Handbook of X-ray and Gamma-ray Astrophysics [2024 ed.] 9811969590, 9789811969591

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Cosimo Bambi Andrea Santangelo Editors

Handbook of X-ray and Gamma-ray Astrophysics

Handbook of X-ray and Gamma-ray Astrophysics

Cosimo Bambi • Andrea Santangelo Editors

Handbook of X-ray and Gamma-ray Astrophysics

With 2227 Figures and 224 Tables

Editors Cosimo Bambi Department of Physics Fudan University Shanghai, China

Andrea Santangelo Institute for Astronomy and Astrophysics University of Tuebingen Tuebingen, Baden-Württemberg, Germany

ISBN 978-981-19-6959-1 ISBN 978-981-19-6960-7 (eBook) https://doi.org/10.1007/978-981-19-6960-7 © Springer Nature Singapore Pte Ltd. 2024 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore Paper in this product is recyclable.

Preface

X-ray and gamma-ray astrophysics concerns the study of the Universe, and thus also of the celestial sources in it, in the energy bands characteristic of X-rays and gamma rays. The X-ray and gamma-ray Universe is a violent, somewhat extreme Universe, often characterized by physical conditions that cannot be reproduced in terrestrial laboratories. Together with the study of astrophysical sources in the UV band, neutrinos, cosmic rays, and gravitational waves, X-ray and gamma-ray astrophysics is a fundamental part of high-energy astrophysics, and of multimessenger astrophysics. X-rays and gamma rays of cosmic origin are blocked by the upper layers of the Earth’s atmosphere. Therefore, X-ray and gamma-ray astrophysics (up to the GeV energies) had to wait for the development of space activities, which began at the end of World War II – from rockets and balloons to satellites – to become an essential discipline of astronomy. At higher energies, those of TeV, the limited fluxes of photons make space research unfeasible. Very high energy gamma astronomy uses ground-based observatories that detect the electromagnetic showers that highenergy gamma rays produce in the Earth’s atmosphere. Since the discovery of the first extrasolar X-ray source in 1962 (Scorpius X-1) by a team led by Riccardo Giacconi, who received the Nobel Prize in Physics in 2002 for his pioneering contributions to the development of X-ray astrophysics, an entire new Universe has been unveiled to the human eyes. Extreme objects like Galactic compact objects and, among others, white dwarfs, neutron stars, and black holes, as well as extragalactic sources such as active galactic nuclei, clusters of galaxies, and gamma-ray bursts, have been discovered as cosmic laboratories for extreme physics. However, studies of X-ray and gamma-ray astrophysics are now rather general and regard a large variety of objects, from planets to potential sources of dark matter. A large number of X-ray and gamma-ray satellites have revolutionized the field, thanks to their improved spectral-timing performance. The launch of IXPE in December 2021 has broken the last uncharted frontier since opened a new window on the study of the polarization of the X-ray radiation from celestial sources. At the same time, TeV observatories have unveiled the very high energy gamma Universe. The future of the discipline is bright. New missions are being developed and some will be launched soon. Large new TeV observatories are being deployed. With

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the emergence of multi-messenger astronomy, we felt it was time of providing the community with a comprehensive handbook for X-ray and gamma-ray astrophysics. The handbook provides an updated coverage of X-ray and gamma-ray astrophysics. All chapters are written by leading experts in the field. The handbook is organized into four subjects: (i) X-ray experimental techniques and observatories (Volumes 1 and 2), (ii) gamma-ray experimental techniques and observatories (Volumes 3 and 4), (iii) science (Volumes 5, 6, and 7), and (iv) analysis techniques in X-ray and gamma-ray astrophysics (Volume 8). Each subject is divided into different “Parts” or “Sections”. Subject I on X-ray experimental techniques and observatories covers optics for X-ray astrophysics (Section Editors: Jessica Gaskin, Rene Hudec, Daniele Spiga), detectors for X-ray astrophysics (Section Editors: JanWillem den Herder, Marco Feroci, Norbert Meidinger), and X-ray missions (Section Editors: Arvind Parmar, Andrea Santangelo, Shuang-Nan Zhang). Subject II on gamma-ray experimental techniques and observatories covers optics and detectors for gamma-ray astrophysics (Section Editors: Lorraine Hanlon, Vincent Tatischeff, David Thompson), space-based gamma-ray observatories (Section Editors: Denis Bastieri, Pablo Saz-Parkinson, Hiroyasu Tajima), and ground-based gamma-ray observatories (Section Editors: Daniel Mazin, Miguel Mostafa, Gerd Pühlhofer). Subject III on science covers Solar System planets (Section Editor: Graziella Branduardi-Raymont), the Sun, stars, and exoplanets (Section Editors: Giuseppina Micela, Beate Stelzer), supernovae, supernova remnants, and diffuse emissions (Section Editors: Aya Bamba, Keiichi Maeda, Manami Sasaki), compact objects (Section Editors: Victor Doroshenko, Andrea Santangelo), galaxies (Section Editors: Giuseppina Fabbiano and Marat Gilfanov), active galactic nuclei in X- and gamma rays (Section Editors: Alessandra De Rosa, Cristian Vignali), galaxy clusters (Section Editors: Etienne Pointecouteau, Elena Rasia, Aurora Simionescu), transient events (Section Editor: Bin-Bin Zhang), and miscellanea (Section Editor: Cosimo Bambi). Subject IV covers spectral-imaging analysis (Section Editors: Victor Doroshenko, Andrea Santangelo, Sergey Tsygankov), timing analysis (Section Editors: Tomaso Belloni, Dipankar Bhattacharya), and polarimetry (Section Editors: Hua Feng, Henric Krawczynski). We hope that the Handbook of X-ray and Gamma-ray Astrophysics can become a valuable reference work for graduate students and research scholars in the high energy astrophysics community for the next two decades. With the living edition, we will keep the handbook always updated. We are extremely grateful to all section editors and authors for their contributions in this project as well as for their future efforts to update their chapters. Shanghai, China Tuebingen, Germany February 2024

Cosimo Bambi Andrea Santangelo

Contents

Volume 1 Part I Introduction to X-ray Astrophysics . . . . . . . . . . . . . . . . . . . . . . . .

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A Chronological History of X-ray Astronomy Missions . . . . . . . . . Andrea Santangelo, Rosalia Madonia, and Santina Piraino

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Part II Optics for X-ray Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jessica Gaskin, Rene Hudec, and Daniele Spiga

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X-ray Optics for Astrophysics: A Historical Review . . . . . . . . . . . . Finn E. Christensen and Brian D. Ramsey

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3

Geometries for Grazing Incidence Mirrors . . . . . . . . . . . . . . . . . . . . Michael J. Pivovaroff and Takashi Okajima

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4

Lobster Eye X-ray Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rene Hudec and Charly Feldman

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5

Single-Layer and Multilayer Coatings for Astronomical X-ray Mirrors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Kristin K. Madsen, David Broadway, and Desiree Della Monica Ferreira

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Silicon Pore Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nicolas M. Barrière, Marcos Bavdaz, Maximilien J. Collon, Ivo Ferreira, David Girou, Boris Landgraf, and Giuseppe Vacanti

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Miniature X-ray Optics for Meter-Class Focal Length Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Jaesub Hong, Suzanne Romaine, Vinay L. Kashyap, and Kiranmayee Kilaru

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Diffraction-Limited Optics and Techniques . . . . . . . . . . . . . . . . . . . Richard Willingale

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Collimators for X-ray Astronomical Optics . . . . . . . . . . . . . . . . . . . Hideyuki Mori and Peter Friedrich

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Technologies for Advanced X-ray Mirror Fabrication . . . . . . . . . . Carolyn Atkins

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Diffraction Gratings for X-ray Astronomy . . . . . . . . . . . . . . . . . . . . Frits Paerels, Jelle Kaastra, and Randall Smith

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Active X-ray Optics for Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . Jacqueline M. Davis, Casey T. DeRoo, and Melville P. Ulmer

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Facilities for X-ray Optics Calibration . . . . . . . . . . . . . . . . . . . . . . . . Bianca Salmaso, Alberto Moretti, and Jessica Gaskin

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Charge Coupled Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . M. W. Bautz, Andrew D. Holland, and D. H. Lumb

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Volume 2 Part III Detectors for X-ray Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . Jan-Willem den Herder, Marco Feroci, and Norbert Meidinger

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X-ray Detectors for Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . J. W. den Herder, Marco Feroci, and Norbert Meidinger

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Proportional Counters and Microchannel Plates . . . . . . . . . . . . . . . Sebastian Diebold

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Silicon Drift Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Andrea Vacchi

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CMOS Active Pixel Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Konstantin D. Stefanov and Andrew D. Holland

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DEPFET Active Pixel Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Norbert Meidinger and Johannes Müller-Seidlitz

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Transition-Edge Sensors for Cryogenic X-ray Imaging Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Luciano Gottardi and Stephen Smith

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Signal Readout for Transition-Edge Sensor X-ray Imaging Spectrometers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Akamatsu, W. B. Doriese, J. A. B. Mates, and B. D. Jackson

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Introduction to Photoelectric X-ray Polarimeters . . . . . . . . . . . . . . Kevin Black, Enrico Costa, Paolo Soffitta, and Anna Zajczyk

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Gas Pixel Detectors for Photoelectric X-ray Astronomical Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Paolo Soffitta and Enrico Costa

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Time-Projection Chamber X-ray Polarimeters . . . . . . . . . . . . . . . . Kevin Black and Anna Zajczyk

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Compton Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ettore Del Monte, Sergio Fabiani, and Mark Pearce

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In-Orbit Background for X-ray Detectors . . . . . . . . . . . . . . . . . . . . . Riccardo Campana

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Filters for X-ray Detectors on Space Missions . . . . . . . . . . . . . . . . . Marco Barbera, Ugo Lo Cicero, and Luisa Sciortino

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Silicon Strip Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . H. Tajima and K. Hagino

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Part IV X-ray Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017 Arvind Parmar, Andrea Santangelo, and Shuang-Nan Zhang 29

The AstroSat Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1019 Kulinder Pal Singh

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The BepiColombo Mercury Imaging X-ray Spectrometer . . . . . . . 1059 Adrian Martindale, Michael J. McKee, Emma J. Bunce, Simon T. Lindsay, Graeme P. Hall, Tuomo V. Tikkanen, Juhani Huovelin, Arto Lehtolainen, Max Mattero, Karri Muinonen, James F. Pearson, Charly Feldman, Gillian Butcher, Martin Hilchenbach, Johannes Treis, and Petra Majewski

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The Chandra X-ray Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1115 Belinda J. Wilkes and Harvey Tananbaum

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The HaloSat and PolarLight CubeSat Missions for X-ray Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1149 Hua Feng and Philip Kaaret

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The Einstein Probe Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1171 Weimin Yuan, Chen Zhang, Yong Chen, and Zhixing Ling

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The Enhanced X-ray Timing and Polarimetry Mission: eXTP . . . 1201 Andrea Santangelo, Shuang-Nan Zhang, Marco Feroci, Margarita Hernanz, Fangjun Lu, and Yupeng Xu

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HERMES-Pathfinder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1231 Fabrizio Fiore, Alejandro Guzman, Riccardo Campana, and Yuri Evangelista

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The Hard X-ray Imager (HXI) on the Advanced Space-based Solar Observatory (ASO-S) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1249 Yang Su, Zhe Zhang, Weiqun Gan, Jian Wu, and Xiankai Jiang

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The Hard X-ray Modulation Telescope . . . . . . . . . . . . . . . . . . . . . . . 1263 Fangjun Lu, Yupeng Xu, Congzhan Liu, Xuelei Cao, Yong Chen, Fan Zhang, and Yunxiang Xiao

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MAXI: Monitor of All-Sky X-ray Image . . . . . . . . . . . . . . . . . . . . . . 1295 Tatehiro Mihara, Hiroshi Tsunemi, and Hitoshi Negoro

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NICER: The Neutron Star Interior Composition Explorer . . . . . . 1321 Keith Gendreau, Zaven Arzoumanian, Elizabeth Ferrara, and Craig B. Markwardt

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Ramaty High Energy Solar Spectroscopic Imager (RHESSI) . . . . 1343 Brian Dennis, Albert Y. Shih, Gordon J. Hurford, and Pascal Saint-Hilaire

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The SMILE Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1369 G. Branduardi-Raymont and C. Wang

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The Spectrometer Telescope for Imaging X-rays (STIX) on Solar Orbiter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1391 Laura A. Hayes, Sophie Musset, Daniel Müller, and Säm Krucker

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Space-Based Multi-band Astronomical Variable Objects Monitor (SVOM) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1409 Jianyan Wei and Bertrand Cordier

44

The Neil Gehrels Swift Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . 1423 Lorella Angelini, S. Bradley Cenko, Jamie A. Kennea, Michael H. Siegel, and Scott D. Barthelmy

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IXPE: The Imaging X-ray Polarimetry Explorer . . . . . . . . . . . . . . . 1455 Martin C. Weisskopf, Paolo Soffitta, Brian D. Ramsey, and Luca Baldini

46

XMM-Newton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1501 Norbert Schartel, Rosario González-Riestra, Peter Kretschmar, Marcus Kirsch, Pedro Rodríguez-Pascual, Simon Rosen, Maria Santos-Lleó, Michael Smith, Martin Stuhlinger, and Eva Verdugo-Rodrigo

Volume 3 Part V Optics and Detectors for Gamma-Ray Astrophysics . . . . . . . . . 1539 Lorraine Hanlon, Vincent Tatischeff, and David Thompson 47

Telescope Concepts in Gamma-Ray Astronomy . . . . . . . . . . . . . . . . 1541 Thomas Siegert, Deirdre Horan, and Gottfried Kanbach

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Coded Mask Instruments for Gamma-Ray Astronomy . . . . . . . . . 1613 Andrea Goldwurm and Aleksandra Gros

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Laue and Fresnel Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1671 Enrico Virgilli, Hubert Halloin, and Gerry Skinner

50

Compton Telescopes for Gamma-Ray Astrophysics . . . . . . . . . . . . 1711 Carolyn Kierans, Tadayuki Takahashi, and Gottfried Kanbach

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Grid-Based Imaging of X-rays and Gamma Rays with High Angular Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1783 Pascal Saint-Hilaire, Albert Y. Shih, Gordon J. Hurford, and Brian Dennis

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Pair Production Detectors for Gamma-Ray Astrophysics . . . . . . . 1817 David J. Thompson and Alexander A. Moiseev

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Readout Electronics for Gamma-Ray Astronomy . . . . . . . . . . . . . . 1851 Marco Carminati and Carlo Fiorini

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Orbits and Background of Gamma-Ray Space Instruments . . . . . 1875 Vincent Tatischeff, Pietro Ubertini, Tsunefumi Mizuno, and Lorenzo Natalucci

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The Use of Germanium Detectors in Space . . . . . . . . . . . . . . . . . . . . 1925 J.-P. Roques, B. J. Teegarden, D. J. Lawrence, and E. Jourdain

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Silicon Detectors for Gamma-Ray Astronomy . . . . . . . . . . . . . . . . . 1969 R. Caputo, Y. Fukazawa, R. P. Johnson, Francesco Longo, M. Prest, H. Tajima, and E. Vallazza

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Cd(Zn)Te Detectors for Hard X-ray and Gamma-ray Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1999 Aline Meuris, Kazuhiro Nakazawa, Irfan Kuvvetli, and Ezio Caroli

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Scintillation Detectors in Gamma-Ray Astronomy . . . . . . . . . . . . . 2035 A. F. Iyudin, C. Labanti, and O. J. Roberts

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Photodetectors for Gamma-Ray Astronomy . . . . . . . . . . . . . . . . . . . 2077 Elisabetta Bissaldi, Carlo Fiorini, and Alexey Uliyanov

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Time Projection Chambers for Gamma-Ray Astronomy . . . . . . . . 2123 Denis Bernard, Stanley D. Hunter, and Toru Tanimori

61

Gamma-Ray Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2173 Denis Bernard, Tanmoy Chattopadhyay, Fabian Kislat, and Nicolas Produit

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CubeSats for Gamma-Ray Astronomy . . . . . . . . . . . . . . . . . . . . . . . . 2215 Peter Bloser, David Murphy, Fabrizio Fiore, and Jeremy Perkins

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Gamma-Ray Detector and Mission Design Simulations . . . . . . . . . 2247 Eric A. Charles, Henrike Fleischhack, and Clio Sleator

Volume 4 Part VI Space-Based Gamma-Ray Observatories . . . . . . . . . . . . . . . . . 2279 Denis Bastieri, Pablo Saz-Parkinson, and Hiroyasu Tajima 64

The COMPTEL Experiment and Its In-Flight Performance . . . . . 2281 James M. Ryan and Werner Collmar

65

The INTEGRAL Mission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2307 E. Kuulkers, P. Laurent, Peter Kretschmar, A. Bazzano, S. Brandt, M. Cadolle-Bel, F. Cangemi, A. Coleiro, M. Ehle, C. Ferrigno, E. Jourdain, J. M. Mas-Hesse, M. Molina, J.-P. Roques, and Pietro Ubertini

66

The AGILE Mission and Its Scientific Results . . . . . . . . . . . . . . . . . 2353 Marco Tavani, Carlotta Pittori, and Francesco Longo

67

Fermi Gamma-Ray Space Telescope . . . . . . . . . . . . . . . . . . . . . . . . . 2383 David J. Thompson and Colleen A. Wilson-Hodge

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The Fermi Large Area Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2415 Riccardo Rando

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The ASTROGAM Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2445 Alessandro De Angelis

Part VII Ground-Based Gamma-Ray Observatories . . . . . . . . . . . . . . . 2457 Daniel Mazin, Miguel Mostafa, and Gerd Pühlhofer 70

Introduction to Ground-Based Gamma-Ray Astrophysics . . . . . . . 2459 Alberto Carramiñana, Emma de Oña Wilhelmi, and Andrew M. Taylor

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How to Detect Gamma Rays from Ground: An Introduction to the Detection Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2483 Manel Errando and Takayuki Saito

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The Development of Ground-Based Gamma-Ray Astronomy: A Historical Overview of the Pioneering Experiments . . . . . . . . . . 2521 Razmik Mirzoyan

73

Detecting Gamma Rays with High Resolution and Moderate Field of View: The Air Cherenkov Technique . . . . . . . . . . . . . . . . . . 2547 Juan Cortina and Carlos Delgado

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Detecting Gamma-Rays with Moderate Resolution and Large Field of View: Particle Detector Arrays and Water Cherenkov Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2575 Michael A. DuVernois and Giuseppe Di Sciascio

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The High-Altitude Water Cherenkov Detector Array: HAWC . . . 2607 Jordan Goodman and Petra Huentemeyer

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Current Particle Detector Arrays in Gamma-Ray Astronomy . . . 2633 Songzhan Chen and Zhen Cao

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The Major Gamma-Ray Imaging Cherenkov Telescopes (MAGIC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2667 O. Blanch and J. Sitarek

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The Very Energetic Radiation Imaging Telescope Array System (VERITAS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2703 David Hanna and Reshmi Mukherjee

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H.E.S.S.: The High Energy Stereoscopic System . . . . . . . . . . . . . . . 2745 Gerd Pühlhofer, Fabian Leuschner, and Heiko Salzmann

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The Cherenkov Telescope Array . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2787 Werner Hofmann and Roberta Zanin

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Future Developments in Ground-Based Gamma-Ray Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2835 Ulisses Barres de Almeida and Martin Tluczykont

Volume 5 Part VIII Solar System Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2895 Graziella Branduardi-Raymont 82

Comets, Mars and Venus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2897 Konrad Dennerl

83

X-ray Emissions from the Jovian System . . . . . . . . . . . . . . . . . . . . . . 2921 W. R. Dunn

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The Earth, the Moon, Mercury, Saturn and Its Rings, and Asteroids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2977 Anil Bhardwaj

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Earth’s Exospheric X-ray Emissions . . . . . . . . . . . . . . . . . . . . . . . . . 3001 Jennifer Alyson Carter

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SMILE: A Novel Way to Explore Solar-Terrestrial Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3029 G. Branduardi-Raymont and C. Wang

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X-ray Emissions from the Ice Giants and Kuiper Belt . . . . . . . . . . 3049 W. R. Dunn

Part IX The Sun, Stars, and Exoplanets . . . . . . . . . . . . . . . . . . . . . . . . . . 3073 Giuseppina Micela and Beate Stelzer 88

The Solar X-ray Corona . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3075 Paola Testa and Fabio Reale

89

Stellar Coronae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3113 Jeremy J. Drake and Beate Stelzer

90

X-ray Emission of Massive Stars and Their Winds . . . . . . . . . . . . . 3185 Gregor Rauw

91

Magnetically Confined Wind Shock . . . . . . . . . . . . . . . . . . . . . . . . . . 3217 Asif ud-Doula and Stan Owocki

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Pre-main Sequence: Accretion and Outflows . . . . . . . . . . . . . . . . . . 3237 P. Christian Schneider, H. Moritz Günther, and Sabina Ustamujic

93

Star-Forming Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3271 Salvatore Sciortino

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Nearby Young Stars and Young Moving Groups . . . . . . . . . . . . . . . 3313 Joel H. Kastner and David A. Principe

95

Extrasolar Planets and Star-Planet Interaction . . . . . . . . . . . . . . . . 3347 Katja Poppenhaeger

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The X-ray Emission from Planetary Nebulae . . . . . . . . . . . . . . . . . . 3365 Martín A. Guerrero

Part X Supernovae, Supernova Remnants, and Diffuse Emission . . . 3387 Aya Bamba, Keiichi Maeda, and Manami Sasaki 97

Stellar Evolution, SN Explosion, and Nucleosynthesis . . . . . . . . . . . 3389 Keiichi Maeda

98

Radioactive Decay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3431 Roland Diehl

99

Supernova Remnants: Types and Evolution . . . . . . . . . . . . . . . . . . . 3467 Aya Bamba and Brian J. Williams

100

Thermal Processes in Supernova Remnants . . . . . . . . . . . . . . . . . . . 3479 Hiroya Yamaguchi and Yuken Ohshiro

101

Nonthermal Processes and Particle Acceleration in Supernova Remnants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3497 Jacco Vink and Aya Bamba

Contents

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102

Pulsar Wind Nebulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3531 A. M. W. Mitchell and J. Gelfand

103

Diffuse Hot Plasma in the Interstellar Medium and Galactic Outflows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3583 Manami Sasaki, Gabriele Ponti, and Jonathan Mackey

104

Interstellar Absorption and Dust Scattering . . . . . . . . . . . . . . . . . . . 3615 E. Costantini and L. Corrales

Volume 6 Part XI Compact Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3655 Victor Doroshenko and Andrea Santangelo 105

Low-Mass X-ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3657 Arash Bahramian and Nathalie Degenaar

106

High-Mass X-ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3719 Francesca Fornasini, Vallia Antoniou, and Guillaume Dubus

107

Accreting White Dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3775 Natalie A. Webb

108

Formation and Evolution of Accreting Compact Objects . . . . . . . . 3821 Diogo Belloni and Matthias R. Schreiber

109

Black Holes: Accretion Processes in X-ray Binaries . . . . . . . . . . . . 3911 Qingcui Bu and Shuang-Nan Zhang

110

Black Holes: Timing and Spectral Properties and Evolution . . . . . 3939 Emrah Kalemci, Erin Kara, and John A. Tomsick

111

Isolated Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3983 Alice Borghese and Paolo Esposito

112

Low-Magnetic-Field Neutron Stars in X-ray Binaries . . . . . . . . . . . 4031 Tiziana Di Salvo, Alessandro Papitto, Alessio Marino, Rosario Iaria, and Luciano Burderi

113

Accreting Strongly Magnetized Neutron Stars: X-ray Pulsars . . . 4105 Alexander Mushtukov and Sergey Tsygankov

114

Fundamental Physics with Neutron Stars . . . . . . . . . . . . . . . . . . . . . 4177 Joonas Nättilä and Jari J. E. Kajava

115

X-ray Emission Mechanisms in Accreting White Dwarfs . . . . . . . . 4231 K. L. Page and A. W. Shaw

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Contents

Part XII Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4275 Giuseppina Fabbiano and Marat Gilfanov 116

Introduction to the Section on Galaxies . . . . . . . . . . . . . . . . . . . . . . . 4277 Giuseppina Fabbiano and Marat Gilfanov

117

X-ray Binaries in External Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . 4283 Marat Gilfanov, Giuseppina Fabbiano, Bret Lehmer, and Andreas Zezas

118

The Hot Interstellar Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4321 Emanuele Nardini, Dong-Woo Kim, and Silvia Pellegrini

119

X-ray Halos Around Massive Galaxies: Data and Theory . . . . . . . 4369 Ákos Bogdán and Mark Vogelsberger

120

The Interaction of the Active Nucleus with the Host Galaxy Interstellar Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4399 Giuseppina Fabbiano and M. Elvis

121

Probing the Circumgalactic Medium with X-ray Absorption Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4445 Smita Mathur

Volume 7 Part XIII Active Galactic Nuclei in X- and Gamma-rays . . . . . . . . . . . . . 4481 Alessandra De Rosa and Cristian Vignali 122

Active Galactic Nuclei and Their Demography Through Cosmic Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4483 Stefano Bianchi, Vincenzo Mainieri, and Paolo Padovani

123

The Super-Massive Black Hole Close Environment in Active Galactic Nuclei . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4515 William Alston, Margherita Giustini, and Pierre-Olivier Petrucci

124

Black Hole-Galaxy Co-evolution and the Role of Feedback . . . . . . 4567 Pedro R. Capelo, Chiara Feruglio, Ryan C. Hickox, and Francesco Tombesi

125

The Dawn of Black Holes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4617 Elisabeta Lusso, Rosa Valiante, and Fabio Vito

Part XIV Galaxy Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4679 Etienne Pointecouteau, Elena Rasia, and Aurora Simionescu 126

X-ray Cluster Cosmology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4681 Nicolas Clerc and Alexis Finoguenov

Contents

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127

Scaling Relations of Clusters and Groups and Their Evolution . . . 4733 Lorenzo Lovisari and Ben J. Maughan

128

Thermodynamic Profiles of Galaxy Clusters and Groups . . . . . . . . 4783 S. T. Kay and G. W. Pratt

129

Cluster Outskirts and Their Connection to the Cosmic Web . . . . . 4813 Stephen Walker and Erwin Lau

130

Absorption Studies of the Most Diffuse Gas in the Large-Scale Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4851 Taotao Fang, Smita Mathur, and Fabrizio Nicastro

131

AGN Feedback in Groups and Clusters of Galaxies . . . . . . . . . . . . 4895 Julie Hlavacek-Larrondo, Yuan Li, and Eugene Churazov

132

Chemical Enrichment in Groups and Clusters . . . . . . . . . . . . . . . . . 4961 François Mernier and Veronica Biffi

133

The Merger Dynamics of the X-ray-Emitting Plasma in Clusters of Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5005 John ZuHone and Yuanyuan Su

134

Plasma Physics of the Intracluster Medium . . . . . . . . . . . . . . . . . . . 5049 Matthew W. Kunz, Thomas W. Jones, and Irina Zhuravleva

Part XV Transient Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5091 Bin-Bin Zhang 135

Gamma-Ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5093 Yun-Wei Yu, He Gao, Fa-Yin Wang, and Bin-Bin Zhang

136

Accretion Disk Evolution in Tidal Disruption Events . . . . . . . . . . . 5127 Wenbin Lu

137

Fast Radio Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5151 Di Xiao, Fa-Yin Wang, and Zigao Dai

Part XVI Miscellanea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5189 Cosimo Bambi 138

Probing Black-Hole Accretion Through Time Variability . . . . . . . 5191 Barbara De Marco, Sara E. Motta, and Tomaso M. Belloni

139

Surveys of the Cosmic X-ray Background . . . . . . . . . . . . . . . . . . . . . 5233 W. N. Brandt and G. Yang

140

Tests of General Relativity Using Black Hole X-ray Data . . . . . . . . 5269 Dimitry Ayzenberg and Cosimo Bambi

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Contents

141

Tests of Lorentz Invariance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5305 Jun-Jie Wei and Xue-Feng Wu

142

X- and Gamma-Ray Astrophysics in the Era of Multi-messenger Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5335 G. Stratta and Andrea Santangelo

Volume 8 Part XVII Spectral-Imaging Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5367 Victor Doroshenko, Andrea Santangelo, and Sergey Tsygankov 143

Modeling and Simulating X-ray Spectra . . . . . . . . . . . . . . . . . . . . . . 5369 Lorenzo Ducci and Christian Malacaria

144

Statistical Aspects of X-ray Spectral Analysis . . . . . . . . . . . . . . . . . . 5403 Johannes Buchner and Peter Boorman

145

Analysis Methods for Gamma-Ray Astronomy . . . . . . . . . . . . . . . . 5453 Denys Malyshev and Lars Mohrmann

Part XVIII Timing Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5507 Tomaso M. Belloni and Dipankar Bhattacharya 146

Basics of Fourier Analysis for High-Energy Astronomy . . . . . . . . . 5509 Tomaso M. Belloni and Dipankar Bhattacharya

147

Time Domain Methods for X-ray and Gamma-ray Astronomy . . . 5543 Eric D. Feigelson, Vinay L. Kashyap, and Aneta Siemiginowska

148

Fourier Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5569 Matteo Bachetti and Daniela Huppenkothen

149

X-ray Polarimetry-Timing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5617 Adam Ingram

Part XIX Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5661 Hua Feng and Henric Krawczynski 150

General History of X-ray Polarimetry in Astrophysics . . . . . . . . . . 5663 Enrico Costa

151

Bayesian Analysis of the Data from PoGO+ . . . . . . . . . . . . . . . . . . . 5683 Mózsi Kiss and Mark Pearce

152

Gamma-Ray Polarimetry of Transient Sources with POLAR . . . . 5717 Merlin Kole and Jianchao Sun

Contents

xix

153

Analysis of the Data from Photoelectric Gas Polarimeters . . . . . . . 5757 Fabio Muleri

154

Neural Network Analysis of X-ray Polarimeter Data . . . . . . . . . . . 5781 A. L. Peirson

155

Soft Gamma-Ray Polarimetry with COSI Using Maximum Likelihood Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5829 John A. Tomsick, Alexander Lowell, Hadar Lazar, Clio Sleator, and Andreas Zoglauer

156

Stokes Parameter Analysis of XL-Calibur Data . . . . . . . . . . . . . . . . 5853 Fabian Kislat and Sean Spooner

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5871

About the Editors

Cosimo Bambi is currently Xie Xide Junior Chair Professor at the Department of Physics at Fudan University. He received the Laurea degree from Florence University in 2003 and the PhD degree from Ferrara University in 2007. He worked as a postdoctoral research scholar at Wayne State University (2007–2008), at IPMU at The University of Tokyo (2008–2011), and in the group of Gia Dvali at LMU Munich (2011–2012). He joined Fudan University at the end of 2012 as Associate Professor under the Thousand Young Talents Program of the State Council of the People’s Republic of China. He was promoted to Full Professor at the end of 2013 and named Xie Xide Junior Chair Professor of Physics in 2016. In 2015, he was awarded a Humboldt Fellowship to collaborate with the group of Kostas Kokkotas at Eberhard Karls Universität Tübingen. Professor Bambi has received a number of awards, including the Magnolia Gold Award in 2022 and the Magnolia Silver Award in 2018 from the Municipality of Shanghai, the International Excellent Young Scientists Award from the National Natural Science Foundation of China in 2022, and the Xu Guangqi Prize from the Embassy of Italy in Beijing in 2018. Professor Bambi has worked on a number of topics in the fields of high-energy astrophysics, particle cosmology, and gravity. His main research interests focus on theoretical and observational studies of black holes. He has published about 200 papers on high impact factor refereed journals as first or corresponding author and has over 10,000 citations. He has authored/edited several academic books xxi

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About the Editors

with Springer: Introduction to Particle Cosmology: The Standard Model of Cosmology and Its Open Problems (Springer-Verlag Heidelberg Berlin, 2016), Astrophysics of Black Holes: From Fundamental Aspects to Latest Developments (Springer-Verlag Heidelberg Berlin, 2016), Black Holes: A Laboratory for Testing Strong Gravity (Springer Singapore, 2017), Introduction to General Relativity (Springer Singapore, 2018), Tutorial Guide to X-ray and Gamma-ray Astronomy: Data Reduction and Analysis (Springer Singapore, 2020), Handbook of Gravitational Wave Astronomy (Springer Singapore, 2022), Regular Black Holes: Towards a New Paradigm of Gravitational Collapse (Springer Singapore, 2023), and HighResolution X-ray Spectroscopy: Instrumentation, Data Analysis, and Science (Springer Singapore, 2023). The book Introduction to General Relativity was published in Chinese by Fudan University Press in 2020, in Spanish by Editorial Reverté in 2021, and in Persian by Jahan-Adib in 2022. Professor Bambi has also written a popular science book, Niente é impossibili: Viaggiare nel tempo, attraversare i buchi neri e altre sfide scientifiche (in Italian), published by Il Saggiatore in 2020 and translated in Chinese and published by Fudan University Press in 2024. Professor Andrea Santangelo studied Physics at the University of Palermo in Italy and later specialized in Astrophysics at the Institute of Cosmic Physics of the Italian National Research Council, with Prof. Livio Scarsi, and at Columbia University, New York, with Prof. Robert Novick. After many years as staff scientist at the Italian CNR and INAF, Andrea Santangelo is since 2004 Professor of High Energy Astrophysics and Director of the High Energy Section of the Institute of Astronomy and Astrophysics of the Eberhard Karls Universität Tübingen in Germany. He has served several terms as Director of the Institute and as Chairman of the physics department. In 2009, he was granted a RIKEN Grant as Senior Scientist, while in 2010 he was co-recipient, as member of the HESS collaboration, of the “Bruno Rossi” Prize for the scientific achievements of the HESS Telescope, and in 2007 he was co-recipient, as member of the HESS collaboration, of the European “Descartes” Prize for the scientific

About the Editors

xxiii

achievements of the HESS Telescope. In 2016, he was granted a CAS President’s International Fellowship as Visiting Full Professor at IHEP (CAS), and since then he has kept a close collaboration with IHEP. He is among the very few scientists who has been granted a second CAS President’s International Fellowship in 2021. Prof. Santangelo’s research interests are in the field of multi-messenger astronomy with focus on High Energy Astrophysics, from a fraction of keV, in the X-rays, to 10^21 eV in the Ultra High Energy Comic rays. He has participated, with leading roles, in many X-ray missions such as BeppoSAX, INTEGRAL, XMM-Newton, eROSITA, and more recently to eXTP, THESEUS, and ATHENA. He is also leading research for the TeV observatories HESS and CTA, and in the past, the EUSO program for the search of Ultra High Energy Cosmic Rays from space. Among the sources populating the High Energy Sky, Prof. Santangelo likes very much X-ray binaries, elusive dark matter sources, and TeV emitters. Andrea Santangelo has published about 500 articles in refereed journals in the fields of Experimental High Energy Astrophysics, Experimental TeV Astrophysics, Space Instrumentation, SpaceBased search for UHECRs, Galactic Compact objects: from accretion to population studies, Dark Matter indirect search, Ultra High Energy Cosmic Rays, Instruments Calibration, and Instrument Background studies.

Section Editors

Aya Bamba Department of Physics Graduate School of Science The University of Tokyo Tokyo, Japan Research Center for the Early Universe School of Science The University of Tokyo Tokyo, Japan Trans-Scale Quantum Science Institute The University of Tokyo Tokyo, Japan Cosimo Bambi Department of Physics Fudan University Shanghai, China

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Section Editors

Denis Bastieri Department of Physics and Astronomy “G. Galilei” Padua University Padua, Italy National Institute for Nuclear Physics (INFN) Section Padua Padua, Italy Center for Astrophysics Guangzhou University Guangzhou, China Tomaso M. Belloni Brera Astronomical Observatory National Institute for Astrophysics (INAF) Merate, Italy

Dipankar Bhattacharya Department of Physics Ashoka University Haryana, India

Tomaso M. Belloni: deceased.

Section Editors

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G. Branduardi-Raymont Mullard Space Science Laboratory Department of Space and Climate Physics University College London London, UK

Alessandra De Rosa National Institute for Astrophysics (INAF) Institute of Space Astrophysics and Planetology (IAPS) Rome, Italy

Jan-Willem den Herder Foundation for Dutch Scientific Research Institutes (NWO) Netherlands Institute for Space Research (SRON) Leiden, The Netherlands University of Amsterdam Amsterdam, The Netherlands Victor Doroshenko Institute of Astronomy and Astrophysics University of Tuebingen Tübingen, Germany

G. Branduardi-Raymont: deceased.

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Section Editors

G. Fabbiano Center for Astrophysics Harvard & Smithsonian Cambridge, MA, USA

Hua Feng Department of Astronomy Tsinghua University Beijing, China

Marco Feroci National Institute for Astrophysics (INAF) Institute of Space Astrophysics and Planetology (IAPS) Rome, Italy National Institute for Nuclear Physics (INFN) Section Roma Tor Vergata Rome, Italy

Section Editors

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Jessica Gaskin NASA Marshall Space Flight Center Huntsville, AL, USA

Marat Gilfanov Max Planck Institute for Astrophysics Garching, Germany

Lorraine Hanlon Centre for Space Research & School of Physics University College Dublin Dublin, Ireland

Rene Hudec Faculty of Electrical Engineering Czech Technical University in Prague Prague, Czech Republic Astronomical Institute Czech Academy of Sciences Ondrejov, Czech Republic

xxx

Section Editors

Henric Krawczynski Washington University in St. Louis St. Louis, MO, USA

Keiichi Maeda Department of Astronomy Kyoto University Kyoto, Japan

Daniel Mazin The University of Tokyo Tokyo, Japan

Norbert Meidinger Max Planck Institute for Extraterrestrial Physics Garching, Germany

Section Editors

xxxi

Giuseppina Micela Palermo Astronomical Observatory Palermo, National Institute for Astrophysics (INAF) Italy

Miguel Mostafá Temple University Philadelphia, PA, USA

Arvind Parmar European Space Agency Noordwijk, The Netherlands

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Section Editors

Etienne Pointecouteau National Center for Scientific Research (CNRS) IRAP, Toulouse, France University of Toulouse Toulouse, France

Gerd Pühlhofer Institute of Astronomy and Astrophysics University of Tuebingen Tübingen, Germany

Elena Rasia Trieste Astronomical Observatory National Institute for Astrophysics (INAF) Trieste, Italy

Andrea Santangelo Institute of Astronomy and Astrophysics University of Tuebingen Tübingen, Baden-Württemberg, Germany

Section Editors

xxxiii

Manami Sasaki Dr. Karl Remeis Sternwarte Erlangen Centre for Astroparticle Physics University of Erlangen-Nuernberg Bamberg, Germany

Pablo M. Saz Parkinson Santa Cruz Institute for Particle Physics University of California Santa Cruz Santa Cruz, CA, USA

Aurora Simionescu Institutes Organization of the Dutch Research Council (NWO) Netherlands Institute for Space Research (SRON) Leiden, Netherlands

Daniele Spiga Brera Astronomical Observatory National Institute for Astrophysics (INAF) Milan, Italy

xxxiv

Section Editors

Beate Stelzer Institute of Astronomy and Astrophysics University of Tuebingen Tübingen, Germany

H. Tajima Solar-Terresterial Enviornment Laboratory Nagoya University Nagoya, Japan

Vincent Tatischeff Paris-Saclay University & National Center for Scientific Research (CNRS)/IN2P3 IJCLab Orsay, France

David J. Thompson NASA Goddard Space Flight Center Greenbelt, MD, USA

Section Editors

xxxv

Sergey Tsygankov Department of Physics and Astronomy University of Turku Turku, Finland

Cristian Vignali Department of Physics and Astronomy “Augusto Righi” University of Bologna Bologna, Italy

Bin-Bin Zhang Nanjing University Nanjing, China

Shuang-Nan Zhang Key Laboratory for Particle Astrophysics Institute of High Energy Physics CAS, Beijing, China University of Chinese Academy of Sciences Chinese Academy of Sciences Beijing, China

Contributors

H. Akamatsu SRON Netherlands Institute for Space Research, The Netherlands

Leiden,

Ulisses Barres de Almeida Brazilian Center for Physics Research (CBPF), Rio de Janeiro, Brazil William Alston Centre for Astrophysics Research, University of Hertfordshire, Hatfield, Hertfordshire, UK Lorella Angelini Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, USA Vallia Antoniou Department of Physics and Astronomy, Texas Tech University, Lubbock, TX, USA Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA Zaven Arzoumanian NASA/GSFC, Greenbelt, MD, USA Carolyn Atkins STFC UK Astronomy Technology Centre, Edinburgh, UK Dimitry Ayzenberg Theoretical Astrophysics, Eberhard-Karls Universität Tübingen, Tübingen, Germany Matteo Bachetti INAF-Osservatorio Astronomico di Cagliari, Selargius, CA, Italy Arash Bahramian International Centre for Radio Astronomy Research – Curtin University, Perth, WA, Australia Luca Baldini Universita’ di Pisa e INFN-Pisa, Pisa, Italy Aya Bamba Research Center for the Early Universe, School of Science, The University of Tokyo, Bunkyo-ku, Tokyo, Japan Cosimo Bambi Center for Field Theory and Particle Physics and Department of Physics, Fudan University, Shanghai, China Marco Barbera Dipartimento di Fisica e Chimica “E. Segrè”, Università degli Studi di Palermo, Palermo, Italy xxxvii

xxxviii

Contributors

Nicolas M. Barrière cosine, Sassenheim, The Netherlands Scott D. Barthelmy Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, USA M. W. Bautz MIT Center for Space Research, Cambridge, MA, USA Marcos Bavdaz European Space Agency, ESTEC, Noordwijk, The Netherlands A. Bazzano IAPS/INAF, Rome, Italy Diogo Belloni Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile Tomaso M. Belloni Osservatorio Astronomico di Brera, INAF, Merate, Italy Denis Bernard LLR, Ecole polytechnique, CNRS/IN2P3 and Institut Polytechnique de Paris, Palaiseau, France Anil Bhardwaj Physical Research Laboratory, Ahmedabad, India Dipankar Bhattacharya Inter-University Centre for Astronomy and Astrophysics, Ganeshkhind, Pune, India Ashoka University, Sonipat, Haryana, India Stefano Bianchi Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre, Roma, Italy Veronica Biffi INAF – Osservatorio Astronomico di Trieste, Trieste, Italy Elisabetta Bissaldi Dipartimento Interateneo di Fisica, Politecnico di Bari, Bari, Italy Sezione di Bari, Istituto Nazionale di Fisica Nucleare, Bari, Italy Kevin Black Rock Creek Scientific and NASA Goddard Space Flight Center, Greenbelt, MD, USA O. Blanch Inistitut de Física d’Altes Energies (IFAE) – The Barcelona Institute of Science and Technology (BIST), Barcelona, Spain Peter Bloser Los Alamos National Laboratory, Los Alamos, NM, USA Ákos Bogdán Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA Peter Boorman Astronomical Institute, Academy of Sciences, Boˇcní, Prague, Czech Republic Alice Borghese Institute of Space Sciences (ICE, CSIC), Barcelona, Spain Departamento de Astrofisica, Universidad de La Laguna, Tenerife, Spain

Tomaso M. Belloni: deceased.

Contributors

xxxix

S. Brandt DTU Space–National Space Institute, Technical University of Denmark, Lyngby, Denmark W. N. Brandt Department of Astronomy & Astrophysics, The Pennsylvania State University, University Park, PA, USA Institute for Gravitation and the Cosmos, The Pennsylvania State University, University Park, PA, USA Department of Physics, The Pennsylvania State University, University Park, PA, USA G. Branduardi-Raymont Mullard Space Science Laboratory, Department of Space and Climate Physics, University College London, Holmbury St Mary, Dorking, Surrey, UK David Broadway NASA Marshall Space Flight Center (MSFC), Huntsville, AL, USA Qingcui Bu Institut für Astronomie und Astrophysik, Kepler Center for Astro and Particle Physics, Eberhard Karls Universität, Tübingen, Germany Johannes Buchner Max Planck Institute for Extraterrestrial Physics, Gießenbachstrasse, Garching, Germany Emma J. Bunce School of Physics and Astronomy, University of Leicester, Leicester, UK Luciano Burderi Dipartimento di Fisica, Universitá degli Studi di Cagliari, Monserrato, Italy Gillian Butcher School of Physics and Astronomy, University of Leicester, Leicester, UK M. Cadolle-Bel Allane Mobility Group, Pullach, Germany Riccardo Campana INAF-OAS, Bologna, Italy F. Cangemi CNRS/LPNHE, Paris, France Xuelei Cao Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Zhen Cao Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Pedro R. Capelo Center for Theoretical Astrophysics and Cosmology, Institute for Computational Science, University of Zurich, Zürich, Switzerland R. Caputo NASA Goddard Space Flight Center, Greenbelt, MD, USA Marco Carminati DEIB, Politecnico di Milano, Milano, Italy

G. Branduardi-Raymont: deceased.

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Contributors

Ezio Caroli INAF/OAS of Bologna, Bologna, Italy Alberto Carramiñana Instituto Nacional de Astrofísica, Óptica y Electrónica, Tonantzintla, Puebla, Mexico Jennifer Alyson Carter University of Leicester, Leicester, UK S. Bradley Cenko Astrophysics Science Division, NASA Goddard Space Flight Center, Greenbelt, MD, USA Eric A. Charles Kavli Institute for Particle Astrophysics and Cosmology, SLAC National Accelerator Laboratory, Menlo Park, CA, USA Tanmoy Chattopadhyay Kavli Institute of Particle Astrophysics and Cosmology, Stanford University, Stanford, CA, USA Songzhan Chen Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Yong Chen Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Finn E. Christensen DTU Space, Technical University of Denmark, Lyngby, Denmark Eugene Churazov Max Planck Institute for Astrophysics, Garching, Germany Space Research Institute (IKI), Moscow,Russia Nicolas Clerc IRAP, Université de Toulouse, CNRS, UPS, CNES, Toulouse, France A. Coleiro AstroParticule et Cosmologie, Université de Paris, CNRS, Paris, France Werner Collmar Max Planck Institute for Extraterrestrial Physics, Giessenbachstrasse 1, 85748 Garching, Germany Maximilien J. Collon cosine, Sassenheim, The Netherlands Bertrand Cordier Lab AIM – CEA, CNRS, Université Paris-Saclay, Université de Paris, Gif-sur-Yvette, France L. Corrales Department of Astronomy, University of Michigan, Ann Arbor, MI, USA Juan Cortina CIEMAT, Madrid, Spain Enrico Costa Istituto di Astrofisica e Planetologia Spaziale – INAF, Roma, Italy E. Costantini SRON Netherlands Institute for Space Research, The Netherlands

Leiden,

Anton Pannekoek Astronomical Institute, University of Amsterdam, Amsterdam, The Netherlands

Contributors

xli

Zigao Dai Department of Astronomy, University of Science and Technology of China, Hefei, China Jacqueline M. Davis NASA Marshall Space Flight Center, Huntsville, AL, USA Alessandro De Angelis Department of Physics and Astronomy “Galileo Galilei”, University of Padua, Padua, Italy INFN and INAF, Padua, Italy IST/LIP, Lisboa, Portugal Barbara De Marco Departament de Fìsica, EEBE, Universitat Politècnica de Catalunya, Barcelona, Spain Emma de Oña Wilhelmi Deutsches Elektronen Synchrotron DESY, Zeuthen, Germany Nathalie Degenaar Anton Pannekoek Institute for Astronomy, University of Amsterdam, Amsterdam, The Netherlands Ettore Del Monte Istituto di Astrofisica e Planetologia Spaziali (IAPS), Roma, Italy INFN – Roma Tor Vergata, Roma, Italy Carlos Delgado CIEMAT, Madrid, Spain J. W. den Herder NWO-I/SRON and the University of Amsterdam, Leiden, The Netherlands Konrad Dennerl Max-Planck-Institut für extraterrestrische Physik, Garching, Germany Brian Dennis Solar Physics Laboratory, Goddard Space Flight Center, Greenbelt, MD, USA Casey T. DeRoo Department of Physics and Astronomy, University of Iowa, Iowa City, IA, USA Tiziana Di Salvo Dipartimento di Fisica e Chimica – Emilio Segré, Universitá di Palermo, Palermo, Italy Sebastian Diebold Institut für Astronomie und Astrophysik, Eberhard Karls Universität Tübingen, Tübingen, Germany Roland Diehl Max Planck Institut für extraterrestrische Physik, Germany

Garching,

W. B. Doriese United States Department of Commerce, National Institute of Standards and Technology (NIST), Boulder, CO, USA Jeremy J. Drake Center for Astrophysics | Harvard & Smithsonian MS-03, Cambridge, MA, USA Guillaume Dubus University of Grenoble Alpes, CNRS, IPAG, Grenoble, France

xlii

Contributors

Lorenzo Ducci Institut für Astronomie und Astrophysik Tübingen, Kepler Center for Astro and Particle Physics, University of Tübingen, Tübingen, Germany ISDC Data Center for Astrophysics, Université de Genève, Versoix, Switzerland W. R. Dunn Department of Physics and Astronomy, University College London, London, UK The Centre for Planetary Science at UCL/Birkbeck, London, UK Michael A. DuVernois Dept of Physics & Wisconsin IceCube Particle Astrophysics Center (WIPAC), University of Wisconsin, Madison, WI, USA M. Ehle European Space Agency (ESA), European Space Astronomy Centre (ESAC), Madrid, Spain M. Elvis Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA Manel Errando Department of Physics, Washington University in St. Louis, St. Louis, MO, USA Paolo Esposito Scuola Universitaria Superiore IUSS Pavia, Palazzo del Broletto, Pavia, Italy INAF–Istituto di Astrofisica Spaziale e Fisica Cosmica di Milano, Milano, Italy Yuri Evangelista IAPS/INAF, Rome, Italy Giuseppina Fabbiano Harvard-Smithsonian Center for Astrophysics (CfA), Cambridge, MA, USA Sergio Fabiani Istituto di Astrofisica e Planetologia Spaziali (IAPS), Roma, Italy INFN – Roma Tor Vergata, Roma, Italy Taotao Fang Department of Astronomy, Xiamen University, Xiamen, China Eric D. Feigelson Department of Astronomy and Astrophysics, Center for Astrostatistics, Penn State University, Pennsylvania, PA, USA Charly Feldman School of Physics and Astronomy, University of Leicester, Leicester, UK Hua Feng Department of Astronomy, Tsinghua University, Beijing, China Marco Feroci Istituto di Astrofisica e Planetologia Spaziali, Istituto Nazionale di Astrofisica, Rome, Italy Elizabeth Ferrara NASA/GSFC and University of Maryland, Greenbelt, MD, USA Desiree Della Monica Ferreira DTU Space – Technical University of Denmark, Kongens Lyngby, Denmark Ivo Ferreira European Space Agency, ESTEC, Noordwijk, The Netherlands

Contributors

xliii

C. Ferrigno ISDC/University of Geneva, Versoix, Switzerland Chiara Feruglio INAF Osservatorio Astronomico di Trieste, Trieste, Italy Institute for Fundamental Physics of the Universe, Trieste, Italy Alexis Finoguenov Department of Physics, University of Helsinki, Helsinki, Finland Fabrizio Fiore INAF-Osservatorio Astronomico di Trieste, Trieste, Italy Carlo Fiorini Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy Sezione di Milano, Istituto Nazionale di Fisica Nucleare, Milano, Italy Henrike Fleischhack Catholic University of America, Washington, DC, USA NASA/GSFC, Greenbelt, MD, USA CRESST II, Greenbelt, MD, USA Francesca Fornasini Stonehill College, North Easton, MA, USA Peter Friedrich Max-Planck-Institut für extraterrestrische Physik, Germany

Garching,

Y. Fukazawa Department of Physical Sciences, Hiroshima University, HigashiHiroshima, Hiroshima, Japan Weiqun Gan Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing, China He Gao Department of Astronomy, Beijing Normal University, Beijing, China Jessica Gaskin NASA Marshall Space Flight Center, Huntsville, AL, USA J. Gelfand NYU Abu Dhabi, Abu Dhabi, UAE Keith Gendreau NASA/GSFC, Greenbelt, MD, USA Marat Gilfanov Max-Planck-Institute for Astrophysics, Space Research Institute, Garching, Germany Space Research Institute, Moscow, Russia David Girou cosine, Sassenheim, The Netherlands Margherita Giustini Centro de Astrobiologia (CAB), CSIC-INTA, Madrid, Hertfordshire, UK Andrea Goldwurm Université Paris Cité, CNRS, CEA, Astroparticule et Cosmologie, Paris, France Département d’Astrophysique/IRFU/DRF, CEA-Saclay, Gif-sur-Yvette, France Rosario González-Riestra Serco Gestión de Negocios S.L., ESAC, Madrid, Spain

xliv

Contributors

Jordan Goodman University of Maryland, College Park, MD, USA Luciano Gottardi NWO-I/SRON Netherlands Institute for Space Research, Leiden, The Netherlands Aleksandra Gros Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, Gif-sur-Yvette, France Martín A. Guerrero Instituto de Astrofísica de Andalucía, IAA-CSIC, Granada, Spain H. Moritz Günther Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA Alejandro Guzman University of Tübingen Institute for Astronomy and Astrophysics, Tübingen, Germany K. Hagino Kanto Gakuin University, Kanazawa-ku, Yokohama, Japan Graeme P. Hall School of Physics and Astronomy, University of Leicester, Leicester, UK Hubert Halloin Université de Paris, CNRS, Astroparticule et Cosmologie, Paris, France David Hanna Physics Department, McGill University, Montreal, QC, Canada Laura A. Hayes European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Noordwijk, The Netherlands Margarita Hernanz Institute of Space Sciences (ICE-CSIC), Barcelona, Spain Ryan C. Hickox Department of Physics and Astronomy, Dartmouth College, Hanover, NH, USA Martin Hilchenbach Max Planck Institute for Solar System Research, Justus-vonLiebig-Weg, Göttingen, Germany Julie Hlavacek-Larrondo Physics Department, Université de Montréal, Montréal, QC, Canada Werner Hofmann Max-Planck-Institut für Kernphysik, Heidelberg, Germany Andrew D. Holland Centre for Electronic Imaging, The Open University, Milton Keynes, UK Jaesub Hong Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA Deirdre Horan Laboratoire Leprince-Ringuet, CNRS/IN2P3, Institut Polytechnique de Paris, Palaiseau, France Rene Hudec Faculty of Electrical Engineering, Czech Technical University in Prague, Prague, Czech Republic

Contributors

xlv

Petra Huentemeyer Michigan Technological University, Houghton, MI, USA Stanley D. Hunter NASA/Goddard Space Flight Center, Greenbelt, MD, USA Juhani Huovelin Department of Physics, University of Helsinki, Helsinki, Finland Daniela Huppenkothen SRON Netherlands Institute for Space Research, Leiden, The Netherlands Gordon J. Hurford Space Sciences Laboratory, University of California, Berkeley, CA, USA Rosario Iaria Dipartimento di Fisica e Chimica – Emilio Segré, Universitá di Palermo, Palermo, Italy Adam Ingram School of Mathematics, Statistics and Physics, Newcastle University, Newcastle upon Tyne, UK A. F. Iyudin Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia B. D. Jackson SRON Netherlands Institute for Space Research, Groningen, The Netherlands Xiankai Jiang Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing, China R. P. Johnson Department of Physics, Santa Cruz Institute for Particle Physics, University of California at Santa Cruz, Santa Cruz, CA, USA Thomas W. Jones School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA E. Jourdain UPS-OMP, IRAP, Université de Toulouse, Toulouse, France Philip Kaaret Department of Physics and Astronomy, University of Iowa, Iowa City, IA, USA Jelle Kaastra SRON, Leiden, The Netherlands Jari J. E. Kajava Serco for ESA, ESA/ESAC, Madrid, Spain Department of Physics and Astronomy, University of Turku, Turku, Finland Emrah Kalemci Faculty of Engineering and Natural Sciences, SabancıUniversity, Istanbul, Turkey Gottfried Kanbach Max Planck Institute for Extraterrestrial Physics, Garching, Germany Erin Kara MIT Kavli Institute for Astrophysics and Space Research, Cambridge, MA, USA Vinay L. Kashyap Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA

xlvi

Contributors

Joel H. Kastner Center for Imaging Science, School of Physics and Astronomy, and Laboratory for Multiwavelength Astrophysics, Rochester Institute of Technology, Rochester, NY, USA S. T. Kay Jodrell Bank Centre for Astrophysics, Department of Physics and Astronomy, The University of Manchester, Manchester, UK Jamie A. Kennea Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA, USA Carolyn Kierans NASA Goddard Space Flight Center, Greenbelt, MD, USA Kiranmayee Kilaru Marshall Space Flight Center, Huntsville, AL, USA Dong-Woo Kim Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA Marcus Kirsch ESA, European Space Operations Centre (ESOC), Darmstadt, Germany Fabian Kislat University of New Hampshire, Durham, NH, USA Mózsi Kiss Department of Physics, KTH Royal Institute of Technology, Stockholm, Sweden The Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Center, Stockholm, Sweden Merlin Kole DPNC, University of Geneva, Geneva, Switzerland Peter Kretschmar European Space Agency (ESA), European Space Astronomy Centre (ESAC), Madrid, Spain Säm Krucker University of Applied Sciences and Arts Northwestern Switzerland, Windisch, Switzerland Space Sciences Laboratory, University of California, Berkeley, CA, USA Matthew W. Kunz Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA E. Kuulkers European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Noordwijk, The Netherlands Irfan Kuvvetli DTU-Space, Kongens Lyngby, Denmark C. Labanti Osservatorio di Astrofisica e Scienza dello spazio (OAS-INAF), Bologna, Italy Boris Landgraf cosine, Sassenheim, The Netherlands Erwin Lau Smithsonian Astrophysical Observatory, Cambridge, MA, USA P. Laurent CEA/DRF/IRFU/DAp, CEA Saclay, Saclay, France

Contributors

xlvii

D. J. Lawrence Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA Hadar Lazar Space Sciences Laboratory, University of California, Berkeley, CA, USA Bret Lehmer University of Arkansas, Fayetteville, AR, USA Arto Lehtolainen Department of Physics, University of Helsinki, Helsinki, Finland Fabian Leuschner Institute for Astronomy and Astrophysics Tübingen, Tübingen, Germany Yuan Li University of North Texas, Denton, TX, USA Simon T. Lindsay School of Physics and Astronomy, University of Leicester, Leicester, UK Zhixing Ling National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China Congzhan Liu Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Ugo Lo Cicero Osservatorio Astronomico di Palermo “G. S. Vaiana”, Istituto Nazionale di Astrofisica, Palermo, Italy Francesco Longo Università degli Studi di Trieste, Trieste, Italy Lorenzo Lovisari INAF – Osservatorio di Astrofisica e Scienza dello Spazio di Bologna, Bologna, Italia Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA Alexander Lowell Space Sciences Laboratory, University of California, Berkeley, CA, USA Fangjun Lu Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Key Laboratory of Stellar and Interstellar Physics and School of Physics and Optoelectronics, Xiangtan University, Xiangtan, Hunan, China Wenbin Lu Departments of Astronomy and Theoretical Astrophysics Center, University of California, Berkeley Berkeley, CA, USA Department of Astrophysical Sciences, Princeton University, Princeton, NJ, USA D. H. Lumb Centre for Electronic Imaging, Open University, Milton Keynes, UK Elisabeta Lusso Dipartimento di Fisica e Astronomia, Università di Firenze, Firenze, Italy INAF-Osservatorio Astrofisico di Arcetri, Firenze,Italy

xlviii

Contributors

Jonathan Mackey Dublin Institute for Advanced Studies, Astronomy & Astrophysics Section, Dunsink Observatory, Dublin, Ireland Rosalia Madonia Institute of Astronomy and Astrophysics, University of Tübingen, Tübingen, Germany Kristin K. Madsen CRESST and X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, USA Keiichi Maeda Department of Astronomy, Kyoto University, Sakyo-ku, Kyoto, Japan Vincenzo Mainieri European Southern Observatory, Garching bei München, Germany Petra Majewski Semiconductor Laboratory of the Max-Planck-Society, Munich, Germany Christian Malacaria International Space Science Institute (ISSI), Switzerland

Bern,

Denys Malyshev Institut für Astronomie und Astrophysik Tübingen, Eberhard Karls Universität Tübingen, Tübingen, Germany Alessio Marino Dipartimento di Fisica e Chimica – Emilio Segré, Universitá di Palermo, Palermo, Italy Astrophysics & Planetary Sciences, Institute of Space Sciences (ICE, CSIC), Barcelona,Spain Craig B. Markwardt NASA/GSFC, Greenbelt, MD, USA Adrian Martindale School of Physics and Astronomy, University of Leicester, Leicester, UK J. M. Mas-Hesse Centro de Astrobiología (CSIC-INTA), Madrid, Spain J. A. B. Mates United States Department of Commerce, National Institute of Standards and Technology (NIST), Boulder, CO, USA Smita Mathur The Ohio State University, Columbus, OH, USA Max Mattero Department of Physics, University of Helsinki, Helsinki, Finland Ben J. Maughan H. H. Wills Physics Laboratory, University of Bristol, Bristol, UK Michael J. McKee School of Physics and Astronomy, University of Leicester, Leicester, UK Norbert Meidinger Max Planck Institute for Extraterrestrial Physics, Garching, Germany

Contributors

xlix

François Mernier European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Noordwijk, The Netherlands Aline Meuris Université Paris-Saclay, Université Paris Cité, CEA, CNRS, AIM, 91191 Gif-sur-Yvette, France Tatehiro Mihara RIKEN, Wako, Saitama, Japan Razmik Mirzoyan Max-Planck-Institute for Physics, Munich, Germany National Academy of Sciences of Republic of Armenia, Yerevan, Armenia A. M. W. Mitchell Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany Tsunefumi Mizuno Hiroshima Astrophysical Science Center, Hiroshima University, Higashi-Hiroshima, Hiroshima, Japan Lars Mohrmann Max-Planck-Institut für Kernphysik, Heidelberg, Germany Alexander A. Moiseev University of Maryland, College Park, MD, USA M. Molina IASF/INAF, Milano, Italy Alberto Moretti INAF Astronomical Observatory Brera, Milano, Italy Hideyuki Mori Japan Aerospace Exploration Agency/Institute of Space and Astronautical Science, Sagamihara, Kanagawa, Japan Sara E. Motta INAF – Osservatorio Astronomico di Brera, Merate, Italy Karri Muinonen Department of Physics, University of Helsinki, Helsinki, Finland Reshmi Mukherjee Department of Physics & Astronomy, Barnard College, Columbia University, New York, NY, USA Fabio Muleri INAF-IAPS, Rome, Italy Daniel Müller European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Noordwijk, The Netherlands Johannes Müller-Seidlitz Max Planck Institute for Extraterrestrial Physics, Garching, Germany David Murphy Centre for Space Research and School of Physics, University College Dublin, Dublin, Ireland Alexander Mushtukov Astrophysics, Department of Physics, University of Oxford, Oxford, UK Leiden Observatory, Leiden, The Netherlands Sophie Musset European Space Agency (ESA), European Space Research and Technology Centre (ESTEC), Noordwijk, The Netherlands Kazuhiro Nakazawa Nogoya University, Nogoya, Japan

l

Contributors

Emanuele Nardini INAF – Arcetri Astrophysical Observatory, Firenze, Italy Lorenzo Natalucci IAPS/INAF, Rome, Italy Joonas Nättilä Center for Computational Astrophysics, Flatiron Institute, New York, NY, USA Physics Department and Columbia Astrophysics Laboratory, Columbia University, New York, NY, USA Hitoshi Negoro Nihon University, Tokyo, Japan Fabrizio Nicastro Istituto Nazionale di Astrofisica (INAF) – Osservatorio Astronomico di Roma, Rome, Italy Department of Astronomy, Xiamen University, Xiamen, China Yuken Ohshiro Institute of Space and Astronautical Science/JAXA, Sagamihara, Japan Takashi Okajima NASA’s Goddard Space Flight Center, Greenbelt, MD, USA Stan Owocki University of Delaware, Newark, DE, USA Paolo Padovani European Southern Observatory, Germany

Garching bei München,

Frits Paerels Columbia Astrophysics Laboratory, Columbia University, New York, NY, USA K. L. Page School of Physics & Astronomy, University of Leicester, Leicester, UK Alessandro Papitto INAF—Osservatorio Astronomico di Roma, Monteporzio Catone, Roma, Italy Mark Pearce Department of Physics, KTH Royal Institute of Technology, Stockholm, Sweden The Oskar Klein Centre for Cosmoparticle Physics, AlbaNova University Center, Stockholm, Sweden James F. Pearson School of Physics and Astronomy, University of Leicester, Leicester, UK A. L. Peirson Kavli Institute for Particle Astrophysics and Cosmology, Stanford University, Stanford, CA, USA Silvia Pellegrini Department of Physics and Astronomy, University of Bologna, Bologna, Italy Jeremy Perkins NASA/GSFC, Greenbelt, MD, USA Pierre-Olivier Petrucci University of Grenoble Alpes, CNRS, IPAG, Grenoble, France

Contributors

li

Santina Piraino Institute of Astronomy and Astrophysics, University of Tübingen, Tübingen, Germany Carlotta Pittori INAF/OAR, Monte Porzio Catone (RM), Italy SSDC/ASI, Roma, Italy Michael J. Pivovaroff Lawrence Livermore National Laboratory, Livermore, CA, USA Gabriele Ponti INAF-Osservatorio Astronomico di Brera, Merate, Italy Max-Planck-Institut für extraterrestrische Physik, Garching, Germany Katja Poppenhaeger Leibniz Institute for Astrophysics Potsdam, Germany

Potsdam,

Institute for Physics and Astronomy, University of Potsdam, Potsdam, Germany G. W. Pratt CEA, CNRS, AIM, Université Paris-Saclay, Université Paris Cité, Gif-sur-Yvette, France M. Prest Università dell’Insubria, Como, Italy Istituto Nazionale di Fisica Nucleare, Sezione di Milano, Italy David A. Principe Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA Nicolas Produit Astronomy Department, University of Geneva, Versoix, Geneva, Switzerland Gerd Pühlhofer Institute for Astronomy and Astrophysics Tübingen, Tübingen, Germany Brian D. Ramsey NASA Marshall Space Flight Center, Huntsville, AL, USA Riccardo Rando University of Padova and I.N.F.N. Padova, Padova, Italy Gregor Rauw Space sciences, Technologies and Astrophysics Research (STAR) Institute, Université de Liège, Liège, Belgium Fabio Reale Dipartimento di Fisica e Chimica, Universita’ di Palermo, Palermo, Italy INAF-Osservatorio Astronomico di Palermo, Palermo, Italy O. J. Roberts Science and Technology Institute, Universities Space Research Association, Huntsville, AL, USA Pedro Rodríguez-Pascual Serco Gestión de Negocios S.L., ESAC, Madrid, Spain Suzanne Romaine Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA

lii

Contributors

J.-P. Roques CNRS, IRAP, Toulouse, France UPS-OMP, IRAP, Université de Toulouse, Toulouse, France Simon Rosen Serco Gestión de Negocios S.L., ESAC, Madrid, Spain James M. Ryan University of New Hampshire, Durham, NH, USA Pascal Saint-Hilaire Space Sciences Laboratory, University of California, Berkeley, CA, USA Takayuki Saito Institute for Cosmic Ray Research, The University of Tokyo, Kashiwa, Japan Bianca Salmaso INAF Astronomical Observatory Brera, Merate, Lecco, Italy Heiko Salzmann Institute for Astronomy and Astrophysics Tübingen, Tübingen, Germany Andrea Santangelo Institute of Astronomy and Astrophysics, University of Tübingen, Tüebingen, Baden-Württemberg, Germany Maria Santos-Lleó European Space Agency (ESA), European Space Astronomy Centre (ESAC), Madrid, Spain Manami Sasaki Dr. Karl Remeis Sternwarte, Erlangen Centre for Astroparticle Physics, Friedrich-Alexander-Universität Erlangen-Nürnberg, Bamberg, Germany Norbert Schartel European Space Agency (ESA), European Space Astronomy Centre (ESAC), Madrid, Spain P. Christian Schneider Hamburg Observatory, Hamburg, Germany Matthias R. Schreiber Departamento de Física, Universidad Técnica Federico Santa María, Valparaíso, Chile Millennium Nucleus for Planet Formation (NPF), Valparaíso, Chile Giuseppe Di Sciascio Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Roma Tor Vergata, Rome, Italy Luisa Sciortino Dipartimento di Fisica e Chimica “E. Segrè”, Università degli Studi di Palermo, Palermo, Italy Salvatore Sciortino INAF-Osservatorio Astronomico di Palermo, Palermo, Sicily, Italy A.W. Shaw Department of Physics, University of Nevada, Reno, NV, USA Albert Y. Shih Solar Physics Laboratory, Goddard Space Flight Center, Greenbelt, MD, USA Michael H. Siegel Department of Astronomy and Astrophysics, The Pennsylvania State University, University Park, PA, USA

Contributors

liii

Thomas Siegert Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Würzburg, Germany Aneta Siemiginowska Center for Astrophysics, Harvard & Smithsonian, Cambridge, MA, USA Kulinder Pal Singh Tata Institute of Fundamental Research, Mumbai, India Indian Institute of Science Education and Research Mohali, Punjab, India J. Sitarek Faculty of Physics and Applied Informatics – Department of Astrophysics, University of Lodz, Lodz, Poland Gerry Skinner University of Birmingham, Birmingham, UK Clio Sleator U.S. Naval Research Laboratory, Washington, DC, USA Michael Smith Telespazio, ESAC, Madrid, Spain Randall Smith Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA Stephen Smith NASA Goddard Space Flight Center, Greenbelt, MD, USA Paolo Soffitta IAPS/INAF, Rome, Italy Sean Spooner University of New Hampshire, Durham, NH, USA Konstantin D. Stefanov Centre for Electronic Imaging, The Open University, Milton Keynes, UK Beate Stelzer Institut für Astronomie & Astrophysik, Eberhard Karls Universität Tübingen, Tübingen, Germany G. Stratta IAPS/INAF, Rome, Italy INFN-Roma, Rome, Italy INAF/OAS, Rome, Italy Martin Stuhlinger Serco Gestión de Negocios S.L., ESAC, Madrid, Spain Yang Su Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing, China Yuanyuan Su University of Kentucky, Lexington, KY, USA Jianchao Sun Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China H. Tajima Solar-Terresterial Enviornment Laboratory, Nagoya University, Nagoya, Japan Institute for Space–Earth Environmental Research, Nagoya University Furo-cho, Chikusa-ku, Nagoya, Japan

liv

Contributors

Tadayuki Takahashi Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba, Japan Harvey Tananbaum Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA Toru Tanimori Graduate School of Science Kyoto University, Kyoto, Japan Vincent Tatischeff CNRS/IN2P3, IJCLab, Université Paris-Saclay, Orsay, France Marco Tavani INAF/IAPS, Roma, Italy Università degli Studi di Roma Tor Vergata, Roma, Italy INFN Roma Tor Vergata, Roma, Italy Consorzio Interuniversitario Fisica Spaziale (CIFS), Torino, Italy Andrew M. Taylor Deutsches Elektronen Synchrotron DESY, Zeuthen, Germany B. J. Teegarden NASA Goddard Space Flight Center, Greenbelt, MD, USA Paola Testa Harvard-Smithsonian Center for Astrophysics, Cambridge, MA, USA David J. Thompson NASA Goddard Space Flight Center, Greenbelt, MD, USA Tuomo V. Tikkanen School of Physics and Astronomy, University of Leicester, Leicester, UK Martin Tluczykont Institute of Experimental Physics, University of Hamburg, Hamburg, Germany Francesco Tombesi Department of Astronomy, University of Maryland, College Park, MD, USA Department of Physics, University of Rome “Tor Vergata”, Rome, Italy INAF Osservatorio Astronomico di Roma, Monteporzio Catone, Rome, Italy NASA Goddard Space Flight Center, Greenbelt, MD, USA John A. Tomsick Space Sciences Laboratory, University of California, Berkeley, CA, USA Johannes Treis Max Planck Institute for Solar System Research, Justus-vonLiebig-Weg, Göttingen, Germany Hiroshi Tsunemi Osaka University, Toyonaka, Osaka, Japan Sergey Tsygankov Department of Physics and Astronomy, University of Turku, Turku, Finland Pietro Ubertini IAPS/INAF, Rome, Italy

B. J. Teegarden: retired.

Contributors

lv

Asif ud-Doula Penn State Scranton, Dunmore, PA, USA Alexey Uliyanov School of Physics, University College Dublin, Dublin, Ireland Melville P. Ulmer Department of Physics, Northwestern University, Evanston, IL, USA Sabina Ustamujic INAF-Osservatorio Astronomico di Palermo, Palermo, Italy Giuseppe Vacanti cosine, Sassenheim, The Netherlands Andrea Vacchi National Institute for Nuclear Physics INFN – Italy, Trieste (I) Branch, Trieste, Italy Rosa Valiante INAF-Osservatorio Astronomico di Roma, Monteporzio Catone, Italy INFN, Sezione di Roma I, Roma, Italy E. Vallazza Istituto Nazionale di Fisica Nucleare, Sezione di Milano Bicocca, Milan, Italy Eva Verdugo-Rodrigo European Space Agency (ESA), European Space Astronomy Centre (ESAC), Madrid, Spain Jacco Vink Anton Pannekoek Institute for Astronomy & GRAPPA, University of Amsterdam, Amsterdam, The Netherlands SRON National Institute for Space Research, Leiden, The Netherlands Enrico Virgilli Istituto Nazionale di Astrofisica INAF-OAS, Bologna, Italy Fabio Vito INAF-Osservatorio di Astrofisica e Scienza dello Spazio, Bologna, Italy Mark Vogelsberger Massachusetts Institute of Technology, Cambridge, MA, USA Stephen Walker Department of Physics and Astronomy, The University of Alabama in Huntsville, Huntsville, AL, USA C. Wang National Space Science Center, Chinese Academy of Sciences, Haidian District, Beijing, China Fa-Yin Wang Key Laboratory of Modern Astronomy and Astrophysics, Ministry of Education, Beijing, China School of Astronomy and Space Science, Nanjing University, Nanjing, China Natalie A. Webb Institute de Recherche en Astrophysique et Planétologie, Toulouse, France Jianyan Wei Key Laboratory of Space Astronomy and Technology, National Astronomical Observatories, Chinese Academy of Sciences, Beijing, People’s Republic of China University of Chinese Academy of Sciences, Beijing, China

lvi

Contributors

Jun-Jie Wei Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China School of Astronomy and Space Sciences, University of Science and Technology of China, Hefei, China Martin C. Weisskopf NASA-MSFC, Alabama, USA Belinda J. Wilkes Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA School of Physics, University of Bristol, Bristol, UK Brian J. Williams X-Ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, USA Richard Willingale University of Leicester, Leicester, UK Colleen A. Wilson-Hodge NASA Marshall Space Flight Center, Huntsville, AL, USA Jian Wu Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing, China Xue-Feng Wu Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China School of Astronomy and Space Sciences, University of Science and Technology of China, Hefei, China Di Xiao Purple Mountain Observatory, Chinese Academy of Sciences, Nanjing, China Yunxiang Xiao Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Yupeng Xu Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China University of Chinese Academy of Sciences, Beijing, China Hiroya Yamaguchi Institute of Space and Astronautical Science/JAXA, Sagamihara, Japan G. Yang Department of Physics and Astronomy, Texas A&M University, College Station, TX, USA George P. and Cynthia Woods Mitchell Institute for Fundamental Physics and Astronomy, Texas A&M University, College Station, TX, USA Yun-Wei Yu Institute of Astrophysics, Central China Normal University, Wuhan, China

Contributors

lvii

Weimin Yuan National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China Anna Zajczyk Center for Space Sciences and Technology, University of Maryland Baltimore County, NASA Goddard Space Flight Center, Center for Research and Exploration in Space Science and Technology, Baltimore, MD, USA Roberta Zanin CTA Observatory, Bologna, Italy Andreas Zezas University of Crete, Crete, Greece Bin-Bin Zhang Key Laboratory of Modern Astronomy and Astrophysics, Ministry of Education, Beijing, China School of Astronomy and Space Science, Nanjing University, Nanjing, China Chen Zhang National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China Fan Zhang Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China Shuang-Nan Zhang Key Laboratory for Particle Astrophysics, Institute of High Energy Physics, CAS, Beijing, China University of Chinese Academy of Sciences, Chinese Academy of Sciences, Beijing, China Zhe Zhang Chinese Academy of Sciences, Purple Mountain Observatory, Nanjing, China Irina Zhuravleva Department of Astronomy and Astrophysics, University of Chicago, Chicago, IL, USA Andreas Zoglauer Space Sciences Laboratory, University of California, Berkeley, CA, USA John ZuHone Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA

Part I Introduction to X-ray Astrophysics

1

A Chronological History of X-ray Astronomy Missions Andrea Santangelo, Rosalia Madonia, and Santina Piraino

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Early Years of X-Ray Astronomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rockets and Balloons in the 1960s and 1970s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ROCKETS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BALLOONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Uhuru and the Others, Opening the Age of the Satellites in the Early 1970s . . . . . . . . . . . . . . UHURU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . APOLLO 15 AND APOLLO 16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SAS-3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HEAO-1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Late 1970s and the 1980s: The Program in the USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EINSTEIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Late 1970s and the 1980s: The Program in Europe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . COPERNICUS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ANS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ARIEL V . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . COS-B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ARIEL VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . EXOSAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Late 1970s and the 1980s: The Program in Japan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HAKUCHO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HINOTORI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TENMA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GINGA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Late 1970s and the 1980s: The Program in Russia and India . . . . . . . . . . . . . . . . . . . . . . . FILIN / SALYUT-4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SKR -02 M . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A. Santangelo · R. Madonia () · S. Piraino Institute of Astronomy and Astrophysics, University of Tübingen, Tübingen, Germany e-mail: [email protected]; [email protected]; [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_147

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A. Santangelo et al. XVANTIMIR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ARYABHATA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

BHASKARA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Golden Age of X-Ray Astronomy, From the 1990s to the Present . . . . . . . . . . . . . . . . . . . THE PROGRAM IN THE USA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ULYSSES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BBXRT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . RXTE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . USA ONBOARD ARGOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . THE PROGRAM IN EUROPE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ROSAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BEPPOSAX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . THE PROGRAM IN JAPAN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ASCA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SUZAKU . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HITOMI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . THE PROGRAM IN RUSSIA AND INDIA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GRANAT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . IRS - P 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 1. List of the Rrockets Launched from 1957 to 1970 . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 2. List of the Balloon Missions Launched by the MIT Group . . . . . . . . . . . . . . . . . . Appendix 3. List of the Balloon Missions Launched by Worldwide Institution . . . . . . . . . . . . Appendix 4. Balloons Flown by AIT and MPI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Appendix 5. Transatlantic Balloons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

In this chapter, we briefly review the history of X-ray astronomy through its missions. We follow a temporal development, from the first instruments onboard rockets and balloons to the most recent and complex space missions. We intend to provide the reader with detailed information and references on the many missions and instruments that have contributed to the success of the exploration of the X-ray universe. We have not included missions that are still operating, providing the worldwide community with high-quality observations. Specific chapters for these missions are included in a dedicated section of the handbook.

Keywords

X-rays astronomy · X-rays balloons · X-rays rockets · X-ray space missions · History of x-ray astronomy

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Introduction The Earth’s atmosphere is not (fortunately!) transparent to X-rays. In the figure published in 1968 by Riccardo Giacconi and colleagues (Giacconi et al. 1968), a figure in many ways now historical, the attenuation of the electromagnetic radiation penetrating the atmosphere due to atmospheric absorption is presented as a function of the wavelength (see Fig. 1). To explore the universe in X-rays or in the soft gammas, it is therefore necessary to fly instrumentation onboard rockets, balloons, or satellites, and this presented new technological challenges at the end of the 1950s. The development of X-ray astronomy therefore had to wait for the development of rockets capable of carrying instrumentation into the upper layers of the atmosphere. Its history thus coincides with the “space race,” which began after the end of World War II and experienced a decisive acceleration with the launch of Sputnik in 1957 and Yuri Gagarin’s first human space flight ever on April 12, 1961 (Santangelo and Madonia 2014).

Fig. 1 Atmospheric absorption as a function of the wavelength (bottom axis). The solid lines indicate the fraction of the atmosphere, expressed in unit of 1 atmosphere pressure (right vertical axis) or in terms of altitude (left vertical axis), at which half of the incoming celestial radiation is absorbed by the atmosphere. Whereas radio and visible wavelength (blue rectangle) can reach without being absorbed the Earth’s surface, infrared, ultraviolet, and X-rays are strongly absorbed. (Credit High Energy Astrophysics Group, University of Tübingen)

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Following the best-known narrative, one usually traces the birth of X-ray astronomy to the program of the AS&E-MIT and especially to the flight of the rocket launched by Giacconi, Paolini, Rossi, and Gursky on June 18 1962 from White Sands (New Mexico), which led to the discovery of the first celestial source of X-rays, Sco X-1 (Giacconi et al. 1962). However, the story, as we will see later, is more complex. This paper, although detailed, is not exhaustive; further read could be found in Giacconi’s book “Secrets of the Hoary Deep” (Giacconi 2008), in Hirsh’s “Glimpsing an Invisible Universe” (Hirsh 1983), and in the review chapter of Pounds “Forty years on from Aerobee 150: a personal perspective” (Pounds 2002).

The Early Years of X-Ray Astronomy At the beginning of the twentieth century, there was great interest among scientific communities in the study of the Earth’s atmosphere. The emanation power of newly discovered radioactive elements, with new types of radiation, and the discovery of cosmic rays (then called “penetrating radiation”) are probably the main reason for this interest. Whether or not some layer of the upper atmosphere could be ionized was of particular interest for investigation (How suggested by Swann (1916a): The subject of the ionization of the upper atmosphere is one of extreme importance to students (SIC). From various points of view there are indications that the upper atmosphere is to be treated as a region of high electrical conductivity.

He further wrote Swann (1916b): both of Terrestrial Magnetism and of Atmospheric Electricity, and from various points of view there are indications that this region of the atmosphere is to be treated as one of relatively high electrical conductivity).

Working on radio waves, Tuve and Breit (1925) noted an interference phenomenon hypothetically due to the existence of an ionized reflecting layer in the upper atmosphere (the Kennelly-Heaviside layer or E layer) (Tuve 1967). The work of Tuve and Breit started a new research’s branch that in the end brought to the invention of the Radar. Between 1925 and 1930, Edward O. Hulburt published different papers on the reflecting properties of the Kennelly-Heaviside layer of the atmosphere (Taylor and Hulburt 1926; Hulburt 1928). He suggested that this should have been related to some Sun activity, because the ionization of the atmosphere could only be due to absorption of the Sun’s ultraviolet light or, more likely, X-rays. When, immediately after World War II, the US military offered research organizations and scientific institutions the opportunity to fly scientific instruments aboard V-2 rockets, developed during the war by Wernher von Braun and Edward Hulburt, head of the Naval Research Laboratory (NRL), enthusiastically accepted the offer to further investigate the reflective power of the atmosphere. Herbert Friedman was working in Hulburt’s department. He was interested in studying the Sun’s UV and X-rays to understand their role in the formation of the ionosphere. Using a combination of filters and gas mixtures, Friedman built several photomultiplier tubes, each sensitive in a narrow frequency range. With the V-2 number

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49 flight, launched in September 1949 from White Sands (Hirsh 1980), Friedman and colleagues confirmed the hypothesis that the ionization of the atmosphere above 87 km was due to solar X-rays emitted by the Sun’s corona (Friedman et al. 1951). For the first time, X-ray instrumentation had been launched above the Earth’s atmosphere. Further developments in the field were obtained, thanks to the construction of a new type of rocket, the Aerobee series, by James van Allen. Using Aerobee rockets, Friedman and colleagues conducted a series of night flights to search for stellar sources that, as the sun, could emit UV and X-ray radiation (Friedman et al. 1951; Kupperian et al. 1959). Only an upper limit of 10−8 ergs cm−2 s−1 Å−1 was obtained. Herbert Friedman (see Fig. 2) was a pioneer of X-ray astronomy: he obtained the first X-ray image of the Sun with a pinhole camera and flew the first Bragg spectrometer for measuring hard X-rays. The first satellite, SOLRAD, for long-term monitoring of the sun was also conceived and developed by Friedman. The prewar interest in the physics of the upper atmosphere and its interaction with the solar radiation was also strong in the UK, at the Imperial College and at the University College London (UCL). Pioneers of ionospheric physics and geomagnetism were Sir Edward Appleton, Sydney Chapman, John Ashworth Ratcliffe, Harrie Massey, and his student David Bates, and James Sayers. In 1942,

Fig. 2 Left: Herbert Friedman (1916–2000) was certainly a pioneer in X-ray research of the celestial sources. Right: Friedman’s US patent No. 2,475,603, for an adaptation of the tube used in a Geiger-Mueller counter. Thanks to a reduced background, Friedman’s tube design increased the counter’s sensitivity to weak sources. The details of the figure can be found at (Friedman 2023). (Credit: Public Domain)

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the Gassiot Committee, a committee concerned with upper atmospheric research, of the Royal Society began to cooperate with the Meteorological Research Committee in order to consider the use of rockets for a program for atmospheric physics (Pounds 2010). The war and the postwar economic difficulty of the nation slowed down the program, but eventually the common interest of military institutions and scientific groups gave the scientific community the possibility to fly instrumentation onboard of rockets and later satellites. Most remarkable was the agreement between the head of the physics department at UCL, Harrie Massey (According to Pounds “... Sir Harrie Massey ... was the key player in establishing the UK as the clear leader – after the USA and the Soviet Union – in the early years of space research (Pounds 2010)) and Sir Arnold Hall, director of the Royal Aircraft Establishment (RAE) Farborough (We cite Pounds (2010): “[...] on 13 May 1953, when the chairman of the Gassiot Committee was about to leave for Shenley to play in the annual UCL staff-students cricket match. Massey’s response to the question, ‘would there be interest in using rockets available from the Ministry for scientific research?’ was an immediate ‘yes’ [...]”). The result was the funding of the Skylark Program and the formation of space research group at UCL (Robert Boyd), Imperial College (Percival Albert Sheppard), Birmingham University (James Sayers), Queen’s University of Belfast (David Bates and Karl George Emeleus), and University College Wales, Aberystwyth (William Granville Beynon). The early Skylark missions were dedicated to the study of the Sun, the Lyman-α and X-ray emission, as well as the study of the upper atmosphere, as already said. The International Geophysical Year (1957/1958) was a motivating occasion for the development of projects and studies. Indeed, the first successful test launch of a Skylark rocket occurred on February 13, 1957, from Woomera Range, Adelaide, Australia. The choice of Woomera was due to the personal Australian relationships of H. Massey (Massey was born on May 16, 1908, in Invermay, Victoria, Australia). Nine months later on November 13, the first Skylark rocket with a scientific payload was launched from Woomera. The program was very successful, new instruments for X-ray were developed by a group of young scientists of the UCL, among them was Ken Pounds who, in 1960, received an assistant lectureship at Leicester with a 3-year grant of £13006 from the Department of Scientific and Industrial Research. This generous fund was indubitably a consequence of the launch of the Sputnik I. The two new instrument developed by UCL and then the Leicester group were as follows: a photographic emulsion, protected in an armored steel cassette with the filter mounted behind aluminum and beryllium foils (“This device was flown successfully in over 20 Skylark flights during the 1960s, providing the first direct broadband X-ray spectra over a wide range of solar activity (Pounds 1986)”), and a proportional counter spectrometer (PCS) that, according to Ken Pounds, was to became the workhorse detector in X-ray astronomy (Pounds 2010). The studies of solar X-rays were pioneered in the Netherlands by Kees de Jager, who started a laboratory for space science at the University of Utrecht. He was supported by the atomic physicist Rolf Mewe, who developed theoretical models

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for data interpretation. Also, the cosmic-ray working group at the University of Leiden, in the 1960s, worked on X-ray with rockets and balloons in collaboration with the Nagoya University and ISAS in Japan. Eventually in 1983, these groups, together with the Groningen University, joined in the SRON (Stichting Ruimte Onderzoek Nederland) with the aim to develop instruments for space science missions. As already mentioned, the turning point for space activities, in general, and therefore for X-ray astronomy was the so-called Sputnik shock of 1957. New opportunities appeared and space research was welcomed and financed. In the USA, in September 1959, Bruno Rossi, chairman of the board of the American Science & Engineering (AS&E), a start-up high-tech company formed in Cambridge a year earlier by Martin Annis, suggested to Riccardo Giacconi, who was called from Princeton to become head of the Space Science Division of the AS&E, to develop some research program on X-ray astronomy. In the next few months, on February 1960, two proposals were submitted to the newly formed NASA: one, rather visionary, to develop an X-ray telescope (Wolter type) and another for a rocket mission to investigate the emission (or scattering) of X-rays from the Moon and from the Crab Nebula. NASA accepted the first proposal and refused the second one. In an oral interview, Nancy Roman, of NASA, said that this proposal was not funded because, in her mind, it was impossible to detect such emission (Roman 1980) (According to Nancy Roman: “Yes. The first X-ray work was ’62, if I remember right, and that was funded by the Air Force. I didn’t fund it. I guess you can blame me for being too good a scientist or you can blame me for not having foresight. Giaconni came to me with a proposal to fly an experiment to measure solar X-rays scattered off the Moon, and it was, to me, absolutely clear that that was impossible. Still is.[...] If they had come to me to say they wanted to do a sky survey in X-ray, I think, admittedly in hindsight, that I would have supported them, because I was very much aware of the desirability of finding out something about new wave length regions. But I could not see supporting an experimental rocket to measure reflected solar X-rays from the moon.” Note that the misspelling of the name of Giacconi is already in the original transcript). Nevertheless, certain of the importance of rocket mission and waiting for the realization of the telescope, Giacconi sent the proposal to the Air Force Cambridge Research Laboratory that, on the contrary to NASA, funded a series of rocket launches. The first and second Aerobee rocket launch failed, but the third one was very successful: it changed the history of astronomy and our perception of the universe. It is fair to mention that in December 1960, a year before the discovery of Sco X-1, Philip Fisher, of the Lockheed Company, had submitted a proposal to NASA to search for cosmic X-ray sources (Fisher 1960). Nevertheless, the launches of the Lockheed rockets (Aerobee 4.69 and 4.70) occurred on September 30, 1962, and March 15, 1963, after the discovery of Sco X-1. However, according to Fisher (2009), his results were not properly taken into account and cited in the subsequent scientific meetings focused on X-Ray astronomy.

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Rockets and Balloons in the 1960s and 1970s ROCKETS On June 18, 1962, an air force Aerobee rocket was launched from White Sands Missile Range in New Mexico with the aim and the appropriate instrumentation to search for X-ray emission from celestial objects. The pioneer AS&E-MIT experiment discovered the first extra solar source of X-rays (see Fig. 3), a diffuse X-ray background component, and the probable existence of a second source in the proximity of the Cygnus constellation (Giacconi et al. 1962). The payload consisted of three Geiger counters, each composed of seven mica windows of 20 cm2 comprising area; the detectors had a sensitivity between 2 and 8 Å. As predicted by Nancy Roman, no X-rays from the Moon were observed. That was just the beginning: an intense program based on rocket launches was started. Rockets observed for only a few minutes, from a maximum altitude of ∼200 km. The list of the rocket experiments launched until 1970 is included in “Appendix 1. List of the Rrockets Launched from 1957 to 1970”. The large majority of rocket launches was performed by US scientists. However, the UK participated to the early race of X-ray astronomy, with the Skylark launches. In particular, Skylark launches SL118 and SL119, from Woomera, Australia, provided for the first time a survey of X-ray sources in the Southern Hemisphere.

BALLOONS The short fly-time of the sound rockets was a clear limit for the study of the X-ray sources, especially once their variability was revealed. With the use of aerostatic

Fig. 3 The discovery plot which marked the beginning of X-ray astronomy. The azimuthal distribution of the count rates of the Geiger-Müller detectors flown in the June 1962 flight is shown. (Credit Giacconi et al. 1962)

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balloons, long-duration observations on the order of hours became possible, even if from a lower altitude. Different research groups undertook intense and fruitful balloon campaigns. In particular, the group at MIT of George W. Clark, Gordon P. Garmire, and Minoru Oda, on leave from Tokyo University, was involved in a robust and successful program for X-ray sky observations with balloons. A detailed list of the MIT Balloon flights is reported in “Appendix 2. List of the Balloon Missions Launched by the MIT Group”. The efforts to fly balloon mission for X-ray astronomy were undertaken by other institutions worldwide. In particular, the following groups were rather active: Leiden University; the GIFCO group at Bologna University and the TESRE Institute of the Consiglio Nazionale delle Ricerche (CNR); the Centre d’Etudes Nucléaires (CEN) de Saclay (France); the Tata Institute in Mumbai (India); the Rice University, Houston (Texas); the Adelaide University (Australia); and Nagoya University (Japan). A detailed list of the Balloon flights launched by these institutions is reported in “Appendix 3. List of the Balloon Missions Launched by Worldwide Institution”. We wish to mention in particular that a balloon program in the hard X-rays (20–200 keV) was pursued by the Institut für Astronomie und Astrophysik der Universität Tübingen (AIT) and the Max Planck-Institut für Extraterrestrische Physics in Garching (MPE) from 1973 to 1980 with nine successful balloon flights from Texas and Australia (Staubert et al. 1981). The program was led by Joachim Trümper who started German X-ray astronomy in Tübingen before moving to the directorship at MPE. A detailed list of the balloon flights launched by these institutions is reported in “Appendix 4. Balloons Flown by AIT and MPI”. The instruments were built and operated by MPE and AIT and consisted of scintillation counters with NaI(Tl) crystals (Kendziorra et al. 1974; Reppin et al. 1978). The close cooperation between AIT and MPI continued in the 1980s with the construction and operation of the high-energy X-ray experiment (HEXE) used during three successful balloon campaigns (May 1980 and September 1981 launched from Palestine/Texas, as well as November 1982 launched from Uberaba/Brazil). At the beginning of the 1970s, the main worldwide available balloon launch site was the NSBF facility in Palestine, Texas, USA. In the period between 1967 and 1976, the average flight duration was about 10–15 h, with a few exceptions (four flights lasted 40–60 h and only one, in 1974, up to 120 h). The opening in 1975 of the stratospheric balloon launch base of Trapani-Milo in Sicily provided the opportunity to use transatlantic flights, with long and stable durations, and the capability to carry payloads with mass up to 2–3 tons at altitudes above 38– 42 km, perfect to realize X-ray investigations of cosmic sources (Ubertini 2008). The flight campaign started with a precursor flight operated by the Italian TrapaniMilo ground operation crew and a launch team from NSBF-NASA. The payload had a total weight of 1500 kg, out of which was 500 kg of scientific experiments and flight services. The flight started on August 5, 1975, and safely landed on the US East Coast after a flight of 81 h. Several successful balloon experiments were performed by the Istituto di Astrofisica Spaziale of Rome (IAS), in collaboration with others Italian and international institutes (Among them are the Istituto di Fisica Cosmica of Milan (IFC), the Laboratorio di Tecnologie e Studio delle Radiazioni Extraterrestri of Bologna (TESRE), the Istituto di Fisica Cosmica con Applicazione

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all’Informatica of Palermo (IFCAI), and international institutions, such as the University of Southampton and RAL (the UK), TATA Institute (Mumbai, India), Tübingen University (Germany), ADFA (Australia), CNES (France), INTA (Spain), etc. (Ubertini 2008)). The list of the major transatlantic balloon missions is reported in “Appendix 4. Balloons Flown by AIT and MPI”.

Uhuru and the Others, Opening the Age of the Satellites in the Early 1970s The first satellite designed for cosmic X-ray observation was the US Vanguard 3 satellite, launched on September 18, 1959. It operated until December 11, 1959. The payload consisted of ion chambers provided by NRL that were intended to detect (solar) X-rays (and Lyman-alpha). Unfortunately as noted in Friedman (1960) “the Van Allen Belt radiation swamped the detectors most of the time and no useful X-ray data were obtained.” On October 13, 1959, the US Explorer 7 satellite was launched from Cape Canaveral. It operated until August 24, 1961, and, like Vanguard 3, carried, among other experiments, ion chambers provided by NRL. The goal was to detect (solar) X-rays (and Lyman-alpha). Unfortunately, no useful X-ray data were obtained similar to the case of Vanguard 3 (Friedman 1960).

UHURU The Small Astronomical Satellite 1 (SAS-1) was the first of small astronomy satellites developed by NASA and was entirely devoted to the observations of cosmic X-ray sources (see Fig. 4). It was launched on December 12, 1970, from the Italian San Marco launch platform off the coast of Kenya, operated by the Italian Centro Ricerche Aerospaziali. December 12 was the seventh anniversary of the independence of Kenya, and in recognition of the kind hospitality of the Kenyan people, Marjorie Townsend, the NASA mission project manager, named the successfully launched mission “Uhuru,” Swahili term for “freedom.” Uhuru was launched into a nearly equatorial circular orbit of about 560 km apogee and 520 km perigee, with an inclination of 3◦ and an orbital period of 96 min. The mission ended in March 1973. The X-ray detectors consisted of two sets of large-area proportional counters sensitive (with more than 10 percent efficiency) to X-ray photons in the 1.7–18 keV range. The lower limit was determined by the attenuation of the beryllium windows of the counter plus a thin thermal shroud, needed to maintain the temperature stability of the spacecraft. The upper energy limit was determined by the transmission properties of the filling gas. Pulse-shape discrimination and anticoincidence techniques were used to reduce the particle background and highenergy photons (Giacconi et al. 1971). The main features of the mission are reported in Table 1.

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Fig. 4 Left: Marjorie Townsend discusses the SAS-1 X-ray Explorer Satellite’s performance with Bruno Rossi during preflight tests at NASA’s Goddard Space Flight Center. Marjorie Townsend was the first woman to become a satellite project manager at NASA. Right: a schematic of the satellite. All major basic elements of an X-ray satellite are shown. (Credit NASA) Table 1 Uhuru

Instrument Bandpass (keV) Eff Area (cm2 ) Field of view (FWHM) Timing resolution (s) Sensitivity (ergs cm−2 s−1 )

Set 1 1.7–18 840 0.52◦ × 5.2◦ 0.192 1.5×10−11

Set 2 1.7–18 840 5.2◦ × 5.2◦ 0.384

The main science achievement of Uhuru was, with no doubt, the completion of the first X-ray all-sky survey up to a sensitivity of 0.5 mCrab (between 10 and 100 times better than what achievable with rockets). Uhuru detected 339 X-ray sources of different classes: X-ray binaries, supernova remnants, Seyfert galaxies, and clusters of galaxies, for which diffuse X-ray emission was discovered (Forman et al. 1978) (Fig. 5).

APOLLO 15 AND APOLLO 16 On July 26, 1971, the Apollo 15 lunar mission carried, inside the Scientific Instrument Module (SIM) of the Service Module, an X-ray fluorescence spectrometer (XRFS (Jagoda et al. 1974; Adler et al. 1975)) and a gamma-ray spectrometer (GRS), with the aim to study the composition of the lunar surface. Similarly, on April 16, 1972, the same suite of instruments was flown on Apollo 16. The XRFS was manufactured by the AS&E. The main objective was indeed to study the Moon’s surface from lunar orbit, in order to better understand the Moon’s overall chemical composition (see Gloudemans et al. 2021). On the way back from the Moon to the

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Fig. 5 The map of the X-ray sky after Uhuru, according to the fourth Uhuru catalog. (Figure adapted from Forman et al. 1978)

Fig. 6 The Scientific Instrument Module of Apollo 15. (Credit HEAG@UCSD High Energy Astrophysics Group at UCSD 2023)

Earth (i.e., during the “trans-Earth coast”), the XRFS observed parts of the X-ray sky. The prime objective of the Apollo observations during the trans-Earth coast was to understand the nature of the X-ray sources discovered earlier (e.g., Cyg X-1, Sco X-1), by observing them continuously for approximately half an hour to an hour, which was unique at that time. UHURU could only observe for approximately 1 or 2 min per sighting. Preliminary results were reported in the Apollo 15 and 16 Preliminary Science Reports (Adler et al. 1972a, b). Further results from the transEarth coast observations include a mysterious (type I?) burst seen by Apollo 15 (see Kuulkers et al. 2009) and a gamma-ray burst seen by Apollo 16 (Metzger et al. 1974; Trombka et al. 1974) (Fig. 6).

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SAS-3 The second small satellite for X-ray astronomy SAS-3 was launched on May 7, 1975 again from the Italian San Marco launch facility. Its initial orbit was equatorial. SAS-3 was designed as a spinning satellite. The spin rate was controlled by a gyroscope that could be commanded to stop rotation. In this way, all instruments could be pointed providing about 30 min of continuous exposures on sources, such as a pulsars, bursters, or transients. The nominal spin period was 95 min, which was also the orbital period having an inclination of 3◦ and an altitude of 513 km. The scientific payload (Mayer 1975), designed and built at MIT, consisted of four X-ray instruments (see Fig. 7): • Two rotating modulation collimator systems (RMCS Schnopper et al. 1976), each of which had an effective area of 178 cm2 and consisted of a modulation collimator and proportional counters active in the energy bands of 2–6 and 6–11 keV. The collimator had an overall FOV of 12◦ ×12◦ , with a FWHM of 4.5 arcmin, centred on the direction parallel to the spin axis (satellite +Z-axis). • Three crossed slat collimators (SME Buff et al. 1977), each with a proportional counter. They were designed to monitor a large portion of the sky in a wideband of directions centred on the plane perpendicular to the rotation axis of the satellite. Each detector had an on-axis effective area of 75 cm2 . The collimators defined three long, narrow FoVs, which intersected on the +Y axis and were inclined with respect to the YZ plane of the satellite at angles of −30◦ , 0◦ , and +30◦ , respectively. During the scanning mode, an X-ray source would appear in the three detectors. Three lines could then be obtained, and their intersection determined the source position. The central collimator had a field of view of 2◦ ×120◦ with FWHM 1◦ ×32◦ . The left and right collimators had narrower but similar responses, i.e., 0.5◦ ×32◦ (FWHM) and 1.0◦ ×100◦ (FW). The proportional counters were filled with argon and were sensitive in the range

Fig. 7 Left: a schematic diagram of the instruments of the science payload. SAS3 was already a complex mission. Note that it also had onboard a set of four grazing-incidence concentrators. Right: an artistic impression of the SAS-3 satellite. (Credit NASA)

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5–15 keV. In addition, the central detector featured a xenon counter, located behind the argon detector, that extended the energy range to 60 keV. Over the energy range 1.5–6 keV, 1 count/s was equivalent to 1.5 × 10−10 erg cm−2 s−1 for a Crab-like spectrum. In any given orbit, at the nominal 95 min spin period, 60% of the sky was scanned by the centre slat detector with an effective area from 300–1125 cm2 . • Three tube collimators (TC Lewin et al. 1976), sensitive to X-rays in the range 0.4–55 keV, located above and below, each of which with an effective area of 80 cm2 . The third was along “the left” with an effective area of 115 cm2 of the slat collimators, that defined a 1.7◦ circular FOV. The tube collimator above the slat collimator was inclined at an angle of 5 degrees above the Y-axis and could therefore be used as a background reference for the other tube collimators aligned along the Y-axis. • One low-energy detector system (LEDS Hearn et al. 1976) to the right of the slat collimators. It consisted of a set of four grazing incidence, parabolic reflection concentrators with two independent gas-flow counters, sensitive to X-rays in the range 0.15–1.0 keV, and with an effective area of 20 cm2 . The major scientific objectives were reaching a position accuracy of bright X-ray sources to ∼15 arcs; studying a selected sample of sources over the energy range 0.1–55 keV; and searching the sky for X-ray novae, flares, and other transient phenomena. The science highlights of the mission included the discovery of a dozen X-ray burst sources (Lewin et al. 1976), among which include the Rapid Burster (Marshall et al. 1979); the first discovery of X-ray from an highly magnetic White Dwarf (WD) binary system, AM Her (Hearn and Richardson 1977); the discovery of X-ray from Algol and HZ 43 (Schnopper et al. 1976); the precise location of about 60 X-ray sources; and the survey of the soft X-ray background (0.1–0.28 kev) (Marshall and Clark 1984).

HEAO-1 In 1977, NASA started launching a series of very large scientific payloads called high-energy astronomy observatories (HEAO). They were launched by Atlas Centaur rockets. The payloads were about 2.5 m×5.8 m in size and ∼3000 kg in mass (Bradt 1992; Tucker 1984; Peterson 1975). The telemetry rate was large, ∼6, 400 bits/s compared to the 1,000 bits/s typical of earlier satellites. The first of these missions, HEAO-1 (HEAO-A before launch), surveyed the X-ray sky almost three times over the 0.2 keV–10 MeV energy band and provided nearly constant monitoring of X-ray sources near the ecliptic poles. More detailed studies of a number of objects were made through pointed observations lasting typically 3–6 h. HEAO-1 operated from August 12, 1977, to January 9, 1979, in a satellite orbit at 432 km, with an inclination of 23◦ and a period of 93.5 min. The science payload included four major instruments (for the details see Table 2):

0.25–25 1350–1900

1◦ ×4◦ -1◦ ×0.5◦

FOV

A1(LASS)

Payload Detector Energy range (keV) Eff area (cm2 )

Table 2 HEAO-1 payload A2(CXE) LED 0.15–3 2×400 MED 1.5–20 800 1.5◦ ×3◦ 3◦ ×3◦ 3◦ ×6◦

HED 2.5–60 3×800 4◦ ×4◦

A3(MC) MC1 0.9–13.3 2×400 300

MC2

1.7◦ ×20◦

A4 LED 15–200 2×100

17◦

MED 80–2000 4×45

37◦

HED 120–10000 100

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• A1 – a large-area sky survey experiment (LASS) consisting of a proportional counter array (seven modules), sensitive in the 0.25–25 keV energy range, designed to survey the sky for discrete sources (Friedman 1979). • A2 – a smaller proportional counter array, the cosmic X-ray experiment (CXE), designed principally to study the diffuse X-ray background from 0.215–60 keV (Rothschild 1979; Boldt 1987). It consisted of six proportional counters: – Low-energy detectors (LED), two detectors operating in the 0.15–3.0 keV energy range – Medium-energy detector (MED) operating in the 1.5–20 keV range – High-energy detector (HED), three detectors in the 2.5–60 keV energy range • A3 – a Modulation Collimator (MC) experiment, covering the energy range of 0.9–13.3 keV, with two detectors (MC1and MC2). It was designed to determine accurate (∼1′ ) celestial positions (Gursky et al. 1978). • A4 – a high-energy experiment, the hard X-ray/low-energy gamma-ray experiment (Matteson 1978; Peterson 1975), extending to ∼10 MeV, consisting in seven inorganic phoswich scintillator detectors: – Low-energy detectors, two detectors in the 15–200 keV range – Medium-energy detectors operating in the 80 keV–2 MeV range – High-energy detector in the range 120 keV–10 MeV Comprehensive catalogs of X-ray sources (one for each experiment) were obtained (see Fig. 8). The LASS and the occasional pointed mode, with 1◦ × 4◦ FWHM collimation, enabled the studies of the rapid temporal variability, with,

Fig. 8 The HEAO-1 A-1 X-ray source catalog includes results from the first 6 months of data from HEAO-1, during which time a scan of the entire sky was completed. It contains positions and intensities for 842 sources. Half of the sources remained unidentified at the time of catalog publication (1984). (Credit NASA)

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e.g., the discovery of aperiodic variability in Cyg X-1 down to a timescale of 3 ms (Meekins et al. 1984), the first eclipse in a low-mass binary system (X1658-298) (Cominsky and Wood 1984, 1989), the 5-Hz quasiperiodic oscillation (QPO) in the “normal-branch” mode of Cyg X-2 (Norris and Wood 1987), and the variability on the timescale of tens of milliseconds in an X-ray burst (Hoffman et al. 1979). The CXE experiment provided a complete flux-limited high galactic latitude survey (85 sources), which yielded improved X-ray luminosity functions for active galactic nuclei and clusters of galaxies (Piccinotti et al. 1982), a classification among AGN types (Mushotzky 1984), and a measurement of the diffuse X-ray background from 3–50 keV (Marshall et al. 1980; Boldt 1987). The celestial positions, accurate to about 1 arcmin, obtained with the MC experiment, led to several hundred optical identifications and source classifications. The results from the high-energy instrument included the observation of the high-energy spectra of AGN, which were key for understanding the origin of the diffuse background (Rothschild et al. 1983); the discovery of the binary system, LMC X-4, with ∼30 d periodic on-off states; and the second example (after Her X-1) of cyclotron absorption in a binary system, 4U0115+63 (Wheaton et al. 1979).

The Late 1970s and the 1980s: The Program in the USA Thanks to Uhuru and HEAO-1, a new sky had been revealed, and X-ray astronomy entered a new mature phase, thanks to collimators and proportional counters. A key step forward was now necessary: X-ray focusing. A step that had been prepared by Riccardo Giacconi since the beginning of the 1960s, with robust R&D plans.

EINSTEIN All efforts to develop X-ray focusing telescopes resulted in a proposal to NASA for a focused large orbiting X-ray telescope (LOXT), whose team was assembled by Giacconi in 1970. Indeed, the second of NASA’s three high-energy astrophysical observatories, HEAO-2, renamed Einstein after launch, revolutionized X-ray astronomy, thanks to its Wolter type-I grazing-incidence X-ray focusing optics (Wolter 1952) (see Fig. 9). It was the first high-resolution imaging X-ray telescope launched into space (Giacconi et al. 1979). Focusing enabled not only a much better position constraint but also was key to dramatically reduce the particle background, since the volume of the detector was now significantly smaller than before. The HEAO2 sensitivity was then several hundred times better than any previous mission. Thanks to its few arcsec angular resolution, tens of arcmin field of view, and greater sensitivity, it was now possible to study the diffuse emission, to image extended objects, and to detect a large number of faint sources. It was a revolutionary mission in X-ray astronomy, and its scientific outcome completely changed our view of the X-ray sky. Einstein operated from November 12, 1978, to April 26, 1981, in a satellite orbit at 465–476 km, with 23.5◦ inclination and a period of 94 min. The

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Fig. 9 Left: a schematic view of the Einstein satellite. Right: the Einstein view of the galactic center of the Andromeda Galaxy (M31). The power of focusing appears in the many point sources resolved. (Both figures credit NASA) Table 3 HEAO 2 science payload Payload Bandpass (keV) Eff area (cm2 )

WolterType 1 IPC HRI 0.4–4 0.15–3 100 5–20

SSS 0.5–4.5 200

Field of view (FOV)

75′

25′

6′

Spatial resolution

∼1′

∼2′′

E ∆E

3–25

FPCS 0.42–2.6 0.1–1 6′ 1′ × 20′ 2′ × 20′ 3′ × 30′ 50–100∗ 100–1000∗∗

MPC 1.5–20 667

OGS

1.5◦

∼20%

∼50

scientific payload consisted of four instruments covering the energy range 0.2– 20 keV, which could be rotated, one at a time, into the focal plane of the optics (see Table 3 for the details of the instrument parameters): • An imaging proportional counter (IPC Gorestein et al. 1981; Giacconi et al. 1979), operating in the 0.4–4.0 keV with high sensitivity • A high-resolution imager (HRI Grindlay et al. 1980) operating in the 0.15– 3.0 keV range • A solid-state spectrometer (SSSn Holt 1976) in the 0.5–4.5 keV range with moderate sensitivity • A focal plane crystal spectrometer (FPCS Lum et al. 1992) in the 0.42–2.6 keV E E of 50–100 for E0.4 keV. Einstein also carried a non-focusing monitor proportional counter array (MPC, Gaillardetz et al. 1978) to measure the higher-energy emission (2–15 keV) of bright

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sources in the view direction of the main telescopes, and an objective grating spectrometer (OGS Harris 1984), with 500 mm−1 & 1000 mm−1 ; energy resolution E ∆E ∼50 was used in conjunction with HRI. Many fundamental and far-reaching results were obtained (NASA’s HEASARC 2023): The high spatial resolution morphological studies of supernova remnants The many faint sources resolved in M31 and the Magellanic Clouds The first study of the X-ray emission from the hot intra-cluster medium in clusters of galaxies revealing cooling inflow and cluster evolution The discovery of X-ray jets from Cen A and M87 aligned with radio jets The first medium and deep X-ray surveys On top of this, Einstein discovered thousands of “serendipitous” sources. Einstein was also the first X-ray NASA mission to have a Guest Observer Program.

The Late 1970s and the 1980s: The Program in Europe COPERNICUS Copernicus or Orbiting Astronomical Observatory 3 (OAO-3) was a collaborative effort between the USA (NASA) and the UK (SERC). The main instrument onboard was the Princeton University UV telescope (PEP) consisting of a Cassegrain telescope with an 80 cm primary mirror, a 7.5 cm secondary, and a Paschen-Runge spectrometer. In addition, the mission carried an X-ray astronomy instrument developed by the Mullard Space Science Laboratory (MSSL) of UCL. OAO-3 was launched on August 21, 1972, into a circular orbit of 7,123 km radius and an inclination of 35◦ . Although some of the instruments ceased to work, it operated for almost 9 years until February 1981. The University College of London X-ray Experiment (UCLXE) consisted of four co-aligned X-ray detectors observing in the energy range 0.7–10 keV, the collimated proportional counter (CPC), and three Wolter type-0 grazing-incidence telescopes (WT-0). At the focus of the telescopes, two proportional counters (PC1, PC2) and one channel photomultiplier (CHP) were used. In Table 4, we report the main parameters of the instruments (Bowles et al. 1974). Science highlights of the mission were the following: the discovery of several long period pulsars (e.g., X Per) (White et al. 1976), the discovery of absorption dips in Cyg X-1 (Mason et al. 1974), the long-term monitoring of pulsars and other bright

Table 4 Aside an instrument for UV astronomy, Copernicus carried onboard four X-ray detectors

Instrument Bandpass (nm) Eff area (cm2 ) FOV (FWHM)

CPC 0.1–0.3 17.8 –

Energy range (keV)

0.7–10

WT-0 PC 1 0.3–0.9 5.5 1′ 3′ 10′

PC 2 0.6–1.8 12.5 2′ 6′ 10′

CHP

2–7 22.9 10′

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X-ray binaries (Branduardi et al. 1978), and the observed rapid intensity variability from Cen A (Davison et al. 1975). ANS

ANS (Astronomische Nederlandse Satelliet) was a collaboration between the Netherlands Institute for Space Research (NIRV) and NASA. Launched on August 30, 1974, the mission reentered the atmosphere on June 14, 1977. Its orbit should have been circular with a radius of 500 km, but due to a failure of the first-stage guidance, the final orbit was highly inclined (98◦ ) and elliptic (258 km perigee and 1173 km apogee) with a period ∼99 min. ANS took onboard three instruments: an ultraviolet telescope spectrometer (UVT) (vanDuinen et al. 1975) by the University of Groningen; a soft X-ray experiment (SXX), den Boggede et al. (1975) developed by the University of Utrecht, that consisted of two parts known as Utrecht soft and medium X-ray detectors; and a hard X-ray experiment (HXX) (Gursky et al. 1975) of the AS&E-MIT group. In particular, the UVT instrument consisted of a Cassegrain telescope followed by a grating spectrometer of the Wadsworthtype; the Utrecht soft X-ray (USXD) consisted of a grazing-incidence parabolic collector, while the Utrecht medium X-ray detector (UMXD) was a 1.7 µ titanium proportional counter; and the HXX experimental package contained three major components: a collimator assembly, a large-area detector (LAD) unit, and a Bragg crystal spectrometer (BCS) tuned for detection of the silicon lines. The details of these experiments are summarized in Table 5. ANS scientific highlights include the discovery of X-ray bursts; flash of X-rays of several seconds, emitted by neutron stars in binary accreting systems (Heise et al. 1976); the detection of X-rays from Stellar Coronae (Capella) (Mewe et al. 1975); and the first detection of X-ray flares from UV Ceti and YZ CMi (Heise et al. 1975)

ARIEL V The Ariel V Satellite, developed by a joint collaboration of the UK and the USA, was launched from the San Marco platform on October 15, 1974, into a low inclination (2.8◦ ), near-circular orbit at an altitude of ∼520 km. The orbital period was 95 min. The mission ended on March 14, 1980. The British Science Research Council managed the project for the UK, the NASA GSFC for the USA. Ariel V Table 5 ANS UVT Instrument Bandpass (keV) Bandpass (Å) Eff area (cm2 ) FOV (FWHM)

1550 Å–3300 Å 266 2.5′ ×2.5′

SXX

HXX

USXD

UMXD

LAD

BCS

0.2–0.28

1–7

1–30

1–4.2

144 34′

45 38′ ×75′

40 10′

3◦

6 3◦

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was dedicated to the monitoring of the X-ray sky. The science payload included six instruments. Four, aligned with the spin axis, were devoted to a detailed study of a small region of the sky within ∼10◦ of the satellite pole. The set included the following: a rotation modulation collimator (RMC or Exp-A), consisting of rotation collimators and three different detectors, a photo-multiplier, an electron multiplier, and a proportional counter; a high-resolution proportional counter spectrometer (Exp-C); a Bragg crystal spectrometer (Exp-D), operating in the energy band 2–8 keV, that used a honeycomb collimator; and a scintillator telescope (ST or ExpF). The remaining two instruments were arranged in a direction perpendicular to the spin axis. The all-sky monitor (ASM or Exp-G), the only experiment of the mission developed by the USA, utilized two X-ray pinhole cameras to image the sky in order to monitor transient X-ray phenomena and all the strong X-ray sources for long-term temporal effects; the Sky Survey Instrument (SSI or Exp-B) (Villa et al. 1976) consisted of two pairs of proportional counters (LE and HE) (Smith and Courtier 1976). Ariel V performed long-term monitoring of numerous X-ray sources. It also discovered several long period (minutes) X-ray pulsars (White et al. 1978) and several bright X-ray transients probably containing a black hole (e.g., A0620-00=Nova Mon 1975) (Pound et al. 1976; Elvis et al. 1975). It also discovered iron line emission in extragalactic sources (Sanford et al. 1975) and established Seyfert I galaxies (AGN) as a class of X-ray emitters. In Table 6, we report details of the scientific payload of the mission.

COS-B Cos-B was an ESA mission built by the so-called Caravane Collaboration that included the following: the Laboratory for Space Research, Leiden, the Netherlands; Istituto di Fisica Cosmica e Informatica del CNR, Palermo, Italy; Laboratorio di Fisica Cosmica e Tecnologie Relative del CNR, Milano, Italy; Max-PlanckInstitut fur Extraterrestrische Physik, Garching, Germany; Service d’Electronique Physique, CEN de Saclay, France; and Space Science Department of ESA, ESTEC, Noordwijk, the Netherlands. The principal scientific objective was to provide a view of the gamma-ray universe; nevertheless, it took onboard a proportional counter sensitive to 2–12 keV

Table 6 Ariel V payload consisted of six instruments: four were aligned with the spin axes (Exp A, Exp C, Exp D, Exp F), and two were offset (Exp G, Exp B) Aligned A (RMC) Instrument Bandpass (keV) Eff area (cm2 ) FOV (FWHM) Energy range (keV)

0.3–30 – 10◦ -20◦ 0.7-10

C

D

F (ST)

1.3–28.6 – 3.5◦

2–8 –

26–1200 8

Offset G (ASM) 3–6

B (SSI) LE

HE

1.2–5.8 290

2.4–19.8

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Table 7 Ariel VI featured two X-ray instruments onboard the SXT and the MXPC

Experiment Bandpass (keV) Eff area (cm2 ) FOV (FWHM)

SXT Grazing telescope + Xe prop. counter 0.1–2 65 1.2◦ –4.6◦

MXPC

1–50 300 3◦

X-rays. As one can read in Bennet (1990) ,“This detector was intended to provide synchronization of possible pulsed gamma-ray emission from pulsating X-ray sources. The pulsar synchronizer was also used for monitoring the intensity of radiation from X-ray sources.”

ARIEL

VI

UK6, named Ariel VI after launch, was launched from the Wallops Island Launch Center in the USA on June 2, 1979. The orbit was elliptical with an apogee of 650 km and a perigee of 600 at an inclination of 55 ◦ . Ariel VI was a national UK mission but, in comparison with the success of its predecessor Ariel V, much less successful due to the problems caused by the interference with powerful military radars. In fact, strong magnetic fields severely hammered the command encoder and the pointing operations. Ariel VI carried three scientific instruments: one was a cosmic-ray experiment consisting of Cerenkov and gas scintillation counters and the other two were X-ray instruments. The soft X-ray telescope (here SXT), developed by MSSL in collaboration with the University of Birmingham, consisted of four grazing-incidence hyperboloid mirrors that reflected X-rays through an aperture/filter to four continuous-flow propane gas detectors (Cole et al. 1981). The medium X-ray proportional counter (MXPC) developed by the Leicester University consisted of four multilayered Xe proportional counters (Hall et al. 1981). Ariel VI continued to observe until February 1982. Table 7 shows some of the features of the X-ray instruments. Although partially, the observations carried with Ariel VI brought some results like the observation of phase variable iron line emission of the source GX 1+4 (Ricketts et al. 1982) or the spectral observation of Active Galaxies (Hall et al. 1981).

EXOSAT

The European Space Agency’s (ESA’s) X-ray Observatory, EXOSAT (Taylor et al. 1981), was active from May 1983 to April 1986. It was launched into a highly eccentric orbit (e∼ 0.93) with a 90.6 h period, inclination of 73◦ , at an apogee and perigee of 191,000 km and 350 km, respectively (at the beginning of the mission). This – at that time – peculiar orbit was chosen to enable long (from 76 h or 90 h),

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Table 8 EXOSAT’s science payload: the LE, ME, and GSPC LE Instrument Bandpass (keV) Eff area (cm2 ) FOV Angular res (FWHM) Energy res (FWHM)

CAM

PSD

0.04–2 0.1–2 0.4–10 – 2.2◦ 1.5◦ on axis 12′′ none

50′′ ∆E/E= 44/E (keV)1/2 %

ME Spectrometer – 1–50

GSPC

–

1800

∼10–100

–

45′ × 45′

45′

21% at 6 keV (Ar)

27/E (keV)1/2 %

2–20

18% at 22 keV (Xe)

uninterrupted observations during a single orbit. Due also to the great distance from the Earth (∼50, 000 km), EXOSAT was almost always visible from the ground station at Villafranca in Spain during science instruments operations. The payload of the satellite consisted of the low-energy telescopes (LE), composed of two identical Wolter-I telescopes. Each could operate in imaging mode by means of channel multiplier array (CMA) or position-sensitive detector (PSD) or in spectroscopy mode with gratings behind the optics and the CMA in the focal plane DeKorte et al. (1981); the medium-energy instrument (ME), the main instrument in the lunar occultation mode (Turner et al. 1981); and the gas scintillation proportional counter (GSPC Peacock et al. 1981). The characteristics of the instruments are shown in Table 8. During the performance verification phase, the PSDs of the two LE failed. About half a year later, one of the channel plates failed. However, overall the LE functioned up to the end, and discoveries were made using the X-ray grating spectrometers (built by SRON) (Bleeker and Verbunt 2013; Bleeker 2022). Most notable were the discoveries of quasiperiodic oscillations (QPOs) of low mass X-ray binaries, the soft excesses from AGN, the red and blue shifted iron K line from SS433, the characterization of many orbital periods of low mass X-ray binaries, and the new transient sources. The scientific highlights of the EXOSAT mission are reported in a special issue of the Memorie della Società Astronomica Italiana (MSAI 1988).

Late 1970s and the 1980s: The Program in Japan Japan, thanks to the leadership of Minoru Oda, contributed to X-ray astronomy with several missions, becoming a well-recognized country in space science. The first of those missions was CoRSa-b renamed, after the successful launch, Hakucho.

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Table 9 HAKUCHO (CoRSa-b). The payload carried three instruments for the detection of very soft (VSX), soft (SFX), and hard (HDX) X-rays VSX Instrument VXP Bandpass (keV) 0.1–1 Eff Area (cm2 )

∼78

FOV (FWHM)

6.3◦ × 2.9◦

SFX VXV

17.6◦

HDX

CMC

FMC

69

1.5–30 FMC 1 40 32 FMC 2 83 5.8◦ 4.4◦ × 10.0◦

24.9◦ × 2.9◦

SVC

10–100 ∼ 45 50.3◦ × 1.7◦

HAKUCHO

Hakucho, Japanese for swan (like one of the archetypal X-ray sources, Cyg X-1) developed by the Institute of Space and Astronautical Science (ISAS), was launched from the Kagoshima Space Center on February 21, 1979. It was placed into a nearcircular orbit with an apogee of 572 km, a perigee of 545 km, an inclination of 29.9◦ , and an orbital period of 96 min (Oda 1980). It was the second of the series CoRSa (Cosmic Radiation Satellite) (Unfortunately the first of the satellite of the series Corsa-a failed to reach the orbit). The mission ended on April 16, 1985. Its main goal was the study of transient phenomena using three different instruments: the very soft X-ray experiment (VSX), based on four units of proportional counters with very thin polypropylene windows. Two of the counters were oriented along the spin axis (VXP) and two were offset (VXV); the soft X-ray instrument (SFX) included six proportional counters with Beryllium windows. Two were equipped with a coarse modulation collimator (CMC), two with a fine modulation collimator (FMC), and the last two aimed at scanning the sky (SVC) operated in offset mode; the hard X-ray (HDX) detector consisted of two Na(T1) scintillators with an offset of 2.7◦ . Table 9 summarizes the principal characteristics of the mission payload (Inoue et al. 1980). Hakucho data led to the discovery of many burst sources and the soft X-ray transient sources Cen X-4 and Apl X-1.

HINOTORI Hinotori, Japanese for phoenix or firebird, was the first of the series of Astra satellites. It was dedicated to the study of solar phenomena, in particular to solar flares during the solar maximum. It was launched from the Kagoshima Space Center (now Ichinoura) on February 21, 1981, and operated until October 8, 1982. The orbit was near-circular with an apogee altitude of 603 km, a perigee of 548 km, an inclination of 31.3◦ , and a period of 96.20 min. For the solar flare studies, Hinitori carried onboard the solar X-ray telescope (SXT), equipped with two sets of bigrid modulation collimators for the imaging of the hard X-ray emission, using the rotating modulation collimator technique. In addition, the solar X-ray aspect sensor (SXA) was a system of collimating lenses to determine the flare position with a

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Table 10 HINOTORI (ASTRO-A). The payload consisted of a solar flare telescope (SXT), an analyzer (SXA), a spectrometer for soft X-ray (SOX), monitors for hard X-rays (HXM), and gamma-rays (SGR), for both solar flares (FLM) and for particle emission (PXM) SXT Instrument Bandpass (keV) Area (cm2 ) Ang. res (FWHM) Time res (ms) Energy res

113

SXA SOX SOX 1 1.72– 1.99 Å 6.69 Å

30′′

5′′

17–40

∼ 6×103

SOX 2

1.83– 1.89 Å 2.36 Å

6–10×103 2mÅ

0.15 m Å

FLM HXM SGR HXM 1 HXM 2 2–12 17–40 40–340 200– 6,700 0.5 57 62

125

7.8

125

PXM 100– 800 2.2

128ch/4s 125/ch 0.1 E1/2 MeV

resolution of 5 arcsec. The soft X-ray crystal spectrometer (SOX, Tanaka et al. 1982) enabled the spectroscopy of X-ray emission lines from highly ionized iron during a flare. It consisted of coarse (SOX1) and fine (SOX2) Bragg spectrometers. Three additional instruments enabled the monitoring of the flares over a large energy band: the soft X-ray flare monitor (FLM), the hard X-ray flare monitor (HXM), and the solar gamma-ray detector (SGR Yoshimori et al. 1983). The FLM was a gas (Xe) scintillation proportional counter, while the HXM and SGR detectors were NaI(T1) and CsI(T1) scintillation counters, respectively. The eight counters of the HXM instrument had different characteristics as reported in Table 10 (Tanaka 1983). In addition to the aforementioned instruments, Hinotori hosted a particle ray monitor (PXM), a plasma electron density measurement instrument (IMP), and a plasma electron temperature measurement instrument (TEL). All instruments were co-aligned with the spacecraft spin (Z) axis that was set 1◦ off the sun center, and therefore no additional driving mechanism for the detectors was necessary. The main scientific results of Hinotori include the following: the time profile and spectrum of the X-ray flares (Tanaka 1987; Yoshimori 1990), monitoring of the electron flux above 100 keV, discovery of high-temperature phenomena reaching up to 50 million ◦ C, and clouds of light-speed electrons floating in coronas (Oyama et al. 1988).

TENMA

Tenma, Japanese for Pegasus, developed by ISAS, was the second satellite of the ASTRO series (ASTRO-B) and the second Japanese satellite for X-ray astronomy. It was launched on February 1983 and placed into a near-circular orbit with an apogee of 501 km, a perigee of 497 km, and an inclination angle of 31.5 degrees. The orbital period was 96 min. Its scientific payload consisted of four instruments:

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Table 11 Tenma.The payload consisted of four instruments: the SPC, the XFC, the TSM, and a the RBM/GBD monitor SPC Instrument Bandpass (keV) Energy res (FWHM) Area (cm2 ) (FOV) FWHM

SPC - A

SPC - B

XFC SPC - C

2–60 9.5% at 5.9 keV 320 80 3.1◦ 2.5◦ 3.8◦

TSM

RBM/GBD

HXT

ZYT

0.1–2

2–25

1.5–25

10–100

15 1.4◦ ×5◦

114 40◦ ×40◦

280 2◦ ×25◦

14 1sr

a scintillation proportional counter (SPC), an X-ray focusing collector (XFC), a transient sources monitor (TSM), and a radiation belt and gamma-ray monitor (RBM/GBD, Tanaka et al. 1984). In particular, the SPC, devoted to spectral and temporal studies, consisted of ten GSPC divided in three groups (SPC-A, B, C) of four, four, and two units, respectively. The XFC, consisting of mirrors and position-sensitive proportional counters, was designed to observe very soft X-ray sources. The TSM served as an X-ray monitor because of its wide FOV. It included two detector groups: an Hadamard X-ray telescope system (HXT) and a scanner counting system (ZYT). Two small scintillation counters monitored the non-X-ray background and the gamma-ray burst emissions. The entire payload was mostly aligned with the stabilized spin-axes (Z) of the satellite. Detailed information about the instruments are reported in Table 11. Tenma observations continued intermittently until November 11, 1985. The main results of the mission were the discovery and the study of the iron line region of many classes of sources. Tenma science highlights include the following: the discovery of hot plasma of several tens of millions of degrees located along the galactic plane (Koyama 1989); the discovery of the iron absorption line in the energy spectra of X-ray bursts, which was red-shifted in the strong gravitational field of the neutron star (Waki et al. 1984; Suzuki et al. 1984; Inoue 1985); and the identification in low-mass X-ray binaries of X-ray emission regions on the surface of the neutron star and in the accretion disk (Mitsuda et al. 1984).

GINGA Ginga, Japanese for galaxy, ASTRO-C before launch, was launched on Feb 5, 1987, and operated until November 1, 1991. Astro-C was the result of a collaboration between Japanese research institutions, the University of Leicester and the Rutherford-Appleton Laboratory in the UK and the Los Alamos National Laboratory (USA). Ginga followed a near-circular orbit at a perigee distance of 505 km and an apogee of 675 km. It was originally planned to make a circular orbit of 630 km, but atmospheric conditions at launch constrained the satellite into an elliptic orbit. The inclination of the orbit was 31◦ , and the period was 96 min.

1 A Chronological History of X-ray Astronomy Missions Table 12 Ginga (ASTRO-C). The primary instrument onboard was the LAC. The ASM and the GBD completed the payload

29 GBD

Instrument Bandpass (keV) Energy res (FWHM) Area (cm2 ) FOV (FWHM)

LAC 1.5–37 18% at 6 keV 4500 0.8◦ × 1.7◦

ASM 1–20

1.5–500

70 1◦ × 45◦

63 60 all sky

PC

SC

The primary mission objective was the study of the time variability of X-rays from active galaxies, such as Seyfert galaxies, BL Lac objects, and quasars in the energy range 1.5–30 KeV. Accurate timing analysis of galactic X-ray sources was also one of the goals of the mission (Makino and Astro-C Team 1987). The payload of the satellite consisted of three instruments: a large-area proportional counter (LAC, Turner et al. 1989), an all-sky monitor (ASM, Tsunemi et al. 1989), and a gamma-ray burst detector (GBD, Murakami et al. 1989). The LAC consisted of eight multicells proportional counters. The ASM consisted of two identical gas proportional counters. Each counter was equipped with a collimator, which had three different FOVs. The GBD included two detectors: a proportional counter and a scintillation spectrometer. The characteristics of these instruments are summarized in Table 12.

The Late 1970s and the 1980s: The Program in Russia and India The X-ray astronomy program of the Soviet Union had modest beginnings in the 1970s with the FILIN X-ray experiment aboard the Salyut-4 space station. It continued in the 1980s with experiments onboard the Astron (1983-1988) and Mir (1987-2000) space stations. This latter program had a strong European involvement. These programs generally suffered from a limited observation time allocation because of other commitments of the manned spacecraft. During the late 1970s and into the 1980s, the Soviet program was focused on studies of gamma-ray bursts. The Konus experiments on the Venera 11-14 spacecraft yielded major advances in this field (Mazets et al. 1981; Higdon and Lingenfelter 1990). A notable result at X-ray wavelengths was the discovery of an unusual gamma burst on March 5, 1979, with sustained X-ray emission that exhibited periodic pulsations (Mazets et al. 1979).

FILIN / SALYUT -4

The FILIN X-ray instrument aboard the manned orbiting space station Salyut4 (December 1974) consisted of three detectors sensitive in the 2–10 keV range (Babichenko et al. 1977) and a smaller proportional counter for soft X-ray studies (0.2–2 keV), with a rather large FOV (see Table 13).

30 Table 13 FILIN. The x-ray instrument onboard the Salyut-4 space station

A. Santangelo et al. Instrument Bandpass (keV) Area (cm2 ) FoV (FWHM)

sFilin Filin 0.2–2 2–10 40 450 3◦ × 10◦

Gas-flow proportional counters were used as the detectors. A gas-flow system supplied a gas mixture for the counters. To determine the source coordinates, two star sensors were installed. The X-ray detectors, all-optical sensors, and the gasflow system were mounted on the outside of the station, while the power supply and electronics were inside. Scanning observations were carried out for about 1 month and pointed observations for about 2 months; studies included observations of Sco X-1, Her X-1, and Cyg X-1 (Babichenko et al. 1977) and the X-ray nova A0620-00 (Bradt 1992; Martynov et al. 1975).

SKR -02 M

The experiment SKR-02M on the Astron station (1983) consisted of a large proportional counter of effective area ∼0.17 m2 sensitive from 2 to 25 keV (Babichenko et al. 1990). The field of view was 3◦ × 3◦ (FWHM). Data were sent via telemetry in ten energy channels. Results have been reported from studies of the Crab Nebula and the Crab Pulsar, Her X-1, A0535 + 26, and Cen X-3 (Babichenko et al. 1990). The prolonged low state of Her X-1 in 1983 was studied, and the 1984 turn-on was reported (Giovanelli et al. 1984).

XVANTIMIR

The Röntgen X-ray observatory was launched in 1987 aboard the Kvant module, which docked to the MIR space station. The complement of detectors (Sunyaev et al. 1990b) included a sensitive high energy 15–200 keV X-ray experiment (HEXE, Reppin et al. 1985), a coded-mask system for imaging high-energy photons (TTM, Brinkman et al. 1985), and a gas scintillation proportional counters (GSPC, Smith (1985)). It also carried two gamma-ray experiments, which reached down to 30–40 keV (Sunyaev et al. 1990b). Röntgen was an international endeavor with contributions from Germany, UK, ESA, and the Netherlands. The highlight of the mission was the discovery and study (with Ginga) of the X-ray emission from SN1987A (Sunyaev 1987). A high-energy tail in the spectrum of the X-ray nova GS2000 + 25 was discovered (Sunyaev 1988a), further indicating its similarity to the black-hole candidate A0620-00. Timing results for the Her X-1 pulsar in 1987–1988 showed it to be continuing its spin up (Sunyaev 1988b). The principal characteristics of the Röntgen X-ray observatory are reported in Table 14.

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Table 14 Röntgen X-ray observatory Instrument Energy range (keV) Energy resolution (FWHM) Area (cm2 ) FOV (FWHM)

TTM 2–32 18% at 6 keV 600 7.8◦ × 7.8◦

GSPC 4–100 10.5% at 6 keV 300 3◦ × 3◦

HEXE 15–200 30% at 60 keV 800 1.6◦ × 1.6◦

ARYABHATA

Aryabhata, named after the Indian mathematician and astronomer of the fifth century, was the first satellite of India completely designed and built by the Indian Space Research Organization (ISRO). It was launched on April 19, 1975, from the Russian rocket launch site Kapustin Yar. Its orbit had a perigee of 563 km, an apogee of 619 km, and an inclination of 50.7◦ . The period was of 96.46 min. The mission ended on March 1981, and the satellite reentered the Earth’s atmosphere on February 10, 1992. Three instruments dedicated to aeronomy, solar physics, and Xray astronomy were onboard. The X-ray detector consisted of a proportional counter filled with a mixture of Ar, CO2 , and He and operated in a parallel mode, in the energy range from 2.5 to 115 keV. The effective area was ∼15.4 cm2 and the FOV, circular, with 12.5◦ (FWHM). In particular Aryabhata made observation of Cyg X-1, finding a hardening in its spectrum, Rao et al. (1976), and of other two X-ray sources, namely, GX17+2 and GX9+9 (Kasturirangan et al. 1976).

BHASKARA

Two satellites Bhaskara I and II were developed by ISRO and named after the two famous Indian mathematicians Bhaskara (or Baskara I) of the seventh century and Bhaskara II (or Bhaskaracharya, Bhaskara the teacher) of the twelfth century. We will report here only about Bhaskara I, since Baskara II didn’t carry X-ray instruments. Bhaskara I was launched on June 7, 1979, from Kapustin Yar. Its orbital perigee and apogee were 512 km and 557 km respectively; the inclination was of 50.7◦ and period 95.20 min. The mission ended on February 17, 1989, after almost 10 years. The main objectives of the mission were as follows: (1) to conduct observations of the earth yielding data for hydrology, forestry, and geology applications; (2) to conduct ocean-surface study using a SAtellite MIcrowave Radiometer (SAMIR); and (3) among other minor investigations, to conduct investigation in X-ray astronomy. The X-ray instrument consisted by a pinhole X-ray survey camera operating in the energy range between 2 and 10 keV with the purpose of observing transient sources and long-term variability of steady sources. At the image plane of the camera, there was a position-sensitive proportional counter, the detector operated with success during the first month after launch. However, it had to be turned off, and when, after some time, was turned on again, it didn’t operate correctly; the reason of the malfunction was never found.

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The Golden Age of X-Ray Astronomy, From the 1990s to the Present The 1990s can be considered as a sort of renaissance of X-ray astronomy. It consisted of years of significant missions that brought X astronomy into its full maturity. The decade begins with the launch of the Soviet mission Granat (December 1989) and of the German mission ROSAT (June 1990) and soon after the Japanese ASCA. In the mid-1990s, BeppoSAX and RXTE were launched, and in the late 1990s, Chandra and XMM-Newton.

THE PROGRAM IN THE USA ULYSSES

The Ulysses mission was a joint mission between NASA and ESA to explore the solar environment at high ecliptic latitudes. Launched on October 6, 1990, it reached Jupiter for its “gravitational slingshot” in February 1992. It passed the south solar pole in June 1994 and crossed the ecliptic equator in February 1995. In addition to its solar environment instruments, Ulysses also carried onboard plasma instruments to study the interstellar and Jovian regions as well as two instruments for studying X- and gamma-rays of both solar and cosmic origins. The mission could send data in four different telemetry modes at rates of 128, 256, 512, and 1024 b/s. The time resolution of the gamma-ray burst instrument depended on the chosen data rate. The maximum telemetry allocation for the instrument was about 40 b/s. The Ulysses solar X-ray and cosmic gamma-ray burst experiment (GRB) had three main objectives: study and monitor solar flares, detect and localize cosmic gamma-ray bursts, and in situ detection of Jovian auroras. Ulysses was the first satellite carrying a gamma burst detector, which went outside the orbit of Mars. This resulted in a triangulation baseline of unprecedented length, thus allowing major improvements in burst localization accuracy. The instrument was turned on November 9, 1990. The GRB consisted of two CsI scintillators (called the hard Xray detectors) and two Si surface barrier detectors (called the soft X-ray detectors). The detectors were mounted on a 3 m boom to reduce background generated by the spacecraft’s radioisotope thermoelectric generator. The hard X-ray detectors operated in the range 15–150 keV. The detectors consisted of two 3 mm thick by 51 mm diameter CsI(Tl) crystals mounted via plastic light tubes to photomultipliers. The hard detector varied its operating mode depending on the measured count rate, the ground command, or a change in spacecraft telemetry mode. The trigger level was normally set for 8 sigma above background corresponding to a sensitivity 2×10−6 erg cm−2 s−1 (Boer et al. 1990). When a burst trigger was recorded, the instrument switched to high-resolution data, recording a 32-kbit memory for a slow telemetry readout. Burst data consisted of either 16 s of 8-ms resolution count rates or 64 s of 32-ms count rates from the sum of the two detectors. There were also

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16 channel energy spectra from the sum of the two detectors (taken either in 1-, 2-, 4-, 16-, or 32-second integration). During “wait” mode, the data were taken either in 0.25 or 0.5 s integration and four energy channels (with shortest integration time being 8 s). Again, the outputs of the two detectors were summed. The soft X-ray detectors consisted of two 500 µm thick, 0.5 cm2 area Si surface barrier detectors. A 100 mg cm−2 beryllium foil front window rejected the low-energy X-rays and defined a conical field of view of 75◦ (half-angle). These detectors were passively cooled and operated in the temperature range −35 ◦ C to −55 ◦ C. This detector had six energy channels, covering the range 5–20 keV. Ulysses results have been mainly about the Sun and its influence on nearby space (Marsden and Angold 2008).

BBXRT

The Broadband X-ray telescope (BBXRT, Serlemitsos et al. 1984) was flown on the Space Shuttle Columbia (STS-35) as part of the ASTRO-1 payload (December 2, 1990–December 11, 1990). It was designed and built by the Laboratory for highenergy astrophysics at NASA/GSFC. BBXRT was the first focusing X-ray telescope operating over a broad energy range 0.3–12 keV, with moderate-energy resolution (90 eV at 1 keV and 150 eV at 6 keV). It consisted of two identical co-aligned telescopes each with a segmented Si(Li) solid-state spectrometer (detector A and B) with five pixels. The telescope consisted of two sets of nested grazing-incidence mirrors, whose geometry was close to the ideal paraboloidal/ hyperboloidal surfaces (modified Wolter type-I). This simplified fabrication and made possible nesting many shells to yield a large geometric area. The effective on-axis areas was 0.03 m2 at 1.5 keV and 0.015 m2 at 7 keV. The focal plane consisted of a five-element lithium-drifted silicon detector with an energy resolution of about 100 eV FWHM. Despite operational difficulties with the pointing systems, the BBXRT obtained high-quality spectra from some 50 selected objects (Serlemitsos et al. 1992), both galactic and extragalactic. Results included the resolved iron K line in the binaries Cen X-3 and Cyg X-2 (Smale et al. 1993), evidence of line broadening in NGC 4151 (Weaver et al. 1992), and the study of cooling flow in clusters (Arnaud et al. 1998). Details are reported in Table 15.

R XTE The Rossi X-ray Timing Explorer (RXTE, Bradt et al. 1993) was launched on December 30, 1995, from the NASA Kennedy Space Center. The mission was managed and controlled by NASA/GSFC. RXTE featured unprecedented time resolution in combination with moderate spectral resolution to explore the time variability of the X-ray sources. Timescales from microseconds to months were studied in the spectral range from 2 to 250 keV. Originally designed for a required lifetime of 2 years with a goal of five, RXTE completed 16 years of observations (!) before being decommissioned on January 5, 2012.

34 Table 15 BBXRT

A. Santangelo et al. Instrument Bandpass (keV) Eff area (cm2 ) (at 1.5 keV) Eff area (cm2 ) (at 7 keV) FOV (diameter) Central pixel FOV diameter Angular resolution Energy resolution (eV, FWHM) at 1 keV Energy resolution (eV, FWHM) at 6 keV

BBXRT on STS-35 0.3–12 765 300 17.4′ 4′ 2′ –6′ 90 150

The spacecraft was designed and built by the Applied Engineering and Technology Directorate at NASA/GSFC. The launch vehicle was a Delta II rocket that put RXTE into a low-Earth circular orbit at an altitude of 580 km, corresponding to an orbital period of about 90 min, with an inclination of 23 degrees. Operations were managed at GSFC. The mission carried onboard two pointed, collimated instruments: the proportional counter array (PCA, Zhang et al. 1993) developed by GSFC to cover the lower part of the energy range, and the high-energy X-ray timing experiment (HEXTE, Gruber et al. 1996) developed by the University of California at San Diego, covering the upper energy range. The PCA was an array of five proportional counters with a total collecting area of 6,500 cm2 . Each unit consisted of a layer propane veto; three layers of xenon, each split in two; and a xenon veto layer. HEXTE consisted of two clusters each containing four NaI/CsI phoswich scintillation counters. Each cluster could “rock” along mutually orthogonal directions to provide background measurements (1.5 or 3.0 degrees away from the source) every 16 to 128 s. Automatic gain control was provided by using a 241Am radioactive source mounted in each detector’s field of view. Part of the RXTE scientific payload was an all-sky monitor (ASM) from MIT that scanned about 80% of the sky every orbit, allowing monitoring at timescales of 90 min or longer. The ASM (Levine et al. 1996) consisted of three wide-angle shadow cameras equipped with proportional counters with a total collecting area of 90 cm2 . The main details of the mission are reported in Table 16. RossiXTE was an extremely successful and productive mission. Science highlights include the following: the discovery of kilohertz quasiperiodic oscillations (KHz QPOs) in NS systems (van der Klis et al. 1996)and high-frequency QPOs in BH systems (Morgan et al. 1997); the discovery of the first accreting millisecond pulsar, SAX J1808.4–3658 (Wijnands and van der Klis 1998), followed by several more accreting millisecond pulsars; the detection of X-ray afterglows from gammaray bursts (Bradt et al. 2003); and the observation of the bursting pulsar over a broad range of luminosity, providing stringent test of accretion theories.

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Table 16 Rossi XTE Instrument Bandpass (keV) Eff area (cm2 ) FOV Time resolution Energy resolution Spatial resolution Sensitivity (milliCrab) Background

Table 17 USA onboard ARGOS

ASM 2–10 90 6◦ × 90◦ e.u. 80% of the sky in 90 min 3′ × 15′ 30

PCA 2–60 6 500 1◦ 1 µs

HEXTE 15–250 2×800 1◦ 8 µs

2) reflections, again reducing the area in the double reflection spot. Figure 6 demonstrates how the variation of the value of ξ , and therefore the thickness of the MPOs, affects the area, gain, and FWHM of the MPO. Here, the gain is a measure of the focusing power of the optic and is the ratio between the total collecting area and the area in the double reflection spot. As shown in Fig. 6, the optimum value of ξ at 1 keV is 1.25. This simplifies Equation 3, at 1 keV, to (4)

0

0

arc min 1 2 3 4 5

area cm2 20 40 60

6 7

L = 2.5dF /r

0.8

1.0

1.2

1.4

1.6

1.8

0.8

1.0

1.2

1.4

1.6

1.8

x

Open symbols -No central MPO

0.0 0.5 1.0 1.5 2.0 2.5

gain cm2/arc min2

x

Solid symbols - Central MPO included Squares - Analysis beam = 2 x FWHM Circles - Analysis beam = FWHM Optimum x = 1.25 0.8

1.0

1.2

1.4

1.6

1.8

Fig. 6 The derivation of the relationship between the MPO’s redial position and optimum thickness is L = 2ξ dF /r. ξ is a scaling factor and all simulations were completed at 1.0 keV. The top left pane details the change in on-axis area as a function of ξ , which is strongly governed by the thickness of the MPO. The top right pain shows the change in the on-axis FWHM of the double reflection spot given ξ , and finally the bottom pane shows the change in gain, the focusing power of the optic, at various values of ξ

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Limitations of MPOs If you have a perfect MPO, which is perfectly spherical, with perfectly smooth pores all pointing to exactly the same position on a curved focal plane at exactly the correct focal distance, the minimum PSF size you could achieve would be the width of the pores at that optic-to-detector distance. The angular size of the pore at the focal length of the optic is the fundamental limit of the resolution of an MPO. If every pore is identical and all point to the same position on the focal plane, then the beam from each pore will pile up on top of each other, perfectly, to the width of a pore. In reality this is not the case, and there are many deformations in the form of the MPO which limit the resolution. The full details of the majority of the deformations can be found in Willingale et al. (2016), but they are summarized here. The three intrinsic aberrations associated with the lobster eye geometry, which limit the angular resolution performance of the optic, independent of the technology used to construct the pore array, are spherical aberrations, the geometric pore size, and diffraction limits. Nonintrinsic aberrations include slumping and formation of the multifibers. Slumping introduces additional radial tilt and shear errors as the pores are stretched and compressed to form the correct profile. Misalignment of multifibers to one another and deformations at the multifiber boundaries and within the multifibers themselves contribute to the total angular resolution. In addition, the pore surface roughness further increases the angular resolution of the MPO. The combination of the above errors imposes a theoretical limit on the angular resolution of ∼2 arcmin for a single MPO; however, the majority of MPOs have an angular resolution far larger than this. The MPOs are slumped by a technique that sandwiches the MPOs between convex and concave diamond-turned mandrels of the appropriate radius of curvature. Equal pressure and heat are applied to both mandrels and across the full surface in order to prevent the shearing of the channels with respect to each other. After slumping, the MPOs and mandrels are left to cool to room temperature which keeps the MPO form. Unfortunately, trying to slump a square MPO onto a sphere causes deformations in the form of the optic. If you think of trying to wrap a basketball with a square piece of paper, at the center, the fit is very good, but toward the corners you get crinkles and folds which distort your piece of paper. This is similar to what happens to an MPO, and the end result is that the form of the corner regions of the optics is not as good as at the center. You can also end up with an astigmatism in the optic where the radius of curvature in one axis does not match that in the other axes. Both of these effects have a massive influence on the net focal length of the optic and the PSF size and shape. At lower energies, the structure of the corners has a strong influence on the PSF, but the astigmatism can affect the PSF at all energies. In addition to the effect of the slumping on individual MPOs, the variation of RoC between the MPOs combined within an assembly will have an effect on the full optic assembly PSF. The optic-to-detector distance of best focus for the optic assembly is governed by the RoC and the form of the frame, but the size of the PSF

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of the assembly is governed by the individual MPOs. If none of the MPOs have the same RoC as the frame, then they will all be out of focus by varying amounts, and this will increase the size of the PSF.

Current Missions Several missions over the next few years are using this technology in order to take advantage of the large FoV and lightweight nature of these optics for various scientific goals, including planetary science and astronomy. Below is a description of some of the current selected missions.

BepiColombo The first instrument is the Mercury Imaging X-ray Spectrometer (MIXS) (Bunce et al. 2020) on board the ESA-JAXA mission BepiColombo. Although it was launched in October of 2018, it will not insert into its scientific orbit around Mercury, its destination, until late 2025–early 2026. MIXS consists of two instruments, the telescope MIXS-T and the wide-field collimator MIXS-C, shown on the left and right, respectively, on the MIXS optical bench in Fig. 7. MIXS-T uses the radial packing of 20 µm square pores and two consecutive sector MPOs, slumped with different radii of curvature to simulate a Wolter geometry (Willingale et al. 1998). In order to create the 1 m focal length, the front sectors have a RoC of 4 m and the rear sectors have a RoC of 1.3 m. The FoV of MIXS-T is ∼1.1◦ and consists of 36 tandem, sector pairs. The inner ring sectors have a thickness of 2.2 mm, the

Fig. 7 The flight MIXS instrument on the optical bench. The MIXS-T is on the left of the bench, and approximates the Wolter geometry. The MIXS-C is on the right of the bench and is a collimator in a 2 × 2 MPO geometry

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middle ring optics are 1.3 mm thick, and the outer ring optics are just 0.9 mm thick. The MIXS-C instrument uses 20 µm, square pore, square packed MPOs which are 40 × 40 mm in size and 1.2 mm thick. These MPOs have been slumped to a radius of curvature of 550 mm and give a FoV of ∼10◦ . The complete MIXS instrument on its optical bench weighs ∼11 kgs. By using these two instruments side by side, an elemental map of the Mercurian surface using X-ray fluorescence from the solar wind (Fraser et al. 2010) will be created.

SVOM The Space-based multiband astronomical Variable Objects Monitor (SVOM) (Mercier et al. 2014) is a Chinese-French mission to be launched in 2023. It is comprised of four spaceborne instruments, including the Microchannel X-ray Telescope (MXT) (Götz et al. 2015). The MXT’s main goal is to precisely localize and spectrally characterize X-ray afterglows of GRBs. The MXT is a narrow-fieldoptimized, lobster eye X-ray focusing telescope, consisting of an array of 25 square MPOs, with a focal length of 1.14 m and working in the energy band 0.2–10 keV. The design of the MXT optic (MOP) is optimized to give a 1◦ detector-limited FoV, but the optic has the unique characteristics of a lobster eye design, with a wide FoV >6◦ , and a PSF which is constant over the entire FoV. The MPOs on the Flight Module (FM) MOP have a pore size of 40 µm giving the optimum thicknesses across the aperture of 2.4 mm in the center and 1.2 mm at the edges. The left of Fig. 8 shows the completed FM MOP. Each MPO is 40 × 40 mm square, and there is a 2 mm gap between each MPO on the frame. The total mass of the fully assembled optic was measured to be 1.43 kg. Einstein Probe Einstein Probe (Yuan 2019) is a Chinese Academy of Science (CAS) mission due for launch in 2023, with its primary goals to discover high-energy transients and monitor variable objects. The mission consists of two instruments, the wide-field

Fig. 8 Left: the flight MXT optic, a 25 MPO array narrow-field lobster eye optic. Right: the full flight MXT lobster eye telescope. (© T De Prada CNES)

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Fig. 9 Left: A qualification WXT module installed in the PANTER beamline, MPE, Germany, prior to calibration. Right: X-ray image with the source centered on the module showing all four MPO quadrants focusing. Image taken with Cu-L (0.93 keV) X-rays at PANTER using the TRoPIC camera (Freyberg et al. 2008). (Image courtesy of MPE)

X-ray telescope (WXT), a lobster eye X-ray telescope consisting of 12 identical modules, and the follow-up X-ray telescope (FXT) (Vernani et al. 2020), which is a traditional Wolter X-ray telescope. The FXT has been jointly developed by the CAS, the European Space Agency (ESA), and the Max Planck Institute for Extraterrestrial Physics (MPE). Each of the WXT modules is comprised of 36 MPOs in a 6 by 6 array (left of Fig. 9), with a 375 mm focal length, a total FoV of more than 3600 square degrees, and an angular resolution goal of 5 arcmin per module and working in the energy range of 0.5–4 keV. Each of the 12 WXT modules has a focal plane comprised of 4 CMOS detectors in a 2 by 2 array. The modules are aligned so that each 3 by 3 quadrant of MPOs focuses onto a single CMOS detector, thus creating 4 discrete telescopes per module with overlapping FoVs (right of Fig. 9).

SMILE Solar wind Magnetosphere Ionosphere Link Explorer (SMILE) (ESA 2020) is a joint mission between the ESA and CAS to investigate the dynamic response of the Earth’s magnetosphere to the impact of the solar wind. From an elliptical polar orbit, it will combine soft X-ray imaging of the Earth’s magnetopause and magnetospheric cusps with simultaneous UV imaging of the Northern aurora, and will monitor in situ the solar wind and magnetosheath plasma conditions so as to set the imaging data into context. It is due for launch in late 2024 or early 2025 with four separate instruments on board, including the Soft X-ray Imager (SXI). The SXI is an elongated lobster eye telescope with an array of 4 by 8 MPOs. Each MPO is 40 × 40 mm, with iridium-coated 40 µm pores and a focal length of 300 mm. The high charge state solar wind ions in collision with hydrogen produce photons at soft X-ray (and EUV) energies within the 0.2–2.5 keV band. The focal plane consists of 2 CCDs and the instrument has a FoV of 26.5◦ by 15.5◦ . The wide FoV enables SXI to spectrally map the location, shape, and motion of Earth’s magnetospheric

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Fig. 10 Clockwise from left: Exploded CAD diagram of the SXI instrument. CAD diagram of the complete instrument. The structural thermal model of the full instrument during vibration testing. Simulation of a typical event and as seen by SXI after 5-min exposure

boundaries. Figure 10 shows an exploded CAD diagram of the SXI instrument on the left, the structural thermal model of the full instrument during vibration testing on the top right, and a simulation of the data expected on the bottom right.

Lobster Eye Optics in MFO/Schmidt Arrangement Schmidt Objectives The lobster eye geometry X-ray optics offer an excellent opportunity to achieve very wide fields of view. One-dimensional lobster eye geometry was originally suggested by Schmidt (1975), based upon flat reflectors. The device consists of a set of flat reflecting surfaces. The plane reflectors are arranged in a uniform radial pattern around the perimeter of a cylinder of radius R. X-rays from a given direction are focused to a line on the surface of a cylinder of radius R/2 (Fig. 11). The azimuthal angle is determined directly from the centroid of the focused image. At glancing angle of X-rays of wavelength 1 nm and longer, this device can be used for the

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Fig. 11 The arrangements of Angel MPO (left), Schmidt MFO 1D (middle), and Schmidt 2D lobster eye optics (Sveda 2003)

focusing of a sizable portion of an intercepted beam of parallel incident X-rays. Focusing is not perfect and the image size is finite. On the other hand, this type of focusing device offers a wide FoV, of up to a maximum of the half sphere of the coded aperture. It is possible to achieve an angular resolution on the order of one tenth of a degree or better. Two such systems in sequence, with orthogonal stacks of reflectors, form a double-focusing device. Such a device offers a FoV of up to 1000 square degrees at a moderate angular resolution. It is obvious that this type of wide-field X-ray telescope could play an important role in future X-ray astrophysics. These innovative very wide-field X-ray telescopes have only recently been suggested for space-based applications. One of the first proposals was the All Sky Supernova and Transient Explorer (ASTRE, Gorenstein (Gorenstein 1979, 1987)). This proposal included a cylindrical coded aperture outside of the reflectors, which provide angular resolution along the cylinder axis. The coded aperture contains circumferential open slits that are 1 mm wide and are in a pseudorandom pattern. The line image is modulated along its length by the coded aperture. The image is cross-correlated with the coded aperture to determine the polar angle of one or more sources. The FoV of this system can be, in principle, up to 360◦ in the azimuthal direction and nearly 90% of the solid angle in the polar direction. To create this mirror system, a development of double-sided flats is necessary. There is also potential for extending the wide-field imaging system to higher energy with the application of multilayers or other coatings in analogy to those described for flat reflectors in the K-B geometry. The angular resolution of the lobster eye optics in the Schmidt arrangement is a function of spacing between the reflecting plates and focal length. In the Schmidt arrangement, the lobster eye consists of plates of thickness t, and depth d (Fig. 12). Spacing between plate planes is s, focal length f , radius r, and focal point F , and β is the angle between optical axis and focused photons. Beam A (Fig. 12) shows the situation where the plate is fully illuminated, and the cross section of the plate is maximal (effective reflection). Beam B is the last beam that can be reflected into the focal point. Beams that are further from the optical axis reflect more than once (critical reflection). If reflected twice from the same set of plates, the photon does not reach the focal point and continues parallel to the incoming photon direction (Sveda 2003).

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Fig. 12 The schematic arrangement of the Schmidt lobster eye type X-ray optics used for simple equations derivation (Sveda 2003)

If t ≪ s ≪ d ≪ f , we can derive the following simple equations (Sveda 2003; Inneman 2001), where α is the estimate of the angular resolution: r 2 (s − t) βE = d f =

βL = 2βE α∼

2s s = r f

The design concept is different for lobster eye systems based on two reflections, a single reflection on a horizontally oriented surface (pore wall or mirror) and a single reflection on a horizontally oriented surface. Particularly, this is a case of Schmidt lobster eye. A paper by Tichý et al. (2019) presents analytical formula allowing direct computing of the effective collecting area for those systems by the formula:

L(r, s, t, ζ ) = 2r

 R(2ζ ) − 2 R(ζ ) + R(0) s  , s+t ζ

(5)

  ¯ )dθ is an arbitrary second antiderivative where  R(θ ) := R(θ )dθ dθ = R(θ of R. Radius of the system measured to mirror center is denoted r, s represents mirror spacing (or pore width), and t is mirror (pore wall) thickness. The effective collecting area equals L2 for the Angel system and L1 L2 for the Schmidt system, where L1 and L2 are related to individual mirror stacks as they have different radii and they may differ in other parameters. The value ζ is the ratio between mirror (pore) depth d and s. The optimal value of this ratio is given by the reflectivity function for given surface and photon energy only. The paper by Tichý et al. (2009) presents the detailed procedure for how the optimal value of this ratio can be analytically calculated. In addition, a paper by Tichý and Willingale (2018) presents a formula for the optimal value of s as s = −t +

 2Rtζ + t 2

(6)

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Here, R = (r + d/2) is the radius of the system measured to the front aperture (d is the mirror depth). This solves a common problem when focal length is limited, e.g., by available space in a spacecraft. Mirror (pore wall) thickness t should be as small as possible but must be large enough to achieve sufficient stress endurance, etc (Fig. 13). The 1D and 2D lobster eye Schmidt modules are illustrated in Fig. 14. To test the design and assembly of lobster eye modules in Schmidt geometry, various test modules were manufactured and tested (Table 1, Fig. 15). The first lobster eye X-ray Schmidt telescope prototype (midi) consisted of 2 perpendicular arrays of flats (36 and 42 double-sided flats 100 × 80 mm each).

Fig. 13 The Schmidt objective midi test module with 100 × 80 mm plates (left) and its optical tests (right)

Fig. 14 The schema of Schmidt lobster eye modules, 1D (left) and 2D (right) arrangements

Table 1 The parameters of selected test Schmidt lobster eye modules assembled and tested. The distance parameter means the separation between reflecting foils. The parameters size, plate thickness, distance, length, and focal distance f are given in mm, resolution in arcmin, FoV in degrees, and optimal energy in keV Module Size Plate thickness Macro 300 0.75 Middle 80 0.3 Mini 1 24 0.1 Mini 2 24 0.1 Micro 3 0.03

Distance

Length

Eff. angle

f

Resolution FoV Energy

10.8 2 0.3 0.3 0.07

300 80 30 30 14

0.036 0.025 0.01 0.01 0.005

6000 400 900 250 80

7 20 2 6 4

16 12 5 5 3

3 2 5 5 10

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Fig. 15 The visual tests for the 1D (left) and 2D lobster eye modules (right) in Schmidt arrangements

The flats were 0.3 mm thick and gold-coated. The focal distance was 400 mm from the midplane. The FoV was about 6.5 degrees (Fig. 13). The results of optical and X-ray tests indicated a performance close to those provided by mathematical modeling (ray tracing). X-ray testing was carried out in the test facility of the X-ray astronomy group at the University of Leicester. At a later date, test modules with a Schmidt geometry were designed and developed using 0.1-mm-thick gold-coated glass plates that were 23 × 23 mm, with a 0.3 mm spacing. The aperture/length ratio is 80. A single module has 60 plates. Two analogous modules represent the 2D system for laboratory tests, providing focus-to-focus imaging with focal distances of 85 and 95 cm. The innovative gold coating technique resulted in a final surface micro-roughness rms to 0.2–0.5 nm. Various modifications of this arrangement have been designed both for imaging sources at final distances (for laboratory tests) and for distant sources (the corresponding double-focusing array has f = 250 mm and FoV = 2.5 deg). In parallel, numerous ray tracing simulations have been performed, allowing for a comparison between theoretical and experimental results (Figs. 16, 17, 18, 19, and 20). Following the aforementioned developments, even smaller (micro) lobster eye modules were constructed and tested in both visible light and X-rays. As an example, we show X-ray test results for the mini and micro lobster eye modules (Fig. 21). These results show the on-axis and off-axis imaging performance of the lobster eye module tested. For mosaics of X-ray test images for various energies see Fig. 22 and for various off-axis angles at 4.5 keV see Fig. 23.

Substrates for Lobster Eye Lenses in Schmidt/MFO Arrangement In general, there is growing need for large segmented X-ray foil telescopes of various geometries and geometrical arrangements. The requirement of minimizing the weight of future large X-ray space telescopes and at the same time achieving large collecting area for future large astronomical telescopes can be met with thin X-ray-reflecting foils (i.e., thin, lightweight, multiple layers that can be easily nested to form precise high-throughput mirror assemblies). This includes the large

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Fig. 16 The large Schmidt lobster eye module macro with aperture of 30 × 30 cm (left) and its optical image in visible light (right)

Fig. 17 The LE Mini and LE Micro modules

Fig. 18 The various sizes of Schmidt MFO lobster modules manufactured by Rigaku Prague. (Photo courtesy of Rigaku Prague)

4 Lobster Eye X-ray Optics Fig. 19 The schematic assembly of 1D lobster eye Schmidt sub-modules and 2D lobster modules

159 Sub-module A

Sub-module B

module (Schmidt arrangement)

Fig. 20 The calculated on-axis gain dependence on energy for lobster eye modules in Schmidt geometry. The f = 375 mm, gold-coated plates 100 microns thick (Sveda 2003)

modules of the Wolter 1 geometry, the large Kirkpatrick-Baez (further referred to as K-B) modules (as they can play an important role in future X-ray astronomy projects as a promising and less laborious to produce alternative), as well as the large lobster eye modules in the Schmidt arrangements. Although these particular X-ray optics modules differ in the geometry of foils/shells arrangements, they do not differ much from the point of the view of the foil/shell production and assembly, and also share all the problems of calculations, design, development, weight constraints, manufacture, assembling, testing, etc. It is evident that these problems are common and rather important for the majority of the large aperture Xray astronomy space-based observatories. Most of the future space projects require light material alternatives (Hudec 2011). We (Czech team with participation of the first author of this chapter) have developed various prototypes of the abovementioned X-ray optics modules based

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Fig. 21 The point-to-point focusing system, lobster eye Schmidt micro (3×3×0.03 mm mirrors), source-detector distance 160 mm, 8 keV photons, left, X-ray experiment vs. simulation, point-topoint focusing system, lobster eye Schmidt mini (25×25×0.1 mm; source-detector distance 1.2 m; 8 keV photons; image width, 2×512 pixels; 24 micron pixel; gain, 570 (measured) vs. 584 (model) (right)

Fig. 22 X-ray images for various energies from MFO Schmidt lobster eye mini, f = 25 cm, Palermo X-ray test facility (Tichý et al. 2009)

on high-quality X-ray-reflecting gold-coated float glass foils (Hudec et al. 2000). The glass represents a promising alternative to electroformed nickel shells used in Wolter optics, the main advantage being much lower specific weight (typically 2.2 g cm−3 if compared with 8.8 g cm−3 for nickel). For the large prototype modules of dimensions equal to or exceeding 30 × 30 × 30 cm, mostly glass foils of thickness of 0.75 mm have been used, although in the future this thickness can be further reduced down to 0.3 mm and perhaps even less (we have successfully designed,

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Fig. 23 Mosaic of X-ray (at 4.5 keV) images for various off-axis positions (demonstrating the offaxis imaging performance), lobster eye REX2 2D module (83 gold-coated glass foils 148 × 57 × 0.42 mm each, FoV 4.7 × 4.3 deg.) (Pina et al. 2021)

Fig. 24 The experimental HORUS modules with Si wafers (Stehlikova et al. 2021)

developed, and tested systems based on glass foils as thin as 30 microns, albeit for much smaller sizes of the modules). More recently, silicon wafers with superior flatness and micro-roughness are serving as alternative substrates for lobster eye MFO modules. The recent HORUS experiment can serve as an example. HORUS has 4 modules, 2 modules with Au surface and 2 modules with Ir surface; each module has 17 silicon foils, i.e., in total 4 × 17 Si wafers 0.625 mm thick, with an aperture of 85 × 65 mm f = 2 m. The goal is to experimentally compare different reflective layers (Fig. 24).

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These substrates, both glass foils and silicon wafers, can be used in various Xray optics arrangements using MFO technology, mostly lobster eye and K-B (Hudec et al. 2006b, 2009).

The Application and the Future of Lobster Eye Telescopes in Schmidt Arrangements It is obvious that the lobster eye Schmidt MFO prototypes confirm the feasibility to design and develop these telescopes with currently available technologies. Considerations for fabricating and assembling a wide-field space-based X-ray observatory include: (1) Reduction of the micro-roughness and slope errors of the reflecting surfaces to optimize the angular resolution and reflectivity/efficiency of the system. The past development has already led to significant micro-roughness improvement (to 0.2–0.5 nm for glass substrates and 0.1 nm for silicon substrates) (2) The design and construction of larger or multiple modules to achieve a larger FoV (of order of 1000 square degrees and/or more) and enhance the collecting area (3) Reduction in the spacing and plate thickness (Schmidt arrangement) to improve imaging performance (angular resolution and system efficiency) and (4) Advanced, alternative layer applications, and/or other approaches applied to the reflecting surfaces to improve the reflectivity and to extend the energy bandpass to higher energies. The application of very wide-field Schmidt MFO X-ray imaging systems could be without doubt very valuable in many areas of X-ray and gamma-ray astrophysics. Results of analyses and simulations of lobster eye X-ray telescopes have indicated that they will be able to monitor the X-ray sky at an unprecedented level of sensitivity, an order of magnitude better than any previous X-ray all-sky monitor. Limits as faint as 10−12 erg cm−2 s−1 for daily observation in the soft X-ray range (typically 1–10 keV) are expected to be achieved, allowing monitoring of all classes of X-ray sources, including X-ray binaries, fainter classes such as AGNs, coronal sources, cataclysmic variables, as well as fast X-ray transients including GRBs and the nearby Type II supernovae (Hudec et al. 2006a, 2008, 2012). For pointed observations, limits better than 10−14 erg cm−2 s−1 (0.5–3 keV) could be obtained, sufficient enough to detect X-ray afterglows to GRBs (Sveda et al. 2004; Hudec et al. 2013).

Lobster Eye Laboratory Modifications The lobster eye soft X-ray optics, originally proposed and designed for astronomical (space) applications, has potential for numerous laboratory applications. As an example, lobster eye optics can be modified for efficient collection of laserplasma radiation for wavelengths longer than 8 nm (Sveda et al. 2006). The optics for this application consist of two orthogonal stacks of ellipsoidal mirrors forming a double-focusing device (Sveda et al. 2006). The ellipsoidal surfaces were covered

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by a layer of gold that has relatively high reflectivity at the wavelength range that is 8–20 nm up to an incident angle of around 10 degrees. The width of the mirrors forming the optics assemblies is 40 mm. As can be noticed, the spacing between adjacent mirrors increases with the distance from the axis. The curvature of the mirrors and the spacing between them were optimized using ray tracing simulations to maximize the optics aperture and to minimize the size of the focal spot.

Hybrid Lobster Eye The lobster eye Schmidt MFO configuration described in the previous sections is a wide-field, relatively low angular resolution optics. Achieving finer angular resolution is challenging given the current limitations of the technological limitation related to the mirror thickness and minimum spacing (Sveda et al. 2005). One possible solution to improving angular resolution is to invoke the typical use case of the standard lobster eye configuration as an all-sky monitor (ASM) for X-ray astronomy. The lobster eye is used onboard a space-based platform and will continuously scan the sky. If an area of the sky is outside the FoV of the optics, it will be inside the FoV sometime later because of scanning. This operational scenario allows for a smaller FoV in the scanning direction, which in turn permits finer angular resolution. The desired optics would have a wide FoV and moderate angular resolution in one direction, and a smaller FoV and better angular resolution in another. It is necessary to use curved mirrors to achieve better angular resolution. However, this puts constraints on the mirror dimensions. A combination of the standard one-dimensional lobster eye optics in one direction and K-B parabolic mirrors in the other direction meets the desired requirements (Sveda et al. 2005), shown in Fig. 25. Preliminary results of this configuration indicate that the hybrid lobster eye works as intended, i.e., it improves the angular resolution in one direction while still having a wide FoV in another. However, the blurring increases rapidly with the off-axis distance in the direction where there is focusing from the parabolic mirrors. Fig. 25 The sketch of the hybrid lobster eye with two plotted rays. Only one parabolic mirror is schematically plotted here. Typically, multiple reflecting surfaces have to be used (Sveda et al. 2005)

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Consequently, it is reasonable to think about such optics for pointed observations if the source and image are expected to be highly asymmetric. The effect of blurring is reduced for scanning observations; hence, the increase in angular resolution is achievable. There is a loss of sensitivity with this configuration, which translates to a significant decrease in the limiting flux. This fact, combined with manufacturing difficulties, makes this configuration of limited use for space-based applications. However, there is potential for use in laboratory applications (Sveda 2006).

Space Experiments with Lobster Eye MFO X-ray Optics The lobster eye optics in the Schmidt/MFO arrangement was placed onboard the Czech nanosatellite VZLUSAT-1 and onboard the NASA Water Recovery Rocket experiment. More systems are in study and/or in preparation for future space missions. For example, the HORUS double test module was designed and tested recently in order to compare modules with various reflective layers; see Fig. 24 (Stehlikova et al. 2021).

VZLUSAT-1 The small lobster eye telescope onboard the VZLUSAT-1 nanosatellite uses the first lobster eye MFO Schmidt X-ray optics in space. The first Czech technological CubeSat satellite VZLUSAT-1 was designed and built during the 2013–2016 period. It was successfully launched into low Earth orbit at an altitude of 505 km on June 23, 2017, as part of international mission QB50 onboard a PSLV C38 launch vehicle. The satellite was developed in the Czech Republic by the Czech Aerospace Research Centre, in cooperation with Czech industrial partners and universities (Dániel et al. 2016). The payload fits into a 2U CubeSat (extended to 3U in space) and includes a 1D (Pína et al. 2015, 2016) miniature X-ray telescope with a Timepix detector in its focal plane (Baca et al. 2016). The main mission goal is the technological verification of the system (Urban et al. 2017; Dániel et al. 2016). However, there is potential for science as the telescope will view bright celestial sources as part of its mission (Blazek et al. 2017). The satellite represents the fifth satellite in space with Czech X-ray optics onboard. The 1D lobster eye module onboard VZLUSAT-1 has focal length of 250 mm and is composed of 116 wedges and 56 reflective double-sided gold-plated foils (thickness 145 microns). The input aperture is 29 × 19 mm2 ; outer dimensions are 60 × 28 × 31 mm3 . The active part of the foils is 19 mm in width and 60 mm in length, and the energy range is 3–20 keV. Images of the optics are shown in Fig. 26. REX Rocket Experiment The Rocket EXperiment 1 (REX1) was a secondary payload instrument on the Water Recovery X-ray Rocket (WRX-R) experiment. WRX-R was launched from the Kwajalein Atoll in the Marshall Islands on April 4, 2018. WRX-R was the first astrophysics sounding rocket mission to use a newly developed NASA water

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Fig. 26 The miniature 1D Schmidt lobster eye module for VZLUSAT1 CubeSat (Urban et al. 2017)

recovery system for astronomical payloads as a cost-effective alternative to typical land recoveries that also may result in payload damage (Miles 2017). The WRX-R was led by the Pennsylvania State University (PSU), USA. The primary payload was the soft X-ray spectroscope of PSU. WRX-R’s primary instrument was a grating spectrometer that consisted of a mechanical collimator, an X-ray reflection grating array, a grazing incidence mirror, and a hybrid CMOS detector. The Czech team provided the REX1 optical instrument as a secondary payload (Urban et al. 2021; Dániel et al. 2017, 2019). It was the first time that an X-ray lobster eye telescope was flown in a rocket experiment to observe an astrophysical object. The design of the REX1 instrument for the WRX-R was based on the concept of an optical baffle, which is normally used for NASA Sounding rocket experiments. This is a simple construction of a quill-shaped boulder with the anchor on one side of the block base, where the baffle is attached to the sounding rocket. The REX1 optical instrument consisted of two parts – vacuum chamber and hermetically sealed box. The vacuum part contained two (one 1D and one 2D) Xray telescopes with Timepix pixel detectors (Pína et al. 2019). The modules were assembled using Multi-Foil Technology (MFT). The material of the housing of the optical module was an aluminum alloy. The 1D X-ray lobster eye system with a focal length of 250 mm had a FoV of 3.3 × 2.0 degrees and spanned the spectral range from 3 to 20 keV. The 1D lobster eye module was composed of 116 wedges and 56 reflective double-sided gold-plated glass foils (thickness of 145 µm). The gold coating allows the material to reflect incoming X-ray photons that have shallow incident angles of 0.5 deg or less. The input aperture was 29 × 19 mm2 , while the outer dimensions were 60 × 28 × 31 mm. The active area of the module was 19 mm in width and 6 mm in length and the energy range was 3–20 keV. The second lobster eye telescope was a 2D X-ray system with a focal length of 1065 mm. The FoV of this system was 0.8 × 0.8 deg with spectral range from

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Fig. 27 The 1D and 2D Schmidt lobster eye modules REX for rocket flight experiment (Urban et al. 2021)

3 to 10 keV. The 2D lobster eye X-ray optics of REX was composed of two 1D sub-modules where one-sided gold-plated glass foils were in the vertical plane of the horizontal arrangement. Each sub-module consisted of 55 pieces of thin at glass foils (thickness of 0.34 mm) which were arranged so that the focal length was around 1.0 m. The external dimensions of the module was approximately 80×80×170 mm. Both REX1 lobster eye modules can be seen in Fig. 27. The second generation of the optical system for the Rocket Experiment (REX2) is currently under study (Pina et al. 2021). This optical device is based on the successful mission REX1 described above. The purpose of REX2 is to verify the Xray optical system that consists of a wide-field 2D X-ray lobster eye assembly with an uncooled Quad Timepix3 detector (512×512 px @ 55 microns and spectrometer (active area 7 mm2 , resolution 145 eV @ 5.9 keV)). The 2D X-ray lobster eye optics is a combination of two 1D lobster eye modules with a focal length of up to 1 m and a FoV larger than 4.0 × 4.0 deg. The proposed optical system has imaging capabilities (2.5–20 keV) and spectroscopy capabilities (0.2–10 keV). The optical system was recently tested in an X-ray vacuum chamber (Pina et al. 2021).

Kirkpatrick-Baez Optics In this section we briefly describe Kirkpatrick-Baez (K-B) X-ray optics. From the standpoint of manufacturing, there is a significant number of similarities to lobster eye optics in MFO Schmidt arrangements as both are based on multiple thin foils. Although the Wolter systems are generally well known, Hans Wolter was not the first who proposed X-ray imaging systems based on the reflection of X-rays. In fact, the first grazing incidence system to form a real image was proposed by Kirkpatrick and Baez in (1948). This system consists of a set of two orthogonal parabolas in the configuration shown in Fig. 28. The first reflection focuses to a line, which the second surface focuses to a point. This was necessary to avoid the extreme astigmatism suffered by a single mirror but was still not free from geometric aberrations. The system is nevertheless attractive for the ease of constructing the reflecting surfaces. These surfaces can be produced as flat plates and then

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Fig. 28 The configuration of the K-B X-ray objective according to Kirkpatrick and Baez (1948)

mechanically bent to the required curvature. In order to increase the aperture, a number of mirrors can be nested together, but it should be noted that such nesting introduces additional aberrations. This configuration is used mostly in experiments not requiring large collecting area (solar, laboratory). Recently, however, large modules of K-B mirrors have been suggested also for stellar X-ray experiments (Hudec et al. 2018a,b). Despite this fact, astronomical X-ray telescopes flown so far on satellites mostly used the Wolter 1 type optics. However, K-B was used in several rocket experiments in the past, and in addition to that, they were proposed and discussed for use on several satellite experiments. Alternately, in the lab, K-B systems are in frequent use, e.g., at synchrotron facilities. In order to increase the collecting area (the frontal area), a stack of parabolas of translation can be constructed for astrophysical applications. However, in contrast to the single double-plate system, the image of a point-like source starts to become increasingly extended in size as the number of plates involved increases. Wolter type I telescopes bend the incident ray direction two times in the same plane, whereas the two bendings in K-B systems occur in two orthogonal planes, which for the same incidence angle on the primary mirror requires a longer telescope (Aschenbach 2009).

K-B Systems in Astronomical Applications As an alternative to Wolter optics-based instruments, van Speybroeck et al. (1971) designed several K-B telescope configurations that focus the X-rays with sets of two orthogonal parabolas of translation. According to van Speybroeck et al. (1971), the crossed parabola systems should find application in astronomical observations such as high sensitivity surveys, photometry, and certain kinds of spectroscopy where a large effective area rather than high angular resolution is the most important factor. The design of a K-B grazing incidence X-ray telescope to be used to scan the sky would allow for the distribution of the reflected X-rays and spurious images over the FoV to be analyzed. Kast (1975) has shown that in order to obtain maximum

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effective area over the FoV, it is necessary to increase the spacing between plates for a scanning telescope as compared to a pointing telescope. Spurious images are necessarily present in this type of lens, but they can be eliminated from the FoV by adding properly located baffles or collimators. X-ray telescopes of the type suggested by Kirkpatrick and Baez (1948) have several advantages over other types of X-ray telescopes for a general sky survey for low-energy X-ray sources. These telescopes use two orthogonal sets of nested parabolas of translation (perpendicular to one another) to provide 2D focusing of an X-ray image. Although their angular resolution for axial rays is somewhat worse compared with telescopes using successive concentric figures of revolution, they can be constructed more easily and have greater effective area (van Speybroeck et al. 1971). Note that more recent papers give somewhat different findings, namely, that the K-B Si stacks provide an alternative solution with a reduced on-axis collecting area but wider field of view and comparable angular resolution (Willingale and Spaan 2009). In either case, these telescopes, in general, can be constructed more easily. The design of K-B-type telescopes has been discussed by several authors, e.g., van Speybroeck et al. (1971), Gorenstein et al. (1973), Weisskopf (1973), and results have been reported from several experiments using 1D focusing from a single set of plates (Gorenstein et al. 1971; Catura et al. 1972; Borken et al. 1972). For a more recent status, see Hudec (2010) and Hudec et al. (2018a).

K-B as a Segmented Mirror Segmentation can also be applied to an array of K-B stacked orthogonal parabolic reflectors (Fig. 29). As shown in Fig. 29, a large K-B mirror can be segmented into rectangular modules of equal size and shape (Gorenstein et al. 1996). A segmented K-B telescope has the advantage of being highly modular on several levels. All segments are rectangular boxes with the same outer dimensions. Along a column, the segments are nearly identical and many are interchangeable with each other. All reflectors deviate from flatness only slightly. On the other hand, the Wolter reflectors are highly curved in the azimuthal direction, and the curvature varies over

Fig. 29 Kirkpatrick-Baez mirror consisting of orthogonal stacks of reflectors. Each reflector is a parabola in one dimension. A large K-B mirror can be segmented into rectangular modules of equal size and shape (Gorenstein et al. 1996)

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Fig. 30 Principle of K-B MFO telescope (left (Marsikova 2009)) Laboratory samples of advanced K-B MFO modules designed and developed at Rigaku Innovative Technologies Europe (RITE) in Prague (right (Marsikova 2009), photo courtesy Rigaku)

a wide range. Furthermore, within a segment, the K-B reflectors themselves can be segmented along the direction of the optical axis. As shown in Fig. 29, a K-B mirror system can be folded more easily than the Wolter mirror into a compact volume for launch and deployment in space. The examples of assembled K-B modules based on superior quality gold-coated Si wafer substrates are illustrated in Fig. 30.

K-B in Astronomical Telescopes: Recent Status and Future Plans The first attempt to create an astronomical K-B module with silicon wafers was reported by Joy et al. (1994). A telescope module that consisted of 94 silicon wafers with a diameter of 150 mm, uncoated, with thickness of 0.72 mm was constructed. The device was tested both with optical light and with X-rays. The measured FWHM was 150 arc-seconds, which was dominated by large-scale flatness. It should be noted that the surface quality and flatness of Si wafers have improved since this time. Recent efforts toward supporting future larger and precise imaging astronomical X-ray telescopes require reconsidering both the technologies and mirror assembly design. Future large X-ray telescopes require new lightweight and thin materials/substrates such as glass foils and/or silicon wafers (Hudec et al. 2015). Their shaping to small radii, as required in Wolter designs, is not an easy task, while the K-B arrangements have potential to represent a less laborious and hence less expensive alternative because of (i) no need of mandrels, (ii) no need of polishing, and (iii) no need of bending to small radii. The use of K-B arrangement for the proposed IXO project (the proposed joint NASA/ESA/JAXA International X-ray Observatory) was suggested and investigated by Marsikova (2009), Hudec (2011), and Willingale and Spaan (2009). These investigations indicate that if superior quality reflecting plates were used and the focal length is large, an angular resolution of order of a few arcsec could be achieved. Recent simulations further indicate that in comparison with Wolter arrangement, the K-B optics exhibit reduced on-axis collecting area but larger FoV, at comparable angular resolution (Willingale and Spaan 2009). A very important factor is the ease of constructing highly segmented modules based on multiply nested thin reflecting substrates if compared with Wolter design.

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While, e.g., the Wolter design for future large space X-ray telescopes such as Athena requires the substrates to be precisely formed with curvatures as small as 0.25 m, the alternative K-B arrangement uses almost flat or only slightly bent sheets. Hence, the feasibility to construct a K-B module with the required Athena 5 arcsecond HEW resolution at an affordable cost is, in principle, lower than the cost of a Wolter arrangement. Note however that in order to achieve the comparable effective area, the focal length of K-B system is required to be about twice of the focal length of Wolter system (Marsikova 2009; Hudec 2010, 2011).

Conclusion The grazing incidence X-ray optical elements of non-Wolter type (lobster eye and Kirkpatrick-Baez) offer alternative solutions for many future space- and lab-based applications. They can offer cheaper, and/or lighter, alternatives, and also a much larger FoV. At the same time, new computer-based systems allow us to consider alternative designs and arrangements (Nentvich et al. 2017). Although both Angel and Schmidt designs were suggested in the 1970s, both have seen rapid development over the past few years with MPO optics in an Angel arrangement already on selected missions and the Schmidt design using MFOs being proven on rocket and CubeSat experiments. A direct and reliable comparison between MFO and MPO designs of lobster eye X-ray optics is difficult, as in both cases the real optics performance deviates from the theoretical. The necessary slumping of the MPOs introduces additional sources of error (Bannister et al. 2007; Willingale et al. 2016), while the MFO design is harder to assemble. Both designs differ in geometry using both Angel and Schmidt designs, and require different manufacturing and assembling technology. The MFO technology enables a larger effective area with easy deposition of reflective layers, while the MPOs are lighter and are easier to assemble into a large array. The effective area at 10 keV for MFOs is higher than for MPOs although alternative coatings are being investigated for MPOs to improve the higher energy response. The prototypes developed and tested for both arrangements confirm that these lightweight telescopes are fully feasible and can achieve angular resolutions of several arcmin or better over a very wide FoV. While both provide a more modest angular resolution compared to Chandra (Weisskopf 2003) and XMMNewton (Jansen et al. 2001), for example, they can still be used to help solve pressing questions in X-ray astrophysics, and can also be used for other applications such as within laboratories. K-B optics have already found wide applications in synchrotrons, and have demonstrated their performance and advantages. Acknowledgments The authors wish to thank the other members of their research groups. The research leading to these results has received funding from the European Union’s Horizon 2020 Programme under the AHEAD2020 project (grant agreement n. 871158)

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References J. Angel, Lobster eyes as x-ray telescopes. ApJ 233, 364–373 (1979) B. Aschenbach, Realization of X-ray telescopes-from design to performance. Exp. Astron. 26 (1–3), 95–109 (2009). https://doi.org/10.1007/s10686-009-9163-8 T. Baca, M. Platkevic, J. Jakubek, A. Inneman, V. Stehlikova, M. Urban, O. Nentvich, M. Blazek, R. McEntaffer, V. Daniel, Miniaturized X-ray telescope for VZLUSAT-1 nanosatellite with Timepix detector. J. Instrum. 11(10), C10007 (2016). https://doi.org/10.1088/1748-0221/11/10/ C10007 N.P. Bannister, E.J. Bunce, S.W.H. Cowley, R. Fairbend, G.W. Fraser, F.J. Hamilton, J.S. Lapington, J.E. Lees, M. Lester, S.E. Milan, J.F. Pearson, G.J. Price, R. Willingale, A Wide Field Auroral Imager (WFAI) for low Earth orbit missions. Ann. Geophys. 25(2), 519–532 (2007). https://doi.org/10.5194/angeo-25-519-2007 M. Blazek, P. Pata, A. Inneman, P. Skala, Astronomical tasks for tests of X-ray optics in VZLUSAT1 nanosatellite. Adv. Astron. 2017, 316289 (2017). https://doi.org/10.1155/2017/3162892 R. Borken, R. Doxsey, S. Rappaport, A soft X-ray survey of the galactic plane from cygnus to norma. apjl 178, L115 (1972). https://doi.org/10.1086/181098 E.J. Bunce, A. Martindale, S. Lindsay, K. Muinonen, D.A. Rothery, J. Pearson, I. McDonnell, C. Thomas, J. Thornhill, T. Tikkanen, C. Feldman, J. Huovelin, S. Korpela, E. Esko, A. Lehtolainen, J. Treis, P. Majewski, M. Hilchenbach, T. Väisänen, A. Luttinen, T. Kohout, A. Penttilä, J. Bridges, K.H. Joy, M.A. Alcacera-Gil, G. Alibert, M. Anand, N. Bannister, C. Barcelo-Garcia, C. Bicknell, O. Blake, P. Bland, G. Butcher, A. Cheney, U. Christensen, T. Crawford, I.A. Crawford, K. Dennerl, M. Dougherty, P. Drumm, R. Fairbend, M. Genzer, M. Grande, G.P. Hall, R. Hodnett, P. Houghton, S. Imber, E. Kallio, M.L. Lara, A. Balado Margeli, M.J. Mas-Hesse, S. Maurice, S. Milan, P. Millington-Hotze, S. Nenonen, L. Nittler, T. Okada, J. Ormö, J. Perez-Mercader, R. Poyner, E. Robert, D. Ross, M. Pajas-Sanz, E. Schyns, J. Seguy, L. Strüder, N. Vaudon, J. Viceira-Martín, H. Williams, D. Willingale, T. Yeoman, The BepiColombo mercury imaging X-ray spectrometer: science goals, instrument performance and operations. Space Sci. Rev. 216(8), 126 (2020). https://doi.org/10.1007/s11214-020-00750-2 J. Camp, N. Gehrels, Whitepaper on Transient Astrophysics Probe (TAP) (2020). https://pcos.gsfc. nasa.gov/physpag/probe/Transient_Astrophysics_Probe.pdf R.C. Catura, P.C. Fisher, H.M. Johnson, A.J. Meyerott, Asymmetry of soft X-ray emission near M87. apjl 177, L1 (1972). https://doi.org/10.1086/181041 H. Chapman, K. Nugent, S. Wilkins, X-ray focusing using cylindrical-channel capillary arrays, I. Theory. Appl. Opt. 32, 6316 (1993) V. Dániel, L. Pína, A. Inneman, V. Zadražil, T. Báˇca, M. Platkeviˇc, V. Stehlíková, O. Nentvich, M. Urban, Terrestrial gamma-ray flashes monitor demonstrator on CubeSat, in CubeSats and NanoSats for Remote Sensing, ed. by T.S. Pagano. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 9978 (2016), p. 99780D. https://doi.org/10.1117/12. 2240299 V. Dániel, A. Inneman, L. Pína, V. Zadražil, T. Báˇca, V. Stehlíková, O. Nentvich, M. Urban, V. Maršíková, R. McEntaffer, J. Tutt, T. Schulz, X-ray Lobster Eye all-sky monitor for rocket experiment, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 10235 (2017), p. 1023503. https://doi.org/10.1117/12.2277515 V. Dániel, R. Hudec, T. Baca, L. Pina, A. Inneman, V. Marsikova, M. Urban, O. Nentvich, V. Stehlikova, J. Tutt, REX LE X-ray telescope experiment overview, in EUV and X-Ray Optics: Synergy Between Laboratory and Space VI. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 11032 (2019), p. 1103206. https://doi.org/10.1117/12.2527288 ESA, SMILE mission description (2020). https://www.cosmos.esa.int/web/smile/mission C. Feldman, P. O’Brien, R. Willingale, H. Lerman, I. Hutchinson, M. McHugh, A. Lodge, R. Speight, J. Seguy, R. Rudot, E. Schyns, R. Fairbend, The development of the THESEUS SXI optics, in Proceedings of SPIE 11444-283 (2020)

172

R. Hudec and C. Feldman

G. Fraser, X-Ray Detectors in Astronomy (Cambridge University Press, Cambridge, 1989) G.W. Fraser, J.E. Lees, J.F. Pearson, M.R. Sims, K. Roxburgh, X-ray focusing using microchannel plates, in Proceedings of SPIE, vol. 1546 (1992) G.W. Fraser, A.N. Brunton, J.E. Lees, J.F. Pearson, R. Willingale, D.L. Emberson, W.B. Feller, M. Stedman, J. Haycocks, Development of Microchannel Plate (MCP) X-ray optics, in Proceedings of SPIE, vol. 2011 (1993) G. Fraser, J. Carpenter, D. Rothery, J. Pearson, A. Martindale, J. Huovelin, J. Treis, M. Anand, M. Anttila, M. Ashcroft, J. Benkoff, P. Bland, A. Bowyer, A. Bradley, J. Bridges, C. Brown, C. Bulloch, E. Bunce, U. Christensen, M. Evans, R. Fairbend, M. Feasey, F. Giannini, S. Hermann, M. Hesse, M. Hilchenbach, T. Jorden, K. Joy, M. Kaipiainen, I. Kitchingman, P. Lechner, G. Lutz, A. Malkki, K. Muinonen, J. Nrnen, P. Portin, M. Prydderch, J. Juan, E. Sclater, E. Schyns, T. Stevenson, L. Strder, M. Syrjasuo, D. Talboys, P. Thomas, C. Whitford, S. Whitehead, The mercury imaging x-ray spectrometer (mixs) on bepicolombo. Planet. Space Sci. 58, 79–95 (2010) M. Freyberg, B. Budau, W. Burkert, P. Friedrich, G. Hartner, K. Misaki, M. Mühlegger, New technology and techniques for x-ray mirror calibration at panter, in Proceedings of SPIE, vol. 7011 (2008). https://doi.org/10.1117/12.789853 P. Gorenstein, X-ray optics for the LAMAR facility, an overview, in Space Optics: Imaging X-Ray Optics Workshop, ed. by M. Weisskopf. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 184 (1979), pp. 63–72. https://doi.org/10.1117/12.957435 P. Gorenstein, All Sky Supernova and Transient Explorer (ASTRE), in Variability of Galactic and Extragalactic X-ray Sources (1987), pp. 253–263 P. Gorenstein, B. Harris, H. Gursky, R. Giacconi, R. Novick, P. vanden Bout, X-ray structure of the cygnus loop. Science 172(3981), 369–372 (1971). https://doi.org/10.1126/science.172.3981. 369 P. Gorenstein, A. Decaprio, R. Chase, B. Harris, Large area focusing collector for the observation of cosmic X-rays. Rev. Sci. Instrum. 44, 539–545 (1973). https://doi.org/10.1063/1.1686178 P. Gorenstein, E. Whitbeck, G.K. Austin, A.T. Kenter, L. Pina, A. Inneman, R. Hudec, Lobstereye x-ray telescope prototype, in Multilayer and Grazing Incidence X-Ray/EUV Optics III, ed. by R.B. Hoover, A.B. Walker. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 2805 (1996), pp. 74–80. https://doi.org/10.1117/12.245080 D. Götz, C. Adami, S. Basa, V. Beckmann, V. Burwitz, R. Chipaux, B. Cordier, P. Evans, O. Godet, R. Goosmann, N. Meidinger, A. Meuris, C. Motch, K. Nandra, P. O’Brien, J. Osborne, E. Perinati, A. Rau, R. Willingale, K. Mercier, F. Gonzalez, Microchannel x-ray telescope on board the SVOM satellite. ArXiv e-prints 1 (2015) R. Hudec, Kirkpatrick-Baez (KB) and Lobster Eye (LE) Optics for Astronomical and Laboratory Applications. X-Ray Opt. Instrum. 2010, 139148 (2010). https://doi.org/10.1155/2010/139148 R. Hudec, Kirkpatrick-Baez x-ray optics: a review, in EUV and X-Ray Optics: Synergy between Laboratory and Space II, ed. by R. Hudec, L. Pina. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 8076 (2011), p. 807607. https://doi.org/10.1117/12. 888268 R. Hudec, A.V. Inneman, L. Pina, Wide-field x-ray optics, in X-Ray Optics, Instruments, and Missions III, ed. by J.E. Truemper, B. Aschenbach. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 4012 (2000), pp. 432–441 https://doi.org/10.1117/12. 391580 R. Hudec, L. Pina, V. Semencova, A. Inneman, M. Skulinova, L. Sveda, M. Mika, V. Brozek, R. Kacerovsky, J. Prokop, J. Sik, Novel x-ray optics with Si wafers and formed glass, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 6266, ed. by M.J.L. Turner, G. Hasinger (2006a), p. 62661H, https://doi.org/10.1117/12.673306 R. Hudec, V. Simon, L. Svéda, L. Pina, A. Inneman, Astrophysics with LOBSTER. Chin. J. Astron. Astrophys. Suppl. 6(S1), 383–387 (2006b). https://doi.org/10.1088/1009-9271/6/S1/52 R. Hudec, L. Švéda, L. Pina, A. Inneman, V. Šimon, Lobster eye telescopes as X-ray all-sky monitors. Chin. J. Astron. Astrophys. Suppl. 8, 381–385 (2008)

4 Lobster Eye X-ray Optics

173

R. Hudec, V. Marsikova, M. Mika, J. Sik, M. Lorenc, L. Pina, A. Inneman, M. Skulinova, Advanced x-ray optics with Si wafers and slumped glass, in Optics for EUV, X-Ray, and Gamma-Ray Astronomy IV, ed. by S.L. O’Dell, G. Pareschi. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 7437 (2009), p. 74370S. https://doi.org/10.1117/12. 827978 R. Hudec, V. Šimon, V. Tichý, Lobster-eye X-ray monitors: astrophysical aspects. Mem. S.A.It. 83, 365 (2012) R. Hudec, L. Pina, V. Marsikova, A. Inneman, GRBs and lobster eye X-ray telescopes, in EAS Publications Series, vol. 61, ed. by Castro-Tirado, J. Gorosabel, I.H. Park (2013), pp. 611–615. https://doi.org/10.1051/eas/1361097 R. Hudec, L. Pina, A. Inneman, Alternative technologies and arrangements for future space x-ray telescopes, in EUV and X-Ray Optics: Synergy Between Laboratory and Space IV, ed. by R. Hudec, L. Pina. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 9510 (2015), p. 951004. https://doi.org/10.1117/12.2177699 R. Hudec, L. Pina, V. Marsikova, O. Nentvich, M. Urban, A. Inneman, Kirkpatrick Baez X-ray optics for astrophysics: recent status. Contrib. Astron. Observ. Skalnate Pleso 48(3), 437–445 (2018a) R. Hudec, L. Pina, V. Marsikova, O. Nentvich, M. Urban, A. Inneman, Lobster Eye X-ray optics for astrophysics: recent status. Contrib. Astron. Observ. Skalnate Pleso 48(3), 456–465 (2018b) A. Inneman, Technological aspects of the development and construction of optical elements for x-rays. PhD thesis, Czech Technical University in Prague (2001) F. Jansen, D. Lumb, B. Altieri, J. Clavel, M. Ehle, C. Erd, C. Gabriel, M. Guainazzi, P. Gondoin, R. Much, R. Munoz, M. Santos, N. Schartel, D. Texier, G. Vacanti, Xmm-newton observatory, 1. The spacecraft and operations. Astron. Astrophys. 365, L1 (2001) M.K. Joy, J.J. Kolodziejczak, M.C. Weisskopf, S.B. Fair, B.D. Ramsey, Imaging properties of a silicon wafer x-ray telescope, in Advances in Multilayer and Grazing Incidence X-Ray/EUV/FUV Optics, ed. by R.B. Hoover, A.B. Walker. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 2279 (1994), pp. 283–286. https://doi.org/10.1117/12.193144 P. Kaaret, P. Geissbuhler, A. Chen, E. Glavinas, X-ray focusing using microchannel plates. Appl. Opt. 31, 7339–7343 (1992) J.W. Kast, Scanning Kirkpatrick-Baez X-ray telescope to maximize effective area and eliminate spurious images; design. 14, 537–545 (1975). https://doi.org/10.1364/AO.14.000537 P. Kirkpatrick, A. Baez, Formation of optical images by x-rays. J. Opt. Soc. Am. 38, 776 (1948) J. Ladislas Wiza, Microchannel plate detectors. Nucl. Instrum. Methods 162(1), 587–601 (1979) V. Marsikova, Axro2009 online proceedings (2009). http://axro.cz A.P. Martin, Exploitation of microchannel plate optics. PhD thesis, University of Leicester (2000) A. Martindale, Novel x-ray instrumentation for astronomy. PhD thesis, University of Leicester (2008) A. Martindale, J. Pearson, C. Whitford, G. Fraser, D. Rothery, D. Talboys, J. Carpenter, T. Stevenson, E. Bunce, R. Fairbend, J. Seguy, E. Sclater, I. Delgado, A. Dixon, J. Treis, J. MasHesse, J.S. Juan, K. Muinonen, C. Sawyers, C. Bulloch, E. Schyns, The mercury imaging x-ray spectrometer: instrument overview. Proc. SPIE 7441, 744115 (2009) K. Mercier, F. Gonzalez, M. Jouret-Perl, J. Atteia, P. Mandrou, R. Pons, S. Basa, B. Cordier, D. Götz, F. Pinsard, S. Schanne, C. Lachaud, J. Wei, S. Zhang, The french payload on-board the SVOM french-chinese mission, in Proceedings of SPIE, vol. 9144 (2014) D. Miles, The Water Recovery X-ray Rocket (WRX-R), in AAS/High Energy Astrophysics Division #16, vol. 16 (2017), p. 103.19 T. Mineo, G. Fraser, A. Martindale, C. Feldman, R. Campana, G. Cusumano, M. Feroci, Effects of capillary reflection in the performance of the collimator of the large area detector on board loft. Exp. Astron. 37 (2014). https://doi.org/10.1007/s10686-013-9368-8 NASA Chandra X-ray Observatory, Telescope system (2006). http://chandra.harvard.edu/about/ telescope_system.html

174

R. Hudec and C. Feldman

O. Nentvich, V. Stehlikova, M. Urban, R. Hudec, L. Sieger, Data processing from lobster eye type optics, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 10235 (2017), p. 102350N. https://doi.org/10.1117/12.2265724 L. Pína, R. Hudec, A. Inneman, D. Cerna, J. Jakubek, L. Sieger, V. Dániel, W. Cash, L. Mikulickova, R. Pavlica, E. Belas, J. Polak, X-ray monitoring for astrophysical applications on Cubesat, in EUV and X-ray Optics: Synergy Between Laboratory and Space IV, ed. by R. Hudec, L. Pina. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 9510 (2015), p. 951005. https://doi.org/10.1117/12.2185091 L. Pína, R. Hudec, A.J. Inneman, T. Baca, M. Blazek, M. Platkevic, L. Sieger, D. Doubravova, R.L. McEntaffer, T.B. Schultz, V. Dániel, Development and tests of x-ray multifoil optical system for 1D imaging (Conference Presentation), in Advances in Laboratory-based X-Ray Sources, Optics, and Applications V, ed. by A.M. Khounsary, G.E. van Dorssen. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 9964 (2016), p. 99640B. https://doi. org/10.1117/12.2243055 L. Pína, R. Hudec, A. Inneman, V. Marsikova, T. Baca, V. Stehlikova, V. Daniel, J. Tutt, Multifoil optics for rocket experiments, in EUV and X-ray Optics: Synergy between Laboratory and Space VI. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 11032 (2019), p. 1103203. https://doi.org/10.1117/12.2525541 L. Pina, R. Hudec, V. Marsikova, A. Inneman, V. Daniel, X-ray testing of the multifoil optical system REX II for rocket experiment, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 11776 (2021), p. 1177608. https://doi.org/10.1117/12.2593763 D.J. Ruggieri, Microchannel plate imaging detectors. IEEE (Inst. Elec. Electron. Eng.), Trans. Nucl. Sci. NS-19(3), 74–84 (1972). https://doi.org/10.1109/TNS.1972.4326705, https://www. osti.gov/biblio/4557273 W.K.H. Schmidt, A proposed X-ray focusing device with wide field of view for use in Xray astronomy. Nucl. Instrum. Methods 127, 285–292 (1975). https://doi.org/10.1016/0029554X(75)90501-7 V. Stehlikova, T. Döhring, M. Stollenwerk, J. Stadtmüller, V. Marsikova, R. Hudec, D. Flachs, V. Burwitz, G. Hartner, S. Rukdee, T. Müller, A. Inneman, T. Schmidt, M. Klementova, S. Zeising, A. Langmeier, Lobster eye type X-ray telescope with chromium-iridium coated trilayer mirrors, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 11776 (2021), p. 1177605. https://doi.org/10.1117/12.2589266 L. Sveda, Astrophysical aspects of lobster eye x-ray telescopes. PhD thesis, Charles University Prague (2003) L. Sveda, Multi-foil x-ray optical systems and image analysis in high-temperature plasma physics. PhD thesis, Czech Technical University in Prague (2006) L. Sveda, R. Hudec, L. Pina, A. Inneman, Lobster all-sky monitor, in Design and Microfabrication of Novel X-Ray Optics II, ed. by A.A. Snigirev, D.C. Mancini. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 5539 (2004), pp. 116–125. https:// doi.org/10.1117/12.559954 L. Sveda, V. Semencova, A. Inneman, L. Pina, R. Hudec, Hybrid lobster optic, in Laser-Generated, Synchrotron, and Other Laboratory X-Ray and EUV Sources, Optics, and Applications II, ed. by G.A. Kyrala, J.C.J. Gauthier, C.A. MacDonald, A.M. Khounsary. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 5918 (2005), pp. 22–30. https://doi. org/10.1117/12.620247 L. Sveda, L. Pina, A. Inneman, V. Semencova, J. Marsik, R. Hudec, A. Bartnik, H. Fiedorowicz, R. Jarocki, J. Kostecki, R. Rakowski, M. Szczurek, Multi-foil optic condenser for a laser plasma EUV source. Phys. Scrip. Vol. T 123, 131–134 (2006). https://doi.org/10.1088/0031-8949/2006/ T123/019 V. Tichý, R. Willingale, Optimization of mirror spacing or pore width of lobster eye optics. Astron. Nachr. 339(5), 363–366 (2018). https://doi.org/10.1002/asna.201813506 V. Tichý, M. Hromˇcík, R. Hudec, A. Inneman, J. Maršík, V. Maršíková, L. Pína, Tests of lobstereye optics for a small X-ray telescope. Balt. Astron. 18, 362–368 (2009)

4 Lobster Eye X-ray Optics

175

V. Tichý, M. Barbera, R. Hudec, R. Willingale, Effective collecting area of lobster eye optics and optimal value of effective angle. Exp. Astron. 47(1–2), 161–175 (2019). https://doi.org/10.1007/ s10686-019-09622-2 M. Urban, O. Nentvich, V. Stehlikova, T. Baca, V. Daniel, R. Hudec, VZLUSAT-1: Nanosatellite with miniature lobster eye X-ray telescope and qualification of the radiation shielding composite for space application. Acta Astronaut. 140, 96–104 (2017). https://doi.org/10.1016/j.actaastro. 2017.08.004 M. Urban, O. Nentvich, T. Báˇca, I. Veˇrtát, V. Maršíková, D. Doubravová, V. Dániel, A. Inneman, L. Pína, L. Sieger, R.L. McEntaffer, T.B. Schultz, D.M. Miles, J.H. Tutt, REX: X-ray experiment on the water recovery rocket. Acta Astronaut. 184, 1–10 (2021). https://doi.org/10.1016/j. actaastro.2021.03.019, 2011.10072 L.P. van Speybroeck, R.C. Chase, T.F. Zehnpfennig, Orthogonal mirror telescopes for X-ray astronomy. 10, 945–949 (1971). https://doi.org/10.1364/AO.10.000945 D. Vernani, G. Bianucci, F. Marioni, G. Valsecchi, A. Keereman, Y. Chen, M. Cong, Y. Yang, J. Wang, M. Bradshaw, V. Burwitz, P. Friedrich, J. Eder, Follow-up x-ray telescope (fxt) for the einstein probe mission, in Proceedings of SPIE 11444-175 (2020) M.C. Weisskopf, Design of grazing-incidence X-ray telescopes. 1. 12, 1436–1439 (1973). https:// doi.org/10.1364/AO.12.001436 M. Weisskopf, The chandra x-ray observatory: an overview. Adv. Space Res. 32(10), 2005 (2003) N. White, The Gamow explorer: a gamma-ray burst mission to study the high redshift universe. Proc. Yamada Conf. LXXI 1, 51 (2020) S. Wilkins, A. Stevenson, K. Nugent, H. Chapman, S. Steenstrup, On the concentration, focusing, and collimation of x-rays and neutrons using microchannel plates and configurations of holes. Rev. Sci. Instrum. 60, 1026–1036 (1989) R. Willingale, F.H. Spaan, The design, manufacture and predicted performance of KirkpatrickBaez Silicon stacks for the International X-ray Observatory or similar applications, in Optics for EUV, X-Ray, and Gamma-Ray Astronomy IV, ed. by S.L. O’Dell, G. Pareschi. Society of PhotoOptical Instrumentation Engineers (SPIE) Conference Series, vol. 7437 (2009), p. 74370B. https://doi.org/10.1117/12.826225 R. Willingale, G. Fraser, A. Brunton, A. Martin, Hard x-ray imaging with microchannel plate optics. Exp. Astron. 8, 281–296 (1998) R. Willingale, J. Pearson, A. Martindale, C. Feldman, R. Fairbend, E. Schyns, S. Petit, J. Osborne, P. O’Brien, Aberrations in square pore micro-channel optics used for x-ray lobster eye telescopes, in Proceedings of SPIE, vol. 9905 (2016) H. Wolter, Generalized schwarzschild mirror systems with glancing incidence as optics for x-rays. Annalen de Physik 445, 286 (1952) A. Woodhead, R. Ward, The channel electron multiplier and its use in image intensifiers. Inst. Electron. Radio Eng. 47, 545–553 (1977). https://doi.org/10.1049/ree.1977.0079 W. Yuan, Exploring the transient x-ray sky with einstein probe (2019). https://www.cosmos.esa. int/documents/332006/1402684/WYuan_t.pdf

5

Single-Layer and Multilayer Coatings for Astronomical X-ray Mirrors Kristin K. Madsen, David Broadway, and Desiree Della Monica Ferreira

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Reflection and Refraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Surface Roughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single-Layer Thin Film Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multilayer Thin Film Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coating and Instrument Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single-Layer Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multilayer Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Depositing Thin Film Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characterization of Thin Film Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Reflectometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Characterization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environmental Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stress in Single and Multilayer Coatings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stress Measurement Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contributions of Stress in Single-Layer Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods of Reducing Film Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stress in Multilayer Thin Films . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Effect of Surface Energy on Film Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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K. K. Madsen CRESST and X-ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, USA e-mail: [email protected] D. Broadway NASA Marshall Space Flight Center (MSFC), Huntsville, AL, USA e-mail: [email protected] D. D. M. Ferreira () DTU Space – Technical University of Denmark, Kongens Lyngby, Denmark e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_4

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Abstract

The bandpass of an X-ray telescope is defined by its reflecting surface, which most commonly is a thin film coating, either as a single-layer, bi-layer, or a multilayer coating. Mirror coatings are made to enhance the telescope performance, and by careful design, they can shape the energy response for very specific applications. In this chapter we review the topic of thin film coating essential for the performance of most astrophysical X-ray missions. We discuss the theory behind X-ray reflection and refraction utilized for thin film coatings and address the design challenges for single-layer, bi-layer, and multilayer coating, as well as the properties of the most typical coating materials. We summarize fabrication methods and discuss the measuring techniques in use for characterizing thin film coatings. Important aspects of stability are presented, and we provide a thorough review on the issue stress, which will play an essential role in next-generation high angular resolution imaging telescope. Keywords

X-ray reflective coatings · X-ray multilayer · X-ray reflectometry · DC magnetron sputtering · X-ray telescope design

Introduction The performance of an X-ray optic can be quantified by just two functions: (1) its point spread function (PSF), which is the size and shape of the focused spot, and (2) the energy-dependent effective area, which is the geometric area of the optic multiplied by the efficiency of the mirror (reflectance and obscuration) at each energy: Aeff (E) = Ageometric × Eff(E). The substrate forming the body of the mirror is primarily responsible for image quality, and typical substrates used for X-ray mirrors are electroformed nickel substrates (Jansen et al. 2001; Gehrels et al. 2004), aluminum and aluminum-cobalt substrates (Serlemitsos et al. 1995, 2007; Takahashi et al. 9905), thermally slumped SiO2 (Harrison et al. 2013; Zhang 2009), and pure Si (Zhang et al. 2010) (see Chap. 2.5), all of which can reflect X-rays, but not very effectively. A mirror coating on top is therefore in most cases required to maximize performance. A coating will contribute to the image quality by adding some additional scatter, but the primary function of a mirror coating is to define the bandpass and effective area. X-ray optics leverage the concept of total external reflection, which is the angle at which a light ray can no longer pass the interface into the second medium. This angle is called the critical angle, θc , and since it has a strong dependency on density, heavy materials such as Au and Ir are favored. For most soft X-ray telescopes that operate below 10 keV, a single layer is often enough to ensure performance over the desired bandpass, but when the majority of the reflection angles become larger than the critical, then a multilayer may be required. In its simplest form, a multilayer is a stack of thinly deposited films of alternating material where one of the films is a

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high-Z material and the other of low-Z material. One such pair forms a bi-layer, and a multilayer of N = 10 is composed of 10 such bi-layer pairs, with a nomenclature of high-Z/low-Z, e.g., W/Si. The stack of bi-layers acts as a periodic crystal lattice, and the Bragg condition will create constructive interference according to λm = 2d sin θi , where d is the lattice spacing, θi the incidence angle, and m the order of reflection. Table 1 summarizes key parameters of the X-ray telescope and coatings used on a selection of past, current, and upcoming X-ray missions. There is a roughly even split between Au and Ir, which generally has to do with the fabrication process of the substrates, and for multilayer telescopes, of which there only have been two, Pt/C and W/Si had been the only combinations in use so far. We will in this chapter first review the basic theory behind X-ray reflection and refraction and then discuss the design considerations behind single- and multilayer coatings. We will review the most common deposition techniques and how to characterize the composition of the mirror coating using a variety of nondestructive and destructive techniques. Finally, we will be discussing the very important subject of stress in mirror coatings.

Theory For a recent overview of the theory behind X-ray reflection and scattering, we refer to Als-Nielsen et al. (2011) and for the classical textbook treatment to Born et al. (1999) and summarize here the important concepts for understanding the performance of X-ray mirror coatings.

X-Ray Reflection and Refraction Light propagating through one medium with refraction index, n1 = 1 − δ + iβ that strikes the plane surface of a second medium with index n2 will undergo a change of direction either as reflection back into the same medium or refraction into the other. This fundamental behavior is governed by Snell’s law n1 cos θ1 = n2 cos θ2 ,

(1)

expressed here as the grazing incidence angle to the surface, θ , which is more appropriate for X-rays. If the first medium is a vacuum then θ2 < θ1 and as the angle of incidence continues to decrease there comes a point when the refracted ray is parallel to the surface (θ2 = 0). The angle of θ1 at which this occurs is called the critical angle, and any angle less than this results in total external reflection of the ray. Because the ray does not enter into the second medium but propagates along the surface as an evanescent wave, the index of refraction does not require the absorption term, β, and with n = 1 − δ, where δ = 2πρr0 /k 2 , the angle is given by (see Als-Nielsen et al. 2011, Eq. (3.3))

Bandpass 0.1–12 keV

0.08–10 keV 0.5–4 keV 0.3–12 keV 0.3–80 keV 2–8 keV 3–80 keV 0.1–2.4 6–30 keV 0.2–12 keV 0.3–10 keV 0.1–12 keV

Mission Athena (Bavdaz et al. 2020)

Chandra (Weisskopf et al. 2002)

Einstein-Probe/FXT (Zhu et al. 2021)

XRISM/XMA (Soong et al. 2011; Iizuka et al. 2018)

Hitomi/HXT (Awaki et al. 2017)

IXPE (Ramsey et al. 2021)

NuSTAR (Harrison et al. 2013)

SRG/eRosita (Predehl et al. 2021)

SRG/ART-XC (Pavlinsky et al. 2018)

Suzaku (Mitsuda et al. 2007; Serlemitsos et al. 2007)

Swift/XRT (Burrows et al. 2005, 2000)

XMM-Newton (Jansen et al. 2001)

Wolter-I 4 shells, F = 10 m, Rmax = 1.2 m Wolter-I 54 shells, F = 1.6 m, Rmax = 17.5 cm Conical approximation Wolter-I 203 shells, F = 5.6 m, Rmax = 22.5 cm Conical approximation Wolter-I 213 shells, F = 12 m, Rmax = 22.5 cm Wolter-I 24 shells, F = 4 m, Rmax = 27.2 cm Conical approximation Wolter-I 133 shells, F = 10.14 m, Rmax = 19 cm Wolter-I 54 shells, F = 1.6 m, Rmax = 36 cm Wolter-I 28 shells, F = 2.7 m, Rmax = 14.5 cm Conical approximation Wolter-I 175 shells, F = 4.75 m, Rmax = 20 cm Wolter-I 12 shells, F = 3.5 m, Rmax = 30 cm Wolter-I 58 shells, F = 7.5 m, Rmax = 70 cm

Telescope type Wolter-Schwartzchild SPO, F = 12 m, Rmax = 1.256 m

Table 1 A selection of past, present, and future X-ray observatories with focusing X-ray optics

Au

Au

Au

Ir

No mirror coating substrate NiCo Shells 1–90: Pt/C Shells 91–133: W/Si Au

Pt/C

Au

Au

(B4C, SiC or C) Cr/Ir

Coating Ir + overcoat

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θc =

 √ 2δ = 4πρr0 /k.

181

(2)

The property of total external reflection is of central importance to the design of X-ray optics and ensures almost unity reflection below θc , which conversely limits the bandpass that can be achieved by a telescope of a particular size and focal length as will be discussed in section “Coating and Instrument Design”. Not all X-ray reflectors, however, operate below the critical angle. An incident wave, E, can be decomposed into a reflected and transmitted component with intensities, E + Er = Et . Together with Snell’s law, they give rise to the Fresnel equations: n ≡ n1 /n2

(3) √

sin θ − n2 − cos2 θ Er = √ E sin θ + n2 − cos2 θ Er 2 sin θ t≡ = , √ E sin θ − n2 − cos2 θ

r≡

(4) (5)

with the corresponding intensity reflectance, R = r 2 , and transmittance, T = t 2 . If the second medium is infinitely thick, the transmitted wave is absorbed, and only the reflected component may be detected. If instead the medium has a finite thickness of ∆ and rests on top of an infinite substrate, then the transmitted wave may again reflect and transmit at the interface to the substrate, and the back-reflected component may also again reflect and transmit at the original interface at the surface. This can proceed in an infinite number of ways, and the superposition of all possible combinations forms a geometric series, which has a finite value at infinity. If medium 0 is vacuum, medium 1 the reflective slab, and medium 2 the infinite substrate, the series becomes (as shown in Als-Nielsen et al. 2011, Eq. (3.23)) rslab =

r01 + r12 eiq∆ , 1 − r10 r12 eiq∆

(6)

where q = 2k sin θ is the vertical component of the momentum transfer vector, q = k − k′ . The expression of reflectivity from a homogeneous slab can be extended to describe a multilayer stack. This was done by Parratt (1954), and in this picture the multilayer is considered to be composed of N layers sitting on top of an infinitely thick substrate. The N’th layer is directly on the substrate, and any layer n ≤ N in the stack has a of thickness ∆n . Progressing from the bottom, the N’th layer on top of the substrate is not subject to multiple scattering from lower levels, and therefore the reflectivity from this surface can be calculated using the Fresnel reflectivity, ′ rN,∞ , from Eq. (3). The next layer, N−1, must include both multiple reflection and refraction, and using the expression in Eq. (6) for reflection from a homogeneous

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slab, where r ′ is the Fresnel reflectivity, the recursive formula becomes

rn−1,n =

′ rn−1,n + rn,n+1 eiqn ∆n

′ 1 + rn−1,n rn,n+1 eiqn ∆n

.

(7)

The reflection is in this way calculated from the bottom up until the total reflective amplitude at the interface between vacuum and the top layer, r0,1 is found.

Surface Roughness For a perfectly sharp interface, Snell’s law (Eq. (1)) dictates that the exit angle must be equal to the incident angle, and the reflection from this condition is called specular. In the preceding sections, it was assumed that the interfaces were perfectly flat and sharp, which will always result in specular reflection, but real surfaces have imperfections and will also scatter outside the specular direction. The imperfections are generally referred to as roughness and can coarsely be grouped by length scale: • Micro roughness [nm, µm]: molecular and crystal imperfections and impurities and bond stresses • Intermediate roughness [µm, mm]: crystal imperfections, bulk impurities, surface abrasion, and stress deformations. • Figure error: [mm0

(10)

Most surfaces are a combination of both. The resulting loss in specular reflectance can be approximated by multiplying the Fresnel reflection coefficients with w(s), ˜ s = 4π cos(θ )/λ, which is the Fourier transform of w(z). The modified Fresnel coefficients then take the form r ′ = r w(s), ˜ and the net reflectivity can as before be calculated using Parratt’s recursive formula. Surface roughness can also be described by its lateral correlation length, ξ , that sets a roughness cutoff above which the rms roughness, σ , is independent of the probe size. For the specular reflection, there are two expressions in general use to describe the reflectivity from a surface with rms roughness, σ , valid for different regimes of the correlation length and scattering angle. For large ξ , describing a surface with low spatial frequency, specular reflection from a diffuse interface can be 2 2 cast as r ′ = re−2k0 σ , where k0 is the perpendicular wave component of the incident wave. This form is the static Debye-Waller (DW) factor, derived from the Born approximation (de Boer 1994, 1996), which requires the interaction and scattering to be weak (θ ≫ θc ). For small ξ , describing high spatial surface frequencies for which the angles and roughness are small, we find the Nevot and Corce (NC) solution 2 (Nevot et al. 1980), r ′ = re2k0 k1 σ , with incidence perpendicular wave component, k0 , and perpendicular refracted component, k1 , valid when k0 σ ≪ 1 and k ≪ kc = |k|2 (1 − n). For typical X-ray optics that operate close to the critical angle and have high-frequency low surface roughness, this is the form used to calculate the specular reflectivity. For non-specular scattering, which are rays exiting from a rough surface at angles either smaller or larger than the incidence, the Born approximation is applicable away from the critical angle where the scattering is considered weak and multiple refractions of the photon can be neglected. The non-specular scattering removes energy out of the specular field, but no energy is coupled from the non-specular field back into the specular, which is an incorrect simplification when the interactions are strong. Near the critical angle, total external and internal reflection becomes possible, and the interaction between matter and incident wave can no longer be considered weak. The distorted-wave Born approximation (DWBA) (Sinha et al. 1988; de Boer 1996) takes into account the multiple reflections between the

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interfaces, and it treats the stack of thin films as the ideal state and regards the deviation of the refractive index to that of a smooth surface as the perturbation. Modeling of non-specular reflectivity is done for the characterization of coatings on individual mirrors. They are complicated calculations that require specialized fitting packages and are not practical for deriving the PSF of an actual X-ray optic. The resulting PSF from an assembled optic is due to the non-specular scattering of its individual components, but as it is a superposition of many scattering elements, which can have different surface roughness properties, it is not feasible to attempt to described the PSF by the fitting of hundreds of non-specular scattering components. In practice, therefore, the PSF of an optic is usually described empirically with geometrical perturbation terms applied to a raytrace that is then used to reproduce the observed PSF. The core of the PSF, though, is usually related to micro surface roughness and the wings from figure error often due to deformations and stress introduced by the manufacture and mounting of the mirror.

Materials The X-ray performance of single- and multilayer coatings is determined by the optical properties of the materials and the quality of the interfaces. For the materials discussed here, there are differences in their surface roughness, but for most cases that is a secondary effect, and we will discuss only the material selection from optical properties themselves.

Single-Layer Thin Film Materials Single-layer coatings have optimal performance for materials for which the critical angle is large, and as shown in Table 1, the preferred choice has been Au or Ir, with the IXPE mission being the only listed exception to utilize the NiCo surface of their substrate instead of a mirror coating. Other possibilities are W and Pt, and to illustrate how the materials relate to one another, we show the attenuation of Au, Co, Ir, Ni, W, and Pt with their M-, L-, and K-edges in Fig. 1 (left). Au, Ir, and Pt are all very similar, and due to the cost of Pt, Au and Ir are preferred. The edges of W are shifted toward lower energies, and this impacts the low-energy throughput of soft X-ray instruments which disfavors W. The M- and L-edges of Au and Ir also appear in the soft X-ray bandpass, and it might, therefore, appear as if Co or Ni would be better choices. However, the critical angle of Ni (and Co) is significantly lower as shown in the right panel, where for scale the horizontal lines correspond to the grazing incidence angles for a telescope with focal length, F , and maximum radius, Rmax . For example, a telescope with a focal length of 10 m and maximum radius of Rmax = 40 cm will, if all the mirrors are coated with Ir or Au, operate at total external reflection up to 10 keV. Because effective area is the most easily controlled parameter to maximize

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Fig. 1 Left: Attenuation with coherent scattering. (Data source: NIST XCOM database (Berger 2010)). Right top: Critical angle. Horizontal lines donate the incidence angel of the shell located at R with focal length F. Right bottom: Delta of the critical angle curves of Ir, Pt, and W with respect to Au

sensitivity, the critical angle of the material is more important than the edges, and unless the mission has a soft bandpass for which the Ni and Co critical angles can deliver the required area, or a science goal compromised by the edges, Au and Ir are the best choices for single-layer thin films.

Multilayer Thin Film Materials Optimal performance for multilayers is achieved with materials that have: (1) large differences in their complex indices of refraction; (2) low absorption in the lowZ material, for which the incident radiation can penetrate into the layers of the stack and reflect from as many interfaces as possible; (3) form smooth, sharp, and chemically inert interfaces to minimize non-specular scattering. Requirement (3) is largely the driver as the stable mating of two materials is the first priority, and the typical multilayer families considered for hard X-ray astrophysical applications are Co-, Ni-, W-, and Pt-based coatings. Which combination suits best is a trade between the above requirements. For example, because Pt has the highest K-edge (78.3 keV) and largest bandpass, Pt/C was favored by NuSTAR and Hitomi. However, the Wbased family has both better interfacial roughness and can be deposited more thinly. For this reason, NuSTAR included both Pt/C and W/Si in its design, applying Pt/C only on mirrors that contributed to area between 70 and 80 keV. To overcome the K-edges of Pt and W, future hard X-ray missions may turn to Ni- and Co- solutions for probing energies beyond 80 kev (Madsen et al. 2018).

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Coating and Instrument Design The choice of a mirror coating is a process that involves many parameters, most of which are related to the fabrication process, such as deposition technique, film stress, uniformity, and surface roughness, but if these environmental parameters are removed, the suitable mirror coating for the application and its performance can be inferred from theory. That is the starting place of all design work, and we outline this process below, deferring the discussion of the fabrication itself to sections “Depositing Thin Film Coatings”, “Characterization of Thin Film Coatings”, “Environmental Stability”, and “Stress in Single and Multilayer Coatings”.

Single-Layer Design As discussed in sections “X-Ray Reflection and Refraction” and “Materials”, the phenomena of total external is of central importance to X-ray mirror design. Below the critical angle, the refracted (transmitted) part of the wave propagates along the surface as an evanescent wave. This wave has some curious properties, and although it creates an electromagnetic field into the second medium, there is no net energy crossing the boundary into the medium, i.e., no ray traverses this medium (Born et al. 1999). The 1/e penetration depth of the wave is 1/qc , where qc = 2k sin θc , and the single layer must therefore have a minimum thickness to effectively take advantage of the total external reflection; otherwise the field may interact with the material or substrate below. A thickness of 10 nm is sufficient for materials such as Ir and Au. Figure 2 shows the critical angle, θc , as a function of energy for Ir, Au, Pt, and W for observatories Chandra, NuSTAR, Swift, XMM-Newton, and Athena. The colored bands are the minimum and maximum graze angle of the observatory, and all energies below the critical angle and energy curve will be externally reflected. For example, Chandra has four large radius shells, and the outermost shell only efficiently reflects energies below 3 keV. That shell, however, contributes most of the area, which mitigates the loss from exceeding the critical angle. In contrast, XMM-Newton has a longer focal length, smaller radii optics, and the outermost shell efficiently reflects all energies below ∼7.5 keV. NuSTAR is not a single-layer observatory, but the top layer of the multilayer coatings was made thick enough to ensure total external reflection up to 15 keV from all shells (Madsen et al. 2009). Despite of the condition of total external reflection, absorption at the interface still occurs below θc . Figure 3 shows the reflectance, R; absorbance, A; and transmittance, T, of a 10 -nm-thick Ir coating at θinc = 15 mrad. For a fixed incidence angle, there is a corresponding critical energy, and the dashed lines in the top left plot of Fig. 2 marks that energy (∼5.8 keV) for Ir at 15 mrad. The Ir Mα complex is a very strong feature, and it causes a drop in R by ∼20% where it remains constant up to the critical energy at ∼5.8 keV when the reflectance decreases down to 0.1. As the critical energy is passed, T increases and adds to A in reducing the intensity of R. As a mitigation against the heavy absorption from Ir, a coating of a less dense

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Fig. 2 Critical angle curves as a function of energy for selected missions. The colored bands mark the minimum and maximum graze angles of each instrument, and all angles below the critical angle curve will see total external reflection

Fig. 3 Reflectance, Transmittance, and Absorptance for a 10 nm Ir single-layer. The curves are at a fixed grazing incidence angle of 15 mrad, which is marked as dashed crosshairs in the upper left plot of Figure 2. The first sharp drop at ∼1.9 keV is Mα1 , and the second less sharp drop at ∼5.8 keV from the critical angle. Also shown is the Reflectance of the same 10 nm Ir with a 8 nm overcoat of SiC

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2.5 baseline Ir/B4C + Pt/B4C + Ir/SiC + W/Si + Ir only +

2.0

2.5 2.0 Aeff

Aeff (m2)

1.5 1.5

1.0 1.0 0.5 0.0

0.5

2

4 Energy (keV)

6

8

2

4 6 Energy (keV)

8

10

Fig. 4 Examples effective area models for different examples of coating design considerations for the Athena mission considering uncoated substrates, a single Ir layer coating and the increased performance at low energies by introduction of a soft material top coating layer (left). The introduction of a multilayer coating underneath the single-/bi-layer can enhance the performance at higher energies. In this example the improvement is around 6 keV (Ferreira et al. 2017)

material can be placed on top of Ir. In this example 8 nm of SiC can significantly boost R below the M-edges up until the SiC critical energy at ∼3 keV (see Fig. 1). Above θc,SiC , the ray is transmitted through the SiC layer to the Ir below, and the absorption of SiC further reduces R. This kind of balancing and trade must often be made when optimizing the instrument bandpass of a mirror coating, and ultimately the decisions must be driven by the mission requirements. In the case of the Athena mission, the science goals have a strict requirement for the effective area below 2 keV and at 6 keV. Several materials were investigated, and Fig. 4 shows the design considerations and illustrates the increase in performance at low energies by adding a soft material top coating layer (left). Improvements of the performance at 6 keV cannot be gained by changing material or top layer alone but achieved by introducing a multilayer coating underneath the single layer of heavy material as shown in the left panel (Ferreira et al. 2017). The X-ray photons impinging on the mirror will primarily be reflected by the Ir and only encounter the multilayer for a subset of mirrors above 4 keV, where the constructive interference generated by the multilayer will enhance reflectivity as discussed in the next section.

Multilayer Design A single-layer coating will be effective up its critical angle, beyond which the reflectivity will drop off rapidly as shown in Fig. 3. By utilizing constructive interference from diffraction, such as can be found in crystals, a multilayer coating can boost the reflectivity beyond the critical angle by considerable amounts through careful construction of the individual bi-layer pairs in the stack. The multilayer stack is turned into a crystal-like structure periodic lattice through the deposition of thin layers of different materials consecutively on top of each other. Due to the Bragg

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condition, which is a special case of the general Laue equations, and occurs when the wavelength is comparable to the thickness of the layer, reflection is enhanced for wavelength, λ, graze angles, θ , and the thickness of the bi-layer, d when: nλ = 2d sin θ,

(11)

where n is the diffraction order. A multilayer stack will have its first order (n = 1) Bragg peak at an energy of E=

hc sin θ, 2d

(12)

for a specific θ and subsequent peaks at higher energies, nE. An example of a Pt/C multilayer with N = 10 bi-layers, each of thickness d = 10 nm, is shown in Fig. 5. The shape of the curve comes directly from Eq. (7), and the oscillations between the peaks are called Kiessig (1931), numbering N−2 between two Bragg peaks. The second principle that makes multilayers so effective goes back to the Fresnel equations for which the intensity of the reflection is maximized at interfaces with a large contrast in the refractive index, or, equivalently, the density. Multilayers, therefore, consist of a dense absorber material paired with a light spacer material. The relative thickness of the bi-layer pair is typically optimal at around 40% absorber and 60% spacer, defined as Γ = dabsorb /dtot ∼ 0.4. A stack of constant thickness bi-layers will result in a spectrum with a good response at a narrow set of energies located at the Bragg peaks as shown in Fig. 5 but otherwise have a poor response in between the peaks. By varying the thickness of the bi-layers through the stack, the Bragg peaks can be shifted through the spectrum and a broadband energy response achieved. This can be done in a number of ways, but we will discuss here only those relevant for X-ray astrophysical application.

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Fig. 5 Left: Cartoon of the power-law graded multilayer stack. The top layers, which are the thickest, reflect the lowest energies and the bottom the highest. Right: multilayer performance at a fixed incidence angle of 2.5 mrad for (1) a single-layer (red), (2) a N = 10 bi-layer constant thickness stack (blue), and (3) a power-law depth-graded multilayer stack (green)

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One such depth-graded profile, commonly used for neutron mirrors and used by NuSTAR (Madsen et al. 2009), is the power-law graded stack (Joensen et al. 1995). The bi-layer thickness of the power-law stack is defined by di =

a (b + i)c

i = 1, N

(13)

where N is the number of bi-layers in the stack and a and b constants that are related to the minimum and maximum thickness of the bi-layer. The power-law index, c, controls the relative shifts of the Bragg peaks, and a low c drives them apart, while a high c pushes them together. In the depth-graded structure, the thinnest layers, which reflect the hardest energies, are at the bottom where the photons have the greatest penetration depth, and the thickest layers at the top as shown in the diagram in the cartoon of Fig. 5. For a fixed set of parameters, increasing N will increase reflectivity due to a more continuous distribution of Bragg peaks, up to a point where the absorption becomes dominant and outweighs the benefit of adding layers. Only two X-ray astrophysical missions have flown multilayers, NuSTAR and Hitomi, both optimized for the same bandpass with similar prescriptions. NuSTAR used the depth-graded power-law, and a multilayer prescription is shown in Fig. 5, which demonstrates the advantage over a single-layer and periodic bi-layer with constant spacing for energies beyond the critical angle. Hitomi used a block method (Tamura et al. 2018), and in this structure, rather than continuously changing the thickness of the bi-layers down through the stack, it contains blocks of bi-layers with periodic constant spacing. The principle is the same as for the power-law depth-graded profile, and by changing the bi-layer thickness for each block, the Bragg peaks are shifted through the spectrum as illustrated in Fig. 6. The power-law and block method yield similar responses and using one over the other a matter of preference and fabrication method. 1 First Block Second Block

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Fig. 6 Left: Reflectivity of block (solid line) and individual blocks (dashed lines) at an incidence angle of 0.208◦ . Right: The coating consists of blocks, which have a constant periodic spacing multilayer. The Bragg energy of each block is different, and the reflectivity profile is determined by superposition of each block. (Reprinted from Tamura et al. 2018)

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Fig. 7 A-periodic multilayer of W/SiC with 200 bi-layers. The coating was optimized against the desired response using IMD and measured with a hard X-ray reflectometer at Reflective X-ray Optics LLC (RXO)

A more radical design intended for use in narrow-band applications (Morawe et al. 2002; Aquila et al. 2006) is the a-periodic structure, in which every bi-layer is tuned individually to achieve a desired target response. Figure 7 shows the energy performance of one such a-periodic W/SiC multilayer at an incidence angle of 0.11◦ against its target response. Multilayers are versatile and can be designed for both narrow and broadband applications. Given a stack of N layers with varying thicknesses, the response as a function of energy can be shaped in a number of ways as described above. All designs, however, have to obey the Bragg condition between energy, bi-layer thickness, and angle, and the starting point is to define the necessary bi-layer thickness needed to obtain the desired bandpass. Once a choice of focal length, F , and radius of the optic, R, is made, the graze angles naturally fall out and the minimum and maximum required thickness computed from: dmin =

hc 2Emax sin θmax

(14)

dmax =

hc . 2Emin sin θmin

(15)

This is usually an iterative process where F and R are changed until a feasible set of dmin and dmax are found. As will be discussed in subsequent sections, there is a practical limit to how thinly a coating of a specific material can be deposited without degrading, and, conversely, how thick it can become before stress sets in. The maximum bi-layer thickness is usually not a constraint and should be set such that there is a smooth transition between the multilayer and the energy

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of the critical angle. This forms the set of baseline parameters from which the multilayer prescriptions are then optimized for performance. There are a number of ways they can be optimized, and the general method is to device a figure of merit (FOM) and walk the design parameters through the possible phase space as done in Madsen et al. (2009) and Tamura et al. (2018) using any phase-space optimization routine appropriate for the number of parameters over which the search is to be conducted. To first order, a FOM can be based on the on-axis effective area, but most instruments also include a weighted off-axis angular response, such as wide-field survey instrument types, and there can be several secondary parameters that enter into the FOM based on the specific application of the instrument as well, such as focal length and the PSF with respect to the detector dimensions (Henriksen et al. 2021). The theoretical optimization process has of course to be taken together with the material and fabrication restrictions, which will be the subject of the subsequent sections.

Depositing Thin Film Coatings There are many techniques in use for the fabrication of thin film coatings, and for a thorough review, we refer to Martin (2010). These techniques are often based on physical or chemical processes, where there is physical ejection of material onto a substrate or the chemical species are reduced or decomposed on the substrate surface. The techniques that have been used for mirror production include grindand-polish technique with DC sputtered Ir (Chandra (Bessey et al. 2011)), the nickel electroforming technique coated with Au via evaporation vacuum (XMMNewton (Chambure et al. 1997)), and thermal glass forming technique coated with Pt/C and W/Si multilayers via DC magnetron sputtering (NuSTAR (Christensen et al. 2011)). The choice of the most appropriate technique will depend on the criteria imposed by the specific mission design, e.g., material selection, mirror substrate, and cost. Direct current (DC) magnetron sputtering is a versatile technique which has been used for Chandra, NuSTAR and Hitomi/HXT and is considered both for the Lynx X-ray observatory, under study by NASA, and for the Athena X-ray observatory, the ESA L-class selected mission. It is a physical, vacuum technique, allowing for deposition of both single element materials and compounds. Figure 8 illustrates the principle of the DC magnetron sputtering technique. High voltage is applied between the cathode and anode attracting positive the ions of an inert gas, e.g., Ar, the desired coating material target, is then bombarded with the energetic gas ions leading the target atoms to be ejected and deposited as a thin film coating on the substrate. The thickness of the film is controlled by moving the substrate past the anode, and by having two or more anode targets of different materials inside the chamber, a multilayer can be deposited with adjustable thickness by controlling the speed of the rotation.

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Fig. 8 Magnetron sputtering diagram. (I) high vacuum minimizes contaminants, (II) ions are attracted to the target, (III) target atoms are bombarded, (IV) sputtered atoms travel toward the substrate, (V) sputtered atoms are deposited to substrate surface forming a thin film (Massahi et al. 2021)

DC magnetron sputtering chambers come in a variety of configurations. They are configured to ease the task of achieving good optical performance of the coatings which rely to various degrees on the coating’s uniformity. One technique for encouraging inherent azimuthal coating uniformity is to spin the substrate about a central axis of symmetry. The substrate spinning mechanism is shown for a flat substrate in Fig. 9a for one of the vacuum deposition systems at MSFC (Broadway et al. 2001; Gurgew et al. 2020). To control the thickness gradient along the radial direction, a contoured mask is added. The mask effectively alters the exposure time for points along the substrate’s radial direction according to the arclength of the mask at a given radius. This technique can be used to achieve a desired lateral thickness gradient on the substrate or to obtain uniform coatings. In this configuration, the circular sputtering cathodes Fig. 9b are pointed upward and rotate past the spinning substrate in an oscillatory fashion at a constant angular velocity. The angular velocity dictates the coating thickness of each material. The film thickness distribution can alternatively be controlled without a mask, in which case the cathodes must rotate at a prescribed angular velocity that changes during their passage past the substrate: a technique referred to as velocity profiling. The smaller diameter cathodes are beneficial for reducing the associated target material cost

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when investigating new material combinations for X-ray optics, particularly when precious metals such as Ir, Au, and Pt are used. The deposition system at MSFC can also be configured to house linear cathodes, which are preferred for coating substrates without an axis of azimuthal symmetry, such as segmented substrates, for example. The linear cathode array, shown in Fig. 9c, also illustrates the mask used for controlling film thickness uniformity. The mask functions to alter the spatial distribution of sputtered flux according to its contoured shape by intercepting sputtered material from the target prior to reaching the substrate. An example of a high production yield DC chamber is shown in Fig. 10. This chamber is located at DTU Space (Jensen et al. 2006) and was used to coat over

Fig. 9 Illustration of the magnetron sputtering chamber at MSFC. See detailed description in section “Depositing Thin Film Coatings” and Broadway et al. (2001) and Gurgew et al. (2020)

Fig. 10 The DC magnetron sputtering coating facility at DTU Space. The coating system was built for the coating development and manufacturing of the depth-graded multilayer coatings used on the NuSTAR telescope mirrors (Christensen et al. 2011)

Fig. 11 Overview of deposition parameters that can be optimized and their effects on the coating characteristics (Massahi et al. 2021)

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8000 segmented mirrors with multilayers for the NuSTAR mission (Christensen et al. 2011). Due its ability to coat a large number of substrates (24 per run for NuSTAR), it is considered as prototype for the present Athena coating system. The cathodes for this chamber are 50 -cm-long and fixed vertically in the center pointing outward, while the substrates are mounted on plates on the entire circumference of the chamber wall and spin around the cathodes. The mechanism of growth of the deposited coating is always dependent on the target material, but properties of the thin film coatings fabricated using DC magnetron sputtering will also depend on the coating conditions. Figure 11 shows an overview of parameters that can be optimized to create specific coating conditions. For example, the working gas pressure and substrate temperature directly affect the growth and microstructure of the coating. It is therefore imperative to control the coating conditions to improve film morphology, composition, uniformity, roughness, and stress, for the increased performance and stability of X-ray mirrors (Massahi et al. 2021).

Characterization of Thin Film Coatings X-Ray Reflectometry The most common way to measure the performance of a thin film coating is with X-ray reflectometry (XRR), which directly probes and verifies the coatings response to X-rays. It also serves as a nondestructive and efficient method to determine the characteristic properties of the coating design (thickness of single and multilayers), surface interface roughness, and material properties such as density and composition as was illustrated in Fig. 5. An example of a reflectometer XRR experimental setup, in use at DTU Space, (Technical University of Denmark) is shown in Fig. 12. The layout is common to most reflectometers, where the X-ray photons are first collimated using slits, filtered in energy, and shaped (paralleling the beam) before reflecting off the coated surface of the specimen being tested. The intensity of the reflected beam as a function of energy or angle is a direct product of the film properties, and desired parameters can be derived by employing a curve minimization model-fitting technique of the measured reflectivity, as predicted by Eq. (7) for the assumed thin film design (section “Coating and Instrument Design”) with the appropriately modified Fresnell functions. Typically, the reflected beam is either measured for a fixed energy as a function of grazing incident angle or for a fixed angle as function of energy. Most XRR setups operate at a single energy since the energy scan capability requires powerful continuum sources, generally only available at synchrotron facilities. Figure 13 (left) shows an example of a XRR angle scan at 8 keV for a single-layer thin film coating, and the distance between and width of the Bragg peaks determines the layer

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Fig. 12 The XRR experimental setup at DTU Space. (1) X-ray generator, (2) slit, (3), evacuated tube, (4) Slit, (5) asymmetric cut Ge crystals, (6) attenuation filters, (7) beam shaping slits, (8) sample holder, (9) evacuated tube, (10) position-sensitive detector (Jafari et al. 2020)

thickness and the decrease in intensity as a function of the angle the roughness. The location of the critical angle, which is responsible for the first sharp decrease in intensity, can be used as a measure for the material density and composition. Figure 13 (right) shows an example of an energy scan at a fixed incidence angle for a W/Si NuSTAR flight coating taken at the RaMCaF NuSTAR calibration facility. Here the frequency and amplitude of the undulations that occur right after the critical angle of W (∼25 keV), taken together with the intensity drop at the W K-edge, determine the bi-layer thickness, relative fraction of W of that bi-layer thickness, and density. As discussed in section “Surface Roughness,” the signature of surface roughness is to remove and redistribute the intensity into angles outside of the specular, and the larger the angle and energy, the greater the effect of roughness on the curve. A large dynamic range is therefore desirable to get an accurate estimate of the roughness. XRR setups operating at softpt energies, such as Al-K (1.487 keV), are designed to characterize the soft materials of a thin C, SiC, or B4 C cap layer, which can be used to boost the telescope performance at lower energies (as illustrated in Fig. 3). XRR setups operating at the more typical 8.048 keV from a Cu K alpha source will be insensitive to the top layer and more suitable for the characterization of a complex multilayer structure. Software used for modeling XRR data have been developed by several research teams and are often available as open source (e.g., IMD for IDL, Windt 1998). The modeling of XRR data is often not a simple process, and the complexity of the material and layer structure will reflect in the complexity of the best-fit model. The X-ray beam will always have a footprint on the sample being measured and effects of nonuniformity and surface contamination will introduce features to the measured reflectance.

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Fig. 13 Top: Example of angle scan at 8.048 keV measured at the DTU Space of a 10 nm Ir single-layer coating on an SPO (Svendsen et al. 2020). Bottom: energy scan at fixed angle for a W/Si NuSTAR mirror measure at at the Columbia University RaMCaF facility (Brejnholt et al. 2011)

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Other Characterization Techniques Even though X-ray reflectometry is an extremely useful tool for characterization of X-ray thin film coatings, several other techniques can also be applied to evaluate the true composition of the coatings after the deposition process and access the level of contamination and the possible effect of contamination on coating quality, performance, and stability. Atomic force microscopy (AFM) enables the mapping of the sample surface and will provide information on roughness and contamination of the mirror surface. A nondestructive force is applied by a sharp tip scanning the investigated area resulting in a topographic map of the sample top surface. Figure 14 exemplifies the AFM map of uncoated Si substrates at different processing levels, clearly showing the difference between a smooth and clean surface and a surface with particle contamination. With AFM it is possible to derive the topological roughness which causes non-specular scattering and affects the coating reflectivity. The surface roughness derived from AFM is not directly comparable to the roughness derived by modeling the XRR data as the AFM is only assessing the very top surface, while the XRR derived roughness will also include the effects of interface roughness, accounting for reduction of the reflectivity of X-rays at the interfaces. The composition and morphology of the films can be investigated using a variety of techniques. Among the most popular are X-ray photoelectron spectroscopy (XPS) and transmission electron microscopy (TEM). XPS is based on the photoelectric effect, and by measuring the electron binding energy of the elements in the coating, it enables the investigation of the composition of the coating material, the state of its chemical bonds, and the relative element

Fig. 14 Atomic force microscopy measurements showing a surface with particulate contamination (left) and a smoother surface (right) of uncoated Si substrates at different processing levels of the photo-resist deposition characteristic of SPO technology (see Chap. 2.5) (Massahi et al. 2015)

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Fig. 15 Example of XPS results. (a) Concentration quantification of selective elements for sample A (Ir/B4 C multilayer) using XPS depth profiling. (b) Schematic of the Ir/B4 C multilayer analyzed and the main bonds detected in each individual layer (Jafari et al. 2020)

concentration (Moulder and Chastain 1992; Greczynski and Hultman 2020). XPS is a destructive characterization technique where the measurements reveal the coating composition at several depths of the coating layer controlled by the etching time as shown in Figs. 15 and 16. TEM technique uses a beam of electrons to obtain images at nano- or atomic scales. The sample preparation for TEM measurements is a destructive process where a sufficiently thin slice of the coating and substrate are extracted from the coated sample and measured via a beam of electrons that pass through the sample forming an image (Martin 2010). In the TEM images presented in Fig. 17, it is possible to visualize the morphology of the coatings and the designed multilayer profiles. STEM is a type of TEM where the beam of electrons raster scan the sample allowing for simultaneous composition assessment via energy dispersive Xray spectroscopy (EDS) or electron energy loss spectroscopy (EELS). Figure 16 shows examples of both XPS and EDS measurements. These techniques combined with XRR provide the means for an in-depth understanding of the chemical composition of the coatings, possible contaminants present in the coatings and the effects they might have on the coating performance when combined with the required process for manufacturing of X-ray mirrors. The true composition of mirror coating is specific of each coating facility; therefore it is necessary that a careful composition analysis of the deposited coatings is performed for both quality assurance and telescope calibration.

Environmental Stability Naturally, it is imperative for the success of any mission that the thin mirror coatings are stable over time and robust to the environment of space and its radiation. But they should also be able to withstand short-term extreme conditions that may occur during fabrication and the forces induced during launch. Of particular interest

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Fig. 16 The composition investigated using X-ray photoelectron spectroscopy (XPS) and scanning transmission electron microscopy (STEM) comparison of (left) XPS survey spectra and (right) TEM-EDS results for Ir and B4 C layers (Jafari et al. 2020)

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Fig. 17 Example of a TEM image of periodic Ir/B4 C multilayer (left) and depth-graded multilayer (right) (Jafari et al. 2020)

are the chemical stability, thermal stability, and stress stability of the thin film coatings. The combined studies of the characterizations techniques discussed in section “Characterization of Thin Film Coatings” are used to investigate the short and long-term evolution of coating performance. An example of chemical change of the B4 C overcoat is shown in Fig. 18 (left) where we observe drastic change is the reflectance performance of the X-ray mirror over a year under normal storage condition (Ferreira et al. 2018). The evolution of the coating properties observed through the change in the reflectance curve can be attributed to a density change of the overcoat material and/or oxidation. An example of a Ir/SiC bi-layer coating presenting consistent performance over time is also shown (right). Some of the processes involved in the manufacturing of modern X-ray optics for large telescopes imposes strong challenges to coating stability (Bavdaz et al. 2020). Exposure of coated mirrors to chemicals and high temperatures can affect the coating performance and stability (Ferreira et al. 2018; Svendsen et al. 2021, 2020; Henriksen et al. 2021). The compatibility of post-coating treatments applied to the X-ray mirrors have to take into account the protection of the reflecting coating. Investigation of the effect of chemical exposure and annealing, part of the manufacturing processes using Silicon Pore Optics (SPO) technology (see Chap. 2.5), show that Ir singlelayer coatings are robust and do not have their performance affected. Figure 19 shows the coating reflectance before and after exposures (Svendsen et al. 2021). The effect on a Ir/B4 C bi-layer shows degradation of the B4 C layer from annealing under atmospheric conditions but not when annealed in low vacuum (Henriksen et al. 2021). Monitoring of the short- and long-term stability of X-ray mirror coatings requires periodic, systematic, and nondestructive assessment of the coating performance, making XRR as an excellent technique for this purpose (Ferreira et al. 2018; Henriksen et al. 2021) (Fig. 20).

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Fig. 18 Example of time evolution of Cr/Ir/B4 C trilayer (Ferreira et al. 2018) and time stability of Ir/SiC bilayer (Svendsen et al. 2019)

Stress in Single and Multilayer Coatings The control of film stress is a leading technological challenge in the development of the next generation of high resolution, large collecting area, lightweight Xray spaceborne telescopes. The X-ray telescope’s grazing incidence, focusing mirror assembly, consists of a large number of concentrically nested, thin shells, whose thickness is on the order of a few hundred microns. This is done to maximize the telescope’s collecting area within prescribed weight and volume launch constraints. The thin film coatings, which are commonly deposited by the process of magnetron sputtering, are applied to enhance the X-ray reflective

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Fig. 19 Ir single-layer coated mirror appears to be robust to the effect of annealing. No reflectance degradation is observed on XRR (Svendsen et al. 2021)

spectral response of the mirrors prior to assembly and alignment. Despite the film’s nanometer-scale thickness, the in-plane forces caused by the residual stress in these coatings can distort the mirror’s precise figure and severely degrade imaging resolution. Therefore, the stress, σ , in the thin film coatings applied to enhance X-ray reflectivity must be reduced to near-zero values in order to preserve the substrate’s precise figure, particularly for the next generation of X-ray telescopes where sub arcsecond resolution imaging is sought. Single-layer thin films, such as Ir, are often used as a reflective coating for grazing incidence, total reflection, X-ray optics due to the large critical angle (L. Note that by construction, the limiting blocking angles for obstructed rays are Φ=

∗ R0 − RM + α0 , ∗ L1

(1)

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R0 − R0∗ , L1

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Σ=

∗ R0 − Rm − 3α0 . ∗ L2

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For focal length f >L1,2 , and L1 = L2 , Φ ≈ Ψ ≈ Σ. Further note that incidence angles vary with azimuthal position φ for sources at off-axis angular position θ : α1 (φ) = α0 − θ cos φ

α2 (φ) = α0 + θ cos φ

(4)

The limiting blocking angle Φ imposes a constraint on the FoV (θFoV ) since for θ > θFoV the geometric area of the shells exposed to the source decreases rapidly due to the rays being blocked. The expression for the available geometric area (Spiga 2011) is    A(θ ) 2θ Φ − α0 =1− 1+S A(θ = 0) π α0 θ

(5)

for off-axis angles Φ − α0 √ < θ < Φ/2 and α0 < Φ < 2α0 , and where 1 S(x) = x cos−1 (w) dw = 1 − x 2 − x cos−1 (x). Notice that A(θ ) decreases monotonically with θ , illustrating a direct relation between the FoV and the shell spacing. A useful measure of the extent of the FoV can be set by considering that off-axis angle where A(θ = θFoV ) drops to, say, A(θ = 0)/2. Note that the actual effective area will be smaller, due to increased vignetting due to both figure and scattering, and energy dependence of reflectivity. From Eq. (5), this sets a constraint on Φ, which in turn fixes the spacing between the shells for any given combination of shell radius and length. This defines a theoretical lower limit to the shell separations; considerations of shell thicknesses and engineering limitations in manufacturing, assembly, alignment, and mechanical support often result in the final designs having larger shell spacings. Nested shell configurations have several benefits. They allow compact designs that can be fit inside a small volume and yet have high effective areas. Critically, these designs are highly customizable and can be adapted to suit a variety of science cases (see section “Mission Concepts Using Miniature X-Ray Optics”). Variations in the coating allow for different energy bands to be better represented: e.g., Fig. 4 compares the effective areas achieved by an iridium (Ir) and an iridium-carbon (IrC) coating for the same shell configuration; the IrC coating, which is a layer of iridium with a carbon overcoating, used to mitigate photoabsorption in the metal layer, smooths out the sharpness of the Ir edge, but at the cost of reduced lowenergy effective area. Furthermore, despite the volume and mass constraints that MiXO designs operate under, adjustments to shell numbers, sizes, and positions allow versatile designs that may be tuned to specific science cases. For instance, missions such as SEEJ are targeted toward observing isolated point sources, so the half-power diameter (HPD) of the on-axis PSF can be optimized at the cost of offaxis performance (see Fig. 5). In contrast, missions like LuXIS that seek to map the

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Fig. 4 Effect of coating on effective area. Effective areas are computed using SAORT at a variety of energies for a SEEJ-like MiXO, for sources located at different off-axis positions. All parameters are held the same except for the coating, which uses iridium (left) and iridium-carbon (right). Including Carbon in the coating reduces the sharpness of the edge structure at 2 keV

Fig. 5 Effect of placing a source at different off-axis angles, simulated for a SEEJ-like configuration. The off-axis position is marked in arcminutes along the upper scale, while the half-power diameter (HPD) is listed in arcseconds below each source. The color table is designed to highlight the scattering wings of the PSF

lunar terrain require a stable imaging performance across a wide field of view, which is achieved with a combination of gradually varying focus offsets and shell lengths (see Fig. 6).

Ray Tracing Ray trace codes are a crucial component of designing telescope optics. They allow detailed explorations of the design in realistic configurations and experimentation of various parameters including shell sizes, lengths, spacings, and focus offsets. They also allow implementation of scattering effects due to micro-roughness as well as

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Fig. 6 As in Fig. 5, but for a LuXIS-like shell configuration that optimizes for stable HPD across the FoV (see Kashyap et al. 2020). An azimuthal distortion of the PSF is apparent at θ20′ , but the HPD is remarkably constant

large-scale variations in the figures of the mirrors, which is crucial to understand the actual performance. There are several ray trace codes that have been developed for specific use cases: e.g., SAOtrace (https://cxc.cfa.harvard.edu/cal/Hrma/SAOTrace.html) for X-ray tracing of Chandra mirrors, XISSIM for X-ray event simulator of Suzaku-XRT (Ishisaki et al. 2007), and generic Wolter Type I reflection gratings ray traces constructed by Rasmussen et al. (2004). The nested shell configuration specifically has been implemented in SAORT (Sethares et al. 2021), and we use this code to compute example ray traces shown here. As an example, we adopt a configuration similar to that used in SEEJ (see Table 1). Scattering due to mirror roughness is included for realistic behaviors. Ray traces are carried out at various energies 0.1–7 keV, for sources at various off-axis positions from 0 arcmin (i.e., on-axis) to 20 arcmin. The PSF degrades rapidly with off-axis (see Fig. 5), and the HPD goes from 20 arcsec on-axis to >2.5 arcmin at 20 arcmin off-axis. This broad disparity can be alleviated by allowing individual shells to come to focus at different offsets, as is done for LuXIS (Fig. 6; adapted from Figure 6 of Kashyap et al. 2020).

ENR and Metal-Ceramic Hybrid MiXO Two different MiXO optics configurations were fabricated using the ENR technique. One of the configurations has 62 mm diameter, 180 mm long, and 1 m focal length, while the other configuration has a 0.7 m focal length with 100 mm diameter × 90 mm length and 80 mm diameter × 80 mm length. Several mirrors were fabricated from each of the configurations and the performance of these optics is discussed in section “Performance of ENR MiXO”. One drawback, however, with the fullshell nickel optics is the high density of nickel, which necessitates thin shells

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Table 1 Key optics parameters of MiXO-based mission concepts: note these may change as each mission concept matures MIXS-Ta Fraser et al. (2010); Bunce et al. (2020) Science discipline Planetary

LuXIS Stupl et al. (2018); Hong et al. (2021a) Planetary

Tel. modules Shellsb Optics massb Ang. Res. (HPD) FoV (Dia.) Focal length Optics ODb On-axis effective areab @ 1 keV Energy range Main requirements

1 N/A 800. If the aperture to image distance is set equal to the focal length of a telescope, the Fresnel number, calculated using Equation 10, is the product of the f -number = D/F , the reciprocal of the diffraction-limited angular resolution, D/λ and the constant 1/4. It constitutes a dimensionless figure of merit for the diffraction-limited focusing power which can be used to provide a comparison of telescopes operating in different wave (energy) bands. For example, the JWST mirror imaging in the near-infrared at a wavelength of 5 microns has diameter of D = 6.5 m and focal length of F = 131.4 m giving NF = 1.6 × 104 . An X-ray mirror imaging at 1 keV (wavelength 1.2 × 10−9 m) with D = 1 m and F = 10,000 m gives NF = 2 × 104 , very close to the JWST value. However, the diffraction-limited angular resolution of JWST is 0.15 arc seconds compared to 0.00026 arc seconds for the X-ray telescope because the X-ray wavelength is so small. The depth of focus of a conventional telescope is determined by the f -number. If the focal plane is displaced by ±dF, then the width of the PSF will increase by ∼dF.D/F . In order to maintain the diffraction-limited angular resolution, we require dF.D/F < F λ/D, dF < F 2 λ/D 2 . Using the focal length of 800 m from above, the depth of focus is dF < 0.77 mm. That is, the imaging detector must be placed at a distance of 800 m from the aperture to an accuracy better than ±1 mm to achieve diffraction-limited imaging. However, the depth of focus of an interferometric system is larger. When the detector is displaced by dF, the fringes seen from the two-slit aperture persist because they exist over a much larger volume above and below the focal plane. The size of this volume depends on the total number of fringes that are visible, determined by the width of the slits (W = 0.025D in the example illustrated in Fig. 2) and the coherence length of the radiation. If the width of the slits is W and the distance between the outer edges of the slits is D, the number of bright fringes visible in the PSF, either side of the central peak, is Nvis ∼ D/W . These fringes will remain visible providing dF < Nvis .F 2 λ/D 2 , a displacement Nvis times greater than the the depth of focus for diffractionlimited imaging. All the diffraction-limited analysis presented so far has assumed monochromatic light, one wavelength, infinite coherence length. All astrophysical X-ray sources are broadband and incoherent, and the coherence length will be set by the spectral resolution of the imaging detector and the quality of the X-ray

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optics. The coherence length can be expressed as the number of fringes visible, Ncl ∼ E/∆E = λ/∆λ. ∆E depends on the type of detector employed. When a single X-ray photon is absorbed in a detector, a cloud of ion pairs is created in the detector material, and the amount of charge released is proportional to the X-ray energy. But the amount of charge fluctuates because of the statistical nature of the ionization process and the fluctuations are characterized by Fano noise (Fano 1947). Currently, Fano limited silicon detectors like CCDs give, at best, ∆E = 65 eV at 1 keV. Alternatively, the energy released when the photon is absorbed can be measured directly using cryogenic detectors like TESs (transition edge sensors) which give ∆E = 2.5 eV. Therefore, the maximum number of fringes produced by interference at 1 keV will be in the range 15 < Ncl < 400 depending on the detector system used. In any diffraction-limited X-ray telescope system, the number of fringes visible will depend on both the limitation set by the bandwidth and the geometry of the optical system.

Diffraction-Limited X-Ray Optics The response of X-ray optics is governed by the complex refractive index for X-rays in materials given by: n = (1 − δ) − iβ

(11)

where both δ and β are positive and small. The linear photoelectric absorption coefficient is: µ = 4πβ/λ

(12)

where λ is the wavelength and therefore the photoelectric mass absorption coefficient is: µ/ρ = 4πβ/(λρ)

(13)

where ρ is the mass density of the material. Figure 4 shows the real (δ) and imaginary (β) decrements as a function of energy, 0.1–10 keV, for iridium, silicon, and beryllium. For energies higher than the absorption edges of the material, both the real and imaginary decrements decay as power laws, δ ∼ E −2 and β ∼ E −4 . There is slight curvature, but these indices give a close match to the broadband decay profile. As a consequence, at high energies, the linear photoelectric absorption falls away as µ ∼ E −3 . Above 10 keV, the attenuation from Compton scattering starts to dominate over photoelectric absorption, and above 1022 keV, pair production will be significant, and these factors must be included when calculating the total linear absorption for hard X-rays and gamma-rays. The real part of n is a slightly less than unity, and therefore the phase velocity of X-rays in materials is a little higher than the velocity of light in vacuum, and likewise

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Fig. 4 The refractive index decrements, δ and β, for iridium, silicon, and beryllium over the energy range 0.1–10 keV

the wavelength in materials is greater than the wavelength in vacuum. Therefore, when X-rays pass from vacuum into a material, the refraction angle (measured from the normal within the material) is greater than the incidence angle, and at a critical grazing angle: cos θt = 1 − δ,

(14)

Total external reflection occurs, analogous to total internal reflection of visible light at a glass-vacuum boundary. Because of the absorption associated with the imaginary part of the refractive index, β, the reflection is not total, but for small √ grazing angles 30 eV), the refractive index can be predicted accurately. In the vicinity of absorption edges, the calculations are limited by the details of the electronic energy structure included in the theory and by extended X-ray absorption fine structure, EXAFS, which is a correction introduced by a second scattering of the outgoing primary scattered wave by nearby atoms in the surface. Tabulations of the refractive index decrements for all atomic types over the entire X-ray energy band are available, and therefore the Fresnel reflectivity of X-rays from mirror surfaces can be calculated in a straightforward manner. The canonical wavelength range defining the X-ray band is 0.1 to 100 Å; therefore, roughness and imperfections in the surface chemistry and geometry on the atomic scale are expected to strongly influence the X-ray reflectivity. Roughness or chemical contamination introduces small phase and amplitude changes in the reflected X-ray wave fronts, and some of the radiation is scattered (or diffracted) away from the specular direction. A complete theory of scattering of electromagnetic radiation from surface roughness was originally developed to describe scattering of radar from land and sea, but the results apply equally well to the much shorter wavelength regime of X-rays. Following the same Fourier optics analysis used in the Introduction section, surface roughness is modeled as a two-dimensional aperiodic diffraction grating, and each Fourier component of the surface height profile, period d, produces diffraction orders m at angles given by the grating equation: sin θs − sin θ =

mλ d

(15)

where θ is the angle of incidence and θs is the angle of scatter measured with respect to the surface normal. The detailed shape of the scattering wings generated by the surface roughness and figure errors will depend on the Fourier spatial frequency power spectrum of the aperiodic diffraction grating, but we can calculate the total integrated scatter (TIS), the fraction of the incident intensity which is scattered out of the specular beam. If the surface is reasonably smooth, first order scattering dominates, and there is no explicit shadowing (which must be the case to approach the diffraction-limited performance), and then: TIS = Rτ (θ, λ)



4π σ cos θ λ

2

(16)

where Rτ is the Fresnel reflectivity for polarization τ and σ is the root mean square of the surface height fluctuations. Typically, working in the energy band 0.1–10 keV σ must be ≤5 Å rms to keep the TIS at an acceptable level. Surface contamination which is distributed unevenly over the surface can be modeled in a similar way and acts like a phase grating. Any particulate or dust contamination will further block or scatter the X-rays. Surface contamination by hydrocarbons or similar compounds often forms a smooth layer or layers. A Fresnel reflection will result from each interface, and

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W

W

Fig. 5 Wave front distortion in optic. Left: grazing incidence reflection. Right: refraction through a thin wedge

the total reflection must be calculated by summing the component wave amplitudes taking into account the phase difference introduced by the thickness of the layers. The contamination acts in the same way as a multilayer coating on a conventional lens. A single monolayer of hydrocarbon contamination can severely compromise or indeed enhance the X-ray reflectivity of a grazing incidence mirror. Figure 5 illustrates the distortion of the X-ray wave fronts as they reflect at grazing incidence or refract through a thin dielectric wedge. If the surfaces are flat, plane wave fronts are reflected or refracted as plane wave fronts. If there is a very small curvature of the surface figure, the reflected or refracted wave fronts will be cylindrical or spherical and will converge or diverge to a very distant line or point. For grazing incidence reflection, the X-ray beam is deflected through twice the grazing angle 2θg , and surface figure errors and surface roughness height variations h(x, y) introduce small phase shifts: ∆φ =

2π h sin θg λ

(17)

and the length scale of the in-plane height variations is compressed by a factor of sin(θg ). So the profile of the gradient errors in the reflecting surface is imprinted on the wave fronts, but the length scale of the fluctuations is compressed and the amplitude diminished. The TIS for grazing incidence reflection described above is

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set by σ sin(θg ) where σ is the root mean square of the height variations, h(x, y), across the entire reflecting surface. In grazing incidence systems, the variation in θg along the surface is very small, so the amplitude of the reflected wave front is constant over the full width of the aperture. For refraction at near-normal incidence, the phase shifts are controlled by the real decrement in the refractive index, δ, such that: ∆φ =

−2π δh λ

(18)

and on transmission through a wedge, both the entrance and exit faces contribute to the wave front distortion. For this case, the TIS is set by δσ where σ is the quadratic sum of the rms fluctuations across both the entrance and exit surfaces. In refractiontransmission optics, the thickness of the optic (wedge in Fig. 5) is a significant factor because of absorption. The thickness and thickness variations across the aperture reduce the wave amplitude and determine the efficiency of the aperture and hence the effective area. Phase errors modify the PSF, shifting flux from the focal spot to elsewhere. Where that flux goes and how the size of the focal spot is changed depend on how the errors are distributed across the aperture. To keep both the HPD and FWHM of the PSF close to the diffraction limit values, the phase shift errors must be ∆φ ≪ 2π for all scale lengths up to the beam width W in both reflection and transmission optics. In some circumstances, the phase errors can be significantly larger than this while maintaining the narrow FWHM, but the HPD will be much broader. In transmission optics, the absorbed fraction is a function of thickness: Fabs = 1 − exp(−µt),

(19)

and the efficiency across the aperture will depend on the thickness profile. For lenses, the profile is parabolic (see section “Transmitting Optics”). The left-hand panel of Fig. 6 is the aperture efficiency as a function of absorbed fraction for both a simple concave lens and a Fresnel lens with maximum thickness variation ∆tmax . If Fabs (∆tmax ) = 0.5 and the minimum thickness is 0, then the aperture efficiency is 72%. If the minimum thickness is t0 > 0, then the absorption will increase across the whole aperture, and the aperture efficiency will be lower than this value. The right-hand panel shows the variation in HPD of the diffractionlimited PSF calculated using Fourier optics analysis including the variation in wave amplitude imposed by the lens thickness. For a simple concave lens (plotted in black), as the absorption increases and Fabs (∆tmax ) < 0.5, the HPD decreases because the absorption profile reduces the step in transmission at the edge of the aperture which in turn suppresses the side lobes in the PSF (a Fourier filtering process called apodization (Mills and Thompson 1986)), but as Fabs increases further, the absorption limits the effective width of the aperture and the HPD increases. For a Fresnel lens with 20 rings and the same ∆tmax , the apodization is reduced and the HPD increases monotonically with increasing Fabs (∆tmax ).

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Fig. 6 Left-hand panel: the aperture efficiency as a function of fraction absorbed at ∆tmax for a concave lens or for a Fresnel lens of the same maximum thickness. Right-hand panel: the HPD of the PSF as a function of fraction absorbed at ∆tmax for a concave lens (black) and Fresnel lens with 20 rings (red)

In order to achieve high aperture efficiency, greater than 50% at thickness ∆tmax , in a transmitting X-ray optic, we require exp(−µ∆tmax ) > 0.5. Under this constraint, the diffraction-limited HPD will be very close to the value imposed by aperture width in the absence of absorption. Figure 7 shows the limiting value of ∆tmax for Be, Si, and Ni as a function of energy. When the change in thickness ∆t across the transmitting wedge is: t1 = λ/δ

(20)

the wedge spans a full period zone within the aperture (corresponding to a phase shift of 2π in transmission). This thickness, proportional to photon energy, t1 ∝ E, is plotted as dashed lines in Fig. 7 for Be, Si, and Ni. It represents the minimum thickness required to produce a Fresnel lens (see subsequent section below). In practice, the thickness of a transmitting focusing optic with high efficiency must be between the solid and dashed lines. For low-Z materials like Be, the entire energy range is accessible, and for Si the energy must be greater than ∼8 keV and for Ni greater than ∼12 keV. Below 10 keV, the optics must be very thin, ∼10 microns and above 100 keV ∼1 mm.

Reflecting Optics Wolter optical systems (Wolter 1952) utilize two grazing incidence reflections to produce a coma-free image. The mirrors are surfaces of revolution about the optical axis, the primary generated by a parabola and the secondary by a hyperbola. Two configurations can be used for X-ray telescopes, Type I and Type II, as illustrated in Fig. 8. The surface generators, parabola and hyperbola, are shown as dotted lines.

303

1e−03

∆tmax cm

1e−01

1e+01

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Berylium Silicon

1e−05

Nickel

1

10

100

1000

10000

keV

Fig. 7 The thickness variation limit for high aperture efficiency, ∆tmax , across the aperture as a function of photon energy for Be, Si, and Ni. The dashed lines represent the full period zone thickness, t1 , as a function of energy for each material

The principal plane of an optic is defined by locus of the intersection between rays incident on the aperture and focused rays converging to the focal plane. For the Wolter geometry, this is the same as the join plane between the surface generators. For Type I, the reflecting surfaces lie either side of the join plane at a distance F , the focal length, from the focal plane. For Type II, the join plane is in front of the mirrors, so the reflecting surfaces are at a distance 800, and the diffraction-limited performance can only be approached using an off-axis sector aperture covering a small angle around the azimuth of the shell annulus. In order to provide good aperture coverage over a sector which is approximately square (azimuthal width the same as the radial width), many shells must be nested and there will be a path difference between successive shells in the nest: ∆L = (r22 − r12 )/(2F )

(21)

where r1 and r2 are the radii of the shells at the join plane. This path difference is always much greater than the coherence length of the astronomical X-rays, so we can calculate the diffraction-limited PSF of the complete aperture by summing the PSFs of the individual shells. The PSF of a nested, square, Wolter sector is illustrated in Fig. 9. The angular resolution in the azimuthal direction (around the shells) is ∆θ ∼ λ/D, but in the radial direction, it is ∆θ ∼ Nnest λ/D where Nnest is the number of shells. The Wolter Type II configuration offers a rather different prospect for diffractionlimited performance. For Type II, the grazing angles are no longer determined by the f -number, so, in principle, complete Type II primary and secondary surfaces of revolution could be used. But nesting is not possible, so the aperture would be a single annulus as illustrated in the top panels of Fig. 2, and the HPD would be determined by the ratio D0 /D. The width of the annular aperture, W = D − D0 ,

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Fig. 9 Left panel: Wolter nest sector aperture size D. Right panel: diffraction-limited PSF

is determined by the axial length, L, of the primary surface. W = L tan θg so for a typical grazing angle of 1 degree W = 0.02L and the diffraction-limited angular resolution set by the HPD performance are determined by the width of the annulus, ∆θ ∼ λ/W , and not the diameter of the primary shell, D. Aside from the performance limitation of the Wolter geometry considered above, the manufacture of Wolter optics that approach a diffraction-limited angular resolution is a formidable task. Currently there is no technology or metrology available which could meet the surface figure requirement of σ sin(θg )/λ ≪ 1 where σ is the rms figure error over the entire reflecting surfaces of the primary and secondary.

Transmitting Optics The radial thickness profile of a simple refracting convex lens is given by the lens maker’s equation and can be expressed as a parabola: t (r) = t0 −

r2 1 2 F (n − 1)

(22)

where t0 is the thickness at the center, F is the focal length, and n is the refractive index. Working in the X-ray band n − 1 = −δ so a converging lens must be concave with profile: t (r) = t0 +

1 r2 2 Fδ

(23)

As the thickness increases toward the edge of the lens, absorption will dominate in the X-ray band because of the relatively large ratio of the decrements in the

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Fig. 10 Top: simple concave lens. Bottom: Fresnel lens with six rings

refractive index, β/δ. Therefore, it’s pertinent to consider using a Fresnel lens as an alternative. In this case, the aperture is split into Nring annular rings with a constant step in thickness of: tring =

1 D2 8 F δNring

(24)

where D is the diameter of the lens. The profile of the Fresnel lens is the same as the simple lens but offset within each ring to keep the thickness below tring + t0 . Figure 10 shows the profiles of a simple concave lens and the equivalent Fresnel lens with six rings. The diffraction-limited PSF of the simple lens is the Airy function as illustrated in Fig. 1 giving the angular resolution FZR = 1.22λ/D. The diffraction-limited PSF of the Fresnel lens is modified by diffraction from the edges of the rings. There is a phase shift of (2π/λ)tring δ at each edge. If the optical path difference corresponding to this phase shift is greater than the coherence length, tring δ > λ2 /∆λ = (E/∆E)λ, then there will be no correlation in phase between rings, and we can calculate the diffraction-limited PSF by performing the summation of amplitude and phase over each ring aperture, squaring to give the intensity, and then summing the intensities over all the rings to yield the combined PSF. Figure 11 illustrates the surface brightness profile of a Fresnel lens calculated in this way compared to the Airy function for the same aperture. The right-hand panel shows the HPD as a function of the number of rings which is approximately HPD = 1.3Nring λ/D. If the step between the rings represents an integer number of wavelengths, m: tring δ = mλ

(25)

and m ≪ E/∆E, then the wave fronts in successive rings will be in phase and the PSF will return to the Airy function. Therefore, the PSF of the Fresnel lens depends critically on photon energy, E, (wavelength, λ) and the bandwidth, ∆E. There are two function forms of diffraction-limited PSF, the narrow Airy function that occurs at specific wavelengths and the wider broadband PSF for which the HPD depends on the number of rings in the Fresnel lens. To reach the diffraction limit of the aperture,

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Fig. 11 Left: broadband PSF surface brightness profile of a Fresnel lens with ten rings (red) compared to Airy function (black). Right: the broadband HPD of a Fresnel lens as a function of the number of rings in the lens

∆θ ≈ λ/D, we require tring δ = mλ where m is an integer, and the bandwidth, ∆E, must be small enough (and hence the correlation length large enough) so that wave fronts from the innermost ring interfere with wave fronts from the outermost ring, E/∆E > m(Nring − 1).

X-Ray Lens Design and Performance To achieve diffraction-limited performance with high efficiency in the Xray/gamma-ray energy band, the thickness of a transmitting optic must lie between t1 and ∆tmax , as plotted in Fig. 7. In the soft band, we require low Z materials with thickness of ∼10 microns. Manufacture of such lenses with aperture D ∼ 1 m is challenging but might be possible by adapting the technology currently used for the production of transmission diffraction gratings. For energies >30 keV, a thin lens with ∆t > 1 mm is a viable proposition and will be much easier to manufacture. At 100 keV, a Fresnel lens made from Si (or similar material) with a thickness of t = 2.5 mm will satisfy the constraints. The real decrement of the refractive index −2 for Si is δ = 4.4 × 10−4 EkeV and at 100 keV λ = 1.24 × 10−11 m so δt = 8.9λ. Setting ∆φ = 2π/10 in Equation 18 gives the sum in quadrature of the rms figure errors on the entrance and exit surfaces as h = 28 microns, so the rms figure error on each surface of the lens must be σ = 20 microns to achieve a phase error equivalent to figure quality of λ/10. This is a modest requirement well within the capabilities of currently available optical figuring techniques. The focal length and diffraction-limited angular resolution will be determined by the number of rings, and the focal length is very large because δ is so small. Using Equation 24 with tring = 2.5 mm, D = 1 m, and δ for Si from above gives F = 1.1 × 109 /Nring m when EkeV = 100. The broadband PSF will have the profile plotted in red on

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Fig. 11 with ∆θ = 2.6Nring micro-arc seconds, and the HPD of the focused spot will be 14 mm on the detector. At a wavelength λ = δt/m, where m = 9 or any nearby integer, and providing the bandwidth is small, E/∆E > 9(Nring − 1), there will be a much narrower PSF, ∆θ = 2.6 micro-arc seconds, with the form of the Airy function and a focused spot with HPD of 14/Nring mm on the detector. The radius  of the nth ring of a Fresnel lens with a total of Nring rings is rn = (D/2) n/Nring so the radial width of the outer (narrowest) ring is ∆rmin ≈ D/(4Nring ). The minimum radial width of the rings and hence the maximum number of rings that can be accommodated will depend on the manufacturing process used to make the lens, Nring = D/(4∆rmin ). The Fresnel number of the lens, calculated by substituting the focal length from Equation 24 for the aperture-image distance, l = F , in Equation 10 is NF = 2Nring (tring δ/λ). Substituting for Nring in terms of rmin from above gives NF = (D/(2∆rmin ))(tring δ/λ). If rmin ∼ 1 mm, then the Fresnel lens described above has Nring = 250 and NF = 4500. Unless some manufacturing process can be developed to produce a Fresnel lens with rmin ≪ 1 mm, the Fresnel number of such a lens and hence the diffraction-limited focusing power will be very modest in comparison with the largest diffraction limited optical or infrared telescopes – the Fresnel number for the JWST mirror was estimated above as NF = 2 × 104 . For a given thickness (t = 2.5 mm above), the broadband focus on the detector is independent of the number of rings, and when Nring = 1, we have a simple lens and the HPD corresponds to the aperture diffraction limit. As the number of rings increases, the focal length and HPD of the narrowband PSF shrink as 1/Nring . To achieve the greatest focusing advantage, the maximum number of rings will be limited by by the energy resolution of the detector: Nmax = E/(m.∆E) + 1

(26)

where m = tδ/λ. The parabolic (spherical) lenses described above produce the optimum diffraction limited PSF (Airy function), on-axis, in the focal plane. If the lens profile is modified, then the off-axis PSF and/or the out-of-focus PSF (depth of focus) can be optimized in a trade-off against the on-axis performance. For example, so-called axilenses use exponential profiles with thickness: t (r) = t0 + a × r b

(27)

where the exponent 0.5 < b < 3.5 controls the aspheric response. When b = 2, we get a parabolic lens. If b < 2 or b > 2, the depth of focus increases but the on-axis PSF is degraded. Such axilens profiles can be applied to full period zones in a Fresnel-type lens although the radii of the zones will depend on the exponent value, b. Further details about the design of axilenses can be found in the literature, e.g., Davidson et al. (1991). Using aspheric profiles may be of use in the final optimization of Fresnel lens design for application in the X-ray and gamma-ray regime.

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Further details about the application of Fresnel lenses in gamma-ray astronomy including construction, the focal length problem, effective area, and chromatic aberration are given by Skinner et al., ⊲ Chap. 49, “Laue and Fresnel Lenses”, Volume 2. Laue lenses are also used to provide focusing of flux in the gamma-ray energy band. They utilize Bragg reflections in transmission, from an array of crystals, to concentrate the flux. The angular resolution is determined by the size and internal structure of the crystals, but the geometry does not give access to diffraction-limited imaging.

Zone Plates If the change in path length across each ring in a Fresnel lens is one wavelength, λ, then m = 1 and the rings are full period zones within the aperture. We can split each ring into two half period zones and replace the refracting rings of the Fresnel lens by alternate open and blocked annuli to form a zone plate. In this case, the open area of the plate is half the area of the full aperture. Or we can introduce a thickness of dielectric in alternate half period zones, tzone = λ/(2δ), to produce a phase shift of π between the adjacent half period zones in which case the open area of the zone plate covers the full aperture. The PSF of the zone plate is then just the diffraction pattern of the aperture, and the complex amplitude at the focal plane is given by the Fresnel integral: exp(ikz) E(x, y, z) = iλz

 

′ 2 ′ 2 ik E(x , y ) exp (x − x ) + (y − y ) + φ dx′ dy′ 2z (28) where x, y are positions in the focal plane at axial position z and x ′ , y ′ are positions in the aperture (axial position z = 0) and φ is the phase change introduced √ by the dielectric. The radius of the nth half period zone of the zone plate is rn = nλz. Therefore, if the aperture diameter is D and there are n half period zones within the aperture, the focal length of the zone plate is z = D 2 /(4λn). The intensity of the PSF is given by the modulus of the complex amplitude squared. Figure 12 shows the PSF of a zone plate calculated using the Fresnel integral. When φ = π or 0 in alternate zones, the PSF is the sum of two components, the Airy function plotted in blue and a very broad residual function plotted in red which is the circular aperture blurred by diffraction. The radius of the first zero of the Airy function is given by the product of the angle 1.22λ/D and the focal length, 1.22(λ/D)(D 2 /(4nλ)) = 1.22D/(4n), while the mean level of the residual remains constant and extends well beyond the radius of the geometric shadow, D/2. The right-hand panel of Fig. 12 shows the encircled energy function for zone plates with 10, 20, 30, 40, and 50 full period zones. The half power radius is ≈0.44D independent of the number of √ half period zones and is always greater than radius D/(2 2) which is the half area radius of the aperture. If the phase term is set to: 

′

′

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Fig. 12 Left: PSF surface brightness profile of a zone plate with 40 half period zones. The dashed line indicates the profile of the geometric shadow. The Airy function component is plotted in blue and the residual in red. The vertical green line indicates the half power radius. Right: the encircled energy function of zone plates with 10, 20, 30, 40, and 50 full period zones (black). Airy function for Fresnel lens with 50 rings (full period zones) in blue

φ = modulo[(r/D)2 4n, 2]π

(29)

2 where r = x ′2 + y ′ , the radius within the aperture, the wave fronts passing through the zone plate are refracted toward the optical axis, and the Fresnel integral gives the PSF of a Fresnel lens, which is identical to the Airy function, and the residual function disappears. The encircled energy function of a Fresnel lens with 50 full period zones is plotted in blue on the right-hand panel. The energy fraction within the radius of the first zero of the Airy function is 84%. For a zone plate PSF, the energy fraction within the Airy component is reduced by a factor 4/π 2 , and the energy fraction within the first zero is 0.84 × 4/π 2 ≈ 0.34. For the Fresnel lens, all wavelet amplitudes at the focal point are in phase, and the integration of the complex amplitudes in the complex plane forms a straight line. For the zone plate, the phase of the wavelets change progressively across a half period zone, and the integration follows the circumference of a semicircle, and the resultant amplitude is reduced by factor 2/π . The refraction of the wave fronts in the Fresnel lens focuses all the flux into the Airy function component with angular half power diameter HPD = 1.06λ/D, while in a zone plate diffraction alone pushes only ∼34% of the flux into the central focused spot (radius to first zero), and the angular half power diameter of the full PSF is HPD = 3.52nλ/D where n is the number of half period zones within the aperture. Although zone plates have much lower efficiency in focusing the incident flux into the central focused spot compared to lenses, simple zone plates with alternate open and blocked half period zones are not subject to low efficiency imposed by the thickness of dielectric and can be used in the soft X-ray band.

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Interferometers When the aperture of an imaging system is reduced to two slits with separation D, as illustrated in Fig. 2, the PSF is dominated by cosine interference fringes with period ∆θ = λ/D. The amplitude and phase of the fringes provide a measurement of the flux and position of sources in the field of view at the spatial frequency corresponding to ∆θ in the direction set by the line of separation of the slits. By measuring the amplitude and phase of fringes with different separations, D, and different position angles of the slits, we can build up an image in the Fourier domain by a process of aperture synthesis. Provided there is adequate coverage in ∆θ and position angle across the Fourier plane, we can achieve diffraction-limited imaging equivalent to an aperture with diameter equal to the maximum value of separation Dmax . Interferometry is the primary method of imaging in radio astronomy and is now providing high angular resolution in the optical band (Baldwin et al. 1996; Monnier 2003). When operating in the long wavelength radio band, very high angular resolution can only be achieved by using very long baseline separations Dmax . However, the wavelengths in the X-ray band are extremely small, so high angular resolutions should be possible using modest baselines providing an X-ray interferometer can be built with sufficient precision to resolve the fringes. In 2000, Cash et al. (2000) reported the detection of X-ray fringes using a simple grazing incidence interferometer utilizing four flat mirrors. Their prototype instrument had a baseline of just one millimeter and gave fringes at 1.25 keV (wavelength 10 Å) equivalent to an angular resolution at source of ∼0.1 arc seconds. More recently the spatial coherence of X-rays from a synchrotron source, wavelength 1 Å, has been measured by Suzuki (2004) using a two-beam interferometer with prism optics. The angular resolution obtained was 0.02 arc seconds using an effective baseline of 0.3 mm. It is tempting to assume that the precision required for interferometry with very high angular resolution is beyond the reach of modern technology, but Cash et al. (2000) have demonstrated this is not the case. Generating a simple two-source fringe pattern is possible using currently available flat mirrors, and increasing the baseline does not require a pro rata increase in mirror precision. The challenge is to build an X-ray interferometer with a collecting area large enough to provide good statistics in the detected fringes while at the same time making the instrument compact and reasonably straightforward to construct. Ideally the dimensions of the instrument should be driven by the upper limit set for the baseline separation rather than being dictated by the geometry required for the mirrors and detectors. If ∆θ is 100 µ arc seconds at 2 keV, then λ = 6.2 Å and D ≈ 1.3 m, a modest aperture about twice the diameter of a single XMM-Newton module (Jansen et al. 2001) (D = 0.7 m) or slightly larger than the largest shell in the Chandra telescope (Weisskopf et al. 2000) (D = 1.2 m). Assuming a detector resolution of ∆y = 10 µm in the focal plane, the focal length must be F ≈ 40 km to give this

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Fig. 13 The geometry of two overlapping beams generating two-source fringes

angular resolution, and the cone angle of rays from the outer edge of the aperture would be 2R/F = 2φ ≈ 7 arc seconds corresponding to an f -number of ∼30,000. In order to achieve diffraction-limited imaging, all the optical paths from the aperture to the focus must be equal in length. As discussed above, for a thin lens operating in the hard X-ray regime, this is accomplished by advancing the wave fronts near the edge of the aperture using a thickness of dielectric. In Xray mirror systems, also discussed above, two grazing incidence reflections in the Wolter Type I or II configuration can provide equal path lengths over a small annular aperture and can, in principle, provide diffraction-limited imaging over a small field of view. Nesting of the Wolter Type I surfaces such as employed in Chandra or XMM-Newton can increase the effective area but cannot provide diffraction-limited imaging over the full aperture covered because the path difference between adjacent shells in the nest is much larger than the coherence length of the radiation. Figure 13 shows the basic geometry needed to generate two-source interference fringes in a wave front splitting interferometer. Parallel beams from two samples of the incident wave fronts enter from the right and converge until they overlap to the left creating a volume containing the interference fringes. Regardless of how the beams are manipulated to the right, a length L, as shown, is required to combine the beams and generate the fringes. If the angle between the beams is θb and the wavelength is λ, then the fringe spacing along the y-axis is: ∆y =

λ θb

(30)

If the beam width is W and the distance along the x-axis from the position where the beams are separate to where the beams fully overlap is L, then: θb =

W L

(31)

The number of fringes seen across the overlapping beams is given by: Nf =

W ∆y

(32)

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Eliminating θb from equations 30, 31 and 32, the fringe separation and beam width are given by:

∆y = W =

λL Nf

 λLNf

(33)

(34)

If we take L = 10 m, λ = 10 Å, and Nf = 10, then ∆y = 30 µm and W = 300 µm. The beam width W is very small, and in order to achieve a large collecting area, the depth of the beams along the Z axis (normal to the X − Y plane shown in Fig. 13) must be large, and/or many identical systems must be operated in parallel. The fringe spacing is small but can be resolved by currently available X-ray imaging detectors. The situation can be improved by increasing L, but we have already chosen a reasonably large distance of 10 m, and because both W and √ ∆y depend on L, a rather large increase is required to make a significant impact. The angle between the beams is small, θb = 6.2 arc seconds.

An X-Ray Interferometer Four flat mirrors can be used to take two samples of width W and separation D = 2R from the aperture and produce overlapping beams as illustrated in Fig. 14. All four mirrors are set at grazing incidence to provide high reflectivity. Operating in the soft X-ray band 0.1–2.0 keV, the grazing angles need to be θg ≈ 2◦ . If M1 and M3 are set at θg with respect to the x-axis, then M2 and M4 must be set at a slightly smaller angle θg − θb /4, where θb is the angle between the beams defined by Equation 31, so that the beams overlap to form fringes. Since θb is very small compared to θg , M2 is almost parallel to M1 and the same is true for M4 and M3 . The effective focal length F is much larger than L and is given by φ = θb /2 = tan−1 (R/F ). The fringe spacing is then ∆y = F δθ = F λ/D where ∆θ is the diffraction-limited angular resolution for the baseline separation D operating at wavelength λ.

Fig. 14 The four flat mirror configuration. The diagram is not drawn to scale. The axial distance between M2 and M3 is much less than the distance L, and F is much larger than L. The vertical scale is exaggerated so that the beam widths are visible

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The arrangement is similar to that used by Cash et al. (2000), but the front of M2 is placed at distance L from the maximum overlap of the beams, whereas in the Cash configuration, this mirror is at a distance 2L from the maximum overlap. The present configuration reduces the overall length required by a useful factor of 2. The physical length of the system is much smaller than the focal length, and the basic geometry is reminiscent of the Wolter Type II telescope in Fig. 8. If W = 300 µm (see above), then the axial length of the mirrors is only 8.6 mm if θg = 2◦ . The axial distance covered by the combination of M1 and M4 needs only be ∼25 mm. The axial distance between M1 and M2 (or M3 and M4 ) is D/(4 tan θg ) ≈ 7D.

A Slatted Mirror The collecting area afforded by a single four mirror arrangement as illustrated in Fig. 14 is going to be small for any sensible depth of mirror (along the z-axis into the plane of the paper). Furthermore, the mirrors required would be incredibly long and thin because the axial length utilized is so small (8.6 mm; see above). A major advantage of the four mirror configuration proposed here and illustrated in Fig. 14 is that a series of parallel systems can be stacked together. The mirror M2 must be split into a slatted mirror, comprising a series of parallel slats, as proposed by Willingale (2004) and Willingale et al. (2005). The axial lengths of mirrors M1 , M3 , and M4 must be increased to cover the full aperture width of all the slats in the slatted mirror. The beam geometry of the slatted mirror is shown in Fig. 15.

Fig. 15 The beam paths using a slatted mirror

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Fig. 16 The layout of an X-ray interferometer using a slatted mirror with 30 elements. Note that the vertical scale is expanded so that the geometry of the beams is easier to discern

Each slat is a long thin mirror facet extending into the plane of the paper. The axial width of a slat is the same as for the mirrors in Fig. 14. The slats are spaced so that the beam from mirror M4 , to the right, is broken into a series of beams of width W . Each slat mirror reflects a fraction of the beam from mirror M1 creating a second set of beams. Each pair of beams overlaps to form interference fringes. Providing there is not too much blocking from support structure needed to hold the slatted mirror together and provided the thickness of the mirror slats is the same order as the beam width W , then about one-third of the flux collected by the apertures of M1 and M3 will form fringes. A slatted mirror with ∼30 slats will provide an effective aperture width of ∼1 cm. The axial length for each slat-gap pair will be ∼26 mm. Figure 16 is a schematic diagram of the layout using a slatted mirror with 30 elements. The length ∆L is the axial separation of M1 and M4 , and the baseline separation D is the same for all the slat-gap pairs. Such a slatted mirror is like a macroscopic transmission grating with mirror facets on each line. It is likely that an optical element of this form could be manufactured using similar techniques to those currently employed in the fabrication of X-ray transmission or reflection gratings. A slatted mirror with dimensions 500 × 500 mm combined with three plane mirrors of the same size would provide a total collecting area of ∼50 cm2 (The final effective collecting area would depend on the X-ray reflectivity of the mirrors and the efficiency of the detectors.). If the mirrors in each arm are set parallel, the path length from the aperture plane at M3 to the detector plane is:

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 P0 = L + ∆L +

D 2 sin(2θg )



1 cos θ

(35)

where θ is the off-axis angle of the source. This is the same for both arms M1 M2 and M3 -M4 and for all positions across the detector. The angle between the incoming wave fronts and the aperture plane introduces a path difference, and when M2 and M4 are tilted by θb /4 to produce an overlap between the beams, we get an extra path contribution. The extra path lengths of the two arms are:  D 1 − 1 + y sin(θb /2) − sin θ =L cos(θb /2) 2

(36)

 D 1 = (L + ∆L) − 1 − y sin(θb /2) + sin θ cos(θb /2) 2

(37)

P12

P34





where y is the position across the detector plane. The path difference between the arms is:   1 ∆ = P12 − P34 = −∆L − 1 + 2y sin(θb /2) + D sin θ (38) cos(θb /2) It is this path difference which gives rise to the fringes. The first term is fixed and of no consequence since it can be eliminated by a small change in the position of M1 or M3 . Ignoring this small correction, the coincidence point of the interferometer (∆ = 0) is given by: y=

−D sin θ ≈ −F θ 2 sin(θb /2)

(39)

Here we have taken the small angle approximation and substituted for the focal length F = R/ tan(θb /2) ≈ D/θb . The interferometer behaves like an imaging telescope of focal length F with the coincidence point (center of the fringe pattern) at the expected position of a point source with off-axis angle θ . The negative sign represents the expected lateral inversion in the focal plane.

The Fringe Pattern If we move away from the coincidence point, the path difference ∆ increases linearly with y ′ = y + F θ , and we expect to observe cosine fringes. Because the wave fronts of the two beams are broken up by the slatted mirror, we must use the Fresnel diffraction formula to calculate the exact form of the fringe pattern. If plane waves of wavelength λ are incident on a slit of width W and we are looking at the fringes at a distance L from the slit, the dimensionless variable used in the Fresnel integrals is given by:

8 Diffraction-Limited Optics and Techniques

u=y

317

′



2 λL

(40)

 Substituting for y ′ = W from Equation 34, we have u0 = 2Nf . Since Nf > 1, the scaled width of the slit u0 is also > 1 and we must use the near field approximation (Fresnel diffraction) rather than the far field limit (Fraunhofer diffraction). We define limits u1 = u − u0 /2 and u2 = u + u0 /2. The complex amplitude at a scaled displacement u from the center of the beam is given by: (41)

A = C(u2 ) − C(u1 ) + i(S(u2 ) − S(u1 )) where C(u) and S(u) are the Fresnel integrals: u

C(u) =



S(u) =



0 u 0

cos(π w 2 /2)dw

(42)

sin(π w 2 /2)dw

(43)

The intensity expected is then given by I = AA∗ . Using the beam parameters from above, u0 = 4.5, and the intensity has the profile shown in the left-hand panel of Fig. 17. The geometric shadow of the edges of the slit (a mirror slat or gap between slats) without diffraction are expected at u = ±2.25. If the mirror slats and gaps are the same size, they will produce identical intensity profiles, but because they are tilted by θb with respect to each other, there is a phase difference between the beams which is a linear function of u, δ = π u0 u, and the complex amplitude in the overlap region is then given by: A2 = A(1 + exp(iπ u0 u))

–4

–2

(44)

3

12

2.5

10

2

8

1.5

6

1

4

0.5

2

0

2

4 u

–4

–2

0

2

4 u

Fig. 17 Left panel: the Fresnel diffraction profile of a single beam. Right panel: the fringe pattern from one slat-gap pair

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Again we can calculate the intensity profile in the same way giving the fringe pattern plotted in right-hand panel of Fig. 17. The intensity of the bright fringes is modulated by the Fresnel diffraction profile shown in the left-hand panel of Fig. 17. The expected Nf = 10 fringes are visible across the center of the beam. The edges of the beam spread into the geometric shadow due to diffraction, but there will be negligible interference between adjacent slat-gap pairs. As the path difference ∆ becomes comparable to the coherence length of the X-rays, the visibility of the fringes will decrease. If E/∆E = N , then we expect to see ∼N fringes across the entire pattern. If N ≫ Nf , then a continuation of the Nf fringes from the slat corresponding to the coincidence position will be visible from slat-gap pairs adjacent to this position, but in the gap between adjacent pairs, the fringes will be much reduced in intensity. These missing fringes can be recovered by splitting the slatted mirror into two halves, reversing the slat and gap positions in the second half. The pattern of slats required is shown in Fig. 18. Combining the fringe patterns from the two halves provides complete coverage of all N fringes. Figure 19 shows the fringe pattern expected from two sources at ±5 milli arc seconds with Nf ∼ 4 and N ∼ 10. The slats introduce a residual modulation, but this can be completely removed during analysis of the interferograms.

Fig. 18 A slatted mirror with complementary halves

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Fig. 19 The fringe pattern expected from two sources at ±5 milli arc seconds. The fringes from the two halves of the slatted mirror are plotted as dashed and dashed-dotted lines

Working at an X-ray wavelength of 10 Å and using L = 10 m, the fringe spacing for Nf = 10 is 30 µm. Such fringes could be resolved using a CCD detector with the smaller pixel sizes currently available. However, the fringes exist through a very long volume in which the two beams overlap. All ten fringes should be visible over an axial depth of ∼L/10. If the detector is set at a grazing angle θd to the beam, the fringe spacing will be increased to: ∆y ′ =

∆y sin θd

(45)

If θd = 5.7◦ , then the magnification factor will be 10, and the fringes will easily be resolved by current detector technology. Unfortunately, a detector operating at such a low grazing angle will have a low efficiency. In order to take advantage of the magnification, a detector with high quantum efficiency operating at small grazing angles would have to be developed. When observing astronomical objects, the X-ray flux will be broadband, and a detector with a moderate energy resolution will be required to detect fringes. We require an energy resolution E/∆E ≥ Nf to resolve the fringes at energy E in a bandwidth ∆E. A CCD typically has E/∆E ≈ 10 at 0.6 keV increasing to ∼15 at 1 keV and ∼50 at 7 keV. This is just adequate for our purpose. However, the imaging and spectral response of a CCD is not well matched to the requirement. High spatial resolution is only needed in 1D (across the fringes), and the sensitivity would be greatly improved if E/∆E > 100.

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Simulation of One-Dimensional Imaging

0

80 60 40 20 0

0

20

40

60

80

The interferometer illustrated in Fig. 14 has been simulated using the slatted mirror layout shown in Fig. 15 and the energy response of the XMM-Newton EPIC-MOS CCDs (Turner et al. 2001). In order to get good coverage in spatial frequency, four parallel systems were used with D-spacings of 35, 105, 315, and 945 mm. The corresponding effective focal lengths are 1.2, 3.7, 11.1, and 33.4 km. Each system has a collecting area of ∼20 cm2 in the energy band of 0.58–2.1 keV (using the reflectivity of gold and the MOS detector efficiency). The E/∆E of the detector provides 21 energy channels across this band. A total source flux equivalent to 1 Crab gives 460,000 counts in a 1000 second exposure. With 4 D-spacings and 21 energy channels, a total of 84 interferograms were recorded in a single exposure. The source distribution assumed was a binary system consisting of an extended source and a point-like companion. Even with ∼460,000 counts, the count per fringe is very small, and it is impossible to see the fringes in the raw simulated data. However, for each interferogram (one energy channel and one D-spacing), the fringe spacing and expected number of fringes are known. It is therefore possible to set up a Fourier filter that picks out the fringe pattern from each interferogram. Figure 20 shows the Fourier power spectra of the 84 interferograms and the Fourier filter constructed to pick out the

1

2 3 frequency moa–1

4

0

1

2 3 frequency moa–1

4

Fig. 20 The left-hand panel shows the Fourier power spectra of 84 interferograms. Each block of 21 corresponds to a given D-spacing. The right-hand panel is the Fourier filter used to pick out the fringes

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Fig. 21 The reconstructed source distribution. The inset shows an expanded detail of the significant peaks. The binary consists of a resolved component with a point source companion

fringes. The 4 blocks of 21 interferograms arise from the 4 D-spacings used. Two peaks are visible in each power spectrum. The vertical white lines to the left at low frequency are the peaks from the modulation caused by the slats. These are completely removed by the filtering. The white patches to the right are the fringes. The visibility of the fringes varies as the frequency increases because of the structure of the binary source under observation. A top-hat profile matched to the E/∆E for each interferogram was used to construct the filter. There is some overlap in the frequency coverage between the four D-spacings. In a practical setup, the overlap regions could provide a means of eliminating phase errors between the four parallel optical systems. Figure 21 shows the reconstruction of the source distribution. The intensity is plotted as counts per 0.058 milli arc second sample, and there are 1800 samples across the field of view. The rms noise level is 2.16 counts per sample, and all the significant samples are detected at >12σ . The total estimated count from the significant samples is 430,000 compared with the actual detected count of 462,000, so 93% of the original count has been successfully imaged. In this simulation and reconstruction, the source distribution was assumed to be independent of energy, and therefore all the detector energy channels could be summed to produce the final image. In reality, this would not always be the case, and more D-spacings would be required to reconstruct a source with a complex spatialenergy structure. To extend the imaging to 2D, more exposures would be required at different roll angles about the pointing axis to give a reasonable coverage in the (u,v) plane. If this were achieved by running several (five to ten) identical systems

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simultaneously at different roll angles not only would 2D imaging be provided, but there would also be a pro rata increase in the total collecting area. The system performs in a similar way to a shadow mask camera (Sims et al. 1980), but a fringe pattern is detected instead of a shadow mask pattern. Each pixel at the detector is multiplexed to many sky elements within the field of view, and therefore the sensitivity of the interferometer is dependent on the source distribution or the number of significantly bright point sources in the field of view. If the energy resolution of the detector were improved, the number of fringes N ≈ E/∆E across the pattern would increase, and the number of pixels multiplexed to a given sky position would be larger. The total area of the Fourier plane covered by the filter (Fig. 20) is ∝ 1/N, and if there √are Nx significant unresolved sources in the field of view, the signal-to-noise is ∝ (N)/Nx .

Tolerances, Alignment, and Adjustment Because the wavelength of X-rays is so small, the tolerances and alignment requirements for an interferometer are very tight, and we must consider figure errors and surface roughness in the flat mirror surfaces, alignment and positional placement of the mirrors, control of the difference between the path lengths in the two beams, and pointing accuracy and stability of the complete system. The mirrors must be flat enough so that incident plane wave fronts are reflected with the minimum perturbation and remain plane as described in sections above. Figure errors will introduce distortions in the wave fronts, and shorter scale surface roughness features will scatter some of the incident light into scattering wings which will reduce the contrast of the fringes. Fortunately, because the mirrors are operating at grazing incidence, the effect of figure errors and surface roughness in the mirror surfaces is reduced by a factor sin θg . A surface height error h introduces a wave front shift of 2h sin θg . To produce clean fringes, the wave fronts must not be perturbed by greater than ∼ λ/10. So we have: h≤

λ 20 sin θg

(46)

If λ = 10 Å and θg = 3◦ , then we require h < 1 nm. A high-quality optical flat has a specification of λ/20 (where λ = 633 nm), so even with the advantage of grazing incidence, we need very high-quality mirrors to obtain clean fringes. The surface height error of 1 nm is equivalent to an axial gradient error over the width of one slat of ∼0.03 arc seconds. Gradient errors over distances larger than the slat width will destroy the register between the overlapping beams produced by a single slat-gap pair and may introduce confusion between adjacent slat-gap pairs. The angular width of the fringe separation is ∆y/L ≈ 3 × 10−6 equivalent

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to 0.6 arc seconds as seen from the mirrors. Therefore, gradient errors between the slats and over the full faces of the other mirrors must be kept to this level. First order perturbation theory gives the total integrated scatter (TIS) after two reflections as: 4π σ sin θg TIS = 2 λ 

2

(47)

where σ is the rms surface roughness. To get TIS < 0.1, we require σ < 3.5 Å integrated over correlation lengths 5σ in 500 seconds. The system can provide imaging in 2D by making exposures at different roll angles. About 40 units (possibly packed into the same tube) running simultaneously with different D-spacings and roll angles could provide good coverage of the (u,v) plane, and because of the tenfold increase in collecting area, the same sensitivity would be achieved in ∼150 seconds using CCDs or detectors with a similar performance. If the detector energy resolution could be improved by a factor of 10 while retaining a spatial resolution of ∼10 µ m in 1D, then the same 2D imaging sensitivity could be achieved in ∼50 seconds. The slatted mirror system is similar to the MAXIM periscope configuration, the tolerances of which are described in detail by Shipley et al. (2003). The introduction of a slatted mirror dramatically reduces the total distance required between the primary mirrors that define the baseline separation and the detector system, and 0.1 mas imaging can be achieved without the requirement for two free-flying spacecraft. Each unit of four mirrors detects two-source fringes, and the combination of several such units provides imaging by aperture synthesis in the same way as conventional interferometers used in the radio and optical bands. This is rather different from the all-up MAXIM approach in which many mirror segments are used to produce a complex interferogram which looks much more like a conventional image.

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All the published proposed designs to date utilize flat mirrors. If technology to introduce a very small cylindrical curvature in the primary optics can be developed, then designs incorporating 1D focusing can be implemented, and the flux sensitivity limit of the X-ray interferometer will be significantly reduced.

Cross-References ⊲ Laue and Fresnel Lenses

References C.S. Adams, I.G. Hughes, Optics f2f from Fourier to Fresnel (Oxford University Press, Oxford, 2019) B.K. Agarwal, X-Ray Spectroscopy: An Introduction (Springer-Verlag, Berlin, Heidelberg, New York, 2013) J.E. Baldwin et al., Astron. Astrophys. 306, L13–L16 (1996) M. Born, E. Wolf, A.B. Bhatia, P.C. Clemmow, D. Gabor, A.R. Stokes, A.M. Taylor, P.A. Wayman, W.L. Wilcock, Principles of Optics: Electromagnetic Theory of Propagation, Interference and Diffraction of Light, 7th edn. (Cambridge University Press, Cambridge, 1999) W. Cash, A. Shipley, S. Osterman, J. Marshall, Nature 407, 160 (2000) N. Davidson, A.A. Friesem, E. Hasman, Opt. Lett. 16, 523–525 (1991) U. Fano, Physical review. APS 72(1), 26–29 (1947) K.C. Gendreau, W.C. Cash, A.F. Shipley, N. White, SPIE 4851, 353–363 (2003) F. Jansen et al., A&A 365, L1 (2001) M. Lieber, D. Gallagher, W. Cash, A. Shipley, SPIE 4851, 557–567 (2003) J.P. Mills, B.J. Thompson, J. Opt. Soc. Am. A 3, 694–703 (1986) J.D. Monnier, Rep. Prog. Phys. 66, 789–857 (2003) H.J. Pain, The Physics of Vibrations and Waves, 6th edn. (John Wiley & Sons Ltd, Chichester, New York, Brisbane, Toronto, Singapore, 2005) A. Shipley, W.C. Cash, K. Gendreau, D. Gallagher, SPIE 4851, 568–576 (2003) M.R. Sims, M.J.L. Turner, R. Willingale, Nucl. Instrum. Methods Phys. Res. 228, 512 (1980) Y. Suzuki, Rev. Sci. Instrum. 75(4), 1026–1029 (2004) M.J.L. Turner et al., A&A 365, L27–L35 (2001) M.C. Weisskopf, H.D. Tananbaum, L.P. Van Speybroeck, S.L. O’Dell, SPIE Proceedings, vol. 4012 (2000) R. Willingale, SPIE 5488, 581–592 (2004) R. Willingale, G. Butcher, T.J. Stevenson, SPIE 5900, 432–437 (2005). Advanced X-ray Astrophysics Facility (AXAF): an overview. Proc. Soc. Photo-Opt. Eng. 2805, 2–7 H. Wolter, Ann. Phys. 10, 94 and 286 (1952)

9

Collimators for X-ray Astronomical Optics Hideyuki Mori and Peter Friedrich

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stray Light and Baffle Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classification of the Stray Light . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Design of the Stray-Light Baffle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XMM-Newton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Suzaku and Hitomi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Suzaku Pre-collimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical Tuning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . On-Ground and In-Orbit X-Ray Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hitomi Pre-collimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . eROSITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

328 331 331 346 349 353 353 357 358 358 361 367 368 369

Abstract

An X-ray collimator, or baffle, can be installed in the X-ray optics of an X-ray telescope. This component is placed in front of an X-ray mirror to protect the mirror from severe in-orbit thermal environment or to limit the mirror’s field of view. Although the latter may be a disadvantage in the viewpoint of observational performance, the collimation of incident X-rays allows us to block X-rays with H. Mori () Japan Aerospace Exploration Agency/Institute of Space and Astronautical Science, Sagamihara, Kanagawa, Japan e-mail: [email protected] P. Friedrich Max-Planck-Institut für extraterrestrische Physik, Garching, Germany e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_10

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large off-axis angles. Thus, the mount of the X-ray collimator results in the reduction of an extended ghost image in the detector field of view that is created by the X-rays, called stray light, with abnormal paths inside the X-ray mirror. The contamination of the stray light hampers both imaging and spectroscopic observations of dim X-ray emission from a spatially extended source or a faint point source. The improvement of the angular resolution and the effective area is intensively pursued for the next-generation X-ray optics. In parallel, it is a vital issue to reduce the stray light as low as possible to fully achieve the expected performance of these future X-ray optics. Keywords

X-ray baffle · Thermal pre-collimator · Stray light · Ghost image · Single reflection · Backside reflection · Alignment process

Introduction We describe an X-ray collimator or baffle mounted on an X-ray mirror in this chapter. Here a collimator (or baffle) is defined to be a component structure as a part of the X-ray astronomical optics, which has some features that enhance the performance of the X-ray mirror. We hereafter use the terms of “collimator” and “baffle” as synonyms. We note that, basically, the collimator is not used for focusing X-rays from celestial sources. Figure 1a shows a schematic drawing of the X-ray mirror and collimator, together with definitions of some terms used in the chapter. The first X-ray mirror was equipped in the Einstein satellite (Giacconi et al. 1979). Even for the X-ray mirror in the Einstein satellite, an X-ray collimator was installed, called forward thermal pre-collimator (see Fig. 1b for its geometrical configuration). This thermal pre-collimator allows us to isolate the X-ray mirror thermally from a space environment and then to reduce heater power required for the thermal control of the mirror. Such a thermal pre-collimator was also introduced in the X-ray mirrors of ROSAT (Truemper 1982; Benz et al. 1983; Aschenbach 1988) and Chandra (Weisskopf et al. 2000; Gaetz and Jerius 2005; Schwartz 2014). Compared with a thermal shield that is mounted on the entrance of the X-ray mirror, another component to isolate the mirror thermally, one of the advantages of the thermal pre-collimator is that it does not block normal X-ray paths. As shown in Fig. 1b, on-axis X-rays reach on a detector plane without any interactions except for the X-ray mirror. Figure 1c indicates the geometrical configuration of the thermal shield. The thermal shield usually consists of an extremely thin film and its support structure. An aluminized polyethylene-terephthalate (PET) film with a thickness of sub-micrometers is utilized for radiation decoupling; thermal radiation is reflected back to the X-ray mirror. Although the aluminized PET film is quite effective to reflect optical/infrared lights completely, X-rays with a relatively low energy (below 0.5 keV) are also absorbed by the film, which prevents the telescope from their detection. For example, the transmission of the thermal shield for the

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Fig. 1 (a) A schematic drawing of a cross-sectional view of an X-ray mirror and collimator. The terms used in this chapter are also indicated. (b) A geometrical configuration of a thermal precollimator. (c) Same as (b), except for a thermal shield

Suzaku XRT was ∼0.7 at 0.5 keV (Serlemitsos et al. 2007). The thickness of the thermal shield was just 0.24 µm. While the thermal shield achieves a lightweight component without additional heater power, careful handling is requested for the extremely thin film not to be torn down. In addition, because the PET film contains carbon (C), severe absorption around the C-K edges (0.28 keV) precludes a clear detection of low-energy X-rays. No absorption of the low-energy X-rays is the advantage of the thermal precollimator because high effective areas of the X-ray mirrors are sustained even in the low-energy band. Moreover, we can avoid uncertainties of observational results caused by the X-ray Absorption Fine Structure (XAFS) of the elements used in the thermal shield. However, the thermal pre-collimator does not isolate the mirror from the space environment completely. Paraboloid shells (and a part of hyperboloid shells that depends on the mirror nesting density) of the X-ray mirror can still see the space directly, which causes radiative cooling. Of course, the cooling is mitigated by the thermal pre-collimator since the solid angle of the space is limited to some extent, depending on the internal structure of the thermal pre-collimator. Furthermore, the thermal coupling by radiation between the mirror shells and the thermal pre-collimator also contributes to thermal stabilization of the X-ray mirror. To keep the thermal environment constant, the temperature of the thermal precollimator is usually controlled by a heater. Hence, compared with the thermal shield, which is a passive component, power consumption is required to operate a thermal collimator.

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Another purpose to install the collimator on the entrance of the X-ray mirror is to reduce incident X-rays with abnormal paths that create a ghost image on a detector plane. These X-rays are called stray light. The stray light itself is a common problem in the design of the optics. For example, a star tracker camera that determines the aspect of the satellite has a baffle in front of the camera lens. Since light paths to the lens are restricted by the baffle, it allows us to reduce a ghost noise by the stray light. Similarly, the collimator installed on the X-ray mirror is expected to reduce the Xray stray light as much efficiently as possible. At the same time, this structure makes the field of view of the X-ray mirror narrower. Hence, the design of the collimator should be determined so as to optimize the total performance of the X-ray optics. So far, a variety of the X-ray collimators has been achieved to reduce the X-ray stray light for the X-ray mirrors on board XMM-Newton (Jansen 1999), Suzaku (Mitsuda et al. 2007), Hitomi (Takahashi et al. 2018), and eROSITA (Predehl et al. 2021). We summarize the missions equipped with the X-ray collimators for stray-light reduction as well as the thermal control in Table 1. Thanks to the X-ray collimators, dim X-ray emission is now able to be detected clearly without contaminations due to the stray light. Especially, new findings were achieved from complicated X-ray structures shown in outskirts of some clusters of galaxies or the regions of the galactic center, where the X-ray contamination from bright X-ray sources hampered accurate X-ray studies of spatially extended dim emission. Since the effectiveness of the X-ray collimators was verified from the in-orbit observations, the collimator with the same concept is an indispensable component even for the X-ray optics in some planned future missions. As the angular resolutions and the effective areas of the X-ray mirrors are improved to detect distant X-ray objects and to investigate fine structures of X-ray sources with extremely low surface brightness, the importance of reducing the X-ray stray light is increased. Indeed, the intensive study of the X-ray collimator design has been carried out for the future

Table 1 Summary of X-ray collimators installed in X-ray imaging optics Mission Einstein ROSAT XMMNewton Chandra

Collimator (or baffle) Thermal precollimator Thermal precollimator X-ray baffle

Swift Suzaku AstroSat Hitomi

Thermal precollimator Thermal baffle Pre-collimator Thermal baffle Pre-collimator

eROSITA

X-ray baffle

Reference Giacconi et al. (1979) Truemper (1982); Benz et al. (1983); Aschenbach (1988) Aschenbach et al. (2000); de Chambure et al. (1996, 1999a,b) Weisskopf et al. (2000); Gaetz and Jerius (2005); Schwartz (2014) Burrows et al. (2003) Serlemitsos et al. (2007); Mori et al. (2005) Singh et al. (2017) Okajima et al. (2016); Awaki et al. (2014); Iizuka et al. (2018); Mori et al. (2018) Predehl et al. (2021); Friedrich et al. (2012, 2014)

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X-ray large missions such as Athena (Bavdaz et al. 2021) and Lynx (Gaskin et al. 2019) (Lynx is also equipped with thermal pre- and post-collimators). We focus on the X-ray collimator for stray-light reduction hereafter because the thermal pre-collimator is a simple component to sustain thermal environment for the X-ray optics as described above. The structure of thermal pre-collimator is related to the thermal design of the X-ray optics, which reenters the domain of thermal engineering. Neither we discuss a simple collimator that only limits the field of view of the X-ray optics such as coded masks, which is beyond our scope. We first describe the classification of the stray light and then give detailed explanations for each component of the stray light. We also mention a basic design to reduce the stray light on the detector plane of the X-ray mirror. The detailed designs of the X-ray collimators are different among the missions, which reflects the requirement for each telescope. Thus, we describe the X-ray collimators separately for XMMNewton, Suzaku, Hitomi, and eROSITA. We also mention briefly the current status of the future collimator design at the end of this chapter.

Stray Light and Baffle Design Classification of the Stray Light In the Wolter-I type optics, X-ray photons are focused on a detector plane by nominal double reflection (see also Fig. 1a). However, since the Wolter-I type mirror is a grazing incident optics, some off-axis X-rays, which form a shallow angle with the common optical axis of the X-ray mirrors, can also arrive at the detector plane. If the off-axis angle becomes large enough, the nominal double reflection no longer occurs for these X-rays. They so create a de-focused and extended ghost image of the corresponding celestial object. However, the image is quite distorted and then does not store correct information on the spatial extent of the object. Such X-rays are called stray light. Figure 2 shows the stray-light image of the Crab Nebula taken by the ASCA GIS. Although the Crab Nebula was located 60′ away from the aim point, i.e., the center of the GIS, and then a source-free region was observed, the stray light was extended in the entire field of view. In this way, a part of the stray light comes into the detector field of view and then comes to represent an important source of X-ray backgrounds for observing targets we are interested in. Especially, for the observation of the source with low surface brightness, the stray light causes an imaging and spectroscopic contamination that makes severe problems to extract correct scientific results. For example, an outskirt of a cluster of galaxies is affected by the stray light from its bright core. Another example of the stray-light contamination is a mapping observation of the galactic diffuse emission in the galactic center where many bright X-ray sources are crowded. As the impact of the stray light on the observations was recognized, countermeasures were studied. The first telescope to be equipped with a stray-light baffle was XMM-Newton. After XMM-Newton, Suzaku (Astro-E2) and Hitomi (ASTRO-H) were equipped with a pre-collimator to reduce the stray light. Before discussing a

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Fig. 2 Stray-light image taken by the ASCA GIS with a circular field of view. The source of the stray light is the Crab Nebula located 60′ away from the aim point. The bright emission shown in the lower left part corresponds to the stray light by the secondary-only reflection, while the upper right part does correspond to the stray light by the backside reflection (This image is adapted from Mori et al. 2005)

structural design suitable for that task, we need to find out the paths of the stray light in the X-ray mirror. A ray-tracing simulation of the X-ray mirror is a powerful tool to understand what occurs inside the X-ray mirror assembly (e.g., Madsen et al. 2017; Saha et al. 2017). X-rays incident onto the mirror assembly are generated as an input file of the Monte Carlo simulation. According to properties of a given X-ray source, an initial direction and an energy are set for each ray. A three-dimensional mirror structure is accurately reconstructed in the computer. Interactions between the X-ray photons and mirror are given by probability functions that represent absorption, reflection, and scattering. We can trace an internal path for each X-ray that allows us to identify the positions at which the reflection occurs. Most X-rays are focused to the detector plane by the nominal double reflection; the ray is reflected in sequence by the primary and secondary mirrors. All the X-rays undergoing a single reflection (on either a primary or a secondary mirror) are not focused and contribute to the stray light. Furthermore, based on the ray path through the mirrors, we can divide the stray light into four types, designated as below: 1. 2. 3. 4.

No reflection or direct component Primary-only reflection or primary component Secondary-only reflection or secondary component Backside reflection or backside component

Figures 3 and 4 show schematic drawings of the paths inside the mirror assembly for the stray light, as well as that for the nominal double reflection. The significant contribution to the stray-light image is created by X-rays with single reflection,

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Fig. 3 X-ray paths inside the X-ray mirror for the (a) nominal double reflection and (b) no reflection. The terms and parameters are also indicated

especially that by the secondary-only reflection (see also Fig. 2). For the nested mirrors, the primary-only reflection has small contribution compared with the secondary-only reflection. Due to dense nesting of mirror shells to enhance the effective area, the majority of the primary-only reflection hits the backside surface of the inner primary or secondary shell, and it is then absorbed inside the mirror shell. The backside surface of the mirror shells is usually very rough compared with the frontside surface to which reflective coating is applied. Hence, the X-ray reflectivity for the backside surface is relatively low, depending on the surface condition. The low reflectivity implies that the flux of the backside reflection is dim. However, the geometrical area on the mirror aperture where the backside reflection occurs is large; therefore the contribution to stray light can be non-negligible. We discuss a simple analytical expression for each stray-light component that represents a relation between basic parameters such as a focal length of the mirror, an off-axis angle of the stray light, and its radial coordinate on the mirror aperture or the detector plane. The relation is useful for understanding the characteristics of each component and for a rough estimation of a collimator’s height explained later. Figure 3a shows a schematic cross-sectional view of the nominal double reflection. For a geometrical calculation, we also define some key parameters with

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Fig. 4 X-ray paths inside the X-ray mirror for the (a) primary-only reflection, (b) secondary-only reflection, and (c) backside reflection

symbols: an off-axis angle (θ ), a focal length (F ), and a tilt angle of a primary mirror shell (τ ). Here, we apply a conical approximation to the mirror shells that allows us to simplify the calculation. Thus, a cross section of each mirror shell is indicated by a straight line, instead of a parabolic or hyperbolic curve. h represents an axial

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height of a mirror shell. According to the mirror design, the axial height is usually different for each mirror shell. However, we assume here that the axial heights of all the primary and secondary mirrors are the same. R is a half size of the detector field of view. We assume that the detector has a square shape. If the detector field of view is a circle, R represents its radius. We designate the radii for the top of the primary mirror and the bottom of the secondary mirror as rp and rs , respectively. The radii for the bottom of the primary mirror and the top of the secondary mirror are slightly different in general since there is a gap between the primary and secondary mirrors produced by a mirrorsupport structure. However, we consider here that both are the same; this radius is designated as rf . We note that the thicknesses of the mirror shells are assumed to be zero to minimize the number of the parameters used in the calculation. Thus, radii of frontside and backside surfaces for a mirror shell are the same. We can easily replace these radii with those of the actual backside surfaces by adding the thickness of the mirror shell. rt represents a radius of an incident X-ray measured at the mirror entrance. There is also a gap between the mirror entrance and the top of the primary mirrors. Hence, strictly speaking, rt for an off-axis X-ray is different from the radius measured in the plane corresponding to the top of the primary mirrors. However, we assume that the gap is negligible hereafter and then compare rt with rp directly. Given a tilt angle of a primary mirror measured from an optical axis, designated as τ , that of the corresponding secondary mirror is set to 3τ so that the incident angle of the reflected X-rays on the primary mirror becomes τ on the secondary mirror (see Fig. 3a). Consequently, the on-axis X-rays (θ = 0) are bent at an angle of 4τ by the nominal double reflection. Hence, rf is given by rf = F tan 4τ . In general, the radii (rf ) for each pair of the primary and secondary mirrors are optimized to enhance the effective area. And then, the tilt angle of the corresponding primary r mirror is set by τ = 14 tan−1 Ff .

No Reflection The direct component is a simple stray light that goes though without any interactions with the mirror shells and their housing. The X-ray performance of the Wolter-I type optics, especially for the effective area, is determined by the focal length and the innermost/outermost radii of the mirror aperture. To enhance the effective area of the grazing incidence optics, the X-ray mirror shells are densely packed, covering a ring-shaped collecting area. Thus, a circular aperture remains clear in the center of the mirror module. Usually, other optical components are equipped in this space, for example, a retroreflector collimator (Chandra) and an alignment cube (Hitomi) that is used for the alignment of the X-ray optical axis. These components allow us to block a part of the direct component. In addition, we can easily seal this central space if necessary, using high-Z metals such as lead to block the direct X-rays. Hence, we ignore the direct component through the central space of the X-ray mirror hereafter. There is the other direct X-ray component that goes through a space between the innermost mirror shells and the inner wall of the mirror housing (see Fig. 3b). This direct component sometimes creates a dim X-ray arc in the detector field of view.

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One countermeasure to block this direct component is to make the space narrower by attaching a roof on the inner wall. However, it may be difficult to align the roof’s position accurately not to intercept the innermost primary shell for on-axis X-rays. Consequently, we need to accept a slight contribution from the direct component. There may be other spaces that the direct component can occur. For example, a space between the outermost mirrors and the outer wall of the housing also contributes to the direct X-ray component. Moreover, if the nesting density of the mirror is low (a sparse nesting), off-axis X-rays can go through a space between the mirror shells. However, since the direct component is not focused and the radial coordinate of these off-axis X-rays (rt ) is significantly larger than the detector size in general, they will rarely contaminate the detector field of view. As shown in Fig. 3b, the direct component for a given off-axis  angle  of θ can reach the detector field of view under a condition of ri ≦ rt ≦ F + h tan θ + rd . Here, rd and ri represent the radial coordinate on the detector plane and the radius of the inner wall, respectively. We note that the discussion below is based on the cross-sectional view limited only in the off-axis plane. An azimuthal effect on the off-axis X-rays is not considered hereafter. Another condition required at the mirror exits, which is given by ri ≦ rt − 2h tan θ ≦ rs . Thus, the condition for rt can be summarized to   ri + 2h tan θ ≦ rt ≦ min (F + h) tan θ + rd , rs + 2h tan θ ,

(1)

which indicates that an allowable radial range for the direct component is quite narrow. Since 2h tan θ is small enough, the blocking of the mirror aperture only with a radial range of ≦ rs provides an effective reduction of the direct component. However, as already mentioned, the alignment of the blocking component is a challenge because nested mirror shells are always affected by alignment errors that make the alignment of a blocking shell a critical step.

Primary-Only Reflection Since the primary and secondary components cause the reflection on the mirror shell, the analytical calculation using the cross-sectional view is a little complicated. Compared with the nominal double reflection, the primary-only reflection is deviated at an angle of τ + (τ − θ ) = 2τ − θ by the single reflection on the primary shell. Note that the condition for the off-axis angle in which the reflection occurs on the primary shell is θ ≦ τ ; if the off-axis angle becomes larger than the tilt angle, the X-rays would come to hit first the frontside of the secondary shell. However, a stronger restriction for the off-axis angle is imposed by the condition that the X-ray reflected on the primary shell should not hit the secondary shell. Since this condition also depends on the hit position on the primary shell, we express here the restriction of the off-axis angle as 2τ − θ  3τ . This restriction of θ  −τ implies that the tilt direction of the primary-only reflection is opposite to that of the primary shell, as shown in Fig. 4a. The tightly nested mirrors seldom meet the condition because of the existence of the inner primary shell. To meet the condition that the reflected X-rays do not hit the

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backside surface of the inner primary shell, another restriction of θ ≧ −τ is required for the off-axis angle as shown in Fig. 5a. For the tightly nested mirrors, the tilt angle of the inner primary shell is almost the same as that of the currently considering primary shell. And then, the radius of the top of the inner primary shell is set to the same as that of the bottom of the primary shell to improve the aperture efficiency. Thus, the minimum off-axis angle for the primary-only reflection is realized when the X-rays are reflected on the middle of the primary shell. Figure 5a shows that τ = ∆r/ h using a small-angle approximation, where ∆r represents the difference in radii between the top and bottom of   shell. This panel also indicates  the primary that the angle of the reflected X-ray is 23 ∆r / h2 = 3 ∆r h = 3τ , which should equal to 2τ − θ . Thus, the minimum off-axis angle is calculated to θ = −τ . Therefore, the off-axis angle for the primary-only reflection is allowable just around −τ . We also show the case of θ > −τ where the reflected X-ray does not hit the secondary shell in Fig. 5a. In summary, the primary-only reflection occurs only at a quite limited radial range of the primary shells for the tightly nested mirrors, except for the innermost primary shell. A correlation plot between the radial coordinates on the mirror aperture and the detector plane is useful to visualize the contribution of the stray-light components and their X-ray paths inside the X-ray mirror. Figures 6 and 7 show the correlation plots obtained from the ray-tracing simulations of the Suzaku XRTs (Shibata et al. 2003). Model lines described below are also indicated in this figure. Here, two segments of the X-ray mirror were considered so that the cross-sectional treatment was applicable. The off-axis angles were set to θ = ±30′ . To make the plot clear, we increased the flux of the stray light by assuming the X-ray energy of 1.49 keV, aluminum Kα X-rays, since we measured the reflectivity and the reflected beam profile at 1.49 keV for aluminum substrates used in the Suzaku XRTs. The direction

Fig. 5 (a) Supplemental drawing of the primary-only reflection in a tightly nested mirror. An offaxis X-ray is hit at the middle of a primary shell. Then, the reflected X-ray passes just behind the inner secondary shell. A blue line shows the case of the primary-only reflection with θ > −τ . (b) Same as (a), except for the secondary-only reflection

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Fig. 6 Correlation plots between the radial coordinates of the mirror aperture and the focal plane for X-ray photons with an off-axis angle of θ = −30′ . The results of the ray-tracing simulations

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of the reflected X-ray was slightly deviated from that of the specular reflection because of the X-ray scattering incorporated into the ray-tracing simulation, which results in the line spread (see the lower panels of Figs. 6 and 7). Moreover, the lines corresponding to multiple reflection, which includes the backside reflection on the inner shells, were removed in the simulation results since the multiple reflection rarely happens in reality. We also run other simulations under the condition that the reflectivity of both frontside and backside surfaces is unity and that only the specular reflection occurs. The results are shown in the upper panels of Figs. 6 and 7, which represent the model lines. The correlation plots clearly show linear relations between the radial coordinates on the mirror aperture and the detector plane although the real relations have scattering to some extent. We note that the nominal double reflection shows a horizontal line regardless of the radial coordinates of the incoming X-rays, according to the principle of the Wolter-I optics. The radial coordinate in the detector plane is F tan θ , if θ is small enough. The labels appended to the model lines represent a tracking path which shows the reflections on the mirror shells. The primary-only reflection corresponds to the label of “1,” implying that the contribution to the stray light in the detector field of view was quite small. In the case of the Suzaku XRTs, the primary-only reflection occurred at the radial coordinates on the mirror aperture of ∼60 mm, consistent with the above statement. There were two other paths of the stray light similar to the primary-only reflection that contaminates the detector field of view. However, these paths include the backside reflection which decreases the flux contribution. Indeed, the corresponding lines were dim in the correlation plots derived from the simulation. We can derive an analytical expression of the relation as described below. According to the sketch shown in Fig. 5a, the radial coordinate on the detector plane (rd ) is calculated by the geometrical optics as follows: rd = rt − (h − l) × tan θ − (F + l) × tan(2τ − θ ). Here, l is a distance from the top of the primary shell to the hit position, which is measured along the optical axis. Since l ≪ F and h ≪ F , the above equation can be reduced to

rd = rt − F tan(2τ − θ ).

(2)

◭ Fig. 6 (continued) for the Suzaku XRT are indicated in the upper panel. Hatched areas show the detector field of view (a width of 25.4 mm). The reflectivity of the frontside and backside surfaces of the mirror shells is set to unity. And then, no scattering of the reflected X-rays is assumed. Model lines estimated from the geometrical calculation are superposed with dashed lines. Labels of the lines represent the X-ray paths, where “1” and “2” represent the reflection on the primary and secondary shells, respectively. A suffix of “B” means the backside reflection. The reflectivity and the reflected beam profile at 1.49 keV measured for the mirrors and the aluminum substrates are used in the lower panel (This figure is adapted from Shibata et al. 2003)

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Fig. 7 Same as Fig. 6, except for a given off-axis angle of θ = +30′

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We already conjectured that the relation of the radial coordinates is expressed by a linear function. Using the addition theorem of tangent and the small-angle approximation of tan 2τ tan θ ≃ 0, we can further reduce it to a simple relation given by rd = rt − F tan 2τ + F tan θ . To evaluate a term of rt − F tan 2τ , let us consider the focusing condition of the nominal double reflection: rf = F tan 4τ . Since rt − rf = h tan θ ≃ 0, we can replace the condition with rt = F tan 4τ . Because 2τ is small angle, F tan 2τ can be also reduced to 2F τ = 21 4F τ ≃ 12 rt . Finally, substituting it to the term of rt − F tan 2τ , we can derive the simple expression of the relation as follows: rd = 0.5rt + F tan θ.

(3)

We again note that the sign of θ is negative, different from that for the secondaryonly and backside reflections.

Secondary-Only Reflection The secondary component is deviated at an angle of 3τ + (3τ − θ ) = 6τ − θ by the reflection on the secondary shell. For the tightly nested mirrors, while offaxis X-rays with θ < τ hit the frontside surface of the primary shell before the reflection on the secondary shell, those with θ > 2τ hit the backside surface of the inner primary shell. Hence, an angle condition for the secondary shells where the secondary component occurs is given by τ < θ < 2τ (see also Fig. 4b). The condition implies that the secondary component also occurs in a limited radial range of the mirror aperture, depending on a given off-axis angle. The condition for the tilt angle also tells us that the secondary component is bent by 4τ –5τ , larger than the bending angle for the nominal double reflection (4τ ). It indicates that the radial coordinates on the mirror aperture and the detector plane of the secondary component are in the opposite directions against the optical axis. Hence, for a given off-axis angle θ , the secondary component appears on only one side of the detector plane. The relation between the radial coordinates on the mirror aperture and the detector plane for the secondary component is shown in Fig. 7. This figure indicates that the area on the mirror aperture where the secondary component occurs is on the opposite side of that for the primary component. Similarly, the relation for the secondary component can be derived. The radial coordinate on the detector plane is given by rd = rt − (h + l) × tan θ − (F − l) × tan(6τ − θ ), as is shown in Fig. 5b. The relation can be reduced to rd = rt − F tan(6τ − θ ),

(4)

by using the approximation of h ≪ F and l ≪ F . We can expand F tan(6τ − θ ) to F tan 6τ − F tan θ . By using the small-angle approximation, the term of F tan 6τ is reduced to 6F τ = 23 4F τ ≃ 32 rt . Therefore, we obtain the relation for the secondary component as follows:

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rd = −0.5rt + F tan θ.

(5)

This expression is a powerful tool for the collimator design in which the secondary component should be blocked. The reduced relations for the primary and secondary components are indicated in the upper panels of Figs. 6 and 7, designated as “primary line” and “secondary line,” respectively. The result of the ray-tracing simulations is consistent with the relations. Since the reflectivity of the backside surface is low, some lines which correspond to the paths of multiple reflection are dim or eliminated. However, the relations allow us to perform a simple geometrical calculation for the collimator design. We note again that the secondary component is the main contribution to the stray light on the detector plane. Since the reflection occurs only once in the mirror, the flux of the secondary component is still large even for soft X-rays. If the incident angle to the secondary shell of 3τ − θ exceeds a critical angle of the reflective material, the contribution becomes rapidly decreased. Hence, the X-ray spectrum of the stray light no longer keeps information on the correct energy spectrum of the source. For the Suzaku XRTs, the effective area of the secondary component is ∼1/100 of the on-axis effective area. Figure 8 shows an angular dependence of the effective areas of the secondary component. One remarkable feature is that the flux of the secondary component is almost independent of the off-axis angle. As the off-axis angle is large, the radial coordinates of the secondary component on the mirror aperture become large, leading to the increase in the tilt angles of the secondary shells. Hence, the incident angle on the secondary shell does not change significantly, which causes slow decrease in the flux of the secondary component. At an off-axis angle of >70′ , the secondary component disappears since there are no primary shells that meet the angle condition (τ > θ/2). A similar trend is shown in the ray-tracing simulations for the eROSITA telescope (see Fig. 9), implying that the fraction of the effective area for the stray light is a common feature of the Wolter-I type optics.

Backside Reflection The backside component is a bit complicated to an analytical treatment. The first hit point is the backside surface of the primary shell. Because of a rough surface of the shell substrates, the reflected X-rays are widely scattered; a large scattering angle makes it difficult to predict the precise direction after the backside reflection. As the number of the backside reflections increases, the probability that the incident X-rays survive without absorption in the mirror becomes quite small. Multiple reflection components including the backside reflection can be found by the raytracing simulation (see Figs. 6 and 7). However, their actual contribution to the stray-light image is negligible so that we focus on here the backside component that causes the backside reflection only once. The dominant X-ray path of the backside component is (1) backside reflection on the substrate of the primary shell → frontside reflection on the primary shell → frontside reflection on the secondary shell or (2) backside reflection on the substrate of the primary shell → frontside reflection on the secondary shell (see Fig. 4c). We

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Fig. 8 Angular dependence of the effective areas of the secondary component. Red-filled circles are the effective areas measured at off-axis angles of 20′ , 30′ , 45′ , and 60′ for the Suzaku XRT before the pre-collimator’s installation. Those measured after the installation are shown by redfilled triangles. The effective areas at 1.49 (red), 4.51 (green), and 8.04 (blue) keV obtained from the ray-tracing simulations are also superposed with dashed and solid curves (This figure is adapted from Mori et al. 2005)

note that, for the second path, the incident angle to the secondary shell amounts to ∼3τ , implying that the reflection probability is relatively small. In addition, if the X-ray is reflected on the secondary shell, the bending angle of the reflected X-ray becomes ∼6τ . Thus, a part of the reflected X-rays are possibly hit on the backside surface of the inner secondary shell although it depends on the hit position of the frontside surface of the secondary shell. For the first X-ray path, we also note that the frontside reflection on the primary shell followed by the backside reflection plays a role of cancelling the reflection. A tilt angle of a primary shell and a tilt angle of its inner one are almost the same, implying that the incident and reflection angles on the backside and frontside surfaces of these two primary shells are all θ − τ . The deviation angle is then (θ − τ ) + τ = θ at the bottom of the primary shell. Hence, this backside component can be considered to be similar to the secondary component. Thus, the reflected X-rays are deviated at an angle of 6τ − θ . This is indeed indicated in Fig. 7, which represents that both the secondary component and the first path of the backside component are on the same line. The angle condition of the backside component which follows the first X-ray path is given by 2τ < θ < 3τ under the assumption that the scatter by the

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Fig. 9 Ray-tracing simulations for the eROSITA telescope, single reflection rejection of the X-ray baffle (for mirrors without profile error or roughness)

backside reflection is negligible. The condition is determined by the requirement that both the backside and the frontside reflections occur on the primary shell. The survived X-rays which escape from the mirror without absorption have a bending angle of 3τ –4τ calculated directly from the deviation angle of 6τ − θ and the angle condition of 2τ < θ < 3τ . Therefore, the stray-light image of the backside component appears on the opposite side of that for the secondary component (see also Fig. 2). Different from the primary and secondary components, the condition described above in which the backside component occurs is not exact. Since the X-ray scattering on the backside surface makes the direction of the reflected X-rays spread, there may be the cases where the shells that do not meet the condition contribute to the stray-light image on the detector plane. Therefore, the aperture area which brings about the backside component is larger than that for the secondary component. From the reflectivity viewpoint, the flux of the backside component created from a given shell is small. Moreover, the reflectivity of the backside reflection has a strong energy dependence. The backside component rapidly disappears above ∼2 keV, which is indicated in Fig. 2 by the difference in the surface brightnesses. However, the large aperture area accumulates the backside component which makes non-negligible contribution to the stray-light image. We note that effective methods to block the backside component have not been developed so far. One reason is a

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technical difficulty in blocking the X-ray path of the backside reflection without affecting the X-ray focusing performance. Because of the large scattering, there seems to be no simple structure to block the backside-reflected X-rays efficiently. The modelling of the X-ray scattering is another difficult issue. So far, many theoretical treatments of the X-ray scattering have been developed: the models invoking a plane-wave Born approximation (Sinha et al. 1988) or bidirectional reflectivity distribution function (Kunieda et al. 1986). However, the surface condition of the shell substrate usually does not meet the requirements for which these theoretical models can be applied. For example, the roughness of the backside surface for the aluminum thin foils, which were used for the Suzaku X-ray mirror, was an order of micrometers (σ = 1–2 µm), much larger than that of the frontside surface (σ = 4 Å). The rough surface of the aluminum foils was created by rolling an aluminum plate, which makes a thin sheet with a thickness of 150 µm. Thus, the roughness had a dependence of the rolling direction. Since the surface condition of the substrates used for the X-ray mirror shells is different from mission to mission, it is almost impossible to establish a unified X-ray scattering model that can be applied to the backside reflection. One method we can mitigate the backside component is that we should select substrates with the X-ray reflectivity as low as possible. In order to the future precise prediction of the backside component, the X-ray scattering theory applied to micrometer-scale surfaces should be examined as well.

Advanced Analytical Treatment The treatment of the stay-light components described above is a simple one where we employed a geometrical optical calculation for a cross section of the X-ray mirror only in the off-axis plane. In addition, we assumed the conical approximation of the Wolter-I type optics and used several approximations to simplify the analytical treatment. In reality, however, the stray X-ray light has an azimuthal dependence. Thus, we usually use a ray-tracing simulator to investigate the stray light for a given optics. Recently, Spiga (2016) developed analytical formalism for the effective areas of the nominal double reflection, the primary component, and the secondary component (see also Spiga 2015). A vignetting coefficient was introduced to take into account the geometrical area of the mirror shells responsible for each component, which gives us a unified treatment for off-axis X-rays. The effective area was easily calculated by performing an integral in the formalism. Although the integrand in the formalism includes reflectivity terms, a numerical integration can be performed to obtain the effective area. Here, we would emphasize that the required resource for the numerical integration is much smaller than that for the ray-tracing simulations. Spiga (2016) also carried out the comparison between the analytical calculation and the ray-tracing results; the ray-tracing simulation was well reproduced by the calculation. In other words, this analytical treatment makes a good estimation of the effective areas for the primary and secondary components without writing a complicated ray-tracing code. Hence, it has the advantage of enabling a quick assessment of the stray light for a given Wolter-I type optics.

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Design of the Stray-Light Baffle As already mentioned, the secondary component is a main source of the straylight image contaminated in the detector field of view. We now discuss a collimator design that focuses on the blocking of the secondary component only. The effective area of the secondary component is about two orders of magnitudes smaller than the on-axis effective area. The secondary component creates a part of a distorted radial pattern on the detector plane. The X-ray path of the secondary component is simple; the incident X-rays go through above the top of the primary shell when entering into the X-ray mirror (see again Fig. 4b). Thus, a structure aligned onto each primary shell can easily block the secondary component. At least, the structure is required not to affect the on-axis X-rays. The simple structure for the reduction of the secondary component is a thin cylindrical shell that is radially aligned with the corresponding primary shell. If the thickness of the cylindrical shell is smaller than that of the primary shell, the on-axis effective area and angular resolution are unaffected. The next problem is what the optimized design parameters for the structure should be to maximize the performance of the X-ray collimator, without degrading the one of the X-ray optics. Hence, the key parameters are the height and thickness of the cylindrical shell. We designate the cylindrical shell as a blade hereafter. Let us consider an X-ray with an off-axis angle of θ and some pairs of the primary and secondary shells inside the X-ray mirror. Similar to the previous subsections, we represent the tilt angle of the primary shell by τ . The angle condition of τ < θ < 2τ for the secondary component indicates that the primary shells with a range of the tilt angle of θ/2–θ contribute to this component. Thus, as is indicated in Fig. 10, a higher blade is required for the outer shell to block the X-ray path of the secondary component. Since the primary shell with a tilt angle of θ is parallel to the incident X-rays, the solid angle subtended to the secondary-shell surface becomes maximum. In other words, the maximum height for a given off-axis angle of θ can be calculated from the case of the primary shell with the tilt angle of θ . We can calculate the blade height, H , required to block this X-ray path completely as below. Again, we define the focal length of the X-ray mirror to be F . The height of the mirror shell is represented by h. We assume here that the radius of the frontside surface of the blade is the same as that of the primary shell, i.e., rp . The case of τ = θ in Fig. 10 shows that the requirement for the blade height is given by rp − (H + h) tan θ ≤ rb ,

(6)

where rb represents the radius of the bottom of the backside surface of the inner primary shell (rb < rp ). This equation can be reduced to H ≥

rp − rb − h. tan θ

(7)

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Fig. 10 Schematic drawing of the blade heights to block the secondary component at an off-axis angle of θ. The larger the tilt angle of the mirror shell becomes, the higher the blade is required (This figure is adapted from Mori et al. 2005)

We then estimate the maximum gap of rp − rb . As is noted in the previous subsection, only a part of the stray-light image created by the secondary component contaminates the detector field of view. The relation between the radial coordinate on the detector plane (rd ) and rt is given by rd = −0.5rt +F tan θ . Hence, if we assume the half size of the detector field of view to be R, only the shells within a radial range between rp,min and rp,min + 2R contribute to the stray-light contamination in the detector field of view. The secondary component occurred at the primary shell with a tilt angle of τ = θ/2 reaches at the center of the detector field of view. Thus, rp,min ∼ F tan 4τ = F tan 2θ . Using a smallangle approximation, the relation can be reduced to rp,min = 2F θ . The maximum radius of the primary shell is thus estimated to be rp,max = 2F θ + 2R. Considering that rp ∼ F tan 4τ = 4F τ , the tilt angle of this primary shell (τmax ) is given by R . We can approximate the gap of rp − rb as 2h tan τ ≃ 2hτ . Thus, τmax = θ2 + 2F the maximum gap is given by 2hτmax = hθ + hR F . Then, the maximum height of the blade can be obtained from

Hmax =

hθ + hR F −h tan θ

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Fig. 11 Radial dependence of the blade height required to block the secondary component. The curve is calculated based on the design of the Suzaku XRTs. Distributions of the blade heights are also indicated by vertical lines. The off-axis angles of the secondary component are assumed to be 20′ , 30′ , 40′ , 50′ , and 60′ . The constant blade height of 30 mm actually adopted for the Suzaku pre-collimator is shown with a dashed line (This figure is adapted from Mori et al. 2005)

≃

hR , Fθ

(8)

where we use a small-angle approximation of tan θ to derive the second equation. This result indicates that the required height can be easily estimated from the basic parameters only. An ideal curve required for the blade heights is an envelope of the maximum heights obtained by changing the off-axis angle θ . Figure 11 shows an example of the calculation carried out for the pre-collimator design for the Suzaku XRTs. Since the maximum height of the blade is proportional to 1/ tan θ and the angle condition of the secondary component is given by τ < θ < τmax , the height of the inner blade becomes larger than that of the outer blade. We note that a radial dependence of the required blade height makes an issue of the mass production of the blades, especially for the thin-nested foil mirrors. The mount of the X-ray collimator on the mirror entrance makes the field of view of the X-ray mirror narrower. Here, the field of view of the mirror is normally defined by the full-width half maximum of the vignetting function of the X-ray optics: the angular response of the effective area. We should determine the optimum design of the X-ray collimator in terms of the reduction rate of the stray light, the field of view of the X-ray mirror, the production, and the structure with enough

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mechanical strength that stands for the launch environment. We show an example of the trade-off study between the stray light and the mirror’s field of view in the section of the Suzaku’s pre-collimator. Another attention induced by the collimator’s mount is that the collimator itself becomes a cause of the stray light. New X-ray paths in which the reflection occurs on the blades in turn become a cause of stray light. If the blade surface is rough, similar to that of the backside surface of the mirror shells, the stray light created by the blade is probably mitigated. However, it is difficult to measure accurately the contribution of the stray light created by the X-ray collimator. For the Suzaku XRTs, the pre-collimator’s blades had line-like marks made by the rolling. To make the X-ray reflectivity as low as possible and to spread the X-ray scattering angles, the marks were arranged normal to the direction of incident X-rays. Similar to the backside reflection, the understanding of the X-ray reflection on rough surfaces is necessary for the suppression of the stray light newly added by the mount of the X-ray collimator.

XMM-Newton The XMM-Newton spaceborne X-ray observatory, an ESA cornerstone mission, was launched in December 1999 and is still operational after 22 years. It consists of three telescopes with identical 7.5 m focal length Wolter optics (Aschenbach et al. 2000; Burger et al. 2000). While the optical and mechanical design of the XMM mirror modules was already fixed in 1995 and demonstration models were built and tested, the X-ray baffle was still under design (de Chambure et al. 1996), since it had been recognized that single reflections from one or more of the hyperboloid surfaces would introduce a high level of confusing stray flux in the field of view of the detectors, created by Xray sources close to, but outside, the field of view from a cone angle of 15 arcmin (de Chambure et al. 1999a). An early conception provided an almost perfect X-ray baffle consisting of a set of cylinders, one for each mirror shell, placed in the shadow zones in front of the mirror shells (see Fig. 12) and each with an individually optimized height (Aschenbach et al. 2000). This, however, was given up because a realization seemed not feasible. de Chambure et al. (1999b) give a detailed description of the design and development of the XMM-Newton X-ray baffle and the following passage, which describes the design trade-offs, quoting his paper: “The only rays, which come to the sensitive area of the focal plane are rays, which can be blocked by an annular concentric cylinder in front of every mirror shell.” Their principle of elimination of singly hyperboloid reflected rays is sketched in Fig. 13. The cylinders have individual lengths between 25 and 160 mm according to the field of view of the associated mirror shell. The baffle cylinders had to be equipped with light traps to prevent additional stray light from their large surfaces. For this purpose, the cylinders should be divided into a stack of “sieve plates,” which both allows a smaller wall thickness than that of the mirror shells and minimizes the areas where

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Fig. 12 Functionality of an X-ray baffle: the single reflections (red) should be blocked, while the double reflections (green) should all pass; an effective way to cut away the single reflections is blades (gray) on top of each mirror shell (yellow); the light gray areas between the mirror shells can be potentially also used for a baffle

light could be scattered toward the mirrors. The tapered edges of the cylindrical rings further reduce the stray light. Due to the limited space in front of the mirror module, which is partly occupied by the “spider” that holds the mirror shells, finally a system of only two sieve plates was adopted. This system cannot fully eliminate the single reflections, but it is able to reduce them by a factor of 5 to 10 depending on the location on the detector. According to de Chambure et al. (1996, 1999a,b), the precise manufacturing of the finely structured sieve plates with 59 × 16 tiny strips was a challenge. It was finally achieved by using wire electrical discharge (WED) machining to cut out material from a massive Invar plate, which, however, led to machining times of 400 to 500 h for each of the two sieve plates. As the final metrology with a coordinate measuring machine (CMM) revealed, the WED technique allowed to limit average radial error to about 25 µm. The requirement on the accuracy of the radial position of the edges of the vane strips of the sieves with respect to the position of the mirrors was to be better than 100 µm, including manufacturing, assembly and integration errors, and displacement due to thermal conditions. As a consequence, the co-centering of all mirror shells (better than 50 µm) became more stringent. To avoid optical stray light from the X-ray baffle directly in front of the optic, the lateral surfaces of the strips were chamfered by 5◦ , and the edges of the strips were made very sharp (radius smaller than 20 µm). All the baffle surfaces (including the edges of the vane strips) facing the mirrors were blackened. The accurate positioning of the X-ray baffle with respect to the optic was achieved by taking both the optic’s and the X-ray baffle’s centers as references, which are defined by two reference points on the mirror module structure and by two

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Fig. 13 Sketch of the opto-mechanical principle of the XMM-Newton X-ray baffle (after de Chambure et al. 1999a): X-rays are coming from the top progressing to the focal plane. Ray #2 is reflected slightly before the end of the hyperboloid is reached and travels to the focus of the telescope. Ray #1 has an inclination against the optical axis which is lower by the radius of the field of view (δε ) and to the edge of the field of view in the focal plane. Any singly hyperboloid reflected ray to be blocked is contained in the bundle bounded by the angles ε0 and εi

reference points on the X-ray baffle structure, respectively. These reference points were used to perform the corresponding alignment of the both parts (de Chambure et al. 1999b). Figure 14 shows the sieve plate baffles mounted in front of the three XMM-Newton mirror modules. The performance verification for all f ive mirror modules (three FM, two FS) was done at the Centre Spatial de Liége (CSL) in Belgium using a parallel EUV beam. The testing included a verification that the imaging performance in terms of on-axis point spread function (PSF) and on-axis effective area did not degrade after the mounting of the X-ray baffle. To demonstrate the stray-light rejection ability of the X-ray baffle, images for effective area measurements were taken from −80 arcmin off-axis to +80 arcmin off-axis in steps of 5 arcmin. In conclusion, the

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Fig. 14 The lower module of the XMM Flight Model during preparation for a 10-day thermal vacuum testing at ESTEC in January 1999; the X-ray baffles are mounted in front of all three X-ray optics (Photograph courtesy of ESA)

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Fig. 15 XMM-Newton data: bright point source (Sco X-1) outside field of view, 40 arcmin offaxis (left) and bright extended sources (Crab) outside field of view, 45 arcmin off-axis (right), data analyses by Michael Freyberg, MPE

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CSL tests confirmed that there was no on-axis performance degradation and that the stray-light rejection rate was 80%, which was close to the predictions. Figure 15 shows the remaining stray light from extremely bright sources, a point-like and an extended one, when they are slightly outside the field of view.

Suzaku and Hitomi Suzaku Pre-collimator Suzaku, the fifth Japanese-US collaborative mission, was equipped with a nested thin-foil X-ray mirror, called X-ray telescope (XRT) (Serlemitsos et al. 2007). The foils used in the X-ray mirror were produced by a replication technique; a reflective gold surface is replicated from a glass mandrel to a thin aluminum foil. Since the thickness of the aluminum foil is 180 µm, a lightweight X-ray optics with a large effective area was achieved. Since the problematic stray light was already recognized for the same nested thin-foil mirrors adopted in ASCA, a collimator to reduce the stray light, called pre-collimator, was planned to be mounted on the Suzaku’s X-ray mirror (see Fig. 16). The detail in the design of the pre-collimator, especially its height to determine the reduction efficiency, is already described. The basic structure of the precollimator is that a thin aluminum blade is arranged onto each mirror foil to block the stray-light path of the secondary-only reflection. As is explained above, the ideal distribution of the pre-collimator heights is proportional to 1/ tan θ , where θ is an off-axis angle of the stray light. However, the different heights of the blades caused a difficulty in the mass production of the blades by heat forming. Alternatively,

Fig. 16 Picture of a pre-collimator quadrant (This figure is adapted from Mori et al. 2005)

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we chose a constant height of the blades. After a trade-off study mentioned below between the field of view and the reduction efficiency by changing the blade height, we decided that the blade height should be 30 mm, roughly 1/3 of the X-ray mirror foil (4 inch = 101.6 mm). A blade with a height of h makes shadows on the mirror aperture for the X-rays with an off-axis angle of θ as is shown in Fig. 17. We first estimated the geometrical areas of the shadows created on the aperture in a radial range of rout –rin by a simple analytical calculation. Here, rin and rout represent the radii of the frontside surface of the top of the primary foil and the backside surface of the top of the inner primary foil, respectively. The blade makes two crescent-shape shadows (S1 , S2 ) on the opposite sides of  the mirror aperture. The angle of AO ′ O is given by  h tan θ/2 θ

AO ′ O = cos−1 ≃ π2 − h2rtan . Thus, the geometrical area of the shadow rout out (S1 ) is calculated by  2π − AOA′

AO ′ A′  − 2π 2π   ′ 2 AO O 2 1− = π rout π = hrout tan θ.

2 S1 = π rout

(9)

Similarly, another area (S2 ) is given by S2 = hrin tan θ . These results imply that the shadow area is radially dependent. While the analytical treatment to estimate the reduction rate of the field of view of the X-ray mirror was difficult, the ray-tracing

Fig. 17 Schematic drawing of shadows on a mirror aperture caused by the pre-collimator mount. Parameters used for the calculation of the geometrical areas (S1 , S2 ) of the shadows are also indicated

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Fig. 18 Trade-off study of the field of view and reduction rate of the secondary component by changing the blade heights

simulation was an easy way to obtain robust results. In addition, the simulation can also estimate the reduction rate of the effective areas of the secondary component in the ideal case of the pre-collimator mount. Thus, we prepared photon files in which incident photons do not go through the shadow area; we performed ray-tracing simulations using these photon files. One advantage of this method is that we do not need to construct the detailed structure of the pre-collimator. This method did not consider full interactions between the X-ray mirrors and the incident photons. However, the result was almost consistent with those by the full simulations, which verifies the method using the blade shadows. We show the relation between the reduction rates of the mirror’s field of view and the effective areas of the secondary component when changing the blade height in Fig. 18. As the blade height becomes large, the reduction rates of the field of view and the effective area increase. The relation shows that the curves have a kink at which the best performance for the X-ray optics is obtained. In the case of the Suzaku pre-collimator, the optimized blade height was 30 mm. If we choose the blade height of >30 mm, the reduction rate of the effective area changes a little. However, the mirror field of view rapidly decreases, which concludes that the height over 30 mm has little benefits. We note that there was a gap between the top of the primary foil and the bottom of the blade since both the foils and the blades were supported separately by structures explained later. Hence, we finally determined that the blade height and length were set to 30 and 22 mm, respectively.

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The blades are made of bare 1000-series aluminum with a thickness of 120 µm. The difference between the blades and foils is that the blades have no reflective coating such as gold, iridium, or multilayer and that the blades have a cylindrical shape. This is why we employed the same procedure for the mass production of the pre-collimator blades as that for the foils (Mori et al. 2005, 2012). Aluminum sheets are cut into a strip shape by electro-discharge machining (EDM) which enables us to obtain the precise height of 22.0 mm. A sparkle generated by the EDM creates tiny thorns with a few micrometers on the edge of the aluminum strip. Since the aluminum strips are stacked on a mandrel, the remaining thorns become a cause of figure errors. Thus, we removed the thorns by shaving the edges using a grinder. After the shaving, each aluminum strip is rolled to add a given curvature. The rolled strips are stacked on a mandrel. The mandrel is a precision-machined aluminum cylinder that has a smooth surface with a sub-micrometer roughness. The stacked strips are surrounded by a silicon sheet with a spacing of ∼1 mm. A Kapton film is attached on the top of the stacked strips and the silicon sheet. The aluminum mandrel has a hole connected to a pump to evacuate air remaining in the space. When the pump is turned on, the Kapton film presses the stacked strips onto the mandrel’s surface by atmospheric pressure. The mandrel with the strips pressed is placed in an oven and then is heated up to 160–180 ◦ C for ∼10 h, which releases internal stress induced by the rolling. This is a heat-forming method that is applied to the foil production. Using a laser profiler, the axial figures of the strips are measured to confirm that the figure errors are small enough for the blades to be inserted into grooves of a supporting structure. Since a length in the azimuthal direction is different for each blade, we cut the extra length of the corresponding strip by a cutter. To hold the blades with a cylindrical shape, we introduced an alignment plate as is shown in Fig. 19. The alignment plate had an open window with grooves carved in the top/bottom sides of the window. The grooves were made by the EDM at Ohishi Co., Ltd. The shape of the groove was a rectangle joined with a trapezoid that was designed for easy insertion. The width of the groove at its bottom was set to 140 µm, which is between the blade thickness and the foil thickness. Thus,

Fig. 19 Picture of an alignment plate used for the Suzaku pre-collimator (This figure is adapted from Mori et al. 2005)

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the accuracy of the radial position of each blade is mechanically limited to 20 µm in vicinity of the alignment plates. The relative uncertainty of the radial positions of the grooves was investigated by an NH series laser profiler, a three-dimensional measuring instrument produced by Mitaka Kohki Co., Ltd. The precise EDM cut for the grooves resulted in the relative uncertainty of 5 µm. Hence, the alignment plates enabled us to give a position determination of an order of ±10 µm, much smaller than an alignment margin of ∼30 µm. The width of the alignment plate was 1 mm, which was narrower than that of the alignment bars, which supported the foils, not to interfere with the mirror aperture. Another important issue of the pre-collimator design was that there was a gap between the primary foils and the pre-collimator blades since the X-ray mirror and pre-collimator were fabricated separately. Carrying out ray-tracing simulations for a trade-off study, we found that the gap should be less than 8 mm to block the stray light going through this gap. Since the blade height is 30 mm and the thicknesses of the foils and the blades are 180 and the stray light with an  120 µm, respectively,  incident angle of θ  64′ = tan−1 (0.18 + 0.12)/2/8 is hit on the top surface of the primary foils. The gap between the top of the primary foils and the top surface of the mirror housing was 5 mm. Hence, an allowable gap between the pre-collimator’s bottom surface and the bottom of the blades is 3 mm. However, the thickness of the bottom frame was designed to be 5 mm to maintain the mechanical strength of the pre-collimator housing. We then determined that the alignment plates were once lifted up by 2 mm for the blade insertion into the grooves and then returned to the original position.

Optical Tuning It was a tough challenge to mount the pre-collimator housing on the X-ray mirror so as to match each blade position to that of the corresponding primary foil. The alignment was a key issue not only to block the stray light as was expected but also not to reduce the on-axis effective area of the X-ray mirror. Since the blades were already inserted into the grooves of the alignment plates, an independent position alignment for each blade cannot be performed. We could only move the alignment plates in the radial direction to adjust the radial position of the whole blades. The alignment margin was ∼30 µm as described above. We performed a tuning of the alignment plates that maximizes the optical throughput. We first measured the optical throughput of the X-ray mirror before and after the pre-collimator mount. A parallel optical beam was illuminated to the mirror and then the throughput was measured by a photo sensor diode. After the pre-collimator mount, the optical throughput was decreased. Next, we placed a mask that limits the aperture only in vicinity of the alignment plate to be tuned. We measured the change of the limited optical throughput while moving the alignment plate radially with a step of several micrometers. The maximum throughput was obtained where the blade positions were best aligned with those of the primary foils. Because of the alignment margin, the profile of the optical throughput had

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a trapezoid-like shape; the position of the maximum throughput was obtained from the center of the flat top. We tuned the radial positions of all the alignment plates one by one in the same manner. Finally, we again measured the optical throughput and then confirmed that the throughput was recovered to that before the pre-collimator mount.

On-Ground and In-Orbit X-Ray Calibrations The X-ray performance of the pre-collimator was measured at the ISAS 30 m beamline facility (Kunieda et al. 1993; Shibata et al. 2001; Hayashi et al. 2014). The key characteristics related to the pre-collimator were the effective area of the stray light, the reduction rate of the on-axis effective area by the pre-collimator mount, and the field of view of the XRTs. The results are shown in the literature (Mori et al. 2005). The ISAS 30 m beamline facility can illuminate an X-ray beam with high parallelism of 15′′ × 15′′ . The X-ray mirror and the detector (a CCD camera or a proportional counter) were separately placed on two three-axis movable stages. These stages were moved synchronously, which enables us to illuminate the parallel X-ray beam to the 1/4 aperture of the X-ray mirror. We measured the stray-light images in the detector field of view (see Fig. 20) and effective areas of the straylight components (secondary-only and backside) by the proportional counter and then confirmed that the pre-collimator blocks the stray light as was expected (see red triangles in Fig. 8). While the stray light was effectively blocked, the on-axis effective area was reduced only by ∼0.5%, implying that the optical tuning method was successfully verified. The results of the in-orbit calibration of the Suzaku XRTs were summarized in Serlemitsos et al. (2007). The in-orbit calibration of the Suzaku pre-collimator was carried out for given off-axis and azimuthal angles because of the limitation of the observational times. The protection of the stray light allowed us to carry out many successful observations such as the galactic center and the outskirts of the cluster of galaxies (Simionescu et al. 2011). At the same time, we found that the reduction of the stray light has a dependence on a roll angle of the satellite. The detailed measurement of the roll-angle dependence is shown in the literature (Takei et al. 2012). This dependence would be caused by a slight difference in curvatures between the foils and the blades. Since the blades were supported by the alignment plates and the alignment plates were moved at the optical tuning, the blade curvature was not perfect compared with the ideal cylindrical design. Although the tuning was a tough problem, we consider that we did the best as much as possible to achieve the effective stray-light reduction for the tightly nested thin-foil mirrors.

Hitomi Pre-collimator Hitomi, the next Japanese-US collaborative mission after Suzaku, was also equipped with four nested thin-foil X-ray mirrors. Two of which were SXTs (Okajima et al.

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Fig. 20 Stray-light images at 20′ , 30′ , 45′ , and 60′ off-axis taken by an X-ray CCD camera installed in the ISAS 30 m beamline. The images were taken without (left panels) and with (right panels) the pre-collimator. A white circle indicates a field of view of a proportional counter by which the effective areas of the secondary component were measured (This figure is adapted from Mori et al. 2005)

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2016) and the others are hard X-ray telescopes (Awaki et al. 2014). The HXT employs the reflective coating of Pt/C multilayers that allows us to perform imaging spectroscopy up to 80 keV. The SXTs were similar to the Suzaku XRTs. The SXTs were provided to a microcalorimeter and an X-ray CCD camera. Since the field of view of the microcalorimeter was small, the stray light was negligible even for the secondaryonly reflection. The X-ray CCD camera had a wide field of view of 50′ × 50′ . Since the similar performance for the stray-light reduction was required to the SXT for the CCD camera, the blade height of the pre-collimator was designed to be 65 mm. For a given off-axis angle of θ , the maximum radius of the primary shell that creates the secondary component is given by 2F tan θ + 2R. Since the focal length of the SXT becomes 5.8 m, larger than that of the Suzaku XRTs, it implies that a radial range for the Hitomi SXTs to be considered for the stray-light reduction was larger than that for the Suzaku XRTs. The thicknesses of the SXT substrates were 150, 200, and 220 µm, dependent of the radial position of the foils. The thicker foils allowed us to mitigate the limitation of the gap between the blades and foils. Hence, we did not need to lower the alignment plate down against the bottom frame of the pre-collimator’s housing. In addition to the change of the design parameters, the supporting method of the blades was slightly changed; the blades were adhered to the grooves of the alignment plates since environmental conditions were severe. The design parameters of the HXT pre-collimator were as follows: the height was 50 mm, the length was 35 mm, and the thickness is 150 µm (Mori et al. 2010). The secondary component emerged at the off-axis angles of 10′ –30′ , according to the mirror design. The aluminum blade was transparent for the X-rays above 10 keV. We examined another material for the blade, SUS304 with a thickness of 50 µm. For the X-rays at 30 keV, the reduction rates of the secondary component were comparable to each other. The difference has occurred at 50 keV. A part of the secondary component with the off-axis angle of 20′ –30′ remained in the detector field of view. However, the reduction rate was still ∼10%, compared with that without the pre-collimator. In addition, the detection limit of the HXT + detector system was determined by the non-X-ray background. Hence, we chose the aluminum blade for the HXT pre-collimator. We also carried out the ray-tracing simulations of two types of scientific cases, the observations of the cosmic X-ray backgrounds (CXB) and the galactic center region, to demonstrate the improvement of the HXT performance. The stray-light contamination from the CXB was reduced to be from 33% to 8.7% by mounting the pre-collimator. The simulated images of the mapping observations of the galactic center also indicated that the stray-light flux was reduced by half in the source-free region. For the HXT pre-collimator, there were two major differences from the SXT pre-collimator. Instead of the alignment plate, we used the alignment bars which had grooves on the both sides for the primary foils and blades. The positional accuracy was determined by the machining accuracy of the EDM. Since the top of the blade is supported by another alignment bar, however, the optical tuning was still required to keep the blade configuration as a cylinder. Since the top and bottom of the blade were supported by two alignment bars, we need to insert the blades

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from the top view of the X-ray mirror, similar to the foil insertion. We note again that we performed the optical tuning of the radial position of the alignment bars in which the optical throughput becomes maximum. The X-ray calibration of the stray-light reduction was carried out at ISAS 30 m beamline facility for the SXTs and SPring-8 for the HXTs. The results showed that the stray light was reduced as expected (Sato et al. 2016; Iizuka et al. 2018; Mori et al. 2018). Unfortunately, since the Hitomi’s in-orbit operation was short, the inorbit performance of the stray-light reduction was not investigated.

eROSITA eROSITA (extended ROentgen Survey with an Imaging Telescope Array) is the primary instrument on the Spectrum-Roentgen-Gamma (SRG) mission, which was successfully launched on July 13, 2019, from the Baikonur Cosmodrome. After the commissioning of the instrument and a subsequent calibration and performance verification phase, an all-sky survey started in December 2019 and shall last until the end of 2023 to be followed by a pointing phase (Predehl et al. 2021). eROSITA’s X-ray telescope consists of 7 identical and co-aligned mirror modules, each with 54 nested Wolter-I mirror shells (Burwitz et al. 2014; Friedrich et al. 2012, 2008). An X-ray baffle in front of each mirror entrance protects against X-ray stray light from single reflections from the Wolter mirrors. Similar to XMM-Newton, the eROSITA X-ray baffle was developed not as part of the mirror module. It has been designed as a separate mechanical piece to be connected and aligned later to the mirror module with a minimum of mechanical and thermal coupling (Friedrich et al. 2014). The need for baffling the eROSITA optic is obvious: The instrument has a large field of view with 61 arcmin diameter, which results in a high grasp during the 4-year all-sky survey. Unlike in pointed observations, the off-axis source detections over the entire field of view contribute essentially to the sensitivity of the survey. However, single reflections, mainly from the hyperbola part of the Wolter mirrors, are frequent at larger off-axis angles. They come from X-ray sources outside the field of view and would contribute an additional background component or, in the case of bright sources, create false sources in the field of view. According to Fig. 4b that illustrates the “θ ≈ 2τ rule,” the single reflections for the eROSITA optic originate from off-axis sources within a range from about 40 to 180 arcmin. This has been confirmed by ray-tracing simulations, which give a more detailed and quantitative picture. The range of contributing off-axis sources shrinks for photons with energies >2 keV, because the reflectivity of an increasing number of mirror shells, starting with the outer ones, drops to zero with increasing photon energy. Ray-tracing has also revealed that there is a minor contribution from single reflections at the parabola part of the innermost mirror shells, which becomes visible already for X-ray sources at an off-axis angle of 20 arcmin so that the X-ray source and its single reflections are both in the field of view. In total, the amount of stray light caused by single reflections at lower energies (calculated for 1 keV)

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Fig. 21 Sketch of a single baffle shell

adds up to 40% of the twice reflected photons resulting in a correspondingly large background contribution, if no baffling would be foreseen. For 4 and 7 keV, the possible background contribution would be 43% and 35%, respectively. The eROSITA X-ray baffle needed a special design adapted to the optical parameters of the mirror module: The aperture ratio of up to 4.5 and the large field of view require that the baffling of single reflections has to happen close to the mirror shells; the baffle has to reach inside the envelope of the mirror spider (see Figs. 21 and 22). Therefore, different from XMM, the X-ray baffle could not be realized as a stack of sieve plates. Instead, a system of co-aligned “baffle shells,” one for each mirror shell, was chosen. Since the mirror diameters range from 77 to 358 mm, the incidence angles vary by a factor 4.7 from the outermost to the innermost mirror shell. As a consequence, the ideal height of the baffle shells also varies by that factor, while it was only a factor of 2.3 for XMM-Newton. Thus, for eROSITA it would have been far from optimum to choose a design with a constant height over the entire baffle, which also speaks against a sieve plate design. The comparison between the eROSITA and XMM-Newton mirror modules, with the latter ones being roughly a factor of 2 bigger in all dimensions, demonstrates that downsizing doesn’t make all things necessarily easier. As the eROSITA mirror thickness ranges from 0.2 to 0.55 mm, which is also about a factor of 2 less than for XMM-Newton, the shadow zone in front of the mirror shells (see Fig. 12) is extremely small and is also relatively short due to the large field of view. It became clear that a 100% rejection of stray light would only work at the price of cutting into the incoming beam. Vice versa, restricting the baffle to the shadow zone would

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Fig. 22 Mechanical design of the eROSITA mirror assembly (vertical cut)

make the stray-light rejection inefficient. Therefore, there was a trade-off between efficient stray-light suppression and an unblocked path for the focused light. Finally, a design was chosen which can reduce the stray light by 95% at 1 keV while the impact on the off-axis area is acceptably low. This design restricts the length of the baffle shells to 60 mm for the outermost shell and 120 mm for the innermost shell resulting in the conical shape of its envelope (Friedrich et al. 2014). Actually, this design corresponds widely to the early baffle concept for XMM-Newton, except that the eROSITA X-ray baffle is not designed for 100% rejection of single reflections as an outcome of the above described trade-off. While the optical design of the X-ray baffle was almost fixed, the question arose how the manufacturing could be realized and which material would be the best choice. Several materials were considered in the beginning, e.g., electroformed nickel, CFRP, eroded aluminum, and Invar. Selection criteria were mass, thermal expansion (the baffle frontside sees the cold space and the rear side the warm mirrors), and manufacturing accuracy. After some prototyping, the decision was in favor of a mechanical design based on concentric Invar foils fixed by an own spider. The thickness of these foils should be on the one hand as low as possible for optical reasons, but on the other hand, mechanical stability could not be neglected. A thickness of 125 µm, which is still less than the thickness of the thinnest mirror shells, turned eventually out to be the best choice, although Invar foils with such thickness were not the lightest option; but they fulfill the other criteria very well. The place of the baffle spider was chosen to be at the entrance aperture because there the exact positions of the baffle shells are most important. Ray-tracing simulations showed that deformations of the baffle rings could be accepted up to ±100 µm when the minimum stray-light suppression factor of 90% is considered acceptable. To avoid mechanical stress in the mirror module, the X-ray baffle is attached to it with 16 “soft” triangular-shaped thermal spacers (see Fig. 23). A major development phase was needed to bring the Invar foils into a precise concentric shape within the allowed tolerances. A material with constant thickness and no other inhomogeneities is an indispensable requirement for the later bending

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Fig. 23 X-ray baffle, top and bottom view (left), and mirror assembly with X-ray baffle on top (right)

Fig. 24 Laser cut Invar foils (left) and welded foil on cylinder (right)

process. The manufacturing process was as follows: The Invar foils were first laser cut (see Fig. 24, left) and then bent by moving them between two rollers: a big one covered with a precisely constant radius-shaped rubber layer and a small one made from steel. The bending radius was controlled by adjusting the pressure of the steel roller onto the soft roller. Actually, two soft rollers with different rubber hardness and three steel rollers with different diameters were used in combination in order to achieve good results for the wide range of radii. The bent foils were fixed on aluminum cylinders with the precise diameter of the corresponding baffle shell and were checked for defects and curvature errors, in particular at the free-standing parts between the cutouts (see Fig. 21). Finally, the foils were welded while fixed on the aluminum cylinder (see Fig. 24, right).

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Fig. 25 Sequence of baffle shell integration, from left to right: inserting a baffle shell on cylinder into the grooves of the spider wheel, gluing and curing for 20 h, removing the cylinder, and measuring the surface with contactless distance sensors

The integration of the baffle shells into the spider was accomplished on an integration stand, which allowed the precisely concentric placement of the shells, the injection of glue into the spider grooves, and final metrology with a contactless optical distance sensor (plus reference sensor) resulting in a roundness map of the just integrated shell. The sequence is pictured in Fig. 25. The curing time of the glue triggered a scheme with one shell integrated per day; the in total eight X-ray baffles for eROSITA were manufactured on two integration stands in parallel. The analyses of the roundness mapping resulted in predicted single reflection efficiencies between 90.6% and 92.1%, while the average loss of on-axis effective area was calculated to 2.4%. Mounting and Alignment: Due to the “soft” mounting interface of the baffle, the unification of mirror module and X-ray baffle required an alignment procedure, in which the baffle could be adjusted in all degrees of freedom. A dedicated assembly and alignment stand (Fig. 26) had been built to mount each X-ray baffle to its mirror module. The granite base was adjusted horizontally with an accuracy of a few arc seconds. After the mirror module and the X-ray baffle were fixed on their platforms, a three-step alignment procedure started: 1. Visual pre-alignment in all degrees of freedom 2. Vertical alignment of mirror module and X-ray baffle with autocollimation on reference mirrors 3. Iterative fine adjustment with fine thread screws under optical monitoring with a telecentric lens and a high-resolution camera The telecentric lens allows a straight view onto the baffle and the mirror shells over its entire field of view. With its image scale of 1 : 10, the edges of the baffle rings appeared with a width of 12.5 µm in the camera corresponding to 7.5 pixels. The edges of the mirror shells appeared accordingly wider. An adjustable diffuse illumination from the top of the alignment stand and a ring of bright LEDs on top of the telecentric lens ensured enough brightness and contrast to distinguish the edges of mirror shells and baffle rings, thus giving a criterion for the correct lateral position of the baffle with respect to the mirror module. A lateral alignment accuracy

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Fig. 26 eROSITA mirror assembly in the baffle mounting and alignment stand (left) and image obtained with the optical monitoring system (right)

Fig. 27 Results from X-ray tests (eROSITA FM1) before and after the X-ray baffle was mounted: comparison of measured and simulated single reflection rate as a function of the off-axis angle (left), measurements at ±90 arcmin, where the inner circle of the PSPC detector corresponds to the eROSITA field of view, data analysis by Gisela Hartner, MPE

of 20 µm had been achieved. When the iterative alignment process was successfully completed, the X-ray baffle was glued to the mirror module with the 16 thermal spacers. The eROSITA FM1 mirror assembly served as a proto-flight model and was tested in much more detail than the following FMs. So, after the baffle mounting, the FM1 mirror assembly was X-ray tested in MPE’s Panter facility to study the efficiency of the baffle and its impact on the imaging performance. Figure 27, left, shows the results of single reflection measurements outside the field of view up to ±200 arcmin and the corresponding predictions for a perfect X-ray baffle. Figure 27,

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right, shows an example of stray-light suppression in the field of view (the inner circle) for a single off-axis angle. In addition, scans to characterize the off-axis PSF performance and to measure the vignetting curves at various photon energies were performed. As expected, the vignetting curves steepened a bit, because the X-ray baffle cuts a small fraction of off-axis rays.

Future Missions XRISM (Tashiro et al. 2020), the recovery mission of ASTRO-H, was equipped with two X-ray mirrors (Okajima et al. 2020) for an X-ray microcalorimeter (Resolve) and an X-ray CCD camera (Xtend). Each XMA has a pre-collimator similar to that of the ASTRO-H SXTs. However, to reduce the stray light with primary-only reflection, “No. 0” primary foil and “No. 0” blade are introduced for the X-ray mirror and pre-collimator, respectively. The “No. 0” primary foil is made by a bare aluminum sheet without a gold reflective surface to avoid X-ray reflection. The gap between the innermost radius of the aperture of the mirror housing and the inner radius of the bottom of the #1 primary foil is large enough for the direct and primary components to go though the inside of the mirror. By introducing the “No. 0” foil and blade, the contribution of the stray light can be reduced, compared with that for the SXT pre-collimator. The FORCE mission (Mori et al. 2016), a planned US-Japanese collaborative mission, aims to elucidate the nonthermal picture of the Universe by the X-ray telescopes covering a wide energy band of 0.5–80 keV. The foil production technique for this X-ray mirror has been extensively investigated to achieve the angular resolution below 15′′ even for the multilayer-coated silicon substrates (Zhang et al. 2019). One of the scientific goals of the FORCE mission is to resolve the cosmic X-ray background into discrete sources at 30 keV. Hence, the stray-light contamination should be reduced as much as possible. An X-ray pre-collimator, similar to those on board Suzaku, Hitomi, and XRISM, is planned to be installed. Athena, the fifth ESA M-class mission, is equipped with an X-ray mirror in which an X-ray silicon pore optics (SPO) is adopted (Bavdaz et al. 2021). The X-ray baffle or collimator that has been used so far has difficulty in mounting the silicon pore optics since the housing structure of the X-ray mirror is quite different from the traditional one. In addition, the alignment of the collimator to reduce the stray light is also severe because of the tight nesting of the silicon mirrors. Regardless of these difficulties, the Athena collaborators are investigating feasibility of a lightweight stray-light baffle (in private communication; see Fig. 28). They consider a meshtype collimator; many stainless-steel meshes with a width of 50 µm and a thickness of 0.7 mm are stacked on the primary structure of the SPO. It is not necessary that cylindrical blades are used to block the paths of the stray light. The mesh-type collimator is developed in terms of the easy production by a chemical etching and achievement of the lightweight module. To increase the structural stiffness, a thin glass spacer is inserted between two meshes. The production trial of the 14-stage stacked BBM is still ongoing.

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Fig. 28 Picture of a glass mesh (left) for a lightweight stray-light baffle and zoomed one taken from an angle (right), by courtesy of Dr. Yoshitomo Maeda and Japanese development team

Conclusion An X-ray collimator is mounted on an X-ray mirror to maintain its expected performance in the viewpoint of the thermal control and the stray-light reduction. The stray light often creates a spatially extended ghost image in the detector field of view, and then affects the observations as X-ray backgrounds. The stray light is mainly caused by off-axis X-rays that go through a single reflection in the Wolter-I type X-ray mirror, different from the nominal double reflection for on-axis X-rays. The stray light that occurs by the reflection on the backside surface of the X-ray mirror shells is also non-negligible. Hence, the X-ray background from the stray light shows an energy dependence that makes it difficult to be removed properly in the X-ray analysis. The single reflection on the secondary (hyperboloid) mirrors is a main contributor of the stray light in the detector field of view. Thus, a collimator, consisting of structures placed on the primary (paraboloid) mirrors to block this single-reflection path, is an effective countermeasure for the stray-light reduction. The field of view of the X-ray mirror becomes narrower by the mounting of the collimator. Therefore, the basic design of the collimator is different from mission to mission, and then needs a trade-off study under the performance requirements for the X-ray optics. Some relations between basic parameters of the X-ray mirror are provided for the collimator’s design. The demand for X-ray optics that achieve supreme angular resolution of a few (to sub) arcseconds and large (1 m2 ) effective areas simultaneously is increasing in recent years, which accelerates the development of the light-weight X-ray optics. To enhance the effective area, we cannot avoid to increase the focal length of the mirror and the mirror nesting. Hence, the detection limit for such highly nested mirror would suffer from stray-light contamination, if no X-ray collimator is installed for its reduction. The X-ray baffle of eROSITA is the state-of-the-art countermeasure of the stray light. However, as the nesting increases drastically, the alignment process between the X-ray mirror and collimator definitely becomes harder challenges. Not only a new fabrication technique such as the mesh-type collimator but also a new method of the fine tuning has been sought in various projects, institutes, and

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companies Ponsor (2017). Also, the use of other new technologies such as precise 3D printing could allow for new advanced designs having been not realized with the current manufacturing techniques.

References B. Aschenbach, Design, construction, and performance of the ROSAT high- resolution x-ray mirror assembly. Appl. Opt. 27(8), 1404–1413 (1988) B. Aschenbach, U. Briel, F. Haberl et al., Imaging performance of the XMM-Newton X-ray telecopes. SPIE Proc. 4012, 731–739 (2000) H. Awaki, H. Kunieda, M. Ishida et al., Hard x-ray telescopes to be onboard ASTRO-H. Appl. Opt. 53(32), 7664 (2014) M. Bavdaz, E. Wille, M. Ayre et al., ATHENA x-ray optics development and accommodation, in SPIE Proceedings (2021), p. 1182205 R.E. Benz, U.G. Hingst, W.J. Schwarzott, Thermal design features of Rosat X-ray telescope. ESA Spec. Publ. 200, 399–406 (1983) F. Burger, J. Eder, G. Grisoni, The Development of the XMM Mirror Modules with 58 nested lightweight nickel mirrors. AIAA 1423, 1:8 (2000) D.N. Burrows, J.E. Hill, J.A. Nousek et al., SPIE Proc. 4851, 1320–1325 (2003). https://doi.org/ 10.1117/12.461279 V. Burwitz, P. Predehl, P. Friedrich et al., The calibration and testing of the eROSITA X-ray mirror assemblies. SPIE Proc. 9144, 91441X 6 (2014) D. de Chambure, R. Laine, K. van Katwijk et al., The status of the mirror production for the ESA XMM spacecraft. SPIE Proc. 2808, 362–375 (1996) D. de Chambure, R. Lainé, K. van Katwijk, P. Kletzkine, XMMs X-ray telescopes. ESA Bull. 100, 30–42 (1999a) D. de Chambure, R. Laine, K. van Katwijk et al., The X-ray baffle of the XMM telescope: development and results. SPIE Proc. 3737, 396-408 (1999b) P. Friedrich, H. Bräuninger, B. Budau et al., Design and development of the eROSITA x-ray mirrors. SPIE Proc. 7011, 70112T 8pp (2008) P. Friedrich, H. Bräuninger, B. Budau et al., Development and testing of the eROSITA mirror modules. SPIE Proc. 8443, 84431S 8pp (2012) P. Friedrich, C. Rohé, R. Gaida et al., The eROSITA X-ray baffle. SPIE Proc. 9144, 91444R 6 pp (2014) T.J. Gaetz, D. Jerius, The HRMA User’s Guide (2005). https://tinyurl.com/52pnwsrh J.A. Gaskin, D.A. Swartz, A. Vikhlinin et al., Lynx X-Ray Observatory: an overview. J. Astron. Telescopes Instrum. Syst. 5, 021001 (2019) R. Giacconi, G. Branduardi, U. Briel et al., The Einstein (HEAO 2) X-ray observatory. ApJ 230, 540–550 (1979) H. Hayashi, T. Sato, K. Tomikawa et al., Upgrade of the thirty-meter x-ray pencil beam line at the Institute of Space and Astronautical Science, in SPIE Proceedings (2014), p 91444A R. Iizuka, T. Hayashi, Y. Maeda et al., Ground-based x-ray calibration of the Astro-H/Hitomi soft x-ray telescopes. J. Astron. Telescopes Instrum. Syst. 4, 011213 (2018) F.A. Jansen, XMM: advancing science with the high-throuighput X-ray spectroscopy mission. ESA Bull. 100, 9–12 (1999) H. Kunieda, S. Hayakawa, T. Hirano et al., Roughness measurement of X-ray mirror surfaces. Jpn. J. Appl. Phys. 25, 1292–1299 (1986) H. Kunieda, Y. Tsusaka, H. Suzuki et al., Thirty-meter X-ray pencil beam line at the institute of space and astronautical science. Jpn. J. Appl. Phys. 32(10R), 4805 (1993) K.K. Madsen, F.E. Christensen, W.W. Craig et al., J. Astron. Telescopes Instrum. Syst. 3, 044003 (2017). https://doi.org/10.1117/1.JATIS.3.4.044003 K. Mitsuda, M. Bautz, H. Inoue et al., The X-ray observatory Suzaku. PASJ 59, S1–S7 (2007)

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H. Mori, R. Iizuka, R. Shibata et al., Pre-collimator of the astro-E2 X-ray telescopes for stray-light reduction. PASJ 57, 245–257 (2005) H. Mori, Y. Haba, T. Miyazawa et al., Current status of the pre-collimator development for the ASTRO-H x-ray telescopes, in SPIE Proceedings (2010), p. 77323E H. Mori, Y. Maeda, M. Ishida et al., The pre-collimator for the ASTRO-H x-ray telescopes: shielding from stray lights, in SPIE Proceedings (2012), p. 84435B H. Mori, T. Miyazawa, H. Awaki et al., On-ground calibration of the Hitomi Hard X-ray Telescopes. J. Astron. Telescopes Instrum. Syst. 4, 011210 (2018) K. Mori, T.G. Tsuru, K. Nakazawa et al., A broadband x-ray imaging spectroscopy with highangular resolution: the FORCE mission, in SPIE Proceedings (2016), p. 99051O T. Okajima, Y. Soong, P.J. Serlemitsos et al., First peek of ASTRO-H Soft X-ray Telescope (SXT) in-orbit performance, in SPIE Proceedings (2016), p. 99050Z T. Okajima, Y. Soong, T. Hayashi, Development of the XRISM X-ray mirror assembly. Am. Astron. Soc. Meeting Abstracts 235, 373.06 (2020) K. Ponsor, Precollimator for X-ray Telescope (stray-light baffle). Mirror Tech/SBIR/STTR Workshop (2017). https://tinyurl.com/yb9fxchd P. Predehl, R. Andritschke, V. Arefiev et al., The eROSITA X-ray telescope on SRG. A&A 647, A1:1–16 (2021) T.T. Saha, W.W. Zhang, R.S. McClelland, Optical design of the STAR-X telescope, in SPIE Proceedings (2017), p. 103990I T. Sato, R. Iizuka, H. Mori et al., The ASTRO-H SXT performance to the large off-set angles, in SPIE Proceedings (2016), p. 99053X D.A. Schwartz, Invited review article: the Chandra X-ray observatory. Rev. Sci. Instrum. 85(6), 061101 (2014) P.J. Serlemitsos, Y. Soong, K.W. Chan et al., The X-Ray Telescope onboard Suzaku. PASJ 59, S9–S21 (2007) R. Shibata, M. Ishida, H. Kunieda et al., X-ray telescope onboard astro-E. II. Ground-based X-ray characterization. Appl. Opt. 40(22), 3762–3683 (2001) R. Shibata, H. Mori, Y. Maeda et al., ASTRO-E2 XRT precollimator for stray light protection I. Design and expected performance. SPIE Proc. 4851, 684–695 (2003) A. Simionescu, S.W. Allen, A. Mantz et al., Baryons at the edge of the X-ray-brightest Galaxy cluster. Science 331(6024), 1576 (2011) K.P. Singh, G.C. Stewart, N.J. Westergaard et al., Soft X-ray focusing telescope aboard AstroSat: design, characteristics and performance. J. Astrophys. Astron. 38(2), id.29 11pp (2017). https:// doi.org/10.1007/s12036-017-9448-7 S.K. Sinha, E.B. Sirota, S. Garoff et al., X-ray and neutron scattering from rough surfaces. Phys. Rev. B 38(4), 2297–2311 (1988) D. Spiga, Analytical computation of stray light in nested mirror modules for x-ray telescopes, in SPIE Proceedings (2015), p. 96030H D. Spiga , X-ray mirror module analytical design from field of view requirement and stray light tolerances, in SPIE Proceedings (2016), p. 99056R T. Takahashi, M. Kokubun, K. Mitsuda et al., Hitomi (ASTRO-H) X-ray Astronomy Satellite. J. Astron. Telescopes Instrum. Syst. 4, 021402 (2018) Y. Takei, H. Akamatsu, Y. Hiyama et al., Stray light of Suzaku XRT from Crab offset observations. Am. Inst. Phys. Conf. Ser. 1427, 239–240 (2012) M. Tashiro, H. Maejima, K. Toda et al., Status of x-ray imaging and spectroscopy mission (XRISM), in SPIE Proceedings (2020), p. 1144422 J. Truemper, The ROSAT mission. Adv. Space Res. 2(4), 241–249 (1982) M.C. Weisskopf, H.D. Tananbaum, L.P. Van Speybroeck et al., Chandra X-ray Observatory (CXO): overview. SPIE Proc. 4012, 2–16 (2000) W.W. Zhang, K.D. Allgood, M.P. Biskach et al., Next generation x-ray optics for astronomy: high resolution, lightweight, and low cost, in SPIE Proceedings (2019), p. 1111907

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Mirror Fabrication: Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Manufacturing Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Mirror Manufacture and Technology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evaluating Optical Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Terminology: Basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Terminology: Optical Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Section Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subtractive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polishing: General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polishing: Robotic . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ion Beam Figuring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Subtractive: Silicon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon Pore Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Monocrystalline Silicon Meta-shell X-Ray Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electroforming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Slumping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differential Deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fabricative . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Active/Adjustable Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Additive Manufacture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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C. Atkins () STFC UK Astronomy Technology Centre, Edinburgh, UK e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_11

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Abstract

X-ray mirror fabrication for astronomy is challenging; this is due to the Wolter I optical geometry and the tight tolerances on roughness and form error to enable accurate and efficient X-ray reflection. The performance of an X-ray mirror, and ultimately that of the telescope, is linked to the processes and technologies used to create it. The goal of this chapter is to provide the reader with an overview of the different technologies and processes used to create the mirrors for X-ray telescopes. The objective is to present this diverse field in the framework of the manufacturing methodologies (subtractive, formative, fabricative, & additive) and how these methodologies influence the telescope attributes (angular resolution and effective area). The emphasis is placed upon processes and technologies employed in recent X-ray space telescopes and those that are being actively investigated for future missions such as Athena and concepts such as Lynx. Speculative processes and technologies relating to Industry 4.0 are introduced to imagine how X-ray mirror fabrication may develop in the future. Keywords

X-ray mirrors · Mirror fabrication · Subtractive · Formative · Fabricative · Additive · Replication · Active control

Introduction The goal of a telescope is to provide the astronomers with photons to analyze, and the objective of a telescope is to deflect the photons from the field of view to the detector. The key component of a telescope is the primary mirror (or lens). The primary mirror must collect as many photons as possible and accurately deflect the photons to the focus or detector. A normal incidence telescope – e.g., Hubble Space Telescope, angle of incidence θi = 90◦ – achieves this by having a mirror as large as possible (2.4 m diameter) and polished as accurately as possible. The primary mirror for a grazing incidence telescope required for X-ray astronomy is based upon the Wolter I geometry, where photons hit the surface at very small angles of incidence (θi ≈ 1°, or less). Therefore to fill the telescope aperture, to collect as many photons as possible, multiple grazing incidence mirrors are nested and as such, the “primary mirror” is made up from many X-ray mirrors. The challenge then becomes how to make the individual X-ray mirrors. Normal incidence mirrors can be made thick (a ∼ 6:1 diameter-to-thickness ratio is often used) to ensure that the mirror surface is rigid; however, thick mirrors for an X-ray telescope reduce the telescope aperture (collecting area) because they are “seen” by the source edge-on and limit the number of mirrors that can be nested in

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the system. In contrast, thin mirrors block less of the telescope aperture and more mirrors can be nested, but the accuracy of the mirror surface is lower. There are multiple methods to create an X-ray mirror. The technology and process used depends upon the science objectives of the telescope/observatory – i.e., imaging, number of photons, or both, required by the telescope. This chapter will explore the plethora of technologies and processes used in X-ray mirror fabrication, both in use today and under development for the future. To limit the scope of the chapter, only the technologies and processes that deliver 1.8% at 6.4 keV 1.5 keV (at 5.9 keV) α. The RGA diffracts the X-rays to an array of nine MOS back-illuminated CCDs. Each has 1024 × 768 pixels, half exposed to the sky and half used as a storage area. During readout, 3 × 3 pixel on-chip binning is performed, leading to a bin size of (81 µm)2 , which is sufficient to fully sample the line spread function, reducing the readout time and the readout noise. In the dispersion direction, one bin corresponds to about 7, 10, and 14 mÅ in first order and about 4, 6, and 10 mÅ in second order for wavelengths of 5, 15, and 38 Å, respectively. The size of one bin projected onto the sky is about 2.5′′ in the cross-dispersion direction and roughly 3, 5, and 7′′ and 4, 6, and 9′′ in the dispersion direction at 5, 15, and 38 Å in first and second order, respectively. After the first week of operations, an electronic component in the clock driver of CCD4 in RGS2 failed, affecting the wavelength range from 20.0 to 24.1 Å. A similar problem occurred in early September 2000 with CCD7 of RGS1 covering 10.6 to 13.8 Å. The total effective area is thus reduced by a factor of two in these wavelength bands (see Fig. 14). In 2007, the readout method in RGS2 was changed from double-node, in which data from the two halves of the chips are retrieved separately, to single-node, in which data from the whole chip are read out through a single amplifier. Hence, RGS2 frame times are twice as long as those from RGS1. The standard mode of operation of the RGS instrument is called “Spectroscopy.” It consists of a two-dimensional readout of one or more CCDs over the full energy range. The accumulation time when reading the eight functional CCDs is 4.8 s for RGS1 and 9.6 s for RGS2. To mitigate the effects of pile-up, very bright sources can be observed in the RGS “Small Window” mode. In this mode, only the central 32 of the 128 CCD rows in the cross-dispersion direction are read. The CCD readout time is therefore decreased by

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Fig. 13 RGS data for an observation of Capella. The dispersion axis runs horizontally and increases to the right. The top panel shows the image of the dispersed light in the detector. The cross dispersion is along the vertical axis. The bottom panel shows the order selection plane, with the energy (PI), on the ordinate. This also illustrates the mechanism used for separation of first, second, and higher grating orders. Standard data extraction regions are indicated by the curves

a factor 4 compared to Spectroscopy mode. It can be further decreased by reading only a subset of the CCDs.

Scientific Performance A consequence of the diffraction equation (1) is that orders overlap on the CCD detectors of the RFC. Separation of the spectral orders is achieved by using the intrinsic energy resolution of the CCDs, which is about 160 eV FWHM at 2 keV. The dispersion of a spectrum on an RFC array is shown in the bottom panel of Fig. 13. First and second orders are very prominent and are clearly separated in the vertical direction (i.e., in CCD energy, or PI, space). Photons of higher orders are also visible for brighter sources. The calibration sources can also be seen in the bottom panel as short horizontal features (Fig. 13). A complete overview of the performance of the RGS, instrumental details, and calibration procedures can be found in de Vries et al. (2015) (Fig. 14). A summary of the RGSs’ performance is given in Table 2.

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Fig. 14 Example of the RGS effective area for a recent observation. Clearly visible are the gaps due to the non-working CCDs and, in RGS1, the prominent instrumental O edge near 23 Å

Table 2 RGS In-orbit Performance

Effective area (cm2 ) Resolution (km s−1 ) Wavelength range Wavelength accuracy

1st order 2nd order 1st order 2nd order 1st order 2nd order 1st order 2nd order

RGS1 RGS2 10 Å 15 Å 35 Å 10 Å 15 Å 51 61 21 53 68 29 15 – 31 19 1700 1200 600 1900 1400 1000 700 – 1200 800 5–38 Å (0.35–2.5 keV) 5–20 Å (0.62–2.5 keV) ±5 mÅ ±6 mÅ ±5 mÅ ±5 mÅ

35 Å 25 – 700 –

The calibration of the RGS effective area is based on a combination of ground measurements and in-flight observations (Fig. 14). Empirical corrections have been introduced along the years, the first one based on the assumed power law form of blazar spectra, followed by the recognition of wavelength-dependent sensitivity changes consistent with a buildup of hydrocarbon contamination on the CCD surface. There are indications of a continuous decrease in effective area over the last years, in both instruments and affecting most of the spectral range. This decrease cannot be explained by only contamination by hydrocarbons. Its origin is not understood. This calibration takes into account this effect, following an empirical

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algorithm. The first-order effective area peaks around 15 Å (0.83 keV) at about 120 cm2 for the two spectrometers. The wavelength scale is determined by the geometry of the various instrument components. The original pre-flight calibration kept the wavelength scale accuracy well within specification. Nevertheless, it has been improved by taking into account some systematic effects. With these corrections, the accuracy of the wavelength scale is now of order of 6 mÅ. The observed line shape is well represented by the model. The empirically determined width of strong emission lines is a slowly varying function of wavelength in both instruments, with a mean FWHM of about 70 mÅ in first order and 50 mÅ in second order, giving a spectral resolution that increases with wavelength. It is estimated that an observed line broadening of more than 10% of the FWHM can be considered to be significant for strong lines. The current status of the instruments and the calibration can be found in the “XMM-Newton Users Handbook” (Ebrero 2021) and in the document “Status of the RGS Calibration” (González-Riestra 2021), both available at the XMM-Newton website.

Optical Monitor (OM) The Optical Monitor (OM) provides simultaneous optical/UV coverage of sources in the EPIC field of view, extending the wavelength range of the mission and enhancing its scientific return. The photon-counting nature of the instrument and the low in-space background mean it is highly sensitive for the detection of faint sources, despite its small size, being able to reach about magnitude 22 (5σ detection) in the B filter in 5 ks of exposure (with maximum depth in the White filter). The provision of UV and optical grisms permits low-resolution spectroscopic analyses, while the fast mode timing options allow detailed studies of temporal variability.

The Instrument The OM is a 2 m-long, 30 cm diameter telescope of Ritchey-Chretien design, with a focal length of 3.8 m (f/12.7). After passing through the primary mirror hole, the light beam impinges on a rotatable 45◦ flat that deflects it to one of two redundant detector chains. Each chain comprises a filter wheel containing 11 apertures (V (500–600 nm), B (380–500 nm), U (300–400 nm), UVW1 (220–400 nm), UVM2 (200–280 nm), UVW2 (180–260 nm), and White-light (180–700 nm) broadband filters, visible (290–600 nm) and UV (180–360 nm) grisms for dispersive (resolving power (λ/∆λ) ∼ 180) spectroscopy, a magnifier (not available for use), and a mirror acting as a blocking filter). A schematic of the OM is shown in Fig. 15, while the photographs in Figs. 16 and 17 show the telescope and the filter wheel assembly, respectively.

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Detector

Baffle

Filter Wheel

Processing Electronics Telescope Power supply

Detector Power Supply Door

Digital Electronics Module(Prime)

Digital Electronics Module(Redundant)

Fig. 15 Schematic of the Optical Monitor Fig. 16 The Optical Monitor at Mullard Space Science Laboratory, UK

The detector, located behind the filter wheel in each chain, is a Micro Channel Plate (MCP)-intensified CCD (MIC), comprising a S20 photocathode, a pair of MCPs, a P-46 phosphor, a fiber taper, and a CCD. An electron liberated from the photocathode by an incident sky photon drifts to the upper MCP where a potential accelerates it along a pore, creating a cascade of electrons by collisions with the pore walls. On passing through the second MCP, this charge cloud is amplified to around 5 × 105 –106 electrons, and these impinge on the phosphor, resulting in a burst of photons. This photon burst, spatially localized by the MCP arrangement, then traverses the fiber taper, onto the CCD, which has 256 × 256 light-facing pixels (each 4 × 4 arcsecs on the sky). The footprint of the photon burst at the CCD covers about 3 × 3 CCD pixels. On readout, an onboard algorithm then centroids each footprint to 1/8 of a CCD pixel, creating an effective image of 2048 × 2048 image pixels (maximum resolution, 0.5 × 0.5 arcsec pixels on the sky). The CCD is read out about 90 times (frames)/s (for the full field). Thus, each sky photon incident on

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Fig. 17 One of the two filter wheels positioned in front of the OM’s CCD detectors

the photocathode that yields a footprint at the CCD within the frame is subject to onboard validation thresholds, recorded as an incident event by the onboard data processing system. The OM has two main modes of operation: Imaging mode, where events from each frame are accumulated into a single image covering the total exposure time, and Fast mode, where, for a small 11′′ ×11′′ window, each event is time-tagged, yielding an event stream. In Imaging mode, the observer has, subject to telemetry-related constraints, significant freedom to define window(s) for optimum sky coverage for their science goals. This may involve coverage of the whole field, at the expense of longer instrument overheads, or coverage of more localized areas of the field via up to five smaller windows. Grism data is taken either in a Full-field mode, potentially yielding spectra from all sufficiently bright objects in the field, or with a narrow, predefined window, designed to concentrate on a specific target observed at the boresight. In Fast mode only two Fast mode windows are allowed, though normally these can be used in conjunction with image mode windows. The highest time resolution in fast mode is 0.5 s. Three important consequences of the OM design on its output data are as follows: (1) When two or more photon bursts arrive at the CCD within the same readout frame and their footprints spatially overlap, the probability of which increases with source count rate and/or longer frame times, they may not be distinguished and so be recorded as a single event. This effect is referred to as coincidence loss and is similar to the pile-up effect in the EPIC cameras. (2) The instrument design, particularly the fiber taper, results in a distortion of the imaged field compared to the real sky. (3) For speed, the onboard algorithm exploits a lookup table to centroid the count distribution in each 3 × 3 CCD-pixel footprint, a simplification that results in a so-called “modulo-8” pattern appearing on a scale of 8 pixels in the 2048 × 2048 output image. These effects are generally corrected for through software tools in the XMM-Newton Science Analysis Software (SAS). Some OM observations also contain low-intensity, diffuse light features, arising from reflections from the back side of the detector entrance window and/or from a chamfer around it. The OM, being a photon-counting instrument, has high sensitivity, and, with the low background (dominated by zodiacal light), it can reach stars as faint as about V = 21 (for a 5σ detection of an A0 star in the B filter) in 1000 s. On the other

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hand, the photocathode can be damaged by high incident photon rates, and this places limits on the brightest sources that the OM can be exposed to. In practice, the limiting magnitude is around V = 7.3 for an A0 star. A more complete description of the OM instrument is given in Mason et al. (2001). For observations not performed in Full-Frame mode, the OM performs a short (20 s) field-acquisition exposure at the start of each observation (Talavera and Rodriguez 2011). This enables a number of pre-specified stars to be recognized in the exposure by the onboard software and the observed and predicted positions compared to measure shifts due to uncertainties in the spacecraft pointing. Consequently, the chosen OM science observation windows can be adjusted in position to ensure the sky coverage is optimal for the observer’s science. This is especially important for accurately positioning the small Fast mode windows, when used, to ensure the target is well centered in the window. In addition, the star positions are also monitored every 20 s, permitting the tracking of any spacecraft drift. This tracking information is used by the onboard software, to relocate events to the correct position in the accumulating image for Image mode data (referred to as “shift and add”). For Fast mode data, this tracking information is not applied onboard but is used for the same purpose in downstream data reduction performed by the SAS.

Scientific Performance The OM has proven to be a very stable instrument. Nevertheless, it has experienced some spatial and temporal changes in sensitivity over the long baseline of the XMMNewton mission, both expected and unexpected (Rosen 2020). Of particular note are the effective areas. These were determined soon after launch, for each photometric filter, based on measurements of spectrophotometric standard stars, alongside the conversions from count rate to absolute flux and the equivalent magnitude zero-point determinations. The effective area for each filter, initially modelled from pre-launch information of the optical components (e.g., mirror area, reflectivities, filter transmissions), and the quantum efficiency of the photocathode were subsequently adjusted, in-flight, to match the observed count rates of standard stars. It was found that all filters showed reduced sensitivity (from 16% to 56% residual throughput) compared to pre-launch expectations, with the UVM2 and especially UVW2 filters most affected. The reduction in sensitivity has been adequately modelled by absorption due to a molecular contaminant layer somewhere in the OM system (Kirsch et al. 2005). The effective areas of the photometric filters, essentially at launch, are shown in Fig. 18. Subsequently, anticipated aging of the detector and, likely, some further contaminant growth have resulted in a gradual decline in sensitivity since launch. This decline, known as the time-dependent sensitivity (TDS) degradation, is filter (wavelength) dependent. It is monitored and characterized via analysis of data from the OM Serendipitous UV Sky Survey (SUSS) catalogues (Page et al. 2012) and is routinely verified via observations of spectrophotometric standard stars. The most

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Fig. 18 The effective area curves for each of the OM photometric filters, essentially at the start of XMM-Newton mission operations (2000)

recent TDS trends for the narrowband filters are shown in Fig. 19. The decline in sensitivity ranges from around 7% in the B filter to about 22% in the UVW2 filter. These curves are used to correct the observed count rates of sources at any epoch within the mission baseline to the rate expected at the start of the mission. That rate can then be converted to absolute photometric values via the at-launch flux and zero-point conversions.

Organization of the XMM-Newton Ground Segment The Mission Operations Centre (MOC) at the European Space Operations Centre (ESOC), Darmstadt, Germany, controls the spacecraft 24 h per day, all year round, using, as main ground stations, Kourou (French Guiana) and Santiago (Chile) and various other additional stations in South America and Australia. The MOC is responsible for the maintenance and operations of the spacecraft and the required ground infrastructure. As XMM-Newton has no onboard data storage capacity, all data are immediately down-linked to the ground in real time. Since 2018 XMMNewton has been operated together with Gaia and INTEGRAL. The Science Operations Centre (SOC) at the European Space Astronomy Centre (ESAC), Villanueva de la Cañada, Madrid, Spain, is responsible for science operations and for supporting the scientific community. The SOC handles Announcements of Opportunity and proposals, including technical evaluation and

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Normalised count rate

Normalised count rate

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0.95 0.90 0.85 0.80

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0.90 0.85 0.80

UVW2

1.00 0.95 0.90 0.85 0.80 0.75

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Normalised count rate

Normalised count rate

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0.75 Normalised count rate

Normalised count rate

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UVW2

1.00 0.95 0.90 0.85 0.80 0.75

2000

4000 6000 MJD-50000.0

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4000 6000 MJD-50000.0

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Fig. 19 Normalized, observed count rates of constant sources in the OM SUSS4 catalogue, binned into 20 time bins (black error bars), for each OM filter. The solid red and dashed blue curves represent the most recent and previously fitted decline trends, respectively, highlighting the ubiquitous flattening of the decline

OTAC support as well as the subsequent planning of observations, including instrument handling, calibration observations, and Targets of Opportunity. Data from these observations are processed from raw telemetry to standard data products at the SOC, before being ingested into the XMM-Newton Science Archive (XSA) and distributed to the users. A Quick-Look Analysis of data and anomaly monitoring of the instruments are part of this process. The SOC also takes a leading role in the continuous calibration of the instruments and the provision of scientific analysis software (SAS) to the users together with experts from the XMM-Newton community. The Survey Science Centre (SSC) (Watson et al. 2001), a consortium of ten institutes in the ESA community, is responsible for the compilation of the XMMNewton Serendipitous Source Catalogue, the follow-up/identification program for the XMM-Newton serendipitous X-ray sky survey, support to pipeline processing at the SOC, and development of parts of the scientific analysis software. NASA provides a Guest Observer Facility (GOF) at the Goddard Space Flight Center (GSFC), Greenbelt, Maryland, USA. The GOF supports the usage of

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XMM-Newton by the scientific community in the USA. It distributes the XMMNewton data to US users and contributes to the SAS development. The GOF is responsible for the organization of the Guest Observer (GO) program funded by NASA.

Observing with XMM-Newton All the scientific instruments onboard XMM-Newton can be operated independently and can obtain science data simultaneously, if operational constraints permit. These constraints are imposed to preserve the safety of the instruments as well as to achieve the conditions for an optimal calibration of the data. The combination of the orbit of the spacecraft with limits in the instruments’ operational parameters (mostly temperatures but also radiation dose) results in observation constraints related to the orientation of the spacecraft with respect to the Sun, Earth, and Moon and to the position of the spacecraft in the Earth’s magnetosphere. XMM-Newton was launched in December 1999 into a highly elliptical orbit, with a high inclination with respect to the Equator and with an apogee height of 115,000 km in the Northern hemisphere and a perigee height of 6000 km in the Southern hemisphere. Due to several perturbations, the orbit of XMM-Newton evolves with time. An orbit correction maneuver was performed in February 2003 to ensure full ground station coverage during the entire science period. But the evolution of the orbit has changed the fraction of the sky visible to science instruments and the effective available science time per orbit along the mission lifetime. The spacecraft has no capacity for data or commanding storage onboard so it requires continuous contact with the ground for science operations. The operations are conducted from the MOC through ground stations in Kourou, Santiago de Chile, and Yatharagga (and in Perth and New Norcia during the early years of the mission and occasionally in Madrid). The EPIC and RGS CCD detectors are sensitive to both X-ray and optical radiation as well as particles. Electromagnetic radiation can affect the scientific analysis of the data collected, but protons striking the detectors can permanently damage the surface of the CCDs. In order to protect the EPIC cameras, their filter wheel is moved into the closed position during intervals of high particle radiation. The RGS spectrographs do not have a similar filter protection so the instruments are placed into a special configuration with minimal equipment switched on during high radiation intervals. Before launch, it was expected that the radiation environment above 46,000 km from the Earth was safe for the mission. This meant that ∼143 ks of the ∼173 ks (∼48-h) orbital period could be devoted to science operations at the beginning of the mission. However, strong fluctuations and variability of the particle background in the cameras were one of the main surprises and concerns following launch. An ad hoc model for radiation belts around the Earth was developed in order to predict the time window within every revolution when science observations could be safely

46 XMM-Newton Fig. 20 The evolution of the XMM-Newton orbit during the mission has changed the spacecraft velocity near perigee passage and the orientation with respect to Earth magnetosphere. As a result the fraction of time available to science has changed with a long-term trend superposed on a seasonal modulation

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0.8

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0.6 2000

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2010

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conducted (Casale and Fauste 2004); see Fig. 20. According to the model and the expected orbital evolution, the science window will be as short as ∼130 ks by 2025. Many parameters in the EPIC cameras and RGS spectrographs are strongly dependent on the temperatures at which the instruments are operated. In order to guarantee a consistent calibration for all observations, the operations are designed to maintain the temperatures of the science payload within a narrow range. Since the main source of heating is illumination by the Sun, strong constraints on temperatures are translated into a strong constraint on the orientation of the spacecraft with respect to the Sun. The solar aspect angle (angle between pointing direction and Sun direction) must be within 70◦ and 110◦ at all times to assure thermal stability and sufficient power from the solar array. This means that ∼65% of the sky is inhibited in every single XMM-Newton revolution. Other celestial constraints are unrelated to temperature or power stability, but to potential electromagnetic radiation damage of the OM. The main sources of dangerous light emission, away from the Sun, are the Earth and the Moon. The Earth limb avoidance angle is 42.5◦ , and the Moon limb avoidance angle is 22◦ , which is increased to 35◦ during eclipse seasons. As in the case of the radiation constraints, the evolution of the XMM-Newton orbit with respect to the ecliptic has had consequences on the fraction of the sky available at any time and on the evolution of the visibility in certain areas of the sky; see Fig. 21. The constraint outlined above apply to any type of observation, independent of the configuration of the instruments. There are a number of constraints that apply only to OM exposures, and some science exposures cannot be performed using the OM, but exposures with the X-ray instruments are permitted. These OM constraints refer to the presence of nearby bright celestial sources that may damage the detector. In addition, OM exposures are forbidden near the following solar system objects (Table 3).

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Fig. 21 The high inclination of the orbit and the high latitude of the perigee have made the South Ecliptic Pole the region of the sky with the best accessibility to XMM-Newton along its lifetime. By contrast, the visibility around the North Ecliptic Pole is constrained by the Earth in most of the revolutions. The image shows the fraction of visible orbits along 21 years (right) and the average maximum visibility in 21 year (left)

46 XMM-Newton Table 3 OM avoidance angles

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Avoidance angle 3.5◦ 4.5◦ 2◦ 0.25◦ 0.25◦

Scientific Data and Analysis XMM-Newton reformatted telemetry is organized in Observation/Slew Data Files (ODF/SDF). Most of the ODF/SDF components have a FITS format. An ASCII summary file provides the astronomers with general information on the observation and an index of the files contained in the ODF. The Science Analysis System (SAS) is the software established to reduce and analyze XMM-Newton science data. It consists of two main blocks: • reduction pipelines, which apply the calibrations to the ODF and the SDF science files and produce calibrated and concatenated event lists for the X-ray cameras, flat-fielded and calibrated OM sky images, source lists, and time series. • a set of file manipulation tools, which include the extraction of spectra, light curves, and (pseudo-)images and the generation of source lists, as well as the generation of auxiliary files such as appropriate instrument response matrices. The SAS reduction pipeline (PPS) is run on all XMM-Newton datasets. Each PPS dataset is manually screened to verify its scientific quality and identify potential processing problems. The PPS output (Rodríguez 2021) includes a wide range of top-level scientific products, such as X-ray camera event lists, source lists, multiband images, background-subtracted spectra, and light curves for sufficiently bright individual sources, as well as the results of a cross-correlation with a wide sample of source catalogues and with the matching ROSAT field. All the XMM-Newton calibration data are organized in a Current Calibration File (CCF). Summary documents, containing an overview of the current calibration status and associated systematic uncertainties, are available from the XMM-Newton Calibration Portal. The XMM-Newton Science Archive (XSA) content is regularly updated with all the newly generated ODF, SDF, and PPS products, with updated versions of the catalogues of EPIC sources, OM sources, and Slew Survey sources, and with ancillary info like associated proposal abstract and publications. On-the-fly data analysis and processing can be performed from the XSA using the SAS without the need of downloading data or software. With all the sources serendipitously detected in the EPIC FOV of XMM-Newton public observations, the SSC compiles and regularly updates the XMM-Newton EPIC source catalogue. At the time of writing, the SSC has created four catalogue

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generations, with 4XMM being the latest, with a few incremental versions for each of them, leading so far to a total of 11 catalogue data releases, 11DR. 4XMMDR11 (Webb et al. 2020) was released in August 2021 and contains 787,963 “clean” detections corresponding to 602,543 unique sources covering 1239 sq. deg. In addition, the 4XMM-DR11s catalogue of serendipitous sources detected from stacked data from overlapping XMM-Newton observations (Traulsen et al. 2020) contains 358,809 unique sources of which 275,440 were multiply observed covering 350 sq. deg. The data acquired during satellite slews are used to build the XMMNewton Slew Survey Catalogue, XMMSL2 (Saxton et al. 2008). The current version contains 55,969 clean detections covering an area of 650,000 sq. deg. The OM team, under the auspices of the SSC, produces and regularly updates a catalogue of sources detected by the Optical Monitor. The 5th version of the XMM-Newton OM Serendipitous Ultraviolet Source Survey Catalogue, XMM-SUSS5, (Page et al. 2012) contains 8,863,922 detections of 5,965,434 sources. Specific queries to all catalogues can be made using the XMM-Newton Science Archive. A database of Upper Limits across the FOV of all public XMM-Newton pointed and slew observations has been built with new observations being added as they become available (Ruiz et al. 2021). The database is searchable from the XSA interface.

Scientific Strategy and Impact

Fig. 22 The over-subscription factors, or requested versus available observing time, for the first 21 XMM-Newton Announcements of Opportunity (AOs) are shown in black. The two blue symbols show the over-subscription of the Multi-Year-Heritage programs

Oversubscrition Factor

XMM-Newton observing time is made available worldwide via Announcements of Opportunity (AOs). The AOs open in the second half of August each year, and the results are publicized in early December. All the AOs were highly over-subscribed, typically by a factor 6 to 7; see Fig. 22. The proposals are peer-reviewed by panels composed of scientists located worldwide. The XMM-Newton observing strategy was discussed with the community at large at two workshops: “XMM-Newton: The next Decade” in 2007 (Schartel 2008) and 2016 (Schartel 2017 and (Schartel et al. 2017)). The unique capabilities of the instruments and the long mean observing time (30 ks) in combination with the possibility of long uninterrupted observations foster XMM-Newton’s

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potential for transformative science. Here transformative science is understood to be scientific results which lead to radically restructuring the scientific understanding or as observational confirmation of central predictions of astrophysical and cosmological theory and modelling. Examples include: (1) the non-detection or weak detection of cooling flows in the galaxy clusters Abell 1835 (Peterson et al. 2001), Abell 1795 (Tamura et al. 2001) and Sérsic 159-03 (Kaastra et al. 2001) which led to the concept of the coupling of the cosmic evolution of supermassive black holes with that of galaxies and clusters of galaxies via feedback. This meant that two object classes which were considered to be completely independent before were from then on understood to undergo a strongly coupled evolution; (2) the detection of transitional millisecond pulsars (Papitto et al. 2013), which confirmed the transition of accretion-powered to rotationpowered emission modes in pulsars; (3) the detection of low magnetic field magnetars (Rea et al. 2010; Tiengo et al. 2013) which changed our understanding of the magnetic fields which cause the short X/gamma ray bursts in repeaters, (4) the identification of neutron stars within ultra-luminous X-ray sources (Fürst et al. 2016; Israel et al. 2017). This changed the understanding of the nature of this source class and allowed the study of super-Eddington accretion (Ciro et al. 2016), (5) the determination of the mass, spin, and X-ray corona size of supermassive black holes (Fabian et al. 2009; Risaliti et al. 2013; Parker et al. 2017; Alston et al. 2020; Wilkins et al. 2021) which quantitatively describe the inner geometry of AGNs, (6) the study of tidal disruption events (Reis et al. 2012; Miller et al. 2015; Kara et al. 2016; Lin et al. 2017, 2018; Pasham et al. 2019; Shu et al. 2020) which shed light on the details of the accretion process and jet launching, (7) the detection of the warm-hot intergalactic medium (Nicastro et al. 2018), which confirmed cosmic simulations by the detection of the missing baryons. Further examples of transformative science resulting from XMM-Newton and Chandra observations are given in two Nature review articles by Santos-Lleo et al. (2009) and by Wilkes et al. (2021). An analysis of the science results and the discussion of the 2017 workshop showed the increased importance of Target of Opportunity observations, large and very large programs, and observations joint with other facilities for transformative science. About 15% of submitted proposals request anticipated target of opportunity (TOO) observations. In addition there are about 45 requests for unanticipated TOOs and/or Director’s discretionary time observations each year, which in general are forwarded to an OTAC (Observing Time Allocation Committee) chairperson for a recommendation. XMM-Newton has not formally limited the time available for TOOs. However, the high amount of fixed-time observations and observations performed simultaneously with other missions limit the time which may be allocated to TOO observations. In the very late 2010s and very early 2020s, XMM-Newton typically performed 80 TOO observations per year. This rate is more than double the rate of TOO observations in the early days of the mission (e.g., 2005); see Figs. 23 and 25. Multi-wavelength and multi-messenger observations are a powerful tool to foster transformative science. With its suite of instruments, XMM-Newton already

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Fig. 23 Performed Target of Opportunity observations

Fig. 24 Observations performed coordinated or simultaneous with other facilities

provides multi-wavelength coverage from the optical to X-ray regimes. XMMNewton SOC staff investigated ways to further extend this approach to “multi”wavelength observations. These can be performed via joint programs. In 2021, XMM-Newton has joint programs with nine facilities. The joint programs allow the time allocation committees of each facility to allocate time on the other mission in connection with the allocation of time on the own facility. Therefore, with one proposal, in response to an XMM-Newton AO, observing time on up to 10 facilities can be requested. Table 4 shows the joint programs and the time exchanged per year. The XMM-Newton joint programs allow the spectral energy distribution of a source to be covered from the radio, optical, UV, and X-ray, Γ -ray all the way to the TeV range. About 30% of the performed high-priority observations (i.e., observations whose execution is guaranteed) are from a joint program, most of them simultaneous with one or more facilities; see Figs. 24 and 26.

46 XMM-Newton Table 4 Joint programs

1533 Facility NRAO VLT(I) HST Chandra Swift NuSTAR INTEGRAL MAGIC H.E.S.S.

Exchanged time 2 × 150 ks 2 × 290 ks 2 × 150 2 × 1 Ms 300 ks 2 × 1.5 Ms 2 × 300 ks 2 × 150 ks 2 × 150 ks

Fig. 25 Observing time performed for Target of Opportunity observations

Requests for observing time longer than 300 ks are submitted as large programs. About 40% of the high-priority observing time (execution guaranteed) is given to large programs, such that they have the same over-subscription as the normal programs. Examples of transforming science resulting from larger programs are given in Fabian et al. (2009), Alston et al. (2020), and Nicastro et al. (2018). To accomplish programs requiring more than 2 Ms, e.g., Pierre et al. (2017), the call for Multi-Year-Heritage (MYH) program was introduced in 2017. Here, up to 6 Ms of observing time are available for distribution, to be executed over a period of three AOs (3 years). The call for MYH programs in 2017 had an over-subscription of a factor 10. The call in 2020 suffered the pandemic constraints showing a lower over-subscription. The distribution of elapsed time between performed observations and publication peaks at 2 years (Ness et al. 2014). Most of the times, TOO observations lead to rapid publications with about 1 year elapsed time between observation and

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Fig. 26 Observing time performed coordinated or simultaneous with other facilities

publication (Ness et al. 2014). The predefined observing modes in combination with the provided support, e.g., pipeline products, calibration, archive, or catalogues, make XMM-Newton data highly comparable and therefore ideally suited for studies based on archival data. In fact 90% of the observing time has been used in at least one publication (Ness et al. 2014). XMM-Newton data also play an important role in education and in the development of new generations of researchers around the world. At the time of writing (November 2021), 406 Ph.D. theses had used XMM-Newton data or included results of research related to the development of the instruments. XMM-Newton is frequently used by young scientists who are starting their career in astrophysics. Since the 5th call for observing time proposals, in 2005, astronomers sending proposals the first time submit about 20% of the proposals of each call. The success rate of these first-time proposers is slightly below the average success rate of all proposers. Remarkably, in more than one third of the calls since 2005, the rate of requested to allocated observing time secured by first-time proposers was similar or even larger than the average rate of all proposers. About 380 articles are published in refereed journals each year making use of XMM-Newton data, describing the instruments, or using pipeline products or the catalogue. Figure 27 gives an analysis of all refereed articles listed in ADS, which mention XMM-Newton, demonstrating not only the usage of XMM-Newton data but also its impact via citations. Articles containing results based on XMM-Newton observations are about three times more cited than all astronomical papers. Figure 28 shows the number of articles making use of XMM-Newton data published in Nature or Science journal demonstrating the high amount of transforming science which typically is published in these two journals.

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Fig. 27 Classification of all refereed articles listed in ADS which contain “XMM” in a full text-search: (1) article makes use of XMM-Newton data or pipeline products; (2) catalogue based on XMM-Newton observations; (3) article makes quantitative predictions for XMM-Newton observations; (4) article describes XMM-Newton, its instruments, scientific impact, etc. (5) article makes use of the primary catalogues (6) article makes use of published XMM-Newton results (7) article refers to papers presenting XMM-Newton results (8) article refers to “XMM-Newton” in general (9) article uses expression derived from XMM-Newton, e.g., names of objects

Authors Contribution Norbert Schartel and Maria Santos-Lleó contributed the “Introduction”, “Scientific Data and Analysis,” and “Scientific Strategy and Impact” sections, Rosario González-Riestra contributed “The Reflection Grating Spectrometers (RGSs)” section, Peter Kretschmar contributed the “Organization of the XMM-Newton Ground Segment” section, Marcus Kirsch contributed “The Spacecraft” section, Pedro Rodríguez-Pascual contributed the “Observing with XMM-Newton” section, Simon Rosen contributed the “Optical Monitor (OM)” section, Michael Smith and Martin Stuhlinger contributed the “European Photon Imaging Camera (EPIC)” section, and Eva Verdugo Rodrigo contributed the “X-Ray Mirrors” section. Norbert Schartel prepared the chapter outline and compiled and homogenized the different contributions.

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Fig. 28 Articles in Nature and Science making use of XMM-Newton data are shown per year as an indicator of the amount of transformative science results

Acknowledgments The authors deeply thank Arvind Parmar for many useful suggestions and Lucia Ballo for help with the statistical numbers for joint programs. The authors also acknowledge the outstanding contribution of the Survey Science Centre to the mission success and the dedication and excellence of the rest of the team members of the XMM-Newton Mission Operations and Science Operations centers, where the authors of this paper feel as an honor to serve.

References W.N. Alston, A.C. Fabian, E. Kara, A dynamic black hole corona in an active galaxy through X-ray reverberation mapping. Nat. Astron. 4, 597–602 (2020) B. Aschenbach, In-orbit performance of the XMM-Newton x-ray telescopes: images and spectra. SPIE 4496, 8–22 (2002) G. Boella, R.C. Butler, G.C. Perola et al., BeppoSAX, the wide band mission for X-ray astronomy. A&AS 122, 299–307 (1997) M. Casale, J. Fauste, Attempt of modelling the XMM-Newton radiation enviroment (2004). http:// xmmweb.esac.esa.int/external/xmm_sched/vischeck/Rad_Model_TN.pdf P. Ciro, M.J. Middleton, A.C. Fabian, Resolved atomic lines reveal outflows in two ultraluminous X-ray sources. Nature 533, 64–67 (2016) J.W. den Herder, A.C. Brinkman, S.M. Kahn et al., The reflection grating spectrometer on board XMM-Newton. A&A 365, L7–L17 (2001) C.P. de Vries, J.W. den Herder, C. Gabrie et al., Calibration and in-orbit performance of the reflection grating spectrometer onboard XMM-Newton. Astron. Astrophys. 573, 128–156 (2015)

46 XMM-Newton

1537

J. Ebrero, XMM-Newton Users Handbook, Issue 2.19 (2021). https://xmm-tools.cosmos.esa.int/ external/xmm_user_support/documentation/uhb/ A.C. Fabian, A. Zoghbi, R.R. Ross et al., Broad line emission from iron K- and L-shell transitions in the active galaxy 1H0707-495. Nature 459, 540–542 (2009) F. Fürst, D.J. Walton, F.A. Harrison et al., Discovery of coherent pulsations from the ultraluminous X-ray source NGC 7793 P13 Astrophys. J. Lett. 831, L14 (2016) P. Gondoin, B.R. Aschenbach, M.W. Beijersbergen et al., Calibration of the XMM flight modules – image quality. SPIE 3444, 278–289 (1998a) P. Gondoin, B.R. Aschenbach, M.W. Beijersbergen et al., Calibration of the first XXM flight mirror module: II. Effective area. SPIE 3444, 290–301 (1998b) R. González-Riestra, Status of the RGS Calibration (2021). https://xmmweb.esac.esa.int/docs/ documents/CAL-TN-0030.pdf G.L. Israel, A. Belfiore, L. Stella et al., An accreting pulsar with extreme properties drives an ultraluminous x-ray source in NGC 5907. Science 355, 817–819 (2017) F. Jansen, D. Lumb, B. Altieri et al., XMM-Newton observatory – I. The spacecraft and operations. A&A 365, L1–L6 (2001) J.S. Kaastra, C. Ferrigno, T. Tamura, XMM-Newton observations of the cluster of galaxies Sérsic 159–03. Astron. Astrophys. 365, L99–L103 (2001) E. Kara, J.M. Miller, C. Reynolds et al., Relativistic reverberation in the accretion flow of a tidal disruption event. Nature 535, 388–390 (2016) M.G.F. Kirsch, A. Abbey, B. Altieri et al., Health and cleanliness of the XMM-Newton science payload since launch. SPIE 5898, 224–235 (2005) M.G.F. Kirsch et al., XMM-Newton, ESAs X-ray observatory, the Loss of Contact Rescue and Mission Operations ready for the next decade. Am. Inst. Aeronaut. Astronaut. 2010, 2123 (2010) M.G.F. Kirsch et al., Extending the lifetime of ESA’s X-ray observatory XMM-Newton. Am. Inst. Aeronaut. Astronaut. 2014, 1608 (2014) D. Lin, J. Guillochon, S. Komossa et al., A likely decade-long sustained tidal disruption event. Nat. Astron. 1, 33 (2017) D. Lin, J. Strader, E.R. Carrasco et al., A luminous X-ray outburst from an intermediate-mass black hole in an off-centre star cluster. Nat. Astron. 2, 656–661 (2018) N. Longdon, G. Melita, An ESA Workshop on a Cosmic X-ray Sepctroscopy Mission. ISSN 0379– 6566, SP-239, ESA Publications Division, Noordwijk (1985) K.O. Mason, A.A. Breeveld, R. Much et al., The XMM-Newton optical/UV monitor telescope. A&A 365, L36–L44 (2001) J.M. Miller, J.S. Kaastra, M.C. Miller et al., Flows of X-ray gas reveal the disruption of a star by a massive black hole. Nature 526, 542–545 (2015) J.U. Ness, A.N. Parmar, L.A. Valencic et al., XMM-Newton publication statistics. Astronomische Nachrichten 335(2), 210–220 (2014) F. Nicastro, J. Kaastra, Y. Krongold et al., Observations of the missing baryons in the warm-hot intergalactic medium. Nature 558, 406–409 (2018) M.J. Page, C. Brindle, A. Talavera et al., The XMM-Newton serendipitous ultraviolet source survey catalogue MNRAS 426, 903–926 (2012) M. Pantaleoni et al., XMM-Newton’s operational challenge of changing the attitude control to 4 active reaction wheels, after 12 years of routine operations. Am. Inst. Aeronaut. Astronaut. AIAA 2012, 1275587 (2012) A. Papitto, C. Ferrigno, E. Bozzo et al., Swings between rotation and accretion power in a binary millisecond pulsar. Nature 501, 517–520 (2013) M.L. Parker, C. Pinto, A.C. Fabian et al., The response of relativistic outflowing gas to the inner accretion disk of a black hole. Nature 543, 83–86 (2017) D.R. Pasham, R.A. Remillard, P.C. Fragile et al., A loud quasi-periodic oscillation after a star is disrupted by a massive black hole. Science 363, 531–534 (2019) J.R. Peterson, F.B.S. Paerels, J.S. Kaastra et al., X-ray imaging-spectroscopy of Abell 1835. Astron. Astrophys. 365, L104–L109 (2001)

1538

N. Schartel et al.

M. Pierre, C. Adami, M. Birkinshaw et al., The XXL survey: first results and future. Astronomische Nachrichten 338(334), 334–341 (2017) N. Rea, P. Esposito, R. Turolla et al., A low-magnetic-field soft gamma repeater. Science 330, 944–946 (2010) R.C. Reis, J.M. Miller, M.T. Reynolds et al., A 200-second quasi-periodicity after the tidal disruption of a star by a dormant black hole. Science 337, 949–951 (2012) G. Risaliti, F.A. Harrison, K.K. Madsen et al., A rapidly spinning supermassive black hole at the centre of NGC 1365. Nature 494, 449–451 (2013) P. Rodríguez, Specifications for Individual SSC Data Products (2021). https://xmmweb.esac.esa. int/docs/documents/XMM-SOC-GEN-ICD-0024.pdf S. Rosen, XMM-Newton Optical and UV Monitor (OM) Calibration Status (2020). https:// xmmweb.esac.esa.int/docs/documents/CAL-TN-0019.pdf A. Ruiz, A. Georgakakis, S. Gerakakis et al., The RapidXMM Upper Limit Server: X-ray aperture photometry of the XMM-Newton archival observations (2021). arXiv:2106.01687v1 M. Santos-Lleo, N. Schartel, H. Tananbaum et al., The first decade of science with Chandra and XMM-Newton. Nature 462, 997–1004 (2009) R.D. Saxton, A.M. Read, P. Esquej et al., The first XMM-Newton slew survey catalogue: XMMSL1. A&A 480, 611–622 (2008) N. Schartel, XMM-Newton: the next decade. Astronomische Nachrichten 329(2), 111–113 (2008) N. Schartel, Editor’s note. Astronomische Nachrichten 388, 139 (2017) N. Schartel, F. Jansen, M.J. Ward, XMM-Newton: status and scientific perspective. Astronomische Nachrichten 388, 354–359 (2017) X. Shu, W. Zhang, S. Li et al., X-ray flares from the stellar tidal disruption by a candidate supermassive black hole binary. Nat. Commun. 11, article id. 5876 (2020) L. Strüder, U. Briel, K. Dennerl et al., The European photon imaging camera on XMM-Newton: the pn-CCD camera. A&A 365, L18–L26 (2001) A. Talavera, P. Rodriguez, Astrometry with the Optical Monitor on board XMM-Newton: OM Field Acquisition and SAS: variable boresight (2011). https://xmmweb.esac.esa.int/CoCo/CCB/ DOC/Attachments/INST-TN-0041-1-0.pdf T. Tamura, J.S. Kaastra, J.R. Peterson et al., X-ray spectroscopy of the cluster of galaxies Abell 1795 with XMM-Newton. Astron. Astrophys. 365, L87–L92 (2001) A. Tiengo, P. Esposito, S. Mereghetti et al., A variable absorption feature in the X-ray spectrum of a magnetar. Nature 500, 312–314 (2013) I. Traulsen, A.D. Schwope, G. Lamer et al., The XMM-Newton serendipitous survey. X. The second source catalogue from overlapping XMM-Newton observations and its long-term variable content. A&A 641, A137 (2020) J. Trümper, The ROSAT mission. Adv. Space Res. 2, 241–249 (1982) M.J.L. Turner, A. Abbey, M. Arnaud et al., The European photon imaging camera on XMMNewton: the MOS cameras. A&A 365, L27–L35 (2001) M.G. Watson, J.L. Auguéres, J. Ballet et al., The XMM-Newton serendipitous survey – I. The role of XMM-Newton survey science centre. A&A 365, L51–L59 (2001) N.A. Webb, M. Coriat, I. Traulsen et al., The XMM-Newton serendipitous survey. IX. The fourth XMM-Newton serendipitous source catalogue. A&A 641, A136 (2020) B.J. Wilkes, W. Tucker, N. Schartel, M. Santos-Lleo, X-ray astronomy comes of age. Nature 606, 261–271 (2022) D.R. Wilkins, L.C. Gallo, E. Costantini et al., Light bending and X-ray echoes from behind a supermassive black hole. Nature 595, 657–660 (2021)

Part V Optics and Detectors for Gamma-Ray Astrophysics Lorraine Hanlon, Vincent Tatischeff, and David Thompson

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Telescope Concepts in Gamma-Ray Astronomy Thomas Siegert, Deirdre Horan, and Gottfried Kanbach

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The “MeV Sensitivity” Gap . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interactions of Light with Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instrument Capabilities and Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Earth’s Atmosphere and Space Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instrumental Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Background Suppression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Astrophysical Sources of Gamma Rays: Not One Fits All . . . . . . . . . . . . . . . . . . . . . . . . . . . Instrument Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Considerations: A Gamma-Ray Collimator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantum Optics in the MeV: Compton Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quantum Optics for Higher Energies: Pair Tracking Telescopes . . . . . . . . . . . . . . . . . . . . Scattering Information: Gamma-Ray Polarimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Apertures: Combinations and Wave Optics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma-Ray Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Understanding Gamma-Ray Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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T. Siegert () Institut für Theoretische Physik und Astrophysik, Universität Würzburg, Würzburg, Germany e-mail: [email protected] D. Horan Laboratoire Leprince-Ringuet, CNRS/IN2P3, Institut Polytechnique de Paris, Palaiseau, France e-mail: [email protected] G. Kanbach Max Planck Institute for Extraterrestrial Physics, Garching, Germany e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_43

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Outlook and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

This chapter outlines the general principles for the detection and characterization of high-energy γ -ray photons in the energy range from MeV to GeV. Applications of these fundamental photon-matter interaction processes to the construction of instruments for γ -ray astronomy are described, including a short review of past and present realizations of telescopes. The constraints encountered in operating telescopes on high-altitude balloon and satellite platforms are described in the context of the strong instrumental background from cosmic rays as well as astrophysical sources. The basic telescope concepts start from the general collimator aperture in the MeV range over its improvements through coded mask and Compton telescopes to pair-production telescopes in the GeV range. Other apertures as well as understanding the measurement principles of γ -ray astrophysics from simulations to calibrations are also provided. Keywords

Gamma-ray measurements · Collimator · Coded mask · Compton telescope · Pair creation telescope · Space environment · Instrumental background

Introduction Gamma rays (γ -rays) are traditionally defined as penetrating electromagnetic radiations that arise from the radioactive decay of an atomic nucleus, and, indeed, for γ -rays produced naturally on Earth, this is the case. Gamma rays constitute the electromagnetic radiation having energy of 100 keV and, therefore, have energies that traverse more than ten decades of the electromagnetic spectrum. In addition to those γ -rays coming from radioactive decays, the extra-terrestrial γ -rays incident on Earth are produced in a variety of different astrophysical scenarios. These include when extremely energetic charged particles accelerate in magnetic fields or upscatter ambient radiation to γ -ray energies, hadronic processes such as cosmic-ray (CR) interactions in the Galaxy, and, indeed, possibly in more exotic interactions, for example, the self-annihilation of dark matter particles (section “Astrophysical Sources of Gamma Rays: Not One Fits All”). In this chapter, an outline of the various techniques and instruments for the detection and characterization of γ -rays will be presented. The limitations and advantages of each particular detection technique, the backgrounds that must be overcome, and the environmental circumstances that must be considered will be reviewed. Only the direct detection of γ -rays will be discussed here, thus effectively

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limiting the upper energy range to approximately 100 GeV. For the detection techniques at the so-called very-high energy (VHE; Eγ  100 GeV), the reader is referred to chapters Introduction to groundbased Gamma-ray astrophysics. In order to detect γ -rays, we rely on one of their three interactions with matter, the photoelectric effect, Compton scattering, and pair production, whose respective cross sections depend on the energy of the γ -ray and on the material in which it interacts (section “Interactions of Light with Matter”). Since γ -rays cannot penetrate the Earth’s atmosphere, it having an equivalent thickness of approximately 0.9 m of lead, a detector needs to be placed above the atmosphere in order to detect γ -rays directly (section “Earth’s Atmosphere and Space Environment”). Like no other energy range, the γ -ray regime is dominated by an irreducible instrumental background (MeV energies) and limited by collection area (GeV energies) and telemetry (MeV and GeV energies; section “Instrumental Background”). Due to these factors and to the energy-dependent cross section of a γ -ray’s interaction with matter, the discussions in this chapter will be split according to the detection technique being employed, which is itself a function of the energy range of the γ rays being studied. Because of CR bombardment, MeV telescopes suffer from a high level of secondary γ radiation. This includes electron bremsstrahlung, spallation, nuclear excitation, delayed decay, and annihilation, all of which contribute to the instrumental background in the MeV range. This orders of magnitude enhanced rate of unwanted events leads to a worse instrument sensitivity – the “MeV sensitivity gap” – compared to neighboring photon energy bands (section “The “MeV Sensitivity” Gap”). The correct identification of background photons from celestial emission leads to an artificial split in the science cases (section “Astrophysical Sources of Gamma Rays: Not One Fits All”) because γ -ray instruments are built to observe either in the MeV or in the GeV. Even though astrophysical high-energy sources can span several decades in the electromagnetic spectrum, the MeV regime is often omitted because the sensitivities of current instruments rarely add much spectral information. In this chapter, we therefore handle MeV- and GeV-type instruments separately. We note, however, that leaving out information, even though it appears weak in the first place, leads to a biased view of the astrophysics to be understood. In the pair-production regime at tens of MeV to GeV energies, the spectra of γ -ray sources phenomenologically follow a power law such that the flux changes rapidly as a function of energy. With the exception of grazing incident mirrors used for hard X-rays in the energy range up to ∼100 keV (section “Other Apertures: Combinations and Wave Optics”), γ -rays cannot be focused and, therefore, in order to be detected, need to enter the detector and interact with it. So, unlike optical telescopes where a large effective area can be achieved by using a huge mirror to focus the optical photons onto a small detector, a large collection area can only be achieved at γ -ray energies by having a large detector volume. This requirement coupled with the constraints of launching a large mass high enough in the atmosphere that it can detect sufficient γ -rays (section “Atmospheric Effects”) limits the upper bound energy at which γ -rays can effectively be detected directly: for the direct detection of γ -rays, the physical volume of the detector is always

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larger than its effective detecting volume and hence the effective area photons see. The requirement to observe from space has the advantage of fewer constraints with respect to observing schedules (e.g., no day and night cycles); however, it limits the sensitive collecting areas of the telescopes because of the mass that can be transferred into an orbit. In this chapter, we will introduce the only 60-year-long history of γ -ray observations (section “Historical Perspective”); describe the least explored range of the electromagnetic spectrum, the MeV range (section “The “MeV Sensitivity” Gap”); and present the basic interactions of high-energy photons with matter that are used in all γ -ray telescopes (section “Interactions of Light with Matter”). Details about the instruments’ current capabilities and requirements to study high-energy sources are given in section “Instrument Capabilities and Requirements”, followed by an extensive discussion of instrumental background origins in section “Instrumental Background” and state-of-the-art suppression mechanisms (section “Background Suppression”). Based on the different science cases in the MeV and GeV range (section “Astrophysical Sources of Gamma Rays: Not One Fits All”), we detail principal instrument designs in section “Instrument Designs”. This includes the basic collimator (section “General Considerations: A Gamma-Ray Collimator”), coded mask telescopes (section “Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes”), Compton telescopes (section “Quantum Optics in the MeV: Compton Telescopes”), pair creation telescopes (section “Quantum Optics for Higher Energies: Pair Tracking Telescopes”), γ -ray polarimeters (section “Scattering Information: Gamma-Ray Polarimeters”), as well as other, alternative, but not necessarily yet realized instruments (section “Other Apertures: Combinations and Wave Optics”). Gamma-ray detectors are briefly explained in section “Gamma-Ray Detectors”, followed by how γ -ray measurements are to be understood, evaluated (section “Understanding Gamma-Ray Measurements”), and compared to simulations (section “Simulations”) and calibrations (section “Calibrations”). We close this chapter with an outlook about future and possible more advanced concepts in section “Outlook and Conclusion”.

Historical Perspective First Observations Gamma-ray astronomy, the highest-energy range of multi-wavelength astronomy, was already recognized in the 1950s as having the potential to provide direct insight into astrophysical processes with particles, fields, and dynamics of extreme conditions in the Universe (chapter “History of Gamma-Ray Astrophysics”). The principal source processes for high-energy γ radiation in space (beyond the energy range of radioactivity) were studied first. These include synchrotron radiation (Iwanenko and Pomeranchuk 1944), Compton scattering (Feenberg and Primakoff 1948), meson production and the decay of π 0 → 2γ (Hayakawa 1952), and bremsstrahlung (Hutchinson 2010).

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The status of particle physics, CR research, and radio astronomy in the 1950s raised widely debated questions such as: “Where do CRs come from and how are they produced?”, “What is the photon fraction in the CR beam?,” “What powers the strong Galactic radio emission?,” “Are there discrete γ -ray sources in the sky and what could be the nature of such sources?,” “Do the observed particle emissions from solar flares lead to γ -ray emissions (nuclear lines and continua)?,” and “Is there antimatter around?.” Estimates for the strength of cosmic γ -ray sources were mainly based on the contemporary knowledge of CRs, the distribution and density of the Galactic interstellar medium (HI radio emission), and the observations of radio emission from individual objects like the Crab Nebula or radio galaxies. Morrison (1958, Morrison 1958) estimated that the active Sun would emit 0.1–1 ph cm−2 s−1 between 10 and 100 MeV and 1–100 ph cm−2 s−1 in the neutron-proton capture line at 2.23 MeV. The Crab Nebula (the pulsar was unknown at the time) and typical radio galaxies should have intensities of 10−2 ph cm−2 s−1 . A thorough study of γ -ray production by CRs interacting with the interstellar medium in the Galaxy by Pollack and Fazio (1963) predicted a flux from the Galactic Center of ∼10−4 ph cm−2 s−1 sr−1 and half that intensity from the Anticenter. All of these flux estimates turned out to be much too high, but nevertheless many experiments were started to detect celestial γ -rays. Short exposures on balloons and a very strong environmental background prevented significant detection of γ -rays from the Milky Way or from discrete sources. The beginning of the space age in 1958 finally provided the facilities to operate γ -ray experiments above the atmosphere. The clear, unabsorbed view of the sky, the longer exposures, the absence of the atmospheric background, and the advanced instruments succeeded in establishing γ -ray astronomy as a new and promising branch of astrophysics. Gamma-ray astronomy is a discipline that depends on the technical resources of the space age. The ground level of Earth-bound observatories is shielded from cosmic γ radiation by the atmosphere (Fig. 1), with roughly 20 (resp. 60) mean free

Fig. 1 Absorption of cosmic electromagnetic radiation in Earth’s atmosphere

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path lengths of attenuation at 1 GeV (resp. 1 MeV) Furthermore, the charged fraction of cosmic radiation, which dominates primary γ -rays by roughly a factor of 104 , generates a high level of secondary γ -ray background in the atmosphere and in detector equipment. It is therefore essential to expose a γ -ray telescope in a low level of external background, i.e., above the atmosphere but below the Earth’s radiation belts, for long periods of observation to obtain the necessary detection statistics. For satellites, this is best achieved in a low Earth orbit (LEO) above the equator with an altitude of 400–500 km. Equally important is the design of the telescope so as to suppress the recording of unwanted charged particles (veto systems) and local γ radiation (material selections). Both requirements directly impact the sensitivity of a γ -ray telescope with detector exposure area A, detection efficiency ε, and angular resolution elements of size θ . Discrete cosmic sources with fluxes of Fγ embedded in a “quasi” continuous background intensity IB observed for an exposure time tobs are then detected with a statistical sensitivity of S:

S=

Fγ Aεtobs (IB Aεtobs π θ 2 )

1/2

=

Fγ θ



Aεtobs IB π

1/2

(1)

It is evident from Eq. (1) that high sensitivity is the result of a large effective area, Aeff = Aε, and long observation times, combined with small angular resolution and low background intensities. Of course this formulation is extremely simplified compared to more appropriate analysis tools using proper instrument response functions for effective detector area, angular and energy resolution, and detailed models for the background radiation, all as a function of primary energy and incidence direction.

Missions 1960–1990 The first successful satellite detectors for high-energy γ -radiation were small ˇ scintillation Cerenkov counter assemblies with anticoincidence shields. As depicted in Fig. 2, they had to fit on the satellites of the 1960s and could only transmit data with limited rates. The emission of >100 MeV photons from the inner Galaxy was, however, clearly established by the OSO-3 measurements (Kraushaar et al. 1972) and confirmed by a spark-chamber imaging balloon experiment (Fichtel et al. 1969). Here, it is interesting to note a performance comparison between the scintillator telescope and the pointed balloon instrument: both could achieve similar results on the Galactic emission with an effective area of 2–8 cm2 even though the former required ∼16 months of observation time, whereas the balloon flight only required several hours. Gamma-ray instruments for the low-energy range 50 MeV) was derived from ∼16 months of observations (Kraushaar et al. 1972), but the coarse angular resolution (15◦ ) prevented the detection of point sources

spectrometer, with its omni-directional response, a massive “well-type” collimator is placed around a central detector. Collimators can be either active radiation detectors, for example, made of BGO or CsI scintillators, or passive structures made of high-Z metals. Two examples of successful instruments are the γ -ray spectrometer (GRS) on the Solar Maximum Mission (SMM, 1981–1990; Fig. 3) and the Oriented Scintillation Spectrometer Experiment (OSSE) on the Compton Gamma-Ray Observatory (CGRO, 1991–2000). The advantage of an imaging telescope for astronomical observations was clearly established and led to the next generation of high-energy detectors, SAS2 and COS-B. Both high-energy satellite telescopes were based on digital readout spark chambers that allowed for the reconstruction of pair-creation events by tracking the electron-positron pairs. Around the central tracker, a charged particle anticoincidence shield made of plastic scintillator and, for COS-B, a calorimeter to measure the deposited pair energy were used. SAS-2 was developed on the basis of previous balloon detectors at NASA/GSFC, and the COS-B instrument was built by a European consortium of research institutes.

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Na I Spectrometer

Am 241

Na I Spectrometer X ray (2)

CsI Back Detector

Co60(3)

Front Plastic

CsI Annulus

Back Plastic

Fig. 3 SMM/GRS (1981–1990): an actively shielded multi-crystal scintillation spectrometer, sensitive to photons in the range 0.3–100 MeV (Forrest et al. 1980). SMM was continuously pointed at the Sun. The open acceptance angle of about (135◦ ) in the forward direction prevented the identification of individual sources, but allowed the instrument to monitor the temporal signatures of solar flares

The “MeV Sensitivity” Gap Figure 4 shows the sensitivities for past and current γ -ray instruments in the range between 10−2 and 105 MeV. While sensitivity should be defined case by case, i.e., depending on the source spectrum, its spatial distribution, and position in the instrument field of view, an order of magnitude estimate of the instrument performance can be given assuming a generic spectral shape at each photon energy. When provided with background estimates, the effective area, and a typical exposure time (here 1 Ms), the sensitivity can be calculated from Eq. (1) to the desired level (here 3σ). In general, the lower the sensitivity, the better the instrument performs. It is evident that the currently flying telescopes NuSTAR (0.03 GeV; chapter “Large Area Telescope”) shape a region in sensitivity space that peaks in the MeV. This several orders of magnitude worse sensitivity is called the “MeV sensitivity gap" and is the direct result of a small collection area (section “Instrument Designs”) combined with a high instrumental background (section “Instrumental Background”). Reducing this MeV gap is currently an active field of technological, methodological, and conceptual development, and attempts to alleviate the problems in the MeV range are described in sections “Other Apertures: Combinations and Wave Optics” and “Outlook and Conclusion”.

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Fig. 4 Continuum sensitivities of hard X-ray to high-energy γ -ray instruments. Shown is the 3σ sensitivity for an observation time of 1 Ms. The Crab’s spectral energy distribution from Meyer et al. (2010) is shown with respect to the sensitivities as it is the “standard candle” of high-energy sources. MilliCrab (mCrab) flux levels can only be seen with deep exposures in the 0.3–100 GeV range or below 100 keV. This defines the “MeV gap” of instrument sensitivities (red shaded area) – the least explored region in the electromagnetic spectrum

In addition to this MeV gap for continuum emission, there is also a similar problem for nuclear γ -ray lines. While COMPTEL on CGRO (⊲ Chap. 64, “The COMPTEL Experiment and Its In-Flight Performance”) could, for example, identify narrow line emission at 1.8 MeV, its spectral resolution was only 10% (FWHM) so that many lines blended together to form one broad feature. High spectral resolution in the MeV range can be achieved by the use of germanium detectors (section “Gamma-Ray Detectors”), such as in RHESSI or SPI. While increased spectral resolution helps to identify background features more easily, the small collecting area still prohibits the investigation of many potential astrophysical sources. As of now, only a dozen nuclear lines of astrophysical origin have been observed with HEAO-3, COMPTEL, RHESSI, and SPI (and NuSTAR). These include the positron annihilation line from the center of the Galaxy at 511 keV (e.g., Mahoney et al. 1994; Purcell et al. 1997; Jean et al. 2006; Churazov et al. 2011; Siegert et al. 2016, 2021); short- and long-lived ejecta from massive stars and their supernovae such as 44 Ti (e.g., Iyudin et al. 1997; Renaud et al. 2006; Grefenstette et al. 2014; Boggs et al. 2015; Siegert et al. 2015; Weinberger et al. 2020, at 68, 78, 1157 keV), 26 Al (e.g., Mahoney et al. 1984; Diehl et al. 2006; Kretschmer et al. 2013; Siegert and Diehl 2016; Pleintinger et al. 2019, at 1809 keV), and 60 Fe (e.g., Harris et al. 2005; Wang et al. 2007, 2020, at 1173 and 1332 keV); short-lived isotopes powering the early light curves of type Ia supernovae (e.g., Diehl et al. 2014, 2015; Churazov et al. 2014; Isern et al. 2016, with 56 Ni and 56 Co at 158, 812, and 847, 1238 keV, respectively); as well as nuclear excitation

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lines from solar flares (e.g., Gros et al. 2004; Kiener et al. 2006, with 511 keV from electron-positron annihilation, 2 H at 2223, 12 C at 4438, and 16 O at 6129 keV, among others). With a factor of 10 improvement in the line sensitivity, the number of detected lines, and therefore the science enabled by this, could increase by the same order of magnitude, eventually finding CR excitation of interstellar medium material, ejecta from classical novae, and multiple supernova lines (e.g., Timmes et al. 2019). The advantage of nuclear line studies is the possibility of finding an absolute measure of ejecta masses, CR fluxes, and kinematics, which may be biased by using observations at other wavelengths.

Interactions of Light with Matter While, for longer-wavelength light, most interactions with matter are either of refractive, reflective, or diffractive nature owing to the wave characteristic of light, higher-energy photons experience processes prone to particles instead of waves. These are used to determine the energy of the incoming light by measuring their partial or total deposits in the detecting material. While more processes can occur, the most relevant reactions for X- and γ -ray photons are photoelectric absorption (photo-effect), Compton scattering, and pair production. The photo effect (Einstein 1905) describes a photon undergoing an interaction with an atom in which the photon deposits its total energy and is removed completely. To conserve momentum and energy, a photoelectron is emitted by the absorbing atom. Since the interaction is with the atom as a whole, having bound electrons in its shells, the photo effect cannot occur on free electrons. The most probable electron to be ejected in photoelectric absorption is the one most tightly bound in the K-shell. The photoelectron has an energy of Ee = Eγ − Eb where Eb is the binding energy of the electron in the atom. The interaction probability for a γ -ray photon to undergo the photo effect is described by the cross section, typically as a function of energy, σPE =

16 √ Z5 2π re2 α 4 3.5 , 3 k

(2)

where re is the classical electron radius, α is the fine-structure constant, Z is the atomic charge number, and k = Eγ /(me c2 ) is the photon energy in units of electron rest masses (Fornalski 2018). Equation (2) is a valid approximation for k  0.9; for higher energies and for more precision over large photon energy ranges, the cross section from Davisson and Evans (1952) should be used. At photon energies of approximately between k = 0.1 and 1.0, depending on the material, the Compton effect (Compton 1923) becomes the dominant interaction process of light with matter. Compton scattering describes the process of a γ -ray undergoing scattering with an electron, assumed to be at rest. The photon changes

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its path as a result of this process and transfers some of its energy to the electron which then recoils. The deflection angle, also called the Compton scattering angle ϕ, is the fundamental property that determines the origin of the γ -rays in Compton telescopes (section “Quantum Optics in the MeV: Compton Telescopes”). Because, in principle, the range of scattering angles covers a full circle, the process of Compton scattering, i.e., the photon loses energy to enhance the kinetic energy of the electron, can also be inverted to inverse Compton scattering, i.e., the photon gains energy by scattering with fast electrons. In the range k = 0.2–20 (Fornalski 2018), the total cross section for Compton scattering is approximated by

σCE =

Z2π re2



   1 + k 2(1 + k) ln(1 + 2k) 1 + 3k ln(1 + 2k) . − − + 1 + 2k k 2k k2 (1 + 2k)2 (3)

Higher-order corrections can again be found in Davisson and Evans (1952). For k > 2, pair production (Blackett and Occhialini 1933), i.e., the conversion of a γ -ray into an electron-positron pair, becomes possible. While, formally, the production of pairs starts at twice the rest mass energy of an electron of 1.022 MeV, the interaction probability stays at a low level until the cross sections dominate, typically above k = 20. Pair production can occur in any electromagnetic field; for the detection of γ -rays, the Coulomb fields of nuclei are to be considered. The γ ray photon loses all of its energy in the process, is removed from the scheme, and is replaced by a pair that carries the total energy of the photon. The kinetic energy of the electron and positron, respectively, is symmetric about half the energy of the incident photon, minus the rest mass energy of the electron. The interaction cross section for pair production (Fornalski 2018; Davisson and Evans 1952) is σPP = Z 2 αre2



 28 218 ln 2k − + O(ln k/k 2 ) , 9 27

(4)

where higher-order terms span several lines of terms. The important feature to note here is that the cross section for pair production in the field of a nucleus increases with the charge number of the nucleus squared. In detail, the cross sections vary for different materials, compositions, and matter structures. In Fig. 5, the mass attenuation coefficients, nσ/ρ, with ρ being the density and n being the number density of the material, for γ -ray detector media that are typically used are shown. The shapes of photo effect, Compton scattering, and pair production are similar for the elements and compounds shown; however, the minuscule details change the behaviors and areas of use of the detectors. For example, plastic shows a much broader Compton scattering regime compared to other scintillating materials (e.g., BGO), making it the scattering material of choice of classic Compton telescopes (section “Quantum Optics in the MeV: Compton Telescopes”).

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Fig. 5 Mass attenuation coefficients for commonly used detector materials as a function of photon energy. The individual interaction processes are shown as colored lines. Left: Germanium (solid) and silicon (dashed). Compton scattering dominates in the energy range ∼200 keV to ∼10 MeV which makes these semiconductors efficient scattering detectors. Right: BGO (solid) and CZT (dashed). In these high-Z materials, absorption through photo effect or pair creation is more pronounced

Instrument Capabilities and Requirements In order to do γ -ray astronomy, the direction from which the γ -ray originated, its time of arrival, its energy, and its polarization would, ideally, be determined accurately. Depending upon the energy of the incident γ -ray and upon the nature of the source of interest, different types of γ -ray detectors are required for this task. As will be discussed in section “Astrophysical Sources of Gamma Rays: Not One Fits All”, some scientific objectives require highly accurate energy resolution, usually achieved at the expense of positional accuracy, i.e., angular resolution. Conversely, when high angular resolution is required, the spectral accuracy of the measurement usually has to be compromised. Gamma-ray polarimetry is an upcoming field, and individual chapters in this book are dedicated to this topic (⊲ Part XIX, “Polarimetry”); a brief overview of measuring the polarization of γ rays is provided later in this current chapter. A massive detector with limited positional but good energy resolution and deep enough to absorb most of the scattered photons can be used as calorimeter to measure spectra of incident γ radiation. Limited angular resolution can be achieved by fitting massive anticoincidence wells around the detectors leaving an “acceptance angle” free or by constraining the field of view with a passive or active collimator. A modern high-resolution Ge spectrometer is the MeV spectrometer SPI on the INTEGRAL mission (Winkler et al. 2003; Vedrenne et al. 2003), which in addition to a massive anticoincidence well encodes the incident γ -ray beam through a coded mask to enable imaging of radiation sources (section “Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes”). In order to detect a γ -ray via its pair-production interaction while extracting as much positional and energy information as possible, two main elements are

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required: Firstly, the γ -ray must be made to interact, i.e., pair produce, in the detector. In order to increase the probability of the γ -ray pair-producing, a high-Z material is required. For the Energetic Gamma Ray Experiment Telescope (EGRET) detector aboard CGRO, this comprised tantalum foils (Thompson et al. 1993), while for both the Large Area Telescope (LAT; ⊲ Chap. 68, “The Fermi Large Area Telescope”) on board the Fermi satellite and the Gamma-Ray Imaging Detector (GRID) on the Astro-rivelatore Gamma a Immagini LEggero (AGILE) satellite (⊲ Chap. 66, “The AGILE Mission and Its Scientific Results”), the high-Z converter material is provided by tungsten (Atwood et al. 2009; Tavani et al. 2009). The resulting electron-positron pair must then be tracked as accurately as possible so that the direction of the incident γ -ray can be reconstructed. This is done by measuring the passage of the electron/positron pair by the tracker. For EGRET, this was achieved by means of a multilevel spark chamber (Thompson et al. 1993). In both LAT and AGILE’s GRID, the trajectory of the charged particles is recorded by layers of silicon strip detectors (Atwood et al. 2009; Tavani et al. 2009) (section “Quantum Optics for Higher Energies: Pair Tracking Telescopes”). To determine the energy of a γ -ray, it is desirable to stop the electron-positron pair in the detector via a calorimeter, where the total energy deposit is measured. For EGRET, a large NaI Total Absorption Shower Counter was the principal energymeasuring device, while in LAT, the calorimeter comprises 16 modules, each of which is composed of 96 CsI(T1) crystals. The calorimeter on AGILE’s GRID is also composed of CsI(T1), in this case 30 bars arranged in 2 planes (Tavani et al. 2009). In addition to providing an energy measurement, a segmented calorimeter can also act as an anchor for the electromagnetic particle shower, providing further positional information to aid with pinpointing the direction of the incident γ -ray and to help with background discrimination (section “Tailored Data Selections”). The required elements of a γ -ray detector operating in the pair-production regime are, therefore, a tracker and a calorimeter. Not essential for the detection of the γ -ray but absolutely necessary so as to reject the overwhelming background of charged CRs that constantly bombard the instrument is an anticoincidence detector (ACD, section “Anticoincidence Shields”). This allows the detector to self-veto upon the entry of a charged particle, so it is essential that it has high detection efficiency for such particles. The ACD of EGRET comprised a large scintillator which surrounded the spark chamber. Backsplash, whereby a charged particle generated inside the detector traversed the ACD and thus caused a false veto, became a problem above 10 GeV (section “Background as a Function of Energy”). To avoid backsplash, the ACD of both the LAT and AGILE are segmented allowing only the segment adjacent to the incident photon candidate to be examined when searching for a veto. This drastically reduces the effects of backsplash allowing for a much more efficient background rejection by the ACD. All these considerations are summarized in the four basic parameters of any γ ray telescope, most importantly the effective area, as well as the energy, angular, and temporal resolution. An overview of current and past γ -ray instruments in the MeV– GeV range is provided in Fig. 6. It is clear that the effective area is the reason why

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Fig. 6 Characteristics of a selection of historic and current instruments as a function of photon energy. Top left: Effective area. Top right: Angular resolution. Bottom left: FWHM energy resolution. Bottom right: Timing accuracy

there is such a great loss in sensitivity in the MeV range (100 cm2 ) compared to the keV or GeV range (both 1000 cm2 ; section “The “MeV Sensitivity” Gap”). However, because of Ge detectors, for example, the spectral resolution of MeV instruments (FWHM/E ≈ 10−3 –10−2 ) can supersede those of GeV instruments by two orders of magnitude. The angular resolution of MeV telescopes can be similar to those of GeV telescopes, but only under specific circumstances, for example, when observing the Sun in the case of RHESSI with a temporal modulation aperture (section “Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes”). Normally, Compton telescopes suffer from their inherently poor angular resolution on the order of degrees, whereas coded mask telescopes could achieve arcminute resolutions or better (see section “Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes”). GeV telescopes can be considered almost direct imaging telescopes as the dispersion is only important for lower energies. Because of the trackers, angular resolutions below the 0.1◦ scale are possible. Finally, the scarcity of γ -rays from celestial sources as well as their intrinsic temporal variability adjusts the timing resolution to typical values around 100 µs.

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Earth’s Atmosphere and Space Environment Atmospheric Effects While at sea level the Earth’s atmosphere blocks almost all low- and high-energy γ -rays to the extent that ground-based observations are impossible, high-altitude observations are still worth the effort and reduce the cost. For instrument prototypes, in particular, balloon flights are often used to test new apertures and concepts. In Fig. 7, the transmissivity of the Earth’s atmosphere is shown for different photon energies, incidence angles (zenith), and altitudes above the surface (Hubbell and Gaithersburg 1996; Berger et al. 2017). The transmissivity is defined as the probability for a photon to reach a certain altitude without previous interaction and therefore to be unabsorbed. At aeroplane cruising altitudes (12 km), for example, the chance for a 1 MeV photon to pass through the upper layers of the atmosphere is 0.001% at most (i.e., at zenith). At this height, the transmissivity is maximized for 40 MeV photons at about 5%. Because of the exponential decrease in the density of the atmosphere, the stratosphere layers of the atmosphere (up to 50 km above ground) provide a useful environment for γ -ray telescopes. At typical balloon flight altitudes of around 30 km, the zenith transmissivity is already around 30% for photon energies of 50 keV. Up to 40 MeV, the transmissivity grows exponentially to about 85% and slightly declines afterward to flatten out at 80% for GeV energies. Clearly, with the beginning of the mesosphere at altitude of approximately 80 km, essentially all γ -ray photons are directly measurable, and only soft and hard X-ray photons remain absorbed. Beyond the von Karman line at around 100 km, which conventionally defines the border between the atmosphere and space, all photons are readily detected as the transmissivity is nearly 100% throughout the electromagnetic spectrum. Most important for γ -ray observations at balloon altitudes, however, is the zenith angle dependence. For the same photon energy and observation altitude, different zenith angles lead to vastly different transmissivities and therefore a much more drastic change in the effective area of the instrument (section “Instrument Designs”). While response functions for balloon experiments take into account the

Fig. 7 Transmissivity of Earth’s atmosphere as a function of incoming photon energy (left) and observation altitude above surface (right) for different zenith angles

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zenith dependence of their effective area, the simulations to provide a reasonable measure of the atmosphere effects require different setups depending on the balloon position around the Earth. This is the case because the local atmospheric conditions, including density and temperature, for example, and, in particular, the magnetic cutoff rigidity change with the Earth’s latitude and longitude (Smart and Shea 2005).

In-Space Observations Passing the 100 km mark, γ -ray instruments experience the space environment which mainly concerns the distributions of charged particles. In terms of onboard electronics, the instruments start to suffer more single event latch-ups and other effects. These are short circuits caused by heavy ions or protons hitting the electronics and triggering semiconductor band transitions. Apart from the latchups, the detectors themselves are also more susceptible to incoming radiation. This can be used as an advantage to measure the in-orbit particle spectrum and therefore provide a measure for the instrumental background (section “Instrumental Background”). Depending on the energy of the charged particles, they produce secondary particles when interacting with the instrument or satellite material. The secondary particles compose most of the instrumental background for γ -ray measurements in space, especially in the MeV range. The concentration of charged particles around Earth is not homogeneous. Because of the Earth’s magnetic field, charged particles are trapped around the planet in torus-like accumulations (Fig. 8). These are known as the Van Allen radiation belts (e.g., Ganushkina et al. 2011). Two tori trap electrons and protons, and to a lesser extent α particles, reaching from 0.2 out to 2 Earth radii (inner belt) and from 3 to 10 Earth radii (outer belt), respectively. While the inner belt contains sub-relativistic electrons (few hundred keV) and protons (∼100 MeV), the outer belt also holds relativistic electrons (up to 10 MeV). The outer belt is more easily influenced by the Sun and therefore more variable than the inner belt.

Fig. 8 Van Allen radiation belts around Earth (left) with inner and outer belts (to scale). Because the Earth’s magnetic field is tilted with respect to its rotational axis (dashed line), the closest part of the inner belt can reach to about 200 km above the southern Atlantic. This is called the South Atlantic Anomaly (SAA, right, adapted from Finlay et al. (2020) and reproduced with permission). Shown is the difference to the mean magnetic field intensity of 45.8 µT (red solid line) in steps of 4.1 µT until the region defining the SAA (solid purple line). Inside the purple region, the steps are 0.6 µT for a minimum around Earth longitude and latitude of 60◦ W and 28◦ S

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Because the magnetic field of the Earth is slightly tilted with respect to its rotational axis and the belts’ centers furthermore shifted from Earth’s center, the inner belt has an anomalously close approach at one specific region to the East of the South American continent. This is called the South Atlantic Anomaly (SAA, e.g., Pavón-Carrasco and De Santis 2016; Finlay et al. 2020). The anomaly represents an area in which the Earth’s magnetic field is weakest relative to its surroundings (Fig. 8, right). In this region, the inner belt approaches within 200 km of the surface which results in higher abundances of energetic particles. This leads to an enhanced instrumental background for satellite observatories (section “Instrumental Background” and ⊲ Chap. 54, “Orbits and Background of Gamma-Ray Space Instruments”).

Orbit Considerations There are options to alleviate the impact of the SAA and Van Allen radiation belts when the orbit of the satellite onboard which the instrument will be mounted is chosen. However, not all instruments suffer from the effects of the increased radiation in the same way. While MeV telescopes without major event selection capabilities (section “Tailored Data Selections”) should avoid the SAA altogether, GeV instruments are typically placed in LEO, i.e., orbits between 200 and 2000 km. Most astronomical observatories in LEO are found between 450 and 600 km. Above an orbit of 1200 km, the radiation belts would again lead to a much increased instrumental background. For MeV transient observatories in particular, for example, Fermi-GBM, the enhanced particle flux at LEO is of only mediocre concern because the background for short timescales (on the order of seconds or less) can easily be determined from adjacent times. For longer and targeted MeV observations, the radiation belts would lead to an insurmountable background rate which would heavily reduce the sensitivity of the instrument. For this reason, MeV observatories like INTEGRAL chose high eccentricity and high inclination orbits to escape the radiation belts for a significant amount of their orbits. The initial INTEGRAL orbit, for example, was a 72-hour orbit with an inclination of 52◦ and an apogee and perigee of 154,000 and 9000 km, respectively. Since the outer belt is populated with charged particles to at most 10 Earth radii (∼65,000 km), most of the time spent in this orbit (∼90%) is far away from the increased radiation. However, the instruments onboard INTEGRAL have to be switched off every time it approaches the Earth. For special tasks which cannot (or can only inaccurately) be performed by single instruments, special orbits can be considered. For example, some transient monitors have hardly any spatial resolution but can, however, be used in combination to provide highly accurate localizations (section “Interplanetary Network”). The difference in the photon arrival times of transients can be used in triangulation to map overlapping annuli onto the sphere of the sky. The larger the leverage arm, i.e., the larger the light travel distance between instruments, the better the localization accuracy. In particular, the gamma-ray spectrometer onboard Mars Odyssey in a Mars orbit provides a valuable baseline for Earth-orbiting transient detectors. This technique led to the term interplanetary network (IPN, e.g., Hurley et al. 2009;

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Fig. 9 Satellite orbits and balloon flight paths. From left to right are shown the Fermi orbit, the INTEGRAL orbit, and the COSI balloon path from a campaign during 2016. The orbits in each panel are to scale

section “Interplanetary Network”), for transient localization with triangulation. Another “orbit” of interest for γ -ray and other observatories is the Lagrange points, L2, of the Sun-Earth system (e.g., Wind, Spektr-RG), which also provide an excellent baseline for IPN measurements. While satellites follow a specified path and can, most of the time, perform maneuvers to correct their orbits (and to make sure that they re-enter the atmosphere when the mission is decommissioned), balloons have no or only little capability to adjust their flight paths. Because of security concerns, among others, balloon flights are typically launched from remote areas, such as Antarctica, or those which are only thinly populated. After the launch, the balloons experience the natural Earth environment and float freely governed by wind (lower atmosphere), temperature (day and night cycle), and torque (rotation of the Earth). Because the power generation has to be secured, which is mostly done with solar panels, the balloon gondolas are rotated toward the Sun during daylight. This also holds the aspect angle of the instruments, which simplifies the analysis. At night, the gondolas can again tumble freely, and minuscule changes in the altitude can lead to extreme variations in the flight paths. As examples, we show two satellite orbits as well as the longduration balloon flight path of the COSI prototype in Fig. 9. For more details on orbital considerations, the reader is referred to ⊲ Chap. 54, “Orbits and Background of Gamma-Ray Space Instruments”.

Instrumental Background Variations of the Background The interaction of charged particles, i.e., in general CRs, with instrument and satellite material leads to several different components that are summarized under the term instrumental background (for a more in-depth treatment of this subject,

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see ⊲ Chap. 54, “Orbits and Background of Gamma-Ray Space Instruments”). These are all unwanted primary and secondary particles and photons which lead to enhanced count rates in the instruments, diluting the celestial signals of interest. The interactions of CRs with matter lead to inverse Compton scattering, bremsstrahlung, nuclear excitation, spallation, radioactive buildup and decay, particle-antiparticle annihilation, and secondary particle production which can also undergo all of the previous interactions again. This results in a cascade of interactions that, depending on the energy range of the instruments, are measured continuously. The largest impact on the amplitudes of these processes is given by the solar activity and the terrestrial and solar magnetic field. Long-term trends in the instrumental background rate of MeV instruments are anticorrelated with the Sunspot number (e.g., Clette et al. 2014, 2016), which is a direct indicator of the solar magnetic activity cycle of 11 years (Fig. 10, top left). The solar modulation of CRs is related to the intensity of the turbulent solar wind, which increases when the Sun’s magnetic field is strong. In other words, this means that when there is a high number

Fig. 10 CR-induced background rates for different processes from different origins. Top left: Prompt MeV background is anticorrelated to the Sunspot number and thus with the solar magnetic field. Top right: Radioactive buildup can occur when the lifetime of isotopes (here 60 Co) is much longer than the activation function (cosmic-ray flux, inverse proportional to Sunspot number). Bottom left: Solar flare events provide a large single dose of mainly protons during a short amount of time. Intermediate lifetime isotopes (here 48 V) are enhanced by a factor of 10 and then decay according to their decay constants. Bottom right: Equatorial LEO satellites pass the SAA every 90 min, activating numerous short-lived isotopes which then decay during the next orbit. (Adapted and updated from Diehl et al. (2018) and Biltzinger et al. (2020) – reproduced with permission)

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of Sunspots, the instruments are better shielded from CRs. This leads to a reduction of the instrumental background rate which is why γ -ray missions are typically launched during or before the solar maximum. One famous example for this is the Solar Maximum Mission (SMM) launched in 1980. Two solar cycles later in 2002, INTEGRAL was launched – also near the solar maximum. Depending in addition on the chosen satellite orbit, the background rate can more than double between the solar maximum and minimum. This effect is visible for prompt background phenomena such as continuous processes (e.g., bremsstrahlung; Fig. 10 top left), nuclear excitation followed by fast de-excitation which typically happens on the order of nanoseconds, and particle production with fast decays from pions or βunstable elements. If the lifetime of the particles produced is (much) longer than the production timescale through CR bombardment, two other temporal evolutions of the background can be found. For example, if the radiation dose hitting the satellite is drastically increased, such as during a solar flare event with a coronal mass ejection, the background rates from γ -rays of all isotopes in the satellite can rise by several orders of magnitude. For isotopes produced during such events that are longer-lived, the background rate then stays at a high level even long after the initial dose. In Fig. 10, bottom left, the rise of the background rate from the element 48 V is shown. From a rather constant background rate of ∼6 × 10−4 cnts s−1 before the X-class solar flare on October 23, 2003 (= MJD 52935), the 48 V rate rises to more than 1 × 10−2 cnts s−1 . Because 48 V has a half-life time of 16 days, its rate decays only according to this decay time; the expected exponential decay is clearly seen. Such nuclear reactions occur continuously, either converting stable satellite materiel to radioactive isotopes, which then decay promptly or with some delay, or directly exciting the nuclei of the instrument which then de-excite by the emission of γ -ray photons. These γ -ray photons have specific energies so that individual isotopes and processes can be identified which helps in suppressing the instrumental background as a whole. In the case of a regularly enhanced dose of radiation, for example, by the passage through the SAA for LEO missions, the decays might not even go back to the base level because after about 90 min, the next passage of enhanced radiation occurs. This is shown in Fig. 10, bottom right, from a measurement of Fermi-GBM over the course of one day. Sixteen subsequent orbits and the different components making up the total measurement are shown. While, after the first three SAA passages, the corresponding levels go back to nearly zero, orbits 4–7 obtain a higher radiation dose so that until 40,000 seconds, the background rate gradually builds up. After orbit 8, only the very short-lived isotopes are seen in the data, while the buildup is still decaying on its own timescale. Other components, such as the Earth albedo, the general CR activation rate outside the SAA, the cosmic γ -ray background, as well as the Sun as a γ -ray source itself, stay constant. Only the change in orientation and aspect of the instrument with respect to the different astrophysical and background sources let the rates appear varying (Biltzinger et al. 2020). If the radioactive decay time of isotopes is much longer than the activation function from CRs, more and more radioactivity is created inside the instruments. In the case of 60 Co,

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for example, with a half-life time of 5.27 years, the decay rate is so small that over very long times, the background rate rises because there is radioactivity that built up. Figure 10, top right, shows the rate of the two γ -ray lines at 1173 and 1332 keV from the decay of 60 Co over 19 years of INTEGRAL/SPI measurements. Clearly, as the Sunspot number goes down, i.e., the activation rate goes up, the 60 Co rate also rises. Since the activation rate drops again after the solar minimum, but the material still decays, the background rate in these lines appears constant. Then after the second maximum, the rate rises again.

Background as a Function of Energy Since most γ -ray telescopes cover one or more decades of the electromagnetic spectrum, their measurements, and in particular their background, can appear quite different. Depending on the spectral resolution, which, technologically, can be much higher at MeV energies compared to GeV energies, the general appearance changes. At MeV energies, the background spectra are dominated by an electron bremsstrahlung continuum with a multitude of γ -ray lines on top (see Fig. 11 for an overview of background processes). Above ∼20 MeV, the decay and de-excitation lines from nuclei cease, and the spectrum is a pure continuum up even to very high energies (TeV). Pion production and decay (e.g., p + p → p + p + π 0 , followed by π 0 → γ γ ) describes the transition region from the MeV to the GeV background. While these interactions would produce a spectrum peaking at 67.5 MeV (half the rest mass of π 0 ) with a high-energy tail mimicking the incident proton spectrum, most of these interactions inside the instrument can be rejected due to their different signatures. The nuclear lines directly reflect the elemental composition of the satellite, the instrument, and the Earth’s atmosphere. For example, shown in Fig. 12, top, are the highly resolved NuSTAR and SPI background spectra. Most of the lines below ∼100 keV are due to X-ray fluorescence of satellite material, i.e., atoms become ionized due to impinging radiation, which leads to an electronic transition from higher to lower shells, followed by the emission of a characteristic photon. Depending on the element, these fluorescence photons can reach up to 115.6 keV (uranium K-shell), formally being an X-ray photon due to its electronic nature, however, falling into the “γ -ray” regime. The strongest instrumental lines in NuSTAR are due to K-shell fluorescences of cesium and iodine at 28 and 31 keV, respectively. Beyond the fluorescence lines, nuclear excitation lines, also appearing below 100 keV, shape the background spectra up to ∼20 MeV. Nuclear excitation is the interaction of an incoming particle with only the nucleus of an atom, therefore enhancing the energy scale of the process. In instruments, either stable nuclei are excited directly by 1–100 MeV particles or nuclear reactions, such as proton or neutron capture, lead to new nuclei which are produced in an excited state and de-excite promptly. For example, many of the strongest background lines in SPI are due to neutron captures and isomeric transitions of germanium isotopes. Isomeric transitions are the spontaneous nuclear transitions of a meta-stable nuclear configuration to a less excited state by the emission of a characteristic γ -ray

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Fig. 11 Instrumental background processes. Top: Nuclear excitation of instrument and satellite material by CR bombardment. An incident particle interacts with a nucleus from the instrument and forms a new isotope. This is formed in an excited state and de-excites by the emission of a prompt photon. The nucleus might still be left radioactive and decays (shown here as βdecay) toward a final nucleus, which may also involve the emission of a then delayed photon. Bottom left: Bremsstrahlung of a charged particle moving in the field of a nucleus. A negatively charged electron approaches the positively charged electric field of a target nucleus. By a change of direction due to electrostatic attraction (or repulsion in the case of positrons), the electron is emitting bremsstrahlung photons equivalent to the change of its kinetic energy. Bottom right: Particle production by relativistic CRs. If the incident CR is energetic enough, particle production can occur (similar to accelerator experiments). The thresholds to produce certain particles depend on the particles’ rest masses and the interacting nuclei. In the case of mesons being produced, for example, neutral pions (π 0 ), they decay on timescales of nanoseconds or less and emit γ -ray photons

photon. In SPI and other germanium detectors, multiple isotopes of germanium are naturally included in the crystals, so that multiple lines according to the different isotopes occur. The SPI lines at 23.4 and 175.0 keV are due to the second isomeric state of 71m Ge (T1/2 = 20 ms) and are coincidentally measured at 23.4 + 175.0 (T1/2 = 79 ns) = 198.4 keV to form its strongest background line (Bunting and Kraushaar 1974).

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Fig. 12 Example of measured (background) spectra. Top left: NuSTAR1 . Top right: INTEGRAL/SPI (Diehl et al. 2018). Bottom left: COMPTEL. (Reproduced with permission from Schoenfelder et al. 1993). Bottom right: Fermi-LAT. (Reproduced with permission from Ackermann et al. 2015)

Another strong line which always occurs in γ -ray measurements is the 511 keV electron-positron annihilation line. Either β + -unstable isotopes decay inside the satellite and produce a positron which quickly finds an electron to annihilate with or CR bombardment leads to secondary positrons which slow down and also annihilate inside the satellite. Compared to SPI, COMPTEL had poorer spectral resolution (Fig. 12, bottom left), so that multiple lines overlapped and merged together as distinct line complexes, or weak lines were just smeared out and drowned in the continuum background. A prominent line in the COMPTEL background was the neutron capture line on protons leading to a strong feature at 2.223 MeV. Most of these interactions occur for high accumulations of protons (hydrogen) which in COMPTEL was found either in its upper detector module filled with the liquid scintillator NE 213A (i.e., xylene, C8 H10 ) or in CGRO’s fuel tanks filled with hydrazine (N2 H4 ) (Schoenfelder et al. 1993). In the pair-production regime, a reduction in the γ -ray detection efficiency can be due to a number of effects including instrumental pile-up, the incorrect vetoing of γ rays, and particle leakage into the detector. One source of instrumental background

1 NuSTAR

observatory guide: https://heasarc.gsfc.nasa.gov/docs/nustar/NuSTAR_observatory_ guide-v1.0.pdf

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is the residual signal that remains from the shower initiated by a charged particle, which has been vetoed, but whose decay time is such that traces still remain when a γ -ray enters the detector volume and causes a trigger (Rochester et al. 2010). In this case, when the signals from the instrument are read out, there will be the signal NuSTAR observatory guide: https://heasarc.gsfc.nasa.gov/docs/nustar/ NuSTAR_observatory_guide-v1.0.pdf due to the genuine γ -ray event but also the residual signal that remains from the previously vetoed event. This can be seen schematically in Fig. 13. In Fermi-LAT, this residual signal is referred to as a “ghost” event, and it can be present in the tracker, the calorimeter, the ACD, or, indeed, in all three as is shown in Fig. 14. The effect has been modelled using simulations, so its effects are well understood and are incorporated in the analysis of LAT data (Ackermann et al. 2012).

Fig. 13 Schematic illustration of a ghost event. The remnants of electronic signals from the particles of a background event (1) that traversed the detector volume prior to the gamma ray (2) that triggered the instrument get read out along with the γ -ray signal

Fig. 14 Left: From Ackermann et al. (2012), an example of ghost activity in the LAT. On the right of the figure is a genuine γ -ray whose reconstructed track is shown by the dashed line. The ghost activity is visible in the ACD, tracker, and calorimeter. Only those ACD tiles with a signal are shown. Right: Reproduced with permission from Moiseev et al. (2007) – an illustration of the effect of backsplash in the simulation of the LAT ACD. Red lines show the charged particles and blue dashed lines show the photons. The red dots show the signals in the ACD due to backsplash

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Other sources of background that have been identified and effectively removed from the LAT data include non-interacting heavy ions and CR electrons that leak through the ribbons of the ACD (Bruel et al. 2018). Improvements to the analysis and simulations post-launch have led to better particle-tracking algorithms (Atwood et al. 2013) and γ -ray selections (Bruel et al. 2018). Thus, the effects of ghost events, leakage, and non-interacting particles result in only a minor loss of efficiency in the LAT’s γ -ray detection capabilities. Another way in which an inefficiency is introduced for the detection of γ -rays at GeV energies is when a true γ -ray gets incorrectly vetoed. In EGRET, this was referred to as “backsplash” (Thompson et al. 1993). Although most of the particles in the electromagnetic shower travel along the direction of the incident γ -ray, a small fraction of them go in the backward direction. The low-energy photons in these showers Compton scatter electrons in the ACD and these charged particles can then cause a veto. The effect became more pronounced at higher energies with EGRET’s detection efficiency degraded by a factor of 2 at 10 GeV compared to that at 1 GeV (Moiseev et al. 2004). The ACD for the Fermi-LAT was then optimized to avoid this issue (Moiseev et al. 2004). An illustration of the effect of backsplash in the LAT ACD simulation model is shown in Fig. 14, right.

Background Suppression As shown in Fig. 12, the measured detector rates from different instruments in the MeV to GeV range are on the order of 10−5 –101 cnts s−1 keV−1 . These rates are already reduced by different suppression mechanisms which decrease the rate of incoming particles and photons by several orders of magnitude. Depending on the energy range and instrument again, the methods to reduce (instrumental) background begin with the choice of the orbit (section “Orbit Considerations”). However, most of the reduction in the MeV–GeV range is achieved by active anticoincidence shields, by discrimination of signals in the readout electronics (⊲ Chap. 53, “Readout Electronics for Gamma-Ray Astronomy”), and through casespecific data selections in the multidimensional data spaces of γ -ray telescopes.

Anticoincidence Shields The general idea of an anticoincidence shield is to veto unwanted particles and/or photons that would enter the detector. This means the active detector is surrounded by another, sometimes U-shaped, active detector with a fast readout system. In the case of a U-shaped detector, the effects are twofold: first, the inner detectors are shielded physically from all directions except for close to zenith (the size of the shield defines the field of view, section “General Considerations: A Gamma-Ray Collimator”), and second, the inner detectors are shielded electronically from events that interact with the anticoincidence system. In Fig. 15, the normal, unvetoed observation case (top) and the vetoed observation case (bottom) with an anticoincidence signal triggered are shown.

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Fig. 15 Anticoincidence systems logics. Top: Two photons, (1) and (2), arrive from inside the field of view of the instrument and deposit their energies in the active detector (left). In the electronics readout (schematic, right), a pulse is registered for each event, and with its start, the detecting system is unable to record any more events during a specified time ∆T (dead time). Either the pulse height or the integral over the entire pulse over the time of measurement ∆T converts the registered event into an electronic channel number, which will be associated with a photon energy after calibration. Bottom: After photon event (1), a particle (2) hits the veto shield from the side. Shortly after, another photon (3) interacts with the detecting system. Because the veto shield triggers an anticoincidence (purple range, right), events (2) and (3) are both vetoed, and only event (1) is recorded

Most modern MeV and GeV telescopes have veto systems made of scintillator crystals with a high light yield. For example, the veto shields of the IBIS and SPI telescopes onboard INTEGRAL are made of BGO and show a typical count rate of up to 105 cnts s−1 . A considerable fraction of these counts would necessarily be measured in the main detectors and would heavily increase the average rate. However, the veto shields also have a huge disadvantage: they are heavy and come with more mass than would actually be needed for the main detectors, effectively reducing their sensitivity. More mass is equivalent to more instrumental background because CRs have more area to interact with. That means that there is a trade-off between the increased mass and the background reduction where the latter typically gets precedence. A major advantage of the massively increased photon collecting area of veto systems is their transient monitoring capabilities thanks to their quasi-all-sky fields of view. While the main detectors of many instruments only observe in the zenith

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Fig. 16 The INTEGRAL satellite as all-sky observatory. Shown are the different instruments and veto shields in the study of Savchenko et al. (2017a, left) and the efficiency of the instruments with respect to the SPI-ACS (right). For a given gamma-ray burst (GRB) spectrum and duration (here Band function (Band et al. 1993) with α = −1, Ep = 300 keV, and β = −2.5 for 8 s), the different instruments would be expected to measure certain rates relative to each other. This describes a “4π response”

direction, the veto shields see the entire sky, unless blocked by the Earth. If multiple instruments and shields onboard a satellite are combined, the sensitivity to transient events is largely enhanced, and the satellite functions as one big observatory. Savchenko et al. (2017a,b) showed and used this for the INTEGRAL observatories (Fig. 16). Because the mass required to shield MeV detectors can comprise a considerable portion of the satellite payload, the effective collecting area supersedes that of the main camera by up to two orders of magnitude. For example, the SPI veto shield ACS weighs 512 kg and reaches a maximum effective area of ∼104 cm2 (e.g., Savchenko et al. 2017a), however, without any spectral information (compared to the 10–102 cm2 of SPI). The veto system on COSI, for example, made of CsI, weighs about 100 kg (Tomsick et al. 2019). This means that whenever an active veto system is installed, careful consideration should be given to whether spectral information can be added to its detection system so that a spectral analysis of transients can also be performed. In the pair-production regime, where the background of charged CR particles outnumbers the γ -ray events by a factor of 104 –105 , plastic scintillator tiles are mostly used nowadays for the ACD; this is the case for both LAT (Moiseev et al. 2007) and AGILE (Tavani et al. 2009). These plastic tiles do not add too much weight and are a well-understood, efficient, reliable, and inexpensive technology (Atwood et al. 2009). The ACD of LAT comprises a total of 89 scintillating plastic tiles, with varying surface areas (between 561 and 2650 cm2 ) and thicknesses (between 10 and 12 mm), 16 of them on each of the 4 sides and 25 on the top of the instrument (Ackermann et al. 2012). The ACD of AGILE comprises 13 independent charged particle detectors (Perotti et al. 2006). As discussed in section “Background Suppression”, the segmentation of the ACDs of both LAT and AGILE allows for a localization of the veto signal to avoid false vetoes due to backsplash. To cover

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the gaps between ACD tiles in the X- and Y-axis, the LAT also has eight flexible scintillating ribbons. In LAT, the signal generated upon the passage of a charged particle is transmitted to the 194 PMTs (two for each ACD tile and two for each of the ribbons) via wavelength shifting fibers and clear fibers so that the veto can be registered. The signals from the AGILE plastic scintillators are read out via optical fibers connected to 16 subminiature PMTs. The total mass of the ACD on the LAT is 284 kg (the combined mass of the LAT is 2789 kg), while that of AGILE is 22.5 kg (the combined mass the AGILE scientific instruments is ∼100 kg).

Pulse Shape Discrimination Another useful technique to filter out particle events, for example, in MeV telescopes, can be achieved by measuring the shape of the incident pulse in the electronics. These pulse shape discriminators (PSD) include templates of rise times to peak and fall times to base level for different particle types so that unwanted particles can efficiently be ignored. The templates depend on the interaction locations in the detectors as well as on the charge carrier mobility as a result of the electric fields and applied voltages (Philhour et al. 1998). The general idea to distinguish, for example, β-particles from photons interacting with the detectors, is that the particles mostly interact in one particular site to deposit parts of their kinetic energy, whereas photons show deposits in multiple sites. This means that single-site events from electrons could potentially be rejected, which enhances the sensitivity of the instrument whenever the photon energies imply a high probability of scattering within the detector volume. Because photons can also be directly absorbed in only one interaction, the energy threshold for a PSD should be set around the turnover from photo-electric absorption to Compton scattering (Fig. 5), which depends on the material and geometry of the instruments. In Fig. 17, a sketch of pulse-shape-discriminated particles compared to photons is shown. PSD electronics have been employed, for example, in INTEGRAL/SPI and are also used to suppress electronic noise which arises from the saturation of its analog front-end electronics (Roques and Jourdain 2019).

Fig. 17 Working principle of a pulse shape discriminator. Events (1) (photon) and (2) (electron) are recorded by the detector. Their pulse shapes are compared to a template (dotted red). If the pulse shape is similar to a β-particle template, it is recognized and filtered out

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Tailored Data Selections The data that can be sent from the satellite to ground stations for further analysis and diagnostics is limited, and so, those that are downloaded must be considered and selected carefully. In the case of the LAT, for example, the onboard trigger is designed to pre-scale the volume of each particular event class that is downloaded so that a maximum of γ -ray candidates can be kept while also sampling a sufficient quantity of particular background and periodic trigger events to help characterize and keep track of the conditions under which the signal is detected. A more detailed discussion can be found in ⊲ Chap. 68, “The Fermi Large Area Telescope”. Once downloaded, the data can be subjected to different sets of analysis cuts, each designed with particular scientific goals in mind. The LAT, these are known as event classes, and they are optimized to address different science cases including, for example, transients, steady point sources or diffuse backgrounds. The quality and efficiency of the cuts are different for each class. Similar data selections can apply for the event selections in Compton telescopes, for example, then utilizing the Compton Data Space (Schoenfelder et al. 1993) to distinguish background and sky photons.

Astrophysical Sources of Gamma Rays: Not One Fits All Depending on the scientific goal of the observations being undertaken, the γ -ray instruments look very different because they are designed for specific tasks. Figure 18 shows a selection of images which highlight the diversity of the science that can be studied at γ -ray energies. The instrument capabilities need to be optimized according to both the energy range of the γ -rays being sought and the science case under study. An in-depth description of both Galactic and extragalactic γ -ray science can be found in Volume 3 of this handbook. Once the instrumental background has been taken into account in the data analysis, the signal that remains is that due to astrophysical γ -rays. Depending upon the energy range being investigated and on the pointing direction on the sky, this could be a superposition of a number of different components. Each of these components needs to be modelled and understood in order to study the γ -ray emission detected. Gamma-ray sources can appear point-like or extended, depending upon the combination of their intrinsic nature and on the angular resolution and exposure time of the instrument. The γ -ray emission from resolved sources will lie on top of that from the diffuse γ -ray background, itself a combination of unresolved point sources, the isotropic diffuse background and possibly containing the so-called exotic components such as contributions from dark matter annihilation and axions. Many solar system objects, for example, the Sun and the Moon, are γ -ray emitters and, in addition to being studied in their own right, constitute a foreground source that has to be accounted for when they pass between the γ -ray telescope and more distant sources for those instruments who can operate in their presence. The spatial, spectral, and temporal nature of the γ -ray sources being investigated are important considerations when designing an instrument and optimizing the observational and analysis strategy.

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Fig. 18 Top left: Gamma-ray spectroscopy using INTEGRAL/SPI. The spectral decomposition into lines is shown for near the 26 Al line (Diehl et al. 2018). Top right: A significance map showing the γ -ray sky above 15 GeV around the supernova remnant γ -Cygni (G78.2+2.1/VER J2019+407) reproduced with permission from Fraija and Araya (2016). Shown are the 1420 MHz observation from the Canadian Galactic Plane Survey at brightness temperatures from 22 to 60 K (green), the VHE source, VER J2019+407, smoothed photon excess contours (magenta), and the location of the γ -ray pulsar, PSR J2021+4026 (blue cross). The boundary of the extended LAT source 3FGL J2021.0+4031e is indicated by the white dashed circle. Bottom left: The light curve of GRB131014 in the 0.03–1 GeV energy range. The polynomial fit to the background is shown by a red line. The data are analyzed using the LAT low-energy technique, designed to optimize the study of bright transient events below ∼1 GeV (Ajello et al. 2019). Bottom right: The spectral energy distribution of the blazar 1ES 1215+304 from Valverde et al. (2020). The data and model are from the source when it was found to be in a low state. Shown are the blob synchrotron and synchrotron self-Compton (SSC) contributions (pale blue), the jet synchrotron and SSC emission (dotted– dashed pink), the intrinsic SSC emission without absorption from the extra-galactic background light (dotted blue), and the sums of all components (thick brown and thick black dotted–dashed)

Some γ -ray sources, certain supernova remnants or radio galaxies, for example, are extended and can have multiple emission components or exhibit different spectral features at different locations. The identification of a position-dependent photon index can help map out the underlying structure of the source, and thus, high angular and spectral resolution is a requirement. Sources can be steady emitters, meaning that they emit a flux that does not vary significantly with time. Often, extended sources of γ -rays have been found to belong to the class of steady emitters. The γ -ray emission from point-like sources can be

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variable over many different timescales from minutes (some AGN) to years (e.g., some binary systems), or, indeed, it can be periodic (pulsars and binaries), quasiperiodic (some AGN), or episodic (AGN, some pulsar wind systems). This variable signal may well sit on top of a more steady component. Other sources of γ -rays, such as GRBs and perhaps fast radio bursts, are one-off events meaning that their detection is dependent upon having a large enough field of view. The spectral properties of the γ -rays being studied should also be considered. Many γ -ray sources have continuous spectra that follow a power law, due to the nonthermal nature of their emission. The spectra of sources whose γ -ray emission is due to nuclear transitions will have a line nature. Many dark matter models also predict mono-energetic γ -ray signals meaning that spectral lines at an energy corresponding to the mass of the annihilating or decaying particle are sought. Similarly, the annihilation signature of neutral pions (an indicator of hadronic processes at work in the γ -ray source) will exhibit a characteristic bump. Many γ -ray sources also exhibit spectral breaks and cutoffs, so, depending upon the importance of accurately measuring these spectral features, the energy resolution of the instrument is an important consideration.

Instrument Designs Gamma-ray measurements in the MeV and GeV range classically rely on the modulation of one or more data space dimensions. Because single photons are counted in individual detector units, such a variation can appear minuscule and still lead to a significant change if treated properly by statistical means. The recognition of one or zero counts in the complex data spaces over a longer period of time leads to almost unique inferences when the full instrument response is applied. The instrument response is, in general, a kernel function that converts an (astro)physical model, such as a point-like or extended source with a certain spectral shape with physical units, into the native data space of the instrument, always counting photons per detector, time, energy (electronic readout channel), or other entities, as a function of its intrinsic coordinates given as zenith and azimuth angle. The instrument’s geometrical detecting area Ageom is therefore reduced to an effective area Aeff which depends not only on the incident photon energy Einc , time T , and zenith and azimuth angle (Z, A) of the source but also on the entire structure of the instrument, on environmental conditions (temperatures, voltages, etc.), and on the satellite mountings and orbit. Even for the simplest of all instrument designs, collimators (section “General Considerations: A Gamma-Ray Collimator”), it holds true that Aeff (Einc , Z, A, T , . . . ) ≤ Ageom .

(5)

For example, the geometrical detecting area of INTEGRAL/SPI’s 19 Ge detectors is 508 cm2 , while the maximum effective area for Z = 0◦ is 125 and 65 cm2 for 0.1 and 1.0 MeV, respectively (Vedrenne et al. 2003; Sturner et al. 2003; Attié et al. 2003).

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In what follows, different instrument designs, i.e., different aspects of modulation in various data spaces, are outlined briefly. The reader is referred to the subsequent chapters in which each of the γ -ray telescope apertures is explained in more detail.

General Considerations: A Gamma-Ray Collimator The basic modulation categories are summarized into temporal, spatial, energetic, and other apertures, as well as combinations thereof. As described earlier in this chapter, the history of low-energy γ -ray detectors started with collimators which should be considered a temporal and spatial modulator by the classification above. They are described as the basic principle from which other designs can be derived in the following. Collimator apertures are designed as large, often cylindrical, tubes with a detector unit (the camera) at the base of the tube (Fig. 19, left). The tube itself shields photons and particles from the side and the back, most of the time being itself an active γ ray detector to veto those unwanted events. In this way, the central camera only observes in the zenith direction with a field of view given by the measurements of the tube. As an example, if we take a cylindrical camera with diameter d, placed in a collimating tube with height h, the field of view, defined by the opening angle α of the aperture, would be given by α = 2 arctan(d/ h).

(6)

Fig. 19 Sketches for collimator and coded mask telescopes. Left: A collimator is built from an active detector that is surrounded by passive or active material to block photons and particles from the side. Only photons within the field of view, defined by the opening angle, α, are recorded. Right: A coded mask telescope adds opaque and transparent mask elements at the opening of the collimator tube. If the active detector is pixelated, this encodes incoming gamma-ray photons spatially, and their origin can be inferred

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If material opacities are ignored for the moment, the angular response of the collimator with one detector unit as the camera can be expressed analytically for a plane-parallel beam of light as Aeff (Z, A) = Ageom (Θ(Z + α/2) − Θ(Z − α/2)), where Θ(x) is the Heaviside step function and Z and A are the zenith and azimuth angle, respectively. This means that if the source is inside the field of view, the camera can detect all of the emitted photons, while it sees zero counts when the source’s aspect angle is greater than half the opening angle. Departing from this ideal view, for example, if the central camera consists of more than one detector and is therefore pixelated, the rise of a source with respect to the camera (decreasing zenith) now leads to a gradual increase of the effective area until the source is directly above the camera. For small fields of view, this results in an effective A area of approximately Aeff (Z, A) = geom π (arccos(τ ) − sin(2 arccos(τ ))), where τ = tan(Z)/ tan(α/2). This is strongly simplified and only serves as a means to describe the zenith dependence of a collimator-type instrument. These ideal treatments are erroneous once a real instrument is considered: The field of view is not a sharply defined region as described above but depends on energy. The higher the photon energy, the higher the probability that the photon is not absorbed by the collimating material so that it may be detected even from “outside” the field of view. If the instrument is not perfectly cylindrical, for example, if it is hexagonal or octagonal, the effective area gains an azimuth dependence. Finally, and probably most importantly for the analysis of γ -ray data, the incident photon energy Einc is not necessarily the measured photon energy Emeas : Because of Compton scattering, escape peaks, and instrumental spectral resolution, the measured photon energy is related to the incident photon energy only by a known but non-invertible redistribution matrix (section “Understanding Gamma-Ray Measurements”). This means that a measured spectrum is never representative of the source spectrum so that the latter must be inferred by forward modelling. The forward modelling then requires complete knowledge of the instrument, which is condensed in the response, often separated into an effective area contribution plus an energy redistribution, and which assumes a certain source model. The responses of γ -ray telescopes are typically determined by particle physics simulations using GEANT (section “Simulations”), which are then validated by calibration measurements on Earth using either radioactive sources or particle accelerator beams (section “Calibrations”). The source model can be versatile but requires the basic parameters of the object of interest, such as position, spatial extent, spectral shape, and temporal behavior. If the spectrum of a point source is being analyzed, the first two properties are typically fixed to known values. With more elaborate techniques, however, all unknown parameters of the observed target can be inferred in a single inference step. Different collimators have already been flown on balloon experiments between the 1960s and 1990s. The most successful collimator aperture was OSSE on CGRO (Johnson et al. 1993). It consisted of four independent, single-axis orientable, and actively shielded NaI(Tl)-CsI(Na) detectors, each surrounded by a tungsten shield. The fields of view of the detectors were 3.8◦ × 11.0◦ and sensitive in the 0.05– 10 MeV photon range. Due to its four independent units, OSSE could measure the

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instrumental background by simultaneously pointing away from and at the source of interest. This has the advantage that only the instruments themselves are moved and not the entire satellite. This technique was then further used to perform the first temporal and spatial modulated measurement which led to the first image reconstruction ever of the Galactic diffuse 511 keV emission (Purcell et al. 1993, 1997). Because the rise into and away from the fields of view of the four detectors changes uniquely with time over several years, an image could be reconstructed by singular value decomposition. It was shown for the first time that the 511 keV emission from the center of the Galaxy was not point-like and variable, but extended and constant.

Temporal and Spatial Modulation Apertures, Geometry Optics: Coded Mask Telescopes Collimators have no spatial, i.e., angular, resolution. The camera is pointed at a source to detect photons and is then moved away so that a background estimate can be provided. This is the simplest form of a temporal (or spatial) modulation: on-off observations. However, if more than one source is in the field of view, they might be difficult to analyze separately, especially if the field of view is large. The apertures are therefore changed to include more information. One way to improve the angular resolution is to place a mask on the top of the collimator’s shielding tube which encodes the incoming light beam to cast shadows onto the detecting area, the so-called shadowgrams. The first mentioning of coding γ -rays appears in Mertz and Young (1962) in the context of Fresnel transformations of images. This mask consists of opaque and transparent elements so that a fraction of the incoming light is blocked and only certain parts of the camera are illuminated. Much finer variations in the aspect angle change between source and telescope can be recorded with such a coded mask. The improvement in angular resolution then depends on the mask element size m, the size of the detector pixels d, and the separation between mask and camera l. In order to separate shadowgrams from different source positions inside the field of view, the detector plane must therefore be pixelated. For technical reasons, the detector size is adjusted to the science case and in particular the photon energy. While in the MeV range this means that one detector (one “pixel”) is several cm in size, which ultimately limits the angular resolution, the pixels can be much smaller (few mm) in the case of 100 keV detectors. This originates from the attenuation lengths required to stop a 1 MeV photon (e.g., in tungsten µ−1 ≈ 1.6 cm) compared to a 100 keV photon (µ−1 ≈ 250 µm). The mask elements should be as small as possible for the angular resolution to be maximized. However, the sensitivity of the instrument suffers when the mask element size is smaller than the detector size. The angular resolution of a coded mask telescope is approximately given by

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δΘ =



(m/ l)2 + (d/ l)2 ,

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(7)

and the positioning accuracy by δα ≈ (S/N )−1 δΘ with S/N being the signal-tonoise ratio of the source given a suitable background estimate. This means that the localization of a coded mask telescope naturally supersedes its angular resolution when the source is strong. The optimal trade-off between angular resolution, localization accuracy, and sensitivity is provided when m ≈ d (Skinner 2008). In order to remove ambiguities in the mask patterns that can emerge if a certain degree of symmetry is involved in the instrument design, targeting coded mask telescopes follow a particular observing strategy. Given the angular resolution and specific geometry of the instrument (symmetries, field of view), an observation pattern can be performed instead of staring at the source of interest for a long time. For example, INTEGRAL performs a rectangular 5 × 5 pattern around the source of interest, called dithering, to optimally sample the different shadowgrams of the mask onto the camera. This can also provide a measure of the unknown instrumental background during this observation because the shadowgrams of the sources inside the field of view smear out over longer periods of time (Siegert et al. 2019). Present and past coded mask telescopes are ISGRI (0.03–0.4 MeV, Ubertini et al. 2003) and SPI (0.02–8 MeV, Vedrenne et al. 2003) onboard INTEGRAL (⊲ Chap. 65, “The INTEGRAL Mission”), Swift-BAT (0.015–0.15 MeV, Krimm et al. 2013; ⊲ Chap. 44, “The Neil Gehrels Swift Observatory”), the CZT Imager onboard AstroSat (0.01–0.15 MeV; ⊲ Chap. 29, “The AstroSat Observatory”), the All-Sky Monitor (ASM) onboard RXTE (0.002–0.012 MeV), and the Wide Field Camera (WFC) onboard BeppoSAX (0.002–0.030 MeV). Details about coded mask telescopes are provided in ⊲ Chap. 48, “Coded Mask Instruments for Gamma-Ray Astronomy”. Another possibility to remedy the need for spatial variation can be achieved if parts of the instrument itself are movable. With several sub-collimators, which had been realized in the RHESSI imaging system (Hurford et al. 2002; Smith 2004), for example, an arcsec angular resolution had been achieved in γ -ray observations of the Sun. In the case of RHESSI, a pair of separated but parallel grids (opaque slats and transparent slit-like elements) inside each of its nine collimator tubes is rotated with respect to the detector plane at 15 revolutions per minute. This leads to the effect that a change in aspect angle produces a modulation of the transmission of the grid pair in time. The rotating shadow of the slats in the top grid then falls on the slits or slats of the read grid which results in a time-modulated transmission from 0 to 50% and back. Similar techniques have been applied for solar flare observations onboard the Hinotori mission with its rotating modulation collimator (RMC, 0.02–0.04 MeV; Sakurai 1991), HXT onboard Yohkoh (0.02–0.1 MeV; Acton et al. 1992), and the balloon-borne HEIDI (High Energy Imaging Device; Crannell et al. 1992) solar telescope with two RMCs. A currently active temporal modulation telescope is Insight-HXMT (0.02–0.25 MeV; Zhang et al. 2018).

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Quantum Optics in the MeV: Compton Telescopes In the 1920s, A. H. Compton introduced the classical concept of elastic scattering for the interaction of photons with matter. He showed that, in the energy range from ∼100 keV to ∼10 MeV, this scattering takes place between the incoming photon and an atomic electron. This results in an energized recoil electron and a deflected photon of reduced energy: in order to characterize the interaction, both secondary components must be measured. Elastic scattering conserves energy and momentum E0 = Escat + Ee , p0 = pscat + pe , where |p0 | = hν0 /c |pscat | = hνscat /c, and |pe | = me vγ with γ = 1/ 1 − β 2 with β = v/c, which leads to the so-called Compton equation: λscat − λ0 =

h (1 − cos ϕ) me c

(8)

where h, me , and c are Planck’s constant, the electron rest mass, and the speed of light, respectively. The fraction h/me c = 2.426 × 10−12 m is often called the Compton wavelength, which is the wavelength shift for a 90◦ scattering. It is important to note that, in a Compton scattering interaction, the incident photon can never lose all of its energy even if it is completely backscattered. Since, in this energy range, the photon energy is much higher than the binding energy of atomic electrons, the target electrons are taken to be free and non-interacting. This is a good approximation at these energies. For low-energy photons interacting with inner-shell atomic electrons, however, “Doppler broadening” of the angular response occurs (Zoglauer and Kanbach 2003; see also ⊲ Chap. 50, “Compton Telescopes for Gamma-Ray Astrophysics”). The total cross section (or absorption coefficient) of Compton scattering in any target material depends directly on the electron density and therefore on the nuclear charge, Z, of the detector material (section “Interactions of Light with Matter”). Equation (8) can be solved for ϕ and the wavelengths converted to energy,    1 1 , − ϕ = arccos 1 − me c2 Escat E0

(9)

where the energy of the scattered photon is Escat = hνscat =

1+

E0 , E0 (1 − cos ϕ) me c 2

(10)

and the kinetic energy of the recoil electron is Ke = E0 − Escat =

E0 (1 − cos ϕ) . me + E0 (1 − cos ϕ) c2

(11)

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Ke can also be expressed in terms of the angle Θ between the incident photon and the direction of the recoil electron, making use of the relation cot(Θ) = (1 + α) tan(ϕ/2) where α = E0 /me c2 , such that Ke =

2E0 α cos2 Θ . (1 + α)2 − α 2 cos2 Θ

(12)

Equations (8), (9), (10), (11), and (12) are directly based on the kinematics of the elastic Compton scattering process and are the basis for various realizations of Compton telescopes. In the “classical” two separated detector designs (e.g., COMPTEL; Fig. 20, left), a scattering detector D1 and an absorbing detector D2 trigger on a time-of-flight delayed coincidence signal and measure the positions and energy deposits of the two interactions. The positions indicate the path of the scattered photon between D1 and D2. Assuming the primary photon’s energy is the sum of both energy deposits (i.e., no undetected energy leakage occurred), the scattering angle is given by Eq. (9). The direction of the incident photon will then be somewhere on a cone around the scattered photon trajectory. If many photons from a distant point source are registered, their individual “event cones” all intersect at the direction to this source. For compact Compton telescopes (Fig. 20, right), the basic principle is the same; however, instead of two interaction layers, a position-sensitive detector volume is

Fig. 20 Compton telescope designs. Left: Classic two-layer Compton telescope. Photons scatter in the upper detector layer 1 via Compton scattering and are absorbed in the lower detector layer 2. Given the Compton scattering Eq. (8), each photon can be associated with a circle in the sky that forms a cone with the interaction point in the upper layer. The opening angle of this cone is given by the Compton scattering angle ϕ. Individual astrophysical sources can be identified by intersections of rings (orange photons). The time of flight (T OF ) between the two layers is indicated with its minimal value (perpendicular path between layers) and maximal value (defined by the opposite edges of the layers). Right: Instead of two layers, a position-sensitive detector, for example, made of several detector strips or with gas, allows the photons potentially to scatter more often (zigzag paths), always according to Compton scattering. The first interaction inside the detector volume again defines the Compton scattering angle. Three or more scatters help to identify the photon origins more clearly. In the case of the yellow photon on the right, only photo-absorption occurs, so that no Compton event reconstruction is possible

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used. This decreases the size of the telescope because no time-of-flight information is used and instead event reconstruction techniques are applied to identify the possible paths of scattering γ -rays inside the instrument. If the pixelation and threshold sensitivity allows recording the track of a Compton recoil electron, its initial direction (before Molière scattering disturbs it) can be used to reduce the event circle to an arc length. This can improve the overall sensitivity considerably. The distribution of closest offsets between the event cones and the true source direction is called the angular resolution measure (ARM). The width and “lopsidedness” of the ARM distribution is caused by uncertainties in the position and energy measurements and by possible energy leakage from the system.

Quantum Optics for Higher Energies: Pair Tracking Telescopes The measurement of the energy of a γ -ray in the pair-production regime is done by measuring the secondary products: electrons, positrons, and recoils on the target nucleus or electron. The latter recoils are not easily measurable, but they are of minor importance for higher γ -ray energies. The energies of the pair particles can be characterized by their scattering behavior (Molière scattering for low-energy electrons), or they can be totally absorbed in a deep calorimeter, where the initiated shower at high energies gives additional information for the total energy. Thus, to first order in most cases, the energy of the γ -ray is calculated by summing the energy deposited in each of the crystals of the calorimeter in the case of the calorimeter on LAT or AGILE or by means of the pulse height analyzers (PHAs) for the Total Absorption Shower Counter (TASC) NaI(T1) calorimeter on EGRET. Of course, some fraction of the energy of the incident γ -ray will have been deposited elsewhere in the detector prior to the shower’s arrival in the calorimeter. So, this energy must be estimated and added on to that deposited in the calorimeter. The tracking information deduced from the tracker and the shower’s position or trajectory into the calorimeter can be used to estimate its path through the detector and, combined with the energy measured in the calorimeter, can be used to estimate the energy deposited elsewhere in the detector (Fig. 21). The 3D passage of the electrons and positrons until they reach the calorimeter is reconstructed using a track finding algorithm. For Fermi-LAT, for example, the algorithm starts by generating a track hypothesis, i.e., a proposed trajectory made of locations and directions, that is accepted or rejected given the detector signals (Atwood et al. 2009). One possibility to fit these tracks and therefore to identify origin of the initial photon on the celestial sphere is by pattern recognition: The algorithm starts by assuming an (x, y) position in the top layer, which is compared to a subsequent hit as well as the energy deposited in the calorimeter. If these positions are close in the multidimensional data space, a candidate track is created by Kalman fitting. This process is repeated into the next layers, always taking into account the covariance matrices of the previous steps, until an adequate figure-of-merit is found. This ensures the correct propagation of uncertainties when scattering in different materials. In the calorimeter-seeded pattern recognition for Fermi-LAT, this process

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Fig. 21 Pair tracking telescope design. Incoming high-energy photons are converted into electronpositron pairs in passive material. With position-sensitive detectors, the electrons and positrons are tracked until they deposit all their energy in a calorimeter. The tracks and final energy deposit are used to determine the total energy and direction of the incoming photons. In contrast to MeV telescopes, the background is dominantly from CRs, so that the anticoincidence system is building a shield above the tracker and calorimeter

provides a χ 2 goodness-of-fit criterion for the Kalman fit, the number of hits in the tracker, and the number of gaps (layers not hit or unrecognized). A quality parameter is derived from a combination of these values, sequencing the possible candidate tracks from “best” to “worst.” In addition, the fitted values also return an error ellipse to each photon’s position in the sky. For the higher-energy γ -rays, the shower will not be completely absorbed by the calorimeter, so this missing energy must also be estimated. For low-energy γ -rays, a significant fraction of their energy can be deposited in the tracker. In these cases, the tracker is considered to be a sampling calorimeter (Atwood et al. 2009), and, in the case of the LAT, the number of silicon strips that had hits in them is used to estimate the energy deposited therein. In the case of EGRET, by the time the shower induced by a low-energy γ -ray reached the TASC, there may not have been sufficient energy deposit to trigger one or both of the PHAs (Thompson et al. 1993). These events were assigned a different class, and the energy was estimated by an alternative means. Another case in which the calorimeter cannot be used to estimate the energy of the incident γ -ray is when the direction is such that the shower misses the calorimeter. In these cases, again, the energy deposited in the tracker can be used to provide an estimate of the energy albeit one with a larger uncertainty. In all cases, energy loss due to leakage must be taken into account. This leakage can occur out the sides and back of the calorimeter, in the various materials that comprise the detector volume and, in the case of the LAT and AGILE, between the internal gaps in the calorimeter modules.

Scattering Information: Gamma-Ray Polarimeters All basic interactions of light with matter from section “Interactions of Light with Matter” are intrinsically sensitive to the polarization properties of the photons.

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In the case of longer wavelengths, filters can be used to distinguish between different polarization angles η and the polarization degree Π . In the case of hard X-rays to high-energy, GeV photons, such filters are impossible to construct so that the polarization parameters of astrophysical sources are inferred from the distribution of secondary particles in the instruments. The differential cross sections for photoelectric effect, Compton scattering, and pair production show an asymmetry with respect to the incoming photon’s polarization angle, whose amplitude is proportional to the polarization degree (also called polarization amplitude). This asymmetry can be measured if position-sensitive detectors for photons and resulting particles are employed. It is important to note that the total cross sections for the three main interactions are unchanged by photon polarization and that, with these techniques, only linear polarization can be measured. Conceptually, the polarization degree can be defined as the maximum variation in the azimuthal scattering probability (Novick 1975; Lei et al. 1997) as Π=

dσ⊥ − dσ , dσ⊥ + dσ

(13)

which is to be compared to the actually possible modulation capabilities of the instruments. In Eq. (13), dσ⊥ and dσ are the scattering cross sections for photons perpendicular and parallel to the emission plane. Photoelectric absorption produces an electron whose angular distribution depends on the polarization of the incident photon. In the classical sense, the electrons accelerate in the direction of the electric field of the incident photon. However, the exact distribution of photoelectrons also depends on the microscopic properties of the absorbing material, for example, the electronic band structure in solids, which makes an exact derivation of the differential cross section as a function of polarization angle cumbersome. In the Born approximation (Sauter 1931; Scofield 1989; Costa et al. 2001; Sabbatucci and Salvat 2016), the differential cross section can be expressed as dσPE (Eγ , η) = re2 Z 5 α 4 dΩ



me c 2 Eγ

7/2 √ 4 2 sin2 θ cos2 η (1 − β cos θ )4

(14)

where Eγ is the total energy of incoming photon, re the classical electron radius, Z the material’s charge number, and α the fine-structure constant. The initial derivation of the Compton scattering cross section already included the polarization angle of incident photons (Klein and Nishina 1929), dσCE (Eγ , η) 1 = re2 dΩ 2



λ λ′

2 

 λ λ′ 2 2 + − 2 sin θ cos η , λ′ λ

(15)

with λ/λ′ = (1 + (Eγ /(me c2 ))(1 − cos θ ))−1 . In this case, the scattered photon obtains a preferred direction with respect to the incident polarization angle.

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The differential cross sections for pair production with polarized photons have been calculated and studied in e.g., Maximon and Olsen (1962); Motz et al. (1969); Depaola and Kozameh (1998); Bakmaev et al. (2008), among others, for numerous cases including form factors, partial screening of the nucleus charge, and pair creation in the electron field, etc. The equations resulting from these calculations are too long to be useful in this summary; however, they all have one factor in common: they depend on the polarization angle η as dσPP (Eγ , η)/dΩ ∝ A(1+B cos2 η). The factor cos2 η appears in all the differential cross sections for the basic interactions of polarized light with matter. Making use of the resulting azimuthal distributions of either scatter photons (Compton scattering) or produced particles (photoelectrons, pairs) will infer the polarization of the incoming photons. Dedicated instruments that use these techniques are, for example, IXPE (Weisskopf et al. 2016) in the photon range 2–8 keV (photoelectric effect) and POLAR in the energy range 50–500 keV (Compton scattering; Produit et al. 2005). Other instruments can measure polarization of low- and high-energy γ -rays; however, they have not been initially designed for this task. These include INTEGRAL/SPI (e.g., Kalemci et al. 2004; Chauvin et al. 2013) by scatterings between its detectors, CGRO-COMPTEL (e.g., McConnell and Collmar 2016), and the COSI balloon (Lowell et al. 2017; see also chapter “COSI Polarisation”), all in the photon range 0.1–10 MeV, and Fermi-LAT (e.g., Giomi et al. 2017).

Other Apertures: Combinations and Wave Optics There are more γ -ray telescope concepts, some of which never flew until today and some of which are not feasible technically without major advances in space flight, for example. In the following, an overview of other such apertures is given.

Coded Mask Compton Telescopes Using the angular resolution from coded mask telescopes, Eq. (7), it is clear that the separation between the detector and the mask impacts the resolution as δΘ ∝ l −1 . Therefore, increasing the collimator tube (anticoincidence shield) length will result in better angular resolution; however, this comes with the problem of enhanced mass and consequently higher background and narrower field of view. One possibility to alleviate this problem is to use a combination of a coded aperture mask with a Compton telescope: in this way, the anticoincidence shield does not necessarily need to fill the gap between the detectors and the mask but only need to cover the position-sensitive detectors. Thus, there are two fields of views, one covering a small region from the mask to the detector and one defined by the veto shield that surrounds the detectors. A deployable mast (see also section “Reflective Optics for Gamma-Rays”) could place the mask several tens of meters above the camera, which narrows the field of view to α ∝ 2l −1 while at the same time improving the angular resolution by a similar factor δΘ ∝ l −1 . The Compton telescope part can then be used to only select photons that passed through the mask which results in considerable background rejection in addition to the veto shield.

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The imager IBIS aboard INTEGRAL is composed of two layers below a coding aperture, ISGRI and PICsiT (Lubi´nski 2009). This may be considered a coded mask Compton telescope; however, it only works up to ≈3 MeV because the mask becomes too transparent at higher energies. The separation between mask and camera is 3.2 m, and the Compton telescope layers are 9 cm apart; however, everything is still shielded by the IBIS veto system. This results in an angular resolution of 12 arcmin within a field of view of 9◦ . A proposed instrument that would extend these capabilities is GECCO, the Galactic Explorer with a Coded Aperture Mask Compton Telescope (Orlando et al. 2021). GECCO’s mask-detector separation would be about 20 m, resulting in a 4◦ field of view with an angular resolution of 1 arcmin. The pixelized camera would be made of CZT, resulting in a spectral resolution of ≈1%.

Reflective Optics for Gamma-Rays X- and γ -rays that approach any material perpendicular to its surface will either be absorbed, undergo Compton scattering, or produce pairs, so that refraction of high-energy photons onto a focal plane – the typical case for optical photons – is difficult. The refractive index for most materials in X- and γ -ray are close to 1.0 (or smaller) so that refractive optics (classical lenses) cannot be used for highenergy photons (see, however, section “Diffractive Optics”). Therefore, the only way to “focus” high-energy photons is to use grazing incident optics that rely on reflection off mirrors in an X-ray Wolter-type telescope (Wolter 1952a,b), for example. For incident angles smaller than some critical value that depends on the photon energy and refraction index of the material, the photons undergo total reflection and thereby avoid photoelectric absorption. In general, the critical angle √ is proportional to ρ/Eγ , where ρ is the density of the material. Thus, for a fixed incidence angle, photons can only be totally reflected up to a cutoff energy that is related to the K-edge of the reflecting material. For photons above 10 keV, the critical angles approach too small values to be used in Wolter telescopes unless the reflective coatings are very thin or the focal length very high: For example, platinum at an incidence angle of 0.07◦ shows a reflectivity of more than 90% up to 68 keV and sharply drops below 20% at higher energies. Wolter telescopes have an effective area that is approximately Aeff (Eγ ) ≈ 8πf Lθ 2 R 2 (Eγ ),

(16)

where f is the instrument’s focal length, L is the mirror length, θ is the incidence angle, and R(Eγ ) is the reflectivity as a function of photon energy Eγ (X-ray Telescopes Based on Wolter-I Optics|The WSPC Handbook of Astronomical Instrumentation). Clearly, for the highest possible effective area, the focal length should be maximized as the material parameters R(E) and L are naturally limited. One instrument in which this focal length maximization, together with Pt/C multilayer coatings to effectively reflect photons below the Pt K-absorption edge at 78.4 keV, is NuSTAR (Harrison et al. 2013). NuSTAR is the first focusing hard

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X-ray telescope ever launched into orbit. It employs 133 nested grazing-incidence shells in a conical approximation to a Wolter telescope to focus photons onto a focal plane made of a pixelated CZT detector. NuSTAR’s focal length of 10 m is achieved by a deployable mast that was extended after the satellite was launched into its orbit. Because reflective optics are ultimately limited by Eq. (16), i.e., focusing higher photon energies would require smaller incidence angles (∝ θ 2 ) and a much larger focal lengths (∝ f ) to accommodate a high level of effective area, these types of apertures are probably not suited beyond photon energies of ∼200 keV. A proposed instrument that is based on reflective optics is PheniX (Roques et al. 2012), which would have a focal length of 40 m, also obtained by an extensible mast.

Diffractive Optics Beyond total reflection, there are the possibilities for refraction and diffraction of γ -ray photons. Yang (1993) who discussed refractive optics for photon energies up to 1 MeV, however, found that absorption and scattering severely limits the ability to form an efficient telescope with large effective area. Therefore, only diffraction permits improvement upon the classic non-focusing γ -ray instruments. In general, the diffraction limit defines the spatial resolution sd = 1.22λf/d, with f being the focal length, λ the photon wavelength, and d lens diameter, and provides the fundamental limit to the achievable angular resolution, θd = sd /f . Thus, for photon energies around 1 MeV (λ ≈ 1.24 pm), the angular resolution approaches microarcseconds (m′′ ). This is possible by the use of phase Fresnel lenses (Miyamoto 1961) in which concentric rings of precisely placed crystals diffract the high-energy photons onto a detector at the focal point. The distance of the focal point where the γ -ray detector is placed, however, is related to the lens diameter d, the photon energy E, and the pitch size of the Fresnel lens p by

p  d  E  km, f = 0.4 × 10 1 mm 1m 1 MeV 6

(17)

which makes the realization of a telescope on a single spacecraft almost impossible (Skinner 2001). It should be noted that Fresnel lenses suffer severely from chromatic aberration, effectively worsening the achievable angular resolution by factors of a few, and distorting the received spectrum. Nevertheless, concepts to build γ -ray-focusing (concentrating) telescopes exist and are discussed in this book (chapter “Gamma-Ray Lens”). An important part of these concepts is the formation flight of two or more spacecrafts in sync. Another possibility to achieve a much enhanced sensitivity would also be to use a deployable boom, such as used in the ASTENA proposal (Frontera et al. 2019, 2021). Here, the goal is not to approach the diffraction limit, but to construct a design feasible with current technologies. With a 20 m focal length, an angular resolution of 30 arcmin could be achieved in the bandpass between 50 and 600 keV, reaching a continuum sensitivity of more than two orders of magnitude better than INTEGRAL/SPI thanks to ASTENA’s effective area of more than 7 m2 (Frontera et al. 2019).

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Interplanetary Network In fact, several spacecrafts are already used in combination in the so-called Interplanetary Network (IPN; e.g. Hurley et al. 2009). While the spacecrafts are not flying in formation, their absolute distances to each other can be used for triangulation of celestial burst-like signals, such as GRBs or soft gamma repeaters. In particular, the localization is performed by a comparison of the arrival times from the different γ -ray instruments wherein the precision is given by the distances of the spacecrafts and the absolute number of detected photons. The further the instruments are separated, i.e., the larger the baseline of potentially several hundred millions of kilometers, the more accurate the localization will be. The triangulation technique is explained in Hurley et al. (2013), for example, and depicted here briefly: A transient event is measured with a delay time δT at two different spacecrafts. Given the separation D of the spacecrafts, the transient is localized onto an annulus on the celestial sphere with half-angle Θ as cos(Θ) =

cδT , D

(18)

with c being the speed of light. The “error box” or width of the annulus is provided by the uncertainty of the time delay as σΘ = cσδT /(D sin(Θ)). Burgess et al. (2021) showed that this classical triangulation method has weaknesses because the choice of uncertainties may be ill-defined. The authors developed a novel method that can robustly estimate the position of a transient via a hierarchical Bayesian model. In particular, they forward-fold the unknown temporal signal evolution, described by random Fourier features, and fit this model to the time series data of each instrument. This takes into account the appropriate Poisson likelihood, and consequently the uncertainties generated by the method are more robust and in many cases more precise compared to the classical method. The IPN started in 1977; its third version, IPN3, was operating with Ulysses, CGRO, Pioneer Venus Orbiter, Mars Observer, and BeppoSAX. Currently, the IPN localizations come from Konus-Wind, Mars Odyssey, INTEGRAL, Swift, AGILE, BepiColombo, and Fermi. In total, more than 32 spacecrafts have been involved in the IPN so far.

Gamma-Ray Detectors Most γ -ray emission processes are continuum-like. Instrumental resolution is, therefore, not too important except for when one wants to do line spectroscopy. Since lines only appear up to the MeV range (20 MeV), spectral resolution is less of an instrument design driving factor above ∼20 MeV. When choosing the materials that compose the target for the incident γ -ray signal, a trade-off between instrumental resolution, weight, sensitivity, and power is always at play. The materials that are used to detect the by-products (charged particles) of the incident γ -ray at these energies broadly comprise two main categories, solid-

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state detectors and scintillators. Solid-state detectors are discussed in detail in chapters (chapters “Germanium Detectors for Gamma-Ray Astronomy” – Roques; and “Silicon Detectors for Gamma-Ray Astronomy” – Caputo; and ⊲ Chap. 57, “Cd(Zn)Te Detectors for Hard X-ray and Gamma-ray Astronomy” – Meuris). They are lightweight, compact, and more tolerant to a space environment than vacuum or gas-based detectors. In general, they comprise a semiconductor material (such as silicon, germanium, or CZT) which is reverse-biased so that the electrons and holes can move freely in the so-called depletion region. When a charged particle (electron or positron) enters this sensitive area of the crystal, ionization is produced. This signal is then transferred via a charge-sensitive preamplifier where it is converted to a voltage pulse proportional to the strength of the ionization signal. For example, the spectrometer SPI uses an array of 19 high-purity cooled germanium detectors to perform high-resolution spectral measurements between 18 keV and 8 MeV (Fig. 22). Silicon strip detectors are used to detect the passage of the electron-positron pairs for both the LAT on Fermi (Atwood et al. 2009) and for the GRID on AGILE (Perotti et al. 2006) Scintillation detectors comprise a material that produces light when it is traversed by a charged particle. They are described in detail in chapter “Scintillators for Gamma-Ray Astronomy” – Iyudin. The scintillation light is recorded by a photodetector (often a photomultiplier tube or photodiode) so that the passage of the charged particle and, in certain cases, its energy can be measured. Scintillator materials can be organic or inorganic in nature. Inorganic scintillators, including NaI and BGO, are usually chosen for calorimeter systems due to their high density and effective atomic number which means that they have a high stopping power. Inorganic scintillators comprise four main categories: plastic, glass, single crystal, and liquid. Plastic scintillators are those most commonly used in γ -ray applications due to their lightweight, low cost, and robustness. The light yield from inorganic scintillators is typically higher than those from organic scintillators so that it is typically used as a material for veto shields.

Fig. 22 General MeV γ -ray measurement features as observed in detectors. A beam of photons with energies Eγ creates a photopeak at this energy. Compton scattering inside the detector leads to a characteristic continuum below the photopeak. If the incoming photon energy is greater than 2me c2 = 1.022 MeV, single and double escape peaks can emerge

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Understanding Gamma-Ray Measurements The nature of γ -ray measurements can be understood as the recording of photons into complex data spaces due to the vastly different apertures. These data spaces are typically shown in the form of back projections, such as the shadow pattern of coded mask instruments or the rings from Compton telescopes. In the case of GeV instruments, this “imaging” is only weakly influenced by dispersion which is why we focus more on the MeV instruments here. Nevertheless, the concepts here apply to all dispersed measurements. The abstract data spaces of γ -ray instruments are spanned by reconstructed or inferred variables, such as the three scattering angles in Compton telescopes or the number of pixels (detectors) in coded mask telescopes. Typically, these data spaces are not necessarily the real instrument spaces because they can have considerable uncertainties which are often omitted in the subsequent data analysis steps or because data filtering due to quality criteria after reconstruction skewed the true generating process: counting photons. The real data space of each instrument goes down to the level of its electronics and the specific geometry – a coding mask, shadow patterns, Compton cones, iterative deconvolutions, polarigrams, scattering angle distributions, a coding mask etc., – are always abstractions of how to possibly visualize raw data. In the reconstructed variables or data spaces, data analysis should be treated with care because there are often (hidden) assumptions which destroy the character of the measurement, change its likelihood, or are ill-defined because the instruments suffer from dispersion. Instead, the method of forward-folding should be used to convolve models with physical units into the raw data space of channel number per detector unit. Forward modelling is the only statistically proper way to analyze γ -ray data d, which, without loss of generality, can be described as matrix equation d = R · m,

(19)

with R being the response matrix and m an (unknown) model that is to be inferred. Except for approximate cases (e.g., mask coding with fully transparent and opaque elements, ⊲ Chap. 48, “Coded Mask Instruments for Gamma-Ray Astronomy”), R is not invertible which means that a solution shaped like m = R−1 d does not exist. The model m is not measured; only the data d are, which means in turn that m must be assumed, i.e., modelled to explain the data. This is done by parameterizing the model with a set of variables, the so-called fit parameters ϕ, so that the model becomes a function of unknown parameters: m(ϕ). The model includes everything that is required to describe the astrophysical source of interest. This means it includes a spectral shape, temporal variability, spatial extent, and polarization parameters, among others. These properties can be interdependent, which can be incorporated in the response function R (Fig. 23). The response is described in units of cm2 and is equivalent to the effective area, i.e.,

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it changes as a function of zenith, azimuth, initial energy, polarization angle, and instrumental environment parameters (temperature, voltage, etc.). Typical features visible in spectral dispersion matrices are the Compton edges (at measured energies Ef = Ei (1 − (1 + 2Ei /(me c2 ))−1 ), approaching Ei − 0.25 MeV for large Ei , Compton continuum (single and multiple scatters), first and second escape peaks (Fig. 22), and emergence of a 511 keV line for initial energies above 1.022 MeV. Conceptually, the data are generated by assuming a source’s position (in astronomical coordinates) which converts to instrument coordinates (zenith/azimuth) for which an instrumental response is created. A differential spectrum (in physical units, e.g., ph cm−2 s−1 keV−1 ) is integrated over the energy to obtain the expected flux per response element (→ ph cm−2 s−1 ), to which the response function is applied, resulting in an expected rate per data space bin (→ cnts s−1 ). Note the change of notation here from physical photons to received number of counts after the application of the response. Given the exposure time, the model counts per data space bin i (→ cnts) can be compared to the data via the Poisson likelihood

Fig. 23 Visualization of MeV telescope responses. Left: Back projection of the SPI coded mask response seen from its central detector (unit 00) at an energy of 66 keV. The same mask pattern is visible for an outer detector (second image, unit 12, which is equivalent to shifting the source position) at an energy of 5 MeV; however, the edges are not as sharp because the transparency of the material increases with photon energy. The inner edge of SPI’s anticoincidence shield is visible (hexagonal shape outside the central ring). Right: Back projection of Compton circles from the COSI balloon response. Shown are 20 Compton circles at an energy of 511 keV, overlapping in the source position. An iterative deconvolution algorithm (fourth image) is applied to reduce improbable regions so that a point source emerges

Fig. 24 Energy dispersion of different γ -ray detectors in units of cm2 . Given a photon with true (initial) energy Ei , there is a probability that the photon is measured at a lower (final) energy Ef . The diagonal represents the photopeak efficiency. Left: NaI detector onboard GBM. Middle: BGO detector from GBM. Right: SPI germanium detector. The scale of the color bar is enhanced by two orders of magnitude for SPI to indicate the features away from the diagonal

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Fig. 25 Forward folding of spectral models into the count data space of different detectors. Top: Selection of five spectral models. A broken power law representing the Crab spectrum (Jourdain and Roques 2009); a Band function (Band et al. 1993) with 10% of the Crab flux, α = −1.5, β = −3.0, and Epeak = 1.5 MeV; a cutoff power law with 10 times the Crab flux, α = −3.0, EC = 100 keV; a positronium (ortho+para, Ore and Powell 1949) spectrum with a line flux of 6 × 10−3 ph cm−2 s−1 ; and a 100 keV broadened 12 C line with the same line flux. Bottom: The models convolved with the energy responses from Fig. 24 for BGO (left), NaI (middle), and Ge (right). The resolution of the detectors is increasing from left to right. It is seen that different spectral models (e.g., the broken power law and the Band function) can appear very similar in the data space. Likewise, components above the maximum considered energy of the instrument contribute to the counts at lower energies because of dispersion

L(d|m(ϕ)) =

mi (ϕ)di exp(−mi (ϕ)) . di !

(20)

i

Finally, the once smooth (infinitesimal) model is transferred into the (possibly) binned data space. Examples of how such a convolution appears are shown in Fig. 25. Here, the same five models are folded through the responses of one of GBM’s NaI and BGO detectors and through the response of SPI’s central detector. Depending on the orientation of the detector with respect to the source in the sky (assumed to be identical here), the response changes (Fig. 24) as the incoming photons are dispersed in different ways in the same detector. It is also seen that different spectral resolutions impact the identification capabilities of different features – for example, lines can be seen more clearly with higher resolution. However, also highresolution germanium detectors suffer from dispersion, distributing more than 50% of photons with an initial energy of 4.4 MeV to lower energies.

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Simulations The above-described response functions, and therefore the entire data analysis and scientific output, rely heavily on simulations. In this handbook, an entire chapter is dedicated to the procedures, requirements, and details of particle and photon simulations (chapter “Simulation”). This also includes details about electronics simulations, detector effects, and methods to handle these in real measurements. Here, a short overview of the basic features and general idea is given to understand the need for simulations as well as a few examples and caveats. Before instrument prototypes are built, they are often simulated in the Geometry and Tracking (GEANT, e.g., Agostinelli et al. 2003) environment. In GEANT, active and passive volume elements are arranged as close as possible to the real geometry of the instrument and irradiated with particles and photons through a Monte Carlo technique. This allows the instrument designer to (1) estimate the performance of the instrument, (2) adjust the geometry and mountings before building the prototype, (3) choose appropriate materials, and (4) determine the response functions of the instrument. Because GEANT includes the most-complete database of cross sections and interactions of many particles, both the instrumental background and the sources of interest can be simulated. Using appropriate statistics, the sensitivity of the instrument can be estimated for different cases, for example, as a function of time, energy, spectral shape, and aspect angle. Including the anticoincidence shield in addition to the active detector(s) in the simulation will provide an estimate of the background reduction. Finally, for the full response as a function of initial energy, zenith, azimuth, and other environmental parameters, also the satellite (or balloon) structure must be included. The more detailed the geometrical mass model of the instrument, the better the scientific output in the end. However, the more sophisticated the mass model is, the longer the simulations will run. In addition, also the computational resources to perform the simulations might be limited. For example, the SPI response simulations (Sturner et al. 2003) have been performed for only 51 individual energies for the more than two decade spanning energy range. This was required because a full, highly resolved energy response would have taken years to simulate. With the ground calibration (Attié et al. 2003) (section “Calibrations”), the simulations have been validated so that a full response can be constructed by interpolation. Although SPI has an energy resolution of 2.7 MeV (Mandrou et al. 1997; Schanne 2002). SPI imaging was calibrated with high-flux sources of 241 Am, 137 Cs, 60 Co, and 24 Na, located outside the laboratory through a transparent window. The beams were strongly collimated to avoid radiation in other directions and scatters inside the experimenting hall. For energy calibration of SPI, the mask was removed so that all detectors could be illuminated simultaneously. Although the field of view of SPI is about 16◦ × 16◦ , the calibration took place only on axis, and no other zenith and azimuth angles have been tested. Instead, the telescope efficiency is derived from the absorption properties of the individually measured transmissivities of opaque and transparent mask elements (Sanchez et al. 2003). A mathematical model was then fit to obtain the correct mask properties given the full set of calibration measurements. For future MeV instruments, such as for COSI, a full field of view calibration is anticipated which will reduce the systematic uncertainties from calibrations with a single beam line plus simulations to obtain the instrument response functions.

Table 1 Radioactive isotopes and resonance photons used for the calibration of MeV instruments between 10 keV and 10 MeV (including K- and L-shell X-rays) with at least a branching ratio of 0.01 (in parentheses) (NUDAT; Kiener et al. 2004; Antilla et al. 1977) Isotope/reaction 241 Am

Half-life time 432.6 years

133 Ba

10.55 years

57 Co

271.74 days

139 Ce

137.64 days

137 Cs 54 Mn

30.08 years 312.20 days

152 Eu

13.517 years

65 Zn

13 C(p,γ )14 N

243.93 days 5.2714 years 2.6018 years –

27 Al(p,γ )28 N

–

60 Co 22 Na

Line energy [keV] 13.9 (0.37), 26.34 (0.02), 59.54 (0.36) 30.63 (0.34), 30.97 (0.62), 34.92 (0.06), 34.99 (0.11), 35.82 (0.04), 53.16 (0.02), 79.61 (0.03), 81.00 (0.33), 276.40 (0.07), 302.85 (0.18), 356.01 (0.62), 383.85 (0.09) 14.41 (0.09), 122.06 (0.86), 136.47 (0.11) 33.03 (0.23), 33.44 (0.41), 37.72 (0.04), 37.80 (0.08), 38.73 (0.02), 165.86 (0.80) 31.82 (0.02), 32.19 (0.04), 661.66 (0.85) 834.85 (1.00) 344.28 (0.27), 411.12 (0.02), 778.90 (0.13), 1089.74 (0.02), 1299.14 (0.02) 1115.54 (0.50), [511.0 (0.03)] 1173.23 (1.00), 1332.49 (1.00) 1274.54 (1.00), [511.0 (1.80)] 1635, 2313, 3948, 5105, 5690, 6445, 6858, 7027, 8062, 9169 1522, 1779, 2839, 3063, 4498, 4608, 4743, 6020, 6265, 7924, 7933, 10763

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GeV: Particle Accelerators There have been different ways to derive the instrument functions for past and present GeV telescopes: in pioneering counter-type instruments (e.g., OSO-3, Explorer XI), design and calibrations were based on analytical estimates (geometry, cross sections, and individual detector responses) which were verified on beam tests using π 0 decay photons or a synchrotron beam and the response to CR muons at ground level. The first imaging telescopes (e.g., SAS-2, COS-B) were calibrated with γ -ray synchrotron beams (up to a few 100 MeV), electron beams (to characterize the tracking), and CR muons (to test the anticoincidence counters). A full-scale beam calibration was performed on the next-generation EGRET instrument (Thompson et al. 1987; Kanbach et al. 1989). The γ -ray beam at the Stanford Linear Accelerator (SLAC) was generated by inverse Compton scattering of laser photons (2.34 eV) on the high-energy electron pulses from the accelerator. Tuning the linac electron energy from about 0.65 to 20 GeV resulted in backscattered photons at ten energies between 15 MeV and 10 GeV, with an energy dispersion of ∼11% FWHM. The beam was constrained to a collimated pencil beam, with an intensity of ∼0.4 photons per 40 ns pulse width and about 15 pulses/s. EGRET, with a total weight of about 1.8 tons, was mounted to an electrohydraulic computer-controlled fixture which could position the telescope with 0.2 mm accuracy laterally and 0.1◦ in attitude angles. A raster scan over and beyond the sensitive volume of the telescope with scan points spaced by 5 cm was performed for attitudes out to 40◦ off-axis. These calibration measurements during 3 months in 1986 provided not only the data for a model of the efficiency of detection but also the efficiency of “recognition” of good γ -ray events in data analysis of real events. This latter point is often difficult to quantify with simulated data (section “Simulations”). Since the space shuttle accident in 1986 delayed the launch of CGRO until April 5, 1991, further calibration measurements could be performed with EGRET. At Brookhaven National Laboratory, a proton beam up to 10 GeV was used to generate background γ -rays in the material outside the anticoincidence system as a test to see the effect of CR particles on the instrumental background. This was found to be significantly below the expected cosmic γ -ray background. Final γ -ray measurements at MIT-Bates accelerator up to 830 MeV were used to verify some technical developments on the instrument after the main calibrations. With the experience from ground-level calibrations and results from EGRET on CGRO using celestial sources, e.g., pulsed photons from strong pulsars for angular resolution, the design, simulation, and calibration of the currently active GeV telescope Fermi-LAT could be undertaken without a full-instrument beam test. Subsystems, called the LAT Calibration Unit, were exposed to a large variety of beams at CERN and the GSI accelerator facilities to probe γ -ray detection and background sensitivity. Beams of photons (10 MeV thanks to the pair-production effect, but there it is more efficient to use the intrinsic directional properties of this interaction on the few detected photons rather than the collective effect of shadow projection by many rays in order to measure the source direction. X/gamma-ray astronomy is also the domain where the high and variable background becomes dominant over the source contributions, which drastically limits the performance of standard on/off monitoring techniques and where the simultaneous measurement of source and background is crucial even for the simple source detection. Coded masks were conceived in the 1970s–1980s and employed successfully in the past 40–30 years in high-energy astronomy, on balloon-borne instruments first and then onboard space missions like Spacelab 2, GRANAT, and BeppoSAX. They have been chosen as imaging systems for experiments on a number of major missions presently in operation, the European INTEGRAL, the American Swift, and the Indian ASTROSAT, and for some future projects like the Chinese-French SVOM mission. Today the NuSTAR and the Hitomi missions have successfully pushed up to 80 keV the technique of grazing incidence X-ray mirrors (Harrison et al. 2013; Takahashi et al. 2014). However the limited field of view (few arcmin) achieved by these telescopes and the variability of the sky at these energies make the coded mask systems still the best options to search for bright transient or variable events in wide field of views. Coded aperture systems have been employed also in medicine and in monitoring nuclear plants, and implementations in nuclear security programs are also envisaged (Cie´slak et al. 2016; Accorsi et al. 2001). Even if basic concepts are still valid for these systems, certain conditions, specific to gamma-ray astronomy, can be relaxed (e.g., source at infinity, high level and variable background, etc.), and therefore designs and data analysis for CMI for terrestrial studies can take a very different form. In particular for close sources (the so-called near-field condition), the system can actually provide three-dimensional imaging because of the intrinsic enlarging effect of shadow projection as the source distance decreases. This interesting property is not applicable in astronomy and we will not discuss it here. In spite of the large literature on the topic, few comprehensive reviews were dedicated to these systems; the most complete is certainly the one by Caroli et al. (1987), which however was compiled before the extensive use of CMI in actual missions. In this paper we review the basic concepts, the general characteristics, and specific terminology (throughout the paper key terms are written in bold when first defined) of coded mask imaging for gamma-ray astronomy (section “Basics Principles of Coded Mask Imaging”), with a historical presentation of the studies dedicated to the search of the optimum mask patterns and best system designs. We present (section “Image Reconstruction and Analysis”) in a simple way the standard techniques of the image reconstruction based on cross-correlation of the detector image with a function derived from the mask pattern, providing the explicit formulae for this analysis and for the associated statistical errors, and the further processing of the images which usually involves iterative noise cleaning.

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We will discuss the performance of the systems (section “Coded Mask System Performances”), in particular the sensitivity and localization accuracy, under some reasonable assumptions on the background and their relation with the instrument design. We cannot be exhaustive in all topics and references of this vast subject. Clearly the analysis of coded mask system data relies, as for any other telescope, on a careful calibration of the instrument, the understanding of systematic effects of the detector, and the measurement and proper modeling of the background. For these aspects these telescopes are not different from any other one, and we will not treat these topics, apart from the specific question of non-uniform background shape over the PSD, because they are specific to detectors, satellites, space operations, and environment of the individual missions. Also we will not discuss detailed characteristics of the PSDs, and we will neglect description of one-dimensional (1-d) aperture designs and systems that couple spatial and time modulation (like rotational collimators), as we are mainly interested in the overall 2-d coded aperture imaging system. We include a section (section “Coded Mask Instruments for High-Energy Astronomy”) on the application of CMI in high-energy astronomy with a presentation of the historical developments from rocket-borne to space-borne projects and mentioning all the experiments that were successfully flown up to today on space missions. Finally we dedicate specific sub-sections to three gamma-ray CMI telescopes: SIGMA that flew on the GRANAT space mission in the 1990s, IBIS currently operating on the INTEGRAL gamma-ray observatory, and ECLAIRs, planned for launch in the next years on board the SVOM mission. These experiments are used to illustrate the different concepts and issues presented and to show some of the most remarkable “imaging” results obtained with CMI, in high-energy astronomy in the past 30 years.

Basics Principles of Coded Mask Imaging Definitions and Main Properties In coded aperture telescopes, the source radiation is spatially modulated by a mask, a screen of opaque and transparent elements, usually of the same shape and size, ordered in some specific way (mask pattern), before being recorded by a position sensitive detector. For each source, the detector will simultaneously measure its flux together with background flux in the detector area corresponding to the projected transparent mask elements and background flux alone in detector area corresponding to the projected opaque elements (Fig. 1). From the recorded detector image (Fig. 2), which includes the shadows of parts of the mask (shadowgrams) projected by the sources in the field of view onto the detector plane and using the mask pattern itself, an image of the sky can, under certain conditions, be reconstructed.

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Fig. 1 Coded aperture principle. Two sources at infinity project a different pattern of the mask on the detector plane (shadow-gram). For a cyclic system, here a mask with a URA basic pattern of 5×3 replicated to 9×5, it is the same pattern but shifted according to the source position

Fig. 2 Coded aperture principle. The resulting images recorded by the position sensitive detector for the configuration of Fig. 1 for the two sources separately (left and right) and combined (center)

Mask patterns must be designed to allow each source in the field of view to cast a unique shadow-gram on the detector, in order to avoid ambiguities in the reconstruction of the sky image. In fact each source shadow-gram shall be as different as possible from those of the other sources. The simplest aperture that fulfills this condition is of course the one that has only one hole, the well-known pinhole camera. The response to a point source of this system is a peak of the projected size of the hole and null values elsewhere. The overall resulting image on the detector is a blurred and inverted image of the object. However the sensitive area and angular resolution, for given mask-detector distance, are inversely proportional to each other: effective area can only be increased by increasing the hole size, which worsens the angular resolution (increases the blurring). A practical alternative is to design a mask with several small transparent elements of the same size (Fig. 1), a multi-hole camera. The resolution still depends on the dimension of one individual hole, but the sensitive area can be increased by increasing the number of transparent elements. In this case however the disposition

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of the holes is important since when more than one hole is used, ambiguity can rise regarding which part of the sky is contributing to the recorded image. For example with a regular chess board pattern mask, different sources would project identical shadows, and disentangling their contributions would be impossible. Mask patterns that have good imaging properties exist, as described below. With the use of a properly designed multiple-hole mask system, an image of the sky can be recovered from the recorded shadow-gram through a convenient computation. In general the sky image reconstruction, or image deconvolution as it is often called, is based on a correlation procedure between the recorded detector image and a decoding array derived from the mask pattern. Such correlation will provide a maximum value for the decoding array “position” corresponding to the source position, where the match between the source shadow-gram and the mask pattern is optimum and generally lower values elsewhere. Note that, unlike focusing telescopes, individual recorded events are not uniquely positioned in the sky: each event is either background or coming from any of the sky areas which project an open mask element at the event detector position. The sky areas compatible with a single recorded event will draw a mask pattern in the sky. It is rather the mask shadow, collectively projected by many source rays, that can be “positioned” in the sky. Assuming a perfect detector (infinite spatial resolution) and a perfect mask (infinitely thin, totally opaque closed elements, totally transparent open elements), the angular resolution of such a system is then defined by the angle subtended by one hole at the detector. The sensitive area depends instead on the total surface of transparent mask elements viewed by the detector. So, reducing hole size or increasing mask to detector distance while increasing accordingly the number of holes improves the angular resolution without loss of sensitivity. Increasing the aperture area will increase the effective surface, but, since the estimation of the background is also a crucial element, this does not mean that the best sensitivity would increase monotonically with the increase of the mask open fraction (the ratio between transparent mask area and total mask area, also sometimes designed as aperture or transparent fraction). In the gamma-ray domain where the count rate is dominated by the background, the optimum aperture is actually one-half. In the X-ray domain, instead the optimum value rather depends on the expected sky to be imaged even if in general, because of the Cosmic X-ray Background (CXB) which dominates at low energies, the optimal aperture is somewhat less than 0.5. The field of view (FOV) of the instrument is defined as the set of sky directions from which the source radiation is modulated by the mask, and its angular dimension is determined by the mask and the detector sizes and by their respective distance, in the absence of collimators. Since only the modulated radiation can be reconstructed, in order to optimize the sensitive area of the detector and have a large FOV, masks larger than the detector plane are usually employed, even if equal dimensions (for the so-called simple or box type CMI systems) have also been used. The FOV is thus divided in two parts: the fully coded (FC) FOV for which all source radiation directed toward the detector plane is modulated by the mask and the partially coded (PC) FOV for which only a fraction of it is modulated by the mask (Fig. 3).

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Fig. 3 Left: A coded aperture telescope geometry with a mask larger than the detector and a shield connecting them. The field of views around the telescope axis are shown: the FCFOV (red), the Half Modulation EXFOV (green), and the Zero Response EXFOV (black). Right: Relation, for a square CMI, between the array sizes of mask (M), detector (D), and sky (S), with indication, in the sky, of the FOVs (same color code than left panel)

The non-modulated source radiation, even if detected, cannot be distinguished from the (non-modulated) background. In order to reduce its statistical noise and background radiation, collimators on the PSD or an absorbing tube connecting the mask and detector are used. The typical CMI geometry and its FOVs are shown in Fig. 3. If holes are uniformly distributed over the mask, the sensitivity is approximately constant in the FCFOV and decreases in the PCFOV linearly because the mask modulation decreases to zero. The total FOV (FC+PC) is often called extended (EX) FOV and can be characterized by the level of modulation of the PC. Figure 3-right shows the relative sizes of the (ZR)EXFOV, detector, and mask. For simple systems the FCFOV is limited to the on-axis direction, and all the EXFOV is PCFOV. Table 1 reports the approximate imaging characteristics provided by a coded aperture system (as illustrated in Fig. 3) as functions of its geometrical parameters along one direction. Values of the IBIS/ISGRI system (section “IBIS on INTEGRAL: The Most Performant Gamma-Ray Coded Mask Instrument”) for which the design parameters are given in the notes are reported as example. The EXFOV dimensions are given for half modulation level and for zero response. Both angular resolution and localization power, which are at the first order linked to the angle subtended by the mask element size to the detector and the detector pixel (or spatial resolution) to the mask, depend actually also on the reconstruction method and even on the distribution of holes in the mask pattern as described below.

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Table 1 Expected imaging properties of a coded aperture system Quantity FCFOV (100% sensitivity) EXFOV (50% sensitivity) EXFOV (0% sensitivity)

Angular value −LD ) 2 · arctan (LM2·H LM 2 · arctan 2·H (LM +LD ) 2 · arctan √ 2·H

Angular resolution on-axis (FWHM) Localization error radius on-axis (90% c.l.)

≈ arctan  ≈ arctan

m2 +d 2 H 1.52 d SN R H



IBIS/ISGRI 8.2◦ 18.9◦ 29.2◦ 13′ m d

−

1 3



22′′ at SNR=30

Notes: LM masklinear size, LD detector linear size, H detector-mask distance, m mask √ element linear size (m > d), d detector pixel linear size for pixelated detector, d = 2 3σD where σD = linear detector resolution (in σ ) for continuous detector. SNR here is the “imaging signal to noise ratio” SN RI for known source position (see below for definitions). IBIS/ISGRI approximate parameters: LM = 1064 mm, LD = 600 mm, H = 3200 mm, m = 11.2 mm, d = 4.6 mm

Coding and Decoding: The Case of Optimum Systems To analyze the properties of coded mask systems, we first simplify the treatment by considering an optimum coded mask system which provides after the image reconstruction a shift invariant and side-lobe-free spatial response to a point source, the so called System Point Spread Function (SPSF), in the FCFOV (see, e.g., Fenimore and Cannon 1978). We assume a fully absorbing infinitely thin mask, a perfectly defined infinitely thin PSD with infinite spatial resolution and perfect detection efficiency. The object, the sky image, described by the term S is viewed by the imaging system composed by a mask described by the function M and a detector that provides an image D. S, M, and D are then continuous real functions of two real variables. M assumes values of 1 in correspondence to transparent elements and 0 for opaque elements, and the detector array D is given by the correlation [The two-dimension integral correlation between two functions, say A and B, is indicated by the symbol ⋆ and is given ¯ by A ⋆ B = C(s, t) = A(x, y) · B(x + s, y + t)dxdy where A¯ is the complex conjugate of the function A.] of the sky image S with M plus an un-modulated background array term B D =S⋆M +B If M admits a so-called correlation inverse function, say G, such that M⋆G = δfunction, then we can reconstruct the sky by performing S′ = D ⋆ G = S ⋆ M ⋆ G + B ⋆ G = S ⋆ δ + B ⋆ G = S + B ⋆ G and S ′ differs from S only by the B ⋆ G term. In certain cases, when, for example, the mask M is derived from a cyclic replication of an optimum basic pattern, if the background is flat, then the term B ⋆G is also constant and can be removed. Since even for very high detector resolution the

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information must be digitally treated in the form of images with a finite number of image pixels, the problem must be generally considered in its discrete form. We can formulate the same process in digital form by substituting the continuous functions with discrete arrays and considering discrete operators instead of integral operators. S, M, G, D, and B terms will therefore be finite real 2-d arrays, and the delta function the delta symbol of Kronecker. The discrete correlation is obtained by finite summations and the reconstructed sky S ′ by ′ Si,j =

 kl

Dk,l Gi+k,j +l

with i, j indices that run over the sky image pixels and k, l over the detector pixels. Mask patterns that admit a correlation inverse array exist (section “Historical Developments and Mask Patterns”) and can be used to design the so-called optimum systems. For instance, for masks M that have an auto-correlation given by a delta function, the decoding array constructed posing G = 2 · M − 1 (i.e., G = +1 for M = 1 and G = −1 for M = 0) is then a correlation inverse. To have such a sidelobe-free response in an optimum system, a source must however be able to cast on the detector a whole basic pattern. To make use of all the detector area and to allow more than one source to be fully coded, the mask basic pattern is normally taken to be the same size and shape as the detector and the total mask made by a cyclic repetition of the basic pattern (in general up to a maximum of 2 times minus 1 in each dimension to avoid ambiguities) (Fig. 4). For such optimum systems, a FCFOV source will always project a cyclically shifted version of the basic pattern, and correlating the detector image with the G decoding array within the limits of the FCFOV will provide a flat side-lobe peak with position-invariant shape at the source position (Fig. 4 right). A source outside the FCFOV but within the PCFOV will instead cast an incomplete pattern, and its contribution cannot be a priori automatically subtracted by the correlation with the decoding array at other positions than its own, and it will produce secondary lobes over all the reconstructed EXFOV including the FCFOV.

Fig. 4 Mask, detector, FC sky of an optimum CMI. Left: A 33×29 replicated mask of basic pattern 17×15 (Hadamard from an m-sequence CDS with N = 255 and m = 8 disposed along the diagonal). Center: Simulated detector image of two sources in the FCFOV and low background for a CMI with the mask on the left and a detector of same size of its basic pattern, with 3×3 pixels per mask element. Right: The relative decoded SNR sky image in the FCFOV

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Following a standard nomenclature of CMI, we refer to these secondary lobes as coding noise. On the other hand, the modulated radiation from PC sources can be reconstructed by extending with a proper normalization the correlation procedure to the PCFOV. The reconstructed sky in the total field (EXFOV) is therefore composed by the central region (FCFOV) of constant sensitivity and optimum image properties, i.e., a position-invariant and flat side-lobes SPSF, surrounded by the PCFOV of decreasing sensitivity and non-perfect SPSF (Fig. 5). In the PCFOV, the SPSF includes coding noise, the sensitivity decreases, and the relative variance increases toward the edge of the field. Also, even FCFOV sources will produce coding noise in the PCFOV, while sources outside the EXFOV are not modulated by the mask and simply contribute to the background level on the detector. When a complete mask is made of a cyclic repetition of a basic pattern, then each source in the FOV will produce eight large secondary lobes (in rectangular geometry) at the positions which are symmetrical with respect to the real source position at distances given by the basic pattern: these spurious peaks of large coding noise are usually called ghosts or artifacts (Fig. 5). These optimum masks also minimize the statistical errors associated to the reconstructed peaks and make it uniform along the FCFOV. Since G is two-valued and made of +1s or −1s, the variance associated to the reconstructed image in the FCFOV is given by V = G2 ⋆ D = ΣD, the variance associated to each reconstructed sky image pixel is constant in the FCFOV and equal to the total counts

Fig. 5 Reconstructed SNR sky image in the full EXFOV for the CMI and simulation of Fig. 4 left/center. The central part corresponds to the FCFOV (same as Fig. 4 right) and shows optimal properties: the shift invariant peaks and flat side-lobes of the two simulated FC sources. In the PCFOV coding noise and the strong eight ghosts of the main source are clearly visible

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recorded by the detector. This implies that the source signal to noise ratio (SNR) is simply Reconstructed Source Counts CS = √ SNR = √ CS + CB T otal Detected Counts where CS and CB are source and background recorded counts. The deconvolution is then equivalent to summing up counts from all the detector open elements (source and background counts) and subtracting counts from the closed ones for that source (background counts only).

Historical Developments and Mask Patterns Following the first idea to modulate incident radiation using Fresnel plates, formulated by Mertz and Young (1961), the concept of a pinhole camera with multiple holes for high energy astronomy (the multiple-pinhole camera) was proposed by Ables (1968) and Dicke (1968) at the end of the 1960s. In these designs multiple holes of the same dimensions are distributed randomly on the absorbing plate and in spite of the inherent production of side-lobes in the SPSF, the increase in the aperture fraction compared to the single pinhole design highly improves the sensitivity of the system, at the same time maintaining the angular resolution. Toward the end of the 1970s, it was realized that special mask patterns could provide optimum imaging properties for coded aperture systems, and then a large number of the early works focused on the search for these optimal or nearly optimal aperture patterns. Most of these are built using binary sets called cyclic different sets (CDS) (Baumert 1971) which have the remarkable property that their cyclic auto-correlation function (ACF) is two-valued and approximates a delta function modulo a constant term. Certain of these sets can be disposed (following certain prescriptions) to form 2-d arrays, the so-called basic patterns, which also have the property of having 2-d cyclic auto-correlations which are bi-dimensional delta functions, thus allowing design of coded aperture systems where a correlation inverse is directly derived from the mask pattern. Thus by disposing, in a rectangular geometry, 2×2 such 2-d basic pattern side by side (actually less than 2 times in each direction in order to avoid full repetition of the pattern and then ambiguity in reconstruction) at a certain distance from a detector plane of the same dimension as the basic pattern, one obtains an optimum system with maximum FCFOV, free of peak repetitions and coding noise. Care must be taken on how the mosaic of the basic pattern is done in order for a source to project on the detector a shifted, but complete, version of the basic pattern.

Patterns Based on Cyclic Different Sets A cyclic different set D(N, k, λ) is a collection of k distinct integer residues d 1 , . . . d k modulo N , for which the congruence d i − d j = q mod(N ) has exactly λ distinct solution pairs (d i ,d j ) in D for every residue q = 0 mod(N ). If such a

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different set D exists, then λ = k(k − 1)/(N − 1). This mathematical definition simply means that for these sets, a cyclic (over the dimension N of the larger set to which they belong) displacement vector between any two elements of the set occurs exactly a constant number of times, given by the parameter λ, which is called the “redundancy” of the set. For this reason binary arrays based on CDS are also called uniformly redundant arrays (URA). From this property immediately follows that a 1-d binary sequence M of dimension N built from a CDS D(N, k, λ) by the following prescription

mi =



1 if i ∈ D

0 if i ∈ /D

has an ACF ai =

 j

mj mj+i =



k

for i = 0 mod N

λ for i = 0 mod N

that is a δ function. The parameter k − λ is also an important characteristic of the set since it determines the difference between the peak and the plateau of the ACF. The higher this value, the better is the signal to noise response to a point source of the derived imaging system. Several types of CDS exist, and early studies on the subject were focused to find as many such sequences as possible and establish the way to build them. A class that was already well known from the coding theory was the Non Redundant Arrays (NRA), which are in fact CDS with redundancy = 1. These have however densities of elements very small (1 are particularly interesting because they have nearly 50% open fraction and when m is even they can be factorized in p × q arrays with p = 2m/2 + 1 and q = 2m/2 − 1 in order to form rectangular (quasi-square) arrays. The first to propose to use different sets for building 2-d imaging optimum systems for X-ray astronomy were independently Gunson and Polychronopulos (1976) and Miyamoto (1977) in 1976. They both identified the m-sequences as the original set to use for the design, but with different mapping in 2-d arrays to obtain the basic pattern. The second author actually started from the Hadamard arrays that were studied in particular for spectroscopy by Harwit, Sloane, and collaborators (1979). The proposed pattern is equivalent to the one obtained by filling up the array with the PN sequence row by row. The first authors instead proposed to build basic patterns from m-sequences filling the array along extended diagonals (this further requires that p and q are mutually primes). In the two cases, the mosaic of cyclic repetition of the basic pattern must be performed in a different way in order to preserve the δ-function ACF property. For the diagonal prescription, the basic patterns can just set adjacent to each other; for the row by row construction, those

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on the side must be shifted vertically by one row (see Caroli et al. 1987 for the details). We call these masks Hadamard masks to distinguish them from the URA described below, even if both can be considered URA. A more complete discussion of the way PN-sequences are used for an imaging coded mask instrument of the type proposed by Gunson and Polychronopulos (1976), including the way of filling the 2-d array by extended diagonal, was provided soon after by Proctor et al. (1979) who also discussed the implementation in the SL1501 experiment (Proctor et al. 1978). Examples of Hadamard masks are shown in Figs. 4 left, 6 left. A particular subset of Hadamard CDS, the twin prime CDS, are those for which p and q are primes and differ by 2 (q = p − 2). These sets can be directly mapped in p × q arrays using the prescription proposed by Fenimore and Cannon (1978) in 1977. In a series of other seminal papers, these authors and collaborators improved the description of coded aperture imaging using these URA arrays and discussed their performances and a number of other associated topics (Fenimore 1978, 1980; Fenimore and Cannon 1981; Fenimore and Weston 1981). These URA masks, as we will call them following Fenimore and Cannon (1978), are generated from quadratic residue sequences of order p and q (p = q + 2) according to the following prescription:

Mij =

⎧ ⎪ 0 if i = 0 ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨1 if j = 0, i = 0 p Ci

q · Cj

⎪ 1 if = 1 where ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩0 otherwise

p Ci

=



+1 if ∃ k ∈ Z, 1 ≤ k < p, i = k2 mod p

−1 otherwise

Other 2-d rectangular arrays presenting delta function ACF were identified as Perfect Binary Arrays (PBA). Again they are a generalization in 2-d of CDS, include the URAs, and are based on different set group theory (Kopilovich and Sodin 1994). Early designs of CMI assumed rectangular geometry, but in 1985 mask patterns for hexagonal geometry were proposed by Finger and Prince (1985). These are based on Skew-Hadamard sequences (Hadamard sequences with order N prime and constructed from quadratic residues) that, for dimensions N = 12t + 7 where t is an integer, can be mapped onto hexagonal lattices, with axes at 60◦ from each other, to form hexagonal URA, the HURA. In addition to be optimum arrays (they have a δ-function ACF), they are also anti-symmetric with respect to their central element (complete inversion of the pattern) under 60◦ rotation. This property allows one to use them to subtract a non-uniform background, if a rotation of the mask of 60◦ can be implemented, and even to smear out the ghosts created by a replicated pattern if a continuous rotation can be performed. The hexagonal geometry is also particularly adapted to circular detectors. The complications induced by moving elements in satellites have limited the use of such mask/anti-mask concept based on mask rotation with respect to the detector plane. A rotating HURA mask (Fig. 6 center) was successfully implemented in the GRIP balloon-borne experiment (Althouse

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Fig. 6 Optimum coded aperture patterns; note the symmetry of URAs with respect to the “more random” Hadamard ones (also Fig. 4 left). Left: The non-replicated 255×257 Hadamard pattern of the COMIS/TTM mask (from in’t Zand 1992), from an m-sequence CDS ordered along the extended diagonal. Center: Replicated HURA mask of 127 basic pattern used in the GRIP experiment (from Althouse et al. 1985, © NASA). Right: The IBIS 95×95 mask, replication of the MURA 53×53 basic pattern (central red square)

et al. 1985) and operated during a few flights allowing for an efficient removal of the background non-uniformity. A fixed non-replicated HURA of 127 elements has been implemented for the SPI/INTEGRAL instrument.

Other Optimum Patterns The limited number of dimensions for which CDS exist coupled to the additional limitation that N must be factorized in two integers for a rectangular geometry or comply with more stringent criteria for the hexagonal one implies that a small number of sequences can actually be used for optimum masks. This led several authors to look for other optimum patterns, and several new designs were proposed in the 1980s and 1990s, even if somehow related to PN sequences. Even though for these patterns the ACF is not exactly a delta function, it is close enough that a simple modification of the decoding arrays from the simple mask pattern allows recovery of a shift invariant and side-lobe-free SPSF. For these masks therefore an inverse correlation array exists, and an optimum imaging system can be designed. The most used of them was certainly the Modified URA or MURA (Fig. 6 right) of Gottesman and Fenimore (1989). Square MURAs exist for all prime number linear dimensions, and this increases by about a factor 3 the number of rectangular optimal arrays with respect to the URA and Hadamard sets. They are basically built like URA on quadratic residues but for the first element (or central element for a 2-d pattern) which is defined as not part of the set. The MURAs also have symmetric properties with respect to the central element which permits a MURA using the complement of the pattern (but keeping the central element to 0 value). The correlation inverse is built like in URAs (+1 for mask open elements and −1 for opaque ones) apart from the central element, and its replications, if any, which are set to +1 even if the element is opaque. With this simple change from the mask

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pattern, the derived decoding array G is a correlation inverse, and the system is optimum. Other optimum rectangular designs for which a correlation inverse can be defined were obtained from the product of 1-d PN sequences, the Pseudo Noise Product (PNP), or 1-d MURAs (MP and MM products patterns).

Real Systems and Random Patterns More recent studies of mask patterns have focused on more practical issues such as how to have opaque elements all connected between them by at least one side in order to build robust self-supporting masks able to resist, without (absorbing) support structures, to the vibration levels of rocket launches. As explained above, even for an optimum mask pattern, any source in the PCFOV will produce coding noise and spurious peaks also in the FCFOV. In order to obtain a pure optimum system, one has then to implement a collimator which reduces the response to 0 at the edge of the FCFOV. This solution was proposed by Gunson and Polychronopulos (1976) who also suggested to include the collimator directly into the mask rather than in the detector plane. However the total loss of the PCFOV (even if affected by noise) and the loss of efficiency also for FC sources not perfectly on-axis are too big a price to pay to obtain a clean system and led to the abandonment of the collimator solution in favor of a shield between the mask edges and detector borders in order to reduce background and out of FOV source contributions. In addition the geometry of optimum systems cannot be, in practice, perfectly realized. Effects like dead area or noisy pixels of the detector plane, missing data from telemetry errors, not perfect alignment, tilt or rotation of the mask with respect to the detector, absorption and scattering effects of supporting structures of the mask or of the detector plane, and several other systematic effects directly increase the coding noise and ghosts and degrade the imaging quality of the system. Since the imperfect design of real instrument generally breaks down the optimum imaging properties of the cyclic optimum mask patterns, today these patterns are not anymore considered essential for a performing coded mask system, and there is a clear revival of random patterns. Indeed for the typical scientific requirements of CMI (detection/localization of sources in large FOV), one prefers to have some low level of coding noise spread over a large FOV rather than few large ghosts produced by the needed cyclic repetition of the optimum patterns giving strong ambiguities in source location. This is why the most recent instruments were designed using random or quasi-random patterns. The drawback is that, for practical reasons, like the need to have solid self-supporting masks, pure random distributions are also difficult to implement and then for these “quasi-random masks” the inherent coding noise becomes less diffuse and more structured. The issue then becomes how to optimize the choice of these quasi-random patterns in order to get best performance in terms of coding noise, SPSF, sensitivity, and localization.

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Image Reconstruction and Analysis Reconstruction Methods A coded mask telescope is a two-step imaging system where a specific processing of the recorded data is needed in order to reconstruct the sky image over the field of view of the instrument. The reconstruction is usually based on a correlation procedure; however, in principle, other methods can be envisaged. Indeed from the simple formulae that describe the image formation in a CMI (section “Coding and Decoding: The Case of Optimum Systems”) and which give the relations between the input sky S, the mask M, and the detector D, it follows that S can be derived by the simple inversion technique, by means of the Fourier transform (FT) of M and D, with S ′ = I F T (F T (D)/F T (M)) = S + I F T (F T (B)/F T (M)), where IFT stands for the inverse FT. However this direct inverse method usually produces a large amplification of the noise in the reconstructed image, since the FT of M always contains very small or even null terms, and the operation on the background component, which is always present, diverges and leads to very large terms. A way to overcome this problem is to apply a Wiener filter as a reconstruction method (Sims et al. 1980; Willingale et al. 1984) in order to reduce the frequencies where the noise is dominant over the signal when performing the inverse deconvolution. It consists in convolving the recorded image D with a filter WF whose FT is F T (W F ) = F T (M)/[(F T (M))2 + (F T (SN R))−1 ] The filter showed to be efficient to recover the input sky image especially when a non-optimal system is employed, but it requires an estimate of the spectral density of the signal to noise ratio (SNR) which is not in principle known a priori. A simple application using a constant SNR value with spatial frequency was used and compared well to correlation and also to Bayesian methods. Indeed Bayesian methods have also been specifically applied to CMI in particular in the form of an iterative Maximum Entropy Method (MEM) algorithm (Sims et al. 1980; Willingale et al. 1984). The results with MEM are not very different from those obtained by the correlation techniques. The heavy implementation of MEM compared to the latter ones and the problems linked to how to establish the criteria for stopping the iterative procedure to avoid over-fitting the data have made these techniques less popular than correlation coupled to iterative cleaning. Most of these data processes are heavy and time-consuming, especially when images are large, and the issue of computation time is relevant in CMI analysis, in particular when iterative algorithms need to compute several times the sky image or a model, like in MEM. Some studies in the past have concentrated on fast algorithms for the deconvolution. Systems based on pseudo-noise mask patterns and Hadamard arrays could exploit the Fast Hadamard Transform (FHT) which reduces

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the convolution processing from an order of N 2 to one proportional to N log N (Fenimore and Weston 1981). Another method exploits the URA/MURA symmetry (large part of these arrays are given by the multiplication of the first line with the first column) in order to reduce significantly the number of operations (Roques 1987; Goldwurm 1995). However today, at least for astronomical applications, the use of the highly optimized routines of 2-d discrete fast Fourier transform (FFT) available in most software packages for any kind of array order, is usually sufficient for the required implementations based on correlation. The search for fast algorithms or for specific patterns that allow fast decoding is therefore, these days, somehow less crucial. Recently deep learning methods mainly based on convolutional neural networks were proposed to improve the performance of image reconstruction from data of CMI in condition of near-field observations. The tests performed for these specific conditions of terrestrial applications, with their additional complexity of the source distance-dependent image magnification, show that these novel techniques provide enhanced results compared to the simple correlation analysis (Zhang et al. 2019b). Further developments in this direction can be expected in the near future.

Deconvolution by Correlation in the Extended FOV The cross-correlation deconvolution described above for the FCFOV can be applied to the PCFOV, by extending the correlation of the decoding array G with the detector array D in a non-cyclic form to the whole field (EXFOV) (Goldwurm 1995; Goldwurm et al. 2003). To perform this a FOV-size G array is derived from the mask array M following a prescription that we describe below and by padding the array with 0 elements outside M in order to complete the matrix for the correlation. Since only the detector section modulated by the PC source is used to reconstruct the signal, the statistical error at the source position and also the significance of the ghost peaks, if any, are minimized. To ensure a flat image in the absence of sources, detector pixels which for a given sky position correspond to mask opaque elements must be balanced, before subtraction, with a proper ratio of the number of transparent to opaque elements for that reconstructed sky pixel. This normalization factor is stored in a FOV-size array, called here Bal, and its use in decoding is equivalent to the so-called balance deconvolution for the FCFOV (Fenimore and Cannon 1978). In order to correctly account for detector pixel contributions or even attitude drifts or other effects, a weighting array W of the size of the detector array and with values comprised between 0 and 1 is defined and multiplied with the array D before correlation (Goldwurm 1995). It is used to neglect the detector areas which are not relevant (e.g., for bad, noisy, or dead area pixels) by setting the corresponding entries to 0. If one is interested in studying weak sources when a bright one is also present in FOV, W may be used to suppress the bright source contamination by setting to 0 the W entries corresponding to detector pixels illuminated by the

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bright source above some given fraction. The array W is also used to give different weights to parts of the detector, for example, when pixels have different efficiencies, e.g., due to different dead times or energy thresholds. The balance array Bal is built using W to properly normalize the balance considering the weights given to the detector pixels. Obviously when W contains some zero values, it means that there is not complete uniform coding of the basic pattern, and this will break the perfect character of an optimum system, introducing coding noise. In case a small fraction of pixels is concerned, the effect will be however small. In order to insure the best imaging sensitivity, G is built from the mask M by G=

1 ·M −1 a

where the factor a gives the aperture of the mask. For a = 0.5 (like in URAs) G = 2 · M − 1 and assumes values +1 or −1 as in the standard prescriptions (Fenimore 1978). Defining the two arrays G+ and G− such that +

G =



G for G ≥ 0 0 elsewhere

−

G =



G for G ≤ 0

0 elsewhere

where of course G = G+ + G− , we obtain the reconstructed sky count image from S=

G+ ⋆ (D · W ) − Bal · (G− ⋆ (D · W )) A

(1)

where dot operator or division applied to matrices indicates here element-byelement matrix multiplication or division. The balance array used to account for the different open to closed mask element ratios is given by Bal =

G+ ⋆ W G− ⋆ W

and ensures a flat image with 0 mean in absence of sources. The normalization array A = (G+ · M) ⋆ W − Bal · ((G− · M) ⋆ W ) allows a correct source flux reconstruction which takes into account the partial modulation. With this normalization the sky reconstruction gives at the source peak the mean recorded source counts within one totally illuminated detector pixel. Note that source flux shall not be computed by integrating the signal around the peak, as this is a correlation image. An additional correction for off-axis effects (including, e.g., variations of material transparency, etc.) may have to be included, once the reconstruction, including ghost cleaning, has been carried out.

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The normalized variance, which is approximately constant in the FCFOV for optimum or pure random masks, and whose relative value increases outside the FCFOV going towards the edges, is computed accordingly [Here X2 = X · X.]: V =

(G+ )2 ⋆ (D · W 2 ) + Bal 2 · ((G− )2 ⋆ (D · W 2 )) A2

(2)

since the cross-terms G+ · G− vanish. Here it is assumed that the variance in the detector image is just given by the detector image itself (assumption of Poisson noise and not processing of the image); however if it is not the case, the D array in this last expression shall be substituted by the estimated detector image variance. The signal to noise image is given by the ratio √S and is used to search for significant excesses. The deconvolution procedure V can be explicitly expressed by discrete summations over sky and detector indices of the type given in section “Coding and Decoding: The Case of Optimum Systems” for Sij (Goldwurm et al. 2003). Different normalizations may be applied in the reconstruction (Skinner and Ponman 1994); for example, one can normalize in order to have in the sky image the total number of counts in the input detector image. However the basic properties of the reconstructed sky image do not change. In particular with the presence of a detector background, there are more unknowns than measurements, and therefore reconstructed sky pixels are correlated. It is possible to show (Skinner and Ponman 1994) that, at least for optimum masks, the level of correlation is of the order of 1/N (where N is again the number of elements in the basic pattern). Clearly if binning is introduced, then the level of correlation increases, depending on the reconstruction algorithm employed as discussed below. All the previous calculations can be performed in an efficient and fast way using the discrete fast Fourier transform algorithm because all operations involved are either element-by-element products or summations or array correlations for which we can use the correlation theorem [For which A ⋆ B = I F T (F T (A) · F T (B)) where FT is the Fourier transform, IFT is the inverse Fourier transform, and the bar indicates complex conjugate.].

Detector Binning and Resolution: Fine, Delta, and Weighted Decoding We have until now implicitly assumed to have a detector of infinite spatial resolution and data digitization for which images are recorded in detector elements (pixels) with the same shape and pitch as the mask elements and that sources are located in the center of a sky pixel, allowing for perfect detector recording of the projected mask shadow. These approximations are of course not verified in a real system, which implies a degradation of the imaging performance. Recorded photons are either collected in discrete detector elements (for pixelated detectors) or recorded

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by a continuous detector (like an Anger camera) subject to a localization error described by the detector point spread function (PSF) and where the measured positions are digitally recorded in discrete steps (pixels). In both cases we will have detector pixels with a finite detector spatial resolution characterized by the detector pixel size d or the σD of a Gaussian describing the detector PSF and the digitization. Pixels may have sizes and pitches different from those of the mask elements, but for a good recording of the mask shadow, resolution and digital pixels must be equal or smaller than the mask element size; otherwise the shadow boundary is poorly measured, and there is a large loss of sensitivity and in source localization. One can define the resolution parameter r as the ratio r = m/d in each direction of the linear sizes of the mask element and the detector pixel (where pixel size means pixel pitch, since the physical pixel may be smaller with some dead area around it). Fenimore and Cannon (1981) considered the case of r integer in both directions and showed that the same procedure of cross-correlation reconstruction can be carried out just by binning the array M with the same pixel grid as the detector, which will give the rebinned mask M R ; by assigning to all its pixels corresponding to one given mask element the value of that element, defining G accordingly (G = 2 · M R − 1, for a = 0.5); and then by carrying out the correlation over all pixels. So, for example, for r × r detector pixels (square geometry) per mask element, each element of the mask is divided in r × r mask pixels. To each of them, one assigns the value of the element and then carries out the G-definition and correlations accordingly. This is the fine cross-correlation deconvolution. Another way, when building the decoding array G, is to assign the value of the mask element to one pixel from the r × r ones that bin this mask element, while the others are set to the aperture a. For a URA (a = 0.5), the G array has +1 or −1 for one pixel per mask element, and the others are set to 0 (and do not intervene in the correlation). This is the so-called delta-decoding (Fenimore 1980; Fenimore and Cannon 1981). This implies that the reconstructed adjacent r × r sky pixels are built using different pixels of the detector, and therefore they are statistically independent. Of course a delta-decoding reconstruction can be transformed in fine decoded image by convolving the delta-decoded image with a r × r box-function of 1s. The delta-decoding also allows one to use the FHT in the case of detector binning finer than the mask element (if M is a Hadamard array, the rebinned array M R build for the fine decoding is not) (Fenimore and Weston 1981). As discussed above, FHT is not relevant anymore as the FFT can do the job, but the relative independence of delta-decoded sky image pixel over sizes of the SPSF peak was found useful in order to apply standard methods of chi-square fitting directly on the reconstructed sky images including parameter uncertainty estimations (Goldwurm 1995). When there is a non-integer number of pixels per mask element, which is a typical, and sometimes desirable [The exact integer ratio, when pixels are surrounded by dead zones, leads to incompressible localization uncertainty, given by the angle subtended by the dead area, for source positions for which mask element borders are projected within the dead zones.] condition of pixelated detectors,

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Fig. 7 IBIS images showing the sky reconstruction process from data of the Cygnus region. From left/top to right/bottom: binned corrected detector image (130×134 pixels) including dead zones (D C ), associated efficiency image (W ), rebinned MURA mask on a detector pixel grid (233×233 pixels) (M R ), decoded intensity sky image (S) (358×362 pixels), associated variance (V ), and final SNR sky image after cleaning of coding noise of the two detected sources (Cyg X-1 and Cyg X-3)

then the mask is rebinned by projecting the M array on a regular grid with same pixel pitch as in the detector and by assigning to the mask pixels the fraction of open element area projected in the pixel. The same decoding array definition and correlation operation given above (Eqs. 1–2 and all associated definitions) are then applied using the rebinned mask array M R at the place of M. M R can take (for non-integer r) fractional values between 0 and 1, and the decoding G array also can have different fractional values accordingly. Weighing the inverse correlation using a filtered mask describing the not-integer binning or the finite detector resolution optimizes the SNR of point sources (Cook et al. 1984; Goldwurm 1995; Bouchet et al. 2001) and is usually implemented (weighted decoding) even if this implies a further smearing of the source peak. Figure 7 shows some of the image arrays involved in the weighted sky reconstruction process described above and applied to IBIS data of a Cygnus region observation (Goldwurm et al. 2003).

Image Analysis Following the prescriptions given above, one obtains a reconstructed sky in the EXFOV of the instrument, composed of an intensity and a variance image. They are “correlation” images; each sky image pixel value is built by a linear operation on all, or part of, the detector pixels. Sky image pixels are therefore highly correlated

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in particular within an area of one mask element. Statistical properties of these images are different from standard astronomical images and their analysis, including fine derivation of source parameters, error estimation, the various steps to reduce systematic noise from background, or source coding noise, and final combination of cleaned images in large mosaics must take into account their characteristics.

Significance of Detection The reconstructed and normalized sky image shall be searched for significant peaks by looking for excesses over the average value that should be, by construction (and neglecting the effect of non uniform background), close to zero. This is done by searching for relevant peaks in the SNR image. In the absence of systematic effects, the distribution of this SNR image shall follow the standard normal distribution. Deviations from such distribution indicates residual systematic effects or presence of sources and their ghosts (Fig. 8 left). Excesses in signal to noise larger than a certain threshold are considered as sources. However the concept of significance level in such a decoded image where each sky pixel is built by correlating all, or part of, the pixels of the detector image needs to be carefully considered. If we are interested to know if one or few sources at given specified positions are detected, then we can use the standard rule of the 3 sigma excess that will give a 99.7% probability that the detected excess at that precise position under test is not a background fluctuation. If, instead, we search all over the whole image for a significant excess, then the confidence level must take into account that we perform a large number of trials (in fact different linear combinations of nearly the same data set) to search for such excess. Assuming standard normal distribution for the noise fluctuations, the probability that an excess (in σ ) larger than α is produced by noise is

Confidence level of detection (%)

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Fig. 8 Left: SNR distribution of a CMI (IBIS/ISGRI) reconstructed sky image without sources before (red) and after (blue) correction of some systematic effects, compared to the expected normal distribution (dashed line). (Reproduced with permission from Krivonos et al. 2010, © ESO). Right: Variation of the confidence level of detection (in %), for no a priori knowledge of source position, as function of number of sky pixels in a CMI sky image for different SNR levels of detection

48 Coded Mask Instruments for Gamma-Ray Astronomy

1 P (α) = √ 2π



+∞ α

e

−x 2 2

1635

  α 1 dx = erf c √ 2 2

The confidence level of a detection (not a noise fluctuation) is then 1 − P (α) in a single trial. Assuming that we have N independent measurements, then the confidence level for such excess to be a source will be reduced to [1 − P (α)]N ∼ 1 − N P (α)

for N P (α) ≪ 1

For a given confidence level and N , the value of α is found from this relation. Curves of α as a function of N can be calculated (see Fig. 8 right and Caroli et al. 1987), and it is found that to have a confidence level of 99% for number of pixels N=104 − 105 , the excess must be in the range 4.5–6.0. For coded mask however, it is difficult to evaluate N , since it does not simply correspond to the number of pixels in the sky reconstructed image, unless this refers to the FCFOV of an optimum system with one detector pixel per mask element. The reason is that in general sky pixels are not fully independent and are highly correlated over areas of the size of the typical SPSF. The best way to evaluate the threshold is therefore through simulations. A value of 5.5–6.5 σ is typically assumed for a secure (may be conservative) source detection threshold in reconstructed images of 200–300 pixel linear size.

System Point Spread Function An isolated significant excess in the deconvolved sky image may indicate the presence of a point-like source, which will be characterized by the System Point Spread Function (SPSF), that is, the spatial response to an isolated bright point source of the overall imaging system, including the deconvolution process (Fig. 9). The SPSF includes a possibly shift-invariant, main peak, proportional to the source intensity, and usually non-shift-invariant, side-lobes of the coding noise, also proportional to the source intensity. For a perfect cyclic optimum coded mask system, the main peak is shift invariant, and the side-lobes are flat within the FCFOV for a source in the FCFOV, but large side-lobes appear in the PCFOV (ghosts) along with a diffuse moderate coding noise, and when the source is in the PCFOV, the width of the main peak may vary depending on the mask pattern, and side-lobes, including the main ghosts, appear all over the field. In random masks, side-lobes are distributed all over the image including in the FCFOV, even for sources in the FCFOV, but, generally, with low amplitude and without the strong ghosts typical of cyclic systems. For a pixelated detector and a sky reconstruction based on the weighted crosscorrelation, the SPSF can be described by a peak function correlated with a set of positive and negative delta functions of different amplitudes (what we will call here the correlation function) that take into account the mask pattern and the decoding operation based on correlation (see, e.g., Fenimore 1980). A positive δ-function of maximum amplitude of this set is of course positioned at the source location and will provide the main peak of the SPSF at the source position. The other positive

A. Goldwurm and A. Gros

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Fig. 9 IBIS/ISGRI SPSF from data of a point source observation. Left: Source peak in the center of the FCFOV of a decoded sky image. Color code highlights the, rather low, coding noise particularly affecting (given the symmetry of the MURA mask) the image axes centered on the source. Right: Source profiles in a decoded image along the 2 axis (black lines) and the Gaussian model, approximation of the SPSF, that best fits the excess (red lines). (From Gros et al. 2012)

and negative deltas, convolved with the peak function, describe the coding noise spread over the image (including ghosts). Assuming from hereon a square geometry with square mask elements of linear dimension m and square detector pixels of linear dimension d (extension to rectangular geometry is trivial, and analog, less trivial, relations can be given for the hexagonal one), the peak function Q is given by the normalized  correlation of four 2-d box functions [A 1-d box function is given

1 for |z| ≤ p/2 .], two of mask element width m (x, y) = m (x) · by p (z) = 0 elsewhere



m (y) and two of pixel width d (x, y) = d (x) · d (y) Q(x, y) = Q(x) · Q(y)

where Q(x) =

m (x) ⋆



m (x) ⋆ d (x) ⋆ 2 d m

d (x)

This function, a blurred square pyramidal function for square geometry, can be expressed analytically. The 1-d analytical function Q that composes it has a peak value (at zero lag) given by the simple equation Q(0) = 1 −

1 3r

(3)

where, as usual, r is the ratio r = m/d. This quantity, which corresponds to the term coding power in Skinner (1995), is important because it appears in the expression of the error estimate for the source flux and location.

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The 2-d function Q can be also √ conveniently approximated by a 2-d Gaussian function with FWHM width of r 2 + 1 along the two axes (Fig. 9 right). For a continuous detector, the SPSF (where now pixel is the data discrete sampling step) is the function above but further convolved with the detector PSF. The explicit formulae of the SPSF for such a system, where the detector PSF is approximated by a Gaussian, were given in the description of SIGMA/GRANAT data analysis (Goldwurm 1995; Bouchet et al. 2001). The use of the SPSF in the analysis of CMI data is important because in general both the detector resolution and the sampling in discrete pixels are finite. Then the discrete images produced by the correlations, with the same steps of the data sampling, do not provide the full information, unless the resolution is exactly given by the sampling, pixels are in integer number per mask element, and the source is exactly located at the center of a sky-projected pixel in order to project a shadow exactly sampled by the detector pixels. Of course an artificial finer sampling can be introduced in the correlation analysis, but this implies rebinning of data with alteration of their statistical properties and increase in computing time for deconvolution (dominant part of the overall processing), and finally the precision may not be adequate to the different level of SNR of the sources, where the brightest ones may be located with higher accuracy than the artificial oversampling used. Therefore, in order to evaluate source parameters, and in particular the position of the source, in a finer way than provided by the sky images with the sampling equivalent to the detector pixels, a practical method is to perform a chi-square fit of the detected excess in the deconvolved sky image with the continuous SPSF peak analytical formula or its Gaussian approximation (see Fig. 9 right). The procedure can also be used to disentangle partially overlapping sources (Bélanger et al. 2006). Once the fine position of the source is determined, a model of the projected image on the detector can be computed and used to evaluate the source flux, subtract the source contribution or its coding noise, and perform simultaneous fit with other sources and background models to extract spectra and light curves. Even though the fit, in the deconvolved image, of the source peak with the model of the SPSF peak will provide a reasonable estimate of the source parameters, the error calculation cannot be performed in the standard way directly using the chisquare value of the best fit and its variation around the minimum, because pixels are too much correlated. Nevertheless formulae for the expected error in source flux and source localization can be derived from the formalism of chi-square estimation in the detector space and can be used to provide uncertainties, after some calibration on real data that will account for residual systematic biases.

Flux and Location Errors One can show that the correlation reconstruction for a single point-like source in condition of dominant Gaussian spatially flat background noise is equivalent to the minimum chi-square determination of source flux and position in the detector image space, where one can determine the errors, using the minimum chi-square paradigm. Using the notations used above for the SPSF and introducing the terms t for integration time, A for detector geometrical area, b (in cts/s/cm2 ) for a background

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count rate, and s0 (in cts/s/cm2 ) for the considered source count rate, both integrated within an energy band, we define σCR =



b A·t

SNRCR =

s0 σCR

fI (x, y) =

SP SF (x, y) −a N ·a

where fI is called the image function and is linked, as shown, to the shape of the SPSF, and N is the average number of mask elements in the detector area A (N = A/m2 ) (and in the basic pattern for an optimum system). σCR and SNRCR are, respectively, the minimum error and maximal signal to noise from purely statistical noise given by the measured count rates in case perfect reconstruction can be achieved and for a mask aperture of 1 (i.e., no mask, where all the area A is used for the measure) with the idealistic assumption that a measurement of the background is available (in the same observation time t). Using the minimum chi-square method applied to the detector image compared to a source shadow-gram model, one obtains, from the inversion of the Hessian matrix of the chi-square function, the expression for source flux and position errors, expressed as 1 σ at 68.3% confidence level in one parameter, which are related to the image function and to its second partial derivatives (Cook et al. 1984; Finger 1988; in’t Zand et al. 1994). The flux error is given by

σS = σCR



1 1 = σCR a · fI (0, 0) Q(0)



1 a(1 − a · fM )

(4)

where the mask function fM is 1 for optimal masks and, in average, for random masks and is given by a more complex relation for the general case, which involves the cross-correlation of the mask pattern. The SNR is then SNR = SNRCR · Q(0) ·



a(1 − a · fM )

(5)

The location error along one direction also can be expressed by an analytical expression and involves the second derivative of the image function:   1 1 d   = KX · σX = ·  2   ∂ f (0,0) SNRCR SNR I a ·  ∂x  2

(6)

For optimal masks (URA, MURA, etc.) with a = 0.5 as well as for random masks in average, the following formula for the constant Kx holds approximately: KX =



r · Q(0) 2

(7)

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The error here, as for the flux, is given at 1 σ along one axis direction. The fact that Eqs. 6–7 hold for both URAs and random masks does not mean that these mask types always have the same localization capability as their signal to noise is not the same if the aperture is different. These expressions are equivalent to those reported in Cook et al. (1984) and Finger (1988) and can be extended to the case of√continuous detectors by replacing the pixel linear dimension d with the value 2 3σD ≈ 1.5wD where σD is the detector spatial resolution in σ and wD in FWHM 1 [Following Skinner (1995) the numerical factor comes from the fact that √ is the 2 3 rms uncertainty in a variable which is known to plus or minus half a pixel.]. A more complicated expression, involving properly computed fM and its second partial derivatives, can be obtained for general (or not-so-random) masks. We do not show it explicitly here because it is too cumbersome, but it has been used to identify which quasi-random masks that cannot be purely random in order to make them self-supporting have optimal sensitivity-location accuracy pairs.

Non-uniform Background and Detector Response In gamma-ray astronomy, the background is generally dominant over the source contribution. Its statistical noise, spatial structure, and time variability are therefore important problems for any kind of instrument working in this energy range. CMI, unlike non-imaging instruments, allow measurement of the background simultaneously with the sources, limiting the problems linked to its time variability. However if the background is not flat over the detector plane, its inherent subtraction during image deconvolution does not work properly. In fact any spatial modulation is even magnified by the decoding procedure (Laudet and Roques 1988). Therefore the non-uniform background shall be corrected before decoding as well as any nonuniform spatial detector response which may affect both the background and the source contributions. Using an estimation of the detector spatial efficiency E for the given observation (spatial efficiency variations due to noisy pixels, dead times, or other time-varying effects) and of the detector non-uniformity U (quantum efficiency spatial variation depending on energy), along with a measure (e.g., from empty field observations already corrected for both E and U ) or a model of the background shape B, a correction of the detector image D affected by non-uniformity can be given by DC =

D −b·B E·U

and use then this corrected image D C to reconstruct the sky (Eqs. 1–2). The background normalization factor b can be computed from the ratio of the averages of the input detector and background images or from their relative exposure times. If one can neglect the variance of both B and b and assuming the Poisson distribution in each detector pixel, the variance of the corrected image can be approximated by σD2 C =

D E2 · U 2

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This implies that in the computation for the sky variance (Eq. 2), this detector variance shall be used instead of simply the detector image D C . Of course the details of the procedures, including other different, more sophisticated correction techniques, to account for spatial modulations not due to the mask, depend on the instrument properties, observing conditions, and calibration data (see, e.g., Goldwurm et al. 2003; Segreto et al. 2010). In general extensive ground and in-flight calibrations, including empty-field observations, will be needed in order to get the best models of the background and of the instrument response. One typical contribution to a non-uniform background is the CXB, dominant at low energies, and whose contribution on the detector plane, despite its isotropic character, becomes significantly non-uniform for large FOVs. In fact the CXB is viewed by each detector pixel through all the instrument opening with different solid angles, dependent on the instrument geometry (mask holes, shield, collimator, supporting structures, etc.). An example of such effect expected on the ECLAIRs detector plane is shown in Fig. 10, which also illustrates the noise that this effect produces in the decoded sky image if not properly corrected before reconstruction. Below we discuss the further modulation of the CXB produced when the Earth enters the instrument FOV. Other observational conditions can also be very important in this regard. For satellite orbits that intersect the radiation belts or the South Atlantic Anomaly, parts of the satellite, instrument, and the detector itself may be activated during the passage through this cloud of high-energy particles. The non-uniform distribution of the material in or around the detector may produce an additional non-flat timevarying background remnant that will spoil the images. A careful study of these effects is often required in order to introduce proper corrections in the analysis.

3000 60

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Fig. 10 Non-uniform CXB in ECLAIRs. Left: Simulation of the CXB intensity (counts/pix) on the ECLAIRs detector during one orbit. Right: Decoded sky SNR map of the detector image (left), when two bright sources (SNR > 60) are also added in the simulation and no correction for the non-uniform background is performed. The sources can be barely seen in spite of their high SNR

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Overall Analysis Procedure, Iterative Cleaning, and Mosaics Once the raw data, possibly in event list form, are calibrated and binned in detector images, along with their weighting array, and then background, non-uniformity, and efficiency are corrected, the decoding can be performed by applying Eqs. 1–2 and prescriptions given in previous sections in order to derive preliminary sky images. Point sources are then searched throughout them by looking for SNR significant peaks. The detected source is finely located by fitting the peak of the SPSF function to the detected excess. A localization error can be associated (Eqs. 6–7) from the source SNR which allows to select the potential candidates for the identification. Iterative cleaning of coding noise from detected sources is performed in order to search for the weaker objects. This is done by modeling each source and subtracting its contribution, either in the detector image, which then must be decoded to look again for new sources, or directly in the deconvolved one. Typically the procedure is iterative, starting with the most significant source in the field and going on to the weaker sources, one by one, until no excess is found above the established detection threshold. Few iterations can be implemented, by restarting the procedure with the source fluxes corrected by the contamination from all other sources, for a deeper search. For close sources with overlapping main peaks, a simultaneous fit of their SPSFs may have to be implemented. A catalog is usually employed to identify, and even to facilitate the search, of the sources. This iterative cleaning procedure has been sometimes called Iterative Removal Of Sources (IROS) (Hammersley et al. 1992; Goldwurm et al. 2003), the most important element of which is the proper estimation of the source contribution in the recorded image which depends on a well-calibrated model of the instrument. As for the background correction, very often the source modelling is not perfect, and the ghost cleaning procedure leaves systematic effects which may dominate the noise in the images of large exposure times or on large sets of combined data. One way to smear out background and source residual systematic noise is to combine reconstructed images from different pointing directions and orientations. Overlapping cleaned sky images can be combined, after a normalization accounting for off-axis losses, in sky mosaics by a proper roto-translation to a common grid frame and then a weighted sum using the inverse of variance as the weight. While this is a standard procedure in astronomy imaging, here again one has to remember that we are treating correlation images and that the combined variance shall be computed including the co-variance term. The combination of images may take different forms depending on the scope of the mosaics (e.g., preserve source flux estimation versus reducing source peak smearing) (Skinner et al. 1987b; Goldwurm et al. 2003). A schematic picture of the overall analysis procedure using the IBIS images as example is shown in Fig. 11 (see also the procedures described by Segreto et al. 2010 and Krivonos et al. 2010).

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UBC Det Ima

CALIBRATED Events

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Cleaned Sky Image

Fig. 11 Simplified scheme of an overall image analysis procedure for CMI data including selection and binning of corrected/calibrated events, background and non-uniformity correction, decoding using the mask pattern, an IROS cleaning procedure on detected sources, and finally image mosaic, illustrated using the IBIS images (Goldwurm et al. 2003)

Coded Mask System Performances From the error estimations one can determine the expected CMI performance as function of instrument parameters and design. It is usually evaluated in terms of sensitivity, angular resolution, localization accuracy, field of view, and shape of SPSF. We already discussed the FOV in Section “Definitions and Main Properties” and the SPSF in Section “System Point Spread Function”.

Sensitivity and Imaging Efficiency The sensitivity of a coded mask system is given by the minimum point-like source flux that can be detected above a certain significance level nσ . The lower the minimum flux, the higher the sensitivity of the instrument. This minimum flux can be derived as function of the CMI parameters from the flux error estimation of Eq. 4. Let ε be the detector efficiency (we neglect here energy redistribution) and τo and τc , respectively, the transparencies of the open

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and closed mask elements, all dependent on the energy E of the incident radiation; then for given observation conditions and detector and mask parameters, with symbol meaning as in previous sections, assuming Gaussian statistics and neglecting systematic effects (see Skinner 2008 for different hypothesis), the continuum sensitivity FS , in units of ph/cm2 /s/keV, of a coded aperture system, on-axis and in the energy interval ΔE around E (keV), is given by

FS = n2σ ·

[(1 − a) · τo + a · τc ] +



[(1 − a) · τo + a · τc ]2 +

4·t·b·A(τo −τc )2 ·a·(1−a) n2σ

2 · ε · A · t · ΔE · (τo − τc )2 · a · (1 − a)

(8)

In the case of dominant background, the same relation holds with the term [(1 − a) · τo + a · τc ] at the numerator set to zero. Equation 8 can be solved toward nσ for a given source flux FS providing the upper signal to noise (SNR) limit attainable on-axis for that exposure or toward time t to have the observation exposure needed to reach the desired detection significance nσ for a given source flux FS . This formula, and the analogous ones for SNR and exposure, usually found in the literature (e.g., Carter et al. 1982; Skinner 2008), neglects both the mask pattern and the finite spatial resolution of the detector. Therefore it approaches the case for optimum or pure random mask systems with infinite resolution or with integer resolution parameter r and the source exactly located in the center of a sky pixel, that is, when detector pixels are all either fully illuminated or fully obscured for that source. This is in fact the most favorable configuration and gives the highest sensitivity, but in the general case, one must take into account the effect of the finite detector spatial resolution which is dependent on source position in the FOV. This gives an additional loss in the SNR due to imaging, which, averaged over source location within a pixel, is given by the term Q(0) of the SPSF, which depends on the resolution parameter r through Eq. 3. We therefore define the imaging efficiency as εI = Q(0) = 1 − 3r1 . The formula of Eq. 8 for the sensitivity can be used as it is also when including an average imaging loss over a pixel size, if one replaces everywhere the value nσ with nσ I = nεσI . In the same way, the SNR derived from Eq. 8 will be reduced to an imaging SNR by a factor given by the imaging efficiency, i.e., SNRI = SNR · εI . This formula, modified with the imaging efficiency, corresponds to Eq. 5 for the SNR discussed in the section “Flux and Location Errors” and approximates well the sensitivity within the FCFOV when the source position is known and the flux evaluation is performed by fitting the SPSF at the source position, or, which is the same, by correlating with a rebinned mask shifted at the exact source position. If one wants to include in the calculation the fact that the source position is not known (e.g., to establish the detection capability of unknown sources in the images), then an additional loss shall be included which takes into account that the deconvolution is performed in integer steps (sky pixels) usually not matching the source position (the phasing error of Fenimore and Weston 1981). If the source location is not

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in the center of a pixel, its peak will be spread over the surrounding pixels in the reconstructed image, and the SNR for the source will appear lower. In this case the prescriptions given above hold, but the expression for the imaging efficiency shall be replaced by the integral over 1 pixel of the SPSF peak, which can be approximated 1 by εI ≈ 1 − 2.1r for pixelated detector and square geometry (Goldwurm et al. 2001). For example, for the IBIS/ISGRI system (r = 2.4), the average (over a pixel) imaging efficiency is εI = 0.86 for known source location (fit of detected peak) and 0.80 for unknown location (peak in the image). The sensitivity formula, and its extensions for different hypothesis, can also be used to determine the optimum open fraction a of the mask (Fenimore 1978; Skinner 2008). One can easily see that for dominant background (b ≫ s) the SNR is optimized for a = 0.5. However if b is not dominant or if the sky component of the background is relevant, or in other applications like nuclear medicine (Accorsi et al. 2001), open fractions lower than 0.5 are optimal. As discussed by in’t Zand et al. (1994) and Skinner (2008) however, the optimum value varies slowly with parameters and remains generally close to 0.4–0.5. Other elements of the CM imaging system have an influence on the sensitivity. They are the used deconvolution procedure, the background shape and its correction, the source position knowledge, and of course the numerous systematic effects that may be present and some mentioned in the subsection on “real systems.” Also a decrease of the sensitivity with the increase of the source distance from the optical axis is present due to reduction of mask modulation, the vignetting effect of the mask thickness, and the possible variation of open and closed mask element transparency with the incident angle. In this case the additional sensitivity loss dependence on source direction angle shall be integrated in the term of the detector efficiency ε in Eq. 8, which then becomes dependent on energy but also on the source direction angle θ , that is, ε = ε(E, θ ).

Angular Resolution The separating power of a CMI system is basically determined by the angle subtended at the detector of one mask element. However the finite detector spatial resolution also affects the resolution. For a weighted cross-correlation sky reconstruction (Eqs. 1–2), the resulting width of the on-axis SPSF peak in one direction, which gives the angular resolution (AR) in units of sky pixels, is well approximated, with the usual meaning of resolution parameter r, for square geometry and a pixelated detector, by AR(F W H M) =



r2 + 1

(9)

To obtain the angular resolution in angular units (radians) on-axis, one has to take the arc-tangent of this value divided by the mask to detector distance H (Table 1).

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Fig. 12 IBIS/ISGRI imaging performance from INTEGRAL early data. (Reproduced with permission from Gros et al. 2003, © ESO). Left: FWHM of the fitted Gaussian to the SPSF along the two central sky image axes: constant at ≈2.6 pix in the FCFOV, it changes wildly in the PCFOV. The upper horizontal line gives the average value in the FCFOV (delimited by 2 vertical lines), the lower one the size of a mask element (2.43 pix). Right: PSLE radius at 90% c.l. from measured offsets of known sources at different signal to noises compared to prediction (solid line). Data are well fitted by a 1/SNR function plus a constant (dashed line)

Of course the angle subtended by a pixel varies along the FOV because of projection effects, and that shall be considered for the off-axis values. Moreover the separating power may vary along the FOV and particularly in the PCFOV because the coding noise may deform the shape of the SPSF main peak while vignetting effect of mask thickness will reduce its width. Figure 12 left shows the fitted width (in pixel units) of the IBIS SPSF, along the two image axes passing by the image center. The width is consistent with the AR value of Eq. 9 and of Table 1 within the FCFOV but changes wildly in the PCFOV (Gros et al. 2003). In any case the SPSF width of a system can be evaluated at any location in the image, and the fitting procedure applied to detected sources can either use the fixed computed value or let the width be a free parameter.

Point Source Localization Accuracy An essential characteristic of an imaging system is the quality of the localization of detected sources. As we have seen in the analysis section, the fine localization of a detected point-like source within the pixels around the significant peak excess shall be derived by a fitting procedure. This is usually implemented as a fit of the source peak in the decoded sky image with a function that describes (Goldwurm 1995; Bouchet et al. 2001) or approximates (e.g., a bi-dimensional Gaussian function) (Goldwurm et al. 2003; Gros et al. 2003) the SPSF, but can in principle (with a more complex procedure which for each tested location models and compares to data the shadow-gram of the studied source) be performed on the detector image. For this last implementation,

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formal errors can be derived and can be related to the SPSF and the source strength. As discussed above the uncertainty on the location is inversely proportional to the significance of the source. The typical procedure is then to express the location error radius for a given confidence level, as a function of the source SNR. Once the function is defined and calibrated for a given system, the error to be associated to the fitted position of a source is derived from its SNR. Using the relation for the location error σx (1-σ error along one direction) of Eqs. 6–7 and assuming that the joint distribution of errors in both directions is bi-variate normal and that they are uncorrelated, one can apply the Rayleigh distribution to obtain and relate to the system parameters (including r), the 90% √ confidence level error radius as P SLE(SN R) = 2 · ln10 · σx (SN R). The error can be expressed in angular units by taking the arc-tangent of the value divided by the mask to detector separation H , with the usual caveat that off-axis projection effects shall be considered. In Skinner (2008) the location error was rather approximated with the expression for the angular resolution (Eq. 9) divided by the SNR, while in Caroli et al. (1987) with the angle subtended by the PSD spatial resolution divided by the SNR. A more accurate and, for optimum or random masks, formally correct approximation with the explicit dependence on r is in fact P SLE(SN R) ≈ arctan

√

ln10 d · · SNR H



1 r− 3



(10)

which gives the 90% c.l. angular error radius of the estimation of a location of an on-axis source with signal to noise SNR. The SNR to use in the above expression is the imaging SNRI for a SPSF fit at the source location. If one wants to use the SNR measured in the images (in average affected by sampling), the value that should be used is the average estimation SNRI for unknown location, in which case the constant of Eq. 10 changes. In any case the PSLE expression above is valid for ideal conditions and shall be considered only as a lower limit obtainable for a given system geometry. In real systems, the non-perfect geometry, systematic effects, and the way to measure the SNR induce generally larger errors in the location than predicted by Eq. 10 and can even change the expected 1/SNR trend. In fact the PSLE will generally tend to a constant value greater than 0 for high SNR, which at the minimum includes the finite attitude accuracy. The PSLE curve as function of SNR is therefore always calibrated with simulations or directly on the data using known sources (Fig. 12). Reducing systematic effects and improving analysis techniques shall lead the calibrated curve to approach the theoretical one. Figure 12 shows the measured offsets of known sources with IBIS compared to the predicted error (Gros et al. 2003). The SNR used to plot the data was the SNR measured in the images, and the theoretical curve is then plotted with a specific constant. Even though the data roughly follow the 1/SNR trend, systematic effects prevent the system to reach the “ideal” performance even at large SNR.

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Sensitivity Versus Localization Accuracy In the design of CMI, it is often important to make a trade-off between sensitivity and localization power. Figure 13 shows the variation of the sensitivity (in terms of the inverse of the flux error σS of Eq. 4) and of the location accuracy (given here by the inverse of the location error σX of Eq. 6) with the resolution parameter r. In the left panel, different r values are obtained maintaining mask element (and mask pattern) fixed and varying the detector pixel size for two types of masks. The formulae correctly predict the performance evaluated through simulations, also shown in the plot: for a fixed mask element size (and then angular resolution), increasing detector resolution improves both sensitivity and accuracy. The cases considered are in condition of dominant background; thus the performance parameters with a 30% aperture mask are slightly worse than those for a 50% aperture.

Fig. 13 Theoretical, computed with full complex formulae, and simulated CMI performance as function of the resolution parameter r = m/d assuming dominant background. Left: Variation of sensitivity (solid line) and location accuracy (dashed) with r for two types of masks, an optimum system with a replicated 95×95 MURA of 53×53 basic pattern (blue) and a random mask of same dimensions and 30% aperture (green). Variation of r is obtained maintaining fixed m (and the mask pattern) and decreasing d (with d < m). Computed curves are compared to simulations, shown by data points and their error bars with the same color code. Right: Normalized accuracy versus normalized sensitivity curves for different r, where r is varied by fixing detector resolution d and varying m for the same masks of left panel (green, blue) plus a random mask with the same dimensions and a = 0.4 (violet). Curves for random masks are obtained by computing, and averaging, error values of a large sample of patterns. Dots give the specific values for integer r, while gray crosses those from the approximate formulae that neglect mask pattern (Eq. 5, 6, and 7). The cyan cross indicates the reference value for IBIS/ISGRI (r = 2.4) in the MURA curve (blue). The red curve is for an optimized quasi-random (auto-sustained) mask of a = 0.4 and dimensions 46×46, which is the pattern chosen for ECLAIRs whose performance is positioned in this plot by the brown cross at r = 2.5. Both sensitivity and accuracy depend on the configuration of the system, and therefore values for different systems are not directly comparable. For example, localization accuracy of IBIS/ISGRI is much higher than for ECLAIRs, because sky pixels are 5′ wide while for ECLAIRs are 30′ wide, even if their accuracy values appear identical in this plot

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In the right panel, the location accuracy is plotted versus sensitivity for different values of r where its variation is obtained by fixing the value of d and varying m. The apparent incoherence with the left panel plot (where accuracy increases with r) is due to the different way r is varied. Clearly by increasing m, which determine the angular resolution, the location accuracy decreases from its maximum at r=1, in contrast to the sensitivity which increases with r. As discussed in Skinner (2008), often the trade-off values of r are set in the range 1.5–3 in order to have, for given detector resolution d, better sensitivity at moderate expenses of positional precision. This opposite trend (for a fixed and finite detector spatial resolution) comes from the fact that localization is determined from a measure on the detector of the position of the boundary between transparent and opaque mask elements; therefore the larger the total perimeter of mask holes (which is maximized for given a when holes are small and are isolated), the better the measure of the source position. On the other hand, signal to noise is optimum when total mask hole perimeter is minimum (i.e., when open elements are large and agglomerated) which reduces the blurring that occurs at the boundary between open and closed mask elements. The above considerations explain not only the dependence on r but also the one on the element distribution (mask pattern). In Fig. 13 right, the curve for the specific quasi-random pattern of ECLAIRs (see section on SVOM) is also plotted. Considering this kind of prediction, the r value for ECLAIRs was finally fixed to 2.5, to reach the desired localization accuracy with the highest possible sensitivity. The formulae of Eqs. 4, 5, 6, and 7, as in general those published before, do not include the terms related to the mask pattern and do not predict the performances precisely other than for optimum systems or, in average, for fully random masks. But these terms can be computed using the mask auto-correlation in particular to select patterns which have best sensitivity/accuracy pair for given science objectives, as was done for ECLAIRs. Indeed, by comparing the values at integer r, its pattern appears better in both sensitivity and localization accuracy than the comparable 40% aperture random mask.

Coded Mask Instruments for High-Energy Astronomy The development of coded mask imaging systems has been, from the beginning, linked to the prospect of employing these devices in high-energy astronomy. We review here the implementation of CMI to this field from the first rocket experiments to the missions presently in operation or expected in the close future. Even if not exhaustive, this summary provides a chronological panorama of CMI in astronomy which illustrates the topics discussed above and recalls the main achievements obtained in imaging the gamma-ray sky with these devices (for a complete list of hard X-ray (>10 keV) experiments including CMI, see Cavallari and Frontera 2017). Specific subsections are dedicated to three major experiments successfully flown, or to be launched soon, on space missions, a representative set of CMI, with different and complementary characteristics. SIGMA, the first gamma-ray CMI

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on a satellite, featured an Anger-type gamma-camera with a continuous spatial resolution depending on energy. Thanks to its imaging capability in the hard Xray range, it became the black hole hunter of the 1990s and provided the first 20-arcmin resolution images of the Galactic bulge at energies above 30 keV, and its success opened the way to the INTEGRAL mission. IBIS, presently operating on INTEGRAL, is the most performing gamma-ray imager ever flown, reaching, for the brightest sources, better than 20′′ location accuracy at 100 keV over a large FOV. It still provides, along with the BAT/Swift experiment, some of the most crucial results in the gamma-ray domain. ECLAIRs/SVOM is the future CMI to be mounted on an autonomously re-pointing platform dedicated to time domain astronomy. The quasirandom mask, optimized to push the threshold at low energies, shall open to the community the efficient detection of cosmological gamma-ray bursts (GRB).

First Experiments on Rockets and Balloons The CMI concept was first applied to high-energy astronomy with instruments mounted on sounding rockets or on stratospheric balloons. Following the first ideas on coded aperture imaging, several such projects were initiated mainly by American, English, and Italian groups. The first experiment that actually probed the CM concept in astronomy was SL1501 (Proctor et al. 1978), built by a UK laboratory and launched on a British Skylark sounding rocket in 1976. Composed of a position sensitive proportional counter (PSPC) and a rectangular 93×11 Hadamard mask, both of the same dimensions (box-type), delimited by the diameter of the rocket, it provided in the few minute flight the first X-ray (2–10 keV) images of the Galactic Center (GC) with an angular resolution of 2.5′ ×21′ (the higher resolution side purposely oriented along the Galactic plane) in a square 3.8◦ FOV (Proctor et al. 1979). SL1501 data were combined with those of Ariel V space mission in order to establish the activity of the X-ray sources of the region, and together they even permitted to detect and localize some GC X-ray bursts. A balloon-borne CMI which was highly successful was the US Gamma-Ray Imaging Payload (GRIP) experiment (Althouse et al. 1985) that flew several times between 1988 and 1995 from Australia. Composed of an NaI(Tl) Anger camera working between 30 keV and 10 MeV coupled to a rotating mask (Cook et al. 1984) of about 2000 elements disposed on multiple repetition of a 127 HURA basic pattern (Fig. 6), this telescope imaged a FOV of 14◦ with 1.1◦ angular resolution and provided some of the first high-quality images of the Galactic Center at energies higher than 30 keV, in particular confirming the results obtained by SIGMA in the same period (Cook et al. 1991). GRIP also detected and located gammaray emission from SN1997a, confirming the discovery from the Kvant Roentgen observatory. Another American balloon experiment, EXITE2 (Lum et al. 1994), based on a phoswich (NaI/CsI) detector but coupled to a fixed rectangular URA, with a collimator that limited the FOV to the 4.5◦ FCFOV, flew several times between

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1993 and 2001 (after a preliminary 1988–1989 flight) giving some results on hard point sources. This project was a technological preparation for a more ambitious CMI space mission, EXIST, not yet included in the US space program. The American Directional Gamma-Ray (DGT) experiment deserves to be mentioned because it aimed to push the CM technique to high energies (Dunphi et al. 1989). Using a set of 35 BGO scintillation crystals working in the range from 150 keV to 10 MeV coupled to a 2-,cm-thick lead mask with 13×9 elements disposed as a replicated 7×5 URA basic pattern, it covered a FCFOV of 23◦ ×15◦ with a 3.8◦ angular resolution. The instrument suffered by a large non-uniform background which limited its performances. Nevertheless DGT could probe the CM concept at high energies with the detection of Crab nebula and the black holes (BH) Cyg X-1 and Cyg X-3 above 300 keV during a 30-hr balloon flight from Palestine (Texas) in 1984 (McConnel et al. 1989). These experiments and several others, only conceived, failed, or operated but for short periods, probed the coded aperture imaging concept and paved the way to the implementation of CMI in space missions.

Coded Mask Instruments on Satellites Table 2 reports the list of the fully 2-d imaging coded mask instruments successfully launched on, or securely planned for, an astronomy satellite mission. Other CMI with 1-d only design (or two 1-d systems disposed orthogonal to each other) were launched on space missions, and some provided relevant results mainly as (all-sky) monitors of point-like sources. These were Gamma-1 on Gamma (URSS-Fr), XRT on Tenma (Japan), ASM on Rossi XTE (US), WXM on HETE2 (US), and SuperAgile on AGILE (Italy); none of them is presently in operation. A 1-d coded mask all-sky monitor system presently in operation is the SSM on the Indian ASTROSAT mission (Singh et al. 2014). We will not describe them, as they are not, fully, imaging systems, even if the 1-d CMI concept, particularly when coupling orthogonal systems that give locations along the two axes, is an interesting one and has certain advantages for which it is still considered for some future missions. The first successful CMI flown on a space mission was the UK XRT experiment, launched as part of Spacelab 2 (SL2) on board the NASA Space Shuttle Challenger for an 8-day flight in August 1985 (Skinner et al. 1988; Willmore et al. 1992). Two modules were included, equipped with the same multi-wire proportional counter working in the 2.5–25 keV range but with two Hadamard masks of different basic pattern, 31×29 for the coarse one and 129×127 for the fine one, and different mask element size which allowed for, respectively, coarse and high resolutions over the same 6.8◦ -wide FOV. Remarkable results were obtained from XRT/SL2, which provided in particular the first GC images with few arcmin resolution at energies >10 keV (Fig. 14 left) (Skinner et al. 1987a). Other XRT results concerned galaxy clusters, X-ray binaries (XRB), and the Vela supernova remnant.

Satellite Challenger SL2 MIR Kvant GRANAT GRANAT SAX INTEGRAL INTEGRAL INTEGRAL Swift ASTROSAT SVOM

Detector type PSPC PSPC Anger PSPC PSPC CdTe CsI HPGe MGC CdZnTe CdZnTe CdTe

Mask type Hadamard Hadamard URA URA Triadic MURA HURA HURA Random Hadamard Random

Notes: [ ] foreseen at the time of writing (Jul 2022) a Second module

CMI XRT TTM SIGMA ART-P WFC IBIS SPI JEM-X BAT CZTI ECLAIRs

Table 2 Coded mask instruments on satellites Pattern or order 129×127a 255×257 31×29 43×41 256×256 53×53 127 22501 54000 17×15 46×46

Energy (keV) 2.5–25 2–32 30–1300 4–30 2–30 15–10000 20–15000 3–35 15–150 20–200 4–150

Ang. Res. (FWHM) 3′ –12′ 1.8′ 15′ 6′ 5′ 12′ 2.5◦ 3.3′ 17′ 17′ 90′

Field of View (at ZR) 6.8◦ 15.8◦ 20◦ 1.8◦ 40◦ 30◦ 45◦ 13.2◦ 120◦ ×85◦ 11.8◦ 90◦

Operations (years) 1985 1987–1999 1989–1997 1989–1993 1996–2002 2002-[2025] 2002-[2025] 2002-[2025] 2004-[2025] 2015-[....] [2024-2029]

Reference (Willmore et al. 1992) (Brinkman et al. 1985) (Paul et al. 1991) (Sunyaev et al. 1990) (Jager et al. 1997) (Ubertini et al. 2003) (Vedrenne et al. 2003) (Lund et al. 2003) (Barthelmy et al. 2005) (Bhalerao et al. 2017) (Godet et al. 2014)

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The following CMI in space was the Coded Mask Imaging Spectrometer telescope (COMIS/TTM) (Brinkman et al. 1985) flown on the Kvant module of the soviet MIR station as part of the Roentgen Observatory which included three other non-imaging experiments. The instrument, built by Dutch and UK laboratories, used again a Hadamard mask (Fig. 6) coupled to a PSPC in a simple system (in’t Zand 1992). It operated at different times between 1987 and 1999 and provided interesting hard X-ray images of the Galactic Center and upper limits of the famous SN1987a in the LMC (Sunyaev et al. 1987). In spite of the progress obtained in the UK and US, it was finally France that built the first soft gamma-ray CMI to fly on a satellite, SIGMA. It was launched in 1989 on the Soviet satellite GRANAT along with few other experiments: the Russian ART-S and CMI ART-P, the Danish rotating collimator monitor Watch, and the French Phebus burst detector. SIGMA spectacular results firmly established the superiority of CM imaging over collimation, on/off chopping, or Earth occultation techniques for gamma-ray astronomy. SIGMA is described in Section “SIGMA on GRANAT: The First Gamma-Ray Coded Mask Instrument on a Satellite.” Soon after SIGMA, the Dutch Wide Field Camera (WFC) (Jager et al. 1997) working in X-rays up to 30 keV was launched in 1996 on the Italian space mission Beppo-SAX (Boella et al. 1997). This instrument was based on a pseudo-random mask, with a pattern called “triadic residues,” with low open fraction (33%), more adapted to the X-ray domain than URAs, arranged in a simple system configuration which provided a 40◦ ×40◦ PCFOV (in’t Zand et al. 1994). Two such cameras

Fig. 14 Left: Image of the Galactic Center obtained by the XRT/SL2 instrument in the 3–30 keV band. (Reproduced by permission from Skinner et al. 1987a, © Springer Nature 1987). Right: Detection of GRB960720 by WFC/SAX. (Reproduced with permission from Piro et al. 1998, © ESO). Top: 3D shadow picture of the WFC 40◦ ×40◦ FOV of the observation showing the GRB peak along with the one from Cyg X-1. Bottom: maps around the GRB before during and after the ≈30 s of the burst

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were disposed orthogonal to each other and to the optical axis of the other SAX instruments and particularly of the X-ray mirror telescope. The WFC allowed the discovery of the first X-ray afterglow of a GRB (Costa et al. 1997) when the satellite could re-point its X-ray mirrors on the transient source positioned with arcmin precision (Fig. 14 right). This was a crucial astrophysical discovery which allowed the community, with follow-up optical observations, to establish that GRBs are extra-galactic events, which now we know are connected to explosion or coalescence of stars in external galaxies. The heritage of SIGMA allowed Europe to maintain and consolidate the advantage in CMI. In fact France, Germany, and Italy took the lead of the development of the two main instruments of the INTEGRAL Mission, both based on coded aperture techniques. The International Gamma-Ray Astrophysical Laboratory (Winkler et al. 2003) of the European Space Agency (ESA) with participation of Russia and the US was launched on the 17th October 2002 from Baikonour by a Proton rocket on a very eccentric orbit, which allows long uninterrupted observations of the sky, about 3 days before entry in the radiation belts. The platform carries four co-axial instruments, the two main gamma-ray CMI, the imager IBIS, and the high-resolution spectrometer SPI, plus the coded mask X-ray monitor JEM-X and the optical telescope OMC. INTEGRAL performs observations in dithering mode where a set of pointing of ≈30 min are carried out along a grid of directions about 2◦ apart around the target source. Data are sent to ground in real time which allows fast analysis and reaction in the case of detection of transient events. The spectrometrer on INTEGRAL (Vedrenne et al. 2003) working in the range 20 keV–8 MeV is composed of 19 individual cooled Germanium detectors of hexagonal shape with 3.2 cm side disposed in an hexagonal array 1.7 m below a thick tungsten non-replicated and non-rotating HURA mask of order 127, with hexagonal elements of the size of the Ge crystals. The very high spectral resolution (2.5 keV at 1.33 MeV) of the 6-cm-thick Ge detectors allows study of gamma-ray lines with moderate imaging capabilities (2.5◦ resolution over a 16◦ FCFOV and a 30◦ half coded EXFOV) thanks to the CM system and the dithering mode which permits a better correction of the background. The SPI CsI anti-coincidence system is by itself a large area detector that is presently used also for the search of GRB events outside the FOV of the CMI. The Danish JEM-X monitor (Lund et al. 2003) working in the range 3–30 keV is also a CMI. Composed of two identical modules with the same non-cyclic fixed HURA of more than 20,000 elements with 25% aperture but rotated by 180◦ in order to have different ghost distribution and highpressure Microstrip Gas Chamber (MGC) detectors, it provides 3′ angular resolution images over a 7◦ FWHM FOV. IBIS is certainly the core of the CM imaging capabilities of INTEGRAL and is described in Section “IBIS on INTEGRAL: The Most Performant Gamma-Ray Coded Mask Instrument.” INTEGRAL provides the community with a large amount of excellent astrophysical results and crucial discoveries, in particular with the mapping of the 511 keV line of the Galaxy; the measurements of gamma-ray lines from SNR and close supernovae (SN); the detection and study of GRBs and BH sources in binary systems and in active galactic nuclei (AGN), of all variety of neutron star (NS)

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systems; and the detailed imaging of the GC region. The mission is still operating today (Kuulkers et al. 2021) with many important results obtained each year, the most recent ones in the domain of time domain astronomy (see, e.g., Ferrigno et al. 2021 and references therein). Meanwhile, on the side of the high-energy time domain astronomy, Beppo [Beppo-SAX, the Italian satellite for X-ray astronomy was named in honor of Giuseppe Occhialini, the eclectic and visionary Italian physicist, to whom we owe, in addition to other things, the strong involvement of Europe in astrophysical space programs.] had, once more, showed the way. The future of this domain would reside on agile spacecrafts with capability of fast (therefore autonomous) re-pointing and a set of multi-wavelength instrumentation, including a large field imaging instrument at high energies, based on coded mask technique, and high-resolution mirror-based telescopes at low energies. Too late to implement these features in INTEGRAL, the US did not miss the opportunity by developing in collaboration with UK and Italy the Neil Gehrels Swift mission (Gehrels et al. 2004), dedicated to GRBs and the transient sky. Using a platform conceived for the military “star-wars” program, with unprecedented, and still unequalled, capability of fast (tens of seconds) autonomous re-pointing, this mission has provided since its launch in 2004 exceptional results in the domain of GRB science (Gehrels and Razzaque 2013) but also of the variable and transient high-energy sky (Gehrels and Cannizzo 2015). Many of these are based on the Burst Alert Telescope (BAT) (Barthelmy et al. 2005) a large coded mask instrument which is still in operation along with the two narrow-field telescopes of the mission, one for X-rays (XRT) and one for ultraviolet-optical frequencies (UVOT). BAT (Fig. 15) is the instrument that detects and localizes the GRB and triggers the platform re-pointing. It is composed of an array of 32,768 individual square CdZnTe semiconductor detectors, for a total area of 5240 cm2 , coupled to a large random mask with a “D” shape and a 50% aperture, made of about 52,000 elements, each of 1 mm thickness and dimensions 5×5 mm2 with a resolution ratio r = 1.2 with respect to the detector pixels. The mask is set at 1 m from the detection plane, and it is connected to the detector by a graded-Z shield that reduces the background. BAT provides a resolution of about 20′ over a huge FOV of 1.4 sr (half coded), a location accuracy of 1′ –4′ , and a good sensitivity in the range 15–150 keV. Ground BAT data analysis is described in Tueller et al. (2010), Segreto et al. (2010), Baumgartner et al. (2013), Oh et al. (2018), and it is quite similar to the standard one described above. Figure 16 left shows the BAT reconstructed image of the Galactic Center from which one can appreciate the imaging capability of this CMI and can compare it to the IBIS one. A specific feature of the instrument is that a BAT data analysis is continuously performed on board in near real time thanks to an image processor which allows the detection and position of GRBs within 12 s from their start and the rapid triggering of the platform re-pointing to the computed location. BAT performances are the key of the large success of the mission. The instrument detects and positions about 100 GRBs per year allowing the following red-shift determination for about 1/3 of them. It provides excellent results on many different variable hard X-ray sources, both Galactic and extra-galactic, like AGNs,

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Fig. 15 Left: Scheme of the BAT CM instrument on board the Swift satellite. (Credit NASA, https://swift.gsfc.nasa.gov/about_swift/bat_desc.html). Right: Assembly of the BAT coded mask, characterized by a “D” shape and a random distribution of elements. (Reproduced by permission from Barthelmy et al. 2005, © Springer Nature 2005)

Fig. 16 Left: Reconstructed image of the Galactic Center from BAT data. (Reproduced with permission from Baumgartner et al. 2013, © AAS). Right: The BAT/Swift catalogue of sources (>15 keV) detected in the first 105 months of operations. (Reproduced with permission from Oh et al. 2018, © AAS)

magnetars, different types of binaries, and others (Gehrels and Cannizzo 2015), for example, it allowed the discovery in 2011 of the first tidal disruption event with a relativistic jet (Burrows et al. 2011). More than 1600 non-GRB hard X-ray sources have been detected by BAT/Swift in the first 105 months of operations (Oh et al. 2018) (Fig. 16 right). The most recent launch of a coded aperture instrument on a space mission is the Cadmium Zinc Telluride Imager (CZTI) (Bhalerao et al. 2017) of the Indian ASTROSAT (Singh et al. 2014) mission in operation since 2015. The CZTI is composed of four identical and co-axial modules disposed 2×2 on the platform. The modules are based on a mask composed of 4×4 arrays, each one following a Hadamard pattern built (in different way) from the same 255 PN sequence, and then coupled to a pixelated CdZnTe detector in a “simple system” configuration. Its overall parameters are given in Table 2, but for more complete and recent reports about the in-flight calibrations and performance of the instrument, see Vibhute

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et al. (2021). Important results have been obtained on transient sources, pulsars, and polarization measurements.

SIGMA on GRANAT: The First Gamma-Ray Coded Mask Instrument on a Satellite SIGMA (Système d’Imagerie Gamma à Masque Aléatoire) is the first gammaray coded mask telescope flown on a satellite (Paul et al. 1991) and provided extraordinary discoveries and results in the domain of black hole astrophysics. Launched on the 1st December 1989 from Baikonour (URSS) by a Proton rocket on the three-axis stabilized Soviet GRANAT satellite, it operated in pure pointing mode till 1995 and then mainly in scanning mode for a couple of years more. A schematic view of SIGMA is given in Fig. 17 where its coded mask is also shown, with its characteristic URA pattern, after the instrument was mounted on the platform. Made of a NaI(Tl) Anger camera, composed of 1.25-cm-thick circular scintillating crystal viewed by 61 photo-multipliers, surrounded by a CsI(Tl) anti-coincidence system, and set at 2.5 m from a 1.5-cm-thick tungsten coded mask, SIGMA could provide images in the 35 keV–1.3 MeV range with angular resolution of 20′ –13′ in a FCFOV of 4.7◦ ×4.3◦ and a half-coded EXFOV of 11.5◦ ×10.9◦ with an onaxis 40–120 keV 3σ sensitivity of the order of 100 mCrabs in 1-day observation. The rectangular mask of 53×49 elements was a replicated 31×29 URA (and not a random mask as implied by the instrument acronym), and the events, detected in the

Fig. 17 The SIGMA/GRANAT coded mask instrument. Left: Scheme of the SIGMA telescope. (Reproduced with permission from Bouchet et al. 2001, © AAS). Right: SIGMA, with its URA tungsten coded mask, mounted on the GRANAT spacecraft. (Credit CEA/IRFU)

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central rectangular 725 cm2 area of the NaI crystal corresponding to the URA basic pattern, were coded in 124×116 pixel detector images and in 95 energy channels. Data analysis and calibration of SIGMA are reported in Goldwurm (1995) and Bouchet et al. (2001) and references therein. A specific feature of the decoding process was the use of the efficiency array to take into account the drifts of the platform (Goldwurm 1995) for the extension of the sky image reconstruction to the PCFOV of the instrument. Another important element was that the continuous spatial resolution of the gamma camera varied with energy (see Fig. 19) and time, and therefore it had to be monitored and modelled along the mission (Bouchet et al. 2001) in order to optimize the analysis of the data. The SIGMA long and repeated observations of the Galactic Bulge (Fig. 18), allowed by the fact that its imaging capabilities could be fully exploited over its huge PCFOV, clarified the situation of the high-energy emission from this very active and variable region by showing in particular that the central degrees at energies >20 keV are fully dominated by the source 1E 1740.7–2942, not particularly bright at low energies, that was soon after identified as the first persistent Galactic BH micro-quasar displaying extended radio jets. They also led to the discovery of the other persistent X-ray BH binary GRS 1758–258 (Mandrou et al. 1991) of the bulge and second identified micro-quasar of the Galaxy (too close to the NS XRB GX5-1 to be studied by previous non-imaging instruments), to a measure of the weakness of the central massive black hole Sgr A∗ at high energies, and to the detection of several other BH and NS X-ray persistent and transient bulge sources (Goldwurm et al. 1994). Again thanks to its huge FOV and imaging capabilities, SIGMA was very efficient in discovering Galactic BH X-ray transients (or X-ray novae) which are particularly hard sources. It detected and positioned seven of them in its 6 years of nominal operations, and between them is the other famous BH

Fig. 18 The Galactic Bulge and Galactic Center observed with SIGMA/GRANAT (Goldwurm et al. 1994). Left: The mosaic of the 40–80 keV sky images reconstructed from SIGMA data from observations of the GC in 1990–1994. Right: Zoom in the central GC region, dominated by the bright micro-quasar 1E1740.7–2942. Very weak emission is present at the position of the SMBH Sgr A*

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35 – 50 keV

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Fig. 19 SIGMA Observation of Nova Muscae 91 in January 1991 (Goldwurm et al. 1992). Left: Sky image sectors around the source in different energy bands which show the large variation of the width of the SPSF due to the changes in the gamma-camera spatial resolution with energy, along with the reappearance of a significant excess in the band around 500 keV. Right: Source spectrum, derived from the deconvolved images, which shows the presence of a high-energy feature

micro-quasar GRS 1915+105 that was the first specimen to reveal super-luminal radio jets. An important result was the detection, in the BH X-ray Nova Muscae 91, of a weak and transient feature around 511 keV (Fig. 19), the energy of the electron-positron annihilation line (Goldwurm et al. 1992). These results showed how well-designed CMI can provide also high-quality spectra and light curves of gamma-ray sources. SIGMA detected, in its 12 Ms 1990–1997 survey, a total of about 35 sources including 14 BH candidates, 10 XRB, 5 AGN, 2 pulsars, and 9 new sources (Revnivtsev et al. 2004b). SIGMA data were complemented at low energies by those of the ART-P coded mask hard X-ray telescope (Sunyaev et al. 1990) which had four identical modules made of a PSPC coupled to a replicated URA mask and providing 6′ angular resolution over less than 2◦ FOV. ART-P’s most relevant results were the hard Xray images of the GC that complemented nicely those of SIGMA (Pavlinsky et al. 1994) and revealed a diffuse emission consistent with the molecular clouds of the region and interpreted as scattering by the clouds of high-energy emission emitted elsewhere. Initially used to put limits on the activity of Sgr A*, the detected emission was later recognized as a signal of the Galactic SMBH past activity and was coupled to the measurements of the molecular cloud Sgr B2 with IBIS/INTEGRAL to constrain the Sgr A* ancient outbursts (Revnivtsev et al. 2004a).

IBIS on INTEGRAL: The Most Performant Gamma-Ray Coded Mask Instrument The main gamma-ray imaging device on INTEGRAL (Fig. 20 left) is the Imager on board the INTEGRAL satellite, a hard X-ray/soft gamma-ray coded mask telescope (Ubertini et al. 2003) developed mainly by Italy and France. IBIS is composed of a

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Fig. 20 IBIS/INTEGRAL coded mask instrument. Left: Artistic view of the INTEGRAL satellite, where the characteristic MURA and HURA patterns of the IBIS and SPI masks are visible. (Credit ESA). Right: The ISGRI detection plane composed of 8 modules of 2048 CdTe detectors integrated in the IBIS instrument. (Reproduced with permission from Lebrun et al. 2003, © ESO)

replicated MURA mask of 95×95, 1.6-cm-thick tungsten square elements (see the pattern in Fig. 6) with 50% open fraction coupled to two position sensitive detectors, the Integral Soft Gamma-Ray Imager (ISGRI) and the Pixellated Imaging Caesium Iodide Telescope (PICsIT), both of the same dimension of the central MURA basic pattern of 53×53 elements. ISGRI (Lebrun et al. 2003) is made of 128×128 individual 2-mm-thick cadmium telluride (CdTe) semiconductor square detectors each of dimensions 4×4 mm2 (for a total area of 2600 cm2 ) (Fig. 20 right), works in the range 15 keV–1000 MeV, and is placed 3.2 m below the mask. The overall IBIS/ISGRI sensitivity is of the order of a mCrab for 1 Ms exposure at 80 keV with typical spectral resolution of 7% (FWHM). PICsIT (Di Cocco et al. 2003) is placed 10 cm below ISGRI and is composed of 64×64 CsI bars, each exposing a collecting area 4 times of an ISGRI pixel and working in the range 175 keV–10 MeV. The detector planes are surrounded by an active anti-coincidence system of BGO blocks, and an absorbing tube connects the unit with the mask allowing for reduction of un-modulated sky radiation. Data of both instruments are recorded, transmitted, and analyzed independently, but coincident events from the two detector layers are combined to provide the so-called Compton mode data which are particularly useful to study polarimetry properties of the incident radiation. In the following we will refer to the IBIS/ISGRI system only, given that it provides the best imaging performances of the telescope, and we will neglect the Compton mode. IBIS has provided the most precise images of the GC (Fig. 21 left) at >20 keV before the recent extension of the grazing incidence technique to 70–80 keV with NuSTAR, and it is still the best imager that can cover such large FOV (>2◦ ) at high energies. The most recent and remarkable discoveries of this telescope have been the detection of emission of a close supernova (SN2014j) in the Na lines and the identification of a magnetar flare (Fig. 21 right) with a fast radio burst (FRB) (Mereghetti et al. 2020).

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Fig. 21 IBIS/INTEGRAL results. Left: Image of the Galactic Center (2.5◦ ×1.5◦ ) in the 20– 40 keV from the mosaic of 5 Ms of observations of the field. (Reproduced with permission from Bélanger et al. 2006, © AAS). Right: IBIS detection of the magnetar SGR 1935+2154 flares coincident with a FRB (Mereghetti et al. 2020): sky image, source location, and light curve (blue) compared to the radio bursts (red) (INTEGRAL POM 07/2020, credits: S. Mereghetti and ESA)

IBIS Data Analysis and Imaging Performance The IBIS coded mask system and the standard analysis procedures of the data are described in Goldwurm et al. (2003) and Gros et al. (2003), but see also Krivonos et al. (2010) for sky surveys at high energies and Renaud et al. (2006) for analysis of extended sources. The instrument analysis software is integrated in the Integral Science Data Center (ISDC) (Courvoisier et al. 2003) through which it is distributed to users as Off-line Scientific Analysis (OSA) packages. After 20 years of operations, the instrument is still providing excellent data, and several new features have been integrated in the analysis procedures (Kuulkers et al. 2021). We have already largely used characteristics and data from this system in order to illustrate CMI design, analysis, and performance concepts: in Table 1 for imaging design/performance, in Fig. 6 for the mask pattern, in Fig. 7 for decoding process, in Fig. 8 for distribution of peaks in reconstructed image, in Figs. 9 and 12 for the resulting SPSF and PSLE, and in Fig. 11 for the overall analysis process. Indeed IBIS represents a typical CMI with a cyclic optimum (MURA) mask coupled to a pixelated detector. The detector spatial resolution is just given by the geometrical dimension of the square pixels, independent from energy. CdTe square pixels have size of 4 mm, but the pitch between them is 4.6 mm with 0.6 mm of dead area. The mask elements are not integer number of pixel pitch also in order to avoid ambiguity in source position due to the dead zones. This does introduce a non-perfect coding even for sources in the FCFOV; however other factors break the perfect coding, and noise is anyway introduced. Imaging performances were studied on different data sets of bright and weak known point-like sources along the years (Gros et al. 2003, 2012; Scaringi et al. 2010). The FCFOV is 8◦ ×8◦ , the halfcoded EXFOV 19◦ ×19◦ , and the zero-response one 29◦ ×29◦ . The detector pixel pitch (and therefore the reconstructed sky pixel for the decoding process described

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above) subtends an angle of 5′ on the sky, while the mask element an angle of 12′ . With a ratio mask element to pixel pitch of 2.43, IBIS is expected to have an average image efficiency (at source location) of 86%; an angular resolution, for weighted reconstruction, of 13′ FWHM in the FCFOV; and a localization better than 0.5′ at SNR > 30. The width of the SPFS however varies wildly along the PCFOV due to the secondary lobes as shown in Fig. 12 left (Gros et al. 2003). The localization error as measured at the beginning of the mission (Fig. 12 right) (Gros et al. 2003), even if it followed well the expected 1/SNR trend and reached values of less than 1 arcmin at SNR > 30, was not as good as the theoretical curve and stalled at a constant level of 20′′ even for very high SNR. With the improvement of the analysis software and the reduction of systematic effects, the PSLE was significantly reduced (Scaringi et al. 2010; Gros et al. 2012) and reaches now about 40′′ at SNR 30. Figure 22 reports the PSLE as a function of the source SNR obtained at later stages of the mission. Systematic effects like pixel on/off, absorption by different detector structures, mask vignetting, and absorption by mask elements including screws and glue and in the mask support honeycomb structure have been studied along the years. All shall be accurately accounted for in source modelling. In fact while the MURA optimum system provides clean and narrow SPSF in the FCFOV, it also creates strong ghosts and coding noise in particular along the image axis passing through the source position, which must be removed in order to search for weaker excesses. An iterative algorithm of search, modelling, and removal of sources is implemented in OSA (Fig. 11) in order to clean the images before summing them in sky mosaics (Fig. 23).

Fig. 22 IBIS/ISGRI imaging performance: recent determination of the PSLE. Left: PSLE vs SNR in FCFOV and PCFOV compared to early measurements (Scaringi et al. 2010). (Credit: IBIS Observer’s Manual, 2017, ESA SOC). Right: Recent PSLE measurements (dots) and derived curves (red, orange, yellow) using refined analysis, compared to previous results and theoretical trend (violet) (Gros et al. 2012)

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Fig. 23 IBIS/ISGRI imaging performance: mosaic in the Cygnus Galactic region after the decoding, analysis, cleaning, roto-translation, and sum of several individual sky images (Goldwurm et al. 2003)

ECLAIRs on SVOM: The Next Coded Mask Instrument in Space The Chinese-French SVOM (Space-based multi-band astronomical Variable Object Monitor) space mission (Wei et al. 2016; Cordier et al. 2015), planned, today, for a launch in 2023–2024, is a multi-wavelength observatory dedicated to the astrophysics of GRBs and of the high-energy variable sky. Between the four instruments of the payload, the hard X-ray coded mask imager ECLAIRs (Godet et al. 2014) (Fig. 24), operating in the 4–150 keV energy range, will autonomously detect onboard GRBs and other high-energy transients providing their localization to the ground (through a fast VHF system) and triggering on board, under certain criteria, the slew of the platform in order to point in few minutes the SVOM narrowfield telescopes working in X-rays (Micro X-ray channel plate Telescope, MXT) and in the optical (VT) toward the event. The ECLAIRs detection plane is made of 6400 pixels of Schottky type CdTe (4×4 mm2 , 1 mm thick) for a total geometrical area (including dead zones) of ≈1300 cm2 . A 54×54 cm2 coded mask with 40% open fraction is located 46 cm above the detection plane to observe a FOV of 2 sr (zero coded) with an angular resolution of 90 arcmin (FWHM). A passive lateral Pb/Al/Cu-layer shield blocks radiation and particles coming from outside the aperture. Sky images will be reconstructed in maps of 199×199 square pixels with angular size ranging from 34′ on-axis down to 20′ at the edges of the FOV. ECLAIRs provides a sensitive area of ≈400 cm2 , a point source localization error better than 12′ for 90% of the sources at the detection limit, and is expected to detect each year about 70 GRBs, several nonGRB extra-galactic transients, dozens of AGNs, and hundreds of Galactic X-ray

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Fig. 24 The ECLAIRs/SVOM coded mask instrument. Left: A scheme of the instrument showing the different elements. (From Godet et al. 2014). Right: The ECLAIRs Mask mounted on the instrument at the CNES premises. (Credit CTS/CNES)

transients and persistent sources. Its low energy threshold of 4 keV will open to SVOM the realm of extra-galactic soft X-ray transients, such as X-Ray flashes or SN shock breakouts, which are still poorly explored, and in particular will allow the detection and study of cosmological GRBs whose emission peak is red-shifted in the X-ray band. The 46×46 square mask elements have linear size 2.53 times the detector pixel pitch, and their distribution follows an optimized quasi-random pattern chosen by requiring connection between elements in order to allow the mask to be autosustained. Thousands of quasi-random patterns of this kind with a 40% aperture, which optimizes performance at these energies, were generated and studied, using the formulae of error estimation for general masks (mentioned but not explicitly given in the section “Flux and Location Errors”), in order to select the one presenting the best compromise between sensitivity and source localization for the GRB science, compatible with the mechanical criteria. The performance as function of the resolution parameter r for the specific chosen mask pattern is shown in Fig. 13 right along with the relative values, at the selected resolution factor which was chosen in order to optimize the system for the scientific objectives of the mission. For the chosen design, the predicted imaging performances are shown in Fig. 25. Left panel shows the peak of the SPSF that, given the non-optimum system based on a quasi-random mask, does present relevant side-lobes even in the center of the FCFOV. Once the source is detected and positioned, the lobes must be cleaned by an IROS procedure in order to search for weaker sources. Right panel shows the localization error curve from simulations of sources at different SNR. The accuracy is expected to be within half the size of the VT FOV (≈26′ ) in order to always have the event within both the optical and the X-ray telescope FOVs after the slew of the platform to the ECLAIRs measured GRB position.

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Fig. 25 ECLAIRs/SVOM imaging performances. Left: Central part of the SPSF for on-axis position. Lobes close to the central source peak are present. Right: Expected PSLE radius at 90% c.l. versus the source signal to noise. Source offsets from true positions obtained from simulations are indicated by black dots and the fitted PSLE, with 1/SNR trend, by the solid line. (From Godet et al. 2014)

The actual mask, integrated in the ECLAIRs instrument, is shown in Fig. 24 right. It is composed by a Ti-Ta-Ti sandwich with the tantalum providing the main absorbing power and the titanium the mechanical strength. A central opaque cross, of width 1.4 times the mask element size, is added, along with fine titanium supporting structures running along the mask elements on the side which avoids vignetting of off-axis sources, to make the overall structure resistant to the expected vibration amplitudes of the launch. The design of the ECLAIRs mask has been optimized in this way in order to allow the instrument to be sensitive at energies as low as 4 keV. That requires to have a solid self-sustained mask without a support structure that would absorb the radiation passing through the mask open elements. The multi-layer thermal coating insulation that envelops the telescope in order to protect the camera from light and micro-meteoroids will stop however X-rays below 3–4 keV and determines the low-energy threshold of the instrument. One particular feature of the SVOM mission is that the general program observations, during which data on other sources are collected while waiting to detect GRB events, will be scheduled giving priority to an attitude law that optimizes the search of GRB. SVOM will generally point opposite to the sun, toward the Earth night, so that detected GRB can be rapidly observed with ground-based observatories, and also, to reduce noise, will avoid the bright Galactic plane and rather observe the sky Galactic poles. These constraints and the low Earth orbit of the satellite (≈650 km) will lead to a frequent and variable occultation of the instrument FOVs by the Earth. ECLAIRs will then often experience partial Earth occultation of its large FOV during which the CXB will be modulated in a variable way during the ≈90 min orbit. Figure 26 shows a simulation of the expected spatial modulation on the detector by this effect, the impact on the imaging performance, and the expected correction results. Given the uncertainties of the CXB model and the additional components of

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Fig. 26 Effect of CXB modulation by partial Earth occultation of the ECLAIRs FOV. From left to right and top to bottom: Simulated detector image of the Earth-modulated CXB in 20 s exposure (during which the Earth can be considered stable in the FOV). Configuration of Earth occultation of ECLAIRs FOV considered in the simulation. Decoded SNR sky image of the simulated detector image and including two not-obscured sources when background is not corrected: large modulation is present, and the sources are not easily detected. Decoded SNR sky image when proper model of CXB modulated by the Earth is used for the background correction: the reconstructed image is flat, and the two sources are detected as the highest peaks

Earth albedo and reflection, the background correction of ECLAIRs images affected by the Earth in its FOV in real conditions will certainly be challenging. However CMI have been proven to be robust and effective imaging systems, and new exciting results are expected from this novel coded mask-based high-energy mission, dedicated to the transient sky, that will be launched soon.

Summary and Conclusions In this review we have described the concept of coded mask instrument for gamma-ray astronomy, discussed the mask patterns, and introduced definitions and terminology useful to understand the large literature on the subject. We have illustrated the correlation analysis procedure to apply to the data of standard CM

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systems, along with some practical recipes for the analysis. We have provided the formulae to evaluate errors and performance of the systems from their design parameters and illustrated them with data, simulations, or calculations for some of the CMI presently in operation or in preparation. Finally we have described the historical development of the field and the main CMI implementations in space missions and recalled some of the important results obtained by these devices in imaging the soft gamma-ray sky. Even if focusing techniques, with their power to reduce background and to reach arcsec scale angular resolutions, are more and more extended to high energies and are definitely performing well in exploring the most dense sky regions like the Galactic center, they are limited to narrow fields, and CMI remain the best options for the simultaneous monitoring of large sky regions. Since the X-/gamma-ray sky is dominated by compact objects which are, most of the time, very variable and even transient, these surveys are crucial to explore this realm, especially in the new era of time-domain and multi-messenger astronomy. Indeed rapid localization at moderate resolutions of high-energy electromagnetic counterparts of gravitational wave or neutrino burst events, which have large positional uncertainties, can trigger the set of high-resolution observations with narrow-field instruments which finally lead to identification of the events. This is what happened for the very first identified GW source (GW170817), and this is the strategy envisaged for the next multi-messenger campaigns of observations. The reaction time for the follow-up of fast transients is obviously very important; therefore the way to go is to couple imaging wide-field monitors with a multiwavelength set of space or/and ground-based narrow-field telescopes with fast autonomous capability to point the sky positions provided by the monitors. This strategy first implemented by Swift and ready to be used by SVOM is still based on CMI. Another technique that is emerging to design large field of view X-ray telescopes is the so-called lobster-eye or micro-pore optics (MPO). The concept, taken from the optical system of the eyes of crustaceans, is to use grazing reflection by the walls of many, very small channels to concentrate X-rays toward the focal plane PSD. By disposing a wide micro-channel plate with a large number of micro-holes with very polished and flat reflecting walls over a properly curved surface, a focusing system with a large FOV can be obtained. MPO is used for the MXT of SVOM (Götz et al. 2014) that will obtain X-ray images with arcmin angular resolution over 1◦ FOV, but larger systems are now being developed, e.g., for the Einstein Probe mission (Yuan et al. 2018). However MPO technique is for now limited to low X-ray energies, and projects for future high-energy missions dedicated to variable sky still plan to implement coded mask wide-field cameras, as, for example, the set of orthogonal 1-d cameras in the Chinese-European eXTP (enhanced X-ray Timing and Polarimetry) mission (Zhang et al. 2019a), or the two full 2-d cameras of the XGIS (X-Gamma ray Imaging Spectrometer) instrument (Labanti et al. 2020) of the Theseus (Transient High-Energy Sky and Early Universe Surveyor) (Amati et al. 2021) project, proposed recently to ESA for a medium size mission (M7) of the Cosmic Vision

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program. This last instrument based on a random mask coupled to Silicon Drift Detectors features a combined ZR-EXFOV of 117◦ ×77◦ , an AR of 120′ , and a localization accuracy of 15′ at SNR = 7 in the 2–150 keV range. A rather complex CMI devoted to soft gamma-rays is also proposed for a future NASA explorer mission, GECCO, an observatory working in the 50 KeV–10 MeV range that combines coded mask imaging at low energies and a Compton mode system for the high energies (Orlando et al. 2021). A specific feature of this CMI is its capability of deploying after launch a mast, which can extend the mask to any distance from the detector up to 20 m, in order to reach the desired imaging performances by tuning this system parameter (H in Table 1). In conclusion, coded mask instruments are very efficient devices to carry out imaging surveys of the hard X-ray/soft gamma-ray sky over large fields of view with moderate angular resolution and localization power and are still considered for future missions dedicated to the time-domain astronomy, for which lighter and more agile systems are now designed. While several such instruments are still presently in operation on INTEGRAL, Swift, and ASTROSAT, the next CMI to fly soon is ECLAIRs, on the SVOM multi-wavelength mission, which pushes the technique to cover a large energy band from X to hard X-rays and is expected to provide exceptional results on GRB and the transient sky science.

References J.G. Ables, Proc Astr. Soc. Aust. 1, 172 (1968) R. Accorsi et al., NIMPR A 474, 273 (2001) W.E. Althouse, et al., Proceedings of 19th ICRC, La Jolla, vol. 3 (1985), p. 299 L. Amati et al., Exp. Astron. 52(3), 183 (2021) S.D. Barthelmy et al., Space Sci. Rev. 120, 3–4, 143–164 (2005) L.D. Baumert, Lecture Notes in Mathematics, vol. 182 (Springer, Berlin, 1971) W.H. Baumgartner et al., ApJS 207, 19 (2013) G. Bélanger et al., ApJ 636, 275 (2006) V. Bhalerao et al., JApA 38, 31 (2017) G. Boella et al., Astron. Astrophys. Suppl. Ser. 122, 299 (1997) L. Bouchet et al., ApJ 548, 990 (2001) A.C. Brinkman et al., International Conference on Proceedings, Rome, ed. by G.C. Perola (1985), p. 263 D.N. Burrows et al., Nature 476, 421 (2011) E. Caroli et al., Space Sci. Rev. 45, 349 (1987) J.N. Carter et al., MNRAS 198, 33 (1982) E. Cavallari, F. Frontera, Space. Sci. Rev. 212, 429 (2017) M.J. Cie´slak et al., Radiat. Meas. 92, 59 (2016) W.R. Cook et al., IEEE Trans. Nucl. Sci. NS-31, 771 (1984) W.R. Cook et al., ApJ 372, L75 (1991) B. Cordier et al., Conference on Proceedings of Swift: 10 Years of Discovery, POS, vol. 233 (2015), p. 5 E. Costa et al., Nature 387, 783 (1997) T.J.-L. Courvoisier et al., A&A 411, L53 (2003) R.H. Dicke, ApJ 153, L101 (1968) G. Di Cocco et al., A&A 411, L189 (2003)

1668

A. Goldwurm and A. Gros

N.L. Dunphi et al., Nucl. Instrum. Methods A274, 326 (1989) E.E. Fenimore, Appl. Opt. 17(22), 3562 (1978) E.E. Fenimore, Appl. Opt. 19(14), 2465 (1980) E.E. Fenimore, T.M. Cannon, Appl. Opt. 17(3), 337 (1978) E.E. Fenimore, T.M. Cannon, Appl. Opt. 20(10), 1858 (1981) E.E. Fenimore, G.S. Weston, Appl. Opt. 20(17), 3058 (1981) E. Ferrigno et al., NewAR 92, 101595 (2021) M.H. Finger, The Imaging of Extra-Galactic Low-Energy Gamma - Sources: Prospects, Techniques, and Instrumentation. PhD Thesis, California Institute of Technology (US) (1988) M. Finger, T.A. Prince, Proceedings of 19th ICRC, La Jolla, vol. 3, (1985), p. 295 N. Gehrels, S. Razzaque, FrPhy 8(6), 661 (2013) N. Gehrels, J.K. Cannizzo, JHEAp 7, 2 (2015) N. Gehrels et al., ApJ 611, 1005 (2004) O. Godet et al., SPIE 9144, 914424 (2014) D. Götz et al., SPIE 9144, 914423 (2014) A. Goldwurm, Exp. Astron. 6, 9 (1995) A. Goldwurm et al., ApJ 389, L79 (1992) A. Goldwurm et al., Nature 371, 589 (1994) A. Goldwurm et al., Proceedings of 4th INTEGRAL Workshop, ESA-SP, vol. 459 (2001), p. 497 A. Goldwurm et al., A&A 411, L223 (2003) S.R. Gottesman, E.E. Fenimore, Appl. Opt. 28, 4344 (1989) A. Gros et al., A&A 411, L179 (2003) A. Gros et al., Proceedings of 9th INTEGRAL Workshop, 2012, POS, vol. 176 (2012), p. 147 J. Gunson, B. Polychronopulos, MNRAS 177, 485 (1976) A. Hammersley et al., N.I.M.P.R. A311, 585 (1992) F. Harrison et al., ApJ 770, 103 (2013) M. Harwit, N.J. Sloane, Hadamard Transform Optics (Academic, New York, 1979) J.J.M. in’t Zand, A Coded-Mask Imager as Monitor of Galactic X-ray Sources, PhD Thesis, University of Utrecht (NL) (1992) J.J.M. in’t Zand et al., A&A 288, 665 (1994) R. Jager et al., Astron. Astrophys. Suppl. Ser. 125, 557 (1997) L.E. Kopilovich, L.G. Sodin, MNRAS 266, 357 (1994) R. Krivonos et al., A&A 519, A107 (2010) E. Kuulkers et al., NewAR 93, 101629 (2021) C. Labanti et al., SPIE 11444, 114442K (2020) P. Laudet, J.P. Roques, NIMPR A267, 212 (1988) F. Lebrun et al., A&A 411, L141 (2003) K.S.K. Lum et al., IEEE Trans. Nuc. Sci. 41, 1354 (1994) N. Lund et al., A&A 411, L231 (2003) P. Mandrou et al., Conf. Proc. AIP 232, 492 (1991) M.L. McConnel et al., ApJ 343, 317 (1989) S. Mereghetti et al., ApJ 898, L29 (2020) L. Mertz, N.O. Young, Conference on Proceedings of Optical Instruments and Techniques (1961), p. 305 S. Miyamoto, Space Sci. Inst. 3, 473 (1977) K. Oh et al., ApJS 235, 4 (2018) E. Orlando et al., Conference on Proceedings of ICRC 2021, POS, vol. 395 (2021), p. 650 J. Paul et al., AdSpR 11(8), 289 (1991) M.N. Pavlinsky et al., ApJ 425, 110 (1994) L. Piro et al., A&A 329, 906 (1998) R.J. Proctor et al., MNRAS 185, 745 (1978) R.J. Proctor et al., MNRAS 187, 633 (1979) M. Renaud et al., A&A 456, 389 (2006) M. Revnivtsev et al., A&A 425, A49 (2004a)

48 Coded Mask Instruments for Gamma-Ray Astronomy M. Revnivtsev et al., AstL 30, 527 [A81] (2004b) J.P. Roques, App. Opt. 26(18), 3862 (1987) S. Scaringi et al., A&A 516, A75 (2010) A. Segreto et al., A&A 510, A47 (2010) M.R. Sims et al., SSI 5, 109 (1980) K.P. Singh et al., SPIE 9144, 91441S (2014) G.K. Skinner, Exp. Astron. 6, 2 (1995) G.K. Skinner, App. Opt. 47(15), 2739 (2008) G.K. Skinner et al., Nature 330, 544 (1987a) G.K. Skinner et al., ASS 136, 337 (1987b) G.K. Skinner et al., ApL&C 27, 199 (1988) G.K. Skinner, T.J. Ponman, MNRAS 267, 518 (1994) R.A. Sunyaev et al., Nature 330, 227 (1987) R.A. Sunyaev et al., AdSpR 10(2), 233 (1990) T. Takahashi et al., SPIE 9144, 25 (2014) J. Tueller et al., ApJS 186, 378 (2010) P. Ubertini et al., A&A 411, L131 (2003) G. Vedrenne et al., A&A 411, L63 (2003) A. Vibhute et al., J. Astrophys. Astron. 42, 76 (2021) J. Wei et al., SVOM White Paper, arXiv:1610:06892 (2016) R. Willingale et al., NIMS 221, 60 (1984) A.P. Willmore et al., MNRAS 258, 621 (1992) C. Winkler et al., A&A 411, L1 (2003) W. Yuan et al., SPIE 10699, 25 (2018) S.-N. Zhang et al., Sci. China Phys. Mech. Astron. 62(2), 029502 (2019a) R. Zhang et al., NIMS 934, 41 (2019b)

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Enrico Virgilli, Hubert Halloin, and Gerry Skinner

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laue Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laue Lenses Basic Principles: Bragg’s Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Crystal Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Focusing Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laue Lens Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Technological Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Examples of Laue Lens Projects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fresnel Lenses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Focal Length Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chromatic Aberration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detector Issues for Focused Gamma Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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E. Virgilli () Istituto Nazionale di Astrofisica INAF-OAS, Bologna, Italy e-mail: [email protected] H. Halloin Université de Paris, CNRS, Astroparticule et Cosmologie, Paris, France e-mail: [email protected] G. Skinner University of Birmingham, Birmingham, UK e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_45

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Abstract

The low-energy gamma-ray domain is an important window for the study of the high-energy Universe. Here matter can be observed in extreme physical conditions and during powerful explosive events. However, observing gamma rays from faint sources is extremely challenging with current instrumentation. With techniques used at present, collecting more signal requires larger detectors, leading to an increase in instrumental background. For the leap in sensitivity that is required for future gamma-ray missions, use must be made of flux concentrating telescopes. Fortunately, gamma-ray optics such as Laue or Fresnel lenses, based on diffraction, make this possible. Laue lenses work with moderate focal lengths (tens to a few hundreds of meters), but provide only rudimentary imaging capabilities. On the other hand, Fresnel lenses offer extremely good imaging, but with a very small field of view and a requirement for focal lengths ∼108 m. This chapter presents the basic concepts of these optics and describes their working principles, their main properties, and some feasibility studies already conducted. Keywords

Laue lenses · Fresnel lenses · Focusing optics · Hard X-ray astronomy · Diffraction

Introduction The “low-energy” gamma-ray band from ∼100 keV to a few tens of MeV is of crucial importance in the understanding of many astrophysical processes. It is the band in which many astrophysical systems emit most of their energy. It also contains the majority of gamma-ray lines from the decay of radioactive nuclei associated with synthesis of the chemical elements and also the 511 keV line tracing the annihilation of positrons. However, observations at these energies are constrained in ways that those at lower and higher energies are not. At lower energies, grazing incidence optics enable true focusing of the incoming radiation, forming images, and concentrating power from compact sources onto a small detector area. At higher energies, the pair production process allows the direction of the incoming photon to be deduced. However, in the low-energy gamma-ray band grazing, incidence optics are impractical (the graze angles are extremely small), and the dominant Compton interaction process provides only limited directional information. Detector background due to particle interactions and to photons from outside the region of interest is a major problem in gamma-ray astronomy. A large collecting area is essential because the fluxes are low, but unless a means is found to concentrate the radiation, this implies a large detector and hence a lot of background. Shielding helps, but it is imperfect, and the materials in the shield themselves

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produce additional background. If the flux from a large collecting area A can be concentrated with efficiency η onto a small area Ad of detector, then √ for backgrounddominated observations there is an advantage in sensitivity of ηA/Ad compared with a “direct-view” instrument of area A having the same background per unit area, energy band, and observation time. At energies where grazing incidence optics are not viable, only two technologies are available for concentrating gamma rays. Both use diffraction. Laue lenses use diffraction from arrays of crystals, while Fresnel lenses utilize diffraction from manufactured structures. Both type of lens can provide a high degree of concentration of flux from a compact on-axis source. Fresnel lenses provides true imaging, albeit with chromatic aberrations, whereas the Laue lens is a “singlereflection” optic, where the off-axis aberrations are severe. MeV astrophysics is now eagerly waiting for the launch of NASA’s COSI mission (Tomsick et al. 2019) which is scheduled for 2025. This will be a survey mission with a large field of view and, consequently, a relatively high background. Nevertheless, COSI is expected to be a factor of 10 more sensitive than Comptel the pioneering instrument for the MeV gamma-ray range (Schoenfelder 1993). A focusing telescope using the techniques discussed here may improve the sensitivity for the study of individual sources by another large factor, allowing studies not possible with scanning, high-background, instruments. Laue lenses and Fresnel lenses are discussed separately.

Laue Lenses The concept of a Laue telescope is shown in Fig. 1. The essential element is a “Laue Lens” containing a large number of high-quality crystals. Each crystal must be correctly oriented to diffract radiation in a narrow spectral range from a distant source towards a detector located at a common focus behind the lens. The crystals are used in the Laue mode (transmission) since the very small diffraction angles make it impractical to rely on surface reflections. Excellent reviews of previous work on this topic can be found in Frontera and Von Ballmoos (2010) and Smither (2014). The term “Laue lens” is actually a misnomer, and it would be more correct to refer to a Laue-mirror. Such a “lens” relies on the mirror reflection of gamma rays from the lattice planes in the crystals. The reflective power of the electrons bound in atoms in a single lattice plane is very small, but the power increases with the square of the number of planes – or electrons – acting coherently.

Laue Lenses Basic Principles: Bragg’s Law The requirement for coherent diffraction is both the strength and the weakness of Laue lenses. It provides for the possibility of high reflectivity, but at the same time,

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Fig. 1 A gamma-ray lens, based on diffraction From crystals in the Laue (transmission) geometry. Crystal tiles are oriented in order to diffract the radiation towards the common focus. In this drawing, five concentric rings of crystals are shown as an example. Crystals can be arranged over a spherical cap, but the lens can also be planar and other radial distributions are possible. Crystals at the same radius from the axis will have the same orientation with respect to the incident radiation, but the orientation will change with radius

it imposes a strict dependence of the diffraction angle, θB , on the wavelength, λ, (or the energy, E) of the radiation. This dependence is expressed by Bragg’s law: sin θB = n

λ 2dhkl

with : n = 1, 2, 3, ...

(1)

where n is the diffraction order, dhkl is the spacing of the crystal lattice planes, and λ is the wavelength of the gamma rays. The first order (n = 1) contributions are by far the most significant. For energies which concern us here, the Bragg angles are always small (≃1◦ ), so we can set tan θ = sin θ = θ . In the following, we shall often prefer to speak in terms of energy, E, rather than wavelength. Bragg’s law then takes the form sin θB = n

hc , 2dhkl E

(2)

where h is Planck’s constant and c the velocity of light. (λ(Å) = 12.39/E (keV)). From the Bragg equation for first diffraction order, with simple geometrical considerations, it can be shown that there is a relation between the distance ri at which the crystal is positioned with respect to the Laue lens axis and the diffracted energy Ei : Ei =

hcF , dhkl ri

where F is the focal length of the Laue lens.

(3)

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Equation 3 shows that for a given focal length, if crystals with a fixed dhkl are used, those placed closer to the lens axis are dedicated to the highest energies, while those positioned further away from the axis diffract the lower energies. Consequently, at a given focal length, there is a direct link between the energy band of a Laue lens and its spatial extent, rin to rout . For a narrow band Laue lens, with the whole surface optimized for a single energy, it would be necessary to arrange that dhkl varies in the radial direction such that dhkl ri is constant (an analogous condition will be seen when the zone widths of Fresnel lenses are discussed in section “Fresnel Lenses”).

Crystal Diffraction Ideal and Mosaic Crystals Before going into details of the calculation of diffraction efficiencies, it is useful to introduce a distinction between “ideal” and “mosaic” crystals. In ideal (defect free) crystals, the crystalline pattern is continuous over macroscopic distances. Examples of such crystals are the highly perfect silicon and germanium crystals now commercially available, thanks to their great commercial interest and the consequent intense development effort. “Mosaic crystals” on the other hand are described by a very successful theoretical model introduced by Darwin (1914, 1922) a century ago. Darwin modeled imperfect crystals as composed of a large number of small “crystallite” blocks, individually having a perfect crystal structure but slightly misaligned one to another. The spread of the deviations, ω, of the orientation of a lattice plane in one block from the mean for the entire mosaic crystal is described by means of a probability distribution Ω ′ (ω), the so-called mosaic distribution function. Darwin’s model has been very useful and quantitatively describes many aspects of real crystals. The mosaic distribution function, Ω ′ can be found experimentally for a given crystal through observation of the ‘rocking curve’, which is the measured reflectivity as function of angle for an incident beam of parallel, monochromatic gamma rays when a crystal is scanned through the angle corresponding to a Braggreflection. The crystal sample should be thin enough that the reflectivity is never close to the saturation value. Examples of measured rocking curves are shown in Fig. 2. For good quality crystals, the mosaic distribution can be well approximated by a Gaussian function. Its width, as observed through the rocking curve, is called the mosaic width of the crystal. Mosaic widths are specified as angular quantities, characterized by either the Full Width at Half Maximum (FWHM) or the standard deviation, σθ , of the rocking curve. Rocking curves are measured at constant diffraction angle, hence constant energy. For Laue lens design where the source direction is the fixed quantity, what is often of interest is the mosaic distribution as a function of the energy offset from the energy, EB , corresponding to the Bragg angle. If the standard deviation of the distribution as a function of energy is σE , then the two quantities are related by

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20

Absolute reflectivity %

Niob (110)

Tantal (110)

MoIybdenum (110)

16

12

8 FWHM 2.70’

FWHM 1.05’

FWHM 1.35’ 4

0 Rocling angle

Fig. 2 Measured rocking curves (at 412 keV) for a few metal crystals having different degrees of mosaicity. The small number triplets shown along with the element names are the “Miller indices” (see Zachariasen 1945) identifying the lattice planes used for diffraction (Reprinted from Lund 1992)

σθ σE = EB θB

(4)

To be useful in a Laue telescope, the rocking curve for each crystal should possess a single, narrow peak. Unless great care is taken in the growth of crystals, the mosaic distribution may not be well behaved, and the rocking curves may be broad or exhibit multi-peaked structures.

Diffraction Efficiency According to Schneider (1981), the crystal reflectivity, ν(E), for mosaic crystals of macroscopic thickness in the Laue-case can be calculated from ν(E) =

1 −µ(E)t e (1 − e−Ω(E−E0 )R(E)t ). 2

(5)

Here µ(E) is the linear attenuation coefficient for photons of energy E, and t is the crystal thickness. Ω(E − E0 ) is the mosaic distribution as function of energy, and R(E) is the specific reflectivity (reflectivity per unit thickness). E0 is defined as the energy where Ω is at its maximum. In the following, we shall assume that the mosaic distribution Ω has a Gaussian shape: Ω(E − E0 ) = √ We then get for the peak reflectivity:

1 2π σ

e−(E−E0 )

2 /2σ 2

.

(6)

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ν(E0 ) =

R(E )t 1 −µ(E0 )t −√ 0 e (1 − e 2π σ ). 2

(7)

The value of the crystal thickness which maximizes the peak reflectivity is ln (1 + α) µ(E0 )α

(8)

R(E0 ) 1 √ µ(E0 ) 2π σ

(9)

tmax = with α=

and the corresponding peak reflectivity is νm (E0 ) =

1+α 1 α(1 + α)− α . 2

(10)

Note that the specific reflectivity, R, and the attenuation coefficient, µ, are characteristic of a particular material and set of crystalline planes, whereas the mosaic width, σ , depends on the method of manufacture and subsequent treatment of the crystals. It is therefore reasonable to start by seeking crystals that maximize the value of R/µ and leave the choice of the mosaic width to the detailed lens design. The specific reflectivity is given by R(E) = 2re2

λ3  Fstruct (x) 2 −2Bx 2 e sin(2θB ) V

(11)

with x = sin(θB )/λ. Here re is the classical electron radius, V is the volume of the unit cell, and Fstruct is the “structure factor” for the crystal unit cell. The structure factor depends on the crystal structure type (e.g., body centered cubic, face centered cubic), on the atoms, and on the choice of lattice planes involved, described by the Miller indices (h,k,l). The exponential factor describes the reduction in the diffraction intensity due to the thermal motion of the diffracting atoms. Considering only crystals of the pure elements, Eq. 11 can be rewritten as R(E) ∝ E −2 a −5/3 (f1 (x, Z))2 e−2Bn

2 /2d 2

,

(12)

where a is the atomic volume, d is the interplanar distance of the diffracting planes, f1 (x, Z) is the atomic form factor, and n is the diffraction order. Here use has been made of the approximations sin(2θB ) ∼ 2 sin(θB ) and x ∼ n/2d. The linear attenuation coefficient, µ(E), can be expressed as a function of the total atomic cross section, κ(E), and the atomic volume: µ(E) =

κ(E) a

(13)

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thus R f1 (x, Z)2 −Bn2 /2d 2 ∝ E −2 a −2/3 e . µ κ(E)

(14)

Since at high energies both f1 (x, Z) and κ(E) are roughly proportional to Z, it is clear that for gamma-ray energies a high atomic number and a small atomic volume (a high atomic density) are important for maximizing R/µ. For energies below ∼100 keV, photoelectric absorption may rule out the use of crystals of the heaviest elements for Laue lenses. The atomic density of crystals of the pure elements varies systematically with the atomic number, Z, as illustrated in Fig. 3. The most suitable elements for Laue lens crystals are found near the peaks in this plot, that is, near Z = 13 (Al), Z = 29 (Ni, Cu,), Z = 45 (Mo, Ru, Rh Ag) or Z = 76 (Ta, W, Os, Ir, Pt, Au). The atomic form factors are tabulated in the literature (International Tables for X-ray Crystallography 1977), and software for their calculation is publicly available (del Rio and Dejus 1997). The thermal factor, B, turns out to be anti-correlated with the atomic density, thereby strengthening somewhat the case for a high atomic density (Warren 1969).

ATOMIC DENSITY x 1022cm-3

10

5

0 0

10

20

30

40

50

60

70

80

90

ATOMIC NUMBER

Fig. 3 The Atomic Density as function of the Atomic Number, Z. (Reprinted from Lund 1992)

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Extinction Effects In the above derivation of the diffraction efficiencies, only the attenuation by incoherent scattering processes was explicitly considered in equation 13. However, losses due to coherent effects also occur. These are termed “extinction effects” (Chandrasekhar 1960). One type of extinction loss is due to the diffraction process itself and occurs in both mosaic and perfect crystals. Photons are removed from both the incoming beam and from the diffracted beam by diffraction. (The diffracted beam is a mirror image of the incoming beam with respect to the lattice planes and fulfills the Bragg condition just as well). This dynamic interaction is termed “secondary extinction” and accounts for the factor 12 in Eq. 5. A more subtle extinction effect, which is only present if phase coherence is maintained through multiple diffractions, is termed the “primary extinction.” Every diffraction instance is associated with a phase shift of π/2. Consequently, after two coherent diffraction processes, the photon has accumulated a phase shift of π and destructively interferes with the incoming beam. In the same way, three coherent diffraction processes will cause destructive interference in the diffracted beam. This effect only occurs in perfect crystals or in mosaic crystals in which the size of the crystallites is large enough that there is a significant probability of multiple successive coherent scatterings. The critical dimension here is the “extinction length” (see Zachariasen 1945) which can be estimated as text ≈

1 V . r0 Fstruct (x)λ

(15)

The extinction length for the Cu(111) reflection at 412 keV is 66 µm (Schneider 1981). As text is proportional to the energy, it will be at the lower gamma-ray energies that extinction effects may become noticeable. For Laue lenses, it is important to find or develop crystals in which the defect density is high enough to keep the crystallite size below text at the lowest energies where the crystals are to be used.

Focusing Elements Classical Perfect Crystals Perfect crystals, where the ideal lattice extends over macroscopic dimensions, are not particularly suitable for the use of Laue lenses in Astrophysics because they are too selective regarding the photon energy, even for Laue lenses intended for narrow line studies. Perfect crystals diffract with high efficiency, but only for an extremely narrow range of energy/angle combinations. For example, at 511 keV a perfect germanium crystal will have an angular width of the diffraction peak (the “Darwin width”) of only 0.25 arc-seconds. This should be compared to the Bragg angle, which at this energy is 750 arc-seconds, i.e., about one part in 3000.

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The corresponding energy bandwidth is then only 0.14 keV! Thus, perfect crystals are not preferred for observations of astrophysical sources.

Classical Mosaic Crystals Fortunately, perfect crystals are not the norm. Most artificial crystals grow as mosaic crystals. According to the Darwin model, such crystals can be viewed as an ensembles of perfect micro-crystals with some spread of their angular alignments. Photons of a specific energy may traverse hundreds of randomly oriented crystallites with little interaction and still be strongly diffracted by a single crystallite oriented correctly for this energy. Mosaic crystals generally perform much better than perfect crystals in the context of Laue lenses. The internal disorder, the mosaic width, may be controlled to some extent during the crystal growth or by subsequent treatment. Mosaic widths of some arc-minutes can be obtained with relative ease for a range of crystal types. For the lenses described further, a mosaic width of about 0.5 arcminutes is typical. Such values can be obtained, but this has required substantial development effort (Courtois et al. 2005). Copper crystals, in particular, have attracted interest because of the need for large size, high quality, Copper crystal for use in low-energy neutron diffraction. It must be kept in mind that Bragg’s law is always strictly valid, even for mosaic crystals. As illustrated in Fig. 4a, after diffraction from a mosaic crystal a polychromatic beam of parallel gamma rays with a spread of energies will emerge as a rainbow-colored fan. Its angular width will be twice the angular mosaic width of the crystal. Even if the crystal is oriented so that the central ray of the emerging beam hits the detector, the extreme rays of the fan may miss it.

Fig. 4 Different crystal options proposed for Laue lenses. Flat mosaic crystals (a) produce a chromatic effect that is evident if the mosaicity is large compared with the angular size of the crystals. Longitudinally bent crystals (b) can in principle reach higher diffraction efficiencies than mosaic crystals. However, they are complex to manufacture. A transverse bent perfect crystal (c) can offer almost achromatic focusing at the expense of the effective area, as the geometric area corresponding to a given energy is a fraction of the total surface of the crystal. In this case, the passband of a crystal depends on its curvature

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At a given energy, the radiation diffracted from a flat mosaic crystal forms in the detector plane a projected image of the crystal. It is important to note that this projected image does not move if the crystal tilt is changed. Its position is fixed by Bragg’s law, and it onlychanges in intensity.

Crystals with Curved Lattice Planes As well as perfect and mosaic crystals, a third group has attracted interest as potential diffractive elements for Laue lenses. These are perfect crystals with curved lattice planes. The curvature of the lattice planes has two remarkable effects: (i) the secondary extinction may be suppressed and (ii) the energy passband is not constrained anymore to the Darwin width but will be defined by the total range of lattice direction, i.e., in principle something under our control. If the lattice curvature is correctly chosen relative to the photon energy, secondary extinction may be suppressed, and the diffraction efficiency can approach 100% – ignoring incoherent absorption, which is always present. Different methods to create such lattice curvature have been proposed and experimentally demonstrated. One involves imposing a thermal gradient on the crystal along its thickness, such that the hot side expands and the cold side contracts. This method is very convenient in the laboratory because both the degree of bending (the bending radius) and the “sign” of the bending can be changed with minimal change in the experimental set up (Smither et al. 2005). Unfortunately, this method cannot be used in space due to the significant power dissipation required to maintain the thermal gradient. A second method relies on specific pairs of elements (or compounds) which can form perfect crystals across a range of component fractions. Stable, curved lattice planes exist in these binary crystals in the regions where a composition gradient is present (Abrosimov 2005). Silicon/germanium composition-gradient crystals have been proposed for the “MAX” Laue lens described in section “The MAX Project (2006)”. A further bending method relies on externally applied mechanical forces to bend the crystals. Mechanically, bent crystals are used in several applications in laboratory experiments including monochromators. However, the mass of the structures necessary to maintain the bending forces is unlikely to be acceptable for a space experiment. Controlled permanent bending of silicon and germanium wafers by surface scratching has been developed by the Institute of Materials for Electronics and Magnetism, (IMEM-CNR) in Parma (Buffagni et al. 2012) in connection with the Italian Laue project (Virgilli et al. 2014). The lapping procedure introduces defects in a superficial layer of a few microns, providing a high compressive stress resulting in a convex surface on the worked side. In such transversally bent crystals, the orientation of the diffraction planes with respect to the incident radiation continuously changes in the direction of the curvature of the crystal. If the bending radius is equal to twice the focal length of the lens, the effect is to produce achromatic focusing as illustrated in Fig. 4.

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A spectrum of finite extent may be focused into an area which is considerably smaller than the crystal cross-section. In this way, the overall Point Source Response Function (PSF) of a Laue lens can be narrower than achievable with flat crystals of the same size. Transversally, bent crystals were studied in the Laue project in which a number of different aspects of the Laue lens technology were faced, from the production of suitable crystals to the definition of an accurate and fast method for their alignment. It was demonstrated through simulations and experimental tests (Virgilli et al. 2013) that a transversally bent crystal focuses a fraction of the radiation arriving on its surface into an area which, depending on mosaicity, can be smaller than the cross section of the crystal itself. For some crystals and crystallographic orientations, if an external (primary) curvature is imposed through external forces, a secondary curvature may arise. This effect is a result of crystalline anisotropy. It has been termed quasi-mosaicity (Ivanov et al. 2005) and leads to an increased diffraction efficiency and angular acceptance (Camattari et al. 2011). A promising manufacturing technology for bent crystals which may overcome some of the limitations of flat crystal diffraction optics is based on the so-called silicon pore optics (SPO) (Bavdaz et al. 2012). This is a bonding technology for silicon wafers which is being developed for the ESA Athena mission. It has made possible the development of novel units for focusing gamma-rays called silicon Laue components (SiLCs (Ackermann et al. 2013; Girou et al. 2017)). These components are being developed at the COSINE company (the Netherlands) in collaboration with the University of California at Berkeley. They are self-standing silicon diffracting elements which can focus in both the radial and the azimuthal directions. SiLCs consist of a stack of thin Silicon wafers with a small wedge angle between adjacent plates such that the diffracted rays from all the plates converge at a common focus. The incidence angle of the radiation is small so the radiation passes through only one plate. The wafer angle with respect to the optical axis of the telescope is selected such that the mean angle enables diffraction at energy E, and the overall range of wedge angles between the wafers dictates the energy bandpass around the centroid E. As can be seen in Fig. 5, the curvature of the wafers allows focusing in the orthoradial direction.

Laue Lens Optimization The response of a Laue lens is strongly energy dependent. For a given focal length and crystal plane spacing, the area diffracting a particular energy passband is inversely proportional to E. Furthermore, the diffraction efficiency of the crystals adopted for realizing these optics decreases with energy. These two reasons, combined with the fact that the gamma-ray emission of astrophysical sources typically decreases with energy according to a power law, make observations at high energies even more challenging. The dependence of the effective area on energy is a geometric effect and can be mitigated only at particular energies in narrow passband Laue lenses. The decrease in diffraction efficiency with energy can be mitigated by choosing crystals to maximize the reflectivity.

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Fig. 5 Sketch of the principle at the basis of the SILCs elements developed at Cosine Measurement System (The Netherlands). A polychromatic beam is focused in two directions. (Published with permission of the authors and adapted from Cosine Measurement Systems Cosine Measurement Systems 2022)

A number of parameters can be tuned in the optimization of a Laue lens. They are mainly related to the crystals properties (mosaicity, crystal material, diffraction planes, crystallite size, crystal thickness), or to the overall lens structure (lens diameter, focal length, inner and outer radius, geometrical configuration). The optimization is complex and depends on the Laue lens requirements (lens bandwidth, point spread function extension, total weight of the lens). The main factors involved in the optimization are described in the following sections.

Crystal Selection As discussed in section “Diffraction Efficiency”, crystals with high atomic density and high atomic number are generally preferable as Laue lens elements except at the lowest energies where photoelectric absorption may render their use less attractive. The technical difficulties involved in the fabrication and handling of crystals of the different chemical elements are also important factors. These difficulties vary significantly among the elements. The mechanical properties of the crystals are an important issue, for example, silicon and germanium are quite hard and rugged, whereas copper, silver, and gold crystals are soft and require special care in treatment and handling. As already observed in section “Extinction Effects”, the crystallite thickness plays an important role in the reflectivity optimization. For given values of the mosaicity and crystal thickness, the highest reflectivity is obtained for a crystallite size much smaller than the extinction length of the radiation. At the energies of interest, this thickness must be of the order of few µm. The crystal mosaicity also has a primary role in the Laue lens optimization. The higher the mosaicity, the larger the integrated reflectivity, and thus the effective the area, but the broader the

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signal on the focal plane detector. These two effects act in opposite senses in the optimization of the sensitivity. The crystal thickness is also an important factor for the optimization of the crystal reflectivity and therefore for the maximization of the Laue lens sensitivity. Equation 8 provides the thickness that maximizes the reflectivity for a given material and for fixed diffraction planes. As the best thickness is also a function of energy, it is expected that, depending on the adopted geometry, crystals dedicated to high energy are thicker than those used to diffract low energies. It must be also taken into account that the choice of the thickness maximizing the reflectivity would often lead to a mass unacceptable for a satellite-borne experiment. A trade-off between lens throughput and mass is then necessary.

Narrow- and Broadband Laue Lenses Depending on the scientific goal to be tackled, Laue lens can be designed, or adjusted, with two different optimizations: lenses for a broad energy passband (e.g., 100 keV–1 MeV) or those configured to achieve a high sensitivity over one or more limited range(s) of energy. The latter can be valuable for studying gamma-ray lines, or narrow-band radiation. Relevant energies of interest might be the 511 keV e+/e− annihilation energy or the 800–900 keV energy range for its importance in Supernova emission. The two classes of Laue lenses need different optimizations and dispositions of the crystals over the available geometric area. For a narrow energy passband, Laue lens as many as possible of the crystals should be tuned to the same energy. According to Eq. 3, the d-spacing of the crystals should ideally increase in proportion to their radial distance from the focal axis in order keep the diffracted energy fixed. The energy range of a broadband Laue lens follows from Eq. 3. With the focal length and d-spacing of the crystalline diffraction planes both fixed, the energy range will be from Emin =

hc F hc F to Emax = , dhkl Rmax dhkl Rmin

where the radial extent of the lens is Rmin to Rmax . If the inner and outer radii are fixed, the simultaneous use of different materials, and thus of different dhkl , would allow enlarging the Laue lens energy passband compared with a single-material Laue lens. Equivalently, for a given energy passband and focal length, the use of multi-material crystals would allow a more compact lens.

Tunable Laue Lens A classical Laue lens with fixed inner/outer radius and focal length has a passband which is uniquely defined by the d-spacing of the crystals used. The red curve in Fig. 6 shows the effective area of an example 100 m focal length Laue lens configured to cover a 300–800 keV energy passband. If all of the crystals could be retuned for different focal lengths, the Laue less could be made sensitive to different passbands. Furthermore, as shown in Fig. 6,

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Fig. 6 The effective area of a single Laue lens which is tunable for different energy passbands. The adjustment of the lens to a different band involves changing both the focal length and the orientation of each crystal. When the focal length increases from 50 to 400 m, the integrated effective area increases and the passband becomes larger. Note that the detector size assumed throughout is matched to the 100 m focal length configuration. (Figure reprinted with permission and adapted from Lund 2020)

the larger the focal length, the broader the passband and the higher the integrated effective area. The adjustment in orbit is not trivial – both the orientation of thousands of crystals and the lens to detector separation must be changed and verified. The former requires thousands of actuators and a sophisticated optical system. An innovative mechanism for the adjustment of the orientation of a crystal, along with an optical system for monitoring alignment of each one, has nevertheless been proposed (Lund 2021a,b). The mechanism is based on a miniature piezo-actuator coupled with a tilt pedestal and does not require power once a crystal has been correctly oriented. It is assumed that the lens and detector are on separate spacecraft that can be maneuvered to adjust their separation.

Multiple Layer Laue Lenses A possible way to increase the flux collection from a lens is to use two or more layers of crystals covering the same area. For instance, two layers of crystals can be used, one on each side of the lens structure. In order to focus at the same position, crystals placed at the same radius but in different layers must diffract at the same angle, so different crystals or Bragg planes must be used to diffract different energies.

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Fig. 7 Blue line: effective area of a single layer of Ag(111) crystals with optimized thickness. Black line: effective area of a Laue lens made with two layers of crystals Ag(111) and Ag(200) whose thickness has been reduced with respect to the optimized thickness in order to save mass. In spite of the thickness reduction, the effective area increases by about 65% and the overall mass is reduced by ∼10%. Both effective areas are obtained with 100 m long focal length, crystals with 0.5 arcmin mosaicity, and detector diameter of 5 cm. (Figure taken and adapted with permission from Lund 2021a)

In a simulation (Lund 2021a), two layers of thin crystals made with Ag(111) and Ag(200) increased the effective area by about 65% (see Fig. 7). A third layer did not further increase the lens throughput. It must be stressed that with multiple layers, the diffracted radiation from any one layer will be attenuated by all of the other layers. The number of layers maximizing the effective area will depend on the crystals parameters (thickness, mosaicity, diffraction efficiency).

Flux Concentration and Imaging Properties of Laue Lenses The sensitivity of a telescope using a Laue lens depends on the effective area over which flux is collected, but because observations will almost always be background limited, it is also a function of the extent to which the collected flux is concentrated into a compact region in the detector plane. For a given lens design, the collecting area at a particular energy is just the sum of the areas of the crystals multiplied by their reflecting efficiency at that energy. Obviously, only those crystals for which the incidence angle is close to the Bragg angle need be considered. In practice, this means that the only crystals that contribute are those with centers that fall inside an annulus whose width depends on the extent, ∆θ , of the rocking curve. For broadband lenses, the incidence angle is a simple inverse function of radius from the axis. Consequently, crystals at the center of the band will contribute most, with the response decreasing towards the edges

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of the annulus. Making the small angle approximation θ = r/2F , the width of the annulus is given by ∆r =

∆θ = 2F ∆θ. dθ/dr

(16)

As the radius of the annulus is also proportional to F , this means that its area is proportional to F 2 . Because each crystal simply changes the direction of the incoming parallel beam, it will illuminate a region in the detector plane identical in size and shape to the profile it presents to the incoming radiation. This immediately means that the focal spot can never be smaller than the size of the crystals. Moreover, crystals that are not at the center of the illuminating annulus will have a “footprint” in the detector plane that is offset from the instrument axis by a corresponding distance. Thus to a good approximation, the radial form of the on-axis PSF of a broadband Laue lens is the convolution of the (scaled) rocking curve and a flat-topped function corresponding to the crystal size (The azimuthal extent of the crystals has been ignored and it is assumed that the crystals are smoothly distributed in radius). As is usual with telescopes, other things being equal, the best signal-to-noise ratio will be obtained with a compact PSF. • In circumstances where use of smaller crystals is feasible and would lead to a significantly narrower PSF, then choosing them will always offer an advantage. • If the PSF width is dominated by the rocking curve width, the situation is more complex. Decreasing the mosaicity will then narrow the PSF but also decrease the area of the diffracting annulus, reducing the advantage to be gained. • Lastly, because of the F 2 dependence of the area of lens over which crystals diffract a given energy, a wider PSF can actually provide an advantage if it is the result of an increased focal length – although the signal will be spread over a detector area proportional to F 2 , the uncertainty due to background only increases as F . This of course assumes that such a design is feasible given the cost and mass of the larger lens and detector. The above discussion concerns the response to an on-axis source. As Laue lenses are single reflection optics, they do not fulfill the Abbe sine condition, and therefore, for off-axis sources, they are subject to coma. The aberrations are very severe as illustrated in Fig. 8. The integrated flux is a little affected by off-axis pointing, but importantly the image is smeared over a larger area, and thus the signal-to-noise ratio of the signal is significantly reduced.

Technological Challenges The development of Laue lenses presents several technological challenges. These can be divided into two categories. The first is associated with the search for, and

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Fig. 8 On- and off-axis images of a point source calculated for the lens of the gamma-ray imager proposal (see section “GRI: The Gamma-Ray Imager (2007)”), based on copper crystals and 100 m focal length. The image aberrations are typical for single-reflection devices

production of, suitable materials and components. Highly reproducible crystals with high reflectivity are needed, as are thin, rigid, and low Z substrates and structures to minimize the absorption. The second category is related to the required accuracy of positioning and alignment, both for the mounting of the crystals in the Laue lens and for the alignment of the lens with respect to the focal plane detector. Some of the main issues that are being faced in studies and development of Laue lenses are described further.

I. Production of Proper Crystals and Substrate In order to cover a competitive geometric area, a Laue lens must contain a large number of crystal tiles. The production of a large quantities of crystals having the optimal properties for providing a reflectivity that is as high as possible is still problematic. Crystal growth has been described as an art as well as a science.

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Advanced technologies present their own problems. For instance, it has been shown that bent crystals reduce the width of the PSF compared with flat crystals, but the advantages depend on very accurate control of the curvature.

II a. Crystal Mounting Methods and Accuracy In a Laue lens, it obviously important that each crystal is properly oriented. It is useful to consider three angles describing the orientation of a generic crystal: • (i) A rotation α about an axis parallel to the instrument axis. If there is an error in α, diffraction will occur with the expected efficiency, but the photons will arrive in the focal plane displaced by a distance R∆α, where R is the distance of the crystal from the instrument axis. This displacement should be kept small compared with the spatial scale of the PSF. • (ii) A rotation φ about an axis normal to the diffracting crystal planes. To first order an error in φ will not have any effect on efficiency or imaging. • (iii) A rotation θ about an axis in the plane of the crystal plane and orthogonal to the instrument axis. If θ does not have the intended value, then the energy at which the reflectivity is highest will change. For any given energy, the position in the focal plane where photons of a given energy are arrived will not be altered. However, the number of photons diffracted by the crystal may either increase or decrease depending on the energy considered. The probable effect is a spreading of the PSF as a result of enhancing the response of crystals that are not at the optimum radius for diffracting photons of a given energy towards the center of the focal spot, at the expense of that of those that are. To avoid such spreading, errors in θ should be kept much smaller than the rocking curve width. The most obvious mounting method is to use adhesives to bond the crystals to a supporting structure at their proper position and orientation. However, due to glue deformation during the polymerization phases, it has not proven easy to maintain the necessary precision (Barrière et al. 2014; Virgilli et al. 2015). The amount of misalignment that is introduced depends on the type of adhesive used and on the polymerization process (two components epoxy adhesive, UV curable, thermal polymerization, etc.). In the CLAIRE experiment, the effects of uncertainties in the bonding process were avoided by the use of a manual adjustment mechanism (Section: “The CLAIRE Balloon Project (2001)”), but this technique is probably not appropriate for space instrumentation.

II b. Laue Lens Alignment Because the MeV sky is poorly known at present, the issue of how to verify the correct alignment of gamma-ray diffraction instruments after launch and during operations is important. It is therefore suggested that some optical means of verifying the shape of the large-scale structure of the lens should be incorporated from the start of the project.

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One possible way is to install mirror reflectors on the lens structure, the orientation of which can be monitored, perhaps from a separate detector spacecraft. If the attachment technique for these mirrors is similar to that used for the Laue crystals, the long-term stability of the mirror alignment will also give some confidence in the stability of the crystal mounting.

Examples of Laue Lens Projects In this section, we will review the Laue lens experiments that have been realized or proposed from the early 2000s until the present. The CLAIRE project is the only Laue lens instrument that has actually flown. Other experiments have been realized in the laboratory as R&D projects and were directed to the advancement of welldefined aspects of the Laue lens technology (mainly crystal production and tiles alignment). Studies have been conducted of several possible space missions based on Laue lenses.

The CLAIRE Balloon Project (2001) A pioneering proof-of-principle Laue telescope, CLAIRE, was built and successfully flown as a balloon payload by the Toulouse group in 2001 and 2002 (Laporte et al. 2000; Halloin et al. 2004). The balloon payload is shown in Fig. 9 during flight preparations.

Fig. 9 The CLAIRE telescope during preparation for the 2001 balloon launch. The instrument features, in addition to the Laue lens, a 3×3-array of cooled germanium detectors, and a pointing platform for the lens. The total weight of the payload was less than 500 kg. (Published with permission from von Ballmoos et al. 2004)

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Fig. 10 Detail of the CLAIRE lens with 659 Ge/Si crystals mounted on adjustable lamellae on a titanium frame

The CLAIRE experiment is an example of a narrow energy passband instrument. It was designed for focusing photons with energy ∼170 keV, with a passband of ∼4 keV at a focal distance of 2.8 m. The lens (Fig. 10) consisted of 659 germanium/silicon mosaic crystals arranged in 8 concentric rings providing a collecting area of 511 cm2 and a field of view (FOV) of 90 arcseconds. The mosaicity of the crystals selected was in the range 60 to 120 arc-seconds, leading to an angular resolution for the instrument of 25–30 arcseconds. Two crystal sizes were used: 10 × 10 mm2 and 7 ×10 mm2 . The crystals focused the radiation onto a germanium detector with 9 elements, each 15 × 15 × 40 mm3 , having an equivalent volume for background noise of 18 cm3 . The fine-tuning of the lens utilized a mechanical system capable of tilting each crystal tile until the correct diffracted energy was detected. The crystals were mounted via flexible lamellae on a rigid titanium frame. The tuning of the individual crystals was done manually with adjustment screws. Due to the finite distance (14 m) of the X-ray source during the crystal tuning phase, the gamma-ray energy used was lowered from 170 to 122 keV. Moreover, also due to the finite source distance used for the crystals alignment, only a limited fraction of each crystal was effectively diffracting at the tuning energy, their subtended angle (about 150 arc-seconds, as seen from the source) being much larger than the crystal mosaicity. The performance of the complete lens was verified using a powerful industrial X-ray source at a distance of 200 m (hence a diffracted energy of 165.4 keV). Seen from a distance of 200 m, each crystal subtended an angle of about 10 arc-seconds, i.e., significantly less than the crystal mosaic width. The CLAIRE lens was flown twice on balloon campaigns in 2000 and 2001. In both flights, the target source was the Crab Nebula. The observed diffracted signal

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at 170 keV was found to be consistent with that expected from the Crab Nebula given the lens peak efficiency, estimated at about 8% from ground measurements (von Ballmoos et al. 2005).

The MAX Project (2006) Following up on the successful CLAIRE project, the French Space Agency, CNES, embarked on the study of a project, “MAX,” for a satellite mission with a Laue lens. MAX was planned as a medium-sized, formation-flying project with separate lens and detector spacecrafts launched together by a single launcher. The scientific aims were (i) the study of supernovae type 1a (through observations of the gamma-lines at 812 and 847 keV), (ii) a search for localized sources of electron-positron annihilation radiation at 511 keV, and (iii) a search for 478 keV line emission from 7 Be-decay associated with novae. These objectives could be met by a Laue lens with two energy Passbands: 460–530 and 800–900 keV. The left panel of Fig. 11 shows the lens proposed for MAX which would contain nearly 8000 crystal tiles 15 × 15 mm2 with a mosaic spread of 30 arc-seconds. The total mass of the Laue crystals was expected to be 115 kg. A focal length of 86 m was foreseen. The predicted response of the MAX lens is shown in the right panel of Fig. 11. In the end, however, CNES decided not to continue the development of MAX. GRI: The Gamma-Ray Imager (2007) The Gamma-Ray Imager (GRI) mission concept was developed by an international consortium and proposed to the European Space Agency in response to the “Cosmic Vision 2015–2025” plan. GRI consisted of two coaligned telescopes each with a focal length of 100 m: a hard X-ray multilayer telescope working from 20 up to 250 keV and a Laue lens with a broad passband 220 keV – 1.3 MeV. The low-energy limit of the GRI Laue lens was driven by the anticipated upper limit of the multilayer technology. The NuSTAR mission has demonstrated the capability of multilayer

Fig. 11 Left panel: The proposed MAX lens layout. Note the two crystal groups corresponding to the two energy bands of the lens. A stable structural octagon supports both. Right panel: The simulated response of the MAX Laue lens. More detailed analysis of the response using Monte Carlo techniques indicated that only about half of the photons collected by the lens are sufficiently well focused to be of use during background limited observations. (From Barriere et al. 2006)

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telescopes of focusing photons up to 70–80 keV. Further developments are expected to allow multilayers to be used up to 200/300 keV. The two optics were proposed to share a single solid-state detector using cadmium zinc telluride (CZT) crystals which are attractive as they can be used without cooling. Thanks to the 3-d capability of pixellated CZT, GRI could also be exploited for hard X-/soft gamma-ray polarimetry. Due to the long focal length, a two spacecraft, formation flying mission was proposed. With these features, GRI was expected to achieve 30 arcsec angular resolution with a field of view of 5 arcmin. Unfortunately, the mission was not selected by CNES or ESA for further assessment.

ASTENA: An Advanced Surveyor of Transient Events and Nuclear Astrophysics (2019) Within the European AHEAD project (integrated Activities in the High Energy Astrophysics Domain) (Natalucci and Piro 2018), a mission was conceived to address some of the current issues in high-energy astrophysics: a high sensitivity survey of transient events and the exploitation of the potential of gamma-ray observations for Nuclear Astrophysics (Fig. 12). This mission concept, named ASTENA (Advanced Surveyor of Transient Events and Nuclear Astrophysics) (Frontera et al. 2019; Guidorzi et al. 2019), has been proposed to the European Space Agency in response to the call “Voyage 2050”. It consists of a Wide Field Monitor, with both spectroscopic and imaging capabilities (WFM-IS), and a Narrow Field Telescope (NFT) based on a broad energy passband (60–700 keV) Laue lens with a field of view of about 4 arcmin and with an angular

Fig. 12 The ASTENA mission concept in its folded configuration at launch (left) and in the operative configuration (right) in which the WFM-IS array and the NFT focal plane detector are unfolded

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resolution of ∼30 arcsec. The Laue telescope exploits bent tiles of Si and Ge using the (111) reflecting planes. The tiles have dimensions of 30 × 10 mm2 in size (the longer dimension being in the focusing direction) and a bending curvature radius of 40 m. The focal length of the lens is 20 m. The crystals are arranged in 18 rings, with an outer diameter of ∼3 m that gives an outstanding geometric area of about 7 m2 . The focal plane detector consists of four layers of CZT drift strip detectors (Kuvvetli and Budtz-Jorgensen 2005) each layer having a cross section of 80 × 80 mm2 and thickness of 20 mm.

Fresnel Lenses Fresnel lenses have been extensively discussed and studied for use in astronomy at X-ray energies (e.g., Dewey et al. 1996; Skinner 2004; Gorenstein 2004; Braig and Predehl 2006; Gorenstein et al. 2008; Braig and Predehl 2012; Braig and Zizak 2018) and missions exploiting them in that band have been proposed (Skinner et al. 2008; Dennis et al. 2012; Krizmanic et al. 2020). For a review see Skinner (2010). The circumstances in which such lenses offer diffraction limited resolution are discussed in ⊲ “Diffraction-Limited Optics and Techniques”. Although the idea of Fresnel lenses for gamma rays was introduced at least as far back as 2001 (Skinner 2001, 2002). When their potential for micro-arc-second imaging was pointed out, the idea has rested largely dormant. It will be seen further that the main reason for this is the extremely long focal lengths of such lenses. A secondary reason is that although they offer effective areas far greater than any other technique, with a simple lens the bandwidth over which this is achieved is narrow because of chromatic aberration. However, if those difficulties can be overcome, gamma-ray Fresnel lenses offer some unique possibilities. Like Laue lenses, Fresnel lenses provide a way of concentrating incoming gamma rays onto a small, and hence low background, detector. A gamma-ray Fresnel lens could focus the flux incident on an aperture that could be many square meters into a millimeter scale spot with close to 100% efficiency. Moreover, such a lens would also provide true imaging in the sense that there is a one-to-one correspondence between incident direction and positions in a focal plane. At photon energies above the limits of grazing energy optics, no other technique can do this. Finally, the imaging can be diffraction-limited, which in the gamma-ray band with a meter scale aperture means sub-micro-arcsecond resolution. What is more, even if missions employing them present challenges, gamma-ray Fresnel lenses are, per se, low-technology items. A conventional refractive lens, operating, for example, in the visible band, focuses radiation by introducing a radius-dependent delay such that radiation from different parts of the lens arrives at the focal spot with the same phase (Fig. 13a). A Fresnel lens (Strictly the term used should be “Phase Fresnel Lens” as the shorter form can also be used for stepped lenses in which coherence is not maintained between steps) (Fig. 13b) achieves the same phase-matching by taking advantage of the fact that the phase of the incoming radiation never needs to be changed by more than 2π . Consequently the maximum thickness of the lens can be reduced to that necessary to produce a phase change of 2π , a thickness termed here t2π . It is

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Fig. 13 (a) A conventional refractive lens for visible radiation (b) An equivalent Fresnel lens (c) A gamma-ray Fresnel lens (d) A gamma-ray Phase Zone Plate

usual to write the complex refractive index as n = 1 − δ − iβ where for gamma rays both δ and β are small and positive. The imaginary component describes absorption and does not affect the phase so t2π = λ/δ where λ is the wavelength. The fact that δ is positive for gamma rays means that a converging lens has a concave profile and a Fresnel lens has the form illustrated in Fig. 13c. It is a more efficient form of a ‘Phase Zone Plate’ (Fig. 13d) in which the thickness profile has just two levels differing in phase shift by π . The parameter δ is given in terms of the atomic scattering factor f1 (x, Z) discussed in section “Crystal Diffraction” by δ=

re λ 2 na f1 (x, Z) 2π

(17)

where re is the classical electron radius and na is the atomic density. For lenses of the type considered here, x is essentially zero. Well above all absorption edges, f1 approaches the atomic number Z and so is constant. Thus, δ is proportional to λ2 or inversely proportional to the square of the photon energy E. In principle in the region of the 1.022 MeV threshold for pair production in the nuclear electric field and above, Delbrück scattering should be taken into consideration. Early reports of an unexpectedly large contribution to δ from this effect (Habs et al. 2012) turned out to be mistaken (Habs et al. 2017) but did lead to experimental confirmations of predicted gamma-ray refractive indices at energies up to 2 MeV (Günther et al. 2017; Kawasaki et al. 2017). Like those from Delbrück

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scattering, contributions from nuclear resonant scattering will also be negligible in most circumstances. Although δ is extremely small at gamma-ray energies, the wavelength is also extremely short, for example, 1.24 pico-metres at 1 MeV. Using δ from Eq. 17 results in the following expression for t2π in terms of some example parameters t2π

 −1  −1  E ρ Z λ mm. = = 2.98 δ A 1 MeV 1g cm−3

(18)

Noting that for materials of interest Z/A is in the range 0.4 to 0.5, this means that a gamma-ray Fresnel lens need have a thickness only of the order of millimeters. The period of the sawtooth profile where it is lowest at the edge of the lens is a crucial parameter. Again in terms of example parameters, for a lens of diameter d and focal length F , the minimum period is given by pmin

  −1   F d −1 E F = 2λ = 2.48 mm. d 1 MeV 1m 109 m

(19)

The difficulties lie in the F term. For reasonable values of pmin , extremely long focal lengths are required. pmin is an important parameter in another respect. The PSF will be an Airy function with a FWHM of 1.03λ/d, so the focal spot size using this measure will be given by w = 1.03

Fλ = 0.501pmin d

(20)

That is to say, the size of the focal spot is about half the period at the periphery of the lens. The corresponding angular resolution is w/F and is given in micro-arcseconds (µ′′ ) by ∆θd = 0.263



E 1 MeV

−1 

d 1m

−1

.

(21)

Thus, gamma-ray Fresnel lenses have the potential to form images with an angular resolution better than available in any other waveband and would be capable of resolving, for example, structures on the scale of the event horizons of extra-galactic massive black holes.

Construction If the full potential of a Fresnel lens is to be realized, then Eq. 20 implies that pmin should be larger than the detector spatial resolution and so should be of the order of millimeters or more. Except at energies above 1 MeV, the required thickness is also of the order of millimeters (Fig. 14a) so high aspect ratios are not then needed.

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Fig. 14 (a) The thickness of some example materials needed to produce a 2π phase shift, plotted as a function of energy. (b) The mean absorption of a lens having as its maximum thickness that is shown in (a). Absorption in any supporting substrate is not taken into account

Almost any convenient material can be used – the nuclei only serve to hold in place the cloud of electrons that produces the phase shifts! Dense materials have the advantage of minimizing thickness but also tend to be of higher Z and hence more lossy at low and high energies. Over much of the gamma-ray band all reasonably low Z materials have similarly low losses (Fig. 14b). Because the refractive index is so close to unity, dimensional tolerances are relatively slack. Using the Maréchal formula (Mahajan 1982), if the rms errors in the profile are kept within 3.5% of the maximum lens thickness (assumed to be t2π), the loss in Strehl ratio (on-axis intensity) will be less than 5%. If the lens is assembled from segments, then the precision needed in their alignment is only at a similar level. Thus, a range of constructional technologies can be considered, including diamond point turning, vapor-phase deposition, photo-chemical etching, and 3-d printing.

The Focal Length Problem As argued above, if the best possible angular resolution is sought, then detector consideration drives one to a pmin ∼ mm. When this is coupled with a requirement for a reasonable collecting area, Eq. 19 implies a focal length of the order of

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105 –106 km. This sort of focal length clearly demands formation flying of two spacecraft, one carrying the lens and the other a focal plane detector. Minimizing station-keeping propulsion requirement suggests locations near to a Sun-Earth Lagrangian point. The line of sight from detector to lens must be controlled with sufficient accuracy to keep the image on the detector, so the precision needed depends on the size of the detector. This could be from a few cm up to perhaps 1 m. Changes in the direction of that line of sight need to be determined with an accuracy corresponding to the angular resolution aimed for, which could be sub-micro-arcsecond. Detailed studies have been performed of missions with requirements that meet all of these requirements separately. Not all are met together in any single study, but on the other hand, the complexity of the instrumentation and spacecraft was in each case much greater than that for a gamma-ray Fresnel telescope. New Worlds Observer requires a 50 m star shade and a 4 m visible-light diffractionlimited telescope to be separated by 8 × 104 km (Cash et al. 2009). The transverse position of the telescope must be maintained to within a few cm. The MAXIM Xray interferometer mission calls for a fleet of 26 spacecraft distributed over an area 1 km in diameter to be separated from a detector craft 2 × 104 km away (Cash 2003, 2005). The requirement for a diffraction-limited gamma-ray Fresnel lens mission to track changes in the orientation of the configuration in inertial space at the submicro-arcsecond level are similar to the corresponding requirement for MAXIM, though only two spacecraft are needed. MAXIM studies envisaged a “super star tracker”. Such a device could locate a beacon on the lens spacecraft relative to a stellar reference frame. In terms of separation distance, the requirement for ∼106 km separation can be compared with the needs of the LISA gravitational wave mission (Joffre et al. 2021) for which three spacecraft must each be separated from the others by 2.5 × 106 km, though in this case it is the rate of change of inter-spacecraft distance that requires strict monitoring rather than the orientation.

Effective Area The focusing efficiency of a gamma-ray Fresnel lens will depend on the fraction of incoming radiation that passes unabsorbed through the lens and on the efficiency with which that radiation is concentrated into a focal spot. In Fig. 14b, the mean transmission of a lens with a maximum thickness of t2π and a typical profile is shown for some example materials. Transmissions in excess of 95% should generally be possible. For an Airy disc, 84% of the radiation falls within the central peak, that is to say, within a radius equal to the resolution according to the Rayleigh criterion. As noted in section “Construction”, allowing for profile errors with an rms level of 3.5% rms of the maximum height could reduce the Strehl ratio by 5%. If the errors are random, the form of the PSF will be little changed and so the effective area will be reduced in proportion. Combining all these factors together indicates a focusing efficiency of about 75%.

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We take as a reference design a 2 m diameter lens made from polycarbonate with a nominal working energy of 500 keV and focal length 106 km. The baseline active thickness is taken to be t2π = 1.15 mm, but absorption in a 2 mm substrate has been allowed for. Additional support against diaphragm mode vibrations would obviously be needed during launch but out of plane distortions during operation have little effect. Allowing for the above factors, an effective area over 20,000 cm2 should be attainable with a simple Fresnel lens having these parameters. The diffractionlimited angular resolution of such a lens would be 0.31 micro-arc-seconds.

Chromatic Aberration Unfortunately, the above indication of a possible effective area applies only at the particular energy and focal distance for which the lens has been designed. An important limit to the performance of a Fresnel lens is the chromatic nature of the imaging. The bandwidth over which the good focusing is achieved is very narrow. For even quite small deviations from the wavelength for which the profile has been designed, the focal length changes, and for a fixed detector position, the focal spot rapidly becomes blurred. The FWHM of the on-axis intensity as a function of energy is approximately δλ δE 1.79 = = λ E NF

(22)

where NF is the Fresnel number, r 2 /(f λ). When the lens thickness is t2π , then NF is equal to twice the number of rings. If the flux within a focal spot the size of the ideal Airy peak is used as a measure of the response, then the bandwidth is somewhat larger, with the numerical factor in Eq. 22 increased to about 2.95, and if the flux from a larger detector region is accepted, then the bandwidth increases further as seen in Fig. 15. The improvement will be at the expense of poorer angular resolution and increased detector background. Note that the diffraction-limited angular resolution will anyway only be available if the detector energy resolution is good enough to select only those photons within ∆E. For a high purity germanium detector (see −3 at ⊲ Chap. 55, “The Use of Germanium Detectors in Space”), then δE E ∼ 4 × 10 500 keV, effectively setting a limit of about 700 on the useful Fresnel Number of a diffraction limited telescope using a simple gamma-ray Fresnel lens. Over a much wider band, good focusing can be recovered by adjusting the detector position (Fig. 15), but only radiation within the narrow bands can be focused efficiently for any given position. There is a direct analogy with the tunable Laue lenses described in section “Tunable Laue Lens”, but for a Fresnel lens, no adjustment is required to the lens, only a change in focal distance. For visible and IR radiation, it has been shown possible to increase the bandpass of Fresnel lenses by correcting the chromaticity of one diffractive lens with that

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Fig. 15 (a) The effective area of a Fresnel lens with the parameters described in Table 1. The curves assume that the flux is collected from a circular region with a radius 1, 2, 4, and 8 times the 1.5 mm Rayleigh width of a diffraction limited response (narrowest peak to widest). The FWHM increases from 2.8 to 17.7 keV. (b) As (a) but assuming that at each energy the configuration is refocused by moving the detector to the focal plane for that energy. The narrowest peak from (a) is reproduced for comparison Table 1 Parameters of example lens designs. All the designs have the following in common – Nominal energy: 500 keV, Diameter: 2 m, Focal distance: 106 km, Fresnel Number: 400, Diffraction limited angular resolution 0.3 micro-arc-seconds, Material: Polycarbonate. A substrate of 2 mm is allowed for in the mass and in calculating the effective area but not included in the “active thickness”. The effective areas quoted are those for the lens and do not include detector efficiency. Those quoted here assume that the flux is collected from a 12 mm diameter region in the image plane. rms figure errors of 3.5% of t2π have been allowed for Type Simple Fresnel Achromatic Doublet ” Multiwavelength

Figure 15a 17a(i) 17a(ii) 17b

Active thickness t mm t/t2π 2.4 1 50 21 191 81 24 10

Mass kg 12 100 332 52

Effective area Peak (cm2 ) Integral (cm2 MeV) 26,735 331 15,768 720 5224 440 17,064 642

of another one of opposite power, but such systems cannot produce a real image as is required for a gamma-ray telescope (Bennett 1976; Skinner 2010). Similarly schemes used in those wavebands to make “Multiorder” or “Harmonic” Fresnel lenses by increasing the maximum thickness of the lens so that it becomes a (different) integer multiple of t2π at each wavelength (Faklis and Morris 1995; Sweeney and Sommargren 1995) do not work in the gamma-ray band. A small part of the surface of such a lens can be regarded as a diffraction grating blazed to direct radiation into the appropriate order, but as t2π for gamma rays is almost universally proportional to λ−1 , the blaze angle cannot be correct at different energies.

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However, various possibilities do exist for alleviating the chromaticity problem: 1. ‘Axilenses’ in which the pitch is varied in ways other than the r −1 variation of a regular Fresnel lens. This can produce an enlarged bandwidth at the expense of efficiency (Skinner 2009). The integral over energy of the effective area is close to that of a corresponding classical Fresnel lens. 2. Achromatic doublets. While the focal length of a diffractive lens for X-rays or gamma rays is proportional to E, that of a refractive lens is even more strongly dependent on energy, being proportional to E 2 . In various contexts, (Skinner 2002; Gorenstein 2003; Wang et al. 2003) it has been pointed out that consequently diffractive and refractive lenses for which the focal lengths are

fd =



 E f0 E0 2

 2 E fr = − f0 E0

(23)

can be combined to form an achromatic doublet for which the combined focal length is to first order independent of wavelength. In the gamma-ray band, the absorption losses for a full refractive lens with useful parameters are likely to be prohibitive, but steps that are many times t2π can be introduced. This leads to a lens having a profile corresponding to the combination of those shown in Fig. 16a and b. Figure 16c is a zoom on parts of the fine structure in the diffractive component, (b). At a given radius, only the total thickness is important, so the two components can be separate as shown, or back to back in s single component, or the diffractive profile can be superimposed on that of the refractive one. With such lens focusing then be achieved at a number of wavelengths over an extended band (Fig. 17a). The peak effective area is less than that for a single lens, but the

Fig. 16 Profile of an achromatic doublet. (a) The refractive component (b) The diffractive component (Fresnel lens) component (c) Zooms on sample regions of (b)

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Fig. 17 (a) The effective area of “achromatic” doublets in which a simple converging Fresnel diffractive lens is combined with a diverging refractive one. The refractive component is assumed to be stepped at points where the thickness would exceed either 20 (green) or 80 (blue) times t2π at the nominal energy of 500 keV. The flux is assumed to be collected from a spot 4 times the diameter of the central peak of a diffraction limited response. The corresponding curve from Fig. 15 is reproduced (red line) for comparison. (b) The corresponding effective area for a multiwavelength lens optimized for response at four energies of astrophysical interest

integral can be several times higher. The mass of the lens will be many times that of a simple lens, and the finest scale of the structure must be a factor of two smaller. 3. Multi-wavelength lenses. Recently, a number of papers have been published describing the design of “achromatic diffractive lenses” for UV/visible/IR radiation (e.g., Banerji et al. 2019). The approach used is to optimize the thickness of a number of concentric rings so that the imaging performance over a number of wavelengths is as good as possible based of some figure of merit. The same technique can be used to design gamma-ray lenses. At first sight, the reported performance of the IR lens designs is remarkably good with, for example, 91% “average efficiency” reported over wavelengths spanning a factor of 2. On detailed examination, though, the efficiency is low except at a few specific wavelengths for which the design was optimized, and analysis suggests that even at these wavelengths the efficiency may have been overestimated (Engelberg and Levy 2021). If the maximum thickness is restricted to be ∼t2π , then the integrated effective area of a lens designed in this way is found to be similar to that of a simple Fresnel lens. If larger thicknesses are allowed, then the performance and limitations are similar to those for an achromat of the same total thickness, but there is the possibility of choosing the energies at which the performance is optimized. An example is illustrated in Fig. 17b which shows the effective area of a lens designed to work simultaneously at the energies of four astrophysical gamma-ray

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lines. The approach used is basically that described by Doskolovich et al. (2020) which maximizes the Strehl ratio averaged over the design energies. However, an additional step was performed in which different target phases were tried and that selected which resulted in the highest value for the minimum over the four energies of the effective area, thus avoiding solutions in which one dominated.

Detector Issues for Focused Gamma Rays A discussion of detectors for gamma-ray astronomy can be found in ⊲ Chaps. 55, “The Use of Germanium Detectors in Space”, ⊲ 56,“Silicon Detectors for Gamma-Ray Astronomy”, ⊲ 57, “Cd(Zn)Te Detectors for Hard X-ray and Gamma-ray Astronomy”, ⊲ 58, “Scintillation Detectors in Gamma-Ray Astronomy” and ⊲ 59, “Photodetectors for Gamma-Ray Astronomy”. Here we present some specific considerations for detectors for focusing gamma-ray telescopes. • Low Background. Gamma-ray observations are almost always limited by background from diffuse sky emission and events arising directly or indirectly from cosmic-rays. It is imperative to suppress these as far as possible. Shielding is heavy and even active shielding is imperfect, some background actually being created by the shielding itself. • Sensitivity to Photon Arrival Direction. A key method of background reduction in the low-energy gamma-ray band involves extracting information about the direction from which a photon arrived. Where the first interaction of a photon in the detector is a Compton scattering and the 3-d locations of that and subsequent interactions can be recorded, a Compton kinematics analysis allows constraints to be placed on the arrival direction. Although there are ambiguities and in the MeV range the precision is limited to a few degrees, background can be drastically reduced by selecting only events whose direction is consistent with having passed through the lens. Obviously, such analysis is not possible for all events, but it is possible to identify a subset of low detection efficiency, very low background, events and give these a high weight during analysis. • Position Resolution. In an imaging system, it is strictly the position where a photon first interacts in the detector that is important, though the location of the centroid of all energy deposits may provide an adequate approximation. Even when the instrument is used as a flux-collector, the position information can be used to define a region of the detector within which events are counted or, better, to attribute to each event a weight depending on the noise level and the expected response at its location. The latter amounts to “PSF fitting”. Of course, Compton kinematics analysis requires recording the positions in 3-d of subsequent interactions as well as the first. • Spatial extent For a Laue lens, a large detector will allow all of the events in the broad wings of the PSF to be captured. With the long focal lengths associated with Fresnel lenses, fields of view tend to be very small and are limited by how large a detector is feasible. In either case, a large detector can provide regions that

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can be used for contemporaneous background estimation, obviating or reducing the need for “off-source” observations • Energy Resolution. As gamma-ray lenses operate over a limited band, good energy resolution reduces the amount of background accompanying the signal. Fresnel lenses, particularly those that are large or have less extreme focal lengths, suffer from severe chromatic aberration so this is crucial where they are used. More generally, insufficient energy resolution will degrade the angular resolution of the Compton kinematic reconstruction and so increase the background. • Detection efficiency Detection efficiency is a major problem in the MeV region. The photons are very penetrating and a non-negligible fraction of photons traverse the detector without interacting at all. The constraints resulting from these objectives are often conflicting. A dense detector is desirable to maximize efficiency, but for Compton reconstruction, low density materials are favored. Compton reconstruction requires measuring position, and the energy deposits at multiple sites, but on the other hand, electronic read-out noise has least impact on energy resolution if all of the charge is fed to a single preamplifier. High purity germanium detectors provide good efficiency and currently the best energy resolution. Germanium-based Compton cameras are well advanced and demonstrated (Tomsick et al. 2019). Cadmium-zinc-telluride (CZT) elements have an energy resolution that is only slightly inferior, do not need cooling, and can be assembled in large arrays. More complex detectors using a 3d-imaging silicon scattering column surrounded by a 3d-imaging CZT-shield absorbing the scattered photons may reach a higher efficiency, but are currently at a development stage (Kuvvetli and Budtz-Jorgensen 2005).

Conclusions Diffractive gamma-ray optics is a field yet to be explored and exploited. Nevertheless, Laue and Fresnel lenses offer unique possibilities. The examples shown in this review illustrate both their capabilities and their limitations. An important consideration in choosing a lens design is the expected signal and how it compares with the likely event rate due to background in the detector. Increasing the effective area is not necessarily an advantage if the background noise increases. For photonstarved observations of continuum sources, though, large integrated effective areas are needed. For applications in which lower effective area or poorer resolution is adequate, reduced diameter or shorter focal lengths can be considered. In some cases, an array of smaller lenses can provide the best solution. Observational MeV astrophysics is still in its infancy. We only know of a handful of low-energy gamma-ray point sources. This is even less than the number known at 100 MeV and above from the SAS-2 and COS-B missions in the 1970s and 1980s. Today high-energy gamma-ray sources are counted in the thousands. For MeV astrophysics, we now await results from the COSI mission (Tomsick et al.

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2019), which in a few years will give us a much clearer picture of the sky at a few MeV, that will be very important in designing future gamma-ray telescopes.

Cross-References ⊲ Diffraction-Limited Optics and Techniques ⊲ The Use of Germanium Detectors in Space

References N.V. Abrosimov, Mosaic and gradient sige single crystals for gamma-ray laue lense. Exp. Astron. 20, 185 (2005) M. Ackermann, N.M. Barrière, M.J. Collon, R. Gunther, G. Vacanti, M.W. Beijersbergen, J. Haneveld, Bending and bonding si single crystals for high performance laue lenses, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 8861 (2013), p. 10. https://doi.org/10.1117/12.2024224 S. Banerji, M. Meem, A. Majumder, C. Dvonch, B. Sensale-Rodriguez, R. Menon, Single flat lens enabling imaging in the short-wave infra-red (SWIR) band, OSA Contin. 2(10), 2968–2974 (2019). https://doi.org/10.1364/OSAC.2.002968, http://www.osapublishing.org/osac/abstract. cfm?URI=osac-2-10-2968 N. Barriere, P. von Ballmoos, G. Skinner, B. Smither, P. Bastie, E. Hinglais, N. Abrosimov, J.M. Alvarez, K. Andersen, P. Courtois, H. Halloin, M. Harris, J. Isern, P. Jean, J. Knödlseder, P. Ubertini, G. Vedrenne, G. Weidenspointner, C. Wunderer, MAX: development of a Laue diffraction lens for nuclear astrophysics. Nucl. Instrum. Methods Phys. Res. A 567(1), 333–336 (2006). https://doi.org/10.1016/j.nima.2006.05.150 N.M. Barrière, J.A. Tomsick, S.E. Boggs, A. Lowell, C. Wade, M. Baugh, P. von Ballmoos, N.V. Abrosimov, L. Hanlon, Developing a method for soft gamma-ray Laue lens assembly and calibration. Nucl. Instrum. Methods Phys. Res. A 741, 47–56 (2014). https://doi.org/10.1016/j. nima.2013.12.006, arXiv:1312.0708 [astro-ph.IM] M. Bavdaz, E. Wille, K. Wallace, B. Shortt, M. Collon, M. Ackermann, M. Olde Riekerink, J. Haneveld, C. van Baren, M. Erhard, F. Christensen, M. Krumrey, V. Burwitz, Silicon pore optics developments and status, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 8443 (2012), p. 29. https://doi.org/10.1117/12.926111 S.J. Bennett, Achromatic combinations of hologram optical elements. Appl. Opt. 15(2), 542–545 (1976). https://doi.org/10.1364/AO.15.000542 C. Braig, P. Predehl, Large-scale diffractive X-ray telescopes. Exp. Astron. 21(2), 101–123 (2006). https://doi.org/10.1007/s10686-006-9077-7 C. Braig, P. Predehl, Toward the diffraction limit with transmissive x-ray lenses in astronomy. Appl. Opt. 51(20), 4638 (2012). https://doi.org/10.1364/AO.51.004638 C. Braig, I. Zizak, Carbon-based Fresnel optics for hard x-ray astronomy. Appl. Opt. 57(8), 1857 (2018). https://doi.org/10.1364/ao.57.001857 E. Buffagni, C. Ferrari, F. Rossi, L. Marchini, A. Zappettini, Preparation of bent crystals as highefficiency optical elements for hard x-ray astronomy. Opt. Eng. 51(5), 056501 (2012). https:// doi.org/10.1117/1.OE.51.5.056501 R. Camattari, V. Bellucci, V. Guidi, I. Neri, Quasi-mosaic crystals for high-resolution focusing of hard x-rays through a laue lens, in Optics for EUV, X-Ray, and Gamma-Ray Astronomy V, vol. 8147 (2011), pp. 81471G–1/–8 W. Cash, X-Ray interferometry. Exp. Astron. 16(2), 91–136 (2003). https://doi.org/10.1007/ s10686-004-2523-5

1706

E. Virgilli et al.

W. Cash, Imaging a black hole: MAXIM. Adv. Space Res. 35(1), 122–129 (2005). https://doi.org/ 10.1016/j.asr.2003.09.057 W. Cash et al., The new worlds observer: the astrophysics strategic mission concept study, in UV/Optical/IR Space Telescopes: Innovative Technologies and Concepts IV, ed. by H.A. MacEwen, J.B. Breckinridge. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 7436 (2009), p. 743606. https://doi.org/10.1117/12.827486 S. Chandrasekhar, Extinction in x-ray crystallography. Adv. Phys. 9, 363–386 (1960). https://doi. org/10.1080/00018736000101219 Cosine Measurement Systems, High-energy Optics (2022). https://www.cosine.nl/technology/ high-energy-optics/ P. Courtois, K.H. Andersen, P. Bastie, Copper mosaic crystals for laue lenses. Exp. Astron. 20(1– 3), 195–200 (2005). https://doi.org/10.1007/s10686-005-9018-x C.G. Darwin, The theory of x-ray reflexion. Philos. Mag. 27(315), 657 (1914) C.G. Darwin, The reflexion of x-rays from imperfect crystals. Philos. Mag. 43, 800–829 (1922) M.S. del Rio, R.J. Dejus, XOP: a multiplatform graphical user interface for synchrotron radiation spectral and optics calculations, in Materials, Manufacturing, and Measurement for Synchrotron Radiation Mirrors, vol. 3152, ed. by P.Z. Takacs, T.W. Tonnessen. International Society for Optics and Photonics (SPIE, 1997), pp. 148–157. https://doi.org/10.1117/12.295554 B.R. Dennis, G.K. Skinner, M.J. Li, A.Y. Shih, Very high-resolution solar x-ray imaging using diffractive optics. Sol. Phys. 279(2), 573–588 (2012). https://doi.org/10.1007/s11207-0120016-7, arXiv:1205.4762 [astro-ph.IM] D. Dewey, T.H. Markert, M.L. Schattenburg, Diffractive-optic telescope for x-ray astronomy, in Multilayer and Grazing Incidence X-Ray/EUV Optics III, ed. by R.B. Hoover, A.B. Walker. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 2805 (1996), pp. 224–235. https://doi.org/10.1117/12.245097 L.L. Doskolovich, R.V. Skidanov, E.A. Bezus, S.V. Ganchevskaya, D.A. Bykov, N.L. Kazanskiy, Design of diffractive lenses operating at several wavelengths. Opt. Express 28(8), 11705 (2020). https://doi.org/10.1364/OE.389458 J. Engelberg, U. Levy, Achromatic flat lens performance limits. Optica 8(6), 834 (2021). https:// doi.org/10.1364/OPTICA.422843 D. Faklis, G.M. Morris, Spectral properties of multiorder diffractive lenses. Appl. Opt. 34(14), 2462 (1995). https://doi.org/10.1364/AO.34.002462 F. Frontera, P. Von Ballmoos, Laue gamma-ray lenses for space astrophysics: status and prospects, Special Issue – X-Ray Focusing: Techniques and Applications (2010). http://arxiv.org/abs/1007. 43081007.4308[astro-ph.IM] F. Frontera, E. Virgilli, C. Guidorzi, P. Rosati, R. Diehl, T. Siegert, C. Fryer, L. Amati, N. Auricchio, R. Campana, E. Caroli, F. Fuschino, C. Labanti, M. Orlandini, E. Pian, J.B. Stephen, S. Del Sordo, C. Budtz-Jorgensen, I. Kuvvetli, S. Brandt, R.M. Curado da Silva, P. Laurent, E. Bozzo, P. Mazzali, M. Della Valle, Understanding the origin of the positron annihilation line and the physics of the supernova explosions, in White Paper in Response to Voyage 2050 Long Term Planning of ESA Science Programme, vol. 1 (2019), p. 20 . D. Girou, C. Wade, N.M. Barrière, M. Collon, R. Günther, L. Hanlon, J.A. Tomsick, A. Uliyanov, G. Vacanti, A. Zoglauer, Development of a second generation silc-based laue lens, in Optical Engineering + Applications (2017), pp. 103991Y–1/–5 P. Gorenstein, Concepts: x-ray telescopes with high-angular resolution and high throughput, in XRay and Gamma-Ray Telescopes and Instruments for Astronomy, ed. by J.E. Truemper, H.D. Tananbaum. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 4851 (2003), pp. 599–606. https://doi.org/10.1117/12.461605 P. Gorenstein, Role of diffractive and refractive optics in x-ray A, in Optics for EUV, XRay, and Gamma-Ray Astronomy, ed. by O. Citterio, S.L. O’Dell. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 5168 (2004), pp. 411–419. https:// doi.org/10.1117/12.506443 P. Gorenstein, W. Cash, N. Gehrels, K. Gendreau, J. Krizmanic, M.C. Miller, C.S. Reynolds, R.M. Sambruna, G.K. Skinner, R.E. Streitmatter, D.L. Windt, The future of high angular resolution

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x-ray astronomy, in Space Telescopes and Instrumentation 2008: Ultraviolet to Gamma Ray, ed. by M.J.L. Turner, K.A. Flanagan. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 7011 (2008), p. 70110U. https://doi.org/10.1117/12.789978 C. Guidorzi, F. Frontera, G. Ghirlanda, G. Stratta, C. Mundell, E. Virgilli, P. Rosati, E. Caroli, L. Amati, E. Pian, S. Kobayashi, G. Ghisellini, C. Fryer, M. Della Valle, E. Margutti, M. Marongiu, R. Martone, R. Campana, F. Fuschino, , C. Labanti, M. Orlandini, J.B. Stephen, S. Brandt, R.M. Curado da Silva, P. Laurent, R. Mochkovitch, E. Bozzo, R. Ciolfi, L. Burderi, T. Di Salvo, Deeper and broder: future observations in the X-/gamma-ray band of known and unknown, in White Paper in Response to Voyage 2050 Long Term Planning pf ESA Science Programme, vol. 1 (2019), p. 20 M.M. Günther, M. Jentschel, A.J. Pollitt, P.G. Thirolf, M. Zepf, Refractive-index measurement of Si at γ -ray energies up to 2 MeV. Phys. Rev.: A 95(5), 053864 (2017). https://doi.org/10.1103/ PhysRevA.95.053864, arXiv:1702.07023 [physics.atom-ph] D. Habs, M.M. Günther, M. Jentschel, W. Urban, Refractive index of silicon at γ ray energies. Phys. Rev. Lett. 108(18), 184802 (2012). https://doi.org/10.1103/PhysRevLett.108.184802, arXiv:1111.3608 [physics.atom-ph] D. Habs, M.M. Günther, M. Jentschel, W. Urban, Erratum: refractive Index of Silicon at γ Ray Energies [Phys. Rev. Lett. 108, 184802 (2012)]; Phys. Rev. Lett. 118(16), 169904 (2017). https://doi.org/10.1103/PhysRevLett.118.169904 H. Halloin, P. von Ballmoos, J. Evrard, G.K. Skinner, J.M. Alvarez, M. Hernanz, N. Abrosimov, P. Bastie, B. Hamelin, P. Jean, J. Knödlseder, R.K. Smither, G. Vedrenne, Gamma-ray astronomy starts to see CLAIRE: first light for a crystal diffraction telescope, in 5th INTEGRAL Workshop on the INTEGRAL Universe, vol. 552, ed. by V. Schoenfelder, G. Lichti, C. Winkler (ESA Special Publication, 2004), p. 739 International tables for x-ray crystallography, Acta Crystallogr. Sect. A 3 (1977). https://doi.org/ 10.1107/S0567739477001314 Y.M. Ivanov, A.A. Petrunin, V.V. Skorobogatov, Observation of the elastic quasi-mosaicity effect in bent silicon single crystals. Sov. J. Exp. Theor. Phys. Lett. 81, 99–101 (2005). https://doi.org/ 10.1134/1.1897998 E. Joffre, D. Wealthy, I. Fernandez, C. Trenkel, P. Voigt, T. Ziegler, W. Martens, LISA: heliocentric formation design for the laser interferometer space antenna mission. Adv. Space Res. 67(11), 3868–3879 (2021). https://doi.org/10.1016/j.asr.2020.09.034 T. Kawasaki, S. Naito, Y. Sano, T. Hayakawa, T. Shizuma, R. Hajima and S. Miyamoto, Measurement of deflection on germanium and gold prisms using 1.7 MeV laser Compton scattering γ -rays. Phys. Lett. A 381(36), 3129–3133 (2017). https://doi.org/10.1016/j.physleta. 2017.07.030 J.F. Krizmanic, N. Shah, P.C. Calhoun, A.K. Harding, L.R. Purves, C.M. Webster, M.F. Corcoran, C.R. Schrader, S.J. Stochaj, K.A. Rankin, D.T. Smith, K. Kota, H. Park, L.E. Boucheron, A. Nasari, VTXO: the virtual telescope for x-ray observations, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 11444 (2020), p. 114447V. https:// doi.org/10.1117/12.2562714, arXiv:2012.15311 [astro-ph.IM] I. Kuvvetli, C. Budtz-Jorgensen, Pixelated cdznte drift detectors. IEEE Trans. Nucl. Sci. 52(5), 1975–1981 (2005). https://doi.org/10.1109/TNS.2005.856882 P. Laporte, N. Abrosimov, P. Bastie, B. Cordier, G.D. Cocco, J. Evrard, L. Gizzi, B. Hamelin, P. Jean, P. Laurent, S. Paltani, G.K. Skinner, R.K. Smither, P. von Ballmoos, CLAIRE – towards the first light for a gamma-ray lens. Nucl. Instrum. Methods Phys. Res. A 442, 438–442 (2000). https://doi.org/10.1016/S0168-9002(99)01270-X N. Lund, A study of focusing telescopes for soft gamma-rays. Exp. Astron. 2(5), 259–273 (1992). https://doi.org/10.1007/BF00690085 N. Lund, Wide band, tunable gamma-ray lenses. Exp. Astron. 51(1), 153–163 (2021a). https://doi. org/10.1007/s10686-020-09680-x, arXiv:2005.03894 [astro-ph.IM] N. Lund, Technologies for tunable gamma-ray lenses. Exp. Astron. 51(1), 165–179 (2021b). https://doi.org/10.1007/s10686-020-09683-8, arXiv:2005.03890 [astro-ph.IM]

1708

E. Virgilli et al.

N. Lund, A new tool for MeV A: the tunable laue-lens, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 11444 (2020), p. 1144430. https://doi.org/10.1117/12. 2560155 V.N. Mahajan, Strehl ratio for primary aberrations: some analytical results for circular and annular pupils. J. Opt. Soc. Am.(1917–1983) 72, 1258–1266 (1982) L. Natalucci, L. Piro, The AHEAD program for integrating activities in high energy astrophysics (Conference presentation), in Space Telescopes and Instrumentation 2018: Ultraviolet to Gamma Ray, vol. 10699, ed. by J.-W.A. den Herder, S. Nikzad, K. Nakazawa. International Society for Optics and Photonics (SPIE, 2018), pp. 1–10 J.R. Schneider, Applications of γ -ray diffractometry. Nucl. Sci. Appl. 1, 227–276 (1981) V. Schoenfelder, H. Aarts, K. Bennett, H. de Boer, J. Clear, W. Collmar, A. Connors, A. Deerenberg, R. Diehl, A. von Dordrecht, J.W. den Herder, W. Hermsen, M. Kippen, L. Kuiper, G. Lichti, J. Lockwood, J. Macri, M. McConnell, D. Morris, R. Much, J. Ryan, G. Simpson, M. Snelling, G. Stacy, H. Steinle, A. Strong, B.N. Swanenburg, B. Taylor, C. de Vries C. Winkler, Instrument description and performance of the imaging gamma-ray telescope COMPTEL aboard the compton gamma-ray observatory. APJS 86, 657 (1993). https://doi.org/ 10.1086/191794 G.K. Skinner, Diffractive/refractive optics for high energy astronomy. I. Gamma-ray phase Fresnel lenses, Astron. Astrophys. 375, 691–700 (2001). https://doi.org/10.1051/0004-6361:20010745 G.K. Skinner, Diffractive-refractive optics for high energy astronomy. II. Variations on the theme. Astron. Asrophys. 383, 352–359 (2002). https://doi.org/10.1051/0004-6361:20011700 G.K. Skinner, Design and imaging performance of achromatic diffractive-refractive x-ray and gamma-ray fresnel lenses. Appl. Opt. 43(25), 4845–4853 (2004). https://doi.org/10.1364/AO. 43.004845, arXiv:astro-ph/0407457 [astro-ph] G.K. Skinner, X-ray and gamma-ray focusing and interferometry, in Optics for EUV, X-Ray, and Gamma-Ray Astronomy IV, ed. by S.L. O’Dell, G. Pareschi. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 7437 (2009), p. 74370J. https://doi. org/10.1117/12.826853 G.K. Skinner, Diffractive x-ray telescopes. X-ray Opt. Instrum. 2010, 743485 (2010). https://doi. org/10.1155/2010/743485, arXiv:1009.2101 [astro-ph.IM] G.K. Skinner, Z. Arzoumanian, W.C. Cash, N. Gehrels, K.C. Gendreau, P. Gorenstein, J.F. Krizmanic, M.C. Miller, J.D. Phillips, R.D. Reasenberg, C.S. Reynolds, R.M. Sambruna, R.E. Streitmatter, D.L. Windt, The milli-arc-second structure imager (MASSIM): a new concept for a high angular resolution x-ray telescope, in Space Telescopes and Instrumentation 2008: Ultraviolet to Gamma Ray, ed. by M.J.L. Turner, K.A. Flanagan. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 7011 (2008), p. 70110T. https://doi. org/10.1117/12.789568 R.K. Smither, Invited review article: development of crystal lenses for energetic photons. Rev. Sci. Instrum. 85(8), 081101 (2014) R. Smither, K. Abu Saleem, M. Beno, C. Kurtz, A. Khounsary, N. Abrosimov, Diffraction efficiency and diffraction bandwidth of thermal-gradient and composition-gradient crystals. Rev. Sci. Instrum. 76, 123107–123107 (2005). https://doi.org/10.1063/1.2130928 D.W. Sweeney, G.E. Sommargren, Harmonic diffractive lenses. Appl. Opt. 34(14), 2469 (1995). https://doi.org/10.1364/AO.34.002469 J. Tomsick et al., The compton spectrometer and imager, in Astro 2020 APC White Paper, vol. Astro2020 (2019), pp. 1–11 J. Tomsick, A. Zoglauer, C. Sleator, H. Lazar, J. Beechert, S. Boggs, J. Roberts, T. Siegert, A. Lowell, E. Wulf, E. Grove, B. Phlips, T. Brandt, A. Smale, C. Kierans, E. Burns, D. Hartmann, M. Leising, M. Ajello, C. Fryer, M. Amman, H.-K. Chang, P. Jean, P. von Ballmoos, The compton spectrometer and imager, in Bulletin of the American Astronomical Society, vol. 51 (2019), p. 98. arXiv:1908.04334 [astro-ph.IM] E. Virgilli, F. Frontera, V. Valsan, V. Liccardo, V. Carassiti, S. Squerzanti, M. Statera, M. Parise, S. Chiozzi, F. Evangelisti, E. Caroli, J. Stephen, N. Auricchio, S. Silvestri, A. Basili, F. Cassese, L. Recanatesi, V. Guidi, V. Bellucci, R. Camattari, C. Ferrari, A. Zappettini, E. Buffagni,

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E. Bonnini, M. Pecora, S. Mottini, B. Negri, The LAUE project and its main results, in Proceedings of the SPIE, vol. 8861 (2013), pp. 121–138. id. 886106 17 E. Virgilli, F. Frontera, V. Valsan, V. Liccardo, V. Carassiti, S. Squerzanti, M. Statera, M. Parise, S. Chiozzi, F. Evangelisti, E. Caroli, J. Stephen, N. Auricchio, S. Silvestri, A. Basili, F. Cassese, L. Recanatesi, V. Guidi, V. Bellucci, R. Camattari, C. Ferrari, A. Zappettini, E. Buffagni, E. Bonnini, M. Pecora, S. Mottini, B. Negri, The laue project and its main results (2014). arXiv:1401.4948[astro-ph.IM] E. Virgilli, F. Frontera, P. Rosati, V. Liccardo, S. Squerzanti, V. Carassiti, E. Caroli, N. Auricchio, J.B. Stephen, Hard x-ray broad band laue lenses (80–600 keV): building methods and performances, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 9603 (2015), p. 960308. https://doi.org/10.1117/12.2190335, arXiv:1509.03416 [astroph.IM] P. von Ballmoos, H. Halloin, J. Paul, N. Abrosimov, K. Andersen, P. Astier, S. Basa, D. Barret, P. Bastie, A. Bazzano, A. Bignami, A. Blanchard, B. Cordier, T. Courvoisier, P. Courtois, A. Ealet, B. Hamelin, M. Harris, M. Hernanz, J. Isern, P. Jean, J. Knödlseder, P. Laurent, F. Lebrun, X. Leyre, O. Limousin, A. Marcowith, V. Martinot, A. Mazure, L. Natalucci, J.F. Olive, R. Pain, S. Paltani, N. Prantzos, H. Riemann, R. Sadat, H. Sainct, G. Skinner, R.K. Smither, P. Ubertini, F. Vedrenne, G. Weidenspointner, The MAX mission: focusing on highsensitivity gamma-ray spectroscopy, in 5th INTEGRAL Workshop on the INTEGRAL Universe, vol. 552, ed. by V. Schoenfelder, G. Lichti, C. Winkler (ESA Special Publication, 2004), p. 747 P. von Ballmoos, H. Halloin, J. Evrard, G. Skinner, N. Abrosimov, J. Alvarez, P. Bastie, B. Hamelin, M. Hernanz, P. Jean, J. Knödlseder and B. Smither, CLAIRE: first light for a gamma-ray lens. Exp. Astron. 20, 253–267 (2005). https://doi.org/10.1007/s10686-006-9071-0 Y. Wang, W. Yun, C. Jacobsen, Achromatic Fresnel optics for wideband extreme-ultraviolet and X-ray imaging. Nature 424(6944), 50–53 (2003). https://doi.org/10.1038/nature01756 B.E. Warren, X-Ray Diffraction (Addison Wesley, 1969) W.H. Zachariasen, Theory of X-ray Diffraction in Crystals. Dover phoenix editions. Dover Publications, Incorporated, (Wiley, 1945). https://books.google.it/books?id=bFcL0bbsDP4C

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Carolyn Kierans, Tadayuki Takahashi, and Gottfried Kanbach

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physics of Compton Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Operating Principles of Compton Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Classic Double-Scattering Compton Telescope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modern Compton Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electron-Tracking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dedicated Polarimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Event Identification and Track Recognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compton Sequencing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two-Site Event Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compton Telescope Performance Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Point Spread Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Imaging Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polarization Capabilities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Limitations and Challenges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Notable Compton Telescope Designs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Semiconductor-Based Compton Imagers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gaseous and Liquid Time-Projection Chambers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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C. Kierans () NASA Goddard Space Flight Center, Greenbelt, MD, USA e-mail: [email protected] T. Takahashi Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba, Japan e-mail: [email protected] G. Kanbach Max Planck Institute for Extraterrestrial Physics, Garching, Germany e-mail: [email protected] © This is a U.S. Government work and not under copyright protection in the U.S.; foreign copyright protection may apply 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_46

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Dedicated Polarimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compton and Pair Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Applications in Other Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Compton telescopes rely on the dominant interaction mechanism in the MeV gamma-ray energy range: Compton scattering. By precisely recording the position and energy of multiple Compton-scattering interactions in a detector volume, a photon’s original direction and energy can be recovered. These powerful survey instruments can have wide fields of view, good spectroscopy, and polarization capabilities and can address many of the open science questions in the MeV range and, in particular, from multimessenger astrophysics. The first space-based Compton telescope was launched in 1991, and progress in the field continues with advancements in detector technology. This chapter will give an overview of the physics of Compton scattering and the basic principles of operation of Compton telescopes; electron-tracking and polarization capabilities will be discussed. A brief introduction to Compton event reconstruction and imaging reconstruction is given. The point spread function for Compton telescopes and standard performance parameters are described, and notable instrument designs are introduced. Keywords

Compton scattering · Gamma-ray astrophysics · Compton telescopes · MeV gamma-rays · Polarimetry · Image reconstruction · Event reconstruction · Spectroscopy

Introduction Megaelectronvolt (MeV) gamma-rays are an excellent tool to explore the cosmos: they travel long distances without deviation or absorption, they probe deeper into dense regions than radiation at other wavelengths, and they are emitted by the most extreme and energetic processes in the universe. In particular, the soft and medium energy regime, from ∼100 keV to 100 MeV, is ripe with scientific opportunities. With recent advances in multimessenger astrophysics, the community’s demand for sensitive medium energy gamma-ray telescopes has grown as the sources which generate gravitational waves, neutrinos, and cosmic rays shine bright in the low end of the gamma-ray spectrum. The MeV range is rich with scientific potential. Neutron stars, black holes, magnetars with extreme magnetic fields, and active galactic nuclei with relativistic jets are natural accelerators that emit gamma-rays through bremsstrahlung, inverse

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Compton, and synchrotron radiation. Emissions in the MeV range constrain the thermal and nonthermal energy budget for high-energy galactic and extragalactic sources. There are also compelling reasons to believe that indirect signatures of dark matter will be found at these energies. And finally, the MeV range is the natural scale to probe nuclear processes in the Galaxy and beyond. Many radioactive isotopes decay by emitting gamma-rays up to the nuclear binding energies 8 MeV per nucleon. Radioactive isotopes generated in stellar and explosive nucleosynthesis are proton rich and often undergo β + decay, emitting a positron which later annihilates and generates signature 511 keV photons. However, the soft to medium energy gamma-ray regime remains one of the least explored energy ranges in multiwavelength astrophysics. This gap in sensitivity, often referred to as the MeV Gap, has greatly hindered progress of science due to limited observations in this thermal to nonthermal transition regime. Figure 1 shows the continuum sensitivity of current and past telescopes in the X-ray and high-energy

Fig. 1 The differential sensitivity for current and past X-ray and gamma-ray missions shows the limited performance achieved in the MeV regime. The reduced sensitivity in the range from 100 keV to 100 MeV is referred to as the MeV Gap. The XMM sensitivity is for a 1.6 Ms observation at 4σ detection significance (Hasinger et al. 2001; XMM-Newton Science Operations Centre). The NuSTAR (Koglin et al. 2005), Suzaku HXD (Fukazawa et al. 2009), INTEGRAL ISGRI (Lebrun 2005), PICsIT (Di Cocco et al. 2003), and SPI (Roques et al. 2003) sensitivities are shown for 3σ detections with 100 ks exposure and ∆E/E = 0.5, assuming statistical error only. The sensitivity of COMPTEL corresponds to the 9 year all-sky survey of CGRO (Schönfelder et al. 2000). CGRO/EGRET sensitivity (3σ ) is taken from Kamae (2005) for a 300 h exposure, which is consistent with the numbers given in Thompson et al. (1993). The sensitivity of Fermi/LAT is for the 10-year survey (Ajello et al. 2021; Fermi LAT Performance). The 5σ sensitivities for MAGIC, H.E.S.S, and CTA (simulated) correspond to 50 h observations (Zanin et al. 2021; CTA Observatory). The dashed gray line representing the Crab flux is calculated from Naima (Zabalza 2015)

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gamma-ray regime, and it is clear that the sensitivity in the MeV Gap is orders of magnitude less than neighboring bands. The lack of sensitive telescopes in the MeV range is not due to a lack of scientific interest, as demonstrated throughout Volume 3 and 4 of this handbook, but instead due to physical, technological, and environmental challenges (i.e., background radiation). The interaction cross section between photons and matter is lowest in this range, and the dominant mechanism is Compton scattering, which produces longrange secondaries. Large detector volumes are needed to stop and contain photons with interaction depths on the order of ∼10 g/cm2 . And with no focusing element, these large detector volumes result in high backgrounds, not only from atmospheric albedo emission but also from activation within and around the instrument. While this high background does not significantly impact the detection sensitivity to highenergy transients due to the short bright signals, studies of steady-state sources in the MeV range require sophisticated background-rejection techniques. To build a sensitive telescope to explore the MeV Gap, it must make use of the dominant interaction mechanism in this range: Compton scattering. In Compton scattering, gamma-rays will partially transfer their energy to bound electrons, and by doing so, the electron recoils, and the gamma-ray is scattered at an angle relative to its initial direction with lower energy. The Compton-scattered photon will then interact a second time, and potentially a third and fourth, before finally absorbing all its energy in the detector. Only the complete measurement of the secondary products, i.e., the energized target electron and the de-energized scattered photon, allows for the determination of the initial energy and direction of the incident photon. The pioneering telescope that opened the MeV range as a new window to astronomy was the Imaging Compton Telescope (COMPTEL (Schönfelder et al. 1993)) aboard the Compton Gamma Ray Observatory (CGRO). COMPTEL covered the energy range 0.8–30 MeV from its launch in 1991 until its termination in 2000. It produced the first all-sky MeV survey, mapped the diffuse galactic emission in the continuum and in the light of radioactive gamma-ray lines (e.g., 26 Al, 44 Ti), and detected more than 30 gamma-ray sources (pulsars, pulsar wind nebulae, black holes, and active galaxies). COMPTEL revolutionized gamma-ray astrophysics, and many of the techniques and tools developed for the mission are still being used in modern Compton telescopes. As the last instrument to observe much of the MeV Gap, there are continuing efforts to build upon COMPTEL’s legacy. The power of Compton telescopes comes from the single-photon detection and imaging capabilities. With a large field-of-view and modest angular resolutions (∼1◦ ), Compton telescopes make powerful survey instruments. The single-photon detections and necessary event reconstruction allow for effective backgroundrejection capabilities. Additionally, Compton scattering is inherently sensitive to the linear polarization of incoming gamma-rays, and there is a class of Compton telescopes designed specifically for polarization measurements of transients, such as gamma-ray bursts. Recent advances in technology have shown the breadth and

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power of Compton telescopes, and looking forward the future is bright with the Compton Spectrometer and Imager (COSI) mission (Tomsick 2022) selected by NASA to launch in 2027. This chapter aims to provide a concise, comprehensive, and up-to date overview of Compton telescopes for astrophysics. The following section “Physics of Compton Scattering” will give an overview of the physics needed to understand Compton telescope operation. An overview of the detection principles, including the COMPTEL-like double-scattering approach, modern compact Compton telescopes, and electron-tracking capabilities, will be given in the section “Basic Operating Principles of Compton Telescopes”. The Section “Event Reconstruction” provides a discussion of modern event reconstruction techniques, and “Compton Telescope Performance Parameters” introduces the standard ways that the capability of Compton telescopes are quantified. And finally, a few illustrious instruments that show the diversity of Compton telescopes will be briefly introduced “Notable Compton Telescope Designs”.

Physics of Compton Scattering A major debate was conducted after the discovery of X-rays (also called Röntgenrays in the early days) in the 1900s on the nature of this new, penetrating radiation. Arthur H. Compton, who received the Nobel Prize in Physics in 1927 for the discovery of Compton scattering, summarized the profound findings in his Nobel lecture (Compton 1927): All phenomena in the realm of light are found in parallel in the realm of X-rays. Reflection, refraction, diffuse scattering, polarization, diffraction, emission and absorption spectra, photoelectric effect, all of the essential characteristics of light have been found also to be characteristic of X-rays. At the same time it has been found that some of these phenomena undergo a gradual change as we proceed to the extreme frequencies of X-rays.

For high-energy X-rays, a modified component of scattered radiation was found at large angles (ϕ) offset from the primary beam (λ0 ) and shifted to longer wavelengths (λscat ), i.e., lower energies. This experimental result could not be explained by coherent scattering of electromagnetic waves on free or bound electrons (Thomson or Rayleigh scattering). Arthur H. Compton introduced the new concept that quanta of light, photons, scattering off electrons can be described by the law of mechanics (Compton 1923). Compton showed that scattering photons conserve energy and momentum, as shown schematically in Fig. 2. For a photon with initial energy E0 , energy conservation gives E0 = Escat + Ee ,

(1)

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Fig. 2 A photon with initial momentum p0 = hν0 /c scatters off an electron assumed to be unbound and at rest. The photon scatters at an angle ϕ relative to the initial direction and has a momentum pscat =  hνscat /c. The electron recoils from the scatter at an angle Θ and with momentum pe = me ν/ 1 − β 2 . Through the conservation of energy and momentum, the relation between the scattering angle and the final photon energy can be determined

where Escat is the scattered photon energy, and the electron, with final energy Ee , is assumed to initially be free and at rest (this limitation is discussed in section “Doppler Broadening as a Lower Limit to the Angular Resolution”). Conservation of momentum gives p0 = pscat + pe ,

(2)

where the initial momentum of the photon is |p0 | = hν0 /c, and the final reduced photon momentum is |pscat | = hνscat /c. The recoil electron  is accelerated and the final momentum is given by |pe | = me vγ , with γ = 1/ 1 − β 2 and β = v/c. This leads to the well-known Compton equation: λscat − λ0 =

h (1 − cos ϕ), me c

(3)

where h, me , and c are Planck’s constant, the electron rest mass, and the speed of light, respectively. The fraction h/me c = 2.426 10−12 m is often called the Compton wavelength, which is the wavelength shift for a 90◦ scattering. It is important to note that a photon can never lose all its energy in a Compton-scattering process, even if it is completely backscattered.

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Equation 3 can be solved for ϕ and with wavelength converted to energy: cos ϕ = 1 − me c2



1 Escat

−

1 E0



,

(4)

where the energy of the scattered photon is Escat = hνscat =

1+

E0 . E0 (1 − cos ϕ) me c 2

(5)

As one can see in Equations 4 and 5, the final energy of the Compton-scattered photon can be uniquely determined with the initial energy and Compton-scattering angle information. As detectors are sensitive to the ionization from the recoil electron, it is important to consider the kinetic energy of the Compton-scattered electron: Ee = E0 − Escat = E0



 E0 (1 − cos ϕ) . me c2 + E0 (1 − cos ϕ)

(6)

The spectral shape of the electron energy is shown in Fig. 3. To better understand this distribution, we consider the extreme cases of grazing-angle scattering and backscattering. For ϕ ≈ 0, Equation 6 gives the recoil electron energy Ee ≈ 0, and Equation 5 gives Escat ≈ E0 . For a head-on collision where the photon backscatters at ϕ = 180◦ , the maximum amount of energy is transferred to the electron, and Equation 6 reduces to

Fig. 3 The spectral shape of the recoil electron energy for a photon with initial energy E0 = hν. There is a continuum of electron energies observed due to the range of allowable Comptonscattering angles. The maximum recoil electron energy is achieved for backscatter interactions when ϕ = 180◦ ; this defines what is referred to as the Compton edge in a measured spectrum. (Modified from Knoll 2000)

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Ee |ϕ=180◦ = E0



2E0 2 me c + 2E0



⎛

= E0 ⎝1 −

1 1+

2E0 me c 2

⎞

⎠.

(7)

The difference between the initial photon energy and the maximum recoil electron energy is given by Ec = E0 − Ee |ϕ=180◦ =

E0 1+

2E0 me c 2

,

(8)

which is often called the Compton edge and is depicted in Fig. 3. The Compton-scattered electron energy Ee can also be expressed in terms of the angle Θ between the incident photon and the direction of the recoil electron (see Fig. 2), making use of the relation cot(Θ) = (1 + α) tan(ϕ/2), where α = E0 /me c2 Ee =

2E0 α cos2 Θ . (1 + α)2 − α 2 cos2 Θ

(9)

The full quantum-mechanical treatment of the scattering of unpolarized energetic photons on single, free target electrons γ +e− → γ +e− was derived by Oskar Klein and Yoshio Nishina in 1928. The differential cross section for Compton scattering is given by the Klein-Nishina formula (Klein and Nishina 1929): r0 2 dσ = dΩ 2



Escat E0

2 

 Escat E0 2 + − sin ϕ , E0 Escat

(10)

where r0 = 2.818 × 10−15 m is the classical electron radius, E0 is the initial energy of the incident photon, Escat is the energy of the scattered photon, and ϕ is the scattering polar angle, as shown in Fig. 2. From this equation, it can be seen that higher energy photons will, in general, have smaller Compton-scattering angles, and lower-energy photons will result in larger scatter angles. The Klein-Nishina differential cross section is shown graphically in Fig. 4 for a number of different energies. Integration of Equation 10 over dΩ gives the total cross section for Compton scattering. In terms of the Thomson cross section (σT = 8π e2 /3me c2 = 0.665 × 10−28 m2 ), and using dimensionless units for the photon energy (ε = E0 /me c2 ), the total cross section is

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Fig. 4 The Klein-Nishina differential cross section (m2 /sr) as a function of Compton-scattering angle shows the energy dependence of the scattering direction. For lower-energy photons, such as 10 keV shown with the blue curve, the magnitude of the differential cross section only changes by a factor of 2 for all Compton-scattering angles. For higher energy photons, such as 2 MeV shown in red, the cross section is maximized for small scattering angles

σC =

3 σT 4



1+ε ε3



 2ε(1 + ε) ln(1 + 2ε) 1 + 3ε (11) − ln(1 + 2ε) + − 1 + 2ε 2ε (1 + 2ε)2

If the gamma-ray energy is much smaller than electron mass, the total cross section is reduced to the Thomson cross section, σT . The differential cross section for linearly polarized photons was derived by Heitler in 1954: r0 2 dσ = dΩ 2



Escat E0

2 

 Escat E0 2 2 + − 2 sin ϕ cos η , E0 Escat

(12)

where the polar Compton-scattering angle ϕ and the azimuthal scattering angle η are explicitly written (Evans 1955). There is a similar dependence on the Comptonscattering angle ϕ in Equation 10; however, the polarized differential cross section is maximized when the cos2 η term equals zero. In other words, photons will predominantly scatter at 90◦ relative to the initial photon’s electric field vector, defined as η = 0. This results in an azimuthal dependence of the cross section, and therefore, Compton telescopes can inherently detect polarization if a measurement of η is made (Lei et al. 1997). The definition of the scattering angles relative to the initial photon electric field vector ξ is shown in Fig. 5. Equation 10 describes not only the energy dependence of the Compton-scattering cross section on single electrons but also implicitly the total cross section for scattering in material of atomic number (Z) and density ρ. Since each single scattering event is independent, the total cross section is the sum of all events and depends directly on the electron density in the target material. Detailed compilations of gamma-ray cross sections for various materials can be accessed with the Internetbased application XCOM (Berger et al. 2017).

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Fig. 5 The Klein-Nishina differential cross section for polarized photons (Equation 12) is maximized when the azimuthal scattering angle η is perpendicular to the photon’s initial electric field vector ξ . By measuring the azimuthal scattering angle η, an instrument can be sensitive to the linear polarization of incoming photons

It is convenient to describe the total cross section in terms of the mass attenuation coefficient µ, particularly when comparing Compton scattering to the dominant photon interactions at lower and higher energies, i.e., photoelectric absorption and pair production. These coefficients, given in units of cm2 /g, are most useful to estimate what fraction of photons from an incoming beam with intensity I0 are lost by interactions, either by absorption or scattering. The intensity I of a beam after traversing matter with thickness x (g/cm2 ) is I = I0 e−µx ,

(13)

where x is the product of the geometrical path length l and density ρ of the transversed material. As an illustrative example, we can calculate the amount of silicon needed to attenuate 50% of incident gamma-rays with initial energy of 511 keV. From XCOM, the µ for silicon at 511 keV is 8.67 × 10−2 cm2 /g, and the density ρ is 2.33 g/cm3 . Rearranging Equation 13 for the path length gives l=

  1 ln(0.5) I = 3.4 cm. = ln ρµ I0 (2.33 g/cm3 )(8.67 × 10−2 cm2 /g)

(14)

Therefore, over 3 cm of silicon are needed to scatter or absorb only half of incident 511 keV photons. This exemplifies the challenges of low interaction cross sections for Compton telescopes where large detector volumes are required. Figure 6 depicts the mass attenuation coefficient µ as a function of energy for three common detector materials: a low-Z plastic scintillator (hydrocarbonbased material of density ρ ≈ 1 g/cm3 ), the ubiquitous semiconductor silicon (ρ = 2.33 g/cm3 ), and the common high-Z sodium iodide doped with thallium NaI(Tl) (ρ = 3.67 g/cm3 ). Compton scattering dominates in the range 30 keV to 30 MeV for the plastic scintillator, while for Na(Tl) this range is reduced to 300 keV to 8 MeV. These differences are the basis for many Compton telescope

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Fig. 6 The mass attenuation coefficients for three common gamma-ray detector materials: (a) plastic scintillator (hydrocarbon-based polymers), (b) silicon, and (c) sodium iodide NaI(Tl). Compton scattering dominates over a much larger energy range from ∼30 keV to 30 MeV for low-Z materials, as shown here for plastic scintillator. For high-Z materials, such as NaI, Compton scattering only is dominant from ∼300 keV to 8 MeV. Calculations are from XCOM (Berger et al. 2017)

Fig. 7 The regions of dominant interaction cross sections for the photoelectric effect, Compton scattering, and pair production are shown as a function of photon energy and for detector materials of atomic number Z. Photoelectric effect and Compton interactions have the same cross section along the boundary σ = τ , and pair creation dominates beyond σ = κ. (Figure From Evans 1955)

designs that separate scattering and absorption processes in multiple interactions, and Fig. 7 shows the interplay between the three major interaction processes as a function of the target material atomic number and initial photon energy. It is evident that materials with low to medium Z, e.g., hydrocarbon-based scintillators or solid-

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state detectors like silicon (Z = 14), are the most efficient Compton scatterers over a wide energy range. Photoabsorption of the Compton-scattered photon is most efficient in a high-Z and high density detector, such as NaI(Tl) or cesium iodide CsI(Tl) scintillators, and solid-state detectors made of cadmium telluride (CdTe) or cadmium zinc telluride (CZT).

Basic Operating Principles of Compton Telescopes In the 1960s and early 1970s, the imaging and spectroscopy of celestial sources in the energy range from 100 keV to several tens of MeV was considered a very difficult task. Instruments relying primarily on photoelectric absorption and pair production were developed but were too inefficient at these energies. The only physical process with reasonable interaction probability in this energy range is Compton scattering (see Fig. 7). However, it is impossible to derive the initial gamma-ray arrival direction and energy (i.e., for imaging or spectroscopy) from only the first Compton-scattering interaction; the photon must be fully absorbed, and the energy and position of each interaction must be recorded to reconstruct a Compton-scattering event. Various work-arounds were attempted to obtain a coarse angular resolution through the use of massive collimators and anticoincidence shields surrounding detectors large enough to contain the full energy of a Compton event and its secondaries. For sources characterized by a clear temporal signal (e.g., pulsars, solar flares, gamma-ray bursts), these instruments could provide important scientific results; however, a more general astronomical imaging instrument at MeV energies was elusive. Progress toward a sensitive MeV telescope was only made with a dedicated effort to measure the locations of energy deposits from Compton interactions. Compton telescopes rely on the precise measurement of the energy and location of Compton-scattering interactions which allow for the arrival direction of the primary gamma-ray to be constrained. For example, let us consider a two-site event, that is, a photon event that consists of a single Compton scatter followed by photoelectric absorption. The basic operating principle is shown in Fig. 8, where a detector volume measures the two interactions, fully containing the event. The Compton-scattering angle ϕ of the first interaction can be derived from the energy measurements. For a two-site event, Equation 4 gives cos ϕ = 1 −

me c 2 me c 2 + , E2 E1 + E2

(15)

where E1 + E2 is the total deposited energy, which is equal to the initial photon energy E0 from Equation 4, Escat = E2 , and Ee = E1 . The direction of the scattered gamma-ray between r1 and r2 defines a cone on the sky with opening angle given by ϕ. The back projection of this cone on the celestial sphere is referred to as the event circle. If the recoil electron direction is not measured (see electron-tracking

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Fig. 8 A Compton telescope works by measuring the energy and position of one or more Compton-scattering interactions. For a two-site event, the initial energy of the photon is determined from the total absorbed energy E0 = E1 + E2 , whereas the direction of the incoming photon is constrained to a circle on the sky defined by the Compton-scattering angle ϕ of the first interaction. When multiple photons are detected originating from the same source, the location of the source is determined by the overlap of each back-projected event circle, as is visualized for ten events on the right. (Modified from Kierans 2018)

Compton telescopes in section “Electron-Tracking”), one cannot determine where on the event circle the single gamma-ray photon originates from. Multiple photons from the same source will have overlapping event circles in image space, revealing the location of the source (see section “Imaging Capabilities” for an overview of imaging reconstruction techniques).

The Classic Double-Scattering Compton Telescope The first Compton telescopes for astrophysics were developed in the 1970s (Schönfelder et al. 1973; Herzo et al. 1975) and were described as “double scatter” telescopes. These classic Compton telescopes consisted of two detectors, referred to as D1 and D2, to measure a Compton-scattering interaction and subsequent photoabsorption in two separated planes, as shown in Fig. 9a. The trajectory of the scattered photon is known by recording the energy and location (E1 , r1 , E2 , r2 ) of the two interaction sites. Equation 15 then affords an estimate for the scattering angle of the primary photon. The first successful Compton telescope operating in space was COMPTEL (Schönfelder et al. 1993) on NASA’s Compton Gamma Ray Observatory (CGRO, 1991–2000). COMPTEL consisted of two detector arrays: D1 contained a low-Z liquid scintillator (NE 213A) to enhance the Compton-scattering cross section, and D2 contains a high-Z NaI(Tl) scintillator to enhance photoelectric

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Fig. 9 (a) A classic Compton telescope uses a scattering plane (D1) and an absorption plane (D2) to measure the position and energy of two interactions in a Compton event. From these measurements, the original photon direction can be constrained to a circle on the sky called the “event circle.” (Adapted from Schönfelder and Kanbach 2013). (b) The first Compton telescope flown was COMPTEL onboard CGRO. COMPTEL used the classic Compton telescope configuration with two planes to map the MeV sky in the 1990s. (Figure from Schönfelder et al. 1993)

absorption (see Fig. 6). COMPTEL was a very large instrument, with D1 and D2 being ∼1.5 m in diameter with a separation of 1.5 m between the two planes and together weighing almost 600 kg. The instrument is shown in Fig. 9b. COMPTEL opened the MeV range with 9 years of groundbreaking observations and provided the first all-sky survey in the 0.75 to 30 MeV energy range. The COMPTEL source catalog (Schönfelder et al. 2000) includes 63 sources, 32 of which are steady state, from spin-down pulsars and stellar black-hole candidates to supernova remnants and active galactic nuclei. Potentially the most notable science achievement from COMPTEL observations was the all-sky map of the 1.8 MeV line from 26 Al decay (Diehl et al. 1993; Plüschke et al. 2001), which showed structure and hot spots consistent with star forming regions. While significant in its contributions, COMPTEL’s achieved sensitivity was still modest (Schönfelder 2004).

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While the instrument was massive, COMPTEL’s efficiency was low. The effective area, which is a measure of the equivalent area of an ideal detector, ranged from only 10 to 50 cm2 depending on energy and event selections, i.e., the efficiency of detecting incident photons was less than 1%. COMPTEL’s angular resolution of a few degrees was limited at low energies by the energy resolution of the scintillators and at higher energies by the position resolution of D1 and D2 (see section “Uncertainties in the Angular Resolution”). COMPTEL’s field-of-view (FOV; ∼1 sr) was limited by the lower-energy thresholds of the two detector planes. COMPTEL employed two essential background reduction features. Due to the large separation between D1 and D2, a time-of-flight measurement was possible to determine the direction of the scattered photons. A selection of downward scattered photons was performed with a time-delay window of 4.5 ns. Secondly, the D1 liquid scintillator allowed for a discrimination of photon and neutron interactions based on differing pulse shapes. This further reduced the background observed in flight. These powerful background-rejection techniques allowed COMPTEL to achieve reasonable sensitivity despite its low effective area and ultimately led to COMPTEL’s unprecedented mapping of the MeV sky.

Modern Compton Telescopes COMPTEL’s double-scattering concept with large separated planes was a limiting factor for the FOV and measurable Compton-scattering angles and thus led to the low efficiency of the instrument. Additionally, COMPTEL was only able to measure two-site events, i.e., a single Compton scatter in D1 and a photoabsorption in D2. However, depending on the atomic number of the detector material, a photon can scatter multiple times before finally stopping in a photoabsorption event. Ideally, one would want to track the photon trajectory by measuring all secondary and tertiary (and beyond) interactions after the initial Compton scatter. While COMPTEL effectively measured interactions in two planes, most modern Compton telescopes are based around the design philosophy of building a 3D position-sensitive detector volume that acts both as the scatterer and absorber. With modern advancements in detector technology achieving (sub)millimeter spatial resolution, the efficiency and performance of Compton telescopes have significantly improved in the past few decades since COMPTEL’s development. Combining the scattering and absorbing detector capabilities without large separation allows for the detection of multiple Compton scatters with no geometric limitation on the scattering angle, as long as the detector volume contains the interactions. Both of these features increase the efficiency of the telescope and improve upon the polarization capabilities (discussed in sections “Dedicated Polarimeter” and “Polarization Capabilities”) compared to the classic Compton telescope design. An example of this is shown in Fig. 10, where a photon Compton scatters twice before fully depositing its energy with a photoelectric absoprtion event. All three interactions are measured within a large 3D position-sensitive detector volume, indicated by the blue area.

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Fig. 10 Most modern Compton telescopes use high position-resolution detectors with good energy resolution to measure the position and energy of multiple interactions, with no geometrical limit on the Compton-scattering angle. As in Fig. 8, the direction of the photon is determined by the Compton-scattering angle of the first interaction. (Modified from Kierans 2018)

For a three-site event, as in Fig. 10, the Compton-scattering angle of the first interaction can be determined in the same way as for two interactions; however, the total absorbed energy is now E0 = E1 + E2 + E3 , and the energy deposited after the second interaction must be accounted for in Escat in Equation 4: cos ϕ = 1 −

me c 2 me c 2 + . E2 + E3 E1 + E2 + E3

(16)

This formula can be scaled to a large number of interactions as long as the initial energy includes all energy deposits from the fully absorbed photon E0 = E1 + E2 + . . . + En , and the scattered photon energy is equal to the total deposited energy excluding E1 : Escat = E2 + . . . + En . The additional event pattern recognition achievable with these multi-scatter Compton telescopes enables sophisticated background-rejection techniques, as discussed further in section “Event Reconstruction”. After COMPTEL, there were multiple competing technologies that were trying to achieve the next-generation MeV telescope design with position-sensitive detectors (Kurfess et al. 2000). One such instrument developed in the 1990s was the Liquid Xenon Gamma-Ray Imaging Telescope (LXeGRIT) (Aprile et al. 2000a,b). LXeGRIT used a time-projection chamber (TPC) filled with liquid xenon to achieve the event-by-event Compton imaging within one large detector volume. Gammarays interact with xenon via ionization and a release of ultraviolet scintillation photons. When a high voltage is applied, the charges drift to the anode and cathode and allow for the total energy deposit to be recorded. The X-Y interaction location is measured by orthogonal sensing wires embedded in the liquid xenon, and the Z coordinate is determined via the drift time. The homogeneous detector volume allowed for a much more efficient design than the classic double-scattering Compton telescope. Similar techniques are used in other modern Compton telescopes SMILE (Tanimori et al. 2015; Takada et al. 2022) and GRAMS (Aramaki et al. 2020).

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The large instrumented detector volume realized by liquid or gaseous TPCs has its advantages but is generally limited in stopping power and energy resolution. Other instrument designs in the 1990s and early 2000s started employing semiconductor detectors, which have the advantage of superior energy resolution. However, it is not possible to fabricate or instrument arbitrarily large active volumes of semiconductors; the detection volume must be segmented into smaller detectors each with energy and internal position sensitivity. This was achieved in the early days through the use of the ubiquitous semiconductor silicon (Kamae et al. 1987). The telescope volume was broken up into thin planes of silicon with 2D resolution, where the Z-dimension of the interaction was defined as the location of the hit detector plane with no internal depth resolution. A multilayered design was developed by both the Medium Energy Gamma-ray Astronomy (MEGA) telescope (Bloser et al. 2002; Kanbach et al. 2005) and the Tracking and Imaging Gamma-Ray Telescope (TIGRE) (Tumer et al. 1994) and proven to be a viable detection technique for Compton telescopes. The added advantage of the thin silicon detector planes was the potential to measure the direction of the Comptonscattered electron in more than one of the silicon planes, which can then be used to further constrain the kinematics of the scatter, as will be discussed further in section “Electron-Tracking”. Other methods of building a 3D position-sensitive detector volume with good energy resolution have been explored since COMPTEL showed the power of Compton imaging. Scintillators, where the internal interaction position within a crystal can be inferred from the light intensity measured at the ends of long scintillating bars, have been used when energy resolution is not a priority, but a large effective area or stopping power is a driver. Semiconductor detectors, with their high spectral resolution, are ideal for Compton telescopes, since the better energy resolution provides a more accurate measure of the Compton-scattering angle ϕ. Other than the thin multilayer silicon detector approach, both germanium (Amman and Luke 2000; Coburn et al. 2003) and CZT (Xu 2006; Du et al. 2001; Lee et al. 2016) with a large form factor have been demonstrated. High-purity doublesided strip germanium detectors will be used in COSI (Tomsick 2022). With an individual crystal size of 8 × 8 × 1.5 cm3 , the total telescope consists of 16 tightly packed germanium crystals with independent readout. The COSI detectors achieve an internal position resolution of 1.5 mm3 : the X-Y position is determined by the charge collection on orthogonal strips, and the Z-dimension is determined from the charge collection timing (Amman and Luke 2000). Other semiconductorbased Compton telescopes are discussed in section “Notable Compton Telescope Designs”. As long as a precise measurement of the energy and 3D location of each interaction is achieved, the actual detector implementation for a Compton telescope can be quite diverse. A summary of three common configurations for modern Compton telescopes is shown in Fig. 11. The classic Compton telescope uses two detector planes, as demonstrated with COMPTEL. Alternatively, a large 3D position-sensitive volume can measure the position and energy of multiple Compton-scattering interactions, increasing the detection efficiency, as demon-

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Fig. 11 There are three common configurations for Compton telescopes. (a) The classic Compton telescope uses two detector planes as a scatterer and absorber to measure the interaction of doublescattering events. (b) The compact Compton telescope uses a single 3D position-sensitive volume to measure multiple Compton-scattering interactions. (c) The multilayer design uses many thin layers of detectors, with the added advantage of electron-tracking. (Modified from Yabu 2022)

strated with LXeGRIT. The third configuration achieves more precise energy and/or position information from each scatter using a detection volume segmented into multiple smaller position-sensitive detectors. One standard design uses thin detectors with 2D resolution, as demonstrated with MEGA. Due to the increased efficiency and smaller resolution elements, most modern Compton telescopes are compact in design. One important point to note is that compact designs no longer have time-of-flight capabilities to determine the temporal order of interactions. While there are still efforts to modernize time-of-flight Compton capabilities (Bloser et al. 2018), most modern Compton telescopes require an extra step for event reconstruction; the relative order of interactions can be determined by the Klein-Nishina cross section and by redundant information in the energy deposits and relative positions of the interactions. The process for determining the most probable sequence of interactions is referred to as Compton sequencing or event reconstruction and is discussed further in section “Event Reconstruction”.

Electron-Tracking In previous discussions, the direction of the incident gamma-ray has been restricted to the Compton event circle where the uncertainty in the azimuthal direction is due to a lack of knowledge of the Compton-scattered electron’s direction. Now, if the direction of the recoil electron is known, momentum conservation can further restrict the direction of each incident gamma-ray. With a more accurate determination of the origin of the gamma-ray, background rejection can be improved (Akyüz et al. 2004). The kinematics of the recoil electron from a Compton interaction can be calculated in an analogous way to the scattered photon as derived in section “Physics of Compton Scattering”. However, since the direction of the Compton-scattered electron Θ is less precise than the direction of the Compton-scattered photon due

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to a short penetration depth and Molièere scattering (Bethe 1953), it is preferable to define the additional kinematic constraint relative to the original photon event circle. With the recoil electron direction, the initial event circle can be reduced to a small segment, defined as the event arc. Figure 12 shows this concept, where a multilayer Compton telescope is used to measure energy deposited from the Compton-scattered electron through multiple detector layers. The length of the event arc is related to the uncertainty in the electron’s recoil direction. Figure 13 shows the backprojected Compton event circles in image space with and without electron-tracking; by using the recoil electron trajectory, the source position is easily discernible with fewer photons. It is important to note that electron-tracking is a powerful background reduction technique and allows for a more clearly defined point spread function in image space, but does not in general improve the angular resolution of a telescope due to the large uncertainties in the recoil electron direction. The details on how electron-tracking affects the point spread function of the instrument will be discussed in detail in section “Scatter Plane Distribution”. The TIGRE and MEGA groups were the first to demonstrate electron-tracking capabilities for Compton imaging; with multiple layers of thin silicon detectors, they were able to measure the momentum direction of the Compton-scattered electrons based on the ionization tracks through multiple silicon layers. Furthermore, electron-tracking Compton imaging has also been demonstrated in large gaseous time-projection chambers (Tanimori et al. 2004; Kabuki et al. 2007; Orito et al. 2005). Any telescope that is capable of detecting the track of the Compton-scattered electron also has the enhanced capability of being sensitive to pair-production events. As the gamma-ray energy increases and pair production becomes dominant,

Fig. 12 By measuring the direction of the Compton-scattered electron of the first interaction, the incident photon direction can be constrained within a reduced arc segment of the original Compton event circle. The measured recoil electron direction is depicted with blue dots representing energy deposits in multiple detector layers, and the length of the event arc is dictated by the precision of the electron trajectory measurement. (Modified from Brewer et al. 2021)

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Fig. 13 The back projection of event circles from untracked Compton events compared with tracked events highlights the benefit of the additional kinematic information. While the angular resolution does not change, the point source is more easily discernible, and background contamination can be significantly reduced. Therefore, electron-tracking can enhance the sensitivity of a telescope. (Figure from Mizumura et al. 2014). (a) Ten untracked Compton events. (b) Ten Compton events with electron-tracking

the direction and energy of incident gamma rays can be constrained by measuring the electron and positron trajectories to reconstruct the vertex and opening angle of the pair conversion. A combination electron-tracking Compton and pair telescope is an enticing technology that can span the majority of the MeV Gap with one telescope. This has been explored by a number of different telescope concepts, as discussed further in section “Notable Compton Telescope Designs”.

Dedicated Polarimeter There also exists a class of Compton telescopes that is not optimized for imaging, but for polarimetry. As Equation 12 shows, there is an asymmetry in the cross section for photons that scatter parallel and perpendicular to the initial photon’s electric field vector. This asymmetry, or the amplitude of the polarization response, is maximized when the sin2 ϕ term is maximized or at polar Compton-scattering angles ϕ = 90◦ . A polarized source will result in a sinusoidal distribution in the azimuthal scattering angle (η in Fig. 5). Therefore, instruments that measure the azimuthal scattering angle, especially at large Compton-scattering angles, can ultimately detect the polarization of a gamma-ray source. The simplest version of a Compton polarimeter is shown in Fig. 14a, where the initial photon is scattered in a central detector element and absorbed in a detector placed at 90◦ . If this secondary detector is rotated to sample the counts in the azimuthal (Fig. 14b), the direction and degree of polarization can be measured, as described in detail in section “Polarization Capabilities”.

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Fig. 14 (a) Photons will predominately scatter at 90◦ relative to their initial electric field vector, according to Equation 12. Therefore, a gamma-ray polarimeter can determine the degree of polarization of a source by measuring the azimuthal scattering direction η of photons. (Modified from Lei et al. 1997). (b) The azimuthal scattering direction for a polarized source gives a sinusoidal response, referred to as the ASAD (azimuthal scattering angle distribution), which is maximized at 90◦ relative to the direction of the initial electric field vector. (Modified from Bellm 2011)

Most dedicated polarimeters are compact in design to be sensitive to 90◦ Compton-scattering angles. As the azimuthal scatter distribution is sinusoidal, the distribution can be coarsely sampled without a significant loss of sensitivity. In addition, the measured energy resolution for dedicated polarimeters is not as crucial as for Imaging Compton Telescopes as the energy information is not used in the reconstruction (but can provide spectral information for the incoming photons). Therefore, most dedicated polarimeters take advantage of scintillator detectors, which are simpler than segmented semiconductor detectors used in most compact and multilayer Compton telescopes. An example of a dedicated polarimeter telescope is the LargE Area burst Polarimeter (LEAP) shown in Fig. 15. LEAP is a NASA Mission of Opportunity concept considered in the 2021 selection round and is similar to other Compton polarimeter designs. LEAP uses two different types of scintillators to measure the azimuthal scattering direction: a low-Z plastic scintillator is optimized for scattering and a high-Z scintillator optimized for absorption. The use of scintillators allows for a simple, high-efficiency, and large field-of-view design. However, without the high-resolution 3D position and energy information for each interaction, Compton imaging is not possible in dedicated polarimeter. These instruments are therefore optimized for transient detections when a large signal-to-background is available.

Event Reconstruction Event reconstruction for Compton telescopes is the process of translating the measured positions and energies of detected photon interactions to the initial gamma-ray direction defined by the event circle (or the event arc for electron-

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Fig. 15 The LargE Area burst Polarimeter (LEAP) telescope is a dedicated Compton polarimeter that measures the azimuthal scattering direction with scintillating bars. LEAP is compact by design, and even with fairly coarse position knowledge of each interaction the scatter vector can be used to precisely measure the polarization of incoming photons (Figure from McConnell et al. 2021)

tracking Compton telescopes). For classic Compton telescopes with a limit of two interactions and time-of-flight information to determine the temporal sequence of hits, event reconstruction is a fairly straightforward process. With the measured energy and Equation 4, the Compton-scattering angle of the first interaction can be determined, and the axis of the event circle can be defined from the measured positions (see Fig. 9a). As modern Compton telescopes become more compact and sophisticated, so too have the event reconstruction techniques. The timing resolution is not sufficient to determine the temporal sequence of interactions in compact Compton telescopes. Therefore, in order to determine the Compton event circle, one must first determine which energy deposits correspond to the first and second interactions for each gamma-ray. This is done by testing all N! combinations of the interactions for an event with N energy deposits and determining the most probable sequence. The process of event reconstruction for modern telescopes is computationally intensive; however, there are also significant benefits. The first is that with the added number of allowable interactions compared to a classic double-scattering Compton telescope, the efficiency of the instrument increases significantly. The average number of interactions depends on the photon energy and the detector material, but higher energy photons can often scatter >5 times in a detector before being photoabsorbed; sophisticated reconstruction techniques are needed to properly trace a high-energy gamma-ray path through a large detector volume. Second, and more importantly, the main advantage of event reconstruction is background rejection (Aprile et al. 1993; Boggs and Jean 2000). Events that have any missing energy, from incomplete absorption or interactions in passive material, or events associated with β + decays within the instrument are effectively background events,

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but with a filtering step in the reconstruction, these unusable events are rejected and the signal-to-background ratio increases. The first step of reconstruction is event identification, outlined in section “Event Identification and Track Recognition”, where it must be determined whether or not the measured energy deposits are consistent with a Compton-scattering event (or a charged-particle track or pair event) and, when applicable, whether there are measured electron tracks. Then the Compton sequence determination can be achieved by taking advantage of redundant information in the kinematics and geometrical information measured for each event. The standard approach is referred to as Compton Kinematic Discrimination (Boggs and Jean 2000), or mean squared difference method. This straightforward and fast sequence reconstruction technique is employed by various research groups and will be detailed in section “Compton Sequencing”. It is difficult to unambiguously determine the correct order for events which only have two interactions and no discernible temporal separation, and thus “Two-Site Event Reconstruction” will be considered separately.

Event Identification and Track Recognition Before determining the correct sequence of interactions for an event, one must characterize the measured energy deposits and determine if they are consistent with a Compton-scattering event, a pair event, a charged-particle track, or any other potential interaction. Telescopes that have tracking capabilities have more possible event types to identify and will be the basis of the presented approach, which follows Zoglauer (2005). Detectors without electron-tracking may use a simplified version of the steps listed below. Photons which interact with multiple Compton scatters within a detector volume leave separated, isolated energy deposits as shown in Fig. 10, i.e., there is no easily identifiable straight path or pattern. Therefore, it is easiest to first confirm if the measured interactions are consistent with event types that do have easily recognizable patterns (i.e., pair events or charged-particle tracks); if no clear pattern is found, then compatibility with Compton interactions can be checked. The general steps for event identification for a tracking Compton telescope are as follows: 1. 2. 3. 4.

Search for pair event vertex Search for high-energy charged-particle straight tracks Search for recoil electron tracks from Compton interactions Search for Compton interaction sequence

Pair events are recognizable by the characteristic inverted “V” from the electron and positron (i.e., the pair) ionization tracks in the detector volume. In a multilayer Compton telescope, as described in section “Modern Compton Telescopes”, the interactions from the electron and positron are measured after conversion in subsequent layers with increasing separation. If a vertex is found with a pattern recognition algorithm, the event can be flagged as a pair event, and the initial photon

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direction can be determined by the trajectory of each particle, weighted by their relative energies. Pair reconstruction is described in detail in Charles and Chiang (2021) and has been matured for the Fermi Large Area Telescope (Atwood et al. 2009). The second easily identifiable event type is the straight tracks left by high-energy charged particles, such as cosmic rays and muons. With linear ionization tracks, the reconstruction of high-energy charged particles is straightforward and can be accomplished by fitting a straight line to the measured energy deposits.

Recoil Electron Track Reconstruction The third step in event identification is to search for tracks left by Compton recoil electrons. In Compton scattering, when a photon interacts with an electron, it will transfer momentum in the scatter, causing the electron to be ejected from its atom and recoil. The recoil electron will then leave an ionization track in the detector material, and the length of the track is based on the initial electron momentum and the density of the material. The track lengths in high-Z materials, such as germanium, CdTe, and CZT, are too short to measure the direction of motion, and the full electron energy is deposited within one position-resolution element of the detector. For lower Z material, such as silicon, or the low densities found in gaseous time-projection chambers, the track length can be longer than a few millimeters and span multiple resolution elements. For example, in multilayer Compton telescopes consisting of thin 2D sensitive silicon detectors, the recoil electron can deposit energy in three to four layers with ∼1 cm spacing. There are two main purposes for electron track recognition in event reconstruction: the initial Compton-scattering interaction location is needed for Compton sequencing (section “Compton Sequencing”), and the direction of motion of the electron can be used to kinematically constrain the incoming photon direction (sections “Electron-Tracking” and “Scatter Plane Distribution”). Unfortunately, the initial interaction location and electron trajectory are not always easy to discern from the measured energy deposit as ionization tracks left by recoil electrons are rarely straight and often short, as seen in Fig. 16. The paths of recoil electrons can make U-shaped tracks, and with poor spatial resolution or coarse sampling in a multilayer Compton telescope, the discrete sampling of the energy deposits complicates the reconstruction. Higher energy electrons (1 MeV) will have long and initially straight tracks, but at lower energies, the track length decreases and the nonlinearity increases. There have been multiple approaches to the electron track reconstruction. The simplest version relies on the assumption that as the electron loses energy, it will tend to deposit more energy, as defined by the Bethe-Bloch equation and the Bragg peak (Particle Data Group et al. 2020). Therefore, the track end point with the smaller measured energy is more likely to be the beginning of the electron’s path. The electron track reconstruction has been performed using different algorithms: a figure-of-merit approach (Zoglauer 2005), Bayesian approach (Zoglauer 2005), momentum analysis (Black et al. 2007), and graph theory (Yoneda et al. 2018). Different approaches are used based on the relative spatial resolution of the track.

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Fig. 16 The measured recoil electron track from Plimley et al. (2011) shows the curving nature of the path and the complication of track reconstruction (see section “Scatter Plane Distribution”). This high spatial resolution measurement, with each pixel being 10.5 × 10.5 µm2 , is the first demonstration of a reconstructed recoil electron track within a 650 µm-thick silicon chargecoupled device (CCD). The deposited energy from the recoil electron is 227 keV. Based on the Bragg peak, the larger energy deposit on the bottom right is likely the end of the track

Measuring the electron-scatter direction allows one to further constrain the kinematics of the Compton-scattering interaction, reducing the photon direction from a back-projected circle to an arc. The precision of the electron recoil direction determines the length of the event arc. Since the precision of the electron’s direction is often much worse than that achieved through the measurements of the scattered photons, this additional kinematic information does not in general improve the angular resolution but can serve as a method to reduce the observational background. As described in section “Electron-Tracking” and shown in section “Physics of Compton Scattering”, the kinematics of the recoil electron can be treated in the same way as the scattered photon. Haefner et al. (2014) demonstrated that the source location can be determined entirely by the recoil electron without needing to measure the Compton-scattered photon, increasing the measurement efficiency. However, the angular resolution and sensitivity of this detection technique is limited. After pair and high-energy charged-particle events have been identified, and Compton recoil electron tracks have been reconstructed to determine the initial interaction position, the measured energy deposits can be tested for compatibility with Compton scattering. The process of determining the most probable sequence of interactions for a single photon is called Compton sequencing.

Compton Sequencing Compton event reconstruction starts with a collection of hits within the detector volume, each with energy and position information. With no prior knowledge or

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Fig. 17 In Compton Kinematic Discrimination, the Compton-scattering angle ϕl of a central interaction l is determined in two ways: kinematically with the energies E and geometrically with the scatter directions g. Minimizing the difference between these two measures for each Compton scatter leads to the most probable sequence of interactions. (Modified from Zoglauer 2005)

assumptions about the first interaction location, all N ! possible combinations of the hit order, where N is the number of interactions, must be analyzed. The first algorithm developed for kinematic event reconstruction was introduced by Aprile et al. (1993) and later formalized by Boggs and Jean (2000). It is referred to as Compton Kinematic Discrimination, the chi-squared approach, or mean squared difference method, and as it remains one of the more popular approaches for events with 3+ interactions, it will be described here. For gamma-ray events which have at least three interactions (two Compton scatters and one photoelectric absorption; see Fig. 17), the Compton-scattering angle of the central interaction(s), denoted by l, can be determined in two ways. The first is kinematically with the Compton equation: cos ϕlkin = 1 −

me c 2 me c 2 + , El+ El + El+

(17)

where El+ is the total energy of all interactions following l; El is not included in El+ . Second, the Compton-scattering angle can be determined geometrically considering the angles: geo

cos ϕl

=

gk · gl , |gk ||gl |

(18)

where gk is the incoming gamma-ray direction and gl is the outgoing direction for interaction l. The two measures of cos ϕl , from Equations 17 and 18, should be identical for the correct order of interactions in an ideal instrument. In the classic Compton Kinematic Discrimination approach, a χ 2 quality factor Q is assigned to each permutation of N interactions (Zoglauer 2005):

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Q=

N−1  i=2

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(cos ϕikin − cos ϕi )2

geo

(d cos ϕikin )2 + (d cos ϕi )2

,

(19)

where d cos ϕi are the uncertainties determined through error propagation and i is the interaction index. The sequence with the lowest quality factor is the best estimate of the correct kinematic ordering of the event. Another common method for Compton sequencing uses a deterministic approach based on the Klein-Nishina formula (Xu et al. 2004). Again, all N ! possible combinations of the interaction sequence must be checked, but the most probable sequence of energy deposits is based on the physics of the interaction. Recent work was done to improve upon the deterministic event reconstruction techniques by developing a more efficient probabilistic method that can account for escape gamma-ray events (Yoneda et al. 2021). For events with three interactions or more, it has been shown that the gamma-ray energy can be estimated even if the event is not fully absorbed (Kurfess et al. 2000; Tashenov and Gerl 2010). In real measurements, the reconstruction becomes more complicated due to the finite spectral and spatial resolution of the detectors, subthreshold interactions, and energy deposits in passive material. Any missing energy will result in a misreconstructed event, and the calculated event circle will not align with the initial photon direction (see section “Uncertainties in the Angular Resolution”). The level of accuracy for event reconstruction is therefore a very important performance parameter for Compton telescopes. The standard Compton Kinematic Reconstruction algorithm was initially found to properly reconstruct 50–70% of 3+ site events (Oberlack et al. 2000; Boggs and Jean 2000). The standard approach has been modified for improved efficiency by a number of groups, for example, by assuming the first interaction is the largest energy deposit, the sequencing performance improves by 20% for 1 MeV gamma-rays (Shy and He 2020). An evaluation of different Compton sequencing approaches can be found in Thrall et al. (2008) and Lee et al. (2021). More recently, advancements in machine learning approaches have shown promise for a much higher reconstruction efficiency (Zoglauer and Boggs 2007; Zoglauer et al. 2021; Cao et al. 2019). One of the main advantages of Compton sequencing is the capability to reject events which do not conform with the expected kinematics of Compton scattering. This is effectively a method of background rejection. Photons that do not deposit all of their energy in the active detector volume will not be properly reconstructed and are thus improperly imaged and contribute to the background during observations. By setting a maximum acceptable level for the quality of the event (e.g., given by Equation 19 for the classic Compton Kinematic Discrimination), any improperly reconstructed Compton event can be rejected. Likewise, pair-production or β-decay events in the instrument can be rejected with this approach. Only events that are statistically determined to be “good” Compton events are kept after Compton sequencing. The challenges of high backgrounds in Compton telescopes are addressed further in section “Background Radiation”.

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Two-Site Event Reconstruction For two-site events, with one Compton scatter followed by a photoelectric absorption, only a small fraction of events can be sequenced unambiguously (Boggs and Jean 2000). A simple comparison test, the Compton Edge Test (Xu 2006), can distinguish the order of some two-site events. We know that the maximum energy deposited in Compton scatter is from backscattering given by Equation 7; this energy defines the Compton edge in Fig. 3. It is therefore easy to compare the two measured energies with this relation, where E0 is the sum of the two energies. If either of the measured energies is larger than the maximum allowable energy of the Compton edge for the given E0 , then that interaction is necessarily a photoelectric absorption and must be the second interaction in the sequence. Another simple relation can be used if the initial photon energy is less than 256 keV (Lehner et al. 2004; Lee et al. 2021). As will be derived below, if E0  me c2 /2 is satisfied, the energy deposit in the first interaction, or in the Compton scatter ES , is deduced to be smaller than the energy deposited through photoelectric absorption in the absorber EA . With E0 = EA + ES , this can be derived starting again with the maximum energy of the first interaction defined by the Compton edge in Equation 7: ⎛

max(ES ) = Ee |ϕ=180◦ = E0 ⎝1 −

1 1+

2E0 me c2

⎞

⎠.

(20)

If 2E0 < me c2 , then max(ES ) < E0 /2,

(21)

and with E0 = EA + ES max(ES )
ϕ geo . The 3D CDS point spread function (Fig. 18) forms the basis for sensitive Compton telescope data analysis. Compared to the image space with overlapping

Fig. 19 (a) It can be illustrative to rotate the CDS coordinates so that the measurement of the scattering direction is made relative to the incident photon direction from a known source location (χ0 , ψ0 ). Then the scattering angles (χ, ψ) in the CDS equate to the geometrically measured polar Compton-scattering angle (ϕ geo ) and the azimuthal Compton-scattering angle (η), as defined in Fig. 5. (b) For on-axis sources, the point spread function in the CDS translates into a twodimensional plane at 45◦ . Modulation from a polarized source will result in a sinusoidal distribution along the ψ dimension

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Fig. 20 When the source position is known, projection of the CDS into two dimensions allows for a direct relation between the kinematically measured Compton-scattering angle (ϕ kin ) and the geometrically measured angle (ϕ geo ). Events that are properly reconstructed lie along the ϕ kin = ϕ geo line, where the spread is defined by uncertainties in the energy and position measurements. (a) A simulation of a 511 keV point source measured in a COSI-like instrument shows this 2D projection of the CDS point spread function. All of the events located off of the ϕ kin = ϕ geo line are improperly reconstructed, most often due to missing energy. (Modified from Kierans 2018). (b) The geometrically measured Compton-scattering angle is given by the angle between the initial photon direction g0 and the scattered gamma-ray direction g1 . The difference between the kinematic and geometric Compton-scattering angle gives the angular resolution measure (ARM), ∆ϕARM , for each event

Compton event circles causing source confusion, the CDS provides strong discriminating power and allows for a better separation of background and source emission regions (Zoglauer et al. 2021).

Angular Resolution Measure The angular resolution of a Compton telescope is given by the width of the CDS cone walls and is generally dominated by the uncertainty in the measured energy and position of interactions. The most common definition of the angular resolution is the full width at half maximum (FWHM) of the angular resolution measure (ARM) distribution, which is a one-dimensional projection of the CDS cone. The ARM for each event is defined as the minimum distance between the geometrically calculated Compton-scattering angle and the kinematically calculated Comptonscattering angle: ∆ϕARM = ϕ geo − ϕ kin .

(24)

The kinematic Compton-scattering angle is determined from the measured energy deposits using the Compton equation:

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Fig. 21 (a) The smallest angular distance between the known source location and each Compton event circle defines the ARM, ∆ϕARM . (b) A histogram of the ∆ϕARM values gives a onedimensional projection of the point spread function, and the FWHM of the ARM distribution defines the angular resolution of a Compton telescope. As an example, the histogram shown here is from a measurement of a far-field laboratory 511 keV source with the COSI balloon detector (Kierans et al. 2017) and has a 6◦ angular resolution

ϕ

kin



= arccos 1 − me c

2



1 Escat

1 − E0



(25)

with E0 being the total deposited energy, as detailed in section “Physics of Compton Scattering”. The geometrically determined Compton-scattering angle is found by taking the dot product of the initial photon direction g0 and the measured scattered gamma-ray direction g1 : ϕ

geo

g0 · g1 , = arccos |g0 ||g1 |

(26)

as defined in Fig. 20b. Note that this is similar to the redundant information used in Compton Kinematic Discrimination (Equations 17 and 18); however, here we must know the initial source location to define g0 . This definition of ∆ϕARM is equivalent to the shortest angular distance between the known source location and the Compton event circle in image space. This is depicted for three event circles in image space in Fig. 21a. The FWHM of the ARM distribution is the standard definition for the angular resolution. A histogram of the measured ∆ϕARM values from a COSI-like detector is shown in Fig. 21b. For an ideal detector, one expects a sharp feature at ∆ϕARM = 0 indicating that the event circle correctly overlaps the known source location. Measurement errors in the position and energy of interactions within the detector broaden this response. Events that are improperly reconstructed, often due to incomplete absorption, end up in the wings of this ARM distribution ∼50◦ . Sophisticated event reconstruction techniques, as discussed in section “Event Reconstruction”,

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and a selection on the quality of the Compton event can reduce the prominence of these off-ARM-peak events (Zoglauer 2005; Zoglauer et al. 2021).

Scatter Plane Distribution Compton telescopes that have electron-tracking allow for a more defined point spread function in image space, as shown in Fig. 13. By measuring the recoil electron trajectory from the first Compton interaction in a telescope, the standard event circle can be reduced to an arc. The measured direction of the recoil electron is less precise than the direction of the scattered gamma-ray (longer lever arm), and, therefore, the ARM is still used to describe the angular resolution of an electron-tracking Compton telescope. It is convenient to define the electron’s kinematics relative to the center of the photon cone defined by g1 , and this is commonly done in terms of the scatter plane deviation (SPD). The SPD describes the angle between the scattered plane defined by the known source location and the true scattered gamma-ray direction (g0 and g1 in Fig. 20b) and the measured scatter plane defined by the scattered gamma-ray direction and the recoil electron direction (e):

∆νSP D = arccos (g1 × g0 ) · (g1 × e) .

(27)

This is equivalent to the angular distance between the known source location and the calculated photon origin for each event circle, as depicted in Fig. 22. The SPD is a measure of the length of the Compton event arc. The Compton Data Space for a tracking telescope includes two more dimensions to describe the recoil electron direction. While a 5+-dimensional data space can be used for the most accurate Compton telescope analysis with enough computation resources, it is currently more common for the SPD to be used as an event selection in list-mode imaging approaches (see section “Imaging Capabilities”). By only using events with a small SPD, the photon direction can be more precisely constrained, and the image-space representation of the source is much more defined. In the presence of background, a selection on the SPD for each gamma-ray event significantly reduces the number of background photons that overlap with the source region, increasing the sensitivity of the telescope.

Fig. 22 The SPD ∆νSP D is defined as the angular distance between the known source location (yellow star) and the measured origin from the scattered electron and gamma-ray kinematics. (Adapted from Zoglauer 2005)

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Electron-tracking capabilities have been achieved in both gaseous and solid-state detectors. The low density in gaseous TPCs allows for the recoil electron to subtend a few centimeters in the detector volume and thus can result in a fairly accurate measure of the initial scattering direction. The SMILE-II instrument demonstrated a FWHM of measured SPDs ∼ 75◦ for events from a 137 Cs source that transferred more than 80 keV to the recoil electron (Tanimori et al. 2015). However, low-density gaseous TPCs require a large detector size and are limited in terms of the energy resolution, which in turn limits the angular resolution. Semiconductor detectors have advantages with high density and high spectral resolution; however, the path length for recoil electrons is generally much shorter. The recoil electron direction can be measured in multilayer silicon Compton telescopes (O’Neill et al. 2003; Kanbach et al. 2005), but the effects of Molière scattering are a limitation; Kanbach et al. (2005) achieved a SPD FWHM of ∼80◦ for a 88 Y source. To more precisely measure the recoil electron direction in silicon, the detector requires a spatial resolution around 10 µm. Track reconstruction within a single solid-state detector layer was first demonstrated for charge-coupled devices (CCDs) with 10.5 × 10.5 µm2 pixel size (Vetter et al. 2011; Plimley et al. 2011); see Fig. 16. More recently, a hybrid detector with complementary metal oxide semiconductor (CMOS) 20 µm pitch readout on one side of a 500 µm-thick silicon wafer, and strip electrodes on the other side, was developed to achieve high spatial resolution tracking information, improved energy resolution, and µs timing information (Yoneda et al. 2018; Yabu 2022).

Uncertainties in the Angular Resolution The angular uncertainty for each event can be determined from the uncertainties in the measured energies, which contribute to the Compton-scattering angle calculation, and the uncertainties in the measured positions of the first two interactions, which determine the axis of the event circle (von Ballmoos et al. 1989). While there is a fundamental limit to the angular resolution of Compton telescopes (see section “Doppler Broadening as a Lower Limit to the Angular Resolution”), in most modern designs, the dominant factor is usually either the position resolution or energy resolution of the detectors for gamma-rays above a few hundred keV. It can be seen from Equation 4 that the measured energy of each interaction plays a role in calculating the Compton-scattering angle for each event and thus is a defining factor for the ARM. The precision with which the energy can be measured, i.e., the energy resolution, depends on the detector properties and readout electronics. A propagation of energy measurement errors for Equation 4 gives the following error on the Compton-scattering angle (Zoglauer 2005; Lehner et al. 2004):

dϕ

kin

E0 = sin ϕ



1 2 Escat

1 − (Ee + Escat )2

2

2 + dEscat

1 dE 2 (Ee + Escat )4 e

(28)

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where E0 is the initial photon energy, dEscat is the uncertainty in the Comptonscattered photon energy, and dEe is the uncertainty in the recoil electron energy, using the same notation in section “Physics of Compton Scattering”. For events with more than two interactions, dEscat will include the measured energy error from each additional interaction added in quadrature. This relation is shown in Fig. 23 where the initial photon energy is assumed to be 2 MeV, and the two different contributions, dEscat and dEe , are plotted separately for set errors of ∆E/E = 0.5%, 2%, 5%, and 10%. The angular resolution is significantly impacted by a poor energy measurement of the scattered gamma-ray, especially at higher Compton-scattering angles. It is clear that to achieve an angular resolution ∼1◦ , the energy resolution of the detector must be 1 − 2%, and by selecting only events which have a smaller Compton-scattering angle, the angular resolution can be improved. The uncertainty in the position measurements for the first two interactions translates to an error in the axis of the Compton circle. When the distance between these two interactions is small, this effect becomes more pronounced. For example, for interactions that are 0.5 cm apart, a spatial resolution of 1 mm results in a significant error on the scattering direction compared to events that are separated by >1 cm. The size of this effect can be simply estimated as dϕ geo  tan( dx D ), where dx is the spatial resolution and D is the distance between interactions. For a 1 mm spatial resolution, the potential angular deviation is as much as 11◦ for a separation of 0.5 cm and only 6◦ at separation of 1 cm. This is only an approximation and likely an upper limit since there is a higher probability of interacting near the center of a spatial resolution element than near the corner when the scattering direction is offaxis (Lehner et al. 2004). For a detailed calculation of the angular uncertainty from

Fig. 23 The error in the angular resolution is affected by both the uncertainty in the measured energy of the scattered gamma-ray and the recoil electron. These are plotted separately assuming a fraction error: the solid lines show the error in the angular resolution from only the error from the scattered gamma-ray energy of ∆E/Escat = 0.5%, 2%, 5%, and 10% of Eg , given by Equation 28. The dashed lines show the contribution from the uncertainty in the recoil electron energy with the same fractional error. The total photon energy was assumed to be 2 MeV. (Adapted from Zoglauer 2005)

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the detector position resolution considering different resolutions in each dimension, see Xu (2006), Takeda (2009), and Xu et al. (2004). In general, the uncertainty in the angular resolution from the error in the position measurements is more pronounced at lower energies since these events will have a smaller distance between the first and second interactions. The total angular uncertainty is given by a sum of the squares of the two independent components: dϕtotal =

 (dϕ kin )2 + (dϕ geo )2 .

(29)

As an example of how the different contributions affect the angular resolution of a telescope, Fig. 24 shows the measured and simulated FWHM of the ARM distribution for a balloon-borne silicon and cadmium telluride Compton telescope (Takeda et al. 2007). The simulated response is broken down into the three main contributing factors: the energy resolution, position resolution, and Doppler broadening (section “Doppler Broadening as a Lower Limit to the Angular Resolution”). The angular resolution is dominated by uncertainties in the energy 100 MeV in the pair regime, depending

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Fig. 35 (a) The POLAR instrument consisted of 25 modules, each with an array of 8 × 8 plastic scintillating bars. With each scintillator being 5.8×5.8×176 mm3 , the total instrument volume was segmented into 2034 bars individually read out through a multi-anode photomultiplier (MAPM) to determine the azimuthal Compton-scattering angle. (Figure from Suarez Garcia 2010). (b) POLAR operated on the Chinese space laboratory Tiangong-2 for 6 months and detected 55 GRBs, where 14 bursts had enough statistics to constrain the polarization fraction, as shown here. (Modified from Kole et al. 2020)

on the size of the instrument. Typically, combined Compton and pair-creation telescopes are designed with two separate detectors: a tracker, in which the initial Compton scatter or pair conversion takes place, and a large, high-Z calorimeter, which absorbs and measures the energy of the Compton-scattered photons and pairproduction components. This concept is shown in Fig. 36. To contain the events and provide enough volume for efficient tracking, these instruments are generally the largest scale of Compton telescope, and combined with the broad energy range, these instruments aim to bring the general capabilities of the Large Area Telescope on Fermi (Atwood et al. 2009) into the MeV range. The first Compton telescopes of this design were pursued in the latter 1990s and early 2000s. Using a similar design TIGRE (Tumer et al. 1994; O’Neill et al. 2003) and MEGA (Bloser et al. 2002; Kanbach et al. 2005) demonstrated the electrontracking and pair capabilities of a multilayer Compton telescope. While MEGA was never flown, the significant laboratory and beam calibrations (Andritschke et al. 2004; Zoglauer 2005), and accompanying software (Zoglauer et al. 2006), have built a solid foundation for future missions. Similar designs with modern advancements are still being explored (De Angelis et al. 2018, 2021; McEnery et al. 2019; Fleischhack 2021).

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Fig. 36 Schematic of a combined Compton and pair-creation telescope. A multilayer tracker and thick calorimeter together detect and characterize Compton and pair events over a large energy range from ∼0.1 to 100 MeV. (Figure from Kanbach et al. 2005)

Medium Energy Gamma-Ray Astronomy Telescope The Medium Energy Gamma-ray Astronomy (MEGA) Telescope prototype was built at the Max Planck Institute for Extraterrestrial Physics (MPE) in Garching, Germany. The prototype detector, described in detail in Kanbach et al. (2005), is shown in Fig. 37. The instrument was built with 11 layers of double-sided silicon strip detectors (DSSD), arranged in 3 × 3 arrays of 500 µm-thick silicon wafers, each 6 × 6 cm2 in size with 470 µm strip pitch. The pixelated calorimeter consisted of 20 modules each with an array of 10 × 12 CsI(Tl) bars (Schopper et al. 2000): the bottom calorimeter was 8 cm thick, and the side calorimeters were either 4 or 2 cm. The CsI bars were read out with silicon PIN diodes. Beyond the significant technology maturation with MEGA which serves as a proof of concept for larger modern missions (Andritschke et al. 2004), the lasting legacy of the MEGA prototype work is in the Medium Energy Gamma-ray Astronomy library (MEGAlib) toolkit (Zoglauer et al. 2006, 2011; Zoglauer and Boggs 2013). MEGAlib was developed for MEGA and has become the state-of-theart simulation and analysis software for Compton telescope development around the world (Zoglauer et al. 2006).

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Fig. 37 The MEGA prototype consisted of a tracker with 11 layers of 3 × 3 arrays of double-sided silicon strip detectors surrounded on the sides and the bottom with CsI calorimeter modules. The MEGA prototype was extensively tested and calibrated, but never flown. (Image from Bloser et al. 2002)

Applications in Other Fields While astrophysical telescopes detect gamma-rays from distant celestial objects, accelerator experiments, medical imaging, and nuclear nonproliferation and environmental monitoring require imaging targets in the near field. Compton imagers, referred to often as Compton cameras for near field and terrestrial applications, provide a wide FOV, high detection efficiency, and the potential for real-time imaging. Compton cameras were first pursued in these other fields at the same time as early Compton telescopes were being developed for astrophysics. One prevalent application for Compton cameras is environmental monitoring and nuclear nonproliferation. A recent example of the power of Compton cameras was the environmental monitoring of radioactive contaminants after the March 2011 Fukushima nuclear power plant accident. Dust containing radioactive materials dispersed throughout the Fukushima Prefecture and gamma-rays emitted through the decay of unstable nuclei gave a way to find contaminated regions. A silicon cadmium telluride (Si/CdTe) Compton camera referred to as the “Ultra-Wide-Angle Compton Camera” was used to image the distribution of radioactive substances in the Fukushima area (Takahashi et al. 2012), where the radiation level ranged from 1 to ∼30 µSv/h. The camera consisted of 2 layers of double-sided strip silicon detectors (DSSDs) and 3 layers of CdTe double-sided strip detectors (CdTe-DSDs), each with a detector area of 3.2 × 3.2 cm2 and a strip pitch of 250 µm. With an energy resolution of 2.2% FWHM at 662 keV, and a wide FOV corresponding to 2π steradian (180◦ × 180◦ ), the Ultra-Wide-Angle Compton Camera was sensitive to nuclear line emissions across a large area. The camera had an angular resolution of 3.8◦ FWHM in the energy range from 500 to 800 keV, which gave the camera the ability to localize radioactive hot spots to areas ∼100 cm2 at a distance of 10 m (Takeda et al. 2015). Other Compton cameras also contributed to radiation monitoring in Fukushima (Vetter et al. 2018; Tomono et al. 2017; Sato et al. 2019).

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Similar to the instrumentation for astrophysical Compton telescopes, the designs of telescopes for environmental monitoring are diverse (e.g., Iltis et al. 2018; Watanabe et al. 2018). Recent techniques have been developed to increase the size of high-quality CZT crystals, resulting in 3D position-sensitive detectors with a thickness over 1 cm and a volume of several cm3 (Shy and He 2020; Lee et al. 2021). By using the ratio of the charge collected on the anode and cathode electrodes, the depth of the interaction can be calculated in pixel coordinates. Even in the case of multiple interactions in a single detector volume, it is possible to obtain three-dimensional position and energy information at each interaction site. CZT is a promising candidate for Compton cameras for radiation monitoring due to its high detection efficiency and excellent energy resolution without the complication of cooling (Xu et al. 2004). Compton cameras are also being used in nuclear medicine to image radioactive tracers used for positron emission tomography (PET) and single-photon emission computed tomography (SPECT) scans (Tumer et al. 1994; Kabuki et al. 2007; Yabu et al. 2021; Chen et al. 2018; H. and G. 2021; Frandes et al. 2010; Mochizuki et al. 2019). SPECT relies on a pin-hole or parallel-hole collimator and becomes less efficient for energies above a few hundred keV because those collimators become transparent. Compton cameras are expected to advance medical imaging technology of radioactive tracers due to their increased efficiency and relatively precise imaging capabilities. Figure 38 shows the Compton image of a patient after administering technetium99m dimercaptosuccinic acid (99m Tc-DMSA), commonly used in the field of nuclear medicine, measured with a silicon cadmium telluride Compton camera. The concentration of the emission is consistent with the left and right kidneys, as expected (Nakano et al. 2020). The range of technology developments is seen through various types of Compton cameras emerging for small animal in vivo imaging (Takeda et al. 2012; Motomura et al. 2013; Suzuki et al. 2013; Kishimoto et al. 2017). In addition to high sensitivity, which minimizes the radiation dose in

Fig. 38 The Compton image of a human torso after the administration of 99m Tc-DMSA is shown in color contours. Overlaid on a computerized tomography (CT) image, these concentrations are consistent, as expected, with the left and right kidneys outlined in red and green. (Figure from Nakano et al. 2020)

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the body, a practical application in medicine requires accurate estimation of the distribution of radionuclides in the body which is achievable through Compton imaging.

Conclusions The MeV range is ripe with scientific potential but remains relatively unexplored. Due to the low interaction cross section, unavoidably high-background radiation, and the inherent difficulties with Compton imaging, progress has been slower than the neighboring energy bands. COMPTEL pioneered Compton imaging in the 1990s and set a baseline performance for the next-generation telescope to exceed. The Hitomi/SGD was the second Compton imaging telescope to be launched. Sensitive in the range of 60 to 600 keV, SGD would have provided crucial observations in the soft gamma-ray energy range, but unfortunately, issues with the spacecraft cut the mission short in 2016 and only allowed for a few days of nominal science observations. The dedicated polarimeter POLAR mission was also cut short but was able to produce a catalog of GRB polarization measurements from its 6 months of observing in 2016–2017. Looking forward, Compton telescopes again have a chance to make significant progress in the low MeV range with the launch of POLAR-2 in 2024 and COSI in 2027. POLAR-2 is expected to provide strong constraints on the measured polarization for many more GRBs. COSI will perform a sensitive all-sky survey of the 0.2–5 MeV sky, with a particular focus on sources of gamma-ray line emissions. Despite all of this progress, the COMPTEL’s sensitivity has yet to be exceeded by an order of magnitude, and there have been no further observations from ∼5 to 30 MeV after CGRO’s termination in 2000. The high observational backgrounds are one of the biggest challenges in Compton imaging. Activation from interactions of charged particles in the detector and spacecraft presents a challenging, and so far unavoidable, background component. The effects of activation can be reduced by minimizing the amount of passive material around the active detector volume and avoiding high-Z materials in the instrument design. Furthermore, a low-inclination (10 MeV. The fine (∼1 keV FWHM) X-ray energy resolution of these detectors allowed accurate measurement of the exponentially falling thermal bremsstrahlung spectra and power-law nonthermal spectra that can be as flat as ε−2 or as steep as ε−10 . The ∼2 to 5 keV gamma-ray energy resolution allows all of the nuclear lines, except for the intrinsically narrow neutron capture line at 2.223 MeV, to be fully resolved and line shapes to be determined. Thicker tungsten grids for two of the coarser collimators with angular resolutions of 35 and 183 arcsec allow for modulation at the highest energies and have enabled RHESSI to make the first ever gamma-ray imaging in the neutron capture line (Hurford et al. 2006) shown in Fig. 16.

Single-Grid Imaging Systems Generalities Detector technologies continue to improve such that the location of where an X-ray or gamma-ray photon first interacts in the detector plane can be determined with a spatial resolution comparable to the size of the grid slits or slats in a bi-grid system.

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Such a sophisticated detector plane can be utilized to modify a bi-grid system into a single-grid system by obviating the need for a rear grid. The resulting single-grid system continues to leverage the principles of bi-grid imaging but with twice the photon throughput compared to the analogous bi-grid system (i.e., ∼50% versus ∼25%). Furthermore, the modulation shape is now square-wave rather than quasitriangular, which increases the signal-to-noise ratio. For a grid with a uniform pitch and held at a fixed orientation relative to the detector, as nominal for a bi-grid collimator, the detector would need to provide spatial information in only 1D (perpendicular to the grid slats). In practice, detectors are commonly able to provide spatial information in 2D, which can be leveraged for further enhancements relative to bi-grid approaches. First, the grid can be of a more complex design, such as having multiple pitches distributed in zones. Second, for approaches based on modulation via rotating, only the single grid needs to be rotated, and the detector plane can stay fixed in orientation. The finest half-pitch of the grid cannot be smaller than the location resolution of the detector, and thus the achievable angular resolution for imaging is dependent on the wavelength of interest and the detector technology. At X-ray energies, the pixels of modern pixelated solid-state detectors can be large enough (hundreds of microns) to fully absorb an X-ray in a single pixel, yet still fine enough to be matched with a fine grid for high-resolution imaging. However, at gamma-ray energies, each incident photon can undergo a sequence of interactions due to Compton scattering and pair production, and the spatial separation between partial energy depositions can be on the order of centimeters. Thus, to achieve fine location resolution for where the gamma-ray first interacted with the detector, the detector needs to be able to determine which of the partial energy depositions occurred first. Otherwise, the location resolution of the detector will not be better than the spatial extents of the gamma-ray scatter tracks.

Rotating Modulator (RM) The rotating modulator (RM), as originally proposed by Durouchoux et al. (1983) as the single-grid analogue of a bi-grid RMC, consists of a uniform-pitch grid rotating in front of a fixed array of identical detectors (Fig. 17). The location of where a photon interacted in the detector plane is determined simply through which detector absorbed the photon, with the individual detectors not providing any further location information. Accordingly, each detector must be large enough to fully absorb the most energetic photons of interest. At gammaray energies, this requirement means that the size scale of the detector, and correspondingly the location resolution of the detector plane, is no smaller than a few centimeters. For a compact gamma-ray instrument, the achievable imaging angular resolution is thus, at best, on the order of 1◦ . Nearly three decades later, Louisiana State University built a laboratory prototype RM shown in Fig. 18 called the Lanthanum Bromide-based Rotating Aperture Telescope (LaBRAT; Budden 2011). The detector plane consisted of 19 cylindrical scintillators, each 3.8 cm in diameter. The rotating grid consisted of lead slats with

51 Grid-Based Imaging of X-rays and Gamma Rays with High Angular Resolution Fig. 17 Illustration of the design for an RM instrument. A rotating grid of coarse slats with a uniform pitch is situated in front of an array of detectors. The location resolution on the detector plane is achieved by knowing which detector absorbed the photon. (From Durouchoux et al. 1983)

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INCIDENT PHOTONS θ ROTATION AXIS

ROTATING MODULATOR

DETECTOR PLANE

a uniform pitch of 7.6 cm, and was situated 1.16 m in front of the detector plane. Thus, the nominal angular resolution was ∼2◦ . Testing with LaBRAT demonstrated the RM imaging concept, and the developed image-reconstruction technique had success with resolving sources below ∼1◦ . As with a bi-grid collimator with a uniform pitch, a given RM is suited for a single angular scale. Although the RM could in principle have multiple grid pitches, the practical size of the grid combined with the required coarse grid pitches limits the number of grid slats. Imaging across a wide range of angular scales would likely require multiple RMs in parallel, spanning a range of grid pitches, especially if good sidelobe response is required. Even so, the limit of ∼1◦ imaging angular resolution is not adequate for purposes such as solar observations, which desire an angular resolution at least as fine as a few arcseconds.

Multi-Pitch Rotating Modulator (MPRM) A multi-pitch rotating modulator (MPRM) has been built as part of the GammaRay Imager/Polarimeter for Solar flares (GRIPS, Duncan et al. 2016) balloon instrument, which had its first Antarctic flight in 2016. The key enabling technology of the MRPM is a detector plane with very high location resolution. GRIPS utilizes 3D position-sensitive germanium detectors to localize individual energy depositions to 0.5 mm (Fig. 19). Each GRIPS detector is of planar

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Fig. 18 Photo of the LaBRAT laboratory prototype RM. The rotating grid (left in photo) consisted of lead slats at a uniform pitch, and the detector plane (right in photo) consisted of 19 cylindrical scintillators. The location resolution of the detector plane is achieved by knowing which detector absorbed the photon. (Reproduced from Budden (2011) with permission from B. Budden)

geometry (7.5×7.5×1.5 cm), with fine-pitch strip contacts on the cathode face and orthogonally oriented fine-pitch strip contacts on the anode face. An energy deposition in the detector is located in 2D by noting which cathode strip and which anode strip measure the pulse of charge, and is further located in the third dimension by measuring the time difference between the cathode pulse and the anode pulse. It is then possible to separately measure the 3D location of each of the individual energy depositions as a gamma-ray Compton scatters through one or more detectors. Using Compton-scatter kinematics, the initial energy deposition can then be determined. With ∼2 orders of magnitude better location resolution than possible with an array of single detectors, the MPRM can achieve high imaging angular resolution and span a wide range of angular scales simultaneously. The GRIPS MPRM is composed of bundles of slats with pitches ranging quasicontinuously from 1 to 13 mm (Fig. 20). To support imaging up to ∼10 MeV, the slats are made of a tungsten-copper alloy with a depth of 2.5 cm. Each bundle of slats uses spacers to hold the slats at the correct pitch, and the bundles are held at their ends by the frame. With a grid-detector separation of 8 m, the imaged angular scales range from 12.5 to 162.5 arcsec FWHM. Measuring 13 different angular scales simultaneously results in the excellent sidelobe response as summarized in the “Conclusions” Section. For a given source direction, a given location on the detector is modulated by a grid pitch and grid orientation that varies over time. Figure 21 displays an example

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Fig. 19 Photo of a GRIPS 3D-position-sensitive germanium detector. The detector dimensions are 7.5 × 7.5 × 1.5 cm, and the visible face shows the strip contacts with a pitch of 0.5 mm. The reverse face (not shown) has strip contacts with the same pitch, but oriented in the perpendicular direction (i.e., approximately horizontal in this photo) Fig. 20 Photo of part of the GRIPS MPRM, showing the variety of grid pitches from 1 mm to 13 mm. The slats are made of tungsten-copper alloy with a depth of 2.5 cm.

back projection from a point source. The image is formed by adding successive probability maps from each captured photon.

Comparison with Coded-Aperture Imaging Modulation-based imaging via a single, complex grid in front of a position-sensitive detector plane has strong similarities to coded-aperture imaging (see ⊲ Chap. 48 in this volume on “Coded Mask Instruments for Gamma-Ray Astronomy”). In both

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Fig. 21 GRIPS back projection of a point source, showing the superposition of successive probability maps of source location. No image deconvolution was applied

cases, the detector plane needs to provide position information that is at least as good as the smallest feature size of the grid/mask, which is set by the desired minimum imageable angular scale. An initial image of the source can be generated by combining the back projections of each photon to the sky based on the transparent parts of the grid/mask. As is typical with indirect imaging, both have limited imaging dynamic range because a bright source in the field of view contributes to the statistical noise of every pixel across the detector plane. We compare the MPRM with the uniformly redundant array (URA), which is a common form of coded-aperture imaging. Both imaging approaches exhibit very good sidelobe response. The obvious drawback of the MPRM is that it requires the grid to be rotating, and the rotation half-period sets the minimum timescale for producing an image. The URA is preferred when imaging on short timescales is needed, or in implementations where it is not tenable to rotate either the mask alone or the instrument as a whole. An alternative to the MPRM would be a single-grid system with a nonrotating multi-pitch grid that is the analogue of a bi-grid fixed collimator, but then the discretization of measured orientations results in less clean sidelobe response. Unlike typical applications of URAs for astrophysical observations, highresolution imaging at gamma-ray energies requires the thickness of the grid/mask to be ∼1 − 2 orders of magnitude greater than the feature size of the grid/mask. The MPRM can be straightforwardly constructed by stacking slats that can be supported at the ends. In contrast, the URA is not inherently self-supporting, so modifications to the design are needed to be able to support such a large aspect ratio for the features. If the necessary mechanical support results in attenuation or scattering in the energy range of interest, the performance of the URA will be degraded.

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In addition, the 1D-like construction of the MRPM lends itself to simpler and less time-consuming characterization and calibration than the 2D URA. The angular scales of the MPRM are also segregated into the individual bundles, as opposed to being highly multiplexed together as in the URA, which allows for straightforward propagation of how fabrication tolerances affect imaging performance. With respect to producing images, image reconstruction for the MPRM is a laborious process of back projection and deconvolution and/or applying forwardfitting image reconstruction techniques. In contrast, image reconstruction for the URA is computationally straightforward because the illumination pattern on the detector plane can, in principle, be “decoded” by a matrix multiplication. That said, for compact sources, it is possible to extract individual visibilities from just the event list of an MPRM and perform visibility-based analysis, which would not be possible for a URA. Finally, an important consideration of single-grid imaging is that nonuniform detector background can distort images. The MPRM inherently enables nonuniform detector background to be characterized because each detector pixel is varied rapidly between exposed and not exposed. The URA nominally requires a dark exposure (i.e., looking away from the source) or an inverse exposure (i.e., with an antimask). One could rotate the URA to obtain the benefits of time modulation, but then that would remove one of the key advantages of the URA: not having to rotate. The MRPM and the URA are both powerful indirect-imaging approaches that can take full advantage of the latest in detector technologies. The choice of one over the other will be driven by the above considerations.

General Grid System Design Initial (“Optical”) design The optical design is almost purely geometric. Most of the steps are common to all grid-based imaging systems: 1. Start with opaque and thin slat assumptions. 2. Angular scales are given by p/2L, where p is the grid pitch and L the grid separation. Select the minimum grid pitches to define the instrument’s best angular resolution and the maximum grid pitches to define the spatial scales beyond which the source will not be properly imaged. 3. Distribute pitches between the two extremes to achieve the desired main-lobe and sidelobe response (uv-plane distribution). When dealing with arrays of collimators each of uniform pitch (e.g., RHESSI, STIX, etc.), the weighting can be easily done in software after the observation. 4. Select desired slat thickness. The slats have to be thick enough to be opaque to the incoming radiation. This results in a limited FWHM field of view of ∼p/2t, where t is the slat thickness, and a varying slit-to-pitch ratio, s/p, across the field

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Fig. 22 Diffraction limit on the possible FWHM angular resolution (θD ) for bi-grid imaging as functions of the X-ray energy (E) and grid-to-grid separation, calculated under the Rayleigh criterion for a single slit. (From Prince et al. 1988)

of view. For the six finest RHESSI grids, the effective s/p ratio varied from ∼60% to ∼40% across solar disk, due to shadowing by the finite depth (thickness along optical axis) of the slats (Fig. 6). This was taken into account during imaging reconstruction. The modulation efficiency (a full discussion of which is beyond the scope of this chapter) is diminished by both partial grid opacity and when s/p does not equal 1/2. The performance of any collimator or mask system is subject to two physical limitations. The first limitation is purely geometrical and is set by a combination of three factors. Specifically, the minimum thickness of the grid is determined by the requirement that the grid be opaque at the maximum energy of interest. This thickness constrains the FOV to an angle given by the ratio of slit width to grid thickness. The slit width in turn is closely tied to the angular resolution (1/2 slit pitch/grid separation). For a collimator of a given length (i.e., grid separation), this combination of factors imposes an unavoidable physics-driven trade-off among angular resolution, FOV, and maximum energy. The second limitation is diffraction. This sets a lower limit to the energy range since at lower energies the front grid can function as a diffraction grating. This is discussed in Section “Diffraction” with the ultimate limitation on the angular resolution that can be achieved shown in Fig. 22 as functions of energy and grid separation. Both of these limitations can be relevant in practice. For example, RHESSI’s angular resolution above ∼1 MeV is limited to 35 arcsec by a requirement that it maintain a 1◦ FOV. With a 1.55-m-long collimator, RHESSI is also prevented from achieving 2.3 arcsec resolution below 4 keV by diffraction.

Diffraction When the wavelength of observations becomes large and the Fresnel number F = s 2 /Lλ becomes 1 (where s is the slit width and L the grid separation), Fresnel diffraction seriously perturbs the geometric optics assumption (λ = 0) that

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Fig. 23 Diffraction “carpet” at 10 keV for the RHESSI finest grid (pitch = 34 microns), assuming an infinite number of slits. The horizontal dashed line corresponds to the 1.55 m distance between the RHESSI front and rear grids. (a) Linear scale. (b) Logarithmic scale

is typically used when computing grid responses. The single-slit Fresnel √ number criterion is akin to constraining the size of the first Fresnel zone ∼ λ/L to be smaller than the angular extent of a slit s/L as seen from the opposite grid. The latter typically corresponds to the angular resolution of the collimator. This consideration leads to the best angular resolution that can be achieved as a function of photon energy and grid separation displayed in Fig. 22. In the diffraction regime, Lindsey (1978) explains in detail the computation of diffraction patterns from one or more grids composed of an infinite series of equally spaced slits (Fig. 23), and Crannell et al. (1991) give the following simplified formula for the factor, D, to multiply the modulation amplitude of a bigrid collimator to account for diffraction: D = cos(π Lh2 λ/p2 ), where L is the grid separation, p is the grid pitch, h is the harmonic number (1, 2, or 3), and λ is the X-ray photon wavelength. As indicated by the periodicity in this formula, the diffraction pattern indeed repeats itself up to a certain distance where, due to the fact that the grid is not infinite in size, the waves from each slit become isophasic, and the pattern becomes that of a classical grating in the far-field. The transition from one regime to the other occurs at a distance of ∼g 2 /2λ (where g is the overall grid size), and each regime is well established an order of magnitude below or above that value.

Grid Manufacture The minimum grating pitch, together with the requirement that the grating be thick enough to stop photons in the desired energy range, drives the choice of manufacturing technique and the material to be used. As a result, several technologies have been used to fabricate the grid or mask “optics” of collimator systems. For coarser grids, mechanical assembly of conventionally machined parts is the typical choice. At intermediate pitches, down to ∼1 mm, electron discharge machining is a viable option (e.g., Crannell et al. 1991). For finer grids, stacking of thin photo-etched foils as shown in Fig. 24 has been used for RHESSI (Lin et al. 2002) and for STIX (Krucker et al. 2020) to achieve pitches as fine as 35 µ m in

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Fig. 24 Grid fabrication techniques. Left: Schematic illustration of stacking photo-etched layers to achieve a thick grid with fine slits. Right: RHESSI 9-cm-diameter, 1-mm-thick grid whose slits have a 35 µ m period and a field of view of ∼1◦ in a plane perpendicular to the slits and >20◦ perpendicular to the slits. (From Lin et al. 2002)

1-mm-thick tungsten. Finer grids cannot be made with this technique because the smallest features that can be produced by chemical etching are of a similar size to the foil thickness and there is a limit to the availability of thinner tungsten foils. Lastufka et al. (2020) investigated new fabrication techniques to make the fine grids needed for their proposed Micro Solar-Flare Apparatus (MiSolFA), a compact X-ray imaging spectrometer designed for a small 6U microsatellite. They were successful in producing engineering grids using the LIGA (Lithographie, Galvanoformung, Abformung; or X-ray lithography, electroplating, and molding) fabrication technology. They used a carbon substrate on which they manufactured gold slats with a thickness of more than 200 µ m and a pitch as fine as 15 µ m, far outperforming etching methods. Laser cutting may also be a future relevant technology.

Alignment, Aspect, and Calibration In this section we provide a broad overview of alignment, aspect, and calibration issues that differ from those used by conventional optical systems.

Bi-grid Collimators The description of such systems in Section “Bi-grid Systems: Fourier Imagers” assumes an idealized hardware implementation. Such an implementation features “ideal grids” that have negligible thickness but are perfectly opaque at X-ray energies of interest, have a 50% slit-to-pitch ratio, and otherwise have perfect metrology. The position and orientation of the grids are perfectly maintained by the metering structure that is, itself, fixed relative to an aspect system that provides pitch, yaw, and roll information on the direction to the star field or to the solar disk.

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The inevitable deviations of the as-built instrument from this ideal state affect the optical performance and so must be determined prior to launch. Directly calibrating the as-built performance using conventional techniques would be problematic since X-ray and gamma-ray beams with the required properties are, in most cases, not available. However, the performance of bi-grid collimators can be well-determined from quasi-two-dimensional characterization of the front and rear grids separately. Specifically, for RHESSI, optical scanning of the surfaces of each grid with micron positional accuracy was used to determine the slat pitch, position, orientation, and uniformity. A good estimate of the slit width can also be made from these measurements. In addition, low spatial resolution X-ray transmission measurements as a function of energy and incident angle were made using radioactive sources to determine the slit width, grid thickness, and overall transmission. These optical and X-ray measurements were combined into a model for each grid from which the transmission as a function of energy and incident angle can be reliably inferred. These combined transmission profiles of the front and rear grids as a function of position then provide the basis for a realistic estimate of the imager response as a function of energy and incident angle. The experience with RHESSI showed that redundant determinations were good at the 2% level. The interpretation of the grid pair data can be done using CAD techniques. In practice, a much more efficient approach is to express the response (as a function of energy and incident angle) in terms of just three parameters – the average transmission, the amplitude, and phase of the periodic response as a function of incident angle. These three parameters fully describe the relevant response and vary smoothly with energy and incident angle. Since the parameters can be analytically adapted to the as-built performance, the calibration is based on knowledge of the as-built hardware, as opposed to requiring that the hardware meet high metrology requirements. Furthermore, this knowledge can be obtained after the fact and applied to previous observations. Thus, in many cases, post facto knowledge of the in-flight metrology can be used to fully compensate for degradation caused by imperfect or misaligned grids and other practical considerations. An example of this knowledge vs. control dichotomy is the relative twist of the front and rear grids. In fact, this need only to be aligned to a precision given by the ratio of grid slit to grid diameter, rather than grid slit to separation. Similarly, if the elements of the aspect system are built into the grids or the grid mounts as was the case for RHESSI (e.g., Zehnder et al. 2003), then mechanical flexure in the overall metering structure is equivalent to a variation in pointing and is reflected in the aspect solution. With photon tagging, short integration times, and a high-cadence aspect system, such variations can be fully compensated for during analysis. In practice, the knowledge vs. control trade-off with RHESSI enabled observations with ∼arcsecond resolution to be obtained with a metering structure that was stable to ∼arcminutes and with pointing stable to ∼a degree. One distinguishing feature of bi-grid systems is that the transverse location of the detector need only be located to an accuracy better than the grid size, not the grid-aperture size. This is particularly useful since it supports late stage integration

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of the detector and grid optics. The distance of the detector from the rear grid is generally not critical, unlike the focus requirements of a focusing imager. The alignment requirements for multi-grid collimators are much more severe than for bi-grid collimators since the intermediate grids must be positioned and maintained to a precision that is small compared to the grid pitch. This requirement was met, however, by the HXIS instrument on SMM with ∼25 µ m grid apertures (van Beek et al. 1980).

Systems with 2D Detectors The significance of internal alignment and tolerance issues depends on the type of mask or collimator system employed. For mask systems that include detectors with two-dimensional spatial capability, the primary requirement is that the relative positions of the mask and detector be known in inertial coordinates to an accuracy small compared to the angular resolution. This must be achieved on timescales that are longer than the integration time. The requirement can be met if both the metering structure and pointing platform are stable. Alternatively, as with RHESSI, one can trade mechanical and pointing stability for data rate by using photon tagging, short binning times, and a high-cadence aspect system. The fact that photons are received in various areas of the spatially sensitive detectors (further reinforced by any jitter the collimator is subject to) ensures that no single source location is disadvantaged. This is in contrast to RMC systems that have limited ability to image a source that is within a pitch angular separation from the spin axis. Also, every detector pixel “sees” all angular scales, and this eases some calibration issues. For example, in a RHESSI-like bi-grid, each detector is associated with a particular angular scale, and inter-detector sensitivity errors lead to certain spatial scales being under- or overemphasized with respect to the others.

Conclusions Grids and masks have provided the basis for X-ray and gamma-ray imaging since the 1960s (Bradt et al. 1968, 1992) (Also see the list of missions found at https://universe.gsfc.nasa.gov/archive/cai/coded_inss.html.). Table 1 compares the capabilities of imagers using the three different schemes: single grid, bi-grid, and multi-grid. Table 2 summarizes the characteristics of a representative set of instruments that have made observations either on spacecraft or on high-altitude balloons, with Fig. 25 displaying a few point spread functions for comparison. Their capabilities have grown as grid and detector technologies have improved. The different techniques that have been employed have both advantages along with significant disadvantages. The design requirement that the detector area be comparable to that of the grid or mask makes it much more difficult to reduce background for applications that require high sensitivity. Sensitivity is further affected since the telescope mask or collimator intentionally blocks between about a half to three quarters of the incident photon flux. In source-limited situations where

Rotating

Fixed

Fixed

Focusing Optics

5⬙

min ∼ p2L

min ∼ p2L

min ∼ p2L

∼ cmin L

on-axis off-axis

none!

good

NSC ≈

2

FOV ang.res.

∼10⬘



statisticslimited

statisticslimited

statisticslimited

≥ 21 period

very good

1◦

statisticslimited

1◦

statisticslimited

1◦ , with vignetting ≥ 21 period

Temp. res. (imaging)

FOV

good

very good

very good

Angular Sidelobe resolution levels

Aoptics Low background

very small

∼ 41 Adet

∼ 21 Adet

∼ 21 Adet

Sensitivity or Aeff

Where detector pixelization is required, it is typically at the level of half the (finest) grid pitch pmin The minimum size of a URA feature (cmin ) is typically half the minimum pitch of a periodic grid (pmin ) The bi-grid row assumes the use of multiple collimators to measure a range of spatial frequencies

Fixed

Multi-grid

Bi-grid (One or two Fixed SC(s) per (cos & sine SCs) pitch) Fixed (moiré)

Single grid (Multi-pitch)

Fixed

URA

Rotating

Fixed/ rotating

Imaging type

required

required

only coarse required

not required

required

required

Pixelized detectors?

HXRs only

´ visibilities moire: robustly formed

“Visibilities”; PSF weighted post-facto in S/W;

PSF ∼fixed

challenging to fabricate and to calibrate

Other notes

Table 1 Qualitative comparison between imaging schemes. Note that rotation-based imaging instruments typically have minimal image accumulations of half a spin period. Color code: blue, best or special mention; green, very good, current cutting edge; yellow, standard or adequate for solar work; orange, below preferred standard for solar applications; red, avoid unless irrelevant!

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Swift/BAT (2004–present) Barthelmy et al. (2005) GRIPS (2016 balloon) Duncan et al. (2016) Solar Orbiter/STIX (2021–present) Krucker et al. (2020) ASO-S/HXI (launch in 2022) Zhang et al. (2019)

Mission/instrument Ariel/B (1974–1980) Villa et al. (1976) SMM/HXIS (1980) van Beek et al. (1980) Hinotori SXT (1981) Enome (1983) Yohkoh/HXT (1991–2001) Kosugi et al. (1991) HEIDI (1993 balloon) Crannell et al. (1991) HETE-2/WXM (2000–2008) Kawai et al. (1999) INTEGRAL/IBIS (2002–present) Ubertini et al. (2003) RHESSI (2002–2018) Lin et al. (2002)

12.5′′ 7.1′′ 6′′

Rotating MPRM mask

30 bi-grid collimators

91 bi-grid collimators (sine & cosine)

2.3′′

9 RMCs 17′

12′

URA

URA

≈10′

40′

2◦ (flares)

1◦ (flares)

burst location

source identification 1◦ solar

burst location

1◦

11′′ & 25′′

two 1-D random masks

solar flares solar flares

30′′ & 38′′ 8′′

2 RMCs 64 bi-grid collimators (sine & cosine) 2 RMCs

FOV survey solar

Ang. res. 0.75′′ 8′′

Description scanner multi-grid direct img

30 to 200

3 to 150

20 to 10,000

15 to 150

3 to 17,000

15 to 10,000

2 to 25

≤20 to 700

17 to 40 15 to 100

Energy band [keV] 0.9 to 18 3.5 to 30

≈96

50 keV:90 2.2 MeV:13 6

50 keV:50 2.2 MeV:3 5200

2500

350

32

70

Aeff [cm2 ] ≈290 0.07

100-byte images

MDP ≈3%

Misc. notes

Table 2 Past instruments. Most nominally require information about all detected photons to be downlinked, although some significant on-board data compression schemes have been used when needed to reduce the telemetered data volume (e.g., STIX on Solar Orbiter). Instruments using URAs and random masks have been added for reference. (Adapted from Hurford 2010)

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Fig. 25 Point spread functions of GRIPS, RHESSI, Solar Orbiter/STIX, and FOXSI (Focusing Optics X-ray Spectroscopic Imager Krucker et al. 2013). The RHESSI subcollimators #6 and #9 were the only ones thick enough to modulate gamma rays at energies above ∼1 MeV, and hence, this combination is shown separately. Top: Natural weighting (all visibilities are weighted equally) and abscissa in arcsecs. Middle: Natural weighting and abscissa in units of the FWHM of the main lobe. Bottom: Uniform weighting (where individual visibilities are weighted such as to preserve the density of uv points in Fourier space) and abscissa in units of the FWHM of the main lobe

background is not an issue, the ability to detect weak sources in the presence of strong ones is limited by the fact that all sources contribute noise to the detection of each source component. Image quality is also significantly constrained for complex sources (single-mask and bi-grid systems).

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In recent years, masks and collimators have been partially supplanted by technical developments in grazing-incidence optics for low-energy applications that require only intermediate resolution and narrow FOVs. In such contexts, focusing optics has a commanding advantage where sensitivity and background rejection are the main drivers or where morphologically complex sources need be imaged. Nevertheless, there will continue to be many applications where mask and gridbased imaging is appropriate. As we have seen, the technique can be adapted to platforms which are three-axis stabilized, rotating, or unstably pointed (as with balloons). It can also be implemented in a wide range of size scales, from compact designs of a few centimeters in scale to configurations requiring extended booms on scales of meters. It can provide angular resolutions from seconds of arc to degrees over FOVs from ∼1◦ × 1◦ to ∼1 sr (see also the Hemispherical Rotational Modulation Collimator Imaging System; Kim et al. 2019). For a given instrument, the same “optics” can be used over a wide range of energies, a feature that greatly aids co-location of images and imaging spectroscopy. Therefore, in applications where either compactness, low mass, wide FOV, high angular resolution, or highenergy response is required, masks, grids, and collimators will continue to provide the imaging technique of choice.

References S.D. Barthelmy, L.M. Barbier, J.R. Cummings, E.E. Fenimore, N. Gehrels, D. Hullinger, H.A. Krimm, C.B. Markwardt, D.M. Palmer, A. Parsons, G. Sato, M. Suzuki, T. Takahashi, M. Tashiro, J. Tueller, Space Sci. Rev. 120, 143 (2005) H. Bradt, G. Garmire, M. Oda, G. Spada, B.V. Sreekantan, P. Gorenstein, H. Gursky, Space Sci. Rev. 8, 471 (1968) H.V.D. Bradt, T. Ohashi, K.A. Pounds, ARAA 30, 391 (1992) B. Budden, PhD thesis, Louisiana State University, 2011 C.J. Crannell, B.R. Dennis, J.P. Norris, L.E. Orwig, E.J. Schmahl, F.L. Lang, R. Starr, M.E. Greene, G.J. Hurford, W.N. Johnson, K.S. Wood, in AIAA International Balloon Conference, Albuquerque, vol. AIM-91-3653-CP, 1991 N. Duncan, P. Saint-Hilaire, A.Y. Shih, G.J. Hurford, H.M. Bain, M. Amman, B.A. Mochizuki, J. Hoberman, J. Olson, B.A. Maruca, N.M. Godbole, D.M. Smith, J. Sample, N.A. Kelley, A. Zoglauer, A. Caspi, P. Kaufmann, S. Boggs, R.P. Lin, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, ed. by J.-W.A. den Herder, T. Takahashi, M. Bautz. Space Telescopes and Instrumentation 2016: Ultraviolet to Gamma Ray, vol. 9905 (2016), p. 99052Q P. Durouchoux, H. Hudson, J. Matteson, G. Hurford, K. Hurley, E. Orsal, Astron. Astrophys. 120, 150 (1983) S. Enome, Adv. Space Res. 2, 201 (1983) M. Fivian, R. Hemmeck, A. McHedlishvili, A. Zehnder, Sol. Phys. 210, 87 (2002) G.J. Hurford, ISSI Sci. Rep. Ser. 9, 223 (2010) G.J. Hurford, S. Krucker, R.P. Lin, R.A. Schwartz, G.H. Share, D.M. Smith, Astrophys. J. Lett. 644, L93 (2006) G.J. Hurford, E.J. Schmahl, R.A. Schwartz, A.J. Conway, M.J. Aschwanden, A. Csillaghy, B.R. Dennis, C. Johns-Krull, S. Krucker, R.P. Lin, J. McTiernan, T.R. Metcalf, J. Sato, D.M. Smith, Sol. Phys. 210, 61 (2002)

51 Grid-Based Imaging of X-rays and Gamma Rays with High Angular Resolution

1815

N. Kawai, M. Matsuoka, A. Yoshida, Y. Shirasaki, M. Namiki, K. Takagishi, M. Yamauchi, I. Hatsukade, E.E. Fenimore, M. Galassi, Astron. Astrophys. Suppl. 138, 563 (1999) H.S. Kim, M. Na, J.G. Ok, G. Kim, S.-J. Ye, IEEE Trans. Nucl. Sci. 66, 2114 (2019) T. Kosugi, K. Makishima, T. Murakami, T. Sakao, T. Dotani, M. Inda, K. Kai, S. Masuda, H. Nakajima, Y. Ogawara, M. Sawa, K. Shibasaki, Sol. Phys. 136, 17 (1991) S. Krucker, S. Christe, L. Glesener, S. Ishikawa, B. Ramsey, M. Gubarev, S. Saito, T. Takahashi, S. Watanabe, H. Tajima, T. Tanaka, P. Turin, D. Glaser, J. Fermin, R.P. Lin, in Society of PhotoOptical Instrumentation Engineers (SPIE) Conference Series, ed. by S. Fineschi, J. Fennelly. Solar Physics and Space Weather Instrumentation V, vol. 8862 (2013), p. 88620R S. Krucker, G.J. Hurford, O. Grimm, S. Kögl, H.P. Gröbelbauer, L. Etesi, D. Casadei, A. Csillaghy, A.O. Benz, N.G. Arnold, F. Molendini, P. Orleanski, D. Schori, H. Xiao, M. Kuhar, N. Hochmuth, S. Felix, F. Schramka, S. Marcin, S. Kobler, L. Iseli, M. Dreier, H.J. Wiehl, L. Kleint, M. Battaglia, E. Lastufka, H. Sathiapal, K. Lapadula, M. Bednarzik, G. Birrer, S. Stutz, C. Wild, F. Marone, K.R. Skup, A. Cichocki, K. Ber, K. Rutkowski, W. Bujwan, G. Juchnikowski, M. Winkler, M. Darmetko, M. Michalska, K. Seweryn, A. Białek, ´ P. Osica, J. Sylwester, M. Kowalinski, D. Scisłowski, M. Siarkowski, M. Ste´slicki, T. Mrozek, P. Podgórski, A. Meuris, O. Limousin, O. Gevin, I. Le Mer, S. Brun, A. Strugarek, N. Vilmer, S. Musset, M. Maksimovi´c, F. Fárník, Z. Kozáˇcek, J. Kašparová, G. Mann, H. Önel, A. Warmuth, J. Rendtel, J. Anderson, S. Bauer, F. Dionies, J. Paschke, D. Plüschke, M. Woche, F. Schuller, A.M. Veronig, E.C.M. Dickson, P.T. Gallagher, S.A. Maloney, D.S. Bloomfield, M. Piana, A.M. Massone, F. Benvenuto, P. Massa, R.A. Schwartz, B.R. Dennis, H.F. van Beek, J. Rodríguez-Pacheco, R.P. Lin, Astron. Astrophys. 642, A15 (2020) S. Krucker, G.J. Hurford, A.L. MacKinnon, A.Y. Shih, R.P. Lin, Astrophys. J. Lett. 678, L63 (2008) E. Lastufka, D. Casadei, G. Hurford, M. Kuhar, G. Torre, S. Krucker, Adv. Space Res. 66, 10 (2020) R.P. Lin, B.R. Dennis, G.J. Hurford, D.M. Smith, A. Zehnder, P.R. Harvey, D.W. Curtis, D. Pankow, P. Turin, M. Bester, A. Csillaghy, M. Lewis, N. Madden, H.F. van Beek, M. Appleby, T. Raudorf, J. McTiernan, R. Ramaty, E. Schmahl, R. Schwartz, S. Krucker, R. Abiad, T. Quinn, P. Berg, M. Hashii, R. Sterling, R. Jackson, R. Pratt, R.D. Campbell, D. Malone, D. Landis, C.P. Barrington-Leigh, S. Slassi-Sennou, C. Cork, D. Clark, D. Amato, L. Orwig, R. Boyle, I.S. Banks, K. Shirey, A.K. Tolbert, D. Zarro, F. Snow, K. Thomsen, R. Henneck, A. McHedlishvili, P. Ming, M. Fivian, J. Jordan, R. Wanner, J. Crubb, J. Preble, M. Matranga, A. Benz, H. Hudson, R.C. Canfield, G.D. Holman, C. Crannell, T. Kosugi, A.G. Emslie, N. Vilmer, J.C. Brown, C. Johns-Krull, M. Aschwanden, T. Metcalf, A. Conway, Sol. Phys. 210, 3 (2002) C.A. Lindsey, J. Opt. Soc. Am. (1917–1983) 68, 1708 (1978) K. Makishima, T. Murakami, J. Nishimura, M. Oda, Y. Ogawara, Y. Tawara, S. Miyamoto, COSPAR, 20th Plenary Meeting, vol. 20, 1977 P. Massa, A.F. Battaglia, A. Volpara, H. Collier, G.J. Hurford, M. Kuhar, E. Perracchione, S. Garbarino, A.M. Massone, F. Benvenuto, F. Schuller, A. Warmuth, E.C.M. Dickson, H. Xiao, S.A. Maloney, D.F. Ryan, M. Piana, S. Krucker (2022). arXiv e-prints, arXiv:2202.09334 S. Masuda, in Multi-Wavelength Observations of Coronal Structure and Dynamics, ed. by P.C.H. Martens, D. Cauffman, vol. 10 (2002), pp. 351–359 L. Mertz, in Modern Optics, ed. by J. Fox (1967), p. 787 M. Oda, Appl. Opt. 4, 143 (1965) M. Piana, A.M. Massone, G.J. Hurford, M. Prato, A.G. Emslie, E.P. Kontar, R.A. Schwartz, Astrophys. J. 665, 846 (2007) M. Piana, A.G. Emslie, A.M. Massone, B.R. Dennis, Hard X-ray Imaging of Solar Flares (Springer, 2022), p. 164 T.A. Prince, G.J. Hurford, H.S. Hudson, C.J. Crannell, Sol. Phys. 118, 269 (1988) B.D. Ramsey, R.A. Austin, R. Decher, Instrumentation for x-ray astronomy, NASA Marshall Space Flight Center Report, 1993 E.J. Schmahl, G.J. Hurford, Sol. Phys. 210, 273 (2002)

1816

P. Saint-Hilaire et al.

H.W. Schnopper, R.I. Thompson, S. Watt, Space Sci. Rev. 8, 534 (1968) D.M. Smith, R.P. Lin, P. Turin, D.W. Curtis, J.H. Primbsch, R.D. Campbell, R. Abiad, P. Schroeder, C.P. Cork, E.L. Hull, D.A. Land is, N.W. Madden, D. Malone, R.H. Pehl, T. Raudorf, P. Sangsingkeow, R. Boyle, I.S. Banks, K. Shirey, R. Schwartz, Sol. Phys. 210, 33 (2002) W. Soller, Phys. Rev. 24, 158 (1924) P. Ubertini, F. Lebrun, G. Di Cocco, A. Bazzano, A.J. Bird, K. Broenstad, A. Goldwurm, G. La Rosa, C. Labanti, P. Laurent, I.F. Mirabel, E.M. Quadrini, B. Ramsey, V. Reglero, L. Sabau, B. Sacco, R. Staubert, L. Vigroux, M.C. Weisskopf, A.A. Zdziarski, Astron. Astrophys. 411, L131 (2003) H.F. van Beek, C. de Jager, A. Schadee, Z. Svestka, A. Boelee, A. Duijveman, M. Galama, R. Hoekstra, P. Hoyng, R. Fryer, G.M. Simnett, J.P. Imhof, H. LaFleur, H.V.A.M. Maseland, W.M. Mels, J. Schrijver, J.J.M. van der Laan, P. van Rens, W. van Tend, F. Werkhoven, A.P. Willmore, J.W.G. Wilson, M.E. Machado, W. Zandee, Astrophys. J. Lett. 244, L157 (1981) H.F. van Beek, P. Hoyng, B. Lafleur, G.M. Simnett, Sol. Phys. 65, 39 (1980) G. Villa, C.G. Page, M.J.L. Turner, B.A. Cooke, M.J. Ricketts, K.A. Pounds, D.J. Adams, Mon. Not. R. Astron. Soc. 176, 609 (1976) A. Zehnder, J. Bialkowski, F. Burri, M. Fivian, R. Henneck, A. Mchedlishvili, P. Ming, J. Welte, K. Thomsen, D. Clark, B.R. Dennis, G.J. Hurford, D.W. Curtis, P.R. Harvey, D.H. Pankow, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, ed. by S.L. Keil, S.V. Avakyan. Innovative Telescopes and Instrumentation for Solar Astrophysics, vol. 4853 (2003), pp. 41–59 Z. Zhang, D.-Y. Chen, J. Wu, J. Chang, Y.-M. Hu, Y. Su, Y. Zhang, J.-P. Wang, Y.-M. Liang, T. Ma, J.-H. Guo, M.-S. Cai, Y.-Q. Zhang, Y.-Y. Huang, X.-Y. Peng, Z.-B. Tang, X. Zhao, H.-H. Zhou, L.-G. Wang, J.-X. Song, M. Ma, G.-Z. Xu, J.-F. Yang, D. Lu, Y.-H. He, J.-Y. Tao, X.-L. Ma, B.-G. Lv, Y.-P. Bai, C.-X. Cao, Y. Huang, W.-Q. Gan, Res. Astron. Astrophys. 19, 160 (2019)

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Counter Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . First-Generation Imaging Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pioneering Balloon Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Satellite Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Second-Generation Imaging Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Advanced Balloon Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Second-Generation Imaging Satellite Instruments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Third Generation: Solid-State Imaging Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Continuing Developments and the Future . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Electron-positron pair production is the essential process for high-energy γ -ray astrophysical observations. Following the pioneering OSO-3 counter telescope, the field evolved into use of particle tracking instruments, largely derived from high-energy physics detectors. Although many of the techniques were developed

D. J. Thompson () NASA Goddard Space Flight Center, Greenbelt, MD, USA e-mail: [email protected] A. A. Moiseev University of Maryland, College Park, MD, USA e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_159

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on balloon-borne γ -ray telescopes, the need to escape the high background in the atmosphere meant that the breakthrough discoveries came from the SAS-2 and COS-B satellites. The next major pair production success was EGRET on the Compton Gamma Ray Observatory, which provided the first all-sky map at energies above 100 MeV and found a variety of γ -ray sources, many of which were variable. The current generation of pair production telescopes, AGILE and Fermi LAT, has broadened high-energy γ -ray astrophysics with particular emphasis on multiwavelength and multimessenger studies. A variety of options remain open for future missions based on pair production with improved instrumental performance. Keywords

Gamma rays · High-energy astrophysics · Active galactic nuclei · Pulsars · Gamma-ray bursts · Gamma-ray telescopes · Pair production

Introduction For energies above a few tens of MeV, photons interact with matter, other photons, or magnetic fields primarily by electron-positron pair production (γ → e− + e+ ). Pair production is an explicit illustration of Einstein’s E = mc2 , where the energy E of the photon is converted into two particles with mass m, with the speed of light c being the conversion factor. This physical process has important implications for detection of astrophysical γ rays: 1. High-energy (greater than about 50 MeV) γ rays cannot be reflected or refracted; there are no mirrors or lenses for these photons. 2. Gamma rays coming from space interact in Earth’s upper atmosphere; therefore direct detection can only be done from space or from the edge of the atmosphere. 3. Properties of high-energy γ rays can only be derived from measurements of the electron and positron resulting from pair production. Gamma-ray instrumentation at these energies consists of charged particle detectors. These considerations drive the most important factor in design of high-energy γ -ray telescopes. The real challenge is not in detecting the electron-positron pair. The critical issue is separating the cosmic pair production events from background. Thanks largely to developments in particle physics, various types of highly efficient particle detectors are available, and many of these have been applied to astrophysical γ -ray instruments. Background comes in two forms: 1. Space is filled with charged particles. Cosmic rays, solar energetic particles, and trapped particles in Earth’s magnetic field outnumber high-energy γ rays by orders of magnitude. These charged particles are highly penetrating for most energies in the pair production regime, so shielding is impractical. Such particles can masquerade as γ -ray interaction products.

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2. Many of the charged particles in space have enough energy to undergo inelastic nuclear interactions, producing secondaries such as neutral pions, which decay very quickly into γ rays in the same energy range as seen by pair production detectors. These secondary γ rays are indistinguishable from cosmic γ rays. The target material for such interactions can be local, as part of the detector or supporting structure, or it can be more diffuse, such as Earth’s atmosphere. Building detectors to deal with these issues was initially stimulated by the recognition that charged-particle cosmic rays in the galaxy must interact with the interstellar gas to produce γ rays in the MeV to GeV energy range (Hayakawa 1952; Morrison 1958). Since that time, detector technologies and access to space have undergone dramatic changes, and pair production telescopes have revealed a broad array of high-energy γ -ray sources in addition to the diffuse galactic radiation that provided the original impetus for the field. In this chapter, we review various approaches that have been taken or proposed as ways to use pair production to conduct astrophysical research. Section “Counter Detectors” describes the early counter instruments; Sections “First-Generation Imaging Detectors” and “Second-Generation Imaging Detectors” present the early imaging γ -ray telescopes; Section “Third Generation: Solid-State Imaging Detectors” outlines the current state of instrumentation; and Section “Continuing Developments and the Future” covers some aspects of the future of pair production telescopes. Additional information can be found in earlier review articles (Kanbach 2019; Tavani 2018).

Counter Detectors The 1960s saw the emergence of several types of pair production telescopes, many of which were carried on high-altitude research balloons. The greatest success from this decade was the use of scintillation counters on satellites. The first hints of cosmic γ -ray detection using this method came from Explorer XI (Kraushaar et al. 1965), and the real breakthrough came from a counter γ -ray instrument on the OSO3 satellite (Kraushaar et al. 1972). Figure 1 is a scale drawing of the OSO-3 γ -ray telescope, showing the variety of instrumentation used to detect the photons and reject the background. The plastic scintillator read out by photomultipliers and surrounding the detectors provides a first-level rejection of charged particles. Plastic scintillator is highly efficient in particle detection while offering minimal absorption of γ rays. A γ ray entering through the top of the instrument undergoes pair production in a cesium iodide (CsI) or plastic scintillator layer. The electron-positron pair produces a signal in the directional Lucite Cerenkov counter. The directionality discriminates against upward-moving particles. Finally, the particles deposit energy in the layers of tungsten and sodium iodide (NaI), allowing a measurement of the original γ -ray energy. An experimental calibration of the instrument showed an effective energy threshold of about 50 MeV and a peak effective area of about 9 cm2 , with an angular response having a full width at half maximum of about 24◦ . No arrival direction information for individual photons within that wide opening angle was possible.

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Fig. 1 Simplified schematic diagram of the OSO-3 γ -ray instrument. (Adapted from Kraushaar et al. 1972)

In an era when rocket reliability was uncertain, three copies of this telescope were made. The first was lost when its satellite failed to reach orbit. The second was the one on OSO-3, launched into a low-Earth orbit on a Delta rocket in 1967 March. The third was used for calibration. The OSO satellites were spin stabilized, with the γ -ray instrument located in the rotating part of the satellite. As the satellite precessed to follow the Sun (its primary mission), the rotation allowed the γ -ray telescope to sweep out the entire sky over the 16 months of operation, ending when the onboard tape recorders failed. During the mission, 621 γ rays from the sky and a much larger number of atmospheric γ rays were detected. Three important results emerged: • As expected, atmospheric γ rays vastly outnumber cosmic photons in the energy range above 50 MeV. The Earth limb is particularly bright, and the east-west effect from geomagnetic screening of the positively charged cosmic rays is visible.

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• The sky events show a clear peak toward the galactic equator and a concentration toward the central region of the Milky Way, confirming the idea of high-energy γ rays being produced by cosmic ray interactions with interstellar gas. • An apparently isotropic emission is visible, with γ rays arriving from all directions in the sky. The OSO-3 results represented a milestone. These were the first very-highconfidence observations in high-energy γ -ray astrophysics. Although the statistics were limited and the angular response quite broad, the careful design of the instrument demonstrated that the challenge of measuring cosmic γ rays in a highbackground environment could be met.

First-Generation Imaging Detectors Counter γ -ray detectors do not take full advantage of the information contained in the electron-positron pair resulting from γ -ray interactions. Imaging of the individual pair production events provides two additional important pieces of information: 1. Visualizing the particle pair originating in a detector offers a distinctive signature of γ -ray pair production. The inverted “V” or “Y” pattern is extremely unlikely to originate from a single charged particle, thus providing an additional valuable discriminator against the huge charged-particle background in the space environment. 2. Measurement of the electron-positron pair provides information about the arrival direction of the incident γ ray. The created particles retain information about both the energy and momentum of the original photon. Deriving the properties of the incoming photon from measurements of the electron and positron involves inherent uncertainties and tradeoffs. Due to conservation of energy and momentum, pair production cannot occur in free space. Some momentum is lost to (usually) an atomic nucleus in the initial interaction. The particles also suffer collisional and radiative losses in passing through whatever target material comprises the detector. Thicker detectors offer higher probability for a photon to undergo pair production but more loss of directional information, primarily due to multiple Coulomb scattering of the electron and positron. The balance between detection efficiency and directional information is a key element in astrophysical pair production instrument design.

Pioneering Balloon Instruments The first efforts to detect high-energy cosmic γ rays through pair production were small instruments carried on high-altitude research balloons. Such balloons can

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carry instruments to altitudes where the residual atmosphere above the balloon is only a few g cm−2 . This is sufficiently little material that γ rays arriving from outside the atmosphere have a relatively small probability of interacting before reaching the detector. Although balloon flights have relatively short durations (days), they offer access to the near-space environment at a small fraction of the cost of a satellite. Particularly for an unproven field of research like high-energy γ -ray astrophysics, balloons offered an opportunity to test pioneering techniques. In the 1960s, particle physicists’ track imaging detector of choice was the spark chamber. Unlike bubble chambers, cloud chambers, or nuclear emulsions, spark chambers can be triggered by an external signal, making them useful for operation in a high-background environment. Figure 2 illustrates the basic principle. A series of conducting layers is stacked in a volume filled with a noble gas (typically neon/argon). When a charged particle passes through the detector, it ionizes the gas while at the same time producing signals in a triggering circuit, in this case a pair of scintillators. The trigger then applies a high voltage to alternating layers while grounding the ones between. Sparks follow the ionization path, and measurement of the spark locations tracks the particle. A number of groups pursuing high-energy γ -ray astrophysics realized that the spark chamber enabled construction of pair production instruments that could visualize the electron-positron tracks. These first-generation imaging detectors employed various triggering systems and readout methods. One of the early balloon-borne spark chamber instruments is shown schematically in Fig. 3 (Frye and Smith 1966). The incoming γ ray produces no signal in the anticoincidence scintillator and then undergoes pair production in one of the steel plates of the spark chamber. The electron and positron produce a coincident signal in trigger scintillators 1 and 2, triggering the high voltage to produce the

Fig. 2 Schematic of the spark chamber principle. (Reproduced with permission Collins 2009)

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Fig. 3 Schematic of an early spark chamber γ -ray telescope. (Adapted from Frye and Smith 1966). The trigger logic was no signal in the anticoincidence scintillator plus coincident signals in the two trigger scintillators

sparks. Stereoscopic views of the sparks were recorded on film, to be analyzed by manual inspection. The instrument could measure γ rays arriving up to 30◦ from the vertical, with the arrival directions of 100 MeV photons accurate to 3◦ . This instrument flew twice in 1964 from the National Center for Atmospheric Research balloon base in Palestine, Texas (later the National Scientific Balloon Facility and now NASA’s Columbia Scientific Balloon Facility). As for many of the early balloon instruments, the flights produced only upper limits for γ rays coming from sources outside the atmosphere. A later version of this instrument incorporated two features to help reduce background: scintillators were added to the sides of the spark chamber, and the lower simple counter was replaced by a directional Cherenkov counter (to discriminate against upward-moving particles) (Frye and Wang 1969). A still-later version included some thicker plates to increase the conversion efficiency and some thinner plates to lower the effective energy threshold (Albats et al. 1972). This instrument produced evidence of pulsed high-energy γ rays from the Crab pulsar. The earliest indications of pulsed high-energy Crab γ -ray emission came from another balloon instrument with a similar design (Browning et al. 1971), also flown from Palestine, Texas. It also had an optical spark chamber with film data recording and a three-element trigger: anticoincidence detectors surrounding five sides of the detector plus coincidence between a scintillator and a directional Cherenkov counter. A similar instrument flown on balloons in 1972, 1974, and 1976 obtained a signal from the high-mass X-ray binary Cygnus X-3 at energies above 40 MeV (Galper et al. 1977) from one of the flights.

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Fig. 4 Schematic of another spark chamber γ -ray telescope. (Adapted from Leray et al. 1972). The trigger logic was no signal in the anticoincidence detector AC plus coincident signals in a scintillator S and Cherenkov detector C. (Reproduced with permission ©ESO)

Still another instrument using similar technology is shown in Fig. 4 (Leray et al. 1972). The spark chamber was optical with film recording. The trigger was a twofold coincidence (mid-instrument scintillator and directional Cherenkov) with anticoincidence scintillators on top and three sides. Based on six successful balloon flights in 1969 from southern France, this instrument yielded a hint of signal from the Crab pulsar, but not at a statistically significant level. One characteristic of all these detectors just described was that the pair production interaction took place in metal plates. The scattering of the electron and positron limited the angular resolution of the measurements. This effect was greatest for energies below 100 MeV, where the scattering significantly changed the particle directions. An approach to avoid this constraint was to use a nuclear emulsion as

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Fig. 5 Schematic of an emulsion plus spark chamber γ -ray telescope. (Adapted from May and Waddington 1969)

the converter material. Fine-grained emulsions allowed measurement of the γ -ray arrival direction before significant scattering of the electron-positron pair. Two examples of detectors using emulsions are shown in Figs. 5 (May and Waddington 1969) and 6 (Share et al. 1974). The triggering was similar to the previous instruments: anticoincidence scintillator to discriminate against charged particles plus a scintillator/Cherenkov detector coincidence to trigger the spark chamber. The tracks in the spark chamber were then used to point back to the part of the emulsion where the pair production event occurred. Scanning of the emulsion could then resolve the incident direction of the γ ray more accurately than a measurement using only a spark chamber. A balloon flight from Paraná, Argentina, in 1971 confirmed the OSO-3 γ -ray excess along the galactic plane surrounding the galactic center, at energy down to 15 MeV (Share et al. 1974). All these balloon-borne instruments that used film or emulsions required recovery of the instrument before any data analysis could be done. They also depended

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Fig. 6 Schematic of another emulsion plus spark chamber γ -ray telescope, in this case using a wide-gap spark chamber instead of a stack. A anticoincidence scintillator, E emulsion, P multiwire proportional chamber, S.C. wide-gap spark chamber, B trigger scintillators (2), C Cherenkov detector, R reflector for Cherenkov light. (©AAS. Reproduced with permission Share et al. 1974)

on extensive manual scanning to convert the images into quantifiable information about the electron-positron pair. While suitable for balloon flights with durations of hours, these approaches would not be applicable to satellite instruments. What was needed was a way to digitize the information on board in such a way that the data could be telemetered to the ground. The first spark chamber pair production instrument designed explicitly as a prototype of a satellite telescope (Fig. 7 (Fichtel et al. 1969)) had several features that differed from most of the other early designs: • The spark chamber modules themselves were wire grids instead of plates. Each module had orthogonal planes of wires separated by about 2 mm. Each wire threaded a magnetic core. When the spark occurred, the set cores would record x and y coordinates that could be transmitted to the ground. • The anticoincidence scintillator was a monolithic dome instead of tiles, providing complete coverage of the active detector. • The pair production took place in separate thin plates made of gold plated onto aluminum for support.

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Fig. 7 Schematic of an early wire grid spark chamber γ -ray telescope (Fichtel et al. 1969). (©AAS. Reproduced with permission)

• The middle triggering scintillator was located within the spark chamber stack instead of coming at the bottom, enabling measurement of the tracks before and after this trigger element. The most important result from this small detector had nothing directly to do with γ -ray astrophysics. Instead, during one balloon flight from Palestine, Texas, the instrument was pointed down to measure the upcoming atmospheric γ radiation (Fichtel et al. 1969) at energies above 100 MeV. This result showed a discrepancy with preliminary OSO-3 atmospheric results. The difference was large enough that the OSO-3 team re-calibrated their flight spare unit, finding reason to adjust their measurements. The final results from OSO-3 reflect these changes (Kraushaar et al. 1972).

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Fig. 8 Schematic of a wire grid spark chamber γ -ray telescope (Mayer-Hasselwander et al. 1972). The trigger was no signal in the anticoincidence signal plus a coincidence between the trigger scintillator and the Cherenkov counter. (©AAS. Reproduced with permission)

Figure 8 is a schematic of another pair production telescope with a similar design, also using a wire grid spark chamber (Mayer-Hasselwander et al. 1972). This instrument had thinner conversion plates, giving it sensitivity to γ rays with energy down to 30 MeV. On two balloon flights from Palestine, Texas, this instrument gave indications of diffuse cosmic γ -ray emission in the 30–50 MeV energy range. Measurement of any diffuse radiation in this energy range from a balloon is particularly difficult, because even at the highest balloon altitudes, most of the detected photons are secondaries from charged particle cosmic rays interacting in the residual atmosphere. The excess from extraterrestrial sources must be derived by subtracting the atmospheric component, based on the atmospheric flux as a function of altitude (the “growth curve”).

Satellite Instruments The plethora of γ -ray telescopes based on pair production and carried on balloons ultimately demonstrated that the atmospheric background presented a nearly insurmountable challenge for all but the brightest sources in the sky. The field would

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have to go to satellite instruments to make substantial progress. The first generation of satellite high-energy γ -ray telescopes was, not surprisingly, based on essentially the same technologies that had been developed and tested using balloon flights. A small spark chamber pair production telescope was included in the Orbiting Geophysical Observatory 5 payload, launched in 1968 (Hutchinson et al. 1970). It used an acoustic readout of the spark data. The highly charged particle fluxes in orbit limited its capabilities, but it did see an excess of γ rays above 40 MeV from the Cygnus region of the galactic plane. The 1969 launch of COSMOS-264 included a small γ -ray telescope with a spark chamber readout using film. The limited supply of film restricted the results from this instrument. It did find an indication of E >100 MeV photons from the Active Galactic Nucleus 3C120 (Volobuev et al. 1972). In early 1972, the TD-1 satellite was launched, and among its instruments was the S-133 γ -ray telescope (Voges et al. 1973). This detector used a vidicon camera system to read out the spark chamber data. High background produced by cosmic ray interactions with the surrounding instruments limited its usefulness, although it did detect one γ -ray burst (Voges and Pinkau 1974). The breakthrough satellite imaging γ -ray telescope was the Second Small Astronomy Satellite (SAS-2), shown schematically in Fig. 9 (Fichtel et al. 1975). The design was similar to some of the balloon instruments: the spark chamber used wire grids with magnetic core readout, and the triggering telescope used a mid-level scintillator and Cherenkov detector coincidence, with a plastic scintillator dome for anticoincidence. SAS-2 had an effective area on axis of about 100 cm2 and a field of view that extended to about 25◦ off axis. A principal consideration for SAS-2 was minimization of background, in order to produce the cleanest possible signal of cosmic γ rays. The discrimination against

Fig. 9 Schematic of the Second Small Astronomy Satellite (SAS-2) γ -ray telescope (Fichtel et al. 1975). (©AAS. Reproduced with permission)

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charged particles relied on the highly efficient, 32-layer spark chamber, where the appearance of a created pair produced a clear signature of a gamma ray (see Fig. 10). Outside the atmosphere, the γ -ray background originates from charged particles interacting in local material to produce γ -ray secondaries. SAS-2 used two approaches to minimize this effect: 1. SAS-2 was launched in late 1972 on a Scout rocket from the Kenya launch facility. This choice put the satellite into a low-Earth orbit very close to the equator, where the geomagnetic field excludes the most cosmic ray flux. 2. The inert material outside the anticoincidence scintillator was minimized and placed directly against the scintillator, so that any γ -ray-producing interactions 0

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had a high probability of being accompanied by a charged particle that could be detected by the anticoincidence system. SAS-2 operated in orbit for about 6 months, until an electronics failure ended the mission. It used 1-week pointed observations to map much of the galactic plane and a number of high-galactic-latitude regions. Its effective energy range was 35– 200 MeV, with the photon energies estimated from the multiple Coulomb scattering of the electron and positron. Key scientific results were the following: • The galactic plane morphology and spectrum confirmed that γ rays trace cosmic ray interactions with the interstellar medium. • The diffuse, isotropic, presumably extragalactic emission has a relatively steep energy spectrum (Fichtel et al. 1978). • The Crab and Vela pulsar γ -ray properties were measured (Kniffen et al. 1974; Thompson et al. 1975). • An unidentified source, which later came to be called Geminga, was discovered in the galactic anticenter (Thompson et al. 1977). The COS-B satellite (Bignami et al. 1975), launched in 1975, provided another major advance for astrophysics in the pair production energy regime. A schematic is shown in Fig. 11. Although it was nearly the same size as SAS-2 and also had a wire grid spark chamber as a primary detector, COS-B had a number of differences: • The triggering telescope had three coincidence elements: two scintillators and a Cherenkov detector. • COS-B included a CsI calorimeter to measure the energies of the electronpositron pair, giving it a much broader effective energy range (30 MeV–10 GeV) than SAS-2. • Because spark chamber gas performance deteriorates with use, COS-B carried a supply of replacement gas, allowing it to operate successfully for more than 6 years. • COS-B had structural material above the anticoincidence scintillator, and the orbit was an elongated one that exposed the instrument to the full flux of chargedparticle cosmic rays. As a result, COS-B suffered from some locally generated γ -ray background. COS-B operations consisted of a series of pointed observations, concentrated mostly, but not entirely, on the galactic plane, where the bright diffuse galactic emission mitigated against the instrumental background. The COS-B longevity and its broad energy range provided a much more extensive view of the γ -ray sky than was obtained by SAS-2. Some scientific highlights were the following: • COS-B produced the first real catalog of high-energy γ -ray sources (Swanenburg et al. 1981). Most of the 25 sources in the 2CG catalog did not have obvious counterparts at other wavelengths.

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Fig. 11 Schematic of the COS-B γ -ray telescope. (Credit: Messerschmitt-Bölkow-Blohm GmbH brochure, URB 5-7-75-25 D, 1975)

• Quasar 3C273 was the first high-confidence detection of an extragalactic highenergy γ -ray source (Swanenburg et al. 1978). • The Orion cloud complex was mapped in γ rays (Caraveo et al. 1980). • Detailed analysis was possible for the galactic diffuse emission and sources seen by SAS-2.

Second-Generation Imaging Detectors During the time SAS-2 and COS-B were operating, other pair production γ -ray telescopes were being planned, built, and tested. These included larger instruments and different experimental techniques from the earlier generation. Some were flown on balloons, often as prototypes of potential future satellite missions. The most successful satellite instrument from this period was the Energetic Gamma-Ray Experiment Telescope (EGRET) on the Compton Gamma Ray Observatory.

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Advanced Balloon Instruments A larger version of a wire grid magnetic core spark chamber instrument flown on balloons provided confirmation of the OSO-3 galactic center region emission (Fichtel et al. 1972). This same instrument was later reconfigured with thinner pair production conversion plates to reduce its energy threshold to about 15 MeV, and balloon flight data measured the galactic emission at lower energies than seen previously (Kniffen et al. 1978). A similar approach of using thin conversion plates to reduce the energy threshold was applied to another balloon-borne spark chamber telescopes, yielding a hint of pulsed 10–30 MeV emission from the Vela pulsar (Albats et al. 1974). An even larger (1 square meter) balloon payload using multi-wire proportional chambers instead of spark chambers introduced a new technology while maintaining the same basic pair production configuration (Frye et al. 1978). Balloon flights of this telescope yielded a pulsed signal from the Crab pulsar in the 10–30 MeV energy range. Another technical innovation was introduced with the Agathe γ -ray telescope (Lavigne et al. 1982). Figure 12 shows a schematic of this instrument. In

Fig. 12 Schematic of the Agathe γ -ray telescope. (Adapted from Lavigne et al. 1982)

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addition to using large-area (1 square meter) optical spark chambers with very thin plates, Agathe used a time-of-flight triggering system to discriminate against upward-moving particles, instead of the Cherenkov detectors used on most previous instruments. Balloon flights from Brazil produced measurements of the atmospheric and diffuse γ -ray flux in the energy range 4–25 MeV. A wire grid spark chamber instrument with a time-of-flight triggering system was flown from Palestine, Texas, as a demonstration of technology for a satellite mission (Thompson et al. 1985). Data analysis included an automated pattern recognition system used to screen out unwanted triggers. Performance matched expectations, confirming the usefulness of the design. Another satellite prototype using wide-gap spark chambers and time-of-flight triggering was also designed for balloon testing (Voronov et al. 1987). A unique feature of this instrument was the use of position-sensitive scintillator strips to trigger the spark chambers only when events arrived close to the direction of a predefined target. A completely different approach to a pair production γ -ray telescope was based on a large gas Cherenkov instrument (Albats et al. 1971). A schematic of this balloon instrument is shown in Fig. 13. A high-energy γ ray entering along the line of sight (upper left in the figure) produces no signal in the anticoincidence scintillator and then undergoes pair production in the thin lead converter. The electron and positron trigger the S2 scintillator and then produce Cherenkov light while moving through the Freon gas. The light is reflected from the spherical mirror segment at the rear and is detected by the cluster of phototubes C. The time of flight between the S2 signal

Fig. 13 Schematic of the large gas Cherenkov γ -ray telescope (Albats et al. 1971). (Reproduced with permission)

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and the C signal is 32 ns. The field of view was about 7◦ in diameter, and the arrival direction of the photons could be measured to about 0.5◦ . The energy threshold was about 100 MeV, although its maximum efficiency came at energies above 700 MeV. In flights from Palestine, Texas, in 1971 and 1973, this instrument clearly detected pulsed emission from the Crab Pulsar, with indications of a change in the pulsed flux between the two flights (McBreen et al. 1973; Greisen et al. 1975).

Second-Generation Imaging Satellite Instruments By the late 1970s, the particle physics community had largely shifted from spark chambers to multiwire proportional chambers or drift chambers. Nevertheless, two satellite pair production telescopes that were approved in this time frame in the USA (EGRET) and in the Soviet Union and France (Gamma-1) used spark chambers as the main detectors. In addition to space-flight experience and high reliability, spark chambers could be operated using much less power than these other technologies, and minimizing power is always a consideration in space. Gamma-1 (Akimov et al. 1989) was conceived based on an extended history of space-borne and balloon-borne small gamma-ray telescopes. The Gamma-1 main detector was a 12-layer stack of wide-gap optical spark chambers with geometrical area of 50 × 50 cm (Fig. 14). The spark chambers were viewed by a mirror system, and the tracks were recorded by a vidicon system. The spark chambers were triggered by the coincidence of the signals of two time-of-flight plastic scintillators and the gas Cherenkov detector placed in between them. This trigger arrangement provided high rejection of upward-moving particles and also additional rejection of cosmic ray protons with energy below the Cherenkov detection threshold of about 12 GeV. The stack of spark chambers was surrounded by efficient anticoincidence plastic scintillators to detect and veto charged cosmic rays. The 7.4-radiation lengththick scintillation calorimeter was placed at the bottom of the telescope to measure the energy of detected photon. The telescope operated in the energy range from 50 MeV to 5 GeV, with angular resolution ∼2◦ at 100 MeV, improving to ∼1.2◦ at 300 MeV. Its energy resolution was 70% at 100 MeV, improving to 35% at 550 MeV. Originally Gamma1 was planned to have a coded-aperture mask which would dramatically improve its angular resolution, but by launch time it was abandoned due to significant complication of the telescope design. Gamma-1 on the Gamma satellite was launched from Baikonur on July 11, 1990, and suffered from a major problem – for a still unknown reason power was not delivered to the spark chambers, so the telescope angular resolution was provided only by the Cherenkov detector at a level of ∼12◦ . Two years after the launch, it was decided to terminate this ill-fated mission. During the orbital operation, Gamma-1 performed observations of Vela pulsar, the galactic center region, the Cygnus X1 and X-3 binaries, and especially Her X-1. Interesting information was obtained about the high-energy emission of the Sun during peak solar activity, including solar flares (Bazer-Bachi et al. 1993).

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Fig. 14 Schematic of the Gamma-1 γ -ray telescope on the Gamma satellite (Akimov et al. 1989). AC anticoincidence scintillator, CA coded mask (planned but not flown), HSC and LSC spark chambers, MS mirrors, ST trigger scintillators, C Cherenkov detector, SC scintillator calorimeter. (Reproduced with permission)

NASA’s choice for a pair production telescope for the Gamma Ray Observatory, later renamed the Compton Gamma Ray Observatory (CGRO), was the Energetic Gamma Ray Experiment Telescope (EGRET). As part of the Great Observatories series, CGRO carried a suite of γ -ray telescopes, so that resources like mass and power on the satellite had to be shared. EGRET, shown schematically in Fig. 15, was in many ways a conventional instrument, incorporating the best features of previous

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Fig. 15 Schematic of the Energetic Gamma Ray Experiment Telescope (EGRET) on the Compton Gamma Ray Observatory (Kanbach et al. 1989). (Reproduced with permission)

satellite and balloon pair production telescopes (Kanbach et al. 1989). Key elements of the design included the following: • A wire grid, magnetic-core spark chamber interleaved with thin tantalum foils served as a converter and tracker for the pair production events. • A time-of-flight coincidence system, operated in anticoincidence with the overlying scintillator dome, formed the trigger. • An 8-radiation-length sodium iodide crystal system provided energy measurements. A minimum signal in this calorimeter was also incorporated into the trigger configuration. • A gas replenishment system enabled refills of the spark chamber gas as it aged. Table 1 shows some of the operational properties of EGRET, based on extensive accelerator calibrations (Thompson et al. 1993). The satellite carrying EGRET was placed into a low-Earth orbit by the Space Shuttle Atlantis on 5 April 1991. Regular science operations started on 15 May 1991. CGRO was operated in a series of pointings with the goal of surveying the γ -

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Table 1 Some characteristics of EGRET Property Energy Range Peak effective area Energy resolution Effective field of view Timing accuracy Point spread function

Value 20 MeV−30 GeV 1500 cm2 at 500 MeV 15% FWHM 0.5 steradians 300 GeV 8000 cm2 above 10 GeV 5 · 105 V/cm), the absorption of

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a single photon in the depleted region of the semiconductor triggers an avalanche of secondary electrons by means of impact ionization. A SPAD, operated in Geiger mode above the breakdown voltage (typically equal to ∼30 V), gives a binary output and requires a quenching circuit to restore the initial armed condition. Instead, the output current of a SiPM, being the sum of SPAD currents, is related to the amount of light collected by its sensitive surface. Each cell thus contains a SPAD and a passive quenching circuit, along with isolation from neighboring cells. Cells have typical dimensions from ∼7 to 100 µm. Due to the saturation of fired cells, the response characteristic is not linear, suffering from saturation at high input light intensities. An approximate equation describing the signal saturation is   N ·P DE − Ph NFired = NCell · 1 − e NCell

(1)

where NP h is the number of incoming photons, NCell the number of cells, NFired the number of fired cells and PDE the photodetection efficiency, at best around 50%. With around 1000 cells per pixel, saturation occurs around 1000 input photons. The choice of the optimal cell size is a balance between efficiency and dynamic range. In fact, by reducing the size of a cell, more cells can be fitted in the sensitive area, thus increasing the dynamic range by reducing the saturation probability. At the same time, due to the dead area caused by the isolation between the cells (realized by means of trenches to reduce optical cross talk), the fill factor (FF), i.e., the ratio between the sensitive area and the total detector area, decreases, thus reducing the sensitivity. Several SiPM pixels can be tiled to form arrays which are commercially available in multiple formats (such as 8 × 8 or 6 × 6) with pixel size of a few mm. SiPMs are produced by several detectors and semiconductor companies such as Hamamatsu, Onsemi, Broadcom, Ketek, and FBK research center. The main properties identifying the performance of SiPM are the gain (∼106 ), the PDE as a function of the wavelength with a maximum ∼50%, the recovery time (∼10 ns), and the dark count rate (DCR, expressed in Hz/mm2 ) which represents a type of noise due to undesired avalanche signals randomly triggered in cells by thermally generated electrons (not correlated to the input light signal). When compared to PMTs, SiPMs provide numerous advantages such as follows: (i) robust solid-state technology, (ii) miniaturization, (iii) operation at lower bias voltage, (iv) compatibility with large magnetic fields, and (v) high versatility in tridimensional tiling geometries. Due to their increasing relevance in multiple applications, from medical imaging to high energy and rare-event physics, the radiation hardness of SiPM is under characterization by many groups, and results are encouraging (Mianowski et al. 2020; Goyal et al. 2022). Usually, the walls of the scintillator are covered by a reflective or diffusive layer, and only one (or a few) faces are left open to be coupled to the photodetectors. As shown in Fig. 1, size matching is typically realized between the scintillator window and the photodetector, either a PMT (a) or a tile of SiPMs (b). The optical coupling between scintillator and photodetector plays a critical role, since refraction and loss of photons should be avoided. A coupling material,

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Fig. 1 Scintillator-based indirect detection of γ -rays by coupling a photodetector with single photon sensitivity: (a) PMT, (b) SiPM to the output window of the crystal

sandwiched between the two rigid surfaces, should adapt the refraction indexes and guide all the light to the detector avoiding optical leak and cross talk. It can be an optical grease (such as BC-631 by Saint-Gobain), a glue (such as Meltmount® ), or an optical pad, for instance made of silicone rubber. Grease can only be used for temporary operation, such as during laboratory experimentation. The pad might introduce more loss but offers the advantage of allowing for some tolerance in the alignment being compressible. In some cases, when the photodetectors have to be placed far from the scintillator, optical fibers can be used. Two approaches can be followed to explore high gamma energies (above ∼30 GeV, which cannot penetrate the atmosphere): installing the detector on a satellite (such as the Fermi Gamma-ray Space Telescope (Michelson et al. 2010)) or leveraging the Cherenkov effect using the atmosphere itself as scintillator producing Cherenkov light which is detected by networks of telescopes on the ground separated by tens to hundreds of meters such as the Cherenkov Telescope Array (Sciascio et al. 2019). Cherenkov light is radiation emitted when a charged particle travels at a speed higher than that of light in a medium. Upon interaction of a γ -ray with the atmosphere, at a height of ∼10 km, a cascade of particles (called shower) is produced, creating fast flashes of faint blue light that can be detected by ground telescopes, usually made of large parabolic reflectors with PMT cameras in the focus. Often the trajectory of the detected gamma photon has to be known. There are two possible approaches to endow the detector with selectivity to the photon direction: (i) physical collimation and (ii) realization of a Compton camera. A collimator is a passive block of high-Z material, typically a heavy metal such as lead or tungsten, which is thick enough to absorb the gamma photons in the energy range of interest. It is placed in front of the detector and is mechanically patterned to select only some trajectories of the rays that are allowed to reach the detector. Different geometries of the openings are possible, especially for gamma imaging (as in the case of tomographic imaging in nuclear medicine): parallel holes, single pinhole, multi pinhole, slits, slats, knife edge, etc. In the case of astronomy, given the distance of the radiation source, parallel openings are commonly used. More details are discussed in ⊲ Chap. 47, “Telescope Concepts in Gamma-Ray Astronomy” in this handbook.

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Coded apertures are special types of collimators, often adopted in telescopes, made of a sophisticated patterned mask that produces different shadows on the detector surface, according to the orientation of the ray, and thus allows its mathematical reconstruction. Interestingly, it has been shown that, in the absence of any collimator, machine learning can be used to train a reconstruction algorithm with rays laterally impinging from different directions on a cylindrical crystal. The classifier is able to identify the direction from the light patterns recorded by the bottom arrays of SiPM (Buonanno et al. 2020). The Compton camera, often also called Compton telescope and largely adopted in astronomical applications, is an instrument able to measure the direction of the incoming gamma photon (Parajuli et al. 2022). It is composed of two detector layers: a scatterer and an absorber. Both have to be position sensitive and provide timing information used to detect coincidence of events. The kinematics of Compton scattering is leveraged to reconstruct the photon trajectory in addition to measuring its energy. The incident photon undergoes scattering in the first layer and then is absorbed in the second one (often called calorimeter, though realized with different detector technologies). The path from the interaction point in the scatterer to the absorber defines a Compton cone, and the position of the gamma source can be estimated by computing the intersection of multiple cones. The scatterer can be a silicon detector, while the absorber is typically a scintillator coupled to a position-sensitive photodetector. COMPTEL is the only Compton telescope flown on a satellite (the Compton Gamma Ray Observatory (Schonfelder et al. 1993)). Compton telescopes can be used for the measurement of the polarization of γ -rays (polarimetry) since Compton scattering depends on the polarization of the photon (Lei et al. 1997). Compton cameras can be made very compact to fit inside CubeSats, such as MeVCube (based on two planes of CZT detectors (Lucchetta et al. 2022)) and ComPol (based on an SDD scatterer and LaBr3 absorber (Toscano et al. 2022; Cojocari et al. 2022) targeting X-ray polarimetry).

Fundamental Concepts Signal and Noise In order to design the readout electronics, we need to understand the properties of the input signal to be processed. The typical shape of the ideal signal at the input of the electronics is shown in Fig. 2. This waveform is assumed here to correspond to the current pulse produced by the detection of a single optical photon triggering the multiplications of electrons in the photodetector such as a SiPM (typically in the order of 106 ). The pulse is characterized by a rise time, usually very fast (in the order of ps), a peak amplitude, and a fall time, characterized by a decay time constant longer than the rise one, typically in the tens of nanosecond range. The decay time is the convolution of different time constants: the scintillator one, the photodetector one, and the one introduced by the front-end circuit. The electronic chain should be

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Fig. 2 Current pulse produced at the output of photodetector (PMT or SiPM) coupled to a scintillator in response to the detection of a gamma photon

designed in such a way that its time constant would be negligible with respect to the ones intrinsic to the detector; however, this is not always possible. Information commonly extracted from the current pulse (to identify the properties of the gamma photon) are the peak amplitude; the pulse area, which is the total generated charge, both of which are proportional to the photon energy; and the photon arrival time. The timing information can be used in multiple ways, in particular to study coincidence events and, for instance, to exclude other types of energetic radiation by simultaneous detection, by means of complementary detectors surrounding the main gamma detector and providing a veto. The signal amplitude is typically in the mA range. Let us consider, for example, a SiPM with 4096 cells, coupled to a LaBr3 scintillator. A 1 MeV gamma photon would produce 75,000 UV photons which correspond, considering SiPM saturation, PDE of 50% and gain of 2 · 106 , to a charge of ∼1.3 nC. Assuming a pulse time constant of 25 ns, the peak current ipeak is 100 mA. The signal has to be compared with the noise of the readout circuit. In fact, the main goal of the filtering stages is the maximization of the signal-to-noise ratio (SNR). In this context, electronic noise is defined as the level of uncertainty affecting electrical quantities in the circuit due to fluctuating sources intrinsic to the electronic components, such as the random motion of charge carriers in a conductor (thermal noise) or crossing a potential barrier in a semiconductor junction (shot noise). Noise is described as a statistical quantity, typically in the frequency domain by means of its power spectral density. The effects of different sources, modeled as equivalent signal sources, are propagated in a linearized abstraction of the circuit like small-signal perturbations. The effects of multiple sources are combined

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and should be summed quadratically (i.e., in power, if uncorrelated). Of course, other sources of fluctuations such as electromagnetic interference originating from external equipment should be minimized as well, by means of filtering and shielding strategies, but belong to another class: that of generic disturbances (not the same category of noise as defined here). Noise is a nonideal, intrinsic property characterizing individual components, such as resistors and transistors, but their impact on the global electrical variables in the chain depends on the topology of the circuit. Since typically signals are amplified along the acquisition chain, the noise of the first stages, undergoing amplification along the chain, is the dominant term and should be carefully minimized. It is possible to minimize noise by design. The detector at the input of the signal chain has a very relevant impact on the noise for three reasons: (i) it introduces its own noise, (ii) its impedance (in particular its capacitance) might enhance the noise of the input stage, and (iii) the parasitics introduced by the interconnection between the sensor and the preamplifier (in particular the stray capacitance) add to the total input impedance, again potentially degrading noise performance. The noise contributions generated in the SiPM are the following: (i) dark counts (DCR is the most relevant effect producing signal-like artifacts, with respect to after pulsing and optical cross talk), and (ii) fluctuations of the multiplication factor, i.e., of the gain, indicated by the excess noise factor (ENF). The total circuit noise, resulting from the combination of all different noise sources, is lumped into a single number, the equivalent noise charge (ENC), representing the value of an input charge that would produce a signal, at the end of the chain, with an amplitude equal to the noise (actually to its standard deviation). Often a minimum SNR = 1 is assumed as limit of detection. Thus, the ENC represents the smallest detectable signal. Actually, the SNR should be larger than 1, at least ∼10 for a more robust detection.

Chain Components The classical electronic chain for indirect detection of gamma photons, for both spectroscopy and imaging applications, is shown in Fig. 3. The detector current pulse is processed by the front-end stage. Often the input current is converted into a voltage by the preamplifier and then processed in the voltage domain. However, current-mode processing is also possible. The different topologies of the input stage are discussed in the next section. Then, the signal path splits into two branches according to the parameter to be acquired. In the energy path, the signal can undergo further amplification and shaping (i.e., filtering) in order to reduce the noise integrated in the bandwidth of interest. Common types of filters are RC and integrators. It can be demonstrated that, for a waveform as the one described in Fig. 2, the optimal filter is a gated integrator (Deighton 1968). At the output of the shaper, the energy of the filtered pulse has to be measured. The peak amplitude can be analogically sampled by a peak stretcher and then digitized by an analog-todigital converter (ADC).

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Fig. 3 Block scheme of the electronic chain for the readout of detectors of γ photons

The second branch is the timing path. The preamplifier signal can be filtered as well, typically by a fast shaper, and then fed to a fast comparator which compares it with a selectable threshold and produces the trigger signal. The delay of this trigger with respect to a reference time frame is measured by a time-to-digital converter (TDC) which digitizes the temporal information. The TDC can be implemented in different ways: as a time-to-amplitude converter (TAC), for instance converting time into a voltage (digitized by an ADC) by charging a capacitor with a constant current. Digital components, such as FPGAs, can be used to measure time intervals as well with very good resolution (∼10 ps): coarse timing is provided by counting periods of the clock signal (in the hundreds of MHz range), while fine, sub-period timing is provided by delay lines. Finally, a simplified approach to estimate the pulse energy with the timing branch is the time-over-threshold (ToT) method. In this case the measurement of the time during which the signal is above the threshold is used as a proxy for the pulse area, since its shape is known.

Analog vs. Digital Pulse Processing In order to process individual signals produced by the absorption of radiation such as X- and γ -ray photons and extract their energy, two main approaches can be followed: analog and digital processing of events. In the first case, an analog filter, called shaper, is applied to each pulse. The output waveform is the convolution of the impulse response of the filter with the output of the preamplifier. The peak amplitude of the shaped pulse has to be sampled. Typically, an analog circuit based on a capacitor, often called peak stretcher, is used to freeze the value of the peak and make it available for the digitization by means of a slow ADC. This approach is named analog pulse processing (APP). The main advantage of this approach is that the analog chain can be fully integrated on-chip, making it compact and scalable to a large number of channels, in an effective way from the point of view of area,

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cost, and power dissipation. The disadvantage is the limited reconfigurability of the filter: only some parameters (such as gain and peaking time) can be programmed among a limited number of options. Great versatility is offered by digital pulse processing (DPP) which instead samples the output of the preamplifier at high rate and applies shaping by means of a digital filter. Clearly the filter properties can be easily modified in the digital domain. Furthermore, since the whole waveform is sampled, additional operations can be applied such as pulse shape analysis (PSA) which comprises a set of operations on the shape of the pulse. For example, PSA can be used to discard events characterized by a slow rise time, reduce the detector background, or discriminate between gamma photons and neutrons looking at the rising edge of the pulses in scintillators (such as Cs2 LiYCl6 ) which generate different shapes of signals depending on the particle type. PSA can be implemented analogically too, but the digital approach is more straightforward. The drawback of DPP is the high cost and power dissipation of the high-sampling-rate ADC and the large data throughput that has to be processed, typically in real time by an embedded digital unit such a DSP or FPGA, which make it more difficult to increase the number of channels. Interestingly, from the point of view of spectroscopic performance, it has been demonstrated that both approaches are comparable (Hafizh et al. 2019). Currently the DPP approach allows reaching higher count rates (above 1 Mcps) with respect to APP which is limited by the bandwidth of fast shapers. The choice of the filter shape impacts on the maximum rate of events that can be processed. In fact, processing introduces a dead time during which additional incoming pulses cannot be correctly processed. Overlapping events cause the phenomenon of pileup which alters the quantification of the photons’ individual energy and thus alters the acquired spectrum.

Integrated vs. Discrete Implementations Before delving into the details of the circuit topologies, it is worth analyzing the available realization technologies. This choice sets some relevant constraints on the electronics design. The major difference is between integrated circuits and standard circuits, realized with discrete components. The latter case is the most traditional one: the circuit is designed and realized employing standard, general-purpose, offthe-shelf components which are then assembled on a printed circuit board (PCB). The advantages of this approach are the quick development time, the abundance of probing points, the possibility to modify the circuit, and the low cost. The main drawback of this realization is the bulkiness. On the other hand, the main advantage of an integrated implementation is the miniaturization: tens to hundreds of sensing channels can be integrated in a single microelectronic chip of a few mm2 in size. In this case the circuit is designed at the level of single transistors on a monolithic silicon platform, typically a CMOS platform including both n-type and p-type MOSFET transistor. The level of scaling, i.e., the minimum length of the transistors, characterizes the technology (such as 350, 180, 130, 65, 28 nm). The silicon foundry provides a design kit for each technology node containing all the detailed models

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needed to design, by means of systematic simulations, the circuits. Miniaturization is important not only to realize very compact and lightweight assemblies (clearly relevant for spaceborne applications) but often to improve the performance. For instance, a miniaturized front-end circuit can be placed closed to the detector, thus reducing the parasitic capacitance due to the interconnection and correspondingly improving the noise behavior of the preamplifier. Moreover, the integrated circuit is custom-designed and custom-tailored to the needs of the application and, thus, optimized (in particular in terms of particular figures of merit such as noise, power dissipation, etc. which are specific of the application), avoiding unnecessary components. For this reason, it is named ASIC (Application Specific Integrated Circuit). Despite these relevant advantages, three critical aspects have to been carefully analyzed: design constraints, development time, and cost. In fact, due to technological constraints, the range of values of passive components (resistors, capacitors, and inductors) that can be integrated onchip are narrower with respect to the discrete case (e.g., capacitor values usually do not exceed tens of pF). Furthermore, the high density of transistors squeezed together implies a large density of power dissipating components, which might introduce limits in the operation of the circuit due to the global thermal design, allowing the removal of heat from the chip. The second aspect concerns the development time: the fabrication of a microelectronic chip, undergoing several steps (photolithography, implantation and doping, metalization), takes a few months in the silicon foundry. Usually research institutions can access these technologies by means of multi-project wafer (MPW) programs offered by consortia (such as Europractice in Europe and MOSIS in the USA) which periodically collect designs from academic institutions and populate a wafer, whose production costs are shared and reduced for educational purposes. Considering the periodicity of the MPW tapeout deadlines (varying among technologies and foundries) and the fabrication time, the total delivery time spans from 3 to 6 months. Of course, the design time has to be added to the fabrication time, and considering the complexity of the design, simulation, and validation, the total design cycle is in the order of 1 year. If, for the initial design from scratch, the development time can be similar among the realizations, the main difference arises for successive iterations and corrections of the design, which takes weeks in the discrete-component case as compared to months with the integrated one. The last drawback of integrated implementations is the cost. Although the cost per chip becomes negligible for large-volume productions, in the case of research use, where batches of tens of chips are commonly produced for each run, the individual cost is typically higher than the equivalent implementation with discrete components (of course depending on the complexity of the circuit). The total ASIC cost is composed of two main contributions: the fabrication cost, which depends on the silicon area used by the circuit, and the cost of software licenses needed for the chip design. In fact, despite the open-source attempts that have been recently activated (for instance by Google https://developers.google.com/silicon), the market of EDA (electronic design automation) is still dominated by very expensive software.

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Since in the aerospace sector, especially in the case of scientific payloads for astronomy, where only a few very sophisticated systems are usually produced, reliability (during long-term missions) is often more important than cost and prototyping time, another key criterion to compare realization technologies is reliability. Different types of faults can affect the lifetime of onboard electronics. Multiple environmental factors impact on the reliability of electronic components and boards: mechanical vibration, thermal stress, and cosmic radiation, the latter often being the dominant concern. In space environment, radiation damage to electronics can be due to the long-term accumulation of radiation (total ionizing dose, TID) which depends on the duration of the mission, or single event effects (SEE) due to the effect of individual particles. On the one hand, since a monolithic ASIC includes several components, it is intrinsically more reliable than discrete components placed on a PCB from the assembly point of view (lack of soldering points and connectors, replaced by bonding wires). However, the ASIC, analogously to commercial chips, is equally prone to radiation damage, such as charge trapping in thin oxides of transistors or increase of dark count in SiPM. Thus, the choice of the most suitable microelectronic technology takes into account also the radiation hardness performance, achievable both by means of process and design techniques (Calligaro and Gatti 2020). In general, more scaled technologies, having, for instance, thinner oxides, are intrinsically radiation harder than older technologies. A final consideration concerns the boundary between on-chip and off-chip circuits, or, in other words, finding the proper answer to the question: which parts of the readout chain are worth being integrated? Looking at the chain of Fig. 3, it is apparent that the early stages of the chain from the front end to the filter and peak detector in the energy branch should be integrated. Should the ADC be integrated? The main motivation to integrate the ADC as well is to provide a digital output to the chip, which is much more robust to electromagnetic interference and noise than an analog output. On the other end, leveraging an external ADC has several advantages: modularity and versatility to change ADC, while keeping the front end, wider choice of state-of-the-art components realized in technologies different from of the one of the front end, less area, and power dissipation issues. A similar consideration holds for the timing branch and the timing block (on-chip vs. off-chip TDC). In conclusion, when multiple readout channels are needed (for instance for imaging purposes or even in spectroscopy applications to achieve high count rates by partitioning the detector area in pixels), or where mass and miniaturization are pivotal for satellite installation of the detector, an integrated circuit is the preferred choice to realize the front-end amplifiers.

Readout Circuits The pulsed current signals produced by the photodetector can be read in different ways, in voltage mode (Fig. 4a), in charge mode (Fig. 4b), and in current mode, by means of an input current buffer either without feedback or leveraging different types of negative (Fig. 4c) and weakly positive feedback (as in the case of the current

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Fig. 4 Taxonomy of circuit topology for readout of a photodetector: (a) voltage mode, (b) charge mode, current mode with (c) negative and (d) positive feedback current buffers

conveyor (CC); Fig. 4d). The different readout topologies will be briefly illustrated in this section. Additional details can be found in review papers (Calò 2019). Here we mostly refer to integrated realizations, describing a selection of the numerous ASICs available for readout of tiles of SiPMs. It must be highlighted that most of these ASICs were developed for medical applications, in particular for positron emission tomography (PET), where the energy of the gamma photons is well defined (511 keV) and much smaller than the high-energy spectral range explored in for γ ray astronomy.

Voltage Mode The most straightforward way to amplify a current is to convert it into a voltage by forcing it to flow through a defined conversion impedance. This approach benefits from the linearity of Ohm’s law relating current and voltage across a known impedance (Fig. 4a). Such impedance can be as follows: (i) a capacitor, often the detector capacitance CD , (ii) a resistor RI N , or (iii) a resistor in series to a capacitor (AC-coupled resistor). The choice of the resistor is the most common since its value is independent of frequency (neglecting the stray capacitance in parallel to it, of the order of 0.1 pF for discrete components and thus negligible up to GHz frequencies), and it can provide a matching termination in case a coaxial cable is

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used to connect the photodetector. The major drawback of this approach is related to the nonzero input impedance which entails the following: (i) variation of the bias voltage across the SiPM due to the Ohmic drop on RI N during the current pulse, producing a nonlinear response, and (ii) a time constant given by the product of the detector capacitance and RI N . For these reasons, the choice of the value of RI N is bound to a compromise: on the one hand, it should be large, to have a large conversion gain from current to voltage, while on the other hand, it should be small to minimize the input impedance. Typical values are a few tens of Ohms. An example of a popular ASIC based on voltage mode readout for SiPM is SPIROC (Ahmad et al. 2021). The input resistor is 50  to provide termination for the coaxial cable, whose shielding is biased at high voltage. The resistor is AC-coupled so that the DC value of the input node is set by an 8-bit DAC useful to compensate variations in the gains of the photodetectors by fine-tuning the bias voltage of individual input channels. The ASIC includes 36 channels. A voltage amplifier with capacitive and selectable gain amplifies the input voltage and drives two shaping branches with CR-RC2 topology. In the energy branch, a slow shaper (50–100 ns) filters the signal whose peak value is stored in an analog memory made of a bank of 16 capacitors. A 12-bit Wilkinson-type ADC converts data with a conversion time of 80 µs. The analog memory allows increasing the sampling rate. The timing branch is composed of a fast shaper (15 ns) whose output is compared to a fast discriminator with an adjustable threshold, triggering a ramp TDC with a timing resolution of 1 ns. An evolution of this ASIC, SPIROC2C adopts a power pulsing technique to reduce the power dissipation, achieving a consumption of 25 mW per channel. The maximum input charge is 320 pC. The same French group (Omega and the WEEROC company) has proposed different generations of chips (Ahmad et al. 2021). One evolution is PETIROC2, sharing the same voltage-mode topology and featuring 32 channels and a TDC with 25-ps timing resolution. Another example of a voltage mode ASIC is the first version of PETA, developed at Heidelberg University (Germany). In this case the AC-coupled voltage preamplifier (with a gain of 32 and endowed with a common-mode feedback loop) has a fully differential configuration. The output voltage of the preamplifier is fed to an integrator (energy path) and to a discriminator (timing path) (Fischer et al. 2009).

Charge Mode In order to address the limitations of the voltage mode, the standard solution adopted in front-end circuits for charge-producing sensors and detectors (SDD and depleted diodes in particular) is the use of negative feedback. Thanks to the high loop gain, the input impedance is ideally zero, within the bandwidth of the loop, and the whole sensor current is forced to flow in the feedback branch, neutralizing the effect of any parasitic path between the input node (virtual ground) and ground. In feedback a known impedance is used to convert the current into a voltage. If a resistor is placed in feedback, the circuit is called transimpedance amplifier (TIA). Instead, if a capacitor is placed in feedback, the circuit becomes a current integrator, often named

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charge-sensitive amplifier (CSA), since the time integral of the current waveform is the charge. In the case of current pulses, the preferable choice is the CSA, since the removal of the feedback resistor RF enables the removal of a source of noise (4kT /RF ). An ideal integrator needs an additional network to handle the input DC current, unavoidably present even in the case of nominal zero-mean signal (for instance due to detector leakage current or to protection diodes of the input node) that would produce a slow drift of the output node, leading to the saturation of the stage. Two approaches are possible: reset or continuous-time schemes. In the first case, the operation of the amplifier is periodically interrupted, and the feedback capacitor is discharged. The discharge can take place through a switch or a current source in parallel to the capacitor CF . The trigger of the reset can be periodic (with a frequency adjusted to the average rate of input events to cover the full swing of the amplifier output) or driven by the passing of a high threshold on the output voltage. Despite its simplicity, this approach introduces a dead time. Alternatively, continuous solutions introduce additional feedback loops that divert the DC current from being integrated in CF (Crescentini et al. 2013). Two aspects need special care when designing a CSA for this application in SiPM readout: the stage stability and the maximum integrable charge. Like any feedback system, operating conditions have to be carefully studied, especially at high frequencies where the loop gain decreases, to avoid instability. The detector capacitance introduces a pole in the loop gain that might cause instability. For standard SiPMs, the detector capacitance is in the order of 100 pF/mm2 . Consequently, values of several nF can be reached in the case of large pixels or when merging multiple pixels, making it very challenging to achieve stability and high speed with standard opamps. In fact, stability could be easily achieved by reducing the amplifier bandwidth, which is against the goal of achieving a fast response (with bandwidths in the 10–100 MHz range) for a fast processing of gamma events. Assuming a maximum input charge in the range from 100 pC to 10 nC and considering a supply voltage of the ASIC of a few volts, the integrator capacitance should have a value in the nF range. This value is far above the maximum capacitance that is commonly integrable on chip, which is of the order of tens of pF. For both reasons discussed above (stability and full-scale range), the SiPM current is very rarely fed to the input of a CMOS integrator directly. Instead, a current buffer is put before, thus partially solving both issues simultaneously, as discussed in the next section.

Current Mode: Negative Feedback Current buffers enable to scale down the input current so that a reduced copy of the input signal is fed to the integrator stage. The current buffer can be realized in different ways: (i) by means of a “cascode” (open-loop transistor, whose source is the input node), (ii) by means of transdiode input configuration and mirrors, (iii) by means of active negative feedback to “boost” the gm of the input transistor, and

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(iv) by means of a current conveyor based on weakly positive feedback. In the first two cases, the input impedance equal to 1/gm . Since the transistor is biased by the signal current, its gm depends on the signal amplitude, thus introducing a nonlinear response. An example of the first approach is the BASIC ASIC developed by Politecnico di Bari (Italy) (Foresta et al. 2009). An input cascode buffers the input current into a mirror (demultiplying the current by a factor 10), which drives a TIA with selectable RC time constant and baseline holder (BHL). The boosted gm allows decreasing the input impedance, thanks to the gain of an additional amplifier put in feedback. Such amplifier can be a second single transistor or a differential stage. There are different ASICs based on this concept, thus resulting in the most popular topology, such as PETA4 (Heidelberg, Germany) (Sacco et al. 2013), SIPHRA (commercially available by IDEAS A.G., Norway, and developed for γ -ray astronomy application) (Meier et al. 2016), FLEXTOT (Barcelona, Spain) (Comerma et al. 2013), TOFPET (Lisbon, Portugal) (Rolo et al. 2013), and FBK (Italy) (Xu et al. 2015). The typical loop gain is the order of 10, leading to an input impedance in the order of 10 . The TOFPET ASIC is commercially available from PETsys Electronics SA (Portugal), thus finding widespread application, especially in medical imaging applications. It features two discriminators. The second threshold has twofold purpose: (i) validation of events for rejection of dark counts and (ii) availability of a second timestamp for ToT amplitude estimation. TOFPET2 includes 64 channels with a FSR of 1.5 nC, operating at a maximum count rate of 600 cps and dissipating 8 mW/channel (in specific conditions). The timestamps are provided by an on-chip TDC with 50-ps resolution (binning of 30 ps). The FLEXTOT ASIC includes 16 channels. Energy is extracted with ToT with an input FSR of 2 nC and a linearity error of 5%. The peculiarity of FLEXTOT is the presence of two feedback loops in the boosted-gm input stage. A low frequency loop stabilizes the bias point of the current buffer, while a second loop operating at higher frequencies lowers the input impedance (34) in the frequency region corresponding to the bandwidth (max. 250 MHz) of the input pulses. Three signal paths follow the input stage: (i) a high-gain branch with a discriminator for timing, (ii) a low-gain one (with an integrator with the Krummenacher solution to discharge the feedback capacitor (Krummenacher 1991)) for energy, and (iii) an AC-coupled discriminator looking at the signal peak amplitude to flag pileup. The trigger jitter is below 30 ps, and the power consumption is 11 mW/channel, among the best in the class. Another ASIC named MUSIC developed at the University of Barcelona (Gómez et al. 2021) provides 8 channels with current input mirrored to energy and timing channels, with zero-pole cancellation, a dissipation of 30 mW per channel, 32  input resistance, and the useful feature of a summed output, where all the 8 input currents are summed in current mode and filtered. This can be very useful per spectral analysis. Interestingly, it operates with a detector capacitance up to 10 nF.

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Current Mode: Positive Feedback In order to address the limitations of negative feedback in the presence of large input capacitance, a totally different approach can be adopted. The Temes current conveyor (CC) (Temes and Ki 1987; Sedra 1989) is based on positive feedback and a symmetrical topology. Our group in Politecnico di Milano has pursued the use of this input topology in a family of ASICs for the readout of SiPMs: ANGUS (Trigilio et al. 2018), GAMMA (Buonanno et al. 2021), and recently SITH (D’Adda et al. 2022). Since this solution is nonstandard, we describe its working principle in detail. The scheme of the CC is shown in Fig. 5: when a current is injected in the source of M1, its voltage would tend to increase, but the voltage at the gate decreases by approximately the same amount, thanks to the mirroring of M3, M4, and M2, thus reducing the input impedance. In order to study the circuit stability, let us compute the loop gain Gloop . At low frequencies, it results: |Gloop,LF | =

gm1 1 gm4 · · gm2 1 + gm1 1r0 gm3

(2)

Due to the strong degeneration of M1, at low frequencies the loop is inactive, and the bias point of the input node is set at VREF only by the symmetry of the circuit. Instead, at medium frequencies, where the detector capacitance CD shunts the Early resistance r0 , we obtain: gm4 gm1 |Gloop,MF | = · = gm2 gm3



W/L4 W/L1 · W/L2 W/L3

(3)

Fig. 5 Scheme of the Temes current conveyor leveraging symmetry and weakly positive feedback to achieve a low input impedance RI N

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which is smaller than one. Interestingly, the value of |Gloop,MF | is independent of the bias current, which can be used to optimize other circuit parameters (such as noise, linearity, and bandwidth), without affecting its stability. At high frequencies, the transistor’s parasitic capacitances become dominant, causing a decrease of Gloop . Among them, the dominant one is Cgate of M3 which is the largest transistor. Thus, Gloop contains three singularities: a zero at fz and two poles at fp1 and fp2 . The low-frequency zero is associated with the recirculation of the input current in CD and r0 , thus resulting: fz =

1 2π · r0 · CD

(4)

The first pole is due to the input impedance and the CD: fp1 =

gm1 2π · CD

(5)

gm3 2π · Cgate

(6)

while the second pole is due to Cgate : fp2 =

The frequency response of Gloop has a band-pass shape, with a flat region between the poles of magnitude close to 1, finely tuned by acting on the transistors form factors. Since the value of fp2 does not depend on CD , the increase of the input capacitance does not affect stability (differently from the classical case of negative feedback). This is confirmed by the circuit simulations reported in Fig. 6 with CD spanning from 0.1 to 20 nF. The increase of CD produces a rigid shift toward lower frequencies of fz and fp1 . In order to find the input resistance RI N , let us split VI N as the sum of V2 at the gate of M1 and ΔV as the Vsg of M1: RI N =

ΔV + V2 VI N = II N II N

(7)

where II N = ΔV · gm1 and v2 can be written as the voltage drop at the gate in response to the injection of II N : V2 = −II N

gm4 gm3 · gm2

(8)

By combining (3) and (8) into (7), we obtain: RI N =

1 gm1

(1 − Gloop,MF )

which confirms that the input impedance is lowered by the positive feedback.

(9)

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Fig. 6 Parametric circuit simulation of the loop gain Gloop(f ) for varying values of the detector capacitance CD up to 20 nF. The circuit is stable across the whole range of values

The main challenge in sizing this stage is to move the value of Gloop as close as possible to 1, avoiding the risk of exceeding it and, thus, producing instability. When approaching unity and decreasing the input impedance, ripples manifest on the output signal, increasing the time needed to process the full input charge, and consequently increasing the dead time and decreasing the maximum input count rate. Taking into account process variations, simulated with both Monte Carlo sampling and corner models, a safe value of 0.9 has been identified. By choosing a bias current of 320 µA, gm1 results equal to 5.4 mS and |Gloop,MF | = 0.9 (in the range from 2 to 10 MHz with CD = 2.5 nF). This value grants RI N smaller than 20 . The layout of the stage (Fig. 7) can be made very compact. The current is copied by the CC with different mirroring factor: large (∼100) demagnification is used to inject the current in the gated integrator (with M6), while higher gain (M5) is used to feed the signal to a current comparator generating the trigger signal. In ANGUS (Trigilio et al. 2018), a 36-channel ASIC targeting application in SPECT (Carminati et al. 2018), the CC was initially coupled with an RC filter (with programmable time constant from 250 ns to 10 µs and endowed with a baseline holder) followed by a peak stretcher. Two multiplexers allow the readout of the analog outputs. Being coupled to a monolithic scintillator, when one channel triggers, all pixels are read. For each channel, a DAC allows to finely tune the DC

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Fig. 7 Example of microelectronic layout of the CC which is very compact

value of the input in order to compensate gain mismatches among SiPM pixels. However, given the good homogeneity of currently available SiPMs, this feature is rarely employed. The GAMMA ASIC (Buonanno et al. 2021) represents an evolution of ANGUS. In the filter stage, a gated integrator (GI) replaces the RC filter, offering better SNR performance. Furthermore, in order to extend the full-scale range (up to 104 photons, necessary to extend the spectroscopy range up to 20 MeV), an automatic gain control (AGC) block has been inserted (Fig. 8). In fact, three capacitors can be connected in the feedback of the GI: the integration begins with the smallest capacitance, which provides the highest gain, and then additional capacitors are automatically connected in parallel to reduce the gain as the signal increases. The peak is sampled and made available at the multiplexed analog output. Other groups have followed our development, for instance improving the on-chip ADC strategies (Sengupta and Johnston 2022).

Conclusions We have presented the key aspects of the design of circuits for γ -ray detection. Since in some cases the amount of secondary photons to detect is limited (due to a low-energy γ -ray or to Cherenkov radiation), photodetectors with internal gain are employed. PMTs, which have dominated this class of applications for decades, are being replaced by their solid-state equivalents, SiPMs. For this reason we have mainly focused on circuits for the readout of SiPMs, but most of the design guidelines here briefly discussed remain valid for other detectors, such as PMTs and SDDs. The value of the detector capacitance and the maximum input charge

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Fig. 8 Block scheme of the GAMMA ASIC: each of the 16 channels includes the CC input stage, the gated integrator with automatic gain control (AGC) that dynamically switches the value of the integration capacitance CF . An additional feedback loop stabilizes the baseline (BHL)

determine the choice of the circuit topology: while voltage mode is very simple and popular, charge and current mode can take advantage of the benefits offered by feedback. The emerging trend in space missions to move toward large constellations of very compact and cheap satellites (such as CubeSats) for a myriad of commercial and scientific applications will also impact strategies for γ -ray astronomy. In this context, radiation hardness requirements are relaxed and make the implementation of readout ASICs very promising, leveraging at the same time miniaturization.

References S. Ahmad, S. Blin, S. Callier, J.B. Cizel, S. Conforti, C. de La Taille, F. Dulucq, J. Fleury, G. Martin-Chassard, L. Raux et al., Omega sipm readout asics. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 986, 164628 (2021) L. Buonanno, D. Di Vita, M. Carminati, C. Fiorini, A directional gamma-ray spectrometer with microcontroller-embedded machine learning. IEEE J. Emerg. Sel. Top. Circuits Syst. 10(4), 433–443 (2020) L. Buonanno, D. Di Vita, M. Carminati, C. Fiorini, Gamma: a 16-channel spectroscopic asic for sipms readout with 84-db dynamic range. IEEE Trans. Nucl. Sci. 68(10), 2559–2572 (2021) C. Calligaro, U. Gatti, Rad-hard mixed-signal ic design, theory and implementation, in NextGeneration ADCs, High-Performance Power Management, and Technology Considerations for Advanced Integrated Circuits (Springer, Springer Nature Switzerland AG 2020), pp. 273–297

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P.P. Calò, F. Ciciriello, S. Petrignani, C. Marzocca, Sipm readout electronics. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 926, 57–68 (2019) M. Carminati, G.L. Montagnani, M. Occhipinti, A. Kuehne, T. Niendorf, K. Nagy, A. Nagy, M. Czeller, C. Fiorini, Spect/mri insert compatibility: assessment, solutions, and design guidelines. IEEE Trans. Radiat. Plasma Med. Sci. 2(4), 369–379 (2018) I. Cojocari, M. Meier, P. Laurent, A. Laviron, M. Arrigucci, M. Carminati, G. Deda, C. Fiorini, K. Geigenberger, C. Glas et al., Calorimeter calibration of the compol cubesat gamma-ray polarimeter. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 1046, 167662 (2022) A. Comerma, D. Gascón, L. Freixas, L. Garrido, R. Graciani, J. Marín, G. Martínez, J.M. Pérez, P.R. Mendes, J. Castilla et al., Flextot-current mode asic for readout of common cathode sipm arrays, in 2013 IEEE Nuclear Science Symposium and Medical Imaging Conference (2013 NSS/MIC) (IEEE, 2013), pp. 1–2 M. Crescentini, M. Bennati, M. Carminati, M. Tartagni, Noise limits of CMOS current interfaces for biosensors: a review. IEEE Trans. Biomed. Circuits Syst. 8(2), 278–292 (2013) I. D’Adda, S. Vacondio, L. Buonanno, M. Carminati, C. Fiorini, Sith: a 16-channel asic for sipms readout in hadrontherapy, in IEEE Nuclear Science Symposium and Medical Imaging Conference (IEEE, 2022) M.O. Deighton, A time-domain method for calculating noise of active integrators used in pulse amplitude spectrometry. Nucl. Instrum. Methods 58(2), 201–212 (1968) C. Fiorini, A. Gola, M. Zanchi, A. Longoni, P. Lechner, H. Soltau, L. Struder, Gamma-ray spectroscopy with labr _3: Ce scintillator readout by a silicon drift detector. IEEE Trans. Nucl. Sci. 53(4), 2392–2397 (2006) P. Fischer, I. Peric, M. Ritzert, M. Koniczek, Fast self triggered multi channel readout asic for time-and energy measurement. IEEE Trans. Nucl. Sci. 56(3), 1153–1158 (2009) F. Corsi, M. Foresta, C. Marzocca, G. Matarrese, A. Del Guerra, Basic: an 8-channel front-end asic for silicon photomultiplier detectors, in 2009 IEEE Nuclear Science Symposium Conference Record (NSS/MIC) (IEEE, 2009), pp. 1082–1087 F. Fuschino, R. Campana, C. Labanti, Y. Evangelista, M. Feroci, L. Burderi, F. Fiore, F. Ambrosino, G. Baldazzi, P. Bellutti et al., Hermes: an ultra-wide band x and gamma-ray transient monitor on board a nano-satellite constellation. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 936, 199–203 (2019) E. Gatti, P. Rehak, Review of semiconductor drift detectors. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 541(1–2), 47–60 (2005) S. Gómez, D. Sánchez, J. Mauricio, E. Picatoste, A. Sanuy, A. Sanmukh, M. Ribó, D. Gascón, Multiple use sipm integrated circuit (music) for large area and high performance sensors. Electronics 10(8), 961 (2021) S.K. Goyal, A.P. Naik, P. Sharma, Characterization of silicon photomultipliers (sipms) for space exploration. Adv. Space Res. 70, 3750–3768 (2022) I. Hafizh, M. Carminati, C. Fiorini, Assessment of analog pulse processor performance for ultra high-rate x-ray spectroscopy. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 945, 162479 (2019) F. Krummenacher, Pixel detectors with local intelligence: an IC designer point of view. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 305(3), 527–532 (1991) F. Lei, A.J. Dean, G.L. Hills, Compton polarimetry in gamma-ray astronomy. Space Sci. Rev. 82(3), 309–388 (1997) G. Lucchetta, M. Ackermann, D. Berge, R. Bühler Introducing the mevcube concept: a cubesat for mev observations. J. Cosmol. Astropart. Phys. 8, 1–15 (2022) D. Meier, J. Ackermann, A. Olsen, H.K.O. Berge, A. Hasanbegovic, M.A. Altan, S. Azman, B. Najafiuchevler, J. Talebi, P. Påhlsson et al., Siphra 16-channel silicon photomultiplier readout asic, in Proceedings of the ESA AMICSA & DSP, 6th International Workshop (2016)

53 Readout Electronics for Gamma-Ray Astronomy

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S. Mianowski, D.M. Borowicz, K. Brylew, A. Dziedzic, M. Grodzicka-Kobylka, A. Korgul, M. Krakowiak, Z. Mianowska, A.G. Molokanov, M. Moszynski et al., Sipm proton irradiation for application in cosmic space. J. Instrum. 15(03), P03002 (2020) P.F. Michelson, W.B. Atwood, S. Ritz, Fermi gamma-ray space telescope: high-energy results from the first year. Rep. Progress Phys. 73(7), 074901 (2010) R.K. Parajuli, M. Sakai, R. Parajuli, M. Tashiro, Development and applications of compton camera–a review. Sensors 22(19), 7374 (2022) C. Piemonte, A. Gola, Overview on the main parameters and technology of modern silicon photomultipliers. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 926, 2–15 (2019) M.D. Rolo, R. Bugalho, F. Goncalves, G. Mazza, A. Rivetti, J.C. Silva, R. Silva, J. Varela, Tofpet asic for pet applications. J. Instrum. 8(02), C02050 (2013) I. Sacco, P. Fischer, M. Ritzert, I. Peric, A low power front-end architecture for sipm readout with integrated adc and multiplexed readout. J. Instrum. 8(01), C01023 (2013) V. Schonfelder, H. Aarts, K. Bennett, H. Deboer, J. Clear, W. Collmar, A. Connors, A. Deerenberg, R. Diehl, A. Von Dordrecht et al., Instrument description and performance of the imaging gamma-ray telescope comptel aboard the compton gamma-ray observatory. Astrophys. J. Suppl. Ser. 86, 657–692 (1993) G. Di Sciascio, Ground-based gamma-ray astronomy: an introduction. J. Phys.: Conf. Ser. 1263, 012003 (2019). IOP Publishing A.S. Sedra, The current conveyor: history and progress, in IEEE International Symposium on Circuits and Systems (IEEE, 1989), pp. 1567–1571 S. Sengupta, M. Johnston, A sipm-based gamma spectrometer with field-programmable energy binning for data-efficient isotope analysis. IEEE Trans. Circuits Syst.–I: Reg. Pap. (2022) G.C. Temes, W.H. Ki, Fast CMOS current amplifier and buffer stage. Electron. Lett. 23(13), 696– 697 (1987) L. Toscano et al., Sdd analog readout system for the compol cubesat compton polarimeter, in IEEE Nuclear Science Symposium and Medical Imaging Conference (IEEE, 2022) P. Trigilio, P. Busca, R. Quaglia, M. Occhipinti, C. Fiorini, A sipm-readout asic for spect applications. IEEE Trans. Radiat. Plasma Med. Sci. 2(5), 404–410 (2018) H. Xu, M. Perenzoni, N. Massari, A. Gola, A. Ferri, C. Piemonte, D. Stoppa, A 16-channel readout asic for pet application, in 2015 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) (IEEE, 2015), pp. 1–3

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Vincent Tatischeff, Pietro Ubertini, Tsunefumi Mizuno, and Lorenzo Natalucci

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orbits of Gamma-Ray Space Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Low-Earth Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High-Earth, Highly Elliptical, and L1/L2 Orbits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stratospheric Balloon Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Background Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Extragalactic Gamma-Ray Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Galactic Gamma-Ray Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Galactic Cosmic Rays and Anomalous Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Solar Energetic Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Secondary Particles in Low-Earth Orbits and the Stratosphere . . . . . . . . . . . . . . . . . . . . . Delayed Background from Activation of Satellite Materials . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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V. Tatischeff () CNRS/IN2P3, IJCLab, Université Paris-Saclay, Orsay, France e-mail: [email protected] P. Ubertini · L. Natalucci IAPS/INAF, Rome, Italy e-mail: [email protected]; [email protected] T. Mizuno Hiroshima Astrophysical Science Center, Hiroshima University, Higashi-Hiroshima, Hiroshima, Japan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_47

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Abstract

Gamma-ray telescopes in space are bombarded by large fluxes of charged particles, photons, and secondary neutrons. These particles and radiation pose a threat to the nominal operation of satellites and limit the detection sensitivity of gamma-ray instruments. The background noise generated in gamma-ray space detectors by impinging particles is always much higher than the astrophysical signal to be detected. In this chapter, we present the different types of orbits suitable for gamma-ray missions, discussing their advantages and disadvantages, as well as the value of experiments embarked in stratospheric balloons. We then review the physical properties of all the background components in the different orbits and the stratosphere. Keywords

Gamma rays · High-energy astrophysics · Gamma-ray telescopes · Instrument background · Low-Earth orbits · High-Earth orbits · Cosmic rays · Solar energetic particles · Earth albedo

Introduction Due to the atmospheric absorption, gamma-ray experiments in the energy range from ∼100 keV to a few tens of GeV must operate in space or in the high stratosphere, at an altitude higher than about 30 km. But while placed in low-Earth orbits (LEO), typically between 400 and 600 km, gamma-ray space missions need to avoid the Van Allen radiation belts filled with energetic charged particles (van Allen and Frank 1959). Similarly, high elliptical orbits around Earth have to limit as much as possible the time passed near perigee (the point of closest approach to Earth), when the spacecrafts pass through the electron and proton belts surrounding the planet. On the other hand, satellites orbiting outside the Van Allen belts, at distances greater than about 40,000 to 60,000 km from Earth, are not shielded by the geomagnetic field, which offers a natural protection against Galactic cosmic rays and solar energetic particles. The environment surrounding high-energy experiments in space has two main effects: (i) radiation damage due to highly energetic particles and (heavy) ions impinging within the detectors’ active volume and electronics and (ii) degradation of the instrument sensitivity due to high counting rate if compared with the usually weak signals from cosmic sources to be studied. To give an order of magnitude, the integrated gamma-ray flux of the Crab Nebula – the most intense (quasi-)stationary source of the gamma-ray sky – is FCrab (≥ 1 MeV) ≈ 2 × 10−3 ph cm−2 s−1 , which can be compared to the flux of Galactic cosmic-ray particles (mostly protons) in the near-Earth interplanetary medium: FGCR (≥ 1 MeV) ≈ 2–5 particles cm−2 s−1 (depending on the strength of the solar modulation). Energetic particles not only

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induce a prompt instrumental background when they deposit energy in gammaray detectors, but they can also be the origin of a delayed background in soft gamma-ray telescopes due to the activation of spacecraft materials. And yet, gamma-ray astronomers are now designing space missions with the aim of reaching the milliCrab sensitivity in the MeV range, that is, detecting tiny fluxes of cosmic gamma-ray photons in a background of surrounding energetic particles that can be a million times more numerous! The first question to consider when preparing a new gamma-ray space mission is the orbit. The pros and cons of placing heavy gamma-ray detectors and spacecrafts in low- versus high-Earth orbits were already a matter of debate in the 1980s. Historically, most of the satellites for high-energy astronomy were placed in LEO because of the lower power needed to reach flight altitude. But at the turn of the millennium, two European Space Agency (ESA) missions, the X-ray satellite XMM-Newton (0.15–15 keV) and the gamma-ray observatory INTEGRAL (20 keV– 10 MeV), were launched to high elliptical orbits, with perigee and apogee at the start of the missions of 7000 × 114,000 km and 2000 × 160,000 km, respectively. Spacecrafts in such orbits spend most of the time outside the radiation belts, which implies a higher average background, though more stable and constant with the yearly orbital evolution. The choice of the best orbit in which to insert a gamma-ray satellite remains a difficult task, depending on multi-parametric issues, including scientific requirements, like the required sky coverage and duration of uninterrupted observations, operational constraints like the tracking station availability, and programmatic constraints like the cost and availability of the launcher and the launch site. In Section “Orbits of Gamma-Ray Space Missions”, we first present the different types of orbits available for gamma-ray space missions. We also devote a sub-Section to stratospheric balloon-borne experiments, which have played a major role in the development of gamma-ray astronomy. In Section “Background Components”, we present in detail the different sources of background of gammaray satellites. We first discuss the origin and overall properties of the background particles and radiation, and then the effects of the internally induced radioactivity in space. Our conclusions are finally given in the last Section.

Orbits of Gamma-Ray Space Missions The Earth’s atmosphere is completely opaque to gamma-ray radiation at ground level. Cosmic photons of energy 100 keV penetrate the atmosphere with an efficiency >30% up to an altitude of ∼30 km, i.e., in the upper stratosphere. These photons can then be detected with large area sensors, although the radiation arriving from cosmic sources provide a minuscule flux if compared with the induced detector background due to the high fluxes of charged particles. For these reasons, softgamma-ray experiments in the energy range between ∼100 keV and a few MeV are operated in space or, for experiments requiring short observing time, in the

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upper stratosphere. Higher-energy gamma-rays, up to 100 GeV, are in principle also detectable at stratospheric altitudes, even if the long observing time needed to detect cosmic sources restricts the usefulness of stratospheric balloon experiments, which maximum floating time is limited to a few weeks in the best case. High-energy gamma-ray experiments are thus mainly conducted with satellites orbiting out of the atmosphere.

Low-Earth Orbits An LEO is defined as a geocentric orbit at an altitude between about 200 and 2000 km. However, most gamma-ray space instruments launched in LEO are placed between 400 and 600 km. At these altitudes, the orbital speed is ∼7.6 km s−1 and the orbital period ∼95 min. Historically, the first scientific satellites to study solar and cosmic X- and gamma rays were injected in LEO: the Orbiting Solar Observatory (OSO) series launched from 1962 to 1975; the three Small Astronomy Satellites (SAS) launched in 1970, 1972, and 1975; the three High Energy Astronomy Observatory (HEAO) missions in 1977, 1978, and 1979; the Solar Maximum Mission (SMM) in 1980, the Compton Gamma Ray Observatory (CGRO) in 1991; and BeppoSAX in 1996, among others. Gamma-ray missions still operative from an LEO comprise AGILE (Astro-Rivelatore Gamma a Immagini Leggero) launched in 2007 and Fermi in 2008. More recently, also a substantial number of CubeSats, small low-cost satellites, have been placed in this family of orbits. One of the major advantages of LEOs is that the Earth’s magnetic field works as a very effective shield against charged particles generated by the Sun and those arriving from the Galaxy. Unfortunately, the effect of the magnetic field shield is strongly modulated, not only in polar orbits (with an inclination of 60◦ –90◦ to the equator), but also in equatorial ones, which are usually chosen for highenergy instruments. The background count rate measured during the typical 95 -min duration of the equatorial or low inclination orbits is strongly modulated. This is basically due to the particular field line profile of the Earth’s magnetic field funneling charged particles in the south Atlantic region, the so-called South Atlantic Anomaly (SAA). As shown in Fig. 1, at an altitude of ∼580 km, the SAA area spans a vast region extending from −50◦ to 0◦ in geographic latitude and from −90◦ to +40◦ in longitude. The SAA has been slowly expanding since the discovery of the radiation belts in 1958 (see van Allen and Frank 1959). This is most likely related to the gradual weakening of the geomagnetic field, which has lost about 9% of its average strength over the last 200 years (See, e.g., https://www.esa.int/Applications/Observing_the_Earth/ FutureEO/Swarm/Swarm_probes_weakening_of_Earth_s_magnetic_field). The top panel of Fig. 2 shows the longitudinal profiles of the geomagnetic field at ∼800 km altitude and a latitude range deeply impinging the minimum of the SAA, as measured in 2001 with the CHAMP satellite and then in 2019 with the Swarm-B

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Fig. 1 South Atlantic Anomaly as detected by the particle background monitor aboard the ROSAT X-ray Observatory, which operated for over 8 years in the 1990s in a LEO of 580 km altitude and 53◦ inclination. (Credits: S.L. Snowden, ROSAT data)

satellite. The bottom panel of this figure shows the corresponding flux of energetic electrons of energies >130 keV. We see that in just 18 years, a general lowering of the internal magnetic field is manifest, with major effects at the eastern SAA minimum. A corresponding variation in the relative intensities of electron flux peaks can be spotted, with cusp deepening (which suggests peaks moving away from each other) and global western drift of the entire SAA area. LEOs are particularly used for high-energy instruments given the relatively low background, despite the strong modulation over a time scale of tens of minutes. It should also be noted that the visibility of a satellite in an LEO by a ground station (such as the Malindi station operated by the Italian Space Agency) is limited to ∼10 min per orbit, which requires an adequate onboard data storage and a fast download of the data at the passage over the receiving station.

High-Earth, Highly Elliptical, and L1/L2 Orbits A high-Earth orbit is a geocentric orbit at an altitude entirely above that of a geosynchronous orbit (35,786 km). To avoid the intense flux of energetic protons and electrons trapped in the outer Van Allen radiation belt, a spacecraft in such an orbit would have to be placed at least 10 Earth radii away (∼64,000 km). A more practical way to escape the Van Allen radiation belts for most of the orbit is to launch the satellite into a highly elliptical geocentric orbit of high eccentricity and high inclination. Several gamma-ray missions were launched to such high elliptical orbits, including COS-B in 1975, the first ESA mission to study cosmic gamma-ray sources, whose orbit perigee and apogee were about 350 and 100,000 km, respectively. COSB spent about 80% of its time outside the radiation belts, i.e., about 30 h per 37.17-h orbital period. Another example is the Soviet (later Russian) X- and gamma-ray space observatory GRANAT, which was placed in December 1989 in a highly eccentric 98-h orbit with an initial perigee/apogee of 1760/202,480 km, respectively, and an inclination of 51.9◦ . However, GRANAT’s orbit has rapidly evolved due to

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Fig. 2 Top: Variation of the geomagnetic field at ∼800 km altitude as a function of longitude in a latitude range of 35◦ –40◦ south crossing the core of the SAA (see Fig. 1). Bottom: corresponding integrated flux of electrons of energies >130 keV as measured by the POES/MEPED-90◦ telescope anti-parallel to the satellite motion. All data were obtained in quiet condition, i.e., during periods of low solar activity. In each graph, the black symbols represent data collected in February–May 2001 (CHAMP satellite for the magnetic field and NOAA16 for particles), while the magenta symbols show data collected in mid-2019 (Swarm-B for the B-field and NOAA19 for particles). (Courtesy of A. Parmentier, private communication)

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Fig. 3 INTEGRAL orbit evolution after the launch, from the Baikonur Cosmodrome in Kazakhstan on October 17, 2002, up to October 2017. The spacecraft travels in a geosynchronous highly eccentric orbit with high perigee in order to provide long periods of uninterrupted observation with nearly constant background away from the radiation belts. Over time, the perigee, apogee, and plane of the orbit evolve. So far, more than 19 years after injection in orbit, INTEGRAL has traveled more than a billion km. (Courtesy of ESA)

lunar and solar perturbations: 5 years later, the perigee had increased to 59,000 km and the inclination to 86.5◦ . The orbit of the INTEGRAL observatory has also evolved over time since its launch in October 2002 (Figs. 3 and 4). The choice of INTEGRAL’s orbit before the launch was dictated by several arguments: (i) orbit stability, without any limitation of the operational lifetime of the observatory, (ii) long uninterrupted observations (about 3 days at the beginning of the mission), (iii) very stable background, (iv) low activation of the two high-energy instruments SPI (Vedrenne et al. 2003) and IBIS (Ubertini et al. 2003), (v) possibility to have a continuous down and upper link with one main ground station, and other minor advantages (Winkler et al. 2003). With the chosen orbit, the instruments can be operated above a distance from Earth of about 40,000 km, corresponding to >85% live observation time. As a result, on top of the almost constant background for the whole orbital duration (to date evolved to 2.8 days), the observatory is most of the time far from Earth with the possibility to observe the whole sky at the time. However, the predicted high background forced the two main instruments IBIS and SPI design to implement heavy active shielding for the high-energy detectors, at the expense of sensitive detection areas. After almost 20 years of scientific observations, it is now clear that the orbital choice was key to the mission success. In fact, the nearly constant background (affected by almost negligible systematic errors), the exploitation of long duration

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Fig. 4 Evolution of INTEGRAL’s perigee altitude and orbital inclination. (From Kuulkers et al. 2021)

uninterrupted observations, the very high fraction of observing time, and the fraction of time spent non-occulted by the Earth have permitted it to achieve the most sensitive surveys of the Galactic Center and plane ever done (Bazzano et al. 2006; Bird et al. 2016; Malizia et al. 2016; Krivonos et al. 2015a,b) and to detect a wealth of gamma-ray bursts, including the first, and so far the only, gamma-ray counterpart of the merging of two neutron stars, i.e., the GW170817–GRB170817A event (Abbott et al. 2017; Savchenko et al. 2017; Ubertini et al. 2019). Farther from Earth, the L1 and L2 Lagrangian points of the Sun–Earth system are attracting more and more interest for gamma-ray space missions. L1 and L2 are two points of gravitational equilibrium located at about 1.5 million km from Earth on the side and opposite side of the Sun, respectively. Among the scientific missions sent to L1 is NASA’s Wind spacecraft, comprising the Russian gamma-ray burst monitor Konus operating since 1994. More recently, in July 2019, the Russian– German soft and hard X-ray observatory Spektr-RG was launched in a halo orbit around L2. Although the background of gamma-ray instruments outside the Earth’s radiation belts is higher than in LEO (see Section “Background Components”), the L1 and L2 orbits have the advantage of greater stability in terms of illumination and thermal conditions. These orbits far away from Earth would be well suited to host a sensitive all-sky gamma-ray imager (with a field of view of almost 4π sr) for multi-messenger astronomy (Tatischeff et al. 2019).

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Stratospheric Balloon Experiments Stratospheric balloons, together with sounding rockets, have been the first historical attempt to understand if the ground measured radioactivity was of terrestrial or cosmic origin. In Fig. 5 is shown one of the first balloon experiments, with a volume of 9000 cubic meters, launched from Sardinia (Italy). The scientific objective of the experiment, designed and exploited under the lead of Prof. Edoardo Amaldi, was to study the production of particles in the high atmosphere, by means of the use of emulsions. The flight was successfully exploited in 1953 (see Ubertini 2008). The background rate of balloon-borne instruments is influenced by the intensity of the incident cosmic-ray radiation, usually represented by the vertical cutoff rigidity, Rcut , which is defined as the lowest rigidity required for a charged particle coming from the zenith direction in order to reach a given point on the Earth surface. Rcut is a function of the geomagnetic latitude and varies with time, with secular changes that are on a time scale of a year or less. The vertical cutoff rigidity is calculated as a function of longitude and latitude through a standard model Fig. 5 The stratospheric balloon, with a volume of about 9000 cubic meters, launched from the Cagliari Elmas Airport (Sardinia, Italy) in the early 1950s. (Courtesy of P. Ubertini)

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of the geomagnetic field, the International Geomagnetic Reference Field (IGRF) maintained by the International Association of Geomagnetism and Aeronomy (IAGA), which is updated regularly, the current model being the 13th generation IGRF (Alken et al. 2021). An approximate formula for estimating Rcut at satellite altitudes, assuming the Earth’s magnetic field to be a simple dipole, is given in Section “Galactic Cosmic Rays and Anomalous Cosmic Rays” (Equation 2). A longitude – latitude map of cutoff rigidity is shown in Fig. 6. Values of Rcut span from nearly zero at the geomagnetic poles to ∼15 GV at the magnetic equator. In Table 1, we provide the cutoff rigidity values at the main balloon launch sites. Although the Earth’s magnetic field shielding is less important at Antarctica and other near-pole stations (e.g., Kiruna, Svalbard, McMurdo, Syowa Station), these launch sites can offer the advantage of long duration flights. In particular, ultra long duration balloons that could sustain flights for weeks/months are currently being developed by NASA (e.g., Jones 2014). The duration of experiments launched from bases at lower latitudes is of the order of a few hours to a few days; as an illustration, the flight profile of an experiment launched in 2016 from L’Aire-surL’Adour (France) is shown in Fig. 7. Different cosmic-ray and gamma-ray experiments have been developed to be launched on stratospheric balloons, mainly in the framework of the NASA balloon program but also exploiting other launch opportunities. Recently, the EU has also created its scientific balloon infrastructure, HEMERA (e.g., Raizonville et al. 2019). Balloon campaigns are a good opportunity to challenge the realization of new experimental techniques in the gamma-ray domain. Relevant examples are the development of Compton and pair-production telescopes, high-resolution spectrometers based on cryogenic detectors, as well as gamma-ray polarimeters.

Fig. 6 Cutoff rigidity map for the year 2020 at the top of atmosphere (20 km altitude). (Reproduced with permission from Gerontidou et al. 2021)

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Table 1 Vertical cutoff rigidity at main balloon launch sites Launch site Kiruna Aire-sur-L’Adour Timmins CSBF Palestine Fort Sumner Alice Springs Svalbard McMurdo Syowa Station Hyderabad Taiki Aerospace Wanaka Airport Spaceport Tucson Trapani

Country Sweden France Canada USA USA Australia Norway USA/Antarctica Japan/Antarctica India Japan New Zealand USA Italy

Latitude 67.889 43.709 48.568 31.780 34.490 -23.799 78.253 -77.841 -67.316 17.474 42.500 -44.720 32.087 37.914

Longitude 21.104 -0.258 -81.373 -95.716 -104.223 133.883 15.467 166.684 39.141 78.579 143.433 169.247 -110.943 12.491

Rcut (GV) 0.36 5.26 1.07 4.38 4.09 8.06 0.01 0.00 0.33 16.77 7.78 2.21 5.05 8.22

Fig. 7 Count rate in the energy range 40–1200 keV of a CeBr3 scintillation detector (green curve) launched by a stratospheric balloon from the base of Aire-sur-L’Adour (France) and balloon altitude (red curve), as a function of local time during the flight on July 2, 2016. The maximum count rate is observed at an altitude between 15 and 20 km, i.e., at an atmospheric depth of ∼100 g cm−2 , which corresponds to the Regener–Pfotzer maximum, i.e., the altitude at which the ionization rate due to cosmic-ray interactions is the highest. At this altitude, the detector’s count rate is about five times higher than that on the ground, which is mainly due to natural radioactivity

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Since the 1960s, pioneering observations on balloons started to provide important results in different fields. In 1967, Fishman and colleagues observed the Crab Pulsar in low-energy gamma rays yielding a measurement of the Crab spin period (Fishman et al. 1969), while Haymes, Johnson et al. detected emission with an energy of ∼500 keV from the Galactic Center in the early 1970s (Haymes et al. 1975). A series of balloon-borne measurements of the cosmic gamma-ray background as well as the atmospheric MeV background were performed in the 1970s (e.g., Schoenfelder et al. 1977; Mandrou et al. 1979). The GRIS instrument (Tueller et al. 1988) developed by NASA/GSFC uses cooled Ge detectors surrounded by a thick NaI anticoincidence shields for highresolution gamma-ray spectroscopy. It was flown two times in 1988 from Alice Springs providing measurements of gamma-ray lines from SN 1987A (Tueller et al. 1990) and had at least seven other successful flights up to 1995. During these flights, it also detected other nuclear lines like the positron annihilation line at 511 keV from the Galactic Center (Gehrels et al. 1991), and the 26 Al line emission from the Galactic plane (Teegarden et al. 1991). The Compton technique allows performing spectroscopy and imaging of the sky in the MeV regime as successfully implemented with the COMPTEL instrument (Schoenfelder et al. 1993) on board CGRO. Further developments came from the Nuclear Compton Telescope (NCT, Coburn et al. 2005) built by a collaboration led by UC Berkeley. It carries 12 crossed-strip cryogenic germanium detectors with 3-D position resolution. NCT was flown successfully in 2005 and 2009 from Fort Sumner, with an additional attempted flight from Alice Spring in 2010. The COSI experiment, its successor, carries newly designed high-purity Ge Detectors (GeDs) as a pathfinder to the recently approved COSI-SMEX mission. More recently, the Kyoto University developed a Compton telescope for soft gamma rays in the framework of the SMILE project. The instrument consists of an Electron Tracking Compton Camera (ETCC), with a gaseous tracker and a position-sensitive scintillation detector. The first prototype, SMILE-I, was flown from the Sanriku Balloon Center of ISAS/JAXA in 2006, reporting observations of the diffuse cosmic background and atmospheric gamma-ray components (Takada et al. 2011). A recent flight of the prototype SMILE-2+ has occurred from Alice Springs in April 2018, reporting observations of the Crab Nebula and the Galactic Center (e.g., Nakamura et al. 2018), and a further prototype, SMILE-3, is being developed for a long-duration balloon flight. At higher energies (E > 20 MeV), the GLAST/BFEM balloon experiment (Thompson et al. 2002) was flown in August 2001 from Palestine. It consisted of an engineering model of one tower element of the Large Area Telescope (LAT; Atwood et al. 2009) currently flying on board the Fermi satellite. The instrument carried a complex combination of detector elements including a Si strip pair conversion tracker, a CsI calorimeter, and an anticoincidence system. As a gamma-ray polarimeter, PoGOLite pathfinder (Pearce et al. 2012) uses the Compton effect and subsequent photo-absorption to detect events within an array of 61 well-type phoswich detector cells made with plastic and BGO scintillators with BGO anticoincidence shield and polyethylene neutron shield. The instrument

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has an effective area for polarization measurements of ∼40 cm2 at E = 40 keV. PoGOLite pathfinder was launched in 2013 from Esrange after two failed attempts and reported a measurement of the Crab polarization. More precise measurements were performed by a more advanced version, PoGO+, launched in 2016 (Chauvin et al. 2017). Finally, one remarkable application in the domain of cosmic-ray research is EUSO-Balloon, flying prototypes developed for the Extreme Universe Space Observatory onboard the Japanese Experiment Module (JEM-EUSO). Launched in 2014 from Timmins, Canada, by the CNES balloon division, it provided measurements of the UV background in different atmospheric and ground conditions (Adams et al. 2015).

Background Components We now discuss each background component, first presenting the origin and overall properties of the background particles and radiation, and then describing their spectrum and angular distribution (Sections “Extragalactic Gamma-Ray Emission”, “Galactic Gamma-Ray Emission”, “Galactic Cosmic Rays and Anomalous Cosmic Rays”, “Solar Energetic Particles” and “Secondary Particles in Low-Earth Orbits and the Stratosphere”). In Section “Delayed Background from Activation of Satellite Materials”, we discuss more specifically the delayed background in soft gamma-ray telescopes due to the activation of satellite materials.

Extragalactic Gamma-Ray Emission The extragalactic gamma-ray emission is both a significant component of background for gamma-ray observations outside of the Galactic plane and an important science topic, especially for astrophysics in the MeV gamma-ray range (de Angelis et al. 2018). The first evidence for an MeV diffuse emission emanating from beyond our Galaxy was found in 1974 with a balloon-borne Compton telescope (Schönfelder and Lichti 1974). At higher energies (>30 MeV), an apparently isotropic emission of extragalactic origin was discovered by the SAS 2 satellite (Fichtel et al. 1978) and has been studied in detail by Fermi/LAT (Abdo et al. 2010). In the hard X-ray range ( 100 MeV), it is more than an order of magnitude larger than the isotropic extragalactic background. In this energy range, the diffuse emission from the Milky Way can be the main source of background when observing a weak source in the Galactic plane. The high-energy gamma-ray emission from the most central part of the Galaxy is even brighter than that from the Galactic plane: the photon intensity detected by Fermi/LAT from the Galactic Center (| ℓ |< 2.5◦ and | b |< 1◦ ) is higher than that from the Galactic disk (| ℓ |< 90◦ and | b |< 2◦ excluding the region of | ℓ |< 2.5◦ around the Galactic Center) by a factor of ∼2.4 between 100 MeV and 1 GeV, increasing to 3.4 at 100 GeV (Cumani et al. 2019).

Galactic Cosmic Rays and Anomalous Cosmic Rays Cosmic rays are composed of bare nuclei for about 99% and electrons for the remaining 1%. Among the nuclei, about 90% are protons and 9% are alpha particles. Most cosmic rays are produced in our Galaxy, probably in strong shock waves induced by supersonic stellar winds and supernova explosions (Tatischeff et al. 2021). Only ultrahigh-energy cosmic rays above ∼1017 eV are thought to be predominantly of extragalactic origin. Solar energetic particles emitted by our star are sometimes called “solar cosmic rays.” These particles and their effects on gamma-ray instruments are discussed in Section “Solar Energetic Particles”.

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Cosmic rays can have several adverse effects on gamma space telescopes. First, they can change the state of components of electronic integrated circuits, causing electronic noise and errors such as single-event upset and latch-up. Space electronics uses radiation-hardened components that are made resistant to damage and malfunction caused by ionizing radiation. Charged cosmic rays can also trigger gamma-ray detectors in space and thus generate bad data contributing to the background noise. This background can be strongly suppressed by shielding the gamma-ray instruments with an anticoincidence detector highly sensitive to charged particles, but less sensitive to gamma-ray photons (see, e.g., Moiseev et al. 2007). Also, cosmic rays can produce radioactive nuclei by spallation reactions in the satellite materials. These radioactivities can induce a delayed background in gamma-ray instruments against which it is more difficult to fight (Section “Delayed Background from Activation of Satellite Materials”). An irreducible background for gamma-ray telescopes in space comes from cosmic-ray interactions in the outermost parts of the instrument, in particular the light shield, thermal blanket, and micrometeroid shield above the anticoincidence detector. Inelastic nuclear collisions of cosmic rays with these materials can produce gamma-ray lines in the MeV range and neutral pions that decay into gamma rays in the primary operating energy range of high-energy instruments. This high-energy emission was the dominant background component of the COS-B gamma-ray telescope for parts of the sky away from the Galactic plane (Strong et al. 1987). For the later developed gamma-ray instruments CGRO/EGRET, Fermi/LAT, and AGILE, a special effort was made to minimize the exterior material to help deal with this irreducible background. Several dozen stratospheric balloon experiments and space instruments have been carried out to study cosmic rays, since the pioneering balloon experiments of Victor Hess in 1912. In the last decade, cosmic-ray flux measurements of extreme precision could be performed with the Alpha Magnetic Spectrometer (AMS-02), a state-of-the-art particle physics detector operating on the International Space Station since 2011. The spectra of cosmic-ray protons, alpha particles, electrons, and positrons measured by AMS-02 (Aguilar et al. 2015a,b, 2019a,b) are shown in Fig. 9. The cosmic-ray flux changes with time in the interplanetary medium, because of the solar modulation effect caused by the magnetized solar wind against which cosmic rays must fight to reach the inner heliosphere. The cosmic-ray flux is found to be anticorrelated with the nearly periodic 11-year cycle of the solar magnetic activity. The force-field approximation (Gleeson and Axford 1968) provides a simple way to estimate the modulated cosmic-ray intensity in the near-Earth interplanetary medium, Fmod , from the steady-state intensity of particles in the local interstellar medium (i.e., just outside the heliosphere), by assuming an effective shift of kinetic energy: Fmod (E) = FLISM (E + Zeφ) ×

(E + Mc2 )2 − (Mc2 )2 , (E + Mc2 + Zeφ)2 − (Mc2 )2

(1)

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Fig. 9 (a) Primary proton and α-particle spectra in the near-Earth interplanetary medium (red and green lines) and in LEO for two geomagnetic cutoff rigidities: Rcut = 4.2 GV (magenta lines) and Rcut = 12.3 GV (black lines). Blue stars show the AMS-02 data from Aguilar et al. (2015a,b) (α-particle intensities have been divided by 10 for clarity). The dashed and solid curves are for minimum and maximum solar activities, respectively. Green curves show the Galactic cosmic-ray model ISO-15390 used in CREME 2009 and red curves are from CREME96, which also includes anomalous cosmic rays (see text). (b) Spectra of primary electrons and positrons. The AMS-02 data (blue stars) are from Aguilar et al. (2019a,b). The electrons and positrons spectra in the nearEarth interplanetary medium (green lines) are calculated from Mizuno et al. (2004), with the solar modulation potential φ = 500 and 1100 MV for minimum (dashed lines) and maximum (solid lines) solar activities, respectively

where Ze and M are the particle charge and mass, c is the speed of light, and φ is a potential representing the level of solar modulation, which typically varies from ∼500 MV for solar activity minimum to ∼1100 MV for solar activity maximum. AMS-02 measurements of the cosmic-ray positron flux showed that φ reached a maximum in 2014 (Aguilar et al. 2019b), which corresponds to the peak of solar cycle 24. Satellites on LEOs are exposed to much lower fluxes of cosmic rays than spacecrafts outside the Van Allen radiation belts (see Section “Orbits of Gamma-Ray Space Missions”), because of the additional modulation due to the Earth’s magnetic field. The transmission of charged particles through the magnetosphere from the local interplanetary medium to a specific location defined by the satellite altitude h and the geomagnetic latitude θM can be estimated from the geomagnetic cutoff rigidity (Smart and Shea 2005): Rcut

 = 14.5 × 1 +

h REarth

−2

(cos θM )4 GV ,

(2)

where REarth = 6371 km is the Earth’s radius. This equation takes the Earth’s magnetic field to be a simple dipole. It should be modified for polar latitudes, where additional magnetospheric effects become important (see Smart and Shea 2005).

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The position of a satellite in the geomagnetic field is sometimes located using the McIlwain L-parameter (also noted Lshell ) rather than the geomagnetic latitude θM (e.g., Fig. 10 and Bidoli et al. 2002). The suppression of particle flux at rigidities lower than Rcut can be modeled as: Fcut (E) =

Fmod (E) , 1 + (R/Rcut )−r

(3)

where R = pc/Ze (p being the particle momentum) and r = 12 for protons and alpha particles or 6 for electrons and positrons (Mizuno et al. 2004). Intensities of protons, alpha particles, electrons, and positrons in LEO are shown in Fig. 9 for two geomagnetic cutoff rigidities, Rcut = 4.2 and 12.3 GV, which were obtained from Equation 2 with h = 550 km and θM = 40◦ and 0◦ , respectively. In good approximation, the angular distribution of these particles can be assumed to be uniform in the range 0◦ ≤ θz ≤ θH (and 0 for θH < θz < 180◦ ), where θz is the (telescope) zenith angle and θH is the horizon angle defined as the angle between the zenith and the top of the atmosphere (HA = 40 km from sea level) at the satellite altitude h: θH = 90◦ + arccos

REarth + HA . REarth + h

(4)

We see in Fig. 9 that the cosmic-ray intensities in LEOs are strongly suppressed below ∼1 GeV, which can be a decisive asset for a gamma-ray mission. However, spacecrafts in LEOs are also exposed to secondary particles of different kinds, which are presented in Section “Secondary Particles in Low-Earth Orbits and the Stratosphere”. But before this, we discuss various models for the intensities of primary particles in the heliosphere.

Protons and Alpha Particles In Fig. 9a, we compare two models for the spectra of primary protons and alpha particles in the near-Earth interplanetary medium. The first one is the Galactic cosmic-ray model ISO-15390, which is the international standard (https://www. iso.org/standard/37095.html) for estimating the radiation impact of cosmic rays on hardware and other objects in space. We extracted this model from the online tool CREME 2009 (https://creme.isde.vanderbilt.edu/), which is the latest version of the cosmic-ray flux model in the CREME (Cosmic Ray Effects on Micro-Electronics) package frequently used in space dosimetry. We also used this tool to estimate the variation of the cosmic-ray intensities between the periods of minimum and maximum solar activity (see Fig. 9). Figure 9a also shows primary proton and α-particle spectra obtained from CREME96 (Tylka et al. 1997), which is the previous and still often used version of the CREME code. In addition to Galactic cosmic rays, this model also describes the intensities in the near-Earth environment of the so-called “anomalous” cosmic rays, which are responsible for the strong rise of the total particle spectra with decreasing

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energy below about 10–20 MeV nucleon−1 (red curves in Fig. 9a). Anomalous cosmic rays were discovered with the IMP (Interplanetary Monitoring Platform) satellites in the early 1970s (Garcia-Munoz et al. 1973) and were soon interpreted as originating from interstellar neutral atoms that drift into the heliosphere, become ionized, and are subsequently accelerated somewhere in the outer heliosphere, perhaps in the solar wind termination shock (Fisk et al. 1974). They are generally considered to be unimportant for the assessment of radiation exposure in space and spacecraft design due to their low energies. However, they can constitute a significant source of background for hard X-ray and soft gamma-ray instruments in high-Earth orbits.

Electrons and Positrons Energetic electrons and positrons are generally less important than ions for the design and operation of satellites due to their lower flux level and ionizing power. However, they can significantly contribute to the background of gammaray instruments by emitting Bremsstrahlung radiation and 511 keV photons from interactions with satellite materials. We used the model of Mizuno et al. (2004) to describe the intensity of primary electrons and positrons in the near-Earth interplanetary medium. Based on a compilation of measurements, this model takes the lepton spectra in the local interstellar medium to be power laws in rigidity: FLISM (E) = Ai



R GV

−3.3

,

(5)

with A− = 0.65 particle m−2 s−1 sr−1 MeV−1 for electrons and A+ = 0.051 particle m−2 s−1 sr−1 MeV−1 for positrons. The modulated and cutoff spectra shown in Fig. 9b are then calculated from Equations 1 and 3.

Solar Energetic Particles Solar energetic particles consist of protons, heavy ions, and electrons with energy ranging from a few tens of keV to a few GeV. They are produced by solar flares in the low corona and by outward moving shock waves driven by coronal mass ejections (CMEs) (Reames 1999). The most harmful solar events for satellite operations and the background of gamma-ray instruments are caused by powerful interplanetary shocks driven by fast CMEs, which take about a day to arrive near Earth from their region of formation in the solar corona. A very active region of the Sun triggering several of such events can cause a strong disturbance of spacecrafts for more than a week (see, e.g., Feynman and Gabriel 2000). The strongest solar particle events produce a peak intensity of protons ≥10 MeV near Earth 4 × 108 protons m−2 s−1 sr−1 , as measured by the Geostationary Operational Environmental Satellites (GOES) since the 1970s (GOES 5-min averaged

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integral proton fluxes are reported almost in real time at https://www.swpc.noaa. gov/products/goes-proton-flux). In comparison, the intensity of Galactic cosmicray protons ≥10 MeV at solar maximum is 1.3 × 103 protons m−2 s−1 sr−1 . Such extreme solar events are not expected to occur more than one or two times per solar cycle of 11 years (two such events occurred during solar cycle 22 in October 1989 and March 1991, but none since then). Relatively strong solar events producing more than 107 protons m−2 s−1 sr−1 are more frequent: 13 during solar cycle 22, 17 during solar cycle 23, and 6 during solar cycle 24, which ended in 2019. These events can generate single-event upsets in onboard electronic systems and slightly degrade the efficiency of solar panels. Moreover, the data accumulated during these events are generally not usable for astronomy, because the background is too high. High-energy protons and heavy ions produced in strong solar particle events can occasionally enter the Earth’s magnetosphere through the polar regions and interact with satellites in LEOs. Contrary to Galactic cosmic rays, solar energetic heavy ions are not fully ionized – they have a charge state characteristic of the ∼2 × 106 K coronal plasma from which they are accelerated (Leske et al. 1995) – which increases their magnetic rigidity and thus enhances their ability to penetrate the Earth’s magnetosphere (see Equation 3). Solar protons and heavy ions in the GeV range creating a nuclear cascade in the Earth’s atmosphere are sometimes detected by neutron monitors as “ground-level enhancements” above the background produced by Galactic cosmic rays.

Secondary Particles in Low-Earth Orbits and the Stratosphere Cosmic rays in or near the Earth’s atmosphere consist of so-called primary and secondary components. The primary cosmic rays, mostly protons and alpha particles, are generated and propagate through extraterrestrial space (Section “Galactic Cosmic Rays and Anomalous Cosmic Rays”). When primary cosmic rays penetrate the air and interact with molecules, they produce low-energy particles (secondary cosmic rays). Hereafter, we will describe the properties of each of particle species. We will first describe the origin and overall properties of the particle fluxes and then give their detailed properties based on measurements and simulations.

Secondary Protons Secondary protons are generated through the interaction of primary protons and alpha particles with the Earth’s atmosphere and are seen below the geomagnetic cutoff rigidity Rcut (Equation 2), with larger flux in higher geomagnetic latitude θM . They are trapped by Earth’s magnetic field and have weak angular dependence. Vertically upward and downward spectra at LEO were measured precisely by the AMS-01 experiment at an altitude of ∼380 km for several θM in the energy range E ≥100 MeV (Alcaraz et al. 2000b). Below 100 MeV, they suffer from severe ionization loss during propagation, and the spectrum flattens as measured by NINA/NINA-2 experiments (Bidoli et al. 2002). The spectra near the geomagnetic

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Fig. 10 Secondary (and primary) cosmic-ray proton spectra at LEO measured by AMS-01 and NINA-2 experiments. Vertically downward fluxes near the geomagnetic equator and pole are plotted

equator and pole are summarized in Fig. 10. Angular and altitude dependencies were studied by Zuccon et al. (2003) through a detailed simulation that takes account of the particle interaction and propagation in the Earth’s atmosphere and magnetic field. They predicted small dependencies at altitudes above 200 km. Secondary cosmic-ray protons (≤1 GeV) generated in the Earth’s atmosphere have a small Larmor radius (≤100 km) and interact with the air. Hence, their flux at balloon altitudes will be higher than that at LEO. Although the measured fluxes at balloon altitudes differ from experiment to experiment and therefore have large systematic uncertainty, they are much higher than that measured by AMS-01. See, e.g., Mizuno et al. (2004) and references therein for more details. One can also use the Model for Atmospheric Ionizing Radiation Effects (MAIRE) (https://www.radmod.co.uk/ maire) to calculate the altitude-dependent proton spectra (integrated over the upper and lower hemispheres) in the atmosphere. Alternatively, one can use EXPACS (https://phits.jaea.go.jp/expacs/) (Sato 2015) to calculate the spectrum as a function of θz and the angle-integrated one.

Secondary Electrons and Positrons Secondary electrons and positrons, produced in the Earth’s atmosphere and trapped by the magnetic field, have similar but not identical properties to those of secondary protons. Firstly, they suffer from less ionization loss and hence their flux near the geomagnetic equator (where Earth’s magnetic field effectively trapped them) will be enhanced. Also, the electron flux is lower than the positron flux near the

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Fig. 11 Secondary (and primary) cosmic-ray lepton spectra at LEO measured by AMS-01 and MARIA-2 experiments. Vertically downward fluxes near the geomagnetic equator (left) and pole (right) are plotted

geomagnetic equator, since electrons oppositely suffer from the east–west effect for (parent) primary protons. Like secondary protons, angular and altitude dependence of secondary electrons/positrons are expected to be small. Vertically upward and downward spectra were measured by the AMS-01 experiment at an altitude of ∼380 km for several θM above 100 MeV (Alcaraz et al. 2000a). The spectrum flattens moderately below 100 MeV as measured by the MARIA-2 experiment (Mikhailov 2002). The spectra near the geomagnetic equator and pole are summarized in Fig. 11; the spectra at 100 MeV do not connect smoothly and hence have large uncertainty. Like for secondary cosmic-ray protons, the fluxes at balloon altitude are much higher than that measured at LEO by AMS-01 (see, e.g., Mizuno et al. 2004). Again, one can also use MAIRE and EXPACS to calculate the altitude-dependent lepton spectra in the atmosphere.

Secondary Gamma Rays (and X-Rays) Secondary gamma rays (≥100 keV) are produced either by interactions of cosmicray protons/alphas or bremsstrahlung of electrons/positrons in the atmosphere and hence have Rcut dependence similar to that of primary cosmic rays. Cosmic rays that enter the atmosphere near grazing incidence produce showers whose forward-moving gamma rays can penetrate the thin atmosphere, making the Earth’s limb bright. The spectrum from the inner part of the Earth’s disk is softer since those gamma rays suffer from multiple scattering during the propagation in the atmosphere. Below about 100 keV (in X-rays), albedo of cosmic X-ray background (CXB) exceeds the atmospheric emission (Türler et al. 2010). Secondary X-rays and gamma rays come from the direction below the horizon angle (i.e., θH ≤ θz < π ). The spectrum and angular dependence of high-energy (≥100 MeV) gamma rays at LEOs (h ∼ 550 km) were measured precisely by Fermi/LAT (Abdo et al. 2009). It reported a sharp peak at the limb (θz ∼ 112◦ ), and a power law spectrum (above a few GeV) with a spectral index of about 2.8 (same as that of primary cosmic rays). The spectrum flattens below 1 GeV because of the cross sections and kinematics of the hadronic interaction. It also reported a softer and weaker spectrum

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−1.13 from the nadir direction. Rcut dependence was reported as Rcut by Gurian et al. (1979) above 80 MeV. The dependence is smaller at higher energies, as described by Madlee et al. (2020). Low-energy (≤100 MeV) gamma rays are produced by bremsstrahlung; they have a harder spectrum (e.g., Imhof et al. 1976; Ryan et al. 1977) and a broader peak at the Earth’s limb (e.g., Graser and Schoenfelder 1977). A similar Rcut dependence to that at a few 100s MeV was reported by Imhof et al. (1976). At balloon altitude, secondary upward gamma rays come from below the horizon (π/2 ≤ θz ). Compared to the flux measured at LEO, those gamma rays have similar flux at the nadir direction and a less sharp peak toward the limb (θz = π/2). The downward gamma-ray flux is much smaller and is proportional to the atmospheric depth (e.g., Daniel and Stephens 1974; Schoenfelder et al. 1980). The gamma-ray spectra above 1 MeV at LEO and balloon altitude are summarized in Fig. 12. One may also use MAIRE and EXPACS to calculate the gamma-ray spectrum in the atmosphere. The CXB albedo was measured by the INTEGRAL satellite. The flux is compatible with that of atmospheric emission at ∼50 keV (see Fig. 10 of Churazov et al. 2007b).

Fig. 12 Secondary upward gamma-ray spectra at LEO and balloon altitude. Abdo et al. (2009) gives Fermi/LAT measurements at the Earth’s limb and the average over θz = 100 − 150 deg. Ryan et al. (1977) gives the result at Palestine, Texas (Rcut = 4.5 GV). Imhof et al. (1976) gives the result by 1972-076B satellite below 2.7 MeV, and we extrapolated their best-fit formulae up to 10 MeV for reference. The downward spectrum by Ryan et al. (1977) at 3 g cm−2 is also plotted for comparison

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Secondary Neutrons Secondary neutrons are produced by cosmic-ray protons/alphas interactions in the atmosphere and have small chance of interaction during the propagation. Therefore, they have similar properties (Rcut , angle, and altitude dependence) as those of secondary gamma rays. Although the neutron spectrum and direction are difficult to measure precisely, there are several observations as well as models that take into account the primary cosmic-ray spectrum and interactions/propagation in the atmosphere. The model calculations by Armstrong et al. (1973) and Selesnick et al. (2007) give spectra below the top of the atmosphere; their spectra steepen progressively toward higher energies. The latter predicted a sharp peak at the Earth’s limb in ≥1 GeV. The limb emission is broader below that energy. Morris et al. (1995) reported an Rcut dependence similar to gamma rays. At balloon altitude, there is also a downward flux proportional to the atmospheric depth (e.g., Preszler et al. 1976). Kole et al. (2015) employed a PLANETOCOSMICS package (Desorgher et al. 2006) to model the secondary neutron spectrum below the top of the atmosphere. They provided settings to calculate upward and downward fluxes integrated over 2π with cos θz multiplied (sometimes called as upward/downward current). As summarized in Fig. 13, their upward spectral model agrees well with measurements at similar geomagnetic locations. One can use their model to predict the upward spectrum at LEOs with a smaller extent of zenith angle. The model spectrum of

Fig. 13 Secondary upward neutron spectral model by Kole et al. (2015) (at Rcut = 4.5 GV and high latitude) and measurements at Rcut = 4.5 GV. The downward spectral model at 4 g cm−2 is also plotted for reference

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downward neutrons is also plotted for reference. One may also use MAIRE and EXPACS to calculate the neutron spectrum in the atmosphere.

Particles Trapped in the Inner Van Allen Radiation Belt A satellite in an LEO can be exposed to intense fluxes of electrons and protons trapped inside the inner Van Allen radiation belt when it passes through the Earth’s polar regions or through the SAA (Fig. 1). As discussed in Section “Low-Earth Orbits”, the SAA has been slowly expanding since the discovery of the radiation belts as a consequence of the gradual weakening of the geomagnetic field (Fig. 2). The particle flux is so intense in the SAA that the scientific instrumentation is often switched off when a high-energy astronomy satellite passes through this region, although some diagnostic data can still be recorded (see, e.g., Abdo et al. 2009). There are several models to describe the fluxes of trapped particles around the Earth. In Fig. 14, we show results of the IRENE (International Radiation Environment Near Earth) AE9/AP9 models (Ginet et al. 2013), which combine data from 33 satellites to produce realistic probabilities of occurrence for varying flux levels along a user-defined orbit. We see that the orbit-averaged particle fluxes are much higher for polar orbits (inclination I ∼ 90◦ ) than for equatorial orbits (I ∼ 0◦ ), by about three orders of magnitude for electrons and two orders of magnitude for protons. The simulated fluxes also increase with altitude, by a factor ˇ of 2 to 3 every 50 km (Cumani et al. 2019; Rípa et al. 2020). The radiation environment in an LEO passing at the edge of the SAA was measured by the Particle Monitor (PM) experiment on board the BeppoSAX X-ray satellite almost uninterruptedly between 1996 and 2002 (Campana et al. 2014). BeppoSAX was initially placed in an orbit of about 600 km altitude and 3.9◦ inclination, but the spacecraft altitude significantly decreased with time due to the atmospheric drag, down to about 470 km when the scientific payload was switched off. Measurements of the particle flux as a function of altitude showed a dramatic decrease in intensity, by about an order of magnitude from 600 to 550 km, which is much more than predicted by the AE9/AP9 models (see Fig. 14). The APE8/AP8 models developed at NASA since the 1970s (See https://ccmc.gsfc. nasa.gov/models/modelinfo.php?model=AE-8/AP-8%20RADBELT) seem to be in ˇ better agreement with these observations (see Rípa et al. 2020). The BeppoSAX/PM measurements also showed a clear anticorrelation of the SAA particle flux and the solar activity, as quantified by the mean number of sunspots. These measurements further showed a significant drift westward of the longitude of the SAA maximum by about 0.40◦ yr−1 , in good agreement with the drift measured with the particle monitor of RXTE at a latitude of −23◦ (Fürst et al. 2009). Trapped electrons in the inner radiation belt have kinetic energies limited to a few MeV (see Fig. 14). These particles can produce significant hard X-ray and soft gamma-ray background by bremsstrahlung in the spacecraft. They can also contribute to an increase in the leakage current of detectors during SAA transits (see, e.g., Dilillo et al. 2022), thus potentially deteriorating the response of high-energy instruments. Trapped protons have energies up to about 1 GeV. These particles can

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penetrate deep into satellites (the range of a 1 GeV proton in Al is ∼1.5 m) and potentially cause damage to onboard electronics and sensors. In addition, energetic protons in the SAA can build up an instrumental background from the activation of spacecraft materials (see, e.g., Wik et al. 2014), as further discussed in the next section.

Fig. 14 Orbit-averaged differential fluxes of electrons (left panels) and protons (right panels) trapped in the inner radiation belt, calculated with the AE9 and AP9 models, respectively, for ˇ three different orbit altitudes (from top to bottom) and various inclinations I . (Adapted from Rípa et al. 2020)

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Delayed Background from Activation of Satellite Materials As a spacecraft is bombarded by energetic hadronic particles, nuclear reactions can produce radioactive isotopes in satellite materials, whose decay radiation can be difficult to distinguish from source gamma rays in the MeV range. Since radioactive decay emissions are delayed compared to the interactions of energetic particles with the spacecraft, most of the background from material activation cannot be suppressed by an anti-coincidence detector of charged particles. The gamma and β + radioactivities can induce several hits in coincidence in the gamma-ray detectors, which can be confused with Compton interactions from celestial gammaray photons. The decay of radioactive nuclei in the detectors by the emission of α or β − particles, or by electron capture, without the concomitant emission of a gamma-ray photon, produces single events that can be rejected from the background of a Compton telescope, but not easily from the one of a coded-mask instrument. A strong background line is generally expected to be the 511 keV positron– electron annihilation line resulting from the decay of various β + radioisotopes (e.g., Weidenspointner et al. 2003; Cumani et al. 2019). The importance of this delayed background depends strongly on the satellite orbit and the nature of the detectors. To illustrate these points, we show in Fig. 15 calculated activation of Si and Ge (two common detector materials) after

Fig. 15 Effective radiation activity of Si and Ge after 1 year of proton irradiation as a function of the perigee altitude of a high elliptical orbit like that of the INTEGRAL satellite (see Section “High-Earth, Highly Elliptical, and L1/L2 Orbits”). Two irradiation conditions are considered: either the semiconductors are directly exposed to the proton flux or they are shielded from the radiation environment by a C layer of 1.3 g cm−2 (see text). The hatched areas reflect the uncertainties arising from the solar activity. Also shown is the activity of these materials in an equatorial LEO at an altitude of 550 km. In this case, the results with and without the C shielding are almost identical

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1 year of proton irradiation in various orbits. Two cases were considered for the irradiation setup: either that a representative block of 100 kg of Si or Ge is directly exposed to the radiation environment or that the detectors are shielded from the proton flux by a C layer of 1.3 g cm−2 . The latter is representative of an anti-coincidence system made of about 1-cm-thick plastic scintillator panels covering the gamma-ray instrument. The radioisotope production is calculated by taking into account both the nuclear reactions induced by the bombarding protons and the reactions from the secondary protons and neutrons produced in the detectors. The cross sections of the proton- and neutron-induced spallation reactions were obtained from the TALYS nuclear reaction code (http://www.talys. eu/) below 250 MeV and from the Liège intranuclear cascade code (https://irfu. cea.fr/dphn/Spallation/incl.html) at higher energies. Once the production of the radioisotopes was evaluated, the decay radiation from these nuclei, as well as from their daughter isotopes, was computed using the NuDat library (https://www.nndc. bnl.gov/nudat3/). The “effective radiation activity” shown in Fig. 15 is defined as the rate of radioactive events that can produce two hits or more in the detectors and thus be confused with Compton events from cosmic gamma rays (J. Kiener, private communication). Two kinds of orbits have been considered for Fig. 15: an equatorial LEO at an altitude of 550 km and a high elliptical (apogee altitude Za = 1.53 × 105 km), high inclination (I = 52◦ ) orbit like that of the INTEGRAL satellite (see section “High-Earth, Highly Elliptical, and L1/L2 Orbits”). INTEGRAL was launched with an initial perigee altitude Zp ≃ 9000 km and initially spent most of the time (more than 80%) above an altitude of 60,000 km, well outside the Earth’s radiation belts. But the perigee altitude varied considerably throughout the mission as a result of the Earth’s oblateness and the lunisolar gravitational perturbations, from Zp ∼ 2000 to 13,000 km. We see in Fig. 15 that when the detectors are shielded from the lowenergy proton flux – the assumed C layer of 1.3 g cm−2 stops protons of less than about 35 MeV – the passage through the Earth’s radiation belts has no significant effect on the detector activation as long as Zp > 10,000 km. However, we also see in Fig. 15 that the predicted effective radiation activities outside the belts are about five to ten times higher than those calculated for detectors on an equatorial LEO, depending on the solar activity. Figure 15 also shows that the activation of Ge is higher than that of Si, by a factor of about 3.1 for high-Earth orbit (see the results for Zp = 30,000 km), 3.3 for an equatorial LEO, and reaching about 17 for an INTEGRAL-like high elliptical orbit with Zp = 5000 km and no shielding of the detectors. The main species contributing to the Si activity are 30 P (half-life T1/2 = 2.498 min), 29 P (4.142 s), 28 Al (2.245 min), and 27 Si (4.15 s). Those for the Ge activity are 74 As (17.77 d), 72 As (26.0 h), 73 Gem (0.499 s), 73 As (80.30 d), 76 As (1.0942 d), and 70 As (52.6 m). It is remarkable that the radioisotopes produced in Si have much shorter lifetimes than the main radioisotopes produced in Ge. As a result, the activity of Si detectors on LEOs passing through the South Atlantic Anomaly (SAA; Section “Particles Trapped in the Inner Van Allen Radiation Belt”) is expected to decrease rapidly when the satellite leaves the SAA, whereas the Ge activity should accumulate over much longer time periods.

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In Fig. 16, we show simulated background spectra of the e-ASTROGAM telescope (De Angelis et al. 2017) for two LEOs with different inclinations, I = 0◦ and 15◦ . e-ASTROGAM is a mission proposal for gamma-ray observations in the energy range between 300 keV and 3 GeV, with a gamma-ray instrument made of three main detectors: a tracker composed of 56 Si layers supported by a mechanical structure in polymer resin and C fibers, a calorimeter comprising a large number of thallium-activated cesium iodide crystals (CsI(Tl)) read out by Si drift detectors, and an anti-coincidence detector made by plastic scintillators coupled to Si photomultipliers covering both the top and the sides of the instrument. The simulations were performed with the Medium Energy Gamma-ray Astronomy library (MEGAlib) toolkit (Zoglauer et al. 2006). For the activation of the spacecraft caused by protons trapped in the SAA, two types of background were considered: a short-term background due to the production of short-lived radioisotopes, which decreases rapidly after the satellite exits the SAA, and a long-term background, which gradually accumulates during the mission. For the latter, the radioisotope production was calculated assuming an irradiation of the spacecraft by the SAA protons for 72 days, which corresponds to the approximate total time the satellite spends in the SAA during 1 year in an equatorial LEO (∼19 min per orbit for a 550 km orbit of period 96 min). This irradiation period was followed by a cool downtime of 48 min in the simulation (half an orbital period), in order to consider only the decay of relatively long-lived radioisotopes (Cumani et al. 2019). We see in Fig. 16 that the Earth albedo and extragalactic gamma-rays are predicted to be the main components of the background below ∼150 keV and above ∼4 MeV, but activation should be dominant between these two energies. The two most prominent lines that appear in the activation spectra are at 511 and 700 keV. The 511 keV line is produced following the β + decay of radioisotopes such as 11 C (T1/2 = 20.364 min) and 15 O (122.24 s). The 700 keV line, which is prominent in all activation spectra except those for the short-term SAA background, is mainly produced by the electron-capture decay of two long-lived isotopes abundantly created in the CsI(Tl) crystals of the calorimeter: 132 Cs (6.480 d) and 126 I (12.93 d). The first radioisotope produces nuclear gamma rays of 668 keV at the same time as Kα X-rays of 30 keV. The second one produces 666 keV gamma rays together with 27 keV X-rays. For an equatorial LEO (upper panel), the main contributor to the total activation comes from the decay of radioisotopes produced by primary Galactic cosmic-ray protons. The total rate of events from the long-term SAA activation is about a fifth of that due to cosmic-ray protons. The total count rate of the short-term SAA background is lower than that of the long-term SAA background by a factor of at least 1.5, even without considering any cool downtime after the SAA passage. On the other hand, for an inclination of 15◦ (lower panel), the long-term SAA activation is predicted to be higher than the sum of all the other components in the ∼150 to ∼720 keV energy range. Moreover, the short-term SAA activation is expected to make a major contribution to the 511 keV line emission for several minutes after the passage through the SAA. In terms of background, an LEO with a low inclination (I < 5◦ ; see Cumani et al. 2019) should generally be the best orbit for a MeV gamma-ray mission.

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Fig. 16 Spectra of the reconstructed background Compton events in the e-ASTROGAM gammaray telescope for an LEO of 550 km altitude and inclination of 0◦ (top) and 15◦ (bottom). The background from the spacecraft activation is calculated from the fluxes of primary protons and alpha particles (i.e., Galactic cosmic rays), secondary protons and neutrons, as well as protons trapped in the SAA. The prompt background is from the extragalactic gamma-ray emission and the Earth’s albedo photons. The “total” emission is obtained from the sum of all the contributions except that from activation in the SAA. The SAA contribution is divided into short-term, with 0 s or 120 s cool downtime after the SAA passage, and long-term background (SAA 1 yr). (Figure adapted from Cumani et al. 2019)

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Conclusions In this chapter, we have presented the different orbits available for gamma-ray space missions and described in detail the properties of the background particles and radiation that limit the detection sensitivity of space-borne gamma-ray instruments. We also discussed the value of stratospheric balloon experiments to prepare and sometimes supplement space missions. A good knowledge of the environment of high-energy experiments is all the more necessary as highly energetic particles and gamma rays can also damage detectors and components of electronic integrated circuits. In terms of background count rate, the best environmental conditions of a gamma-ray mission are found in near-equatorial, low altitude (typical altitude of 500–600 km) circular orbit. A satellite on such LEO is well shielded from lowenergy cosmic rays and solar energetic particles by the Earth’s magnetic field. Proton and alpha particle fluxes beyond the Earth’s radiation belts are typically an order of magnitude higher than those in equatorial LEO, resulting in lower activation of spacecraft materials and lower instrumental background in low- than in highEarth orbits, especially in the MeV gamma-ray range. Anyway, this conclusion is valid only for LEO inclinations below ∼10◦ , as for higher inclinations the orbitaveraged flux of protons trapped in the inner radiation belt can exceed that in high-Earth orbit. The intense electron and proton fluxes experienced by a gammaray satellite crossing the South Atlantic Anomaly also have the drawback of significantly limiting the observation duty cycle. A satellite in high-Earth orbits or at the L1 or L2 Lagrange points can benefit from a more stable environment, in particular not subject to the day–night variations of the equatorial LEO and the accompanying temperature changes. Moreover, in these distant orbits, the lack of Earth’s albedo radiation and secondary particles produced in the atmosphere can allow the conception of gamma-ray instruments with very large fields of view capable of continuously monitoring almost the entire gamma-ray sky with good detection efficiency. But a caveat is due to direct exposure to solar energetic particles that can be a source of an additional background component not shielded by the Earth’s magnetic field. During periods of intense solar activity, this may limit the observing time, as happened, for example, for INTEGRAL observations. In view of the above mentioned issues, the choice of the “best orbit” for a gamma-ray satellite has to be optimized taking into account not only the detection sensitivity of the onboard experiments but also other important requirements such as: • The required duration of uninterrupted observations: LEOs have an average science window for observations of less than 1 h, while high elliptical orbits can provide observations lasting up to 3 days and L1–L2 orbits can allow even longer uninterrupted observations. • The required sky coverage: LEOs are compatible with a coverage of about half of the sky at any moment, while the field of view in high elliptical orbits is barely obscured by the Earth when the satellite is transiting with high speed

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close to perigee, granting large part of the orbit with almost all-sky visibility. Thus, Fermi/GBM monitors the whole sky with about 60% duty cycle, while it is 85–90% for the anti-coincidence shield of INTEGRAL/SPI. • The main operational constraints, i.e., satellite lifetime, tracking station availability and hand-over constraints, data download requirements (i.e., real-time versus in-board storage), and telecommand need. In the era of multi-messenger astronomy recently opened by the simultaneous detection of gamma rays and gravitational waves, as well as the detection of highenergy neutrinos, it is essential to have in-space instruments with good imaging and monitoring capabilities able to detect and localize 24 h/7 d weak signals from energetic transients in the energy range from ∼0.1 MeV to a few hundred MeV. The required highly efficient coverage of the whole sky should be associated with excellent, omnidirectional sensitivity above 100 keV and rapid reaction time for target-of-opportunity observations.

Cross-References ⊲ Compton Telescopes for Gamma-Ray Astrophysics ⊲ Fermi Gamma-Ray Space Telescope ⊲ Gamma-Ray Detector and Mission Design Simulations ⊲ In-Orbit Background for X-ray Detectors ⊲ Pair Production Detectors for Gamma-Ray Astrophysics ⊲ Surveys of the Cosmic X-ray Background ⊲ Telescope Concepts in Gamma-Ray Astronomy ⊲ The AGILE Mission and Its Scientific Results ⊲ The COMPTEL Experiment and Its In-Flight Performance ⊲ The INTEGRAL Mission ⊲ X- and Gamma-Ray Astrophysics in the Era of Multi-messenger Astronomy

Acknowledgments The research presented in this chapter has received funding from the European Union’s Horizon 2020 Programme under the AHEAD2020 project (grant agreement n. 871158). PU acknowledge the continuous support of the ASI-INAF Agreement N.2019-35-HH.0. We thank Pierre Cristofari for his careful reading of the manuscript.

References B.P. Abbott, R. Abbott, T.D. Abbott, F. Acernese, K. Ackley, C. Adams, T. Adams, P. Addesso, R.X. Adhikari, V.B. Adya, C. Affeldt, M. Afrough, B. Agarwal, M. Agathos, K. Agatsuma, N. Aggarwal, O.D. Aguiar, L. Aiello, A. Ain, P. Ajith, B. Allen, G. Allen, A. Allocca, M.A. Aloy, P.A. Altin, A. Amato, A. Ananyeva, S.B. Anderson, W.G. Anderson, S.V. Angelova, S. Antier, S. Appert, K. Arai, M.C. Araya, J.S. Areeda, N. Arnaud, K.G. Arun, S. Ascenzi, G. Ashton, M. Ast, S.M. Aston, P. Astone, D.V. Atallah, P. Aufmuth, C. Aulbert, K. AultONeal,

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C. Austin, A. Avila-Alvarez, S. Babak, P. Bacon, M.K.M. Bader, S. Bae, P.T. Baker, F. Baldaccini, G. Ballardin, S.W. Ballmer, S. Banagiri, J.C. Barayoga, S.E. Barclay, B.C. Barish, D. Barker, K. Barkett, F. Barone, B. Barr, L. Barsotti, M. Barsuglia, D. Barta, J. Bartlett, I. Bartos, R. Bassiri, A. Basti, J.C. Batch, M. Bawaj, J.C. Bayley, M. Bazzan, B. Bécsy, C. Beer, M. Bejger, I. Belahcene, A.S. Bell, B.K. Berger, G. Bergmann, J.J. Bero, C.P.L. Berry, D. ersanetti, A. Bertolini, J. Betzwieser, S. Bhagwat, R. Bhandare, I.A. Bilenko, G. Billingsley, C.R. Billman, J. Birch, R. Birney, O. Birnholtz, S. Biscans, S. Biscoveanu, A. Bisht, M. Bitossi, C. Biwer, M.A. Bizouard, J.K. Blackburn, J. Blackman, C.D. Blair, D.G. Blair, R.M. Blair, S. Bloemen, O. Bock, N. Bode, M. Boer, G. Bogaert, A. Bohe, F. Bondu, E. Bonilla, R. Bonnand, B.A. Boom, R. Bork, V. Boschi, S. Bose, K. Bossie, Y. Bouffanais, A. Bozzi, C. Bradaschia, P.R. Brady, M. Branchesi, J.E. Brau, T. Briant, A. Brillet, M. Brinkmann, V. Brisson, P. Brockill, J.E. Broida, A.F. Brooks, D.A. Brown, D.D. Brown, S. Brunett, C.C. Buchanan, A. Buikema, T. Bulik, H.J. Bulten, A. Buonanno, D. Buskulic, C. Buy, R.L. Byer, M. Cabero, L. Cadonati, G. Cagnoli, C. Cahillane, J. Calderón Bustillo, T.A. Callister, E. Calloni, J.B. Camp, M. Canepa, P. Canizares, K.C. Cannon, H. Cao, J. Cao, C.D. Capano, E. Capocasa, F. Carbognani, S. Caride, M.F. Carney, J. Casanueva Diaz, C. Casentini, S. Caudill, M. Cavaglià, F. Cavalier, R. Cavalieri, G. Cella, C.B. Cepeda, P. Cerdá-Durán, G. Cerretani, E. Cesarini, S.J. Chamberlin, M. Chan, S. Chao, P. Charlton, E. Chase, E. Chassande-Mottin, D. Chatterjee, K. Chatziioannou, B.D. Cheeseboro, H.Y. Chen, X. Chen, Y. Chen, H.-P. Cheng, H. Chia, A. Chincarini, A. Chiummo, T. Chmiel, H.S. Cho, M. Cho, J.H. Chow, N. Christensen, Q. Chu, A.J.K. Chua, S. Chua, A.K.W. Chung, S. Chung, G. Ciani, R. Ciolfi, C.E. Cirelli, A. Cirone, F. Clara, J.A. Clark, P. Clearwater, F. Cleva, C. Cocchieri, E. Coccia, P.-F. Cohadon, D. Cohen, A. Colla, C.G. Collette, L.R. Cominsky, M. Constancio Jr., L. Conti, S.J. Cooper, P. Corban, T.R. Corbitt, I. Cordero-Carrión, K.R. Corley, N. Cornish, A. Corsi, S. Cortese, C.A. Costa, M.W. Coughlin, S.B. Coughlin, J.-P. Coulon, S.T. Countryman, P. Couvares, P.B. Covas, E.E. Cowan, D.M. Coward, M.J. Cowart, D.C. Coyne, R. Coyne, J.D.E. Creighton, T.D. Creighton, J. Cripe, S.G. Crowder, T.J. Cullen, A. Cumming, L. Cunningham, E. Cuoco, T. Dal Canton, G. Dálya, S.L. Danilishin, S. D’Antonio, K. Danzmann, A. Dasgupta, C.F. Da Silva Costa, V. Dattilo, I. Dave, M. Davier, D. Davis, E.J. Daw, B. Day, S. De, D. DeBra, J. Degallaix, M. De Laurentis, S. Deléglise, W. Del Pozzo, N. Demos, T. Denker, T. Dent, R. De Pietri, V. Dergachev, R. De Rosa, R.T. DeRosa, C. De Rossi, R. DeSalvo, O. de Varona, J. Devenson, S. Dhurandhar, M.C. Díaz, L. Di Fiore, M. Di Giovanni, T. Di Girolamo, A. Di Lieto, S. Di Pace, I. Di Palma, F. Di Renzo, Z. Doctor, V. Dolique, F. Donovan, K.L. Dooley, S. Doravari, I. Dorrington, R. Douglas, M. Dovale Álvarez, T.P. Downes, M. Drago, C. Dreissigacker, J.C. Driggers, Z. Du, M. Ducrot, P. Dupej, S.E. Dwyer, T.B. Edo, M.C. Edwards, A. Effler, H.-B. Eggenstein, P. Ehrens, J. Eichholz, S.S. Eikenberry, R.A. Eisenstein, R.C. Essick, D. Estevez, Z.B. Etienne, T. Etzel, M. Evans, T.M. Evans, M. Factourovich, V. Fafone, H. Fair, S. Fairhurst, X. Fan, S. Farinon, B. Farr, W.M. Farr, E.J. Fauchon-Jones, M. Favata, M. Fays, C. Fee, H. Fehrmann, J. Feicht, M.M. Fejer, A. Fernandez-Galiana, I. Ferrante, E.C. Ferreira, F. Ferrini, F. Fidecaro, D. Finstad, I. Fiori, D. Fiorucci, M. Fishbach, R.P. Fisher, M. Fitz-Axen, R. Flaminio, M. Fletcher, H. Fong, J.A. Font, P.W.F. Forsyth, S.S. Forsyth, J.-D. Fournier, S. Frasca, F. Frasconi, Z. Frei, A. Freise, R. Frey, V. Frey, E.M. Fries, P. Fritschel, V.V. Frolov, P. Fulda, M. Fyffe, H. Gabbard, B.U. Gadre, S.M. Gaebel, J.R. Gair, L. Gammaitoni, M.R. Ganija, S.G. Gaonkar, C. Garcia-Quiros, F. Garufi, B. Gateley, S. Gaudio, G. Gaur, V. Gayathri, N. Gehrels, G. Gemme, E. Genin, A. Gennai, D. George, J. George, L. Gergely, V. Germain, S. Ghonge, A. Ghosh, A. Ghosh, S. Ghosh, J.A. Giaime, K.D. Giardina, A. Giazotto, K. Gill, L. Glover, E. Goetz, R. Goetz, S. Gomes, B. Goncharov, G. González, J.M. Gonzalez Castro, A. Gopakumar, M.L. Gorodetsky, S.E. Gossan , M. Gosselin, R. Gouaty, A. Grado, C. Graef, M. Granata, A. Grant, S. Gras, C. Gray, G. Greco, A.C. Green, E.M. Gretarsson, P. Groot, H. Grote, S. Grunewald, P. Gruning, G.M. Guidi, X. Guo, A. Gupta, M.K. Gupta, K.E. Gushwa, E.K. Gustafson, R. Gustafson, O. Halim, B.R. Hall, E.D. Hall, E.Z. Hamilton G. Hammond, M. Haney, M.M. Hanke, J. Hanks, C. Hanna, M.D. Hannam, O.A. Hannuksela, J. Hanson, T. Hardwick, J. Harms, G.M. Harry, I.W. Harry, M.J. Hart, C.-J. Haster, K. Haughian, J. Healy, A. Heidmann, M.C. Heintze, H. Heitmann, P. Hello, G. Hemming, M. Hendry, I.S. Heng, J. Hennig, A.W. Heptonstall, M.

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Heurs, S. Hild, T. Hinderer, D. Hoak, D. Hofman, K. Holt, D.E. Holz, P. Hopkins, C. Horst, J. Hough, E.A. Houston, E.J. Howell, A. Hreibi, Y.M. Hu, E.A. Huerta, D. Huet, B. Hughey, S. Husa, S.H. Huttner, T. Huynh-Dinh, N. Indik, R. Inta, G. Intini, H.N. Isa, J.-M. Isac, M. Isi, B.R. Iyer, K. Izumi, T. Jacqmin, K. Jani, P. Jaranowski, S. Jawahar, F. Jiménez-Forteza, W.W. Johnson, N.K. Johnson-McDaniel, D.I. Jones, R. Jones, R.J.G. Jonker, L. Ju, J. Junker, C.V. Kalaghatgi, V. Kalogera, B. Kamai, S. Kandhasamy, G. Kang, J.B. Kanner, S.J. Kapadia, S. Karki, K.S. Karvinen, M. Kasprzack, W. Kastaun, M. Katolik, E. Katsavounidis, W. Katzman, S. Kaufer, K. Kawabe, F. Kéfélian, D. Keitel, A.J. Kemball, R. Kennedy, C. Kent, J.S. Key, F.Y. Khalili, I. Khan, S. Khan, Z. Khan, E.A. Khazanov, N. Kijbunchoo, C. Kim, J.C. Kim, K. Kim, W. Kim, W.S. Kim, Y.-M. Kim, S.J. Kimbrell, E.J. King, P.J. King, M. Kinley-Hanlon, R. Kirchhoff, J.S. Kissel, L. Kleybolte, S. Klimenko, T.D. Knowles, P. Koch, S.M. Koehlenbeck, S. Koley, V. Kondrashov, A. Kontos, M. Korobko, W.Z. Korth I. Kowalska, D.B. Kozak, C. Krämer, V. Kringel, B. Krishnan, A. Królak, G. Kuehn, P. Kumar, R. Kumar, S. Kumar, L. Kuo, A. Kutynia, S. Kwang, B.D. Lackey, K.H. Lai, M. Landry, R.N. Lang, J. Lange, B. Lantz, R.K. Lanza, A. Lartaux-Vollard, P.D. Lasky, M. Laxen, A. Lazzarini, C. Lazzaro, P. Leaci, S. Leavey, C.H. Lee, H.K. Lee, H.M. Lee, H.W. Lee, K. Lee, J. Lehmann, A. Lenon, M. Leonardi, N. Leroy, N. Letendre, Y. Levin, T.G.F. Li, S.D. Linker, T.B. Littenberg, J. Liu, R.K.L. Lo, N.A. Lockerbie, L.T. London, J.E. Lord, M. Lorenzini, V. Loriette, M. Lorm, G. Losurdo, J.D. Lough, C.O. Lousto, G. Lovelace, H. Lück, D. Lumaca, A.P. Lundgren, R. Lynch, Y. Ma, R. Macas, S. Macfoy, B. Machenschalk, M. MacInnis, D.M. Macleod, I. Magaña Hernandez, F. Magaña-Sandoval, L. Magaña Zertuche, R.M. Magee, E. Majorana, I. Maksimovic, N. Man, V. Mandic, V. Mangano, G.L. Mansell, M. Manske, M. Mantovani, F. Marchesoni, F. Marion, S. Márka, Z. Márka, C. Markakis, A.S. Markosyan, A. Markowitz, E. Maros, A. Marquina, F. Martelli, L. Martellini, I.W. Martin, R.M. Martin, D.V. Martynov, K. Mason, E. Massera, A. Masserot, T.J. Massinger M. Masso-Reid, S. Mastrogiovanni, A. Matas, F. Matichard, L. Matone, N. Mavalvala, N. Mazumder, R. McCarthy, D.E. McClelland, S. McCormick, L. McCuller, S.C. McGuire, G. McIntyre, J. McIver, D.J. McManus, L. McNeill, T. McRae, S.T. McWilliams, D. Meacher, G.D. Meadors, M. Mehmet, J. Meidam, E. Mejuto-Villa, A. Melatos, G. Mendell, R.A. Mercer, E.L. Merilh, M. Merzougui, S. Meshkov, C. Messenger, C. Messick, R. Metzdorff, P.M. Meyers, H. Miao, C. Michel, H. Middleton, E.E. Mikhailov, L. Milano, A.L. Miller, B.B. Miller, J. Miller, M. Millhouse, M.C. Milovich-Goff, O. Minazzoli, Y. Minenkov, J. Ming, C. Mishra, S. Mitra, V.P. Mitrofanov, G. Mitselmakher, R. Mittleman, D. Moffa, A. Moggi, K. Mogushi, M. Mohan, S.R.P. Mohapatra, M. Montani, C.J. Moore, D. Moraru, G. Moreno, S.R. Morriss, B. Mours, C.M. Mow-Lowry, G. Mueller, A.W. Muir, A. Mukherjee, D. Mukherjee, S. Mukherjee, N. Mukund, A. Mullavey, J. Munch, E.A. Muñiz, M. Muratore, P.G. Murray K. Napier, I. Nardecchia, L. Naticchioni, R.K. Nayak J. Neilson, G. Nelemans, T.J.N. Nelson, M. Nery, A. Neunzert, L. Nevin, J.M. Newport, G. Newton, K.K.Y. Ng, T.T. Nguyen, D. Nichols, A.B. Nielsen, S. Nissanke, A. Nitz, A. Noack, F. Nocera, D. Nolting, C. North, and L.K. Nuttall and J. Oberling, G.D. O’Dea, G.H. Ogin, J.J. Oh, S.H. Oh, F. Ohme, M.A. Okada, M. Oliver, P. Oppermann, R.J. Oram, B. O’Reilly, R. Ormiston, L.F. Ortega, R. O’Shaughnessy, S. Ossokine, D.J. Ottaway, H. Overmier, B.J. Owen, A.E. Pace, J. Page, M.A. Page, A. Pai, S.A. Pai, J.R. Palamos, O. Palashov, C. Palomba, A. Pal-Singh, H. Pan, H.-W. Pan, B. Pang, P.T.H. Pang, C. Pankow, F. Pannarale, B.C. Pant, F. Paoletti, A. Paoli, M.A. Papa, A. Parida, W. Parker, D. Pascucci, A. Pasqualetti, R. Passaquieti, D. Passuello, M. Patil, B. Patricelli, B.L. Pearlstone, M. Pedraza, R. Pedurand, L. Pekowsky, A. Pele, S. Penn, C.J. Perez, A. Perreca, L.M. Perri, H.P. Pfeiffer, M. Phelps, O.J. Piccinni, M. Pichot, F. Piergiovanni, V. Pierro, G. Pillant, L. Pinard, I.M. Pinto, M. Pirello, M. Pitkin, M. Poe, R. Poggiani, P. Popolizio, E.K. Porter, A. Post, J. Powell, J. Prasad, J.W.W. Pratt, G. Pratten, V. Predoi, T. Prestegard, M. Prijatelj, M. Principe, S. Privitera, G.A. Prodi, L.G. Prokhorov, O. Puncken, M. Punturo, P. Puppo, M. Pürrer, H. Qi, V. Quetschke, E.A. Quintero, R. Quitzow-James, F.J. Raab, D.S. Rabeling, H. Radkins, P. Raffai, S. Raja, C. Rajan, B. Rajbhandari, M. Rakhmanov, K.E. Ramirez, A. Ramos-Buades, P. Rapagnani, V. Raymond, M. Razzano, J. Read, T. Regimbau, L. Rei, S. Reid, D.H. Reitze, W. Ren, S.D. Reyes, F. Ricci, P.M. Ricker, S. Rieger, K. Riles, M. Rizzo, N.A. Robertson, R. Robie, F. Robinet, A. Rocchi, L. Rolland, J.G. Rollins, V.J. Roma,

54 Orbits and Background of Gamma-Ray Space Instruments

1909

R. Romano, C.L. Romel, J.H. Romie, D. Rosi´nska, M.P. Ross, S. Rowan, A. Rüdiger, P. Ruggi, G. Rutins, K. Ryan, S. Sachdev, T. Sadecki, L. Sadeghian, M. Sakellariadou, L. Salconi, M. Saleem, F. Salemi, A. Samajdar, L. Sammut, L.M. Sampson, E.J. Sanchez, L.E. Sanchez, N. Sanchis-Gual, V. Sandberg, J.R. Sanders, B. Sassolas, B.S. Sathyaprakash, P.R. Saulson, O. Sauter, R.L. Savage, A. Sawadsky, P. Schale, M. Scheel, J. Scheuer, J. Schmidt, P. Schmidt, R. Schnabel, R.M.S. Schofield, A. Schönbeck, E. Schreiber, D. Schuette, B.W. Schulte, B.F. Schutz, S.G. Schwalbe, J. Scott, S.M. Scott, E. Seidel, D. Sellers, A.S. Sengupta, D. Sentenac, V. Sequino, A. Sergeev, D.A. Shaddock, T.J. Shaffer, A.A. Shah, M.S. Shahriar, M.B. Shaner, L. Shao, B. Shapiro, P. Shawhan, A. Sheperd, D.H. Shoemaker, D.M. Shoemaker, K. Siellez, X. Siemens, M. Sieniawska, D. Sigg, A.D. Silva, L.P. Singer, A. Singh, A. Singhal, A.M. Sintes, B.J.J. Slagmolen, B. Smith, J.R. Smith, R.J.E. Smith, S. Somala, E.J. Son, J.A. Sonnenberg, B. Sorazu, F. Sorrentino, T. Souradeep, A.P. Spencer, A.K. Srivastava, K. Staats, A. Staley, M. Steinke, J. Steinlechner, S. Steinlechner, D. Steinmeyer, S.P. Stevenson, R. Stone, D.J. Stops, K.A. Strain, G. Stratta, S.E. Strigin, A. Strunk, R. Sturani, A.L. Stuver, T.Z. Summerscales, L. Sun, S. Sunil, J. Suresh, P.J. Sutton, B.L. Swinkels, M.J. Szczepa´nczyk, M. Tacca, S.C. Tait, C. Talbot, D. Talukder, D.B. Tanner, M. Tápai, A. Taracchini, J.D. Tasson, J.A. Taylor, R. Taylor, S.V. Tewari, T. Theeg, F. Thies, E.G. Thomas, M. Thomas, P. Thomas, K.A. Thorne, K.S. Thorne, E. Thrane, S. Tiwari, V. Tiwari, K.V. Tokmakov, K. Toland, M. Tonelli, Z. Tornasi, A. Torres-Forné, C.I. Torrie, D. Töyrä, F. Travasso, G. Traylor, J. Trinastic, M.C. Tringali, L. Trozzo, K.W. Tsang, M. Tse, R. Tso, L. Tsukada, D. Tsuna, D. Tuyenbayev, K. Ueno, D. Ugolini, C.S. Unnikrishnan, A.L. Urban, S.A. Usman, H. Vahlbruch, G. Vajente, G. Valdes, N. van Bakel, M. van Beuzekom, J.F.J. van den Brand, C. Van Den Broeck, D.C. Vander-Hyde, L. van der Schaaf, J.V. van Heijningen, A.A. van Veggel, M. Vardaro, V. Varma, S. Vass, M. Vasúth, A. Vecchio, G. Vedovato, J. Veitch, P.J. Veitch, K. Venkateswara, G. Venugopalan, D. Verkindt, F. Vetrano, A. Viceré, A.D. Viets, S. Vinciguerra, D.J. Vine, J.-Y. Vinet, S. Vitale, T. Vo, H. Vocca, C. Vorvick, S.P. Vyatchanin, A.R. Wade, L.E. Wade, M. Wade, R. Walet, M. Walker, L. Wallace, S. Walsh, G. Wang, H. Wang, J.Z. Wang, W.H. Wang, Y.F. Wang, R.L. Ward, J. Warner, M. Was, J. Watchi, B. Weaver, L.-W. Wei, M. Weinert, A.J. Weinstein, R. Weiss, L. Wen, E.K. Wessel, P. Weßels, J. Westerweck, T. Westphal, K. Wette, J.T. Whelan, S.E. Whitcomb, B.F. Whiting, C. Whittle, D. Wilken, D. Williams, R.D. Williams, A.R. Williamson, J.L. Willis, B. Willke, M.H. Wimmer, W. Winkler, C.C. Wipf, H. Wittel, G. Woan, J. Woehler, J. Wofford, K.W.K. Wong, J. Worden, J.L. Wright, D.S. Wu, D.M. Wysocki, S. Xiao, H. Yamamoto, C.C. Yancey, L. Yang, M.J. Yap, M. Yazback, H. Yu, H. Yu, M. Yvert, A. Zadrozny, M. Zanolin, T. Zelenova, J.-P. Zendri, M. Zevin, L. Zhang, M. Zhang, T. Zhang, Y.-H. Zhang, C. Zhao, M. Zhou, Z. Zhou, S.J. Zhu, X.J. Zhu, A.B. Zimmerman, M.E. Zucker, J. Zweizig, LIGO Scientific Collaboration, Virgo Collaboration, E. Burns, P. Veres, D. Kocevski, J. Racusin, A. Goldstein, V. Connaughton, M.S. Briggs, L. Blackburn, R. Hamburg, C.M. Hui, A. von Kienlin, J. McEnery, R.D. Preece, C.A. Wilson-Hodge, E. Bissaldi, W.H. Cleveland, M.H. Gibby, M.M. Giles, R.M. Kippen, S. McBreen, C.A. Meegan, W.S. Paciesas, S. Poolakkil, O.J. Roberts, M. Stanbro, Gamma-ray Burst Monitor, Fermi, V. Savchenko, C. Ferrigno, E. Kuulkers, A. Bazzano, E. Bozzo, S. Brandt, J. Chenevez, T.J.-L. Courvoisier, R. Diehl, A. Domingo, L. Hanlon, E. Jourdain, P. Laurent, F. Lebrun, A. Lutovinov, S. Mereghetti, L. Natalucci, J. Rodi, J.-P. Roques, R. Sunyaev, P. Ubertini, INTEGRAL, Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A. Astrophys. J. 848(2), L13 (2017). https://doi.org/10.3847/2041-8213/aa920c, 1710.05834 A.A. Abdo, M. Ackermann, M. Ajello, J. Ampe, B. Anderson, W.B. Atwood, M. Axelsson, R. Bagagli, L. Baldini, J. Ballet, G. Barbiellini, J. Bartelt, D. Bastieri, B.M. Baughman, K. Bechtol, D. Bédérède, F. Bellardi, R. Bellazzini, F. Belli, B. Berenji, D. Bisello, E. Bissaldi, E.D. Bloom, G. Bogaert, J.R. Bogart, E. Bonamente, A.W. Borgland, P. Bourgeois, A. Bouvier, J. Bregeon, A. Brez, M. Brigida, P. Bruel, T.H. Burnett, G. Busetto, G.A. Caliandro, R.A. Cameron, M. Campell, P.A. Caraveo, S. Carius, P. Carlson, J.M. Casandjian, E. Cavazzuti, M. Ceccanti, C. Cecchi, E. Charles, A. Chekhtman, C.C. Cheung, J. Chiang, R. Chipaux, A.N. Cillis, S. Ciprini, R. Claus, J. Cohen-Tanugi, S. Condamoor, J. Conrad, R. Corbet, S. Cutini, D.S. Davis, M. DeKlotz, C.D. Dermer, A. de Angelis, F. de Palma, S.W. Digel, P. Dizon, M. Dormody, E. do

1910

V. Tatischeff et al.

Couto e Silva, P.S. Drell, R. Dubois, D. Dumora, Y. Edmonds, D. Fabiani, C. Farnier, C. Favuzzi, E.C. Ferrara, O. Ferreira, Z. Fewtrell, D.L. Flath, P. Fleury, W.B. Focke, K. Fouts, M. Frailis, D. Freytag, Y. Fukazawa, S. Funk, P. Fusco, F. Gargano, D. Gasparrini, N. Gehrels, S. Germani, B. Giebels, N. Giglietto, F. Giordano, T. Glanzman, G. Godfrey, J. Goodman, I.A. Grenier, M.H. Grondin, J.E. Grove, L. Guillemot, S. Guiriec, M. Hakimi, G. Haller, Y. Hanabata, P.A. Hart, P. Hascall, E. Hays, M. Huffer, R.E. Hughes, G. Jóhannesson, A.S. Johnson, R.P. Johnson, T.J. Johnson, W.N. Johnson, T. Kamae, H. Katagiri, J. Kataoka, A. Kavelaars, H. Kelly, M. Kerr, W. Klamra, J. Knödlseder, M.L. Kocian, F. Kuehn, M. Kuss, L. Latronico, C. Lavalley, B. Leas, B. Lee, S.H. Lee, M. Lemoine-Goumard, F. Longo, F. Loparco, B. Lott, M.N. Lovellette, P. Lubrano, D.K. Lung, G.M. Madejski, A. Makeev, B. Marangelli, M. Marchetti, M.M. Massai, D. May, G. Mazzenga, M.N. Mazziotta, J.E. McEnery, S. McGlynn, C. Meurer, P.F. Michelson, M. Minuti, N. Mirizzi, P. Mitra, W. Mitthumsiri, T. Mizuno, A.A. Moiseev, M. Mongelli, C. Monte, M.E. Monzani, E. Moretti, A. Morselli, I.V. Moskalenko, S. Murgia, D. Nelson, L. Nilsson, S. Nishino, P.L. Nolan, E. Nuss, M. Ohno, T. Ohsugi, N. Omodei, E. Orlando, J.F. Ormes, M. Ozaki, A. Paccagnella, D. Paneque, J.H. Panetta, D. Parent, V. Pelassa, M. Pepe, M. Pesce-Rollins, P. Picozza, M. Pinchera, F. Piron, T.A. Porter, S. Rainò, R. Rando, E. Rapposelli, W. Raynor, M. Razzano, A. Reimer, O. Reimer, T. Reposeur, L.C. Reyes, S. Ritz, S. Robinson, L.S. Rochester, A.Y. Rodriguez, R.W. Romani, M. Roth, F. Ryde, A. Sacchetti, H.F.W. Sadrozinski, N. Saggini, D. Sanchez, A. Sander, L. Sapozhnikov, O.H. Saxton, P.M. Saz Parkinson, A. Sellerholm, C. Sgrò, E.J. Siskind, D.A. Smith, P.D. Smith, G. Spandre, P. Spinelli, J.L. Starck, T.E. Stephens, M.S. Strickman, A.W. Strong, M. Sugizaki, D.J. Suson, H. Tajima, H. Takahashi, T. Takahashi, T. Tanaka, A. Tenze, J.B. Thayer, J.G. Thayer, D.J. Thompson, L. Tibaldo, O. Tibolla, D.F. Torres, G. Tosti, A. Tramacere, M. Turri, T.L. Usher, N. Vilchez, N. Virmani, V. Vitale, L.L. Wai, A.P. Waite, P. Wang, B.L. Winer, D.L. Wood, K.S. Wood, H. Yasuda, T. Ylinen, M. Ziegler, The on-orbit calibration of the Fermi Large Area Telescope. Astropart. Phys. 32(3–4), 193–219 (2009). https://doi.org/10.1016/j.astropartphys.2009.08.002, 0904.2226 A.A. Abdo, M. Ackermann, M. Ajello, W.B. Atwood, L. Baldini, J. Ballet, G. Barbiellini, D. Bastieri, B.M. Baughman, K. Bechtol, R. Bellazzini, B. Berenji, E.D. Bloom, E. Bonamente, A.W. Borgland, A. Bouvier, J. Bregeon, A. Brez, M. Brigida, P. Bruel, R. Buehler, T.H. Burnett, S. Buson, G.A. Caliandro, R.A. Cameron, P.A. Caraveo, J.M. Casandjian, C. Cecchi, O. Çelik, E. Charles, A. Chekhtman, J. Chiang, S. Ciprini, R. Claus, J. Cohen-Tanugi, J. Conrad, F. de Palma, S.W. Digel, E. do Couto e Silva, P.S. Drell, R. Dubois, D. Dumora, C. Farnier, C. Favuzzi, S.J. Fegan, W.B. Focke, P. Fortin, M. Frailis, Y. Fukazawa, S. Funk, P. Fusco, F. Gargano, N. Gehrels, S. Germani, B. Giebels, N. Giglietto, F. Giordano, T. Glanzman, G. Godfrey, I.A. Grenier, M.H. Grondin, J.E. Grove, L. Guillemot, S. Guiriec, E. Hays, D. Horan, R.E. Hughes, G. Jóhannesson, A.S. Johnson, T.J. Johnson, W.N. Johnson, T. Kamae, H. Katagiri, J. Kataoka, N. Kawai, M. Kerr, J. Knödlseder, M. Kuss, J. Lande, L. Latronico, M. Lemoine-Goumard, F. Longo, F. Loparco, B. Lott, M.N. Lovellette, P. Lubrano, A. Makeev, M.N. Mazziotta, J.E. McEnery, C. Meurer, P.F. Michelson, W. Mitthumsiri, T. Mizuno, C. Monte, M.E. Monzani, A. Morselli, I.V. Moskalenko, S. Murgia, P.L. Nolan, J.P. Norris, E. Nuss, T. Ohsugi, A. Okumura, N. Omodei, E. Orlando, J.F. Ormes, D. Paneque, J.H. Panetta, D. Parent, V. Pelassa, M. Pepe, M. Pesce-Rollins, F. Piron, T.A. Porter, S. Rainò, R. Rando, M. Razzano, A. Reimer, O. Reimer, T. Reposeur, L.S. Rochester, A.Y. Rodriguez, M. Roth, H.F.W. Sadrozinski, A. Sander, P.M. Saz Parkinson, C. Sgrò, G.H. Share, E.J. Siskind, D.A. Smith, P.D. Smith, G. Spandre, P. Spinelli, M.S. Strickman, D.J. Suson, H. Takahashi, T. Tanaka, J.B. Thayer, J.G. Thayer, D.J. Thompson, L. Tibaldo, D.F. Torres, G. Tosti, A. Tramacere, Y. Uchiyama, T.L. Usher, V. Vasileiou, N. Vilchez, V. Vitale, A.P. Waite, P. Wang, B.L. Winer, K.S. Wood, T. Ylinen, M. Ziegler, Fermi large area telescope observations of the cosmic-ray induced γ -ray emission of the earth’s atmosphere. Phys. Rev. D 80, 122004 (2009). https://doi. org/10.1103/PhysRevD.80.122004 A.A. Abdo, M. Ackermann, M. Ajello, W.B. Atwood, L. Baldini, J. Ballet, G. Barbiellini, D. Bastieri, B.M. Baughman, K. Bechtol, R. Bellazzini, B. Berenji, R.D. Blandford, E.D. Bloom, E. Bonamente, A.W. Borgland, J. Bregeon, A. Brez, M. Brigida, P. Bruel, T.H. Burnett, S.

54 Orbits and Background of Gamma-Ray Space Instruments

1911

Buson, G.A. Caliandro, R.A. Cameron, P.A. Caraveo, J.M. Casandjian, E. Cavazzuti, C. Cecchi, O. Çelik, E. Charles, A. Chekhtman, C.C. Cheung, J. Chiang, S. Ciprini, R. Claus, J. CohenTanugi, L.R. Cominsky, J. Conrad, S. Cutini, C.D. Dermer, A. de Angelis, F. de Palma, S.W. Digel, G. Di Bernardo, E.D.C. e Silva , P.S. Drell, A. Drlica-Wagner, R. Dubois, D. Dumora, C. Farnier, C. Favuzzi, S.J. Fegan, W.B. Focke, P. Fortin, M. Frailis, Y. Fukazawa, S. Funk, P. Fusco, D. Gaggero, F. Gargano, D. Gasparrini, N. Gehrels, S. Germani, B. Giebels, N. Giglietto, P. Giommi, F. Giordano, T. Glanzman, G. Godfrey, I.A. Grenier, M.H. Grondin, J.E. Grove, L. Guillemot, S. Guiriec, M. Gustafsson, Y. Hanabata, A.K. Harding, M. Hayashida, R.E. Hughes, R. Itoh, M.S. Jackson, G. Jóhannesson, A.S. Johnson, R.P. Johnson, T.J. Johnson, W.N. Johnson, T. Kamae, H. Katagiri, J. Kataoka, N. Kawai, M. Kerr, J. Knödlseder, M.L. Kocian, F. Kuehn, M. Kuss, J. Lande, L. Latronico, M. Lemoine-Goumard, F. Longo, F. Loparco, B. Lott, M.N. Lovellette, P. Lubrano, G.M. Madejski, A. Makeev, M.N. Mazziotta, W. McConville, J.E. McEnery, C. Meurer, P.F. Michelson, W. Mitthumsiri, T. Mizuno, A.A. Moiseev, C. Monte, M.E. Monzani, A. Morselli, I.V. Moskalenko, S. Murgia, P.L. Nolan, J.P. Norris, E. Nuss, T. Ohsugi, N. Omodei, E. Orlando, J.F. Ormes, D. Paneque, J.H. Panetta, D. Parent, V. Pelassa, M. Pepe, M. Pesce-Rollins, F. Piron, T.A. Porter, S. Rainò, R. Rando, M. Razzano, A. Reimer, O. Reimer, T. Reposeur, S. Ritz, L.S. Rochester, A.Y. Rodriguez, M. Roth, F. Ryde, H.F.W. Sadrozinski, D. Sanchez, A. Sander, P.M.S. Parkinson, J.D. Scargle, A. Sellerholm, C. Sgrò, M.S. Shaw, E.J. Siskind, D.A. Smith, P.D. Smith, G. Spandre, P. Spinelli, J.L. Starck, M.S. Strickman, A.W. Strong, D.J. Suson, H. Tajima, H. Takahashi, T. Takahashi, T. Tanaka, J.B. Thayer, J.G. Thayer, D.J. Thompson, L. Tibaldo, D.F. Torres, G. Tosti, A. Tramacere, Y. Uchiyama, T.L. Usher, V. Vasileiou, N. Vilchez, V. Vitale, A.P. Waite, P. Wang, B.L. Winer, K.S. Wood, T. Ylinen, M. Ziegler, Spectrum of the isotropic diffuse gamma-ray emission derived from firstyear fermi large area telescope data. Phys. Rev. Lett. 104, 101101 (2010). https://doi.org/10. 1103/PhysRevLett.104.101101 M. Ackermann, M. Ajello, W.B. Atwood, L. Baldini, J. Ballet, G. Barbiellini, D. Bastieri, K. Bechtol, R. Bellazzini, B. Berenji, R.D. Blandford, E.D. Bloom, E. Bonamente, A.W. Borgland, T.J. Brandt, J. Bregeon, M. Brigida, P. Bruel, R. Buehler, S. Buson, G.A. Caliandro, R.A. Cameron, P.A. Caraveo, E. Cavazzuti, C. Cecchi, E. Charles, A. Chekhtman, J. Chiang, S. Ciprini, R. Claus, J. Cohen-Tanugi, J. Conrad, S. Cutini, A. de Angelis, F. de Palma, C.D. Dermer, S.W. Digel, E.D.C. e Silva , P.S. Drell, A. Drlica-Wagner, L. Falletti, C. Favuzzi, S.J. Fegan, E.C. Ferrara, W.B. Focke, P. Fortin, Y. Fukazawa, S. Funk, P. Fusco, D. Gaggero, F. Gargano, S. Germani, N. Giglietto, F. Giordano, M. Giroletti, T. Glanzman, G. Godfrey, J.E. Grove, S. Guiriec, M. Gustafsson, D. Hadasch, Y. Hanabata, A.K. Harding, M. Hayashida, E. Hays, D. Horan, X. Hou, R.E. Hughes, G. Jóhannesson, A.S. Johnson, R.P. Johnson, T. Kamae, H. Katagiri, J. Kataoka, J. Knödlseder, M. Kuss, J. Lande, L. Latronico, S.H. Lee, M. LemoineGoumard, F. Longo, F. Loparco, B. Lott, M.N. Lovellette, P. Lubrano, M.N. Mazziotta, J.E. McEnery, P.F. Michelson, W. Mitthumsiri, T. Mizuno, C. Monte, M.E. Monzani, A. Morselli, I.V. Moskalenko, S. Murgia, M. Naumann-Godo, J.P. Norris, E. Nuss, T. Ohsugi, A. Okumura, N. Omodei, E. Orlando, J.F. Ormes, D. Paneque, J.H. Panetta, D. Parent, M. Pesce-Rollins, M. Pierbattista, F. Piron, G. Pivato, T.A. Porter, S. Rainò, R. Rando, M. Razzano, S. Razzaque, A. Reimer, O. Reimer, H.F.W. Sadrozinski, C. Sgrò, E.J. Siskind, G. Spandre, P. Spinelli, A.W. Strong, D.J. Suson, H. Takahashi, T. Tanaka, J.G. Thayer, J.B. Thayer, D.J. Thompson, L. Tibaldo, M. Tinivella, D.F. Torres, G. Tosti, E. Troja, T.L. Usher, J. Vandenbroucke, V. Vasileiou, G. Vianello, V. Vitale, A.P. Waite, P. Wang, B.L. Winer, K.S. Wood, M. Wood, Z. Yang, M. Ziegler, S. Zimmer, Fermi-lat observations of the diffuse γ -ray emission: implications for cosmic rays and the interstellar medium. Astrophys. J. 750(1), 3 (2012). https://doi.org/10. 1088/0004-637X/750/1/3, 1202.4039 M. Ackermann, M. Ajello, A. Albert, W.B. Atwood, L. Baldini, J. Ballet, G. Barbiellini, D. Bastieri, K. Bechtol, R. Bellazzini, E. Bissaldi, R.D. Blandford, E.D. Bloom, E. Bottacini, T.J. Brandt, J. Bregeon, P. Bruel, R. Buehler, S. Buson, G.A. Caliandro, R.A. Cameron, M. Caragiulo, P.A. Caraveo, E. Cavazzuti, C. Cecchi, E. Charles, A. Chekhtman, J. Chiang, G. Chiaro, S. Ciprini, R. Claus, J. Cohen-Tanugi, J. Conrad, A. Cuoco, S. Cutini, F. D’Ammando, A. de Angelis, F. de Palma, C.D. Dermer, S.W. Digel, E.D.C. e Silva, P.S. Drell, C. Favuzzi,

1912

V. Tatischeff et al.

E.C. Ferrara, W.B. Focke, A. Franckowiak, Y. Fukazawa, S. Funk, P. Fusco, F. Gargano, D. Gasparrini, S. Germani, N. Giglietto, P. Giommi, F. Giordano, M. Giroletti, G. Godfrey, G.A. Gomez-Vargas, I.A. Grenier, S. Guiriec, M. Gustafsson, D. Hadasch, K. Hayashi, E. Hays, J.W. Hewitt, P. Ippoliti, T. Jogler, G. Jóhannesson, A.S. Johnson, W.N. Johnson, T. Kamae, J. Kataoka, J. Knödlseder, M. Kuss, S. Larsson, L. Latronico, J. Li, L. Li, F. Longo, F. Loparco, B. Lott, M.N. Lovellette, P. Lubrano, G.M. Madejski, A. Manfreda, F. Massaro, M. Mayer, M.N. Mazziotta, J.E. McEnery, P.F. Michelson, W. Mitthumsiri, T. Mizuno, A.A. Moiseev, M.E. Monzani, A. Morselli, I.V. Moskalenko, S. Murgia, R. Nemmen, E. Nuss, T. Ohsugi, N. Omodei, E. Orlando, J.F. Ormes, D. Paneque, J.H. Panetta, J.S. Perkins, M. Pesce-Rollins, F. Piron, G. Pivato, T.A. Porter, S. Rainò, R. Rando, M. Razzano, S. Razzaque, A. Reimer, O. Reimer, T. Reposeur, S. Ritz, R.W. Romani, M. Sánchez-Conde, M. Schaal, A. Schulz, C. Sgrò, E.J. Siskind, G. Spandre, P. Spinelli, A.W. Strong, D.J. Suson, H. Takahashi, J.G. Thayer, J.B. Thayer, L. Tibaldo, M. Tinivella, D.F. Torres, G. Tosti, E. Troja, Y. Uchiyama, G. Vianello, M. Werner, B.L. Winer, K.S. Wood, M. Wood, G. Zaharijas, S. Zimmer, The spectrum of isotropic diffuse gamma-ray emission between 100 MeV and 820 GeV. Astrophys. J. 799(1), 86 (2015). https://doi.org/10.1088/0004-637X/799/1/86, 1410.3696 J.H. Adams, S. Ahmad, J.N. Albert, D. Allard, L. Anchordoqui, V. Andreev, A. Anzalone, Y. Arai, K. Asano, M. Ave Pernas, P. Baragatti, P. Barrillon, T. Batsch, J. Bayer, R. Bechini, T. Belenguer, R. Bellotti, K. Belov, A.A. Berlind, M. Bertaina, P.L. Biermann, S. Biktemerova, C. Blaksley, N. Blanc, J. Błe¸cki, S. Blin-Bondil, J. Blümer, P. Bobik, M. Bogomilov, M. Bonamente, M.S. Briggs, S. Briz, A. Bruno, F. Cafagna, D. Campana, J.N. Capdevielle, R. Caruso, M. Casolino, C. Cassardo, G. Castellinic, C. Catalano, G. Catalano, A. Cellino, M. Chikawa, M.J. Christl, D. Cline, V. Connaughton, L. Conti, G. Cordero, H.J. Crawford, R. Cremonini, S. Csorna, S. Dagoret-Campagne, A.J. de Castro, C. De Donato, C. de la Taille, C. De Santis, L. del Peral, A. Dell’Oro, N. De Simone, M. Di Martino, G. Distratis, F. Dulucq, M. Dupieux, A. Ebersoldt, T. Ebisuzaki, R. Engel, S. Falk, K. Fang, F. Fenu, I. Fernández-Gómez, S. Ferrarese, D. Finco, M. Flamini, C. Fornaro, A. Franceschi, J. Fujimoto, M. Fukushima, P. Galeotti, G. Garipov, J. Geary, G. Gelmini, G. Giraudo, M. Gonchar, C. González Alvarado, P. Gorodetzky, F. Guarino, A. Guzmán, Y. Hachisu, B. Harlov, A. Haungs, J. Hernández Carretero, K. Higashide, D. Ikeda, H. Ikeda, N. Inoue, S. Inoue, A. Insolia, F. Isgrò, Y. Itow, E. Joven, E.G. Judd, A. Jung, F. Kajino, T. Kajino, I. Kaneko, Y. Karadzhov, J. Karczmarczyk, M. Karus, K. Katahira, K. Kawai, Y. Kawasaki, B. Keilhauer, B.A. Khrenov, J.S. Kim, S.W. Kim, S.W. Kim, M. Kleifges, P.A. Klimov, D. Kolev, I. Kreykenbohm, K. Kudela, Y. Kurihara, A. Kusenko, E. Kuznetsov, M. Lacombe, C. Lachaud, J. Lee, J. Licandro, H. Lim, F. López, M.C. Maccarone, K. Mannheim, D. Maravilla, L. Marcelli, A. Marini, O. Martinez, G. Masciantonio, K. Mase, R. Matev, G. Medina-Tanco, T. Mernik, H. Miyamoto, Y. Miyazaki, Y. Mizumoto, G. Modestino, A. Monaco, D. Monnier-Ragaigne, J.A. Morales de los Ríos, C. Moretto, V.S. Morozenko, B. Mot, T. Murakami, M.N. Murakami, M. Nagata, S. Nagataki, T. Nakamura, T. Napolitano, D. Naumov, R. Nava, A. Neronov, K. Nomoto, T. Nonaka, T. Ogawa, S. Ogio, H. Ohmori, A.V. Olinto, P. Orlea´nski, G. Osteria, M.I. Panasyuk, E. Parizot, I.H. Park, H.W. Park, B. Pastircak, T. Patzak, T. Paul, C. Pennypacker, S. Perez Cano, T. Peter, P. Picozza, T. Pierog, L.W. Piotrowski, S. Piraino, Z. Plebaniak, A. Pollini, P. Prat, G. Prévôt, H. Prieto, M. Putis, P. Reardon, M. Reyes, M. Ricci, I. Rodríguez, M.D. Rodríguez Frías, F. Ronga, M. Roth, H. Rothkaehl, G. Roudil, I. Rusinov, M. Rybczy´nski, M.D. Sabau, G. Sáez-Cano, H. Sagawa, A. Saito, N. Sakaki, M. Sakata, H. Salazar, S. Sánchez, A. Santangelo, L. Santiago Crúz, M. Sanz Palomino, O. Saprykin, F. Sarazin, H. Sato, M. Sato, T. Schanz, H. Schieler, V. Scotti, A. Segreto, S. Selmane, D. Semikoz, M. Serra, S. Sharakin, T. Shibata, H.M. Shimizu, K. Shinozaki, T. Shirahama, G. Siemieniec-Ozie¸bło, H.H. Silva López, J. Sledd, K. Słomi´nska, A. Sobey, T. Sugiyama, D. Supanitsky, M. Suzuki, B. Szabelska, J. Szabelski, F. Tajima, N. Tajima, T. Tajima, Y. Takahashi, H. Takami, M. Takeda, Y. Takizawa, C. Tenzer, O. Tibolla, L. Tkachev, H. Tokuno, T. Tomida, N. Tone, S. Toscano, F. Trillaud, R. Tsenov, Y. Tsunesada, K. Tsuno, T. Tymieniecka, Y. Uchihori, M. Unger, O. Vaduvescu, J.F. Valdés-Galicia, P. Vallania, L. Valore, G. Vankova, C. Vigorito, L. Villaseñor, P. von Ballmoos, S. Wada, J. Watanabe, S. Watanabe, J. Watts, M. Weber, T.J. Weiler, T. Wibig, L. Wiencke, M. Wille, J. Wilms, Z. Włodarczyk, T.

54 Orbits and Background of Gamma-Ray Space Instruments

1913

Yamamoto, Y. Yamamoto, J. Yang, H. Yano, I.V. Yashin, D. Yonetoku, K. Yoshida, S. Yoshida, R. Young, M.Y. Zotov, A. Zuccaro Marchi, The EUSO-Balloon pathfinder. Exp. Astron. 40(1), 281–299 (2015). https://doi.org/10.1007/s10686-015-9467-9 M. Aguilar, D. Aisa, B. Alpat, A. Alvino, G. Ambrosi, K. Andeen, L. Arruda, N. Attig, P. Azzarello, A. Bachlechner, F. Barao, A. Barrau, L. Barrin, A. Bartoloni, L. Basara, M. Battarbee, R. Battiston, J. Bazo, U. Becker, M. Behlmann, B. Beischer, J. Berdugo, B. Bertucci, G. Bigongiari, V. Bindi, S. Bizzaglia, M. Bizzarri, G. Boella, W. de Boer, K. Bollweg, V. Bonnivard, B. Borgia, S. Borsini, M.J. Boschini, M. Bourquin, J. Burger, F. Cadoux, X.D. Cai, M. Capell, S. Caroff, J. Casaus, V. Cascioli, G. Castellini, I. Cernuda, D. Cerreta, F. Cervelli, M.J. Chae, Y.H. Chang, A.I. Chen, H. Chen, G.M. Cheng, H.S. Chen, L. Cheng, H.Y. Chou, E. Choumilov, V. Choutko, C.H. Chung, C. Clark, R. Clavero, G. Coignet, C. Consolandi, A. Contin, C. Corti, E.C. Gil, B. Coste, W. Creus, M. Crispoltoni, Z. Cui, Y.M. Dai, C. Delgado, S. Della Torre, M.B. Demirköz, L. Derome, S. Di Falco, L. Di Masso, F. Dimiccoli, C. Díaz, P. von Doetinchem, F. Donnini, W.J. Du, M. Duranti, D. D’Urso, A. Eline, F.J. Eppling, T. Eronen, Y.Y. Fan, L. Farnesini, J. Feng, E. Fiandrini, A. Fiasson, E. Finch, P. Fisher, Y. Galaktionov, G. Gallucci, B. García, R. García-López, C. Gargiulo, H. Gast, I. Gebauer, M. Gervasi, A. Ghelfi, W. Gillard, F. Giovacchini, P. Goglov, J. Gong, C. Goy, V. Grabski, D. Grandi, M. Graziani, C. Guandalini, I. Guerri, K.H. Guo, D. Haas, M. Habiby, S. Haino, K.C. Han, Z.H. He, M. Heil, J. Hoffman, T.H. Hsieh, Z.C. Huang, C. Huh, M. Incagli, M. Ionica, W.Y. Jang, H. Jinchi, K. Kanishev, G.N. Kim, K.S. Kim, T. Kirn, R. Kossakowski, O. Kounina, A. Kounine, V. Koutsenko, M.S. Krafczyk, G. La Vacca, E. Laudi, G. Laurenti, I. Lazzizzera, A. Lebedev, H.T. Lee, S.C. Lee, C. Leluc, G. Levi, H.L. Li, J.Q. Li, Q. Li, Q. Li, T.X. Li, W. Li, Y. Li, Z.H. Li, Z.Y. Li, S. Lim, C.H. Lin, P. Lipari, T. Lippert, D. Liu, H. Liu, M. Lolli, T. Lomtadze, M.J. Lu, S.Q. Lu, Y.S. Lu, K. Luebelsmeyer, J.Z. Luo, S.S. Lv, R. Majka, C. Mañá, J. Marín, T. Martin, G. Martínez, N. Masi, D. Maurin, A. Menchaca-Rocha, Q. Meng, D.C. Mo, L. Morescalchi, P. Mott, M. Müller, J.Q. Ni, N. Nikonov, F. Nozzoli, P. Nunes, A. Obermeier, A. Oliva, M. Orcinha, F. Palmonari, C. Palomares, M. Paniccia, A. Papi, M. Pauluzzi, E. Pedreschi, S. Pensotti, R. Pereira, N. Picot-Clemente, F. Pilo, A. Piluso, C. Pizzolotto, V. Plyaskin, M. Pohl, V. Poireau, E. Postaci, A. Putze, L. Quadrani, X.M. Qi, X. Qin, Z.Y. Qu, T. Räihä, P.G. Rancoita, D. Rapin, J.S. Ricol, I. Rodríguez, S. Rosier-Lees, A. Rozhkov, D. Rozza, R. Sagdeev, J. Sandweiss, P. Saouter, C. Sbarra, S. Schael, S.M. Schmidt, A.S. von Dratzig, G. Schwering, G. Scolieri, E.S. Seo, B.S. Shan, Y.H. Shan, J.Y. Shi, X.Y. Shi, Y.M. Shi, T. Siedenburg, D. Son, F. Spada, F. Spinella, W. Sun, W.H. Sun, M. Tacconi, C.P. Tang, X.W. Tang, Z.C. Tang, L. Tao, D. Tescaro, S.C.C. Ting, S.M. Ting, N. Tomassetti, J. Torsti, C. Türkoˇglu, T. Urban, V. Vagelli, E. Valente, C. Vannini, E. Valtonen, S. Vaurynovich, M. Vecchi, M. Velasco, J.P. Vialle, V. Vitale, S. Vitillo, L.Q. Wang, N.H. Wang, Q.L. Wang, R.S. Wang, X. Wang, Z.X. Wang, Z.L. Weng, K. Whitman, J. Wienkenhöver, H. Wu, X. Wu, X. Xia, M. Xie, S. Xie, R.Q. Xiong, G.M. Xin, N.S. Xu, W. Xu, Q. Yan, J. Yang, M. Yang, Q.H. Ye, H. Yi, Y.J. Yu, Z.Q. Yu, S. Zeissler, J.H. Zhang, M.T. Zhang, X.B. Zhang, Z. Zhang, Z.M. Zheng, H.L. Zhuang, V. Zhukov, A. Zichichi, N. Zimmermann, P. Zuccon, C. Zurbach, AMS Collaboration, Precision measurement of the proton flux in primary cosmic rays from rigidity 1 GV to 1.8 TV with the alpha magnetic spectrometer on the international space station. Phys. Rev. Lett. 114(17), 171103 (2015a). https://doi.org/10. 1103/PhysRevLett.114.171103 M. Aguilar, D. Aisa, B. Alpat, A. Alvino, G. Ambrosi, K. Andeen, L. Arruda, N. Attig, P. Azzarello, A. Bachlechner, F. Barao, A. Barrau, L. Barrin, A. Bartoloni, L. Basara, M. Battarbee, R. Battiston, J. Bazo, U. Becker, M. Behlmann, B. Beischer, J. Berdugo, B. Bertucci, V. Bindi, S. Bizzaglia, M. Bizzarri, G. Boella, W. de Boer, K. Bollweg, V. Bonnivard, B. Borgia, S. Borsini, M.J. Boschini, M. Bourquin, J. Burger, F. Cadoux, X.D. Cai, M. Capell, S. Caroff, J. Casaus, G. Castellini, I. Cernuda, D. Cerreta, F. Cervelli, M.J. Chae, Y.H. Chang, A.I. Chen, G.M. Chen, H. Chen, H.S. Chen, L. Cheng, H.Y. Chou, E. Choumilov, V. Choutko, C.H. Chung, C. Clark, R. Clavero, G. Coignet, C. Consolandi, A. Contin, C. Corti, E.C. Gil, B. Coste, W. Creus, M. Crispoltoni, Z. Cui, Y.M. Dai, C. Delgado, S. Della Torre, M.B. Demirköz, L. Derome, S. Di Falco, L. Di Masso, F. Dimiccoli, C. Díaz, P. von Doetinchem, F. Donnini, M. Duranti, D. D’Urso, A. Egorov, A. Eline, F.J. Eppling, T. Eronen, Y.Y. Fan, L. Farnesini, J. Feng,

1914

V. Tatischeff et al.

E. Fiandrini, A. Fiasson, E. Finch, P. Fisher, V. Formato, Y. Galaktionov, G. Gallucci, B. García, R. García-López, C. Gargiulo, H. Gast, I. Gebauer, M. Gervasi, A. Ghelfi, F. Giovacchini, P. Goglov, J. Gong, C. Goy, V. Grabski, D. Grandi, M. Graziani, C. Guandalini, I. Guerri, K.H. Guo, D. Haas, M. Habiby, S. Haino, K.C. Han, Z.H. He, M. Heil, J. Hoffman, T.H. Hsieh, Z.C. Huang, C. Huh, M. Incagli, M. Ionica, W.Y. Jang, H. Jinchi, K. Kanishev, G.N. Kim, K.S. Kim, T. Kirn, M.A. Korkmaz, R. Kossakowski, O. Kounina, A. Kounine, V. Koutsenko, M.S. Krafczyk, G. La Vacca, E. Laudi, G. Laurenti, I. Lazzizzera, A. Lebedev, H.T. Lee, S.C. Lee, C. Leluc, H.L. Li, J.Q. Li, J.Q. Li, Q. Li, Q. Li, T.X. Li, W. Li, Y. Li, Z.H. Li, Z.Y. Li, S. Lim, C.H. Lin, P. Lipari, T. Lippert, D. Liu, H. Liu, H. Liu, M. Lolli, T. Lomtadze, M.J. Lu, S.Q. Lu, Y.S. Lu, K. Luebelsmeyer, F. Luo, J.Z. Luo, S.S. Lv, R. Majka, C. Mañá, J. Marín, T. Martin, G. Martínez, N. Masi, D. Maurin, A. Menchaca-Rocha, Q. Meng, D.C. Mo, L. Morescalchi, P. Mott, M. Müller, T. Nelson, J.Q. Ni, N. Nikonov, F. Nozzoli, P. Nunes, A. Obermeier, A. Oliva, M. Orcinha, F. Palmonari, C. Palomares, M. Paniccia, A. Papi, M. Pauluzzi, E. Pedreschi, S. Pensotti, R. Pereira, N. Picot-Clemente, F. Pilo, A. Piluso, C. Pizzolotto, V. Plyaskin, M. Pohl, V. Poireau, A. Putze, L. Quadrani, X.M. Qi, X. Qin, Z.Y. Qu, T. Räihä, P.G. Rancoita, D. Rapin, J.S. Ricol, I. Rodríguez, S. Rosier-Lees, A. Rozhkov, D. Rozza, R. Sagdeev, J. Sandweiss, P. Saouter, S. Schael, S.M. Schmidt, A.S. von Dratzig, G. Schwering, G. Scolieri, E.S. Seo, B.S. Shan, Y.H. Shan, J.Y. Shi, X.Y. Shi, Y.M. Shi, T. Siedenburg, D. Son, J.W. Song, F. Spada, F. Spinella, W. Sun, W.H. Sun, M. Tacconi, C.P. Tang, X.W. Tang, Z.C. Tang, L. Tao, D. Tescaro, S.C.C. Ting, S.M. Ting, N. Tomassetti, J. Torsti, C. Türkoˇglu, T. Urban, V. Vagelli, E. Valente, C. Vannini, E. Valtonen, S. Vaurynovich, M. Vecchi, M. Velasco, J.P. Vialle, V. Vitale, S. Vitillo, L.Q. Wang, N.H. Wang, Q.L. Wang, R.S. Wang, X. Wang, Z.X. Wang, Z.L. Weng, K. Whitman, J. Wienkenhöver, M. Willenbrock, H. Wu, X. Wu, X. Xia, M. Xie, S. Xie, R.Q. Xiong, N.S. Xu, W. Xu, Q. Yan, J. Yang, M. Yang, Y. Yang, Q.H. Ye, H. Yi, Y.J. Yu, Z.Q. Yu, S. Zeissler, C. Zhang, J.H. Zhang, M.T. Zhang, S.D. Zhang, S.W. Zhang, X.B. Zhang, Z. Zhang, Z.M. Zheng, H.L. Zhuang, V. Zhukov, A. Zichichi, N. Zimmermann, P. Zuccon, AMS Collaboration, Precision measurement of the helium flux in primary cosmic rays of rigidities 1.9 GV to 3 TV with the alpha magnetic spectrometer on the international space station. Phys. Rev. Lett. 115(21), 211101 (2015b). https://doi.org/10.1103/PhysRevLett.115.211101 M. Aguilar, L. Ali Cavasonza, B. Alpat, G. Ambrosi, L. Arruda, N. Attig, P. Azzarello, A. Bachlechner, F. Barao, A. Barrau, L. Barrin, A. Bartoloni, L. Basara, S. Ba¸seˇgmez-du Pree, R. Battiston, U. Becker, M. Behlmann, B. Beischer, J. Berdugo, B. Bertucci, V. Bindi, de Boer W, K. Bollweg, B. Borgia, M.J. Boschini, M. Bourquin, Bueno EF, J. Burger, W.J. Burger, X.D. Cai, M. Capell, S. Caroff, J. Casaus, G. Castellini, F. Cervelli, Y.H. Chang, G.M. Chen, H.S. Chen, Y. Chen, L. Cheng, H.Y. Chou, V. Choutko, C.H. Chung, C. Clark, G. Coignet, C. Consolandi, A. Contin, C. Corti, M. Crispoltoni, Z. Cui, K. Dadzie, Y.M. Dai, A. Datta, C. Delgado, S. Della Torre, M.B. Demirköz, L. Derome, S. Di Falco, V. Di Felice, F. Dimiccoli, C. Díaz, P. von Doetinchem, F. Dong, F. Donnini, M. Duranti, A. Egorov, A. Eline, T. Eronen, J. Feng, E. Fiandrini, P. Fisher, V. Formato, Y. Galaktionov, R.J. García-López, C. Gargiulo, H. Gast, I. Gebauer, M. Gervasi, F. Giovacchini, D.M. Gómez-Coral, J. Gong, C. Goy, V. Grabski, D. Grandi, M. Graziani, K.H. Guo, S. Haino, K.C. Han, Z.H. He, M. Heil, T.H. Hsieh, H. Huang, Z.C. Huang, M. Incagli, Y. Jia, H. Jinchi, K. Kanishev, B. Khiali, T. Kirn, C. Konak, O. Kounina, A. Kounine, V. Koutsenko, A. Kulemzin, G. La Vacca, E. Laudi, G. Laurenti, I. Lazzizzera, A. Lebedev, H.T. Lee, S.C. Lee, C. Leluc, J.Q. Li, Q. Li, T.X. Li, Z.H. Li, C. Light, C.H. Lin, T. Lippert, F.Z. Liu, H. Liu, Z. Liu, S.Q. Lu, Y.S. Lu, K. Luebelsmeyer, F. Luo, J.Z. Luo, X. Luo, S.S. Lyu, F. Machate, C. Mañá, J. Marín, T. Martin, G. Martínez, N. Masi, D. Maurin, A. Menchaca-Rocha, Q. Meng, D.C. Mo, M. Molero, P. Mott, L. Mussolin, T. Nelson, J.Q. Ni, N. Nikonov, F. Nozzoli, A. Oliva, M. Orcinha, M. Palermo, F. Palmonari, M. Paniccia, A. Pashnin, M. Pauluzzi, S. Pensotti, C. Perrina, H.D. Phan, N. Picot-Clemente, V. Plyaskin, M. Pohl, V. Poireau, A. Popkow, L. Quadrani, X.M. Qi, X. Qin, Z.Y. Qu, P.G. Rancoita, D. Rapin, A.R. Conde, S. Rosier-Lees, A. Rozhkov, D. Rozza, R. Sagdeev, C. Solano, S. Schael, S.M. Schmidt, A.S. von Dratzig, G. Schwering, E.S. Seo, B.S. Shan, J.Y. Shi, T. Siedenburg, J.W. Song, Z.T. Sun, M. Tacconi, X.W. Tang, Z.C. Tang, J. Tian, S.C.C. Ting, S.M. Ting, N. Tomassetti, J. Torsti, T. Urban, V. Vagelli, E. Valente, E. Valtonen, M.V. Acosta, M. Vecchi,

54 Orbits and Background of Gamma-Ray Space Instruments

1915

M. Velasco, J.P. Vialle, J. Vizán, L.Q. Wang, N.H. Wang, Q.L. Wang, X. Wang, X.Q. Wang, Z.X. Wang, J. Wei, Z.L. Weng, H. Wu, R.Q. Xiong, W. Xu, Q. Yan, Y. Yang, H. Yi, Y.J. Yu, Z.Q. Yu, M. Zannoni, S. Zeissler, C. Zhang, F. Zhang, J.H. Zhang, Z. Zhang, F. Zhao, Z.M. Zheng, H.L. Zhuang, V. Zhukov, A. Zichichi, N. Zimmermann, P. Zuccon, AMS Collaboration, Towards understanding the origin of cosmic-ray electrons. Phys. Rev. Lett. 122(10), 101101 (2019a). https://doi.org/10.1103/PhysRevLett.122.101101 M. Aguilar, L. Ali Cavasonza, G. Ambrosi, L. Arruda, N. Attig, P. Azzarello, A. Bachlechner, F. Barao, A. Barrau, L. Barrin, A. Bartoloni, L. Basara, S. Ba¸seˇgmez-du Pree, R. Battiston, U. Becker, M. Behlmann, B. Beischer, J. Berdugo, B. Bertucci, V. Bindi, W. de Boer, K. Bollweg, B. Borgia, M.J. Boschini, M. Bourquin, E.F. Bueno, J. Burger, W.J. Burger, X.D. Cai, M. Capell, S. Caroff, J. Casaus, G. Castellini, F. Cervelli, Y.H. Chang, G.M. Chen, H.S. Chen, Y. Chen, L. Cheng, H.Y. Chou, V. Choutko, C.H. Chung, C. Clark, G. Coignet, C. Consolandi, A. Contin, C. Corti, M. Crispoltoni, Z. Cui, K. Dadzie, Y.M. Dai, A. Datta, C. Delgado, S. Della Torre, M.B. Demirköz, L. Derome, S. Di Falco, F. Dimiccoli, C. Díaz, P. von Doetinchem, F. Dong, F. Donnini, M. Duranti, A. Egorov, A. Eline, T. Eronen, J. Feng, E. Fiandrini, P. Fisher, V. Formato, Y. Galaktionov, R.J. García-López, C. Gargiulo, H. Gast, I. Gebauer, M. Gervasi, F. Giovacchini, D.M. Gómez-Coral, J. Gong, C. Goy, V. Grabski, D. Grandi, M. Graziani, K.H. Guo, S. Haino, K.C. Han, Z.H. He, M. Heil, T.H. Hsieh, H. Huang, Z.C. Huang, M. Incagli, Y. Jia, H. Jinchi, K. Kanishev, B. Khiali, T. Kirn, C. Konak, O. Kounina, A. Kounine, V. Koutsenko, A. Kulemzin, G. La Vacca, E. Laudi, G. Laurenti, I. Lazzizzera, A. Lebedev, H.T. Lee, S.C. Lee, C. Leluc, J.Q. Li, Q. Li, T.X. Li, Z.H. Li, C. Light, C.H. Lin, T. Lippert, F.Z. Liu, H. Liu, Z. Liu, S.Q. Lu, Y.S. Lu, K. Luebelsmeyer, F. Luo, J.Z. Luo, X. Luo, S.S. Lyu, F. Machate, C. Mañá, J. Marín, T. Martin, G. Martínez, N. Masi, D. Maurin, A. Menchaca-Rocha, Q. Meng, D.C. Mo, M. Molero, P. Mott, L. Mussolin, T. Nelson, J.Q. Ni, N. Nikonov, F. Nozzoli, A. Oliva, M. Orcinha, M. Palermo, F. Palmonari, M. Paniccia, A. Pashnin, M. Pauluzzi, S. Pensotti, C. Perrina, H.D. Phan, N. Picot-Clemente, V. Plyaskin, M. Pohl, V. Poireau, A. Popkow, L. Quadrani, X.M. Qi, X. Qin, Z.Y. Qu, P.G. Rancoita, D. Rapin, A.R. Conde, S. Rosier-Lees, A. Rozhkov, D. Rozza, R. Sagdeev, C. Solano, S. Schael, S.M. Schmidt, A. Schulz von Dratzig, G. Schwering, E.S. Seo, B.S. Shan, J.Y. Shi, T. Siedenburg, J.W. Song, Z.T. Sun, M. Tacconi, X.W. Tang, Z.C. Tang, J. Tian, S.C.C. Ting, S.M. Ting, N. Tomassetti, J. Torsti, T. Urban, V. Vagelli, E. Valente, E. Valtonen, M. Vázquez Acosta, M. Vecchi, M. Velasco, J.P. Vialle, J. Vizán, L.Q. Wang, N.H. Wang, Q.L. Wang, X. Wang, X.Q. Wang, Z.X. Wang, J. Wei, Z.L. Weng, H. Wu, R.Q. Xiong, W. Xu, Q. Yan, Y. Yang, H. Yi, Y.J. Yu, Z.Q. Yu, M. Zannoni, S. Zeissler, C. Zhang, F. Zhang, J.H. Zhang, Z. Zhang, F. Zhao, Z.M. Zheng, H.L. Zhuang, V. Zhukov, A. Zichichi, N. Zimmermann, P. Zuccon, AMS Collaboration, Towards understanding the origin of cosmic-ray positrons. Phys. Rev. Lett. 122(4), 041102 (2019b). https://doi.org/10.1103/PhysRevLett.122. 041102 J. Alcaraz, B. Alpat, G. Ambrosi, H. Anderhub, L. Ao, A. Arefiev, P. Azzarello, E. Babucci, L. Baldini, M. Basile, D. Barancourt, F. Barao, G. Barbier, G. Barreira, R. Battiston, R. Becker, U. Becker, L. Bellagamba, P. Béné, J. Berdugo, P. Berges, B. Bertucci, A. Biland, S. Bizzaglia, S. Blasko, G. Boella, M. Boschini, M. Bourquin, L. Brocco, G. Bruni, M. Buenerd, J.D. Burger, W.J. Burger, X.D. Cai, C. Camps, P. Cannarsa, M. Capell, D. Casadei, J. Casaus, G. Castellini, C. Cecchi, Y.H. Chang, H.F. Chen, H.S. Chen, Z.G. Chen, N.A. Chernoplekov, T.H. Chiueh, Y.L. Chuang, F. Cindolo, V. Commichau, A. Contin, P. Crespo, M. Cristinziani, J.P. da Cunha, T.S. Dai, J.D. Deus, N. Dinu, L. Djambazov, I. D’Antone, Z.R. Dong, P. Emonet, J. Engelberg, F.J. Eppling, T. Eronen, G. Esposito, P. Extermann, J. Favier, E. Fiandrini, P.H. Fisher, G. Fluegge, N. Fouque, Y. Galaktionov, M. Gervasi, P. Giusti, D. Grandi, O. Grimm, W.Q. Gu, K. Hangarter, A. Hasan, V. Hermel, H. Hofer, M.A. Huang, W. Hungerford, M. Ionica, R. Ionica, M. Jongmanns, K. Karlamaa, W. Karpinski, G. Kenney, J. Kenny, W. Kim, A. Klimentov, R. Kossakowski, V. Koutsenko, M. Kraeber, G. Laborie, T. Laitinen, G. Lamanna, G. Laurenti, A. Lebedev, S.C. Lee, G. Levi, P. Levtchenko, C.L. Liu, H.T. Liu, I. Lopes, G. Lu, Y.S. Lu, K. Lübelsmeyer, D. Luckey, W. Lustermann, C. Maña, A. Margotti, F. Mayet, R.R. McNeil, B. Meillon, M. Menichelli, A. Mihul, A. Mourao, A. Mujunen, F. Palmonari, A. Papi, I.H. Park, M. Pauluzzi, F. Pauss, E. Perrin, A. Pesci, A. Pevsner, M. Pimenta, V. Plyaskin, V. Pojidaev, V.

1916

V. Tatischeff et al.

Postolache, N. Produit, P.G. Rancoita, D. Rapin, F. Raupach, D. Ren, Z. Ren, M. Ribordy, J.P. Richeux, E. Riihonen, J. Ritakari, U. Roeser, C. Roissin, R. Sagdeev, G. Sartorelli, A. Schultz von Dratzig, G. Schwering, G. Scolieri, E.S. Seo, V. Shoutko, E. Shoumilov, R. Siedling, D. Son, T. Song, M. Steuer, G.S. Sun, H. Suter, X.W. Tang, S.C.C. Ting, S.M. Ting, M. Tornikoski, J. Torsti, J. Trümper, J. Ulbricht, S. Urpo, I. Usoskin, E. Valtonen, J. Vandenhirtz, F. Velcea, E. Velikhov, B. Verlaat, I. Vetlitsky, F. Vezzu, J.P. Vialle, G. Viertel, D. Vité, H. Von Gunten, S. Waldmeier Wicki, W. Wallraff, B.C. Wang, J.Z. Wang, Y.H. Wang, K. Wiik, C. Williams, S.X. Wu, P.C. Xia, J.L. Yan, L.G. Yan, C.G. Yang, M. Yang, S.W. Ye, P. Yeh, Z.Z. Xu, H.Y. Zhang, Z.P. Zhang, D.X. Zhao, G.Y. Zhu, W.Z. Zhu, H.L. Zhuang, A. Zichichi, B. Zimmermann, Leptons in near earth orbit. Phys. Lett. B 484(1–2), 10–22 (2000a). https://doi.org/10.1016/ S0370-2693(00)00588-8 J. Alcaraz, D. Alvisi, B. Alpat, G. Ambrosi, H. Anderhub, L. Ao, A. Arefiev, P. Azzarello, E. Babucci, L. Baldini, M. Basile, D. Barancourt, F. Barao, G. Barbier, G. Barreira, R. Battiston, R. Becker, U. Becker, L. Bellagamba, P. Béné, J. Berdugo, P. Berges, B. Bertucci, A. Biland, S. Bizzaglia, S. Blasko, G. Boella, M. Boschini, M. Bourquin, G. Bruni, M. Buenerd, J.D. Burger, W.J. Burger, X.D. Cai, R. Cavalletti, C. Camps, P. Cannarsa, M. Capell, D. Casadei, J. Casaus, G. Castellini, Y.H. Chang, H.F. Chen, H.S. Chen, Z.G. Chen, N.A. Chernoplekov, A. Chiarini, T.H. Chiueh, Y.L. Chuang, F. Cindolo, V. Commichau, A. Contin, A. Cotta-Ramusino, P. Crespo, M. Cristinziani, J.P. da Cunha, T.S. Dai, J.D. Deus, N. Dinu, L. Djambazov, I. D’Antone, Z.R. Dong, P. Emonet, J. Engelberg, F.J. Eppling, T. Eronen, G. Esposito, P. Extermann, J. Favier, C.C. Feng, E. Fiandrini, F. Finelli, P.H. Fisher, R. Flaminio, G. Fluegge, N. Fouque, Y. Galaktionov, M. Gervasi, P. Giusti, D. Grandi, W.Q. Gu, K. Hangarter, A. Hasan, V. Hermel, H. Hofer, M.A. Huang, W. Hungerford, M. Ionica, R. Ionica, M. Jongmanns, K. Karlamaa, W. Karpinski, G. Kenney, J. Kenny, W. Kim, A. Klimentov, R. Kossakowski, V. Koutsenko, G. Laborie, T. Laitinen, G. Lamanna, G. Laurenti, A. Lebedev, S.C. Lee, G. Levi, P. Levtchenko, C.L. Liu, H.T. Liu, M. Lolli, I. Lopes, G. Lu, Y.S. Lu, K. Lübelsmeyer, D. Luckey, W. Lustermann, C. Maña, A. Margotti, F. Massera, F. Mayet, R.R. McNeil, B. Meillon, M. Menichelli, F. Mezzanotte, R. Mezzenga, A. Mihul, G. Molinari, A. Mourao, A. Mujunen, F. Palmonari, G. Pancaldi, A. Papi, I.H. Park, M. Pauluzzi, F. Pauss, E. Perrin, A. Pesci, A. Pevsner, R. Pilastrini, M. Pimenta, V. Plyaskin, V. Pojidaev, H. Postema, V. Postolache, E. Prati, N. Produit, P.G. Rancoita, D. Rapin, F. Raupach, S. Recupero, D. Ren, Z. Ren, M. Ribordy, J.P. Richeux, E. Riihonen, J. Ritakari, U. Roeser, C. Roissin, R. Sagdeev, D. Santos, G. Sartorelli, A. Schultz von Dratzig, G. Schwering, E.S. Seo, V. Shoutko, E. Shoumilov, R. Siedling, D. Son, T. Song, M. Steuer, G.S. Sun, H. Suter, X.W. Tang, S.C.C. Ting, S.M. Ting, M. Tornikoski, G. Torromeo, J. Torsti, J. Trümper, J. Ulbricht, S. Urpo, I. Usoskin, E. Valtonen, J. Vandenhirtz, F. Velcea, E. Velikhov, B. Verlaat, I. Vetlitsky, F. Vezzu, J.P. Vialle, G. Viertel, D. Vité, H. Von Gunten, S. Waldmeier Wicki, W. Wallraff, B.C. Wang, J.Z. Wang, Y.H. Wang, K. Wiik, C. Williams, S.X. Wu, P.C. Xia, J.L. Yan, L.G. Yan, C.G. Yang, M. Yang, S.W. Ye, P. Yeh, Z.Z. Xu, H.Y. Zhang, Z.P. Zhang, D.X. Zhao, G.Y. Zhu, W.Z. Zhu, H.L. Zhuang, A. Zichichi, Protons in near earth orbit. Phys. Lett. B 472(1–2), 215–226 (2000b). https://doi.org/10.1016/S03702693(99)01427-6, hep-ex/0002049 P. Alken, E. Thébault, C.D. Beggan, H. Amit, J. Aubert, J. Baerenzung, T.N. Bondar, W.J. Brown, S. Califf, A. Chambodut, A. Chulliat, G.A. Cox, C.C. Finlay, A. Fournier, N. Gillet, A. Grayver, M.D. Hammer, M. Holschneider, L. Huder, G. Hulot, T. Jager, C. Kloss, M. Korte, W. Kuang, A. Kuvshinov, B. Langlais, J.M. Léger, V. Lesur, P.W. Livermore, F.J. Lowes, S. Macmillan, W. Magnes, M. Mandea, S. Marsal, J. Matzka, M.C. Metman, T. Minami, A. Morschhauser, J.E. Mound, M. Nair, S. Nakano, N. Olsen, F.J. Pavón-Carrasco, V.G. Petrov, G. Ropp, M. Rother, T.J. Sabaka, S. Sanchez, D. Saturnino, N.R. Schnepf, X. Shen, C. Stolle, A. Tangborn, L. Tøffner-Clausen, H. Toh, J.M. Torta, J. Varner, F. Vervelidou, P. Vigneron, I. Wardinski, J. Wicht, A. Woods, Y. Yang, Z. Zeren, B. Zhou, International geomagnetic reference field: the thirteenth generation. Earth Planets Space 73(1), 49 (2021). https://doi.org/10.1186/s40623020-01288-x

54 Orbits and Background of Gamma-Ray Space Instruments

1917

T.W. Armstrong, K.C. Chandler, J. Barish, Calculations of neutron flux spectra induced in the Earth’s atmosphere by galactic cosmic rays. J. Geophys. Res. 78(16), 2715 (1973). https://doi. org/10.1029/JA078i016p02715 W.B. Atwood, A.A. Abdo, M. Ackermann, W. Althouse, B. Anderson, M. Axelsson, L. Baldini, J. Ballet, D.L. Band, G. Barbiellini, J. Bartelt, D. Bastieri, B.M. Baughman, K. Bechtol, D. Bédérède, F. Bellardi, R. Bellazzini, B. Berenji, G.F. Bignami, D. Bisello, E. Bissaldi, R.D. Blandford, E.D. Bloom, J.R. Bogart, E. Bonamente, J. Bonnell, A.W. Borgland, A. Bouvier, J. Bregeon, A. Brez, M. Brigida, P. Bruel, T.H. Burnett, G. Busetto, G.A. Caliandro, R.A. Cameron, P.A. Caraveo, S. Carius, P. Carlson, J.M. Casandjian, E. Cavazzuti, M. Ceccanti, C. Cecchi, E. Charles, A. Chekhtman, C.C. Cheung, J. Chiang, R. Chipaux, A.N. Cillis, S. Ciprini, R. Claus, J. Cohen-Tanugi, S. Condamoor, J. Conrad, R. Corbet, L. Corucci, L. Costamante, S. Cutini, D.S. Davis, D. Decotigny, M. DeKlotz, C.D. Dermer, A. de Angelis, S.W. Digel, E. do Couto e Silva, P.S. Drell, R. Dubois, D. Dumora, Y. Edmonds, D. Fabiani, C. Farnier, C. Favuzzi, D.L. Flath, P. Fleury, W.B. Focke, S. Funk, P. Fusco, F. Gargano, D. Gasparrini, N. Gehrels, F.X. Gentit, S. Germani, B. Giebels, N. Giglietto, P. Giommi, F. Giordano, T. Glanzman, G. Godfrey, I.A. Grenier, M.H. Grondin, J.E. Grove, L. Guillemot, S. Guiriec, G. Haller, A.K. Harding, P.A. Hart, E. Hays, S.E. Healey, M. Hirayama, L. Hjalmarsdotter, R. Horn, R.E. Hughes, G. Jóhannesson, G. Johansson, A.S. Johnson, R.P. Johnson, T.J. Johnson, W.N. Johnson, T. Kamae, H. Katagiri, J. Kataoka, A. Kavelaars, N. Kawai, H. Kelly, M. Kerr, W. Klamra, J. Knödlseder, M.L. Kocian, N. Komin, F. Kuehn, M. Kuss, D. Landriu, L. Latronico, B. Lee, S.H. Lee, M. Lemoine-Goumard, A.M. Lionetto, F. Longo, F. Loparco, B. Lott, M.N. Lovellette, P. Lubrano, G.M. Madejski, A. Makeev, B. Marangelli, M.M. Massai, M.N. Mazziotta, J.E. McEnery, N. Menon, C. Meurer, P.F. Michelson, M. Minuti, N. Mirizzi, W. Mitthumsiri, T. Mizuno, A.A. Moiseev, C. Monte, M.E. Monzani, E. Moretti, A. Morselli, I.V. Moskalenko, S. Murgia, T. Nakamori, S. Nishino, P.L. Nolan, J.P. Norris, E. Nuss, M. Ohno, T. Ohsugi, N. Omodei, E. Orlando, J.F. Ormes, A. Paccagnella, D. Paneque, J.H. Panetta, D. Parent, M. Pearce, M. Pepe, A. Perazzo, M. Pesce-Rollins, P. Picozza, L. Pieri, M. Pinchera, F. Piron, T.A. Porter, L. Poupard, S. Rainò, R. Rando, E. Rapposelli, M. Razzano, A. Reimer, O. Reimer, T. Reposeur, L.C. Reyes, S. Ritz, L.S. Rochester, A.Y. Rodriguez, R.W. Romani, M. Roth, J.J. Russell, F. Ryde, S. Sabatini, H.F.W. Sadrozinski, D. Sanchez, A. Sander, L. Sapozhnikov, P.M.S. Parkinson, J.D. Scargle, T.L. Schalk, G. Scolieri, C. Sgrò, G.H. Share, M. Shaw, T. Shimokawabe, C. Shrader, A. Sierpowska-Bartosik, E.J. Siskind, D.A. Smith, P.D. Smith, G. Spandre, P. Spinelli, J.L. Starck, T.E. Stephens, M.S. Strickman, A.W. Strong, D.J. Suson, H. Tajima, H. Takahashi, T. Takahashi, T. Tanaka, A. Tenze, S. Tether, J.B. Thayer, J.G. Thayer, D.J. Thompson, L. Tibaldo, O. Tibolla, D.F. Torres, G. Tosti, A. Tramacere, M. Turri, T.L. Usher, N. Vilchez, V. Vitale, P. Wang, K. Watters, B.L. Winer, K.S. Wood, T. Ylinen, M. Ziegler, The large area telescope on the Fermi gamma-ray space telescope mission. Astrophys. J. 697(2), 1071–1102 (2009). https://doi.org/10.1088/0004-637X/697/2/1071, 0902.1089 A. Bazzano, J.B. Stephen, M. Fiocchi, A.J. Bird, L. Bassani, A.J. Dean, A. Malizia, P. Ubertini, F. Lebrun, R. Walter, C. Winkler, INTEGRAL IBIS census of the sky beyond 100 keV. Astrophys. J. 649(1), L9–L12 (2006). https://doi.org/10.1086/508171, astro-ph/0608164 V. Bidoli, M. Casolino, M. de Pascale, G. Furano, A. Iannucci, A. Morselli, P. Picozza, R. Sparvoli, A. Bakaldin, A. Galper, S. Koldashov, M. Korotkov, A. Leonov, V. Mikhailov, S. Voronov, M. Boezio, V. Bonvicini, A. Vacchi, G. Zampa, N. Zampa, M. Ambriola, F. Cafagna, M. Circella, C. de Marzo, O. Adriani, P. Papini, P. Spillantini, S. Straulino, E. Vannuccini, M. Ricci, G. Castellini, Energy spectrum of secondary protons above the atmosphere measured by the instruments NINA and NINA-2. Ann. Geophys. 20(10), 1693–1697 (2002). https://doi.org/ 10.5194/angeo-20-1693-2002 A.J. Bird, A. Bazzano, A. Malizia, M. Fiocchi, V. Sguera, L. Bassani, A.B. Hill, P. Ubertini, C. Winkler, The IBIS soft gamma-ray sky after 1000 integral orbits. Astrophys. J. Suppl. 223(1), 15 (2016). https://doi.org/10.3847/0067-0049/223/1/15, 1601.06074 L. Bouchet, E. Jourdain, J.P. Roques, A. Strong, R. Diehl, F. Lebrun, R. Terrier, INTEGRAL SPI all-sky view in soft gamma rays: a study of point-source and galactic diffuse emission. Astrophys. J. 679(2), 1315–1326 (2008). https://doi.org/10.1086/529489, 0801.2086

1918

V. Tatischeff et al.

R. Campana, M. Orlandini, E. Del Monte, M. Feroci, F. Frontera, The radiation environment in a low earth orbit: the case of BeppoSAX. Exp. Astron. 37(3), 599–613 (2014). https://doi.org/10. 1007/s10686-014-9394-1, 1405.0360 M. Chauvin, H.G. Florén, M. Friis, M. Jackson, T. Kamae, J. Kataoka, T. Kawano, M. Kiss, V. Mikhalev, T. Mizuno, N. Ohashi, T. Stana, H. Tajima, H. Takahashi, N. Uchida, M. Pearce, Shedding new light on the Crab with polarized X-rays. Sci. Rep. 7, 7816 (2017). https://doi.org/ 10.1038/s41598-017-07390-7, 1706.09203 E. Churazov, R. Sunyaev, M. Revnivtsev, S. Sazonov, S. Molkov, S. Grebenev, C. Winkler, A. Parmar, A. Bazzano, M. Falanga, A. Gros, F. Lebrun, L. Natalucci, P. Ubertini, J.P. Roques, L. Bouchet, E. Jourdain, J. Knödlseder, R. Diehl, C. Budtz-Jorgensen, S. Brandt, N. Lund, N.J. Westergaard, A. Neronov, M. Türler, M. Chernyakova, R. Walter, N. Produit, N. Mowlavi, J.M. Mas-Hesse, A. Domingo, N. Gehrels, E. Kuulkers, P. Kretschmar, M. Schmidt, INTEGRAL observations of the cosmic X-ray background in the 5–100 keV range via occultation by the Earth. Astron. Astrophys. 467(2), 529–540 (2007a). https://doi.org/10.1051/0004-6361: 20066230, astro-ph/0608250 E. Churazov, R. Sunyaev, M. Revnivtsev, S. Sazonov, S. Molkov, S. Grebenev, C. Winkler, A. Parmar, A. Bazzano, M. Falanga, A. Gros, F. Lebrun, L. Natalucci, P. Ubertini, J.P. Roques, L. Bouchet, E. Jourdain, J. Knödlseder, R. Diehl, C. Budtz-Jorgensen, S. Brandt, N. Lund, N.J. Westergaard, A. Neronov, M. Türler, M. Chernyakova, R. Walter, N. Produit, N. Mowlavi, J.M. Mas-Hesse, A. Domingo, N. Gehrels, E. Kuulkers, P. Kretschmar, M. Schmidt, INTEGRAL observations of the cosmic X-ray background in the 5–100 keV range via occultation by the Earth. Astron. Astrophys. 467(2), 529–540 (2007b). https://doi.org/10.1051/0004-6361: 20066230, astro-ph/0608250 E. Churazov, L. Bouchet, P. Jean, E. Jourdain, J. Knödlseder, R. Krivonos, J.P. Roques, S. Sazonov, T. Siegert, A. Strong, R. Sunyaev, INTEGRAL results on the electron-positron annihilation radiation and X-ray & Gamma-ray diffuse emission of the Milky Way. New Astron. Rev. 90, 101548 (2020). https://doi.org/10.1016/j.newar.2020.101548 W. Coburn, S.E. Boggs, J.D. Bowen, M.E. Bandstra, M.S. Amman, M.T. Burks, W. Craig, P. Jean, R.P. Lin, P.N. Luke, N.W. Madden, D.M. Smith, P. von Ballmoos, First results from the balloon flight of the NCT prototype, in UV, X-Ray, and Gamma-Ray Space Instrumentation for Astronomy XIV, ed. by O.H.W. Siegmund. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 5898, (2005), pp. 13–21. https://doi.org/10.1117/12.615876 P. Cumani, M. Hernanz, J. Kiener, V. Tatischeff, A. Zoglauer, Background for a gamma-ray satellite on a low-Earth orbit. Exp. Astron. 47(3), 273–302 (2019). https://doi.org/10.1007/s10686-01909624-0, 1902.06944 R.R. Daniel, S.A. Stephens, Cosmic-ray-produced electrons and gamma rays in the atmosphere. Rev. Geophys. Space Phys. 12, 233 (1974). https://doi.org/10.1029/RG012i002p00233 A. De Angelis, V. Tatischeff, M. Tavani, U. Oberlack, I. Grenier, L. Hanlon, R. Walter, A. Argan, P. von Ballmoos, A. Bulgarelli, I. Donnarumma, M. Hernanz, I. Kuvvetli, M. Pearce, A. Zdziarski, A. Aboudan, M. Ajello, G. Ambrosi, D. Bernard, E. Bernardini, V. Bonvicini, A. Brogna, M. Branchesi, C. Budtz-Jorgensen, A. Bykov, R. Campana, M. Cardillo, P. Coppi, D. De Martino, R. Diehl, M. Doro, V. Fioretti, S. Funk, G. Ghisellini, E. Grove, C. Hamadache, D.H. Hartmann, M. Hayashida, J. Isern, G. Kanbach, J. Kiener, J. Knödlseder, C. Labanti, P. Laurent, O. Limousin, F. Longo, K. Mannheim, M. Marisaldi, M. Martinez, M.N. Mazziotta, J. McEnery, S. Mereghetti, G. Minervini, A. Moiseev, A. Morselli, K. Nakazawa, P. Orleanski, J.M. Paredes, B. Patricelli, J. Peyré, G. Piano, M. Pohl, H. Ramarijaona, R. Rando, I. Reichardt, M. Roncadelli, R. Silva, F. Tavecchio, D.J. Thompson, R. Turolla, A. Ulyanov, A. Vacchi, X. Wu, A. Zoglauer, The e-ASTROGAM mission. Exploring the extreme Universe with gamma rays in the MeV – GeV range. Exp. Astron. 44(1), 25–82 (2017). https://doi.org/10.1007/s10686-017-9533-6, 1611.02232 A. de Angelis, V. Tatischeff, I.A. Grenier, J. McEnery, M. Mallamaci, M. Tavani, U. Oberlack, L. Hanlon, R. Walter, A. Argan, P. von Ballmoos, A. Bulgarelli, A. Bykov, M. Hernanz, G. Kanbach, I. Kuvvetli, M. Pearce, A. Zdziarski, J. Conrad, G. Ghisellini, A. Harding, J. Isern, M. Leising, F. Longo, G. Madejski, M. Martinez, M.N. Mazziotta, J.M. Paredes, M. Pohl, R. Rando,

54 Orbits and Background of Gamma-Ray Space Instruments

1919

M. Razzano, A. Aboudan, M. Ackermann, A. Addazi, M. Ajello, C. Albertus, J.M. Álvarez, G. Ambrosi, S. Antón, L.A. Antonelli, A. Babic, B. Baibussinov, M. Balbo, L. Baldini, S. Balman, C. Bambi, U. Barres de Almeida, J.A. Barrio, R. Bartels, D. Bastieri, W. Bednarek, D. Bernard, E. Bernardini, T. Bernasconi, B. Bertucci, A. Biland, E. Bissaldi, M. Boettcher, V. Bonvicini, V. Bosch-Ramon, E. Bottacini, V. Bozhilov, T. Bretz, M. Branchesi, V. Brdar, T. Bringmann, A. Brogna, C. Budtz Jørgensen, G. Busetto, S. Buson, M. Busso, A. Caccianiga, S. Camera, R. Campana, P. Caraveo, M. Cardillo, P. Carlson, S. Celestin, M. Cermeño, A. Chen, C.C. Cheung, E. Churazov, S. Ciprini, A. Coc, S. Colafrancesco, A. Coleiro, W. Collmar, P. Coppi, R. Curado da Silva, S. Cutini, F. D’Ammando, B. de Lotto, D. de Martino, A. De Rosa, M. Del Santo, L. Delgado, R. Diehl, S. Dietrich, A.D. Dolgov, A. Domínguez, D. Dominis Prester, I. Donnarumma, D. Dorner, M. Doro, M. Dutra, D. Elsaesser, M. Fabrizio, A. FernándezBarral, V. Fioretti, L. Foffano, V. Formato, N. Fornengo, L. Foschini, A. Franceschini, A. Franckowiak, S. Funk, F. Fuschino, D. Gaggero, G. Galanti, F. Gargano, D. Gasparrini, R. Gehrz, P. Giammaria, N. Giglietto, P. Giommi, F. Giordano, M. Giroletti, G. Ghirlanda, N. Godinovic, C. Gouiffés, J.E. Grove, C. Hamadache, D.H. Hartmann, M. Hayashida, A. Hryczuk, P. Jean, T. Johnson, J. José, S. Kaufmann, B. Khelifi, J. Kiener, J. Knödlseder, M. Kole, J. Kopp, V. Kozhuharov, C. Labanti, S. Lalkovski, P. Laurent, O. Limousin, M. Linares, E. Lindfors, M. Lindner, J. Liu, S. Lombardi, F. Loparco, R. López-Coto, M. López Moya, B. Lott, P. Lubrano, D. Malyshev, N. Mankuzhiyil, K. Mannheim, M.J. Marchã, A. Marcianò, B. Marcote, M. Mariotti, M. Marisaldi, S. McBreen, S. Mereghetti, A. Merle, R. Mignani, G. Minervini, A. Moiseev, A. Morselli, F. Moura, K. Nakazawa, L. Nava, D. Nieto, M. Orienti, M. Orio, E. Orlando, P. Orleanski, S. Paiano, R. Paoletti, A. Papitto, M. Pasquato, B. Patricelli, M.Á. PérezGarcía, M. Persic, G. Piano, A. Pichel, M. Pimenta, C. Pittori, T. Porter, J. Poutanen, E. Prandini, N. Prantzos, N. Produit, S. Profumo, F.S. Queiroz, S. Rainó, A. Raklev, M. Regis, I. Reichardt, Y. Rephaeli, J. Rico, W. Rodejohann, G. Rodriguez Fernandez, M. Roncadelli, L. Roso, A. Rovero, R. Ruffini, G. Sala, M.A. Sánchez-Conde, A. Santangelo, P. Saz Parkinson, T. Sbarrato, A. Shearer, R. Shellard, K. Short, T. Siegert, C. Siqueira, P. Spinelli, A. Stamerra, S. Starrfield, A. Strong, I. Strümke, F. Tavecchio, R. Taverna, T. Terzi´c, D.J. Thompson, O. Tibolla, D.F. Torres, R. Turolla, A. Ulyanov, A. Ursi, A. Vacchi, J. van den Abeele, G. Vankova-Kirilovai, C. Venter, F. Verrecchia, P. Vincent, X. Wang, C. Weniger, X. Wu, G. Zaharijaš, L. Zampieri, S. Zane, S. Zimmer, A. Zoglauer, E-Astrogam Collaboration, Science with e-ASTROGAM. A space mission for MeV-GeV gamma-ray astrophysics. J. High Energy Astrophys. 19, 1–106 (2018). https://doi.org/10.1016/j.jheap.2018.07.001, 1711.01265 L. Desorgher, E.O. Flückiger, M. Gurtner, The planetocosmics Geant4 application, in 36th COSPAR Scientific Assembly, vol. 36 (2006), p. 2361 G. Dilillo, N. Zampa, R. Campana, F. Fuschino, G. Pauletta, I. Rashevskaya, F. Ambrosino, M. Baruzzo, D. Cauz, D. Cirrincione, M. Citossi, G.D. Casa, B. Di Ruzza, Y. Evangelista, G. Galgóczi, C. Labanti, J. Ripa, F. Tommasino, E. Verroi, F. Fiore, A. Vacchi, Space applications of GAGG:Ce scintillators: a study of afterglow emission by proton irradiation. Nucl. Instrum. Methods Phys. Res. B 513, 33–43 (2022). https://doi.org/10.1016/j.nimb.2021. 12.006, 2112.02897 J. Feynman, S.B. Gabriel, On space weather consequences and predictions. J. Geophys. Res. 105(A5), 10543–10564 (2000). https://doi.org/10.1029/1999JA000141 C.E. Fichtel, G.A. Simpson, D.J. Thompson, Diffuse gamma radiation. Astrophys. J. 222, 833–849 (1978). https://doi.org/10.1086/156202 G.J. Fishman, J.F.R. Harnden, I.W.N. Johnson, R.C. Haymes, The Period and Hard-X Spectrum of NP 0532 IN 1967. Astrophys. J. 158, L61 (1969). https://doi.org/10.1086/180432 L.A. Fisk, B. Kozlovsky, R. Ramaty, An interpretation of the observed oxygen and nitrogen enhancements in low-energy cosmic rays. Astrophys. J. 190, L35 (1974). https://doi.org/10. 1086/181498 F. Fürst, J. Wilms, R.E. Rothschild, K. Pottschmidt, D.M. Smith, R. Lingenfelter, Temporal variations of strength and location of the South Atlantic Anomaly as measured by RXTE. Earth Planet. Sci. Lett. 281(3–4), 125–133 (2009). https://doi.org/10.1016/j.epsl.2009.02.004, 0902.2873

1920

V. Tatischeff et al.

ˇ G. Galgóczi, J. Rípa, R. Campana, N. Werner, A. Pál, M. Ohno, L. Mészáros, T. Mizuno, N. Tarcai, K. Torigoe, N. Uchida, Y. Fukazawa, H. Takahashi, K. Nakazawa, N. Hirade, K. Hirose, S. Hisadomi, T. Enoto, H. Odaka, Y. Ichinohe, Z. Frei, L. Kiss, Simulations of expected signal and background of gamma-ray sources by large field-of-view detectors aboard CubeSats. J. Astron. Telescopes Instrum. Syst. 7, 028004 (2021). https://doi.org/10.1117/1.JATIS.7.2. 028004, 2102.08104 M. Garcia-Munoz, G.M. Mason, J.A. Simpson, A new test for solar modulation theory: the 1972 May–July low-energy galactic cosmic-ray proton and helium spectra. Astrophys. J. 182, L81 (1973). https://doi.org/10.1086/181224 N. Gehrels, S.D. Barthelmy, B.J. Teegarden, J. Tueller, M. Leventhal, C.J. MacCallum, GRIS observations of positron annihilation radiation from the galactic center. Astrophys. J. 375, L13 (1991). https://doi.org/10.1086/186077 M. Gerontidou, N. Katzourakis, H. Mavromichalaki, V. Yanke, E. Eroshenko, World grid of cosmic ray vertical cut-off rigidity for the last decade. Adv. Space Res. 67(7), 2231–2240 (2021). https://doi.org/10.1016/j.asr.2021.01.011 R. Gilli, A. Comastri, G. Hasinger, The synthesis of the cosmic X-ray background in the Chandra and XMM-Newton era. Astron. Astrophys. 463(1), 79–96 (2007). https://doi.org/10.1051/00046361:20066334, astro-ph/0610939 G.P. Ginet, T.P. O’Brien, S.L. Huston, W.R. Johnston, T.B. Guild, R. Friedel, C.D. Lindstrom, C.J. Roth, P. Whelan, R.A. Quinn, D. Madden, S. Morley, Y.J. Su, AE9, AP9 and SPM: new models for specifying the trapped energetic particle and space plasma environment. SSpace Sci. Rev. 179(1–4), 579–615 (2013). https://doi.org/10.1007/s11214-013-9964-y L.J. Gleeson, W.I. Axford, Solar modulation of galactic cosmic rays. Astrophys. J. 154, 1011 (1968). https://doi.org/10.1086/149822 U. Graser, V. Schoenfelder, Theoretical zenith angle distribution of atmospheric MeV gamma radiation at high balloon altitudes. J. Geophys. Res. 82(7), 1055 (1977). https://doi.org/10.1029/ JA082i007p01055 D.E. Gruber, J.L. Matteson, L.E. Peterson, G.V. Jung, The spectrum of diffuse cosmic hard X-rays measured with HEAO 1. Astrophys. J. 520(1), 124–129 (1999). https://doi.org/10.1086/307450, astro-ph/9903492 I.A. Gurian, E.P. Mazets, M.P. Proskura, I.A. Sokolov, Investigation of hard gamma radiation of the atmosphere on Cosmos 461. Geomagn. Aeron. 19, 11–17 (1979) R.C. Haymes, G.D. Walraven, C.A. Meegan, R.D. Hall, F.T. Djuth, D.H. Shelton, Detection of nuclear gamma rays from the galactic center region. Astrophys. J. 201, 593–602 (1975). https:// doi.org/10.1086/153925 W.L. Imhof, G.H. Nakano, J.B. Reagan, High-Resolution Measurements of Atmospheric Gamma Rays from a Satellite. J. Geophys. Res. 81(16), 2835 (1976). https://doi.org/10.1029/ JA081i016p02835 W.V. Jones, Evolution of scientific ballooning and its impact on astrophysics research. Adv. Space Res. 53(10), 1405–1414 (2014). https://doi.org/10.1016/j.asr.2013.12.028 M. Kole, M. Pearce, M. Muñoz Salinas, A model of the cosmic ray induced atmospheric neutron environment. Astropart. Phys. 62, 230–240 (2015). https://doi.org/10.1016/j.astropartphys. 2014.10.002, 1410.1364 R. Krivonos, M. Revnivtsev, E. Churazov, S. Sazonov, S. Grebenev, R. Sunyaev, Hard X-ray emission from the Galactic ridge. Astron. Astrophys. 463(3), 957–967 (2007). https://doi.org/ 10.1051/0004-6361:20065626, astro-ph/0605420 R. Krivonos, S. Tsygankov, A. Lutovinov, M. Revnivtsev, E. Churazov, R. Sunyaev, INTEGRAL 11-year hard X-ray survey above 100 keV. Mon. Not. R. Astron. Soc. 448(4), 3766–3774 (2015a). https://doi.org/10.1093/mnras/stv150, 1412.1051 R. Krivonos, S. Tsygankov, A. Lutovinov, M. Revnivtsev, E. Churazov, R. Sunyaev, INTEGRAL 11-year hard X-ray survey above 100 keV. Mon. Not. R. Astron. Soc. 448(4), 3766–3774 (2015b). https://doi.org/10.1093/mnras/stv150, 1412.1051

54 Orbits and Background of Gamma-Ray Space Instruments

1921

E. Kuulkers, C. Ferrigno, P. Kretschmar, J. Alfonso-Garzón, M. Baab, A. Bazzano, G. Bélanger, I. Benson, A.J. Bird, E. Bozzo, S. Brandt, E. Coe, I. Caballero, F. Cangemi, J. Chenevez, B. Cenko, N. Cinar, A. Coleiro, S. De Padova, R. Diehl, C. Dietze, A. Domingo, M. Drapes, E. D’uva, M. Ehle, J. Ebrero, M. Edirimanne, N.A. Eismont, T. Finn, M. Fiocchi, E.G. Tomas, G. Gaudenzi, T. Godard, A. Goldwurm, D. Götz, C. Gouiffès, S.A. Grebenev, J. Greiner, A. Gros, W. Hajdas, L. Hanlon, W. Hermsen, C. Hernández, M. Hernanz, J. Hübner, E. Jourdain, G. La Rosa, C. Labanti, P. Laurent, A. Lehanka, N. Lund, J. Madison, J. Malzac, J. Martin, J.M. Mas-Hesse, B. McBreen, A. McDonald, J. McEnery, S. Mereghetti, L. Natalucci, J.U. Ness, C.A. Oxborrow, J. Palmer, S. Peschke, F. Petrucciani, N. Pfeil, M. Reichenbaecher, J. Rodi, J. Rodriguez, J.P. Roques, E.S. Doñate, D. Salt, C. Sánchez-Fernández, A. Sauvageon, V. Savchenko, S.Y. Sazonov, S. Scaglioni, N. Schartel, T. Siegert, R. Southworth, R.A. Sunyaev, L. Toma, P. Ubertini, E.P.J. van den Heuvel, A. von Kienlin, N. von Krusenstiern, C. Winkler, U. Zannoni, INTEGRAL reloaded: Spacecraft, instruments and ground system. New Astron. Rev. 93, 101629 (2021). https://doi.org/10.1016/j.newar.2021.101629 F. Lebrun, R. Terrier, A. Bazzano, G. Bélanger, A. Bird, L. Bouchet, A. Dean, M. Del Santo, A. Goldwurm, N. Lund, H. Morand, A. Parmar, J. Paul, J.P. Roques, V. Schönfelder, A.W. Strong, P. Ubertini, R. Walter, C. Winkler, Compact sources as the origin of the soft γ -ray emission of the Milky Way. Nature 428(6980), 293–29 (2004). https://doi.org/10.1038/nature02407 R.A. Leske, J.R. Cummings, R.A. Mewaldt, E.C. Stone, T.T. von Rosenvinge, Measurements of the ionic charge states of solar energetic particles using the geomagnetic field. Astrophys. J. 452, L149 (1995). https://doi.org/10.1086/309718 S. Madlee, W. Mitthumsiri, D. Ruffolo, S. Digel, W. Nuntiyakul, First analysis of earth’s stratospheric gamma-ray emission in geographical coordinates with fermi lat. J. Geophys. Res.: Space Phys. 125, 28151 (2020) A. Malizia, R. Landi, M. Molina, L. Bassani, A. Bazzano, A.J. Bird, P. Ubertini, The INTEGRAL/IBIS AGN catalogue: an update. Mon. Not. R. Astron. Soc. 460(1), 19–29 (2016). https://doi.org/10.1093/mnras/stw972, 1604.06303 P. Mandrou, G. Vedrenne, M. Niel, Diffuse cosmic gamma-ray observations from 0.3 to 6 MeV in two regions near the galactic center and anticenter. Astrophys. J. 230, 97–105 (1979). https:// doi.org/10.1086/157065 F.E. Marshall, E.A. Boldt, S.S. Holt, R.B. Miller, R.F. Mushotzky, L.A. Rose, R.E. Rothschild, P.J. Serlemitsos, The diffuse X-ray background spectrum from 3 to 50 keV. Astrophys. J. 235, 4–10 (1980). https://doi.org/10.1086/157601 V.V. Mikhailov, Low energy electron and positron spectra in the earth orbit measured by Maria2 instrument. Int. J. Modern Phys. A 17(12–13), 1695–1704 (2002). https://doi.org/10.1142/ S0217751X02011199 T. Mizuno, T. Kamae, G. Godfrey, T. Handa, D.J. Thompson, D. Lauben, Y. Fukazawa, M. Ozaki, Cosmic-ray background flux model based on a gamma-ray large area space telescope balloon flight engineering model. Astrophys. J. 614(2), 1113–1123 (2004). https://doi.org/10. 1086/423801, astro-ph/0406684 A.A. Moiseev, R.C. Hartman, J.F. Ormes, D.J. Thompson, M.J. Amato, T.E. Johnson, K.N. Segal, D.A. Sheppard, The anti-coincidence detector for the GLAST large area telescope. Astropart. Phys. 27(5), 339–358 (2007). https://doi.org/10.1016/j.astropartphys.2006.12.003, astro-ph/0702581 D.J. Morris, H. Aarts, K. Bennett, J.A. Lockwood, M.L. McConnell, J.M. Ryan, V. Schoenfelder, H. Steinle, X. Peng, Neutron measurements in near-Earth orbit with COMPTEL. J. Geophys. Res. 100(A7), 12243–12250 (1995). https://doi.org/10.1029/95JA00475 Y. Nakamura, T. Tanimori, A. Takada, Y. Mizumura, S. Komura, T. Kishimoto, T. Takemura, K. Yoshikawa, T. Tanigushi, K. Onozaka, K. Saito, T. Mizumoto, S. Sonoda, H. Kubo, Y. Matsuoka, Y. Nakamasu, S. Kurosawa, K. Miuchi, T. Sawano, SMILE-2+: the 2018 balloon flight and the instrument design of the electron-tracking Compton camera, in Space Telescopes and Instrumentation 2018: Ultraviolet to Gamma Ray, ed. by J.W.A. den Herder, S. Nikzad, K. Nakazawa. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 10699, (2018), p. 106995W. https://doi.org/10.1117/12.2309920

1922

V. Tatischeff et al.

M. Pearce, H.G. Florén, M. Jackson, T. Kamae, M. Kiss, M. Kole, E. Moretti, G. Olofsson, S. Rydström, J.E. Strömberg, H. Takahashi, Balloon-borne hard X-ray polarimetry with PoGOLite (2012). arXiv e-prints arXiv:1211.5094, 1211.5094 T.A. Porter, I.V. Moskalenko, A.W. Strong, E. Orlando, L. Bouchet, Inverse compton origin of the hard X-ray and soft gamma-ray emission from the galactic ridge. Astrophys. J. 682(1), 400–407 (2008). https://doi.org/10.1086/589615, 0804.1774 A.M. Preszler, S. Moon, R.S. White, Atmospheric neutrons. J. Geophys. Res. 81(25), 4715 (1976). https://doi.org/10.1029/JA081i025p04715 P. Raizonville, A. Vargas, F. Friedl-Vallon, K. Dannenberg, P. Ubertini, M. Abrahamsson, Hemera research Balloon Infrastructure, in 24th ESA Symposium on European Rocket & Balloon (ESA’s Publication, 2019), pp. 214–218 D.V. Reames, Particle acceleration at the Sun and in the heliosphere. SSpace Sci. Rev. 90, 413–491 (1999). https://doi.org/10.1023/A:1005105831781 J.M. Ryan, B. Dayton, S.H. Moon, R.B. Wilson, A.D. Zych, R.S. White, atmospheric gamma ray angle and energy distributions from 2 to 25 MeV. J. Geophys. Res. 82(25):3593 (1977). https:// doi.org/10.1029/JA082i025p03593 T. Sato, Analytical model for estimating terrestrial cosmic ray fluxes nearly anytime and anywhere in the world: Extension of parma/expacs. PLOS ONE 10(12), 1–33 (2015). https://doi.org/10. 1371/journal.pone.0144679 V. Savchenko, C. Ferrigno, E. Kuulkers, A. Bazzano, E. Bozzo, S. Brandt, J. Chenevez, T.J.L. Courvoisier, R. Diehl, A. Domingo, L. Hanlon, E. Jourdain, A. von Kienlin, P. Laurent, F. Lebrun, A. Lutovinov, A. Martin-Carrillo, S. Mereghetti, L. Natalucci, J. Rodi, J.P. Roques, R. Sunyaev, P. Ubertini, INTEGRAL detection of the first prompt gamma-ray signal coincident with the gravitational-wave event GW170817. Astrophys. J. 848(2), L15 (2017). https://doi.org/ 10.3847/2041-8213/aa8f94, 1710.05449 V. Schoenfelder, U. Graser, J. Daugherty, Diffuse cosmic and atmospheric MeV gamma radiation from balloon observations. Astrophys. J. 217, 306–319 (1977). https://doi.org/10.1086/155580 V. Schoenfelder, F. Graml, F.P. Penningsfeld, The vertical component of 1-20 MeV gamma rays at balloon altitudes. Astrophys. J. 240, 350–362 (1980). https://doi.org/10.1086/158239 V. Schoenfelder, H. Aarts, K. Bennett, H. de Boer, J. Clear, W. Collmar, A. Connors, A. Deerenberg, R. Diehl, A. von Dordrecht, J.W. den Herder, W. Hermsen, M. Kippen, L. Kuiper, G. Lichti, J. Lockwood, J. Macri, M. McConnell, D. Morris, R. Much, J. Ryan, G. Simpson, M. Snelling, G. Stacy, H. Steinle, A. Strong, B.N. Swanenburg, B. Taylor, C. de Vries, C. Winkler, Instrument description and performance of the imaging gamma-ray telescope COMPTEL aboard the compton gamma-ray observatory. Astrophys. J. Suppl. 86, 657 (1993). https://doi. org/10.1086/191794 V. Schönfelder, G. Lichti, Energy spectrum and evidence for extragalactic origin of diffuse gammaradiation in the MeV range. Astrophys. J. 191, L1 (1974). https://doi.org/10.1086/ 181528 R.S. Selesnick, M.D. Looper, R.A. Mewaldt, A theoretical model of the inner proton radiation belt. Space Weather 5(4), S04003 (2007). https://doi.org/10.1029/2006SW000275 D.F. Smart, M.A. Shea, A review of geomagnetic cutoff rigidities for earth-orbiting spacecraft. Adv. Space Res. 36(10), 2012–2020 (2005). https://doi.org/10.1016/j.asr.2004.09.015 A.W. Strong, Interstellar gamma rays and cosmic rays: new insights from fermi-lat and integral, in Cosmic Rays for Particle and Astroparticle Physics, ed. by S. Giani, C. Leroy, P.G. Rancoita (2011), pp. 473–481. https://doi.org/10.1142/9789814329033_0059, 1101.1381 A.W. Strong, J.B.G.M. Bloemen, F. Lebrun, W. Hermsen, H.A. Mayer-Hasselwander, R. Buccheri, The final COS-B database – in-flight calibration of sensitivity and instrumental background behaviour. Astron. Astrophys. Suppl. 67(2), 283–296 (1987) A. Takada, H. Kubo, H. Nishimura, K. Ueno, K. Hattori, S. Kabuki, S. Kurosawa, K. Miuchi, E. Mizuta, T. Nagayoshi, N. Nonaka, Y. Okada, R. Orito, H. Sekiya, A. Takeda, T. Tanimori, Observation of diffuse cosmic and atmospheric gamma rays at balloon altitudes with an electron-tracking compton camera. Astrophys. J. 733(1), 13 (2011). https://doi.org/10.1088/ 0004-637X/733/1/13, 1103.3436

54 Orbits and Background of Gamma-Ray Space Instruments

1923

V. Tatischeff, A. De Angelis, M. Tavani et al., All-Sky-ASTROGAM – the MeV gamma-ray companion to multimessenger astronomy. MmSAI 90, 137 (2019), 1905.07806 V. Tatischeff, J.C. Raymond, J. Duprat, S. Gabici, S. Recchia, The origin of Galactic cosmic rays as revealed by their composition. Mon. Not. R. Astron. Soc. 508(1), 1321–1345 (2021). https:// doi.org/10.1093/mnras/stab2533, 2106.15581 B.J. Teegarden, S.D. Barthelmy, N. Gehrels, J. Tueller, M. Leventhal, C.J. MacCallum, GRIS observations of 26Al gamma-ray line emission from two points in the galactic plane. Astrophys. J. 375, L9 (1991). https://doi.org/10.1086/186076 D.J. Thompson, G. Godfrey, S.M. Williams, J.E. Grove, T. Mizuno, H.F.W. Sadrozinski, T. Kamae, J. Ampe, S. Briber, J. Dann, E. Do Couto E Silva, R. Dubois, Y. Fukazawa, B. Giebels, G. Haller, T. Handa, R.C. Hartman, K. Hirano, M. Hirayama, R.P. Johnson, W.N. Johnson, A. Kavelaars, H. Kelly, S. Kliewer, T. Kotani, J. Krizmanic, W. Kroeger, M. Kuss, D. Lauben, T. Linder, M. Lovellette, N. Lumb, J. Manildi, P. Michelson, H. Mizushima, A. Moiseev, P.L. Nolan, S. Ogata, J.F. Ormes, M. Ozaki, G. Paliaga, B.F. Phlips, S. Ritz, L.S. Rochester, F.M. Roterman, W.A. Rowe, J.J. Russell, R. Schaefer, T. Schalk, D. Sheppard, S. Singh, M. Sjogren, G. Spandre, T. Usher, P. Valtersson, A.P. Waite, J. Wallace, A. Webster, D. Wood, Gamma-ray Large-Area Space Telescope (GLAST) balloon flight engineering model: overview. IEEE Trans. Nuc. Sci. 49(4), 1898–1903 (2002) . https://doi.org/10.1109/TNS.2002.801548, astro-ph/0209615 J. Tueller, S. Barthelmy, N. Gehrels, B.J. Teegarden, M. Leventhal, C.J. MacCallum, The GammaRay Imaging Spectrometer (GRIS) instrument and plans for serving SN 1987A, in Nuclear Spectroscopy of Astrophysical Sources, ed. by N. Gehrels, G.H. Share. American Institute of Physics Conference Series, vol. 170 (1988), pp. 439–443, https://doi.org/10.1063/1.37243 J. Tueller, S. Barthelmy, N. Gehrels, B.J. Teegarden, M. Leventhal, C.J. MacCallum, Observations of gamma-ray line profiles from SN 1987A. Astrophys. J. 351, L41 (1990). https://doi.org/10. 1086/185675 M. Türler, M. Chernyakova, T.J.L. Courvoisier, P. Lubi´nski, A. Neronov, N. Produit, R. Walter, INTEGRAL hard X-ray spectra of the cosmic X-ray background and Galactic ridge emission. Astron. Astrophys. 512, A49 (2010). https://doi.org/10.1051/0004-6361/200913072, 1001.2110 A.J. Tylka, J.H. Adams, P.R. Boberg, B. Brownstein, W.F. Dietrich, E.O. Flueckiger, E.L. Petersen, M.A. Shea, D.F. Smart, E.C. Smith, CREME96: a revision of the C_osmic R_ay E_ffects on M_icro-E_lectronics code. IEEE Trans. Nucl. Sci. 44(6), 2150–2160 (1997). https://doi.org/10. 1109/23.659030 P. Ubertini, Scientific balloons: historical remarks. Memorie della Società Astronomica Italiana 79, 783 (2008) P. Ubertini, F. Lebrun, G. Di Cocco, A. Bazzano, A.J. Bird, K. Broenstad, A. Goldwurm, G. La Rosa, C. Labanti, P. Laurent, I.F. Mirabel, E.M. Quadrini, B. Ramsey, V. Reglero, L. Sabau, B. Sacco, R. Staubert, L. Vigroux, M.C. Weisskopf, A.A. Zdziarski, IBIS: The Imager on-board INTEGRAL. Astron. Astrophys. 411, L131–L139 (2003). https://doi.org/10.1051/0004-6361: 20031224 P. Ubertini, A. Bazzano, L. Natalucci, J. Rodi, S. Mereghetti, E. Bozzo, T.J.L. Courvoisier, C. Ferrigno, V. Savchenko, E. Kuulkers, S. Brandt, J. Chenevez, R. Diehl, A. von Kienlin, L. Hanlon, A. Martin-Carrillo, E. Jourdain, J.P. Roques, P. Laurent, F. Lebrun, A. Lutovinov, R. Sunyaev, INTEGRAL search for GW counterparts and the GRB170817A/GW170817 detection. Rendiconti Lincei Scienze Fisiche e Naturali 30, 65–70 (2019). https://doi.org/10.1007/s12210019-00767-y J.A. van Allen, L.A. Frank, Radiation around the earth to a radial distance of 107,400 km. Nature 183(4659), 430–434 (1959). https://doi.org/10.1038/183430a0 G. Vedrenne, J.P. Roques, V. Schönfelder, P. Mandrou, G.G. Lichti, A. von Kienlin, B. Cordier, S. Schanne, J. Knödlseder, G. Skinner, P. Jean, F. Sanchez, P. Caraveo, B. Teegarden, P. von Ballmoos, L. Bouchet, P. Paul, J. Matteson, S. Boggs, C. Wunderer, P. Leleux, G. Weidenspointner, P. Durouchoux, R. Diehl, A. Strong, M. Cassé, M.A. Clair, Y. André, SPI: The spectrometer aboard INTEGRAL. Astron. Astrophys. 411, L63–L70 (2003). https://doi. org/10.1051/0004-6361:20031482

1924

V. Tatischeff et al.

ˇ J. Rípa, G. Dilillo, R. Campana, G. Galgóczi, A comparison of trapped particle models in low Earth orbit, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 11444 (2020), p. 114443P. https://doi.org/10.1117/12.2561011, 2101.03090 G. Weidenspointner, J. Kiener, M. Gros, P. Jean, B.J. Teegarden, C. Wunderer, R.C. Reedy, D. Attié, R. Diehl, C. Ferguson, M.J. Harris, J. Knödlseder, P. Leleux, V. Lonjou, J.P. Roques, V. Schönfelder, C. Shrader, S. Sturner, V. Tatischeff, G. Vedrenne, First identification and modelling of SPI background lines. Astron. Astrophys. 411, L113–L116 (2003). https://doi. org/10.1051/0004-6361:20031209 D.R. Wik, A. Hornstrup, S. Molendi, G. Madejski, F.A. Harrison, A. Zoglauer, B.W. Grefenstette, F. Gastaldello, K.K. Madsen, N.J. Westergaard, D.D.M. Ferreira, T. Kitaguchi, K. Pedersen, S.E. Boggs, F.E. Christensen, W.W. Craig, C.J. Hailey, D. Stern, W.W. Zhang, NuSTAR observations of the bullet cluster: constraints on inverse compton emission. Astrophys. J. 792(1), 48 (2014). https://doi.org/10.1088/0004-637X/792/1/48, 1403.2722 C. Winkler, T.J.L. Courvoisier, G. Di Cocco, N. Gehrels, A. Giménez, S. Grebenev, W. Hermsen, J.M. Mas-Hesse, F. Lebrun, N. Lund, G.G.C. Palumbo, J. Paul, J.P. Roques, H. Schnopper, V. Schönfelder, R. Sunyaev, B. Teegarden, P. Ubertini, G. Vedrenne, A.J. Dean, The INTEGRAL mission. Astron. Astrophys. 411, L1–L6 (2003). https://doi.org/10.1051/0004-6361:20031288 A. Zoglauer, R. Andritschke, F. Schopper, MEGAlib the medium energy gamma-ray astronomy library. New Astron. Rev. 50(7–8), 629–632 (2006). https://doi.org/10.1016/j.newar.2006.06. 049 P. Zuccon, B. Bertucci, B. Alpat, G. Ambrosi, R. Battiston, W.J. Burger, D. Caraffini, C. Cecchi, L. Di Masso, N. Dinu, G. Esposito, E. Fiandrini, M. Ionica, R. Ionica, G. Lamanna, M. Menichelli, M. Pauluzzi, A calculation of the radiation environment for satellite experiments operating below the Van Allen Belts, in International Cosmic Ray Conference, vol. 7 (2003), p. 4249

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Germanium as a Solid-State Detector for High Energy . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Germanium Detector (GeD) Configurations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Charge Carriers Inside the GeD: Speed-Trapping-Collection . . . . . . . . . . . . . . . . . . . . . . Implementation of Germanium Detector in View of Space Usage . . . . . . . . . . . . . . . . . . . . . Thermal Constraints . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Irradiation by Heavy Particles, Detector Degradation, and Recovery . . . . . . . . . . . . . . . . Background Issue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Germanium Detectors for Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HEAO-3/HGRS: The First Space HPGeD . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma-Ray Imaging Spectrometer (GRIS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transient Gamma-Ray Spectrometer (TGRS) Onboard WIND : Hermetically Sealed Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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B. J. Teegarden: retired. J.-P. Roques () CNRS, IRAP, Toulouse, France e-mail: [email protected] B. J. Teegarden NASA Goddard Space Flight Center, Greenbelt, MD, USA D. J. Lawrence Johns Hopkins University Applied Physics Laboratory, Laurel, MD, USA e-mail: [email protected] E. Jourdain UPS-OMP, IRAP, Université de Toulouse, Toulouse, France e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_163

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RHESSI : Segmented GeDs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . INTEGRAL/SPI: maintaining Ged more than 20 years in space . . . . . . . . . . . . . . . . . . . . . COSI: In Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Use of Germanium Detectors in Planetary Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Benefits of Germanium Detectors for Planetary Composition Measurements . . . . . . . . . Challenges for Using Germanium Detectors with Planetary Missions . . . . . . . . . . . . . . . Summary of Planetary Germanium Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Instrumental Perspectives and conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electronics and Digital Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cryogenics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Germanium Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A 3D Germanium Focal Plane for a Hard X-Ray Telescope . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Germanium detectors are the best solution to study γ -ray radiation with an excellent energy resolution. The high atomic number, together with low ionization and band gap energies, ensures a good detection efficiency and an accurate knowledge of the energy deposits. Whereas its use for scientific experiments conducted on Earth is mastered, the technological challenges are more numerous in the case of space missions. However, many astrophysical or planetary topics require high-precision measurements of γ -ray energies, which encourages technical developments in various domains, in particular Ge crystal manufacturing and operating mode as well as cooling techniques. The current status of some of the space-specific issues is described, together with several major instruments based on germanium detectors (GeD), implemented on astrophysics and planetary space missions or balloon-borne experiments in the past 50 years. Keywords

High-energy space instrumentation · High-purity germanium detector · Gamma-ray lines · Gamma-ray emission

Introduction Among the various techniques used to detect and measure high-energy photons (i.e., γ -rays), the use of a “germanium detector” is certainly among the prime choices when the energy of the incoming radiation has to be precisely determined. In many cases, the photon energy is a key parameter to reveal the origin (physical process) of the observed emission. For example, the detection of photons at 511 keV identifies an electron-positron annihilation; a possible shift of the line centroid is the signature of a gravitational or a Doppler shift, while a broadening of the line may be related to the temperature of the annihilation site. Thus, the best achievable energy resolution is the ultimate quest for several areas of astrophysical research. Mono-energetic emission processes are the first to benefit from such a capability and thus the first to

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motivate development and research of high-performance spectrometers. However, our understanding of many high-energy emitters also experienced major advances, thanks to accurate energy measurements that allow a reliable determination of their spectral emission shape, as well as the distinction of separate components. Since the discovery of γ -rays around the year 1900, several detection techniques have been developed. Among them, the first germanium detectors have been realized in the early 1960s (Freck and Wakefield 1962; Tavendale and Ewan 1963), showing their excellent spectroscopic properties. Since then, constant progress has been done allowing a variety of usage of germanium detectors, in particular for use in space applications. The intrinsic quality of germanium, in particular its low band gap, allowing precise energy measurement, is accompanied by implementation constraints. The germanium detector needs to be cooled around liquid nitrogen temperature and is damaged by heavy particle irradiation. This imposes constraints for space usage that will be discussed. Nevertheless, several instruments have been successfully operated in space.

The Germanium as a Solid-State Detector for High Energy Radiation Detection The detection and measurement of a high-energy photon is a two-step process. When a high-energy photon interacts with matter, an energy deposit occurs. The different energy deposition processes are photoelectric absorption, Compton scattering, and pair creation. The energy is released in the form of moving electron(s) (more than one in case of multiple interactions) and positron(s) if pair creation is involved. These secondary electrons lose their energy by ionization. Then, several techniques can be used to convert it into an electrical signal that will be measured. The first step of the process requires a detector with a “good” interaction/detection efficiency for a reasonable size. Thus, high Z/dense materials are preferred. For the second step, one needs a mechanism that converts the kinetic energy of the secondary electrons into a signal to be measured.

Energy Measurement The secondary electrons produced by a photon interaction “quickly” lose their energy in the material. The order of magnitude of an electron path is 0.1 mm per 100 keV in a solid absorber. The energy is lost mainly by ionization and is converted into an electric signal through a detector-dependent process. In a scintillator, light photons are produced along the electron path, and a photomultiplier tube is used to produce an electrical signal proportional to the emitted light. In a semiconductor, secondary electrons lose energy by creating electron/hole pairs. These charge carriers are accelerated with an electric field applied between

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two electrodes and collected separately, producing an electrical signal proportional to the energy deposit. The precision of the energy measurement is driven by the fluctuations of the recorded signal. An intrinsic source of uncertainty comes from the number of the main carriers of information (quanta) released during the energy conversion process and its associated statistical fluctuation. In a detector system formed by an inorganic scintillator and a photomultiplier tube, the number of photoelectrons created by the photocathode is 8–10 per keV. In a semiconductor detector, the quanta are the electron/hole pairs generated by the slow-down of the secondary electron. The pair energy is related to the band gap of the material and to its temperature. The energy of an electron/hole pair in semiconductors is, for instance, CdTe : 4.43 eV – CdZnTe : 4.64 eV – Si: 3.62 eV @300 K; 3.76 eV @77 K – Ge 2.96 eV @77 K. In a germanium semiconductor, the energy of the pair (2.96 eV) leads to ∼338 charge carriers per keV. It is thus clear that the intrinsic energy resolution is much better than in scintillators. In practice, the typical energy resolution of a germanium detector is 2.1 keV Full Width Half Maximum (FWHM) at 1332 keV. For comparison, in a NaI crystal, the energy resolution (FWHM) reaches 65 keV and in a CZT detector, 15 keV. This immediately shows the interest of germanium to build a hard X-ray/ γ -ray spectrometer. We note that several other sources of uncertainty affect the energy measurement: detector homogeneity, electronic noise, charge trapping, and temperature variation. Some of these sources are discussed below.

The Germanium Detector (GeD) Configurations Since the development of high-purity germanium crystals (HPGe), conventional (classical) detectors feature a P and a N contact on either side of an intrinsic region. A germanium detector is thus a semiconductor diode, which is reverse biased to create an electric field across the intrinsic region. Therefore, charge carriers created after a photon interaction will move along the electric field and will be collected by the P and N electrodes, respectively. Following the energy band theory in solids, the forbidden band, or band gap, in a germanium crystal is small enough so that electrons can cross it, thus entering the conduction band. However, the band gap is so low that thermal excitation can generate charge carriers in the conduction band. This phenomenon gives rise to a leakage current that is superimposed to the pulses produced by photon interactions. This current is drastically reduced by cooling the detector. In practice, a germanium detector is usually cooled around liquid nitrogen temperature (∼77 K), but can be usefully operated up to 110 K. The conventional contacts of a GeD are classically blocking P and N electrodes. The P-type contact is typically implanted boron ∼0.3 µ thick, while the N-type contact is lithium diffused 0.5–1.5 mm thick. Other type of contacts has been developed. The Most advanced are the “amorphous semiconductor contacts.” One of the aims is the fabrication of highly segmented detectors (Looker 2014). Photolithography techniques or shadow masks allow the germanium electrodes to be split with a variety of patterns. Each segment is associated with its own

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charge collection, allowing the localization of charge carrier generation within the germanium crystal. As an example, the two sides of a planar detector can be segmented with orthogonal strips (double-sided strip detector or DSSD). The interstrip gap can be as small as ∼50 µ, while the pitch can be as low as ∼200 µ, to realize a position-sensitive detector (visit, for instance, https://www.canberra.com/ fr/produits/detectors/special-ge-si-li-detectors.html). This is a key issue to get a precise localization of the incoming photons in the detector and thus access to the position of the emitting source on the sky. Concerning the intrinsic region, the refining process of germanium enables what is known as “intrinsic germanium,” i.e., a germanium crystal with an impurity concentration below 1010 atoms/cm3 . With this process, high-purity germanium (HPGe) detectors can be manufactured, with the main advantage of allowing reverse bias voltages up to ∼1000 V/cm. Two main detector geometries exist. In the planar geometry, the charge collection is done by two parallel planes on the two sides of the detector. The detector can be a disk or a rectangular parallelepiped. The maximum thickness of such detectors is 2 cm, which limits their usage below a few hundred keV. The electric field is thus perpendicular to the electrodes. In the coaxial geometry, the detector is a cylinder with an axial well. The crystal height can reach 10 cm and its diameter, 8 cm. One electrode is on the outer surface, while the other is in the central well. In the reverse electrode configuration, the P-type electrode is on the outside surface, while the N-type electrode is inside. The low-energy threshold achievable with a germanium detector depends on the thickness of the contact in front of the incoming radiation and the electronic noise of the preamplifier. A P-type contact, boron implanted, allows a low-energy threshold of typically 3 keV, while a lithium-diffused contact will stop photons below ∼30 keV. The electronic noise of a preamplifier depends on the capacitance seen at its input. There is thus a strong dependence between the electronic noise and the detector geometry. For instance, a stripped detector with very low inter-strip capacitance will allow a low-energy threshold below 1 keV if thin electrodes are used.

Charge Carriers Inside the GeD: Speed-Trapping-Collection The precise measurement of energy deposition in a germanium detector is related to the completeness of the charge-carrier collection. Moreover, to ensure an optimal usage, the charge collection should be homogeneous in the detector volume as well as stable in time. The following points have to be considered: • An extensive study of the drift velocity of holes and electrons in germanium can be found in Ottaviani et al. (1975). The important facts to note are as follows: (i) Hole and electron drift velocities are similar in magnitude. (ii) They both reach a saturation level at high electric field (∼1 kV/cm). (iii) The drift velocity increases as the temperature of the material decreases. (iv) At maximum speed, the chargecarrier velocity magnitude is around 107 cm/s. For an interaction point situated at 1 cm from an electrode, the current pulse appears ∼100 ns after the interaction.

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• In practice, a germanium crystal contains impurities and also exhibits defects in the crystalline lattice. Thus, during their travel toward the electrodes, a fraction of holes and electrons is lost either by trapping (capturing and releasing holes or electrons) or by recombination (capturing carriers that ultimately annihilate). These effects reduce the charge-carrier mean lifetime. If the lifetime of some charge carriers becomes lower than the collection time, they will not contribute to the output pulse. • Therefore, the distribution of the electric field inside the detector should ensure a drift velocity (of the charge carriers) close to the saturation level in order to minimize the trapping effects. • The electric field distribution depends not only on the geometry of the detector and its electrodes but also on the distribution and concentration of impurities. • A high-quality crystalline lattice is mandatory as defects create trapping sites for the charge carriers. Manufacturers are able to produce high-volume crystals with near-perfect quality. However, the irradiation of a detector in accelerator or space environment may degrade the crystalline lattice. The degradation occurs when heavy particles, neutrons, protons, or nuclei knock out and displace atoms from their original position in the crystalline lattice. A fluence of 109 n/cm2 of fast neutrons produces measurable effects (Stelson et al. 1972; Kraner et al. 1975). This phenomenon, particularly important for space missions, is discussed in detail below.

Implementation of Germanium Detector in View of Space Usage The excellent spectroscopic features of the germanium are accompanied by important implementation constraints. In particular, germanium detectors (GeD) need to be cooled down to cryogenic temperatures, which has strong implications on the instrument design. The aim of this section is to review the specific needs of a germanium-based experiment and the solutions to meet them.

Thermal Constraints The germanium detector needs to be cooled, at least below 100–110 K, to reduce the thermal generation of charge carriers and associated noise. A lower temperature around 80 K is aimed at, as that mitigates trapping effects. These low temperatures are obtained inside a cryostat, which enables a direct thermal contact between the detector and a cold source. When intended for use in space, the cryostat design should comply with strong constraints. • While a cryostat ultimately needs to operate in the vacuum of space, it should also be operable under one atmosphere, which simplifies ground-based integration and test. This constraint means that the cryostat has to be sealed or pumped during lab operations and can be sealed or opened in space conditions. The

55 The Use of Germanium Detectors in Space

•

•

•

•

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outside skin of the cryostat is submitted to thermal exchanges by convection in the lab, while only radiative and conductive effects are at work in space. In general, the cryostat envelope cannot be cooled in laboratory conditions. As with all resources in a space mission, cryogenic power is limited. The thermal power drain from the cold finger should be as small as possible. Extensive use of MLI (multi-layer insulation) allows reduction of radiative heat transfer. Careful design of mechanical support should select low-conductivity materials (i.e., fiber glass). Electric wires (thermal sensors-heaters-high voltage and signal connections) should be made of low thermal conductivity material. Copper whose thermal conductivity is 400 W/m.K can be replaced by constantan whose thermal conductivity is 22 W/m.K. Conversely, the cold finger should be as conductive as possible, and the number of thermal interfaces has to be minimized in order to keep a low-temperature drop between the cold source and the germanium detector. A two-temperature-stage cooling system can be used to reduce the heat load on the cryogenic stage. In such a design, the envelope of the cryostat is maintained at an “intermediate” temperature (164 K for TGRS, 207 K for INTEGRAL SPI). This intermediate temperature can be obtained through a radiator (INTEGRAL SPI design) looking at the outer space. This design allows the preamplifiers to be cooled without impacting the performance of the cryogenic stage. The band gap of the germanium, which determines the energy/charges conversion, varies with the temperature. The thermal stability of the cold finger directly impacts the stability of the measurement. Typically, a drift of 0.18 keV/K at 1 MeV has been measured for INTEGRAL SPI (Roques et al. 2003). In this particular case, a temperature stability around 1 K per day allows use of the same energy calibration parameters for one day. The cryogenic cooling system is one of the primary technical issues for a germanium-based instrument. A few solutions exist: – A dewar filled with liquid nitrogen has often been used to cool balloon-borne germanium experiments. This is a very simple and effective solution when the flight time is a few days. A more complex configuration was used for HEAO3/HGRS instrument. It consists of a two-temperature solid cryogen system using solid methane (71 K) and solid ammonia (148 K) (Mahoney et al. 1980). This system worked 8 months in orbit. The main feature of these systems is that a stable temperature can be easily obtained. However, its short lifetime is a strong limitation. – A passive cooling radiator, properly shielded from the Sun, can be used to radiate energy toward deep space. The main advantage is the null power consumption, which is particularly important for planetary applications. The cooling power is roughly proportional to T4 × S, T being the temperature in K and S the radiator surface. For a given cooling power, the size of the radiator increases dramatically when the target temperature decreases, which can lead to physical implementation difficulties on a spacecraft. In addition, for reasons of temperature stability, it is highly desirable to keep the radiator directed toward the deep space all the time. Moreover, if annealing capabilities are

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required (see below), a thermal switch between the cold rod and the radiator is required; otherwise, the radiator will prevent the detector from heating. – The first mechanical coolers for space applications have flown in the early 1970s, and since the 1990s, several of them have been developed and used. Such systems need resources (mass, power, volume) and can be challenging to build with requirements on lifetime – launch survival and operation in zero gravity. There are several implementation constraints: the temperature of the coolers has to be controlled, cold surfaces need to be kept clean of pollution, instrument and spacecraft outgassing has to be minimized, and damping of machine vibration and micro-vibration is needed. In addition, these systems are complex to test on ground (need of vacuum chamber). In the case of INTEGRAL SPI, the machines provide a controlled temperature and a heat lift of a few watts, and the cold tip can accept the annealing temperature of 373 K. The INTEGRAL SPI cryocoolers work nominally after 20 years in space. • Contamination of cold surfaces by outgassed products has to be limited, for a number of reasons: it reduces the thermal efficiency of radiators; it induces leakage current around high-voltage paths; and on germanium surface, it also produces leakage current and consequently affects the noise performance of the sensor. This effect needs to be taken into account from the beginning in the instrument design by using low outgassing materials, by fully baking out the system, and by using a venting design that minimizes material accumulation. However, the main contaminant is water, which is difficult to avoid. Moreover, due to van der Waals forces, pollution migrates from hot surfaces to cold ones and is difficult to fully eliminate. • The protection of germanium from contaminants is a primary difficulty to accommodate. The first level of protection is the passivation of the surface (usually silicon oxides). The detector manufacturers have made progress in this process, and in some cases, the germanium detectors can be vented and exposed to a clean atmosphere. This is the case for the INTEGRAL SPI detectors. However, the classical solution is to keep the detector in ultra-high vacuum within a sealed housing that includes a getter. Alternatively, the detector housing can be filled with a neutral gas. For instance, the housings of the TGRS and MESSENGER detectors were filled with nitrogen. • Annealing of germanium detectors is a highly desirable feature as it enables periodic restoration of the detector energy resolution. This is achieved by heating the germanium crystal at 373 K or higher (see below). The cryostat design should therefore allow a temperature range from 80 K to 380 K. As a drawback, such temperature variations can produce outgassing products (see above).

Irradiation by Heavy Particles, Detector Degradation, and Recovery As already mentioned, the quality (completeness) of the charge collection in a germanium detector relies on the perfection of its crystalline lattice. Yet, irradiation, primarily by heavy particles, induces defects in the crystal that act as trapping

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sites for the charge carriers. The charge collection is then no longer perfect, and the energy resolution of the detector degrades. In space, the satellites and their instruments are exposed to cosmic rays and solar protons which, in turn, lead to secondary neutrons. The germanium detectors are thus irradiated by the primary protons and secondary neutrons. This irradiation produces measurable effects in the energy resolution in a few days’ time and produces significant effects in a few months’ time (Mahoney et al. 1981; Roques et al. 2003; Lonjou et al. 2005). Some aspects of radiation damages on germanium detectors are: • Detector configuration: the most sensitive charge carrier to trapping are the holes. Thus, in a coaxial detector, less trapping occurs in an N-type Ge as the holes are collected in the external electrode and thus their average path is small (compared to P-type Ge). • A number of irradiation tests in accelerators have been conducted to quantify the radiation damages. Some of them include studies of the possible recovery through an annealing process (see, for instance, Mahoney et al. 1981; Borrel et al. 1999; Leleux et al. 2003; Peplowski et al. 2019, and references therein). For example, for 1.5 GeV protons, induced damages become significant above a dose of 3 × 107 proton/cm2 , while for 6–70 MeV neutrons, damage appears above a few 108 neutron/cm2 . • For a given irradiation dose, the detector energy resolution degrades as the operating temperature increases. This is related to the germanium charge carrier’s velocity dependence with the temperature which has a direct impact on the charge trapping. There is therefore great interest in keeping germanium at low temperature. For a space mission, this implies a compromise between complexity (lower temperature) and performance (slower degradation of energy resolution). The irradiation-induced damage can be repaired by heating the detector above ∼373 K. This annealing process restores the quality of the crystalline lattice and suppresses the trapping sites. Annealing capability has been included in some space instruments with different implementation details. Some conclusions can be drawn: • Annealing is efficient in space despite continuous irradiation during transition states (cooling down). • Annealing temperature below ∼358 K (85C) does not allow full recovery of energy resolution. • INTEGRAL SPI has shown that a temperature of ∼378 K (105C) during 200 h restores the original energy resolution of the detectors. The INTEGRAL SPI irradiation conditions are those of a highly eccentric orbit which is equivalent to interplanetary conditions. • To date (January 2023), INTEGRAL SPI experienced 39 annealings that demonstrates that germanium can be operated with good performance during nearly 20 years (see INTEGRAL SPI instrument subsection).

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More details on annealing implementation and results can be found in individual instrument subsections. Improvements in annealing procedures continue to be made, with recent studies directed toward the use of high-temperature anneals to mitigate effects of long-term charged particle exposure in planetary missions (Peplowski et al. 2019).

Background Issue Given the low signal-to-noise ratio of the γ -ray measurements (with the exception of γ -ray bursts or solar flares), the background determination is a key issue. The two main sources of background radiation are photons traveling through the galaxy and cosmic rays, which interact within the structures surrounding the instrument, inducing an abundant production of neutrons as well as successive generations of γ -rays by radioactive decay or de-excitation of heavy nuclei. In particular, these nuclear interactions result in a large number of lines, corresponding to the materials present in the spacecraft and the detectors. For instance, various lines related to the element Ge are identified in the cosmic ray-induced background recorded by HEAO-3/HGRS (Wheaton et al. 1989) and INTEGRAL SPI (Weidenspointner et al. 2003). There are two ways to reduce this phenomenon: to put the detector assembly far from the main satellite (with a mast, for instance) or to shield it with scintillators (usually BGO, NaI, CsI, or plastic scintillator), which will both stop the particle (passive shield) and detect them to identify the background signal among the global photon flux (active anti-coincidence system). However, the shield itself can also be a source of background since it increases the material present around the instrument. Simulations are thus crucial to determine the best trade-off when designing the instrument shielding. The choice of the detector material should also be carefully considered. For instance, the GRIS team has used an isotopically enriched germanium detector. This choice results in an obvious reduction of the background contribution, in particular in a broad feature present between 54 and 67 keV, as well as in the line at 139 keV, two regions strongly affected by Ge isotope decay (see below, the GRIS instrument description). However, this kind of detector is hard to produce, and subsequent instruments have been designed with natural isotopic composition.

Energy Calibration All space instruments are carefully studied before launch to determine their characteristics (e.g., sensitivity and energy/spatial resolution versus energy). During the ground calibration procedures, a set of specific “normalized” radioisotope sources are available. Their mono-energetic radiations, with known flux and lifetimes, are the ideal tools to measure the peak efficiency and energy resolution at different steps of the instrument integration, up to a few MeV (see, for instance, Mahoney et al. 1980; Vedrenne et al. 2003; Peplowski et al. 2012a). For higher energies,

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the HEAO-3 team has conceived a specific device based on the high-energy γ -ray accompanying a neutron capture (Mahoney et al. 1980). Then, along the mission, the instrument performance is monitored, and optimized when it is possible, by adapting some house-keeping parameters. Concerning the Ge detectors, a special attention is paid to ensure the highest return in terms of energy resolution. This issue relies, in a first step, on the channel-energy relation, which connects the energy of an incoming photon to the signal measured by the electronic chain (electronic gain). This relation must be regularly determined for each individual detector and taken into account in the data analysis processing. Fortunately, the background radiation recorded on a space detector exhibits several narrow features (see the above section “Background Issue”), with known theoretical energy peak, which play the same role as the radioisotope sources during ground calibration campaign. Together with the channel-energy relation (i.e., the electronic gain monitoring), these mono-energetic radiations allow tracking the energy resolution of each detector, over the whole energy domain. However, while the mono-energetic nature of many prompt lines (i.e., with short lifetime) makes the process easy at the beginning of the mission, after a while, the number of features due to radioactive decay of longer-living elements created by particle interactions in the satellite materials increases (build-up), and some of them may “grow” near prompt lines, distorting the originally Gaussian shape. It is therefore crucial to carefully check the fit procedure results to keep the correct parameters (peak energy and width). Since the energy resolution is closely related to the crystal structure, the constant irradiation by heavy particles from cosmic rays causes cumulative damages which impair the detector performance. A major property of germanium detectors is the capacity to control the energy resolution degradation due to particle interaction, by performing regular annealing processes (see above). However, a continuous monitoring of the detector state (in terms of energy resolution) is necessary to follow the instrument performance. On this aspect, INTEGRAL SPI is, as of today, the best illustration of GeD comportment in space, as controlled by periodic (∼ every 6 months) annealings.

Germanium Detectors for Astrophysics In the astrophysics domain, the first experiments based on germanium detectors were dedicated to investigating narrow-line emissions throughout the galaxy. More precisely, the main subjects of study were positron annihilation, which leads to the emission of two photons around 511 keV, and 26 Al decay, witness of the nucleosynthesis of heavy elements, and characterized by the production of photons at 1.809 MeV. The excellent energy resolution of Ge detectors is required to precisely determine the characteristics of the emission lines, in terms of peak energy and line shape. Also, the possibility to determine fluxes in narrow energy bins limits the background contribution and thus increases the signal-to-noise ratio.

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In the 1970s and 1980s, most of the Ge-based experiments were launched aboard balloons. They were first based on GeD doped with Li ions [Ge(Li)] (e.g., Jacobson et al. 1975; Albernhe et al. 1978). The introduction of Li donors aims to decrease the impurity rate and allows depletion by reverse bias voltage over ∼1 cm in depth . However, such detectors require continuous cooling around liquid nitrogen temperature, to avoid the Li ions to drift within the Ge crystal. This issue makes the detector maintenance particularly constraining. When new refining processes were developed, the Ge(Li) detectors were replaced by high-purity germanium detectors (HPGe). Those latter must still be operated at liquid nitrogen temperature; however, they withstand room temperatures without degrading. Balloon experiments have both allowed the technical developments of these specific detectors and brought the first results on the spatial distribution and spectral shape of the emissions observed at 511 keV and 1.809 MeV. A brief review of the first developments and results obtained by several teams can be found in Leventhal et al. (1982). In 1972, two Ge(Li) detectors were flown aboard a low-altitude polar orbiting satellite (Nakano et al. 1980). Then, the HEAO-3 mission carried out an instrument based on high-purity germanium crystals. HRGRS operated from September 1979 to May 1981 in a scanning mode, allowing a continuous survey of the galactic γ -ray narrow-line emissions (Mahoney et al. 1980). Three bright high-energy point sources were detected, namely, Cyg X-1 (Ling et al. 1983), the Crab Pulsar (Mahoney et al. 1984), and the Galactic Center (GC) region (Riegler et al. 1981). While the spectral emission of the two point sources has been extracted from 50 to 300 keV, the signal detected from the GC region was limited to the 511 keV positron annihilation radiation. At the end of the 1980s, major efforts in balloon-borne instrumentation were dedicated to germanium detectors. They resulted in a number of flights with different gondolas (see Table 1 and https://asd.gsfc.nasa.gov/archive/gris/gris. html, http://www.ucsdhighenergyastrophysicsgroup.com/high-altitude-ballooning). Beyond various scientific outcomes on bright sources (Cyg X-1, Crab, Galactic Center) and on nucleosynthesis processes (with, for instance, the observation of the supernova SN1987A by GRIS and HEXAGONE), they have also driven important developments of innovative subsystems, including solar power arrays and controllers, on-board data logging, or autonomous control system for operations. While HEXAGONE was completely destroyed after a free fall due to a parachute shock at the end of the second flight, GRIS and HIREGS systems have been flown six and four times, respectively. Fifteen years after HEAO-3/HGRS, another germanium spectrometer was mounted aboard the WIND spacecraft (Owens et al. 1995), with the aim to observe γ -ray bursts and solar flares. Thanks to an occultation technique, it provided the first high-precision measurement of the annihilation line emitted from the Galactic Center region (description below). No lines were detected in the numerous burst spectra recorded. In 2001, an original design for high-energy astrophysics has been tested: the CLAIRE project is based on the association of a Laue diffraction lens with a 3

Mission/instrument Operation [ref] HEAO-3/HGRS 1979–1981 (Mahoney et al. 1980) WIND /TGRS 1994–∼1998a (Owens et al. 1995) RHESSI 2002–2018 (Lin et al. 2002) INTEGRAL SPI 2002–(2029) (Vedrenne et al. 2003) Balloon-borne GRIS 1988–1992c (https://asd.gsfc.nasa. gov/archive/gris/gris. html) HEXAGONE 1989 (Durouchoux et al. 1993)

Cooling type Op. temp (K) Ammonia + methane 92 2-stage passive radiators 100 Stirling machine 75 Stirling machine 90 and then 80

7 low-mass Al Liquid nitrogen

Liquid nitrogen

4 HPGeD Ø = 5.5 cm, h = 4.5 cm

1 HPGeD, co-axe Ø = 6.7 cm, h = 6.1 cm

9 HPGeD Ø = 7.1 cm, h = 8.5 cmb

19 co-axe HPGeD hexa ∼ 6 cm, h = 7 cm

7 co-axe Ø∼ 6.5 cm 1 isotopically enriched GeDc

12 N-type co-axe HPGe Ø = 5.6 cm, h = 5.6 cm

Sensor information

Table 1 Listing of astrophysics missions using HPGe γ -ray sensors

ACS 5-cm-thick BGO (+ CsI)

ACS 15-cm-thick NaI

ACS 5-cm-thick BGO

Positioned at L1 (1996)

ACS 6.6-cm-thick CsI

Configuration

20 keV–2.5 MeV 2.2 keV @ 511 keV

25 keV–8.2 MeV 3 keV @1 MeV

20 keV–8 MeV 2 keV @ 1 MeV

3–100 keV–17 MeV 2 keV @ 1 MeV

25 keV–8.2 MeV 3 keV @1 MeV

Energy range Energy resolution 50 keV–10 MeV 3 keV @1.4 MeV

/

/

(continued)

Every ∼6 months 200 h; Tmax 105C

6

No

Anneal Details No

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c

b

a

Liquid nitrogen

Liquid nitrogen

Cryocooler 77

CryoTel Stirling cryocooler

12 HPGeD Ø = 6.7 cm, h = 6.1 cm

3X3 HPGeD, co-axe 1.5 × 1.5 × 4 cm3 each

12 (8 × 8 × 1.5 cm3 ) HPGeD 37 strips each side

16 (8X8X1.5 cm3 ) HPGeD 64 strips each side ACS BGO

ACS+collimator CsI+BGO

Technical flight Focalization by Laue lens

ACS 5-cm-thick BGO

0.2–5 MeV ∼3 keV

0.2–5 MeV 3.5 keV @ 0.5 MeV

170 keV (Mono-energetic)

20 keV–17 MeV 2.0 keV @ 0.6 MeV

/

/

/

∼4 years after launch, TGRS instrument did no longer produce useful data, due to detector degradation; the WIND satellite is still operating A two-contact electrode splits each detector into a planar (∼1-cm-thick) + a co-axe (∼7-cm-thick) detectors; see Lin et al. (2002) for details GRIS was flown six times. The isotopically enriched GeD was added to the payload which flew in April 1992

HIREGS 1992–1998 (Pelling et al. 1992) CLAIRE 2001 (Halloin et al. 2003) COSI-B 2016 (Lowell et al. 2016) In development COSI-SMEX 2025 (target) (Tomsick et al. 2022)

Table 1 (continued)

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× 3 HPGeD matrice (1.5 × 1.5 × 4 cm3 each). With a 2.77 m focal length, the fine-tuning of the 556 crystals lens focused 170 keV photons (3 keV bandpass) within 1.5-cm-diameter focal spot. The small detector volume ensures a minimal background contribution. The early 2000s was also marked by the launch of two Ge-based instruments, one aboard the solar mission RHESSI and the second aboard the INTEGRAL observatory, dedicated to the exploration of the high-energy sky. For these two instruments, the main objectives were not only the study of specific emissions in narrow energy ranges but also the precise determination of the overall spectral shape of the emission produced by solar particles and compact objects, respectively. The advantages of the germanium detectors in studying the continuum of hard X-ray/γ -ray emissions deserve to be highlighted: These detectors operate over a broad energy band, from ∼20 keV to a few MeV, i.e., two orders of magnitude. Most of the time, several mechanisms compete to produce photons, as evidenced by the complex spectral shapes observed from X-ray binaries (XRB). While the inverse Comptonization of soft photons by a population of electrons in thermal equilibrium explains the bulk of the observed emission above 10 keV, the presence of a reflection component, revealed through the iron line in many persistent or transient sources, is an obvious example of this. Also, the discovery of an emission in excess of the Comptonized component (hereafter “hard tail”) at energies greater than ∼200 keV has become a common feature in XRB. To disentangle these various components, the energy resolution in the spectral measurements is crucial to precisely identify the locations where each contribution vanishes or takes the lead. The estimation of the underlying continuum emission is another key point when investigating specific features, related, for instance, to cyclotron absorption or annihilation emission. The accuracy in determining the corresponding position and shape directly drives the reliability of the details of the information extracted from the data. Also, the reflection component valuation depends on the knowledge of the (underlying) primary emission. As both Compton and reflection components present a curved shape, the sharpness of the measured fluxes around the location where one component appears or disappears above the other is a crucial issue. The same is true for the emergence of the hard tail, which appears above the Compton component. Below are described in more details some of these Ge-based instruments, with their specific features:

HEAO-3/HGRS: The First Space HPGeD Launched in September 1979, HEAO-3 (Mahoney et al. 1980) was the first space mission to carry on board a high-purity germanium γ -ray spectrometer (HRGRS experiment; see Fig. 1). Four high-purity germanium crystals, approximately 45 mm height for a 55 mm diameter, cooled to 92 K in a single cryostat, were surrounded by an active CsI(Na) shield that was 6.62 cm thick. The collimator part, on the top of the instrument, is drilled with four 5.65-cm-diameter holes centered above each

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Csl (Na) Shield

Cryostat Cover

Ge Crystal Solid Methane & Ammonia Refrigerator

Photo multiplier Tube

Charged Particle Detector

Cs I (Na) Collimator

Cs I (Na) Shield

Fig. 1 Diagram of the HRGRS experiment aboard HEAO-3. (Credit: W. Mahoney of the JPL)

crystal, defining an (energy-dependent) aperture of ∼30◦ FWHM. The instrument operated between 50 keV and 10 MeV in a scanning mode (∼20 min scan period), which allowed a complete sky survey in about 6 months. Each P-type cylindrical crystal was converted into a N-type detector, through a junction made with lithium diffused in the outer surface and at the top. An 8-mm-diameter hole was drilled from the bottom over two-thirds of the height and gold plated. A spring-loaded segment of a sphere ensured the bottom electrical contact, while the aluminium cup assembly holding each detector completed the contact. The four detector cups were open at the top and mounted on a common cold plate. A two-stage solid cryogen cooler (methane and ammonia, resp.) vented to free space.

Gamma-Ray Imaging Spectrometer (GRIS) Introduction The Gamma-Ray Imaging Spectrometer (GRIS) was a balloon-borne multi-detector high-resolution germanium spectrometer. It was developed by a collaboration between NASA/Goddard Space Flight Center and AT&T Bell Laboratories. GRIS was operational during the period from 1988 to 1992 and was representative of the state-of-the-art cosmic γ -ray spectrometers of that epoch. During its observational lifetime, it was flown a total six times from Alice Springs, Australia, and Fort Sumner, New Mexico. Its most notable observations included the 511 keV electronpositron annihilation line from the Galactic Center and iron and cobalt lines from supernova 1987A. The iron and cobalt line detections demonstrated conclusively that these elements are primarily produced by explosive nucleosynthesis in supernovae. Figure 2a shows the GRIS detection of the 847 keV cobalt line from SN1987A.

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Fig. 2 GRIS balloon. (a) GRIS data for the 847 keV line from the decay of 56 Co in SN1987A (from Tueller et al. 1990). The solid line is the best fit Gaussian profile. The dashed line is the predicted line profile for the 10 HMM model of Woosley (1988). A clear departure from the model prediction is evident. (b) GRIS layout in flight configuration. Figure from https://asd.gsfc.nasa. gov/archive/gris/grisover.html

Technical Description Figure 2b shows the overall layout of the GRIS instrument in its flight gondola. The central γ -ray detector array consists of seven N-type, closed-end coaxial germanium detectors, each ∼6.5 cm in diameter. These were the largest germanium detectors available at the time. GRIS spanned the energy range from 25 keV to 8 MeV with a typical energy resolution of 2.1 keV. Each detector was enclosed in its own individual low-mass cryostat. Minimizing the passive material inside the active shield was essential for maintaining a low instrumental background. The detector array was surrounded by a 15-cm-thick active sodium iodide collimator/shield with a field of view of 20◦ . Active γ -ray shielding was essential due to the high level of γ -ray background in the upper atmosphere. The seven germanium detectors were cooled to a temperature of ≈100 K by a single liquid nitrogen dewar. The detector/shield assembly was mounted on an azimuth over elevation gondola with a pointing accuracy of a fraction of a degree. The gondola was typically rotated off target by 180◦ every 20 min to permit background subtraction. The GRIS instrument parameters are summarized in Table 1. Isotopically Enriched Germanium The idea of using isotopically enriched germanium to reduce the background in astrophysical γ -ray spectrometers was first proposed by Gehrels (1990). Naturally occurring germanium has five isotopes in the following proportions: 70 Ge, 21%; 72 Ge, 27%; 73 Ge, 8%; 74 Ge, 36%; and 76 Ge, 8%. Two of these isotopes, 72 Ge and 74 Ge, were particularly bad because they have high neutron capture cross-sections.

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In particular, the strong background lines at 54 and 67 keV are from 72 Ge, the strong line at 140 keV is from 74 Ge, and the beta decay continuum is dominated by 74 Ge. These background lines and continuum can be significantly reduced by removing all or most of the 72 Ge and 74 Ge isotopes. Calculations have shown (Gehrels 1990) that the lowest background is obtained with a detector made from pure 70 Ge. The GRIS team entered into a collaboration with scientists in Russia led by Dr. V Lebedev who provided an isotopically enriched germanium detector. It was added to the GRIS payload and flown from Alice Springs, Australia, in April 1992. Figure 3 compares normal and enriched detectors. The reduction in background is immediately evident. Particularly important for hard X-ray spectroscopy and cyclotron line studies is the virtual elimination of the 54 and 67 keV line complex. The GRIS results conclusively demonstrate that there is a significant improvement in performance with isotopically enriched germanium.

Transient Gamma-Ray Spectrometer (TGRS) Onboard WIND : Hermetically Sealed Detectors Introduction The Transient Gamma-Ray Spectrometer employed a high-resolution germanium detector to perform spectroscopy of transient γ -ray events such as cosmic γ -ray bursts and solar flares over the energy range 25 keV to 8.2 MeV (Owens et al. 1995). A passive occulter was used to modulate the signal from the Galactic Center region permitting the detection and study of the 511 keV annihilation radiation from that region. This very simple instrument produced what was at that time the highestquality spectrum of the narrow 511 keV electron-positron annihilation line from the center of our galaxy (see Fig. 4). Numerous spectra of γ -ray bursts were obtained. No γ -ray lines were found. A passive radiator was used to cool the germanium detector to its required operating temperature of approximately 100 K. The detector was flown on the WIND spacecraft launched in November 1994 into a “halo” orbit around the inner Lagrangian point L1. Because the L1 orbit is significantly outside the radiation belts, the detector was not exposed to trapped radiation that typically degrades the performance of high-resolution γ -ray systems in low-Earth orbits. TGRS also provided a node in the interplanetary network of γ -ray detectors for the determination of γ -ray burst locations by multi-spacecraft timing. Technical Description General Configuration An exploded view of the instrument and its location on the spacecraft are shown in Fig. 5 (left). It has four principal components, a detector/cooler assembly, preamplifier, analog processing unit (APU), and a digital processing unit (DPU). The detector/cooler assembly was mounted atop the WIND spacecraft with an essentially clear view of the northern ecliptic hemisphere. The spacecraft was spinning with its axis pointing in the north ecliptic direction. The Galactic Center lies very close to the ecliptic plane. TGRS takes advantage of this configuration by

55 The Use of Germanium Detectors in Space

105 Counts keV-1 cm-3

9.00+05

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GRIS Ballon

8.00+05

Enriched Detector

26 April 1992

7.00+05 6.00+05 5.00+05 4.00+05 3.00+05 2.00+05 1.00+05

105 Counts keV-1 cm-3

9.00+05

Normal Detector 8.00+05 7.00+05 6.00+05 5.00+05 4.00+05 3.00+05 2.00+05 1.00+05

50

100

150

200

Energy (keV)

Fig. 3 Comparison of backgrounds in normal and enriched Ge detectors. A significant reduction of the background in the isotopically enriched detector is evident (from Barthelmy et al. 1994)

using passive occulter to modulate the signal in a region that includes the Galactic Center. With no active shielding, TGRS has a high background. However, as a stable high-resolution detector with 100% duty cycle and a long (>2 yr) accumulation time, it was able to produce the high-quality spectrum shown in Fig. 4.

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Fig. 4 511 keV annihilation line from the Galactic Center detected by the TGRS germanium spectrometer on board the WIND spacecraft. (From Harris et al. 1998)

Fig. 5 Exploded view of TGRS on the WIND spacecraft (left) and TGRS detector/cooler assembly (right). (From Owens et al. 1995)

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The Germanium Detector The detector assembly is shown in Fig. 5 (left). The instrument was designed around a 215 cm3 high-purity Ge crystal fabricated into a detector by the semiconductor spectrometer group at the Lawrence Berkeley Laboratory (LBL). Its specifications are listed in Table 1. The detector assembly is unusual, in that it has been designed as an integral hermetically sealed unit that can be thermally cycled from room temperature to liquid nitrogen temperature without degradation. The detector is an N-type closed-end coaxial of diameter 6.7 cm and length 6.1 cm in a reverse electrode configuration. The detector size is representative of the largest available germanium crystals at the time. The Radiative Cooler A cross-section of the cooler is shown in Fig. 5 (right). It has two stages: an outer stage and an inner stage coupled to each other and the spacecraft by three lowconduction supports of small cross-section. The outer stage is designed to operate at an intermediate temperature (164 K) and thereby provide a thermal buffer between the detector and the spacecraft. The mechanical interface between the outer stage and the spacecraft is a support ring which is maintained near room temperature. As the outer stage cools, it contracts slightly. The support points are designed such that this contraction breaks the thermal path between the support ring and the outer stage, thereby thermally isolating the cooler. Similar support points for the inner stage break the thermal path between the inner and outer stages.

RHESSI : Segmented GeDs The Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) was launched on February 5, 2002, as a NASA SMEX mission. It covered the X to γ -ray line energy domain from ∼3 keV to ∼20 MeV, with the highest spectral resolution, thanks to internally segmented GeD, developed by the University of California, Berkeley (Luke 1984). Its prime objectives were the spectro-imaging of solar flares. The RHESSI spectrometer design (Smith et al. 2002) was based on the largest, readily available, hyperpure (N-type) coaxial Ge material ( 7.1 cm diam × 8.5 cm long). Nine were enclosed in a single cryostat and cooled below 75 K for optimized operation. For each detector, the inner electrode was segmented into three independent detecting areas, resulting in a 1-cm-thick planar GeD on the top, a thick 7 cm coaxial GeD, and a ∼≤0.5 cm “guard ring” at the base. A ∼0.3 µm boron layer on the front segment ensured detecting photons down to ∼3 keV, while its thickness enabled photoelectric absorption of photons up to ∼150 keV. Its minimal volume reduced the background component. In addition, a passive, graded-Z (Pb, Cu, Sn) ring around the planar part stopped hard X-rays incident from the side, whereas anti-coincidence with the rear segment rejected other undesirable particles. Also, the cryostat was covered by 30 mils aluminium, with a window of 20 mils rolled foil beryllium above the 0.2 cm2 central part of each GeDs to prevent the absorption

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of low-energy photons (heritage of the HEXAGONE balloon). With this design, the energy coverage extends down to 3 keV. The coaxial segments, 7 cm thick, aim at stopping photons from 150 keV to 20 MeV. Some of them deposit energy in both the front and the coaxial part, or in more than one GeD, that is taken into account in the instrument response. Annealing Like all instruments in space, the RHESSI detectors suffered from high-energy particle radiations. For GeD, the main damage is a strong degradation of the energy resolution. To restore it, the solution is to interrupt the operations at cryogenic temperature and to heat the crystal at high temperature (typically 373 K; see above). Worrying about possible troubles on the segmented configuration, the RHESSI team waited more than 5 years before realizing the first anneal (https://sprg.ssl.berkeley.edu/~tohban/wiki/index.php/Annealing_RHESSI_ for_the_first_time). Reassured by the results, they repeated the operation every ∼2 years after that. However, after five anneals (i.e., in 2016), only four of the nine detectors kept their segmented configuration. The others presented a lowenergy threshold close to 15 keV and a degraded spectral resolution (https://sprg. ssl.berkeley.edu/~tohban/wiki/index.php/RHESSI_has_resumed_operations). Also, because of a continuous loss in the cryocooler efficiency, the cold plate temperature, supporting the detector plane, reached ∼130 K, strongly affecting the detector functioning. In order to preserve the core objective of the mission, some detectors are switch-on only during high solar activity periods. Due to communication issues, it was not possible to turn back on the RHESSI detectors after the sixth anneal. The last observation dates back to April 11, 2018, after more than 16 years of operation, covering (more than) a complete solar cycle, while the decommissioning operation has been carried out on August 2018. Operational details all along the mission are available through the website https:// hesperia.gsfc.nasa.gov/rhessi3/mission/operations-health/index.html.

INTEGRAL/SPI: maintaining Ged more than 20 years in space The SPI (Spectromètre Pour INTEGRAL) instrument has been launched in October 2002 aboard the INTEGRAL mission. Operating between 20 keV and 8 MeV, it observes the high-energy sky with a modest imaging capability (spatial resolution of ∼2.2◦ ) over a 30◦ × 30◦ field of view, thanks to a coded mask located 1.7 m above the detector plane. Its main scientific objectives, as a spectrometer, are the nucleosynthesis signatures and the electron-positron annihilation line emission, but its performance is also ideal to investigate the emission of all high-energy sources, mainly galactic compact objects, transient or permanent. The detector plane consists in 19 high-purity germanium (HPGe) crystals, cooled below 90 K. Each Ge detector is an hexagonal crystal, 6 cm (face to face) by 7 cm height, for a total geometrical surface of ∼500 cm2 (see Fig. 6). An active ACS system, made of 92 BGO blocks, surrounds the telescope, with a plastic scintillator on the top.

55 The Use of Germanium Detectors in Space

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Fig. 6 Left: Cutaway view of the SPI lower assembly. The detection plane is at the center. The cryo-machines are on the right. Right: SPI flight model camera assembly prepared for tests in vacuum chamber

The two-stage cooling system is based on a passive radiator that cools the cryostat envelope and the preamplifiers at 207 K, while Stirling cryocoolers maintain the detection plane at 80 K (the temperature, fixed at 90 K at the beginning of the mission, has been decreased to 85 K after 6 months and then to 80 K since October 2006.) within 1 K. From the conception phase, SPI has been designed to withstand recurrent annealings. Various tests have been performed, during the development phase, to optimize the annealing procedure (Leleux et al. 2003). As the time of writing (January 2023), after more than 20 years of operation, 39 annealings have been carried out, and the energy resolution degradation remains minimal. The annealing configurations were continuously adapted to the detector behavior. For instance, the annealing duration has been progressively extended up to a trade-off value of 200 h. Also, to reduce the degradation speed of the detectors (due to irradiation), their operating temperature has been decreased down to 80 K. Figure 7 displays the energy resolution measured all along the mission for the 214 Bi line at 1764 keV. The energy resolution has been kept under control during roughly 10 years, whereafter a regular drift can be observed; nevertheless, a very good energy resolution is maintained for 10 more years. Meanwhile, the annealing process poses a primary downside for detectors with lithium-implanted electrodes. At high temperature, the lithium drifts in the crystal. As a result, the thickness of the contact increases, while the active volume of the detector decreases. This leads to a loss of efficiency for high-energy photons, which require a thicker depth to be stopped than low-energy ones. For INTEGRAL SPI, the loss of efficiency has been measured by using the 40 K line at 1460 keV, visible in the background spectrum, and whose flux is expected to remain stable. In fact, this element originates from natural radioactivity only, and its lifetime is greater than 109 yr. By monitoring the flux measured in this line along the mission, the loss of efficiency of the INTEGRAL SPI detector plane at high energy has been estimated to be of the order of 25% after 17 yr (Jourdain and Roques 2020).

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1764,3 keV line

3,76 3,71 3,66 3,61 3,56 3,51

ResoluƟon in keV

3,46 3,41 3,36 3,31 3,26 3,21 3,16 3,11 3,06 3,01 2,96 2,91 2,86 2,81 2,76 10

110

210

310

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510

610

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1010 1110 1210 1310 1410 1510 1610 1710 1810 1910 2010 2110 2210 2310 2410 2510

RevoluƟon number

Fig. 7 Evolution of the energy resolution at 1764 keV (214 Bi) for the SPI instrument, along the INTEGRAL mission. Vertical lines spaced by ∼6 months indicate the 39 annealings realized before end 2022

COSI: In Development COSI (Compton Spectrometer and Imager) has been selected by NASA for a launch in 2025, as a small explorer mission (https://cosi.ssl.berkeley.edu/). COSI-SMEX is developed on the heritage of COSI balloon experiment. This latter was composed of 12 HPGe planar detectors, each with 37 electrode strips on each face (see Fig. 8). COSI detection plane features 16 planar GeD 8 × 8 × 1.5 cm, each crystal having 64 strips (2 mm wide) on each side. The detectors are in a cryostat cooled by active cryocoolers. These 16 planar detectors will form a Compton telescope that will observe the sky in the 0.2 to 5 MeV energy range. In each of the planar GeD, the incoming photons are localized in X-Y by the activated strips around the interaction site. For 2 mm strips, the pixel size is 4 mm2 . In addition, the difference on arrival times of electron and hole allows determination of a z-position within the planar thickness. Associated with the Compton mode, the 3D localization provides accurate information about the photon characteristics, raising expectations of breaking results, in particular in the polarimetry domain.

Use of Germanium Detectors in Planetary Science Planetary nuclear spectroscopy is a measurement technique in planetary science that quantifies the elemental compositions of airless or nearly airless planetary bodies. These compositional measurements provide information about how various

55 The Use of Germanium Detectors in Space

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Fig. 8 Cutaway view of the COSI cryostat. (From Tomsick et al. 2022)

planetary bodies formed and changed over time. While the focus here is on γ -ray measurements, it is noted that the full technique uses both γ -rays and neutrons to fully characterize the elemental compositions of planetary surfaces. γ -Rays provide composition measurements for specific elements, whereas neutrons quantify hydrogen and other compositional parameters (e.g., average atomic mass, abundance of elements with strong neutron absorption properties). To date, the majority of planetary γ -ray measurements have been accomplished using sensors in orbit around planetary bodies. Most of the detected planetary γ -rays are produced by nuclear spallation reactions of galactic cosmic ray (GCR) protons into the planetary surfaces. The GCR-generated γ -rays result from either neutron-capture or inelastic scatter reactions. In general (with some exceptions), elements with abundances greater than 1 wt.% are detectable using GCR-generated γ -rays. For typical planetary surfaces, such elements are major and minor “rock-forming” elements. The following elements have been detected and quantified using GCR-generated γ -rays on different planetary bodies: Al, C, Ca, Cl, Fe, H, Mg, Na, O, S, and Ti. There are also a few naturally radioactive elements – K, Th, and U – with γ -ray fluxes large enough to be detected from orbit from which elemental abundances have been derived. An early review of planetary γ -ray spectroscopy is given by Gorenstein and Gursky (1970), and the first orbital planetary measurements were made of the Moon using inorganic scintillator γ -ray sensors (see, e.g., Metzger et al. 1973). Additional planetary missions made further use of scintillator γ -ray sensors (Near Earth Asteroid Rendezvous, Lunar Prospector) (Goldsten et al. 1997; Feldman et al. 2004) and accomplished significant scientific results (e.g., Lawrence et al. 1998; Evans et al. 2001; Prettyman et al. 2006; Peplowski et al. 2015). Engineering and technical developments enabled the use of HPGe γ -ray detectors for planetary missions that are generally constrained in resources (e.g., mass and power). Proposed missions

MMX/MEGANE (Japan/USA)

Mars Odyssey (Boynton et al. 2004) Kaguyac (Japan) (Hasebe et al. 2008) MESSENGER (Goldsten et al. 2007) In development Psyche (USA)

Mission (country)[ref] Mars Observer (USA) (Boynton et al. 1992)

(16) Psyche TBD Phobos 9 months

10/2023 100 df 8/2024 100 df

Launch Operation dur. 9/1992 No orbital operations Mars (USA) 04/2001 7 months 6.5 yr Moon 9/2007 20 d 243 d Mercury (USA) 8/2004 6.5 yr 15 months

Planet Cruise Mars 11 months

5 × 5 cm

5 × 5 cm

5 × 5 cm

6.5 × 7.7 cm

6.7 × 6.7 cm

5.5 × 5.5 cm

Sensor size

Table 2 Listing of planetary missions using HPGe γ -ray sensors

Passive radiator

No ACS 6 m boom Stirling cryocooler Two ACS 0.1 MeV) which are energies of particular interest for high-energy and gammaray astrophysics. It will also give an overview of silicon semiconductor detectors.

Photon Interactions in Silicon At different energies, different phenomena dominate the photon-silicon interaction. For a complete review, please see Particle Data Group (2020). The various interactions that contribute to the photon cross section in silicon are shown in Fig. 1. As illustrated at energies below ∼0.1 MeV, the photoelectric effect dominates. The photoelectric cross section is characterized by a discontinuity (absorption edge) which illustrates the threshold for photoionization of the silicon’s atomic levels. At higher photon energies, scattering becomes the dominant interaction. Photons can penetrate into the atomic structure, and their direction can no longer be bent by mirrors or lenses – a unique challenge for gamma-ray astrophysics.

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Fig. 1 Photon interactions in silicon plotted as the cross section as a function of photon energy (Particle Data Group 2020; Berger et al. 2010)

From ∼0.1 to 30 MeV, Compton scattering takes over as the dominant siliconphoton interaction. Photons in this energy range are particularly interesting for gamma-ray astronomy because this is a region where nuclear emission lines from heavy elements are produced. This is also a region where gamma-ray bursts, some pulsars, and active galaxies are bright. Compton scattering is the inelastic scattering of an incoming gamma ray after an interaction with the electrons in the silicon bulk material. Part of the energy of the gamma ray is transferred to the recoiling electron, which is liberated from the electron shell assuming the energy transferred is larger than the binding energy of the atomic electron. The cross section is represented by the Klein-Nishina equation (Particle Data Group 2020) and is as follows: σCompton ∝ Z 2π re2 which is proportional to the atomic number, Z. re is the classical electron radius and can be calculated as e2 /(4π ε0 me c2 ), where e is the electron charge, me is the electron mass, c is the speed of light, and ε0 is the permittivity of free space. Figure 2a illustrates Compton scattering of a photon (γ ) off of an electron. Depending on its energy, the gamma ray (γ ′ ) scatters probabilistically at various angles (θ ) while imparting some energy into the electron (Particle Data Group 2020). Both the scattered photon and the electron will then either be absorbed in the bulk material or escape the active area of the detector. As the photon energy increases, the primary photon-silicon interaction mechanism changes to pair production (Fig. 1). Pair production occurs when a gamma ray penetrates the electron shell and interacts with the electric field generated by the atomic nucleus creating an electron–positron pair. For pair production to occur, the incoming energy of the gamma ray must be above a threshold of the total rest mass energy of the electron and positron created. The probability of pair production in photon–matter interactions increases with photon energy and also

56 Silicon Detectors for Gamma-Ray Astronomy

(a) Compton Scattering

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(b) Pair Production

Fig. 2 Compton scattering (a) of an incoming gamma ray (γ ) off of an electron (gray circle) resulting in a scattered and lower-energy outgoing gamma ray (γ ′ ). An incoming gamma ray (γ ) (b) at sufficiently high energy interacts with the nucleus of an atom (gray circle) and produces an electron-positron (e+ e− ) pair which are scattered at angles θ and φ respectively (JabberWok 2006)

increases approximately as the square of atomic number of the nearby atom. The cross section represented in the Maximon equation (Maximon 1968): σpair production ∝ α re2 Z 2 where α is the fine-structure constant and Z is the atomic number of the material. Figure 2b illustrates the conversion of a photon (γ ) into an electron-positron pair and the subsequent scattering angles (θ and φ respectively) in the presence of an atomic nucleus. Full details can be found in Particle Data Group (2020). Gamma-ray telescopes are designed with these types of interactions in mind to determine the energy and direction of the incident particle. In general, they can be optimized for a certain type of interaction and are generally classified as a “Compton” or “pair-conversion” telescope or a combination of both.

Silicon Semiconductors Detectors The intrinsic properties of silicon, some of which were listed in the previous section, have enabled their use as the go-to detector for particle physics experiments and gamma-ray and X-ray telescopes. Silicon is an easy material to manufacture and can be operated as a semiconductor at room temperature. A silicon sensor is a diode with a p-n junction. The silicon is doped to form the junction where elements are added to the bulk material to increase the number of electrons (n-type) or holes (p-type) to enhance the conductivity of the material. When a bias voltage is applied, electrons diffuse from n-type to p-type semiconductor. This creates a space charge region, which is the depletion zone or active area of the sensor, and a linear electric field (Leo 1994). The depletion voltage is the minimum voltage at which the bulk of the sensor is fully depleted. This is illustrated in Fig. 3.

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Fig. 3 A diagram of a pn-junction. When a bias voltage is applied, a depletion zone is created and is devoid of mobile charge carriers. An electron or hole created will be pushed by the electric charge

Ionizing radiation entering the depletion zone will create electron-hole pairs. The bias voltage causes the electrons and holes to drift to n-type implant (anode) and p-type implant (cathode), respectively. The charge collection is dependent on the amount of energy deposited by the particle which is given by the Bethe-Bloch equation (Particle Data Group 2020): −

dE Zρ ∝ dx A

where Z is the atomic number, ρ is the density, and A is the atomic mass. For a minimum ionizing particle (MIP) in a detector with active thickness, x MIPmaterial (x) =

dE x. dx

For silicon, the following equation gives the number of ion pairs produced in terms of the incident particle energy, E0 , and the mean energy to produce an ionization pair, Ei = 3.65 eV. Nion pairs =

E0 Ei

The depletion voltage is determined by the effective doping concentration (impurity density), ρd , and the depletion depth, ldep : Vdep =

eρd 2 l . 2ε dep

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The timing depends on the electron-hole mobility, the electric field profile, and the active area. The sensor readout amplifies the signal, removes noise, and converts the analog signal to digital.

Characterizing Silicon Devices Generally the quality of silicon devices is determined by the quality of the crystalline structure, the fabrication process including doping, and any surface or implant defects. Since silicon is easy to manufacture, defects more often arise from a complicated fabrication process than in the crystalline material itself. The detector properties can be characterized by measuring how the leakage current and capacitance change as a function of voltage (IV and CV curves respectively) (Leo 1994; Seidel 2019). It is particularly important to measure the response of devices up to and beyond the full depletion voltage. Small fluctuating current, or leakage current, can flow through semiconductor junctions when a voltage is applied. It is mainly caused by defects in devices. The current appears as noise at the detector output and sets a limit on the smallest signal pulse height which can be observed. In the detector bulk, leakage current is mainly caused by thermal excitation of electron-holes pairs in the depletion region and is temperature-dependent. Another source of leakage current is the diffusion of free carriers from the undepleted region. Measurements of leakage current are a strong diagnostic of detector defects. Detectors that have a strong increase of current after reaching the depletion voltage likely have a defect in the backside which is causing the injection of charge into the depletion region. Detectors that have a similar increase before reaching depletion voltage likely have a defect in the implant. A full overview of characterizing silicon devices is given in Seidel (2019) and the references therein. For charged particles, the intrinsic detection efficiency of semiconductors is close to 100%. The limiting factor on sensitivity is noise from leakage currents in the detector and the associated electronics which set a lower limit on the pulse amplitude which can be detected. To ensure adequate signal, the depletion depth must be chosen such that enough ionization will be produced to form a signal larger than the noise level.

Noise in Silicon Detectors Semiconductor detectors have an intrinsic noise, which determines the threshold energy and energy resolution. The noise performance of semiconductor detectors is determined by the properties of semiconductor detector and amplifiers. The theory of noise for semiconductor detectors is described in the Radeka (1988), and the equivalent noise charge (ENC) is formulated as the following:

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Q2ENC = 2Ap (eI +

2 4kT RS Cin 4kT )τ + As + Af RP τ

(2)

where e is electron charge, I is the leakage current, τ is the shaping time, k is the Boltzmann constant, T is temperature, RP is an equivalent parallel resister, RS is an equivalent series resister, and Cin is an input capacitance to the charge-sensitive preamplifier. Ap , As , and Af are constant parameters, and Ap and As depend on the shaping function, and their values are around 0.6. The first term represents the parallel noise attributed to the shot noise of leakage current and the parallel resistor such as feedback resistors or bias resistors. Semiconductor detectors are often operated at a lower temperature so as to reduce this noise term. The second term is attributed to the thermal fluctuation of carriers in the series resistors. The transconductance of the input field-effect transistor (FET), gm , can be related with the equivalent series resistor as RS = 3g2m . The third term represents other noise sources such as the 1/f noise of the preamplifier. Typically, the second term and the third term depend on the charge-sensitive preamplifier and can be approximated by the linear function of Cin as aCinτ +b , where a and b are intrinsic values for each charge-sensitive preamplifier. The above equation means that the ENC can be minimized at a certain shaping time τ . Accordingly, the energy resolution is represented as ΔE = 2.355εQENC (FWHM) in unit of eV, where ε = 3.65 eV is an average ionization energy of photo electrons for Si.

Radiation Damage Because of the crystalline structure of silicon detectors, they can be susceptible to radiation damage. The radiation damage is caused by ionization and non-ionizing collisions with the lattice atoms. The ionizing damage is caused by trapped holes at defects at the silicon/silicon dioxide (SiO2 ) interface (SiO2 is deposited on the silicon surface as a protective layer) and is proportional to the total radiation dose until all interface defects trap charges. Fixed charge is saturated at 1012 /cm2 which is the density of the interface defects. This positive fixed charge attracts negative carriers at the surface if the doping density is less than 1012 /cm2 and forms the accumulation layer which acts as n+ implant and is a source of the leakage current. This means highly doped regions (e.g., p+ and n+ implanted regions) are not affected by this effect. Because of this, the leakage current increase is proportional to the area of low-doping interface and the total dose. The coefficient is 1.7 nA/cm2 /krd (Kaneko et al. 2002). Non-ionizing collision displaces the lattice atoms and produces charged defects with intermediate band gaps, which increases the leakage current. This effect is complicated to characterize because the damage factor depends on the type and the energy of the particle. The damage factor is usually translated to the damage equivalent to a 1 MeV neutron, which is equivalent to ∼100 MeV protons. Above 100 MeV, the non-ionizing radiation damage reduces gradually to about a half of

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1 MeV neutron equivalent. The leak current increase is proportional to the fluence of 1 MeV neutron equivalent particles and the depleted volume. The coefficient is 4 × 10−17 A/cm3 /cm−2 (Moll 2018). Assuming the fluence of 4 × 107 /cm2 /year in the orbit, the increased leak current of 1 mm3 silicon detector in 10 years is 0.2 pA.

Silicon Detector Technologies The simplest type of silicon device is a large surface diode. A simple example is n-type silicon, with a large pad of p+ -implants on top and n+ on the back plane. The pad and back plane are metalized (usually with aluminum), and a natural layer of SiO2 forms as part of production. This forms the pn-junction of a single-channel detector. This detector could just as easily be made with p-type silicon, with the reversed implants, but for simplicity only n-type silicon will be discussed further. From this basic form, we can optimize the position resolution by dividing the large pad into strips or smaller pixels. These types of silicon detectors have been used extensively in particle physics and gamma-ray astronomy for decades.

PIN Diode Detectors A PIN diode is pn-junction but with an intrinsic silicon layer, sometimes referred to as the bulk of the diode, placed in between the p- and n-type materials and illustrated in Fig. 4. Intrinsic silicon has an equal number of electrons and holes per unit volume. PIN diodes are more commonly used in photodetectors than PN diodes since the intrinsic region presents a larger volume in which photons can produce electron-hole pairs, and so the thickness of this region can be adapted to increase quantum efficiency. The thickness of this region also gives them a lower capacitance than a typical PN diode. With a forward bias, the PIN diode behaves

Fig. 4 Silicon positive-intrinsic-negative (PIN) diode detector schematic

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like a variable resistor for high-frequency signals. With a reverse bias, it acts as a parallel plate capacitor. The PIN diode detector is particularly useful for the detection of low-energy gamma rays. It generates a high signal in a small active volume, has a fast response time, and has better relative energy resolution than NaI:Tl or BGO scintillation detectors (Lee et al. 2016).

Strip Detectors Silicon strip detectors (SSDs), or microstrip detectors, are an arrangement of strip implants that act as charge-collecting electrodes. Strips are patterned on a silicon wafer and form a 1D array of diodes. By measuring the charge collected by each of the metalized strips, we can measure the position of the interaction within the bulk material. The strips are passive, and each strip is wire bonded to separate readout electronics which amplify, shape, and digitize the signal and trigger. Figure 5 illustrates an example sensor with n-doped bulk material. The cut through the structure shows the p+ -implants on top, covered by layers of an insulator (e.g., SiO2 ), and an aluminum layer on top (not shown). The input of an amplifier is connected to an aluminum pad. The backside of the detector is n+ doped and also covered by an aluminum layer. The doped region together with the aluminum layer allows for a proper ohmic contact to the backside. This basic strip detector is DC coupled to the readout system. However, an insulation layer can be deposited between the p+ -doped silicon and aluminum strips to form an integrated capacitor, which blocks the leakage current of the strips, but allows the high-frequency signal

Fig. 5 Cartoon schematic of a single-sided silicon strip detector (SSD). Ionization from interactions with a charged particle drift to electrodes where the associated signal is collected, digitized, amplified, and read out to provide timing and pulse height information

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Fig. 6 An example of a part of an AC coupled Silicon Strip detector. The strips are surrounded by a guard ring (shown on the left) and the large pads inside the guard ring are for testing and wire bonding. The strips extend from the pads to the end of the image.

to pass. This type of strip is AC-coupled, and these detectors need biasing structures to apply the bias voltage to the strip implants. The noise in a strip detector depends on the capacitance of the amplifier load  (∝C), the leakage current (∝ Ileakage ), the temperature and bias resistance √ √ (∝ kT /Rbias ), and resistance in the metal readout (∝ Rseries ). The parameters of a single strip can be measured via a probe pad (an Al contact) to the strip implant. A guard ring structure shields the active sensor area from the edge of the detector. Figure 6 shows a microscope image of a silicon strip detector. The distance between the strip implants is the dominant parameter determining the position resolution of the detector. The pulse height of each individual strip is measured via the readout electronics which are wire bonded to the strip pads. The upper limit of the position resolution in the case of a binary readout or low signal-to-noise ratio is the digital √ resolution given by the strip pitch/ 12. Two-dimensional readout is achieved by layering multiple strip sensors orthogonally. SSDs work particularly well at higher energies, where pair production interactions dominate because the electron-positron pairs create tracks within layers of the strip sensors. In the Compton interaction regime, inactive material has particularly negative consequences for the instrument sensitivity, so a 2D readout is required within a single layer. In this case, orthogonal strips are patterned onto the backside of the wafer producing double-sided silicon strip detectors (DSSDs) allowing two coordinates in one detector layer and minimizing material. In DSSDs the back plane is also structured into n+ strips (in an n-doped wafer). A basic functional diagram is shown in Fig. 7. These strips can be offset or positioned at an angle with the topside p+ strips. However, there are challenges with this design: static, positive oxide charges accumulate in the Si-SiO2 interface. The positive charge attracts electrons which form an accumulation layer underneath the oxide. The n+ strips are therefore no longer isolated and short. For a functioning detector, this accumulation layer has to be mitigated using either p+ implants (p-stops) or an additional p+ layer (p-spray). In the p-stop technique, p+ implants between the n+ strips interrupt the electron accumulation layer. Another option is the p-spray technique, where the

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Fig. 7 Double-sided silicon detector. In this illustration the strips are parallel (on the top and bottom of the device); however, the strips are generally perpendicular (or at least at an angle) so that the device provides 2D position information

whole surface of the sensor is implanted with a low density of acceptor atoms (p+ ). In either case, for large instruments, the strips must be long and can be daisy chained together via wire bonds (the detectors generally are not larger than 10 cm on a side because of limitations in the fabrication process).

Pixel Detectors With the increased needs for both improved position resolution and 2D readouts within a single sensor, pixel detectors have become increasingly popular. The implants in these detectors are small pixels rather than strips, with dimensions as small as 5 µm on a side and up to ∼1 mm.

Hybrid Pixel Detectors Each pixel of the sensor, patterned on high-resistivity silicon material, is electrically connected to the corresponding input channel of the electronic chip via a process called bump bonding. A schematic drawing of a cell of a hybrid pixel detector is shown in Fig. 8. Small conductive bump balls (using materials such as In or SnPb) connect the pixels to the input pads of the electronic chip at the top. The layout of the electronic chip has to match the pattern of the pixel sensor (Seidel 2019). The achievable position resolution depends, as in the case of strip detectors, on the pixel dimensions and on the electronics. If the signal height is measured and used to interpolate between the pixels, a position resolution of a few micrometers is achievable. Versions of hybrid silicon pixel detectors (i.e., Timepix (https://home. cern/tags/timepix)) have been used on board the International Space Station to measure cosmic ray fluxes (Turecek et al. 2011).

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Fig. 8 Hybrid pixel detector with bump bonds connecting the active silicon material to the readout electronics

Fig. 9 Previous and currently operating high-energy X-ray, gamma-ray, and cosmic-ray telescopes that use silicon-based detectors. The area of silicon used in the instrument is plotted vs. the year launched. (Inspired by Sadrozinski 2001)

Gamma-Ray Telescopes Silicon detectors in gamma-ray telescopes have become ubiquitous for the reasons outlined in the previous sections of the chapter (see Fig. 9). This section goes into detail of the motivation, design, and performance of a selection of such instruments.

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Fermi Large-Area Telescope The Fermi large-area telescope (LAT) followed upon the success of the EGRET pair-conversion gamma-ray telescope of the Compton Gamma-Ray Observatory (CGRO). The use of SSDs in the LAT contributed to several major improvements with respect to EGRET, which used spark chambers for tracking: • Long life and reliability: the solid state detectors use no consumables, other than solar-electric power, employ relatively low voltage, and do not degrade significantly over time in the benign environment within Fermi. Whereas the EGRET spark chambers were limited in lifetime by degradation of the sparkchamber gas as well as the high-voltage spark generators, the LAT tracking has not degraded significantly after more than a decade of operation on orbit (Ajello et al. 2021). • Large effective area: the LAT instrument geometric area was limited by the size of the Delta-2 rocket shroud, but the high efficiency of the SSDs helped to achieve an effective area about six times that of EGRET. • Large field of view: LAT science has been greatly enhanced by the enormous field of view that allows the entire sky to be viewed every two orbits. The SSDs allowed the instrument to be relatively thin, maximizing the field of view, and the crucial ability of the silicon strip tracking system to self-trigger eliminated the need for a tall, narrow time-of-flight hodoscope system, such as was used on EGRET for triggering. • Improved angular resolution: pair-conversion telescope resolution is drastically limited by multiple scattering in the converter and detector material, but the high spatial resolution and efficiency of the SSDs, combined with their thin geometry, allowed optimization of the angular resolution, to achieve significant improvements relative to EGRET’s performance. The basic idea behind a pair-conversion telescope is to interleave tracking layers between layers of dense, hi-Z converter material. The degradation in angular resolution caused by scattering of electrons and positrons in the converter material puts a premium on obtaining the maximum information on the gamma-ray propagation direction from the first detector layers that follow the conversion. Furthermore, the impact of multiple scattering is minimized if the distance between the converter material and the following detector layer is minimized, making thin silicon sensors superior to relatively thick gas volumes. Consider two layers of tungsten converter foils, each immediately followed by thin sensors, and a gamma-ray conversion in the first foil. Assuming the sensors and mechanical structure to be negligible in radiation lengths compared with the converter foil, then only scattering in the material in the foil where the conversion takes place degrades a measurement of the electron or positron direction. That is because there is insufficient lever arm between the subsequent layer of foil and the sensors that follow it for scattering in that second foil to degrade the direction

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measurement. Furthermore, on average only half of the material in the conversion foil contributes to scattering, since the conversion depth in the foil is uniformly distributed. This simple analysis motivated the LAT design, but for it to be effective, the efficiency for an individual layer to measure an electron must be close to 100%, which can be and was, achieved by the use of SSDs. For a more complete description of the LAT tracker design, see Atwood et al. (2007). The Fermi-LAT tracker uses two separate silicon strip layers, oriented at 90 degrees, to make each 2D coordinate measurement. DSSDs could do the same in a single layer with less material. However, the number of radiation lengths in the silicon is so small compared with the tungsten foils that the material savings afforded by DSSDs would not be worth their extra complexity. Also, the design would need to accommodate extraction of signals from the high-voltage side via long flexible circuits, which would result in inferior signal-to-noise performance. This would result in the need to route signals from one side via long flexible circuits. Supporting the detectors and converter foils securely and accurately during a rocket launch can be a challenge. The LAT design is based on rigid, lightweight panels made of honeycomb aluminum cores and carbon-composite face sheets. Each panel is the size of a 4 × 4 array of SSDs, requiring the overall instrument to be made of 16 identical modules called “towers,” each composed of 18 panels called “trays.” The panel closeouts on the four edges are made of machined carboncarbon material, and the trays are supported on all four sides by carbon-composite sidewalls. See Fig. 10 for an exploded view of a tray assembly. Except for the top and bottom of a tower, each tray has SSDs on the top and bottom surfaces, with strips parallel. The tungsten foils are just above the silicon on the tray bottom and are cut to match the silicon strip active area, to avoid conversions between sensors. All trays are nearly identical, except for the top and bottom trays, but each tray is stacked in the tower with its strip orientation at a right angle with respect to the strips on the neighboring trays. The gap between trays is small, only

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Fig. 10 Exploded view of a Fermi-LAT tray, illustrating the integration of the silicon strip sensors and the “MCM,” which holds the readout electronics (Atwood et al. 2007)

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2 mm, so this arrangement results in each tungsten foil being closely followed by a pair of sensors, one for each of the orthogonal views. The bottom three trays have no tungsten, since a conversion in those layers would result in few tracking measurements before entering the calorimeter and would not satisfy the sixfold coincidence used in the trigger. Also, the bottom-most four layers of tungsten foils are about six times thicker than the foils in the other layers, a design choice that was made to enhance the effective area at the expense of greater multiple scattering for conversions in the thick layers. The effective area enhancement is most important at high, multi-GeV energies, where the photon intensity from a source is relatively low and also where multiple scattering in the tungsten is diminished. The trays with the heavier tungsten have heavier aluminum cores and face sheets, to support the additional load, so in all there are five variations of trays within a tower. Figure 11 illustrates the integration of trays in a single tower. The SSD design was optimized for high reliability and simplicity. Each is 8.95 cm on a side, with 384 strips spaced at 0.228 mm pitch and a 1-mm-wide inactive border, and they were produced by Hamamatsu Photonics on 0.4-mmthick 15-cm diameter n-type intrinsic wafers. The strip implants are 56 µm wide and AC coupled to 64 µm-wide aluminum strips to optimize the insterstrip capacitance and tolerance against breakdown and are biased by ≈50 M polysilicon resistors (Ohsugi et al. 2005). The SSD readout electronics are based on a 64-channel IC specifically designed for the LAT tracker and optimized for low power (180 µW per channel) as well as good noise performance (Baldini et al. 2006a). A single threshold, adjustable Fig. 11 Illustration of a Fermi-LAT tower, one of 16 (Atwood et al. 2007). Each “MCM” is a printed circuit holding 24 amplifier ASICs and 2 digital readout-controller ASICs

MCM

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per chip, is used to digitize the signal after it is processed by a two-stage chargesensitive amplifier. Avoiding transmission of analog signals to external multi-bit ADCs, and keeping the digitization at the front-end to a single bit, minimizes power consumption and results in a system with excellent noise performance, high efficiency, and adequate spatial resolution, such that the gamma-ray angular resolution is multiple scattering dominated up to over 10 GeV. Each of the application-specific integrated circuits (ASICs) includes a calibration system that can inject a specified charge into an arbitrary selection of channels; masks for noisy channels; an OR of hits from all channels, which forms the basis of the instrument trigger; readout buffers four-events deep, to keep dead time near zero; and dual, redundant readout for reliability. A second, digital ASIC sits at both ends of the row of 24 amplifier chips in each layer, to coordinate the readout of the layer, zero-suppress the data, and communicate with the data-acquisition electronics. The readouts on the two edges of each of the four sides of a tower are redundant, and each amplifier chip can be reprogrammed to communicate along either path. To minimize the dead area between the 16 towers, the tracker front-end readout electronics are all located on the edges of the trays, on boards mounted to the panel closeouts. That greatly complicated the coupling of the silicon strip sensors to the amplifier chips, which was accomplished by means of a flexible circuit bent 90 degrees around a 1 mm radius. Eight long, four-layer flexible circuits connect the front-end electronics to the data acquisition on each tower. The fabrication of the readout in this aggressive design proved to be challenging but ultimately successful (Baldini et al. 2006b), resulting in only 18 mm distance between the active silicon of one tower and its neighbor, of which 2 mm is due to the inactive edge regions of the sensors themselves. Overall, this gives an 89.9% active fraction of the 16-tower tracker aperture. The mechanical and thermal design of the tracker towers was also aggressive and challenging. Carbon composites were used as much as possible to maximize transparency to electrons and positrons as well as to minimize gamma-ray conversions in the structural material, but the mechanical tolerances were tight for such composite construction. The 16 towers had to be cantilevered from the aluminum structural backbone (“grid”) of the instrument with nominal gaps between them of only 2.5 mm, which had to be maintained during vibration and thermal cycling, a feat that was achieved by the tight mechanical tolerances, a very stiff structure, and a sophisticated alignment procedure for the attachments to the grid via titanium flexures. The cooling of the electronics had to be entirely passive, with the heat flowing down the carbon-composite sidewalls and into the grid via copper straps. That aspect was made relatively straightforward by the low-power design. The entire tracking system, with 884,736 amplifier channels, uses only 160 W of conditioned power.

Fermi-LAT Tracker Testing and Calibration About 11,500 detectors were produced by Hamamatsu and tested by INFN, and only 0.5% were rejected. The SSDs were glued and bonded in groups of four to form a ladder: a single detector with 36-cm-long strips. Each SSD and flight ladder

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had IV and CV scans performed. The full tracker tower underwent environmental tests: thermal cycling from −15◦ to +45◦ and vibration testing to simulate launch. All tracker modules satisfied the requirements in terms of detector performance: the average layer efficiency (within the active area) is more than 99.4% with a strip noise occupancy lower than 10−6 (Sgro et al. 2007). A Monte Carlo model of the LAT was developed based on the GEANT4 toolkit to verify the instrument response. A beam test campaign was carried out using the Proton Synchrotron (PS) and Super Proton Synchrotron (SPS) CERN beam lines in summer 2006. The T9 line at CERN PS was used in August 2006 for ∼15 days of data collection and provided proton, electron, and photon beams in energies of 0.5– 15 GeV. In September 2006, the calibration unit (CU) was moved to the H4 beam line at the CERN SPS which provided electrons and protons with energies up to 400 GeV. Full details and results are given in Sgro et al. (2007).

Fermi-LAT Tracker On-Orbit Performance Since the Fermi satellite was launched in 2008, the detector has been operating very stably for more than 13 years. None of the changes that have been observed have affected significantly its science performance. The most noticeable change on-orbit has concerned the number of hot strips (defined as hit occupancy greater than 2%), which increased from 203 to 578, out of 0.9 million strips, as shown in Fig. 12a, corresponding to only a 0.03% increase. A majority of the new hot strips, 308 out of 375, belong to two silicon sensors, as shown in Fig. 12b. The LAT team observed a sudden increase a half year after launch. Most of the new hot strips appeared in a particular silicon sensor, confined to its first quadrant, and there has been no increase since then in that sensor. They observed a relatively rapid increase over the first half year for the remaining sensors

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Fig. 12 (a) Total number of hot strips as a function of the time since the launch. (b) Number of hot strips in two offending silicon sensors. Open circles indicate one silicon sensor, solid circles for another silicon sensor, and solid triangles for the increased number of hot strips for the rest of 9214 silicon sensors. Black, red, blue, and green indicate the first, second, third, and fourth quadrants of each sensor, respectively

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as well. This could be considered to be infant mortality of the silicon strips. They also observed another epoch (2.5–4 years after the launch) during which the number of hot strips increased gradually in a second sensor. In this sensor, the new hot strips were located in the first, third, and fourth quadrants. It is unknown why those disparate silicon sensors developed many hot strips over a similar time period. The third epoch started 7.5 years after launch, and the hot strips were concentrated in the second and third quadrants of the second sensor. The LAT team also monitored hit efficiencies, trigger efficiencies, and peak pulse height of minimum ionizing particles. They observed negligible decreases (0.003% for the hit efficiency and 0.002% for the trigger efficiency) over 13 years (Ajello et al. 2021). The peak pulse height rapidly increased by 10% in the first one month, and the increased rate slowed down to 1% over 13 years.

AGILE The AGILE mission is a powerful observatory for gamma-ray astrophysics in the energy range 30 MeV–50 GeV. AGILE was launched on April 27, 2007, by Polar Satellite Launch Vehicle (PSLV) on an equatorial orbit at 550 km with Malindi as ground base, and it has been the first gamma-ray mission based on a large deployment of SSDs in orbit. The instrument (Barbiellini et al. 2001) is light (≈100 kg) and is able to detect and monitor gamma-ray sources within a large field of view (≈1/4 of the whole sky). The instrument consists of: • A silicon-tungsten tracker that detects the electron-positron pair created in the photon conversion in order to provide the trigger to the whole instrument and to provide a complete representation of the event topology allowing the reconstruction of the incoming direction of the gamma ray. • A 1.5 X0 deep CsI(Tl) minicalorimeter (Celesti et al. 2004) that measures the energy released by the pair. • An anticoincidence system (AC) made of segmented plastic scintillators that is used to reject charged particle background. • SuperAGILE, a silicon X-ray detector in the 15–45 keV range with a coded mask system (Soffitta et al. 2000), based on the same silicon detectors of the tracker but with a different readout ASIC, optimized for X-ray detection, the XAA1.2, by IDE AS, Norway (AS 2022). The detailed description of the instrument can be found in Feroci et al. (2007).

The AGILE Silicon Tracker The silicon tracker is the heart of the AGILE mission. It is a compact, low-power ≈37,000 channel detector with self-triggering capabilities, fast timing possibility, full analog readout, and low dead time (3 orders of magnitudes less than the previous gamma-ray mission, EGRET) (Prest et al. 2003). The AGILE tracker is made of 12 planes of SSDs organized in 13 trays. Each tray is configured as follows:

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Fig. 13 (Left) The first silicon tracker flight tray: the four ladders are glued with a silicone glue (Dow Corning 3145) on the fiber surface, and the four detectors of each ladder are bonded together. Each ladder is connected to a test adapter board which is disconnected and substituted with a flexible cable in a second phase of the assembly. (Right) The assembled AGILE silicon tracker

• Active part: 2 views of 16 silicon pads each (except trays 1 and 13 which have a single view) organized in 4 ladders of 4 detectors each; the strip orientation of the first view is perpendicular to the one of the second view resulting in a x-y detector. • Passive converter: one tungsten layer 245 µm thick (corresponding to 0.07 radiation lengths) positioned above the silicon layer; the last two planes do not have this converter layer because of the trigger configuration. Figure 13 (left) shows the first silicon tracker flight tray still on the assembly structure. The bonding between SSDs belonging to the same ladder is visible. Each ladder is connected to a test adapter board which is used during the assembly and test phase. The four boards are disconnected in a second assembly phase and substituted with a flexible cable which is wire bonded to the front-end boards. Each tray is made of a 14 mm core of aluminum honeycomb covered on both sides by a 0.5-mm-thick carbon fiber layer obtained from four 0.125 mm plies (0-90-90-0). The active element of the AGILE tracker is a single-sided, AC-coupled, 410 µ-m-thick, 9.5 × 9.5 cm2 SSD (Barbiellini et al. 2002) with a readout pitch of 242 µm and one floating strip and polysilicon resistors for the bias. It has been manufactured on high resistivity (≥4 k ·cm) 6” substrate by Hamamatsu PK. Each ladder is read by the TAA1 (IDE AS, Norway) (AS 2022), an analogdigital, low-noise, self-triggering ASIC used in a very low-power configuration (200 V/mm), a moderate cooling (−20 ◦ C) and a periodic bias cycling are efficient solutions to perfectly operate this kind of device and obtain high spectral resolution. Charge buildup effect also exists in CZT detectors with quasi ohmic contacts. Deep trapping levels can decrease the electrical field especially at low temperatures and make the detectors not usable below −40 ◦ C typically. Note that a polarization effect as a modification of the electrical field in the CdZnTe detectors can also occur under high flux conditions (>106 photons/s/mm2 ), which is not much of a concern for astrophysics applications but which may have to be taken into account in future solar physics missions involving focusing optics.

Electrode Segmentation One step of the electrode deposition process consists in the electrode segmentation to form an imaging detector, generally before cutting the crystal to its final dimensions. The most common technique is the photolithography with a photoresist etching mask and an ion or chemical etching process. This allows the realization of metallic electrodes of various shapes: strip width down to ∼20 µm or pixel size down to ∼50 µm. This technique is not applicable to indium electrodes since it degrades the properties of the Schottky contact; patterning is then obtained by micro sawing the electrode so the strip or pixel gap is at least of 100 µm with no possibility of guard ring pattern. For Schottky CdTe detectors, it was noticed that the leakage is not proportional to the area but to the length of the periphery. This means that the leakage current is not dominated by the bulk current of Eq. (2) or Eq. (3) but by surface currents introduced by defects in the cutting edges. One effective solution to solve this issue is to introduce a guard ring anode surrounding the pixel pattern. Thanks to improvements in the cutting process, guard rings as thin as 50 µm do not significantly reduce the effective crystal detection area. In order to interconnect readout electrodes to the anodes with limited risk of short circuits, electrode passivation is a common and effective process. A thin dielectric film is deposited between the electrodes by photolithography process as well.

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Interconnects The technological constraints to produce fine pitch imaging devices rest not only on the segmentation capacities of electrodes but also on the capacities to connect them to readout electronics. Here, we propose to review space-proven techniques for interconnecting the detector electrodes with the inputs of the front-end electronics to produce so-called hybrid detectors. CdTe and HgCdTe imaging devices (for X-ray imaging and infrared imaging, respectively) can be connected to read-out integrated circuits with pixel pitches down to 15 µm by using indium bump bonding technique. This low-temperature process (118 ◦ C) is applied for industrial X-ray applications (medical imaging) and infrared space applications in a number of Earth observation missions or astrophysics missions (Hubble, Cassini, James Webb Space Telescope . . . ). However, this melting temperature turns out to be not low enough for X-ray imaging spectroscopy applications with Cd(Zn)Te detectors: it can damage the electrodes and alter the already modest charge transport properties of the devices in a non-acceptable manner. Moreover, larger pixel pitches of typically 100 µm relevant for X-ray and gamma-ray astronomy implies the development of bumps with good height to withstand the thermoelectric constraints of the space environment. For those reasons, a process of double gold stud polymer bump bonding was invented. Gold stud-bumps are twice thermo-sonically bonded to the ASIC chip pads to get bump height to ∼50 µm. Then indium bumps with a “cold-weld” process or conductive isotropic epoxy bumps with a stencil printed technique are deposited on the detector or on the ASIC before a flip-chip of the detector on the ASIC. The gold stud bonding technique was successfully used in the NASA NuSTAR mission and the JAXA Hitomi mission. Some users reported the possible contamination of the electrode by indium and the migration of indium that modify the charge transport properties of Cd(Zn)Te detectors at the vicinity of the electrode (lifetime of charge carriers in particular). Polymer epoxy filled with silver is nowadays largely employed for the hybridization of Cd(Zn)Te detectors. Alternative solutions are gold and silver epoxy bump bonding developed for the CdZnTe detectors of the ASIM instrument suite in the International Space Station and the laser-assisted bump bonding technique with silver epoxy developed for the CdTe detectors for the ESA mission Solar Orbiter.

Detectors Technologies to grow crystals, to pattern electrodes, and to interconnect them have been improved for decades to produce good Cd(Zn)Te material for radiation detection. For astrophysics applications, the detector is part of a telescope; its efficiency to detect photons will contribute to the instrument’s sensitivity. The detector is in addition able to measure the time of arrival of the photons, their energy, and their position of interaction in the sensor; this allows time-resolved

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spectroscopic imaging of the sources. Moreover, light polarization has become a powerful observable to give information about the magnetic environment of the source. All these capabilities can be covered with a single Cd(Zn)Te detector or a system of detectors of this kind. This part explains the principles, the typical performance, and the key parameters to optimize a photon counter, a spectrometer, an imager, or a polarimeter. The performance limitations are linked to the intrinsic properties of the material and the front-end electronics.

Quantum Efficiency Cd(Zn)Te detectors are high Z materials that were studied at first for their high detection efficiency above 30 keV. The quantum efficiency (QE) of a material of thickness L is the probability of a photon interaction, and is given by: QE = 1 − exp (−μL)

(10)

where μ is the total absorption coefficient, illustrated in Fig. 3, as the sum of the contributions of the absorptions by photoelectric effect, Compton scattering, and pair production. For orders of magnitude, 90% efficiency is obtained with 30 µm CdTe at 10 keV, 180 µm at 30 keV, 3.7 mm at 100 keV, and 4.2 cm at 500 keV. Given the μ curve, flat at high energy with a minimum at 5 MeV, at least 50% of gamma-rays, whatever their energy, are detected with 3 cm of CdTe. However, this corresponds to the technological limit of the available thickness of these crystals. The complete detection in the gamma-ray domain implies the stacking of detection layers, either in the horizontal or in the vertical dimensions. Thanks to the improved noise performance of front-end electronics over the last decades, it is now possible to use CdTe detectors for X-ray detection down to a few keV, in order to cover a wide energy range with a single device. In this case, special attention must be paid to the detector entrance window. Measurements with CdTe detectors illuminated by the Pt planar cathode showed a detection efficiency of ∼50% at 2 keV. The quantum efficiency characteristics at low energy of the curve in Fig. 4 is explained by the presence of an interface layer made of TeO2 below the thin Pt layer.

Spectroscopy Spectroscopy is the measurement of the photon energy. It is based on two principles in ionization detectors: (i) the complete conversion of the energy into charges and (ii) the complete charge collection.

Energy Conversion and Spectral Analysis The interaction of high energy photon may not result in a complete absorption, in case of Compton scattering or pair production or X-ray fluorescence escape.

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4

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Fig. 4 Quantum efficiency between 1 keV and 1 MeV of 1 mm or 2 mm-thick CdTe detectors irradiated through the Pt electroless planar cathode. The model at low energy is based on experimental data (flux-calibrated spectroscopy and material analysis by Rutherford backscattering spectroscopy) demonstrating the presence of ∼40 nm Pt and ∼ 400 nm TeO2 interface layers. (Source: Dubos et al. 2013)

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Table 4 X-ray fluorescence lines in keV by the atom of the Cd(Zn)Te detectors. Kα line corresponds to the transition from L to K shells, Kβ line to the transition from M to K shell, Lα and Lβ lines to the transitions from M and N to L shells. (Source: NIST database) Element Cd Zn Te

Kα 23.1 8.6 27.2

Kβ 26.0 9.6 31.0

Lα /Lβ 3.7 1.1 4.5

We can see in Fig. 3 that photoelectric effect stays the prominent interaction physical process until 300 keV (unlike Si with a predominance up to 50 keV), which is highly favorable for hard X-ray spectroscopy. As a matter of fact, the relevant parameter for spectroscopy is the peak detection efficiency, involving the effective absorption coefficient μen ; it is the probability of a complete absorption of a photon by photoelectric effect, and it will result in a line in the spectrum for a monochromatic source. ηpeak = 1 − exp (−μen L)

(11)

The interaction of photons by Compton effect creates a scattering photon of lower energy and therefore with a higher probability of full absorption in the sensor. In case of pair production above 1.02 MeV, the electron of the pair (like the photoelectron in photoelectric or Compton effects) will ionize the matter and produce a charge cloud; the positron of the pair will annihilate with an electron to produce two 511 keV photons emitted in opposite directions. These photons can in turn be detected by Compton scattering and then photoelectric effect. If the volume of the sensing media is large enough, the full energy can be converted into charges. If this is not the case and for monochromatic sources, a continuum spectrum will be obtained in addition to the photopeak (continuum with a Compton edge). Secondary spectral lines called escape lines can occur when photons of precise energies escape the detectors. This is possible with the 511 keV photons of pair creation. This is also possible at lower energy with a photoelectric effect: the relaxation of the electronic cortege can occur by a radiative transition producing X-ray fluorescence lines at energies characteristic for each atom and detailed in Table 4. If the detector has segmented electrodes, the secondary photons can be detected in the adjacent channels. As a result, a gamma-ray spectrum can be quite complex to analyze and model, as illustrated in Fig. 5. This is a mandatory exercise to build the response matrix of the detector in an astrophysics instrument for instance.

Charge Collection To measure the charges created by ionization, the detector must be fully depleted. For 1-mm-thick compensated Cd(Zn)Te, this is the case when biased at −50 V. The signal is measured on the electrode by charge induction: as soon as both charge carrier types separate under the influence of the applied electric field, a mirror charge is formed and an output signal is created (charge induction does not only take place

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model: all P (137Cs = 662 keV) P (60Co1 = 1.17 MeV) P (60Co2 =1.33 MeV) P (Ba Kα) P (Ba Kβ) Ce (60Co1) CγP (60Co1) CγCe (60Co1) CγCγP (60Co1) CγCγCe (60Co1) CγCγCγP (60Co1)

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Fig. 5 Spectrum of 137 Cs and a 60 Co sources measured with a CdTe planar detector and modeled with the different physical processes at stake, involving photoelectric effect (P), single and multiple Compton scattering (Cγ), photon escapes. (Source: Maier et al. 2018)

when the electrodes are reached but as soon as the charge carriers drift starts). The instantaneous current induced by a charge q is described by the Shockley-Ramo theorem: −→ → − Iind (t) = q EW − x ·→ v (12)

−−→ → where EW is the weighting field, x the position of the charge and − v its instantaneous drift velocity. Incomplete charge collection can have various origins that have to be clearly distinguished in order to manage it properly: (i) shaping time of the readout electronics shorter than the charge carrier drift time prevents integrating the full charge signal, hereafter called ballistic deficit; (ii) charge recombination before the full induction of the signal by trapping in the lattice defects, hereafter called charge trapping effect; (iii) charge drifting in the gap between electrodes instead of reaching an electrode, hereafter called charge loss. For an interaction at a depth z from the cathode, electrons and holes drift times te and th to their respective electrodes are expressed as follows in a planar detector of thickness L and bias voltage V:  th = μz·L h ·V (13) te = (L−z)·L μe ·V The time required for holes to drift 1 mm in a CdTe detector biased under 200 V/mm is ∼1 µs. Front-end electronics with shaping times of several µs are recommended to avoid ballistic deficit when using detection material with low charge carrier mobility.

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The lifetime of a charge carrier is a time constant that describes in one macroscopic parameter all the processes that can occur in the semiconductor after the charge generation, i.e., charge capture and release by donors or acceptors and electron-hole recombination. From an initial number N of electron-hole pairs, the instantaneous numbers of free electrons Ne and holes Nh are given by: ⎧  ⎪ ⎨ Ne (t) = N · exp − τte (14)  ⎪ ⎩ Nh (t) = N · exp − t τh The charge trapping effect can be easily expressed in the simple case of a planar detector. Assuming no detrapping and no charge cloud diffusion and from the Eqs. (12), (13) and (14), the fraction of charge that will contribute to the induced signal is given by the Hecht equation:  

 t te Q V − h (15) = 2 · μe τe 1 − e− τe + μh τh 1 − e τh Qtot L

Charge trapping depends on the µτ products of the charge carriers, explaining why this parameter is a general concern for Cd(Zn)Te detectors. In addition, both charge trapping effect and ballistic deficit depend on the ratio between the drift time and the lifetime of the charge carriers; increasing the bias voltage is very beneficial to maximize charge collection for both of these reasons. Charge trapping can be corrected in the experimental data if the drift time of the charge carriers, i.e., the depth of interaction of the photon is measured. This is generally managed by measuring the signals on both cathode and anode sides (see more details on the methods in the polarimetry section). Charge loss between electrodes was first observed in pixel CZT detectors in the 1990s. The physical interpretation is the presence of a residual conductive layer in-between the electrodes, which is caused by electric field lines that do not end at the electrodes but in the gaps. These surface defects due to fabrication process of the segmented electrode have more or less impact depending on the geometry of the detector and in particular, the ratio between the electrode size and the gap size. One way to characterize the charge loss is to select the events producing charge signals in two adjacent electrodes and to plot the correlation graph between the energy detected in an electrode versus the energy of its neighbor (see Fig. 6). The maximum deviation between the data curve and the reference line gives the charge loss and can be as high as 10–20% for some devices. The charge loss can be corrected in the experimental data by using this kind of correlation graph obtained with monoenergetic sources and by measuring for each double event the ratio between the energy measured at each electrode.

Energy Resolution Even when energy conversion and charge collection are complete, the energy measurement is affected by uncertainties of two different kinds, one caused by the energy conversion process in the sensor and one caused by the signal processing

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Fig. 6 Charge sharing correlation graph and charge loss. (Adapted from Koch-Mehrin et al. 2020)

in the front-end electronics. The energy resolution of a spectrometer for a photon energy E, defined as the full width at half maximum (FWHM) of the spectral line, is given by: E 2 = Estat 2 + Eelec 2 + EICC 2

(16)

where ICC refers to the incomplete charge collection justified earlier. In semiconductor detectors, the creation of electron-hole pairs by photon interaction is a statistical process which produces on average a number of electron-hole pairs proportional to the absorbed energy. The factor of proportionality called pair creation energy ε is a constant of the material (see Table 1) and is roughly equal to three times the semiconductor band gap; one third of the photon energy is actually spent in the production of electron-hole pairs and the other two thirds goes into exciting lattice vibrations (phonons). The fluctuation on the number of created pairs cannot be described by Poisson statistics because the ionization events are not all independent due to the fact that the total absorbed energy is fixed. The Fano factor F gives the deviation from Poisson statistics, so that the contribution of the detector to the energy resolution can be written as: Estat = 2.35 ×

√

F ·ε·E

(17)

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The Fano factor is determined experimentally; values between 0.1 and 0.15 are reported for Cd(Zn)Te (Devanathan et al. 2006; Sammartini et al. 2018) and are finally very close to silicon (0.115) and germanium (0.13). Thus, the intrinsic energy resolution of a semiconductor detector is at first order given by its band gap, hence the excellent spectral performance of germanium detectors. The Fano limit of Cd(Zn)Te detectors is ∼140 eV FWHM at 6 keV, ∼400 eV FWHM at 60 keV, and 1.1 keV FWHM at 511 keV (0.2%). The front-end electronics amplifies the charge signal induced on the electrodes and generally shapes it into a pulse to reduce the bandwidth of the signal and thus improve the signal to noise ratio. The basic architecture of a front-end electronics for a spectroscopic channel with Cd(Zn)Te detectors includes a charge sensitive preamplifier (CSA) and a filter stage. Electronic noise can be of three types: the thermal or Johnson noise in resistors, the shot noise in presence of current sources and the low frequency or 1/f noise whenever the fluctuations are not purely random in time (for example carriers in the electronics are released with a time constant). All three components are present in the front-end electronics with different predominance depending on the transistor technology (CMOS, bipolar, FET) and the circuit design. All architectures are sensitive to one detector parameter: the leakage current, which is the main contribution to the shot noise of the electronics. The detector capacitance also constrains the design of the CSA and the management of the Johnson noise of the input transistor. Versatile and accessible, the CMOS technology is the most commonly used technology for our applications. We can today consider that the intrinsic limitation of this technology defining some floor noise is due to charge trapping and detrapping in the crystalline defects of the transistors responsible for the 1/f noise. The best electronics for Cd(Zn)Te detectors have equivalent noise charge of ∼30 electrons rms, which makes the energy resolution close to the Fano limit in the hard X-ray range (but not yet in the X-ray range): ∼500 eV FWHM at 60 keV (∼300 eV FWHM at 6 keV). As a conclusion, spectrometers require Cd(Zn)Te material of high resistivity to allow operation at high bias voltage to limit incomplete charge collection and low leakage current to limit electronic noise, both impacting at first the energy resolution in the Cd(Zn)Te detectors.

Detector Design for Spectral Performance Enhancement In the 1990s, several electrode geometries were tested to modify the weighting field and improve the charge collection. In CZT coplanar-grid devices, a differential bias is applied between the adjacent electrodes so that a strong electric field inside the gap forces the electrons on the surface to move toward one contact. Moreover, signals from the two grids can be processed independently with two charge sensitive preamplifiers and subtracted one from the other, removing the hole depth-dependent component of the induced signal. The main drawback of using steering electrodes is the extra surface leakage current component that increases the total leakage current. In capacitive Frisch grid structures, the lateral faces of the CZT crystal

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are surrounded with a metal screen connected to the cathode and isolated from the crystal by a thin dielectric film. The electric field is not modified while the transient behavior of the detector changes through the new weighting field distribution. The hole trapping is considerably reduced by applying a high voltage (Limousin 2003; Bolotnikov et al. 2005). Energy resolution of 1–2% at 511 keV can be obtained. Last but not least, segmenting the anode with a fine pixel array modifies the weighting field such that the potential strongly increases close to the anode. As a consequence, the induction of the signal is mainly due to the charges when approaching the anode, i.e., the electrons; this has an effect of screening on the hole signal which is the most sensitive to charge trapping. This so-called small pixel effect has been widely exploited thanks to the progress in interconnects and offers the benefit of better charge collection and fine spatial resolution for one system (see HEFT, NuSTAR projects hereafter). A recent electrode configuration to provide a high resolution CZT spectrometer, inherited from the Frisch strip concept and the silicon drift detectors (SDD), is the drift strip detector (see Fig. 7). The entrance window is a planar electrode. On the opposite side, a number of drift strips are separated by anode readout strips and biased with a voltage divider. The photon position accuracy is given by the size of the cell, which corresponds to the pitch between two anodes. In addition, and as for SDD, the full volume of the cell is sensitive and the size of the anode can be reduced to limit the input capacitance on the front-end electronics impacting the series and the 1/f noise.

Fig. 7 Principle of CZT drift strip detectors. The anode is segmented in cells including one readout strip and drift strips. The cathode can also be segmented in strips in the opposite direction to obtain a 3D-sensitive sensor. (Source: Kuvvetli et al. 2010)

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Imaging With the progress of X-ray focusing optics at high energy, the motivation for Cd(Zn)Te detectors with high spatial resolution has increased since the 2000s. The precision of the localization of the photon interaction in the detection plane (two dimensions) is based on the combined exploitation of two factors: (i) the segmentation of the electrodes (ii) the charge sharing by diffusion.

Charge Sharing The charge cloud created by photoelectric effect can be initially considered as pointlike in the X-ray range and typically of 1 µm/keV at higher energy due to the electrostatic repulsion of the created charges. The charge cloud will expand with time due to the diffusion described by the Fick’s law in the presence of charge concentration gradients. Practically, the hole cloud on one hand and the electron cloud on the other hand can be modeled with a 2D-Gaussian charge distribution (2D is presented for the sake of simplicity but the diffusion obviously occurs in 3D) whose variance at an instant t after the charge creation is given by: σ 2 = σ0 2 + 2 · D · t

(18)

With D the diffusion coefficient of the Einstein equation: 

Dh = De =

kT q kT q

μh μe

(19)

At the end of the charge drift, the charge cloud size in variance (σ h 2 for holes and σ e 2 for electrons) is then: 

L σh 2 = σ0 2 + 2kT qV z 2kT L 2 σe = σ0 + qV (L − z) 2

(20)

which is independent of the material property, and only dependent on the detector geometry and operating conditions. Typically, the initially punctual charge cloud is ∼20 µm (FWHM) wide after 1 mm drift (0 ◦ C, 200 V). The fraction S of shared events can be at first order analytically modeled by using the geometry of the detector, i.e., the pixel size a and the inter-pixel size g (for a pixelated readout anode) (Iniewski et al. 2007): S =1−

(a + 2c − 2.35σe )2 (a + g)2

(21)

where c describes the width over which a pixel collects the total charge, empirically determined as g/2 for small inter-pixel gap and a/20 for large inter-pixel gap. To fit with experimental data, two other important effects have to be taken into

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account to refine this model, especially at low energy: (i) the influence of the noise threshold, (ii) the abundance of X-ray fluorescence. A Monte Carlo model implementing Coulomb repulsion, X-ray fluorescence, and Compton scattering and the noise response of the system (threshold and energy resolution) can be used to properly model the initial charge cloud size, the stochastic effects, and the final event multiplicity. The segmentation of the imager can be chosen such that the probability of inducing signals on several electrodes is important. The energy measurement in each electrode is then used to determine with a barycentric method the centroid of the charge cloud in a more precise way than the electrode pitch itself. In this method, multiple events that do not correspond to charge sharing can be extracted and treated separately: the photon position corresponds in these cases to the pixel recording the first interaction and not the secondary (fluorescence or Compton scattering) photon. The spectroscopic capability is then exploited to design imagers with subpixel resolution. Designing a large gap to favor shared events is nevertheless not advised because it increases charge loss in-between pixels. The worst position accuracy is obtained for the single events; however, with a precision better than the pixel size, especially for systems with very low detection threshold.

Segmentation Geometries To determine the position of interaction in the two dimensions of a focal plane, two geometries are competing and present different attractive features (see Fig. 8). The Cd(Zn)Te pixel detectors have a planar cathode as an entrance window and a pixelated anode to favor the small pixel effect and screen the hole signal. Thanks to the progress for medical applications, pixel pitch can be as low as 50 µm. The difficulty in this geometry for imaging spectrometers is in the front-end electronics design and its connection to the sensor; it requires mastering the safe process of interconnection not to alter the properties and the low noise integrated circuit that can fit with the pixel pitch. This hybrid concept, available in few groups in the world, offers the great advantages of measuring a position interaction without ambiguity, possibly below the physical size of the pixel and measuring with high resolution the energy of the photon taking advantage of the low capacitance of the small anodes. The double sided strip detectors are interesting alternative concepts, especially appealing in large systems. They have strip cathodes on one side and strip anodes in the orthogonal direction on the opposite side. Readout electronics can be interconnected on the side of the device by wire bonding. This can be of great interest in the case of a stacking of detectors for a Compton camera or a gamma-ray focal plane since no sensitive matter is placed between the layers. Moreover, with the same position, accuracy of an equivalent pixel detector, 2 N readout channels are necessary instead of N2 , which saves power. 3D Position-Sensitive Sensors Imaging can also been achieved in three dimensions on the sensors. Experimental techniques and algorithms have been tested since the end of the 1990s with thick CZT detectors. The initial motivation was the improvement of the spectral

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Fig. 8 Segmentation geometries for Cd(Zn)Te imagers implemented for hard X-ray and gammaray astronomy. (a) Parallel Frisch grid detector, (b) Single pixel detector with guard ring (c) Pixel detector (d) Orthogonal (or double sided) strip detector. The two first structures are optimized for spectroscopy with no imaging capabilities

performance and the correction for charge trapping as explained previously. The devices can now reach sub-millimeter resolution in the three dimensions, which opens the way to new concepts of gamma-ray focal planes. The detector layers can be stacked parallel to the focal plane or perpendicular to it to gain in quantum efficiency, in so-called photon parallel field (PPF) and planar transverse field (PTF) configurations (Kuvvetli et al. 2010). As for 2D imagers, two concepts of 3D position sensitive CZT detectors have been first proposed, one based on pixel arrays at the anode (He et al. 1999), one based on orthogonal strip anodes and cathodes (see Fig. 9) (Xu et al. 2005); more recently, the CZT drift detectors (associated to suitable algorithms (Budtz-Jørgensen and Kuvvetli 2016)) have also shown excellent performance for this prospect (see Fig. 7). Methods to estimate the depth of interaction (DOI) of the photon in the sensor are generally based on the measurements of the signals on both cathode and anode side. In the anode to cathode ratio methods, the ratio between the charges collected at both sides is computed; the DOI is then extracted based on a reference ratio curve obtained by calibration or simulations. The accuracy of the measurement is given by the energy resolution on both electrodes and can be of the order of 100 µm. Other methods use the time properties of the induced signal (on one or both sides) with fast readout systems to evaluate the electron drift time or rise time and then the DOI. Moreover, it was demonstrated that a fast readout of the electrode’s signals allows measuring multiple- interaction events, even within the same electrode: the drift times of the

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Fig. 9 Three-dimensional position sensitive CdZnTe pixel detectors. The lateral position is given by the location of individual pixels collecting electrons, and the interaction depth is obtained by measuring the drift time of electrons from the interaction location to the collecting anode. (Source: Xu et al. 2005)

two events are different due to their difference in DOI. This principle can be used to detect Compton events, for Compton imaging or polarimetry, as we will see hereafter.

Polarimetry As in gas detectors for X-ray polarization measurement, the Compton effect – predominant in hard X-rays with high Z material – can be exploited to measure the light linear polarization in the hard X-ray domain with Cd(Zn)Te detectors. According to the Klein-Nishina formula, the Compton scattering cross section for a linearly polarized gamma ray is: dσ =

k1 2 r0 2 d 2 4 k0



k1 k1 + − 2 sin2 θ cos2 η k0 k0



(22)

in which dσ is the differential cross section, dΩ = sin sin θ dθ dη is the differential solid angle around , r0 is the classical electron radius, k1 and k0 are the respective momenta of the scattered and initial gamma rays, θ is the scattering angle, and the azimuthal angle η is the angle between the electric vector of the incident gamma ray and the scattering plane. As a result, for any specific scattering angle, the scattering probability is maximized when η = 90◦ , which means the scattered photon prefers to be ejected at directions perpendicular to the polarization plane of the incident photon. By measuring the azimuthal angular distribution of the scattered photons, the polarization information of the incident photons can be deduced. The polarization of an astrophysical source with a CdTebased detector was for the first time measured by the two layers of detector of the

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Fig. 10 (a) Principle of polarimetry with two layers of 2D position-sensitive semiconductor detectors. The scatterer collects the charges after a Compton scattering at position P1 and with an angle θ, whereas the absorber collects the charge after a photoelectric effect at position P2 . The distribution of the azimuthal scattering angle η given by the count distribution in the second layer is modulated according to Eq. (23) in the case of a linearly polarized incident light. (b) Compton scattered photon distribution measured by a 1-mm thick CdTe detector (both scatterer and absorber) with a 200 keV photon beam, 98◦ linearly polarized with a 30◦ polarization angle. Events are selected by time coincidence and energy, by excluding the events in two adjacent pixels. (Adapted from Antier et al. 2015)

imager of the INTEGRAL mission in the Crab Nebula (CdTe and CsI) in 2008 (Forot et al. 2008). Since then, several polarimeter concepts based on Cd(Zn)Te only were proposed, characterized on ground (Antier et al. 2015) and successfully implemented in balloon or space experiments (Beilicke et al. 2012). The polarimeter should include a scatterer and an absorber (see Fig. 10a). One great advantage of a highly segmented Cd(Zn)Te detector is the possibility to have the Compton scattering and the photoelectric absorption in a single device, which makes the energy calibration and the coincidence detection easier (see Fig. 10b). For a source linearly polarized with an angle α and by selecting the Compton events only in the sensor, the counts of the photoelectric interactions as a function of the azimuthal angle will follow the equation: N (η) = N0 (1 + μ · cos (2η − 2η0 ) ) With η0 = α +

π 2

(23)

and the µ so-called modulation factor defined as:

  N (η0 ) − N η0 + π2 Nmax − Nmin   = μ= Nmax + Nmin N (η0 ) + N η0 + π2

(24)

For a 100% polarized source without background, the modulation factor µ100 with Cd(Zn)Te polarimeters can reach 40–90%, depending of the geometry and the spectral performance of the devices to detect and select the good Compton events (1 Compton scattering +1 photoelectric effect) (Howalt Owe et al. 2019). Generally, events are selected using two non-adjacent pixels to avoid the confusion

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with charge sharing. So, polarimetry in the hard X-ray range requires small pixels to get the scattered photon traveling more than a pixel size. After characterizing experimentally and by simulations the response of a polarimeter, the phase of the modulation gives the angle of polarization of the source and the amplitude of the modulation gives the fraction F of polarization of the source (µ = F.µ100 ). In astrophysics applications, the relevant parameters for polarimetry performance are the minimum detectable polarization (MDP), and the systematic errors on the polarization angle and the polarization fraction. The minimum detectable polarization is the minimum fraction of polarization that can be detected at the 99% confidence level and is defined as (Weisskopf et al. 2010): 4.29 MDP = μ100 · NS



NS + NB T

(25)

With NS and NB the count rates of the source and the background and T the time of observation. This formula is more appropriate to compare the performance of polarimeters for astrophysics because it also takes into account the polarimetry efficiency of the devices, i.e., the number of photons of the source NS detected as Compton counts. To get both a high modulation factor and a good detection efficiency (i.e., not discarding good Compton events), key parameters for the detector are a good event time-tagging capability, a good energy resolution, and a good photon interaction position reconstruction in three dimensions. The concepts of 3D position sensitive sensors are the best trend to reach optimal performance in polarimetry. It is worth implementing it even in thin detectors to reduce the ambiguity in the selection of Compton events.

Trade-Offs for the Design of a Detector CdTe Versus CZT If CZT appears as excellent material for industrial spectroscopy applications requiring room temperature and high flux counting capabilities, the choice is more balanced for astrophysics applications where high flux is not much of a concern and moderate cooling is usually affordable. CdTe is probably easier to fabricate, less brittle, and with better edge pixels, which makes a good candidate for large X-ray detection planes. CdZnTe is more resistive and available in thick dimensions, which makes it so far the best choice for gamma-ray applications. Concerning hard X-ray focal planes with fine pitch electrodes, both CZT and CdTe have experience with excellent performance. The characterization tests and the onground calibration are critical to select defect-free samples with uniform response, in particular with CZT material known for high concentrations of performance limiting defects (non-uniformity in the Zn doping profile, Te inclusions, networks of subgrain boundaries). CdZnTe was proven to be more tolerant to radiation damage but feedback experience of CdTe in space presented hereafter also gives good confidence in this material for future applications.

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Detector Geometry The definition of the pattern electrode for a new imaging spectrometer has to be optimized to the instrumental concept and the science requirements. The guard ring around the pixel pattern insures low and uniform leakage currents in the pixels for high spectral resolution but introduces dead zones that can be critical to design a focal plane for focusing optics based on a mosaic of pixel detectors. With the progress in crystal quality, a guard ring as thin as 20–50 µm was proven to be efficient enough. The pixel pitch is a key parameter to optimize. On one side, smaller pixels or voxels increase the accuracy in position interaction, which is mandatory for space hard X-ray telescopes (focal length not higher than ∼15 m so far for a single satellite mission, ∼10 m without a deployable system to fit in a rocket fairing). It can be also beneficial for photometry and spectroscopy to limit photon pile-up in the pixels in case of bright sources. It improves the polarimetry efficiency in the hard X-ray range by detecting more Compton events in two non-adjacent pixels. On the other side, the contribution of the electronic noise to the energy resolution increases with the number of hit channels (multiplicity m) whose mean value depends on the pixelization: Eelec = 2.35 ×

√ m × ε × EN C

(26)

where ENC is the equivalent noise charge of one readout channel. For space astrophysics applications where spectroscopic information is crucial and power resources are limited, segmentation of ∼200 µm is a good compromise; it can result in spatial resolution of 100 µm or better. It allows polarimetry from 50 keV. Then, the optimal ratio between the pixel size and the inter-pixel size can be defined experimentally and by simulations: reducing this ratio can be beneficial for the input capacitance of the readout electronics (a critical point for pixel detectors directly connected to 2D ASICs) but can introduce charge loss between the pixels affecting the charge collection efficiency (residual surface capacitance in the gap, process dependent). Finally, the thickness of the devices can also be a trade-off between the efficiency and the spectroscopy: if the full detection efficiency is not required, as for solar physics applications with strong photon signals for instance, thin devices with high voltage will have good charge collection, and better stability in time in case of Schottky CdTe detectors. Moreover, for gamma-ray polarimetry applications where Compton efficiency is critical, thick detectors associated to depth sensing methods compete with stacks of thin layers to offer the best performance. Design optimization often requires Monte Carlo simulations in that case. For low background measurements, optimal thickness is where the detection efficiency reaches 70–90%. A Cd(Zn)Te device in space is activated by cosmic rays, and in too thick devices material does not contribute to photon detection and is then just a background generator. Nevertheless, a high segmentation of the sensitive volume in voxels, as in 3D spectrometers, allows reducing this background with appropriate rejection techniques.

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Readout Strategy A detector system (sensor and its front-end electronics) is generally read out in frame mode or in so-called self-triggered mode (photon counting mode). So far, for astrophysics applications, frame modes have been implemented for large silicon arrays only in the X-ray range. The most common architecture of the front-end electronics of Cd(Zn)Te detectors is the self-triggered architecture: the detector, or a fraction of it, is read out only when an event is detected, i.e., a signal above a predefined threshold. This readout strategy is almost mandatory for hard X-ray and gamma-ray astrophysics applications: Compton imaging, polarimetry, and rejection of non-X-ray background are required to detect events in time coincidence. For space missions at this energy range (100–1000 keV) which are background dominated, the timing resolution directly drives the sensitivity of the instrument. Post processing for event detection is very power consuming on board and often not available on ground due to the telemetry limitations. Even for solar physics applications where signal to background ratio is highly favorable, the self-triggered readout mode is attractive: it can sustain with a reasonable power allocation very high photon count rate without photon pile-up implying spectral distortions, and it allows time-resolved spectroscopy of eruptive events (solar flares) that typically last a few minutes.

Space Systems and Instruments The previous section presented the key parameters to optimize for the best imaging spectrometers or polarimeters based on Cd(Zn)Te detectors. The noise performance of the front-end electronics below 30 electrons rms and the reduction of the pixel size down to 200 µm can provide optimal solutions for hard X-ray applications. Complex electrode configuration can also be set up in small groundbased experiments to improve the charge collection efficiency in CZT detectors for gamma-ray spectroscopy (coplanar, Frisch-grid, drift strip). However, in the context of a space instrument, other challenges have to be considered: the system design of large focal planes, resource limitations, radiation damage. Here, we present an overview of astrophysics and solar physics flown missions as the best illustrations of successful implementations of the detection concepts explained before. We extend the panorama to some rocket and balloon missions, as promising pathfinders for future space missions.

Detection Planes for Indirect (or Multiplexing) Imaging Systems ISGRI was the first CdTe based focal plane operated for astrophysics ever implemented (realized by CEA-Saclay, France, see Fig. 11a). It is the soft gamma-ray imager of the IBIS coded mask aperture telescope on board the ESA INTEGRAL

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Fig. 11 Pictures of flight models of detection planes for indirect imaging telescopes. (a) ISGRI, The full detection unit of INTEGRAL/IBIS with 16,384 single-pixel crystals. (Source: https:// sci.esa.int/web/integral) (b) The full detector plane of the Fourier telescope STIX with 32 pixel detectors. (Courtesy of S. Krucker/FHNW)

mission, launched in 2002 (Lebrun et al. 2003). It was shortly followed by the CZTbased imager BAT (realized by NASA Goddard, USA, Barthelemy et al. 2005), a coded mask instrument on board the NASA Swift mission, launched in 2004. Both instruments are still in operation 20 years later. They are equipped with large focal plane arrays with single pixel crystals for coded-mask aperture telescopes. The 16,384 IBIS crystals are 4 × 4 × 2 mm3 CdTe detectors with Pt ohmic contacts produced by Acrorad whereas the 32,768 BAT crystals are CZT detectors of the same dimensions produced by eV products. The energy range of these focal planes is 15 keV–150 keV. The IBIS mask made of tungsten is placed 3.2 m away from the detection whereas the BAT mask made of lead is placed 1 m away from the detector plane (Lebrun et al. 2003). Consequently, the latter has a larger field of view but a worse angular resolution. The first Indian astronomy mission Astrosat, launched in 2015, implements a suite of instruments from the UV to the hard X-ray range. Hard X-ray imaging is performed by the CZTI instrument, based on a coded mask and a 976 cm2 CZT detection plane to cover a similar energy range (Singh et al. 2014). A few years later, the ECLAIRs instrument (realized by CNRS-IRAP, France) on board the CAS SVOM mission is based on this instrumental concept but with a major improvement on the low energy threshold to observe gamma-ray bursts and compact objects with high redshift. The detection threshold can be as low as 4 keV thanks to two new technologies in the focal plane: the use of Schottky CdTe crystals with indium anode to reduce the leakage current and a low noise full-custom frontend ASIC (IDeF-X) integrated into the ceramic detection module. Consequently, the energy resolution has been improved from 6 keV down to 1.4 keV FWHM at 60 keV. The design of the imaging part was upgraded accordingly to limit all kinds of matter that could affect the instrument efficiency at 4 keV (self-supported mask structure, thin multi-layer-insulation . . . ) (Lacombe et al. 2018). The Modular X- and Gamma-ray Monitor (MXGS) is the first coded-mask aperture telescope with pixelated CZT detectors; it was launched in 2018 in the ESA Atmospheric Space Interaction Mission on board the International Space Station. It includes 64 Detector Modules (realized by DTU-Space, Denmark). One module

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consists of four 20 × 20 × 5 mm CZT detectors with 16 × 16 pixels produced by Redlen Technologies and tiled together. The energy resolution is 4.3 keV at 662 keV (0.6%) after applying a depth-of-interaction correction (charge trapping). Pixel CdTe detectors (realized by CEA-Saclay, France) were also implemented in the Spectrometer Imaging X-ray Telescope (STIX) of the ESA Solar Orbiter mission launched in 2020. The indirect imaging technique is not based on a coded mask but on pairs of collimation grids forming a Fourier telescope. This technique is very attractive for the Sun observation in hard X-rays because it can allow angular resolution of few arcsec with compact systems, 10–100 times better than with a coded-mask telescope and close to the best X-ray focusing optics; this is at the expense of the instrument field of view and flux sensitivity, which are of lower concern for solar physics than for astrophysics. The imaging technique was previously used for space solar missions in the Yohkoh satellite (1991–2005) with scintillators and in the RHESSI satellite (2002–2018) with germanium detectors. The detection plane of STIX is made of 32 Al-Schottky CdTe detectors with a special pattern of 12 pixels surrounded by a guard ring (see Fig. 11b). The lowlevel threshold is 3 keV and the energy resolution is 1.2 keV FWHM at 31 keV (Limousin et al. 2016).

Focal Plane for Focusing Optics The first hard X-ray focusing optics telescope in space was on board the NASA NuSTAR mission, launched in 2012, with a deployable boom to reach a focal length of 10 m and an energy range up to 80 keV. The focal plane is a mosaic of 2 × 2 pixel CZT detectors (realized by Caltech, USA). The CZT detectors of 20 × 20 × 2 mm have a 32 × 32 pixel array with a pixel pitch of 605 µm and are directly connected to a 2D full-custom ASIC (see Fig. 12a) (Rana et al. 2009). The filter stage is not included within the pixel area; a digital filtering is done out of the focal plane. The low-level threshold is 3 keV and the energy resolution is 0.9 keV FWHM at 68 keV. Technologies have been developed from the 2000s and validated with the HEFT experimental balloons. Other focal planes launched in the same decade involve strip detectors connected to on-the-shell ASICs (VATA family). Each of the two telescope modules of the HXT instrument on board the JAXA mission launched in 2016 implements a focal plane with 4 layers of silicon double sided strip detectors and one layer of CdTe double sided strip detector (realized by JAXA-ISAS, Japan). The Schottky CdTe detector of 34 × 34 × 0.75 mm has strips of 250 µm pitch connected to the front-end electronics by means of a ceramic board with through holes. This is so far the finest spatial resolution in a space instrument with CdTe-based detectors (see Fig. 12b) (Nakazawa et al. 2018). On board the Roscosmos Spektrum Rontgen Gamma mission, launched in 2019, each of the seven telescope modules of the ART-XC instrument implements a focal plane (realized by IKI, Russia) with a 30 × 30 × 1 mm Schottky CdTe detector (see Fig. 12c). The detector has 2 × 48 strips of 625 µm pitch. The low-energy threshold with this type of detector systems is 5 keV and the energy resolution is around 1.7 keV FWHM at 14 keV due to the

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Fig. 12 Pictures of flight models of focal planes. (a) The focal plane of NuSTAR based on CZT pixel detectors. (Source: Rana et al. 2009). (b) The CdTe layer of the Hard X-ray Imager of Imager of Hitomi. (Courtesy of JAXA). (c) The seven focal planes of ART-XC based on double sided strip detectors. (Source: https://www.russianspaceweb.com/spektr-rg-art-xc.html)

quite important input capacitance with such large electrodes (Pavlinsky et al. 2021). Based on this concept, focal planes with enhanced spatial and spectral performance were demonstrated in rocket flights. The last FOXSI-3 sounding rocket launched in 2018 embedded a CdTe double strip detector with 128 × 128 strips of 60 µm pitch with an energy resolution of 0.8 keV at 14 keV (Furukawa et al. 2019).

Compton Camera Above 80 keV, no focusing optics have flown so far. To extend the observation into the 100–300 keV range, JAXA has proposed for the first time instrumental concepts based on Compton imaging and room-temperature semiconductor detectors only (after similar concepts based on germanium detectors implemented by Berkeley, USA) (Watanabe et al. 2005). One semiconductor layer acts as the scatterer and a second one acts as the absorber (see Fig. 10). The energy resolution is used to identify good Compton events (and measure their energy) and the spatial resolution is used to reconstruct the source position in the sky using the Compton kinematics. The uncertainties in the angle reconstruction come from the Doppler broadening (related to quantum uncertainty of bound electron momentum, typically 3◦ FWHM at 511 keV and 10◦ FWHM at 100 keV, Ordonez et al. 1997) and the interaction position reconstruction in the detection system. In case of a stacking of several detection layers with segmented electrodes, the latter error can be quite low. In case of a system with a single thick detector, the depth sensing method is recommended (as discussed for polarimetry). The Soft Gamma-Ray Detector (SGD) of the JAXA Hitomi mission implemented 32 layers of Si sensors and 8 layers of CdTe sensors surrounded by 2 layers of CdTe sensors, to optimize the probability of absorption of a photon scattered in the Si layer (see Fig. 13). A silicon detection layer consisted of a 51.2 × 51.2 × 0.62 mm pixel silicon detector (0.6 mm depletion layer) whereas a CdTe detection layer consisted of a 2 × 2 array of 25.6 × 25.6 × 0.75 mm Schottky pixel CdTe detectors (since detector surface as large as for Si devices is not available) (Tajima et al. 2018). In both cases, the pixel pitch is 3.2 mm (Compton imaging does not require as fine pitch as focusing optics due to the

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Fig. 13 Pictures of the flight model of the Semiconductor Compton camera of Hitomi (SGD) (a) Full assembly of Si and CdTe layrs (b) Si module (c) CdTe module. (Courtesy of S. Watanabe/JAXA)

intrinsic performance given by the Doppler broadening). BGO scintillator detectors surrounded the semiconductor systems to reduce in-orbit background by active shielding. In addition to soft gamma-ray imaging spectroscopy, SGD provided polarimetry, with a modulation factor of 57% for a 100% polarized source. Hitomi, despite its short mission life, has paved the way to future instruments operating up to 600 keV (for the observation of the 511 keV annihilation line in particular). In parallel, progress in the reconstruction methods for Compton imaging (pushed by other applications such as medical imaging and nuclear safety) allows improving the imaging and sensitivity performance of the system, moving from classical back projection methods to maximum likelihood or Bayesian methods (Daniel et al. 2020).

Radiation Damage Protons are mainly responsible for radiation damage in space experiments. They come from the radiation belts for low-Earth orbit missions, or from the cosmic rays and the solar flares. The electrons are generally stopped with a moderate shielding. By construction and in contrast to high purity germanium, Cd(Zn)Te detectors are compensated material, i.e., they includes several types of impurities to have a high resistivity. The moderate transport properties of these devices are the signs of non-negligible concentrations of defects (Te inclusions, Cd vacancies, etc.). The positive consequence is a good hardness to displacement damage. In the ISGRI experiment flying for 20 years on-board INTEGRAL, the degradation of the spectral performance has been identified as the consequence of a continuous decrease in the electron lifetime only; this important result is in agreement with ground-based experiments of proton irradiation with CdTe:Cl detectors (Fraboni et al. 2007). The transport properties for holes are unchanged. This is confirmed in the STIX experiment for which the charge loss (visible in the left tailing of the spectral lines) mainly due to hole trapping has not changed after 2 years operation. The gain decrease due to electrons trapping is more severe with ohmic CdTe in ISGRI than Schottky CdTe in STIX (2% per year versus 0.5% per year typically). This is the combination of two effects. On one hand, the electrical field can be

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increased in Schottky detectors, increasing the collected charge for given µ and τ parameters. On the other hand, ISGRI is surrounded by BGO scintillators for anticoincidence (rejection of non-X-ray background). Proton irradiation though BGO has proved to induce more radiation damage due to secondary particles, gamma-rays, and neutrons in particular (Limousin et al. 2015). The modeling of the experiment and the detector environment (based on Monte-Carlo simulations coupled to models of non-ionizing energy loss for each particle type) is a key step of the design of the space instrument to limit the displacement damage dose and maintain the spectral performance of the detectors.

Future Challenges Crystal Growth Technological developments in the raw material have continued to work to overcome the limitations of both CdTe and CZT detectors. To reduce the leakage current in CdTe detectors, structures based on homoepitaxial p-i-n diodes have been proposed in the 2000s but most of the studies were focused on the epitaxy of HgCdTe for infrared applications. To reduce the charge trapping centers and the spatial inhomogeneity of charge transport in CZT, active studies are going on conversely, with the addition of a selenium in small quantity (production of Cd0.9 Zn0.1 Te0.98 Se0.2 ). The introduction of selenium allows a better compositional homogeneity and enhances the mechanical hardness (Roy et al. 2021). Promising results have been obtained for high resolution gamma-ray spectroscopy (0.8% FWHM at 662 keV). Detector Developments for Future Hard X-Ray Missions New Cd(Zn)Te hybrid detectors with pixel arrays are in development in several groups in the world to prepare the next generations of hard X-ray focusing telescopes for solar physics or astrophysics with ∼250 µm pixels connected to lownoise low-power front-end electronics. This allows following the progress of the focusing mirrors in angular resolution while maintaining high spectral resolution compared to strip detectors even for bright sources. One remaining critical point to design a system is the way to build a large array, as it is now available with waferscale silicon detectors. Due to the constraints in the detector size (even if progress has been made in 10 years to go from 1 cm2 to 9 cm2 detection surfaces while maintaining the quality), one should think of 4-side buttable detection modules to build focal planes with a mosaic of modules with limited dead zones in-between. Several technologies are under investigation for that, trying to avoid wires most of the time: 2D ASIC with through silicon via, 3D packaging with wireless die on die processes. Detector Developments for Future Soft Gamma-Ray Missions Focal planes for a broadband Laue lens requires the development of detectors that can at the same time implement fine spectroscopy, 3D spatial resolution (sub millimetric 0.3–0.5 mm) and high detection efficiency in the gamma-ray domain (>80% at the upper limit of the passband). Developments with CZT detectors in

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photon parallel field or planar transverse field configurations are under study and will increase in maturity in the coming years. This challenging instrumentation domain is extremely promising to cover a band, e.g., 50–700 keV that is still rather difficult to observe. Furthermore, this implementation, given the reachable sensitivity, would also open the window of polarimetry in this region of the energy spectrum of cosmic sources.

Conclusion From 2002, the five main space agencies in the world have launched astrophysics and solar physics missions with CdTe-based detection planes. This illustrates how mature and widely spread is the use of this high-density high Z compound semiconductor for imaging spectroscopy in space instruments. Important gain in the telescope sensitivity was obtained in the hard X-ray range with this technology, allowing major astrophysics discoveries (at 30 keV from ∼0.2 mcrab with ISGRI and to ∼1 µcrab with NuSTAR). Continuous progress in the crystal growth, the electrodes patterning and their interconnects, and the associated front-end electronics, as well as in detector design, instrumental methods, modeling, and signal processing have been made to provide reliable and performant solutions with limited electrical and thermal power. As a result, compact focal planes can be contemplated to cover an energy range as wide as 2–600 keV with Cd(Zn)Te crystals only. This is of great importance in the era of multiwavelength astrophysics, which often requires several telescopes in different energy bands on the same satellite platform. This is also an asset in the new field of multi-messenger astrophysics and the transient sky to have lightweight instruments for easily repointing the spacecraft in case of an alert. The association of CdTe with other light materials and in particular silicon is interesting to extend the energy range below 2 keV and to offer polarimetry capability below 50 keV. The technology offers the possibility to design various instrumental configurations adapted to the specific scientific needs to enhance either detection efficiency, spectroscopy, imaging, or polarimetry. The new challenges for instrumentation are in the development of large hard X-ray focal planes with highly pixelated 4-side buttable detection modules and CZT-based gamma-ray focal planes.

References S. Antier, P. Ferrando, O. Limousin, et al., Hard X-ray polarimetry with Caliste, a high performance CdTe based imaging spectrometer. Exp. Astron. 39, 233–258 (2015). https://doi.org/10.1007/ s10686-015-9442-5 S. Barthelemy et al., The Burst Alert Telescope (BAT) on the SWIFT Midex Mission. Space Sci. Rev. 120(3–4), 143–164 (2005) M. Beilicke et al., Design and tests of the hard X-ray polarimeter X-Calibur. Nucl. Instrum. Methods Phys. Res. A 692, 283–284 (2012). https://doi.org/10.1016/j.nima.2011.12.111

2032

A. Meuris et al.

A.E. Bolotnikov, G.C. Camarda, G.W. Wright, R.B. James, Factors limiting the performance of CdZnTe detectors. IEEE Trans. Nucl. Sci. 52(3), 589–598 (2005). https://doi.org/10.1109/TNS. 2005.851419 C. Budtz-Jørgensen, I. Kuvvetli, New position algorithms for the 3D CZT drift detector. 2016 IEEE Nuclear Science Symposium, Medical Imaging Conference and Room-Temperature Semiconductor Detector Workshop (NSS/MIC/RTSD), 1–7 (2016). https://doi.org/10.1109/ NSSMIC.2016.8069957 P. Capper, Properties of Narrow Gap Cadmium-Based Compounds (INSPEC, 1994) E. Cavallari, F. Frontera, Hard X-ray/soft gamma-ray experiments and missions: Overview and prospects. Space Sci. Rev. 212, 429–518 (2017). https://doi.org/10.1007/s11214-017-0426-9 G. Daniel, O. Limousin, D. Maier, A. Meuris, F. Carrel, Compton imaging reconstruction methods: a comparative performance study of direct back-projection, SOE, a new Bayesian algorithm and a new Compton inversion method applied to real data with Caliste. 2020EPJ Web of Conferences. 225. 06006 (2020). 6th International Conference on Advancements in Nuclear Instrumentation Measurement Methods and their Applications (ANIMMA). https://doi.org/10. 1051/epjconf/202022506006 A.W. Davies, A. Lohstroh, M.E. Özsan, P.J. Sellin, Spatial uniformity of electron charge transport in high resistivity CdTe. Nucl. Instrum. Methods Phys. Res. A 546(1–2), 192–199 (2005). https://doi.org/10.1016/j.nima.2005.03.024 S. Del Sordo, L. Abbene, E. Caroli, A.M. Mancini, A. Zappettini, P. Ubertini, Progress in the development of CdTe and CdZnTe semiconductor radiation detectors for astrophysical and medical applications. Sensors 9, 3491–3526 (2009). https://doi.org/10.3390/s90503491 R. Devanathan, L.R. Corrales, F. Gao, W.J. Weber, Signal variance in gamma-ray detectors – a review. Nucl. Instrum. Methods Phys. Res. A 565(2), 637–649 (2006). https://doi.org/10.1016/ j.nima.2006.05.085 S. Dubos et al., Low energy characterization of Caliste HD, a fine pitch CdTe-based imaging spectrometer. IEEE Trans. Nucl. Sci. 60(5), 3824–3832 (2013). https://doi.org/10.1109/TNS. 2013.2281572 M. Forot, P. Laurent, I.A. Grenier, C. Gouiffes, F. Lebrun. Polarization of the Crab Pulsar and Nebula as Observed by the Integral/IBIS Telescope (2008). hal-00319540v1 B. Fraboni, A. Cavallini, N. Auricchio, M. Bianconi, Deep traps induced by 700 keV protons in CdTe and CdZnTe detectors. IEEE Trans. Nucl. Sci. 54(4), 828–833 (2007). https://doi.org/10. 1109/TNS.2007.902364 M. Funaki, T. Ozaki, K. Satoh, R. Ohno, Growth and characterization of CdTe single crystals for radiation detectors. Nucl. Instrum. Methods Phys. Res. A 436(1–2), 120–126 (1999). https:// doi.org/10.1016/S0168-9002(99)00607-5 K. Furukawa et al., Development of 60 µm pitch CdTe double-sided strip detectors for the FOXSI3 sounding rocket experiment. Nucl. Instrum. Methods Phys. Res. A 924, 321–326 (2019). https://doi.org/10.1016/j.nima.2018.07.011 Z. He, W. Li, G.F. Knoll, D.K. Wehe, J. Berry, C.M. Stahle, 3-D position sensitive CdZnTe gammaray spectrometers. Nucl. Instrum. Methods Phys. Res., Sect. A 422(1–3), 173–178 (1999). https://doi.org/10.1016/S0168-9002(98)00950-4 S. Howalt Owe, I. Kuvvetli, C. Budtz-Jørgensen, A. Zoglauer, Evaluation of a Compton camera concept using the 3D CdZnTe drift strip detectors. JINST 14, C01020 (2019) K. Iniewski, H. Chen, G. Bindley, I. Kuvvetli, C. Budtz-Jorgensen, Modeling charge-sharing effects in pixellated CZT detectors. IEEE Nuclear Science Symposium Conference Record 2007, 4608–4611 (2007). https://doi.org/10.1109/NSSMIC.2007.4437135 K.A.L. Koch-Mehrin, J.E. Lees, S.L. Bugby, A spectroscopic Monte-Carlo model to simulate the response of pixelated CdTe based detectors. Nucl. Instrum. Methods Phys. Res. A 976, 164241 (2020). https://doi.org/10.1016/j.nima.2020.164241 I. Kuvvetli, C. Budtz-Jørgensen, E. Caroli, N. Auricchio, CZT drift strip detectors for high energy astrophysics. Nuclear Instruments and Methods in Physics Research Section A 624(2), 486–491 (2010). https://doi.org/10.1016/j.nima.2010.03.172 K. Lacombe et al., Spectral performance of ECLAIRs flight detectors on SVOM mission. Astropart. Phys. 103, 131 (2018)

57 Cd(Zn)Te Detectors for Hard X-ray and Gamma-ray Astronomy

2033

F. Lebrun et al., ISGRI: the INTEGRAL soft gamma-ray imager. Astron. Astrophys. 411, L141 (2003) O. Limousin, Mise en oeuvre et étude des propriétés spectrales de la gamma-caméra ISGRI, Thèse de doctorat, Université Toulouse III Paul Sabatier (2001) O. Limousin, New trends in CdTe and CdZnTe detectors for X- and gamma-ray applications. Nucl. Instrum. Methods Phys. Res. A 504(1–3), 24–37 (2003). https://doi.org/10.1016/S01689002(03)00745-9 O. Limousin et al., ASTRO-H CdTe detectors proton irradiation at PIF. Nucl. Instrum. Methods Phys. Res., Sect. A 787, 328–335 (2015). https://doi.org/10.1016/j.nima.2015.01.062 O. Limousin, A. Meuris, O. Gevin, et al., Flight production of Caliste-SO: the hard x-ray spectrometers for solar orbiter/STIX instrument. Proc. SPIE 9905, 99050F (2016) D. Maier et al., Second generation of portable gamma camera based on Caliste CdTe hybrid technology. Nucl. Instrum. Methods Phys. Res. A 912, 338–342 (2018). https://doi.org/10.1016/ j.nima.2017.12.027 A. Meuris, O. Limousin, C. Blondel, Characterization of polarization phenomenon in Al-Schottky CdTe detectors using a spectroscopic analysis method. Nucl. Instrum. Methods Phys. Res. A 654(1), 293–299 (2011). https://doi.org/10.1016/j.nima.2011.05.084 K. Nakazawa, G. Sato, M. Kokubun, et al., Hard x-ray imager onboard Hitomi (ASTRO-H). J. Astron. Telesc. Instrum. Syst. 4(2), 021410 (2018). https://doi.org/10.1117/1.JATIS.4.2.021410 C.E. Ordonez, A. Bolozdynya, W. Chang, Doppler broadening of energy spectra in Compton cameras. 1997 IEEE Nuclear Science Symposium Conference Record 2, 1361–1365 (1997). https://doi.org/10.1109/NSSMIC.1997.670574 S.H. Owe, I. Kuvvetli, C. Budtz-Jørgensen, Carrier lifetime and mobility characterization using the DTU 3-D CZT drift strip detector. IEEE Trans. Nucl. Sci. 68(9), 2440–2446 (2021). https:// doi.org/10.1109/TNS.2021.3068001 A. Owens, A. Peacock, Compound semiconductor radiation detectors. Nucl. Instrum. Methods Phys. Res. A 531(1–2), 18–37 (2004). https://doi.org/10.1016/j.nima.2004.05.071 M. Pavlinsky et al., The ART-XC telescope on board the SRG observatory. Astron. Astrophys. 650, A42 (2021). https://doi.org/10.1051/0004-6361/202040265 V. Rana, W. Cook, F. Harrison, et al., Development of focal plane detectors for the Nuclear Spectroscopic Telescope Array (NuSTAR) Mission. SPIE Proc. 7435, 743503–743501 (2009) U.N. Roy, G.S. Camarda, Y. Cui, et al., Impact of selenium addition to the cadmium-zinc-telluride matrix for producing high energy resolution X-and gamma-ray detectors. Sci. Rep. 11, 10338 (2021). https://doi.org/10.1038/s41598-021-89795-z M. Sammartini, M. Gandola, F. Mele, B. Garavelli, D. Macera, P. Pozzi, G. Bertuccio, A CdTe pixel detector–CMOS preamplifier for room temperature high sensitivity and energy resolution X and γ ray spectroscopic imaging. Nucl. Instrum. Methods Phys. Res. A 910, 168–173 (2018). https://doi.org/10.1016/j.nima.2018.09.025 K.P. Singh et al., Astrosat mission. SPIE Proc. 9144, 91441S (2014) H. Tajima, S. Watanabe, Y. Fukazawa, et al., Design and performance of soft gamma-ray detector onboard the Hitomi (ASTRO-H) satellite. J. Astron. Telesc. Instrum. Syst. 4(2), 021411 (2018). https://doi.org/10.1117/1.JATIS.4.2.021411 T. Takahashi, S. Watanabe, Recent progress in CdTe and CdZnTe detectors. IEEE Trans. Nucl. Sci. 48(4), 950–959 (2001). https://doi.org/10.1109/23.958705 H. Toyama, Quantitative analysis of polarization phenomena in CdTe radiation detectors. Jpn. J. Appl. Phys. 45(11), 8842–8842 (2006) S. Watanabe et al., A Si/CdTe semiconductor Compton camera. IEEE Trans. Nucl. Sci. 52(5), 2045–2051 (2005) M.C. Weisskopf, R.F. Elsner, S.L. O’Dell, On understanding the figures of merit for detection and measurement of x-ray polarization. Proc. SPIE 7732, Space Telescopes and Instrumentation 2010: Ultraviolet to Gamma Ray, 77320E (2010). https://doi.org/10.1117/12.857357 D. Xu, Z. He, F. Zhang, Detection of gamma-ray polarization using a 3-D position-sensitive CdZnTe detector. IEEE Trans. Nucl. Sci. 52(4), 1160–1164 (2005). https://doi.org/10.1109/ TNS.2005.852703

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Principles of Scintillating Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Inorganic Scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Organic Scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gas Scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Neutron Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation Hardness, Internal Background and Induced Radioactivity of Scintillators . . . . . Radiation-Induced Degradation of Scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Creation of Defects Under Ionizing Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Damage Properties in Scintillating Materials Under Gamma Radiation . . . . . . . Phosphorescence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radio-Luminescence due to Produced Radioisotopes in Heavy and Light Scintillation Crystalline Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of Background Produced Effects in the Scintillator . . . . . . . . . . . . . . . . . . . . . . Photosensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photo-Multipliers (PMT) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scintillator-Photodetector Optical Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Concept for Scintillator Detectors Signal Electronics System . . . . . . . . . . . . . . . . . Scintillator Detectors Used in Space Observatories for Gamma-Ray Astronomy . . . . . . . . . Background Noise in Gamma-Ray Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A. F. Iyudin () Skobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow, Russia e-mail: [email protected] C. Labanti Osservatorio di Astrofisica e Scienza dello spazio (OAS-INAF), Bologna, Italy e-mail: [email protected] O. J. Roberts Science and Technology Institute, Universities Space Research Association, Huntsville, AL, USA e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_48

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Scintillator Detectors in Early Gamma-Ray Observatories . . . . . . . . . . . . . . . . . . . . . . . . Scintillator Detectors Used as Active Anti-Coincidence Detectors . . . . . . . . . . . . . . . . . . The Phoswich Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Position Sensitive Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scintillators in Pair-Production Based Telescopes: Calorimeters and Hodoscopes . . . . . . Scintillators in Compton Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scintillators in Polarimetry Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gas Scintillators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scintillating Detectors for Gamma-Ray Astronomy at Ground-Based Observatories . . . . . Conclusions and Outlook for Scintillators in Gamma-Ray Astronomy . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Inorganic Scintillators and Organic Plastic Scintillators are widely used for many applications in modern-day observational astronomy and cosmic-ray experiments. We review the different detection techniques, the optical and physical characteristics of scintillator detectors, and methods of light collection. We review the main gamma-ray instruments that have used scintillation materials up to the present day and discuss their great promise for future space- and ground-based gamma-ray experiments. This is due to their fundamental properties, possibility for high segmentation, radiation hardness, and ability to use wave-length shifting fibers for light collection and multi-pixel Silicon photomultipliers as alternatives to more conventional directly coupled optical readout (i.e., photomultiplier tubes). The combination of scintillation detectors and their photosensors will enable the search for new states of matter, antiparticles, neutrino oscillations, and will be used to study a wide range of astrophysical phenomena. Keywords

Nuclear detectors · Scintillators · Photosensors

Introduction Scintillators were first used during the accidental discovery of X-rays in 1895 by W.C. Roentgen (1895), who used a barium platinocyanide screen. After the discovery of natural radiation the following year, radiation detection methods that used scintillators, including devices such as the spinthariscope (Crookes 1903), were developed. However, most of these primitive detection methods were relatively inconvenient as they relied on the use of the human eye as a photosensor. The commercial introduction of the Photomultiplier Tube (PMT) was in 1941, and its later use with a ZnS coating by (Curran and Backer 1944; Marshall et al. 1947) produced a scintillation counter that didn’t require the human eye. This was soon followed by the discovery of NaI(Tl) in 1949, which was used primarily for

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applications involving the detection of gamma-rays (Hofstadter 1948, 1949), and changed scintillators into practical radiation spectrometers. After the discovery of NaI(Tl), there was tremendous research activity aimed at producing bright radiation scintillators, which resulted in hundreds of documented scintillators (see (Melcher 2005; Derenzo et al. 2016; Gobain; Eljenvtechnology; Yanagida 2018; Dujardin et al. 2018; Glodo et al. 2017; Cherepy 2015; Moses 2002; Lecoq et al. 2017) for example). Yet for many decades, NaI(Tl) has remained one of the best scintillation materials. Recently, new and exciting scintillators with properties that in many ways outperform traditional scintillators like NaI(Tl) (Knoll 2010) have been discovered, proving that this research field is far from complete. Over the last 20 years, the introduction of the lanthanide halide, elpasolite, and new ceramic scintillators have resulted in a wider selection of high-performance scintillation materials. Furthermore, there are several commercially available scintillators that are used for special applications such as fast timing, medical imaging, neutron detection, and for radiation measurements in harsh environments (Lecoq 2020). Traditionally, scintillators are distinguished as Inorganic or Organic, to which one can add the category of gaseous scintillators and specialized scintillators like, for example, the ones used for neutron detection. Among the properties listed in Table 1, the light output is the most important, as it affects both the efficiency and the energy resolution of the detector. The detection Table 1 Most common inorganic scintillators (IOSs) and their key scintillation characteristics. (From (Derenzo et al. 2016; Lecoq et al. 2017)). *The light output value is from luminescence produced by alpha particles. ZnS(Ag) is presented here for its historical role, nowadays it is currently used for detecting α-particles, protons, and neutrons when embedded in transparent plastic, loaded with light isotopes with a high neutron-alpha capture cross-section Scintillator NaI(Tl) CsI(Tl) CsI(Na) CsI(pure) BGO CdWO4 ZnS(Ag) PbWO4 BaF2

Light yield [ph/keV] 38 54 41 2 15–20 12–15

50 (*) 2 Fast (F) 1.8 Slow (S) 10 LaBr3 (Ce) 63 SrI2 (Eu) 80 CeBr3 45 GYGAG(Ce) 40 GAGG(Ce) 40

Emission λmax [nm] 415 550 420 315 480 475 450 450–550 F 220 S 310 360 480 370 540 520

Decay Time [ns] 230 680, 3340 460, 4180 2, 16 300 1100, 14,500 200 5, 14, 110 F 0.8, S 630 17 1500 17 250 60, 150

Density [g/cm3 ] 3.67 4.51 4.51 4.51 7.31 7.90

FWHM res. @ 661 keV 7.1% 5.7% 7.4% 16.7% 9.05% 6.3%

Hygroscopic? y n y n n n

4.09 8.28 4.8

– >20% 11.4%

n n n

5.1 4.6 5.2 5.8 6.7

2.7–3.2% 3.7% 3.2% 8% 1017 eV) subatomic particles in the upper troposphere and stratosphere (Fig. 11). The amount of scintillation light generated by an EAS is proportional to the energy deposited in the atmosphere and nearly independent of the primary species. The energies of an EAS extend beyond 1020 eV, making these the highest-energy subatomic particles known to exist. In addition to particle arrival directions, energy spectra, and primary composition, the astro-particle science investigated with FDs also includes multimessenger studies, searches for high-energy photons, neutrinos, monopoles, and deeply penetrating forms of dark matter. The current generation of experiments with FDs include the Telescope Array (TA) (Tokuno et al. 2012) in the northern hemisphere and the much larger Pierre Auger Observatory (Auger) (Abraham et al. 2010) in the southern hemisphere. Both are hybrid observatories; their FD telescopes overlook sparse arrays of SDs on the ground. They each have one FD site populated with additional telescopes that view up to 60◦ in elevation to measure lower EASs using a combination of scintillation and direct Cherenkov light. The Auger FD also measures UV scintillation that traces the development of atmospheric transient luminous events called “Elves,” which are initiated by lightning (Mussa and Ciaccio 2012).

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A good example of SDs used in cosmic ray research was the neutrino detection from the nearby extragalactic supernova SN1987A, which exploded on February 23, 1987, in the Large Magellanic Cloud (Arnett et al. 1989). SN1987A was an amazing and extraordinary event because it was detected in real time by different neutrino experiments (νs) around the world. Approximately 25 neutrino events were observed in three different experiments ; ∼12 in Kamiokande II (KII) (Hirata et al. 1987), about eight in Irvine-Michigan-Brookhaven (IMB) (Bionta et al. 1987), and about five in Baksan (Alekseev et al. 1987) (Kamiokande-II and IMB are water Cherenkov detectors. They really do not qualify as scintillator detectors, while Baksan does use scintillator). Neutrinos have an important role to play in the origin of a new-born neutron star, as the SN compact object remnant loses ∼99% of its energy in the first few seconds of the explosion. This is due to neutrinos escaping from the explosion region, a process known as “neutrino freezing.”

Conclusions and Outlook for Scintillators in Gamma-Ray Astronomy More than 120 experiments dedicated to space exploration of the gamma-ray sky have flown to date. In section “Basic Principles of Scintillating Detectors,” the desirable attributes of the “perfect” scintillator were listed, which included parameters such as fast decay times, high light output, linearity, high stopping power, good energy resolution, among other things. Over the last 20–30 years many new scintillators have been investigated and tested to push the boundaries of research in this area closer to realizing such an ideal scintillator. These include the study of ceramics and other new materials (Cherepy et al. 2010; de Faoite et al. 2018), and co-doping wellestablished scintillator crystals with more exotic ions (Soundara et al. 2021) to improve some of these desirable traits. However, despite this, NaI(Tl), CsI(Tl), and CsI(Na) are still currently the most popular. It’s not just new materials being investigated that are driving new instrument concept studies in astrophysics. The advent of 3D-printing is currently being investigated as a way of making customizable shapes of plastic scintillators for gamma-ray detection at reduced cost (Kim et al. 2020), which could provide attractive alternatives for making anti-Compton shields in future space telescopes. Additionally, due to the increasing interest in smaller, compact, cheaper payloads, detection methods such as phoswiches are being reinvestigated for future mission concept studies with increasing popularity using newly available technologies (Fletcher et al. 2020). There are many new scintillators that can be combined to drive advances in phoswich design, for example, using faster scintillators as the main detector element (i.e., LaBr3 (Ce) (Ulyanov et al. 2016) and CeBr3 (Ulyanov et al. 2017)), with a slower, denser active shield. Of course, this is just one of many methods that can currently be improved upon utilizing current technologies. One can argue that scintillation detectors are critical for future space research, given the heritage they have seen. They remain an important component of space

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experiments and are used in many presently active and planned future gamma-ray telescopes. They represent a reliable, flight-proven technology that is robust under a variety of operating conditions, are relatively low in cost, and can be fabricated into a variety of shapes and sizes. New readout technology, such as SiPMs, make scintillators even more attractive by reducing mass and volume, while maintaining the desirable characteristics of PMT-based solutions. Similarly, developing new technologies, or upgrading already operational instruments in the on-ground arrays are being considered to further study sources of extremely high-energy cosmic rays. While space research may have not been the initial driving force for the rapid production and development of modern scintillating crystals, it certainly has benefited from improvements in that technology and now drives the production of even faster, brighter, and cheaper scintillators for future missions.

References J. Abraham, P. Abreu, M. Aglietta, et al., The fluorescence detector of the Pierre Auger Observatory. Nucl. Instrum. Methods Phys. Res., Sect. A 620(2–3), 227–251 (2010). https:// doi.org/10.1016/j.nima.2010.04.023 M. Aglietta, et al., (LVD coll), The 1 kton LVD neutrino observatory, in Proc. 27th ICRC, Hamburg, Vol. 3, p. 1093, Hamburg, (2001) M. Aguilar, J. Alcaraz, J. Allaby, et al., The alpha magnetic spectrometer (AMS) on the International Space Station: Part I – Results from the test flight on the space shuttle. Phys. Rep. 366(6), 331–405 (2002). https://doi.org/10.1016/S0370-1573(02)00013-3 E.N. Alekseev, L.N. Alekseeva, V.I. Volchenko, I.V. Krivosheina, Possible detection of neutrino signal on 23 February 1987 at the Baksan underground scintillation telescope of the Institute of Nuclear Research. Soviet J. Exp. Theor. Phys. Lett. 45, 589–592 (1987) https://ui.adsabs. harvard.edu/abs/1987JETPL..45..589A V. Alenkov et al., Irradiation studies of a multi-doped Gd3 Al2 Ga3 O12 scintillator. Nucl. Instrum. Methods Phys. Res., Sect. A 916, 226–229 (2019). https://doi.org/10.1016/j.nima.2018.11.101 J. Angle, E. Aprile, F. Arneodo, et al., 3D position sensitive XeTPC for dark matter search. Nucl. Phys. B – Proc. Suppl. 173, 117–120 (2007) A. Annenkov, E. Auffray, M. Korshik, J.P. Peigneux, On the origin of the transmission damage in lead tungstate crystals under irradiation. Phys. Status Solidi A 170, 47–62 (1998) E. Aprile, A. Curioni, K.L. Giboni, M. Kobayashi, U.G. Oberlack, S. Zhang, Compton imaging of MeV gamma-rays with the liquid xenon gamma-ray imaging telescope (LXeGRIT). Nucl. Instrum. Methods Phys. Res., Sect. A 593(3), 414–425 (2008). https://doi.org/10.1016/j.nima. 2008.05.039 W.D. Arnett, J.N. Bahcall, R.P. Kirshner, S.E. Woosley, Supernova 1987A. Annu. Rev. Astron. Astrophys. 27(1), 629–700 (1989). https://doi.org/10.1146/annurev.aa.27.090189.003213 W.B. Atwood, A.A. Abdo, M. Ackermann, et al., The large area telescope on the Fermi gamma-ray space telescope Mission. Astrophys. J. 697, 1071–1102 (2009) arXiv:0902.1089 E. Auffray, et al., Improvement of several properties of lead tungstate crystals with different doping ions, CMS NOTE 97/54, CERN Geneva, Switzerland, (1997) E. Auffray, G. Dosovitskiy, A. Fedorov, I. Guz, M. Korjik, N. Kratochwill, et al., Irradiation effects on Gd3 Al2 Ga3 O12 scintillators prospective for application in harsh irradiation environments. Radiat. Phys. Chem. 164, 108365 (2019) H. Bethe, J. Ashkin, in Experimental Nuclear Physics, ed. by E. Segré, (Wiley, New York, 1953), p. 253

2072

A. F. Iyudin et al.

G.F. Bignami, G. Boella, J.J. Burger, et al., The COS-B experiment for gamma-ray astronomy. Space Sci. Instrum. 1, 245–268 (1975) R.M. Bionta, G. Blewitt, C.B. Bratton, et al., Observation of a neutrino burst in coincidence with supernova 1987A in the large magellanic cloud. Phys. Rev. Lett. 58, 1494–1496 (1987). https:// doi.org/10.1103/PhysRevLett.58.1494 J.B. Birks, Theory and Practice of Scintillation Counting (Pergamon Press, Oxford, 1964) S. Boggs, J. Kurfess, J. Ryan, E. Aprile, et al., The advanced compton telescope, in Proceedings of SPIE – The International Society for Optical Engineering Vol 6266, (2006) A. Bonura, S. Giarrusso, L. Lombardo et al., High-pressure gas-scintillation proportional counter: performance characteristics of the scientific model, in Proc. SPIE 1743, EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy III, (1992). https://doi.org/10.1117/12.130712 N. Borghi, B. Lauritzen, L. Lindvold, N. Poolton, Characterization of optical components for the ESS target imaging system. Radiat. Meas. 136, 106329 (2020). https://doi.org/10.1016/j. radmeas.2020.106329 L. Bouchet, P. Roques, J. Ballet, et al., The sigma/GRANAT telescope: calibration and data reduction. Astrophys. J. 548, 990–1009 (2001). https://doi.org/10.1086/318997 S. Brandt, N. Lund, A.R. Rao, The watch all-sky monitor for the GRANAT project. Adv. Space Res. 10(2), 239–242 (1990). https://doi.org/10.1016/0273-1177(90)90148-S V. Brudanin, Element-loaded organic scintillators for neutron and neutrino physics. Phys. Part. Nucl. 6, 69 (2001). https://doi.org/10.1142/9789812811363_0080 E. Caroli, J.B. Stephen, G. Di Cocco, et al., Coded aperture imaging in X- and gamma-ray astronomy. Space Sci. Rev. 45, 349–403 (1987) N.J. Cherepy, Transparent ceramic scintillators for gamma spectroscopy and MeV imaging, LLNLPROC-676780, Lawrence Livermore Natl. Lab., (2015) N.J. Cherepy, S.A. Payne, S.J. Asztalos, G. Hull, J.D. Kuntz, T. Niedermayr, et al., Scintillators with potential to supersede lanthanum bromide. IEEE Trans. Nucl. Sci. 56, 873–880 (2009). https://doi.org/10.1109/TNS.2009.2020165 N.J. Cherepy, J.D. Kuntz, Z.M. Seeley, et al., Transparent ceramic scintillators for gamma spectroscopy and radiography, in Hard X-Ray, Gamma-Ray, and Neutron Detector Physics XII, 78050I, 20 September (2010). https://doi.org/10.1117/12.862503 E.L. Chupp, D.J. Forrest, P.R. Higbie, et al., Solar gamma ray lines observed during the solar activity of August 2 to August 11, 1972. Nature 241, 333–335 (1973). https://doi.org/10.1038/ 241333a0 W. Crookes, The emanation of radium. Proc. R. Soc. Lond. 71, 405–408 (1903) S.C. Curran, W.R. Backer, A photoelectric alpha particle detector, U.S. Atomic Energy Commission Rpt. MDDC 1296, 17 November 1944 (declassified 23 September 1947) A. De Angelis, V. Tatischeff, I.A. Grenier, J. McEnery, M. Mallamaci, M. Tavani, U. Oberlack, L. Hanlon, et al., Science with e-ASTROGAM. A space mission for MeV-GeV gamma-ray astrophysics. J. High Energy Astrophys. 19, 1–106 (2018) arXiv:1711.01265 D. de Faoite, I. Tobin, A. Ulyanov, et al., Growth of trigonal gadolinium fluoride in a glass-ceramic for scintillation and optical applications. J. Eur. Ceram. Soc. 38(14), 4739–4748 (2018). https:// doi.org/10.1016/j.jeurceramsoc.2018.05.037 A.J. Dean, L. Fan, K. Byard, et al., Radioactivity induced background noise in space-borne astronomical gamma-ray telescopes employing inorganic scintillation spectrometers. Exp. Astron. 1, 35–45 (1989). https://doi.org/10.1007/BF00414794 S. Derenzo, M. Boswell, M. Weber, K. Brennan, Scintillation properties, (2016). http://scintillator. lbl.gov C. Dujardin et al., Trends, and advances in inorganic scintillators. IEEE Trans. Nucl. Sci. 65(8), 1977–1997 (2018). https://doi.org/10.1109/TNS.2018.2840160 Eljenvtechnology., “Scintillation products,” Scintillation products. http://www.eljentechnol ogy.com/ C.E. Fichtel, R.C. Hartman, D.A. Kniffen, et al., High-energy gamma-ray results from the second small astronomy satellite. Astrophys. J. 198, 163–182 (1975). https://doi.org/10.1086/153590

58 Scintillation Detectors in Gamma-Ray Astronomy

2073

C. Fiorini, A. Longoni, F. Perotti, et al., Gamma ray spectroscopy with CsI(Tl) scintillator coupled to silicon drift chamber. IEEE Trans. Nucl. Sci. 44(6), 2553–2560 (1997). https://doi.org/10. 1109/23.650862 C. Fletcher, C.M. Hui, A. Goldstein, O. Roberts, et al., The moon burst energetics all-sky monitor (MoonBEAM) CubeSat concept. Am. Astron. Soc Meeting Abstracts 235, 271.04 (2020) S.O. Flyckt, C. Marmonier, Photomultiplier Tubes, Principles & Applications (Photonis, Brive, 2002) https://usermanual.wiki/Document/FlycktMarmonier.1962139817 F. Frontera, D. Dal Fiume, M. Pamini, et al., The high energy X-ray experiment PDS on board the SAX satellite. Adv. Space Res. 11(8), 281–285 (1991). https://doi.org/10.1016/02731177(91)90180-R C. Furetta, Handbook of Thermoluminescence (World Scientific Publishing, Singapore, 2010) Garzon J.A, for the TRAGALDBAS collaboration, TRAGALDABAS. First results on cosmic ray studies and their relation with the, in XXV European Cosmic Ray Symposium, Turin, Sept. 4–9, (2016). https://arxiv.org/pdf/1701.07277.pdf N. Gehrels, Instrumental background in gamma-ray spectrometers flown in low Earth orbit. Nucl. Instrum. Methods Phys. Res., Sect. A 313(3), 513–528 (1992). https://doi.org/10.1016/01689002(92)90832-O N. Gehrels, C.E. Fichtel, G.J. Fishman, et al., The Compton gamma ray observatory. Sci. Am. 269, 68–77 (1993) S. Giarrusso, G. La Rosa, G. Manzo, et al., Performance characteristics of the medium energy gas scintillation proportional counter on board the Italian Dutch x-ray astronomy satellite SAX, in Proc. SPIE 1344, EUV, X-Ray, and Gamma-Ray Instrumentation for Astronomy, (1990). https:// doi.org/10.1117/12.23284 A. Giaz, G. Hull, V. Fossati, N. Cherepy, F. Camera, N. Blasi, et al., Preliminary investigation of scintillator materials properties: SrI2:Eu, CeBr3 and GYGAG:Ce for gamma rays up to 9 MeV. Nucl. Instrum. Methods Phys. Res., Sect. A 804, 212–220 (2015). https://doi.org/10.1016/j. nima.2015.09.065 R.J. Ginther, New cerium activated scintillating glasses. IRE Trans. Nucl. Sci. 7, 28–31 (1960) J. Glodo, R. Hawrami, E. van Loef, et al., Dual Gamma Neutron detection with Cs2 LiLaCl6 , in Proc. SPIE 7449, Hard X-Ray, Gamma-Ray, and Neutron Detector Physics XI, 74490E, (2009). https://doi.org/10.1117/12.830127 J. Glodo, R. Hawrami, K.S. Shah, Development of Cs2 LiYCl6 scintillator. J. Cryst. Growth 379, 73–78 (2013). https://doi.org/10.1016/j.jcrysgro.2013.03.023 J. Glodo, Y. Wang, R. Shawgo, et al., New developments in scintillators for security applications. Phys. Procedia 90, 285–290 (2017). https://doi.org/10.1016/j.phpro.2017.09.012 S. Gobain, Scintillation products. http://www.detectors.saint-gobain.com/uploadedFiles/Sgdetecto rs/Documents/Brochures/Organics-Brochure.pdf J.O. Goldsten, E.A. Rhodes, W.V. Boynton, et al., The MESSENGER gamma-ray and neutron spectrometer. Space Sci. Rev. 131(1–4), 339–391 (2007) D.E. Gruber, J.L. Matteson, L.E. Peterson, G.V. Jung, The spectrum of diffuse cosmic hard X-rays measured with HEAO 1. Astrophys. J. 520, 124–129 (1999) Hamamatsu-Photonics, Photomultiplers Tubes, Basics and Applications, 4th ed, Hamamatsu Photonics K.K. Electron Tube division, (2017). https://www.hamamatsu.com/resources/pdf/etd/ PMT_handbook_v4E.pdf K. Hirata, T. Kajita, M. Koshiba, et al., Observation of a neutrino burst from the supernova SN1987A. Phys. Rev. Lett. 58(14), 1490–1493 (1987). https://doi.org/10.1103/PhysRevLett. 58.1490 R. Hofstadter, Alkali halide scintillation counters. Phys. Rev. 74(1), 100–101 (1948) R. Hofstadter, The detection of gamma-rays with thallium-activated sodium iodide crystals. Phys. Rev. 74, 796–810 (1949) A.F. Iyudin, V.V. Bogomolov, V.I. Galkin, et al., Instruments to study fast neutrons fluxes in the upper atmosphere with the use of high-altitude balloons. Adv. Space Res. 56(10), 2073–2079 (2015)

2074

A. F. Iyudin et al.

A.S. Jacobson, The HEAO-3 high resolution gamma-ray spectrometer, in 17 International Cosmic Ray Conference 13–25 July 1981, Paris, France, (1981) K. Kamada, M. Nikl, S. Kurosawa, A. Beitlerova, A. Nagura, Y. Shoji, et al., Alkali earth co-doping effects on luminescence and scintillation properties of Ce doped Gd3 Al2 Ga3 O12 scintillator. Opt. Mater. 41, 63–66 (2015) T. Kamae, V. Andersson, M. Arimoto, et al., PoGOLite – a high sensitivity balloon-borne soft gamma-ray polarimeter. Astropart. Phys. 30(2), 72–84 (2008). https://doi.org/10.1016/j. astropartphys.2008.07.004 D.-g. Kim et al., Performance of 3D printed plastic scintillators for gamma-ray detection. Nucl. Eng. Technol. 52–12, 2910–2917 (2020). https://doi.org/10.1016/j.net.2020.05.030 G.F. Knoll, Radiation Detection and Measurement, 4th edn. (Wiley, Hoboken, 2010). ISBN 9780470131480 M. Kobayashi et al., Improvement in radiation hardness of PbWO4 scintillating crystals by Ladoping. Nucl. Instrum. Methods Phys. Res., Sect. A 404(1), 149–156 (1998). https://doi.org/10. 1016/S0168-9002(97)01137-6 M. Korjik, Limits of scintillation materials for future experiments at high luminosity LHC and FCC. J. Instrum. 12(8), C08021 (2017). https://doi.org/10.1088/1748-0221/12/08/C08021 M. Korjik, E. Auffray, Limits of inorganic scintillating materials to operate in a high dose rate environment at future collider experiments. IEEE Trans. Nucl. Sci. 63(2), 552–563 (2016). https://doi.org/10.1109/TNS.2016.2527701 M.V. Korzhik, A general approach to increasing the radiation hardness of complex structure oxide scintillation crystals. Nucl. Instrum. Methods Phys. Res., Sect. A 500(1–3), 116–120 (2003). https://doi.org/10.1016/S0168-9002(03)00328-0 W.L. Kraushaar, G.W. Clark, G.P. Garmire, et al., High-energy cosmic gamma-ray observations from the OSO-3 satellite. Astrophys. J. 177, 341–363 (1972). https://doi.org/10.1086/151713 V.D. Kuznetsov, L.M. Zelenyi, I.V. Zimovets, et al., The sun and heliosphere explorer – the interhelioprobe mission. Geomagn. Aeron. 56(7), 781–841 (2016) C. Labanti, G. Di Cocco, G. Ferro, et al., The IBIS-PICsIT detector onboard INTEGRAL. Astron. Astrophys. 411, L149–L152 (2003). https://doi.org/10.1051/0004-6361:20031356 C. Labanti, M. Marisaldi, F. Fuschino, et al., Design and construction of the mini-calorimeter of the AGILE satellite. Nucl. Instrum. Methods Phys. Res., Sect. A 598(2), 470–479 (2009). https:// doi.org/10.1016/j.nima.2008.09.021 F. Lebrun, J.P. Leray, P. Lavocat, et al., ISGRI: the INTEGRAL soft gamma-ray imager. Astron. Astrophys. 411, L141–L148 (2003). https://doi.org/10.1051/0004-6361:20031367 P. Lecoq, Scintillation detectors for charged particles and photons, in Particle Physics Reference Library, ed. by C. Fabjan, H. Schopper, (Springer, Cham, 2020). https://doi.org/10.1007/978-3030-35318-6_3 P. Lecoq, A. Gektin, M. Korzhik, Inorganic Scintillators for Detecting Systems (Springer, 2017), p. 408 F. Lei, A.J. Dean, G.L. Hills, Compton polarimetry in gamma-ray astronomy. Space Sci. Rev. 82(3/4), 309–388 (1997). https://doi.org/10.1023/A:1005027107614 D. Marcuse, Compression of a bundle of light rays. Appl. Opt. 10, 494–497 (1971) N. Markevich, I. Gertner, J. Elsteiner, Low energy X-ray and γ spectroscopy using silicon pin photodiodes. Nucl. Instrum. Methods Phys. Res., Sect. A 269(1), 219–221 (1988). https://doi. org/10.1016/0168-9002(88)90881-9 F.-H. Marshall, J.W. Coltman, A.I. Bennet, Photomultiplier radiation detector. Nucleonics 3(1), 58–64 (1947) D.S. McGregor, Materials for gamma-ray spectrometers: inorganic scintillators. Annu. Rev. Mater. Res. 48(1), 245–277 (2018) C. Meegan, G. Lichti, P.N. Bhat, et al., The Fermi gamma ray burst monitor. Astrophys. J. 702, 791–804 (2009). https://doi.org/10.1088/0004-637X/702/1/791 C.l. Melcher, Perspectives on the future development of new scintillators. Nucl. Instrum. Methods Phys. Res., Sect. A 537(1–2), 6–14 (2005). https://doi.org/10.1016/j.nima.2004.07.222

58 Scintillation Detectors in Gamma-Ray Astronomy

2075

W.W. Moses, Current trends in scintillator detectors and materials. Nucl. Instrum. Methods Phys. Res., Sect. A 487, 123–128 (2002). https://doi.org/10.1016/S0168-9002(02)00955-5 M. Moszynski, T. Ludziejewski, D. Wolski, W. Klamra, L.O. Norlin, Properties of the YAG:Ce scintillator. Nucl. Instrum. Meth. Phys. 345, 461 (1994). https://doi.org/10.1016/01689002(94)90500-2 M. Moszynski et al., A comparative study of silicon drift detectors with photomultipliers, avalanche photodiodes and PIN photodiodes in gamma spectrometry with LaBr3 crystals. IEEE Trans. Nucl. Sci. 56(3), 1006–1011 (2009). https://doi.org/10.1109/TNS.2008.2005110 N.F. Mott, R.W. Gurney, Electronic Process in Ionic Crystals (Oxford, New York, 1948) R. Mussa, G. Ciaccio, for the Pierre Auger Collaboration, Observation of ELVES at the Pierre Auger Observatory. Eur. Phys. J. Plus 127, 1–6 (2012). https://doi.org/10.1140/epjp/i201212094-x P.W. Nicholson, Nuclear Electronics (Wiley, London, 1974) J. Paul, F. Lebrun, P. Mandrou, et al., The SIGMA space telescope for low-energy gamma-ray astronomy, in 20 International Cosmic Ray Conference 2–15 Aug 1987, Moscow (USSR), (1987) M. Pearce, Balloon-borne gamma-ray polarimetry, in 20th Symposium on European Rocket and Balloon Programmes and Related Research, Hyére, France, (2011). https://ui.adsabs.harvard. edu/abs/2011ESASP.700.561P F. Perotti, M. Fiorini, S. Incorvaia, et al., The AGILE anticoincidence detector. Nucl. Instrum. Methods Phys. Res., Sect. A 556(1), 228–236 (2005). https://doi.org/10.1016/j.nima.2005.10. 016 L.E. Peterson, R.L. Howard, Gamma-ray astronomy in space in the 50 keV to 3 MeV region. IRE Trans. Nucl. Sci. 8(4), 21–29 (1961). https://doi.org/10.1109/TNS2.1961.4315853 P. Picozza, A.M. Galper, G. Castellini, PAMELA – a payload for antimatter matter exploration and light-nuclei astrophysics. Astropart. Phys. 27, 296–315 (2007) arXiv:astro-ph/0608697 C. Piemonte, A. Gola, Overview on the main parameters and technology of modern silicon photomultipliers. Nucl. Instrum. Methods Phys. Res., Sect. A 926, 2–15 (2019). https://doi. org/10.1016/j.nima.2018.11.119 K. Pinkau, Die Messung solarer und atmosphaerischer Neutronen. Naturforschung A 21, 2100– 2101 (1966) O.J. Roberts, Lanthanum halide and cerium bromid scintillators, in Solid-State Radiation Detectors, ed. by S. Awadalla, K. Iniewski, (CRC Press, Boca Raton, 2017), pp. 261–284 W. Röntgen, Ueber eine neue Art von Strahlen. Vorläufige Mitteilung, Aus den Sitzungsberichten der Würzburger Physik.-medic. Gesellschaft Würzburg, pp. 137–147, (1895) R.S. Saunders, R.E. Arvidson, G.D. Badhwar, W.V. Boynton, et al., 2001 Mars Odyssey mission summary. Space Sci. Rev. 110, 1–36 (2004). https://doi.org/10.1023/B:SPAC.0000021006. 84299.18 V. Schönfelder, U. Graser, J. Daugherty, Diffuse cosmic and atmospheric MeV gamma radiation from balloon observations. Astrophys. J. 217, 306–319 (1977) V. Schönfelder, H.J.M. Aarts, K. Bennett, et al., Instrument description and performance of the imaging gamma-ray telescope COMPTEL aboard the Compton gamma-ray observatory. Astrophys. J. Suppl. Ser. 86, 657–692 (1993) Z.M. Seeley, N. Cherepy, S. Payne, Homogeneity of Gd-based garnet transparent ceramic scintillators for gamma spectroscopy. J. Cryst. Growth 379, 79–83 (2013) C. Sgrò, The calorimeter of the Fermi large area telescope, in Proceedings, International Conference on Calorimetry for the High Energy Frontier (CHEF 2013): April 22–25, pp. 447– 453, Paris, France, (2013) L. Soundara et al., TlSr2I5:Eu2+− a new high density scintillator for gamma-ray detection. Nucl. Instrum. Methods Phys. Res., Sect. A 988, 164876 (2021). https://doi.org/10.1016/j.nima.2020. 164876 E.C. Stone, C.M.S. Cohen, W.R. Cook, et al., The cosmic ray isotope spectrometer for the advanced composition explorer. Space Sci. Rev. 86, 284–356 (1998). https://doi.org/10.1023/ A:1005075813033

2076

A. F. Iyudin et al.

G. Stratta, R. Ciolfi, L. Amati, et al., THESEUS: a key space mission concept for multi-messenger astrophysics. Adv. Space Res. 62(3), 662–682 (2018). https://doi.org/10.1016/j.asr.2018.04.013 T. Tadayuki, A. Keiichi, E. Manabu, et al., Hard X-ray detector (HXD) on board Suzaku. arXiv:astro-ph/0611232, (2006) G. Tamulaitis, A. Vasil’ev, M. Korzhik, A. Mazzi, A. Gola, S. Nargelas, et al., Improvement of the time resolution of radiation detectors based on Gd3 Al2 Ga3 O12 scintillators with SiPM readout. IEEE Trans. Nucl. Sci. 66(7), 1879–1888 (2019). https://doi.org/10.1109/TNS.2019.2919898 M. Tavani, G. Barbiellini, A. Argan, et al., The AGILE mission. Astron. Astrophys. 502, 995–103 (2009). https://doi.org/10.1051/0004-6361/200810527 D.J. Thompson, D.L. Bertsch, C.E. Fichtel, et al., Calibration of the energetic gamma-ray experiment telescope (EGRET) for the Compton gamma-ray observatory. Astrophys. J. Suppl. Ser. 86, 629–656 (1993). https://doi.org/10.1086/191793 H. Tokuno, Y. Tameda, M. Takeda, et al., New air fluorescence detectors employed in the telescope array experiment. Nucl. Instrum. Methods Phys. Res., Sect. A 676, 54–65 (2012). https://doi. org/10.1016/j.nima.2012.02.044 S. Torii, CALET for high energy electron and gamma-ray measurements on ISS. Nucl. Phys. B – Proc. Suppl. 150, 345–348 (2006) S. Torii, M. Hareyama, N. Hasebe, et al., The CALET mission on the ISS, in Proc. SPIE 7021, High Energy, Optical, and Infrared Detectors for Astronomy III, 702114, (2008). The calorimeter of the Fermi large area telescope. https://doi.org/10.1117/12.788524 P. Ubertini, F. Lebrun, G. Di Cocco, et al., IBIS: The imager on-board INTEGRAL. Astron. Astrophys. 411, L131–L139 (2003). https://doi.org/10.1051/0004-6361:20031224 A. Ulyanov et al., Performance of a monolithic LaBr3:Ce crystal coupled to an array of silicon photomultipliers. Nucl. Instrum. Methods Phys. Res., Sect. A 810, 107–119 (2016) A. Ulyanov et al., Localisation of gamma-ray interaction points in thick monolithic CeBr3 and LaBr3:Ce scintillators. Nucl. Instrum. Methods Phys. Res., Sect. A 844, 81–89 (2017) V.A.J. Van Lint, The physics of radiation damage in particle detection. Nucl. Instrum. Methods Phys. Res., Sect. A 253(3), 453–459 (1987). https://doi.org/10.1016/0168-9002(87)90532-8 E. Van Loef, J. Glodo, W.M. Higgins, K.S. Shah, Optical and scintillation properties of Cs/sub 2/LiYCl/sub 6/:Ce/sup 3+/ and Cs/sub 2/LiYCl/sub 6/:Pr/sup 3+/ crystals. IEEE Trans. Nucl. Sci. 52(5), 1819–1822 (2005). https://doi.org/10.1109/TNS.2005.856812 G. Vedrenne, J.P. Roques, V. Schönfelder, et al., SPI: The spectrometer aboard INTEGRAL. Astron. Astrophys. 411, L63–L70 (2003). https://doi.org/10.1051/0004-6361:20031482 C. Winkler, T.J.L. Courvoisier, G. Di Cocco, et al., The INTEGRAL mission. Astron. Astrophys. 411, L1–L6 (2003). https://doi.org/10.1051/0004-6361:20031288 X. Wu et al., PANGU: a high resolution gamma-ray space telescope. Proc. SPIE Int. Soc. Opt. Soc. 9144 (2014). https://doi.org/10.1117/12.2057251 T. Yanagida, Inorganic scintillating materials and scintillation detectors. Proc. Jpn Acad. 94B, 75 (2018). https://doi.org/10.2183/pjab.94.007 Y. Chuan, M. Peng-Xiong, S. Di Margherita, et al., Correction method for the readout saturation of the DAMPE calorimeter. Nucl. Instrum. Methods Phys. Res., Sect. A 984, 164645 (2020). https://doi.org/10.1016/j.nima.2020.164645 N. Zaitseva, B.L. Rupert, I. Paweczak, et al., Plastic scintillators with efficient neutron/gamma pulse shape discrimination. Nucl. Instrum. Methods Phys. Res., Sect. A 668, 88–93 (2012). https://doi.org/10.1016/j.nima.2011.11.071 N. Zaitseva, A. Glenn, L. Carman, et al., Scintillation properties of solution-grown trans-stilbene single crystals. Nucl. Instrum. Methods Phys. Res., Sect. A 789, 8–15 (2015). https://doi.org/ 10.1016/j.nima.2015.03.090

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Elisabetta Bissaldi, Carlo Fiorini, and Alexey Uliyanov

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photomultiplier Tubes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photocathodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photoelectron Collection Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electron Multiplication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Single-Photoelectron Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Timing Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dark Current and Dark Counts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Afterpulses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Position-Sensitive Multi-Anode PMTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Environmental Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PMTs in Imaging Atmospheric Cherenkov Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . PMTs in Spaceborne Scintillation Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Photodiodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon Photomultipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ground-Based Gamma-Ray Detectors Adopting SiPMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . The SCT Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The ASTRI-Horm Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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E. Bissaldi () Dipartimento Interateneo di Fisica, Politecnico di Bari, Bari, Italy Sezione di Bari, Istituto Nazionale di Fisica Nucleare, Bari, Italy e-mail: [email protected] C. Fiorini Dipartimento di Elettronica, Informazione e Bioingegneria, Politecnico di Milano, Milano, Italy Sezione di Milano, Istituto Nazionale di Fisica Nucleare, Milano, Italy e-mail: [email protected] A. Uliyanov School of Physics, University College Dublin, Dublin, Ireland e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_49

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Space-Based Gamma-Ray Detectors Adopting SiPMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Current Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Missions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon Drift Detector as scintillator photodetector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Silicon Drift Detector Fundamentals for Scintillation Detection . . . . . . . . . . . . . . . . . . . . SDD-Based Detectors for Gamma-Ray Astronomy Applications . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Photodetectors are widely employed as optical receivers to convert light into electrical signals in many applications ranging from communications to electronics, medicine, automotive, and transport. In gamma-ray astronomy, photodetectors are extensively used by space experiments to detect and measure the energy of X-rays and gamma rays (from a few keV to hundreds of GeV) interacting in various scintillator materials. Moreover, they are required in the cameras of Imaging Atmospheric Cherenkov Telescopes (IACTs) on the ground to measure very short light pulses produced by the interaction of high-energy gamma rays in the atmosphere down to a level of several photons. In this chapter, we introduce representative photodetectors used for high-energy astronomy, including photomultiplier tubes (PMTs), solid-state (semiconductor) photodetectors, with particular emphasis on silicon photomultipliers (SiPMs), and silicon drift detectors (SDDs). We address their basic properties and highlight past, present, and future applications, with particular emphasis to their employment in many small CubeSat missions devoted to the study of the highenergy, multimessenger sky. Keywords

Photomultiplier tubes · Photodiodes · Avalanche photodiodes · Silicon photomultipliers · Silicon drift detectors · Scintillators · Readout electronics

Introduction Photodetectors are devices that convert light in the optical range to a measurable electric signal. The two main applications of photodetectors in gamma-ray astronomy are Imaging Atmospheric Cherenkov Telescopes (IACTs) and scintillation detectors. IACTs are ground-based telescopes which are used to detect very highenergy gamma rays in the energy range of ∼30 GeV to a few hundred TeV. Interacting with the atmosphere such gamma rays produces extensive cascades of electromagnetic particles. The Cherenkov light emitted by the ultrafast electrons as they move through the air is observed by the telescopes. IACTs are similar to conventional optical telescopes, but need to detect and record an image of very

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short (a few ns) flashes of light. As the night sky background at this time scale is very low, the photodetectors are required to measure light pulses down to a level of several photons. Scintillators emit light in response to ionizing particles. They are extensively used by space experiments to detect and measure the energy of X-rays and gamma rays in the range of ∼8 keV to several hundred GeV (large calorimeter systems, such as the Fermi-LAT CsI calorimeter, are required to fully absorb and measure the energy of GeV gamma rays). Scintillation decay time of common scintillator materials varies from nanoseconds to several microseconds. Depending on the instrument design and intended energy range, photodetectors for scintillator readout are required to measure light pulses in a range of 102 –106 photons. The photomultiplier tube (PMT) has so far been the most common optical detector employed in gamma-ray astronomy both for scintillator readout and for use in IACT cameras. It is a very sensitive device with low-noise internal amplification, capable of detecting very low amounts of light down to a single-photon level. Solidstate (semiconductor) photodetectors have significant advantages over PMTs: they are compact, are mechanically robust, operate under low operation, are insensitive to magnetic fields, allow fine pixelization, and often have better quantum efficiency, especially in the long-wavelength part of the spectrum. The performance of early solid-state detectors, such as silicon photodiodes, did not match the low-light detection capabilities of PMTs. Lacking internal gain, conventional photodiodes produce very small signals which require external amplification and suffer from electronics noise. However, combined with low-noise amplifiers, they are suitable for detection of relatively large light pulses and have been successfully used in space instruments with bright CsI(Tl) scintillator to detect gamma rays above ∼100 keV. Development of avalanche photodiodes (APDs) and, more recently, silicon photomultipliers (SiPMs) has brought to the market silicon photodetectors with an internal gain which can compete with PMTs and detect low-intensity light pulses down to one-photon level. Over the last decade, SiPMs have replaced PMTs in many terrestrial applications and are now being qualified for use in space instruments. The silicon drift detector (SDD) is another promising photodetector for scintillator readout in future space instruments. Although it doesn’t have an internal gain, the SDD uses a unique design with very low output capacitance to greatly reduce the electronics noise. This chapter describes the properties of PMTs, silicon photodiodes, SiPMs, SDDs, and their usage in the past and future gamma-ray instruments.

Photomultiplier Tubes The basic structure of a typical PMT is schematically shown in Fig. 1. All photomultiplier elements are located inside an evacuated tube, usually made of glass, which has a dedicated window for light entrance. The inner surface of the window is covered with a thin semitransparent layer of photoemissive material called the

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Fig. 1 Schematic view of an end-window photomultiplier tube and its operation

photocathode. The photocathode absorbs incident photons and emits photoelectrons via the external photoelectric effect. The photoelectrons are then accelerated by the electrostatic field toward a dynode, a secondary-emission electrode which emits several secondary electrons for each impinging electron. A typical PMT includes a chain of 8–12 dynodes to achieve a total electron multiplication gain of 105 –107 . The electrons emitted from the last dynode are collected by the anode, which delivers the generated electric current to an external readout circuit. When the PMT is operated under continuous illumination, the measured anode current is used to evaluate the incident radiant flux. In a typical gamma-ray application, however, the PMT is operated in pulse mode where the readout electronics detects pulses of anode current above a certain threshold and usually employs an integrating circuit to measure the total charge of each pulse. Unless the light pulse is too intense, the output charge is proportional to the number of emitted photoelectrons and hence to the number of incident photons. Modern PMTs range in size from 10 mm wide by 11 mm deep by 2 mm thick for Hamamatsu Micro PMT to very large tubes with photocathode diameters of 50 cm. Apart from the end-window PMT (also called the end-on or head-on PMT) with a semitransparent (transmission-mode) photocathode shown in Fig. 1, the other common PMT type is the side-window (side-on) PMT with an opaque (reflection-mode) photocathode. In that case the light enters the PMT through a side of the tube and impinges on the photocathode deposited on a separate metal plate. The photoelectrons are then emitted (“reflected”) from the illuminated side of the photocathode and directed toward the first dynode. Although side-window PMTs are good for applications where the light can be beamed or focused onto the photocathode plate, they cannot be efficiently coupled to scintillators. To accelerate and focus photoelectrons and secondary electrons onto the respective dynodes, a voltage of 100–200 V is applied between the photocathode and first dynode and between the successive dynodes. The PMT therefore requires an operating voltage of 1–3 keV between the photocathode and anode. A resistive voltage divider is commonly used to divide the voltage from a single high-voltage source and to supply it to the individual electrodes as required.

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Photocathodes When an incident photon is absorbed by the photocathode, the photon energy is transferred to an electron which has a chance to migrate to the photocathode surface and escape into vacuum if its energy exceeds the work function W of the photocathode material (typically 1–2 eV). The photoemission is therefore usually described as a binomial process with each photon producing zero or one photoelectron. The sensitivity of the photocathode is characterized by the quantum efficiency (QE), which is defined as the average number of photoelectrons emitted from the photocathode per one incident photon: η=

Number of emitted photoelectrons . Number of incident photons

(1)

The quantum efficiency is a function of photon energy Eph or wavelength λ = hc/Eph and is primarily defined by the photocathode material and its manufacturing process as well as the material and thickness of the PMT window. The PMT window is usually transparent for visible and infrared light but limits the photocathode sensitivity in the UV range. Common window materials include borosilicate glass suitable for infrared to near-UV light (λ > 300 nm) , UV glass (λ > 190 nm), fused silica (quartz) glass (λ > 160 nm), sapphire (λ > 150 nm), and MgF2 crystals (λ > 115 nm). The quantum efficiency of various PMT photocathodes is shown in Fig. 2. At long wavelengths it reduces to zero when the photon energy becomes insufficient to allow the photoelectron to escape from the photocathode into vacuum (Eph < W ). The most common photocathode materials used in modern PMTs for detection of visible and near-UV light are bialkali antimonides, such as KCsSb and RbCsSb. The spectral sensitivity of bialkali photocathodes peaks at 350–400 nm and is a good match for the blue Cherenkov radiation of atmospheric showers and the emission spectra of many common inorganic and organic scintillators including NaI:Tl, LaBr3 :Ce, CeBr3 , LYSO, CsI:Na, BGO, and BC404 (Fig. 2). Until recently the maximum quantum efficiency of transmission-mode bialkali photocathodes was limited to 25–30%, and the majority of PMTs on the market are still produced with such standard bialkali photocathodes. However, in 2007 Hamamatsu improved the fabrication process of a bialkali photocathode and introduced “super bialkali” (SBA) and “ultra bialkali” (UBA) photocathodes achieving a maximum quantum efficiency of 35% and 43% at 350 nm, respectively (Nakamura et al. 2010). This was followed by the development of an “extended green bialkali” (EGBA) photocathode with a maximum quantum efficiency of 39% at 380 nm. A number of PMT models with these improved photocathodes are now commercially available. The enhanced quantum efficiency of the new photocathodes helps to improve the energy resolution of scintillator detectors and the sensitivity of IACTs. Multialkali (trialkali) photocathodes have better red light sensitivity extending up to 850 nm. This type of photocathode is commonly used in wideband optical

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Fig. 2 Top: Typical quantum efficiency of various transmission-mode photocathodes with a borosilicate entrance window. Using a UV-transparent window, the sensitivity of the bialkali and multialkali photocathodes can be extended to the UV region. Bottom: Emission spectra of several common scintillators and a typical spectrum of atmospheric Cherenkov radiation

spectrometers, but it is not particularly well suited for scintillator applications due to a lower quantum efficiency and much higher thermionic emission compared to bialkali photocathodes. All traditional alkali photocathodes exhibit relatively low sensitivity to yellow and red light, particularly compared to semiconductor photodetectors. Hamamatsu recently made available PMTs with transmission-type III–V semiconductor photocathodes such as GaAs and GaAsP. The latter in particular features an excellent quantum efficiency over the entire visible spectrum. However, compared to alkali photocathodes, the GaAsP photocathode exhibits much higher thermionic emission and is more likely to degrade when exposed to intense light (Hamamtsu Photonics 2017). Only a few specialized PMT models using this photocathode are currently available off the shelf. Other photocathode types used in PMTs include solar-blind photocathodes for UV applications (CsI and CsTe) and photocathodes for nearinfrared applications (InGaAs and InGaAsP).

Photoelectron Collection Efficiency To be efficiently multiplied and contribute to the output signal, photoelectrons have to strike the active area of the first dynode. Photoelectrons that land on other electrodes produce much smaller or zero signals at the anode output. The

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photoelectron collection efficiency of a PMT is defined as the ratio of the number of photoelectrons reaching the first dynode to the total number of photoelectrons emitted by the photocathode. This parameter is determined by the design of the dynode system and focusing electrode. Typical values for various PMTs range from 60% to 90% (Hamamtsu Photonics 2017; Wright 2017). Collection efficiency depends on the voltage between the photocathode and first dynode and may suffer if an insufficient voltage is applied. It also depends on the light wavelength as it affects the initial velocities of emitted photoelectrons. Combined with quantum efficiency, collection efficiency essentially defines what fraction of photons is detected by the PMT. Although it is an important performance parameter, it is difficult to measure and is not specified by PMT manufacturers.

Electron Multiplication When an accelerated electron strikes a surface of a dynode, it ionizes the dynode material transferring its kinetic energy to other electrons. As a result, several secondary electrons are typically emitted from the dynode. The electrons are then accelerated toward the next dynode, and the process repeats until the electrons are collected by the anode. Secondary emission is a random process, and a Poisson distribution is often assumed to describe the number of emitted electrons. However, an excess of events with a small number of secondary photons is often observed due to inelastic scattering of primary electrons (Wright 2017). The average number of secondary electrons emitted per one incident electron is called the multiplication factor (gain) of the dynode: δ=

Number of emitted electrons . Number of incident electrons

(2)

It is common to combine the electron multiplication factor δi of the ith dynode with the collection efficiency αi+1 of the next electrode to define the effective gain of the dynode as gi = δi αi+1 .

(3)

The combined gain of all dynodes in an n-stage PMT is then given by the product of the individual dynode gains: G0 = g1 g2 g3 · · · gn .

(4)

It should be distinguished from the PMT gain (current amplification), which is defined as the ratio of the anode current to the photocathode current and therefore takes into account the photoelectron collection efficiency α of the first dynode: G = αG0 = αg1 g2 g3 · · · gn .

(5)

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The average signal (anode charge) of the PMT in response to a light pulse of Nph photons can be calculated as Q = Nph ηGe = Nph ηαG0 e,

(6)

where η is the quantum efficiency and e is the electron charge. Electron multiplication factors typically range from 3 to 15 depending on the dynode material and the applied voltage, resulting in a total PMT gain of 104 –108 . However, multiplication factors of several dozens can be achieved for certain dynode materials using a large voltage (Wright 2017; Knoll 2010). The multiplication factor of each dynode is proportional to a power of the interstage voltage ∆V (which defines the energy of incident electrons): g ∝ ∆V a ,

(7)

where the index a (typically 0.6–0.8 (Hamamtsu Photonics 2017; Flyckt and Marmonier 2002)) is defined by the dynode geometry and material. The total gain of an n-stage PMT thus increases with the supplied PMT bias voltage V as G ∝ V an .

(8)

The strong dependence of the PMT gain on the bias voltage puts stringent requirements on the stability of the power supply.

Single-Photoelectron Response The average output charge generated by the PMT for one photoelectron striking the first dynode is Qpe = eG0 = eg1 g2 g3 · · · gn .

(9)

This is a sizeable signal which can be observed for the majority of PMTs using suitable readout electronics (low-gain tubes would require a low-noise amplifier). However, electron multiplication is a random process which results in a relatively wide distribution of the output signal (pulse-height distribution) for one photoelectron as shown in Fig. 3. The shape of the distribution is primarily defined by fluctuations in the number of secondary electrons emitted from the first dynode. Electron multiplication at subsequent dynodes introduces additional fluctuations blurring the distribution, but the effect of each following multiplication stage becomes progressively less important because of the increasing number of electrons that are multiplied at each stage. To a first approximation, secondary electron emission from a dynode is often described by a Poisson distribution. In that model the relative variance of the single-photoelectron response can be calculated (Wright 2017; Donati 2021) as

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Fig. 3 Typical single-photoelectron response distribution. The PMT signal is expressed in photoelectrons by dividing the measured output signal by the average value of single-photoelectron signal. This distribution is obtained by illuminating the PMT with a very dim light source to prevent two-photoelectron events

2 σQ

Q2pe

=

1 1 1 1 + + + ··· + , g1 g1 g2 g1 g 2 g3 g1 g2 g3 · · · gn

(10)

where the different terms represent the diminishing contributions from electron multiplication by successive dynodes. Assuming equal gains gi = g for all dynodes, Equation 10 can be simplified to 2 σQ

Q2pe

=

1 1 1 1 1 + 2 + 3 + ··· + n ≈ . g g g−1 g g

(11)

Figure 4 shows two simulated response distributions for very weak light pulses, assuming Poisson statistics for photoelectrons collected by the first dynode. The actual number of photoelectrons varies from pulse to pulse, and for PMTs with a high gain of the first dynode, it may be possible to observe peaks in the spectrum corresponding to 1, 2, and 3 photoelectrons. These peaks overlap and are usually poorly resolved because of the relatively large variance of the single-photoelectron response and cannot be resolved at all for PMTs with a low gain of the first dynode. The narrow peak near zero corresponds to emission of zero photoelectrons. The width of the peak is usually defined by the noise of the readout electronics. This peak can be observed when measurements are synchronized with incident light pulses, e.g., a pulse generator is used to drive a light source and to trigger signal measurement at the same time. Gamma-ray detectors normally operate by measuring signals above a certain threshold, in which case “zero” signals cannot

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Fig. 4 Simulated pulse-height distributions for weak light pulses producing, on average, two photoelectrons. The left plot represents a PMT operating with a relatively high gain of the first dynode (g1 = 10); the right plot is for a lower gain (g1 = 5). Different curves in each plot show contributions from events with a specific number of photoelectrons

be observed. The distributions in Fig. 4 assume the Poisson model for the singlephotoelectron response. In reality, single-photoelectron response spectra have larger variance than predicted by the Poisson model and typically show an excess of lowsignal events due to photoelectron inelastic scattering from the first dynode (Wright 2017). This further degrades the capability of the PMT to resolve individual photoelectrons.

Timing Characteristics Anode current pulses produced by various PMTs in response to instantaneous light pulses typically have rise times of 0.7–7 ns (measured from 10% to 90% of the peak current) and somewhat longer fall times. Typical values of the full width at half maximum (FWHM) of the pulse range from 1.3 to 25 ns. The transit time of electrons from the photocathode to the anode is usually around several tens of nanoseconds, resulting in a noticeable delay between the incident light pulse and produced signal. The electron transit time depends on the initial position and velocity of the emitted photoelectron. This results in a transit time spread (T.T.S.) or transit time jitter, which defines the time resolution of the PMT and is usually specified as the FWHM of the transit time distribution obtained with single photoelectrons. Typical values range from 0.4 to several nanoseconds. Timing properties of a PMT are mainly determined by its dynode structure, with linearfocused and metal-channel PMTs showing the best timing performance.

Dark Current and Dark Counts When a PMT is operated in complete darkness, it still produces a small output current called dark current. This current has a DC component and random pulses

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similar to pulses produced by incident photons. These pulses are called dark counts and their rate is referred to as dark count rate (DCR). Dark counts form background for detection of incident light. The sources of PMT dark current include thermionic emission, ohmic leakage current, field emission, and background radiation. Thermionic emission from the photocathode is usually the main source of dark current and dark counts in a PMT operating at room temperature and nominal voltage. Electrons spontaneously emitted from the photocathode are multiplied by the dynode structure and thus produce signals that are equivalent to single-photoelectron signals. Thermionic emission rate is defined by the photocathode material and exponentially increases with temperature according to Richardson’s law (Hamamtsu Photonics 2017; Engstrom 1980). The resulting dark current is proportional to the PMT gain; therefore, it has the same power-law dependence on voltage. Ohmic leakage current is caused by residual conductivity of the glass envelope and plastic base of the PMT. It becomes a major dark current component when the PMT is operated at low voltage or low temperature. Ohmic leakage does not produce dark counts. Field emission is electron emission from PMT dynodes caused by strong electric fields. It rapidly increases when the PMT is operated at an excessive voltage, becoming the main source of dark current. Field emission limits the maximum safe voltage (and hence the gain) at which the PMT can be operated. Background radiation can generate light in the window and glass envelope of a PMT through scintillation and Cherenkov emission. In particular, Cherenkov emission of a cosmic muon traveling through a 4-mm-thick quartz window can produce about 200 photoelectrons (Wright 2017).

Afterpulses Output signal pulses produced by light flashes (such as scintillation events) may sometimes be followed by additional pulses separated from the main pulses by a constant delay, typically hundreds of nanoseconds to microseconds. These afterpulses are primarily caused by positive ions which may be generated by ionization of residual gases inside the PMT by accelerated electrons. Guided by the electric field, the positive ions slowly travel back to the photocathode and typically generate upon impact tens to hundreds electrons. These electrons are the multiplied by dynodes in the usual manner, producing a large anode signal. The afterpulse probability is proportional to the size of the true signal, but the magnitude of the afterpulse is determined by the ion type and its final energy. Afterpulses are a major concern for IACTs as they are copiously produced in PMTs exposed to night sky.

Energy Resolution Monoenergetic gamma rays that are fully absorbed in the scintillator generate detector signals of similar magnitudes, thereby producing a peak in a recorded

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pulse-height distribution. The position of the peak (mean pulse height) is defined by the gamma-ray energy, while the width of the peak is defined by fluctuations of the detector response, which can be considered as measurement noise. Energy resolution (or pulse-height resolution) of the detector is defined as the ratio of the full width at half maximum (FWHM) to the mean signal. When the peak is described by a Gaussian distribution with a mean pulse height Q and a standard deviation σQ , the energy resolution of the detector can be calculated as R=

FWHM Q

≈

2.355σQ Q

(12)

.

The definition of energy resolution assumes that the mean detector signal is proportional to the absorbed gamma-ray energy. For a nonlinear detector, the detector response scale must be calibrated or at least linearized before using Eq. 12 to calculate the energy resolution. Energy resolution of a scintillation detector is determined both by characteristics of the scintillator and by properties of the photodetector. It can be represented by the sum of two terms:  2 + R2 . R = Rstat (13) scint

The first term Rstat represents the statistical limit of the energy resolution, which is calculated assuming Poisson statistics for emitted scintillation photons (Wright 2017; Engstrom 1980): 

Rstat = 2.355

ENF N pe



= 2.355

ENF N ph ηα

,

(14)

where N ph is the mean number of photons striking the photocathode, η and α are the average values of quantum efficiency and photoelectron collection efficiency for scintillation photons and N pe = N ph ηα is the mean number of photoelectrons collected by the first dynode. ENF is the excess noise factor, which represents the effect of electron multiplication on the signal variance. ENF is determined by the relative variance of the single-photoelectron response (Wright 2017): 2 ENF = 1 + σQ /Q2pe .

(15)

Assuming the Poisson model of secondary electron emission, ENF can be deduced from the dynode gain using Eq. 11: ENF = g/(g − 1).

(16)

PMTs with good single-photoelectron response typically have ENF of about 1.1– 1.2 (Wright 2017). Rstat is thus mainly determined by the number of photoelectrons

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collected by the first dynode and hence crucially depends on the light yield of the scintillator, quantum efficiency, and photoelectron collection efficiency of the PMT. The second term Rscint in Eq. 13 is called intrinsic energy resolution of the scintillator and represents additional (non-Poisson) fluctuations of the scintillator light output associated with such effects as scintillator nonuniformities and nonproportionality of the scintillator response. It is determined by the deviation of the relative variance of the number of output photons from the value predicted by the Poisson distribution:   2  σNph 1 Rscint = 2.355 2 − , (17) N ph N ph

Depending on scintillator and gamma-ray energy, Rscint can be a significant component of the detector energy resolution given by Eq. 13.

Position-Sensitive Multi-Anode PMTs Hamamatsu provides a range of position-sensitive PMTs which use a special metal channel dynode structure and multiple anodes. Photoelectrons and secondary electrons travel through numerous metal channels in the dynode structure to the anodes with very little lateral spread. Those channels effectively map the photocathode area to the multiple anodes, with each anode collecting electrons from a specific part of the photocathode (photocathode pixel). Multi-anode PMTs are available in the form of linear arrays and two-dimensional arrays of up to 256 pixels. Minimizing the dead space, multi-anode PMTs can be conveniently used with scintillator arrays, in Anger cameras and in cameras of Cherenkov telescopes.

Environmental Considerations Performance of a PMT can be affected by environmental factors such as temperature, pressure, mechanical stress, magnetic fields, and ionizing radiation. PMTs with bialkali photocathodes can operate in a wide range of temperatures, typically from −30 ◦ C to +50 ◦ C. Special PMTs are available for operation at very low temperatures down to −186 ◦ C and high temperatures up to 200 ◦ C (Hamamtsu Photonics 2017). As discussed above, temperature has a strong effect on the dark current of a PMT. In addition, both the quantum efficiency and gain of a PMT, and hence its response to light, depend on temperature. The temperature dependence of the PMT response does not typically exceed a few tenths of a percent per degree (Hamamtsu Photonics 2017; Wright 2017). Although PMTs can operate in high vacuum without any issues, usage of high voltage in a low-pressure atmosphere (e.g., on a balloon flight) may be impaired by a high risk of an electric discharge according to Paschen’s law (Wadhwa 2007).

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Made of glass, PMTs are relatively fragile devices and should be protected from mechanical shock and stress. The majority of PMTs can tolerate up to 50–100 m/s2 of vibration and up to 750–1000 m/s2 of shock (Hamamtsu Photonics 2017). To survive launch vibrations and shocks, space applications may require the use of ruggedized PMTs, which are based on conventional tubes with improved electrode support and dynode structure. Magnetic fields can change electron trajectories in a PMT, thereby affecting the output signal. This is particularly true for large head-on tubes with a large distance between the photocathode and the first dynode. Such PMTs are sensitive to very weak fields such as the geomagnetic field (∼10−4 T) and require the use of magnetic shields. The magnetic shield is typically a cylindrical housing or simply a thin layer of mu-metal or another high-permeability material around the PMT. Special PMTs with fine-mesh dynodes capable of operating in strong magnetic fields of over 1 T have been developed for use in high-energy physics experiments (Hamamtsu Photonics 2017). PMTs are relatively radiation-tolerant detectors. The most important effect of radiation is progressive darkening of the glass window, which results in a loss of optical transmission (especially at short wavelengths) and thus reduces the quantum efficiency of the PMT. This becomes a noticeable effect for PMTs with borosilicate glass windows exposed to doses of several kilorads. UV glass and particularly fused silica glass are much less affected by radiation (Hamamtsu Photonics 2017; Bell et al. 2001).

PMTs in Imaging Atmospheric Cherenkov Telescopes An IACT uses a large mirror with an area of about ten to several hundred square meters to focus the Cherenkov light emitted by atmospheric electromagnetic showers onto an imaging camera, which typically consists of hundreds or thousands of densely packed photodetectors (camera pixels). Since IACTs observe very dim and short (a few nanoseconds) flashes of light, they require sensitive and fast photodetectors. PMTs are currently the most established photodetectors for IACTs: they have been used in nearly all telescopes constructed to date, from the first Whipple 10 m IACT (Cawley et al. 1990) to the current generation of telescopes (VERITAS (Weekes et al. 2002), MAGIC (Aleksi´c et al. 2016), H.E.S.S. (Hinton 2004)), and selected for use in the new-generation large and medium telescopes of the Cherenkov Telescope Array (CTA) (Actis et al. 2011). IACTs typically use 1–1.5-inch-diameter head-on PMTs with flat or hemispherical entrance windows and employ Winston cone light guides in front of the PMTs to reduce the dead space between the camera pixels and shield the PMTs from stray light. New telescope designs with short focal lengths may require a smaller pixel size of about 6 mm, which can be conveniently provided by multi-anode PMTs. Multi-anode PMTs were considered, for example, for the dual-mirror (Schwarzschild-Couder) telescopes of CTA (Vandenbroucke et al. 2011); however, this camera design was later abandoned in favor of silicon photomultipliers.

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Photodetectors in IACTs operate in the presence of strong night sky background (NSB) with typical photoelectron rates of about 100–200 MHz per pixel (Actis et al. 2011), which by many orders of magnitudes exceed the dark count rate of conventional PMTs. To distinguish dim signals produced by atmospheric showers from the NSB noise, the IACT trigger requires multiple (neighboring) pixels above a certain threshold within a coincidence window of several nanoseconds. The trigger threshold for each pixel is typically several photoelectrons and is mainly defined by the rate and amplitude of PMT afterpulses generated by the NSB (Mirzoyan et al. 1997). The main PMT criteria for IACTs are the following (Actis et al. 2011; Kohnle et al. 2000): • High quantum efficiency in the 300–600 nm range. While PMTs with standard bialkali photocathodes were used in the older telescopes, super bialkali photocathodes are now employed by VERITAS (Nepomuk Otte 2011), MAGIC (Tridon et al. 2010), and CTA (Mirzoyan et al. 2017). • Dynamic range from one to several thousand photoelectrons. • Good single-photoelectron response to discriminate dim events against noise. • Low afterpulse rate to reduce the trigger threshold. • Short pulse width of a few nanoseconds to minimize the charge integration window and thereby reduce the noise produced by the NSB. • Short rise time to minimize the coincidence window in the trigger. • Operation at low gain (3 × 104 − 2 × 105 ) to reduce the relatively large current through the dynode system caused by the NSB and extend the lifetime of the dynodes. Specifically to meet the CTA requirements, Hamamatsu developed R12992-100, a 1.5-inch 7-stage PMT with an SBA photocathode and a low afterpulse probability of 0.02% at a threshold of 4 photoelectrons (Mirzoyan et al. 2017). This is a stateof-the-art tube with a peak quantum efficiency of over 38% at 390 nm, an excellent photoelectron collection efficiency of 95–98%, and a pulse width of 30 keV), with a size of 4.5 × 4.5 mm2 each and a pitch of 5 mm. Other examples of projects which foresee the use of SDD as readout photodetector for scintillators are HERMES (Fuschino et al. 2020), GrailQuest (Burderi et al. 2021), and Astena (Frontera et al. 2021).

Conclusions In this chapter we explored the capabilities of photodetectors, in the context of their two main applications in gamma-ray astronomy, namely, Imaging Atmospheric Cherenkov Telescopes (IACT) and scintillation detectors. In the first case, photodetectors are required to measure very short light pulses produced by the interaction of high-energy (>10 GeV) gamma rays in the atmosphere down to a level of several photons, while in the latter case, they are extensively used by space experiments to detect and measure the energy of X-rays and gamma rays (from few keV to hundreds of GeV) interacting in various scintillator materials.

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Fig. 14 Exploded view of the CsI(Tl)-SDD detector arrays foreseen in Theseus-XGIS, with the double-side SDD readout

We started by discussing the main characteristics of the photomultiplier tube (PMT), which has so far been the most common optical detector employed in gamma-ray astronomy both for scintillator readout and for use in IACT cameras. Then, we moved to present solid-state (semiconductor) photodetectors as natural successors of PMTs. Their advantages include compactness, mechanical robustness, insensitivity to magnetic fields, and the capability of operating at low voltages, reaching very high values of quantum efficiency. PIN photodiodes combined with low-noise amplifiers have been successfully used in space instruments coupled to CsI(Tl) scintillator to detect gamma rays above ∼100 keV. Rapid development of avalanche photodiodes (APDs) and, more recently, silicon photomultipliers (SiPMs) has led to the replacement of PMTs in many terrestrial applications. SiPMs are now being qualified for use in space instruments, particularly in many small CubeSat missions devoted to the study of the multimessenger sky. Finally, we focused on the properties of silicon drift detectors (SDDs) as promising photodetectors for scintillator readout in future space instruments. Acknowledgments AU acknowledges support from Science Foundation Ireland grant 19/FFP/6777.

References B.P. Abbott et al., Multi-messenger observations of a binary neutron star merger. Astrophys. J. Lett. 848, L12 (2017a) B.P. Abbott et al., Gravitational waves and gamma-rays from a binary neutron star merger: GW170817 and GRB 170817A. Astrophys. J. Lett. 848, L13 (2017b)

59 Photodetectors for Gamma-Ray Astronomy

2117

F. Acerbi et al., Characterization of single-photon time resolution: from single SPAD to silicon photomultiplier. IEEE Trans. Nucl. Sci. 61, 2678–2686 (2014) M. Actis, G. Agnetta, F. Aharonian et al., Design concepts for the Cherenkov Telescope Array CTA: an advanced facility for ground-based high-energy gamma-ray astronomy. Exp. Astron. 32, 193–316 (2011) C.B. Adams et al., Detection of the crab nebula with the 9.7 m prototype Schwarzschild-Couder telescope. Astropart. Phys. 128, 102562 (2021) C.B. Adams et al., Design and performance of the prototype Schwarzschild-Couder telescope camera. J. Astron. Telesc. Instrum. Syst. 8, 014007 (2022) M. Ahangarianabhari et al., VEGA: a low-power front-end ASIC for large area multi-linear X-ray silicon drift detectors: design and experimental characterization. Nucl. Instr. Methods A 770, 155 (2015) J. Aleksi´c, S. Ansoldi, L. Antonelli et al., The major upgrade of the MAGIC telescopes, Part I: the hardware improvements and the commissioning of the system. Astropart. Phys. 72, 61–75 (2016) F. Altamura et al., Preliminary results from the LAZIO-Sirad experiment on board of the International Space Station, in Proceedings of the 29th International Cosmic Ray Conference, vol. 2 (2005), p. 343 H. Anderhub et al., Design and operation of FACT – the first G-APD Cherenkov telescope. J. Instrum. 8(06), P06008 (2013). Article id. P06008 R.L. Aptekar, D.D. Frederiks, S.V. Golenetskii et al., Konus-W gamma-ray burst experiment for the GGS wind spacecraft. Space Sci. Rev. 71(1–4), 265–272 (1995) R.L. Aptekar et al., Konus-W gamma-ray burst experiment for the GGS wind spacecraft. Space Sci. Rev. 71, 265–272 (1995) J.L. Atteia, M. Niel, M. Cassignol et al., FREGATE, a gamma-ray spectrometer for HETE. Astrophys. Space Sci. 231(1–2), 471–474 (1995) W.B. Atwood et al., The large area telescope on the fermi gamma-ray space telescope mission. Astrophys. J. 697, 1071–1102 (2009) S. Bacholle et al., Mini-EUSO mission to study Earth UV emissions on board the ISS. Astrophys. J. Suppl. S. 253(2), 36–53 (2021) K. Bechtol et al., TARGET: a multi-channel digitizer chip for very-high-energy gamma-ray telescopes. Astropart. Phys. 36(1), 156–165 (2012) K. Bell, R. Brown, D. Cockerill et al., The development of vacuum phototriodes for the CMS electromagnetic calorimeter. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 469(1), 29–46 (2001) G. Bertuccio et al., A silicon drift detector-CMOS front-end system for high resolution X-ray spectroscopy up to room temperature. J. Instrum. 10(01), P01002 (2015) L. Bombelli, C. Fiorini, T. Frizzi, R. Alberti, A. Longoni, CUBE, A low-noise CMOS preamplifier as alternative to JFET front-end for high-count rate spectroscopy, in Nuclear Science Symposium Conference Record 2011 (2012). ISBN 978-1-4673-0118-3 J. Buckley et al., The Advanced Particle-astrophysics Telescope (APT) Project Status, in Proceedings of Science, 37th International Cosmic Ray Conference (ICRC2021), vol. 395 (2021), p. 665. Id. 665 L. Burderi et al., GrailQuest: hunting for atoms of space and time hidden in the wrinkle of spacetime. Experimental Astronomy, 51, 1255–1297 (2021) A.D. Butt et al., Development of a detector for gamma-ray spectroscopy based on silicon drift detector arrays and 2 lanthanum bromide scintillator. IEEE Trans. Nucl. Sci. 62(5), 2334–2342 (2015) A.D. Butt et al., Application of silicon drift detectors for the readout of a CdWO4 scintillating crystal. IEEE Trans. Nucl. Sci. 65(4), 1040–1046 (2018) P. Buzhan et al., Silicon photomultiplier and its possible applications. Nucl. Instrum. Methods Phys. Res. A 504, 48–52 (2003) N. Cannady et al., Characteristics and performance of the CALorimetric Electron Telescope (CALET) calorimeter for gamma-ray observations. ApJS 238, 5 (2018)

2118

E. Bissaldi et al.

M. Casolino et al., SiPM development for space-borne and ground detectors: from Lazio-Sirad and Mini-EUSO to Lanfos. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 986, 164649 (2021). Article 164649 O. Catalano et al., The ASTRI camera for the cherenkov telescope array, in Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 10702 (2018), p. 1070237. Id. 1070237 M. Cawley, D. Fegan, K.K. Harris et al., A high resolution imaging detector for TeV gamma-ray astronomy. Exp. Astron. 1, 173–193 (1990) C. Chen et al., Design and test of a portable Gamma-Ray Burst simulator for GECAM. Exp. Astron. 52, 45 (2021) A.A. Compagnino et al., Evaluating the night sky background directly from the signal images detected by the ASTRI telescopes. Exp. Astron. 53, 1017–1035 (2022) A. De Angelis et al., The e-ASTROGAM mission (exploring the extreme Universe with gamma rays in the MeV-GeV range). Exp. Astron. 44, 25–82 (2017) A. De Angelis et al., Science with e-astrogam. J. High Energ. Astrophys. 19, 1–106 (2018) S. Donati, Photodetectors: Devices, Circuits and Applications, 2nd edn. (Wiley, Hoboken, New Jersey, United States, 2021) R.W. Engstrom, Burle industries, in Photomultiplier Handbook (1980) C. Fiorini, Gamma detectors for spectroscopy and imaging based on scintillators coupled to semiconductor detectors, invited paper, in Proceedings of SPIE, Hard X-Ray, Gamma-Ray, and Neutron Detector Physiscs II, vol. 4141 (2000), pp. 97–110 C. Fiorini, A. Longoni, F. Perotti, C. Labanti, P. Lechner, L. Strüder, Gamma ray spectroscopy with CsI(Tl) scintillator coupled to silicon drift chamber. IEEE Trans. Nucl. Sci. 44(6), 2553 (1997) C. Fiorini, A. Longoni, P. Lechner, Single-side biasing of Silicon Drift Detectors with homogeneous light entrance window. IEEE Trans. Nucl. Sci. 47(4), 1691–1695 (2000) C. Fiorini, A. Gola, M. Zanchi, A. Longoni, P. Lechner, H. Soltau, L. Struder, Gamma-ray spectroscopy With LaBr3:Ce scintillator readout by a silicon drift detector. IEEE Trans. Nucl. Sci. 53(4), Part 2 2392–2397 (2006) C. Fiorini et al., The DRAGO gamma camera. Rev. Sci. Instrum. 81(4), 044301–044301-7 (2010). Art. no. 044301 C. Fiorini et al., The HICAM gamma camera. IEEE Trans. Nucl. Sci. 59(3), 537–544 (2012) C. Fiorini et al., Silicon drift detectors for readout of scintillators in gamma-ray spectroscopy. IEEE Trans. Nucl. Sci. 60(4), Part: 2, 2923–2933 (2013) G.J. Fishman, C.A. Meegan, T.A. Parnell et al., Burst and Transient Source Experiment (BATSE) for the Gamma Ray Observatory (GRO), in 19th International Cosmic Ray Conference (ICRC19), vol. 3 (1985), pp. 343–346 H. Fleischhack et al., AMEGO-X: MeV gamma-ray Astronomy in the Multi-messenger Era, in Proceedings of Science 37th International Cosmic Ray Conference (ICRC2021), vol. 395 (2022), p. 649. Id. 649 S. Flyckt, C. Marmonier, Photomultiplier Tubes: Principles and Applications (Philips Photonics, Brive, France, 2002) F. Frontera, E. Costa, D. Dal Fiume et al., The high energy instrument PDS on-board the BeppoSAX X–ray astronomy satellite. A & A Suppl. Ser. 122, 357–369 (1997) F. Frontera et al., Understanding the origin of the positron annihilation line and the physics of supernova explosions. Exp. Astron. 51, 1175–1202 (2021) F. Fuschino, et al., An innovative architecture for a wide band transient monitor on board the HERMES nano-satellite constellation, in SPIE Proceedings, Space Telescopes and Instrumentation 2020: Ultraviolet to Gamma Ray, vol. 11444 (2020), p. 114441S H. Gao et al., On-ground calibrations of the GRID-02 gamma-ray detector. Exp. Astron. 53, 103– 116 (2022) E. Gatti, P. Rehak, Semiconductor drift chamber – an application of a novel charge transport scheme. Nucl. Instrum. Methods A 225, 608–614 (1984) E. Gatti, P.F. Manfredi, M. Sampietro, V. Speziali, Suboptimal filtering of 1/f -noise in detector charge measurements. Nucl. Instrum. Methods 297(3), 467–478 (1990)

59 Photodetectors for Gamma-Ray Astronomy

2119

N. Gehrels et al., The swift gamma-ray burst mission. Astrophys. J. 611(2), 1005–1020 (2004) A. Goldstein et al., An ordinary short gamma-ray burst with extraordinary implications: fermiGBM detection of GRB 170817A. Astrophys. J. Lett. 848, L14 (2017) V. Golovin, V. Saveliev, Novel type of avalanche photodetector with Geiger mode operation. Nucl. Instrum. Methods Phys. Res. A 518, 560–564 (2004) J.Greiner et al., GRIPS – The potential of a future MeV survey. Il Nuovo Cimento 34, 3 (2011) E. Grove et al., Glowbug, a low-cost, high-sensitivity gamma-ray burst telescope, in Proceedings of the Yamada Conference LXXI: Gamma-Ray Bursts in the Gravitational Wave Era (2020), pp. 57–59 S. Gundacker, A. Heering, The silicon photomultiplier: fundamentals and applications of a modern solid-state photon detector. Phys. Med. Biol. 65, 17TR01 (2020) K.K. Hamamtsu Photonics, Photomultiplier Tubes: Basics and Applications, 4th edn. Hamamtsu Photonics K.K., Electron Tubes Division, Japan (2017) D.J. Herbert et al., First results of scintillator readout with silicon photomultiplier. IEEE Trans. Nucl. Sci. 53 389–394 (2006) J. Hinton, The status of the HESS project. New Astron. Rev. 48(5), 331–337 (2004). 2nd VERITAS Symposium on the Astrophysics of Extragalactic Sources N. Hirade et al., Annealing of proton radiation damages in Si-PM at room temperature. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 986, 164673 (2021) E.B. Hughes, R. Hofstadter, A. Johansson et al., Characteristics of the telescope for high energy – ray astronomy selected for definition studies on the gamma ray observatory. IEEE Trans. Nucl. Sci. 27(1), 363–369 (1980) Z. Hughes et al., Characterization of a prototype imaging calorimeter for the Advanced Particleastrophysics Telescope from an Antarctic balloon flight and CERN beam test, in Proceedings of Science 37th International Cosmic Ray Conference (ICRC2021), vol. 395 (2021), p. 137. Id. 137 M. Hui, Moon burst energetics all-sky monitor: a beyond earth-orbit gamma-ray burst detector for multi-messenger astronomy. Bull. Am. Astron. Soc. 54(3), Presentation #305.05 (2022). e-id 2022n3i305p05 C.M. Hui et al., MoonBEAM: a beyond-LEO gamma-ray burst detector for gravitational-wave astronomy, in Proceeedings of the Deep Space Gateway Concept Science Workshop, vol. 2063 (2018), p. 3060. Id. 3060 D. Impiombato et al., Characterization and performance of the ASIC (CITIROC) front-end of the ASTRI camera. Nucl. Inst. Methods Phys. Res. A 794, 185–192 (2015) D. Impiombato et al., Procedures for the relative calibration of the SiPM gain on ASTRI SST-2M camera. Exp. Astron. 43, 1–17 (2017) G.F. Knoll, Radiation Detection and Measurement, 4th edn. (Wiley, Hoboken, New Jersey, United States 2010) A. Kohnle, J. Mattes, G. Hermann et al., Photodetectors for HESS. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 442(1), 322–326 (2000) J. Kurfess, W. Johnson, R. Kinzer et al., The oriented scintillation spectrometer experiment for the gamma-ray observatory. Adv. Space Res. 3(4), 109–112 (1983) C. Labanti et al., The Ibis-Picsit detector onboard integral. Astron. Astrophys. 411, L149 (2003) C. Labanti et al., The mini-calorimeter of the AGILE satellite. Proc. SPIE 6266, 62663 (2006) C. Labanti et al., Array of X and gamma ray scintillator detector for space gamma ray telescope application, 2008 IEEE Nuclear Science Symposium Conference Record, Dresden, Germany, (2008), pp. 749–756, https://doi.org/10.1109/NSSMIC.2008.4774586 C.Labanti et al., The X/Gamma-ray Imaging Spectrometer (XGIS) on-board THESEUS: design, main characteristics, and concept of operation, in Proceedings of SPIE, SPIE Astronomical Telescopes + Instrumentation (2020) P.Lechner et al., Silicon drift detectors for high resolution room temperature X-ray spectroscopy. Nucl. Instrum. Methods A 377, 346–351 (1996)

2120

E. Bissaldi et al.

X. Li, C. Liu, Z. Chang et al., Ground-based calibration and characterization of the HE detectors for Insight-HXMT. J. High Energy Astrophys. 24, 6–14 (2019) C. Li et al., Ground electron calibration of Charged Particle Detectors onboard GECAM satellite. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 1022, 165969 (2022). Id. 165969 S. Lombardi et al., First detection of the Crab Nebula at TeV energies with a Cherenkov telescope in a dual-mirror Schwarzschild-Couder configuration: the ASTRI-Horn telescope. Astron. Astrophys. 634, A22 (2020). Id. A22 P. Lv et al., A low-energy sensitive compact gamma-ray detector based on LaBr3 and SiPM for GECAM. J. Instrum. 13, P08014 (2018) M.C. Maccarone et al., The site of the ASTRI SST-2M telescope prototype, in Proceedings of the 33th International Cosmic Ray Conference (ICRC2013) (2013). arXiv:1307.4639 W. Mahoney, J. Ling, A. Jacobson, R. Tapphorn, The HEAO 3 gamma-ray spectrometer. Nucl. Instrum. Methods 178(2), 363–381 (1980) M. Marisaldi, C. Labanti, H. Soltau, C. Fiorini, A. Longoni, F. Perotti, X- and gamma-ray detection with a silicon drift detector coupled to a CsI(Tl) scintillator operated with pulse shape discrimination technique. IEEE Trans. Nucl. Sci. 52(5), 1842–1848 (2005) I. Martinez et al., BurstCube: status and public alerts, in 37th International Cosmic Ray Conference (ICRC2021), vol. 395 (2021), p. 656. Id. 656 M.L. McConnell, M. Baring, P. Bloser et al., The LargE Area burst Polarimeter (LEAP) a NASA mission of opportunity for the ISS, in UV, X-Ray, and Gamma-Ray Space Instrumentation for Astronomy XXII, ed. by O.H. Siegmund. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 11821 (2021), p. 118210P J. McEnery et al., All-sky Medium Energy Gamma-ray Observatory: exploring the Extreme Multimessenger Universe. Bull. Am. Astron. Soc. 51(7), 245 (2019). Id. 245 C. Meegan, G. Lichti, P.N. Bhat et al., The fermi gamma-ray burst monitor. Astrophys. J. 702(1), 791–804 (2009) C. Meegan et al., The fermi gamma-ray burst monitor. Astrophys. J. 702, 791–804 (2009) F. Mele et al., The ORION Chipset for the X-Gamma Imaging Spectrometer Onboard of the THESEUS Space Mission,” 2020 IEEE Nuclear Science Symposium and Medical Imaging Conference (NSS/MIC) (2020) F. Mele, M. Gandola, G. Bertuccio, SIRIO: a high-speed cmos charge-sensitive amplifier for highenergy-resolution X-γ ray spectroscopy with semiconductor detectors. IEEE Trans. Nucl. Sci. 68(3), 379–383 (2021) R. Mirzoyan, E. Lorenz, D. Petry, C. Prosch, On the influence of afterpulsing in PMTs on the trigger threshold of multichannel light detectors in self-trigger mode. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 387(1), 74–78 (1997). New Developments in Photodetection R. Mirzoyan, D. Mueller, J. Hose et al., Evaluation of novel PMTs of worldwide best parameters for the CTA project. Nucl. Instrum. Methods Phys. Res. Section A: Accel. Spectrom. Detect. Assoc. Equip. 845, 603–606 (2017). Proceedings of the Vienna Conference on Instrumentation 2016 B.F. Mitchell et al., Strontium iodide radiation instrumentation (SIRI). Proc. SPIE 10397, 103970B (2021). Id. 103970B L. Mitchell et al., Radiation damage assessment of SensL SiPMs. Nucl. Inst. Methods Phys. Res. 988, 164798 (2021). Id. 164798 I.G. Mitrofanov, A.S. Kozyrev, D.I. Lisov et al., The mercury gamma-ray and neutron spectrometer (MGNS) onboard the mercury planetary orbiter of the bepicolombo mission: design updates and first measurements in space. Space Sci. Rev. 217(5), 67 (2021) D. Murphy et al., Proceedings of the 2nd Symposium on Space Educational Activities (SSEA 2018) (2018), pp. 201–205 D. Murphy et al., A compact instrument for gamma-ray burst detection on a CubeSat platform I. Exp. Astron. 52, 59–84 (2021)

59 Photodetectors for Gamma-Ray Astronomy

2121

D. Murphy et al., Balloon flight test of a CeBr−3 detector with silicon photomultiplier readout. Exp. Astron. 52, 1–34 (2021) D. Murphy et al., A compact instrument for gamma-ray burst detection on a CubeSat platform II. 1572 Exp. Astron. 53, 961–990 (2022) K. Nakamura, Y. Hamana, Y. Ishigami, T. Matsui, Latest bialkali photocathode with ultra high sensitivity. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 623(1), 276–278 (2010). 1st International Conference on Technology and Instrumentation in Particle Physics A. Nepomuk Otte, The upgrade of VERITAS with high efficiency photomultipliers (2011). arXiv e-prints , arXiv:1110.4702 M. Ohno et al., CAMELOT: design and performance verification of the detector concept and localization capability. Proc. SPIE 10699, 15 (2018). Id. 106992P A. Pál et al., GRBAlpha: a 1U CubeSat mission for validating timing-based gamma-ray burst localization. Proc. SPIE 11444, 9 (2020). Id. 114444V G. Pareschi et al., The dual-mirror small size telescope for the cherenkov telescope array, in Proceedings of the 33rd International Cosmic Ray Conference (ICRC 2013) (2013), p. 1151 J. Perkins et al., BurstCube: a CubeSat for gravitational wave counterparts. Proc. SPIE 11444, 114441X 9 (2020) C. Piemonte et al., Characterization of the first prototypes of silicon photo-multiplier fabricated at ITC-irst. IEEE Trans. Nucl. Sci. 54, 236–244 (2007) N. Produit, T. Bao, T. Batsch et al., Design and construction of the POLAR detector. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 877, 259–268 (2018) R. Quaglia, L. Bombelli, P. Busca, C. Fiorini, M. Occhipinti, G. Giacomini, F. Ficorella, A. Picciotto, C. Piemonte, Silicon drift detectors and CUBE preamplifiers for high-resolution X-ray spectroscopy. IEEE Trans. Nucl. Sci. 62(1), 221–227 (2015). Art. no. 7027255 A. Rashevsky, V. Bonvicini, P. Burger, S. Piano, C. Piemonte, A. Vacchi, Large area silicon drift detector for the ALICE experiment. NIMA 485(1–2), 54–60 (2002) D. Renker, E. Lorenz, Geiger mode avalanche photodiodes, history, properties and problems. Nucl. Instrum. Methods Phys. Res. A 567, 48–56 (2006) D. Renker, E. Lorenz, Advances in solid state photon detectors. J. Instrum. 4, P04004 (2009) P. Sangiorgi et al., The software architecture of the camera for the ASTRI SST-2M prototype for the Cherenkov Telescope Array, in Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), vol. 9913 (2016), p. 99133T. Id. 99133T V. Schoenfelder, H. Aarts, K. Bennett et al., Instrument description and performance of the imaging gamma-ray telescope COMPTEL aboard the compton gamma-ray observatory. Astrophys. J. Suppl. 86, 657 (1993) J. Smith et al., BurstCube: mission overview, status, and testing, AAS High Energy Astrophysics Division meeting n.19, id. 305.06. Bull. Am. Astron. Soc. 54(3), e-id 2022n3i305p06 (2022) G. Sottile et al., ASTRI SST-2M camera electronics, in Proceedings of the Society of Photo-Optical Instrumentation Engineers (SPIE), vol. 9906 (2016), p. 99063D. Id. 99063D H. Takahashi et al., Silicon photomultiplier (Si-PM) comparisons for low-energy gamma ray readouts with BGO and CsI (Tl) scintillators. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 989, 164945 (2021) M. Tavani et al., The AGILE mission. Astron. Astrophys. 502, 995 (2009) The Cherenkov Telescope Array Consortium et al., Science with the Cherenkov Telescope Array (World Scientific Book, 2019). ISBN 978-981-3270-08-4 D.B. Tridon, T. Schweizer, F. Goebel et al., The MAGIC-II gamma-ray stereoscopic telescope system. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 623(1), 437–439 (2010). 1st International Conference on Technology and Instrumentation in Particle Physics A. Ulyanov et al., Radiation damage study of SensL J-series silicon photomultipliers using 101.4 MeV protons. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. 164203, 97 (2020)

2122

E. Bissaldi et al.

J. Vandenbroucke, K. Bechtol, S. Funk et al., Development of an ASIC for dual mirror telescopes of the cherenkov telescope array (2011). arXiv e-prints , arXiv:1110.4692 G. Vedrenne, J.-P. Roques, V. Schönfelder et al., SPI: the spectrometer aboard INTEGRAL. Astron. Astrophys. 411(1), L63–L70 (2003) C. Wadhwa, High Voltage Engineering, 2nd edn. (New Age International, Delhi, India, 2007) X.I. Wang et al., GRB 210121A: a typical fireball burst detected by two small missions. ApJ 922, 237 (2021) Wavelength Electronics, Application Note AN-LD17 Rev. A, “Photodiode Basics: Selection and Operation” (2020) T. Weekes, H. Badran, S. Biller et al., VERITAS: the very energetic radiation imaging telescope array system. Astropart. Phys. 17(2), 221–243 (2002) J. Wen et al., GRID: a student project to monitor the transient gamma-ray sky in the multimessenger astronomy era. Exp. Astron. 48(1), 77–95 (2019) J. Wen et al., Compact cubesat gamma-ray detector for GRID mission. Nucl. Sci. Tech. 32, 99 (2021) N. Werner et al., Proc. SPIE 10699, 15 (2018). Id. 106992P C. Winkler et al., The INTEGRAL mission. Astron. Astrophys. 411, L1 (2003) R. Woolf et al., Glowbug, a telescope for gamma-ray bursts and other transients. Bull. Am. Astron. Soc. 54(3), Presentation #204.04 (2022). e-id 2022n3i204p04 A.G. Wright, The Photomultiplier Handbook (Oxford University Press, Oxford, United Kingdom 2017) S. Xiao et al., On-ground and on-orbit time calibrations of GECAM. MNRAS 511, 964–971 (2022) K. Yamaoka, A. Yoshida, T. Sakamoto et al., The CALET gamma-ray burst monitor (CGBM) (2013). arXiv e-prints , arXiv:1311.4084 R. Zanin et al., CTA – the World’s largest ground-based gamma-ray observatory, in Proceedings of Science – 37th International Cosmic Ray Conference (ICRC2021), vol. 395 (2021), p. 005 D.L. Zhang et al., Energy response of GECAM gamma-ray detector based on LaBr3:Ce and SiPM array. Nucl. Instrum. Methods Phys. Res. A 921, 8–13 (2019) S. Zhang et al., Overview to the hard x-ray modulation telescope (Insight-HXMT) satellite. Sci. China (Phys. Mech. Astron.) 59(1), 1–8 (2020) D.L. Zhang et al., Quality assurance test and failure analysis of SiPM arrays of GECAM satellites. Radiat. Detect. Technol. Methods 6, 35–42 (2021) X. Zheng et al., In-orbit radiation damage characterization of SiPMs in GRID-02 CubeSat detector. Nucl. Instrum. Methods Phys. Res. Sect. A: Accel. Spectrom. Detect. Assoc. Equip. (2022), Submitted to. arXiv:2205.10506v1

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Denis Bernard, Stanley D. Hunter, and Toru Tanimori

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Charged Particles Production and Transport in a Medium . . . . . . . . . . . . . . . . . . . . . . . . . . . Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Drift, Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Negative Ion Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic Field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Absolute Time Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electron-Tracking Compton Camera with Gaseous Time-Projection Chamber . . . . . . . . . . How to Realize Complete Bijection Imaging for MeV Gamma Rays . . . . . . . . . . . . . . . . Background Rejection in ETCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Estimation of Sensitivity of ETCC in MeV Gamma Astronomy . . . . . . . . . . . . . . . . . . . . How to Obtain a Good PSF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Development of ETCC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SMILE-2+ Balloon Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Analysis for Background Reduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . TPCs as Pair Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polarimetry with Pair Conversions and Multiple Scattering . . . . . . . . . . . . . . . . . . . . . . . . Past Experimental Achievements and Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . .

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D. Bernard () LLR, Ecole polytechnique, CNRS/IN2P3 and Institut Polytechnique de Paris, Palaiseau, France e-mail: [email protected] S. D. Hunter NASA/Goddard Space Flight Center, Greenbelt, MD, USA e-mail: [email protected] T. Tanimori Graduate School of Science Kyoto University, Kyoto, Japan e-mail: [email protected]; [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_50

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HARPO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AdEPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid or Solid TPCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effective Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Angular Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sensitivity: Gas Choice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dense Phase TPCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LXeGRIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Liquid TPCs as High-Resolution Homogeneous Calorimeters . . . . . . . . . . . . . . . . . . . . . Summary/Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

The detection of photons with energies greater than a few tenths of an MeV, interacting via Compton scattering and/or pair production, faces a number of difficulties. The reconstruction of single-scatter Compton events can only determine the direction of the incoming photon to a cone, or an arc thereof, and the angular resolution of pair-conversion telescopes is badly degraded at low energies. Both of these difficulties are partially overcome if the density of the interaction medium is low. Also no precise polarization measurement on a cosmic source has been obtained in that energy range to date. We present the potential of low-density high-precision homogeneous active targets, such as time-projection chambers (TPC) to provide an unambiguous photon direction measurement for Compton events, an angular resolution down to the kinematic limit for pair events, and the polarimetry of linearly polarized radiation. Keywords

Gas time-projection chamber (TPC) · Compton scattering · Pair conversion · Point spread function · Micropattern gas detector (MPGD) · Electron-tracking Compton camera (ETCC) · Polarization

Introduction Gamma-ray astronomy proceeds by the analysis of the conversion of individual photons with an atom of a telescope, either • the Compton scattering on an electron, γ e− → γ e− , in the approximate energy range 1 keV < E < 100 MeV, or • by the creation of an e+ e− pair (γ Z → e+ e− Z “nuclear” conversion, above a threshold E > 2mc2 ; γ e− → e+ e− e− “triplet” conversion, E > 4mc2 ), where m is the electron mass.

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At lower energies, X-rays are detected via their photo-electric interaction with matter, see Volume 1 of this handbook. A number of detector techniques have been developed (see the ⊲ Chap. 47, “Telescope Concepts in Gamma-Ray Astronomy” in Vol. 2, Sect. IV), among which some use a homogeneous active target, that is, a device in which the photon converts and the trajectory of the charged particle(s) in the final state (electron and/or positron) are measured, that consists of an homogeneous medium. Among these, a TPC (time projection chamber) (Marx and Nygren 1978) is a device in which a chunk of matter is immersed in an electric field; charged particles ionize the atoms/molecules on their way through the detector, after which the produced electrons and positive ions drift in the electric field toward an anode and a cathode, respectively, where their arrival creates an electric signal that can be measured. The collecting anode can be segmented in a two-dimensional (2D) series of pads, or in a two-fold set of strips, something which provides a 2D image of the flow of electrons that are “falling” on the anode at a particular time. The measurement of the drift duration provides the third coordinate: the collection and the analysis of these images as a function of time provides a full, 3D, picture of the charged particles in the final state for the particular event of the conversion of the photon. For gases, the amount of charge produced by ionization is small, typically tens to hundreds of electrons per (cm · bar), so an amplification in the gas is needed, that was performed with multi-wire proportional chambers (MWPC), that have later been replaced by micropattern gas detectors (MPGD) such as micromegas (Giomataris et al. 1996), gas electron multiplier (GEM) (Sauli 1997b), or micropixels (Ochi et al. 2000). For two-track final states, in the case of a two-fold series of strips, reconstructing the full 3D image of the event requires solving a two-fold ambiguity (i.e., the matching of either of two tracks in the (x, t) plane to either of two tracks in the (y, t) plane) something that is made easy (Fig. 11 of Bernard et al. 2014) by the violent variation of the energy deposited along the track, the distribution of which presents a large tail at high values (the Landau distribution). The ambiguity can also be solved with a threefold series of strips, for example, at 120◦ of each-other, in a configuration known as (x, u, v). In contrast with MWPCs for which the wire pitch is limited to values larger than a couple of millimeters, the collecting structure of MPGDs can be much smaller, enabling spatial resolutions down to 50 µm (Thers et al. 2001). In addition to measuring precisely the geometry of the conversion, TPCs can also provide precise measurements of the energy deposition in the gas, something which is key to high-precision Compton scattering, and of the energy deposition per unit length, dE/dx, which enables the rejection of z > 1 cosmic-ray ions, as dE/dx is proportional to z2 (Eq. (34.5) of Zyla et al. 2020). The TPC concept proves to be particularly powerful for the polarimetry of the incoming radiation, see the chapter ⊲ Chap. 24, “Time-Projection Chamber X-ray Polarimeters” in Sec. II of Vol. 1 (X-rays) and chapter “Design of Gamma-Ray Polarimeters” in Sec. IV of Vol. 2. Reviews on TPCs can be found in Sec. 35.6.5 (gas TPCs) and in

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Sec. 36.4 (liquid TPCs) of Zyla et al. (2020) and in Hilke (2010) and Fujii (2014). The transport of electric charges in matter, drift detectors, and their use is described in Sauli (1977a, 2014) and Blum and Rolandi (2008), the simulation of gas detectors can be performed by the Garfield++ software package (Veenhof 1998), and the RD51 Collaboration (RD51 2008) is coordinating the efforts of the community to develop gas detector technologies. Various configurations have been developed to meet various needs, such as “cartesian” TPCs (uniform electric field, e.g., Atwood et al. 1991), “radial” TPCs (e.g., Obertelli et al. 2014), and “spherical” TPCs (e.g., Giomataris et al. 2008). TPCs are mainly used as inexpensive (in terms of the number of electronics channels) hyper-high-granularity trackers for low (Hz to kHz) rate experiments, due to the duration of the drift (microseconds for the electrons to milliseconds for the ions), as most users wish to avoid event pile-up. The TPC itself, though, can cope easily with much higher rates (e.g., a p annihilation rate of 20 MHz (Fabbietti et al. 2011; Ball et al. 2012)), as long as the electric charge of the ion back-flow does not disturb the electric field, in which case gating the amplification device is advised (Nemethy et al. 1983). The complexity load is then transferred to the eventreconstruction software (see Fig. 13 of Rauch 2012). It should be noted that most of the positive ions are created in the amplification volume of the MPGD and that in the case of the micromegas and of the GEM, a large fraction of them is collected by the grid, and therefore does not escape to the drift volume, something that limits the induced nuisance. An important limitation of TPCs in their use for high-energy physics (HEP) is their reliance on the information provided by other sub-detectors to build a trigger and in particular to define the start time of the drift. Difficulties in obtaining a sufficiently large background noise rejection factor can induce data acquisition (Daq) dead time and lead to a severe reduced trigger efficiency, as observed, for example, during the balloon test flight of the Liquid Xenon Gamma-Ray Imaging Telescope (LXeGRIT) TPC prototype (Curioni et al. 2007). For a stand-alone TPC in space, a trigger-less, continuous, autonomous mode (Rauch 2012; Hunter et al. 2014) can be considered. Dielectric gases that allow the free drift of injected electric charges, such as noble gases or alkanes, can be used that have negligible electron attenuation over drift lengths of several meters. As electro-negative impurities in the gas can trap drifting electrons, maintaining a good gas purity on the long term is important. For example, the degradation of the gas in the EGRET spark chambers required regular gas changes and caused the instrument to be operated only intermittently in the later part of the Compton Gamma Ray Observatory mission (Esposito et al. 1999). Actually the dose rate of ionizing radiation that is inducing the production of these deleterious chemical species is much lower in orbit than in detectors on HEP experiments, and spark chambers are well known to be very powerful quencher polymerizing devices. Using the HARPO TPC prototype that includes a number of elements that are potentially harmful to the gas purity (PVC, epoxy, etc.), continuous, perfectly stable operation was demonstrated for over 6 months just filtering out the oxygen contamination (Frotin et al. 2018). The test of a TPC prototype designed using

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high-vacuum technology for the Gravity and Extreme Magnetism Small Explorer (GEMS) X-ray Polarimeter Instrument (XPI) demonstrated a gas-fill estimated lifetime larger than 23 years (Hill et al. 2013); they estimated the integrated charge expected on a space mission to be of the order 10−3 mC/mm2 (Hill et al. 2013). This can be compared to the performance of micromegas and GEM devices for LHC detectors that can stand >20 mC/mm2 (which corresponds to >6. 1011 MIP/mm2 ) without degradation (Titov 2004), though with flushing some amount of fresh gas. A gas purifier system for the close-loop operation of resistive plate chambers (RPC) at the LHC, with high recirculation fractions, has shown stable operation up to an integrated charge of 0.5 mC/mm2 (Capeans et al. 2013). Alkanes can be replaced by CO2 to alleviate the polymerization issue. In that case, at extreme irradiation doses, the next contaminant of concern is found to be silicone, in particular from pump-oil outgassing (see, e.g., Zimmermann and Cernoch 2004). Despite the huge body of knowledge accumulated on aging of detectors exposed to extreme irradiation doses (but with some amount of fresh gas flushing), or sealed detectors in operation for an extended duration (but without an irradiation dose rate commensurate with that on a space mission), it is fair to state that a smooth decade-long operation of a sealed (possibly with recirculation and filtering) proportional gas detector exposed to an appropriate level of ionizing radiation is still to be demonstrated. MPGDs are prone to sparking, especially when exposed to a charged-particle beam, with a rate that increases with the applied amplification voltage. The limiting mechanism was understood after it was observed that the spark production rate is much larger from a pion beam than from a muon beam of similar energy and intensity (Thers et al. 2001): hadrons can undergo hadronic interactions with the atoms of the detectors, after which a nuclear fragment can deposit a huge amount of energy in a very small volume at the end of its trajectory, due to the 1/β 2 variation of dE/dx (the Bragg peak) (Zyla et al. 2020). The phenomenon is particularly prevalent for micromegas, for which the transverse size of the avalanche is small, of the order of 5–10 µm, and/or when a magnetic field is applied, that clamps the transverse diffusion of the drifting electrons. The problem is now routinely solved using an additional resistive layer (Alexopoulos et al. 2011).

Charged Particles Production and Transport in a Medium Ionization The average energy lost by a charged particle traversing a piece of matter is described by the Bethe equation (eq. (33.5) of Zyla et al. 2020) that shows a sharp rise proportional to 1/β 2 at low energies, a minimum at about γβ = 3, and a slow rise at higher energies (β is the particle velocity normalized to that of light and γ is its Lorentz factor). The specific loss rate at the minimum (MIP, minimum ionizing particle) is proportional to (z2 Z)/(Aβ 2 ) and is therefore approximately independent of the nature of the gas, at (1/ρ)dE/dx ≈ 2 MeVg−1 cm2 , where ρ, Z, and A are

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the density, the atomic number, and the mass number of the target (Tab. 6.1 of Zyla et al. 2020), and z is the electric charge of the particle normalized to the charge of an electron. Part of the interactions results in the ionization of the atoms, with an effective energy lost per produced electron of 20 to 40 eV (Tab. 1 of Sauli 1977a).

Drift, Diffusion As the ionization electrons drift in the electric field of the TPC, they undergo elastic collisions with the atoms and molecules of the gas, a process by which they lose some of their kinetic energy and by which they are deflected. Between two collisions, the electrons are accelerated in the field and follow a ballistic trajectory. At low electric fields, the resulting average drift velocity, v, is proportional to the electric field, E, with typical values of the mobility µ ≡ v/E of µp = (0.5 − 2) cm2 bar V−1 s−1 for most positive ions (Tab. 4 of Sauli 1977a), and µp = (0.5 − 2) 104 cm2 bar V−1 s−1 for electrons, where p is the gas pressure. On average, the deflections result in an isotropic, Gaussian-distributed spread of the distribution of the electron position that√is named diffusion, with an RMS along any of the three directions of space σ = 2Dt with L = vt, where t and L are the duration and the length of the drift and D is the diffusion coefficient (Sauli 1977a): 

2kT L . (1) eE √ The spread can also be expressed as σ = dL where d = 2kT /(eE): the lowfield RMS spread is independent on the material used; at a given temperature, the only way to decrease σ is to increase the electric field. At high electric fields, the rise of the electron drift velocity with the electric field saturates, the electron velocity distribution is characterized by a temperature that is larger than the ambient, and the diffusion process becomes anisotropic, with a diffusion coefficient in the transverse plane DT and in the longitudinal direction DL that differ increasingly √ at higher field. In pure argon, for example, the spread would amount to 0.11 cm/ cm √ at E/p = 1 kV/(cm · bar) while the thermal limit at 300 K at that field is 80 µm/ cm. Therefore a (usually small) fraction of multi-atomic (means here >2 atoms) molecular gas is added. These molecules have vibration and rotation degrees of freedom that enlarge the cross section of inelastic interactions from fast electrons, something which “cools” the electron bunch, and also they have absorption bands that mitigate the potentially catastrophic discharges induced by photo-electric effect on the detector cathode by impacts of avalanche-created UV photons – hence their appellation of “quenchers.” Most gas TPCs use a mixture based on a large fraction of a noble gas together with a multi-atom molecular quencher (e.g., an alkane). These “fast gases” allow at σ =

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the same time a high electron drift velocity of several cm/µs and a small diffusion coefficient. For argon-isobutane mixtures, for example, the transverse coefficient √ dT plateaus above E/p ≈ 50 V/(cm · bar) at a value that is√ proportional to 1/ pr , where pr is the quencher partial pressure (e.g., 170 µm/ cm for a 4-bar 90:10 mix). In these conditions, the longitudinal coefficient dL is a smoothly decreasing function of E, with little √ dependence on the quencher fraction and gas pressure, and amounts to 180 µm/ cm for 4-bar 90:10 at E = 500 V/cm). It should be noted that some amount of diffusion, with a spread commensurate with the pitch size of the signal collection segmentation, enables the optimization of the spatial resolution of individual measurements (Fig., 7 of Arogancia et al. 2009). Charge amplification can be easily performed in these gases with gains of several 104 (Attié 2009; Veenhof 2010) in current MPGD structures such as a multilayer GEM (Sauli 1997b) or a micromegas (Giomataris et al. 1996).

Negative Ion Technique Another option to reduce the diffusion of a TPC is to add a mildly electronegative component to the TPC gas. This is referred to as the negative ion (NI) technique, developed for TPC dark matter searches, which originally used carbon disulfide (CS2 ) (Martoff et al. 2000, 2005). Subsequently, nitromethane (CH3 NO2 ) was also used (Martoff et al. 2009). The NI technique has been used in several different applications (Snowden-Ifft et al. 2003; Son et al. 2010). In the gas of a negative ion TPC (NI TPC), the NI component scavenges the free, ionization, electrons, within ≈100 µm of their point of origin, to form negative ions, which then drift in the TPC gas. Compared to the electrons, which drift at super-thermal speed, the negative ions, being much more massive, remain in thermal equilibrium with the gas molecules and drift at the thermal velocity of the gas. Consequently, the diffusion of the NIs is reduced to the thermal diffusion limit, see Figure 6 in Dion et al. (2011). The NI √ technique reduces the diffusion coefficient to the thermal limit of d = 80 µm/ cm, but at the cost of a much lower drift velocity v = 2 cm/ms (Hunter 2018). This velocity is three to four orders of magnitude smaller than for electrons in a typical fast TPC gas (Peisert and Sauli 1984). This slow velocity can make the detector more susceptible to background pile-up. However, the high granularity of a TPC and the reduced diffusion and slow drift velocity allow image processing techniques to be employed to differentiate the high-energy photons interacting to produce electron pairs from the Compton low-energy recoil electrons produced by sub-MeV photons and cosmic ray tracks. Software techniques have been explored to address this problem (Garnett et al. 2021). Application of the negative ion technique to the Advanced Energetic Pair Telescope, and software solutions to deal with the slow drift velocity, is discussed in section “Past Experimental Achievements and Future Prospects”.

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Energy Measurements Gas TPCs are thin detectors from which high-energy electrons escape (1 MeV electrons have an 0.5 − 0.7 g/cm2 range in most gases (Berger et al. 2010a), e.g., 3.6 m in 1-bar argon). Also, the measurement of the track momentum by the analysis of the multiple deflections induced by multiple scattering in the detector, which is a powerful method for denser detectors, is too imprecise for gas TPCs (Frosini and Bernard 2017). So it is difficult to measure the energy of the leptons, and therefore of the candidate photon, from the TPC alone. Either the TPC can be immersed in a magnetic field, to become a high-precision magnetic spectrometer, or the TPC can be complemented with an additional detector that either measures the momentum of the track(s), such as a transition-radiation detector (TRD) (Wakely et al. 2004) or the total energy of the final state, such as a calorimeter.

Magnetic Field Most gamma-ray telescopes on space missions do not include a magnetic spectrometer. The AMS experiment on the ISS does (Bourquin 2005), however, and has a sensitivity to gamma rays (Beischer 2020). The presence of a magnetic field has important consequences on the performances of the detector; • In the first place, the curvature enables a measurement of track momenta; • Also, low-momentum electrons are clamped to spiral and deposit their energy in a small volume, something that can help the trigger system survive the large Compton-induced single-track background; • Spiraling electrons might be an issue though, for the correct tracking of lowenergy electrons in a Compton camera; • The transverse diffusion of the drifting electrons is greatly reduced, as the ballistic flight between collisions is along spiraling helices instead of parabolas. • Last but not least, at very high electron momenta where multiple scattering can be neglected, in the presence of a non-zero magnetic field, B, the track fit includes a track curvature while for B = 0 a straight line is fitted. The non-zero correlation between the curvature and the angle of the track at vertex induces a degradation of the single-track angle resolution of a factor of 4 with respect to the fit that assumes B = 0 (compare, e.g., eqs. (5) and (9) of Regler and Fruhwirth 2008).

Absolute Time Measurement The ability to measure precisely the absolute time of a gamma-ray conversion can be of interest, for example, for pulsars or for transients. MPGD are fast devices that enable event-time measurements with a precision of a couple of nanoseconds with a suitable electronics for tracks that are crossing them. This could allow building a

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trigger from a telescope consisting of a 3D set of individual TPC modules (Bernard et al. 2014), by forming multi-module coincidences. For events for which the track(s) exit(s) by the side of the TPC without crossing the amplification structure, the degenerescence between the start time and the vertical position of the event in the TPC fundamental relation, z = v(t − t0 ), makes it difficult to determine separately the vertex vertical position and the conversion time. In these cases, the variation with drift time of the track width due to diffusioninduced spread enables a measurement (Antochi et al. 2021), though with a much degraded resolution.

Electron-Tracking Compton Camera with Gaseous Time-Projection Chamber The simplest Compton telescopes are based on the analysis of one-scatter events, γ e− → γ e− , after which the scattered photon propagates in the detector until it is absorbed: the position and the energy of the scattered electron and photon are measured, and the properties of the incident photon are inferred from this information. With that method, the direction of the incident photon is found to lie on a cone, something which makes the analysis of an extended field of view containing several sources complicated. In more elaborate telescopes, the direction of propagation of the recoiling electron is tracked, so that the cone is reduced to an arc, something that simplifies the image analysis (Fig. 1 left). The present section addresses the extreme case for which the tracking of the electron is so precise that the analyst can use a bijection between the measured observables for a given Compton scatter event and the direction of the incoming photon (one-to-one mapping, Fig. 1 right), in a scheme that is named ETCC

Fig. 1 Images of a point source with a Compton camera (CC, left) and with an electron-tracking Compton camera (ETCC, right). (Adapted from Tanimori 2020)

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(electron-tracking Compton camera) (Tanimori et al. 2004, 2015, 2017). We will see that a low-density high-precision active target, such as a gas TPC, is well suited for that purpose.

How to Realize Complete Bijection Imaging for MeV Gamma Rays In astronomical imaging, the intensity of each point in the image is independent, and linearity is preserved, as shown in Fig. 2. This is the minimum requirement for maintaining quantitativeness in image analysis in general. Quantitative imaging is an essential technology, e.g., in radio and X-rays, because the electromagnetic waves can generally be refracted and reflected, as well as simply focused according to optical principles using a reflector and a lens. As shown in Fig. 3, reflectors and lenses make a bijection to each point on the image surface while preserving the intensity of rays in each direction at a size larger than the point spread function (PSF). Therefore, the intensity of each point separated from the PSF of the image is guaranteed to be linear, and the intensity can be accurately measured. The PSF is

Fig. 2 Explanation of the linear imaging system, which is essential for quantitative imaging analysis

Fig. 3 Schematic of the bijection image and PSF

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defined as the minimum angular distance that guarantees linearity. Here, we use a half-power angular radius (degrees) as the PSF. The linear optical system is shown in Fig. 2. However, gamma rays have strong quantum properties, and refraction/reflection cannot be used. Therefore, the only way to determine the direction of the incident gamma ray is to solve the kinematics of Compton scattering for each gamma ray. This was attempted using a CC, starting in the 1970s. However, because the CC solves the equation of motion of Compton scattering incompletely owing to the lack of the direction of the recoil electron, only the elevation angle in the arrival direction can be obtained, as shown in Fig. 4. Therefore, the gamma-ray direction is given only as an annulus. The gamma-ray distribution is estimated by superimposing this annulus on the image. The annulus spreads over the entire field of view (FoV) to several tens of degrees or more, making it difficult to define the PSF, and the information at each point on the image is strongly mixed and influenced, as shown in Fig. 5, where bijection cannot be satisfied by a CC. Thus, the CC lacks nearly half the information and loses quantification, which is the essence of image analysis. Sometimes, the CC employs the “effective PSF” using only the angular resolution of the zenith angle obtained by the CC, which is identical to the proper twodimensional (2D) PSF (Schoenfelder et al. 1993). However, gamma rays within the “effective PSF” are surely and strongly influenced by the large flux of gamma rays outside of it and are never separated from background gamma rays coming outside the effective PSF, whereas telescopes for other wave bands having a proper PSF easily separate gamma rays within and outside the PSF. Thus, the CC is certainly a nonlinear optical point system, but all other telescopes, including the ETCC, are linear systems. In particular, considering the large radiation background from the

Fig. 4 Schematic of the Compton scattering kinematics. The parameters θ and ϕ represent the Compton-scattering angle and electron-azimuthal angles of the incident gamma ray, respectively, on the Compton coordinates. (right) Schematic explanation of the PSF(Θ) of the CC and ETCC. See the text for the definition of Θ

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Fig. 5 Schematic of the nonlinear system of the CC and the linear one of the ETCC. The observed spectra for each target point clearly indicate that the CC cannot perform imaging spectroscopy

satellite and instruments due to collision with cosmic rays, as mentioned in the next section, a rigid quantitative imaging system is needed to remove this background. To overcome this problem, it is necessary to completely solve the kinematics of Compton scattering, which can be achieved by measuring the direction of the recoil electron. As shown in Fig. 1, the ETCC focuses MeV gamma rays emitted from the point source to one point, similar to optical telescopes. Only the determination of both the angles of incident gamma rays surely enables selection of the gamma rays in the FoV from background gamma rays coming from the outside with the resolution of the PSF and to estimate the leakage of the background from the outside of the FoV, as shown in Fig. 5 (Tanimori et al. 2015, 2017). Additionally, such a proper PSF gives us the ON region, as well as the interested region and OFF regions, which are hardly affected by the ON region in the same FoV. The background-subtracted signal is obtained using the ON-OFF method, as shown in Fig. 6 (Tanimori et al. 2015). Thus, the precise definitions of the FoV and background regions make it possible to quantitatively evaluate the detection of the signal. These methods and concepts are essential and common in all fields of astronomy and science using imaging analysis. Furthermore, the intensity

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Fig. 6 Image of the 137 Cs source at the off-axis with a polar angle of 20◦ measured by SMILEII. Red and black circles, each having a radius of 15◦ , indicate source and background regions, respectively. (right) The spectrum after air-scattered gamma rays within the PSF are removed, by using the region symmetric about the center of the FoV (black circle) as the background region. (Adapted from Tanimori et al. 2017)

independence of each point above the PSF in the image ensures that the spectrum of each point comes from that location, as shown schematically in Fig. 5, which is called imaging spectroscopy (Tanimori et al. 2015). As explained previously, most universal imaging analysis methods are based on a clear definition of the PSF, and a sharper PSF provides better quantities from imaging analyses in general.

Background Rejection in ETCC Another serious problem is the large radiation background in space. Although gamma backgrounds coming outside the FoV are significantly reduced by the linear imaging system, other types of backgrounds, such as neutrons, missing charged cosmic rays, accidental events, and misreconstructed events, are difficult to remove completely via this method. In the reconstruction method in particle physics, additional physical parameters that are not used to solve the kinematics are usually needed to suppress such a background. In MeV gamma-ray telescopes using the reconstruction of Compton scattering, residual physical parameters are considered necessary (Tanimori et al. 2017). We have good examples. COMPTEL successfully opened MeV gamma-ray astronomy by detecting approximately 30 celestial objects using a CC (Schoenfelder et al. 1993; Schoenfelder 2000), although the actual sensitivity was degraded by 25% compared with that expected before launching (Schönfelder 2004). According to the experience of SMILE-2+, this success is mainly attributed not to the imaging of the CC method but to the efficient background rejection based on the time of flight (ToF), the pulse analysis of the forward liquid scintillator, the reduction of the FoV (limited to 30◦ ), and the adoption of a light material as a scatterer of the forward detector (FD). In principle, the CC cannot distinguish correctly reconstructed Compton scattering events (signal) from misreconstructed background events, owing to the incompleteness of the

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event reconstruction. COMPTEL adopted several tools to reduce the background; in particular, the ToF was effective for removing most of the background coming from the downward direction, which accounted for approximately 90% of the total background (Schönfelder 2004). Additionally, the pulse-shape analysis provided a good reduction of the neutron background, and the adoption of a light material was effective for reducing the accidental background to reduce the single hit counts in the FD. The narrow FoV was effective for reducing the large background coming from outside the FoV, although it also reduced the detection area. COMPTEL appears to be able to reduce the background by more than one order of magnitude and thus detect the celestial objects. However, there remains a large background exceeding that of cosmic diffuse MeV gamma rays by approximately one order of magnitude, as shown in Fig. 2 of Kappadath et al. (1996). Thus, the study of COMPTEL indicates that additional parameters, except for those needed to solve the kinematics of Compton scattering, must be employed in MeV gamma-ray telescopes. The measurement of the track of the recoil electron provides additional parameters such as the energy loss rate (dE/dx) of the particle track (Figs. 7 and 19), the scattering angle α between the recoil electron and the scattered gamma rays in Compton scattering (Figs. 1 and 4), and the event topology, as shown in Fig. 8 (Tanimori et al. 2015, 2017). The correlation between dE/dx and the energy of the tracks is useful for particle identification, enabling to distinguish recoil electrons from cosmic rays, high-energy electrons, and neutrons. The angle α can be determined using the kinetic form of the kinematic equation and from the measurements of the directions of the recoil electrons and scattered gamma rays. Then, the two angles can be compared to determine whether the gamma direction calculated via the kinematical equation is correct or false, which is referred to as the kinematic test. Furthermore, an event topology enables easy determination of

Fig. 7 Observed and simulated scatter plots of track energy and its length in SMILE-II. The ratio is dE/dx, and Compton recoil electron is clearly identified from background events. (Adapted from Tanimori et al. 2015)

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Fig. 8 Event topologies observed by the SMILE-2+ TPC during the balloon ascent in 2018. (Adapted from Tanimori 2020)

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Fig. 9 Schematic explanation of background reduction by the PSF. (right) Energy spectra of a super-weak point source (27 kBq 22 Na) at a distance of 5.5 m. (b) Image observed by the SMILEII ETCC with 7.1σ . (Adapted from Tanimori et al. 2015)

whether the measured event is due to Compton events caused by gamma rays by requiring only one fully contained track in the tracking instrument, as shown in Fig. 8. From the results of the ground experiments (Fig. 9) and two balloon experiments, dE/dx and the event topology were confirmed to be more efficient than the ToF in COMPTEL without the loss of the true signal events (Takada et al. 2011). The combination of the two reduced the background by more than two orders of magnitude at an altitude of >35 km to maintain a wide FoV of >3 sr. To realize the aforementioned requirements for almost all recoil electrons ranging from a few kiloelectronvolts (keV) to several MeV, an ideal three-dimensional (3D) tracking device such as a cloud chamber that provides a fine image of betadecay electrons is necessary. A gaseous TPC enables the measurement of the 3D image of such a fine track of the above energy region electrically by using a micropattern gas detector (MPGD), as shown in Fig. 10 (Tanimori et al. 2004), where the 3D position of the track can be measured with a sub-mm pitch. Herein, such a TPC is referred to as a µTPC. Because a 10-keV electron track runs along

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Fig. 10 Schematic of the µPIC and the operating principle of the TPC using µPIC

5 mm in 1 atm Ar gas, >10 points in one track can be measured, whose pitch is similar to the diffusion of the drift electron passing through a distance of a few tens of centimeters in the µTPC.

Estimation of Sensitivity of ETCC in MeV Gamma Astronomy For celestial objects, the sensitivity of telescopes is generally calculated by knowing the effective area, proper PSF, and background flux (Tanimori et al. 2015). The background comprises the flux of cosmic diffuse gamma rays (CDG), which has a celestial origin and is the minimum background that is never removed; albedo gamma rays from the atmosphere; and instrumental radiation generated by cosmic rays. First, let us consider the minimum effective area and worst PSF to reach a sensitivity of 1 mCrab during the observation time of 106 s for the ideal case in which all background except CDG could be removed. For a PSF of a few degrees, a relatively small effective area of a few 100 cm2 is needed because the typical fluxes of celestial gamma rays in the MeV region are three orders of magnitude stronger than those in the GeV region. If the PSF was 1 MeV provide a good sub-degree SPD (Scatter Plane Deviation) for gamma rays above a few MeV, as shown in Fig. 14, while the ARM is saturated to a few degrees above a few MeV (Mizumura et al. 2017).

How to Obtain a Good PSF The PSF is the most significant factor for attaining a good sensitivity. In Compton scattering, the PSF is determined equivalently by the two angular resolutions of the

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Fig. 14 Energy dependence of angular resolution-related parameters. Red and blue lines indicate the ARM and SPD, respectively. The PSF is indicated by a black thick line; assuming a point source, the PSF is improved by weighting the SPD, as indicated by the thick green line. (Adapted from Mizumura et al. 2017)

Fig. 15 Cumulative ratios of events within a radius of θ (50% corresponds to the PSF). (Adapted from Tanimori et al. 2015)

elevation and azimuth in general, as shown in Figs. 14 and 15. The former is the ARM, and the other is a function of the SPD (Tanimori et al. 2015, 2017). To obtain a good PSF, the two angular resolutions must be similar. The ARM depends on the energy resolution of the telescope, and as the Compton scattering angle increases, the ARM becomes worse. Although the theoretical ARM of the forward scattering region is better (by a few degrees) than those in larger scattering regions, the ARM is degraded by geometrical errors owing to the position resolutions of the scatterer and absorbers and systematic errors of the instrument structure. Because the position resolutions of semiconductors or gaseous TPCs are sub-mm, the real ARM depends on the distance between the hit points of the scatterers and absorbers, which is the instrument size. For COSI with Ge (Kierans et al. 2020) and SDGs (Soft Gamma Ray Detector) on Hitomi satellite with cooling Si and CdTe (Watanabe et al. 2014), an ARM of 6◦

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Fig. 16 Relationship of the multiple scattering (SPD) of a recoil electron and the length of tracking in 3-atm CF4 and Ar gases for several energies of recoil electrons. (Adapted from Tanimori et al. 2015)

at 511 and 662 keV were reported, respectively, with energy resolutions of 104 in MPGDs, which are mostly operated with a gain of 2. Operations with CF4 is planned, so as to attain an effective area of 10 cm2 for a (30 cm)3 cubic TPC. The energy resolution of the ETCC with GSO scintillators using a photomultiplier tube was 11% (FWHM) at 662 keV. New PSAs with GSO + SiPM and GAGG + SiPM can yield 8% and 5% (FWHM) at 662 keV, respectively. In 2004, for the first time the successful full electron tracking in a laboratory experiment with a small (10 cm)3 cubic ETCC was reported (Tanimori et al. 2004; Takada et al. 2005). Then the “Sub-MeV gamma ray Imaging Loaded-on-balloon Experiment” (SMILE) project was conducted with the improved (10 cm)3 cubic ETCC (SMILE-I in Fig. 17) to measure the diffuse cosmic MeV gamma rays via a balloon-borne experiment in 2006 (Takada et al. 2011). An excellent particleidentification ability according to the dE/dx of an electron track in the gas was demonstrated as shown in Fig. 18, from which the background level was reduced by a factor of ∼3.

Fig. 17 Photographs of SMILE-I, SMILE-II, and SMILE-2+

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A (30 cm)3 cubic ETCC (Figs. 1 and 17) was then developed to achieve an effective area of 1 cm2 at 300 keV (Fig. 13) for the detection of celestial MeV-gamma-ray objects such as the Crab with a balloon experiment in the Northern Hemisphere (SMILE-II) (Tanimori et al. 2015). In this ETCC, the tracking efficiency in the TPC is improved significantly (from 10% to 100%) compared to SMILE-I owing to the improved readout electronics and algorithm. This provides better noise reduction of dE/dx and good angular resolutions of 5.9◦ (FWHM) at 662 keV, which is consistent with that calculated using the detector energy resolution (Mizumoto et al. 2015). For the ETCC, obtaining the direction of the recoil electron is crucial. In the µPIC of the TPC, orthogonal strips of the X and Y coordinates were used to significantly reduce the number of readout channels from the pixel readout. However, this readout method causes a well-known left-right uncertainty in tracking multiple hits simultaneously as shown in Fig. 19 (Tanimori et al. 2015), which

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degrades the SPD considerably to 200◦ (FWHM) with SMILE-I. In the new readout electronics of SMILE-II, the pulse width of each electrode in the µPIC is recorded as the timing width over the threshold (TOT) (Mizumoto et al. 2015), which provides a coarse charge deposit at each hit point. In 2015, using the TOT, the coincidence width between the X and Y strips could be reduced from 10 to ∼1 ns and the SPD improved to ∼100◦ (FWHM), thus reducing the uncertainty in tracking (Tanimori et al. 2015). Consequently, a half-power radius of 25◦ for the PSF at 662 keV was obtained (Tanimori et al. 2015).

SMILE-2+ Balloon Experiment SMILE-2+ was improved from SMILE-II for a sufficient sensitivity estimated according to the PSF for the Galactic Center (GC) diffuse gamma-ray flux (Tanimori 2020; Takada et al. 2022). SMILE-II was the first (30 cm)3 cubic ETCC with 1atm Ar gas, and PSAs were set outside the gas vessel of the TPC. SMILE-II was designed to use the ARM as a PSF for detecting Crab with >3σ via several hours of observation in the Northern Hemisphere (Tanimori et al. 2015). However, given the importance of the proper PSF for the estimation of sensitivity (Tanimori et al. 2017), SMILE-II was redesigned to SMILE-2+ to realize the same sensitivity as that expected for SMILE-II, taking into account that the flux of Crab is reduced by half owing to the smaller zenith angle of 45◦ in the southern-sky observation (Takada et al. 2022). The effective area of SMILE-2+ was increased three times at 511 keV and several times above 1 MeV with Ar gas at 2 atm and the use of a GSO of double thickness in the bottom pixel scintillation arrays (PSAs). Additionally, because a fully contained electron in the TPC restricts the energy range of gamma-rays to 3 sr) for the entire southern sky during the JAXA balloon launching at Alice Springs of Australia on April 7–8, 2018 (Takada et al. 2022). The balloon was successfully flown at an altitude of 37–39 km for 30 h, and the southern sky was observed, including the GC, half of the galactic disk, Crab, Cen-A, and the Sun.

Analysis for Background Reduction 4 × 107 triggered events were recorded and finally reduced to 105 events (by more than two orders of magnitude) with the requests of the fully contained and good dE/dx for the recoil electron in the TPC. Here, the clear event topology enabled the efficient identification of Compton scattering. The number of final events is consistent with that estimated from the SMILE-I results, indicating a signal-tobackground ratio of >1. This is clearly confirmed by the obvious enhancements of the detected gamma flux at ∼10% during the passage of the GC through the FoV,

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for both low- and high-energy events, as reported in Takada et al. (2022). The ratio is consistent with previously reported data, and as a result, the final data contained only a few 10% of the instrumental background. Until now, for all observations of MeV gamma rays done before SMILE-2+, the background was approximately 1–2 orders of magnitude higher than the signal. For SMILE-2+, because 3/5 of the whole sky was observed via bijection imaging, the OFF region could be set simply with both the GC and the disk outside the FoV, and the significance showed enhancements of the GC and disk were observed. ETCC has been demonstrated to enable MeV gamma-ray astronomy in the same manner as for astronomy at other wavelengths, i.e., bijection imaging and complete background rejection.

Future Prospects The next step will be the construction of SMILE3, a 40 cm φ× 30 cm cylindrical ETCC with 3-atm CF4 gas and a 3-coordinate µPIC, which give a 10-cm2 effective area and a good PSF of ∼5◦ (Takada et al. 2020, 2022). Thanks to the excellent rejection of background events, this detector will enable the study of the MeV gamma sky with a sensitivity several times higher than that of COMPTEL for only 1-month-long balloon observation, as shown in Fig. 20. Such a detector on a space mission would yield a sensitivity enabling the detection of faint sources at the sub-mCrab level, as shown in Fig. 20 (Tanimori et al. 2015). A few hundred cm2 and a PSF of a few degrees are required. Such a

Fig. 20 Observed and expected sensitivities of SMILE-2+ and expected sensitivities of SMILE3 and ETCC-satellite. (Adapted from Hamaguchi et al. 2019; Takada et al. 2022)

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fine PSF requires a good SPD of ∼10◦ , which is only possible when gas is used as a scatterer. With molecular gases, the needed effective area can be obtained from a 1-m3 sensitive volume. A proposal of such an ETCC on a satellite mission was submitted to the 2020 NASA Decadal Survey (Hamaguchi et al. 2019).

TPCs as Pair Telescopes After the first exploration of the gamma-ray sky by COS-B and EGRET, it was recognized that further improvement in the crowded and/or bright part of the sky, such as the galactic plane, and further improvement at low energies would imply the removal of the high-Z converters and the use of low-multiple-scattering active targets, such as those consisting of gas drift chambers (Mukherjee et al. 1996). Later, and for similar reasons, the potential of such telescopes for the gamma-ray polarimetry, the measurement of the fraction, and direction of the linear polarization of the incoming radiation, was underlined (Bloser et al. 2004).

Polarimetry with Pair Conversions and Multiple Scattering Due to the J P C = 1−− nature of the photon, the reduced differential cross section of the interaction of photons with a charged particle, as a function of the azimuthal angle, ϕ, that measures the orientation of the final state in the plane orthogonal to the photon direction of flight, has the form: dΓ ∝ (1 + AP cos [2(ϕ − ϕ0 )]), dϕ

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• P is the fraction of the linear polarization of the photon beam; • A is the polarization asymmetry of the conversion process; its value depends on the conversion process (pair, Compton, photo-electric) and on the photon energy. A number of experimental effects affect the measurement of the azimuthal angle, among which multiple scattering is certainly the fiercest and has been one of the major obstacles to polarimetry with the past and present pair-conversion gammaray telescopes. The presence of a non-zero resolution σϕ on the azimuthal angle changes Eq. (4) to   2 dN ∝ 1 + A e−2σϕ P cos[2(ϕ − ϕ0 )] , dϕ

(5)

so the effective polarization asymmetry is afflicted with a dilution factor D = 2 Aeff /A = e−2σϕ . The classical calculation (Kel’ner et al. 1975; Kotov 1989; Mattox et al. 1990) of σϕ is performed assuming the small-polar-angle approximation,

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the most probable value θˆ+− = E0 /E of the pair opening angle θ+− , with E0 = 1.6 MeV (Olsen 1963), and an approximate expression for the √ R.M.S. multiple scattering deflection (eq. (34.16) of Zyla et al. 2020), θ0 ≈ p0 /p x/X0 (p0 = 13.6 MeV/c, p the track momentum, x and X0 are the material thickness traversed by the electron and the radiation length). Assuming an equal energy √ share, p ≈ E/(2c), we obtain (eq. (15) of Bernard 2013a) σϕ = σ0 x/X0 with σ0 ≈ 24 rad. A dilution of D = 1/2 would be reached after a propagation of ≈110 µm in silicon, for example, that is before the leptons could even exit the conversion wafer in a silicon-strip detector (SSD) active target. The catastrophic exponential dependence of the dilution as a function of thickness so obtained, D ≈ exp(−σ02 x/(2X0 )) is not confirmed by the results of full simulations, actually, (Fig. 7 of Bernard 2019b, Fig. 3 of Eingorn et al. 2018). At high thicknesses, the dilution is found to be much larger (i.e., less degraded) for the full simulation, something which is the consequence of the θ+− distribution having a huge tail at large values (Olsen 1963). An optimal fit (such as a Kalman filter (Fruhwirth 1987)) can be performed that takes into account multiple scattering and the space resolution of each of the detector layers σ . For homogeneous detectors, the single-track angular resolution 1/6  at the vertex is found to be σtrack ≈ (p/p1 )−3/4 , with p1 = p0 4σ 2 l/X03 , l being the longitudinal sampling (along the track). Given the 1/E scaling of the θ+− distribution (Olsen 1963), the induced dilution is then found to be higher (less degraded) at low energies (Fig. 20 of Bernard 2013a).

Past Experimental Achievements and Future Prospects Gamma-ray beams are currently produced in the laboratory using the Compton scattering of a laser beam on a high-energy mono-energetic electron beam. Gammaray pseudo-monochromaticity is achieved by selecting the “Compton-edge” with a cylindrical collimator on the forward axis. The linear polarization of the incident laser beam is then transferred almost exactly to the gamma-ray beam (Sun and Wu 2011).

HARPO The HARPO project (Hermetic ARgon POlarimeter) has developed a gas TPC prototype (Bernard 2019a) and characterized it on the gamma-ray beam of the BL01 beam line at LASTI (Gros et al. 2018), with a gamma-ray energy that could be tuned from 1.7 to 74 MeV. The drift volume was cubic, (30 cm)3 , filled with a (95-5%) argon-isobutane gas mixture at a pressure that was varied from one to four bar. Most of the data were taken at 2.1 bar, for which a 220 V/cm uniform electric field provided an electron drift velocity of vdrift ≈ 3.3 cm/µs. The signal was amplified by a then

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1.4 1.2 1 0.8 0.6 1 + A cos(2(φ - φ )) 0 A = 10.5 ± 0.6% φ = -3.5 ± 1.6o

0.4 0.2 0

0

−3

−2

−1

0

1

2

3

φ+- [rad] Fig. 21 TPC polarimeter characterization on beam: Left: conversion of a photon from the BL01 gamma-ray beam line at NewSUBARU, into the 2.1 bar argon-isobutane (95-5%) gas mixture of the HARPO TPC prototype; the two “maps” are shown, that is, the two x, t and y, t projections of the conversion event; the vertical dashed lines denote the physical limits of the detector, i.e., the cathode (left) and the anode (right). Right: distribution of the azimuthal angle of 11.8 MeV gamma-rays (ratio of the fully linearly polarized to the linearly non-polarized) (Gros et al. 2018) (with permission)

novel GEM+micromegas combination, the performance of which was characterized carefully (Gros 2014). The anode was segmented to two series of orthogonal strips (x, y) at a pitch of 1 mm, and the signal sampled at a pace of 30 ns, equivalent to 1 mm given the value of the drift velocity. The prototype was routinely exposed to beam for 5 weeks, with an incoming single-track background rate of several kHz, that is larger than that expected on a space mission, a background that created negligible pile-up and no visible gas degradation in a sealed configuration. An excellent value of the polarization-asymmetry dilution was observed (Fig. 21 and Gros et al. 2018).

AdEPT The Advanced Energetic Pair Telescope (AdEPT) is currently being developed at NASA/GSFC. The primary science goal of AdEPT is to study the polarization of photons with energies above 1 MeV, interacting via pair production (Hunter et al. 2014). The polarization angle of the photon is observable as the azimuthal angle of the electron-positron pair. To preserve the azimuthal angle of the pair, and subsequently measure it, requires that Coulomb scattering of the pair in the interaction medium be minimized. Thus, the density of the medium must be low. A low interaction medium density is easily achieved with a gaseous TPC detector (ρAr = 1.782 × 10−3 (P /bar) g/cm3 ). However, the gaseous medium has a corresponding large radiation length (X0,Ar =19.55 g/cm2 =1.1×104 (1 bar/P ) cm).

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Maximizing the interaction probability (µnuclear (E=10 MeV)=1.03 × 10−2 cm2 /g) requires increasing the overall instrument interaction depth to compensate for the low interaction medium density. However, the maximum interaction depth is limited by the maximum allowable diffusion of the ionization electrons as they drift through the TPC. The diffusion of the ionization electrons obscures the tracks and consequently reconstruction of the azimuth angle of the electron-positron pair. A useful limit to the maximum TPC drift distance is that distance which results in an electron diffusion equal to twice the pitch of the readout plane (Arogancia et al. 2009). Increasing the total detector depth beyond this limit requires adding additional readout planes or reducing the diffusion of the drifting ionization charge. The NI technique, discussed above, is an effective approach to reducing the diffusion in a TPC. The introduction of an electronegative component into any TPC gas mixture affects the operation of the TPC in three ways. One, the diffusion of the ionization charge is reduced to the thermal limit; two, the drift velocity of the ions, which depends on the major component of the gas, is reduced by 3– 4 orders of magnitude compared to the drift velocity of free electrons in the gas; and three, the effective gas gain of the readout plane is reduced. This reduction in gas gain, corresponding to a reduction of the path over which the Townsend avalanche develops, is due to the initial acceleration of the NI process leading to knocking the ionization electron free from the NI and allow the avalanche to occur. To take advantage of the reduced diffusion in a NI-TPC, the effects of the reduced drift velocity and increased gain must be accounted for in the TPC design.

Design of a NI-TPC Pair Telescope The NI diffusion is reduced to the thermal limit, independent of the TPC gas mixture (Dion et al. 2011); however, the NI drift velocity depends on the molecular mass of the TPC gas. The velocity in low mass gases, e.g., argon, is faster compared with heavier gases, e.g., xenon. The NI drift velocity in argon is ≈20 m/s, corresponding to a total drift time of ≈50 ms/m of drift. This slow drift velocity allows the spatial resolution of the TPC readout to be very high while at the same time reducing the speed (bandpass) and power of the readout electronics. Reduction in the diffusion from the free electron diffusion rate, Eq. (1), to the thermal limit is dramatic. For example, at 1 kV/(cm · bar), the√electron diffusion in a mixture √ of argon and CO2 is reduced from 300 µm/ cm (Piuz 1983) to 80 µm/ cm at 300 K. This reduction allows the drift distance, or detector interaction depth, corresponding to a given amount of diffusion, to be increased by a factor of ≈16, thereby dramatically increasing the interaction probability of the instrument without additional layers of readout electronics. The slow drift velocity of the electron-positron tracks in a NI-TPC does not absolutely rule out the use of a calorimeter. If the electron and positron from an interacting photon cross the readout plane and enter a calorimeter directly underneath the readout plane, their energies from a position-sensitive calorimeter could be correlated in time with the TPC signals of the electron-positron crossing

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the readout plane. Requiring this pair event geometry, however, severely reduces the effective area of the telescope and eliminates the nearly isotropic (2π steradian) sensitivity achievable with a TPC-based gamma-ray telescope operating in low Earth orbit. The slow drift velocity does, however, introduce timing coincidence problems for a gamma-ray telescope if a design similar to previous gamma-ray telescopes (e.g., EGRET, Fermi -LAT) is followed. All previous imaging telescope designs have consisted of a multilayered tracker system mounted above a calorimeter and the tracker surrounded by an anti-coincidence system (ACS). Using a NI-TPC as the interaction medium and electron-positron pair tracker for a pair telescope and realizing the elimination of the ACS and calorimeter subsystems from the telescope design requires instrument solutions to overcome the slow drift velocity of the NIs. The advantages of eliminating the ACS and calorimeter subsystems are twofold. First, eliminating these two massive and complex detector subsystems reduces telescope complexity, mass, and hardware cost. Second, the geometric size of the telescope, and hence its sensitivity, is determined by the dimensions of the launch vehicle payload shroud rather than total telescope mass. We discuss the AdEPT instrument solutions being developed to these concerns below. Elimination of the ACS Previous telescope designs utilized an ACS to veto the instrument triggering circuit for a few µs after a cosmic ray traverses the detector volume. The slow drift velocity of a NI-TPC would require the veto signal to last tens of milliseconds in order for the ionization charge left by a cosmic ray traversing the volume to completely drift through the volume. In a 550–600 km circular low Earth orbit, the cosmic ray proton flux is 2.6 × 104 protons/s/m2 (SPENVIS 2021). This proton flux and the long veto signal period would result in the TPC readout being gated off 100% of the time. Thus, we conclude that the ACS is ineffective and can be eliminated from the design of a gamma-ray telescope using a NI TPC. Since the ionization charge produced by the cosmic rays cannot be discriminated, the problem becomes how to locate the interacting gamma rays in the background of cosmic ray tracks. Modern computer hardware, particularly graphics processing units (GPU) and field programmable gate arrays (FPGA), have evolved to the point where artificial intelligence/machine learning techniques can be used to search the NI TPC data for the electron-positron pair vertex signature of interacting gamma rays. The raw data is read out continuously and segmented into overlapping time intervals of about 50 ms duration. Each interval is then searched for the inverted “Λ” signature of a pair interaction. Those intervals containing an interaction are discriminated from the large number of background tracks from cosmic ray and low-energy photon interactions (Garnett et al. 2021). These background events are eliminated from the raw data and only those intervals containing pair interactions form the instrument science data.

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Eliminating the Calorimeter As discussed in section “Charged Particles Production and Transport in a Medium”, the energy loss of a charged particle traversing a medium is described by the Bethe formula, see eq. (33.5) of Zyla et al. (2020). The mean energy loss of electrons is tabulated as a function of energy in ESTAR (Berger et al. 2010a). The mean energy loss is then compared to the calculated average energy loss (Berger et al. 2005) to determine the energy of the original electron (Allison et al. 1974, 1976; Allison and Cobb 1980; Cobb et al. 1976). The positron energy loss and electron energy loss differ by a few percent (Rohrlich and Carlson 1954). This difference, however, is too small to be used to differentiate the pair electron from the positron. For charged particles traversing a gaseous TPC, the actual energy loss, in terms of ion pairs per cm, is Poisson distributed about the mean and fluctuates widely. Thus, any single sample of the dE/dx is a poor indication of the particle energy. The high granularity (sampling rate) of a TPC provides a large number of samples of the dE/dx loss in the gas. The mean energy loss can be determined from these samples and the actual energy of the electron and positron can be estimated. The energy loss as a function of particle energy is double valued about its minimum ionization value. Thus, any mean energy loss corresponds to two possible particle energies, one above the minimum ionizing energy and one below. The lower value can be confirmed or discarded based on the total range of the particle range. A particle with dE/dx below (dE/dx)min will have more pronounced Coulomb scattering or will stop in the gas. AdEPT Instrument Design The AdEPT instrument takes advantage of the NI-TPC technique to provide a low density interaction medium and to optimize the sensitivity for pair polarization. The gas mixture, 90%/10% argon/methane plus ≈40 torr of CS2 , was chosen to provide, 20 m/s, drift velocity. A total pressure of 1.5 atm was chosen to provide significant pair interaction depth, while minimizing the Coulomb scattering of the electronpositron and allows for a thin (3 mm aluminum) pressure vessel (Hunter 2018). The AdEPT instrument is composed of two gaseous NI-TPCs stacked so their drift electrode is common to the two TPCs and the two readout planes are at the top and bottom of the stack (Hunter 2018). Each TPC has large, 4 m2 , geometric area and 1 m depth and two-dimensional readout plane based on the micro-well detector (MWD) (Deines-Jones et al. 2002). This configuration of the TPCs allows the largest physical separation between the common high voltage drift electrode and the lower voltage readout planes, spacecraft structures, and pressure vessel, which are at ground potential. The two-dimensional MWD readout plane has electrodes in both the X- and Ydimensions on 400 µm pitch. The readout sampling frequency, 20 m/s/400 µm = 50 kHz, is chosen so that the vertical coordinate digitization is also 400 µm. This results in a very high granularity of ≈25 samples per cm of track for the AdEPT NI TPC and only ≈4 cm segment of the electron or positron track provides ≈100 samples of the dE/dx energy loss of the particle.

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Micro-Well Detector Readout Plane The MWD readout plane is fabricated using flex printed circuit board techniques. The currently available flex circuit technology allows for fabrication of multilayer circuits with line and gap separations as small as 75 µm on areas up to about 50 × 50 cm2 . This allows for large area TPC readouts to be implemented by tiling detector smaller pieces together. The only limitation to the readout dimension and area is the capacitance of the electrodes. The micro-well detector is fabricated as a two layer flex circuit with subsequent laser ablation to form the micro-wells (Deines-Jones et al. 2002). The cathode electrode strips, about 200 µm wide on 400 µm pitch, are on the top surface of the flex circuit, and the orthogonal anode electrode strips, similarly about 200 µm wide on 400 µm pitch, are on the lower layer. The cathode electrodes are perforated with 150 µm diameter openings aligned with the crossings of the underlying anode electrodes. A subsequent operation, using excimer laser ablation, is used to open the 100 µm diameter micro-wells in the center of each hole in the cathode electrode. The thickness of the insulating layer determines the depth of the wells and the maximum gas gain (Deines-Jones et al. 2002). This MWD geometry was considered to be a promising detector technology since the avalanche occurs in the strong gradient of the electric field in the wells and the charge is collected onto the anodes. Motion of the positive ions resulting from the avalanche induces an equal but opposite signal on the cathodes. Fabrication of large area MWDs using laser ablation coupled with real-time optical alignment to ensure that the wells were centered on the cathode openings was investigated over many years at GSFC ultimately producing detectors as large as 30 × 30 cm2 . These detectors were operated with gas gain as high as 104 (Son et al. 2010). A wide range of laser and chemical etching techniques were explored with industrial vendors to transfer the MWD to industrial fabrication. However, we realized that the position of the micro-wells had to be concentric, within a few microns, of the circular openings in the cathode electrodes. This accuracy requirement rendered industrial fabrication impractical. Deviation of the well from being centered in the cathode holes, by more than a few µm, led to breakdown of the anode-cathode voltage which limited the gas gain performance. The high gain lifetime of these detectors was also decreased by reduced breakdown voltage. This effect, attributed to charge migration in the insulating layer caused by the very strong electric field in the wells, limited the lifetime of these detectors to only a few months of operation. These considerations led us to discontinue development of MWDs at GSFC.

The µ-PIC Detector Readout Plane We are currently updating the design of the AdEPT instrument, retaining the NI TPC concept and size, but replacing the MWD readout with the Japanese µ-PIC+GEM detector developed for the ETCC discussed in section “Electron-Tracking Compton Camera with Gaseous Time-Projection Chamber” (Takada et al. 2011). A schematic diagram of the µ-PIC, without the GEM layer, is shown in Fig. 10.

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The electrode structure of the µ-PIC detector is similar to the MWD and is fabricated as a multilayer flex circuit. The cathode electrodes, on the top surface, are separated from the anodes on an underlying layer with a polyimide insulating layer. The anode electrodes have posts (filled vias) extending up through the insulating layer, typically about ≈100 µm thick, and exposed in the center of vias in the cathodes. These exposed anode posts and surrounding cathode strips form the proportional detector structures. The anode-cathode gap is ≈100 µm and the Townsend avalanche forms in the gas above the cathode layer. Readout Electrode Design The front-end electronics of the readout plane, typically a charge-sensitive amplifier on each electrode, can be implemented either with discrete electronics or as an ASIC. These implementations have an intrinsic minimum equivalent RMS noise value of about 103 electrons. Thus, a reasonable minimum detector gain for a non-NI TPC is ≈3 × 103 to provide a minimum three-to-one signal-to-noise ratio. Implementation of the NI technique reduces the effective gain of the readout because the NI must move deeper into the strong electric field until the ionization electron is knocked off of the NI at which point the free electron begins the avalanche process. This motion of the NI reduces the effective gain of the TPC readout by a factor of ≈200. The minimum gain of a NI TPC must be increased by this factor to retain the minimum signal-to-noise ratio. Thus, the required minimum TPC gain is 200×3×103 = 6×105 which is higher than is achievable with a single micromegas amplification stage (Veenhof 2010). The solution, for a NI TPC, is an additional gain stage in the form of a gas electron multiplier (GEM). The anode and cathode signals of a TPC are negative and positive charge, respectively. Thus the charge amplifier must have bi-polar response, or two different versions of the amplifier are needed for the anodes and cathodes. These amplifiers can be implemented using operational amplifiers and other discrete components or an application-specific integrated circuits (ASIC) can be used. The discrete approach offers a means to quickly develop a modest number of channels when beginning detector development. This approach is not the lowest power solution, in most cases, but does allow for easy modification of parameters such as gain and shaping time. The readout electrodes, which operate at high voltage, require a high voltage blocking capacitor to couple the charge signal to the amplifier inputs. These capacitors are large compared to the detector pitch and are a design problem for the electronics. An option, explored for AdEPT instrument, is to float the amplifier grounds to the corresponding anode or cathode voltages, thereby eliminating the need for high voltage blocking capacitors. This approach also requires that the grounds of all the subsequent analogue electronic stages be floated. This is done up to the digitizer stage where the serial output of which is easily level shifted and the remainder of the event selection and background discrimination is done at spacecraft ground.

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ASIC Readout Electronics The advantages of discrete electronics are quickly lost when the channel count exceeds a few hundred channels at which point selection of an integrated circuit becomes appealing. Over the past several years, there have been many general purpose ASICs developed for large experiments at CERN and by industry, e.g., IDEAS (2021). The design of an ASIC unique to a specific detector is another option that offers the advantages of tailoring the electronics to the detector and incorporating specific features into the electronics. Such development requires several years of lead time, is expensive, and cannot typically be done until the detector performance is well defined. An ASIC design investigated for AdEPT is a bidirectional switched capacitor charge integrating amplifier. The adjustable integration time, 20–15 µs, provided direct digitization of the TPC charge for each electrode with 400 µm resolution. The advantage of integrating the charge in the front-end electronics is that the discrete charge density corresponding to a discrete TPC voxel (three-dimensional volume) is directly measured. This ASIC design was completed and the performance simulated; however, funding issues prevented fabrication of test ASICs. AdEPT Performance Expected performance of the AdEPT gamma-ray polarimeter based on a NI TPC in low Earth orbit is summarized below. The detailed calculations are given in Hunter et al. (2014). The effective area compared to the Fermi LAT front is only ≈20% at 100 MeV but increases rapidly at lower energies and is about five times higher than Fermi LAT at 20 MeV. The point spread function approaches the kinematic limit for pair production (the angular resolution due to the unmeasurable nuclear recoil) and is less than twice the kinetic limit (Bernard 2013b) up to ≈150 MeV, where θ68 ≈ 0.6◦ . This excellent angular resolution contributes to a continuum sensitivity of about 10 mCrab over the energy range from 5 to 200 MeV. The minimum sensitivity, 2 × 10−6 MeV cm−2 s−1 , is reached at 70 MeV. The minimum detectable polarization (MDP) for a 10 mCrab source is ≈4% and for a brighter, 100 mCrab source, the MDP decreases to ≈0.7% at 15 MeV. AdEPT Future Prospects The next phase of the AdEPT mission development will assemble a prototype of the AdEPT TPC using the µ-PIC+GEM readout plane and existing discrete electronics. Testing of this prototype with radioactive sources will provide data with realistic level of backgrounds. This data will be used to develop the software solutions to discriminate the electron-positron pair interactions from the background and determine the electron-positron momenta. Additional software will determine the gamma-ray incident direction, energy, and polarization angle from the pair momenta.

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Liquid or Solid TPCs Given the volume limitation on a space mission and the weight of the pressure vessel needed for a gas detector, using a liquid detector seems to be tempting (Caliandro et al. 2013), with a density gain of a factor of 840 for argon, with respect to 1 bar gas. For polarimetry, the performance of the tracking system must scale accordingly, something which presents several difficulties. In particular, the typical collected electrical charge is left unchanged by the double scaling (same collected charge on a 1 cm track segment in 1 bar gas as on a 12 µm segment in a liquid): an issue arises from the fact that gas detectors allow charge amplification in the gas while liquid argon does not, so single-phase liquid argon detectors do not allow such a small-scale tracking. Some amplification can be achieved, on Earth, by the use of a two-phase system in which the active target consists of liquid, from which the electrons are extracted for amplification in the gas. In zero gravity on orbit, the stability of the gasliquid interface might be an issue, possibility solved by performing amplification in bubbles inside the holes of GEMs (Erdal et al. 2019). Another possibility to fix the dense-gas interface is to use a solid TPC, as the electron-transport properties of solid noble gases are similar to those of liquid noble gases (though with a somewhat larger drift velocity) (Aprile et al. 1985). Another issue is diffusion, as the coefficient saturates in liquid argon for high √ electric field, at a value of d ≈ 100 µm/ cm. The diffusion of the electron cloud during drift cannot scale with density, and the two tracks merge to a common blurred single track close to the vertex. Polarimetry with conversions to pairs, with a dense (liquid or solid) TPC, seems to be out of reach. The Compton Spectrometer and Imager (COSI) project is using a set of 1.5-cmthick germanium slabs as a combined (active-target + calorimeter) telescope, read with a twofold series of strips; as the interaction depth in the detector is inferred from the charge collection time difference between the two sides (Kierans et al. 2020), COSI can rightfully be described as a germanium TPC. More on dense-phase TPCs and their possible use in gamma-ray astronomy is presented in section “Dense Phase TPCs”.

Effective Area In contrast to “thick” active targets, in which the conversion probability of the photon is close to unity and the effective area is the product of the geometric area by the efficiency, here for “thin” active targets, it is better expressed as the product of the detector sensitive mass, M, by the attenuation coefficient, H , which is found to be approximately proportional to Z 2 /A (atomic number and mass, respectively) (Berger et al. 2010b). H (E) tends asymptotically, at high energy, to 7/(9 X0 ). The number of events is

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N = tM



ε(E)f (E)H (E)dE

(6)

t mission duration; ε(E) efficiency. For a “Crab-like” source with a spectral index of Γ = 2, with flux f (E) = F0 /E 2 , with F0 = 10−3 MeVcm−2 s−1 and perfect efficiency, N = tMF0



H (E) dE E2

(7)



H (E) dE for some materials commonly used in gamma-ray E2 telescopes are listed in Table 1. The variation of f (E)H (E) as a function of E is available in Fig. 2 of Bernard (2013a). For a 1 kg · year argon-mission with full efficiency, acceptance, exposure, and perfect dilution down to threshold, (ε = 1), and D = 1, we would observe N ≈ 105 events with an average polarization asymmetry of A ≈ 0.33  and, 2 1 ≈ therefore, a precision of the measurement of P , for small P , of σP ≈ A N 0.0135. Note though that the median energy E1/2 above which half of the collected data would lie is as low as E1/2 ≈ 10 MeV, which questions the ability to trigger/select/reconstruct/analyze low-energy conversions in the polarimeter. In the more realistic case of a 1 kg · year argon mission with a 10 MeV threshold, ε = 0.1 above threshold, and D = 0.5 dilution, we would obtain N ≈ 5000 events with A ≈ 0.232, Aeff ≈ 0.116, and σP ≈ 0.17. Therefore the polarimetry of a cosmic source with pairs should focus on the brightest sources of the MeV sky, in Values of

Table 1 Properties of some material. See text Z A X0 ρ

Ne 10 20.2 28.9

Si 14 28.1 21.8

Ar 18 40.0 19.5

Ge 32 72.6 12.2

Xe 54 131. 8.48

g/cm2

H (100 MeV)

17.0

23.5

27.0

45.3

67.1

cm2 /kg



H (E) dE E2  H (E) dE F0 E2

1.90

2.67

3.17

5.32

8.28

cm2 /(kg MeV)

60

84

100

168

261

103 (kg year)−1

E1/2

9.8

9.7

9.3

9.4

8.8

MeV

Atomic number Mass number Specific radiation length Photon attenuation coefficient @ 100 MeV

Number of (thousands) events per kg per year, ε=1

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the first place, and with a good-dilution, low-threshold, large-sensitive mass detector in orbit for several years.

Angular Resolution The primary interest of developing a telescope with an active target consisting in a gas TPC is the excellent angular resolution and, consequently, a sizeable sensitivity to the linear polarization of the incoming radiation. After a photon of momentum k converted to a pair of leptons with momenta p+ for the positron, p− for the electron and q for the recoiling nucleus, with k = p+ + p− + q, we want to reconstruct the direction of the candidate photon from the measured values of p+ and p− , as in general the track of the recoiling nucleus cannot be reconstructed. Therefore the single-photon angular resolution receives contributions from the following sources: (1) the missing recoil momentum; (2) the uncertainty in the magnitude of the momentum of each lepton. (3) the uncertainty in the direction of the tracks; (1) The kinematic limits for large, for nuclear √ the recoil momentum are extremely√ conversion from qm = k − k 2 − 4m2 ≈ 2m2 /k to qM = (k + k 2 − 4m2 )(k + M)/(2k + M), where M is the nucleus mass, but in practice the high (q ≫ mc) part of the q spectrum is strongly suppressed, both by the presence of a 1/q 4 factor and of 1/(E− − p− cos θ− ) and 1/(E+ + p+ cos θ+ ) terms in the differential cross section (the recoil direction is mainly transverse to the direction of the photon, and all the more so, asymptotically, at high energy). The induced contribution to angular resolution at 68% containment is found to be (Bernard 2013b, 2019b) θ68 ≈ b × E −5/4 ,

with b = 1.5 rad MeV5/4

(8)

As the angular kick is not Gaussian distributed, 95% and 99.7%-containment values might be of interest too; see Gros and Bernard (2017) and Bernard (2019b). (2) The contribution from the uncertainty in the magnitude of the momentum of each lepton varies like 1/E, as the fraction of the photon energy carried away by the positron, x+ ≡ E+ /E has a distribution that has a mild variation with energy, and as the distributions of the polar angles of the electron and of the positron, θ+ and θ− , scale like 1/E. The relative track momentum precision, σp /p, depends on the device that is used for the measurement and is not detailed here. For σp /p = 10%, the induced contribution on the single-photon angular resolution is found to be negligible, compared to the two other contributions (Fig. 6 of Bernard 2013b). (3) Tracking, the determination of the direction of the tracks, faces the limited spatial resolution of the detector and the deleterious effect of multiple scattering. A tracking method that takes into account the two effects in an optimal way is the Kalman filter (Fruhwirth 1987).

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• For continuous media, and for momenta for which multiple scattering is sizeable, and under the hypothesis that the detector is thin enough that momentum stays nearly constant throughout propagation, the precision of the measurement of the track angle at “origin” is (eq. (1) of Bernard 2019b)  

2 + −4j − x 2

2 x3 4j − x σ

  , σθ =   l 4j − x 2 + j x −4j − x 2 − j x

(9)

where x is the longitudinal track sampling pitch, l, normalized to the detector scattering length λ (Innes 1993), σ is the precision of a measurement of the track position, and j is the imaginary unit. – At low momenta (high x), only the two first measurements contribute significantly, and the angular precision is σθ ≈

√

2σ/ l.

(10)

l 3/2 √ . Above that value, the full 21/3 σ X0 power of the Kalman filter is at work, and the precision is This takes place for p < px ≡ p0

σθ ≈ (p/p1 )−3/4 .

(11)

– At high momenta, such that multiple scattering can be neglected, track-fitting turns out to be a simple linear regression, and the angular resolution (for no magnetic field) is (Regler and Fruhwirth 2008) 2σ σθ = l

3 (N − 1)N (N + 1)

This takes place for p > pu ≡ p0



l l N2 X0 σ 2 × 91/3

2σ l

≈ =



3 . N3

(12)

1 L2 p0 √ . σ lX0 2 × 91/3

For a 4-bar, argon-based TPC (X0 ≈ 29 m, ρ ≈ 6.6 kg/m3 ) with σ = 200 µm spatial resolution, l = 1 mm longitudinal sampling, N = 100 measurements along each track on average (L = 10 cm), we obtain p1 ≈ 58 keV/c, px ≈ 0.3 MeV/c, and pu ≈ 950 MeV/c: on most of the electron momentum range relevant for TPCbased gamma-ray telescopes, the single-track angular resolution is described by Eq. (11), something which translates to a similar expression for the contribution to the single-photon angular resolution (Sec. 3.1.1 of Bernard 2013b). At E = 100 MeV, the kinematic contribution amounts to θ68 ≈ 0.27◦ and the tracking contribution to σθ ≈ 0.22◦ (the two contributions are of similar magnitude −3/2 for p = pl = b2 p1 , pl ≈ 160 MeV/c).

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Sensitivity: Gas Choice Any of the noble gases is appropriate as a base for TPC and MPGD design, from helium to xenon, with the exception of krypton, that is generally avoided for the radioactive decays of 85 Kr would produce a permanent background noise in the detector, at a level of 3.7 × 105 Bq per kg of natural Kr. It could be tempting to use a high-Z gas, as the photon attenuation coefficient, and therefore the effective area per unit √ mass, is proportional to Z 2 /A, but the radiation length X0 decreases, so p1 ∝ 1/ X0 increases, and so the single-photon angular resolution, σθ ∝ (p1 /p)3/4 , degrades. The sensitivity to faint√sources, s, defined as the source flux at significance limit, is proportional to σθ / H (E) (eq. (8) of Bernard 2013b). √ • Below pl , with the angular resolution at the kinematic limit, s ∝ A/Z, presenting an interest for high Z. −3/8 • Above pl , with σθ ∝ (p1 /p)3/4 ∝ X0 , and H (E) ∝ 1/X0 , the sensitivity −1/8 becomes ∝ X0 , presenting a mild preference for low Z. For polarimetry, an analysis that is so badly demanding for high statistics, one would favor high Z too, but the dilution degrades for higher values of p1 (Fig. 20 of Bernard 2013a). At low pressures (several bar), statistics is the dominant factor and high Z is preferred, while for densities tending toward that of the liquid (hundreds of bar), it is the opposite (Fig. 22 of Bernard 2013a).

Dense Phase TPCs The use of noble gases in a dense phase, that is, liquid or solid, is similar to that in the gas phase, but a number of differences must be mentioned: • Most often pure noble gases are used, i.e., without a quencher (Note though that saturation value of the electron drift velocity in liquid noble gases can be enlarged by the addition of ≈1% in concentration of various alkanes (Yoshino et al. 1976).), so diffusion could be an issue; these pure materials are transparent to their own scintillation light, so the scintillation signal can be used to generate a trigger and/or to measure the energy deposited in the material. • Upon ionization of the material, a large electric charge is generated in a small volume (electrons and positive ions), after which recombination takes place, something that affects both the efficiencies of charge collection and of the detection of scintillation. Recombination can be mitigated, to some extent, by a swift separation of the positive and negative charges, in an electric field. The fractions of the energy of the incident particle that ends up in ionization and in scintillation show an important fluctuation, but they are strongly anti-correlated,

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• •

• •

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so a combined analysis enables a precision measurement of the total deposited energy. An energy resolution of 1.7% could be obtained in that way with a LXe (liquid xenon) detector with 662 keV photons at 1 kV/cm, for example, Aprile et al. (2007). Scintillation and ionization yields reported in Table 2 were obtained with incident electrons. Note that charge amplification in the liquid is either difficult (Xe, with maximum gains of a couple of hundreds) or impossible (Ar), as it needs to operate close to breakdown voltage. Note that electrons cannot drift freely in liquid neon, as they attract a group of atoms that make a heavy negative-charge, low-mobility “bubble.” But solid neon is of interest, still. Scintillation takes place in the vacuum ultraviolet (see Fig. 3.27 of Aprile et al. 2008a), so light collection is performed through VUV transparent windows or after wavelength-shifting (WLS) inside the experimental vessel. The spectra are similar for the gas, for the liquid, and for the solid phases (see Fig. 3.32 of Aprile et al. 2008a), with typical width (FWHM) of ≈10 nm. Refraction indices are computed by Grace and Nikkel (2017) at the scintillation wavelength, from data collected at higher wavelengths. The ionization electron yield depends on the experimental conditions, in particular on the nature and the energy of the incident particle, and on the value of the applied electric field that mitigates the loss due to electron-ion recombination (solids: Table 1 of Guarise et al. 2020; liquids: Table 1 of Chepel and Araujo 2013). The electron drift velocity depends on the temperature, especially for solids (see Fig. 3.11 of Aprile et al. 2008a for argon). The values of the electron drift mobility are provided close to the triple point (Miller et al. 1968). Diffusion of the drifting electrons is larger than the thermal limit over most of the electric field practical range, with larger values for Xe than for Ar (see Fig. 3.12 of Aprile et al. 2008a) and for transverse diffusion than for longitudinal (DL /DT ≈ 0.1 for Xe), see the discussion in section 4.3.1 of Chepel and Araujo 2013. of DT = 25 cm2 /s and v = 0.5 cm/µs the RMS spread √ For typical values√ is 2DT /v ≈ 100 µm/ cm.

High-mobility liquid hydrocarbons have been considered in the past, so as to avoid the complexity of a cryogenic apparatus. Also the drift velocity saturates at a much larger electric field and at a much larger value than for liquid noble gases (Sowada et al. 1976) so the diffusion spread can be extremely small (Bakale and Beck 1986). Alkanes can be used and higher effective-Z materials can be obtained by replacing the central carbon atom by a heavier atom, such as for tetramethylsilane (CH3 )4 Si, tetramethylgermane (CH3 )4 Ge, etc. Unfortunately, these materials are opaque to their own scintillation.

Electron transport ionization yield e− drift velocity v at 1 kV/cm e− drift velocity v at saturation low field e− drift mobility µ DT

n @ λscint

T (boil @ 1 atm, melt) ρ X0 Scintillation yield λscint 74 80

K g cm−3 cm

γ /keV nm

cm2 /s at 1 kV/cm

e− /keV cm/µs cm/µs

Ne Liq. 27.07 1.204 24.03

1.9 600

46

170

Sol. 24.56 1.444 20.0

40 0.225 1.0 475 15

1.45 ± 0.07

40 128

Ar Liq. 87.30 1.396 14.00

42 0.38 1.07 1000

1.50 ± 0.07

Sol. 83.79 1.623 12.0

44 0.2 0.30 2200 60 – 80

1.69 ± 0.04

42 178

Xe Liq. 165.1 2.953 2.872

64 0.4 0.56 4500

1.81 ± 0.03

id Liq.

Sol. 161.4 3.41 2.49

Table 2 Properties of the dense (liquid or solid) phases of noble gases, used in TPCs. Values of the radiation lengths are from Zyla et al. (2020), of the scintillation yields from Michniak et al. (2002) and Doke et al. (2002), of the refractive indices from Grace and Nikkel (2017), of the ionization yields from Chepel and Araujo (2013) and Guarise et al. (2020), of the electron drift velocities from Aprile et al. (1985), Yoo and Jaskierny (2015), and Sakai et al. (1982), of the low-field mobilities from Sakai et al. (1982) and Miller et al. (1968)

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Cathode

HV

E

z=v*t

Shaping Rings

1st Compton

Liquid Xenon

2nd Compton Photoabsorption

(x, y)

HV

Mesh X−wire Y−wire Anode

Quartz Window

HV UV PMT

UV PMT

HV

Amplifiers

X−Y Induction Anode Collection Signal Signals

Fig. 22 Schema (left, Aprile et al. 1998) and picture of the TPC structure (right (Aprile and Doke 2010)) of the LXeGRIT telescope. A 2-scatter, 3-site event is represented on the schema

LXeGRIT LXeGRIT (Liquid Xenon Gamma-Ray Imaging Telescope) is a balloon-borne Compton telescope based on a liquid xenon TPC for imaging cosmic gamma rays in the energy range 0.15–10 MeV with a FoV at FWHM of ≈1 sr. The active target has a 20 × 20 cm2 sensitive area, a 7 cm thickness and contains high-purity liquid xenon at a temperature of −95 ◦ C, immersed in a 1 kV/cm electric field. The full drift duration is of 35 µs. The scintillation light is collected by a set of four PMTs located below the sensitive volume through quartz windows. After drift, the ionization electrons traverse a set of two orthogonal wire sheets at a pitch of 3 mm, on which they induce a signal, after which they are collected on a fourfold segmented anode (Fig. 22). LXeGRIT has undergone calibration with radioactive sources, full simulation, √ and a series of balloon-borne flights. The telescope shows a ∆E = 8.8%/ E/MeV FWHM energy resolution and a single-interaction position resolution better than 1 mm in the transverse and than 0.3 mm in the longitudinal directions, from which an ARM angular resolution of 3.8◦ was obtained at 1.836 MeV (the energy dependence for 2- and 3-site events can be found in Fig. 14 of Aprile et al. 2008b). A 27 h balloon flight was performed in 2000, of which 5 h of consecutive data were taken at an altitude of 39 km, or an atmospheric thickness of 3.2 gcm−2 (Curioni et al. 2003). A first-level, fast trigger was formed from an OR of the PMT signals. A second-level trigger, including a cut on the number of wire hits, enabled a rejection of single-site and charged cosmic-ray background noise events. The background rate in flight was actually found to be larger than anticipated, so it was decided to reduce the trigger efficiency so as to mitigate the data acquisition

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bottleneck (Curioni et al. 2007). The energy spectrum (Fig. 9 of Curioni et al. 2003) shows a continuum, plus a 1.46 MeV peak due to 40 K radioactivity, from the potassium present in the ceramic part of the structure of the detector. The Crab nebula/pulsar has been within the field of view for several hours of that flight; it has been estimated that hints of a detection were within reach at the 2–3 σ significance level (Aprile et al. 2004).

Liquid TPCs as High-Resolution Homogeneous Calorimeters Homogeneous liquid xenon calorimeters have been considered as high energyresolution active targets for gamma-ray lines in the GeV energy range (Doke et al. 1989; Okada et al. 2000; Baranov et al. 1990). The angular resolution has been estimated to be ≈1 mrad at 10 GeV (Seguinot et al. 1990), to be compared to the PSF at 68% (front) of the Fermi -LAT tracker, of ≈7 mrad (P8R3 release).

Summary/Conclusions Gamma-ray astronomy is suffering from the lack of high-sensitivity instruments at the frontier of the Compton and of the pair-conversion energy ranges and from the difficulty of performing a polarimetry of the incoming radiation from gamma-ray sources. On the Compton side, one of the issues is the complexity of the analysis induced by the determination of the incoming photon direction on a cone for one-scatter events, while on the pair side, the degradation of the angular resolution at low energy due to multiple scattering of the leptons in their way through the detector is the main limitation. In both cases, the ability of selecting signal photons and reject background noise is affected, the sensitivity is degraded, and in both cases a key issue is the precision of the tracking of low-energy electrons. On both sides of the frontier, major improvements have been achieved since the beginning of this century, thanks to the development of low-density highprecision active targets such as gas TPCs. For Compton events, it was recognized and demonstrated experimentally that the tracking of the scattered electron can be so precise that for each event, the cone arc can be brought down to an almost isotropic PSF. TPC prototypes have undergone balloon test flights, during which the detector and in particular the trigger system survived the intense single-track background in the upper atmosphere, and cosmic photons were observed. For pair-conversion events, TPCs enable an excellent angular resolution down to the kinematic limit (that is due to the non-observation of the recoiling nucleus). A measurement of the linear polarization fraction and angle of the incoming radiation has been demonstrated both by the analysis of simulated data and by the characterization of a TPC prototype on a γ -ray beam. Several MPGD techniques have been developed that provide a high-gain, high-rate, spark-resistant, low-jitter, low-ion backflow amplification of the

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time-dependent signal that is flowing on the readout electrodes. These amplification devices work in the so-called proportional mode, far from the sparking mode of the EGRET spark chambers that is suspected to have inflicted the radiation-induced chemistry processes that have degraded the gas to the point that EGRET had to change it to fresh gas by the year. The design of low-aging gas detectors can benefit from the experience gained by the experiments at the Large Hadron Collider (LHC) that have been routinely exposed for years to much higher radiation dose rates than for a detector in orbit. Higher-density TPCs using a liquid or solid material have been considered, but the tracking precision is an issue as charge amplification is limited in noble-gas liquid and mitigating diffusion during drift by the addition of a quencher is difficult, so having the tracking pitch and precision scale down with density is not an option. For Compton events, furthermore, the charge collection statistics is much lower than for semiconductor materials like silicon or germanium, so the energy resolution is not as good and nuclear spectroscopy seems to be out of reach. The “vertical” coordinate is determined from a time-of-flight difference in the COSI detector, so the first gamma-ray TPC in orbit might well consist of germanium.

Cross-References ⊲ Gamma-Ray Polarimetry

List of Variables A A Aeff Aeff α

β b B B D D d e E

mass number polarization asymmetry polarization asymmetry, with detector effects effective area Compton scattering angle α between the recoil electron and the scattered gamma ray particle velocity normalized to that of light single-photon resolution-angle kinematic-limit constant magnetic field the background flux (polarization asymmetry) dilution factor diffusion coefficient pseudo diffusion coefficient elementary electric charge particle energy

b = 1.5 rad MeV5/4

60 Time Projection Chambers for Gamma-Ray Astronomy E0 E

ε f γ H j k k L l λ m M M µ N p p pr p0 p1 P ϕ q ρ S σ σ t T θ θ+− θ0 v X0 x+ x x

Olsen constant electric field efficiency source flux energy distribution particle Lorentz factor photon attenuation coefficient the imaginary unit Boltzmann’s constant photon momentum length longitudinal sampling along the track detector scattering length electron mass nucleus mass detector sensitive mass mobility number of events pressure particle momentum quencher partial pressure multiple scattering constant detector characteristic scattering momentum (linear) polarization fraction of light azimuthal angle recoil momentum density signal intensity resolution of track position single-measurement electron cloud spread due to diffusion time temperature polar angle (wrt the incident photon direction) pair opening angle multiple scattering RMS angle with logarithmic correction factor neglected velocity detector material radiation length fraction of the incident photon energy carried away by the positron longitudinal track sampling pitch, l, normalized to detector scattering length λ transverse coordinate

2167 E0 = 1.6 MeV (Olsen 1963)

Berger et al. (2010b)

Innes (1993)

p0 = 13.6 MeV/c (Zyla et al. 2020)

x = l/λ

2168 y z z Z

D. Bernard et al. transverse coordinate “vertical” position, i.e., along the electric field particle electric charge in elementary electric charge units atomic number

Acknowledgments This study was supported by the Japan Society for the Promotion of Science (JSPS) Grant-in-Aid for Challenging Research Pioneering 20K20428.

References M. Abe et al., Development of a µ-PIC with glass substrate aiming at high gas gain. J. Phys. Conf. Ser. 1498, 012002 (2020) T. Alexopoulos, J. Burnens et al., A spark-resistant bulk-micromegas chamber for high-rate applications. Nucl. Instrum. Methods A 640, 110–118 (2011) W.W.M. Allison, J.H. Cobb, Relativistic charged particle identification by energy loss. Ann. Rev. Nucl. Part. Sci. 30(1), 253–298 (1980) W. Allison, C. Brooks et al., The identification of secondary particles by ionisation sampling (ISIS). Nucl. Instrum. Methods A 119, 499–507 (1974) W.W.M. Allison, C.B. Brooks et al., The ionization loss of relativistic charged particles in thin gas samples and its use for particle identification: 2. Experimental results. Nucl. Instrum. Methods A 133, 325 (1976) V.C. Antochi et al., Performance of an optically read out time projection chamber with ultrarelativistic electrons. Nucl. Instrum. Methods A 999, 165209 (2021) E. Aprile, T. Doke, Liquid xenon detectors for particle physics and astrophysics. Rev. Mod. Phys. 82, 2053–2097 (2010) E. Aprile, K.L. Giboni et al., A study of ionization electrons drifting large distances in liquid and solid argon. Nucl. Instrum. Methods A 241, 62–71 (1985) E. Aprile et al., The electronics read out and data acquisition system for a liquid xenon time projection chamber as a balloon-borne Compton telescope. Nucl. Instrum. Methods A 412(2), 425–436 (1998) E. Aprile et al., Calibration and in-flight performance of the Compton telescope prototype lxegrit. New Astron. Rev. 48(1), 257–262 (2004) E. Aprile, K.L. Giboni, P. Majewski, K. Ni, M. Yamashita, Observation of anti-correlation between scintillation and ionization for MeV gamma-rays in liquid xenon. Phys. Rev. B 76, 014115 (2007) E. Aprile et al., Noble Gas Detectors (Wiley, Weinheim, 2008a) E. Aprile et al., Compton imaging of MeV gamma-rays with the liquid xenon gamma-ray imaging telescope (LXeGRIT). Nucl. Instrum. Methods A 593, 414–425 (2008b) D.C. Arogancia et al., Study in a beam test of the resolution of a Micromegas TPC with standard readout pads. Nucl. Instrum. Methods A 602, 403–414 (2009) D. Attié, TPC review. Nucl. Instrum. Methods A 598, 89–93 (2009) W.B. Atwood et al., Performance of the ALEPH time projection chamber. Nucl. Instrum. Methods A 306, 446–458 (1991) G. Bakale, G. Beck, Field-dependent electron attachment in liquid tetramethylsilane. J. Chem. Phys. 84(10), 5344–5350 (1986) M. Ball et al., Technical design study for the PANDA time projection chamber. Technical report, The GEM-TPC Collaboration (2012). arXiv:1207.0013 [physics.ins-det] A. Baranov et al., Liquid xenon calorimeter for the detection of electromagnetic showers. Nucl. Instrum. Methods A 294, 439–445 (1990)

60 Time Projection Chambers for Gamma-Ray Astronomy

2169

B. Beischer, Measurement of high energy gamma rays from 200 MeV to 1 TeV with the alpha magnetic spectrometer on the international space station. PhD thesis, RWTH Aachen University (2020) M.J. Berger et al., ESTAR, PSTAR, and ASTAR: computer programs for calculating stoppingpower and range tables for electrons, protons, and helium ions (version 2.0.1) (2005) M.J. Berger et al., Estar: stopping powers and ranges for electrons. NIST: National Institute of Standards and Technology, Gaithersburg (2010a) M.J. Berger et al., Xcom: photon cross sections database, nist standard reference database 8 (xgam). NIST: National Institute of Standards and Technology, Gaithersburg (2010b) D. Bernard, Polarimetry of cosmic gamma-ray sources above e+ e− pair creation threshold. Nucl. Instrum. Methods A 729, 765–780 (2013a) D. Bernard, TPC in gamma-ray astronomy above pair-creation threshold. Nucl. Instrum. Methods A 701, 225–230 (2013b) [Erratum: Nucl. Instrum. Methods A 713, 76–77 (2013)] D. Bernard, HARPO, a gas TPC active target for high-performance γ -ray astronomy; demonstration of the polarimetry of MeV γ -rays converting to e+ e− pair. Nucl. Instrum. Methods A 936, 405–407 (2019a) D. Bernard, Performance of the MeV gamma-ray telescopes and polarimeters of the future. γ → e+ e− in silicon-detector active targets. Mem. Soc. Ast. It. 90(1–2), 149–153 (2019b) D. Bernard et al., HARPO: a TPC as a gamma-ray telescope and polarimeter. Proc. SPIE Int. Soc. Opt. Eng. 9144, 91441M (2014) P.F. Bloser, S.D. Hunter et al., A concept for a high-energy gamma-ray polarimeter. Proc. SPIE Int. Soc. Opt. Eng. 5165, 322 (2004) W. Blum, L. Rolandi, Particle Detection with Drift Chambers (Springer, Berlin/Heidelberg, 2008) M. Bourquin, The AMS tracking detector for cosmic-ray physics in space. Nucl. Instrum. Methods A 541, 110–116 (2005) G.A. Caliandro, B. Rossi et al., A new concept of y-ray telescope. LArGO: Liquid Argon Gammaray Observatory, in 15th International Workshop on Neutrino Telescopes (2013). 1312.4503 M. Capeans, R. Guida et al., RPC performances and gas quality in a closed loop gas system for the new purifiers configuration at LHC experiments. JINST 8, T08003 (2013) V. Chepel, H. Araujo, Liquid noble gas detectors for low energy particle physics. JINST 8, R04001 (2013) J.H. Cobb, W.W.M. Allison, J.N. Bunch, The ionization loss of relativistic charged particles in thin gas samples and its use for particle identification. 1. Theoretical predictions. Nucl. Instrum. Methods A 133, 315 (1976) A. Curioni et al., On the background rate in the LXeGRIT instrument during the 2000 balloon flight. Proc. SPIE Int. Soc. Opt. Eng. 4851, 1281 (2003) A. Curioni, E. Aprile et al., A Study of the LXeGRIT detection efficiency for MeV gamma-rays during the 2000 balloon flight campaign. Nucl. Instrum. Methods A 576, 350–361 (2007) P. Deines-Jones, J. Black et al., Imaging micro-well proportional counters fabricated with masked UV laser ablation. Nucl. Instrum. Methods A 477(1), 55–58 (2002). 5th International Conference on Position-Sensitive Detectors M.P. Dion, S. Son et al., Negative ion drift velocity and longitudinal diffusion in mixtures of carbon disulfide and methane. Nucl. Instrum. Methods A 648(1), 186–191 (2011) T. Doke et al., Liquid xenon calorimeter for observation of cosmic line gamma-rays in the GeV region. Nucl. Phys. B Proc. Suppl. 10, 150–158 (1989) T. Doke et al., Absolute scintillation yields in liquid argon and xenon for various particles. Jpn. J. Appl. Phys. 41, 1538–1545 (2002) M. Eingorn, L. Fernando et al., High energy photon polarimeter for astrophysics. J. Astron. Telesc. Instrum. Syst. 4(1), 011006 (2018) E. Erdal, A. Tesi et al., First demonstration of a bubble-assisted Liquid Hole Multiplier operation in liquid argon. JINST 14(11), P11021 (2019) J.A. Esposito, D.L. Bertsch et al., In-flight calibration of EGRET on the Compton gamma-ray observatory. Astrophys. J. Suppl. 123(1), 203–217 (1999)

2170

D. Bernard et al.

L. Fabbietti et al., The PANDA GEM-based TPC prototype. Nucl. Instrum. Methods A 628, 204– 208 (2011) M. Frosini, D. Bernard, Charged particle tracking without magnetic field: optimal measurement of track momentum by a Bayesian analysis of the multiple measurements of deflections due to multiple scattering. Nucl. Instrum. Methods A 867, 182–194 (2017) M. Frotin et al., Sealed operation, and circulation and purification of gas in the HARPO TPC, in Proceedings, 4th International Conference on Micro Pattern Gaseous Detectors (MPGD2015), Trieste, EPJ Web Conference, vol. 174 (2018), p. 05002 R. Fruhwirth, Application of Kalman filtering to track and vertex fitting. Nucl. Instrum. Methods A 262, 444–450 (1987) K. Fujii, Fundamental processes in the TPC, in Presented at iSTEP 2014, IHEP Beijing (2014) (Part I, Part II) R.L. Garnett, A.R. Hanu et al., Event selection and background rejection in time projection chambers using convolutional neural networks and a specific application to the AdEPT gammaray polarimeter mission. Nucl. Instrum. Methods A 987, 164860 (2021) Y. Giomataris, P. Rebourgeard et al., MICROMEGAS: a high granularity position sensitive gaseous detector for high particle flux environments. Nucl. Instrum. Methods A 376, 29–35 (1996) I. Giomataris et al., A novel large-volume spherical detector with proportional amplification readout. JINST 3, P09007 (2008) Goddard Space Flight Center, Introduction to EGRET, EGRET data products, and EGRET data analysis (2021) E. Grace, J.A. Nikkel, Index of refraction, Rayleigh scattering length, and Sellmeier coefficients in solid and liquid argon and xenon. Nucl. Instrum. Methods A 867, 204–208 (2017) P. Gros, HARPO – TPC for high energy astrophysics and polarimetry from the MeV to the GeV. PoS TIPP2014, 133 (2014) P. Gros, D. Bernard, γ -ray telescopes using conversions to e+ e− pairs: event generators, angular resolution and polarimetry. Astropart. Phys. 88, 60–67 (2017) P. Gros et al., Performance measurement of HARPO: a time projection chamber as a gamma-ray telescope and polarimeter. Astropart. Phys. 97, 10–18 (2018) M. Guarise, C. Braggio, R. Calabrese, G. Carugno, A. Dainelli, A. Khanbekyan, E. Luppi, L. Tomassetti, Particle detection in rare gas solids: DEMIURGOS experiment. Nucl. Instrum. Methods A 958, 162434 (2020) K. Hamaguchi et al., A space-based all-sky MeV gamma-ray survey with the electron tracking compton camera (2019). arXiv:1907.06658 [astro-ph.IM] H.J. Hilke, Time projection chambers. Rep. Prog. Phys. 73, 116201 (2010) J.E. Hill, J.K. Black et al., Lifetime estimation of a time projection chamber x-ray polarimeter, in UV, X-Ray, and Gamma-Ray Space Instrumentation for Astronomy XVIII, ed. by O.H. Siegmund. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 8859 (2013), p. 88590O S.D. Hunter, The advanced energetic pair telescope for gamma-ray polarimetry. Proc. SPIE Int. Soc. Opt. Eng. 10699, 106992M (2018) S.D. Hunter et al., A pair production telescope for medium-energy gamma-ray polarimetry. Astropart. Phys. 59, 18–28 (2014) IDEAS, IDEAS, integrated detector electronics AS (2021) W.R. Innes, Some formulas for estimating tracking errors. Nucl. Instrum. Methods A 329, 238–242 (1993) S.C. Kappadath, J. Ryan et al., The preliminary cosmic diffuse γ -ray spectrum from 800keV to 30MeV measured with COMPTEL. A&A Suppl. Ser. 120, 619–622 (1996) S. Kel’ner et al., Methods of measuring linear polarization of gamma quanta. Yad Fiz 21, 604 (1975) C.A. Kierans et al., Detection of the 511keV galactic positron annihilation line with COSI. Astrophys. J. 895(1), 44 (2020) I.D. Kotov, Methods of measurement of gamma-ray polarization. Space Sci. Rev. 49(1–2), 185– 195 (1989)

60 Time Projection Chambers for Gamma-Ray Astronomy

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C.J. Martoff, D.P. Snowden-Ifft et al., Suppressing drift chamber diffusion without magnetic field. Nucl. Instrum. Methods A 440(2), 355–359 (2000) C.J. Martoff, R. Ayad et al., Negative ion drift and diffusion in a TPC near 1 bar. Nucl. Instrum. Methods A 555(1–2), 55–58 (2005) C.J. Martoff, M.P. Dion et al., A benign, low Z electron capture agent for negative ion TPCs. Nucl. Instrum. Methods A 598(2), 501–504 (2009) J.N. Marx, D.R. Nygren, The time projection chamber. Phys. Today 31N10, 46–53 (1978) J.R. Mattox, H.A. Mayer-Hasselwander, A.W. Strong, Analysis of the COS B data for evidence of linear polarization of VELA pulsar gamma rays. Astrophys. J. 363, 270 (1990) R. Michniak et al., Alpha and beta particle induced scintillations in liquid and solid neon. Nucl. Instrum. Methods A 482(1), 387–394 (2002) L.S. Miller, S. Howe, W.E. Spear, Charge transport in solid and liquid ar, kr, and xe. Phys. Rev. 166, 871–878 (1968) T. Mizumoto et al., New readout and data-acquisition system in an electron-tracking Compton camera for MeV gamma-ray astronomy (SMILE-II). Nucl. Instrum. Methods A 800, 40–50 (2015) Y. Mizumura, T. Tanimori, A. Takada, Possibility of systematic study of supernova explosions by nuclear imaging spectroscopy. JPS Conf. Proc. 14, 020607 (2017) R. Mukherjee, B.L. Dingus et al., AGATE: a high-energy gamma-ray telescope using drift chambers. Space Sci. Rev. 75, 97–108 (1996) P. Nemethy, P.J. Oddone, N. Toge, A. Ishibashi, Gated time projection chamber. Nucl. Instrum. Methods A 212, 273 (1983) A. Obertelli et al., MINOS: a vertex tracker coupled to a thick liquid-hydrogen target for in-beam spectroscopy of exotic nuclei. Eur. Phys. J. A 50, 8 (2014) A. Ochi et al., A new design of the gaseous imaging detector: micro pixel chamber. Nucl. Instrum. Methods A 471, 264–267 (2000) H. Okada et al., Liquid Xe homogeneous electro-magnetic calorimeter. Nucl. Instrum. Methods A 451, 427–438 (2000) H. Olsen, Opening angles of electron-positron pairs. Phys. Rev. 131, 406–415 (1963) A. Peisert, F. Sauli, Drift and diffusion of electrons in gases: a compilation (with an introduction to the use of computing programs). Technical report, CERN, CERN-84-08, CERN-YELLOW84-08 (1984) F. Piuz, Measurement of the longitudinal diffusion of a single electron in gas mixtures used in proportional counters. Nucl. Instrum. Methods A 205(3), 425–436 (1983) J. Rauch, Pattern recognition in a high-rate GEM-TPC. J. Phys. Conf. Ser. 396, 022042 (2012) RD51, RD51 collaboration, development of micro-pattern gas detectors technologies (2008) M. Regler, R. Fruhwirth, Generalization of the Gluckstern formulas. I: Higher orders, alternatives and exact results. Nucl. Instrum. Methods A 589, 109–117 (2008) F. Rohrlich, B.C. Carlson, Positron-electron differences in energy loss and multiple scattering. Phys. Rev. 93(1), 38 (1954) Y. Sakai, E.H. Boettcher, W.F. Schmidt, On the electron drift velocity in solid neon. Zeitschrift für Naturforschung A 37(1), 87–90 (1982) F. Sauli, Principles of operation of multiwire proportional and drift chambers. Technical report, CERN, CERN-77-09 (1977a) F. Sauli, GEM: a new concept for electron amplification in gas detectors. Nucl. Instrum. Methods A 386, 531–534 (1997b) F. Sauli, Gaseous Radiation Detectors; Fundamentals and Applications (Cambridge University Press, Cambridge, 2014) V. Schoenfelder, The first comptel source catalogue. Astron. Astrophys. Suppl. Ser. 143, 145 (2000) V. Schoenfelder, H. Aarts others, Instrument description and performance of the imaging gammaray telescope COMPTEL aboard the Compton gamma-ray observatory. ApJS 86, 657 (1993) V. Schönfelder, Lessons learnt from COMPTEL for future telescopes. NewAR 48(1–4), 193–198 (2004)

2172

D. Bernard et al.

J. Seguinot et al., A totally active liquid xenon or krypton electromagnetic calorimeter for high luminosity hadron colliders, in INFN Eloisatron Project, 12th Workshop: New Technologies for Supercolliders (1990), pp. 9–28 D.P. Snowden-Ifft, T. Ohnuki et al., Neutron recoils in the drift detector. Nucl. Instrum. Methods A 498(1), 155–164 (2003) S. Son, G.A. de Nolfo et al., Neutron imaging camera, in IEEE Nuclear Science Symposuim Medical Imaging Conference (2010), pp. 298–301 U. Sowada et al., Electron transport in high mobility liquid hydrocarbons and tetramethylsilane, in Fifth International Conference on Conduction and Breakdown in Dielectric Liquids, 1975, Noordwijkerhout (1976), pp. 1–4 SPENVIS, SPENVIS is developed by a consortium led by the royal belgian institute for space aeronomy for ESA’s space environments and effects section through its general support technology programme (2021) C. Sun, Y.K. Wu, Theoretical and simulation studies of characteristics of a Compton light source. Phys. Rev. ST Accel. Beams 14, 044701 (2011) A. Takada et al., Development of an advanced Compton camera with gaseous TPC and scintillator, in Proceedings, 6th International Workshop on Radiation Imaging Detectors (IWORID 2004), Glasgow, Nucl. Instrum. Methods A, vol. 546 (2005), pp. 258–262 A. Takada et al., Observation of diffuse cosmic and atmospheric gamma rays at balloon altitudes with an electron-tracking compton camera. Astrophys. J. 733, 13 (2011) A. Takada, T. Tanimori et al., SMILE-3: sky survey in MeV gamma-ray using the electron-tracking Compton telescope loaded on balloons, in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 11444 (2020), p. 1144467 A. Takada et al., First observation of the MeV gamma-ray universe with bijective imaging spectroscopy using the electron-tracking compton telescope on board SMILE-2+. Astrophys. J. 930(1), 6 (2022) T. Tanimori, MeV Gamma-ray imaging spectroscopic observation for Galactic Centre and Cosmic Background MeV gammas by SMILE-2+ Balloon Experiment. J. Phys. Conf. Ser. 1468(1), 012046 (2020) T. Tanimori, H. Kubo et al., MeV gamma-ray imaging detector with micro-TPC. New Astron. Rev. 48, 263–268 (2004) T. Tanimori et al., An electron-tracking compton telescope for a survey of the deep universe by MeV gamma-rays. Astrophys. J. 810(1), 28 (2015) T. Tanimori et al., Establishment of imaging spectroscopy of nuclear gamma-rays based on geometrical optics. Sci. Rep. 7, 41511 (2017) D. Thers et al., Micromegas as a large microstrip detector for the COMPASS experiment. Nucl. Instrum. Methods A 469, 133–146 (2001) M.P. Titov, Radiation damage and long term aging in gas detectors, in Proceedings, 42nd Workshop of the INFN ELOISATRON Project, Erice, ICFA Instrum. Bull., vol. 26 (2004), p. 002 R. Veenhof, GARFIELD, recent developments. Nucl. Instrum. Methods A 419, 726–730 (1998), software page R. Veenhof, Gain limits, Hints from measurements of Ar mixtures, in RD51 mini week, CERN (2010) S.P. Wakely, D. Muller et al., Transition radiation detectors for energy measurements at high Lorentz factors. Nucl. Instrum. Methods A 531, 435–444 (2004) S. Watanabe et al., The Si/CdTe semiconductor Compton camera of the ASTRO-H Soft Gammaray Detector (SGD). Nucl. Instrum. Methods A 765, 192 (2014) J. Yoo, W.F. Jaskierny, Electron drift in a large scale solid xenon. JINST 10(08), P08011 (2015) K. Yoshino, U. Sowada, W.F. Schmidt, Effect of molecular solutes on the electron drift velocity in liquid Ar, Kr, and Xe. Phys. Rev. A 14, 438–444 (1976) S. Zimmermann, C. Cernoch, MDT Ageing Studies: Results of the measurements conducted at the Gamma Irradiation Facility GIF between autumn 2001 and summer 2003. Technical report, CERN, CERN-ATL-MUON-2004-019 (2004) P.A. Zyla et al., Review of particle physics. PTEP 2020(8), 083C01 (2020)

Gamma-Ray Polarimetry

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Denis Bernard, Tanmoy Chattopadhyay, Fabian Kislat, and Nicolas Produit

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Science Drivers of Gamma-Ray Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Scattering Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Experimental Approaches . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pair Production Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Differential Cross-Section . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polarization Asymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiple Scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polarimetry with Triplet Conversions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Past Experimental Achievements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Effective Area and Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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D. Bernard LLR, Ecole polytechnique, CNRS/IN2P3 and Institut Polytechnique de Paris, Palaiseau, France e-mail: [email protected] T. Chattopadhyay Kavli Institute of Particle Astrophysics and Cosmology, Stanford University, Stanford, CA, USA e-mail: [email protected] F. Kislat () University of New Hampshire, Durham, NH, USA e-mail: [email protected] N. Produit Astronomy Department, University of Geneva, Versoix, Geneva, Switzerland e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_52

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Abstract

While the scientific potential of high-energy X-ray and gamma-ray polarimetry has long been recognized, measuring the polarization of high-energy photons is challenging. To date, there have been very few significant detections from an astrophysical source. However, recent technological developments raise the possibility that this may change in the not-too-distant future. Significant progress has been made in the development of gamma-ray burst (GRB) polarimeters and polarization-sensitive Compton telescopes. A second-generation dedicated GRB polarimeter, POLAR-2, is under development for launch in 2024, and COSI, a second-generation polarization sensitive Compton telescope, has been selected by NASA for launch in 2025. This chapter reviews basic concepts and experimental approaches to scattering polarimetry of hard X-rays to MeV γ -rays and pair production polarimetry of higher-energy photons. Keywords

Gamma-rays · Polarization · Instrumentation · Compton polarimetry · Pair production polarimetry · Gamma-ray bursts · Black hole accreting systems · Neutron stars

Introduction The polarization of X-rays and γ -rays provides important observables, in addition to imaging, spectroscopy, and timing. While this potential has been recognized for a long time, measuring the polarization of high-energy photons is technically challenging. In fact, the only detection of γ -ray polarization at ≥5σ significance was AstroSat ’s measurement of the Crab (Vadawale et al. 2018). However, in the last two decades, there has been tremendous progress in the development of polarizationsensitive γ -ray detectors, and several highly promising missions are currently under consideration and under development. Gamma-ray polarimetry covers a broad energy range from tens of keV to GeVs. No single experimental approach can cover this entire energy range nor is there a single approach suitable to the broad range of scientific and observational objectives. In the energy range up to a few MeV, the azimuthal dependence of the Compton scattering cross-section can be exploited, whereas at higher energies the kinematics of electron-positron pair production is used. This is illustrated in Fig. 1 and discussed in more detail in sections “Basic Concepts” and “Differential Cross-Section”. In essence, the measured azimuthal distribution is modulated sinusoidally with a period of 180°, an amplitude proportional to linear polarization fraction and a phase related to polarization angle. At lower energies, the emission direction of photo-electrons can be used to measure polarization. However, that is outside the scope of this chapter. The ideal instrument design depends on whether the target of observation is a steady, predictable source or an unpredictable

61 Gamma-Ray Polarimetry 2 1.8 1.6 Relative Counts

Fig. 1 Azimuthal scattering angle distribution of an 80 keV beam with a polarization fraction of 85% at the Cornell High-Energy Synchrotron Source (CHESS) measured with X-Calibur. With the particular event selection, the instrument has a modulation factor of about 0.6. (Data from Beilicke et al. 2014)

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transient, such as gamma-ray bursts (GRBs). This paper gives an overview of the basic concepts of Compton and pair production polarimetry and compares the predominant experimental approaches and their trade-offs. While there is some astrophysical interest in circular polarization of γ -rays (e.g., Elagin et al. 2017; Huang et al. 2020; Shakeri and Allahyari 2018; Yang et al. 2017; Heyl and Caiazzo 2018), there is currently no sufficiently sensitive experimental approach to measure circular polarization. In principle, both Compton scattering (Clay and Hereford 1952; Tashenov 2011; Beard and Rose 1957; Trautmann et al. 1977) and pair production (Olsen and Maximon 1962; Kolbenstvedt and Olsen 1965; Olsen and Maximon 1959; Gakh et al. 2012) are sensitive to circular polarization, for example, when conversion or scattering takes place on polarized electrons (e.g., in magnetized iron targets), or when the polarization state of the final state electron(s) can be measured. The complete polarization state can be described by the four Stokes parameters I (intensity), Q and U (linear polarization), and V (circular polarization) (Stokes 1852; Kislat et al. 2015). The linear polarization state is fully described by I , Q, and U or, alternatively, polarization fraction and angle:  Q2 + U 2 p= I

and

ψ=

  1 U arctan . 2 Q

(1)

Due to the current lack of viable circular polarization detectors for astrophysics, this chapter focuses entirely on the measurement of linear polarization. A key challenge of γ -ray polarimetry is that source fluxes are typically low and backgrounds high. For example, assuming a not uncommon signal-to-background ratio of 1, on the order of 1 × 106 to 1 × 107 , photons must be collected to detect a 1% polarized signal at the 99% confidence level. The reason for this is that from a statistical perspective only the 1% of polarized photons contribute to the signal. Furthermore, the relative amplitude of the azimuthal modulation may not reach

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100% for a fully polarized signal. An important characteristic of any instrument is the so-called modulation factor for a 100% polarized signal: μ100 =

Amax − Amin , Amax + Amin

(2)

where Amax and Amin are the maximum and minimum of the azimuthal distribution, respectively. This modulation factor is determined by the kinematics of the photon interaction and by the ability of the instrument to measure the inherent azimuthal modulation. The latter depends on the process by which azimuth is measured and the geometry of the instrument. Figure 1 illustrates the azimuthal modulation measured with the scattering polarimeter X-Calibur during a beam test at the Cornell HighEnergy Synchrotron Source (CHESS). The beam is about 85% polarized, and the instrument has a modulation factor of ∼0.6. Typical modulation factors are in the μ100 = (10–50)% range. The statistical sensitivity to polarization of an observation is determined by the modulation factor, signal and background event rates, and observation time. The minimum detectable polarization (MDP) is commonly defined as the polarization fraction below which 99% observations fall in the absence of any polarization of the signal: 4.29 MDP = μ100 RS



RS + RB , T

(3)

where RS and RB are signal and background event rates, respectively, and T is observation time. Polarization is an inherently positive quantity. While the resulting statistical challenges are well understood, this also leads to systematic issues that must be understood in detail. For example, any azimuthal asymmetry of the instrument can lead to a false-positive signal if not mitigated or treated correctly in the data analysis. One mitigation strategy is to rotate the instrument during observations. However, that is not always possible. Statistical treatment of asymmetries requires their precise knowledge, which is typically gained from detailed Monte Carlo simulations, often using the Geant4 framework (Agostinelli et al. 2003). Of course, any simulation result must be verified through laboratory measurements with both polarized and unpolarized sources. The polarization sensitivity energy range of most Compton polarimeters lies in the sub-MeV domain, as both the Compton cross-section and the Compton polarization asymmetry are decreasing functions of energy. For pair polarimeters, for photons with an energy close to threshold (2me c2 ≈ 1 MeV), the limiting factor is the ability to detect, reconstruct, select, and trigger on pairs of low-momentum tracks, as the cross-section decreases and the angular resolution of the telescope degrades at low energy. Therefore, the energy range between 1 and ∼10 MeV will remain the most challenging for γ -ray polarimetry.

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A γ -ray polarimeter is not only a physical instrument; it involves also a simulation that is required to be able to transform the measured quantities to usable scientific measurements. This simulation has to be checked, tuned, and validated by using polarized and unpolarized sources in the laboratory. The instrument also has to be fully calibrated before the launch in conditions as close as possible to those on orbit. The ride aboard a rocket has the danger of disturbing the instrument due to depressurization, vibrations, shocks, and temperature excursions. Thus, calibration obtained on Earth must be verified and monitored in space. Energy response and detection efficiency can in general be monitored using radioactive sources. However, verification of the polarization response in space is complicated by the fact that most gamma-ray emission is expected to be at least partially polarized, resulting in a lack of a reliable unpolarized standard. Furthermore, while there are γ -ray polarization measurements of the Crab nebula, it certainly cannot be considered a true established calibration reference. Finally, it is very hard to accurately simulate the instrumental background conditions in space. A typical approach, thus, is to model measured backgrounds in order to understand their origin and then incorporate those results in the data analysis. Knowledge of the instrument response, typically obtained from simulations, is summarized in Response Matrix Files (RMFs) and Ancillary Response Files (ARFs). These response files fully characterize the instrument and are used in the analysis of measured data. The Geant4 simulation library (Agostinelli et al. 2003) accurately simulates polarized Compton scattering and can be used to derive the necessary response files, provided a sufficiently accurate mass model is implemented. For pair conversion, after it was found (Gros and Bernard 2017b) that the existing polarized “Physics Model” fails to generate events with the known polarization asymmetry (Gros and Bernard 2017a), a new “G4BetheHeitler5DModel” Physics Model (Semeniouk and Bernard 2019; Bernard 2018) that samples the 5D polarized Bethe-Heitler differential cross-section (May 1951) has been implemented and has been available since Geant4 release 10.6 (Ivanchenko et al. 2020). This paper is structured as follows. Section “Science Drivers of Gamma-Ray Polarimetry” provides an overview of the scientific motivation for γ -ray polarimetry. Basic concepts and experimental approaches to scattering polarimetry are discussed in section “Scattering Polarimetry”, and pair-production polarimetry is reviewed in section “Pair Production Polarimetry”. The paper closes in section “Summary and Outlook” with a summary, discussion of unresolved issues, and future outlook.

Science Drivers of Gamma-Ray Polarimetry Science drivers for polarimetry in energies, ranging from a few tens of keV to the MeV region, focus on a number of X-ray and gamma-ray sources that are bright in this energy range. Scientific potential in hard X-rays and the recent findings from

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some of the recent X-ray spectro-polarimetric instruments have been summarized in Chattopadhyay (2021). The following is a brief description of the science cases for some of the bright gamma-ray sources. • Gamma-Ray Bursts: Measurement of gamma-ray polarization has the potential to test the proposed models for GRB prompt burst emission mechanism (Covino and Gotz 2016; McConnell 2016; Toma et al. 2009), e.g., synchrotron emission from relativistic electrons either in a globally ordered magnetic field (Lyutikov et al. 2003; Nakar et al. 2003; Granot and Königl 2003) or in a random magnetic field generated in the shock plane within the jet (Medvedev and Loeb 1999) or emission due to Comptonization of soft photons (Shaviv and Dar 1995) by the relativistic jet. In the past decade, several dedicated X-ray polarimetry experiments and some of the spectroscopic instruments have reported measurements of X-ray/γ -ray polarization for several GRBs (see reviews by McConnell 2016; Gill et al. 2021; Chattopadhyay 2021). Gamma-ray burst polarimeter (GAP) and CZT imager (CZTI) aboard AstroSat reported high polarization fractions (>50%) for a few GRBs (Yonetoku et al. 2011, 2012; Chattopadhyay et al. 2019). For CZTI, GRB intervals were optimized for best detection of polarization. On the other hand, POLAR, a dedicated GRB polarimeter aboard Chinese space station, found most of the GRBs to have low or null polarization in their full burst intervals (Zhang et al. 2019; Kole et al. 2020). Although a firm conclusion on the prompt emission requires polarization measurements of a larger number of GRBs, the existing results indicate that GRB prompt emission is highly structured which can lead to possible variation in polarization angle within a burst as has been seen in a number of GRBs (Sharma et al. 2019; Burgess et al. 2019). • Active Galactic Nuclei (AGN): The power-law component seen in AGN spectra corresponding to the coronal emission is expected to be polarized owing to the scattering of disk photons by corona. Measurement of polarization of this component can be useful in investigating the corona geometry (Schnittman and Krolik 2010). • Blazars: In the case of low-energy peaked blazars, polarization in MeVs is expected to explain the origin of the high-energy peak in their spectral energy distribution. For example, while the synchrotron self-Compton model (SSC model, Celotti and Matt 1994) predicts around 30% polarization in a uniform magnetic field, the external Compton model (EC) predicts null polarization (50%) for Cygnus X-1 at energies above ∼300 keV, while the emission at relatively lower energies was found to be weakly polarized (Laurent et al. 2011; Jourdain et al. 2012). • Accreting Neutron Stars: Phase-resolved polarization study of accreting neutron stars in hard X-rays can be useful in determining the beam shape of the pulsar, e.g., to distinguish between the pencil and fan beam radiation patterns where oscillations in polarization fraction with the pulse phase are predicted to be opposite to each other (Meszaros et al. 1988). In case of millisecond X-ray pulsars, polarization measurement has the potential to test the origin of highenergy photons and put tighter constraints on geometrical parameters like orbital and dipole axis inclinations (Viironen and Poutanen 2004; Sazonov and Sunyaev 2001). Recently, the balloon-borne hard X-ray polarimeter X-Calibur , during a balloon flight in December 2018, reported a phase-integrated 15 keV to 35 keV polarization fraction of 27+38 −27 % for GX 301-2 as well as on-pulse and bridge polarizations of 32+41 % and 27+55 −32 −27 %, respectively, which does not constitute a non-zero detection (Abarr et al. 2020). • Magnetars: Gamma-ray polarization for magnetars can test the RICS model (Resonant Inverse Compton Scattering, see Wadiasingh et al. 2017; Beloborodov 2012; Baring and Harding 2006) explaining the origin of hard X-ray tail seen in the spectra of a several magnetars. A high level of linear polarization in hard X-rays would be a direct confirmation of RICS process in magnetar’s lower magnetosphere (Wadiasingh et al. 2019). Polarimetry studies of magnetars also offer unique opportunity to test the QED effects in strong magnetic field. • Pulsars: Phase-resolved γ -ray polarization has the potential to investigate the emission sites of high-energy radiation from rotation-powered pulsars. The theoretical models, e.g., polar cap model (Daugherty and Harding 1982), outer gap model (Cheng et al. 2000), slot gap model (Dyks and Rudak 2003),

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and striped pulsar wind (Kirk et al. 2002; Pétri and Kirk 2005), propose different acceleration sites for the relativistic electrons and predict distinct phasedependent polarization signatures which can be tested by gamma-ray polarimetry studies of X-ray pulsars. In recent times, there have been a number of reports on measurements of polarization of Crab pulsar and nebula in hard X-rays from instruments like SPI, IBIS, PoGO+, CZTI, Soft Gamma-ray Detector (SGD ) on board Hitomi, and POLAR (Jourdain and Roques 2019; Forot et al. 2008; Chauvin et al. 2018b; Vadawale et al. 2018; Aharonian et al. 2018; Li et al. 2021). All these instruments found high polarization 20 % for both phaseaveraged Crab and nebula separately with polarization angle closely aligned with the pulsar spin axis, 124.0±0.1◦ (Ng and Romani 2004). • Solar Flares: Gamma-ray polarization measurement of solar flares has the potential to investigate the emission mechanism behind the high-energy photons which is widely believed to be from nonthermal Bremsstrahlung emission by the high-energy electrons. Polarization measurements are expected to probe multiple crucial model parameters like beaming of the electrons, magnetic field structure, back-scattering of the photons from the photosphere, and dependence of polarization on the location of the flare on the disk (Bai and Ramaty 1978; Leach et al. 1985; Zharkova et al. 2010; Jeffrey and Kontar 2011). Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI ) and a polarimeter SPR-N on board CORONAS-F reported polarization for a sample of M and X class flares in hard X-rays (Suarez-Garcia et al. 2006; Zhitnik et al. 2006). Due to the large uncertainties in the measurements, any firm conclusion on the hard X-ray origin of the flares was not feasible from these measurements.

Scattering Polarimetry Basic Concepts Rayleigh and Compton scattering, like essentially all electromagnetic interactions, conserve polarization. Because photons are massless, their polarization is perpendicular to their momentum vector. As an immediate consequence, photons preferentially scatter perpendicular to their polarization. In fact, in the low-energy limit, a 90° scattered photon scattering along the polarization direction would lead to a longitudinally polarized photon, which is forbidden. Rayleigh scattering and photo effect dominate at low energy and are more important for material of high atomic number Z. Compton scattering dominates for energies between ∼50 keV and ∼10 MeV, depending on the target material. The cross-section of the Compton process (see Fig. 2) follows the Klein-Nishina formula (e.g., Evans 1955): dσ 1 = re2 dΩ 2



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with  E λ′ 1 + E/me c2 (1 − cos θ ) = ′ = E λ

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Here, re = e2 /4π ǫ0 me c2 ≈ 2.818 × 10−15 m is the classical electron radius; E, λ, E ′ , λ′ are the energy and wavelength before and after scattering, respectively; θ is the scattering angle; and φ is the azimuthal scattering angle with respect to polarization (see Fig. 2). The cross-section is illustrated in Fig. 3. It depends on polarization through the φ angle, which must be measured by any scattering polarimeter. The dependence is in cos2 φ (or 2φ as cos2 φ = (cos 2φ + 1)/2) as it should be because polarization lives in the projective plane so must have a π symmetry. The cross-section is strongly forward-backward enhanced by the

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sin2 θ term, with a strong forward enhancement in the high-energy limit. The polarization sensitivity is strongest when θ is π/2. Hence, there is an advantage to have a detector that can detect perpendicular scatterings. The direction of the recoil electron in Compton scattering is also sensitive to polarization. While this is being exploited by some experimental approaches (see section “3D Instruments”), directional information of the electron is rapidly lost due to multiple scattering.

Experimental Approaches A range of instruments based on these general principles has been designed, built, tested, and in some cases flown on spacecraft or high-altitude balloons (Table 1). Differences in instrument design result from specific scientific objectives, as well as a range of detailed trade-offs. One of the most important considerations in the design of a Compton polarimeter is the selection of detector materials. This is illustrated in Fig. 4, which shows the fractional cross-section for scattering for a selection of commonly used materials. Low-Z materials are ideally suited as scattering targets over a broad energy range. In fact, below ∼20 keV purity of the scattering material is critically important, and even a small contamination with high-Z elements can degrade performance. On the other hand, high-Z materials such as inorganic CsI scintillator or CZT semiconductor detectors provide a large photon absorption crosssection though it should be noted that scattering is the dominant interaction process over an energy range from a few hundred keV to a few MeV, regardless of target material. As a consequence, many detector designs consist of dedicated low-Z scattering and high-Z detector elements, although some instruments use only a single material. Compton polarimeters can broadly be divided into two classes: wide field and point source instruments. Wide-field instruments are ideally suited for studies of bright transient events such as gamma-ray bursts and for extended sources. Wide-field instruments can further be subdivided into wide-field polarimeters and Compton telescopes, which in addition to polarimetry have significant imaging capabilities. Point source instruments are optimized for in-depth observations of point-like sources. Their background tends to be lower resulting in a higher sensitivity for steady sources. Point source instruments can further be subdivided into collimated large area instruments and focal plane instruments. The latter utilize imaging or light-collecting optics allowing a significant reduction of the detector size, and as a consequence background, while maintaining a significant effective area. While the optics tend to have less effective area than large area polarimeters, the improved signal-to-background ratio enhances sensitivity to weak sources and objects with low polarization fraction. The following sections describe examples of each of these four classes, and the trade-offs that led to the various designs. The instruments were chosen based on their relevance to the field and to highlight certain aspects and trade-offs of each implementation. This section is not intended to represent an exhaustive list.

FOV Full Sun disk

2π sr

4.8°

45° × 45°

45° × 45°

30° × 30°

2π sr

2°

π sr

Instrument SPR-N

MEGA

PHENEX

TIGRE

PENGUIN-M

GAP

GRAPE

POGO+

COSI (Balloon)

200 keV to 2000 keV

20 keV to 180 keV

50 keV to 500 keV

50 keV to 300 keV

256 cm2

1400 cm2

144 cm2

176 cm2

80 cm2 at1 MeV 78 cm2

400 keV to 1 × 105 keV

20 keV to 150 keV

44 cm2

324 cm2

Effective area 50 cm2

40 keV to 200 keV

300 keV to 5 × 104 keV

Energy range 20 keV to 100 keV

Technology Be scatterer and scintillators Silicon strips and CsI Plastic scintillator and CsI Silicon strips and CsI Plastic scintillator and NaI Plastic scintillator and CsI Plastic scintillator and CsI Plastic scintillator and CsI Segmented Ge 3.2°

2°

Non-imaging

Non-imaging

2° ARM at 1 MeV Non-imaging

Non-imaging

Some degree

Angular resolution Non-imaging

Satellite wide-field Balloon wide-field Balloon collimated Balloon 3D

Satellite

Balloon collimated Balloon 3D

Balloon 3D

Type Satellite

Point sources GRB Point sources

GRB

Science Solar flares GRB Point sources Point source GRB Point sources Solar flares GRB

2016

2016

(continued)

2011 and 2014

2010–2011

2009–2010

2010

2006 and 2009

Prototype

Status 2001–2005

Table 1 Hard X-ray and γ -ray polarimetry missions, important prototypes, and proposed missions and key characteristics, representing a broad cross-section of past and current experimental efforts. The order is approximately chronological. The numbers in the table are only indicative; the energy range and the effective area may be different for polarization measurements and in case of balloons may not include absorption in atmosphere. “Type” lists the type of mission and of the instrument according to the classification used in section “Experimental Approaches”

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6′

X-Calibur / XL-Calibur INTEGRAL IBIS

9° × 9°

4.6° × 4.6°

2π sr

2π sr

45° × 45°

INTEGRAL SPI

AstroSat

POLAR

POLAR-2

PING-P

9° × 9°

FOV 0.6° × 0.6°

Instrument SGD

Table 1 (continued)

20 keV to 150 keV

10 keV to 500 keV

50 keV to 500 keV

100 keV to 350 keV

15 keV to 1 × 104 keV

20 keV to 60 keV 20 keV to 80 keV 15 keV to 1 × 104 keV

Energy range 50 keV to 200 keV

Technology Si pixels and CdTe Be scatterer and CZT CdTe, CsI

Ge

CZT

Plastic scintillator Plastic scintillator Plastic scintillator and CsI

10 cm2 at 50 keV 100 cm2 at 50 keV 2600 cm2

500 cm2

924 cm2 above 100 keV 300 cm2 at 300 keV

1250 cm2 at 300 keV 30 cm2

Effective area 210 cm2

Non-imaging

5° bright GRB

10° bright GRB

Non-imaging

1°

12′′

Non-imaging

Angular resolution 30°

Space station wide-field Space station wide-field Satellite

Satellite coded mask

Satellite coded mask

Type Satellite collimated Balloon Focal plane Satellite coded mask

Solar flares

GRB

GRB, Point sources GRB

Science Point sources Point sources Point sources GRB Point source

2025

Manifested 2024

2016–2017

2016, 2019, 2022 Flying since Oct 2002 Flying since Oct 2002 Flying since 2015

Status 2016

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π sr

1.5π sr

2.5 sr

2.5 sr

COSI (SMEX)

LEAP

AMEGO

e-ASTROGAM ASTROMEV

Segmented Ge

Plastic scintillator and CsI Silicon strips CZT and CsI

256 cm2

1000 cm2 608 cm2

10 000 cm2

50 keV to 500 keV

200 keV to 1 × 106 keV

300 keV to 3 × 106 keV

200 keV to 2000 keV

Silicon strips and CsI

Plastic scintillator and GSO

3.2 cm2

10 keV to 80 keV

0.15° at 1 GeV

2.5° at 1 MeV

1 − 5°

3.2°

1°

Satellite 3D

ISS wide-field Satellite 3D

Satellite 3D

Satellite Focal plane

Point sources, GRB Point sources, GRB

GRB, Galactic sources GRB

Point sources

Proposed

Proposed

Proposed

Under development, Launch TBD Selected 2025

References: SPR-N (Bogomolov et al. 2003), MEGA (Bloser et al. 2006), PHENEX (Gunji et al. 2008), TIGRE (O’Neill et al. 1996; Bhattacharya et al. 2004), PENGUIN-M (Dergachev et al. 2009), GAP (Yonetoku et al. 2006), GRAPE (Bloser et al. 2009), POGO+ (Friis et al. 2018), COSI (Balloon) (Yang et al. 2018), SGD (Aharonian et al. 2018), X-Calibur (Kislat et al. 2018), XL-Calibur (Abarr et al. 2021), IBIS (Ubertini et al. 2003), SPI (Vedrenne et al. 2003), AstroSat (Vadawale et al. 2015), POLAR (Produit et al. 2018), POLAR-2 (Kole 2019), PING-P (Kotov et al. 2016), PolariS (Hayashida et al. 2014), COSI (SMEX) (Tomsick et al. 2019), LEAP (McConnell et al. 2021), AMEGO (McEnery et al. 2019), e-ASTROGAM (De Angelis et al. 2018)

10′′ × 10′′

PolariS

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1

σc/ σ

0.8 0.6 Be EJ-200 Si Ge CZT CsI

0.4 0.2 0 1

10

102 Energy [keV]

3

10

104

Fig. 4 Ratio of scattering to total cross-section of a selection of commonly used materials. EJ-200 (base material polyvinyltoluene) is shown as an example of a common plastic scintillator material. At low energy, photoelectric absorption dominates, whereas above a few MeV electron-positron pair production dominates. (Data from the NIST XCOM photon cross-section database)

Wide-Field Instruments Wide-field γ -ray polarimeters are characterized by a field of view that covers a significant fraction of the sky, typically on the order of (1−2)π sr, and a large photon collection area. This class of γ -ray polarimeters is primarily designed to measure the polarization of short transient events, such as gamma-ray bursts and magnetar outbursts. The unpredictable nature and short duration of these events makes the wide field of view necessary. Another key requirement is a large effective area in order to detect a sufficient number of photons during a short event, typically a few seconds for a short GRB and up to a few hundred seconds for a long GRB (von Kienlin et al. 2020). The instruments discussed in this section are designed with these primary requirements in mind. Imaging and spectroscopy are not driving factors. All instruments discussed here are optimized for an energy range around the GRB peak flux, typically ranging from tens to hundreds of keV. Several instruments in this category have been flown or are currently under development: the Gamma-Ray Burst Polarimeter GAP (Yonetoku et al. 2004) aboard the Japanese IKAROS satellite; POLAR (Produit et al. 2018) on the Chinese space laboratory Tiangong2 ; the balloon-borne Gamma-ray Polarimeter Experiment GRAPE (Bloser et al. 2009); POLAR-2 (De Angelis 2021) currently under construction; and the proposed Large Area Burst Polarimeter LEAP for the International Space Station (McConnell et al. 2021). They are all based on an array of scintillator detectors that serve both as scattering target for the incoming photons and as photoabsorber material for the scattered photons. The scintillators are typically in the form of long bars read out by photomultiplier tubes or SiPMs on one end. Figure 5 shows a detector module of POLAR consisting of 64 plastic scintillator bars, illustrating the concept.

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Fig. 5 One of the 25 modules of POLAR. The 64 plastic scintillator bars are read out by a multichannel PMT. Triggering and analog-to-digital conversion are handled by the Front-End Electronics (FEE) board

Events in which a photon Compton scatters in one scintillator element and is absorbed in another are ideally suited to measure polarization. In that case, determination of polarization information from the azimuthal scattering angle is completely geometrical. Due to the π symmetry of polarization, it is not necessary to determine the order of interactions. On the other hand, if the incident photon is immediately absorbed in one detector element, no polarization information can be obtained. The exact detector geometry is the result of an optimization, and different conclusions may be reached depending on different requirements and priorities. For example, POLAR consists of an array of 1600 plastic scintillator bars of 6 × 6 × 200 mm3 arranged on a square grid and read out by multi-anode photomultiplier tubes (Produit et al. 2018). The goal of this design is to maximize the fraction of photons that interact in two separate elements regardless of incident angle, creating a field of view of about 2π sr. The designers also found that this approach maximizes the mean free path between photon interactions, which improves the quality of the azimuth angle determination. Usage of very fast plastic scintillator also enable to reduce the coincidence window to 50 ns, so there are virtually no random coincidences even during most bright GRB or heavy background conditions. The successor mission of POLAR, POLAR-2, will use the same design but four times the number of detector modules. Use of SiPMs instead of photomultiplier tubes (PMTs) will improve quantum efficiency and thus reduce the detector threshold to about 10 keV. LEAP, on the other hand, consists of 7 modules of 144 scintillator bars, each of which 84 are plastic scintillators and 60 are inorganic CsI(Tl) scintillators. The

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bars are 17 × 17 × 100 mm3 in size, optically isolated, and read out by individual photomultiplier tubes. The CsI elements are arranged around the edge of each module as well as forming an X in the middle. This design limits the field of view to about 1.5π sr because most photons at large zenith angles would have to pass through a CsI element before scattering in a plastic element. On the other hand, the likelihood that scattered photons are absorbed is increased, and CsI provides a better energy resolution than plastic scintillator. GAP has a better defined scattering geometry in featuring a single plastic scintillator in the middle and a ring of high-Z scintillators. This geometry enables very accurate azimuthal angle measurement, but the effective area and the angular acceptance are small. Neither design allows direct single-photon imaging capabilities. However, all instruments have the ability to localize transient events by comparing event rates in different detector elements. For example, the statistical localization error for a burst with an MDP 300 GeV within a single mission. The GBM 10-year GRB catalog (von Kienlin et al. 2020) includes 2356 GRBs, while the LAT 10-year GRB catalog (Ajello et al. 2021) includes only 186 GRBs, resulting in 100 keV. The bottom panel shows the time-frequency map of GW170817 from LIGO-Hanford and LIGOLivingston

with respect to the lower energy emission, typically by a few seconds. Emission above 100 MeV typically lasted longer than the lower energy emission. Specific individual bursts resulted in additional key advances. Here we highlight results from GRB 090510, GRB 130427A, GRB 190114C, and GRB 200415A.

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For the short GRB 090510 with a known distance (z = 0.903 ± 0.003, Rau et al. 2009), a LAT observation of a single 31-GeV photon coinciding with the last of seven GBM pulses set the most stringent limits to date on variations in the speed of light with energy, called Lorentz invariance. This is an important component of Einstein’s special relativity, the idea that the speed of light is the same for all observers and does not vary with energy. Sharp features in GRB light curves could reveal tiny variations in the speed of light if they were present (Abdo et al. 2009c). GRB 130427A was the most fluent GRB observed with GBM and had the second highest spectral peak energy ever recorded with GBM. However, existing models cannot simultaneously explain all of the observed spectral and temporal behaviors (Preece et al. 2014). GRB 130427A was the longest burst detected above 100 MeV and had the most energetic photon detected, at 95 GeV. The widely accepted external shock model cannot explain the high-energy spectral component seen in this GRB (Ackermann et al. 2014a). GRB 190114C was remarkable because it was the first reported GRB detected on the ground at TeV energies, by the MAGIC telescope (MAGIC Collaboration et al. 2019), starting about 1 min after the initial GBM detection. Joint observations with Fermi and Swift reveal GRB 190114C to be the second most luminous GRB above 100 MeV, surpassed only by GRB 130427A. The prompt emission shows typical GRB spectral components. An additional power-law component that extends to higher energies explains the delayed onset of the LAT emission. This additional power-law component is also seen as a low-energy excess in GBM data. A long-lived afterglow component is also present in the GBM data and in Swift. The detection of photons above 300 GeV with MAGIC suggests that an additional emission mechanism is required to explain the full extent of the observed emission. GRB 200415A turned out not to be a traditional GRB at all. Instead it revealed a new progenitor. The Interplanetary Network localized GRB 200415A to the nearby Sculptor Galaxy (NGC 253) (Svinkin et al. 2021). Fermi GBM measured an extremely rapid rise time of 77 µs and a hard spectral slope and along with Swift BAT, measured an unusually short duration of 140 ms (Roberts et al. 2021). These features point to an extragalactic giant magnetar flare instead of a neutron star merger as the origin of this short GRB. Magnetars are neutron stars with very large magnetic fields (>1013 G). The Fermi LAT detected three high-energy photons, with energies of 480 MeV, 1.3 GeV, and 1.7 GeV at 19 s, 180 s, and 284 s after the GBM trigger time. These events were spatially associated with the Sculptor Galaxy and are the first ever GeV detections associated with a giant magnetar flare (The FermiLAT Collaboration 2021).

Magnetars In addition to the likely extragalactic giant magnetar flare detected by GBM as GRB 200415A, GBM has triggered on a number of other magnetars, exhibiting a variety of bursting activity (Collazzi et al. 2015; van der Horst et al. 2012; Kaneko et al. 2010), including bursts from a magnetar that has been associated with a Fast Radio Burst (FRB) (Younes et al. 2021; Lin et al. 2020). It also detected many more

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magnetar bursts through subthreshold analyses and discovered a new magnetar, SGR J0418+5729 (van der Horst et al. 2010). The GBM Magnetar catalog (Collazzi et al. 2015) describes spectral and temporal analyses for 440 magnetar bursts from the first 5 years of the Fermi mission. Magnetar bursts are typically sub-second in duration and spectrally softer, with a lower peak energy, than γ -ray bursts. Persistent emission from magnetars shows slow spin periods (∼2–12 s) and large period derivatives (∼10−13 –10−10 s s−1 ). Historically, the magnetar population has been divided into two classes, soft γ -ray repeaters (SGRs) and anomalous X-ray pulsars (AXPs), with the SGR class describing bursting sources and the AXP class describing those with only persistent emission, but it is now known that sources move between the two classes. On April 27, 2020, SGR J1935+2154 emitted a storm of hundreds of bursts. One burst, detected by INTEGRAL (Mereghetti et al. 2020), Konus-Wind (Ridnaia et al. 2021), and Insight-HMXT (Li et al. 2021), was remarkable because it was temporally associated with an FRB, but Fermi GBM was not observing the source at the time of the FRB. Comparisons of 24 bursts (Younes et al. 2021) observed from the burst storm with GBM and NICER only 13 h before the FRB and 148 bursts (Lin et al. 2020) observed with GBM in 2019 and 2020 revealed that the FRB-associated burst had a much higher cutoff energy and steeper power-law than the large number of GBM bursts. The likely explanation for the difference is that the FRB-associated burst originated in quasi-polar regions at high altitudes, while the typical GBM bursts originated in quasi-equatorial regions (Younes et al. 2021). Early in the Fermi mission in October 2008 and January and March 2009, SGR J1550-5418 underwent three burst active episodes. Untriggered burst searches of GBM data revealed about 450 bursts during a 24-hour interval at the peak of the second episode. At the onset of the second bursting episode, a 150-s-long interval of enhanced persistent emission was found. This interval showed clear pulsations up to about 110 keV at the spin period of 2.07 s, additional spectral components, and an energy-dependent pulsed fraction that was largest (55%) in the 50–74 keV band (Kaneko et al. 2010).

Crab Variations Observed by GBM and LAT The Crab Nebula, powered by its 33-ms pulsar, has long been considered a stable “standard candle” in high-energy astrophysics. Fermi’s GBM and LAT, together with other observatories, have now overturned that concept, showing two very different types of variability in this bright γ -ray source. From 2008 to 2010, Fermi GBM along with the Rossi X-ray Timing Explorer (RXTE) Proportional Counter Array (PCA), Swift Burst Alert Telescope (BAT), and the Imager on-Board the INTEGRAL Satellite (IBIS) found a 7% decline in the 15–50 keV Crab Nebula flux. Similar declines were seen in lower and higher energy bands. Variations of ±3% per year were also seen from 2001 to 2008 with RXTE (Wilson-Hodge et al. 2011). Similar variations, typically 0.1 TeV. Ground-based detection of gamma rays relies on the M. Errando () Department of Physics, Washington University in St. Louis, St. Louis, MO, USA e-mail: [email protected] T. Saito Institute for Cosmic Ray Research, The University of Tokyo, Kashiwa, Japan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_61

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electromagnetic showers that gamma rays initiate in the Earth’s atmosphere. In this chapter we will review the properties of electromagnetic air showers as well as the differences with respect to cosmic-ray showers that enable the rejection of the cosmic-ray background. The experimental techniques that have been developed for ground-based detection of gamma rays will be introduced. These fall onto three main categories: air shower particle detectors, sampling Cherenkov arrays, and imaging atmospheric Cherenkov telescopes. Hybrid concepts and other experimental approaches are also discussed. Keywords

Gamma rays · TeV · Cherenkov · Air showers · Cosmic rays · Ground-based observatories

Introduction The Earth’s atmosphere is opaque to gamma rays. Cosmic gamma rays interact with the upper atmosphere producing showers of energetic electrons, positrons, and photons. The detection and characterization of these electromagnetic showers enables the study of cosmic gamma-ray sources from the ground. Current-generation ground-based observatories achieve their peak sensitivity for gamma rays in the TeV energy scale. The gamma-ray flux from the Crab Nebula above 1 TeV is ∼2×10−7 m−2 s−1 . TeV observatories need to realize effective areas >104 m2 to detect a few photons from the Crab Nebula in one hour of exposure. Such large instruments cannot be mounted on an orbital platform and must be installed on the Earth’s surface, making the Earth’s atmosphere an integral part of any ground-based gamma-ray observatory. Rather than detecting the passage of primary gamma rays through an instrument, ground-based detection is achieved in an indirect fashion by recording the secondary particles and radiation produced by the interaction of the primary gamma-ray with the atmosphere. These secondaries comprise what is known as extensive air showers. There are two main techniques to detect cosmic gamma rays from the ground. The first measures the passage of the secondary charged particles that make the extensive air shower through a surface detector array. The direction of the primary gamma ray is determined by arrival time differences recorded at different detectors as the shower front sweeps through the detector plane. The second technique uses optical telescopes to focus Cherenkov light produced by shower particles onto photon detectors. The first generation of Cherenkov telescopes had a single photomultiplier seeing each mirror. The second generation used the imaging technique with multi-pixel photomultiplier cameras and exploited results from Monte Carlo simulations of electromagnetic and hadronic air showers to improve the angular resolution and background rejection. This led to the detection of the Crab Nebula by the Whipple 10 m observatory in 1989 (Weekes et al. 1989), the first significant detection of an astrophysical gamma-ray source with a ground-based observatory.

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Three decades later, the LHAASO reported the detection of a population of galactic PeV sources using a particle sampling array. Many observatories have been in operation during this time, including sampling and imaging Cherenkov telescopes as well as particle sampling arrays, leading to the development of ground-based gamma-ray astronomy (Hinton and Hofmann 2009). This chapter discusses the development of electromagnetic and hadronic showers in the Earth’s atmosphere and describes the operating principles of the different types of ground-based gamma-ray observatories. For a more comprehensive discussion on electromagnetic and hadronic showers, along with a review of the basic physics processes that influence their development, the reader is directed to the book by Gaisser et al. (2016). A classic discussion of electromagnetic air showers that includes parameterizations that are still used to this day can be found in the review by Rossi and Greisen (1941). Finally, a more compact description of shower physics along with the principles of ground-based detection of gamma rays is given in the review by Aharonian et al. (2008).

Electromagnetic Air Showers Gamma-ray photon incident in the Earth’s atmosphere will pair produce in the presence of the Coulomb field of an atmospheric nucleus. The resulting electron– positron pair will subsequently produce multiple generations of secondary photons and pairs via bremsstrahlung and pair production, leading to the development of an electromagnetic cascade (Fig. 1). Eventually, the energy is dissipated by ionization of the medium (the Earth’s atmosphere) by all the electrons and positrons in the cascade. Photon or cosmic-ray-initiated cascades in the Earth’s atmosphere are often referred to as air showers. In this section we will provide some analytical approximations that will give the reader a quantitative understanding of the aspects of electromagnetic showers that are most relevant to the indirect detection of gamma rays from the ground. The three processes that govern the development of electromagnetic particle showers initiated by gamma rays are bremsstrahlung, pair production, and ionization losses. Bremsstrahlung energy losses for electrons and positrons can be characterized by a radiation length X0 that depends on the medium and is defined as the amount of matter a high-energy electron has to traverse to lose all but 1/e of its energy. The processes of pair production and bremsstrahlung are very closely related. Their Feynman diagrams are variants of one another. As a result, the radiation length for bremsstrahlung is 7/9 of the mean free path for pair production. Given the similarity of length scales between the two main processes driving the development of electromagnetic air showers, one can derive a simple analytical approximation for the development of the shower in which every ln(2) X0 every particle (photon, electron, or positron) produces two more particles that share its energy (Heitler 1954). Eventually, the energy of the electrons and positrons reaches a critical energy Ec where ionization takes over from bremsstrahlung as the dominant energy loss mechanism for charged leptons and the electromagnetic

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0.1 TeV photon

0.1 TeV proton

Fig. 1 Simulated showers initiated by a 100 GeV gamma ray (left) and a 100 GeV proton (right) in the Earth’s atmosphere. Red tracks indicate secondary electrons, positrons, and photons with energy E > 0.1 MeV. Green and blue tracks show muons and hadrons with E > 0.1 GeV. The first interaction is fixed at 30 km height and the lateral scale is ±5 km. (Adapted from Schmidt and Knapp 2005)

shower dies out. In air, Ec = 88 MeV for electrons and 86 MeV for positrons (Particle Data Group et al. 2020). All particles in the shower are strongly collimated along the incident direction of the primary gamma ray that defines the shower axis. Multiple Coulomb scattering and, at the second order, the deflection of charged particle trajectories by the Earth’s magnetic field contribute to broadening the shower profile. Figure 1 shows the simulated particle tracks of an atmospheric air shower initiated by a gamma ray.

The Earth’s Atmosphere Particle showers develop on a medium (the Earth’s atmosphere) that has increasing density as the shower progresses from high altitudes toward the ground level. The density profile of the atmosphere at midlatitudes can be reasonably approximated by an exponential function ρ(z) = ρ0 exp(−z/H )

(1)

where z is the vertical height measured above sea level, ρ0 ∼ 1.225 × 10−3 g cm−3 , and H ∼ 8.4 km is the atmospheric scale height. The most practical applications use

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Table 1 Atmospheric parameters from the U.S. Standard Atmosphere model that are relevant for the development of air showers and the production of Cherenkov light. Columns indicate the vertical height measured from sea level, vertical atmospheric depth in radiation lengths, local density of the atmosphere, threshold for production of Cherenkov light and Cherenkov angle for electrons, and the average expected number of shower particles for showers initated by gamma rays with Eγ = 0.1, 1, 10, and 100 TeV. (Data from National Aeronautics Space Administration 1976; Gaisser et al. 2016) Height z [km] 20 10 5 3 1.5 0

Vert. depth x ′ /X0 1.52 7.25 15.0 19.5 23.6 28.2

Density ρ [10−3 g/cm3 ] 0.088 0.42 0.74 0.91 1.06 1.23

Ch. th. [MeV] 80 37 28 25 23 21

Ch. ang. θCh [◦ ] 0.36 0.79 1.05 1.17 1.26 1.36

N (z) for Eγ /TeV 1.0 10 100

0.1

21 3.0 0.4 0.04

490 110 21 2.6

7800 2800 740 120

92000 51000 19000 4100

top of the atmosphere

x= 0 x′

x

z T

l

z= 0

ground level

Fig. 2 Definition of the variables used to describe the Earth’s atmosphere. (Adapted from Gaisser et al. 2016)

tabulated atmospheric models based on atmospheric profiling data that describe the experimental sites where gamma-ray observatories are located. An example of the atmospheric properties at certain relevant altitudes for one such model is given in Table 1. Temperature effects close to the Earth’s surface produce seasonal changes in density of the order of 3–5% at 10 km height increasing to ∼15% at 15 km. Let us define the total path length in the atmosphere of a particle with incident zenith angle θ moving on a straight trajectory from a vertical height z to the ground as ℓ (Fig. 2). For small zenith angles (θ  65◦ ), the curvature of the Earth can be neglected and ℓ = z/ cos θ . To remove the effect of the changing density of the atmosphere, it is common to quote the depth x of the particle track in units of g cm−2 instead of the geometric path length ℓ and to scale it by the radiation length of the material, which is X0 = 36.6 g cm−2 for dry air at 1 atm of pressure (Particle Data Group et al. 2020). The atmospheric depth of a particle entering the atmosphere and moving down to a height z will then be x=



ℓ

∞

ρ(z = ℓ cos θ ) dℓ

(2)

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which reduces to ′

x =



∞

ρ(z′ ) dz′

(3)

z

for a vertically incident particle. In this framework, the atmosphere of the Earth can be considered an electromagnetic calorimeter with approximately 28 radiation lengths of low Z material (Table 1).

Longitudinal and Lateral Development of Electromagnetic Showers A primary gamma ray with energy Eγ will develop an electromagnetic shower in the atmosphere. At the ground level, a typical shower front has a radius of 130 m and a thickness of 1–2 m at the shower core, growing wider toward the edges of the front. The number of electromagnetic particles in the shower as a function of atmospheric depth is shown in Fig. 3 and can be described by the analytical Approximation B approach from Rossi and Greisen (1941). After the first interaction, the number of electrons and positrons grows rapidly until reaching a shower maximum, which will occur at an atmospheric depth xmax = X0 ln(Eγ /Ec )

(4)

For a 1 TeV primary gamma ray, the shower maximum occurs at ∼10 km above the sea level. After the shower maximum, the number of particles decreases by a factor of ∼1.65 for each additional radiation length that is transversed. The number N of secondary electrons and positrons at a given atmospheric depth x can be approximated by Hillas (1982)   0.31 N (x) =  exp Xx0 (1 − 1.5 ln s) ln(Eγ /Ec )

(5)

where s is the shower age parameter that describes the stage of development of the shower and is given by s=

3 1 + 2 ln(Eγ /Ec )/(x/X0 )

(6)

Table 1 lists the average number of particles that reach different altitudes for gammaray showers with Eγ = 0.1, 1, 10, and 100 TeV. At the shower maximum, the total number of particles is approximately N (xmax ) ∼ 103 Eγ /TeV. The leading factor responsible for shower-to-shower variance is fluctuations in the depth of the first interaction. The probability that a primary gamma ray will propagate to an atmospheric depth x without interacting is P (x) = exp(−9x/7X0 ). If we consider a collection of showers with the same Eγ measured at the same

number of electrons

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Fluka gamma 500 GeV Fluka gamma 300 GeV Fluka gamma 200 GeV Fluka gamma 150 GeV Fluka gamma 100 GeV Fluka gamma 80 GeV Fluka gamma 50 GeV Fluka gamma 30 GeV Fluka gamma 10 GeV

102

10

1 100

200

300

400

500

600 700 800 900 2 atmospheric depth [g/cm ]

Fig. 3 Longitudinal development of electromagnetic air showers in the Earth’s atmosphere. The average number of electrons as a function of atmospheric depth is shown for 1000 simulated vertical incidence showers with different primary energies. Simulations were performed using the CORSIKA package (Heck et al. 1998). (Courtesy of Maier 2022)

atmospheric depth, the fluctuations in the number of secondary particles can be parameterized as (Gaisser et al. 2016) δ ln N ∼

9 (s − 1 − 3 ln s) 14

(7)

Shower fluctuations are proportional to N and are the smallest if the shower is sampled at or close to the shower maximum (s = 1), emphasizing the need for particle-sampling arrays to be located at high altitudes. The effect of shower-toshower fluctuations can be visualized in Fig. 4. The lateral spread of electromagnetic showers determines the size of the particle pool on the ground that particle sampling arrays can use to detect gamma-ray showers. The size of the shower front can be characterized by the Molière radius, which is a property of the material in which the shower develops and can be expressed as RM = 0.24

X0 ρ

(8)

The Molière radius indicates the radius of the cylinder that contains 90% of an electromagnetic shower in a given medium. At sea level RM ∼ 80 m, but it increases with altitude as the atmosphere becomes less dense (see Table 1). The lateral spread of the shower is driven by Coulomb scattering of the low-energy secondaries close

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Fig. 4 Effect of shower-to-shower variations in electromagnetic cascades. The figures show the density of Cherenkov photons hitting the ground for 10 simulated 100 GeV photon showers. Observatory altitude is set at 1,800 m above sea level. Simulations were performed using the CORSIKA package (Heck et al. 1998). (Courtesy of Maier 2022)

to the critical energy and is well characterized by RM . Higher energy particles have their characteristic lateral spread reduced by a factor of ∼Ec /E. While the geometry of a full electromagnetic shower resembles a cone (Fig. 1), its actual time-resolved development is, at the first order, a down-going disk centered at the shower axis and moving at the speed of light. In fact, the shower front has a concave shape similar to that of a contact lens although thinner in the center and thicker toward the edges. This geometry of the shower front is due to particles at the edges of the shower having longer travel times as well as a broader arrival time distribution due to multiple Coulomb scattering. Near the core of the shower, the thickness of the shower front is 10 ns (Fig. 5). The density distribution of electrons and positrons (ρe ) as a function of the radial distance r from the shower core can be parameterized using the Nishimura-Kamata–Greisen lateral distribution function (Greisen 1960) Γ (4.5 − s) N(x) ρe (r, s, x) = 2 RM 2π Γ (s) Γ (4.5 − 2s) valid for shower ages ranging 0.5 ≤ s ≤ 1.5.



r RM

s−2 

r 1+ RM

s−4.5

(9)

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Fig. 5 Left: Air Shower Front of a γ -ray-like event from Crab Nebula. The horizontal axis denotes the distance from the shower core, while the vertical axis denotes the residual of the plane fit to the actual particle detection time of each air shower array (HAWC) counter. It shows that the air shower front is not a plane but a curved surface, and the time spread is several nanoseconds within the radius of ∼100 m. The original figure is from Abeysekara et al. (2017). Right: arrival time distribution of Cherenkov photons on the ground as a function of radial distance to the shower core for a vertical incidence 300 GeV photon shower. Observatory altitude is set at 1,800 m above sea level. The curvature of the shower front with a width of a few nanoseconds can be distinguished. Simulations were performed using the CORSIKA package (Heck et al. 1998). (Courtesy of Maier 2022)

The Earth’s magnetic field has a second-order effect on the development of electromagnetic showers, as the directions of electrons and positrons are deflected in opposite directions by the geomagnetic field (Commichau et al. 2008; Szanecki et al. 2013). This effect is non-negligible when compared to multiple Coulomb scattering, and its relative importance increases for low-energy showers. In addition, the Lorentz force systematically deflects particles in opposite directions depending on the sign of their charge, while the effects of multiple Compton scattering are random. At the first order, geomagnetic fields stretch the lateral distribution of shower secondaries, reducing the particle density on the ground and making detection more difficult. The Earth’s magnetic field also introduces systematic differences that depend on the azimuthal direction of the shower axis for nonvertical showers that complicate the reconstruction of shower parameters from experimental ground-based data.

Cherenkov Light Charged particles in a medium with refractive index n moving with speed v > c/n will emit Cherenkov radiation. Cherenkov light is observed in underwater nuclear reactors and has recently been detected in the vitreous humor of patients undergoing radiation therapy (Tendler et al. 2020). Cherenkov light produced by charged secondaries can be used in ground-based detection of gamma rays.

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Considering the Earth atmosphere as a dielectric medium with refractive index n(z), particles with mass m and energy E = γ mc2 will produce Cherenkov light if their Lorentz factor is γ ≥

n(z)

(10)

n(z)2 − 1

The dependence of the atmospheric refractive index with height is a function of the air density and can be approximated by n(z) = 1.0 + 0.000283

ρ(z) ρ(z = 0)

(11)

Fluka gamma 500 GeV Fluka gamma 300 GeV Fluka gamma 200 GeV Fluka gamma 150 GeV Fluka gamma 100 GeV Fluka gamma 80 GeV Fluka gamma 50 GeV Fluka gamma 30 GeV Fluka gamma 10 GeV

2

Cherenkov photon densitiy [1/m ]

Cherenkov radiation is emitted at the Cherenkov angle θCh such that cos θCh = c/v n(z). At z = 10 km, θCh = 12 mrad or 0.8◦ and the Cherenkov energy threshold ECh is approximately 40 MeV for electrons and positrons and 8 GeV for muons. The geometry of the Cherenkov light emission at 10 km height would result in a blurry Cherenkov ring with radius ∼10 km · 0.013 = 130 m that determines the size of the light pool for a typical gamma-ray shower (Figs. 6 and 7). For a 1 TeV primary, the photon density inside the light pool is ∼100 m−2 . The paths of charged secondaries follow an angular distribution ∝ exp (θ/θ0 ) with respect to the shower axis, where θ0 = 0.83 (ECh )−0.67 . The values of θ0 are

2

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Fig. 6 Lateral distribution of Cherenkov photons as a function of radial distance to the shower core, averaged for 1,000 vertical-incidence simulated showers with different primary energies. Observatory altitude is set at 1,800 m above sea level. A light pool with radius ∼130 m can be seen. Simulations were performed using the CORSIKA package (Heck et al. 1998). (Courtesy of Maier 2022)

500 400

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Fig. 7 Density of Cherenkov photons on the ground for a vertical incidence 300 GeV photon shower and a 500 GeV proton shower. Observatory altitude is set at 1,800 m above sea level. The proton shower shows additional clumpyness due to subshowers initiated to be the production of pions with large transverse momentum. Simulations were performed using the CORSIKA package (Heck et al. 1998). (Courtesy of Maier 2022)

typically in the range between 4◦ and 6◦ . The combination of the height-dependent Cherenkov angle and the longitudinal development of the shower gives rise to a characteristic lateral distribution of photons on the ground shown in Fig. 6. The Cherenkov light flash has a width of only a few nanoseconds (Fig. 5) and can be the brightest source of light in the sky during the short duration of the pulse. The total number of Cherenkov photons Nph produced by secondaries is proportional to Eγ and is ∼100 photons per square meter for a 1 TeV shower. The emitted ˇ Cherenkov radiation spectrum follows the Franck–Tamm relation (Cerenkov 1937; Frank and Tamm 1937) d2 Nph 2π α = 2 sin2 (θCh ) dx dλ λ

(12)

which gives the differential number of Cherenkov photons per unit wavelength dλ and path length dx, with α being the fine-structure constant. Cherenkov photons are affected by atmospheric absorption as they propagate toward the ground level. Rayleigh scattering off of particles smaller than the photon wavelength has a λ−4 dependence and suppresses the propagation of short wavelengths. Mie scattering on particles with sizes comparable to the photon wavelength depends on the aerosol content of the atmosphere, which can present seasonal or transient variability that needs to be corrected (Dorner et al. 2009; Hahn et al. 2014). Ozone O3 + γ −→ O2 + O absorption process that filters off photons in the 200 nm top 315 nm range. A combination of the λ−2 dependence of the Cherenkov emission spectrum and ozone absorption leads to a Cherenkov light distribution at the ground level that peaks at λ ≈ 300–350 nm with a detailed spectral shape depending on the height of the observatory, the height of the shower maximum, and the zenith angle of the observation.

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Geographical differences in atmospheric density profiles lead to differences in Cherenkov light density on the ground of up to 60%. Seasonal variations at midlatitude sites have an effect on the order of 15–20% (Bernlöhr et al. 2000). Finally, scattering by water vapour in clouds limits the use of atmospheric Cherenkov light to cloudless conditions. The introduction of LIDAR cloud monitoring at observatory sites (Bregeon et al. 2016) allows for determination of the height of the cloud layer. Gamma-ray observations in the presence of high cloud layers located above the typical location of the shower maximum (10–12 km) have been conducted with an increased systematic uncertainty in the flux and spectral characterization (Abeysekara et al. 2017).

Differences Between Electromagnetic and Cosmic-Ray Showers Protons and heavier nuclei also produce air showers in the atmosphere that constitute the main source of background for ground-based gamma-ray observations. Even for strong gamma-ray sources, the signal-to-background shower rates are 10−3 –10−4 . Hadronic interactions in cosmic-ray showers lead to the production of secondary nucleons and pions. A characteristic difference with respect to pair production and bremsstrahlung is the larger transverse momentum carried by hadronic interactions, leading to showers with larger lateral spread (Fig. 1). Neutral pions decay quickly into two gamma-ray photons producing an electromagnetic subshower. Charged pions decay into a muon and a neutrino. Muons do not suffer from multiple Coulomb scattering and propagate straight to the ground, producing a characteristic Cherenkov light ring. With a lifetime of 2.2 ns, a significant fraction of muons reach the ground level before decaying due to relativistic time dilation. Differences in morphology (Figs. 1 and 7) between electromagnetic and cosmic ray showers, as well as their muon content, constitute the main means of discrimination between gamma-ray-initiated showers and cosmic rays.

Air Shower Simulations Monte Carlo simulations are used in modern particle physics and cosmic ray experiments to understand the development of electromagnetic and hadronic cascades in a complex medium. The study of air showers through simulations has been key to the success of ground-based gamma-ray astronomy. In seminal work from 1985 Hillas exposes that “it should be possible to distinguish very effectively between background hadronic showers and TeV gamma-ray showers from a point source on the basis of the width, length and orientation of the Cherenkov light images of the shower” (Hillas 1985). These Monte Carlo studies, as well as hardware developments such as the use of pixelated cameras, enabled the development of the imaging Cherenkov technique that led to the detection of TeV emission from the Crab Nebula (Weekes et al. 1989) and the blossoming of ground-based gamma-ray astronomy seen in the following decades.

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Over the years, the CORSIKA software package (Heck et al. 1998) has become the field standard for simulations of particle showers in the Earth’s atmosphere. Other standard simulation packages include GEANT4 (Agostinelli et al. 2003; Allison et al. 2016), EGS (Kawrakow 2000), and FLUKA (Battistoni et al. 2014; Ahdida et al. 2022) and are used to simulate specific aspects of the shower development as well as the response of detectors and telescopes.

Air Shower Particle Detectors Electromagnetic cascades (air showers) initiated by very high-energy gamma rays develop deep in the atmosphere (Fig. 3). At a sufficient altitude above sea level, a significant number of secondary particles will reach the ground and can be detected with air shower particle detectors, also known as particle sampling arrays. At 4000 m height, for example, the typical spread of secondary particles in an air shower is ∼100 m in radius, and they arrive in a few nanoseconds long bunch (see the left panel of Fig. 5). An array of particle detectors deployed in the area of ∼10,000–1,000,000 m2 can detect these particles and reconstruct the arrival direction and the energy of the primary high-energy gamma rays. One method to detect air shower particles is to use scintillators. Arrays of plastic scintillators with ∼1 m2 surface and a few centimeters thick can be used to sparsely cover a large surface area. Electrons and positrons with energies down to a few MeV produce scintillation light that can be collected and detected with photomultipliers. Photons carry a significant fraction of the total shower energy, but plastic scintillators only produce a response to charged particles. To overcome this limitation, it is common to cover the scintillator with ∼1 radiation lengths of lead or another metal with high atomic number to convert the photons to electron–positron pairs without significantly absorbing the electron flux. The Chicago Air Shower Array (CASA), the Tibet Air Shower gamma experiment (Tibet-ASγ ), and the Large High Altitude Air Shower Observatory (LHAASO) are some of observatories that use scintillator arrays. Resistive plate counters can also be used as surface particle detectors. Resistive plate counters are composed of a thin, gas-filled detector with two metal plates and two high-resistance (∼1010 Ω cm) plates setup as a large planar capacitor. A high voltage of about ∼10 kV is applied between the metal plates. When a charged particle passes though the detector, the gas along the particle track is ionized, producing an electrical discharge between the plates. Due to the highresistivity layer, the avalanche effect is quenched quickly and stays confined in the region along the particle track, providing good time (∼1 ns, Aielli et al. 2006) and spatial (∼100 µm, John et al. 2022) resolution. Resistive plate counters are used in particle collider experiments (e.g., ATLAS). The ARGO-YBJ experiment adopted this technology for air shower detection, realizing a carpet particle detector over an area of ∼6,700 m2 that achieves a gamma-ray detection threshold as low as 100 GeV (Bacci et al. 1999).

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The third method to detect air shower particles is to use Cherenkov light emission in water. The refractive index of the water is ∼1.33 and electrons and positrons with energy above 0.78 MeV emit Cherenkov light (see Equation 10). This Cherenkov radiation is emitted at a Cherenkov angle of ∼40◦ for charged particles with β ≃ 1. A large container of water such as a pool or a lake can be used as a particle sampling array by installing photomultiplier tubes in it to collect Cherenkov light, with every single photomultiplier acting as an independent counter. The Milagro gamma-ray observatory realized a water Cherenkov array on a 4,800 m2 pool with an array of photomultipliers placed under 1.3 m of water with a spacing of ∼3 m between photomultipliers (Abdo et al. 2007). A smaller array of photomultipliers at 6 m depth was used to measure the penetrating component of the showers. The second way to realize a water Cherenkov array is to deploy isolated water tanks instrumented with one or more photomultipliers. The HAWC observatory is an example of such array with 300 7 m diameter × 5 m depth water tanks that are densely packed to cover an area on 22,000 m2 (Abeysekara et al. 2017).

Event Reconstruction with Air Shower Particle Detectors The lateral distribution of air shower secondaries peaks at the shower axis and decays exponentially away from it (see Eq. 9). The location of the intersection between the shower axis and the detector plane is called the shower core. The location of the shower core can be estimated by computing the center of gravity of the particle densities detected across several detector units of the air shower array. Moreover, as can be seen in the left panel of Fig. 5, the shower front arriving on the ground has a characteristic curved shape. Using the arrival time information of the particles in the shower front on each detector together with the estimated core location, the arrival direction of the primary gamma-ray can be estimated. The precision of estimation depends on the number of detected particles as well as the density of the array and the number of detectors that have a signal above threshold. The energy of the primary gamma-ray can be estimated from the number of detected secondary particles that can be derived from the total signal in the detector array. In most cases, the detector array is located at a height that lies below the shower maximum. Therefore, the conversion from the number of detected particles to the primary gamma-ray energy is not fully deterministic and relies on an indirect assumption of the location of the shower maximum that is generally based on comparison of the observed data with Monte Carlo simulations of electromagnetic showers. Observatories with densely packed or carpet arrays (water detectors or resistive plate counter arrays) have a low energy threshold with sufficient gamma/hadron separation ability, while their effective area is limited by the surface covered by the array. A more sparse deployment of detectors on the ground improves the effective area at high energies at the cost of also rising the energy threshold of the observatory.

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Cosmic-Ray Rejection with Air Shower Particle Detectors The flux of charged cosmic rays hitting the Earth’s atmosphere is significantly higher than the gamma-ray flux, even for the brightest gamma-ray sources. Means to distinguish between cosmic-ray and gamma-ray induced showers are essential for observatories to reach sufficient signal-to-noise ratio to detect and study gamma-ray sources. There are several differences between electromagnetic and hadronic showers. One key feature is the muon content of air showers. Muons are produced in hadronic interactions mainly via the decay of charged pions. On the other hand, electromagnetic showers can produce muon secondaries only via photo-pion production or the infrequent creation of a muon–antimuon pair. Therefore, estimating the number of muons detected in air showers can discriminate between hadronic and electromagnetic (photon or electron) primaries. From the detection point of view, the behavior of muons and electron/positrons inside the detector medium is significantly different. The largest difference is the probability to cause bremsstrahlung. Below ∼500 GeV, the bremstrahlung cross section is inversely proportional to the square of mass of the particle. Therefore, muon bremstrahlung is suppressed by a factor (me /mμ )2 ≈ 40,000 compared to electrons. This means that muons are much more difficult to shield from than electrons. The radiation length for electrons in typical soil is about ∼20 cm. About seven radiation lengths (∼1.4 m) of soil reduce the energy of a 3 GeV electron down to 3 MeV, and then ionization takes away the remaining energy. On the other hand, muons lose their energy by ionization. After crossing 1.4 m of soil, a 3 GeV muon loses only a tenth of its energy. Because of this penetrating power of muons, detectors installed under soil or metal shielding will not be sensitive to the electron and photon component of the shower but will detect the muons in the air shower. The CASA-MIA experiment installed scintillation counters 3 m underground as muon detectors, while the Tibet ASγ observatory used water Cherenkov counters 2 m underground as primary mean for cosmic-ray rejection through identifying muons. In the absence of dedicated muon detectors, discrimination of cosmic-ray events can also be accomplished based on the increased irregularity of distribution of electromagnetic particles in the air shower front in hadronic showers when compared to electromagnetic showers that present smoother particle distribution. Hadronic showers can be considered as the collection of electromagnetic subshowers originating from the decay of neutral pions. Consequently, the air shower front is not as regular as in electromagnetic showers. A dense coverage of particle detectors on the ground is necessary to detect the inhomogeneities than can allow for a morphological discrimination between cosmic-ray showers and gamma-ray candidates. Figure 8 shows examples of simulated proton and photon-induced showers as for the Milagro observatory. A large water pond with a dense coverage of photomultipliers is suitable for capturing these discriminating features.

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Fig. 8 Simulated air showers seen by Milagro observatory. Top panels are gamma-ray events and bottom panels are proton events. A clear difference in irregularity is seen between gamma rays and protons. (Adapted from Atkins et al. 2003)

Sampling Cherenkov Arrays Charged particles in air showers emit Cherenkov light. While UV photons suffer from Rayleigh scattering by aerosols and absorption by ozone molecules, visible light photons reach the Earth’s surface where they can be collected and detected using fast photon detectors. Cherenkov photons produced during the development of the air shower travel together with the particle shower front, keeping a time spread of a few nanoseconds when they reach the ground level. Air showers are seen from the Earth’s surface as brief, nanosecond-long light flashes that are easy to detect against the weak and continuous light background from the night sky. An example of the spatial and time delay distribution of a simulated Cherenkov light shower front from air showers initiated by a gamma-ray photon and a proton is shown in Fig. 9. Sampling Cherenkov arrays use photomultiplier tubes or mirrors deployed on the ground to cover a large fraction of the ∼130 m radius Cherenkov light pool of gamma-ray showers. This can be accomplished either by using bare upward-looking photomultipliers, short focal length mirrors viewed by individual photon sensors,

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Fig. 9 Simulation of Cherenkov photon front. X and Y axes denote the position on the ground and the Z axis shows the arrival time. Smoothness is different between a gamma ray (left) and protons (right). (Adapted from Oser et al. 2001)

or with long focal length mirrors each focused onto a photomultiplier in a central camera. In both cases, each mirror is seen by a single photomultiplier that records the light intensity and timing at each position. Distributed sampling Cherenkov arrays have been used in air shower experiments such as Tunka (Budnev et al. 2017), Yakutsk (Dyakonov et al. 1986), EAS-TOP (Aglietta et al. 1995), or AIROBICC (Arqueros et al. 1996). The AIROBICC detectors in the HEGRA experiment consisted of 97 large photomultipliers were deployed in an ∼200 × 200 m2 area. Each photomultiplier had a 20 cm diameter and was pointing toward zenith to directly detect Cherenkov photons from air showers. In photomultiplier arrays, shower events can be distinguished from fluctuations of the night sky background by requiring a coincident signal over a number of neighboring detectors within a time window of the order of the duration of the Cherenkov shower light flash. The second implementation of sampling Cherenkov arrays is to use heliostat arrays. STACEE (Ong et al. 1996) and CELESTE (Smith et al. 1997) are the two examples of this technique (Fig. 10), which among other similar experiments played a pioneering role in exploring the energy domain below 100 GeV. Both observatories made use of existing mirror arrays and infrastructure at solar power stations. When operating as a power plant, individual mirrors deployed on the ground are actively operated to track the Sun reflecting its light onto a single heat collector located on a tower at a certain height above the ground. At night, when the sun is below the horizon and the solar power plant is not in operation as such, the individual mirrors of the heliostat array can be used to collect Cherenkov photons from air showers and focus them on a photomultiplier camera located on the solar tower. The pointing direction of each mirror is actively adjusted so that Cherenkov photons from a given

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Fig. 10 A concept of STACEE and CELESTE. (Adapted from Ong et al. 1996). Cherenkov light illuminates the large area of the ground and the mirrors distributed over a large area focus the light to the camera on the tower. Each mirror focuses the light to different photosensors, enabling imaging of the air shower front

arrival direction falling on each heliostat are focused onto a specific photomultiplier in the camera. The output signal of photomultipliers can be used to reconstruct the timing and the light density of Cherenkov photons on the corresponding heliostat, mapping the Cherenkov light pool of the shower on the ground. In other words, the distribution of Cherenkov photons hitting the ground from a given direction over a ∼10,000 m2 area is projected onto the ∼1 m2 scale photomultiplier camera.

Event Reconstruction and Cosmic-Ray Rejection with Sampling Cherenkov Arrays Sampling Cherenkov arrays use the positional and arrival time information of Cherenkov photons to reconstruct the main properties of gamma-ray showers. After reconstructing the core position, the arrival direction of the primary gamma-ray is estimated using the reconstructed light intensity and arrival time distribution on the ground as inferred from the pulse height and timing of signals from each individual photomultiplier. The shower direction can be geometrically determined from the individual timing of the photomultiplier signals, applying the appropriate corrections due to the curvature of the Cherenkov photon front (Fig. 5). Numerical simulations show that the density of photons inside the 130 m radius Cherenkov light pool is directly proportional to the energy of the primary gamma-ray (Fig. 6). Outside of the light pool, the photon density decays with a slope that is related to the atmospheric depth of the shower maximum (Hillas 1982). Local inhomogeneities in the timing and intensity of the signals across the Cherenkov light pool (Fig. 9) can be used to identify and reject showers initiated by cosmic rays.

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Imaging Atmospheric Cherenkov Telescopes Imaging air Cherenkov telescopes (IACTs) use focusing mirror optics and photomultiplier cameras to exploit the angular arrival direction of Cherenkov photons and form images of air showers. An imaging Cherenkov telescope is composed of a wide-field optical telescope with a fast photomultiplier camera on its focal plane (Fig. 11). The typical optical assembly consists of a short focal ratio (f/D ∼ 1, focal length f divided by the aperture D) parabolic or Davies-Cotton (Davies and Cotton 1957) reflector constructed with smaller individual mirror segments. The total mirror surface per telescope is typically 100 m2 (up to >600 m2 (Collaboration et al. 2017)) to collect enough photons from a Cherenkov light pool with photon densities of ∼10–100 m−2 (Fig. 6). Alternative approaches to a single-mirror optical design have been tested in recent years. Two-mirror designs based on Ritchey-Chrétien optics (Ritchey and Chretien 1927) can be optimized to cancel aberrations and reduce the plate-scale of the camera resulting on a flat focal plane. Dual mirror Schwarzschild-Couder telescopes have been implemented and commissioned in preparation for the future Cherenkov Telescope Array observatory (Lombardi et al. 2020; Adams et al. 2021). Focal plane instrumentation consists of an array of photosensors that captures a Cherenkov image of each shower. Single-anode photomultiplier tubes are typically used, providing reasonable photon detection efficiency (20%), clean amplification (∼105 ), and nanosecond response. Silicon devices feature in some modern Cherenkov telescope designs (Dorner et al. 1502; Adams et al. 2022). The impact

Fig. 11 Schematic view of Imaging Atmospheric Cherenkov Telescope technique. The Cherenkov photons emitted at different altitudes are focused on the different part of the camera by the telescope optics. With this technique, the air shower development can be imaged

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parameter of shower is defined as the distance between the shower axis projected on the ground and the telescope location. In order to contain shower images with impact parameter out to ∼130 m, the camera field of view (FoV) has to be 3◦ in diameter, requiring hundreds to a few thousand pixels. The angular size of a 100 GeV shower seen at zenith is ∼0.1◦ . Showers with higher energy primaries, observed at higher zenith angles or with large impact parameters, have larger angular extents. To resolve the shower structure, it is important that the optical angular resolution of the telescope, the angular size of the camera pixels, and the pointing accuracy of the telescope should all be 0.1◦ . A single Cherenkov telescope located inside the shower light pool can record and potentially reconstruct the energy and the arrival direction of the primary gammaray from the shower image. Therefore, the effective area of an IACT is determined by the size of the Cherenkov light pool, which is of the order of 5 × 105 m2 . To record Cherenkov images, IACTs are triggered when a number m of pixels (typically 2–4) in the camera exceed a certain discrimination threshold (in photoelectrons) within a narrow time window τ which is typically a few nanoseconds long. This reduces the rate of false triggers from fluctuations of the night sky background RNSB well below the individual pixel rate R1 following RNSB ∼ R1m τ m−1 . Most IACTs use topological requirements such as forcing the triggering pixels to be adjacent or located in the same camera sector to further reduce the accidental trigger rate. Most observatories consist of more than one imaging Cherenkov telescope, making use of the stereoscopic imaging technique. Having multiple views of a given shower from different perspectives enhances the geometrical reconstruction of the shower. In addition, requiring showers to trigger in more than one camera further reduces the accidental trigger rate due to the night sky background as well as from local muons that at high impact parameters produce gamma-like shower images. The sensitivity of an IACT array increases roughly as the square root of the number of telescopes. The optimal spacing depends on the energy rage to be covered, with wider spacing improving the sensitivity at higher energies. Finally, the performance of the array improves when the array becomes significantly larger than the Cherenkov light pool, achieving better sensitivities for low energy showers even with telescopes of modest size (Colin and LeBohec 2009; Bernlöhr et al. 2013).

Event Reconstruction and Cosmic-Ray Rejection with IACTs The optics of an imaging Cherenkov telescope convert photon angular arrival directions into positional information in the focal plane camera (Fig. 11). Electromagnetic air showers produce elliptical shower images when recorded by an imaging Cherenkov telescope. The longitudinal development of the shower is mapped onto the major axis of the elliptical shower image, with the image being offset from the arrival direction of the shower primary by an angular distance proportional to the shower impact parameter. In a stereoscopic system, the intersection of the major axes of the image ellipses obtained by different telescopes indicates the arrival direction of the primary particle. This results in an energy-dependent angular

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resolution that typically reconstructs 68% of the gamma rays from a point source within ∼0.1◦ of the source position. The Cherenkov photon yield of a shower is proportional to the number of secondaries, which is in turn proportional to the energy of the primary particle. The amount of light collected in shower images is a good indicator of the primary gamma-ray energy, although it also depends on the impact parameter of the shower. Stereoscopic energy reconstruction dramatically improves the energy resolution of IACTs, with images from multiple telescopes allowing to break the degeneracy between shower energy and impact parameter. This leads to energy resolutions of ∼15% above 1 TeV. Showers induced by cosmic rays are the dominant background for ground-based detection of gamma rays. Event selection based on the width and length of shower images can efficiently reject cosmic-ray showers while keeping most gamma-ray events (Hillas 1985). These cuts exploit the more compact nature of gamma-ray showers, which have a smaller lateral spread than hadronic showers. Cosmicray showers are essentially a superposition of multiple electromagnetic cascades originating from the decay of individual neutral pions. These irregularities in the shower development propagate to the shower images and can also be exploited for cosmic ray rejection. Gamma-ray-looking cosmic ray showers that survive background rejection cuts will have an isotropic distribution of arrival directions. Searches for point sources of gamma rays use the clustering of the arrival directions of gamma-ray events around the source location as one final means to extract the gamma-ray signal from the background.

Complementarity Between Ground-Based Techniques Typical performance parameters for a selection of ground-based gamma-ray observatories are summarized in Table 2. Air shower arrays and IACTs have complementary capabilities. A combined coverage of sky regions with both techniques provides sensitivity to detect and study a wide variety of source classes. Some of the main differences between techniques are operational: IACTs run as pointed telescopes and cover a limited 5◦ region of the sky at any given time, while air shower arrays are sensitive to gamma-ray sources located directly overhead of the observatory within a ∼2 sr cone. In addition, IACTs are essentially optical telescopes and can only operate during clear nights without significant moonlight, leading to duty cycles 90% >90% >90% >90% ∼10% ∼10% ∼10% ∼12% ∼12% ∼10%

Ang. res.a [◦ ] 0.3 0.2 0.4 0.4 0.3 ∼0.5 ∼0.5 0.05 0.08 0.09

Energy thresh. [TeV] 3 0.5 0.1 30 15 0.03 0.1 0.02 0.03 0.15

Point source sensitivityb [Crab Unit] 20% 6% 10% 1% ∼100% 12% 40% 0.7% 0.7% 0.7%

a Values

reported at 1 TeV except for air shower arrays and AIROBICC, for which the angular resolution is reported at 30 TeV b The value at the best energy threshold is reported. Sensitivity assumes 1 year of operation for air shower arrays and 50 h of dedicated exposure for Cherenkov telescopes c Ref. Amenomori et al. (2009) d Refs. Abeysekara et al. (2012, 2013, 2017) e Ref. Cao et al. (2019) f Refs. Arqueros et al. (1996) and Aharonian et al. (2002) g Refs. Paré et al. (2002) and Manseri (2005) h Refs. Williams et al. (2004), Hanna et al. (2002), and Mueller et al. (2011) i Refs. Aharonian et al. (2006), LU et al. (2013), and H.E.S.S. Collaboration et al. (2018) j Refs. Aleksi´ c et al. (2016) and MAGIC Collaboration et al. (2020) k Ref. Park and VERITAS Collaboration (2015)

energy resolution, and background rejection capabilities compared to air shower arrays. In the energy range above 10 TeV, the sensitivity of detectors based on the Cherenkov technique is limited by the effective area of the observatory. Wavefront sampling experiments can deploy small and widely separated detectors and achieve very large effective areas in a more efficient way than regular IACTs. The number of Cherenkov photons in a shower is proportional to the energy of the primary Eγ . Large-aperture mirrors are required for IACTs to collect enough light to trigger on and reconstruct showers with Eγ  100 GeV. Smaller Cherenkov telescopes are cheaper to produce, simpler to operate, and could be deployed in large numbers over a larger surface area resulting on a bigger effective area at high energies. A combination of imaging Cherenkov telescopes with different mirror apertures to cover a wide energy range with good sensitivity is the design basis of the future Cherenkov Telescope Array (Bernlöhr et al. 2013). The H.E.S.S. collaboration is currently operating 4 × 12 m telescopes surrounding a 28 m telescope in what constitutes the first hybrid Cherenkov instrument of this kind. The system triggers on events detected either only by the large-aperture telescope (mono) or by any combination of two or more telescopes (stereo) (Collaboration et al. 2017).

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The combined use of different detection techniques in a single observatory has also been explored. The HEGRA array combined up to five 3.3 m-aperture imaging Cherenkov telescopes with an array of more than 200 × 1 m2 scintillator counters (Krawczynski et al. 1996), a matrix of 77 × 1 sr open photomultipliers acting as a sampling Cherenkov array (AIROBICC), and 17 × 16 m2 lead-concrete Geiger tracking calorimeters (Rhode et al. 1996). Detectors were operated in a truly hybrid mode, with all systems except for the calorimeter towers contributing to the trigger. For example, AIROBICC would not only require a signal in six counters to selftrigger but also received external triggers when the imaging Cherenkov telescope array detected a shower (Arqueros et al. 1996). The Geiger towers would measure the total energy deposition of particles in the shower tail and reconstruct and identify muon and electron tracks. The LHAASO observatory is designed on similar hybrid operation principles with a sparse 1.3 km2 array of scintillator detectors and muon detectors, three large pools that act as water Cherenkov detectors, and 18 wide-field Cherenkov telescopes (Cao et al. 2019).

Other Detection Concepts A number of alternative techniques have been explored for the detection of gamma rays from the ground. An excellent survey of detection concepts with a historical perspective can be found in Hillas (2013). Several hybrid concepts have been considered to reduce the sensitivity of imaging Cherenkov telescopes to the cosmic ray background, which was one of the main challenges that frustrated early attempts to detect TeV sources. One technique was to install offset photomultipliers that would detect light originating from ∼1◦ angular distance from the shower axis (Grindlay et al. 1975). An excess of off-axis light would indicate the presence of a muons and would cause the event to be rejected. However, cosmic-ray rejection may have been about a factor of two and exploiting the shape of the Cherenkov images with multi-pixel cameras achieved better results. Different implementations of the imaging Cherenkov technique have also been proposed to lower the energy threshold below 100 GeV. A large effective area could be achieved using a large number of small telescopes (>100 × 2.5 m aperture). The signals from individual telescopes can be delayed and combined before a trigger is generated, with the potential to achieve a low energy threshold and sensitivity equivalent to that of a single 20–50 m aperture IACT at a fraction of the cost (Falcone et al. 2005). Another concept would consist in deploying imaging Cherenkov telescopes at an altitude of ∼5 km above sea level. At these altitudes, a 5 GeV shower produces photon densities ∼1 m−2 inside the light pool (compare to Fig. 6) enabling a stereoscopic system of 20 m telescopes to operate with an energy threshold of ∼5 GeV (Aharonian et al. 2001). Shower-to-shower fluctuations and the background from electromagnetic showers initiated by cosmic-ray electrons become increasingly important at such low energies. Fresnel lenses enable optics with large apertures and wide fields of view with moderate angular resolution. With a lower weight and cost than reflective optics, a

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system composed of a 3 m Fresnel lens and a multi-anode photomultiplier camera could have a similar threshold and sensitivity than a 10 m class IACT (Cusumano 2011). Another concept based on Fresnel lenses proposes to use 0.5 m telescopes developed for the PANOSETI project (Maire et al. 2020b). Each telescope is equipped with a silicon photomultiplier camera and uses a commercial telescope mount for pointing and tracking. Two PANOSETI telescopes have been tested at the Whipple Observatory site and successfully detected air showers from the Crab Nebula that were identified as gamma rays with energies of 15–50 TeV using VERITAS (Mair et al. 2022a). The compact size of the telescopes and the use of commercial technologies reduce the cost by two orders of magnitude compared to classical IACTs. A large array of such low-cost telescopes could bring the benefits of the imaging Cherenkov technique (energy resolution, angular resolution, and background rejection) at energies >100 TeV. Alternative techniques have been proposed to improve the sensitivity and lower the energy threshold of particle sampling arrays. One possibility is to use particle tracking detectors such as time projection chambers (Lohse and Witzeling 1992) instead of scintillator detectors. Tracking detectors do not only record the passage of secondary cosmic-ray particles but can also reconstruct their path and arrival direction with 105 m2 . Such an array reaches a sensitivity of a few millicrabs at 100 GeV energies in 50 h of observations, an angular resolution of ∼5 arcmin, and a spectral resolution of ∼10%. This chapter describes the technical implementation of Imaging Atmospheric Cherenkov telescopes and also describes how the data are analyzed to reconstruct the physical parameters of the primary gamma rays. Keywords

IACTs · Cherenkov telescopes · Very high-energy gamma rays · Cosmic rays · Instrumentation

Introduction The imaging atmospheric Cherenkov technique was pioneered by the Whipple Collaboration in the USA (⊲ Chap. 72, “The Development of Ground-Based Gamma-Ray Astronomy: A Historical Overview of the Pioneering Experiments”). After more than 20 years of development, Whipple discovered the Crab nebula, the first VHE gamma-ray source, in Weekes et al. (1989). The Crab nebula is one of the most powerful sources of very high-energy gamma rays and is often used as a “standard candle.” Modern instruments, which use multiple telescopes to follow the cascades from different perspectives and employ fine-grained photon detectors to enhance the images, can detect sources with a flux below 1% of the Crab Nebula flux. Finely pixelated images were first employed on the French CAT telescope (Barrau et al. 1998), and the use of “stereoscopic” telescope systems to provide images of the cascade from different viewpoints was pioneered on the European HEGRA IACT system (Daum et al. 1997). Irrespective of the technical implementation details, as far as its performance is concerned, an Imaging Atmospheric Cherenkov Telescope (IACT) is primarily characterized by its light collection capability, i.e., the product of mirror area, photon collection efficiently, and photon detection efficiency, by its field of view and by its pixel size, which limits the size of image features which can be resolved. The larger the light collection efficiency, the lower the gamma-ray energy that can be successfully detected. The optical system of the telescope should obviously be able to achieve a point spread function matched to the pixel size. The electronics for signal capture and triggering should provide a bandwidth matched to the length

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of Cherenkov pulses of a few nanoseconds. The performance is also dependent on the triggering strategy; the Cherenkov emission from air showers has to be separated in real time from the high flux of night sky background photons, based on individual images and global information in case the showers are observed from several viewpoints. In addition, the huge data stream from IACTs does not allow to deal with untriggered recording easily. The collection area of an array of 2–4 telescopes is of the order of the area of the light pool, i.e., >105 m2 . This collection area may grow by simply adding more telescopes to the array. An array of 2–4 telescopes of the 10-m diameter mirror class reaches a sensitivity of a few millicrabs at 100 GeV energies in 50 h of observations, an angular resolution of ∼5 arcmin, and a spectral resolution of ∼10%. Larger mirrors (20–30 m) bring the energy threshold of the array to few tens of GeV, while increasing the number of 10 m diameter telescopes to 10–20 can improve the sensitivity well under 1 millicrab. However, telescope optics prevents the field of view (FOV) of IACTs to exceed 8–10◦ diameter, and the Cherenkov light of atmospheric showers can only be detected during the astronomical night, typically without Moon, and with good weather conditions, so the duty cycle of IACTs rarely exceeds 15%. These collection areas are orders of magnitude larger than the collection areas of satellite-based detectors (⊲ Part VI, “Space-Based Gamma-Ray Observatories”). This makes IACTs the instruments of choice in the energy range between a few tens of GeV and tens of TeV. During the last two decades, IACTs have opened a new astronomical window: the VHE γ -ray range offers a new tool to study sources of non-thermal radiation such as supernova remnants, star forming regions, or the surroundings of compact objects (jets and winds around black holes and pulsars). VHE γ -ray astronomy also allows us to study the extragalactic background light and intergalactic magnetic fields or to search for dark matter and effects of quantum gravity (Sections 7–15). At larger energies, from hundreds of TeV to a few PeV, one requires even larger collection areas, larger FOVs, and/or a duty cycle approaching 100%, as offered by detector arrays sampling the particles in the atmospheric shower. However, IACTs still offer unbeatable angular and spectral resolutions.

Air Shower Properties and Imaging When a very high-energy gamma-ray interacts with the Earth’s upper atmosphere, it converts into an electron–positron pair. Subsequent Bremsstrahlung and pair production interactions generate an electromagnetic shower in the atmosphere, in which the total number of electrons, positrons, and photons approximately doubles every log(2) times the radiation length for Bremsstrahlung in the atmosphere (roughly 37.2 g cm−2 ) (Heitler 1954). The splitting of the energy of the primary gamma-ray stops when the losses due to ionization of the secondary electrons and positrons dominate over the other processes. This happens when the average lepton

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energy is about E0 = 84 MeV and, as a result, the maximum number of leptons in the shower is E/E0 , where E is the energy of the primary. Given their energy, the electrons and positrons move faster than the speed of light in air, thus emitting the Cherenkov radiation (Cherenkov 1934). The maximum intensity of this emission occurs when the number of particles in the cascade is largest, at an altitude of ∼10 km for primary gamma-ray energies of 100 GeV to 1 TeV near the zenith. During their propagation, these particles undergo multiple Coulomb scattering, distributing then in the direction perpendicular to the shower propagation, increasing the spread of their individual direction of propagation. Together with the Cherenkov emission angle of about 1.4◦ , this results on a pool of photons nearly uniformly distributed within a circle of about 130 m of radius around the extrapolation of the primary trajectory to ground, with a density of about 100 photons m−2 s−1 for a primary gamma ray of about 1 TeV. These photons arrive to the ground in a single pulse of few nanoseconds of duration. An IACT detects these photons and determines the energy and direction of the primary gamma ray. The detection technique is based on a simple concept: photons are collected in a large mirror which focuses them in a fast camera with photodetectors coupled to digital samplers (Actually, the first detection of Cherenkov from an air shower was done with a free running analog oscilloscope and a single photomultiplier.). However, as usual, the devil is in the details: even if the detection is relatively simple, the rejection of cosmic ray showers, night sky photons, and determination of the gamma-ray kinematics are challenging problems. Cosmic rays (mainly protons and He nuclei) collide with atmospheric nuclei to generate secondary hadronic or leptonic particles. After further interactions, they develop several electromagnetic sub-showers and muons. Compared to a gamma-ray shower and due to the larger transverse momentum of hadronic interactions, cosmicray shower particles spread away from the incident direction. The corresponding shower image at an IACT is broader and more irregular. This fact is key to cosmicray rejection techniques. In addition, IACTs implement the stereoscopic imaging technique, illustrated in Fig. 1: two or more large convex reflector placed within the light pool focus the Cherenkov light of a single shower onto the same number of cameras equipped with photodetectors. These cameras record the image of the shower from different perspectives, and the geometrical properties of these images allow us to determine the properties of the primary particle. In particular, the crossing point of the longitudinal axis of these images projected into the sky provides a determination of the direction of the primary, and the total recorded number of photons is directly linked with the energy. In order to accurately identify and reconstruct the primary particle properties, it is necessary to make use of complex Monte Carlo simulations of the shower development and the detector response. In order to implement this technique, it is necessary to design a telescope with a very large optical aperture that allows to collect as many Cherenkov photons as possible and a large FOV since the shower images can have an angular extend of up to few degrees and are shifted another few degrees from the source position in the sky. In addition, it is common to point slightly off-source to use a source-less portion

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Fig. 1 Two or more IACTs record the Cherenkov photons (purple) emitted by the electrons and positrons (red) of a single electromagnetic shower. The right panel illustrates the projection of the recorded images into the sky

of the sky within the FOV to estimate the background due to diffuse gamma rays and hadronic cosmic rays. These constraints lead to designs of the optics explained later in this chapter. To cover the required FOV, cameras of 10-m type IACTs are usually large, with sizes measured in meters. Their focal plane is instrumented with fast detectors, with response times of the order of nanoseconds, high photodetection efficiencies (20% or more), large detection areas, and very clean amplification, which allows to resolve single phe (phe) signals. These are described later in this chapter together with the associated electronics. The size of focal plane pixels is a parameter which requires careful optimization in IACTs. Figure 2 illustrates how a shower image is resolved at pixel sizes of 0.10◦ and of 0.20◦ . The gain due to the use of small pixels depends strongly on the analysis technique. In the classical second-moment analysis (Hillas analysis Hillas 1985), the performance seems to saturate for pixels smaller than 0.15◦ . On the other hand, analysis techniques that use the full image distribution can extract the information contained in the well-collimated head part of high-intensity images, as compared to the more diffuse tail, and benefit from smaller pixel sizes. Pixel size also influences trigger strategies, since gamma-ray images are contiguous for large pixel sizes, allowing straightforward topological triggers compared with the case with smaller pixel sizes.

Telescope Optics Let us first consider the requirements for the telescope optics: • As a general rule of thumb, a γ -ray atmospheric shower produces 1 photon per m2 and GeV. This means that one needs mirror collection areas of hundreds of

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Fig. 2 Simulation of the recorded image, the same shower with two different pixel sizes

m2 to study γ -rays of ≤100 GeV energy. As a result, IACTs currently have the largest optical mirrors in the world. • However, as we have seen, shower images have an angular extent of tens of arcminutes and undergo intrinsic fluctuations due to the shower development in the atmosphere. Consequently, IACTs only require an optical point spread function (PSF) roughly of the size of a pixel, i.e., about ∼5 arcminute in diameter. This contrasts sharply with the optical requirements of telescopes in the optical range of light, for which the PSF must be better than 1 arcsecond, and allows to relax the quality requirements for the mirrors and mirror support structure. • The FOV must have an angular diameter of at least 2 arcdeg to contain the images of low-energy showers produced by point-like γ -ray sources and at least 4 arcdeg if the telescope is pointed slightly away from the source (“wobble mode”) and the intention is to observe high-energy showers. Larger FOVs are needed if one plans to observe sources with an extent of a few arcmin or to perform sky surveys. • As mentioned above, time is also of the essence in the identification and reconstruction of showers. The telescope optics must also satisfy a requirement for photon arrival time: the shape of the reflector must be isochronous to very few nanoseconds. Most IACTs follow a simple optical design. Light is collected by a convergent reflecting mirror surface (“reflector”) into a photodetector camera located at the focal plane. Like all large optical telescopes, IACT reflectors are multifaceted. Mirror facets have a typical surface area of 0.25–2 m2 . A spherical reflector shows too poor an optical performance. Two other reflector concepts are used:

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• A parabola. The overall shape of the reflector is parabolic, while each facet has a spherical shape with a curvature corresponding to the local curvature of the parabola. All facets in a ring around the center of the reflector are equal. In principle, the individual facets should be aspherical, but in practice they are manufactured with the same radius of curvature in the sagittal and tangential directions. A parabolic reflector has an excellent PSF at the center of the FOV but suffers from off-axis coma aberration. The main advantage of a parabolic is its excellent temporal resolution. • A “Davies–Cotton” design. Many IACTs have opted for the Davies–Cotton design (Davies and Cotton 1957), which can only be applied when the reflector is multifaceted. Figure 3 shows how this design compares to a spherical reflector. For a given focal length f , the radius of curvature of a spherical reflector Rsphere is 2×f and the normal vectors of the individual facets point to the center of the sphere. Instead, in a Davies–Cotton design, the reflector follows a global spherical shape with a smaller Rsphere = f , whereas the individual facets have a constant Rfacet = 2 × f . However, their normal vectors do not cross the center of the reflector sphere but a point at a distance 2 × f along the optical axis. Figure 4 illustrates how the tangential RMS changes with an incident angle for different optical designs (the sagittal RMS does not change with the incident angle). The results are based on a ray-tracing simulation (Schliesser and Mirzoyan 2005). For any of these optical designs, increasing the ratio of focal length and reflector diameter (focal ratio, f/D) reduces aberrations but increases the cost and complexity of the telescope mechanics, so IACTs do not exceed a focal ratio of 1.5.

Fig. 3 The left panel shows a spherical design: the radius of curvature Rsphere is 2×f and the normal vectors of the individual facets point to the center of the sphere. The right panel shows a Davies–Cotton design. For the same f , the global shape of the reflector is spherical but has a smaller radius of curvature. At the same time, the normal vectors of the individual facets are no longer aligned with the normal vector of the global sphere, and their curvature does not follow its curvature

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0.05

tangential rms [°]

0.04 0.03 elliptic

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Davies-Cotton parabolic

0.01 -0.2 f

0

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Fig. 4 Tangential RMS for given incident angle for a spherical design (green circles), a DaviesCotton design (purple squares), a parabolic design with adjusted radii (blue rhomboids), and a more sophisticated elliptical design (orange crosses). The focal ratio is fixed to 2 and the tessellation ratio (the ratio of area of facet and area of reflector) to 0.03. The inset shows the actual gross shape of the different configurations

Such a simple telescope optics has significant advantages: the design is simple, production is less expensive, and there is no loss of light in the secondary optical elements. However, some IACTs have opted for more complex optics in order to achieve a larger FOV and to reduce the plate scale. The latter allows to use smaller photosensors, namely Silicon PMs. The so-called Schwarzschild–Couder design (Couder et al. 1926) has two aspheric mirrors that can be configured to correct for spherical and coma aberrations, achieving good optical quality over a large FOV of ∼10◦ with a small focal ratio and plate scale.

Mechanical Structure Compared to telescopes in the visible range where the optical precision is higher, IACTs can be built with relatively simple mechanics and without a protecting dome. This reduces the cost considerably. However, both the mirrors and the mechanical structure must be particularly resistant to the harsh atmospheric conditions common in astronomical observatories, more specifically to high ice loads or strong wind gusts. Working outdoors also requires low-maintenance technical solutions. In addition, some phenomena in VHE astrophysics are very fast. In particular, the prompt emission of gamma-ray bursts lasts only a few seconds. In general, IACTs are expected to re-point in about 1–2 min, but some IACTs have been designed to

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re-point to any position on the sky in a time as short as 20–30 s. Acceleration during rapid re-pointing introduces additional forces in the structure. Except for the initial smaller (GByte/s) “raw data stream.” Raw events are delivered by the DAQ and contain information from each pixel. The Cherenkov pulse is typically digitized at the front-end electronics with sampling rates up to 2 Gsample/s. The pixel information included in a raw event may vary from just the total integrated charge and one single arrival time to the whole digitized waveform over a period of a few tens of nanoseconds. In addition, the event includes an event number, a time tag with a precision of at least a few hundred nanoseconds, a tag with information of trigger type (shower, calibration, pedestal, stereo, single-telescope. Etc.), and other control and auxiliary tags.

Photosensors The photosensors most commonly used in IACTs are photomultipliers with alkaline photocathodes and dynode chain-based electron multipliers, which provide ultrafast signals and allow measuring single phe. They can reach a relatively high peak quantum efficiency (QE), of about 40%, with a dynamic range of about 5,000 phe. However, these are not the only possible photosensors that can be employed in IACTs, and new devices, like solid-state Silicon Photomultipliers (SiPMs), are becoming viable candidates for new telescopes. Generally speaking, any device is a viable photosensor if it fulfills the following criteria:

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• The photosensor should allow to determine the arrival time of the photons to each pixel with sub-nanosecond precision for light pulses of sufficiently large amplitude. This is necessary to avoid distorting the intrinsic time evolution of the recorded shower. • The Cherenkov spectrum peaks at 350 nm and has a cutoff below 300 nm, and therefore the peak of the efficiency of the photosensor must match this wavelength range. In addition, given that the NSB contribution increases with the wavelength, it is desirable that the sensor efficiency drops to zero above 550 nm (This is not completely correct: there are re-emission lines of Cherenkov radiation above 650 nm due to the rotation states of OH molecules.) to reduce the background. • The dynamic range of the sensor must be broad enough to accurately reconstruct showers initiated by gammas across a wide range of energies. Typically, a range that starts at one phe and extends to a few thousand phe provides a good balance between cost and performance, allowing for the reconstruction of showers over a range of three orders of magnitude in energy without the need for extrapolation of truncated signals. • The contribution of spurious signal to the trigger thresholds, and to the trigger rate, shall be negligible. This is especially important for photomultipliers, in which ionized atoms trapped in its interior can give rise to large signals long after true phe have been identified. For SiPM, a similar phenomenon takes place, the optical crosstalk, although the mechanism is completely different. The rate of spurious signal is typically required to be at the 10−4 level or below with respect to the true signal. • In order to reduce the variance of the signal, the uniformity of the response within a single sensor must be better than 10%. This requirement can be extended to the uniformity between different sensors in the same camera. • Given that the sensors can be exposed to indirect sunlight during maintenance operations or to indirect moonlight during observations, they have to be able to survive to strong illumination. In particular, this survival requirement during observations imposes the use of a current limiter in the high voltage supplier for photomultipliers, whereas SiPMs do not require such protection. • The size of the sensor should match the typical angular size of the fluctuation of the shower images in the camera focal plane and should not introduce dead areas in the camera. This cannot be usually fulfilled by off-the-shelf sensors. However, it can be achieved by coupling a light guide to it, designed to have a pixel FOV of about 0.1 degrees. Moreover, this design allows to reject most of the background light outside this FOV and to keep the dead area of the camera small, without having to use custom geometries for the sensors. Apart from these criteria, there are other operational aspects that have to be considered when selecting photosensors for IACTs. In particular, their lifetime, stability, and cost are important aspects to consider in order to keep the performance of the camera up to the expectations, with a bounded maintenance cost.

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Camera Trigger and DAQ Triggering in telescopes has two goals: to reduce the load of the data acquisition system to manageable levels and to reject background events, mainly due to NSB fluctuations. IACTs are usually triggered in a staged manner. Firstly, individual Cherenkov telescope cameras produce a camera trigger signal by making use of topological properties in the pixel signals. This camera trigger may be staged itself and is designed to minimize the probability of triggering due to fluctuations of the NSB. The signal is sent either to a centralized facility or to neighboring telescopes to build a higher level trigger signal by exploiting the temporal coincidence of camera trigger images within the array of telescopes, the so-called stereo trigger or array trigger. The array trigger is sent back to the cameras to proceed recording the images. Therefore, an individual telescope typically buffers the shower image from the moment the camera trigger is issued to the moment it receives the stereo trigger. This can be done without introducing dead times in scales of milliseconds for digital buffering or microseconds for analog buffering. Therefore, the kind of buffer has a strong influence in the trigger design. Regardless of the chosen implementation, the trigger system must be flexible and software-configurable since operation modes vary from deep observations, where all telescopes follow the same source, to monitoring or survey applications, where groups of a few telescopes or even single telescopes point in different directions.

Camera Trigger The camera trigger must keep the trigger rate due to fluctuations of the NSB low. For this purpose, it exploits the recognition of the pattern due to the concentrations of Cherenkov signals in local regions of the camera. Nowadays, this recognition is based on looking for a number of pixels above threshold or a number of neighboring pixels above threshold, within the camera. This is typically implemented by dividing the camera up into sectors, which must overlap to provide a uniform trigger efficiency across the camera. In an alternative approach, the sum of all pixel signals in a patch of neighboring pixels, capped to a maximum value to reduce the influence of afterpulsing, is formed, and a threshold is set to initiate a trigger. In both cases, the implementation can be digital or analogue, although the second one is usually employed. The decision signal is sent in digital format, sometimes together with additional timing information, to neighboring telescopes or to a central decision system to form the stereo trigger.

Stereo Trigger The stereo trigger schemes for systems of IACTs provide asynchronous trigger decisions, delaying individual telescope trigger signals by an appropriate amount

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to compensate for the time differences when the Cherenkov light reaches the telescopes, and scanning trigger signals for patterns of telescope coincidence. The time to reach a trigger decision and to propagate it back to neighboring telescopes is of the order of microseconds. This can rise up to the millisecond scale when the signals have to be propagated to a central unit to take the decision. If the data is digitized and buffered with the individual camera trigger or with a lower level stereo trigger that combines individual triggers of neighboring telescope, restrictions on array trigger latency of a centralized decision are greatly relaxed, and the decision can be software-based. In this scheme, along with each local trigger, an absolute timestamp with an accuracy of 1 ns is sent to the central decision system, which searches for time coincidences of the events and defines the telescope system trigger. The centralized trigger system sends the information of the coincidence time back to the cameras. The cameras then select the events that fulfil the global trigger condition and should be recorded and transmitted for further stereoscopic processing. This centralized scheme is software-based but still makes uses of the properties of the individual camera trigger system in an optimal way.

DAQ Electronics As already commented, shower images have a pulse width of a few nanoseconds, with a background due to the NSB with typical rates from tens to hundreds of megahertz per pixel depending on mirror and pixel size and the photodetection efficiency. Thus, recording the shower induced signals efficiently requires high bandwidth and short integration times. On top of that, the dynamic range and electronics noise should be such that signals from one phe up to at least few thousands are recorded without truncation. Given the latency of the trigger signal, the electronics must delay or buffer the signals until the decision to store the signal arrives, which can take up to about 10 µs if the trigger signal of several telescopes is combined. The current available signal recording and processing technologies allow recording a range of signal parameters, from the integrated charge to the full pulse shape, over a fixed time window. The latter option seems optimal for low energies (below few TeV), which requires a more sophisticated background reduction, whereas for higher energies the former parameter is usually enough, complemented with other few parameters like time and time width of the signal. Two techniques for signal recording and processing are in use nowadays. The first technique is based on the use of Flash Analogue-to-Digital Converters (FADCs), while the second one uses analogue sampling memories: • FADC technology: these digitize the photosensor signal at sampling rates between 100 megasamples/s and few gigasamples/s. The digitized stream can be subsequently stored digitally for further processing, which allows for longer trigger latencies. Moreover, this technology allows the implementation of fully

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digital trigger systems that exploit the recorded image in real time. The main disadvantages of using FADCs with respect to analogue sampling memories are their cost and power consumption, which makes difficult its integration in cameras, although recent developments on low-power and low-cost FADCs with sampling speeds of up to 300 MS/s make them competitive for some IACT cameras. • Analogue sampling memories technology: these consist of banks of switched capacitors which are used in turn to record the signal shape. The maximum recording depth is given by the number of capacitors and the sampling time. The implementation in ASICs is such that they allocate enough capacitors to cope with few microseconds of trigger latency at sampling speeds 1 GS/s or faster for several channels simultaneously, making them very competitive in terms of cost and power scalability, and allowing a full implementation inside the camera. Once the event signals have been sampled and digitized, either they can be processed in FPGAs to perform a first reduction of the information by storing only pixel charges and pulse time width, or they can be fully stored for subsequent offline processing. In either case, the transmission system and consumer electronics and software must be able to deal with trigger rates of up to 20 kHz per camera, in which the signal of few thousand pixels, and few tens of time samples, if not reduction is performed, has to be buffered and eventually transmitted for archival. Currently, this can be implemented using local digital buffers in the cameras and commercial hardware for transmitting the data from the camera to high-end computers, which can assemble the events in real time and store them on disk.

Analysis Techniques The analysis of gamma rays detected using IACTs has to cope with different sources of background at different stages. At the earliest one, when the signal collected on individual pixels is integrated to obtain the number of phe, the integration has to be performed in such a manner as to reduce the contribution of electronic noise and the fluctuations of the ambient random photon field, which is mainly due to NSB and diffuse Moon Light. At later stages, the recorded shower images have to be treated to minimize further the contribution of the fluctuations of that random photon field. The techniques used in these two first stages are called Signal Extraction and Image Cleaning, respectively. Finally, at the latest stage of the analysis, it is necessary to reject the population of recorded images that are not initiated by gamma rays from the object of interest for the data analysis. In doing so, the technique to be used depends on the physical origin of the image, which is mostly showers initiated by hadrons and gammas from the object source, but could also include Cherenkov rings due to atmospheric muons, diffuse gammas, or electrons. Let us discuss the rejection techniques and the main properties of the backgrounds.

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Signal Extraction The NSB light level near the zenith at typical locations of IACTs is about 2.4 · 103 photons sr−1 ns−1 m−2 for wavelengths between 300 and 650 nm (Preuß et al. 2002). For typical IACTs, this results in a time average detection level of about 0.1 phe ns−1 per pixel, which can increase up to 10-fold in the presence of diffuse Moon Light. On the other hand, the total number of phe detected with a typical IACT in a gamma ray with an energy of 0.1 TeV is of the order of few hundreds spread over few nanoseconds, scattered in about 10 pixels (For pixels of a typical size of 0.1◦ and a 10-m type IACT). The goal of the signal extraction algorithm is to identify the time of arrival and the number of phe in each pixel within a recorder window that lasts few tens of nanoseconds. It profits from the clustering in time of the phe due to showers reaching a given pixel. To this end, it has to identify the most probable location in time of the signal on each pixel and integrate it in a time window large enough to capture it, but small enough to minimize the amount of noise accounted. This width relates to the bandwidth of the system, which usually dominates the time width of the signal recorded for a single phe. Most signal extraction algorithms rely on minimizing the following goodness of fit Gof between the recorded signal of a pixel in a given time window and the expected response function: Gof =

 2 Si − N Ri,T i∈n

=

 

Si2

i





constant





+N

2

 

2 Ri,T

i





constant



−2 × N ×

 



Si Ri,T







i

,

(1)

correlation between R and S

where the summation is in the n samples in time, Si is the signal in sample i, Ri,T is a given normalized response function centered in time sample T and evaluated in sample i, and N is a normalization factor. The rightmost hand side of the equation above separates the Gof in the terms which are relevant for the discussion of the signal extraction. The minimization of Gof is usually with respect to N and T , which gives a time and amplitude for the signal. Depending on the response function R and how the minimization is performed, the usual strategies are: • Fixed window: T is kept fixed, and R is constant in a window around this sample and zero out of it, that is, a square function of a given width. With this, N is proportional to the average of the signal within this window. • Sliding window: R has the same shape as for the fixed window, but Gof is minimized with respect to T . In this case, T is the one that maximizes the correlation between the signal and the square function R, and N is the proportional to the average around this T . • Digital filter (Albert et al. 2008a): Ri,T has the expected shape for a single phe arriving at T . The minimization gives the value of T that maximizes the

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correlation between the signal and R, and N is proportional to the weighted average of the signal around the sample T with the chosen response. The main drawback of these methods relies in the assumption of the response function shape in Eq. 1. Selecting the right one is a key parameter to reduce the influence of the electronic noise in the extracted signal and noise. On top of that, independently on the chosen response function, variations of the shape of the true signal result in a fluctuation in both the reconstructed time T and the extracted signal normalization N , which are undesirable. These are not the only possible strategies, and there are algorithms in the literature which aim to improve the background rejection and to reduce the systematic error in the value of the extracted signal, like using smooth basis functions to describe R, using the information from neighboring pixels to predict the expected arrival times of the Cherenkov photons, or employing state-of-the-art techniques like deep learning methods. Except for the methods based on the whole image processing, like some deep learning ones, the result of the image cleaning algorithm, i.e., a list of arrival time and total signal for each signal, is used as input for the next step in the analysis: the image cleaning.

Image Cleaning The task of an image cleaning procedure is to identify as many pixels as possible which are dominated by the signal from the shower, rejecting the pixels dominated by noise. To this end, the method exploits the correlation of the signal due to a single shower between neighboring pixels, which is not present for the background noise. To understand how this algorithm works, it is useful to introduce a simple model that describes the mean instantaneous signal at time t of a pixel with coordinates x and y with respect to the maximum of a recorded electromagnetic shower. This simple model is based on the Hillas parameterization (Hillas 1985) of shower images, approximating the time dependence of the arrival time of photons to the telescope by a linear function along the axis of the shower images. With this, we have that the recorded signal S(x, y, t) is 

S(x, y, t) = b + Ae

− 12

 x2 w

2

y 2+ 2 l



×e

− 21

(y−vt)2 σt2



∆,

(2)

where the shower axis moves along the Y-axis, the shower image maximum amplitude is A, w is its width and l its length, σt is the typical time length of a single phe pulse, v gives the shower image development speed, b gives the background signal per unit time, and ∆ is the sampling time width. The values of A, w, l, and v depend on the shower characteristics (like gamma or hadron energy, impact point of the shower axis on the ground, . . . ) as well as the optics of the telescope, camera pixel size, and detection efficiency. On the other hand, ∆ and σt are mostly due to

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instrumental characteristics like the sampling speed and the full chain electronics bandwidth. The signal extraction algorithm previously described extracts the time for each pixel in which Eq. 2 is maximized as a function of t, which is called Sextracted (x, y). For pixels that record a large number of phe due to the shower compared with the NSB contribution, the resulting amplitude of the signal extraction will be shower Sextracted (x, y) = Ae

− 21

 x2

w2

2

+ y2 l



∆,

and the time will be given by y/v. On the other hand, for pixels that only contain background phe, the average number of recorded phe would be b × ∆ × N , where N is the total number of time samples per pixel used as input for the signal extraction algorithms. These photons ∆ will be uniformly distributed among all the N samples, and if b × ∆ × N < 2σ N, t they will likely not overlap. Under these usually realistic conditions, the extraction algorithm will result in the maximum amplitude for a single phe SN SB , and the time will be random among all samples. The first approach to reject pixels dominated by noise is to select only those such that extracted signal is larger than SNSB +F , where F is a safety factor to account for uncertainties in the response, electronic noise, and statistical fluctuations. However, this is not fully satisfactory because requires to adjust the rejection level without any a priori knowledge of the shower image parameters. Since the required rejection efficiency will depend on the number of pixels, this results in either keeping NSBdominated background as part of the image or rejecting pixels of the shower image. Both possibilities result in introducing a systematic error for showers produced by low-energy gammas or by high-energy gammas far away from the telescope, and in the rejection of full images in case of showers with a small, but significant, number of photon–electrons detected. An improved approach is built by realizing pixels dominated by the shower cluster around the image maximum, so given a pixel which is safely considered not due to the background, its next-neighbors are likely due to shower photons too. This idea is implemented by using two background rejection levels instead of one. The first one is tight enough to select a list of pixels which are due to shower photons, typically selecting pixels with a signal larger than the one expected for 10 phe. Then, other pixels are added recursively to this list if they are neighbors of pixels already contained in the list and other signals are above a second looser rejection level, which usually are close to 5 phe. To improve the performance of the selection, as well as its robustness against background signals that do not fulfill the conditions for the background considered above, some additional constraints are required to add pixels to the list: (a) pixel above the first level is only added if they have at least a next-neighbor pixel also above this level (these are called core pixels) and (b) pixels which are above the second but not the first level are only added if at least one of its next-neighbors is above the first level (these are called boundary pixels). An additional improvement to this consists in taking into account the extracted time

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t between pixels (Aliu et al. 2009) or performing a global fit in time and space to a model similar to that of Eq. 2 (Emery et al. 2021), thus increasing the signal over noise ratio of the reconstructed shower image. Employing sophisticated models, this latest approach allows to relax the necessity of the event cleaning or even eliminate it completely.

Gamma–Hadron Separation The abovementioned techniques deal mainly with the NSB. However, once the images have been cleaned, the main background is shower images produced by the interaction of non-gamma primaries with the atmosphere. These are dominated by protons and He nuclei, which constitute more than 95% of primaries. The traditional rejection method for this background is based on the aforementioned Hillas parameterization (Hillas 1985) and the exploitation of the stereoscopic observation of the showers. This consists in fitting the distribution of photons in the cleaned images of the same shower observed by all Cherenkov Telescopes to bivariate Gaussian distributions (one per image). The result of this parameterization is the total amount of light contained in the shower, the position of the core of the shower in the sky, the projection of the axis of the shower in the sky, and the length of the major and minor axes of the shower, shown in Fig. 5. Since the image of an electromagnetic shower is well described by a single compact distribution except for very low-energy events, a first level of rejection is

Fig. 5 Sketch of some of the Hillas parameters obtained by fitting the image of a shower recorded in a single telescope

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traditionally obtained by discarding events in which at least one telescope recorded an image that contains more separated shower. On top of that, given that the shower axis follows the original direction of the gamma, a second level is achieved by rejecting events in which the projected shower axis of the parameterization of all the recorded images of the same shower does not cross, within the expected resolution obtained from Monte Carlo simulation, in the same point in the sky. A final rejection level is the rejection of non-electromagnetic initiated events. In traditional analyses, it exploited the width parameter, which is directly linked with the Molière radius in the upper atmosphere, and, contrary to other Hillas parameters, has a weak dependence on direction or energy of the primary gamma. A discriminating variable can be built using the width obtained from each telescope scaled by adding them in quadrature scaled by the expected one obtained from Monte Carlo simulations as a function of the cleaned image amount of light on each telescope and the distance of the telescope to the extrapolated impact point of the shower direction on the ground (the so-called impact parameter).

Wscaled = 

1 Ntelescope



i ∈ images

Widthi − < Widthi > (Size, D) , σi (Size, D)

(3)

where Size is the measured amount of light and D is the impact parameter, < Widthi > (Size, D) is the expected Width for telescope i, and σi (Size, D) is the expected variance of the width. Figure 6 shows the distribution of the Wscaled for gammas of 1 TeV and the proton background for observations with 4 telescopes and gammas, showing that a simple cut can reject most of the proton initiated showers.

Fig. 6 Distribution of Wscaled for 4 telescopes and 1 TeV gammas and protons, obtained from a Monte Carlo simulation

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More sophisticated methods make use of all Hillas parameters simultaneously using multivariate classificators like Random Forests or Boosted decision trees (Albert et al. 2008b). There are also an extension of the Hillas parameterization, for example, the use of templates in the so-called Model Analysis (de Naurois et al. 2003) or fitting all the images to a 3D model for the shower (Lemoine-Goumard et al. 2005) or lately using deep neutral network models (Nieto et al. 2017). These provide an improved background rejection efficiency over the traditional one, at the cost of a larger complexity. They are especially useful to enlarge the lower end of the energy range covered by the telescope, where the statistical fluctuations of the images make the classification based on Hillas parameters less performing.

Determination of Gamma-Ray Energy and Incident Direction The final stage of the analysis of a sample of shower images taken with IACTs, once backgrounds have been rejected, is the determination of primary gamma-ray direction and energy on an image by image basis. The accurate determination of the direction is possible thanks to the stereoscopic observation of the shower, as already sketched in Fig. 1: since the development of the electromagnetic shower is symmetric around the incident direction of the primary gamma ray, the axis of symmetry of each registered image represents the direction projected into the FOV as observed from the position of each telescope. Actually, this projection, together with the position of the center of the telescope mirror, defines a plane in real space. If the telescopes are pointing to the same position in the sky, then the crossing point of these projections is, within the statistical and systematic errors of the determination of the images axes, the primary gamma-ray incident direction because it is the only direction common to all image axes. Additional information can be extracted if the description based on planes in real space is used since the intersection of these planes does not only provide the direction but also the impact point if the extrapolation of the trajectory to the ground. It is obvious that the accuracy of this determination then depends on the number of collected photons, which correlates with the energy of the primary gamma ray, and the number of telescopes that register the same shower. The resolution reached for a single gamma ray for the current generation of IACTs is the range 0.1–0.05◦ for a primary energy above few hundreds of GeV. Figures 7 and 8 are typical results obtained with current-generation IACTs. The first one displays a distribution of reconstructed directions of γ -rays around a source and the latter one the distribution of angular distances between these reconstructed directions and the known or inferred position (so-called θ 2 ) of the source. A cut of θ 2  0.02 is typically applied to define the signal region and estimate the significance of the source detection. The reconstruction of the primary gamma-ray energy relies on two facts already described: (i) the number of electrons and positrons of the shower is approximately proportional to the primary energy and (ii) the Cherenkov photons reaching the ground are nearly uniformly distributed within a radius of 130 m of the impact

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Fig. 7 Distribution of the reconstructed direction of the identified gammas projected on the sky directions for a typical VHE gamma-ray source measured by a typical Cherenkov telescope. The color scale reflects the number of background subtracted gammas detected, smoothed to reduce the visual effect of statistics fluctuations

Fig. 8 Distribution of the square of the angular distance of the inferred incoming direction of the γ -ray showers with respect to the known source position (black points) for the source of Fig. 7, superimposed with the estimated irreducible background (red solid line), and a fit to a point like source (dashed blue line)

point on ground. Based on these, the energy reconstruction relies on building a parameterized estimate of the primary energy given the impact parameter and the register number of photons of each image after cleaning, which are combined accounting for the statistical fluctuations. The parameterization is built by means of complex Monte Carlo simulations of the shower development, based on models of the atmosphere and electromagnetic interactions (see Heck et al. 1998 for example) and the telescope response using ray-tracing codes and detailed descriptions of the photosensors and DAQ. As usual, there are more sophisticated methodologies which improve the accuracy and precision of the reconstruction of the primary properties at the cost of complexity and computational resources (Albert et al. 2008b; de Naurois et al. 2003; Lemoine-Goumard et al. 2005; Nieto et al. 2017).

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Typical Performance and Scientific Plots Key parameters characterizing the performance of IACTs are flux sensitivity, angular resolution, and energy resolution. While angular resolution refers to the accuracy of measuring the incoming direction of the gamma ray, energy resolution refers to the accuracy of measuring its energy. Flux sensitivity is the minimum flux of a gamma-ray source that can be detected beyond a certain statistical significance, usually five sigma, in a given amount of time. Performance figures are calculated by means of Monte Carlo simulations tailored to the observed properties of the detectors, resulting in typical angular resolutions in the range of 0.15 to 0.05 degrees and typical energy resolutions in the range of 10–15%. This dependency on the energy of the gamma rays being observed is evident in Figs. 9 and 10 for the sensitivity and angular resolution of some representative instruments. Regarding typical results for IACTs, the reader can refer to Section 16–19 for a comprehensive overview of high-level analysis techniques. Figures 7, 11, and 12 provide examples of what can be obtained through the analysis of a gamma-ray source with IACTs: they show, respectively, (1) the distribution of reconstructed directions of gammas in a given energy range, (2) the reconstructed energy spectrum for a bright source, and (3) the light curve, that is, the reconstructed flux as a function of time for a given energy range, for an exceptionally variable gamma-ray source.

Fig. 9 Sensitivity for several arrays of IACTs, that is, detectable flux with a statistical significance above the background fluctuations of five sigma in 50 h. (Extracted from MAGIC collaboration 2016; VERITAS; Preliminary Sensitivity Curves for H.E.S.S.-I 2015)

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Fig. 10 Angular resolution for a typical IACT array as a function of the gamma energy. (Adapted from MAGIC collaboration 2016)

Fig. 11 Reconstructed flux for the Crab Nebula with the MAGIC telescopes. (Adapted from MAGIC collaboration 2015)

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Fig. 12 Typical light curve for a VHE bin, that is flux in the bin as a function of time, for a highly variable gamma-ray source. The x-axis corresponds to Modified Julian Date (MJD)

Current Telescopes and Future Evolution of the Technique The second-generation IACT arrays such as H.E.S.S. in Namibia, MAGIC in Spain, and VERITAS in USA have brought the technique to maturity and are still operational. The reader is referred to Chapters VIII to X for the status and a review of the roughly last 20 years of scientific results of these three instruments. The community behind these three IACT arrays has come together to design and build a full-sky open observatory called the Cherenkov Telescope Array Observatory (CTAO Chapters XI of Section 6). CTAO will consist of two arrays of IACTs in the northern and southern hemispheres. CTAO-North will be located at the Roque de los Muchachos observatory (La Palma, Spain) and CTAO-South at Cerro Paranal (Chile). The CTAO IACTs will have mirrors of three different sizes optimized for overlapping energy ranges: the Large-Sized Telescopes (LST) will be equipped with the largest mirrors (23 m diameter) and target the lowest energies down to an energy of ∼20 GeV, the Medium-Sized Telescopes (MST) will be equipped with 12 m diameter mirrors and cover the range from roughly 100 GeV to a few TeV, and Small-Sized Telescopes (SSTs) with ∼4 m diameter mirrors will be sensitive to the highest energies up to hundreds of TeV. CTAO is designed to operate for 30 years. Over this long period of time, most probably the mechanics and optics of the CTAO telescopes will remain unchanged, but the cameras will be upgraded with higher efficiency photodetectors and faster trigger and readout electronics. Data analysis methods are expected to improve, especially with the application of new machine learning techniques, which may still be limited by computing power.

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With an increase in photodetection efficiency, the IACT may expand to even lower energies, probably even below 10 GeV. Extracting physical information may prove challenging, given the fact that γ -ray showers develop farther and farther away from the telescope with decreasing energy and their images get correspondingly smaller and smaller. A low zenith 300 GeV γ -ray shower reaches its maximum at 8 km altitude above the sea level, while a 3 GeV shower does so at 14 km altitude. For higher zenith angles, the distance to the shower maximum is even larger. Both camera pixelization and optical PSF will need to improve in order to resolve the relevant features of the shower image. The IACT technique may also evolve through innovative optics to increase the FOV, reduce the threshold, or improve the optical quality (Mirzoyan and Andersen 2009; Cortina et al. 2016; Mueller and Cherenkov-Plenoscope 2019). See Chapter XII of Section 6 for a more extensive review of future initiatives in ground-based gamma-ray astronomical detectors, including large FOV shower particle detector arrays.

References Handbook of X-Ray and Gamma-Ray astrophysics, The Major Gamma-ray Imaging Cherenkov Telescopes (MAGIC), The Very Energetic Radiation Imaging Telescope Array System (VERITAS) and The High Energy Stereoscopic System (H.E.S.S.), Section 6 (Springer) Handbook of X-Ray and Gamma-Ray astrophysics, The Cherenkov Telescope array (CTA): a worldwide endeavor for the next level of ground-based gamma-ray astronomy, Section 6 (Springer) Handbook of X-Ray and Gamma-Ray Astrophysics, Future developments in ground-based gammaray astronomy, Section 6 (Springer) Handbook of X-Ray and Gamma-Ray Astrophysics, Sections 7–15 (Springer) Handbook of X-Ray and Gamma-Ray Astrophysics, Section 16–19 (Springer) J. Albert et al., (MAGIC collaboration), FADC signal reconstruction for the MAGIC telescope. NIM A 594, 407–419 (2008a) J. Albert et al., (MAGIC collaboration), Implementation of the random forest method for the imaging atmospheric Cherenkov telescope MAGIC. NIM A 588, 424–432 (2008b) E. Aliu et al., (MAGIC collaboration), Improving the performance of the single-dish Cherenkov telescope MAGIC through the use of signal timing. Astropart. Phys. 30, 293 (2009) A. Barrau et al., The CAT imaging telescope for very-high-energy gamma-ray astronomy. NIM A 416, 278–292 (1998) P.A. Cherenkov, Visible emission of clean liquids by action of γ radiation. Dokl. Akad. Nauk SSSR 2, 451 (1934) J. Cortina, A. Moralejo, R. Lopez-Coto, MACHETE: a transit imaging atmospheric Cherenkov telescope to survey half of the very high energy gamma-ray sky. Astrop. Phys. 72, 46–54 (2016). A. Couder, Sur un type nouveau de télescope photographique. Compt. Rend. Acad. Sci. Paris 45, 1276 (1926) A. Daum et al., (The HEGRA Collaboration), First results on the performance of the HEGRA IACT array. Astropart. Phys. 8, 1–11 (1997) J.M. Davies, E.S. Cotton, Design of the quartermaster solar furnace. J. Sol. Energy Sci. Eng. 1, 16 (1957) G. Emery et al., Reconstruction of extensive air shower images of the first Large Size Telescope prototype of CTA using a novel likelihood technique, in PoS (ICRC2021) (2021), p. 716

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D. Heck et al., CORSIKA: a Monte Carlo code to simulate extensive air showers, Technical Report, FZKA-6019, Forschungszentrum Karlsruhe (1998) W. Heitler, The Quantum Theory of Radiation (1954) (Oxford University Press), ISBN-10 0198512120 A. Hillas, Cherenkov light images of EAS produced by primary gamma, in Proceedings of 19th ICRC (La Jolla), vol. 3 (1985), p. 445 M. Lemoine-Goumard et al., 3D-reconstruction of gamma-ray showers with a stereoscopic system, in Proceedings of toward Network of Atmospheric Cherenkov Detectors VII (2005), pp. 173–182 MAGIC collaboration, Measurement of the Crab Nebula spectrum over three decades in energy with the MAGIC telescopes. J. High Energy Astrophys. 5–6, 30–38 (2015) MAGIC collaboration, The major upgrade of the MAGIC telescopes, part II: A performance study using observations of the Crab Nebula. Astropart. Phys. 72, 76 (2016) R. Mirzoyan, M.I. Andersen, A 15 deg wide field of view imaging air Cherenkov telescope. Astrop. Phys. 31, 1–5 (2009) S.A. Mueller, Cherenkov-Plenoscope (2019). arXiv:1904.13368 M. de Naurois et al., Application of an analysis method based on a semi-analytical shower model to the first H.E.S.S. telescope, in Proceedings of 28th ICRC (2003), p. 2907 D. Nieto et al., Exploring deep learning as an event classification method for the Cherenkov Telescope Array, in Proceedings of 35th ICRC, (2017) Preliminary Sensitivity Curves for H.E.S.S.-I (stereo reconstruction), based on/adapted from Holler et al., in Proceedings of the 34th ICRC (2015) S. Preuß, G. Hermann, W. Hofmann, A. Kohnle, Study of the photon flux from the night sky at La Palma and Namibia, in the wavelength region relevant for imaging atmospheric Cherenkov telescopes. NIM A 481, 229–240 (2002) A. Schliesser, R. Mirzoyan, Wide-field prime-focus imaging atmospheric Cherenkov telescopes: a systematic study. Astrop. Phys. 24, 382 (2005) VERITAS: public specifications webpage. https://veritas.sao.arizona.edu/about-veritas/veritasspecifications C.T. Weekes et al., (Whipple collaboration), Observation of TeV gamma rays from the crab nebula using the atmospheric Cerenkov imaging technique. Astrophys. J. 342, 379–395 (1989)

Detecting Gamma-Rays with Moderate Resolution and Large Field of View: Particle Detector Arrays and Water Cherenkov Technique

74

Michael A. DuVernois and Giuseppe Di Sciascio

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ground-Based Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Air Shower Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Example Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HAWC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LHAASO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Detector Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sensitivity to a γ -Ray Point Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Energy Threshold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relative Trigger Efficiency R . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Angular Resolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Background Discrimination from the Ground . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

The Earth is continuously bombarded by cosmic rays and gamma-rays extending over an immense range of energies. Discovered in 1912 by Victor Hess, the cosmic radiation has been studied from balloons, from space, from the ground, and from underground. The resulting fields of cosmic-ray astrophysics (focused

M. A. DuVernois () Dept of Physics & Wisconsin IceCube Particle Astrophysics Center (WIPAC), University of Wisconsin, Madison, WI, USA e-mail: [email protected] G. Di Sciascio Istituto Nazionale di Fisica Nucleare (INFN), Sezione di Roma Tor Vergata, Rome, Italy e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_64

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on the charged particles), gamma-ray astrophysics, and neutrino astrophysics have diverged somewhat. But for the air showers in the GeV and TeV energy ranges, the ground-based detector techniques have considerable overlaps. Very high-energy (VHE) gamma-ray astronomy is the observational study measuring the directions, flux, energy spectra, and time variability of the sources of these gamma-rays. These measurements constrain the theoretical models of the sources and their interactions between the sources and detection at Earth. With the low flux of gamma-rays, and the background of charged particle cosmic rays, the distinguishing characteristic of gamma-ray air shower detectors is large size and significant photon to charge particle discrimination. Air shower telescopes for gamma-ray astronomy consist of an array of detectors capable of measuring the passage of particles through the array elements. To maximize signal at energies of a TeV or so, the array needs to be built at high altitude as the maximum number of shower particles is high in the atmosphere. These detectors have included sparse arrays of shower counters, dense arrays of scintillators or resistive plate counters (RPC), buried muon detectors in concert with surface detectors, or many-interaction-deep water Cherenkov detectors (WCD). In general, these detectors are sensitive over a large field of view, and the whole of the sky is a typical sensitivity and perhaps two-thirds of the sky selected for clean analysis, but with only moderate resolution in energy, typically due to shower-to-shower fluctuations and the intrinsic sampling of the detector. These telescopes, though, operate continuously, despite weather, moonlight, day or night, and without needing to be pointed to a specific target for essentially a 100% duty cycle. In this chapter, we will examine the performance and characteristics of such detectors. These are contrasted with the Imaging Air Cherenkov Telescopes which also operate in this energy range, and both current and future proposed experiments are described. Keywords

Gamma-ray astronomy · Instrumentation · Air shower physics

Introduction The large energy range that can be investigated in gamma-ray astronomy (≈MeV → PeV) requires different detection techniques and implies a great variety of generation phenomena. The experimental techniques that can be used are determined by the properties of the gamma radiation and by the huge background of cosmic rays (CRs): (1) The γ -ray flux is very small (≤10−3 with respect to the background of CRs detected in a 1◦ angle around the direction of the source) and rapidly decreasing with increasing energy. All the known sources exhibit a power-law energy spectrum:

74 Detecting Gamma-Rays with Moderate Resolution and Large Field. . .

dN ∝ E −γ dE

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(1)

with an index γ ∼2–3. Small detectors onboard satellites (e.g., Fermi Gamma Ray Observatory) allow observations up to around 10 GeV. To detect the low flux at higher energies, it is necessary to build up ground-based detectors where it is possible to have larger effective collecting areas. (2) The Earth’s atmosphere is opaque to γ −rays being about 28 radiation lengths thick at sea level. Therefore, γ −rays cannot be directly observed by groundbased detectors. (3) The isotropic cosmic-ray flux forms a huge background exceeding by many orders of magnitude even the strongest steady photon flux. It consists largely of protons and helium nuclei. It is important to consider the atmosphere also as part of the extended detector system, with atmospheric monitoring especially critical to both telescope measurements but also affecting air shower ground particle measurements.

Ground-Based Detection The ground-based detection of VHE photons is indirect: the nature, direction, and energy of the primary particle have to be inferred from the measurable properties of the secondary particles (in the case of shower arrays) or of the Cherenkov flash in the atmosphere (for Cherenkov telescopes). Gamma-rays interact electromagnetically, producing an electron-positron pair. The mean free path of photons for pair production is almost the same as the electron radiation length, X0 ∼37 g/cm−2 , in air. These secondary particles yield a new generation of γ -rays through bremsstrahlung, starting an electromagnetic extensive air shower (EAS). The properties of electromagnetic cascades are well established for many decades (Heitler 1994; Matthews 2005), even for very small showers from low-energy, few GeV, primaries (D’Ettorre Piazzoli and Di Sciascio 1994; Di Sciascio et al. 1997). The detection of air showers from the ground is carried out by means of two different experimental techniques, both exploiting the atmosphere as a calorimeter (Fig. 1): • An active inhomogeneous calorimeter, with the detection of the Cherenkov light produced in air by means of telescopes. • A sampling calorimeter, sampling the number of secondary charged particles only at ground level (in practice, often a high altitude above sea level). Unlike Cherenkov telescopes, the detectors of shower arrays directly exploit secondary particles that reach the ground sampling their lateral distribution. Typically they consist of a large number of charged particle detectors, usually scintillation

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-0.1-10 GeV

~ 1 TeV

g

~ 100 TeV

Area: - 0.15 m2

Atmosphere

-8 km

Cerenkov Light Cone

~0.8∞

4 2 Area: -10 m

Optical Detector

Air-shower Array

Fig. 1 Experimental techniques used for the detection of high-energy γ −rays from ground. IACT on the left and air shower array on the right

counters, Resistive Plate Chambers (RPCs), or water Cherenkov tanks, spread over an area of 104 –105 m2 with a spacing of 10–20 m. The tail particles of the shower are sampled at a single depth (the observational level) and at fixed distances from the shower core position. In High Energy Physics language, an array is a so-called tail catcher sampling calorimeter. The key observables in all air shower arrays are the local shower particle densities and the secondary particle arrival times with which to reconstruct the shower arrival direction, the energy, and the kind of the primary particle. The resolutions of these measurements are limited by the large shower-to-shower fluctuations mainly due to the depth of the first interaction, which fluctuates by one radiation length (∼37 g/cm2 ) for electromagnetic particles and by one interaction length (∼90 g/cm2 ) for protons. From an experimental point of view, the sampling of secondary particles at ground can be realized with two different approaches: (1) Particle Counting. A measurement is carried out with thin (≪1 radiation length) counters providing a signal proportional to the number of charged particles (as an example, plastic scintillators or RPCs). The typical detection threshold is in the keV energy range.

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(2) Calorimetry. A signal proportional to the total incident energy of electromagnetic particles is collected by a thick (many radiation lengths) detector. An example is a detector constituted by many radiation lengths of water to exploit the Cherenkov emission of secondary shower particles. The Cherenkov threshold for electrons in water is 0.8 MeV and the light yield ≈320 photons/cm or ≈160 photons/MeV emitted at 41◦ . The critical parameters of a detector are the time and the amplitude resolutions. The direction of the incoming primary particle is reconstructed with the time of flight method, making use of the relative times at which the individual detection units are triggered by the shower front. The time resolution can affect the angular resolution of the apparatus if it is not comparable with the rising edge of the shower front (∼ns). Time resolution is the convolution of the shower front leading edge, the photodetector transit-time spread, the timing jitter in the trigger system, and the finite resolution of the data acquisition. Sampling fluctuations are typically very large; therefore, a modest amplitude resolution (∼30%) is required. A large dynamic range is on the contrary needed due to the strong dependence of the signal from the shower core distance. In general, not all detectors allow an optimization of both observables at the same time. As an example, in a water Cherenkov detector, reflecting inner surface allows a very good calorimetric measurement but with a narrower arrival time distribution. Generally, the instrumented area A determines the rate of high-energy events recorded, i.e., the maximum energy via limited statistics. The grid distance d determines the low-energy threshold (small energy showers are lost in the gap between detectors) and the quality of the shower sampling. The particular kind of detector (scintillator, RPC, or water tank) determines the detail of measurement (efficiency, resolutions, energy threshold, granularity of the readout) and impact on the cost per detector Cd . In principle, best physics requires large area A, small distance d, and high quality of the sampling. But the cost of an array increases with Cd · A/d 2 ; therefore, a compromise is always needed. The total sensitive area of a classical array is less than 1% of the total enclosed area. This results in a high degree of uncertainty in the reconstruction due to sampling fluctuations which add to the shower fluctuations. The sparse sampling sets the energy threshold and determines a poor energy resolution (∼100%). Also the angular resolution is limited by the shower fluctuations. Denser arrays (see discussion of the Milagro, HAWC, and LHAASO water detectors elsewhere) can reduce the sampling fluctuations significantly while also improving the chances of catching muons in the air shower. This comes at a cost of reduced total detector area which in practice has been compensated for with a less dense outer (“outrigger” in Milagro and HAWC parlance) detector array added onto the dense inner array. In addition, dependence of threshold and reconstruction capabilities on the zenith angle is higher than for Cherenkov telescopes: since the active area is horizontal, its projection onto a plane perpendicular to the shower axis is smaller than the geometrical area. (Cherenkov telescopes point the source; therefore, their area is

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Table 1 Air shower arrays compared to Imaging Air Cherenkov Telescopes (IACT) Energy threshold Max energy Field of view Duty cycle Energy resolution Background rejection Angular resolution Zenith angle dependence Effective area

Air shower array Low (≈100 GeV) Very high (≈1015 eV) Very large (≈2 sr) Very large (≈100%) Modest (≈100–20%) Good (>80%) Good (≈1–0.2 deg) Very strong (≈cosθ −(6−7) ) Shrinks with zenith angle

IACT Very low (≈10 GeV) Limited (≈100 TeV) Limited (≈5 deg) Very small (≈15%) Good (≈15%) Excellent (>99%) Excellent (≈0.05 deg) Small (≈osθ −2.7 ) Increases with zenith angle

always orthogonal to the shower axis. The degradation of the detector performance with zenith is simply due to the increasing thickness of atmosphere). On the other hand, EAS arrays have a large field of view (∼2 sr) and a 100% duty cycle. These characteristics give them the capability to serve as all-sky monitors, important to detect flaring, or transient, gamma emissions. The main characteristics and differences between air shower arrays and Cherenkov telescopes are summarized in Table 1.

Air Shower Physics High-energy cosmic rays or gamma-rays collide with the nucleus of some atmospheric gas, high in the atmosphere. The resulting collision produces additional high-energy particles. These also collide with air nuclei, and each additional interaction adds to the growing particle cascade. That is Npart ∝ 2depth as the shower develops. These particles include neutral pions, which decay immediately to a pair of gamma-rays, with the gamma-rays producing e± pairs near other nuclei. Electrons and positrons regenerate gamma-rays via bremsstrahlung, building up the electromagnetic cascade.

Simplified Treatment Decays and interactions in the atmosphere cause a Npart ∝ e−depth scaling. Thus, there is a point in depth of maximum number at which an air shower reaches a maximum size Nmax which is approximately E/(1.6 GeV) depending on some details such as incoming species and the hadronic interactions. Gamma-ray initiated showers are purely electromagnetic, so let’s consider that subset of cosmic-ray air showers. In the electromagnetic shower π 0 , mesons decay into gamma-rays, with gammas converting in to e± pairs, which produce new gammas by bremsstrahlung. The  radiation length X0 is the grammage path length ( density(x) dx) in which their energies attenuate by a factor of 1/e. In air, the radiation length X0 is about 37 g/cm2 .

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One can picture the cascade as a series of generations. For each generation, every existing gamma-ray converts to electron-positron pair, while each existing electron or positron produces a new gamma-ray in addition to itself. Each generation doubles the number of cascade particles. This continues until the average particle energy is reduced to a critical energy scale at which the charged particles lose energy to ionization in less than a radiation length. Ionizing energy loss is about 2.2 MeV/g/cm2 , so the critical energy is (2.2 MeV/g/cm2 ) × (37 g/cm2 ) = 81 MeV. At this point, the shower size is Nmax = E/Ec . The number of generations n needed to reach this maximum size depends on the total energy E. At maximum, 2n = Nmax = E/Ec , so n = ln(E/Ec )/ln(2). The maximum size occurs at a (slant) depth of Xmax = n × X0 × ln(2) = X0 × ln(E/Ec ) along the shower axis. The number of particles as a function of depth is typically called the electromagnetic longitudinal profile and is described by the Greisen formula: 0.31 T −3T /s Ne = √ e s . Tmax

(2)

Here T is the atmosphere depth measured in radiation length X/X0 in slant distance, Tmax = ln(E/Ec ), and s is the shower age s = 3T/(T+2Tmax ). Shower maximum is at shower age s = 1 (Greisen 1956). Hadronic interactions, from a charged cosmic ray, additionally produce charged pions, π ± , and muons, μ± , in addition to forward nuclear fragments. For a good reference on the structure of hadronic air showers, see here Engel et al. (2011). The secondary muons at the ground therefore form an observable consequence of a charged primary cosmic ray and can be used as a veto to suppress the (dominant) charged cosmic-ray flux.

Adding Complexity to the Air Shower Model The simplified form of the air shower physics described above gives us some qualitative understanding, but in practice, the air shower development is studied via Monte Carlo-based simulations using either CORSIKA or AIRES to handle the overall atmospheric simulation and some combination of GEANT and hadronic simulation codes such as QGSJET for the underlying micro-physics (CORSIKA: https:// www.iap.kit.edu/corsika/70.php; AIRES: http://aires.fisica.unlp.edu.ar/; GEANT4: https://geant4.web.cern.ch/node/1; QGSJET: arXiv:hep-ph/0412332). This allows for the shower-to-shower fluctuations to be taken into account and also addresses the atmosphere as a detector element (see below), timing and positions of groundlevel particles, and the shape of the shower front which is critical for timing. The atmosphere is composed of about 78% N2 , 21% O2 , and 1% Ar, with an average atomic mass of ∼14.6. This average atomic mass is generally used as the target “nucleus.” The starting point for an atmospheric model is generally the US Standard Atmosphere developed by NOAA, NASA, and the US Air Force (NOAO, NASA, and USAF, US Standard Atmosphere 1976). This has a typical parameterization into five layers with simple coefficients (CORSIKA: https://www.

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Fig. 2 US Standard Atmosphere mass overburden as function of altitude and parameterization of the atmospheric overburden in five layers

iap.kit.edu/corsika/70.php; Sinnis 2021) shown in Fig. 2. These parameterization functions for the first four layers are exponential: X(h) = ai + bi × e−h/ci

(3)

and the fifth layer is linear in altitude and overburden: X(h) = a5 − b5 ×

h . c5

(4)

The US Standard Atmosphere is approximately valid for most low altitude sites around the world with minor deviations, at higher altitudes, and in climatically complicated sites such as the South Pole, there are modified forms appropriate to the local sites.

Example Experiments The earliest air shower arrays used for gamma-ray astronomy were composed of small plastic scintillator panels distributed over a large area. With low active area fractions of less than 1% of the enclosed area, these arrays had high-energy thresholds near 100 TeV. The CYGNUS (Alexandreas et al. 1992) and CASA

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(Borione et al. 1994) arrays were the largest of this sort of instrument. No evidence of sources were seen in these experiments. We will look more closely at two experiments of the next generation of gammaray observatories using the experimental approaches mentioned above, but with a goal of lowering the detector thresholds. The following are the two different groundbased TeV survey instruments and their techniques: (1) Water Cherenkov (Milagro) (Atkins et al. 2000). (2) Resistive Plate Chambers (ARGO-YBJ) (Di Sciascio 2014). The Milagro detector consisted of a large central water reservoir (60×80 m2 ), which operated between 2000 and 2008 in New Mexico (36◦ N, 107◦ W), at an altitude of 2630 m above sea level (a.s.l.) (Atkins et al. 2000). The reservoir was covered with a light-tight barrier and instrumented with two layers of 8” PMTs to improve the detection of muons. In 2004, an array of 175 small tanks was added, irregularly spread over an area of 200×200 m2 around the central reservoir. With this array, the Milagro collaboration developed analysis techniques for CR background discrimination (gamma-hadron separation). The Tibet ASγ experiment utilized a sparse array of plastic scintillators with an energy threshold higher than ≈10 TeV (Amenomori et al. 2015). The ARGO-YBJ experiment, located at the Yangbajing Cosmic Ray Observatory (Tibet, PR China, 4300 m a.s.l., 606 g/cm2 ), is constituted by a central carpet ∼74 ×78 m2 , made of a single layer of Resistive Plate Chambers (RPCs) with ∼93% of active area, enclosed by a guard ring partially instrumented (∼20%) up to ∼100×110 m2 . The apparatus has a modular structure, the basic data acquisition element being a cluster (5.7×7.6 m2 ), made of 12 RPCs (2.85×1.23 m2 each). Each chamber is read by 80 external strips of 6.75×61.80 cm2 (the spatial pixels), logically organized in 10 independent pads of 55.6×61.8 cm2 which represent the time pixels of the detector (Aielli et al. 2006). The readout of 18,360 pads and 146,880 strips is the experimental output of the detector. In addition, in order to extend the dynamical range up to PeV energies, each chamber is equipped with two large size pads (139×123 cm2 ) to collect the total charge developed by the particles hitting the detector (Bartoli et al. 2015a). The RPCs are operated in streamer mode by using a gas mixture (Ar 15%, isobutane 10%, tetrafluoroethane 75%) optimized for high altitude operation (Bacci et al. 2000). The high voltage settled at 7.2 kV ensures an overall efficiency of about 96% (Aielli et al. 2009). The central carpet contains 130 clusters, and the full detector is composed of 153 clusters for a total active surface of ∼6700 m2 (Fig. 3). The total instrumented area is ∼11,000 m2 . Because of the small pixel size, the detector is able to record events with a particle density exceeding 0.003 particles · m−2 , keeping good linearity up to a core density of about 15 particles · m−2 . The median energy of the first multiplicity bin (20–40 fired pads) for photons with a Crab-like energy spectrum is ∼340 GeV (Bartoli et al. 2015b). The granularity of the readout at centimeter level and a noise of accidental coincidences of 380 Hz/pad allowed to sample events with only 20 fired pads, out of 15,000, with a noise-free topological-based trigger logic.

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12 RPC =1 Cluster 2 (5.7 × 7.6 m )

1

2

3

4

5

6

7

8

9

10

ELECTRONIC FRONT-END CARDS

PAD

99 74 m m

1 2 3

4

5

6

Local station

7

8 9 10 11 12

10 Pads = 1 RPC 2 (2.80 × 1.25m ) 78 m 111 m

Fig. 3 Layout of the ARGO-YBJ experiment (see text for a description of the detector)

The benefits in the use of RPCs in ARGO-YBJ are as follows(Di Sciascio 2014; Bartoli et al. 2011): (1) high efficiency detection of low-energy showers by means of the high density sampling of the central carpet (the detection efficiency of 100 GeV photoninduced events is ≈50% in the first multiplicity bin); (2) unprecedented wide energy range investigated by means of the digital/charge readouts (∼300 GeV → 10 PeV); (3) good angular resolution (σθ ≈ 1.66◦ at the threshold, without any lead layer on top of the RPCs) and unprecedented details in the core region by means of the high granularity of the different readouts. RPCs allowed one to also study charged cosmic-ray physics (energy spectrum, elemental composition, and anisotropy) up to about 10 PeV. By contrast, the capability of water Cherenkov facilities in extending the energy range to PeV and in selecting different primary masses must be still investigated. In both experiments (Milagro and ARGO-YBJ), the limited capability to discriminate the background was mainly due to the small dimensions of the central detectors (pond and carpet). In fact, in the new experiments HAWC (Abeysekara et al. 2013) and LHAASO (Di Sciascio 2016; Cao et al. 2021), the discrimination of the CR background is made studying shower characteristics far from the shower core (at distances R > 40 m from the core position, the dimension of the Milagro pond and ARGO-YBJ carpet).

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HAWC The Milagro results, as well as the potential for continuous monitoring of a large fraction of the sky, have motivated the construction of larger EAS detectors like the High-Altitude Water Cherenkov Observatory (HAWC). HAWC is located on the Sierra Negra volcano in central Mexico at an elevation of 4100 m a.s.l. (see Fig. 4). It consists of an array of 300 water Cherenkov detectors made from 5 m-high, 7.32 mdiameter water storage tanks covering an instrumented area of about 22,000 m2 . Water in the tanks totals about 55 kilotons. Four upward-facing photomultiplier tubes (PMTs) are mounted at the bottom of each tank: a single 10′′ high quantum efficiency (HQE) PMT positioned at the center and three 8′′ PMTs formerly from Milagro positioned halfway between the tank center and rim. The central PMT has roughly twice the sensitivity of the outer PMTs, due to its superior quantum efficiency and larger size. The WCDs are filled to a depth of 4.5 m, with 4.0 m (more than ten radiation lengths) of water above the PMTs. This large depth guarantees that the electromagnetic particles in the air shower are fully absorbed by the HAWC detector, well above the PMT level, so that the detector itself acts as an electromagnetic calorimeter providing an accurate measurement of electromagnetic energy deposition (Abeysekara et al. 2012, 2013, 2017). HAWC operates with a two stage triggering system: PMT pulses above threshold generate signal edges for two levels of small and large events; and all of these digital edges are brought together in software to form interesting event triggers. The purely software second level trigger allows for significant flexibility in addressing horizontal showers and potentially lowered thresholds in certain directions in addition to facilitating the basic air shower trigger (Abeysekara et al. 2018a).

Fig. 4 Layout of the HAWC experiment as seen from aerial photograph. The sketch of a water tank is shown on the right side

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LHAASO A new project, developed starting from the experience of ARGO-YBJ and the Milagro and HAWC water tanks, is LHAASO (Cao et al. 2021). The experiment is strategically built to study with unprecedented sensitivity the energy spectrum, the elemental composition, and the anisotropy of CRs in the energy range between 1012 and 1017 eV, as well as to act simultaneously as a wide aperture (∼2 sr), continuously operated gamma-ray telescope in the energy range between 1011 and 1015 eV. The first phase of LHAASO consists of the following major components (see Fig. 5): • 1.3 km2 array (LHAASO-KM2A) for electromagnetic particle detectors (ED) divided into two parts: a central part including 4931 scintillator detectors 1 m2 each in size (15 m spacing) to cover a circular area with a radius of 575 m and an outer guard ring instrumented with 311 EDs (30 m spacing) up to a radius of 635 m. • An overlapping 1 km2 array of 1146 underground water Cherenkov tanks 36 m2 each in size, with 30 m spacing, for muon detection (MD, total sensitive area ∼42,000 m2 ). • A close-packed, surface water Cherenkov detector facility with a total area of about 78,000 m2 (LHAASO-WCDA). • 18 wide field-of-view air Cherenkov telescopes (LHAASO-WFCTA).

Fig. 5 Layout of the LHAASO experiment. Central pond and outer particle detector array

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LHAASO is located at high altitude (4410 m a.s.l., 600 g/cm2 , 29◦ 21′ 31′′ N, 100◦ 08′ 15′′ E) in the Daochen site, Sichuan province, P.R. China. In Tables 2 and 3, the main characteristics of a selection of air shower arrays operated in the last two decades to study gamma-ray astronomy and galactic cosmic-ray physics from ground are summarized. The atmospheric depths of the arrays, the main detectors used, the energy range investigated, the sensitive areas of electromagnetic and muon detectors, the instrumented areas, and the coverage (i.e., the ratio between sensitive and instrumented areas) are reported. The depth in the atmosphere (altitude of the site) is crucial to fix the energy threshold, the energy resolution, and the impact of shower-to-shower fluctuations. As can be seen, the new experiment LHAASO will operate with a coverage of ∼0.5% over a 1 km2 area. The sensitive area of the muon detectors is unprecedented and about 17 times larger than CASA-MIA, with a coverage of about 5% over 1 km2 .

Table 2 Characteristics of a selection of air shower arrays e.m. sens. Instr. area (m2 ) area (m2 ) Coverage 6700 11,000 0.93

Experiment ARGO-YBJ (Bartoli et al. 2011)

g/cm2 Detector 606 RPC/hybrid with wideFoV Cˇ Tel.

HAWC (Abeysekara et al. 2013) TIBET ASγ (Amenomori et al. 2011) CASA-MIA (Glasmacher et al. 1999) KASCADE (Antoni et al. 2005) KASCADEGrande (Apel et al. 2012) Tunka (Prosin et al. 2016) IceTop (Aartsen et al. 2019) LHAASO (Cao et al. 2021)

620

Water Cˇ

1012 − 1014

1.2 × 104 2 × 104

606

scint./burst det.

5 × 1013 − 1017

380

860

scint./muon

1014 − 3.5 × 1016

1.6 × 103 2.3 × 105 7 × 10−3

1020

scint./mu/had 2 × 1015 − 1017

5 × 102

4 × 104

1.2 × 10−2

1020

scint./mu/had 1016 − 1018

370

5 × 105

7 × 10−4

900

open Cˇ det.

3×1015 − 3 × 1018 –

106

–

680

ice Cˇ det.

1016 − 1018

600

Water Cˇ 1012 − 1017 scint./mu/had wide-FoV Cˇ Tel.

ΔE (eV) 3 × 1011 − 1016

(carpet) 0.61

3.7 × 104 10−2

4.2 × 102 106

4 × 10−4

5.2 × 103 1.3 × 106 4 × 10−3

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Table 3 Characteristics of muon detectors operated in a selection of shower arrays Experiment LHAASO TIBET ASγ KASCADE CASA-MIA

Altitude (m) 4410 4300 110 1450

μ Sensitive area (m2 ) 4.2 × 104 4.5 × 103 6 × 102 2.5 × 103

Instrumented area (m2 ) 106 3.7 × 104 4 × 104 2.3 × 105

Coverage 4.4 × 10−2 1.2 × 10−1 1.5 × 10−2 1.1 × 10−2

Detector Performance To understand the overall performance, and trade-offs in design, we look here at some measures of a successful TeV-scale gamma-ray observatory: (1) (2) (3) (4) (5)

Sensitivity to γ -point source Energy threshold Trigger relative efficiency Angular resolution Background discrimination

The recent construction of the first portions of LHAASO has shown the direction taken by that collaboration in light of the previous generations of experiments. LHAASO is using multiple technologies, greatly expanding the scale of the detector, and taking advantage of the multiple technologies to offer different “handles” on managing the cosmic-ray background. We’ll also look at prospects for the future, which include the SWGO (Southern Wide-field Gamma-ray Observatory) effort, currently in the design process, and actively manage these different detector performance metrics for potential high altitude sites in South America to give a Southern Hemisphere sensitivity at TeV gamma-ray energies. For one approach to this trade study, see this recent work (Schoorlemmer et al. 2019). Outside of the air shower measurements, an important feature of the wide field-of-view gamma-ray experiments is their sensitivity to transient, and multimessenger, events. The uptime of the HAWC detector has been better than 98% with an instantaneous coverage of about one-third of the sky. As astronomy becomes increasingly focused on transient events, always-on, no-pointing-required, observations are especially important at high energies which for many phenomena are peaked early in the emission. Additionally, following up from neutrino or gravitational-wave observations can be done using the archived data of these detectors rather than an attempt at quickly repositioning and targeting the followon signals. Multi-messenger networks of communications, such as AMON (Ayala Solares et al. 2020), allow for the distribution of observations of different messengers, from very different styles of telescopes, in near real time.

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Sensitivity to a γ -Ray Point Source The main drawback of ground-based measurement is the huge background of charged CRs. This means that ground-based instruments detect a source as an excess of events from a certain direction over an overwhelming uniform background. Suppression of the cosmic-ray signal can be achieved by the use of muon detector veto or other gamma-hadron distinguishing variables in the air shower signal. Due to the background, though, the detector sensitivities are often expressed in units of standard deviations of the cosmic-ray background (see, e.g., Di Sciascio 2019). Φγ Nγ S= ∝ ·R· Φbkg Nbkg



γ

Aeff ·

1 √ · T ·Q σθ

(5)

where Φγ and Φbkg are the integral fluxes of photon and background, σθ is the angular resolution,  bkg γ R = Aeff /Aeff ,

(6)

the γ /hadron is the relative trigger efficiency, and T is the observation time. The so-called Q-factor Q= 

ǫγ 1 − ǫbkg

(7)

represents the gain in sensitivity due to the background discrimination capability, where ǫγ and ǫbkg are the efficiencies in identifying γ -induced and backgroundinduced showers, respectively. For a point source, the angular term to evaluate the isotropic background is given by the opening angle of the detector, i.e., the point spread function PSF (ΔΩ = 2 ). If we have an extended source with a photon flux equal to that of ΔΩPSF ∼ π θPSF the point source, we must integrate over the extension of the source to have the same number of photons: ΔΩPSF → ΔΩext , and the background will increase. Therefore,

and

   Φγ θext θPSF 1 γ Sext ∝  · · · R · Aeff · Q · θext θPSF θext Φbkg Sext ∝ Spoint ·

θPSF θext

(8)

(9)

where θext is the dimension of the extended source. As it can be seen, detectors with a poor angular resolution, like shower arrays, are favored in the extended source studies.

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Because for the integral fluxes we can write −γ

Φγ ∼ Ethr and Φbkg ∼ Ethr bkg −γ

(10)

we obtain Φγ −(γ −γbkg /2) −2/3  ∼ Ethr ∼ Ethr Φbkg

(11)

being γ ∼1.5 and γbkg ∼1.7. Energy threshold, relative trigger probability R, angular resolution, and Q-factor are the main parameters, the drives, which determine the sensitivity of a groundbased γ -ray telescope. The wide angular acceptance of air shower arrays also leads to a somewhat complicated extended source sensitivity. In particular, extended source sensitivities of large field-of-view instruments are often superior compared to narrow field instruments which require multiple exposures to image the full object due to background subtraction. Difference between the HAWC and HESS, for example, galactic plane extended sources, has been noted in this area (Abdalla et al. 2021).

The Energy Threshold The energy threshold of EAS arrays is not well defined due to the large fluctuations affecting the number of particles at ground from shower to shower for identical primaries. The main source of fluctuations is the depth of first interaction. As a consequence, an array can be triggered by very low-energy showers if the primary particles interacted by chance deeper into atmosphere than expected. On the contrary, it may fail to detect high-energy events when the initial interaction is unusually high in the atmosphere. Therefore, the trigger probability increases slowly with energy and is not a step function at the threshold energy Ethr . The shower fluctuations can be reduced placing the detector at high altitude, close to the maximum of the shower development. As a rule of thumb, we can estimate the energy threshold of an array from the effective area and trigger rate (Cronin 1996). If we assume that the efficiency as a function of cosmic-ray energy has a turn-on at an energy E0 , the rate is given by the following: R = ΦCR (≥ E0 ) × (∼ 1sr) × A

(12)

where ΦCR is the integral CR flux and A is the effective area of the array. The rate of cosmic rays peaks at the zenith, and more than 90% of the recorded showers lie within a cone of 1 sr around the zenith. Therefore, we assume the effective solid angle of an array is equal to 1 sr. This is also the angular range over which the array

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has a reasonable acceptance for a source passing overhead. According to a wellknown parametrization (Horandel 2003), the integral flux is given by the following: ΦCR (≥ E0 ) = 1.3 ·



E0 1GeV

−1.66

cm−2 s−1 sr−1 .

(13)

Solving for the energy, we find the following:

E0 = 1.2 ·



RH z Acm2

−0.6

GeV.

(14)

For ARGO-YBJ, a rate of 3.5 kHz and an instrumented area of 108 cm2 imply E0 ∼ 470 GeV, in fair agreement with the median energy of the first multiplicity bin of 340 GeV. The energy threshold of a shower array is mainly determined by the combination of altitude and coverage, i.e., the ratio between sensitive and instrumented areas. In addition, the threshold of the particular detector and the trigger logic of the apparatus can affect the final energy threshold. An important limiting factor is the rate of accidental coincidences of the detector unit. In the ARGO-YBJ experiment, the single particle counting rate is about 1 kHz/m2 , to be compared with the rate of single muons of about 200 Hz/m2 . In the LHAASO experiment, the counting rate of a single 8′′ PMT used in WCDA is about 40 kHz. HAWC has a similar hardware trigger rate of a single 8′′ PMT of around 20 kHz at 1/4 SPE (single photo electron). These higher PMT rates require a larger number of channels triggered for a reconstructable event to rise above the noise floor. In Fig. 6, the average sizes produced by showers induced by primary photons and protons of different energies at different observation levels are plotted. The left plot shows the total number of secondary particles (charged plus photons), and the right one shows the number of particles contained inside an area 150 × 150 m2 centered on the shower core. As can be seen, the number of particles in proton-induced events exceeds the number of particles in γ -induced ones at low altitudes. This implies that, in gamma-ray astronomy, the trigger probability is higher for the background than for the signal. The small number of charged particles in sub-TeV showers within 150 m from the core imposes to locate experiments at extreme altitudes (>4500 m a.s.l.). At 5500 m a.s.l. 100 GeV γ -induced showers contain about eight times more particles than proton showers within 150 m from the core. This fact can be appreciated in Fig. 7 where the ratio of particles (charged + photons) in photon- and proton-induced showers of different energies as a function of the observation level is shown.

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Relative Trigger Efficiency R The effective area Aeff is mainly a function of the number of charged particles at the observation level, the dimension and coverage of the detector, and the trigger logic. Moving a given detector at different altitudes Aeff is proportional to the number of charged particles.

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Figure 7 shows the ratio R = Nγ /Np of secondary particles (charged plus photons) in photon- and proton-induced showers as a function of the altitude. The left plot refers to the total size and the right one to particles contained inside an area 150 × 150 m2 centered on the shower core. When R1, the trigger probability, and thus the effective area, of the detector is larger for γ -showers than for protons, and an intrinsic γ /hadron separation is available at higher altitudes. Since R is proportional to the ratio of effective areas, an altitude >4500 m a.s.l. is required to increase the sensitivity of a gamma-ray telescope into the hundreds GeV energy range. Comparing the two plots of Fig. 7, we can see that, as expected, the γ -showers show a more compact particle distribution at the observation level. Therefore, at extreme altitudes, the trigger efficiency of photon event at hundreds GeV is highly favored if we consider only secondary particles within 150 m from the core. We note that, as shown in Fig. 6, the cosmic-ray showers that fake gamma showers are not of the same energies. As an example, at an altitude of 1000 m a.s.l., a 100 GeV, proton-induced shower has the same size of a 300 GeV photon shower. Showers of all energies have the same slope well after the shower maximum: ≈1.65x decrease per radiation length (r.l.). This implies that if a given detector is located one radiation length higher in atmosphere, the result will be a ≈1.65x decrease of the energy threshold. But the energy threshold is also a function of the detection medium and of the coverage, the ratio between the detector and instrumented areas. Classical extensive air shower arrays are constituted by a large number of detectors (typically plastic scintillators) spread over an area of order of 104 –105 m2 with a coverage factor of about 10−3 . This poor coverage limits the energy threshold because small lowenergy showers cannot be efficiently triggered by a sparse array. To exploit the potential of the coverage, a high granularity of the readout must be coupled to image the shower front with high resolution. Another important factor to lower the energy threshold of a detector is the secondary photon component detection capability. Gamma-rays dominate the shower particles on ground: at 4300 m a.s.l., a 100 GeV photon-induced shower contains on average seven times more secondary photons than electrons (Di Sciascio et al. 1997). In γ -showers, the ratio Nγ /Nch decreases if the comparison is restricted to a small area around the shower core. For instance, we get Nγ /Nch ∼3.5 at a distance r < 50 m from the core for 100 GeV showers (Di Sciascio et al. 1997). In Fig. 8, the ratio of secondary photons within 150 m from the shower core for gamma- and proton-induced showers of different energies is plotted as a function of the altitude. The number of secondary photons in low-energy γ -showers exceeds by large factors the number of gammas in p-showers with increasing altitude (Fig. 9). Secondary photons can be converted into an electron-positron pair in two different ways: (1) with one radiation length of lead above the counters; (2) with a suitable depth of water in a water Cherenkov detector.

Fig. 8 Ratio of secondary photons in gamma- and proton-induced showers of different energies as a function of the observation level. The particles have been selected inside an area 150 × 150 m2 centered on the shower core (Di Sciascio et al. 2018). We note that the kink at about 3000 m a.s.l. is only a graphical artifact

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The Angular Resolution The direction of the primary particle is obtained after reconstructing the time profile of the shower front by using the information from each timing pixel of the experiment. Shower particles are concentrated in a front of a nearly spherical shape.

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A good approximation for particles not far from the shower core is represented by a cone-like shape with an average cone slope of about 0.10 ns/m. The accuracy in the reconstruction of the shower arrival direction mainly depends on the capability of measuring the relative arrival times of the shower particles. The angular resolution of a shower array is a combination of the temporal resolution of the detector unit; the dimension of apparatus, i.e., the dimension of the lever arm in the fitting procedure of the shower front; and the number of temporal hits, i.e., the granularity of the sampling. The time resolution of each detector is determined by the intrinsic time resolution, the propagation time of the signal, and the electronic time resolution. As an example, for the ARGO-YBJ experiment, the total detector resolution is ≈1.3 ns (including RPC intrinsic jitter, strip length, and electronic time resolution). The dependence of the angular resolution on the time resolution of RPCs in the ARGOYBJ experiment is shown in Fig. 10 (Aielli et al. 2009). Events with Npad ≥60, 100, and 500 fired pads on the central carpet have been selected. As it can be seen from the figure, a time resolution in the range between 1 and 2 ns corresponds to a very small change in the angular resolution because the time jitter of the earliest particles in high multiplicity events (>100 hits) is estimated ≈1 ns (Di Sciascio et al. 1997; Bacci et al. 2002). Following the same arguments as given in Karle et al. (1995), the angular resolution σθ , averaged on the azimuthal angle φ, is found to depend on multiplicity N and zenith angle θ as follows: σt (N ) √ sec θ σθ ∝ √ N

(15)

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where σt (N ) is the average time fluctuation for events with N particles. The factor √ sec θ accounts for the geometrical effect related to the reduction with increasing θ of the effective distance between detectors (Bacci et al. 2002). The dependence of σθ upon N is well explained in terms of the combined effect of the time thickness of the extensive air shower disk, as imaged by the detector, and the density of shower particles. Placing a thin sheet of lead converter (one radiation length) above the detector (scintillator or RPC) is a well-known technique to improve the angular resolution, mainly at the threshold, due to, qualitatively (1) absorption of low-energy electrons (and photons) which no longer contribute to the time signal; (2) multiplication process of high-energy electrons (and photons) which produce an enhancement of the signal. A similar effect is provided by a suitable water depth in a water Cherenkov detector. The enhanced signal reduces the timing fluctuations: the contributions gained are concentrated near the ideal time profile because the high-energy particles travel near the front of the shower while those lost tend to lag far behind. The ARGO-YBJ experiment has been the only gamma-ray detector operated without a layer of lead above the detectors. The observation of a number of gamma sources showed the capability of the high granularity sampling provided by the RPC readout in imaging the temporal profile of air showers. The angular resolution σθ is related to the opening angle ΔΩ. If the point spread function of the angular resolution is Gaussian

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(16)

then the opening angle that maximizes the signal/bkg ratio is given by Δθ = 1.58σθ , and it tallies with a fraction of ǫ = 0.72 of the events from the direction of the source in the solid angle ΔΩ = 2π(cos Δθ ). Therefore, ǫ(ΔΩ) 0.72 0.45 ≃ = (Protheroe and Clay 1984). ΔΩ 1.6σθ σθ

(17)

The usual method for reconstructing the shower direction is performing a χ 2 fit to the recorded arrival times ti by minimization of the following: χ2 =

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(18)

where the sum includes all detectors with a time signal. Usually the function f describes a plane, a cone with a fixed cone slope, or a plane with curvature corrections as a function of core distance r and multiplicity m. A time offset and two

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direction cosines are fitted. The weights w are generally chosen to be an empirical function of the number m of particles registered in a counter, a function of r, or a function of r and m. This represents in general terms the usual fitting procedure of the “time of flight” technique. Improvement to this scheme can be achieved by excluding from the analysis the time values belonging to the non-Gaussian tails of the arrival time distributions by performing some successive χ 2 minimizations for each shower (Di Sciascio et al. 2005; Bartoli et al. 2011). In fact, the distribution of the arrival times shows non-Gaussian tails at later times, mainly due to multiple scattering of low-energy electrons but also to incorrect counter calibrations and to random coincidences. These non-Gaussian tails are expected typically to be 20% of all measured time values. The resolution in the reconstruction of the shower core position, i.e., the point where the shower axis intersects the detection plane, can affect the angular resolution when functions depending on r are used to describe the temporal profile. The core position is usually obtained fitting the lateral density distribution of the secondary particles to a modified Nishimura-Kamata-Greisen (NKG) function (Di Sciascio et al. 2003). In Fig. 11, an example of angular resolution vs. shower core position resolution for the ARGO-YBJ carpet is shown. As it can be seen, resolutions worse than about 2 meters affect the angular resolution of the detector. The standard method to measure the angular resolution and the pointing accuracy of a shower array is to exploit the so-called Moon shadow technique which provides unique information on its performance. CRs blocked in their way to the Earth by the

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Moon generate a deficit in its direction usually mentioned as “Moon shadow.” At high energies, the Moon shadow would be observed by an ideal detector as a 0.52◦ wide circular deficit of events, centered on the Moon position. The actual shape of the deficit as reconstructed by the detector allows the determination of the angular resolution, while the position of the deficit allows the evaluation of the absolute pointing accuracy. In addition, charged particles are deflected by the geomagnetic field by an angle depending on the energy. As a consequence, the observation of the displacement of the Moon shadow at low rigidities can be used to calibrate the relation between the shower size and the primary energy (Bartoli et al. 2011). The HAWC Moon shadow is shown in Fig. 12 and has been used to place constraints on the fraction of antiprotons in the high-energy cosmic rays (from the opposite bending from the proton signal seen in the figure) (Abeysekara et al. 2018b).

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Background Discrimination from the Ground In 1960, Maze and Zawadzki (1960) suggested that in gamma-ray astronomy with shower arrays, the background of CRs can be identified and rejected by identifying EAS with an abnormally small number of muons Nμ , the so-called muon-poor technique. The existence of such “unusual” showers is due to the relatively small photonuclear cross section compared with the corresponding value for the protonnucleus and nucleus-nucleus cross sections. In gamma showers, muons are produced mainly by the photoproduction of hadrons: γ + air → nπ ± + mπ 0 + X(σγ −air ∼ 1 − 2mb),

(19)

followed by the pion decays in muons and photons and by muon pair production with a cross section σγ −air ∼12 µb. The relevant quantity for the muon content is the total hadronic part of the cross section. In fact, it is the ratio of the total hadronic part of the cross section to the Bethe-Heitler cross section one that determines the fraction of the events induced by photons that are hadronic in character. If this ratio is small, then most photon-induced showers must start out an electromagnetic process, and no muons are present in the cascade. The probability of pion production, with respect to the probability to produce a e+ e− pair, is ∼3·10−3 . This implies that the muon content in a gamma shower is only ∼10% the muon content in a shower induced by charged cosmic rays. For a given shower size Ne and muon number Nμ , the selection of muon-poor showers reads (Nμ / < Nμ >)Ne ≤ Sμ ,

(20)

where < Nμ > is the average muon multiplicity expected for a fixed size Ne and Sμ is an optimum threshold value to optimize the sensitivity. In principle, γ γ Sμ =< Nμ > / < Nμh > where < Nμ > and < Nμh > are the average muon numbers in showers produced by gamma and “normal” (hadron) primaries, respectively. The selection threshold Sμ is not universal but depends on the specific experimental configuration, i.e., the total area of the muon detector and its coverage, the ratio between the sensitive area and the instrumented one. But the key point is the knowledge of the properties of the gamma showers and of the fluctuations of the observed muon number in EAS initiated by photons and primary CRs. In fact, in order to evaluate the rejection power, it is crucial to study how frequently hadronic showers fluctuate in such a way to have a low muon content indistinguishable from gamma-induced events. On general ground, there is a close relationship between the adopted model for photonuclear interactions and the muon distribution F (Kμ ) with Kμ = Nμ / < Nμ >. As an example, for models assuming a fast increase of the photonuclear

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cross section, the number of muons expected in high-energy gamma and proton showers becomes comparable (Krys et al. 1991). This implies that the detection of any gamma-ray flux with the muon-poor technique would be impossible. Therefore, an accurate knowledge of the photonuclear process, starting from the cross section, is mandatory. In fact, measurements of the photoproduction cross section are limited √ to s 200 GeV. The efficacy of background rejection exploiting the muon content is limited by the number of muons that can be detected. According to Monte Carlo simulations, in a proton-induced shower, the number of muons is approximately proportional to the energy of the primary, with about 20 muons above 1 GeV for a 1 TeV proton (200 muons for a 10 TeV muon) but only 4 muons within 150 m of the shower core. As a consequence, the muon-poor technique is effective above a few TeV. In addition, the fluctuations in the muon number(for a fixed proton energy) are larger than Poisson, with a Gaussian width of ≈2.5 Nμ ; thus, there are more events with zero muons than a Poisson calculation. This is an important limiting factor for background discrimination at low energy. Another limiting factor is the high rate of single muons unassociated with any showers at the ground. The need for large full coverage muon detector is evident to exploit the muon-poor technique in the TeV energy range. The topological differences in muon-poor, or purely electromagnetic showers, and those with muon sub-cascades can be seen, for example, in simulated HAWC gamma and proton results across the array. See Fig. 13 left panel for gamma simulation; note the single core with only random hits across the rest of the array and the right hand panel for proton simulation where there are multiple strong (muon) hits distinct from the shower core (Westerhoff et al. 2014). Similar gamma-hadron

Fig. 13 HAWC proton shower (left panel) and electron shower (right panel) with a similar number of PMTs triggered. Note the energy difference and the single shower core structure for the electromagnetic cascade for the gamma-ray shower and the multiple “centers of gravity” for the shower core and muon sub-showers in the hadronic simulation

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separation is shown in the HAWC data mentioned earlier and essential for separation of the photon-induced showers from the cosmic-ray background. Different experiments in the past (CASA-MIA (Borione et al. 1997), EAS-TOP (Aglietta 1995), and HEGRA (Aharonian et al. 2004)) operated muon detectors to measure a possible emission of photons in the 100 TeV energy range, but they set only upper limits mainly due to the small area of the detectors (order of 100 m2 ) combined with a small efficiency in the muon counting. Only recently, the Tibet ASγ (Amenomori et al. 2019) and HAWC (Abeysekara et al. 2020) experiments, detecting muons over areas larger than 1000 m2 , report evidence of emissions above 100 TeV. In the last year, the breakthrough in VHE gammaray astronomy is represented by the LHAASO experiment that observed gamma emission beyond 1015 eV opening for the first time the PeV energy range to the observations (Cao et al. 2021). The large muon detector operated (∼40,000 m2 ) allows a discrimination at a level of 10−5 in the PeV range and a background-free measurement starting from about 100 TeV. The background-free regime is very important because in this case the sensitivity is the inverse of the effective area of the array multiplied by the time spent observing a source. Thus, an EAS array with a comparable effective area to a IACT array, with more than one order of magnitude larger time on source, will have a much better sensitivity to the highest energy sources.

Future Prospects All of the wide field-of-view experiments mentioned above have been built in the Northern Hemisphere. The construction of a new, wide field-of-view instrument at sufficiently southern latitude to continuously monitor the Galactic Center and the inner Galaxy should be a high priority. In order to sensibly find complementarity to the CTA-South IACT effort, this observatory should have the following characteristics: (1) an energy threshold near 100 GeV, to observe transients; (2) a sensitivity of a few percent of the Crab level flux below a TeV, for flaring activity detection; (3) an angular resolution around 1◦ , to reduce source confusion along the galactic plane; (4) a real-time trigger facility, and event look-back, to allow multi-messenger astrophysics with CTA, IceCube, LIGO, and other gamma-ray, cosmic-ray, and neutrino experiments; (5) a discrimination against protons at the level of 10−5 above 100 TeV to observe the cosmic-ray spectrum knee in the gamma-rays; (6) an ability to measure the cosmic rays, with some elemental resolution, also up to the knee of the spectrum, to observe the maximum energy of accelerated particles in the cosmic-ray sources and also the anisotropy of the cosmic rays.

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Following the ideas above, energy threshold, angular resolution, relative trigger efficiency, effective area, and background rejection, there are a number of efforts in this direction currently under study. These include ALTO, ALPACA, LATTES, STACEX, and SWGO (Becherini et al. 2018; Asaba et al. 2018; Assis et al. 2018; Di Sciascio et al. 2019; Albert et al. 2019). ALTO is a follow-on design from HAWC, with an eye toward higher altitudes, denser tank-packing (including hexagonal tanks), faster electronics, and a scintillator panel under the tanks for muon tagging. This effort is a direct push forward on the critical design variables with some innovative ideas on tank construction techniques (Becherini et al. 2018). ALPACA (Andes Large area PArticle detector for Cosmic ray physics and Astronomy) is a project launched in 2016 between Bolivia and Japan aiming at a 83,000 m2 surface air shower array and a 5400 m2 underground muon detector array. The site is on a highland pad at an altitude of 4740 m a.s.l. halfway up the road to Mount Chacaltaya on the outskirts of La Paz. The layout of the array is similar to the Tibet ASγ experiment but sited in the Southern Hemisphere (Asaba et al. 2018). LATTES (Large Array Telescope for Tracking Energetic Sources) is a proposed hybrid detector utilizing a layer of RPC over a water Cherenkov tank. The base element of the array is a 3 × 1.5 m water tank of 0.5 m depth covered by a pair of 1.5 × 1.5 m RPCs with a 5.6 mm (one radiation length) layer of lead on top. There would be 60×30 of these detector elements comprising roughly 10,000 m2 of active area installed at 5400 m a.s.l. (Assis et al. 2018). STACEX (Southern TeV Astrophysics and Cosmic rays EXperiment) is a similar RPC plus WCDs proposed detector. In this proposed experiment, the RPC panels “carpet” the roof of a round, HAWC-like WCD. Total RPC coverage would be 150× 150 m (Di Sciascio et al. 2019). SWGO (Southern Wide-field Gamma-ray Observatory) is a consortium (previously called SGSO, Southern Gamma-ray Survey Observatory) examining a very large area water Cherenkov detector employing either a pond or tanks at high altitude in South America (Albert et al. 2019). Some possible design calls for tanks with two layers for enhanced muon vs. electromagnetic shower discrimination. See Fig. 14 for an illustration of this and more information in the reference Kunwar et al. (2021). Outside of the Southern Hemisphere detector concept, there are a number of detector-specific notions which have been raised, often within the context of the aforementioned detectors, which have not yet been implemented in a gamma-ray observatory, but which still merit further investigation: • Neutron detection for cosmic-ray shower rejection; boron-doped plastic scintillator panels are sensitive to up-scattered neutrons from hadronic showers as they hit the ground. • Wavelength-shifting (WLS) fiber readout within a WCD for enhanced photon collection; a “mop” of WLS fibers can collect blue Cherenkov photons, convert them to green light, and waveguide that light to smaller photodetectors.

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• Fast FPGA-based photon correlator allowing for low signal level, few sensor hit, and reconstruction; for example, search for all 5–10 PMT hits which point to the Crab, along with a location at the same zenith but differing orientation for background subtraction. Sometimes called a “vector telescope.” • Large area photodetectors potentially built up from silicon PMs; lower cost, lower voltage, and lower transit-time spread are possible. • Scintillator additions within the WCD; liquid scintillator or quantum dots to enhance photon yield and potentially help with particle ID as well. • Freezing point depression of the fluid in a WCD; to allow for no freezing even at the highest South American site locations. • Low power electronics; improving the sustainable footprint of the detector, potentially combined with the use of renewable energy, recyclable detector elements, and a minimally invasive installation at the site. New detector designs typically are fairly conservative, improving incrementally on previous designs, especially in a fairly mature design environment such as the ground-based VHE gamma-ray observatory. The proposed Southern Hemisphere telescopes reflect that path but do allow for the exploration of other potential improvements. LHAASO represents the current state-of-the-art pushing the design primarily in scale and the aggressive combination of multiple detector techniques rather than novel technologies.

Conclusions Current and future gamma-ray telescopes exploiting the air shower physics of the incident particles continue to advance with both approaches of water Cherenkov and ground-particle detection. These experiments provide the highest-energy gamma-

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ray observations available. Right now there are a considerable number, and variety, of Galactic sources, and a handful of extra-Galactic sources. Some of these sources show significant time variability. With new observatories coming online, the source catalog is likely to expand, and the time domain astronomy aspects are sure to increase in interest. It is in these two ways that these detector arrays are especially powerful.

References M.G. Aartsen, M. Ackermann, J. Adams, J.A. Aguilar et al. ICETOP Collaboration, Cosmic ray spectrum and composition from PeV to EeV using 3 years of data from IceTop and IceCube. Phys. Rev. D 100, 082002 (2019) H. Abdalla et al. (2021) arXiv:2107.01425 A.U. Abeysekara et al. (HAWC), Astropart. Phys. 35, 641–650 (2012). (Preprint 1108.6034) A.U. Abeysekara et al. (HAWC), Astropart. Phys. 50–52, 26–32 (2013). (Preprint 1306.5800) A.U. Abeysekara et al. (HAWC), Astrophys. J. 841, 100 (2017). (Preprint 1703.06968) A.U. Abeysekara et al., NIM A888, 138 (2018a) A.U. Abeysekara et al. (HAWC Collaboration), Phys. Rev. D 97, 102005 (2018b) A.U. Abeysekara et al. (HAWC Collaboration), Phys. Rev. Lett. 124, 021102 (2020) M. Aglietta, G. Di Sciascio et al. (EAS-TOP Collaboration), Astropart. Phys. 3, 1 (1995) F. Aharonian et al. (HEGRA Collaboration), Astroph. J. 614, 897 (2004) G. Aielli et al. (ARGO-YBJ Collaboration), Nucl. Instrum. Methods Phys. Res. Sect. A 562, 92 (2006) G. Aielli et al. (ARGO-YBJ Collaboration), Nucl. Instrum. Methods Phys. Res. Sect. A 608, 246 (2009) A. Albert et al., (2019). arXiv:1902.08429; M. Mostafa et al., PoS ICRC2017, 851 (2018). https:// www.swgo.org/ D.E. Alexandreas et al., Nucl. Instrum. Methods A 311, 350 (1992) M. Amenomori, X.J. Bi, D. Chen, S.W. Cui, L.K. Ding et al., Tibet ASγ Collaboration, Cosmicray energy spectrum around the knee obtained by the Tibet experiment and future prospects. Adv. Space Res. 47, 629 (2011) M. Amenomori et al., Tibet ASγ collaboration. ApJ 813, 98 (2015) M. Amenomori et al. (Tibet ASγ Collaboration), Phys. Rev. Lett. 123, 051101 (2019); M. Amenomori et al. (Tibet ASg Collaboration), Phys. Rev. Lett. 126, 141101 (2021) T. Antoni, W.D. Apel, A.F. Badea, K. Bekk, A. Bercuci et al., KASCADE Collaboration, KASCADE measurements of energy spectra for elemental groups of cosmic rays: results and open problems. Astropart. Phys. 24, 1 (2005) W.D. Apel, J.C. Arteaga-Velázquez, K. Bekk, M. Bertainaet et al., KASCADE-Grande Collaboration, The spectrum of high-energy cosmic rays measured with KASCADE-Grande. Astropart. Phys. 36, 183 (2012) T. Asaba et al. (ALPACA Collaboration), PoS ICRC2017, 827 (2018). https://alpaca-experiment. org/ P. Assis et al., Astropart. Phys. 99, 34 (2018) R. Atkins et al., Nucl. Instrum. Methods Phys. Res. 449 478 (2000) H.A. Ayala Solares et al., Astropart.Phys. 114, 68 (2020). https://www.amon.psu.edu/ C. Bacci et al. (ARGO-YBJ Collaboration), Nucl. Instrum. Methods Phys. Res. Sect. A 443, 342 (2000) C. Bacci et al., Astropart. Phys. 17, 151 (2002) B. Bartoli, P. Bernardini, X.J. Bi, C. Bleve, I. Bolognino et al., ARGO-YBJ Collaboration, Observation of the cosmic ray moon shadowing effect with the ARGO-YBJ experiment. Phys. Rev. D84, 022003 (2011)

74 Detecting Gamma-Rays with Moderate Resolution and Large Field. . .

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B. Bartoli et al. (ARGO-YBJ Collaboration), Astropart. Phys. 67, 47 (2015a) B. Bartoli et al. (ARGO-YBJ), Astrophys. J. 798, 119 (2015b). (Preprint 1502.05665) Y. Becherini et al., PoS ICRC2017, 782 (2018) A. Borione et al., Nucl. Instrum. Methods A 346, 329 (1994) A. Borione et al. (CASA-MIA Collaboration), Phys. Rev. D 55, 1714 (1997) Z. Cao, LHAASO Collaboration, Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 γ -ray Galactic sources. Nature 594, 33–36 (2021) J.W. Cronin, Nuovo Cimento 19C, 847 (1996) B. D’Ettorre Piazzoli, G. Di Sciascio, Astropart. Phys. 2, 199 (1994): erratum 327 G. Di Sciascio, Int. J. Mod. Phys. D23, 1430019 (2014); [Erratum: Int. J. Mod. Phys. D24(02), 1592001 (2014)] G. Di Sciascio (LHAASO), Nucl. Part. Phys. Proc. 279–281, 166–173 (2016). (Preprint 1602.07600) G. Di Sciascio, J. Phys. Conf. Ser. 1263, 012003 (2019) G. Di Sciascio et al. (STACEX Collaboration), (2019) arXiv:1907.06686 G. Di Sciascio, B. D’Ettorre Piazzoli, M. Iacovacci, Astropart. Phys. 6, 313 (1997) G. Di Sciascio et al., Proceedings of the 28th International Cosmic Ray Conference (ICRC 03), Tsukuba, Japan vol. 5 (Universal Academy Press, Inc., Tokyo, 2003), p. 3015 G. Di Sciascio et al. (ARGO-YBJ Collaboration), in International Cosmic Ray Conference (ICRC 05), Pune, India, ed. by B.S. Acharya, S. Gupta, S. Tonwar, vol. 6 (Tata Institute of Fundamental Research, Mumbai, 2005), p. 33 G. Di Sciascio, S. Miozzi, P. Montini, G. Piano, R. Santonico, M. Tavani, PoS ICRC2017, 781 (2018) R. Engel, D. Heck, T. Pierog. Annu. Rev. Nucl. Part. Sci. 61, 467 (2011) M.A.K. Glasmacher, M.A. Catanese, M.C. Chantell et al., CASA-MIA Collaboration, The cosmic ray composition between 1014 and 1016 eV. Astropart. Phys. 12, 1 (1999) K. Greisen, Progr. Cosmic Rays 3, 1 (1956) W. Heitler, The Quantum Theory of Radiation (Clarendon Press/Oxford, London, 1994) J.R. Horandel, Astrop. Phys. 19, 193 (2003) A. Karle et al., Astropart. Phys. 3, 321 (1995) A. Krys et al., J. Phys. G: Nucl. Part. Phys. 17, 1261 (1991) S. Kunwar et al., Eur. Phys. J. C in submission (2021) J. Matthews, Astropart. Phys. 22, 387 (2005) R. Maze, A. Zawadzki, Nuovo Cimento 17, 625 (1960) NOAO, NASA, and USAF, US Standard Atmosphere 1976, US Government Printing Office (1976) V.V. Prosin, S.F. Berezhnev, N.M. Budnev et al., TUNKA Collaboration, Results from Tunka-133 (5 years observation) and from the Tunka-HiSCORE prototype. EPJ Web Conf. 121, 03004 (2016) R.J. Protheroe, R.W. Clay, Proc. ASA 5, 586 (1984) H. Schoorlemmer et al., Eur. Phys. J. C 79, 427 (2019) G. Sinnis, WSPC Handb. Astron. Instrum. 7, 137 (2021) S. Westerhoff (HAWC Collaboration), Adv. Space Res. 53, 1492 (2014)

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Science Goals of the HAWC Observatory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observatory Site and Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observatory Site . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water Cherenkov Detectors (WCDs) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Water . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electronics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Methods of Data Reconstruction and Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview of Important Scientific Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Synergies with Imaging Atmospheric Cherenkov Telescopes . . . . . . . . . . . . . . . . . . . . . . . . Conclusion and Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

The High-Altitude Water Cherenkov (HAWC) Gamma-Ray Observatory is one of the most sensitive wide field of view, continuously operating ground-based instruments in astrophysics that is exploring the origin of cosmic rays, studying the acceleration of particles in extreme physical environments, and searching for new physics at the TeV-PeV scale. HAWC is providing an unprecedented look at the TeV sky, discovering new sources and new source classes, setting new limits on dark-matter and Lorentz Invariance Violation in previously inaccessible phase

J. Goodman () University of Maryland, College Park, MD, USA e-mail: [email protected] P. Huentemeyer () Michigan Technological University, Houghton, MI, USA e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_65

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spaces, and playing a crucial role in multi-messenger and multi-wavelength observations. HAWC is located in the high mountains of Mexico at 4100 m a.s.l. and has been operating with greater than 95% on-time since March of 2015. This chapter will describe the science goals of the project, explain the technological design and current status of the detector array, and present noteworthy scientific results from six years of operation. Keywords

γ rays · Particle detection array · Extensive air showers · High altitude · Water Cherenkov detectors · PeVatrons · γ -ray halos · Pulsar wind nebulae · Star-forming regions · Wide-field surveys

Introduction The HAWC Observatory in the high mountains of Mexico consists of 300 large water Cherenkov detectors (WCDs) surrounded by an “outrigger” array of 345 smaller WCDs, see Fig. 1. HAWC science operation began in March of 2015 and is expected to continue operating until at least 2025. The goal of this ground-based observatory is to explore non-thermal astrophysical processes in the Galaxy and beyond and provide valuable information to the multi-messenger/multi-wavelength community to enhance scientific knowledge. HAWC’s wide field of view (∼2 sr) and high duty cycle (>95% on-time) simultaneously allow it to monitor the same sky as is observed by other wide field-of-view observatories, such as Fermi, LIGO/Virgo, and IceCube and provide an instantaneous sky view complimentary to that of the Large High-Altitude Air Shower Observatory (LHAASO). This is crucial to search for transient phenomena such as gamma-ray bursts (GRBs) and emission from Active Galactic Nuclei (AGNs). HAWC sends alerts to other observers so they can make correlated observations at other wavelengths or of other messengers. In addition to delivering wide-field surveys in time-domain astronomy, the HAWC Observatory provides regularly updated, integrated maps of the TeV γ -ray sky in the Northern Hemisphere to the astrophysics community. This makes it possible to jointly analyze confirmed signals or measured upper limits across the full electromagnetic spectrum and in multi-messenger data, for example via combined fits. Based on stand-alone studies of their sky maps, the HAWC Collaboration has reported the discovery of ultra-high-energy (UHE) γ -ray sources, which since have been confirmed to be good candidates for galactic PeVatrons (Abeysekara et al. 2020), and of a new source class surrounding middle-aged pulsars, γ -ray halos (Abeysekara et al. 2017a), which led to follow-up observations by other instruments (Mauro et al. 2019; Mitchell et al. 2021). More detailed morphology studies of HAWC sky maps have revealed very-high-energy (VHE) to UHE γ -ray emission from the lobes of micro-quasar SS 433 and from a “Cocoon” surrounding the Cygnus OB2 star-forming region pointing to particle acceleration to PeV energies in jets and young star clusters (Abeysekara et al. 2021a,b).

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Fig. 1 The completed HAWC detector. It consists of a core array of 300 WCDs, each containing 188,000 liters of water and instrumented with four upward-facing photomultipliers tubes (PMTs) at the bottom, surrounded by an outrigger array of 345 smaller WCDs, equipped with one PMT, also upward-facing and anchored at the bottom. The site is at an elevation of 4,100 m at 19◦ N in Mexico. Visible in the background is the volcano Pico de Orizaba

The HAWC design extends the capabilities of the first-generation water Cherenkov TeV γ -ray observatory, Milagro. Milagro had performed several widefield surveys of the TeV sky by 2009 and reported the detection of new TeV γ -ray sources, diffuse TeV emission from the galactic plane, and a correlation of TeV emission excess locations with GeV γ -ray source locations (Abdo et al. 2007a,b, 2008a, 2009, 2012; Atkins et al. 2005). The observatory also discovered an unexpected small-scale cosmic-ray anisotropy (Abdo et al. 2008b). The expanded active detector area of HAWC (∼10× that of Milagro), increased altitude of the site (4,100 m vs. 2,630 m a.s.l.), and optical isolation of the detector elements lead to more than an order of magnitude increase in sensitivity relative to Milagro. The HAWC Observatory reuses the 900 Milagro photomultiplier tubes (PMTs) and front-end electronics, but a new Data Acquisition (DAQ) system was developed and 300 larger, higher quantum efficiency PMTs were added to increase the sensitivity of the HAWC instrument to γ rays, particularly with energies 10 TeV of HAWC help increase our understanding of Nature’s highest energy particle accelerators and allow us to use this understanding to search for new physics in extreme physical environments that cannot be replicated on the Earth.

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Fig. 2 The quasi-differential 5-year sensitivity of the HAWC Observatory as a function of photon energy, compared to Imaging Atmospheric Cherenkov Telescopes (IACTs) (Aleksi´c et al. 2016; Holler et al. 2016; Park et al. 2016) and the Fermi Large Area Telescope (LAT) (Atwood et al. 2012). Also shown is an inferred quarter-decade differential upper limit for the Crab at 141 TeV from the CASA-MIA experiment (Borione et al. 1997). The HAWC curve is calculated assuming a source at a declination of 22◦ within HAWC’s field of view with a differential energy spectrum of E−2.63 and for a 5σ detection 50% of the time. The sensitivity surpasses a 50-hour observation by current-generation IACTs at around 4 TeV. It becomes equal to a projected 50-hour observation of the Cherenkov Telescope Array (CTA) just below 100 TeV (CTAO Consortium 2021). (Courtesy of Sohyoun Loreto Yun and Andrew Smith, University of Maryland/HAWC Collaboration)

Observatory Site and Design The HAWC Observatory belongs to the category of ground-based particle detection arrays, which measure the footprints of extensive air showers (EAS) initiated by gamma and cosmic rays on the ground. There are three main technologies in use: Scintillation Counters (SCs), Resistive Plate Chambers, and Water Cherenkov Detectors (WCDs). While some arrays use a combination of these technologies – LHAASO for example uses SCs and WCDs – the HAWC Observatory solely consists of WCDs.

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Observatory Site HAWC is located at an altitude of 4100 m a.s.l. inside the Parque Nacional Pico de Orizaba (The park is named after the peak of Orizaba called Citlaltépetl in Nahuatl, which translates to Starmountain.) in Mexico. While there was basic infrastructure (roads, power, Internet) running up the mountain (∼1 km away) to the Large Millimeter Telescope, the HAWC site was completely green (see Fig. 3). HAWC funding began in Feb. 2011. In 19 months, the ∼25,000 m2 site was leveled, the HAWC utility building (complete with water filtration system, workrooms, and meeting space) and counting house were built, and electrical power and Internet to both buildings installed allowing to begin full-scale construction. Construction of the core 300 tank array took just over four years from the funding start and was substantially completed in March of 2015. The construction progress during this time can be seen in Fig. 3. The core array is surrounded by a sparse array of smaller 345 WCDs, known as outrigger array. The outrigger array was deployed between September 2017 and September 2018, distributed on the slopes around the core array, extending the instrumented area by about a factor of four.

Water Cherenkov Detectors (WCDs) The core (or main) array of 300 WCDs covers an area of about 22,500 m2 . The surrounding outrigger array of 345 WCDs covers an area of about 100,000 m2 . The WCDs of the core array are placed in joint pairs of rows, with enough clear space to allow for maintenance and repairs on any of them if necessary (see Fig. 4). The gap near the center is the location of the counting house, where the WCDs of the array are controlled and data are acquired. Each of the WCDs (see Fig. 5) consists of a 5 m high by 7.3 m diameter steel barrel containing a custom light-tight bladder. Each bladder holds 188,000 liters of filtered water corresponding to a depth of 4.5 m. Four upward-facing PMTs are attached to the bottom of the bladder: one high-quantumefficiency 10-inch Hamamatsu R7081-MOD PMT at the center and three 8-inch Hamamatsu R5912 PMTs at 1.8 m from the center, see Fig. 5. The design of the large WCDs of the main array allows them to be constructed at the site, from the top down, meaning that the top ring and roof are constructed first and then raised by jacks. This process is repeated so that the remaining four rings can be installed from the ground. The sand-colored, dome-shape roofs, visible in Fig. 1, are chosen to minimize any rain water or snow accumulation. Once the metal barrel is completed, it is lowered into a 60-cm-deep trench and buried. This provides stability in case of earthquakes. When the metallic structure is complete, a light dark plastic bladder is installed through a hatch and inflated in order to reduce wrinkles. At the bottom of each bladder, there are four plates that are welded and have mounts for holding the PMTs in the inside part, while the outside part of the plate is attached to a pre-survey anchor so each PMT position is fixed and measured.

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Fig. 3 This figure shows the progress of HAWC construction. Starting from a nearly “green” site in 2011 to a completed detector in four years

Once the bladder is inflated and in position, it is filled with high purity water (about 10-m attenuation length) and the PMTs are lowered into place via strings that go through the custom mount that captures the enclosure above the pre-survey spot. The PMTs can easily be retrieved for servicing (Fig. 6). The signals from each of the 300 detectors are sent back to the electronics room though a cabling network. This network is composed of conduits transporting three different kinds of cables: RG59, CAT5, and optical fiber. The RG59 cable carries the signal and high voltage (HV) for the PMTs. The optical fiber and CAT5 are part

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Fig. 4 Top view schematic of the HAWC core and outrigger array. The red dots represent the nodes that contain the readout electronics and power supply for the 65 WCDs in each zone A through E (Marandon et al. 2020)

of the laser calibration and water-level monitoring system. This cabling network is buried underground to minimize temperature fluctuations that may affect the transmitted signals. At γ -ray energies of around 10 TeV, the size of the footprint the related air shower produces starts to become bigger than the size of the main array. Most of the cores of these air showers while triggering the main array fall outside the area it covers. This poses a challenge to angular and energy reconstruction making them less accurate. The sparse outrigger array significantly improves the reconstruction of these VHE to UHE γ -ray events, thus increasing the instrument sensitivity above 10 TeV. Each of the 345 outrigger WCDs is a Rotoplas tank of 1.55-m diameter and 1.65-m height. The tanks are separated by distances of between 12 and 18 m. They are equipped with a single Hamamatsu R5912 8′′ PMT upward facing and anchored to the bottom. The outrigger array is divided into five sections, labeled A through E (see Fig. 4), which each consists of 69 WCDs. Run control and DAQ system are integrated into nodes that are located in the center of each section. A White Rabbit system (Serrano et al. 2009) provides synchronization between the different nodes and the main array with sub-nanosecond precision.

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Fig. 5 Schematic of the HAWC main (top right) and outrigger (bottom left) WCDs. The three outer PMTs in each main array WCDs are standard 8′′ PMTs, previously used in the Milagro Experiment and then refurbished. The center PMT is 10′′ high-quantum-efficiency tube that has about twice the light collection of the 8′′ PMTs. The outrigger WCDs each have one 8′′ PMT anchored at the bottom (Joshi et al. 2020)

Water Each HAWC WCD of the core array contains ∼188,000 liters of water. Water for the project was obtained from two sources. The large majority of the water was brought by tanker trucks from a well at an elevation of 2,400 m to the HAWC site at 4,100 m. The well water was softened near the well location. The remaining water was obtained from a spring on the mountain. This water was brought by a pipe ∼1 km from the spring to a storage tank about 1.5 km below the HAWC site where it was then trucked to the site. This water did not require softening. It took ∼13 tanker trucks full of water to fill each WCD of the core array. So ∼3,900 truckloads of water were used to fill the main array. At the site, the water was filtered and run through a UV lamp before distributing it to the array. Water quality is monitored regularly and with a few exceptions remains stable over a period of years without refiltering.

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Fig. 6 Shown above (left) is a PMT being attached to a string in the hatch in the top of a tank. Shown on the right is a PMT mount that is attached to the bottom of the tank over pre-survey anchor point under the tank. The mount (bottom) captures a small ball on the bottom of the PMT and holds the PMT in place. By tugging on the string, the ball can be released and the PMT can be retrieved. This design allows deployment and servicing from outside the tank

Electronics The PMTs detect the Cherenkov light inside the WCDs that is produced by relativistic particles from the EAS initiated by a gamma or cosmic ray. The PMT signals propagate through ∼200 m of RG59 cable to the data acquisition system in the counting house, where they are processed by custom made front-end boards. The pulses are shaped and sampled with a low and high threshold. A time stamp of a pulse that crosses a threshold is recorded by CAEN VX1190A time-to-digital converter modules with a precision of 0.1 ns. The arrival time and ultimately the charge can be inferred from the time-over-threshold (TOT). A laser calibration system measures the TOT-charge conversion and the response time of each PMT to different pulse sizes (Huentemeyer et al. 2011; Kelley-Hoskins 2012; Lauer et al. 2013). The raw data rate from the TDCs is ∼500 MB/s (separate VME backplanes are used for each TDC with a single board computer in each). Once in the main online computer a trigger formed and the data reconstructed (as described in the next section), the data rate to disk is reduced to ∼22 MB/s. Note this produces nearly 2TB of data a day, which is archived on site and then transferred to repositories at the Universidad Nacional Autónoma de México and University of Maryland.

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The analog signals recorded by the PMTs in the outrigger array are also sent through RG59 cables to one of the nodes A through E. The signals are separated from the HV that powers the PMT using a pick-off module and sent to the readout electronics. The readout electronics at each node consists of three Flash Analog-toDigital Converter (FADC) boards. The FADC boards convert the analog signal of up to 24 channels into a 12-bit digital signal with a sampling rate of 250 MHz rate. These boards have originally been developed for a prototype of camera proposed for the CTA, called the FlashCam (Pühlhofer et al. 2016). Of the 24 channels, 23 are used for PMT signals. The remaining channel is used as readout trigger during laser calibration runs.

Methods of Data Reconstruction and Analysis Once an air shower triggers the detector, i.e., it produces signals in more than a predefined number of PMTs in a preset time window (for example, >20–50 PMTs in 150 ns, depending on the exact array configuration Abeysekara et al. 2017b), the charge and time of each calibrated PMT signal are used to reconstruct the shower core, which is the intersection point of the primary particle direction with the detector level. The Nishimura–Kamata–Greisen (NKG) function (Greisen et al. 1960) describes the lateral distribution of charged particles produced by a gammaray initiated EAS. A modified NKG function can be used to find the position of the shower core (Abeysekara et al. 2017b). The direction of the primary particle is reconstructed using the relative times among the recorded PMT signals as the air shower sweeps across the array. Figure 7 visualizes how the arrival times are

Fig. 7 PMT signal times (red columns, already corrected for the shower front curvature) are used to reconstruct the shower front formed by air shower particles arriving on the HAWC array (in blue). The figure shows how the signal times vary across the array due to the angle of shower arrival (see text for details)

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used to reconstruct the arrival plane direction. The picture represents a simplified view of the shower front, which in reality is of convex shape and a few meters thick with a higher particle density near the shower core. Thus the accuracy and precision of the directional reconstruction of HAWC depend on the ability to first correctly reconstruct the shower core and then introduce corrections for curvature and shower front particle sampling (Abeysekara et al. 2017b). The higher concentration of secondary particles near the shower core for both γ -ray-induced air showers and a proton-induced air showers is evident in Fig. 8. The figure shows the event display of the HAWC main array only, with bigger black circles indicating a WCD and smaller black circles indicating the PMT locations inside the WCDs. The footprints of the air showers are overlaid with the disk colors

Fig. 8 This figure shows simulated γ -ray-induced air shower footprints (top) and hadron-induced air shower footprints (bottom). Each filled circle is a PMT signal, with the color and the size indicating the charge. The reconstructed shower core is marked with a light-green star, and the red circle indicates the 40-m radius around the reconstructed core. For the hadronic shower footprints, there is significant energy and hence charge deposited outside the 40-m radius far from the shower core

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and sizes indicating the amount of charge corresponding to the amount of light detected by each PMT. The charge distribution of the footprint in the HAWC main array can be fit with a function, which represents a simplification of the modified NKG function constructed from a Gaussian to describe the charge distribution near the central core location, and an additional term to describe the decreasing charge with increasing distance from the shower core in the tail. The charge signal in the ith PMT is given by  Si = A

 N 1 −|xi −x|2 /2σ 2 , e + 2π σ 2 (0.5 + |xi − x|/Rm )3

(1)

where x is the location of the shower core, xi is the location of the ith PMT, Rm is the Moliére radius of the atmosphere at the altitude of the HAWC detector, σ is the Gaussian width, and N is the normalization of the tail. The Gaussian width (10 m) and the normalization (5 × 105 ) are fixed. The core location and overall amplitude are fit. The algorithm is called the Super-Fast Core Fit (SFCF) (Abeysekara et al. 2017b). The SFCF is an approximation of the NKG function but has one less free parameter and contains simpler functional dependencies avoiding for example the use of the Γ function in the original NKG function, whose evaluation is computationally intensive. The numerical minimization of the SFCF converges faster with the derivatives being computed analytically and a softer slope toward the core location. Methods the HAWC Collaboration developed for rejecting the background of hadron-induced showers and estimating the energy of the γ -ray primary rely crucially on the proper reconstruction of the shower core. They are briefly described below. Air showers induced by hadrons are the primary background when measuring astrophysical γ -ray fluxes from the ground. Hadronic showers have a higher abundance of muons, and the muons that are produced tend to follow a broader lateral distribution. The shape of the lateral distribution of γ -induced air showers differs in general from that of hadron-induced showers. Figure 8 shows simulated γ -ray and proton EAS footprints observed by the HAWC Observatory. The γ -ray footprints follow a “smooth” charge signal distribution, while proton footprints appear “clumpier.” The HAWC Collaboration has been using three algorithms to identify γ -ray and hadron signatures. The first algorithm is based on a method developed for the Milagro Observatory and computes a parameter, called compactness, C=

Nhit , CxP E40

(2)

where Nhit is the number of PMTs with a significant signal produced by the EAS, and CxPE40 is the maximum charge measured by a PMT beyond a radial distance of 40 m from the shower core (Atkins et al. 2003). A small value of compactness corresponds to a small likelihood of an EAS to be originating from a γ ray. The other two algorithms are testing the shape of the whole EAS footprint. One approach is to

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calculate a χ 2 -like expression as a measure of the footprint smoothness and radial symmetry, P =

N 1  (ζi − ζi )2 , N σζ2i i=0

(3)

where ζi = log10 (Qi ) is the logarithm of the charge, which is calibrated and normalized to indicate the light level measured by the ith PMT that participates in the shower fit (Abeysekara et al. 2017b). The parameter ζi  is the average of the logarithms of charge, measured by all triggered PMTs in an annulus of 5-m width centered on the shower core position containing the ith PMT. The errors σζi are obtained from an analysis of a test sample of γ -like EAS events originating from the direction of the Crab Nebula. Hadronic EAS footprints are on average more uneven and less symmetric, which is reflected in a considerable number of PMT charge measurements that are significantly different from the average value at certain radial distance from the EAS core. This results in large P values. The second approach of testing the EAS footprint shape is based on the NKG function, which was originally formulated to describe the lateral distribution of purely electromagnetic EAS generated by a gamma-ray primary. Fitting such a function to shower footprints in a particle detection array like HAWC results in smaller χ 2 values for γ -like EAS. While HAWC and Milagro publications in the past have used parameters C and P of equations 2 and 3 to separate gamma ray from cosmic-ray primaries, HAWC has most recently switched to utilizing χ 2 values of shower lateral profile fits. The latter performs better than C and P . Unlike IACTs, which observe the EAS progression through the atmosphere, particle detection arrays, such as the HAWC Observatory, only rely on parameters associated with the EAS footprint in the array to estimate the energy of the primary particle. The simplest variable developed to measure the energy of a primary particle is to count the number of PMTs that are triggered by the EAS it causes. The downside of this variable is that it ignores the shower core location and shower profile shape, which results in a relatively weak correlation to the primary particle energy. Particularly at the upper bound of the detectable energy range, the correlation is limited by saturation of the number of possible PMTs triggered in the array as all PMTs in the HAWC main array tend to be triggered for EAS from primary particles with energies of 10 TeV and above. Therefore, HAWC researchers have developed two additional methods to estimate γ -ray energies. One of them is based on an idea first put forth by Hillas in the 1970s (Hillas et al. 1971). The charge profile of the EAS footprint in the HAWC array is fit with a modified NKG function, and the radial distance from the shower core is found at which the uncertainty in the density of the shower energy deposited in the array is smallest. For the HAWC layout and altitude, this radius has been found to be 40 m. The (extrapolated) PMT signal at this distance and an empirically determined function that depends on the reconstructed zenith angle of the EAS are used to convert the deposited charge into the primary particle energy (Abeysekara et al. 2019). The second method uses an

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artificial neural network and as input variables the fraction of PMTs and WCDs triggered by the EAS and the logarithm of the amplitude of the function used in the SFCF (Eq. 1). These input variables are proxies for the amount of energy deposited and how much of the EAS footprint is contained in the array. They also indirectly measure the attenuation of the EAS in the atmosphere. The energy resolution achieved with these two algorithms on the log scale is around 10% at 100 TeV (Abeysekara et al. 2019). Fluctuations intrinsic to the shower development, e.g., the fluctuations of the first interaction depth, combined with limited sampling at the ground level present a fundamental boundary for the energy resolution. The two methods are illustrated in Fig. 9. EAS events that trigger the HAWC array are dealt with as needed for different scientific analyses, which may focus on γ -ray or cosmic-ray emission, energy, spatial or time dependence of the emission, or self-triggered and externally triggered burst searches. The investigation of point, extended, and diffuse γ -ray emission usually involves the creation of the so-called sky maps integrated over the detector on-time. Reconstructed shower events are allocated to bins that correlate with the

Fig. 9 Charge distribution of a single EAS event. The black points represent the log of the effective charge measured by the PMTs in the array as a function of the radial distance from the shower core. There are two types of PMTs in the main array of the HAWC Observatory, an 8-inch Hamamatsu R5912 and a 10-inch Hamamatsu R7081-02. To equalize the light measurements of the two types, an effective charge is calculated by applying a scaling factor. The red line is the best fit to an NKG-like function described in Abeysekara et al. (2019). The red dot marks the charge at a distance of 40 m from the shower axis. The blue histogram represents the relative fraction of the charge in several rings around the shower core. While the width of the rings up to an outer radial distance of 90 m is 10 m, the charge fraction outside of the 90 m radius is combined in just one bin. The 10 charge fractions are a measure of the lateral shower distribution and serve as input to a neural network. See text for more details

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primary particle energy. They are further sorted into directional bins providing information about where the primary came from (e.g., the particles R.A. and δ according to the J2000 epoch). The HEALPix binning scheme is used to produce pixels on a spherical surface that covers the same surface area for every pixel (Górski et al. 2005). Gamma-hadron separation cuts described above are applied to reduce the background of EAS caused by cosmic-ray primaries as well as additional data quality cuts ensuring only well-reconstructed EAS are considered in an analysis (see, for example, Abeysekara et al. 2017b, 2019, 2017c). Yet, even after data have been prepared in this way, a significant number of hadronic EAS remain in the sample. The HAWC collaboration has used two alternative ways to estimate this background (Surajbali et al. 2020). The main reconstruction and analysis pipeline applies an algorithm that was developed for the analysis of Milagro data, called direct integration (Atkins et al. 2003; Alexandreas et al. 1993). Direct integration is based on the assumption that the all-sky rate is independent of the distribution of EAS arrival directions for a certain time period. For the interval of 2 h that HAWC analyses typically use, this is accurate to a few parts in a thousand corresponding to the level of the cosmic anisotropy (Abeysekara et al. 2017b). The background rate at a certain (R.A.,δ) point is then calculated by convolving the all-sky rate with the spatial distribution of EAS events in detector coordinates. To exclude potential signal events from the computation of the background, regions near the galactic plane, the Crab Nebula, Mrk 421, and Mrk 501 are masked out. The γ -ray flux maps created in this way are further analyzed using a maximum likelihood formalism in which an energy- and morphology-dependent emission model is convolved with the instrument response and compared to the data (Vianello et al. 2015; Younk et al. 2015). Figure 10 shows the all-sky γ -ray test statistics (TS) map resulting from a putative point-source search using this formalism to construct the Third HAWC

Fig. 10 All-sky significance map of γ -ray emission in celestial coordinates for 1523 days of data taking, assuming a point source hypothesis. The bright emission band on the left is the galactic plane as seen from the Northern Hemisphere, and the bright region on the right is the galactic anticenter region with the Crab Nebula and the Geminga and Monogem halos. There are two bright off-plane regions associated with the two blazars Mrk 421 (right) and Mrk 501 (left)

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Catalog (3HWC) (Albert et al. 2020a). In the following section, we will provide an overview of impactful scientific results that the HAWC Collaboration derived using the tools we just outlined.

Overview of Important Scientific Results Three core capabilities of the HAWC Observatory have played a crucial role in all of its most high-impact results: the high duty cycle, wide field of view, and a detection sensitivity for γ rays of energies >10 TeV that is superior to that of IACTs currently in operation. Compared to its predecessor, the Milagro Experiment, the HAWC Observatory has produced a significantly larger number of publications – about three to four times more – a reflection of the vastly improved instrument sensitivity of the latter. A comprehensive compilation of HAWC publications can be found elsewhere (Abreu et al. 2020; HAWC 2022). Here, we will only summarize a few high-impact results. These results can be categorized into the following broad groups: Discovery of new VHE γ -ray sources and source classes, PeVatrons, and fundamental physics. Discovery of new VHE γ -ray sources and source classes The HAWC Observatory detected TeV γ -ray emission around two nearby middle-aged pulsars Geminga and Monogem (PSR B0656+14) that extend over several degrees (see Fig. 11). The wide field-of-view instrument Milagro had measured extended emission surrounding Geminga in the past, but the significantly improved sensitivity of the HAWC data

Fig. 11 Surface Brightness of the Geminga and Monogem pulsars (Abeysekara et al. 2017a). The color scale in the left-hand image indicates the statistical pre-trial significance of the excess counts above the background for γ -ray energies between ∼1 and ∼50 TeV. The right-hand image shows the surface brightness as a function of distance from the Geminga pulsar. The solid red line is the best-fitting diffusion model. The distance from the pulsar in parsecs is calculated based on the nominal distances of 250 pc to the Geminga pulsar (Manchester et al. 2005)

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allowed to study the emission profile in more detail. HAWC researchers developed a simple leptonic progenitor model based on Atoian et al. (1995) and by fitting the model to emission profile showed that the leptons diffuse away from the pulsar more slowly than previously assumed (Abeysekara et al. 2017a). Assuming that the diffusion coefficient does not change dramatically between the source and the Earth, this challenged the supposition that the positron excess flux measured near the Earth (Adriani et al. 2009; Aguilar et al. 2013) could be explained by local pulsars instead of alternative hypothesis such as dark-matter annihilation. Other models suggest that there are possible significant changes to the diffusion coefficient that would allow these positrons to reach earth (Tang and Piran 2019; Wu n.d.). Following this discovery of γ -ray halos by the HAWC Observatory, it was widely recognized that extended halos are a common feature associated with pulsars and distinct from the classical X-ray PWN thus representing a new class of γ -ray sources (Linden et al. 2017; Linden and Buckman 2018; Sudoh et al. 2019; Giacinti et al. 2020). There are slightly differing assumptions about the halo formation, but interpretations have in common that the γ rays are produced by an electron/positron plasma that has escaped from the PWN via inverse Compton up-scattering with cosmic microwave background (CMB) photons. Since their discovery by the HAWC Observatory, halos have also been detected by the LHAASO (Aharonian et al. 2021) and at lower γ -ray energies by the Fermi-LAT (Mauro et al. 2019). SS 433 is a micro-quasar that has been extensively studied in many wavelengths from radio to MeV. Its orientation with jets nearly perpendicular to our line of sight makes both jets visible. Previous observations by the H.E.S.S., MAGIC, and VERITAS telescopes set upper limits on TeV emission from the jets. HAWC detected TeV emission from the SS 433/W50 system where the lobes are spatially resolved (Abeysekara et al. 2021a). The TeV emission is localized to structures in the lobes, far from the center of the system where the jets are formed (see left hand Fig. 12). The HAWC Observatory measured photon energies of at least 25 TeV, and these are not Doppler boosted, because of the viewing geometry. The HAWC Collaboration used these observations to show that the data are consistent with electrons that inverse-Compton scatter off of the CMB in the region of the terminated shocks and that hadronic acceleration is disfavored (see right-hand image in Fig. 12). The acceleration mechanism is still unknown. The discovery of SS 433 as a TeV γ -ray source particularly shows the benefits of wide field-of-view observations coupled with good detection sensitivity for γ -ray energies >10 TeV. New source searches can be performed without the need for a strategically designed campaign that has to take into account competing interests and may be rather time-consuming. PeVatrons In 2020, the HAWC Collaboration reported the detection of γ rays above 100 TeV from the direction of the Crab Nebula (Abeysekara et al. 2019). Since then, several more PeVatron candidates were found in HAWC data with one possibly associated with an SNR (Abeysekara et al. 2020; Albert et al. 2020b). Figure 13 shows the γ -ray signal significance map in galactic coordinates along a galactic plane region. One of the PeVatron candidates is found in HAWC data

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Fig. 12 Left-hand image: Significance map of VHE-γ -ray emission from SS 433/W50. The color scale indicates the statistical pre-trial significance of the excess counts above the background. The dark contours show X-ray emission from SS 433 and its jets. The jet termination regions e1, e2, e3, w1, and w2 observed in the X-ray data are also marked, as well as the location of the central binary. Right-hand image: Broadband spectral energy distribution of the eastern emission region e1. The plot shows a combined fit of radio (Geldzahler et al. 1980), soft and hard X-ray (Brinkmann et al. 2007; Safi-Harb and Petre 1999), and VHE γ -ray (Ahnen et al. 2018; Kar et al. 2018) emission data including the HAWC measurement. The thick and thin error bars on the HAWC flux represent the statistical and systematic uncertainties. Downward arrows represent flux upper limits. The leptonic multi-wavelength spectra assume a single electron population. The hadronic spectrum assumes that 10% of the jet kinetic energy converts into protons

Fig. 13 Significance γ -ray signal map of the galactic plane for reconstructed primary particle ◦ energies of >56 TeV. A disk of radius √ 0.5 is assumed as the source morphology. Black triangles denote spots in the sky where the TS of the high-energy emission is >5 (Malone 2022)

of the Cygnus region. In a dedicated analysis that involves the construction of an emission model that consists of three source components and is fit to the data in the region, 1 to 100 TeV γ rays were identified to come from the “Cygnus Cocoon” (Fig. 14) (Abeysekara et al. 2021b). This structure is associated with a superbubble that surrounds a region of massive star formation. These γ rays are likely produced by 10–1,000 TeV previously accelerated cosmic rays that originate from the enclosed star-forming region Cyg OB2. Until then, it was not known that such regions could accelerate particles to these energies. The measured flux is well modeled as originating from the interaction of protons colliding with ambient gas after they were accelerated to PeV energies by powerful shock waves generated by strong stellar winds in the star cluster.

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Fig. 14 Two left-hand images: γ -ray signal significance map of the Cocoon region before (a) and after (b) subtraction of the known sources J2031+415 (a PWN) and 2HWC J2020+403 (γ Cygni). The blue contours are four annuli centered at the OB2 association. The green contour is the region of interest (ROI) to which an emission model fits. The bright source 2HWC J2019+367 is excluded from the ROI. The light-blue, medium-blue, and dark-blue dashed lines are contours for 0.16, 0.24, and 0.32 photons per 0.1◦ ×0.1◦ spatial bin, respectively, as measured by the FermiLAT (Ackermann et al. 2011). Both maps are made assuming a 0.5◦ extended disk source and a spectral index of −2.6 with 1,343 days of HAWC data. Right-hand image: The plot shows the spectral energy distribution (SED) of the γ -ray emission from the Cygnus Cocoon measured by different instruments (Ackermann et al. 2011; Bartoli et al. 2014; Abdollahi et al. 2020; Aharonian et al. 2019). The gray solid and dashed lines are γ -ray SED derived from modeling the emission as a result of proton progenitors

Fundamental Physics The HAWC Observatory with its wide field of view and sensitivity at energies >10 TeV is particularly well-suited to search for γ -ray excess fluxes and structures that stem from dark-matter interactions. Such searches often rely on the ability to observe extended emission regions or stack data gathered from a significant enough number astrophysical sources of the same class, like for example dwarf spheroidal galaxies, which are expected to contain significant amounts of dark matter. Furthermore, because astrophysical source accelerates particles to energies that cannot be reached by earthbound accelerators and are located at very large distances from us, the observer, they offer unique opportunities for testing Lorentz Invariance. Grant Unified Theories, String Theory, or Quantum Gravity all motivate some Lorentz Invariance Violation (LIV) allowing photons of sufficient energy to decay over short timescales. Putting lower limits on the highest photon energies detected by the HAWC Observatory will translate to tighter limits on the LIV scale. Figure 15 shows dark matter, and LIV limits the HAWC Collaboration published in recent years and compares them to those published by other γ -ray observatories.

Synergies with Imaging Atmospheric Cherenkov Telescopes Until recently, it has been unclear if the results of observations by both types of instruments are consistent. Several of the discovered HAWC sources were followed up by IACTs, resulting in a confirmed detection only in a minority of cases. A paper

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Fig. 15 Left-hand image: Joint 95% CL upper limits derived on the channel-specific annihilation cross-section from the observation of local, dark matter dominated, dwarf galaxies in the HAWC field of view compared to other experiments (Albert et al. 2020c). Right-hand image: Limits on Eγ can be translated into limits on the LIV energy scale. The latter are shown here. HAWC (1) measurements exclude the LIV energy scale of new physics, ELI V , to greater than >1031 eV. This 28 is over 1800 times above the Planck energy scale (EP l ∼ 10 eV). Both sets of limits are more constraining than limits computed prior to the HAWC measurements (Albert et al. 2020d)

published by the HAWC and H.E.S.S. Collaborations together attempts to resolve the tensions between previous results by performing a new analysis of the H.E.S.S. Galactic plane survey data and applying a technique that makes a comparison of H.E.S.S. and HAWC results more straightforward (Abdalla et al. 2021). To create the γ -ray sky maps in Fig. 16, EAS events above 1 TeV are selected for both data sets, the kernel size in the computation of the H.E.S.S. maps is increased to approach the point spread function of the HAWC instrument, and a similar background estimation method is used. This is the first detailed comparison of the galactic plane observed by both instruments. H.E.S.S. confirms the γ -ray emission of four HAWC sources among seven previously undetected by IACTs. The three remaining sources have measured fluxes below the sensitivity of the current H.E.S.S. data set. Outstanding differences in the overall γ -ray flux can be explained by the systematic uncertainties. Thus, we confirm a consistent view of the γ -ray sky between the WCD and IACT techniques. At the same time, it is obvious that particle detection arrays such as HAWC provide a complementary view on the VHE/UHE γ -ray sky.

Conclusion and Outlook Studies of the non-thermal universe probe some of the most significant unresolved questions in astrophysics, including the location and properties of cosmic accelerators, the nature of dark matter, and searches for physics beyond the standard model. The HAWC Gamma-Ray Observatory is an extremely efficient survey instrument, which has been applying its high duty cycle (approaching 100%) and large field of view (∼2 sr) to discover new TeV γ -ray sources and a new class of TeV sources, set world-leading limits on dark matter and Lorentz Invariance Violation, and play

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Fig. 16 HAWC and H.E.S.S. γ -ray signal significance maps of a section of the galactic plane (Abdalla et al. 2021). The green circles mark the 68% containment of the H.E.S.S. Galactic Plane Survey (HGPS) sources and the black dots the location of the HAWC sources in the region. The white boxes are highlighting areas where new sources were detected in HGPS data using a HAWC-like map-making process. The green dotted lines point to H.E.S.S. sources not detected by the HAWC Observatory, and the orange dotted lines point to HAWC sources previously not detected by the H.E.S.S. Telescope. The maps from top to bottom are: (1) H.E.S.S. data for energies above 1 TeV reconstructed with the Image Pixel-wise fit for Atmospheric Cherenkov Telescopes (ImPACT) algorithm using a Gaussian kernel size of 0.1◦ (Parsons and Hinton 2014); the ring background method (Abdalla et al. 2018) is applied on each observation run separately with an adaptive radius and the standard exclusion regions around sources are used. (2) Same H.E.S.S. data using a Gaussian kernel of 0.4◦ . (3) Same H.E.S.S. data using the so-called field-of-view background method, which is closest to the method of direct integration used by the HAWC collaboration and is based on using H.E.S.S. exposure maps as background. Again a Gaussian kernel of 0.4◦ is used. For the background normalization, in addition to the standard exclusion regions around sources, a 2◦ wide mask covering the galactic plane is used. (4) 1523 days of HAWC data for energies above ∼1 TeV

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a crucial role in multi-messenger observations. The science gleaned from HAWC measurements demonstrates the complementarity to and synergies with current and planned observatories such as H.E.S.S., MAGIC, VERITAS, and CTA, as well as Fermi, IceCube, and LIGO/Virgo. The HAWC achievements have inspired a more ambitious Chinese effort also in the Northern Hemisphere, the LHAASO, which uses a similar WCD design and features a bigger effective detection area. Recent discoveries such as a GRB associated with merging neutron stars, GRBs detected up to energies above hundreds of GeV, and a detection of neutrinos from a flaring AGN also points to the need for a wide field-of-view instruments, which almost continuously survey the sky in the space and time domain, like the HAWC Observatory. The pioneering work by the HAWC Observatory coupled with a recognition that ground-based high duty cycle, wide-field, γ -ray facilities will play a crucial role in Multi-messenger Astrophysics motivates the design a next-generation ground-based survey instrument for VHE γ -ray astronomy to be deployed at a high-altitude site in the Southern Hemisphere: The Southern Wide-Field GammaRay Observatory (SWGO). SWGO will provide daily unbiased monitoring for variable sources including GRBs or nearby AGNs and near-real-time alerts to other instruments, such as CTA. Here, archival data sets are also important because they enable regions of the sky to be studied both before and after alerts from other experiments are reported. High-impact HAWC results have shown that sensitivity to particle accelerators in the local galactic neighborhood is one of the greatest strengths of wide fieldof-view observatories. The detection of very extended TeV γ -ray emission around the pulsars Geminga and Monogem revealed that nearby pulsars likely strongly influence their surroundings, leading to an interpretation of this newly discovered emission as halos of GeV to TeV γ rays that are produced by electrons and positrons interacting with the ambient interstellar radiation fields outside the classical PWNe. The HAWC Observatory also uniquely contributed to the search for and study of sources of cosmic rays with energies in excess of 1 PeV. Next-generation instruments such as SWGO will build on groundbreaking accomplishments of the HAWC instrument.

References H. Abdalla et al., [HESS], The H.E.S.S. Galactic plane survey. Astron. Astrophys. 612, A1 (2018). https://doi.org/10.1051/0004-6361/201732098 H. Abdalla et al., [H.E.S.S.], TeV emission of galactic plane sources with HAWC and H.E.S.S. Astrophys. J. 917, 6 (2021). https://doi.org/10.3847/1538-4357/abf64b A.A. Abdo et al., [Milagro], Discovery of TeV gamma-ray emission from the Cygnus Region of the galaxy. Astrophys. J. Lett. 658, L33-L36 (2007a). https://doi.org/10.1086/513696 A.A. Abdo et al., [Milagro], TeV gamma-ray sources from a survey of the galactic plane with Milagro. Astrophys. J. Lett. 664, L91-L94 (2007b). https://doi.org/10.1086/520717 A.A. Abdo et al., [Milagro], A measurement of the spatial distribution of diffuse TeV gamma ray emission from the galactic plane with Milagro. Astrophys. J. 688, 1078–1083 (2008a). https:// doi.org/10.1086/592213

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J. Goodman and P. Huentemeyer

A.A. Abdo et al., [Milagro], Discovery of localized regions of excess 10-TeV cosmic rays. Phys. Rev. Lett. 101, 221101 (2008b). https://doi.org/10.1103/PhysRevLett.101.221101 A.A. Abdo et al., [Milagro], Milagro observations of TeV emission from galactic sources in the fermi bright source list. Astrophys. J. Lett. 700, L127–L131 (2009); [erratum: Astrophys. J. Lett. 703, L185 (2009); erratum: Astrophys. J. 703, L185 (2009).] https://doi.org/10.1088/0004637X/700/2/L127 A.A. Abdo et al., [Milagro], Spectrum and morphology of the two brightest Milagro sources in the Cygnus region: MGRO J2019+37 and MGRO J2031+41. Astrophys. J. 753, 159 (2012). https:// doi.org/10.1088/0004-637X/753/2/159 S. Abdollahi et al., [Fermi-LAT], F ermi large area telescope fourth source catalog. Astrophys. J. Suppl. 247(1), 33 (2020). https://doi.org/10.3847/1538-4365/ab6bcb A.U. Abeysekara et al., [HAWC], Extended gamma-ray sources around pulsars constrain the origin of the positron flux at Earth. Science 358(6365), 911–914 (2017a). https://doi.org/10.1126/ science.aan4880 A.U. Abeysekara et al., [HAWC], Observation of the crab nebula with the HAWC gamma-ray observatory. Astrophys. J. 843(1), 39 (2017b). https://doi.org/10.3847/1538-4357/aa7555 A.U. Abeysekara et al., The 2HWC HAWC observatory gamma ray catalog. Astrophys. J. 843(1), 40 (2017c). https://doi.org/10.3847/1538-4357/aa7556 A.U. Abeysekara et al., [HAWC], Measurement of the Crab Nebula at the highest energies with HAWC. Astrophys. J. 881, 134 (2019). https://doi.org/10.3847/1538-4357/ab2f7d A.U. Abeysekara et al., [HAWC], Multiple galactic sources with emission above 56 TeV detected by HAWC. Phys. Rev. Lett. 124(2), 021102 (2020). https://doi.org/10.1103/PhysRevLett.124. 021102 A.U. Abeysekara et al., [HAWC], Very high energy particle acceleration powered by the jets of the microquasar SS 433. Nature 562(7725), 82–85 (2021a); [erratum: Nature 564(7736), E38 (2018).] https://doi.org/10.1038/s41586-018-0565-5 A.U. Abeysekara et al., [HAWC], HAWC observations of the acceleration of very-high-energy cosmic rays in the Cygnus Cocoon. Nat. Astron. 5(5), 465–471 (2021b). https://doi.org/10.1038/ s41550-021-01318-y P. Abreu, A. Albert, R. Alfaro, C. Alvarez, R. Arceo, P. Assis, F. Barao, J. Bazo, J.F. Beacom, J. Bellido et al., The Southern Wide-Field Gamma-Ray Observatory (SWGO): a next-generation ground-based survey instrument for VHE gamma-ray astronomy. (2020) [arXiv:1907.07737 [astro-ph.IM]] M. Ackermann, M., et al. Science, 334 (2011), 1103 https://doi.org/10.1126/science.1210311 O. Adriani et al., [PAMELA], An anomalous positron abundance in cosmic rays with energies 1.5–100 GeV. Nature 458, 607–609 (2009). https://doi.org/10.1038/nature07942 M. Aguilar, G. Alberti, B. Alpat, A. Alvino, G. Ambrosi, K. Andeen, H. Anderhub et al., [AMS], First result from the alpha magnetic spectrometer on the international space station: precision measurement of the positron fraction in primary cosmic rays of 0.5–350 GeV. Phys. Rev. Lett. 110(14), 141102 (2013). https://doi.org/10.1103/PhysRevLett.110.141102 F. Aharonian, R. Yang, E. de Oña Wilhelmi, Massive stars as major factories of galactic cosmic rays. Nat. Astron. 3(6), 561–567 (2019). https://doi.org/10.1038/s41550-019-0724-0 F. Aharonian et al., [LHAASO], Extended very-high-energy gamma-ray emission surrounding PSR J0622+3749 observed by LHAASO-KM2A. Phys. Rev. Lett. 126(24), 241103 (2021). https://doi.org/10.1103/PhysRevLett.126.241103 M. L. Ahnen et al., [MAGIC and H.E.S.S.], Constraints on particle acceleration in SS433/W50 from MAGIC and H.E.S.S. observations. Astron. Astrophys. 612 (2018), A14 https://doi.org/ 10.1051/0004-6361/201731169 A. Albert et al., [HAWC], 3HWC: the third HAWC catalog of very-high-energy gamma-ray sources. Astrophys. J. 905(1), 76 (2020a). https://doi.org/10.3847/1538-4357/abc2d8 A. Albert et al., [HAWC], HAWC J2227+610 and its association with G106.3+2.7, a new potential Galactic PeVatron. Astrophys. J. Lett. 896, L29 (2020b). https://doi.org/10.3847/2041-8213/ ab96cc

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A. Albert et al., [HAWC], Search for gamma-ray spectral lines from dark matter annihilation in dwarf galaxies with the High-Altitude Water Cherenkov observatory. Phys. Rev. D 101(10), 103001 (2020c). https://doi.org/10.1103/PhysRevD.101.103001 A. Albert et al., [HAWC], Constraints on Lorentz invariance violation from HAWC observations of gamma rays above 100 TeV. Phys. Rev. Lett. 124(13), 131101 (2020d). https://doi.org/10.1103/ PhysRevLett.124.131101 J. Aleksi´c et al., [MAGIC], The major upgrade of the MAGIC telescopes, Part II: a performance study using observations of the Crab Nebula. Astropart. Phys. 72, 76 (2016). https://doi.org/10. 1016/j.astropartphys.2015.02.005 D.E. Alexandreas, D. Berley, S. Biller, G.M. Dion, J.A. Goodman, T.J. Haines, C.M. Hoffman, E. Horch, X.Q. Lu, C. Sinnis et al., Point source search techniques in ultrahigh-energy gammaray astronomy. Nucl. Instrum. Meth. A 328, 570–577 (1993). https://doi.org/10.1016/01689002(93)90677-A R. Atkins et al., [Milagro], Observation of TeV gamma-rays from the Crab Nebula with MILAGRO using a new background rejection technique. Astrophys. J. 595, 803–811 (2003). https://doi.org/ 10.1086/377498 R. Atkins et al., [Milagro], Evidence for TeV gamma-ray emission from the galactic plane. Phys. Rev. Lett. 95, 251103 (2005). https://doi.org/10.1103/PhysRevLett.95.251103 A.M. Atoian, F.A. Aharonian, H.J. Volk, Electrons and positrons in the galactic cosmic rays. Phys. Rev. D. 52, 3265 (1995). https://doi.org/10.1103/PhysRevD.52.3265 W. Atwood et al., [Fermi-LAT], Pass 8: toward the full realization of the fermi-LAT scientific potential. (2012) [arXiv:1303.3514 [astro-ph.IM]] B. Bartoli et al., [ARGO-YBJ], Identification of the TeV gamma-ray source ARGO J2031+4157 with the Cygnus Cocoon. Astrophys. J. 790(2), 152 (2014). https://doi.org/10.1088/0004-637X/ 790/2/152 A. Borione et al., [CASA-MIA], A search for ultra-high-energy gamma-ray emission from the crab nebula and pulsar. Astrophys. J. 481(1), 313 (1997). https://doi.org/10.3847/1538-4357/aa7555 W. Brinkmann, G.W. Pratt, S. Rohr, N. Kawai, V. Burwitz, XMM-Newton observations of the eastern jet of SS433. Astron. Astrophys. 463, 611–620 (2007). https://doi.org/10.1051/00046361:20065570 CTAO Consortium, CTAO Performance (2021). Cited June 2022. https://www.cta-observatory.org/ science/cta-performance B.J. Geldzahler, T. Pauls, C.J. Salter, Continuum observations of the SNR W50 and G 74.9+1.2 at 2695 MHz. Astron. Astrophys. 84(1–2), 237–244 (1980) G. Giacinti, A.M.W. Mitchell, R. López-Coto, V. Joshi, R.D. Parsons, J.A. Hinton, Halo fraction in TeV-bright pulsar wind nebulae. Astron. Astrophys. 636, A113 (2020). https://doi.org/10.1051/ 0004-6361/201936505 K.M. Górski, E. Hivon, A.J. Banday, B.D. Wandelt, F.K. Hansen, M. Reinecke, M. Bartelman, HEALPix – A framework for high resolution discretization, and fast analysis of data distributed on the sphere. Astrophys. J. 622, 759–771 (2005). https://doi.org/10.1086/427976 K. Greisen, Cosmic ray showers. Ann. Rev. Nucl. Part. Sci. 10, 63–108 (1960). https://doi.org/10. 1146/annurev.ns.10.120160.000431 HAWC, HAWC Publications (2022). Cited June 2022. https://www.hawc-observatory.org/ publications/ A.M. Hillas, D.J. Marsden, J.D. Hollows, H.W. Hunter, in Proceedings of 12th International Cosmic Ray Conference (Hobart), vol. 3 (1971), p. 1001 M. Holler et al., [H.E.S.S.], Observations of the crab nebula with H.E.S.S. Phase II. PoS ICRC2015, 847 (2016). https://doi.org/10.22323/1.236.0847 P. Huentemeyer, E. Bonamente, B. Dingus, Calibration of the HAWC Observatory. (2011) https:// doi.org/10.7529/ICRC2011/V09/0767 V. Joshi et al., [HAWC], Air shower reconstruction using HAWC and the outrigger array. PoS ICRC2019, 707 (2020). https://doi.org/10.22323/1.358.0707

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P. Kar, [VERITAS], VERITAS Observations of High-Mass X-Ray Binary SS 433. PoS ICRC2017, 713 (2018). https://doi.org/10.22323/1.301.0713 N.C. Kelley-Hoskins, Calibration of the HAWC Gamma-Ray Observatory. Master’s Thesis, Michigan Technological University, 2012. https://doi.org/10.37099/mtu.dc.etds/109 R. Lauer, Calibration and Reconstruction Performance of the HAWC Observatory, in 33rd International Cosmic Ray Conference, ICRC2013 (2013), p. 2960 T. Linden, B.J. Buckman, Pulsar TeV halos explain the diffuse TeV excess observed by Milagro. Phys. Rev. Lett. 120(12), 121101 (2018). https://doi.org/10.1103/PhysRevLett.120.121101 T. Linden, K. Auchettl, J. Bramante, I. Cholis, K. Fang, D. Hooper, T. Karwal, S.W. Li, Using HAWC to discover invisible pulsars. Phys. Rev. D 96(10), 103016 (2017). https://doi.org/10. 1103/PhysRevD.96.103016 K. Malone, HAWC’s view of the highest-energy gamma-ray sky. AAS High Energy Astrophysics Division Meeting #19, 202.01. BAAS, 54, 3 (2022) R.N. Manchester, G.B. Hobbs, A. Teoh, M. Hobbs, The Australia Telescope National Facility pulsar catalogue. Astron. J. 129, 1993 (2005). https://doi.org/10.1086/428488 V. Marandon et al., [HAWC], Latest news from the HAWC outrigger array. PoS ICRC2019, 736 (2020). https://doi.org/10.22323/1.358.0736 M. Di Mauro, S. Manconi, F. Donato, Detection of a γ -ray halo around Geminga with the Fermi LAT data and implications for the positron flux. Phys. Rev. D 100(12), 123015 (2019); [erratum: Phys. Rev. D 104(8), 089903 (2021).] https://doi.org/10.1103/PhysRevD.104.089903 A.M.W. Mitchell et al., [H.E.S.S.], Detection of extended TeV emission around the Geminga pulsar with H.E.S.S. PoS ICRC2021, 780 (2021). [arXiv:2108.02556 [astro-ph.HE]] N. Park, [VERITAS], Performance of the VERITAS experiment. PoS ICRC2015, 771 (2016). https://doi.org/10.22323/1.236.0771 R.D. Parsons, J.A. Hinton, A Monte Carlo Template based analysis for Air-Cherenkov Arrays. Astropart. Phys. 56, 26–34 (2014). https://doi.org/10.1016/j.astropartphys.2014.03.002 G. Pühlhofer et al., [CTA], FlashCam: a fully-digital camera for the medium-sized telescopes of the Cherenkov Telescope Array. PoS ICRC2015, 1039 (2016). https://doi.org/10.22323/1.236. 1039 S. Safi-Harb, R. Petre, Rossi x-ray timing explorer observations of the Eastern Lobe of W50 associated with SS 433. Astrophys. J. 512, 784 (1999). https://doi.org/10.1086/306803 J. Serrano et al., [HAWC], The White Rabbit Project, in Proceedings of ICALEPCS TUC004 (Kobe, Japan, 2009) T. Sudoh, T. Linden, J.F. Beacom, TeV halos are everywhere: prospects for new discoveries. Phys. Rev. D 100(4), 043016 (2019). https://doi.org/10.1103/PhysRevD.100.043016 P. Surajbali, Observing large-scale structures in the gamma-ray sky. Ph.D. Thesis, U. Heidelberg, 2020. https://doi.org/10.11588/heidok.00028625 X. Tang, T. Piran, Positron flux and γ -ray emission from Geminga pulsar and pulsar wind nebula, Mon. Notices Royal Astron. Soc. 484(3), 3491–3501 (2019). https://doi.org/10.1093/mnras/ stz268 G. Vianello, R.J. Lauer, P. Younk, L. Tibaldo, J.M. Burgess, H. Ayala, P. Harding, M. Hui, N. Omodei, H. Zhou, The multi-mission maximum likelihood framework (3ML). (2015) [arXiv:1507.08343 [astro-ph.HE]] D. Wu, New estimate for the contribution of the Geminga pulsar to the positron excess. (n.d.) [arXiv:2206.07621 [astro-ph.HE]] P.W. Younk, R.J. Lauer, G. Vianello, J.P. Harding, H.A. Ayala Solares, H. Zhou, M. Hui, A highlevel analysis framework for HAWC. (2015) [arXiv:1507.07479 [astro-ph.IM]]

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Progress of the Particle Detector Array in China . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tibet ASγ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ARGO-YBJ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Identification of the First TeV Gamma-Ray Super-Bubble . . . . . . . . . . . . . . . . . . . . . . . . . Long-Term Monitoring at VHE Band and Multiwave Band Study of AGN . . . . . . . . . . . LHAASO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . KM2A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . WCDA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Major Achievement of LHAASO in Gamma-Ray Astronomy . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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LHAASO, which was fully completed and started taking data in July 2021, is currently the most sensitive particle detector array. It has high sensitivity to measure both the very high-energy and ultra-high-energy gamma rays. In particular, the sensitivity for ultra-high-energy gamma rays is more than ten times better than all previous experiments. Recently, a breakthrough has been made in ultra-high-energy gamma-ray observations. Twelve ultra-high-energy gammaray sources accompanied by several PeV photons were detected. ARGO-YBJ and Tibet ASγ , the predecessors of LHAASO, are also famous gamma-ray particle detector arrays. They have made important contributions in the observations of

S. Chen · Z. Cao () Key Laboratory of Particle Astrophysics, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing, China e-mail: [email protected]; [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_66

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very high-energy gamma rays, which are important stages in the development of particle detector arrays. The development history of Tibet ASγ , ARGO-YBJ, and LHAASO, as well as their achievements in gamma-ray astronomy, will be introduced in this chapter. Keywords

Very high-energy gamma ray · Ultra-high-energy gamma ray · LHAASO · ARGO-YBJ · Tibet ASγ · Crab nebula · Extensive shower array

Introduction Cosmic rays are high-energy particles from the universe. They were discovered by Hess in 1912 during a balloon flight (Hess 1912). Up to now, the maximum energy of cosmic ray particles observed by people has reached 1020 eV, which is ten million times higher than that of particles accelerated by the largest human particle accelerator – the large hadron collider (LHC). What kind of celestial object do cosmic rays originate from? How are they accelerated to such extreme energies? These questions have been major scientific issues in the field of particle astrophysics for a long time. The most basic and important problem is its origin, which is called “the mystery of the century.” Cosmic rays are charged particles. During their propagation, they will be deflected by the cosmic magnetic field and lose their original direction information. However, cosmic rays will collide with the ambient gas near their acceleration site which yields neutral high-energy gamma rays. The detection of gamma rays can shed light on our understanding of the origin and acceleration mechanisms of cosmic rays. Therefore, since the birth of extensive air shower particle detector arrays, detection of gamma-ray sources has become one of the most important scientific targets. However, limited by sensitivity, ground-based particle detector arrays did not detect gamma-ray signals in the first few decades. The energy spectrum of all cosmic ray particles from 1011 to 1020 eV generally exhibits a power law shape, showing features of nonthermal origin. The spectrum softens at about 3×1015 eV, which is known as the “knee” structure. This structure was first discovered by the MSU group in Kulikov et al. (1958) and later confirmed by many other experiments and contains important information about the origin and propagation of cosmic rays. According to the estimation of the maximum acceleration energy of cosmic rays, based on the size and magnetic field of the known celestial objects, it is generally believed that the cosmic rays with energies around and below the “knee” region originate from Galactic objects. Therefore, searching for evidence of PeV cosmic ray acceleration from Galactic objects through gamma-ray observations is an important way to solve the origin of cosmic rays within the Milky Way. In 1983, the ground-based particle detector array made an amazing breakthrough. A very active cosmic ray research group from the Kiel University in Germany observed a PeV gamma-ray signal at 4.4σ from the Cygnus X-3 direction using a

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small cosmic ray array (Samorski and Stamm 1983). The PeV gamma-ray signal has a periodicity of 4.8 h as that in X-ray band. Although the reliability of this result is still controversial up to now, it triggered an upsurge of ultra-high-energy gamma-ray detection and promoted the rapid development of ground-based cosmic ray experiments. At that time, the Chinese cosmic ray research group was in the transition period from particle physics to particle astrophysics and was planning to propose a particle array project in Tibet, which takes into account the geographical advantages of Tibetan Plateau. This encouraging result undoubtedly accelerated the process of the project. Soon later, the China cosmic ray group and the Japan cosmic ray group were collaborated together to build an extensive atmospheric shower array in Yangbajing, Tibet, which took the detection of gamma-ray sources as one of the important scientific contents. This collaboration opened the development of particle detector arrays in China. After entering the atmosphere, high-energy gamma rays will induce extensive atmospheric cascade showers, and the number of secondary particles increases rapidly with the development of the shower. However, when it reaches the maximum, the number of particles begins to decrease. The ground-based particle detector array can reconstruct the direction and energy of primary particles by measuring secondary particles. At the position of the shower maximum, the fluctuation of the number of secondary particles is the smallest; therefore, it is the best detection position for ground-based particle arrays. The maximum position of showers caused by PeV gamma rays is about 4500 m above sea level (a.s.l.). At the same time, such a high altitude is also more conducive to the detection of low-energy gamma ray. Therefore, when detecting gamma rays, ground-based particle arrays generally need to be built at an altitude of more than 4000 m a.s.l.. In addition, at such a high altitude, the construction and maintenance of the detector should also be considered, which requires convenient transportation and power supply. The operation of ground-based particle arrays is not affected by the weather and can work 24 h a day. It also has a large field of view. All the overhead sky region with zenith angle less than 50◦ can be observed at any time. With the daily rotation of the Earth, it can cover a wider sky region. These are different from the imaging atmospheric Cherenkov telescope (IACT), which usually has a 3◦ to 5◦ field of view of and can only work on a clear and moonless night. The particle array can carry out sky surveys in a large sky region and also has technical advantages for the observation of extended sources and long-term monitoring of variable sources. These characters surely make up for the shortcomings of IACTs due to the narrow field of view. At the same time, the particle array can also measure higher-energy gamma rays and extend the observation to the ultra-high-energy regime (UHE, >0.1 PeV). In the following content, we will introduce the three-generation particle detector arrays established in China at high altitude areas and their physical achievements. The scientific objectives of ground-based particle arrays mainly include two research areas: cosmic ray physics and gamma-ray astronomy. Limited by the objective of this book, we will only introduce the achievements in gamma-ray astronomy in the following content.

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Progress of the Particle Detector Array in China Yangbajing International Cosmic Ray Observatory (90.522◦ E and 30.102◦ N) is located in an intermountain basin in the southeast of Nianqing Tanggula Mountain, 90 km northwest of Lhasa, the capital of Tibet Autonomous Region, on the Tibetan Plateau. At an altitude of 4300 m, it has flat and open terrain, mild climate, no accumulated snow, and smooth traffic all the year-round and is adjacent to geothermal power plants and a permanent residential area. These made the Yangbajing International Cosmic Ray Observatory the best high-altitude cosmic ray observatory in the world at that time. The Tibet ASγ experiment, the result of a collaboration among Chinese and Japanese institutions, adopt plastic scintillator detectors to detect EAS by sampling. The detector construction started in 1989, and the first batch of detectors began to operate in 1990. Since then, the particle array has been expanded or encrypted three times. In 1999, the gamma-ray emission from the Crab Nebula was successfully detected at the 3–30 TeV (Amenomori et al. 1999). Therefore, the Tibet ASγ experiment became the first particle detector array to detect the gamma-ray source. At the same time, the threshold energy of the particle array was reduced from about 100 to 3 TeV, which clearly shows the advantage of high altitude. Hereafter, the ground-based particle array aiming at gamma-ray astronomy has taken high altitude as the standard for selecting the site. In 1989, the Whipple experiment, an imaging atmospheric Cherenkov telescope (IACT), successfully discovered the first TeV gamma-ray source, the Crab Nebula (Weekes et al. 1989), marking the beginning of the very high-energy (VHE) gammaray astronomy era. In the following 14 years, the number of VHE gamma-ray sources increased to be about ten, contributed by many IACTs in the world. The Compton Gamma-Ray Observatory (CGRO) satellite launched in 1991 realized the full-sky survey for high-energy gamma ray for the first time. The gamma-ray detector EGRET onboard CGRO observed 271 high-energy gamma-ray sources at energy above 100 MeV (Hartman et al. 1999), which guide us look sight into the high-energy phenomena of the universe and also provide an important motivation for ground-based detectors to carry out gamma-ray sky survey at VHE. In this context, China and Italy have cooperated to start another project ARGO-YBJ at Yangbajing observatory. The ARGO-YBJ detector adopted a single layer of Resistive Plate Chambers (RPCs), developed by Italian collaborators, to detect the secondary particles of air shower with almost full coverage. This detector can almost fully collect the secondary particles compared to the traditional sampling method. With the help of both full coverage and a high altitude, the energy threshold is further reduced to 100 GeV, which is comparable with the energy range of space-based detectors. The sensitivity for gamma rays is also improved. The ARGO-YBJ experiment began long-term stable operation at the end of 2007. It has realized continuous observation of the active galactic nucleus Mrk 421 at VHE band for 5 years, and the evolution of the multiwave band radiation spectrum was systematically studied, combined with the observations of Fermi-LAT and X-ray satellites (Bartoli et al. 2016). In addition, the ARGO-YBJ has also made important

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measurements on Galactic plane diffuse gamma-ray emission and several extended VHE sources. These results surely exhibit the important role of particle detector arrays in VHE gamma-ray astronomy due to the characteristics of large field of view and full duty cycle, which is a crucial complement to the technology of IACT with a narrow field of view. During the construction of ARGO-YBJ, the second-generation IACTs, such as H.E.S.S., MAGIC, VERITAS, and CANGROOIII, began to operate since 2003. Compared with the first-generation IACTs, their angular resolution and sensitivity have been greatly improved. After several years of accumulation, the number of detected VHE gamma-ray sources has increased to more than 100, which has greatly promoted the development of VHE gamma-ray astronomy. Compared with the great success of IACTs, the contribution of ground-based particle detector arrays in gamma-ray astronomy is dwarfed. The main bottleneck of Tibet ASγ and ARGOYBJ particle arrays is that they cannot distinguish between gamma rays and huge cosmic ray backgrounds, which significantly limits their sensitivity. Previously, although it was well known that detecting muons in showers can effectively eliminate the cosmic ray background, muon detectors need to be covered by a thick shielding layer and have a large detection area, which makes the cost of detectors much more expensive. Therefore, muon detectors were not widely used in early particle arrays. With the success of Milagro water Cherenkov detector array, water, as a cheap detector medium, began to be widely used in cosmic ray experiments. About in 2006–2009, the ASγ collaboration proposed the upgrading plan of ASγ array (Sako et al. 2009). The key point is to construct 10,000 m2 underground water Cherenkov detector as a large-area muon detector to eliminate cosmic ray background. The main goal is to realize the detection of 100 TeV gamma rays. In 2013, the ASγ collaboration completed only 4 of the 12 underground water pools originally planned. In 2019, the Crab Nebula was clearly detected as a >100 TeV gamma-ray source for the first time (Amenomori et al. 2019). Based on the experience of Tibet ASγ and ARGO-YBJ experiments, China’s cosmic ray group in IHEP, CAS, proposed a more ambitious plan for the nextgeneration particle detector array in 2009 (Cao 2010), i.e., the LHAASO project. LHAASO includes three sub-arrays, two of which are mainly for VHE and UHE gamma-ray detection, respectively. The sub-array WCDA adopts large-area water Cherenkov detection technology and are mainly for VHE gamma-ray detection. The detector area is four times of HAWC experiment. The sub-array KM2A adopts a scintillator to detect shower particles and an underground water Cherenkov detector to detect the muons of the shower. This array covers an area of 1.3 km2 , which is 20 times the area of ASγ array. Its sensitivity for UHE gamma-ray sources is about ten times of the upgraded ASγ experiment. The LHAASO detectors were completed in July 2021. A breakthrough in UHE gamma-ray astronomy has been made by LHAASO by detecting 12 UHE gamma-ray sources with gamma-ray energies exceeding 1 PeV. Figure 1 shows the sensitivity of major ground-based gamma-ray detectors in the world. The sensitivity and energy range of the three-generation experiments constructed in China are clearly exhibited. Compared with the primary ASγ

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10−10 ARGO-YBJ −11

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detector, the sensitivity of upgraded ASγ is improved by a factor of 10 at energies above 10 TeV, and the LHAASO detector improves the sensitivity by a factor of 100. At energies around 1 TeV, the sensitivity of LHAASO is also about 100 times higher than that of ARGO-YBJ. In the following, the details of the experiments, performance, and scientific achievements of Tibet ASγ , ARGO-YBJ, and LHAASO will be introduced.

Tibet ASγ The Tibet ASγ experiment utilizes a plastic scintillator detector, and its structure is an inverted pyramid, as shown in Fig. 2. The size of the plastic scintillator is 70.7 × 70.7 × 3 cm. The scintillator is covered by a 5-mm-thick lead plate to absorb low-energy charged particles in showers and convert gamma rays into electronpositron pairs, which can improve the angular resolution of the array by a factor of 1.5. When charged particles or gamma rays pass through the scintillator, atoms or molecules in the scintillator are ionized and excited, and fluorescence photons are

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707mm (Scintillator) 9mm plywood 5mm Thick Lead 30mm Scintillator

Painted by VH white enamel

1mm stainless steel

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Fast Timing (FT) PMT

Denisty (D) PMT H.V. cable

Signal cable Fig. 2 The structure of the scintillator detector used in the Tibet ASγ experiment. (This figure is taken from Zhang 2008)

emitted in the process of de-excitation. A stainless steel light guide box is under the scintillator, which transmits the scintillation light to the photomultiplier tube (PMT) at the bottom. The PMT is used to record the arrival time and number of particles. In order to improve the uniformity and collection efficiency of scintillation light, the inside walls of the light guide box is coated with white enamel. The lower surface of the scintillator is rough, so as to enhance the scattering and reduce the reflection of scintillation light. The whole detector is covered with a layer of white plastic film, which is used to reflect sunlight and reduce the variation of internal temperature of the detector. Figure 2 shows the structure of a single scintillator detector. ASγ detectors can be divided into three types according to the PMT and it is equipped with Zhang (2008). The first type is the fast-time (FT) detector, which adopts the Hamamatsu H1161 PMT to measure the arriving time of each hit. At the same time, it can also record the number of secondary particles hitting the detector, with a dynamic range of 1–30 particles. The second type is the fast-time and wide-range density detector. It is equipped with two PMTs, namely, Hamamatsu H1161 and Hamamatsu H3178. It can record the time of each hit and corresponding number of secondary particles with a dynamic range of 1–10,000 particles. The

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third is the density detector equipped with two PMTs, namely, Hamamatsu H1949 and Hamamatsu H3178. It can measure the number of secondary particles with a dynamic range of 1–10,000 particles. The hits recorded by FT-type detectors are used for trigger selection. The Tibet ASγ experiment is triggered when any four hits from FT-type detectors are registered within 600 ns. The construction of Tibet ASγ experiment started in 1989. The first 65 detectors, covering an area of 7650 m2 , were put into operation in 1990. The array is denoted as Tibet I. In 1995, the number of detectors was expanded to 221 with a spacing of 15 m. The area was 36,900 m2 , which was denoted as Tibet II. In 1996, 168 detectors were added to encrypt an area of 5175 m2 in the northwest corner of the Tibet II array. The interval between detectors was reduced to be 7.5 m, denoted as Tibet HD. This encryption lowered the mode energy of the array to 3 TeV. The event rate of the array was 110 Hz. The angular resolution was 0.8◦ . With this Tibet HD array, the gamma-ray emission from Crab Nebula was detected with a significance of 5.5σ (Amenomori et al. 1999). This is the first time for the ground-based particle detector array to successfully detect gamma-ray signals. Later, a gamma-ray signal from Mrk 501, an active galactic nucleus (AGN), is also detected with a significance of 4.7σ in 1997 during a huge flare (Amenomori et al. 2000). This is also the first time for the ground-based particle detector array to successfully detect extragalactic gamma-ray signals. In 1999, the encrypted area was further enlarged to 22,050 m2 , and the number of detectors was 533, which was denoted as Tibet III. Figure 3 shows the layout of the array. The event rate of the array is 680 Hz. Based on this array, the emission of AGN Mrk 421 was observed with a significance of 5.1σ during

Fig. 3 Tibet III detector layout. Open squares are FT-type detectors equipped with a fast-timing (FT) PMT. Filled squares are FT detectors with a wide dynamic range PMT. Filled circles are density detectors with a wide dynamic range PMT. The area enclosed by the dotted line outlines the fiducial area for shower core selection used by the ASγ collaboration. (This figure is taken from Amenomori et al. 2003)

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its activities in 2000 and 2001 (Amenomori et al. 2003). The observed emission above 3 TeV is clearly correlated with the flux variation at X-ray band. In 2003, the encrypted area was enlarged to 36,900 m2 . Finally, the total number of detectors was 789 with a spacing of 7.5 m. The event rate of the array was 1700 Hz and the mode energy was 3 TeV. With this configure, the observation significance of the Crab Nebula reached to 6.9σ , while no other source was detected by the Tibet ASγ experiment with significance above 5σ (Amenomori et al. 2010). The Tibet ASγ experiment adopts a traditional particle detector array, with an area of 0.5 m2 for each detector and detector spacing of 7.5 m. The sampling proportion of shower is 1/100, which is higher than that of the previous similar detector arrays. At the same time, the Tibet ASγ array is located at a high altitude of 4300 m a.s.l.. These two characteristics lower its threshold energy to 3 TeV and also make it become the first particle detector array to detect gamma-ray sources. These achievements are important in the history of the development of groundbased particle detector arrays. The Tibet ASγ experiment exhibits the advantage of high altitude in ground-based gamma-ray observations. Hereafter, similar detectors such as ARGO-YBJ, HAWC, and LHAASO are located at an altitude of more than 4000 m a.s.l. The Tibet ASγ experiment adopted a single type of scintillator detector, which cannot distinguish between gamma rays and a large number of cosmic ray background. This shortcut significantly limits the sensitivity for gamma-ray observations. In 2006–2009, the Tibet ASγ collaboration proposed the upgrading plane, denoted as Tibet ASγ +MD (Sako et al. 2009). The crucial point is to build water Cherenkov detectors under the scintillator array as large-area muon detectors (MDs) to eliminate the cosmic ray background. The main scientific motivation is to detect gamma rays with an energy around 100 TeV. The MD is buried below 2.4 m of soil, which can shield a large number of the secondary electrons/positrons and gamma rays in showers and retain muons with energy above 1 GeV to pass through. The MD adopts modular design. Each module is a 30 × 30 × 1.5 m water tank and then divided into detection units, i.e., 16 7.5 × 7.5 × 1.5 m. After deducting the wall, the detection area is 7.35 × 7.35 m. The surrounding walls are coated with a white Tyvek film to reflect Cherenkov photons generated by the muon in the water. A 20-inch PMT facing down is placed on the top of each unit to detect Cherenkov photons; thus, the muon signal is recorded. In 2014, the Tibet ASγ collaboration built four underground water tanks, namely, 64 MD units, and began scientific data collection. Based on the measurement of muons by MD, the gamma-ray and cosmic ray backgrounds can be distinguished. Figure 4 shows the comparison between gamma rays and cosmic rays. Based on the number of muons, 99.92% of the cosmic ray backgrounds can be excluded at energy above 100 TeV. Based on 719 days of effective observation data from February 2014 to May 2017, the Tibet ASγ collaboration observed 24 photon-like events with E > 100 TeV against 5.5 background events, which corresponds to a 5.6σ statistical significance (Amenomori et al. 2019). This is the first detection of photons with E > 100 TeV from an astrophysical source. Figure 5 shows the angular distribution of the detected photons from the Crab Nebula direction. Based on the same data, the

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Tibet ASγ collaboration also detected Galactic plane diffuse gamma-ray radiation at energies above 100 TeV (see Fig. 6) (Amenomori et al. 2021). This provides evidence that cosmic rays are accelerated beyond PeV energies in our Galaxy.

ARGO-YBJ The ARGO-YBJ experiment, the result of a collaboration among Chinese and Italian institutions, is also located at the Yangbajing International Cosmic Ray Observatory, close to the Tibet ASγ experiment. Figure 7 shows the picture of the Yangbajing International Cosmic Ray Observatory with two experiments. The ARGO-YBJ detector consists of a single layer of Resistive Plate Chambers (RPCs), which are a gas detector operated at streamer mode and organized with a modular configuration (Aielli et al. 2006). The basic module is a cluster (5.7×7.6 m) composed of 12 RPCs (2.850×1.225 m each). The RPCs are equipped with pickup strips (6.75×61.80 cm each), and the logical OR of the signal from eight neighboring strips constitutes a logical pixel (called a “pad”) for triggering and timing purposes. One hundred thirty clusters are installed to form a carpet of about 5600 m2 with an active area of 93%. This central carpet is surrounded by 23 additional clusters (a “guard ring”), with an active area of 22%, to improve the reconstruction of the shower core location. The total area of the array is 110 × 100 m. The whole detector array is inside a huge hall, which can shelter RPCs from wind and rain and keep the inside temperature not too low in winter due to the temperature requirement of RPCs for normal working. In order to increase the number of measured particles and extend the energy range to the knee region, two large pads are set for each RPC under the air chamber, which use analog readout signals. The maximum number of particles measured by each large pad can exceed 1000. The layout of the whole detector is shown in Fig. 8.

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Fig. 5 Angular distribution of events from the Crab direction detected by the Tibet ASγ experiment. (This figure is taken from Amenomori et al. 2019)

RPC is the basic detector entity of the ARGO-YBJ array. In the middle of RPC is a 125 × 280 × 0.2 cm air chamber. The upper and lower parts of the air chamber consists of two 2-mm-thick Bakelite plates. These plates have a high resistivity (4.9×1011 .cm). The outer surface is coated with a layer of conductive graphite layer as two electrodes. The upper electrode is grounded, and the lower electrode is with high voltage, which form a strong electric field in the RPC chamber. Outside the graphite layer, there is a 200-µm insulating layer, and then a signal reading strip is arranged on it with an interval of about 3 mm. A ground wire is embedded between the intervals to reduce the interference of signals between the reading strips. Two large 20-µm-thick copper foil plates are laid under the lower insulating film as large pad readout plates. The whole system is contained in an aluminum box, and the aluminum shell is grounded, which can shield the external electromagnetic radiation and internal streamer discharge. At the same time, the aluminum plate frame also plays a role in protecting the internal electronics and air chamber.

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(a) 25º 15◦ and excluding the areas near the Large and Small Magellanic clouds, out of about 106,500 sources, at least 10% of them have a galactic object (i.e., with a detectable proper motion) as a counterpart (Salvato et al. 2018). The RASS X-ray sources associated with stars/YSOs dominate the galactic plane region and overall about 30% are stars/YSOs (Schmitt 1999 and references therein). With the RASS a widespread population of active, X-ray luminous, stars have been found not only within or in proximity of known SFRs, but also rather far away from them (a detailed account is provided by Neuhäuser (1997) and references therein). This was perceived as a major surprise, even if the analysis of the stellar content of the EMSS (Extended Medium Sensitivity Survey) (Gioia et al. 1984; Fleming et al. 1988) based on the lithium abundances derived from high-resolution optical spectra (Favata et al. 1993) and on the modeling of the X-ray stellar content of the Galaxy, X-Count (Based on a modified version of the Bahcall and Soneira, thin-disk population model (Bahcall and Soneira 1980)) (Favata et al. 1992; Sciortino et al. 1995), has had already shown the existence of a stellar population with an age of about 100 Myr (Pleiades-like or ZAMS) and a ∼100 pc vertical scale height. The Hipparcos distances of the EMSS stars have shown that, in majority, they are main-sequence stars (Micela et al. 1997). X-Count predicted their presence in any X-ray survey (Micela et al. 1993). The nature of this widespread stellar population has been debated between those that claimed to consist of weak-lined

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T Tauri stars (i.e., Class III YSOs) (e.g., Krautter et al. 1997) and others that instead show compelling evidence that most of them should be explained with a ZAMS population, still young, but no so-young as for the case of the putative Class III YSOs (Favata et al. 1997; Briceno et al. 1997; Micela et al. 1997). The analysis of the stellar sample selected by cross-correlating the RASS and the Tycho catalogues (Fig. 2) has confirmed the existence of a galactic density gradient from the plane to the pole (Guillout et al. 1998a, b) predicted by X-Count and by another, independently developed, age-dependent stellar population model (Guillout et al. 1996). More surprising was the occurrence of a low galactic latitude feature asymmetric with respect to the galactic plane and located between l = 15◦ and l = 195◦ , where the concentration of X-ray active, very young late-type stars (Log LX [erg/s] = 29.5 – 30.5) is higher than expected. Such an excess was interpreted as due to young late-type (mostly F and G) stars belonging to the so-called Gould Belt or ring (It could be a ringlike structure of which we recognize only the part nearest to the Sun.) (Guillout et al. 1998a). This structure encompasses several star formation sites and very likely hosts a population of bona fide Class III YSO, while most

Fig. 2 Galactic coordinated all sky representation of the 8593 RASS sources (black dots) – at the limiting fX ∼ 2 10−13 erg/s/cm2 – having as counterpart one of the Tycho catalogue stars. Note the density enhancement at low galactic latitudes and the asymmetry with respect to the galactic plane. The dashed line indicates the position of the Gould Belt, while the solid line is the best fit to the density of matching stars using an exponential flat disk distribution. Black circles indicate the positions of the more conspicuous young open clusters and SFRs that show up in the RASSTycho sample. Note the enhancement between IC 2602 and Lupus-Centaurus toward the Lower Centaurus Crux OB association. (Adapted from Guillout et al. 1998a)

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of the widespread population consists of near ZAMS stars. The lithium abundances derived from high-resolution spectra provided convincing evidence that the ROSATdiscovered stars near the Lupus SFR are Class III YSOs (Wichmann et al. 1999). As extensively discussed in this study, the area around the Lupus is very likely the best place to find as clean as possible a population of bona fide WTTS, while around other nearby SFRs like Chameleon, Taurus-Auriga, etc., the situation is much less favorable and substantial intermixing of ZAMS stars and bona fide YSOs occurs. In this scenario, the solar neighborhood would be located in a region of the Galaxy characterized by a high spatial density of young stars. The origin of the (young) flare stars around the Sun is an old astrophysical problem (Ambazsumian 1955) connected to the characteristics of the birth environment of the solar system (cf. Adams (2010) for a pre-GAIA review). The RASS and follow-up observations provided additional hints for a tentative explanation on the nature of the nearby stellar population. However, the recent GAIA results are challenging the paradigm of the nearby (distance 1031 ergs/s) protostars are rare. No bona fide Class 0 YSO was found to emit X-rays. There have been attempts to explore the effectiveness of X-rays in tracing the low- and intermediate-mass SFRs at distances >1 kpc (Gregorio-Hetem et al. 1998). In this study, plausible optical counterparts were found for most of the ROSAT sources, except for about 25% of them that are probably embedded in the clouds. Near-IR data were consistent with the sources being YSOs with LX in the 1030 –1032 erg/s range, like in the nearby SFRs. The detection of individual YSOs confirmed that X-rays do efficiently trace low- and intermediate-mass star formation at significant distances across the Galaxy. The limited PSPC angular resolution resulted in source confusion from groups of embedded sources, as it was already the case in the ρ Oph core F. Source confusion was problematic in the center of the most crowded regions, like the Orion Trapezium (Gagne et al. 1995), even if the observations were performed with the HRI having an angular resolution of ∼5′′ . Last, but not least, both ROSAT and Einstein were operating on a low-earth orbit with a period of about 1.5 h, and then data gathering has to stop during each south-Atlantic anomaly passage because of elevated particle background; hence, continuous uninterrupted observations were rather short (∼1 h) clearly affecting the studies of YSO variability, a clear signature of their X-ray emission known since the Einstein observations. An illustrative example is provided by the ROSAT HRI study of the Orion Nebula Cluster (ONC) region (cf. Fig. 11 in Gagne et al. 1995) where ten low-mass YSOs have shown evidence of intense flare-like variability. The short duration of the observation windows prevented to observe in five YSOs the flare rise and in two more YSOs the end of flare decay, and all light curves were affected by substantial data gaps. In two cases – P1846 (LY Ori, K7e) and P1977 (AG Ori, G8-K0e) – the inferred rise times were 8 and 9 ks and the decay times 35 and 45 ks, respectively; these values are at odds with those of solar flares and pose the question of these flare nature. The characteristics and nature of the magnetic structures where the YSO flares occur are a question that only the Chandra data have permitted to investigate (see section “The YSO Flares: Nature and Effects on Circumstellar Disks”).

ASCA: Looking for X-Rays from Class I and Class 0 YSOs In 1993, the Japan-US X-ray mission ASCA has provided, for the first time, CCDresolution (∼150 eV) time-resolved X-ray spectra of a few nearby YSOs up to the Fe 6.7 keV line and even above. Several ASCA observations have investigated the onset of the (hard) X-ray emission among Class 0 and Class I YSOs, something that was impossible with ROSAT whose sensitivity drops above ∼2.4 keV. However, even in the nearby SFRs, a limiting factor was the angular resolution (2.9 arc-min, HEW) (This was mitigated by the mirror point spread function shape with a sharp central peak that has allowed to distinguish two sources with a separation of ∼0.5 arc-min).

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Several observations have surveyed the core of nearby molecular clouds hosting groups of YSOs in several SFRs: R Cra, L1630, the core F of ρ Oph, Monoceros R2, NGC 2023 and NGC 2024, and two cores in the Perseus complex. About ten pointlike sources have been typically detected in each observation, most of them have had as counterpart one or more YSOs of Class I or II and more rarely of Class III. Several Class 0 YSOs were observed and, notwithstanding the amount of devoted observing time, no bona fide Class 0 YSO was detected. In R CrA hard X-ray emission from Class I YSOs has been found for the first time (Koyama et al. 1996). The quiescent X-ray spectrum was modeled as an absorbed (NH = 4.2 × 1022 cm−2 ) thermal bremsstrahlung (kT = 7.2 keV) plus a line emission at 6.45 keV. In ρ Oph during a flare that occurred on the Class I YSO Elias 29, the spectrum has shown a factor 10 increase in the absorbing column (NH ), consistent with a scenario in which the flare emission comes from a more “external” region than the one emitting the quiescent emission and is affected by additional absorption due to an anisotropic distribution of circumstellar matter, like in the case of a circumstellar disk. In YLW 15, a Class I YSO in ρ Oph previously detected with the ROSAT HRI (Grosso et al. 1997), three subsequent flares occurred every ∼20 h have been detected. The last two flares were consistent with the reheating of the same magnetic structure hosting the first flare due to the interaction between the star and the disk as a result of the differential rotation (Tsuboi et al. 2000; Montmerle et al. 2000). The ASCA observations have shown that the X-ray emission mechanism from Class I and II YSOs during the quiescent state requires plasmas with kT  6 keV, but keeping almost the same LX /LBol ratios typical of Class III YSOs. The enhanced disk-magnetosphere interaction model (Shu et al. 1997) was suggested to account for such high-temperature plasmas. The observed hard X-ray flares were consistent with a model based on a magnetic loop connecting the central star and its disk (Hayashi et al. 1996). Still today their existence is an intriguing, and controversial, issue (see section “The YSO Flares: Nature and Effects on Circumstellar Disks”).

The Transformational Impact of Chandra and XMM-Newton The boost of observational capabilities enabled by Chandra and XMM-Newton has made it possible to perform up to ∼150-ks-long uninterrupted high-sensitivity observations with energy resolution of ∼100 eV and angular resolution of 0.5– 10 arc-s over field of view (FOV) ranging from ∼0.08 to 0.18 sq. deg. Time-resolved X-ray CCD spectroscopy of YSOs in SFRs up to a distance of a few kpcs has become possible and, together with high-resolution X-ray spectroscopy of a handful of nearby YSOs, has had a profound impact on our knowledge. Thanks to Chandra superb PSF, the sensitivity and angular resolution have allowed us to survey SFRs up to distances of ∼4 kpc, even in their denser subgroups (Fig. 3). These data have given rise to transformational investigations along two major avenues: (1) the study of the processes originating the YSO X-ray emission and their changes with evolution, something that was started before but mostly left unsolved,

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Fig. 3 (Left ACIS view of NGC 2264. The RGB image is obtained from data in three energy bands: [200:1150] eV (red), [1150:1900] (green), and [1900:7000] (blue). Soft and unabsorbed sources are shown in red, while hard and/or absorbed sources in blue. (Right) XMM-Newton-EPIC false-color image toward the core F of the ρ Oph SFR. The image is obtained by summing together the 500 ks DROXO and 350 ks Elias-29 joint NuStar-XMM-Newton Large projects data. High background time interval has been screened out

and (2) the study of the complex processes that result in star cluster formation, especially of those hosting OB stars, that was essentially impossible before. The former has been tackled already with the very early observations and has been mostly based on the SFRs within ∼1 kpc, while the latter has emerged more vigorously when enough data have been available and uniformly analyzed and has been based on a much larger number of SFRs up to ∼4 kpc. A crucial role has been played by optical/IR/NIR observations that have enabled a successful multiwavelength approach. The shape of the star cluster mass function, dN/dM ∼ M −2 , implies that >50% of stars form within massive SFRs containing OB stars where rich clusters born, likely constituting the main mode of star formation in the Galaxy. In the early 2000s, several aspects of the stellar cluster formation were poorly known or controversial, as discussed in various reviews and papers (Lada and Lada 2003, Allen et al. 2007, Kennicutt and Evans 2012, Motte et al. 2018, Feigelson et al. 2013 and references therein). Let me recap a few of them: (i) the effect of the new born OB stars on cloud ionization and dispersal (Bate 2009; Howard et al. 2016; Rumble et al. 2021); (ii) the duration of star formation with the two alternative scenarios of a very rapid star formation (Elmegreen 2000), and of a star formation process progressing actively for millions of years (Tan et al. 2006); (iii) the issue of rich cluster formation as a global process or as the result of the merging of smaller groups (McMillan et al. 2007; Maschberger et al. 2010); (iv) the origin of the age spread often found in the Hertzsprung-Russell diagram (Baraffe et al. 2009; Hosokawa et al. 2011; Jeffries et al. 2011; Jensen and Haugbølle 2018; Prisinzano et al. 2019) and its relation to

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the duration of star formation process; (v) the relevance of HII region expansion in triggering star formation (e.g., Ogura et al. 2007; Getman et al. 2009); (vi) the most relevant mechanism of massive star formation among the many proposed: monolithic collapse, stellar mergers, rapid disk accretion, and competitive accretion (cf. (Motte et al. 2018) and references therein); (vii) the effect on protoplanetary disk survival of the massive star irradiation (Johnstone et al. 1998; Ercolano et al. 2008; Gorti and Hollenbach 2009) and/or stellar density (e.g., Clarke and Pringle 1993; Thies et al. 2010) within rich clusters. For decades cluster formation studies have been hampered by the observational difficulty to obtain a reliable and unbiased member census. At low galactic latitude, in the optical, (older) field stars have a surface density 10–100 times higher than SFR members at the peak of their IMF, while AV can be as high as 30 and can vary by tens of magnitudes within a given SFR. YSOs are difficult to detect as faint infrared objects toward the background emission due to heated dust in HII nebulae. As a result, often only the SFR bright cores, where stellar density is very high, have been identified, and the OB stars have been recognized by their color and affordable spectroscopic studies; instead low-mass YSOs have been identified by their photometric infrared excess due to the circumstellar disk. This procedure recognizes the disk-bearing YSO members, but fails to select the, usually, larger population of YSO members that have already lost (most of) their circumstellar disk. This latter population is “easily” selected with medium-deep imaging X-ray observations because the low-mass YSO X-ray luminosity is at least 3 dex higher than the low-mass field stars (The contaminant AGNs seen through the galactic plane can be discarded since they lack the infrared counterparts). In a 100 ks Chandra observation of a SFR at a distance of 2–3 kpc, about 1–2 103 YSO members are typically detected allowing to sample the IMF typically down to ∼0.5 M (e.g., Damiani et al. 2004) and even to BDs in the nearby SFRs (e.g., Imanishi et al. 2003) or farther away in deeper observations (e.g., Preibisch et al. 2005b). With a judicious combination of X-ray and IR-selected YSO members, recent and ongoing studies based on almost unbiased samples have been possible. New avenues to investigate some of the questions on cluster formation process have recently been opened by GAIA (Brown 2021). The quality of DR2 and EDR3 GAIA data allows, within ∼1 kpc, detailed studies of the low-mass, down to ∼0.1 M , star population of the young clusters and stellar associations. On the other hand, given the GAIA bandpass, the very young, more absorbed and/or more embedded, stellar population is much more difficult to recognize and characterize (cf. Prisinzano et al. 2022). As an example, in the case of NGC 2264 with the EDR3 data, about 50% of the very likely members selected/confirmed by X-ray and IR data are recovered as members, and a sizeable fraction of the embedded ones are missed ((Prisinzano et al. 2022) as well as an ongoing analysis by E. Flaccomio). This effect is expected to become more consistent as the young cluster/SFR distance increases. In summary, while GAIA is adding and will add superb pieces of information on the study of cluster formation, still X-ray and IR surveys will continue to play a relevant role to build as much as possible an unbiased low-mass member list of young clusters/SFRs beyond ∼0.5–1 kpc.

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A first round of Chandra studies, usually based on 50–100-ks-long ACIS observations, has concentrated on the Orion Nebula Cluster (ONC) region (Garmire et al. 2000; Feigelson et al. 2002, 2003; Flaccomio et al. 2003a, b), Orion outer regions (Ramírez et al. 2004b), NGC 1333 (Getman et al. 2002), RCW 38 (Wolk et al. 2002), W3 (Hofner et al. 2002), OMC 2 and OMC 3 (Tsuboi et al. 2001; Tsujimoto et al. 2002), the ρ Oph core (Imanishi et al. 2001, 2003), Mon R2 (Kohno et al. 2002; Nakajima et al. 2003), Sgr B2 (Takagi et al. 2002), NGC 2264 (Ramírez et al. 2004a; Flaccomio et al. 2006; Rebull et al. 2006), M17 and Rosette (Townsley et al. 2003), Lagoon (NGC 6530) (Damiani et al. 2004, 2006), Trifid (Rho et al. 2004), NGC 2068 (Grosso et al. 2004), and Sh 2-106 (Giardino et al. 2004). In the same years, the XMM-Newton/EPIC studies of nearby SFRs or young associations deserve attention such as L1551 (Favata et al. 2003), NGC 1333 (Preibisch 2003b), Serpens (Preibisch 2003a), Chameleon I (Stelzer et al. 2004; Telleschi et al. 2006; Robrade and Schmitt 2007), ρ Ophiuchi (Ozawa et al. 2005), and Upper Sco (Argiroffi et al. 2006). In a 100ks ACIS observation toward the ρ Oph central region, ∼100 sources with LX > 1028 erg/s have been found, and about 65% have optical/IR counterparts with a substantial number of Class I to Class III YSOs and few brown dwarfs (Imanishi et al. 2001). About 70% of Class I YSOs have been detected and about 40% of the brown dwarfs have been detected with Log (LX /LBol ) ∼ −5 to −3, similar to the values of main-sequence stars. In YLW 16A, a Class I YSO, for the first time, a neutral Fe fluorescent line at 6.4 keV has been firmly detected. The line equivalent width (EW) requires an origin from circumstellar gas distributed with a nonspherical geometry as for a face-on circumstellar disk. Combining the data from a later ACIS observation of the same region, a total of 195 sources with 71 X-ray flares have been found in YSOs and brown dwarfs (Imanishi et al. 2003). Most of them have the typical solar flare shape with fast rise and slow decay, except a few bright flares with unusually long rise phase. By modeling the spectra and light curves, the time-averaged temperature (kT ), luminosity (LX ), and rise and decay timescales (τrise and τdecay ) have been derived showing that Class I–II YSOs have usually high kT , in some case up to 5 keV; the Log LX [erg/s] distributions during flares span the 29.5–31.5 range for all YSO classes, with a marginal evidence of higher LX among Class I YSOs; positive and negative log-linear correlations have been found between τrise and τdecay , and kT and τrise . Assuming that the emission is due to magnetic reconnection within a magnetic loop in the presence of heat conduction and chromospheric evaporation, those correlations are, in most of the cases, consistent with nearly the same loop length, of the order of the central star radius (1010 –1011 cm), for all YSO classes, regardless of the existence of an accretion disk. However, a few flares on ROX 31 and YLW 16A with larger rise timescale (∼104 s), require longer loops with length up to 1012 cm (i.e., of the same size of the co-rotation radius). Thanks to a 100-ks-long ACIS observation toward NGC 2264, a total of 420 X-ray point-like sources have been detected, 85% with optical and NIR catalogued counterparts. Given their LX values, more than 90% of identified X-ray sources are NGC 2264 members, thereby significantly increasing the known low-mass

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member population by about 100 YSOs (Flaccomio et al. 2006). About 50% of X-ray sources without counterparts are likely associated with members, most of which previously unknown (obscured) YSOs. X-ray activity has been investigated as a function of stellar and circumstellar characteristics by correlating the X-ray luminosities, temperatures, and absorptions with published optical and NIR data. This analysis has confirmed previous findings: LX is related to stellar mass, although with a large scatter; except during some flares, Log (LX /LBol ) is close to, but always below, the −3 saturation level. A comparison between Class I–II and Class III YSOs shows several differences: the former have, at any given mass, activity levels that are both lower and more scattered than the latter; emission from Class I–II may also be more time variable and is on average slightly harder than for Class III. In some Class I–II YSOs, there is evidence of extremely cool, ∼0.1–0.2 keV, plasma which is consistent with being heated by accretion shocks and emitted by plasma at higher density, ne ∼ 1011 – 1013 cm−3 , than the coronal one as it has been found in TW Hya (Kastner et al. 2002) and in other YSOs. This emission component has been recently reviewed by Argiroffi (2019). The very young cluster NGC 6530 in the Lagoon Nebula has been the target of a 60-ks-long ACIS observation; 884 X-ray point sources have been detected, and 90%–95% are likely members, mostly low-mass YSOs resulting in a substantial increase of the NGC 6530 YSO population with respect to previous optical and Hα surveys (Damiani et al. 2004; Delgado et al. 2006). Only ∼25% of the X-ray sources have a counterpart down to V = 17, mostly having fainter counterparts, and 2MASS IR counterparts have been found for ∼83% of the X-ray sources. The H-R diagram of the optical counterparts shows that they are above the main sequence and fall in the locus of 0.5–1.5 Myr YSOs, with masses down to 0.5–1.5 M . An age gradient from north-west to south is evident and is qualitatively consistent with a sequence of star formation events reported in earlier studies. By combining the Chandra, optical, and 2MASS data and considering various different indicators of IR excesses and reddening-free indices, 333 YSOs with optical-IR excess have been found, 196 in the ACIS fov, and 76 undetected in X-rays. The total number of estimated cluster members thus has become ≥1100. The estimated disk frequency in the ACIS field was 20%. YSOs with optical-IR excess in the north of NGC 6530 are nearly cospatial with a subpopulation of older members than the ones in the cluster center. Hence, in these northern regions, far from massive cluster stars, star formation and disk evolution have proceeded almost undisturbed for a long time, while near the cluster center, where most massive stars are found, most of the members lack substantial disks and strong accretion. The Serpens dark cloud at a distance of ∼260 pc was studied with a deep XMMNewton/EPIC observation detecting 45 individual X-ray sources. Among their counterparts, only one Class I and two flat-spectrum YSOs have been found, but none of the Class 0 YSOs was detected (Preibisch 2003b). The core of the Serpens cloud was studied also with a 90 ks Chandra ACIS observations with the specific aim to search for the X-ray emission from the six known bona fide Class 0 YSOs falling in the ACIS FOV (Giardino et al. 2007a). None of them was detected, and their X-ray emission has remained undetected even by co-adding the data at the six

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individual Class 0 positions (reaching an equivalent observing time of ∼540 ks); the derived upper limit to the Class 0 source X-ray emission was LX < 4 1029 erg/s (for NH = 4 1023 cm−2 and kT = 2.3 keV). Such a value is below the typical persistent X-ray emission of the other YSOs in the region. Hence, either Class 0 X-ray emission is intrinsically much weaker or they are hidden behind an absorbing column density substantially higher than 4 × 1023 cm−2 , and/or, admittedly less likely, their X-ray emission is extremely variable. In the ONC ACIS-based study, more than 1000 sources have been found, 91% of them were known members ranging from brown dwarfs to O stars (Garmire et al. 2000; Feigelson et al. 2002, 2003). About 7% of X-ray sources were newly identified deeply embedded cloud members. For ONC sources, log LX,[0.5−8.0 kev] [erg/s] ranges from the sensitivity limit of ∼28 to 33.3, and absorption ranges from Log NH [cm−2 ] < 20.0 to ∼23.5. Thanks to the availability of bolometric luminosities, masses, ages, disk indicators, and rotational periods, it was concluded that the presence of rapid variability in 2 A Ori, a O9.5, 31 M , star, and in several early B stars, is at odd with a mechanism of X-ray production due to shocks distributed throughout the radiatively accelerated wind; the low-mass YSOs exhibit large flares but usually LX /LBol remain well below the saturation level; the YSO plasma temperature is often very high with T > 100 MK, irrespective of luminosity level and flare presence; a large number of very low-mass objects showing flares with intensity like for the ∼1 M YSOs were found, as well as evidence of the decline of the magnetic activity among L- and T-type brown dwarfs; LX is strongly correlated with LBol , and the average Log (LX /LBol ) value is −3.8 for YSOs with masses 0.7 < M < 2 M , about one order of magnitude below the main-sequence saturation level; LX /LBol drops rapidly below this value in some YSOs with 2 < M < 3M with no compelling evidence that the intermediate-mass (mid-B – A type) YSOs are by themselves significant X-ray emitters; LX shows, if any, a slight increase with rotational periods, in contrast to the strong LX decline with increasing period seen in main-sequence stars. This very different behavior indicates that the YSO mechanism of magnetic field generation is different from that operating in main-sequence stars (e.g., an α − Ω dynamo). One of the most promising possibilities was, and still is, the so-called turbulent dynamo distributed throughout the deep convection zone, but other proposed models are possible as well. The Chandra HRC-based study of ONC (Flaccomio et al. 2003a, b) has found, for the first time, convincing evidence of a dependence of LX and LX /LBol on circumstellar accretion indicators for which three tentative explanations have been advanced: (i) accreting YSOs are less active since they rotate slowly because of disk braking, while those accreting less can “freely” spin up and thus saturate their activity. Since no dependence on rotational period nor on Rossby number has emerged, this hypothesis lacks support unless assuming a strong bias on rotational data. (ii) Accretion and/or the presence of a disk and/or out-flows decreases the fraction of the stellar surface covered with the closed magnetic structures from which X-ray emission originates. A similar outcome would result from “nonstandard” geometry, as in the case of coronal structures extending to the inner part of disk (e.g., Montmerle et al. 2000). Because of the inhomogeneous and

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time-variable nature of accretion, variability studies and simultaneous X-ray/optical observations could help clarify this matter. (iii) Accreting stars have higher X-ray extinction than assumed, so the difference in inferred LX and LX /LBol is only apparent. This could be possible either if the assumed AV -NH relation, i.e., the gasto-dust ratio, is different for accreting stars with respect to the average interstellar value or in a scenario in which accretion gas columns that cross the line of sight would obscure X-rays and let optical/IR radiation through. This hypothesis can be and has been tested (see sections “XEST and the Origin of YSO Mass-LX and Accretion-LX Relations” and “COUP: LX vs. Rotation and Age, Insights on the Dynamo, and the Origin of Saturation”) with longer exposures that have allowed to confirm that the observed difference is real. The case of Orion and of other early observations made it clear the need for long continuous observations as well as for simultaneous multiwavelength observations. The early results have stimulated a large number of guest observing programs that have covered tens of different SFRs up to distances of 4 kpc investigating a range of ages, environmental conditions, metallicities, massive vs. non-massive SFRs, etc. Thanks to superb quality X-ray data, about 50 distinct SFRs have been studied often jointly to optical/NIR/MIR archive or purposely taken observations, with a key role played by the IRAC/Spitzer observations that in some cases have been part of coordinated programs. A somehow outdated, but still useful, list of Chandra studies can be found in Table 2 of Feigelson et al. (2013) and Table 1 of Getman et al. (2017).

Systematic Studies of the Star Cluster Formation Process The very rich Chandra/ACIS and Spitzer/IRAC archives have made possible two projects: MYStIX (Massive Young star-forming complex Study in Infrared and X-ray) aimed to characterize 20 OB-dominated young clusters and their environments within a distance ≤4 kp (cf. Feigelson et al. 2013 and references therein) and SFiNCS (Star Formation in Nearby Clouds), based on MyStIX heritage, aimed at providing a detailed study of the young cluster stellar populations and cluster formation in the nearby (0.2 < d < 1 kpc) 22 SFRs to be compared with MYStIX richer, more distant clusters (Getman et al. 2017 and references therein). Both projects have been based on a homogeneous reanalyses of the Chandra/ACIS, the IRAC/Spitzer, and the UK InfraRed Telescope observations in order to construct catalogues of SFR members with well-defined criteria and map the nebular (hot) gas and dust. The adopted sophisticated analysis has pushed to the very limit the available observations; a thorough discussion of the advantages and possible limitations of produced catalogues is provided by the team (cf. Appendix B of Feigelson et al. 2013). The motivations and results of the MYStIX project have been recently reviewed in detail (Feigelson 2018). The MYStIX project has produced a catalogue of 31,784 probable SFR members. The analysis of this catalogue has shown that the age spreads within clusters are real with the cluster core formed after the cluster halo (Getman et al. 2014a). There is

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evidence of older dispersed populations and cluster expansion, and of long-lived, nonsynchronous, star formation, and, at the same time, there is not conclusive evidence of subcluster merging (Kuhn et al. 2015). To investigate the spatiotemporal history of the star formation within the studied SFRs, a reliable age estimation of various stellar subgroups was needed. The MYStIX team has developed a simple, but effective, estimator (Getman et al. 2014b) based on the well-established, but poorly physically understood, empirical correlation between LX and YSO mass, M, (cf. Telleschi et al. 2007) that accounts for most of the four decades LX range found in SFRs. In a nutshell, individual LX , corrected for absorption, provides an estimate of M, while the de-reddened J magnitude provides a proxy for LBol . Using standard evolutionary tracks, M and LBol provide a (crude) age estimator for each YSO (nicknamed AgeJ X ). While individual values are rather inaccurate, median values for spatial defined subgroups appear adequate enough to follow the star formation history within and between SFRs/young clusters. The SFiNCs project has built a catalogue of ∼8500 likely members increasing by 40% the census of the 22 analyzed nearby SFR regions. The comparative analysis of the SFiNCs and MYStIX clusters has shown that the former are typically smaller, younger, and more heavily obscured than the latter. The SFiNCs clusters associated with molecular clouds have an elongated shape whose major axis is aligned with their host molecular filaments, a firm of the morphology imprint of their parental clouds. Cluster expansion is evident from many indicators. Core radii increase by one order of magnitude (from ∼0.08 to ∼0.9 pc) over the age range 1–3.5 Myr, implying that gas removal timescale is longer than 1 Myr. There is evidence of an early generation of star formation that has left conspicuous, spatially distributed, stellar populations. Another project, based on the reanalysis of archival Chandra ACIS observations, is the Massive Star-Forming Regions (MSFRs) Omnibus X-ray Catalog (MOXC) (Townsley et al. 2019) that includes X-ray point sources from a selection of 12 MSFRs across the Galaxy, with distances ranging from 1.7 to 50 kpc, plus 30 Doradus in the Large Magellanic Cloud. MOXC reports 20,623 X-ray point sources. Taking advantage of the point source catalogue, and removing their contributions, it has been possible to study the morphology of the remaining diffuse X-ray emission that traces the bubbles, ionization fronts, and photon-dominated regions that are found in all MOXC MSFRs. As already found in the cases of M17 and Rosetta, this unresolved X-ray emission is dominated by hot plasma from massive star wind shocks (Townsley et al. 2003). This diffuse X-ray emission shows that massive star feedback (and the accompanying several-million-degree plasmas) is a key element of MSFR physics.

Long-Look, Large-Area, and Multiwavelength Simultaneous Surveys In the current scenario of Class I–II YSOs (Hartmann 2008), magnetically funneled accretion streams connect the central star with its circumstellar disk. In such a system, X-rays could be emitted by the PMS star corona, by the funnel plasma

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that is shocked as it accretes on the star, by the fluorescing disk matter, or by gas shocked in a jet. X-ray studies allow us to disentangle those contributions and to investigate the processes at work. Among the many studies, particularly notable are the long-look programs and the large-area surveys that have consolidate emerging scenarios or opened new perspectives.

NGC 1893: Exploring Star Formation in the Outer Galaxy The young cluster NGC 1893 in the external region of the Galaxy at about 12 kpc from the galactic center has been observed with Chandra for 450 ks. This program, led by G. Micela, has allowed to study the IMF in a region of the Galaxy where the environmental conditions are different than in the vicinity of the Sun. A catalogue extending from X-rays to NIR has allowed to derive the cluster membership as well as other cluster parameters: 415 diskless candidate members and 1061 disk-bearing candidate members, 125 of which are also Hα emitters, have been found showing that NGC 1893 contains a conspicuous population of YSOs, together with the wellstudied main-sequence cluster population. The fraction of disk-bearing members is about 70% as found in similar age clusters in the solar vicinity. Hence, despite expected unfavorable conditions for star formation, evidence has been found that very rich young clusters can also form in the outer regions of our Galaxy (Prisinzano et al. 2011). DROXO and Follow-On: The Enigmatic Variability of YSO Fe 6.4 keV Line Two long-look programs, led by S. Sciortino, have been devoted to study the ρ Oph core F region. The first is nicknamed DROXO (Deep Rho Ophiuchi XMM-Newton Observation) and consists of a 500-ks-long continuous EPIC observation (Sciortino et al. 2006). The DROXO time-resolved spectroscopy has allowed us to study the X-ray emission of the 1-Myr-old ρ Oph YSOs. A successive joint XMM-NewtonNuStar has been devoted to investigate the existence (if any) and origin of the very hard X-ray emission and to further perform time-resolved X-ray spectroscopy of the ρ Oph YSO Elias 29, specifically of its Fe 6.4 keV Kα line. This line EW had shown intense variability, not clearly associated with YSO flares (Giardino et al. 2007b) and tantalizing evidence of line centroid displacement that could either be due to Doppler shift of emitting matter or rapid changes of its ionization (Pillitteri et al. 2019). Since its first firm discovery in YLW 16A, the Fe 6.4 keV Kα has been now found in several tens of YSO (e.g., Tsujimoto et al. 2005; Favata et al. 2005b; Stelzer et al. 2011) but only in few YSOs observed with DROXO line variability has been investigated in some detail (Giardino et al. 2007b; Stelzer et al. 2011; Pillitteri et al. 2019). XEST and the Origin of YSO Mass-LX and Accretion-LX Relations Another program devoted to the study of YSO physics was XEST (XMM-Newton Extended Survey of Taurus (Güdel et al. 2007) and references therein), led by M. Guedel, based on a mosaic of many medium-deep exposures to cover most of the Taurus region. The XEST has confirmed the existence of an LX vs. mass relation that has been interpreted as a consequence of the X-ray saturation and of the

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mass vs. bolometric luminosity (LBol ) relation occurring among YSOs in a narrow age range (Telleschi et al. 2007). In the saturation regime, LX ∼ C × LBol with Log(C) = −3.73 for Class II and −3.39 for Class III YSOs, confirming the findings of the intrinsic factor ∼2 lower LX of Class II with respect to Class III YSOs. As a possible explanation, the same authors have suggested that some of the accreting material in Class II is cooling active regions preventing them from contributing to the X-ray emission. An alternative scenario assumes that YSO X-rays modulated the accretion flow by the X-rays heating the gas in the surface layer of the disk (e.g., Drake et al. 2009). If the local temperature excesses the escape temperature, a thermal-driven wind will start and the accretion rate will decrease: in a few Myr, a gap will develop in the inner disk, the erosion will start, and the accretion rate will drop. The YSOs with higher LX will reach sooner the low-accretion rate condition. Detailed models (Picogna et al. 2019, 2021) predict a weak anticorrelation between LX and the mass accretion rates (see section “Circumstellar Disk Evolution and High-Energy Radiation”).

COUP: LX vs. Rotation and Age, Insights on the Dynamo, and the Origin of Saturation The Orion central region has been extensively studied with COUP (Chandra Orion Ultradeep Project, led by E. Feigelson, cf. Getman et al. 2005), 10 days (850 ks) of ACIS integration during a continuous time span of 13 days, yielding a total of 1616 detected sources in the 17′ × 17′ field of view which has allowed us to study the X-ray properties of known Orion YSOs as well as to discover and characterize the Orion YSO embedded population. The analysis of COUP data (Preibisch et al. 2005a) has confirmed with a high confidence level that the LX level of non-accreting YSOs is consistent with that of rapidly rotating main-sequence stars, while the accreting YSOs have, a factor 2–3 on average, weaker LX . This weakening is not due to the absorption since LX has been properly absorption-corrected, nor to possible disk-star rotational locking given the lack of correlation of LX with rotation. The other possible explanations are (i) the accretion effects on YSO magnetosphere and the loading by the accreting matter on part of field lines resulting in higher density, reduced temperature and weaker LX , or (ii) modification of the internal stellar structure due to the accretion that weakens the dynamo action. The COUP data have also confirmed the strong, almost linear, correlation between LX , LBol and YSO mass already reported in the early studies (Feigelson et al. 2003; Flaccomio et al. 2003b). LX /LBol increases slowly with mass over the 0.1–2 M range. The scatter about these relations is larger than explainable in terms of data uncertainties, unresolved binaries, and intrinsic X-ray variability, and it is likely due to the effect of accretion on LX . Taking advantage of the exceptional COUP time coverage, rotational modulation of X-ray emission was searched on a subsample of 233 (out of 1616 sources) X-ray bright stars with known rotational periods and was found in at least 23 YSOs with periods between 2 and 12 days and relative amplitudes ranging from 20% to 70%. In 16 cases, the X-ray modulation period is similar to the stellar rotation period, while in 7 cases, it is about half that value, possibly due to the presence of X-ray-emitting structures at opposite

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stellar longitudes (Flaccomio et al. 2005). The observed modulation indicates that the X-ray-emitting regions are distributed nonhomogeneously in longitude and, usually, do not extend to distances significantly larger than the stellar radius. Modulation is observed in stars with saturated activity levels (LX /LBol ∼ 10−3 ) showing that saturation is not due to the filling of the stellar surface with X-rayemitting regions. COUP has reached a sensitivity better than LX = 1027 erg/s providing a large unbiased sample of YSOs down to BDs, and it is more than 95% complete (Preibisch et al. 2005a). It arguably still is the best sample to study age-activity relationship in a very reliable way allowing, for the first time, to consider mass-stratified subsamples. The evolution of low-mass stars/YSOs magnetic activity – of which LX is a proxy – provides, together with the age-rotation relation, the observational constraints on stellar magnetic dynamo models and theories. For the range of ONC member ages 0.1–10 Myr (Palla and Stahler 1999), a mild decay of LX with stellar age τ roughly as LX ∼ τ −1/3 has been found (Preibisch and Feigelson 2005). Comparing ONC YSOs with main-sequence stars up to Log τ [yr] = 9.5, in the 0.5 M < M < 1.2 M mass range, LX decays more rapidly as LX ∼ τ −0.75 . Taking LX /LBol and the X-ray surface flux FX as activity indicators, the decay is similar for the first 1–100 Myr but larger for older stars. For masses in the 0.1 M < M < 0.4 M range, i.e., M-type on MS, activity indicators have a different evolution. In the first 1–100 Myr, a mild decrease of LX , LX /LBol , and FX has been found, followed by the three-activity indicator decay over long timescales on the main sequence. Given also the confirmed lack of a rotation-activity relationship, the activityage decay characterizing the evolution of solar mass stars cannot be attributed to rotational deceleration during the early epochs. For 0.5M < M < 1.2 M , the results may be explained with a combination of tachocline and distributed convective dynamos at work up to ∼10 Myr, while for 0.1 M < M < 0.4 M , the results are consistent with the convective dynamo dominance during the entire evolutive history.

CSI-2264: Unveiling Circumstellar Disks with Simultaneous Multiwavelength Variability Studies The “Coordinated Synoptic Investigation of NGC 2264” (CSI-2264) was led by G. Micela and J. Stauffer, during which in December 2011, simultaneous observations of a large sample of YSOs in NGC 2264 have been obtained with three spaceborne telescopes, Chandra (X-rays), CoRoT (optical), and Spitzer (mIR) (e.g., Cody et al. 2013, 2014; Stauffer et al. 2016). CSI-2264 is the only program of this kind that has so far been done (Few selected interesting individual sources (e.g., AB Dor, V4046 Sgr, V2129 Oph, etc.), some of which are YSOs, have also been the subject of simultaneous multiwavelength observations.). The main mechanisms responsible for the YSO X-ray variability besides flares are variable extinction (e.g., warped rotating disk), unsteady accretion, and rotational modulation due to hot, accretion-induced, and cold photospheric spots and X-ray-active regions. In disk-bearing YSOs, this variability is related to the

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morphology of the inner circumstellar region (≤0.1 AU) and that of the photosphere and corona, all impossible to be spatially resolved with present-day techniques. Thanks to the CSI-2264 data, the X-ray spectral properties during optical bursts and dips to unveil the nature of these phenomena have been studied (Guarcello et al. 2017). The simultaneous CoRoT and Chandra/ACIS-I observations have been analyzed to search for coherent optical and X-ray flux variability. In YSOs with evidence of variable extinction, by looking for a simultaneous increase of optical extinction and X-ray absorption during the optical dips; in YSOs showing accretion bursts, by searching for soft X-ray emission and increasing X-ray absorption during the bursts. In 38% of the 24 YSOs with optical dips, a simultaneous increase of X-ray absorption and optical extinction has been found. In seven dips, it was possible to calculate the NH /AV ratio in order to infer the composition of the obscuring material. In 25% of the 20 YSOs with optical accretion bursts, increasing soft X-ray emission during the bursts arguably associated with the emission of accreting gas has been reported. Since favorable geometric configurations are required, these phenomena have been observed only in a fraction of YSOs with dips and bursts. The proposed scenario is that the observed variable absorption during the dips is mainly due to dust-free material in accretion streams. In YSOs with accretion bursts, a larger soft X-ray spectral component has been, on average, observed, while it has not been seen in weakly accreting YSOs.

X-Rays from Class 0 YSOs Notwithstanding large observational efforts (see section “ASCA: Looking for X-Rays from Class I and Class 0 YSOs”) for a long time, there has been no clear evidence of X-ray emission from the Class 0 YSO. While X-rays are quite penetrating, Class 0 sources can be subject to extinction up to 100 magnitudes and even higher preventing the escape of any X-rays. The most constraining upper bound to Class 0 LX was ∼4 × 1029 erg/s (Giardino et al. 2007a) that, however, is about two dex higher than the X-ray luminosity of active Sun. After several controversial reports, more firm evidences have been recently reached. By assembling the deepest and most, at the time, complete photometric catalogue of objects in the ONC region from the UV to 8 μm, a sample of high-probability YSOs members from Class 0 to Class III have been selected, and the properties of their X-ray emission have been studied concluding that Class 0–Ia YSOs are significantly less X-ray luminous than the more evolved Class II YSOs with M > 0.5 M (Prisinzano et al. 2008). Data are consistent with the onset of X-ray emission occurring at a very early stage. Class 0–I have X-ray spectral properties similar to those of the Class II and III, except for a larger absorption likely due to gas in the envelope or disk of the protostars. Recently, it has been reported that HOPS 383, a bona fide Class 0 YSO, has been detected above 2 keV with Chandra during a flare of a duration of ∼3.3 h (Grosso et al. 2020). In the 2–8 keV bandpass, the YSO peak LX has reached ∼3.4×1031 erg/s, at least ten times higher than its undetected “quiescent” emission. The 28 collected counts have secured the detection, but required a careful analysis

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to extract spectral information. The flare spectrum is highly absorbed (NH ∼ 7 × 1023 cm−2 ), and the quality of the spectral fit does slightly improve when a Fe 6.4 keV emission line with an equivalent width of ∼1.1 keV is added, suggesting emission component arising from neutral or low-ionization iron. This result, if representative of all Class 0 YSOs, points toward an early development of the intense X-ray emission of YSOs, and, as a result, the X-ray emission likely starts to regulate very early the further evolution of star formation process, for example, by determining the effectiveness of ambipolar diffusion (see section “YSO X-Ray Emission Effects on Small and Large Scales”). Since the Class 0 data are still too sparse, further deep observations with current or future X-ray observatories are needed.

The YSO Flares: Nature and Effects on Circumstellar Disks The issue of the existence of star-disk interconnecting flaring arches has been a matter of debate over the last two decades. The issue is particularly relevant since, depending on the actual occurrence rate of those large flares, they can affect the early evolution of circumstellar disks with far-reaching effects even on the formation of planetary systems. Detailed MHD model investigation has also shown that the flare location (and geometry) likely plays a key role (e.g., Colombo et al. 2019) in disk evolution. A flare is a manifestation of the impulsive release of energy in a tenuous plasma confined in a “magnetic bottle” that loses energy by optically thin radiation and by efficient thermal conduction to the chromosphere (cf. the extensive discussion in Reale 2007, 2014). The magnetic confinement determines the typical flare light curve shape (The shape would be very different in the case of unconfined plasma) characterized by a very rapid increase of the emission (due to the rapid heating of the plasma) followed by a slow, almost exponential decay (due to the cooling by thermal conduction and radiative losses). Most of the observed flares conform to very general conditions (Reale 2007) such that the time evolution of the emission√and of the peak temperature, as well as the cooling, traced in the Log (T ) − Log ( EM) diagram provide a “direct” estimate of the length of the flaring magnetic structure. Adopting this robust interpretative framework, the analysis of a sample of 32 large COUP flares has reached the conclusion that about 10 of them show flare decay times of about 1–2 days (cf. the published light curves) and the flaring structure has a length of 3–20 stellar radii, R∗ , Favata et al. (2005a). Such length structures have never been found in the many analogous analyses of flares in more evolved normal stars. Structures of such extent, if anchored on the stellar surface, should suffer of likely stability problem due to the centrifugal force since 1–2-Myr-old YSOs are fast rotators with rotation period, P ∼3 − 6 days. The study of the coronal loop equilibrium condition in fast rotating stars assuming a magnetic field with potential configuration has shown that loops longer than ∼ three times the stellar radius are a possible stable solution in diskless YSOs only assuming that the wind cooperates to support them (Aarnio et al. 2012). In other configurations, long loops anchored only

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on the star would be very likely ripped open during a long flare whose duration is of the order of rotational period (for further details, cf. the discussion section of Favata et al. 2005a). As a solution to this problem, since the co-rotation radius of those YSOs is typically at 4–5 R∗ , it has been suggested that the loop, on which the flare occurs, is connecting the star and the disk (at the co-rotation radius). The existence of such magnetic “funnels” in Class I–II YSOs is postulated by magnetospheric accretion scenario (e.g., Hartmann 2008 and references therein). In DROXO, in seven YSOs, intense flares have been observed (Flaccomio et al. 2009) and the length of the flaring loops has been derived, and in two cases (DROXO 63 and DROXO 67), the flaring loops are several stellar radii long. The fraction of the very long flaring structures in ρ Oph is similar to the one observed in Orion, namely, ∼30% . By adopting a novel spectral analysis technique that avoids nonlinear parametric modeling, the full set of 216 COUP flares on 161 YSOs have been analyzed (Getman et al. 2008a, b) deriving the length of the flaring loop, Lloop . Only 98 of them, classified with the available IR photometry, have been retained in the further analysis. Based on estimation of the stellar radius, R∗ , and disk Keplerian co-rotation radius, Rcor (The distance from stellar surface at which the angular velocity of disk equates that at stellar surface) (when the rotational period is known), the scatter plots of (Lloop + R∗ )/Rcor as a function of indicators (when available) of the presence of circumstellar disk or of ongoing accretion process have been built for a final subsample of ∼70 flares (see Fig. 4) concluding that (1) circumstellar disks have no effect on flare morphology and (2) circumstellar disks may truncate PMS magnetospheres, i.e., (Lloop +R∗ )/Rcor < 1. Moreover, the study has found that circumstellar disks are unrelated to flare energetics, and superhot (>100 MK) “nonstandard” flares do occur in accreting YSOs (in agreement with

Fig. 4 (left) Scatter plot of (Lloop + R∗ )/Rcor vs. excess of (H − KS ) color, an indicator of the presence of circumstellar disk. (right) Scatter plot of (Lloop + R∗ )/Rcor vs. the EW of CaII triplet, an indicator of accretion process. In both panels, the vertical wavy gray curve marks the transition to accreting/inner disks. COUP 1608, that is outlined, clearly behaves very differently from the rest of (most of) the other YSOs. COUP 43 and COUP 332, for which all the different analysis techniques discussed in the text have derived long flaring structure, are not shown in the plots for lack of period and/or EW data. (Adapted from Getman et al. 2008b)

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Favata et al. 2005a). Points (1) and (2) are at odd with the likely existence of stardisk interconnecting magnetically confined flaring structures (Favata et al. 2005a). A detailed analysis of the 68 flares on 65 YSOs simultaneously observed in the CSI-2264 program comparing the light curves obtained in X-rays (with Chandra), in optical (with COROT), and in the infrared (with Spitzer) has been performed (Flaccomio et al. 2018). The simultaneity of those observations – crucial for studying fast variability phenomena like flares – makes this really a unique dataset that includes the first, and still unique, simultaneous X-ray and IR observations of flare in a Class I YSO. Over the studied sample, the flare released energy in the X-ray bandpass ranges from ∼6 × 1033 to ∼2 × 1036 erg. Some firm conclusions have been drawn, namely, (i) the flare peak luminosity measured in the optical, IR, and X-ray bandpasses are tightly correlated; with a small (.3 dex) scatter, a similar relation (with a similar amplitude scatter) holds also for the flare energy released in the optical, IR, and X-ray bandpasses; and the relationships hold over three orders of magnitude; (ii) the flare energy emitted in “soft” X-rays is about 10% to 20% of the flare energy emitted in the optical band; (iii) the flare energies are up to ∼5 decades higher than those of the brightest solar flares, and the simple extrapolation of solar flares to this extreme regime requires some cautions. As an example, the data indicate that the flare photospheric temperature is significantly lower than 104 K, which is the typical solar value; (iv) the occurrence of X-ray flares without optical counterparts can be due to flaring loop geometry since optical/IR emission comes from loop footprints, whereas the X-rays are likely emitted along most of the loop. Based on a simple model, the fraction of flares without optical counterparts ranges from 19% to 48%. (v) there is evidence of a strong IR excesses for flares in stars with circumstellar disks: likely a result of the direct response (heating) of the inner disk to the flare. This is still the more direct observational signature of the interaction between flare emission and disks. Taking advantage of the MYStIX and SFiNCs data products, a large sample of powerful YSO flares has been recognized and studied (Getman and Feigelson 2021; Getman et al. 2021) deriving the peak X-ray luminosity (LX,p ) and released energy in the X-ray bandpass (EX ). The sample has been subdivided in 636 super-flares (34 36.2). This latter subsample is the most complete of the two; the “best-fitting” flare energy distribution is dN/dEX ∝ EX −1.95±0.07 over the entire mass range. The derived slope is in agreement with previous analyses (Stelzer et al. 2007; Caramazza et al. 2007; Albacete Colombo et al. 2007). The occurrence rate is 1.7 [+1,-0.6] flares/YSO/year over the entire mass range, reduces to 0.3 [+0.2,0.1] for M < 1 M , and is 11.0 [+6.4, −4.1] for M > 1 M . From the derived flare intensity distribution and mass-dependent occurrence rate, the contribution of observed mega-flares to the YSO X-ray fluence has been estimated to typically be 8–19% and to decrease with YSO mass. This contribution could be even more conspicuous if much bigger flares sustained by extremely strong magnetic field would exist. However, so far, the maximum measured averaged YSO magnetic field reaches ∼3.3 kG (cf. Sokal et al. 2020 and references therein); in a region of 0.1

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R∗ , the associated stored magnetic energy would be ∼1039 erg, not far from the maximum measured energy of mega-flares. By adopting the near and mid-IR photometric excess (More specifically, the infrared spectral energy distribution slope αI RAC with the value of -1.9 separating diskless and disk-bearing YSOs (Richert et al. 2018)) as a proxy of the presence of the (gaseous) inner circumstellar disk, the distributions of LX,p or EX of diskless and disk-bearing YSOs have shown to be statistically indistinguishable confirming previous results on smaller samples (Stelzer et al. 2007; Flaccomio et al. 2012, 2018). Since big flares have been reported both in diskless and disk-bearing YSOs, this is not too surprising since duration, LX,p , and EX are determined by the same physics governing all flares, irrespective of the YSO nature. It is worth to remember that the subdivision in diskless and disk-bearing YSOs is likely a simplification as the ample range of accretion rates measured among Orion YSOs clearly shows (Manara et al. 2012). Possibly more relevant, it would be a comparative study of the (big) flare occurrence rates between the accreting and non-accreting YSO samples. In the Taurus-Auriga region, XEST data have shown a marginal hint that large amplitude and fast rise flares are more frequent on cTTS than on wTTS (The classification scheme adopted in XEST is predominantly based on accretion signature (Güdel et al. 2007).) (31 ± 7% vs. 22 ± 7%) (Stelzer et al. 2007). A similar effect has also been found with a time-resolved analysis of all available COUP data (cf. Fig. 6 of Flaccomio et al. 2012), but the differences in flare detectability among the fainter Class II and Class III YSO populations could bias the flare occurrence rates (cf. Appendix A of Flaccomio et al. 2012) making difficult to draw firm conclusion. This same analysis has shown that disk-bearing stars are definitively more X-ray variable than diskless ones; this could be explained as the effect of time-variable absorption by warped and rotating circumstellar disks, but some other effects due to disk presence cannot firmly be ruled out (at least in some of the YSOs). The MYStIX/SFinCs flare study does not include the Carina complex and COUP nor CSI-2264. Let me stress that the COUP sample because of the time coverage, duration of continuous observations, accumulated count statistics, and sample size and the CSI-2264 sample for its multiwavelength simultaneous coverage remain the best ones to investigate the origin of (big) flares. Even in a systematic analysis of COUP data (Getman et al. 2008b), there are a few YSOs whose data can hardly be reconciled with the lack of any evidence of a possible effect of circumstellar disk, notably COUP 1608 and COUP 332 (LópezSantiago et al. 2016) and COUP 43 (Reale et al. 2018), three of the about ten COUP YSOs with long flaring loop (Favata et al. 2005a). A novel analysis of the light curves based on the so-called Morlet wavelet (e.g., López-Santiago (2018) and references therein) has been applied to some of the aforementioned big COUP flares. This analysis has shown to be very powerful in detecting quasiperiodic oscillations occurring in some stellar coronal flares (cf. Fig. 5). On the basis of simple physical argument, it is possible to derive from measured period the length of the flaring structure where the oscillating X-ray

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Fig. 5 The data and the summary of the wavelet analysis results for two COUP big flares. Time is measured from the beginning of the observation; the analyzed flare data segment is highlighted in yellow. The central panel shows the analyzed data segment after subtraction of the running average, while the bottom panel shows the intensity curve as a function of period and time. The statistical significance maps are also shown; they allow to discriminate the statistically significant period and the duration of the periodic signal. The dashed outer region marks the so-called cone of influence, inside which the analysis provides meaningful results. The right and left panels are for COUP 1608 (OW Ori) and for COUP 332 (2MASS J05350934-0521415), respectively. (Adapted from López-Santiago et al. 2016)

emission comes from López-Santiago et al. (2016). In the case of some of the COUP big flares, it has been shown the existence of oscillations during the flare decay phase allowing to determine the oscillation period (Reale et al. 2018). More specifically, the analysis has found large-amplitude (∼20%), long-period (∼3 h) pulsations in the light curve of two daylong COUP flares. Detailed hydrodynamical modeling, including all the relevant physical effects, of the flares observed on COUP 43 (V772 Ori) (shown in Fig. 6) and COUP 1068 (OW Ori) shows that these pulsations track the sloshing of plasma along an elongated magnetic tube, triggered by a heat pulse whose duration (∼1 h) is much shorter that the sound crossing time along the loop. From this simple and robust modeling, the authors have concluded that

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Fig. 6 The smoothed and running average subtracted light curve of COUP 43 flare (black line) is compared with the hydrodynamical model synthesized light curve in the case of a short-duration heating pulse (blue dashed line) and of a long-duration heating (red line) on the same long length flaring structure. Only a long loop with a length of about 10–20 R and a short heating pulse can reproduce the observed oscillations both in intensity and period. (Adapted from Sciortino et al. 2019)

the involved magnetic tubes are ∼20 solar radii long, and, very likely, connect the stars (near a polar region) with their surrounding disks (near the co-rotation radius). Such a geometry is consistent with the observed daylong stability of the flaring loop. All those evidences taken together indicate that we still lack a clear understanding of the nature of those big (flaring) loops; even their stable existence in diskless YSOs requires a specific modeling (Aarnio et al. 2012) involving the YSO winds; the extension to the case of disk-bearing YSOs should be properly investigated (A recent study of protoplanetary disk winds shows that both fast and slow winds are consistent with expectations from a thermal-magnetized disk wind model and are generally inconsistent with a purely thermal wind (Xu et al. 2021)). On the possible effect of circumstellar disks, further studies with higher-quality data on truly unbiased samples are needed; there is a large quantity of data, but their relevance/quality and/or absence of, often subtle, biases requires a critical analysis; a few points worth to consider are the following: (i) the large flaring loops are a coronal phenomenon involving hot gas, and the presence of dust is not really required; however, the IR excess to distinguish diskless and disk-bearing YSOs is sensitive to the presence of dust; (ii) for the star-disk interaction, it is likely relevant the accreting status of the disk (and not only its mere existence), something that

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should be evaluated by specific, and as “direct” as possible, accretion signatures; and (iii) subtle biases induced by the “selective” lack of accretion signature and/or rotational period should be carefully analyzed. The fact that most of the scaling laws of observed flares are similar and/or extensions of the solar case (Getman et al. 2021) are interesting, but not too much surprising since the physical nature of flares is always that of an explosion in a (magnetic) bottle with conductive and radiative losses. Perhaps more revealing could be the comparison of flare occurrence rates of well-defined samples of (strongly) accreting and non-/weakly accreting YSOs.

Circumstellar Disk Evolution and High-Energy Radiation The issue of the effect of high-energy radiation on circumstellar disk evolution has been studied and debated. Disks around low-mass stars can be strongly perturbed or even destroyed before they form planets by photoevaporation induced by incident X-ray and UV radiation (e.g., Störzer and Hollenbach 1999; Picogna et al. 2019; Ercolano et al. 2021) or gravitational interaction during close encounters with other cluster members (e.g., Pfalzner et al. 2005; Vincke et al. 2015). Evaporating disks have been observed in the Orion Trapezium (e.g., Bally et al. 2000), Cygnus OB2 (Wright et al. 2012; Guarcello et al. 2014), NGC 2244 (Balog et al. 2006), NGC 1977 (Kim et al. 2016), and Carina (Mesa-Delgado et al. 2016). Indirect evidence supporting a fast erosion of protoplanetary disks in proximity of massive stars was deduced by the decline of the disk fraction observed close to massive stars or in regions with high local UV fields in massive clusters/associations such as NGC 2244 (Balog et al. 2007), using Spitzer data alone, and NGC 6611 (Guarcello et al. 2007, 2009, 2010) and Pismis 24 (Fang et al. 2012) using a multiwavelength approach with a pivotal role played by Chandra data. In contrast with these results, in the MYStIX massive cluster sample, no evidence supporting a lower disk fraction near massive stars was instead reported (Richert et al. 2015), suggesting that evidence supporting the external disks photo-evaporation found by earlier studies was affected by selection effects. Subsequent Chandra-enabled studies of, e.g., NGC 6231 (Damiani et al. 2016), Cygnus OB2 (Guarcello et al. 2016), and Trumpler 14 and 16 (Reiter and Parker 2019) have refuted this hypothesis supporting the evidence that the star-forming environment plays an important role in the survival and enrichment of protoplanetary disks and confirming disk photoevaporation role. A recent study of Dolidze 25 suggests that disk evolution may be impacted by the environment; given the small number of O stars and the low stellar density, disk dispersal timescale is likely determined by cluster low metallicity rather than photo-evaporation or dynamical encounters (Guarcello et al. 2021a). A signature of X-ray-driven disk photo-evaporation due to the low-mass YSO emission is provided by the dependence of stellar accretion rates on X-ray luminosities, LX ; models predict that, in a coeval, similar mass sample, stars with higher LX should show, on average, lower accretion rates. By using the COUP-derived LX (Getman et al. 2005) and accretion derived from the Orion HST Treasury

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Program (Manara et al. 2012), it has been found evidence for a weak anticorrelation, as predicted by the models, even after correcting for the LX and accretion rate dependence on mass that could produce a spurious anticorrelation (Flaischlen et al. 2021). Since massive stars are the primary sources of X-ray/UV radiation and the chances of close encounters are high in dense stellar environments, both processes can be relevant depending on massive stars’ numbers and space density, the most extreme environment being a massive starburst region like Westerlund 1 (WD1). Thus, likely better evidence would be obtained testing protoplanetary disk survival in such an extreme environment; this is really a challenging experiment, at the limit of the capability both of Chandra and JWST. It is one of the main objectives of the currently ongoing “Extended Westerlund One Chandra, and JWST, Survey” (EWOCS) (Guarcello et al. 2021b).

YSO X-Ray Emission Effects on Small and Large Scales The role of YSO X-rays as a major local ionization component has been modeled and discussed by Lorenzani and Palla (2001) who have introduced the concept of the Röntgen sphere as the region around each YSO where the ionization rate due to the YSO X-rays is greater than the one due to cosmic rays. With the typical LX of YSOs, the resulting ionization is 4–20 times higher than the value due to the cosmic rays. In SFRs like Orion and ρ Oph, the YSO space density is sufficient to affect regions of 1 pc size (Fig. 7). Due to the greater ionization, the coupling of magnetic field to the cloud should increase and the cloud core collapse should take longer due to ambipolar diffusion. Hence, the X-rays from YSOs could naturally slow down an accelerating star formation process. More recently, a much detailed treatment of the X-ray transfer and energy deposition into a gas with solar composition, with an accurate description of the electron cascade after the primary photoelectron energy deposition (Locci et al. 2018), has confirmed that in molecular clouds embedding low-mass YSOs substantial volumes of gas are affected by ionization levels much higher than the cosmic-ray background ionization. In dense SFRs, X-rays create an ionization network pervading densely the interstellar medium, and providing a natural feedback mechanism. These results support the idea that X-ray could be among the most relevant ingredients in the evolution of a variety of astronomical regions. Let me add that in the COUP data, at least three YSOs have flare peak LX higher than the one found on HOPS 383 (Wolk et al. 2005) and many more have been recently reported (see section “The YSO Flares: Nature and Effects on Circumstellar Disks”) in many other SFRs. Big flares, with an estimated rate of ∼1.7 flares/YSO/year (Getman and Feigelson 2021), are common among Class I, and may be Class 0, YSOs. During the first 5 Myr of its evolution, a solar mass YSO will generates about 107 big flares which will very likely play a role in the ionization of YSO circumstellar environments and disks.

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Fig. 7 A two-dimensional projection of a model predicted ionization rate for the BN-KL cloud core in the Orion Molecular Cloud 1 region based on COUP-derived LX . Across the entire core, the ionization rate exceeds the value due to cosmic rays (2 × 10−17 s−1 ), and around each of the embedded X-ray-emitting YSOs develops a Röntgen sphere where the X-ray-induced ionization rate is several orders of magnitude higher than the background level. (Model data courtesy of the late F. Palla.)

A Glance into the Future Making predictions is often rooted on biased opinions and is a slippery exercise, and I do believe that astronomy is really driven by the advancement of observational capabilities; paradigm changing discoveries have often been the outcome of the increase in discovery space fostered by new telescopes and instruments (Fabbiano et al. 2019).

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Having this in mind, there are still some obvious predictions: (1) the ongoing (Since March 2022, the survey is in hold due to international tensions; survey restarting date can hardly be predicted.) eRosita all-sky survey (∼30 times deeper than the RASS) will permit to investigate the YSO population in the nearby SFRs also, thanks to the availability of GAIA and IR data. A first example is provided by the study of the Sco-Cen OB association (Schmitt et al. 2022). The foreseen eRosita pointed program will open the opportunity to perform long dedicated observations of interesting SFRs; if performed simultaneously at other wavelengths, they will have a huge impact as we have learned with CSI-2264. Given the eRosita angular resolution, these studies should concentrate on rather nearby SFRs. Already at the distance of Orion, confusion, unless reaching the superb Chandra angular resolution, could be a problem; (2) the XRISM microcalorimeter promises groundbreaking 7 eV spectral resolution, namely, a resolving power, R ∼ 1000 at Fe Kα 6.7 keV line(s) even if with limited angular resolution. The best targets for XRISM YSO studies will be the nearby heavily obscured SFRs, e.g., ρ Oph and R CrA. The strong Fe 6.7 keV and Fe fluorescent 6.4 keV lines, often found in YSO X-ray spectra, can diagnose plasma conditions and dynamics of the innermost region of Class I and Class II YSO where the free-fall and Keplerian velocities of matter and X-ray-emitting plasma are expected to be a few hundreds km/s. At ∼7 keV Chandra (The XMM-Newton reflection grating bandpass extends only to about 2.4 keV.), high-resolution grating spectrometers lack the sensitivity and resolution to resolve such velocity shifts whose investigation at much lower energies (1 keV) is hampered by absorbing circumstellar matter. For the first time, XRISM should be able to investigate (a) the geometry of X-ray plasmas around the central object from Doppler shift or broadening measurements of highly ionized Fe emission lines, (b) the emitting plasma equilibrium state from multiple Fe emission lines, (c) the dynamics of the innermost accretion disk from Doppler shifts or broadening of the fluorescent Fe Kα line, (d) the dynamics of plasma from Doppler shifts of emission lines during X-ray flares; (3) on a longer timescale, with a possible launch around 2035, the under-study ESA L-class ATHENA X-ray observatory with its large collecting area (∼1.4 sq.m at 1 keV), spectral resolution (>2.5 eV up to 7 keV), and long continuous observations will have a deep, transformational impact. As an example, it would be possible to study with a time resolution of a few ks the possible time variations of the energy of the Fe Kα fluorescent line complex centroid of which we have found tantalizing evidence in a deep XMM-Newton/EPIC observation (Pillitteri et al. 2019). An analysis, admittedly somewhat outdated, of the ATHENA capabilities on YSOs research is provided by Sciortino et al. (2013); two white papers discuss the foreseen synergy between ATHENA and the ESO current and under construction telescopes (Padovani et al. 2017), and those between ATHENA and SKA (Cassano et al. 2018). They include, among the many, a discussion of multiwavelength investigations of the star formation process, YSO physics, and evolution of circumstellar and protoplanetary disks.

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In order to reach the cores of faraway massive SFRs, as an (X-ray) astronomer, I continue to envisage an X-ray observatory having a Chandra-like resolution, a few square meter effective area, a ∼500 square arc-min field of view, a ∼1 eV spectral resolution, and a ∼1 ms time; when feasible – substantial technological developments are required – this will be a wonderful play field for the next generations of astronomers. Acknowledgments I sincerely thank the many colleagues whose long-standing dedication to astronomy have made possible the writing of this review; among the many I want to remember some of my younger colleagues in Palermo: Francesco Damiani, Ettore Flaccomio, Mario Giuseppe Guarcello, Ignazio Pillitteri, and Loredana Prisinzano. Some of the exposed ideas have benefited of the many pleasant friendly discussions I have had with the late Francesco Palla. This research has made use of NASA’s Astrophysics Data System.

References A. Aarnio, J. Llama, M. Jardine, S.G. Gregory, Mechanical equilibrium of hot, large-scale magnetic loops on T Tauri stars. MNRAS 421(2), 1797–1802 (2012) F.C. Adams, The birth environment of the solar system. ARA&A 48, 47–85 (2010) F.C. Adams, M. Fatuzzo, L. Holden, Background x-ray radiation fields produced by young embedded star clusters. PASP 124(919), 913 (2012) J.F. Albacete Colombo, M. Caramazza, E. Flaccomio et al., X-ray flaring from the young stars in Cygnus OB2. A&A 474, 495–504 (2007) L. Allen, S.T. Megeath, R. Gutermuth et al., The Structure and Evolution of Young Stellar Clusters, in Protostars and Planets V, ed. by B. Reipurth, D. Jewitt, K. Keil (University of Arizona Press, Tucson, AZ, USA, 2007), p. 361 V.A. Ambazsumian, in Non-stable Stars proceedings from IAU Symposium. Stars of T Tauri and UV Ceti types and the phenomenon of continuous emission, International Astronomical Union. Symposium 3, ed. by George H. Herbig (Cambridge University Press, Cambridge, UK, 1955), pp. 177–185 P. Andre, T. Montmerle, From T Tauri stars to protostars: circumstellar material and young stellar objects in the rho ophiuchi cloud. ApJ 420, 837 (1994) C. Argiroffi, High-energy emission and its variability in young stellar objects. Astron. Nachr. 340(4), 284–289 (2019) C. Argiroffi, F. Favata, E. Flaccomio et al., XMM-Newton survey of two upper Scorpius regions. A&A 459(1), 199–213 (2006) J.N. Bahcall, R.M. Soneira, The universe at faint magnitudes. I. Models for the Galaxy and the predicted star counts. ApJS 44, 73–110 (1980) J. Bally, C.R. O’Dell, M.J. McCaughrean, Disks, microjets, windblown bubbles, and outflows in the orion nebula. AJ 119(6), 2919–2959 (2000) Z. Balog, G.H. Rieke, K.Y.L. Su et al., Spitzer MIPS 24 μm detection of photoevaporating protoplanetary disks. ApJ 650(1), L83–L86 (2006) Z. Balog, J. Muzerolle, G.H. Rieke et al., Spitzer/IRAC-MIPS survey of NGC 2244: protostellar disk survival in the vicinity of hot stars. ApJ 660(2), 1532–1540 (2007) I. Baraffe, G. Chabrier, J. Gallardo, Episodic accretion at early stages of evolution of low-mass stars and brown dwarfs: a solution for the observed luminosity spread in H-R diagrams? ApJ 702(1), L27–L31 (2009) M.R. Bate, The dependence of star formation on initial conditions and molecular cloud structure. MNRAS 397(1), 232–248 (2009)

93 Star-Forming Regions

3305

T. Boller, M.J. Freyberg, J. Trümper et al., Second ROSAT all-sky survey (2RXS) source catalogue. A&A 588, A103 (2016) C. Briceno, L.W. Hartmann, J.R. Stauffer et al., X-rays surveys and the post-T Tauri problem. AJ 113, 740–752 (1997) A.G.A. Brown, Microarcsecond astrometry: science highlights from gaia (2021). arXiv e-prints arXiv:2102.11712 M. Caramazza, E. Flaccomio, G. Micela et al., X-ray flares in Orion low-mass stars. A&A 471(2), 645–654 (2007) L. Carkner, J.A. Kozak, E.D. Feigelson, An x-ray survey of very young stellar objects. AJ 116(4), 1933–1939 (1998) S. Casanova, T. Montmerle, E.D. Feigelson, P. Andre, ROSAT x-ray sources embedded in the rho ophiuchi cloud core. ApJ 439, 752 (1995) R. Cassano, R. Fender, C. Ferrari et al., SKA-Athena synergy white paper (2018). arXiv e-prints arXiv:1807.09080 J.P. Cassinelli, J.H. Swank, X-ray spectra of Orion OB supergiants. ApJ 271, 681–690 (1983) C.J. Clarke, J.E. Pringle, Accretion disc response to a stellar fly-by. MNRAS 261(1), 190–202 (1993) A.M. Cody, J.R. Stauffer, G. Micela et al., A multiwavelength view of star-disk interaction in NGC 2264. Astron. Nachr. 334, 63 (2013) A.M. Cody, J. Stauffer, A. Baglin et al., CSI 2264: simultaneous optical and infrared light curves of young disk- bearing stars in NGC 2264 with CoRoT and spitzer—evidence for multiple origins of variability. AJ 147, 82 (2014) S. Colombo, S. Orlando, G. Peres et al., New view of the corona of classical T Tauri stars: effects of flaring activity in circumstellar disks. A&A 624, A50 (2019) F. Damiani, G. Micela, Einstein observations of T Tauri stars in taurus-auriga. II. Relationships between x-ray emission and pre-main-sequence activity. ApJ 446, 341 (1995) F. Damiani, G. Micela, S. Sciortino, J.F.R. Harnden, Einstein observations of T Tauri stars in taurus-auriga. I. Properties of x-ray emission. ApJ 446, 331 (1995) F. Damiani, E. Flaccomio, G. Micela et al., A deep chandra x-ray observation of the rich young cluster NGC 6530. I. The x-ray source catalog and the cluster population. ApJ 608(2), 781–796 (2004) F. Damiani, L. Prisinzano, G. Micela, S. Sciortino, The rich young cluster NGC 6530: a combined x-ray-optical-infrared study. A&A 459(2), 477–488 (2006) F. Damiani, G. Micela, S. Sciortino, A chandra x-ray study of the young star cluster NGC 6231: low-mass population and initial mass function. A&A 596, A82 (2016) A.J. Delgado, O. González-Martín, E.J. Alfaro, J. Yun, Multiwavelength analysis of the young open cluster NGC 2362. ApJ 646(1), 269–274 (2006) A.J.F. den Boggende, R. Mewe, E.H.B.M. Gronenschild et al., ANS: x-rays from the direction of the orion nebula (M42). A&A 62, 1–7 (1978) J.J. Drake, B. Ercolano, E. Flaccomio, G. Micela, X-ray photoevaporation-starved T Tauri accretion. ApJ 699(1), L35–L38 (2009) B.G. Elmegreen, Star formation in a crossing time. ApJ 530(1), 277–281 (2000) B. Ercolano, J.J. Drake, J.C. Raymond, C.C. Clarke, X-ray-irradiated protoplanetary disk atmospheres. I. Predicted emission-line spectrum and photoevaporation. ApJ 688(1), 398–407 (2008) B. Ercolano, G. Picogna, K. Monsch et al., The dispersal of protoplanetary discs – II: photoevaporation models with observationally derived irradiating spectra. MNRAS 508(2), 1675–1685 (2021) G. Fabbiano, M. Elvis, A. Accomazzi et al., Increasing the discovery space in astrophysics – a Collation of six submitted white papers (2019). arXiv e-prints arXiv:1903.06634 M. Fang, R. van Boekel, R.R. King et al., Star formation and disk properties in Pismis 24. A&A 539, A119 (2012) F. Favata, G. Micela, S. Sciortino, G.S. Vaiana, The stellar coronal component of the Galaxy. I. The X-COUNT numerical model. A&A 256(1), 86–94 (1992)

3306

S. Sciortino

F. Favata, M. Barbera, G. Micela, S. Sciortino, A search for yellow young disk population stars among EMSS stellar x-ray sources by means of lithium abundance determination. A&A 277, 428–438 (1993) F. Favata, G. Micela, S. Sciortino, On the widespread weak-line T-Tauri population detected in the ROSAT all-sky survey. A&A 326, 647–654 (1997) F. Favata, G. Giardino, G. Micela et al., An XMM-Newton-based x-ray survey of pre-main sequence stellar emission in the L1551 star-forming complex. A&A 403, 187–203 (2003) F. Favata, E. Flaccomio, F. Reale et al., Bright x-ray flares in orion young stars from COUP: evidence for star-disk magnetic fields? ApJS 160, 469–502 (2005a) F. Favata, G. Micela, B. Silva et al., A survey for Fe 6.4 keV emission in young stellar objects in ρ Oph: the strong fluorescence from Elias 29. A&A 433, 1047–1054 (2005b) E.D. Feigelson, X-ray insights into star and planet formation. Proc. Natl. Acad. Sci. 107(16), 7153– 7157 (2010) E.D. Feigelson, Multiwavelength studies of young OB associations, in The Birth of Star Clusters, vol. 424, ed. by S. Stahler (Springer International Publishing AG, Cham, Switzerland, 2018), p. 119 E.D. Feigelson, G.A. Kriss, Soft x-ray observations of pre–main-sequence stars in the chamaeleon dark cloud. ApJ 338, 262 (1989) E.D. Feigelson, T. Montmerle, High-energy processes in young stellar objects. ARA&A 37, 363– 408 (1999) E.D. Feigelson, S. Casanova, T. Montmerle, J. Guibert, ROSAT x-ray study of the chamaeleon I dark cloud. I. The stellar population. ApJ 416, 623 (1993) E.D. Feigelson, P. Broos, J.A. Gaffney et al., X-ray-emitting young stars in the orion nebula. ApJ 574(1), 258–292 (2002) E.D. Feigelson, J.A. Gaffney, G. Garmire et al., X-rays in the orion nebula cluster: constraints on the origins of magnetic activity in pre-main-sequence stars. ApJ 584(2), 911–930 (2003) E.D. Feigelson, L.K. Townsley, P.S. Broos et al., Overview of the massive young star-forming complex study in infrared and x-ray (MYStIX) project. ApJS 209(2), 26 (2013) A. Feldmeier, J. Puls, A.W.A. Pauldrach, A possible origin for x-rays from O stars. A&A 322, 878–895 (1997) E. Flaccomio, F. Damiani, G. Micela et al., Chandra X-ray observation of the oOrion nebula cluster. I. Detection, identification, and determination of x-ray luminosities. ApJ 582(1), 382– 397 (2003a) E. Flaccomio, F. Damiani, G. Micela et al., Chandra x-ray observation of the orion nebula cluster. II. Relationship between x-ray activity indicators and stellar parameters. ApJ 582(1), 398–409 (2003b) E. Flaccomio, G. Micela, S. Sciortino et al., Rotational modulation of x-ray emission in orion nebula young stars. ApJS 160, 450–468 (2005) E. Flaccomio, G. Micela, S. Sciortino, ACIS-I observations of NGC 2264. Membership and x-ray properties of PMS stars. A&A 455(3), 903–921 (2006) E. Flaccomio, B. Stelzer, S. Sciortino et al., The disk/activity connection results from DROXO, in 15th Cambridge Workshop on Cool Stars, Stellar Systems, and the Sun, vol. 1094 (2009), pp. 317–320 E. Flaccomio, G. Micela, S. Sciortino, X-ray variability of pre-main-sequence stars. Toward an explanation of the different X-ray properties of classical and weak-line T Tauri stars. A&A 548, A85 (2012) E. Flaccomio, G. Micela, S. Sciortino et al., A multi-wavelength view of magnetic flaring from PMS stars. A&A 620, A55 (2018) S. Flaischlen, T. Preibisch, C.F. Manara, B. Ercolano, Testing the models of x-ray driven photoevaporation with accreting stars in the orion nebula cluster. A&A 648, A121 (2021) T.A. Fleming, J. Liebert, I.M. Gioia, T. Maccacaro, M dwarfs from the Einstein extended mediumsensitivity survey. ApJ 331, 958 (1988) M. Gagne, J.P. Caillault, J.R. Stauffer, Deep ROSAT HRI observations of the orion nebula region. ApJ 445, 280 (1995)

93 Star-Forming Regions

3307

Gagné M, G. Fehon, M.R. Savoy et al., Carina OB stars: x-ray signatures of wind shocks and magnetic fields. ApJS 194(1), 5 (2011) G. Garmire, E.D. Feigelson, P. Broos et al., Chandra x-ray observatory study of the orion nebula cluster and BN/KL region. AJ 120(3), 1426–1435 (2000) K.V. Getman, E.D. Feigelson, X-ray superflares from pre-main-sequence stars: flare energetics and frequency. ApJ 916(1), 32 (2021) K.V. Getman, E.D. Feigelson, L. Townsley et al., Chandra study of young stellar objects in the NGC 1333 star-forming cloud. ApJ 575(1), 354–377 (2002) K.V. Getman, E. Flaccomio, P.S. Broos et al., Chandra orion ultradeep project: observations and source lists. ApJS 160, 319–352 (2005) K.V. Getman, E.D. Feigelson, P.S. Broos et al., X-ray flares in orion young stars. I. Flare characteristics. ApJ 688, 418–436 (2008a) K.V. Getman, E.D. Feigelson, G. Micela et al., X-ray flares in orion young stars. II. Flares, magnetospheres, and protoplanetary disks. ApJ 688, 437–455 (2008b) K.V. Getman, E.D. Feigelson, K.L. Luhman et al., Protoplanetary disk evolution around the triggered star-forming region cepheus B. ApJ 699(2), 1454–1472 (2009) K.V. Getman, E.D. Feigelson, M.A. Kuhn, Core-halo age gradients and star formation in the orion nebula and NGC 2024 young stellar clusters. ApJ 787(2), 109 (2014a) K.V. Getman, E.D. Feigelson, M.A. Kuhn et al., Age gradients in the stellar populations of massive star forming regions based on a new stellar chronometer. ApJ 787(2), 108 (2014b) K.V. Getman, P.S. Broos, M.A. Kuhn et al., Star formation in nearby clouds (SFiNCs): x-ray and infrared source catalogs and membership. ApJS 229(2), 28 (2017) K.V. Getman, E.D. Feigelson, G.P. Garmire, X-ray super-flares from pre-main sequence stars: flare modeling (2021). arXiv e-prints arXiv:2106.08262 R. Giacconi, G. Branduardi, U. Briel et al., The Einstein (HEAO 2) x-ray observatory. ApJ 230, 540–550 (1979) G. Giardino, F. Favata, G. Micela (2004) Chandra observations of the massive star-forming region S106. X-ray emission from the embedded massive protostellar object IRS 4. A&A 424, 965–978 (2004) G. Giardino, F. Favata, G. Micela et al., The onset of X-ray emission in young stellar objects. A Chandra observation of the Serpens star-forming region. A&A 463(1), 275–288 (2007a) G. Giardino, F. Favata, I. Pillitteri et al., Results from Droxo. I. The variability of fluorescent Fe 6.4 keV emission in the young star Elias 29. High-energy electrons in the star’s accretion tubes? A&A 475(3), 891–900 (2007b) I.M. Gioia, T. Maccacaro, R.E. Schild et al., The medium sensivity survey: a new sample of X-ray sources with optical identifications and the revised extragalactic log N-log S. ApJ 283, 495–511 (1984) U. Gorti, D. Hollenbach, Photoevaporation of circumstellar disks by far-ultraviolet, extremeultraviolet and x-ray radiation from the central star. ApJ 690(2), 1539–1552 (2009) J. Gregorio-Hetem, T. Montmerle, S. Casanova, E.D. Feigelson, X-rays and star formation: ROSAT observations of the Monoceros and Rosette molecular clouds. A&A 331, 193–210 (1998) N. Grosso, T. Montmerle, E.D. Feigelson et al., An x-ray superflare are from an infrared protostar. Nature 387(6628), 56–58 (1997) N. Grosso, T. Montmerle, E.D. Feigelson, T.G. Forbes, Chandra observation of an unusually long and intense X-ray flare from a young solar-like star in M 78. A&A 419, 653–665 (2004) N. Grosso, K. Hamaguchi, D.A. Principe, J.H. Kastner, Evidence for magnetic activity at starbirth: a powerful X-ray flare from the Class 0 protostar HOPS 383. A&A 638, L4 (2020) M.G. Guarcello, L. Prisinzano, G. Micela et al., Correlation between the spatial distribution of circumstellar disks and massive stars in the open cluster NGC 6611. Compiled catalog and cluster parameters. A&A 462(1), 245–255 (2007) M.G. Guarcello, G. Micela, F. Damiani et al., Correlation between the spatial distribution of circumstellar disks and massive stars in the young open cluster NGC 6611. II. Cluster members selected with Spitzer/IRAC. A&A 496(2), 453–463 (2009)

3308

S. Sciortino

M.G. Guarcello, G. Micela, G. Peres et al., Chronology of star formation and disk evolution in the Eagle Nebula. A&A 521, A61 (2010) M.G. Guarcello, J.J. Drake, N.J. Wright et al., Accretion and outflow in the proplyd-like objects near cygnus OB2. ApJ 793(1), 56 (2014) M.G. Guarcello, J.J. Drake, N.J. Wright et al., Photoevaporation and close encounters: how the environment around Cygnus OB2 affects the evolution of protoplanetary disks (2016). arXiv e-prints arXiv:1605.01773 M.G. Guarcello, E. Flaccomio, G. Micela et al., CSI 2264: simultaneous optical and x-ray variability in pre-main sequence stars. I. Time resolved X-ray spectral analysis during optical dips and accretion bursts in stars with disks. A&A 602, A10 (2017) M.G. Guarcello, K. Biazzo, J.J. Drake et al., Dispersal timescale of protoplanetary disks in the low-metallicity young cluster Dolidze 25. A&A 650, A157 (2021a) M.G. Guarcello, R. Bonito, S.J. Clark et al., Testing protoplanetary disk evolution and brown dwarf formation in starburst: NIRCAM and MIRI observations of the young cluster Westerlund 1. JWST Proposal. Cycle 1 (2021b) M. Güdel, Y. Nazé, X-ray spectroscopy of stars. A&A Rev. 17(3), 309–408 (2009) M. Güdel, K.R. Briggs, K. Arzner et al., The XMM-Newton extended survey of the Taurus molecular cloud (XEST). A&A 468, 353–377 (2007) P. Guillout, M. Haywood, C. Motch, A.C. Robin, The stellar content of soft X-ray surveys. I. An age dependent numerical model. A&A 316, 89–101 (1996) P. Guillout, M.F. Sterzik, J.H.M.M. Schmitt et al., The large-scale distribution of x-ray active stars. A&A 334, 540–544 (1998a) P. Guillout, M.F. Sterzik, J.H.M.M. Schmitt et al., Discovery of a late-type stellar population associated with the Gould Belt. A&A 337, 113–124 (1998b) H.M. Günther, Accretion, winds and outflows in young stars. Astron. Nachr. 334(1–2), 67 (2013) L. Hartmann, Accretion Processes in Star Formation (Cambridge University Press, New York, USA, 2008) M.R. Hayashi, K. Shibata, R. Matsumoto, X-ray flares and mass outflows driven by magnetic interaction between a protostar and its surrounding disk. ApJ 468, L37 (1996) P. Hofner, H. Delgado, B. Whitney et al., X-ray detection of the ionizing stars in ultracompact H II regions. ApJ 579(2), L95–L98 (2002) T. Hosokawa, S.S.R. Offner, M.R. Krumholz, On the reliability of stellar ages and age spreads inferred from pre-main-sequence evolutionary models. ApJ 738(2), 140 (2011) C.S. Howard, R.E. Pudritz, W.E. Harris, Simulating radiative feedback and star cluster formation in GMCs – I. Dependence on gravitational boundedness. MNRAS 461(3), 2953–2974 (2016) K. Imanishi, K. Koyama, Y. Tsuboi, Chandra observation of the ρ ophiuchi cloud. ApJ 557(2), 747–760 (2001) K. Imanishi, H. Nakajima, M. Tsujimoto et al., A systematic study of x-ray flares from low-mass young stellar objects in the ρ ophiuchi star-forming region with chandra. PASJ 55, 653–681 (2003) R.D. Jeffries, S.P. Littlefair, T. Naylor, N.J. Mayne, No wide spread of stellar ages in the Orion Nebula Cluster. MNRAS 418(3), 1948–1958 (2011) S.S. Jensen, T. Haugbølle T, Explaining the luminosity spread in young clusters: proto and premain sequence stellar evolution in a molecular cloud environment. MNRAS 474(1), 1176–1193 (2018) D. Johnstone, D. Hollenbach, J. Bally, Photoevaporation of disks and clumps by nearby massive stars: application to disk destruction in the orion nebula. ApJ 499(2), 758–776 (1998) P.G. Judge, S.C. Solomon, T.R. Ayres, An estimate of the sun’s ROSAT-PSPC x-ray luminosities using SNOE-SXP measurements. ApJ 593(1), 534–548 (2003) J.H. Kastner, D.P. Huenemoerder, N.S. Schulz et al., Evidence for accretion: high-resolution x-ray spectroscopy of the classical T Tauri star TW hydrae. ApJ 567(1), 434–440 (2002) R.C. Kennicutt, N.J. Evans, Star formation in the milky way and nearby galaxies. ARA&A 50, 531–608 (2012)

93 Star-Forming Regions

3309

J.S. Kim, C.J. Clarke, M. Fang, S. Facchini, Proplyds around a B1 star: 42 orionis in NGC 1977. ApJ 826(1), L15 (2016) M. Kohno, K. Koyama, K. Hamaguchi, Chandra observations of high-mass young stellar objects in the monoceros R2 molecular cloud. ApJ 567(1), 423–433 (2002) K. Koyama, K. Hamaguchi, S. Ueno et al., Discovery of hard x-rays from a cluster of protostars. PASJ 48, L87–L92 (1996) J. Krautter, R. Wichmann, J.H.M.M. Schmitt et al., New “weak-line”–T Tauri stars in lupus. A&AS 123, 329–352 (1997) M.A. Kuhn, E.D. Feigelson, K.V. Getman et al., The spatial structure of young stellar clusters. III. Physical properties and evolutionary states. ApJ 812(2), 131 (2015) C.J. Lada, E.A. Lada, Embedded clusters in molecular clouds. ARA&A 41, 57–115 (2003) U. Lebreuilly, P. Hennebelle, T. Colman et al., Protoplanetary disk birth in massive star-forming clumps: the essential role of the magnetic field. ApJ 917(1), L10 (2021) D. Locci, C. Cecchi-Pestellini, G. Micela et al., Röntgen spheres around active stars. MNRAS 473(1), 447–456 (2018) J. López-Santiago, On the use of wavelets to reveal oscillatory patterns in stellar flare emission. Philos. Trans. R. Soc. Lond. A 376, 20170253 (2018) J. López-Santiago, I. Crespo-Chacón, E. Flaccomio et al., Star-disk interaction in classical T Tauri stars revealed using wavelet analysis. A&A 590, A7 (2016) A. Lorenzani, F. Palla, Effects of the x-ray emission from young stars on the ionization level of a fractal star forming cloud, in From Darkness to Light: Origin and Evolution of Young Stellar Clusters, ed. by T. Montmerle, P. André. Astronomical Society of the Pacific Conference Series, vol. 243 (2001), p. 745 L.B. Lucy, R.L. White, X-ray emission from the winds of hot stars. ApJ 241, 300–305 (1980) C.F. Manara, M. Robberto, N. Da Rio et al., Hubble space telescope measures of mass accretion rates in the Orion Nebula Cluster. ApJ 755(2), 154 (2012) T. Maschberger, C.J. Clarke, I.A. Bonnell, P. Kroupa, Properties of hierarchically forming star clusters. MNRAS 404(2), 1061–1080 (2010) S.L.W. McMillan, E. Vesperini, S.F. Portegies Zwart, A dynamical origin for early mass segregation in young star clusters. ApJ 655(1), L45–L49 (2007) A. Mesa-Delgado, L. Zapata, W.J. Henney et al., Protoplanetary disks in the hostile environment of carina. ApJ 825(1), L16 (2016) G. Micela, S. Sciortino, S. Serio et al., Einstein x-ray survey of the pleiades : the dependence of x-ray emission on stellar age. ApJ 292, 172–180 (1985) G. Micela, S. Sciortino, G.S. Vaiana et al., The Einstein observatory survey of stars in the hyades cluster region. ApJ 325, 798 (1988) G. Micela, S. Sciortino, F. Favata, Stellar birthrate in the galaxy: constraints from x-ray flux-limited surveys. ApJ 412, 618 (1993) G. Micela, F. Favata, S. Sciortino, HIPPARCOS distances of x-ray selected stars: implications on their nature as stellar population. A&A 326, 221–227 (1997) T. Montmerle, What can x-rays tell us about accretion, mass loss and magnetic fields in young stars?, in Star-Disk Interaction in Young Stars, vol. 243, ed. by J. Bouvier, I. Appenzeller (Cambridge University Press, Cambridge, UK, 2007), pp. 23–30 T. Montmerle, L. Koch-Miramond, E. Falgarone, J.E. Grindlay, Einstein observations of the Rho Ophiuchi dark cloud: an x-ray christmas tree. ApJ 269, 182–201 (1983) T. Montmerle, N. Grosso, Y. Tsuboi, K. Koyama, Rotation and x-ray emission from protostars. ApJ 532(2), 1097–1110 (2000) F. Motte, S. Bontemps, F. Louvet, High-mass star and massive cluster formation in the milky way. ARA&A 56, 41–82 (2018) H. Nakajima, K. Imanishi, S.I. Takagi et al., X-ray observation on the monoceros R2 star-forming region with the chandra ACIS-I array. PASJ 55, 635–651 (2003) R. Neuhäuser, Low-mass pre-main sequence stars and their x-ray emission. Science 276, 1363– 1370 (1997)

3310

S. Sciortino

R.W. Noyes, N.O. Weiss, A.H. Vaughan, The relation between stellar rotation rate and activity cycle periods. ApJ 287, 769–773 (1984) K. Ogura, N. Chauhan, A.K. Pandey et al., Age sequence in small clusters associated with brightrimmed clouds. PASJ 59, 199–204 (2007) H. Ozawa, N. Grosso, T. Montmerle, The x-ray emission from young stellar objects in the ρ ophiuchi cloud core as seen by XMM-Newton. A&A 438(2), 661–661 (2005) P. Padovani, F. Combes, M. Diaz Trigo et al., ESO-Athena synergy white paper (2017). arXiv e-prints arXiv:1705.06064 F. Palla, S.W. Stahler, Star formation in the Orion Nebula Cluster. ApJ 525(2), 772–783 (1999) R. Pallavicini, L. Golub, R. Rosner et al., Relations among stellar X-ray emission observed from Einstein, stellar rotation and bolometric luminosity. ApJ 248, 279–290 (1981) S. Pfalzner, S. Umbreit, T. Henning, Disk-disk encounters between low-mass protoplanetary accretion disks. ApJ 629(1), 526–534 (2005) G. Picogna, B. Ercolano, J.E. Owen, M.L. Weber, The dispersal of protoplanetary discs – I. A new generation of x-ray photoevaporation models. MNRAS 487(1), 691–701 (2019) G. Picogna, B. Ercolano, C.C. Espaillat, The dispersal of protoplanetary discs – III. Influence of stellar mass on disc photoevaporation. MNRAS 508(3), 3611–3619 (2021) I. Pillitteri, S. Sciortino, F. Reale et al., Deep x-ray view of the class I YSO Elias 29 with XMMNewton and NuSTAR. A&A 623, A67 (2019) N. Pizzolato, A. Maggio, G. Micela et al., The stellar activity-rotation relationship revisited: dependence of saturated and non-saturated x-ray emission regimes on stellar mass for late-type dwarfs. A&A 397, 147–157 (2003) M.S. Povich, H.A. Busk, E.D. Feigelson et al., Candidate x-ray-emitting OB stars in MYStIX massive star-forming regions. ApJ 838(1), 61 (2017) T. Preibisch, XMM-Newton study of the serpens star-forming region. A&A 410, 951–959 (2003a) T. Preibisch, XMM-Newton study of the star forming region NGC 1333. A&A 401, 543–555 (2003b) T. Preibisch, E.D. Feigelson, The evolution of x-ray emission in young stars. ApJS 160(2), 390– 400 (2005) T. Preibisch, Y.C. Kim, F. Favata et al., The origin of T Tauri x-ray emission: new insights from the chandra orion ultradeep project. ApJS 160(2), 401–422 (2005a) T. Preibisch, M.J. McCaughrean, N. Grosso et al., X-ray emission from young brown dwarfs in the orion nebula cluster. ApJS 160(2), 582–593 (2005b) L. Prisinzano, G. Micela, E. Flaccomio et al., X-ray properties of protostars in the orion nebula. ApJ 677(1), 401–424 (2008) L. Prisinzano, Sanz-Forcada J, G. Micela et al., Star formation in the outer galaxy: membership and fundamental parameters of the young open cluster NGC 1893. A&A 527, A77 (2011) L. Prisinzano, F. Damiani, V. Kalari et al., The gaia-ESO survey: age spread in the star forming region NGC 6530 from the HR diagram and gravity indicators. A&A 623, A159 (2019) L. Prisinzano, F. Damiani, S. Sciortino et al., Low mass young stars in the milky way unveiled by DBSCAN and gaia EDR3. Mapping the star forming regions within 1.5 Kpc (2022). arXiv e-prints arXiv:2206.00249 S.V. Ramírez, L. Rebull, J. Stauffer et al., Chandra x-ray observations of young clusters. I. NGC 2264 data. AJ 127(5), 2659–2673 (2004a) S.V. Ramírez, L. Rebull, J. Stauffer et al., Chandra x-ray observations of young clusters. II. Orion flanking fields data. AJ 128(2), 787–804 (2004b) G. Rauw, Y. Nazé, X-ray emission from interacting wind massive binaries: a review of 15 years of progress. Adv. Space Res. 58(5), 761–781 (2016) F. Reale, Diagnostics of stellar flares from X-ray observations: from the decay to the rise phase. A&A 471, 271–279 (2007) F. Reale, Coronal loops: observations and modeling of confined plasma. Living Rev. Sol. Phys. 11, 4 (2014) F. Reale, J. Lopez-Santiago, E. Flaccomio et al., X-ray flare oscillations track plasma sloshing along star-disk magnetic tubes in the orion star-forming region. ApJ 856, 51 (2018)

93 Star-Forming Regions

3311

L.M. Rebull, J.R. Stauffer, S.V. Ramirez et al., Chandra x-ray observations of young clusters. III. NGC 2264 and the orion flanking fields. AJ 131(6), 2934–2948 (2006) M. Reiter, R.J. Parker, A tale of two clusters: dynamical history determines disc survival in Tr14 and Tr16 in the Carina Nebula. MNRAS 486(3), 4354–4364 (2019) J. Rho, S.V. Ramírez, M.F. Corcoran et al., Chandra observation of the trifid nebula: x-ray emission from the O star complex and actively forming pre-main-sequence stars. ApJ 607(2), 904–912 (2004) A.J.W. Richert, E.D. Feigelson, K.V. Getman, M.A. Kuhn, No evidence for protoplanetary disk destruction by OB stars in the MYStIX sample. ApJ 811(1), 10 (2015) A.J.W. Richert, K.V. Getman, E.D. Feigelson et al., Circumstellar disc lifetimes in numerous galactic young stellar clusters. MNRAS 477(4), 5191–5206 (2018) J. Robrade, J.H.M.M. Schmitt, A deep XMM-Newton x-ray observation of the chamaeleon I dark cloud. A&A 461(2), 669–678 (2007) R. Rosner, L. Golub, G.S. Vaiana, On stellar x-ray emission. ARA&A 23, 413–452 (1985) D. Rumble, J. Hatchell, H. Kirk, K. Pattle, The JCMT gould belt survey: radiative heating by OB stars (2021). arXiv e-prints arXiv:2105.03353 M. Salvato, J. Buchner, T. Budavári et al., Finding counterparts for all-sky x-ray surveys with NWAY: a Bayesian algorithm for cross-matching multiple catalogues. MNRAS 473(4), 4937– 4955 (2018) J.H.M.M. Schmitt, X-ray emission from normal stars, in Highlights in X-ray Astronomy, vol. 272, ed. by B. Aschenbach, M.J. Freyberg (Max-Planck-Institut für extraterrestrische Physik, Garching, 1999), p. 371 J.H.M.M. Schmitt, S. Czesla, S. Freund et al., X-raying the Sco-Cen OB association: the low-mass stellar population revealed by eROSITA. A&A 661, A40 (2022) N.S. Schulz, The Formation and Early Evolution of Stars (Springer, Berlin/Heidelberg, 2012) S. Sciortino, Stellar coronal emission: what we have learned from pre-ROSAT observations, in Physics of Solar and Stellar Coronae, vol. 183, ed. by J.L. Linsky, S. Serio (Kluwier Academic Publishers, Dordrecht, The Netherlands, 1993), p. 211 S. Sciortino, F. Favata, G. Micela, The stellar coronal component of the Galaxy. II. An analysis of the stellar content of the Einstein extended medium sensitivity survey. A&A 296, 370 (1995) S. Sciortino, I. Pillitteri, F. Damiani et al., The Deep Rho Ophiuchi XMM-Newton Observation (DROXO), in The X-Ray Universe 2005, vol. 604, ed. by A. Wilson (ESA Special Publication, 2006), p. 111 S. Sciortino, G. Rauw, M. Audard et al., The hot and energetic universe: star formation and evolution (2013). arXiv e-prints arXiv:1306.2333 S. Sciortino, E. Flaccomio, I. Pillitteri, F. Reale, The complex phenomena of young stellar objects revealed by their x-ray variability. Astron. Nachr. 340(4), 334–339 (2019) F.H. Shu, H. Shang, A.E. Glassgold, T. Lee, X-rays and fluctuating x-winds from protostars. Science 277, 1475–1479 (1997) K.R. Sokal, C.M. Johns-Krull, G.N. Mace et al., The mean magnetic field strength of CI Tau. ApJ 888(2), 116 (2020) S.W. Stahler, F. Palla, The Formation of Stars (Wiley-VCH, Weinheim, 2004) J. Stauffer, A.M. Cody, L. Rebull et al., CSI 2264: characterizing young stars in NGC 2264 with stochastically varying light curves. AJ 151, 60 (2016) B. Stelzer, G. Micela, R. Neuhäuser, XMM-Newton probes the stellar population in Chamaeleon I South. A&A 423, 1029–1044 (2004) B. Stelzer, G. Micela, K. Hamaguchi, J.H.M.M. Schmitt, On the origin of the x-ray emission from Herbig Ae/Be stars. A&A 457(1), 223–235 (2006) B. Stelzer, E. Flaccomio, K. Briggs et al., A statistical analysis of x-ray variability in pre-main sequence objects of the Taurus molecular cloud. A&A 468(2), 463–475 (2007) B. Stelzer, J. Robrade, J.H.M.M. Schmitt, J. Bouvier, New x-ray detections of Herbig stars. A&A 493(3), 1109–1119 (2009) B. Stelzer, E. Flaccomio, I. Pillitteri et al., Time-resolved spectroscopy of DROXO x-ray sources: flares and Fe Kα emission, in 16th Cambridge Workshop on Cool Stars, Stellar Systems, and

3312

S. Sciortino

the Sun, Astronomical Society of the Pacific Conference Series, vol. 448, ed. by C. Johns-Krull, M.K. Browning, A.A. West (2011), p. 1279 H. Störzer, D. Hollenbach, Photodissociation region models of photoevaporating circumstellar disks and application to the proplyds in orion. ApJ 515(2), 669–684 (1999) S.I. Takagi, H. Murakami, K. Koyama, X-ray sources and star formation activity in the sagittarius B2 cloud observed with chandra. ApJ 573(1), 275–282 (2002) J.C. Tan, M.R. Krumholz, C.F. McKee, Equilibrium star cluster formation. ApJ 641(2), L121–L124 (2006) A. Telleschi, M. Güdel, K. Briggs, M. Audard, XMM-Newton survey of the Chamaeleon I star forming region, in The X-ray Universe 2005, vol. 604, ed. by A. Wilson (ESA Special Publication, 2006), p. 45 A. Telleschi, M. Güdel, K.R. Briggs et al., X-ray emission from T Tauri stars and the role of accretion: inferences from the XMM-Newton extended survey of the Taurus molecular cloud. A&A 468(2), 425–442 (2007) I. Thies, P. Kroupa, S.P. Goodwin et al., Tidally induced brown dwarf and planet formation in circumstellar disks. ApJ 717(1), 577–585 (2010) L.K. Townsley, E.D. Feigelson, T. Montmerle et al., 10 MK gas in M17 and the rosette nebula: x-ray flows in galactic H II regions. ApJ 593(2), 874–905 (2003) L.K. Townsley, P.S. Broos, Y.H. Chu et al., The chandra carina complex project: deciphering the enigma of carina’s diffuse x-ray emission. ApJS 194(1), 15 (2011a) L.K. Townsley, P.S. Broos, Y.H. Chu et al., The integrated diffuse x-ray emission of the carina nebula compared to other massive star-forming regions. ApJS 194(1), 16 (2011b) L.K. Townsley, P.S. Broos, G.P. Garmire, M.S. Povich, The massive star-forming regions omnibus x-ray catalog, third installment. ApJS 244(2), 28 (2019) Y. Tsuboi, K. Imanishi, K. Koyama et al., Quasi-periodic x-ray flares from the protostar YLW 15. ApJ 532(2), 1089–1096 (2000) Y. Tsuboi, K. Koyama, K. Hamaguchi et al., Discovery of x-rays from class 0 protostar candidates in OMC-3. ApJ 554(2), 734–741 (2001) M. Tsujimoto, K. Koyama, Y. Tsuboi et al., X-ray properties of young stellar objects in OMC-2 and OMC-3 from the chandra x-ray observatory. ApJ 566(2), 974–981 (2002) M. Tsujimoto, E.D. Feigelson, N. Grosso et al., Iron fluorescent line emission from young stellar objects in the orion nebula. ApJS 160, 503–510 (2005) G.S. Vaiana, J.P. Cassinelli, G. Fabbiano et al., Results from an extensive Einstein stellar survey. ApJ 245, 163–182 (1981) G.S. Vaiana, A. Maggio, G. Micela, S. Sciortino, Coronal emission and stellar evolution. Mem. Soc. Astron. Italiana 63, 545–561 (1992) K. Vincke, A. Breslau, S. Pfalzner, Strong effect of the cluster environment on the size of protoplanetary discs? A&A 577, A115 (2015) F.M. Walter, J.L. Linsky, S. Bowyer, G. Garmire, HEAO 1 observations of active coronae in mainsequence and subgiant stars. ApJ 236, L137–L141 (1980) R. Wichmann, E. Covino, J.M. Alcalá et al., High-resolution spectroscopy of ROSAT-discovered weak-line T Tauri stars near Lupus. MNRAS 307(4), 909–918 (1999) S.J. Wolk, T.L. Bourke, R.K. Smith et al., Discovery of nonthermal x-ray emission from the embedded massive star-forming region RCW 38. ApJ 580(2), L161–L165 (2002) S.J. Wolk, F.R. Harnden Jr., E. Flaccomio et al., Stellar activity on the young suns of orion: COUP observations of K5-7 pre-main-sequence stars. ApJS 160, 423–449 (2005) N.J. Wright, J.J. Drake, E.E. Mamajek, G.W. Henry, The sStellar-activity-rotation relationship and the evolution of stellar dynamos. ApJ 743(1), 48 (2011) N.J. Wright, J.J. Drake, J.E. Drew et al., Photoevaporating proplyd-like objects in Cygnus OB2. ApJ 746(2), L21 (2012) Z. Xu, G.J. Herczeg, C.M. Johns-Krull, K. France, Probing protoplanetary disk winds with C II absorption (2021). arXiv e-prints arXiv:2107.11188 E. Zari, H. Hashemi, A.G.A. Brown et al., 3D mapping of young stars in the solar neighbourhood with Gaia DR2. A&A 620, A172 (2018)

Nearby Young Stars and Young Moving Groups

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Young Stars and Stellar Groups Within ∼100 pc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nearby Young Moving Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Identifying NYMG Members: X-Rays, UV, and Gaia . . . . . . . . . . . . . . . . . . . . . . . . . . . . Well-Studied NYMGs and Their Members . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High-Energy Stellar Astrophysics: Exploiting Nearby, Young Stars . . . . . . . . . . . . . . . . . . . Early Evolution of Magnetic Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Emission from Young, Intermediate-Mass Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . Pre-MS Accretion and Coronae at High (X-Ray) Spectral Resolution . . . . . . . . . . . . . . . High-Energy Irradiation of Planet-Forming Environments . . . . . . . . . . . . . . . . . . . . . . . . Future Prospects: Impacts of Forthcoming X-Ray Missions and Facilities . . . . . . . . . . . . . . The eROSITA All-sky Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High-Resolution Spectroscopy: Athena, Lynx, Arcus, and XRISM . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

The past two decades have seen dramatic progress in our knowledge of the population of stars of age 150 Myr that lie within ∼100 pc of the Sun. Most such stars are found in loose kinematic groups (“nearby young moving groups,”

J. H. Kastner () Center for Imaging Science, School of Physics and Astronomy, and Laboratory for Multiwavelength Astrophysics, Rochester Institute of Technology, Rochester, NY, USA e-mail: [email protected] D. A. Principe Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, Cambridge, MA, USA e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_83

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NYMGs). The proximity of NYMGs and their members facilitates studies of the X-ray properties of coeval groups of pre-main-sequence (pre-MS) stars as well as of individual pre-MS systems. In this review, we focus on how NYMG X-ray studies provide unique insight into the early evolution of stellar magnetic activity, the X-ray signatures of accretion, and the irradiation and dissipation of protoplanetary disks by high-energy photons originating with their host pre-MS stars. We discuss the likely impacts of the next generation of X-ray observing facilities on these aspects of the study of NYMGs and their members. Keywords

Accretion · Circumstellar disks · Early stellar evolution · Moving clusters · Star formation · Stellar associations · Stellar coronae · X-ray astronomy

Introduction Only a quarter of a century has elapsed since the identification of the TW Hydrae association (TWA), a sparse but physically associated group of pre-main-sequence (pre-MS) stars located at a mean distance of just ∼50 pc (Kastner et al. 1997, and references therein). The TWA represented the first example then known of a young stellar group found significantly (a factor ∼3) closer to Earth than the nearest starforming molecular clouds. Its existence was established, in large part, on the basis of the anomalously bright X-ray emission from the (mere) five TWA member stars then known (Kastner et al. 1997), capitalizing on the fact that such luminous X-ray emission constitutes a defining characteristic of low-mass (∼0.1–1.5 M⊙ ), pre-MS stars (see Feigelson and Montmerle 1999, and references therein). The intervening two-and-a-half decades have seen dramatic progress in our knowledge of the population of stars of age 150 Myr that lie within ∼100 pc (Zuckerman and Song 2004; Torres et al. 2008; Zuckerman et al. 2011; Gagné et al. 2019; Kastner et al. 2019). Thanks to their proximity and the lack of both ambient molecular cloud material and intervening ISM, such nearby, young stars – most of which are found in loose kinematic groups (nearby young moving groups, hereafter NYMGs; Mamajek 2016) – provide unique tests of pre-MS stellar evolution and the late stages of evolution of planet-forming circumstellar disks (Kastner et al. 2016b) and presently represent the best targets for direct-imaging searches for exoplanets and brown dwarfs (e.g., Chauvin 2016; Carter et al. 2021). Considerable effort is now being invested in expanding the known memberships of NYMGs and the number of known NYMGs, so as to exploit the potential of nearby, young stars to advance our knowledge of the early evolution of stars and planetary systems. Whereas X-ray-based identifications utilizing the ROSAT All-sky Survey (hereafter RASS) were a major factor in the early identification of NYMGs and their members, the high-precision stellar parallax and proper motion measurements now flowing from the Gaia Space Astrometry Mission (Gaia Collaboration et al. 2016, 2018,

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2021) are driving much of this recent progress in the census and characterization of nearby young stellar groups (see overviews in Gagné et al. 2019; Kastner et al. 2019). The proximity of NYMGs and their members facilitates studies of the X-ray properties of coeval groups of pre-MS stars as well as of individual pre-MS systems. In this review, we focus on how such studies provide unique insight into the early evolution of stellar magnetic activity, the X-ray signatures of accretion, and the irradiation of protoplanetary disks and the atmospheres of young planets by highenergy photons originating with their host pre-MS stars. We also provide a brief prospectus on some likely advances in the study of nearby young stars and young stellar groups that will be enabled by forthcoming and planned next-generation X-ray missions.

Young Stars and Stellar Groups Within ∼100 pc Nearby Young Moving Groups As of the writing of this chapter, roughly a dozen known young moving groups had been identified within ∼100 pc of the Sun (see Fig. 1). These NYMGs are (essentially, by definition) significantly closer than the nearest well-studied dark clouds and their associated young (T Tauri) stellar populations, which are all located beyond ∼120 pc. For purposes of this chapter, “young” is defined as ∼5–150 Myr – a range whose lower end roughly corresponds to the evolved T Tauri star and zero-age main-sequence evolutionary stages of solar- to intermediate-mass (i.e., G- to A-type) stars and which spans the full extent of the pre-MS evolution of stars with lower masses (K and M stars), down to the (eventual) H-burning limit. Comprehensive reviews of the status of the study of stars in these age and distance ranges as of the early-mid 2000s are contained in Zuckerman and Song (2004) and Torres et al. (2008). (For a brief review of the early history of the discovery and study of young stars and young moving groups within ∼100 pc, the reader is directed to Kastner 2016.) By the mid-2000s, the aggregate total of confirmed and candidate members of NYMGs in the age range ∼5–150 Myr within ∼100 pc numbered ∼300 stars, plus a few hundred more associated with the more distant Scorpius-Centaurus (Sco-Cen) complex. Due in large part to recent releases of data from the Gaia Space Astrometry Mission (see below), the dozen NYMGs of age ∼5–150 Myr within ∼100 pc now comprise, in total, >300 well-established members and ∼1600 candidate members, and these numbers continue to grow (J. Gagné, private communication). If one includes the combined populations of the sprawling ∼10–20 Myr-old Sco-Cen, Lower Centaurus Crux (LCC), and Upper Centaurus Lupus (UCL) complexes (which generally lie beyond ∼100 pc and are hence not a focus of this chapter), the present census of nearby, young stars stands at several thousand stars within ∼145 pc of the Sun (Luhman and Esplin 2020; Kerr et al. 2021).

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Fig. 1 The spatial, distance, and age distribution of known NYMGs within ∼120 pc. Left: the groups’ heliocentric positions and approximate extents as seen in projection within the plane of the Galaxy, i.e., X, Y in the galactic reference frame (such that the groups’ positions are collapsed along the Z direction, perpendicular to the plane). The position of the Sun is indicated by the black cross at (X, Y ) = (0, 0). Right: mean NYMG distance vs. age. Groups specifically highlighted or mentioned in this chapter are (from left to right in the right panel) the ε Cha Association (EPSC), the η Cha cluster (ETAC), the TW Hya association (TWA), the β Pic Moving Group (BPMG), the Columba and Argus Associations (COL, ARG), the Tuc-Hor Association (THA), and the AB Dor Moving Group (ABDMG). The purple triangles indicate open clusters. These plots do not include the Scorpius-Centaurus, Lower Centaurus Crux, and Upper Centaurus Lupus complexes, which are comprised of several thousand ∼10–20 Myr-old stars located ∼100–145 pc from the Sun (Pecaut and Mamajek 2016; Luhman and Esplin 2020). (Figures adapted from Gagné et al. 2019, courtesy J. Gagné (private communication))

The origins of NYMGs, and even the existence of some NYMGs, have been the subject of interest and debate for more than two decades (e.g., Mamajek et al. 1999; Zuckerman et al. 2011; Mamajek 2016; Zuckerman et al. 2019). We will not cover the problem of NYMG origins in this chapter, other than to point out that recent Gaia-based kinematic studies appear to directly connect NYMGs to well-studied young clusters and star-forming clouds within a few hundred pc of the Sun (Kounkel and Covey 2019; Gagné et al. 2021; Kerr et al. 2021). The X-ray emission properties of protostars and pre-MS stars in these rich star formation regions, all of which lie well beyond ∼100 pc, are covered elsewhere in this Handbook (see ⊲ Chaps. 93, “Star-Forming Regions” and ⊲ 92, “Pre-main Sequence: Accretion and Outflows”).

Identifying NYMG Members: X-Rays, UV, and Gaia Throughout the late 1990s and early 2000s, the majority of NYMG members of spectral-type F through early M (i.e., late-type member stars) were identified, or their youth was confirmed, via their anomalously strong coronal X-ray emission relative to the field star population (e.g., Kastner et al. 1997; Mamajek et al. 1999; Sterzik et al. 1999; Webb et al. 1999; Zuckerman and Webb 2000; Torres et al. 2000;

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Stelzer and Neuhäuser 2000; Mamajek et al. 2002). The intense coronal emission characteristic of such young and (hence) rapidly rotating, late-type stars is the external manifestation of their strong internal magnetic dynamos that are generated via the combination of differential rotation and convection and result in large surface magnetic fields (see ⊲ Chap. 89. “Stellar Coronae”). As a consequence, late-type pre-MS and very young (“zero age”) main-sequence stars display X-ray luminosities (LX ) relative to bolometric (Lbol ) that lie in the range −4  log (LX /Lbol )  −3; in stark contrast, the vast majority of main-sequence field stars, which are of age 1 Gyr, display log (LX /Lbol )  −5 (the Sun exhibits log (LX /Lbol ) ∼ − 6 to −7). As it became clear that there existed a local population of such X-ray-luminous, young stars, it was quickly recognized that this population was also kinematically coherent, i.e., that these stars occupied a relatively small volume of the overall field star galactic space motion (U V W ) parameter space and that, furthermore, individual stellar groups (“moving groups”) were distinguishable within this U V W space (Zuckerman and Song 2004; Torres et al. 2008, and references therein). The combination of stellar kinematics and relative X-ray luminosity (LX /Lbol ) remains a particularly effective means to identify candidate late-type members of NYMGs, with follow-up ground-based optical spectroscopy – to obtain measurements of lithium absorption lines and emission lines indicative of chromospheric or accretion activity (e.g., Hα) – then serving to confirm the youth of such candidates (e.g., Song et al. 2003). (During the pre-MS evolution of (highly convective) late-type stars, surface Li is rapidly mixed to the stellar interior, where it is destroyed via nuclear reactions. Therefore, the presence (and strength) of Li absorption lines in a stellar photospheric spectrum serves as an indicator of youth (e.g., Zuckerman and Song 2004; Kraus et al. 2014; Binks et al. 2020b, and references therein).) However, the sensitivity of the only existing all-sky X-ray survey – the RASS – is insufficient to detect the coronae of young, lower-mass (M-type) stars at distances much beyond ∼50 pc (Wright et al. 2011; Rodriguez et al. 2013). The combination of IR photometry from the Two Micron All-Sky Survey (2MASS) and Wide-field Infrared Science Explorer (WISE) all-sky surveys and UV photometry from the Galaxy Evolution Explorer (GALEX) all-sky survey also efficiently selects cool field stars displaying strong chromospheric emission, facilitating identification of candidate nearby, young M-type stars to somewhat larger distances (Shkolnik et al. 2011; Rodriguez et al. 2011, 2013; Bowler et al. 2019). Nevertheless, prior to the availability of Gaia data, the census of stars of age 150 Myr within ∼100 pc was significantly lacking in stars of spectral type later than mid-K (e.g., Kraus et al. 2014; Gagné et al. 2017; Bowler et al. 2019) due, in large part, to the limited sensitivities of the ROSAT and GALEX all-sky surveys and the lack of sufficiently precise stellar distances and proper motions. With data releases that include high-precision stellar parallaxes and proper motions (PMs) for over a billion stars (Gaia Collaboration et al. 2018, 2021), Gaia is now providing the raw material for expansive investigations of the nearby field star population in search of candidate young, low-mass stars. Gaia parallaxes and PMs, combined with Gaia and ground-based spectroscopic radial velocity (RV)

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measurements, provide the precise galactic positions (XY Z) and space motions (U V W ) necessary to “sweep up” hundreds of new candidate members of known NYMGs, via the application of various statistical young star search methodologies (e.g., Gagné and Faherty 2018; Lee and Song 2018, 2019; Riedel et al. 2017). These new candidates are dominated by M dwarfs, thereby demonstrating the potential of Gaia data to reveal the suspected “missing” low-mass NYMG members (Faherty et al. 2019; Gagné and Faherty 2018). The RASS and GALEX all-sky survey data available for the new Gaia-identified candidates, though generally limited to the brighter stars, demonstrate that their high-energy emission properties are overall consistent with youth (Gagné and Faherty 2018; Schneider et al. 2019). Conversely, Gaia data enable confirmation or refutation of nearby, young star status for candidates that have been previously identified on the basis of, e.g., their chromospheric and/or coronal activity levels (Rodriguez et al. 2013; Binks et al. 2020a) or their Li absorption line strengths (Binks et al. 2020b). In particular, Gaia parallax distances can establish the ages of candidate nearby young stars that have been selected through such kinematically unbiased means, via comparison of their color-magnitude (or HR) diagram positions with theoretical pre-MS isochrones (e.g., Kastner et al. 2017; Binks et al. 2020a,b). More generally, Gaia colormagnitude data for NYMGs serve both to test theoretical isochrones (e.g., Gagné et al. 2018a) and to define empirical isochrones so as to establish or confirm the relative ages of NYMGs as deduced via other methodologies (e.g., DicksonVandervelde et al. 2021).

Well-Studied NYMGs and Their Members We highlight here a half-dozen of the more heavily studied NYMGs, in order of estimated age (youngest to oldest): the ε Chamaeleonis Association, the TW Hydrae Association, the β Pictoris Moving Group, the Tucana-Horologium and Columba Associations, and the AB Doradus Moving Group. In Table 1, we list two dozen of the most intensively studied young stars of age 150 Myr within ∼110 pc, most of which belong to one of these groups. Table 1 lists these noteworthy stars in order of distance from Earth and summarizes the properties of their X-ray emission and their circumstellar disks (or lack thereof), with references to papers establishing or detailing these X-ray and disk properties. All of the Table 1 stars are discussed in this section and/or subsequent sections of this chapter.

The ε Cha Association, age ∼5 Myr Even previous to Gaia, the ε Cha Association (εCA) had been considered to be among the youngest NYMGs (Murphy et al. 2013). The εCA lies near the ∼10 Myrold η Cha cluster, which was identified on the basis of pointed ROSAT observations (Mamajek et al. 1999). The two groups likely share a common origin, as both appear to be physically associated with the more distant, well-studied Chamaeleon starforming regions (Feigelson et al. 2003); however, the εCA is evidently even younger than the η Cha cluster. The widely dispersed εCA and its compact “sibling” stellar

Sp. Typea M1VeBa1

K0V

A6V M2Ve

M4Ve+M4Ve F0+Vk K5V(e) M2Ve M4+M5 M2Ve K6Ve

A0V K5+K7

Name AU Mic

AB Dor

β Pic CE Ant

Hen 3-600 HR 8799 HD 98800 CD-29 8887 TWA 30A CD-33 7795 TW Hya

HR 4796A V4046 Sgr

70.8 71.5

37.1 40.9 42.1 45.9 47.4 49.7 60.1

19.6 34.1

14.9

TWA βPMG

ND Drake et al. (2014) Acc+SCor Günther et al. (2006), Argiroffi et al. (2012)

X-raysc SCor

Refs.d Testa et al. (2004); Mitra-Kraev et al. (2005) AB Dor SCor Drake et al. (2015), Schmitt et al. (2021) βPMG WCor Günther et al. (2012) TWA SCor Webb et al. (1999), Uzawa et al. (2011) TWA SCor+Acc Huenemoerder et al. (2007) Columba WCor Robrade and Schmitt (2010) TWA SCor Kastner et al. (2004) TWA SCor Kastner et al. (1997) TWA AbsCor Principe et al. (2016) TWA SCor Kastner et al. (1997) TWA Acc+SCor Kastner et al. (2002), Brickhouse et al. (2010)

D b (pc) Group 9.7 βPMG

Table 1 Well-studied pre-main-sequence stars within ∼100 pc

D PP

PP D D NE PP NE PP

D D

Qi et al. (2013), Andrews et al. (2016), van Boekel et al. (2017) Milli et al. (2017) Kastner et al. (2008b), Kastner et al. (2018)

Looper et al. (2010)

Czekala et al. (2021) Faramaz et al. (2021) Ronco et al. (2021)

Smith and Terrile (1984) Ren et al. (2021)

diske Refs.f D Schneider and Schmitt (2010); Grady et al. (2020) NE

(continued)

Two M companions Circumbinary PP disk

Hierarchical triple Multiple exoplanets Hierarchical quadruple TWA 2 Highly inclined PP disk TWA 5 Well-studied PP disk

Massive exoplanet TWA 7

Rapid rotator

Comments Flare star; two exoplanets

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K0e A9Ve A0sh A0Vaek A2Vek K7IVe F1Vek

T Cha HD 100453 HD 104237A HD 100546 HD 141569 PDS 70 HD 169142

102.7 103.8 106.6 108.1 111.6 112.4 114.9

D b (pc) 76.5 97.9 101.0

εCA LCC? εCA LCC? Sco-Cen? UCL Sco-Cen?

Group TWA εCA Sco-Cen? AbsCor WCor ND? Acc? ND SCor Acc?

X-raysc SCor Acc+SCor Acc? Sacco et al. (2014) Collins et al. (2009) Feigelson et al. (2003) Skinner and Güdel (2020) Stelzer et al. (2006) Joyce et al. (2020) Grady et al. (2007)

Refs.d Webb et al. (1999) Argiroffi et al. (2007) Swartz et al. (2005)

diske Refs.f NE PP Kastner et al. (2010) PP Guidi et al. (2018), Öberg et al. (2021b) PP Sacco et al. (2014) D Collins et al. (2009) PP Hales et al. (2014) PP Pineda et al. (2019) D White et al. (2016) PP Keppler et al. (2018) PP Grady et al. (2020)

Two protoplanets? Protoplanet?

X-ray-bright comp. Two protoplanets?

highly inclined PP disk

Protoplanet?

Comments TWA 9A

b

Stellar spectral type as listed in the SIMBAD database (https://simbad.u-strasbg.fr/simbad/) Gaia Early Data Release 3 (EDR3) parallax distance. Typical EDR3 statistical parallax uncertainties are ∼0.1% c X-ray class: SCor = strong coronal (log (LX /Lbol )  −4); WCor = weak coronal (log (LX /Lbol )  −6); AbsCor = absorbed coronal (intrinsic log (LX /Lbol )  −4 with log (NH [cm−2 ])  21); Acc = X-ray signatures of accretion; ND = X-rays not detected d Selected references for observations/classification of X-ray emission e Disk class: D debris (gas-poor), PP protoplanetary (gas-rich), NE no evidence of disk (i.e., no detection of excess thermal mid-IR emission from warm circumstellar dust) f Selected references for observations/classification of disk

a

Sp. Typea K5V K1Ve A1Vep

Name CD-36 7429A MP Mus HD 163296

Table 1 (continued)

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group, the η Cha cluster, also serve to illustrate the (somewhat fuzzy) distinction between NYMGs (i.e., loose associations of comoving stars) and young (open) star clusters. The implicit assumption is that – unlike an association – a cluster is potentially gravitationally bound. A stellar group’s mass density (relative to the field) and tidal radius serve as quantitative measures of its status as a cluster vs. association (e.g., Zuckerman et al. 2019; Dickson-Vandervelde et al. 2021, and references therein). Gaia data provided the basis for a recent reassessment of the membership status of previously identified εCA candidates and refined estimates of the distance, age, multiplicity, and disk fraction of the group (Dickson-Vandervelde et al. 2021). This analysis yielded a census of ∼50 members and candidate members and confirmed that, at a mean distance of 101 pc and age of ∼5 Myr, the εCA represents the youngest stellar group within ∼100 pc of Earth. Consistent with its young age, ∼30% of εCA members display infrared excesses indicative of the presence of circumstellar disks, and the εCA’s multiplicity fraction of 40% is intermediate between those of young T Tauri star associations and the field (Dickson-Vandervelde et al. 2021). The confirmed εCA members with circumstellar disks include MP Mus and T Cha, two of the nearest stars of roughly solar mass that are known to host primordial protoplanetary disks (Sacco et al. 2014), and the “classical” Herbig Ae/Be (actively accreting, intermediate-mass) star HD 104237A, the anchor of a complex multiplestar system (Feigelson et al. 2003) that includes yet another gaseous-disk-bearing, solar-mass star (HD 104237E). All of these disk-bearing stars have been the subject of Chandra and/or XMM-Newton studies, as described in later sections of this review. The ∼5 Myr age of the εCA is similar to that of heavily scrutinized young clusters such as IC 348 (Stelzer et al. 2012) and NGC 2264 (Bouvier et al. 2016); however, the εCA is a factor ∼3.5 and ∼7 closer to Earth, respectively, than these well-studied clusters, and the line of sight in the direction of the εCA is largely free of extinction by either a host molecular cloud or intervening ISM (Murphy et al. 2013). This makes the εCA particularly fertile ground for future X-ray- and UVbased investigations of the early evolution of stellar magnetic activity, dispersal of protoplanetary disks, and irradiation of young exoplanets.

The TW Hya Association, age ∼8 Myr The TW Hya association was the first pre-MS stellar group identified within ∼100 pc of the Sun (Kastner 2016, and references therein). Its namesake, TW Hydrae, is one of the most intensively studied pre-MS stars. This scrutiny is due in large part to the fact that, at a mere 60.1 pc, TW Hya presents the nearest-known example of a near-solar-mass star orbited by, and actively accreting from, a gasrich protoplanetary disk (unless otherwise noted, distances listed in this review are obtained from Gaia EDR3 parallaxes). Since the TWA’s identification, and the accompanying recognition of its proximity to the Earth, TW Hya itself has become among the most popular targets for high spatial and spectral resolution studies

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Fig. 2 Multiwavelength views of the nearly face-on protoplanetary disk orbiting the nearby young star TW Hydrae (top panels) and schematic and observational views of the X-ray manifestation of disk material accreting onto the star (bottom panels). Top panels, from left to right: maps of emission from rotational transitions of the CO and N2 H+ molecules obtained by the Submillimeter Array and Atacama Large Millimeter Array (ALMA), respectively, in the 0.8 mm wavelength range (Qi et al. 2013); near-infrared (1.6 µm) polarimetric/coronagraphic image of starlight scattered off small (submicron) dust grains at the disk surface (van Boekel et al. 2017); 0.8 mm continuum emission from larger (mm-sized) dust grains in the cold disk midplane, with inset blowup of the central few au around the star (Andrews et al. 2016). Note the ringed disk structure, which has been interpreted as potentially revealing the location of the disk “CO snow line,” in the case of the molecular line imaging (Qi et al. 2013), and the locations and masses of protoplanets forming in the disk, in the case of the near-IR and sub-mm continuum imaging (Andrews et al. 2016; van Boekel et al. 2017, and references therein). Bottom right: X-ray spectral models for coronal emission and accretion shock sources (top and middle panels) compared with the observed Chandra/HETGSspectrum of TW Hya (bottom panel) (Brickhouse et al. 2010). The comparison indicates that the X-ray spectrum of TW Hya is in fact a combination of corona and accretion shocks (see also Fig. 4 and associated text). Bottom left: the interpretation of the X-ray data vs. model comparison at right in terms of an “accretion-fed corona” (Brickhouse et al. 2010) (see section “X-Ray Signatures of Accretion: TW Hya as Archetype”).

aimed at understanding protoplanetary disk physics and chemistry as well as preMS accretion processes (Fig. 2). The mean distance (∼50 pc) and youth of the TWA’s original contingent of just five stars – which included the well-studied, dusty binary systems HD 98800 (TWA 4) and Hen 3–600 (TWA 3), both discussed further below – were originally ascertained from the combination of RASS X-ray luminosity measurements and Li line equivalent widths (Kastner et al. 1997). The common space motions of the

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TWA member stars were established not long thereafter (Webb et al. 1999), and its known membership then steadily expanded; as of the writing of this chapter, the TWA comprised at least 30 single stars and binary systems (Lee and Song 2019; Carter et al. 2021). Various methods (Li absorption line equivalent widths, pre-MS isochrones, kinematic traceback) indicate that the age of the TWA is ∼8 Myr (Gagné et al. 2018b; Lee and Song 2018, and references therein). The TWA’s presently known membership is notably deficient in early-type stars, its most massive member being HR 4796A (= TWA 11A), which is host to a well-studied debris disk (e.g., Milli et al. 2017). This A-type star, which is not an X-ray source (see below), is accompanied by two comoving, X-ray-luminous M-type companions, the second of which (TWA 11C, at ∼13,000 au projected separation) having been identified via serendipitous XMM-Newton X-ray observations (Kastner et al. 2008a). Thanks to its proximity and young age, the TWA has served as a prime subject for studies of the early evolution of coronal activity for ultralow-mass stars and (future) brown dwarfs (BDs) – i.e., pre-MS objects that lie near or below the (∼0.08 M⊙ ) mass lower limit for eventual core hydrogen burning via core nuclear fusion, which constitutes the definition of a main-sequence star. Chandra X-ray observations of a handful of TWA BD candidates – which, at the age of the TWA, corresponds to pre-MS stars with spectral types later than ∼M6 – yielded evidence for a wide range of X-ray activity levels (Gizis and Bharat 2004; Castro et al. 2011; Tsuboi et al. 2003). A systematic study of X-ray data available for TWA M stars spanning the future H-burning limit revealed that the fractional X-ray luminosity appears to decline from log (LX /Lbol ) ∼ − 3 for early-M stars to log (LX /Lbol )  − 3.5 for most (though not all) stars of spectral-type M4 and later (Kastner et al. 2016a). This decline in X-ray flux is possibly related to the persistence of circumstellar accretion disks to late pre-MS ages for ultralow-mass stars and BDs; the resulting, long-lasting magnetospheric coupling between star (or BD) and accretion disk may inhibit stellar spin-up and, hence, suppress coronal activity (see below).

The β Pic Moving Group, age ∼24 Myr The nearby A star β Pictoris (D = 19.6 pc) gained notoriety almost four decades ago, for hosting the first debris disk to be directly (coronagraphically) imaged in scattered light (Smith and Terrile 1984). The star has become even more heavily scrutinized with the discovery of a massive planet orbiting within its nearly edgeon disk (Lagrange et al. 2010). Though the early-1980s discovery of the disk suggested that β Pic was quite young, its youth was not firmly established until the identification of a contingent of comoving late-type stars, which was dubbed the β Pic Moving Group (Zuckerman et al. 2001a; hereafter βPMG). The age of the βPMG, which comprises at least 60 (perhaps as many as ∼120) members very widely distributed on the sky (Lee and Song 2019; Carter et al. 2021), is presently estimated at ∼24 Myr (Gagné et al. 2018b, Lee and Song 2018 and references therein). Though β Pic itself is a weak X-ray source (Günther et al. 2012), the βPMG membership includes the X-ray-luminous, late-type, disk-bearing stars V4046 Sgr and AU Mic. The latter star, at a distance of just 9.7 pc, is the nearest-known example

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of a young M-type flare star orbited by a debris disk (e.g., Grady et al. 2020). The AU Mic disk (like the β Pic disk) is viewed nearly edge-on, and Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2014) observations have recently established that, consistent with this viewing geometry, AU Mic hosts two transiting exoplanets (Plavchan et al. 2020; Martioli et al. 2021). Meanwhile, the near-solarmass V4046 Sgr binary and its (circumbinary) disk share many properties with the (only slightly closer) TW Hya star-disk system; but V4046 Sgr is, in many respects, even more interesting. It consists of a close (2.4 d period) 0.9 + 0.85 M⊙ pair orbited by and accreting from a circumbinary, protoplanetary disk that harbors ∼0.1 M⊙ of gas and dust (see Kastner et al. 2014 and references therein). This is a remarkably large disk mass, given the system’s advanced pre-MS age: V4046 Sgr is roughly three times older than TW Hya, which is widely regarded as unusually “old” (evolved) for an actively accreting T Tauri star. The V4046 Sgr system is furthermore a hierarchical multiple. As in the case of the companion to TWA member HR 4796A, the early-M-type tertiary of V4046 Sgr (GSC 07396–00759, itself likely a close binary) is loosely bound (projected separation ∼12,000 au) and was identified via X-ray imaging (Kastner et al. 2011).

The Tuc-Hor and Columba Associations, age ∼40–50 Myr The Tucana and Horologium Associations (Tuc-Hor) were identified independently and subsequently recognized as a single kinematically and spatially coherent group (Torres et al. 2000; Zuckerman and Webb 2000; Zuckerman et al. 2001b). Prior to their union, Tucana was the first NYMG subjected to a comprehensive (ROSAT) X-ray study, which supported the general age range determined by the initial studies of the group (Stelzer and Neuhäuser 2000). The Columba Association is very similar to Tuc-Hor in both kinematics and age (∼40–50 Myr; Torres et al. 2008; Zuckerman et al. 2011). Like the βPMG, the membership of Tuc-Hor and Columba – which (combined) now totals in excess of 200 stars (Lee and Song 2019) – is very widely distributed on the sky. These groups furthermore may be associated with the newly identified χ 1 For cluster (Zuckerman et al. 2019), one of only a handful of known open clusters within ∼100 pc (the others being the far older Hyades and Coma Berenices clusters; Fig. 1). The Columba Association membership is notable for including the chemically peculiar late-A star HR 8799, which hosts the first (and still only) directly imaged multiple-exoplanet system (Marois et al. 2010). The TucHor Association and the χ 1 For cluster provide vivid illustrations of the limited capabilities of the RASS where X-ray detection of low-mass NYMG members is concerned (Rodriguez et al. 2013; Zuckerman et al. 2019). The AB Dor Moving Group, age ∼120 Myr

The young, rapidly rotating K-type star AB Dor has been intensively studied in X-rays since the days of the Einstein, EXOSAT, and GINGA facilities (Vilhu et al. 1993; Collier Cameron et al. 1988; Alev et al. 1996). Only decades later was it recognized as the anchor of a comoving group of (∼30) young stars (Zuckerman et al. 2004). The AB Dor Moving Group (ABDMG), like the younger βPMG, thereby serves as an illustration of how the membership of a NYMG, which was

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first established primarily on the basis of pre-Gaia stellar kinematics, was slowly and painstakingly increased via spectroscopic follow-up of candidate members identified, in many cases, on the basis of sufficiently large X-ray fluxes to be detected in the RASS (Zuckerman et al. 2011; Schlieder et al. 2012; Binks and Jeffries 2016). The presently established membership of the ABDMG now stands at over 100 stars (Lee and Song 2019). At an estimated age of 119±20 Myr, the ABDMG appears to be physically associated with the Pleiades (Ortega et al. 2007), perhaps originating as a tidal tail of this iconic cluster (Gagné et al. 2021). At a distance of just 14.9 pc, AB Dor itself remains a readily accessible target for multiwavelength studies of the temporal behaviors and energetics of flares at rapidly rotating, highly magnetically active late-type stars (Schmitt et al. 2021).

High-Energy Stellar Astrophysics: Exploiting Nearby, Young Stars Early Evolution of Magnetic Activity The connection between stellar rotational evolution and the strength and characteristics of stellar high-energy radiation fields represents a primary means to understand the generation of stellar magnetic fields via dynamo processes and to constrain magnetic dynamo models (see accompanying chapter on stellar coronae by J. Drake & B. Stelzer). Stars in the mass range ∼0.1–1.5 M⊙ spin up during their pre-MS (gravitational contraction) stages, with spin-up rates governed largely by star-disk interactions (Gallet and Bouvier 2013). Peak rotation rates should be attained as the stars approach the ZAMS – the aforementioned AB Dor being a “poster child” for such spin-up at the end of the pre-MS contraction stage – after which they spin down on timescales ∝ t 1/2 due to stellar wind-induced angular momentum loss (Skumanich 1972; Kawaler 1988). Measurements of the surface rotation periods (Prot ) of the members of young open clusters across the age range 13–700 Myr (e.g., Wright et al. 2011; Stauffer et al. 2016; Argiroffi et al. 2016, and references therein) have yielded empirical relationships between Prot and stellar mass and age that are generally consistent with the predictions of rotational evolution models. The spread in Prot among coeval cluster members can be more than an order of magnitude at a given mass, however, reflecting the wide range of disk lifetimes and internal core-envelope coupling strengths among pre-MS stars (see discussions in Gallet and Bouvier 2013; Binks et al. 2015). These and other observational investigations of the rotation-activity connection (e.g., Stelzer et al. 2016; Magaudda et al. 2020; Pineda et al. 2021) have further explored the correlation between Prot and stellar UV and/or X-ray emission intensity. However, with the exception of the nearest-known young open clusters (e.g., the Pleiades; Stauffer et al. 2016), such Chandra and/or XMM-Newton X-ray imaging photometry studies are deficient in K and (even more so) M stars with ages 100,000 K) CSPNe can extend into the X-ray domain. The Wien tail of the spectral distribution can be detectable as a weak soft X-ray emission peaking at 0.1–0.2 keV, with no emission above 0.4 keV. This X-ray emission, however, can be highly absorbed in metal-rich atmospheres of CSPNe with high content of helium, carbon, nitrogen, and oxygen. Interestingly, the heaviest atoms in the atmosphere of CSPNe settle down with time, while the stellar effective temperature increases. Therefore, sources of very soft ≤0.3 keV X-ray emission can be expected from the atmosphere of hot, hydrogen-rich CSPNe. The wild variety of morphologies of PNe, with many showing extremely axisymmetric or point-symmetric shapes (Schwarz et al. 1992; Manchado et al. 1996), and the detection of fast collimated outflows (jets) (Guerrero et al. 2020) have evidenced the effects of the late evolution of CSPNe in binary systems (Soker and Livio 1994; Soker 1997). It can thus be expected that a significant fraction of CSPNe are actually binary systems (De Marco 2009) where the companion is a main-sequence low-mass star. Late-type companions of CSPNe may present coronal emission or accrete material from a disk or directly from the CSPN wind, which can be detected in X-rays. These sources will exhibit harder X-rays than the photospheric emission from hot CSPNe. Moreover, the Interacting Stellar Winds (ISW) model of PN formation (Kwok et al. 1978; Balick 1983) implies the interaction between the present fast stellar wind of the CSPN and the previous slow and dense AGB wind. The physics of this interaction is described by the wind-blown bubble model (Weaver et al. 1977), where a forward shock compresses and snowplows the AGB wind and a reverse shock heats the fast stellar wind at temperatures in excess of 107 K, producing a hot bubble. The fast stellar wind is so tenuous that negligible X-ray emission can be expected. However, at the interphase between the hot bubble and the optical nebula, processes of heat conduction, turbulent mixing, and mass evaporation raise the density and emissivity of the hot gas while reducing its temperature to a few times 106 K. These are optimal conditions for the emission of soft X-rays with limbbrightened diffuse morphology inside the innermost cavities of PNe, which soon became an essential prediction of ISW models of PN formation (Mellema and Frank 1995).

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Early X-Ray Observations of PNe The first detection of X-ray emission from a PN was presented in the mid1980s, when EXOSAT observations of NGC 1360 were reported (de Korte et al. 1360). Soon afterwards, an analysis of the Einstein archive (Tarafdar and Apparao 1988) discovered X-ray emission from another four PNe, namely, A 33, NGC 246, NGC 6853, and NGC 7293. A subsequent analysis of the EXOSAT archive by the same authors (Apparao and Tarafdar 1989) revealed X-ray emission from four more PNe: A 36, NGC 1535, NGC 4361, and NGC 3587. Despite the apparent success in detecting X-ray emission from PNe by these early X-ray missions, some misidentifications and erroneous analyses were soon noticed. A detailed comparison between X-ray and optical images revealed that the X-ray sources attributed to some PNe are actually located outside their optical boundaries. The misidentifications include A 33 (Conway and Chu 1997) and NGC 1535 (Chu et al. 3587). Before the launch of ROSAT, there were seven PNe with credible X-ray detections. All of them harbored hot (100,000–200,000 K) CSPNe, and thus, all these detections were interpreted as soft X-ray emission from the photosphere of their CSPNe. ROSAT observations then yielded additional X-ray detections of A 12, BD+30◦ 3639, LoTr 5, and NGC 6543 (Kreysing et al. 1992), K 1-27 (Rauch et al. 1994), K 1-16 (Hoare et al. 1995), and A 30 (Chu and Ho 1995). Note, however, that as for A 33 and NGC 1535, the comparison of the X-ray and optical images of A 12 confirmed that the X-ray source is actually located outside the nebular optical boundary (Hoare et al. 1995). Removing A 12 from the list of X-ray PNe, ROSAT had thus almost doubled the number of X-ray PNe up to a total of 13 sources. Among the sources investigated using ROSAT observations, the emission from LoTr 5, NGC 4361, NGC 6543, and NGC 6853 (Kreysing et al. 1992), A 30 (Chu and Ho 1995), and BD+30◦ 3639 (Leahy et al. 2000) was claimed to be diffuse. This diffuse X-ray emission would likely originate from shock-heated gas confined within hot bubbles, as expected in the ISW model of PN formation. The diffuse nature of the X-ray emission reported for LoTr 5, NGC 4361, and NGC 6853, however, can be questioned. In particular, the low signal-to-noise ratio of the ROSAT all-sky survey observations of LoTr 5 and NGC 4361 may cause their apparent extended morphology, which is not seen in deep pointed ROSAT observations (Chu and Ho 1995), while an electronic ghost image for photon energies below 0.2 keV may be behind the apparent extended morphology of NGC 6853 (Chu et al. 1993). ROSAT provided the capability to investigate the spectral properties of the Xray sources associated with PNe. Accordingly, three different X-ray spectral types among PNe could be identified at that time (Conway and Chu 1997): (1) Soft X-ray spectra with emission only below 0.4 keV, for example, NGC 246, NGC 1360, NGC 6853, and K 1–16 (Kreysing et al. 1992; Hoare et al. 1995) (2) “Hard” X-ray spectra that peak above 0.5 keV, for example, BD+30◦ 3639 and NGC 6543 (Kreysing et al. 1992; Arnaud and Harrington 3639)

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(3) Mixed spectra with both soft and hard components, for example, NGC 7293 (Leahy et al. 1994) The origin of these different sources of X-ray emission was at that time uncertain and highly disputed. Then in 2000 we presented a comprehensive investigation of the entire ROSAT archive searching for PSPC observations of PNe (Guerrero et al. 2000). ROSAT had obtained pointed or serendipitous PSPC observations of 63 PNe, with only 16 detections among them. These detections were mostly found in sources located closer than 2 kpc and with optical extinctions AV lower than 0.5 mag (Fig. 1–top), confirming that the weakness and softness of the X-ray emission from PNe make their detection to depend critically on their distance, extinction, and evolutionary status of their CSPNe and associated PNe. Most of these detections correspond to the soft photospheric emission from late CSPNe, implying large Teff and little photospheric metal content, of nearby and tenuous PNe with small absorption column densities (Fig. 1–bottom). Only three of these ROSAT X-ray PNe, namely, BD+30◦ 3639, NGC 6543, and NGC 7009, with type 2 X-ray spectra (Conway and Chu 1997), could be tentatively attributed to diffuse hot gas. Interestingly, the comparison between these three sources and those associated with type 1 or 3 X-ray spectra implied that the former were associated with denser, smaller PNe surrounding cooler CSPNe with lower surface gravity (Fig. 1–bottom).

The early X-ray results provided by Einstein, EXOSAT and most importantly ROSAT hinted at the presence of different sources of X-ray emission in PNe (soft photospheric emission, shock-heated plasma inside hot bubbles, etc.), but the limited spatial resolution of the ROSAT PSPC observations precluded a detailed study of the spatial distribution of the X-ray emission in PNe. These studies had to wait until the advent of Chandra and XMM-Newton.

PNe in the Era of Chandra and XMM-Newton The unprecedented spatial resolution of Chandra and sensitivity of XMM-Newton promised a leap forward in our knowledge of high energy processes in PNe. It took very little for it to come, as soon as the first observations of PNe came out. The first Chandra high-resolution image and CCD spectra of a PN, namely, BD+30◦ 3639 (Fig. 2), one of the ROSAT X-ray type 2 PN, was presented in 2000 (Kastner et al. 2000). The X-ray emission was then revealed to be diffuse and confined within the innermost cavity of the shell of ionized gas of this young PN (see inset in Fig. 2). The authors noted an asymmetry of the spatial distribution of this X-ray emission, which is discussed below. Its ACIS spectrum (black dots in Fig. 2) implied a hot plasma at a temperature ≃3 × 106 K with the notable contribution

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Fig. 1 Observed distributions of the hydrogen column density NH and distance (top), nebular electron density Ne and linear radius (bottom left), and stellar surface gravity g and effective temperature Teff of the PNe and CSPNe with ROSAT PSPC observations (Guerrero et al. 2000). Undetected sources are shown by open diamonds, whereas sources detected in X-rays are shown as solid dots colored according to their spectral type (Conway and Chu 1997): blue for type 1 with spectra peaking below 0.4 keV, black for type 2 with spectra peaking above 0.5 keV, and red for type 3 with mixed spectra

of O VII, O III, and Ne IX line emission. These emission lines, particularly the abundance anomaly implied by the bright Ne line, are indicative of products of nuclear burning (Maness et al. 2003). Soon afterward, a Chandra high-resolution image and CCD spectra of NGC 6543, the Cat’s Eye Nebula (Fig. 3), another ROSAT X-ray type 2 PN, were released (Chu et al. 2001). These observations reinforced the prevalence of hot plasma emission in ROSAT X-ray type 2 PN, with a plasma temperature ≃1.7 × 106 K, and revealed clearly for the first time the expected limb-brightened

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Fig. 2 Chandra ACIS-S (black dots) and LETG (red histogram) X-ray spectra of BD+30◦ 3639. The inset shows the HST WFPC2 Hα image (grayscale) overlaid by Chandra ACIS-S X-ray contours (red). The most relevant emission lines are labeled. (Picture courtesy of R.Jr. Montez and J.H. Kastner Kastner et al. 2000)

Fig. 3 Chandra ACIS-S 0.3–1.0 keV (left) and Chandra (blue) and HST Hα (red) and [N II] (green) color-composite picture (right) of NGC 6543, the Cat’s Eye Nebula. The X-ray emission is clearly resolved into a point source at the central star and diffuse emission confined within the central elliptical shell and two extensions along the major axis. No X-ray emission is associated with the fast collimated outflows piercing through the extensions along the major axis

morphology of the diffuse X-ray emission within the hot bubble of PNe, lending strong support to the wind-wind interaction as a major agent in the shaping and evolution of PNe. Indeed, it was found that the thermal pressure of the hot gas

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drives the ongoing expansion and evolution of the nebula. The details of the spectral analysis, however, disclosed a puzzling situation: the abundances of the X-rayemitting gas are similar to those of the fast stellar wind, not those of the nebula, but its temperature is 100 times lower than the expected postshock temperature of the fast stellar wind. The plasma temperatures implied mixing, but the chemical abundances do not. The Chandra observations of NGC 6543 also revealed an unexpected source of harder X-ray emission, peaking above 1 keV, at the location of its CSPN. The nature of this source was investigated at this same time (Guerrero et al. 2001), together with the hard X-ray emission detected at the CSPN of NGC 7293, the Helix Nebula, one of the rare ROSAT X-ray type 3 PN. Both in NGC 6543 and NGC 7293, the source of hard X-ray emission was a point source at the location of their CSPNe. In the latter case, the small distance of the nebula and faintness of its CSPN precluded the origin of the X-ray emission from a background or foreground X-ray source. The possible chromospheric emission from a late-type companion was constrained at a spectral type later than M5. Just one year later, in 2002, the first XMM-Newton detection of hot gas in a PN was reported (Guerrero et al. 2002). The diffuse X-ray emission from NGC 7009, the Saturn Nebula, was found inside the innermost cavity of this famous PN. The X-ray emission could be associated with a hot plasma at temperatures of ≃1.8 × 106 K, similar to those found in NGC 6543. Contrary to previous expectations, there was no X-ray emission associated with the fast outflows detected in NGC 6543 nor NGC 7009. This was exactly the opposite to that found in the proto-PN Hen 31475 (Sahai et al. 2003). In this case, Chandra observations found X-ray emission associated with the ≃1,000 km s−1 fast outflow emanating from its central source, exactly at the location of the brightest optical knot northwest of the CSPN (Fig. 4). The X-ray emission arises from a region with an inverted V-shape morphology indicative of strong shocks. Emission could be expected from the similar structure towards the southeast, but extinction is much higher. The number of PNe with Chandra and XMM-Newton detections grew steadily in the next years, and a number of detailed studies on individual sources helped us to gain insights on the role of X-ray-emitting plasmas in PNe and their central stars (Kastner et al. 2001, 2003; Kastner et al. 2008; Guerrero et al. 2005; Montez et al. 2005, 2009, 2010; Gruendl et al. 2006; Frew et al. 2011; Ruiz et al. 2011). The complexity of the physical properties of the hot plasma in PNe was most highlighted in the only high-quality Chandra LETG high-dispersion spectrum of a PN, namely, BD+30◦ 3639 (Yu et al. 2009). The LETG spectrum reveals a twotemperature plasma and the prevalence of the H-like resonance lines of O VIII and C VI, and the He-like triplets of O VII and Ne IX (red spectrum in Fig. 2). The nonsolar abundances implied by the spectral analysis (Yu et al. 2009) point at the present stellar wind composition of the shocked X-ray-emitting plasma. These observations also suggest complex physical processes at the interphase between the hot plasma and the optical nebula, with carbon ions crossing the interphase and recombining into the optical nebular shell (Nordon et al. 2009). So far, no other high-quality high-dispersion spectra of PNe have been obtained due to their extreme surface brightness faintness (Guerrero et al. 2015).

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Fig. 4 Chandra ACIS-S 0.3–1.5 keV (blue) and HST Hα (red) and [N II] (green) color-composite picture of the proto-PN Hen 3–1475. The fast ≃1,000 km s−1 collimated outflow shows a notable S shape indicative of precession of the ejection engine. The X-ray emission is coincident with the brightest northwest knot of the fast outflow (Sahai et al. 2003). North is top; east is to the left

A coherent vision of the effects of hot gas in PN evolution and on the nature of the hard X-ray emission from CSPNe was emerging at that time (Ruiz et al. 2013) but still lacking (Soker and Kastner 2002; Kastner and Soker 2003). The PN community joined forces and presented an ambitious Chandra Large Program proposal to acquire observations of all PNe closer than 1.5 kpc, the Chandra Planetary Nebulae Survey (ChanPlaNS).

This program produced a notable increase of PNe with X-ray observations in the time period between 2010 and 2015 that has revealed X-ray emission in almost 40 PNe (Kastner et al. 2012; Freeman et al. 2014; Montez et al. 2015). This has resulted in an unprecedented progress in the understanding of the nature of point and extended sources of X-rays in PNe as described in the next section. This was also a fortunate circumstance, as the sensitivity of the Chandra ACIS instrument to the soft X-ray emission of PNe has declined considerably in the last years due to the contamination of its CCD window.

What Has Been Learned from the X-Ray Observations of PNe All Chandra and XMM-Newton observations, either from pointed or serendipitous observations of individual sources or in the framework of the ChanPlaNS project, have produced a tremendous impact in our knowledge of the hot gas in PNe. We are now aware of the effects of the hot gas in the formation and evolution of PNe and also the implications of X-ray point sources at their CSPNe to search for binary companions or to compare their stellar winds to those of massive stars.

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Diffuse X-Ray Emission The ChanPlaNS program managed to gather X-ray observations for almost 60 PNe, detecting diffuse X-ray emission in 21 (Kastner et al. 2012; Freeman et al. 2014) and X-ray point sources at their CSPNe for 16 (Montez et al. 2015). After the observing program was completed, two additional detections of diffuse X-ray emission were reported in a serendipitous Chandra observation of NGC 5189 (Toalá et al. 2019) and a pointed observation of IC 4593 (Toalá et al. 2020). Another two peculiar sources, of the type born-again PNe, presented both diffuse and pointsource X-ray emissions (Guerrero et al. 2012; Toalá et al. 2015), as will be discussed below. Considering all these detections, the occurrence of diffuse emission among the sample of PNe with Chandra and XMM-Newton observations amounts to 32% of the whole sample, whereas it adds to 37% for point sources. The large observational body of X-ray observations of PNe in the ChanPlaNS has allowed us to investigate quantitatively the effects of the hot gas in PN evolution and their physical structure.

PN Evolution A very clear (and obvious!) first result arose from the ChanPlaNS. Diffuse X-ray emission is mostly confined to PNe with elliptical sharp, closed inner rims or bipolar lobes (Kastner et al. 2012; Freeman et al. 2014), and only in a few cases it is found in PNe with bipolar morphology (Kastner et al. 2001; Gruendl et al. 2006; Montez et al. 2009). As soon as the hot bubble (whether its morphology is round, elliptical, or bipolar) gets pinched or broken, the hot gas within hot bubble quickly escapes and the density and temperature sudden drops make its emissivity falls below the detection limit. The detailed statistical analysis of the occurrence of diffuse X-ray emission within the hot bubbles of PNe allowed by ChanPlaNS (Freeman et al. 2014) set solid limits on the time duration of the X-ray-emitting phase in PNe. Diffuse X-ray emission is preferentially found in PNe younger than ≃5,000 yr, with compact (0.30 pc in size) hot bubbles and dense (1,000 cm−3 ) nebular shells. With time, the stellar wind power diminishes and the volume occupied by the hot bubble expands. The wind-diminishing energy input and the adiabatical cooling of the hot gas cannot support the production of plasma at X-ray-emitting temperatures. The pressure drop of the hot bubble makes also the snowplowed gas at the inner nebular rim to broaden, acquiring a more diffuse appearance. The sharp and closed morphology of the rim of a PN can be used as a prime criterion for the presence of a hot bubble filled with X-ray-emitting gas. A nebular age younger than 5,000 yr and rim size smaller than 0.30 pc are also indicative of X-ray emission.

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Refining Models of PN Formation The first predictions for diffuse X-ray emission from PNe were based on the early models of wind-blown bubbles for bubbles around massive stars (Weaver et al. 1977) and ISW models of PNe with limited physical processes (Mellema and Frank 1995; Zhekov and Perinotto 1996). The detailed physical parameters of the hot bubbles of PNe (plasma temperature and density, emission measure, chemical abundances, X-ray luminosity, etc.) revealed by Chandra and XMMNewton confronted these simple models. One of the most critical contradictions was posed by the relatively low temperature of the X-ray-emitting plasma in PNe, in the range of 1–3×106 K, and its chemical abundances, which suggested it consisted mostly of fast stellar wind (Chu et al. 2001; Yu et al. 2009). Soon after the first Chandra and XMM-Newton observations of PNe, the effects of the declining stellar wind and heat conduction at the interphase between the hot bubble and the PN were explored using 1D hydrodynamical models, including a sophisticated and complete treatment of heat conduction and mass evaporation (Steffen et al. 2008). These models were capable to reproduce the physical conditions and X-ray luminosity of the PNe with diffuse X-ray emission (Ruiz et al. 2013). The treatment of the effects of turbulent mixing at the interphase requires 2D models. These have been explored using high-resolution two-dimensional radiationhydrodynamic numerical simulations also accounting for heat conduction at the interphase (Toalá and Arthur 2014, 2016, 2018). These models have been able to reproduce many of the observational properties of hot bubbles in PNe, including the ∼1 × 106 K low temperature of the X-ray-emitting plasma and the quick decline of their X-ray emission. We must note here that the X-ray observations of PNe led to the recognition of two different families of hot bubbles, those produced by H-rich CSPNe and those associated with [WR] CSPNe. The latter CSPNe have optical spectra with broad emission lines of carbon, nitrogen, and/or oxygen, similar to those of genuine Wolf-Rayet (WR) stars descending from massive OB stars. In both cases, they have H-poor atmospheres and powerful stellar winds, with mass-loss rates and terminal wind velocities in the case of [WR] CSPNe much larger than those of H-rich CSPNe. As a result, their energy input within hot bubbles are larger, whereas the chemical composition of the stellar wind, richer in heavy elements, implies larger emissivities than those of H-rich CSPNe (Toalá and Arthur 2018; Sandin et al. 2016; Heller 2018). As a consequence, PNe with a [WR] CSPN have larger X-ray luminosities than PNe with a H-rich CSPN (Freeman et al. 2014), as are the case for BD+30◦ 3639 (Kastner et al. 2000) or NGC 5189 (Toalá et al. 2019). The Physics at the Interphase Between the PN and Its Hot Bubble The sudden temperature drop from a few 106 K to 10,000 K and density jump from a few cm−3 to a few 10−3 cm−3 suggest the presence of an interphase region with intermediate properties between the hot bubble and the photoionized optical PNe.

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The production of hot gas in a PN and therefore the formation and evolution of its hot bubble and the PN itself can be expected to depend on the physical processes at this interphase. This region was revealed in shallow absorptions of the O VI λλ1032,1038 Å resonance doublet in FUSE far-UV spectra of the CSPNe of a number of X-ray-emitting PNe (Ruiz et al. 2013; Gruendl et al. 2004). Its spatial distribution and physical properties were finally revealed in HST STIS UV spectroscopic observations of the N V λλ1239,1243 Å resonance doublet in NGC 6543 (Fang et al. 2016). Its temperature (a few 100,000 K) and density (≃200 cm−3 ) are intermediate between those of the hot bubble and photoionized optical PN. These physical conditions, determined by the effects of heat conduction from the hot bubble and mass evaporation from the innermost regions of the rim of the photoionized optical PN, in conjunction with turbulent mixing, define a hydrostatical equilibrium between the X-ray hot bubble and optical PN.

The Connection Between PNe and WR Wind-Blown Bubbles PNe have hot bubbles filled with X-ray-emitting plasma with linear sizes up to 0.30 pc that are fed by the stellar wind of their CSPNe with mechanical luminosities of 1032 –1035 erg s−1 . The physical processes of wind-wind interactions that occur within the PN hot bubbles are similar to those taking place in WR bubbles, but a much larger spatial scales. These WR bubbles are formed around the descendants of OB stars, which develop during the WR phase the most powerful stellar winds, with mechanical luminosities 1037 –1038 erg s−1 , i.e., 102 –106 times larger than those of CSPNe. These evolved stars blow circumstellar bubbles by pushing the material ejected in the previous phase of stellar evolution, the red or yellow supergiant phase, through a dense and slow stellar wind. The linear sizes of WR bubbles are a few tens pc, in contrast with the size of the X-ray-emitting hot bubbles of PNe below the parsec scale. The physical properties of these WR bubbles can be expected to be similar to those of hot bubbles in PNe, but the X-ray spectra of the diffuse emission from WR bubbles peak even at lower energies, 0.4–0.5 keV. Spectral analyses imply two-temperature plasma components at ≃1 × 106 K and ≃10 × 106 K (Chu 2003; Toalá et al. 2012, 2014, 2016). The large angular size of WR bubbles results in very low X-ray surface brightness (Fig. 5), which together with the softness of their X-ray spectrum and small distance to the Galactic Plane (and thus high extinction) explains that only four have X-ray detections, namely, NGC 2359 (Toalá et al. 2015), NGC 3199 (Toalá et al. 2017), NGC 6888 (Toalá et al. 2014; Toalá and Arthur 2016), and S 308 (Chu 2003; Toalá et al. 2012). The production of hot gas in PNe and WR bubble both imply the interaction of stellar winds affected by processes of heat conduction and turbulent mixing, and thus, they can be studied altogether to understand these phenomena at different energy, length, and time scales. Indeed the much larger angular size of WR bubbles with respect to PNe (as expected from their notable difference in size) allows an accurate determination of the interphase size and physical conditions spatial variations of the X-ray-emitting plasma.

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Fig. 5 XMM-Newton EPIC 0.3–1.0 keV (blue) and optical Hα (red) and [O III] (blue) color-composite picture of the WR bubble NGC 6888. The diffuse X-ray emission is clearly confined within the crescent-shaped nebula, with higher surface brightness towards the northeast and southwest tips. X-ray emission is also found at the blowout towards the northwest. North is top; east is to the left

Differential Extinction PNe and their immediate progenitors, the AGB stars, are known to be prime places for dust production. The overall spatial distribution of this dust would result in gradients and/or patches of enhanced absorption of nebular emission, as well as shadows of dusty filaments and knots. These have been searched using optical Hα and Hβ images, as well as radio continuum images, to build maps of the logarithmic extinction coefficient c(Hβ), but the results have been ambiguous and become only reliable when using integral field spectroscopic observations (Walsh et al. 2016). The extreme sensitivity of the soft X-ray emission from PNe to the absorption along the line of sight makes this spectral regime an excellent probe for spatially varying extinction across the images of PNe. Indeed, asymmetries of the X-ray emission in BD+30◦ 3639 (Kastner et al. 2000), NGC 7027 (Kastner et al. 2001), and Hen 3–1475 (Sahai et al. 2003) were soon ascribed to spatially varying extinction across the nebulae. Detailed studies of the relationship between X-ray emission and extinction have been used to provide a fair interpretation of the X-ray morphology of PN hot bubbles (Kastner et al. 2002; Montez and Kastner 2018). X-Ray Emission from Born-Again PNe Born-again PNe are a peculiar subset of PNe. These are formed when a very late thermal pulse occurs on the surface of a post-AGB star that is already descending the WD cooling track. This violent process is actually a thermo-nuclear runaway event that transforms the helium at the stellar surface into carbon, nitrogen, and oxygen. The envelope of the CSPN grows and its temperature subsequently drops, somehow resembling a “born-again” CSPN, for a few decades or centuries. By the time the CSPN effective temperature increases and its size shrinks, the increasing

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ionizing flux and the fast stellar wind photo-evaporate and ablate the hydrogen-poor material ejected in the born-again event. Quite surprisingly, two born-again PNe, namely, A 30 (Fig. 6) and A 78, have been found to produce extremely soft X-ray emission (Guerrero et al. 2012; Toalá et al. 2015). The X-ray spectra are so soft, and the temperatures implied so low, that it is difficult to explain those with the present conditions of the fast stellar wind. There is evidence of significant C VI line emission with very reduced levels of thermal continuum, which has been suggested to be better reproduced by chargeexchange reaction processes, as it is the case for the X-ray emission detected in comets of the solar system.

X-ray observations of the hot plasma inside hot bubbles of PNe have revealed new physical processes in the interaction of the fast stellar wind with the surrounding nebula. In addition to heat conduction and turbulent mixing, other processes such as ions crossing the interphase between the hot bubble and the nebula and charge-exchange reaction may be active in PNe. X-ray observations also disclose dusty regions and very importantly can be used to help us understand bubbles around their more massive sibling WR stars, casting light on the evolution of WR bubbles just before SN explosions. Once again, PNe offer a unique laboratory for the detailed investigation of physical processes in ionized plasmas.

Fig. 6 XMM-Newton EPIC X-ray (purple) and optical Hα (green) and [O III] (blue) colorcomposite picture of A 30 (left) and Chandra ACIS X-ray (purple) and HST WFC3 [O III] (orange) color-composite picture of its innermost regions (right). The diffuse X-ray emission fills the [O III]bright petal-like region inside the old, round PN (left) and is coincident with one of the brightest optical knot (right). In addition, there is a point source of X-ray emission at the CSPN (right). North is top; east is to the left

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Point Sources of X-Ray Emission In addition to the diffuse X-ray emission from hot bubbles, their CSPNe can also present point sources of X-ray emission. ChanPlaNS found 21 of those sources, some being the only source of X-ray emission in the PN and some others embedded within the diffuse emission of hot bubbles (Freeman et al. 2014; Montez et al. 2015). Different spectral properties and even time behaviors have been reported for the X-ray CSPNe as described in the next sections.

Photospheric X-Ray Emission from CSPNe The soft (≤0.3 keV) photospheric emission from the Wien tail of hot CSPNe was suspected to be the origin for the X-ray emission from most PNe detected by ROSAT (Guerrero et al. 2000). On the opposite, Chandra and XMM-Newton have detected only a small fraction of CSPNe whose X-ray emission can really be attributed to photospheric emission (Kastner et al. 2012; Montez et al. 2015). The different spectral responses of Chandra and XMM-Newton make them more sensitive to harder X-ray emission than ROSAT, detecting X-ray emission at higher energy from CSPNe. Indeed, only the X-ray spectrum of the CSPN of NGC 6853, the Dumbbell Nebula, fulfills the expectations for photospheric emission from a hot CSPN. A few more hot CSPNe, namely, NGC 246, NGC 1360, NGC 2371, and NGC 4361, have X-ray spectra consistent with those expectations but exhibit median energies slightly higher than expected (Freeman et al. 2014).

Binary CSPNe The next obvious source or “hard” ≥0.5 keV X-ray emission from a CSPN is the chromospheric emission from a late-type companion. The identification of the “hard” X-ray sources at the CSPNe of LoTr 5, DS 1, and HFG 1 (Montez et al. 2010) strongly supported this hypothesis. The star rotation and variable level of coronal activity even provide an interpretation of the variations seen in the X-ray light curves of some of these sources. A comprehensive analysis of the ChanPlaNS observations indeed found a class of X-ray CSPNe with high-temperature plasma emission and levels of X-ray luminosity uncorrelated with the CSPN bolometric luminosity that would originate from magnetically active companions (Montez et al. 2015). The high X-ray luminosities of some of these sources suggest that they have been spun-up during the binary evolution of the CSPN, transferring orbital energy to the rotation of the companion (Montez et al. 2010). The presence of an unresolved late-type companion star will contribute to the general emission from the CSPN particularly in the IR regime. This is the case for some of those CSPNe, but not for the nearby central star of NGC 7293, whose bright X-ray emission remained enigmatic until a recent detection of a binary companion has been reported based on TESS data (Aller et al. 2020).

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The then unknown nature of the X-ray source at the CSPN of NGC 7293 led a search for X-ray emission above 0.5 keV in WD, the next stage in the evolution of CSPN. A handful of “hard” X-ray WDs without known binary companions despite their close distance has been reported (O’Dwyer et al. 2003; Chu et al. 2004; Bilíková 2010). A recent Chandra and XMM-Newton joint investigation of the hot WH KPD 0005+5106 (Chu et al. 2021) has found evidence for a 4.7 hr periodicity in the X-ray 0.6–3.0 keV light curve. Assuming that this period corresponds to a binary orbital period, only a substellar companion would have a size larger than its Roche radius to fuel accretion-powered hard X-ray emission. Another intriguing case of hard X-ray emission is that of the CSPN of NGC 2392 (Ruiz et al. 2013), the first PN where a fast collimated outflow was detected (Gieseking et al. 1985) and may be the only one where it is currently being collimated and launched (Guerrero et al. 2021). The discovery of a WD companion with an orbital period of 1.9 day (Miszalski et al. 2019) and X-ray variability even in a shorter time-scale of 6.2 hour (Guerrero et al. 2019) argue for accretion of material from the CSPN wind onto a WD companion as the most plausible origin for its hard X-ray emission.

Shock-In Winds The ChanPlaNS investigation of X-ray CSPNe also confirmed the presence of another class of sources whose X-ray emission has lower plasma temperatures than those of binary CSPNe and is correlated with the bolometric luminosity as LX /Lbol ≃ 10−7 (Montez et al. 2015). This relationship is very close to that found for the OB stars in the rich open cluster NGC 6231, LX /Lbol = 10−6.912±0.153 (Sana et al. 2006), which results from strong stochastic shocks within the dense layers of the winds of massive stars induced by the strong instability of their radiatively driven nature (Lucy and White 1980; Gayley and Owocki 1995). Indeed the most relevant member of this class is the CSPN of NGC 6543 (Guerrero et al. 2001), whose strong stellar wind exhibits variability in time-scales of minutes to hours indicative of changes in its structure (Prinja et al. 2012; Guerrero and De Marco 2013). It has thus been concluded that the X-ray emission of this second class of “hard” X-ray CSPNe can be attributed to shock-in winds with smaller efficiency of conversion of mechanical wind energy into X-rays than OB stars. Most X-ray point sources at CSPNe have X-ray emission peaking ≥0.5 keV that are unlikely to be due to their photospheric emission. In many cases, this X-ray emission can be attributed to the coronal activity of companions or even to accretion of the CSPN wind onto those companions. In other cases, shockin winds, as those detected in WR and OB stars, are also found to be active in CSPNe with strong and variable stellar winds.

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The Future of X-Ray Observations of PNe Most modern X-ray observations of PNe have been obtained using the Chandra and XMM-Newton observatories, which were launched more than 20 years ago in 1999. Still, they have been used rather than other more modern X-ray observatories such as Swift or AstroSat due to their larger effective areas in the energy range of interest (≤1.5 keV) for PNe. In the long run, the Advanced Telescope for High ENergy Astrophysics (Athena) and the Lynx X-ray Observatory (Lynx), with their enhanced collecting areas, high-dispersion instruments, and/or spatial resolution, will play major roles in a better understanding of the production of hot gas in the interior of PNe and its role in their evolution and shaping. A comparison between the available 345 ks XMM-Newton RGS exposure (highly affected by high background that reduced the net exposure time to only 70 ks) and a simulated Athena XIFU 20 ks exposure clearly shows that Athena can look into the details of the plasma physics to accurately determine the physical conditions and chemical abundances of many PNe (Fig. 7). The Athena IFS is otherwise expected to detect the diffuse X-ray emission from a larger number of PNe, allowing detailed CCD spectroscopic analyses. Meanwhile, the eROSITA All Sky Survey (eRASS) can reach a sensitivity in the range from 1 × 10−14 down to 3 × 10−17 erg cm−2 s−1 , depending on the final exposure time of a particular position on the sky. About 200 PNe will be observed with exposure times greater than 20 ks in the eRASS, and almost 500 PNe will have observations as sensitive, ≤ 2 × 10−15 erg cm−2 s−1 , as those of ChanPlaNS (Guerrero 2020).

We can thus expect major improvement in our knowledge of the physical properties and chemical abundances and on the statistics of the presence of X-ray emission in PNe.

Fig. 7 Available XMM-Newton RGS 70 ks spectrum of NGC 6543 (left) and simulated Athena XIFU 20 ks exposure (right). The obvious superior signal-to-noise ratio of the Athena XIFU spectrum detects more clearly different emission lines that would allow a detailed spectral analysis to derive accurate physical conditions and chemical abundances

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Acknowledgments This chapter uses graphical material kindly provided by Joel H. Kastner, Rodolfo Jr. Montez, and Jesús A. Toalá. The author acknowledges support of the Spanish Ministerio de Ciencia, Innovació y Universidades (MCIU) grant PGC2018-102184-B-I00 and from the State Agency for Research of the Spanish MCIU through the “Center of Excellence Severo Ochoa” award to the Instituto de Astrofísica de Andalucía (SEV-2017-0709).

References A. Aller et al., Planetary nebulae seen with TESS: discovery of new binary central star candidates from Cycle 1. Astron. Astrophys. 635, id.A128 (2020) K.M.V. Apparao, S.P. Tarafdar, X-ray observations of planetary nebulae with the EXOSAT satellite. Astrophys. J. 344, 826–829 (1989) K. Arnaud, K.J. Borkowski, J.P. Harrington, X-ray emission from the wind-blown bubble in the planetary nebula BD+30◦ 3639. Astrophys. J. Lett. 462, L75–L78 (1996) B. Balick, The evolution of planetary nebulae. I. Structures, ionizations, and morphological sequences. Astron. J. 94, 671–678 (1983) B. Balick, A. Frank, Shapes and shaping of planetary nebulae. Ann. Rev. Astron. Astrophys. 40, 439–478 (2002) J. Bilíková et al., Hard x-ray emission associated with white dwarfs. III. Astron. J. 140, 1433–1443 (2010) Y.-H. Chu et al., Hot gas in the circumstellar bubble S 308. Astrophys. J. 599, 1189–1195 (2003) Y.-H. Chu, C.-H. Ho, Diffuse x-ray emission from the hydrogen-deficient planetary nebula abell 30. Astrophy. J. Lett.448, L127–L130 (1995) Y.-H. Chu, K.B. Kwitter, J.B. Kaler, Diffuse x-ray emission from the dumbbell nebula. Astron. J. 106, 650–655 (1993) Y.-H. Chu et al., Chandra reveals the x-ray glint in the cat’s eye. Astrophys. J. 553, L69-L72 (2001) Y.-H. Chu et al., Hard x-ray emission associated with white dwarfs. II. Astron. J. 127, 477–480 (2004) Y.-H. Chu et al., Hard x-ray emission associated with white dwarfs. IV. Signs of accretion from substellar companions. Astrophys. J. 910, id.119 (2021) Y.-h. Chu, R.A. Gruendl, G.M. Conway, ROSAT x-ray observations of two planetary nebulae: NGC 1535 and NGC 3587. Astron. J. 116, 1882–1885 (1998) H.C. Kreysing, C. Diesch, J. Zweigle et al., Extended x-ray emission from planetary nebulae. Astron. Astrophys. 264, 623–628 (1992) G.M. Conway, Y.-H. Chu, X-ray emission from Planetary Nebulae. Planetary nebulae, in Proceedings of the 180th Symposium of the International Astronomical Union, vol. 180 (Kluwer Academic Publishers, Dordrecht, 1997), p. 214 P.A.J. de Korte, J.J. Claas, F.A. Jansen, S.P. McKechnie, X-ray emission from the planetary nebula NGC 1360. Adv. Space Res. 5, 57–59 (1985) O. De Marco, The origin and shaping of planetary nebulae: putting the binary hypothesis to the test. Publ. Astron. Soc. Pac. 121, 316–342 (2009) X. Fang et al., HST STIS observations of the mixing layer in the cat’s eye nebula. Astrophys. J. Lett. 822, id.L19 (2016) M. Freeman et al., The Chandra planetary nebula survey (ChanPlaNS). II. X-Ray emission from compact planetary nebulae. Astrophys. J. 794, id.99 (2014) D.J. Frew et al., K 1–6: an asymmetric planetary nebula with a binary central star. Publ. Astron. Soc. Aust. 28, 83–94 (2011) K.G. Gayley, S.P. Owocki, Line-driven instability growth rates in Wolf-Rayet winds. Astrophys. J. 446, 801–811 (1995) F. Gieseking, I. Becker, J. Solf, High-velocity bipolar mass flow in the planetary nebula NGC 2392. Astrophys. J. Lett. 295, L17–L20 (1985)

96 The X-ray Emission from Planetary Nebulae

3383

R.A. Gruendl, Y.-H. Chu, M.A. Guerrero, Far ultraviolet spectroscopic explorer observations of nebular O VI emission from NGC 6543. Astrophys. J. 617, L127–L130 (2004) R.A. Gruendl et al., XMM-Newton observations of the bipolar planetary nebulae NGC 2346 and NGC 7026. Astrophys. J. 653, 339–344 (2006) M.A. Guerrero, X-ray Observations of planetary nebulae since WORKPLANS I and beyond. Galaxies 8, 24 (2020) M.A. Guerrero, O. De Marco, Analysis of far-UV data of central stars of planetary nebulae: occurrence and variability of stellar winds. Astron. Astrophys. 553, A126 (2013) M.A. Guerrero, Y.-H. Chu, R.A. Gruendl, ROSAT observations of x-ray emission from planetary nebulae. Astrophys. J. Suppl. Ser. 129, 295–313 (2000) M.A. Guerrero et al., The enigmatic x-ray point sources at the central stars of NGC 6543 and NGC 7293. Astrophys. J. 553, L55–L58 (2001) M.A. Guerrero, R.A. Gruendl, Y.-H. Chu, Diffuse x-ray emission from the planetary nebula NGC 7009. Astron. Astrophys. 387, L1–L5 (2002) M.A. Guerrero et al., XMM-Newton detection of hot gas in the eskimo nebula: shocked stellar wind or collimated outflows? Astron. Astrophys. 430, L69–L72 (2005) M.A. Guerrero et al., Rebirth of x-ray emission from the born-again planetary nebula A 30. Astrophys. J. 755, id.129 (2012) M.A. Guerrero et al., XMM-Newton Reflection grating spectrometer observations of the cat’s eye nebula. Astron. Astrophys. 574, id.A1 (2015) M.A. Guerrero, J.A. Toalá, Y.-H. Chu, Variable hard x-ray emission from the central star of the eskimo nebula. Astrophys. J. 884, id.134 (2019) M.A. Guerrero, J.S. Rechy-García, R. Ortiz, Space velocity and time span of jets in planetary nebula. Astrophys. J. 890, id50 (2020) M.A. Guerrero et al., Tomography of the unique ongoing jet in the planetary nebula NGC 2392. Astrophys. J. 909, id.44 (2021) R. Heller et al., Hot bubbles of planetary nebulae with hydrogen-deficient winds. II. Analytical approximations with application to BD+30◦ 3639. Astron. Astrophys. 620, id.A98 (2018) M.G. Hoare, A.B. Martin, K. Werner, T. Fleming, ROSAT observations of EUV-bright planetary nebula central stars. Mon. Not. R. Astron. Soc. 273, 812–820 (1995) I. Iben Jr., On the frequency of planetary nebula nuclei powered by helium burning and on the frequency of white dwarfs with hydrogen-deficient atmospheres. Astrophys. J. 277, 333–354 (1984) J.H. Kastner, N. Soker, On the luminosities and temperatures of extended x-ray emission from planetary nebulae. Astrophys. J. 583, 368–373 (2003) J.H. Kastner et al., Chandra x-ray observatory detection of extended x-ray emission from the planetary nebula BD+30◦ 3639. Astrophys. J. 545, L57–L59 (2000) J.H. Kastner, S.D. Vrtilek, N. Soker, Discovery of extended x-ray emission from the planetary nebula NGC 7027 by the Chandra x-ray observatory. Astrophys. J. 550, L189–L192 (2001) J.H. Kastner et al., On the asymmetries of extended x-ray emission from planetary nebulae. Astrophys. J. 581, 1225–1235 (2002) J.H. Kastner et al., A compact x-ray source and possible x-ray jets within the planetary nebula menzel 3. Astrophys. J. 591, L37–L40 (2003) J.H. Kastner et al., Serendipitous Chandra x-ray detection of a hot bubble within the planetary nebula NGC 5315. Astrophys. J. 672, 957–961 (2008) J.H. Kastner et al., The Chandra x-ray survey of planetary nebulae (ChanPlaNS): probing binarity, magnetic fields, and wind collisions. Astron. J. 144, id.58 (2012) S. Kwok, The Origin and Evolution of Planetary Nebulae. Cambridge Astrophysics Series, vol. 33 (Cambridge University Press, Cambridge, 2000) S. Kwok, C.R. Purton, P.M. Fitzgerald, On the origin of planetary nebulae. Astrophys. J. Lett. 219, L125–L127 (1978) D.A. Leahy, C.Y. Zhang, S. Kwok, Two-temperature x-ray emission from the planetary nebula NGC 7293. Astrophys. J. 422, 205–207 (1994)

3384

M. A. Guerrero

D.A. Leahy, S. Kwok, D. Yin, Extended X-ray emission from the planetary nebula BD+30◦ 3639, Astrophys J. 540, L442–L446 (2000) L.B. Lucy, R.L. White, X-ray emission from the winds of hot stars. Astrophys. J. 241, 300–305 (1980) A. Manchado, M.A. Guerrero, L. Stanghellini, M. Serra-Ricart et al., The IAC Morphological Catalog of Northern Galactic Planetary Nebulae (Instituto de Astrofísica de Canarias (IAC), La Laguna, 1996) H.L. Maness et al., Abundance anomalies in the x-ray spectra of planetary nebulae NGC 7027 and BD+30◦ 3639. Astrophys. J. 589, 439–443 (2003) G. Mellema, A. Frank, Radiation gas dynamics of planetary nebulae – V. Hot bubble and slow wind dynamics. Mon. Not. R. Astron. Soc. 273, 401–410 (1995) B. Miszalski et al., The post-common-envelope X-ray binary nucleus of the planetary nebula NGC 2392. Publ. Astron. Soc. Aust. 36, id.e018 (2019) R. Montez Jr., J.H. Kastner, Dissecting the x-ray emission in the young planetary nebula NGC 7027. Astrophys. J. 861, id.45 (2018) R. Montez Jr et al., X-Ray imaging of planetary nebulae with Wolf-Rayet-type central stars: detection of the hot bubble in NGC 40. Astrophys. J. 635, 381–385 (2005) R. Montez Jr et al., Serendipitous XMM-Newton detection of x-ray emission from the bipolar planetary nebula Hb 5. Astrophys. J. 694, 1481–1484 (2009) R. Montez Jr et al., X-ray emission from the binary central stars of the planetary nebulae HFG 1, DS 1, and LoTr 5. Astrophys. J. 721, 1820–1828 (2010) R. Montez Jr et al., The Chandra planetary nebula survey (ChanPlaNS). III. X-Ray emission from the central stars of planetary nebulae. Astrophys. J. 800, id.8 (2015) R. Nordon et al., Narrow radiative recombination continua: a signature of ions crossing the contact discontinuity of astrophysical shocks. Astrophys. J. 695, 834–843 (2009) B. O’Dwyer et al., Hard x-ray emission associated with white dwarfs. Astron. J. 125, 2239–2254 (2003) R.K. Prinja, D.L. Massa, M. Cantiello, Looking deep into the cat’s eye: structure and rotation in the fast wind of the PN central star of NGC 6543. Astrophys. J. Lett. 759, id.L28 (2012) T. Rauch, J. Koeppen, K. Werner, Spectral analysis of the planetary nebula K 1–27 and its very hot hydrogen-deficient central star. Astron. Astrophys. 286, 543–554 (1994) N. Ruiz et al., Physical structure of the planetary nebula NGC 3242 from the hot bubble to the nebular envelope. Astron. J. 142, id.91 (2011) N. Ruiz et al., Detection of diffuse x-ray emission from planetary nebulae with nebular O VI. Astrophys. J. 767, id.35 (2013) R. Sahai et al., X-ray emission from the pre-planetary nebula henize 3-1475. Astrophys. J. 599, L87–L90 (2003) H. Sana et al., An XMM-Newton view of the young open cluster NGC 6231 – II. The OB star population. Mon. Not. R. Astron. Soc. 372, 661–678 (2006) C. Sandin et al., Hot bubbles of planetary nebulae with hydrogen-deficient winds. I. Heat conduction in a chemically stratified plasma. Astron. Astrophys. 586, id.A57 (2016) D. Schönberner, Late stages of stellar evolution. II. Mass loss and the transition of asymptotic giant branch stars into hot remnants. Astrophys. J. 272, 708–714 (1983) H.E. Schwarz, R.L.M. Corradi, J. Melnick, A catalogue of narrow band images of planetary nebulae. Astron. Astrophys. Suppl. Ser. 96, 23–113 (1992) N. Soker, Properties that cannot be explained by the progenitors of planetary nebulae. Astrophys. J. Suppl. Ser. 112, 487–505 (1997) N. Soker, J.H. Kastner, X-ray emission from central binary systems of planetary nebulae. Astrophys. J. 570, 245–251 (2002) N. Soker, M. Livio, Disks and jets in planetary nebulae. Astrophys. J. 421, 219–224 (1994) M. Steffen, D. Schönberner, A. Warmuth, The evolution of planetary nebulae. V. The diffuse X-ray emission. Astron. Astrophys. 489, 173–194 (2008) S.P. Tarafdar, K.M.V. Apparao, Einstein x-ray observations of planetary nebulae and their implications. Astrophys. J. 327, 342–346 (1988)

96 The X-ray Emission from Planetary Nebulae

3385

J.A. Toalá, S.J. Arthur, Formation and x-ray emission from hot bubbles in planetary nebulae – I. Hot bubble formation. Mon. Not. R. Astron. Soc. 443, 3486–3505 (2014) J.A. Toalá, S.J. Arthur, Formation and x-ray emission from hot bubbles in planetary nebulae – II. Hot bubble x-ray emission. Mon. Not. R. Astron. Soc. 463, 4438–4458 (2016) J.A. Toalá, S.J. Arthur, On the x-ray temperature of hot gas in diffuse nebulae. Mon. Not. R. Astron. Soc. 478, 1218–1230 (2018) J.A. Toalá et al., X-Ray emission from the Wolf-Rayet bubble S 308. Astrophys. J. 755, id.77 (2012) J.A. Toalá et al., X-Ray emission from the Wolf-Rayet bubble NGC 6888. I. Chandra ACIS-S observations. Astron. J. 147, id.30 (2014) J.A. Toalá et al., The Born-again planetary nebula A 78: an x-ray twin of A 30. Astrophys. J. 799, id.67 (2015) J.A. Toalá et al., On the diffuse X-ray emission from the Wolf-Rayet bubble NGC 2359. Mon. Not. R. Astron. Soc. 446, 1083–1089 (2015) J.A. Toalá et al., X-ray emission from the Wolf-Rayet bubble NGC 6888 – II. XMM-Newton EPIC observations. Mon. Not. R. Astron. Soc. 456, 4305–4314 (2016) J.A. Toalá et al., Hot gas in the Wolf-Rayet nebula NGC 3199. Astrophys. J. 846, id.76 (2017) J.A. Toalá, R. Montez Jr., M. Karovska, A carbon-rich hot bubble in the planetary nebula NGC 5189. Astrophys. J. 886, id.30 (2019) J.A. Toalá et al., Chandra observations of the planetary nebula IC 4593. Mon. Not. R. Astron. Soc. 494, 3784–3789 (2020) J.R. Walsh et al., The extinction and dust-to-gas structure of the planetary nebula NGC 7009 observed with MUSE. Astron. Astrophys. 588, id.A106 (2016) R. Weaver et al., Interstellar bubbles. II. Structure and evolution. Astrophys. J. 218, 377–395 (1977) Y.S. Yu et al., The x-ray spectrum of a planetary nebula at high resolution: chandra gratings spectroscopy of BD+30◦ 3639. Astrophys. J. 690, 440–452 (2009) S.A. Zhekov, M. Perinotto, Modelling the x-ray, EUV and infrared coronal-line emission from PNe. Astron. Astrophys. 309, 648–654 (1996)

Part X Supernovae, Supernova Remnants, and Diffuse Emission Aya Bamba, Keiichi Maeda, and Manami Sasaki

Stellar Evolution, SN Explosion, and Nucleosynthesis

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Massive Star Evolution and Core-Collapse Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Core Evolution Toward the Iron-Core Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Core-Collapse Supernova (CCSN) Explosion Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . Core-Collapse Supernova Progenitors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . White Dwarfs in a Binary and Thermonuclear Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . Thermonuclear Supernovae: Progenitors and Explosion Mechanisms . . . . . . . . . . . . . . . Binary Evolution of a White Dwarf Toward Thermonuclear Runaway . . . . . . . . . . . . . . . Explosive Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Emissions from Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristic Behaviors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Power Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SN Progenitors and Explosions as Seen in Observations . . . . . . . . . . . . . . . . . . . . . . . . . . High-Energy Emissions from Supernovae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Massive stars evolve toward the catastrophic collapse of their innermost core, producing core-collapse supernova (SN) explosions as the end products. White dwarfs, formed through evolution of the less massive stars, also explode as thermonuclear SNe if certain conditions are met during the binary evolution. Inflating opportunities in transient observations now provide an abundance of data, with which we start addressing various unresolved problems in stellar evolution and SN explosion mechanisms. In this chapter, we overview the stellar K. Maeda () Department of Astronomy, Kyoto University, Sakyo-ku, Kyoto, Japan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_85

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evolution channels toward SNe, explosion mechanisms of different types, and explosive nucleosynthesis. We then summarize observational properties of SNe through which the natures of the progenitors and explosion mechanisms can be constrained. Keywords

Stellar evolution · Circumstellar matter · Supernovae · Nuclear reactions · Nucleosynthesis · Abundances · Radiative transfer · Transient sources · Multiwavelength emission

Introduction Supernovae (SNe) announce catastrophic demise of stars. Their luminosities typically reach to ∼1043 erg s−1 (with large variations), i.e., comparable to the typical luminosity of a galaxy in the optical wavelengths. The kinetic energy of the ejected materials, which is eventually inserted to its surroundings, is typically ∼1051 erg which is comparable to the whole energy budget of the Sun in its entire life of ∼1010 yr. With the rate of ∼0.01 SN yr−1 , SNe provide the total energy of ∼1059 erg in the Hubble time into a galaxy they belong to, which is not negligible as compared to (or can even exceed) the binding energy of a galaxy. SNe thus play an important role in shaping the local, or even global, environment of a galaxy, e.g., by affecting the star-formation rate in the surrounding region. SNe are one of the most important events as the origin of heavy elements in the cosmic inventory. They not only eject heavy elements synthesized during the hydrostatic stellar evolution into the space but create various elements, especially intermediate mass elements (IMEs) and iron-group elements (IGEs, or Fe-peak elements), at the moment of the explosion. SNe are thus key players in the Galactic chemical evolution. SNe show diverse observational properties, which reflect various pathways in the stellar evolution toward the end of their lives. To demonstrate this point, Fig. 1 shows a classical classification scheme based on spectral properties of SNe at their brightest (maximum-light) phase (Filippenko 1997) (see section “Emissions from Supernovae” for details); this classical classification scheme relies mostly on the chemical composition in the outermost layer of the ejected material and thus in the progenitor stars; type Ia SNe are believed to be a thermonuclear explosion of a massive C+O white dwarf (WD), while the other classes shown in Fig. 1 are all from the core collapse of a massive star; type II SNe are an explosion of a redsupergiant (RSG); type Ib and Ic SNe are an explosion of a (nondegenerate) He and C+O star, which are produced during the evolution of massive stars in which the outer H-rich envelope (or even He-rich layer) has been stripped away either by a strong stellar wind or binary interaction. There is a class of type IIb SNe (not shown in Fig. 1), which show transitions from type II to Ib in their spectral features; the SN IIb progenitors are believed to be similar to those of SNe Ib (i.e., a He star) but with

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Fig. 1 Classification of SNe based on the properties of spectral-line features seen in their maximum-light spectra

a small amount of the H-rich envelope still attached at the time of the SN explosion. In summary, SNe are the end products of both intermediate mass stars (after the formation of a WD) and massive stars (at the formation of a neutron star, NS, or even a black hole, BH). SNe thus provide an irreplaceable opportunity to study stellar evolution in the final phase, which is otherwise difficult by other means. In this chapter, we will first summarize the basic principles of stellar evolution toward SN explosions, and provide basic pictures on the explosion mechanism(s); massive star evolution and core-collapse SNe in section “Massive Star Evolution and Core-Collapse Supernovae”, and evolution of a WD in a binary and thermonuclear SNe in section “White Dwarfs in a Binary and Thermonuclear Supernovae”. Key concepts of explosive nucleosynthesis are introduced in section “Explosive Nucleosynthesis”. In section “Emissions from Supernovae”, we will summarize emission processes of SNe, and discuss how observational features of SNe can be interpreted in terms of their progenitors and explosion mechanisms. We will also briefly mention mechanisms for high-energy and radio emissions from SNe. The review is closed in section “Conclusion” with a Conclusion.

Massive Star Evolution and Core-Collapse Supernovae Core Evolution Toward the Iron-Core Formation Theory of stellar evolution forms a basic framework for many branches of astronomy and astrophysics. It is a matured and classical field, but at the same time, it continues to be in the forefront of astronomy with many outstanding problems yet to be solved. In this section, we provide some key (minimal) concepts that control the stellar evolution as basic rules, in an introductory and rather qualitative/simplified

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manner. Even within the standard framework of quasi-static evolution of a spherical star, it is already a highly nonlinear problem, and many interesting and important phenomena and processes are not described by such a simplified treatment. We therefore recommend the readers to access classical textbooks with high reputation, such as Clayton (1984) and Kippenhahn et al. (2012). There are also many modern textbooks at an introductory level, which may serve as the run-up before tackling to these standard textbooks. As a very rough, zeroth-order approximation, we may describe a star as a uniform sphere with the mass M and radius R, with the sharp drop of the pressure at its surface. By integrating the hydrostatic balance (dP /dr = −GMr ρ/r 2 together with dMr /dr = 4πρr 2 , where Mr is the enclosed mass below given radius r within the star) for the whole star, it then requires the following: P ∝

M2 , R4

(1)

where P is the (central) pressure. Here, we are concerned with the scaling relation thus omit the coefficient (which is dependent on the detailed structure). It can also be viewed as the balance between the internal energy and the gravitation energy, i.e., (4π R 3 /3)P ∝ (GM 2 /R) which reduces to the same relation, noting the pressure is proportional to the internal energy. Assuming that the pressure is provided by the ideal gas (P ∝ ρT , with ρ and T the (central) density and temperature), we can derive the relation between the central density and temperature as ρ ∝ T 3 M −2 or T ∝ ρ 1/3 M 2/3.

(2)

This relation has two important consequences: (1) For a given hydrostatic configuration (or roughy for given T if the energy balance is maintained by the nuclear energy generation), a more massive star is less dense. (2) When the release of the gravitational binding energy is the only energy-generation process, the star collapses toward the higher density following the path in the (T , ρ) plane as given by Equation 2 (which is essentially parallel for stars with different masses). Not only the density but the temperature increase through the contraction, which is also viewed as a consequence of the virial theorem for an object bound by the selfgravity. This behavior relies on the ideal gas equation of state (EOS). Once the pressure is mainly provided by degenerate electrons, the binding energy released by the contraction is no more channeled into the increase in the thermal energy (i.e., no or little temperature increase anymore). The boundary can be estimated by equating the degenerate pressure at zero temperature (P ∝ ρ 5/3 in the nonrelativistic regime which is of main interest during the stellar evolution) and the thermal pressure (P ∝ ρT ), yielding ρ ∝ T 3/2 or T ∝ ρ 2/3 .

(3)

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Importantly, the line defining this boundary is flatter than the path of the contraction (Eq. 2) in the (T − ρ) plane, or steeper in the (ρ − T ) plane. The basic picture of stellar evolution obtained through detailed numerical calculations (an example shown in Fig. 2) can be roughly understood by the general and simple rules as derived above. An opaque gas as born through contraction of the interstellar matter (ISM), as a seed of a star, keeps contracting toward the higher density and temperature. A more massive (proto-)star follows a track in the (T − ρ) plane at a lower-density side. When the central temperature reaches to ∼107 K, the hydrogen burning is initiated at the center, which balances the energy loss from the surface of the star; it is the main-sequence (MS) stage. Once hydrogen is (completely) consumed in the central region, the star is now described as a He core plus a H-rich envelope. The bottom of the envelope is still energized by the (shell) H-burning, but the nuclear energy generation is now missing in the He core. The core then starts contracting, with a track in the T − ρ plane again described by Equation 2 (with M and R now replaced by the core properties, noting that the core mass is generally correlated with the zero-age main-sequence (ZAMS) mass (MZAMS ) and a more massive star/core always takes a lower-density track). The H-rich envelope reacts to the core contraction in a way that it expands to

Fig. 2 The evolutionary pathways of stars with different masses in their central properties. (Reproduction of Kovetz et al. 2009 with modifications)

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become a giant. Eventually the He-burning can be ignited, if the He core (therefore the initial mass) is sufficiently massive to avoid the dominance of the degenerate pressure before reaching to ∼108 K. The subsequent evolution follows essentially the same way, i.e., repeated sequences of exhaustion of fuels in the present burning stage, core contraction, and then initiation of a new burning stage, toward more advanced burning stages ultimately toward the formation of an Fe core. The key that mainly determines the fate of a star is whether the electron degenerate pressure overwhelms the thermal pressure during the evolution, and if so, when it takes place. Given the lower-density track for a more massive star in the (T −ρ) plane, a sufficiently massive star ends up with the formation of the Fe core. A less massive star will reach to the degenerate regime before the formation of the Fe core; for example, if the core becomes degenerate after the He-burning but before the C-burning, the core is essentially a C+O WD; this will become a C+O WD once the envelope is ejected to form a planetary nebula. Based on these considerations (and results of detailed stellar evolution calculations), the end points of stellar evolution are summarized as follows (but note that the masses defining the boundaries can be dependent on the details, with different predictions from different simulations) (e.g., Nomoto 1984; Woosley and Weaver 1995; Rauscher et al. 2002; Heger et al. 2003; Limongi and Chieffi 2003; Langer 2012): • MZAMS  8M⊙ : Formation of a WD. The dividing mass between a C+O WD and He WD is MZAMS ∼ 0.5M⊙ . • 8M⊙  MZAMS  10M⊙ : The ONeMg core is formed but degenerates before entering into the next burning stages. The outcome will be either a ONeMg WD or an SN explosion following the ONeMg core collapse. • MZAMS  10M⊙ : Formation of an Fe core, followed by a subsequent core collapse and an SN explosion. The time scale of the nuclear burning becomes shorter toward more advanced stages (e.g., Heger et al. 2003). For example, for a star with MZAMS ∼ 10M⊙ , the whole life time is ∼107 yrs. The star stays in the H-burning MS stage for ∼90% of the whole life time, followed by the core He-burning stage lasting for ∼106 yrs. The core C-burning is set in ∼1,000 yrs before the core collapse. The O-burning lasts only for ∼1 yr, and further burning stages have much shorter time scale.

Core-Collapse Supernova (CCSN) Explosion Mechanism In this section, we overview the processes that are relevant to the Fe core collapse (Fig. 3). Studying the CCSN explosion mechanism is a rapidly evolving field tackled with state-of-the-art simulations for which readers can find good reviews and/or recent articles, such as Fryer (2004), Mezzacappa (2005), Kotake et al. (2006), Janka (2012), Bruenn et al. (2016), and Burrows and Vartanyan (2021).

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Fig. 3 Core-collapse supernova (CCSN) explosion mechanism. The left panel shows a schematic picture. The right panel is an example of numerical simulations (Suwa et al. 2015)

In the advanced burning stages, the cooling via neutrinos becomes dominant, and the core evolution is accelerated. Once the Fe core is formed, the lack of the nuclear energy generation leads to the core collapse. Due to the increasing density and temperature, the core reaches to nuclear statistical equilibrium (NSE; see section “Explosive Nucleosynthesis” for details), through which Fe (or Ni) is photodisintegrated to nucleons and alpha particles: 54 26 Fe + γ

↔ 1342 He + 2n,

56 26 Fe + γ

↔ 1342 He + 4n,

4 2 He + γ

↔ 2p + 2n.

(4)

Through the photodisintegration, the thermal energy is further extracted from the core, accelerating the collapse. At the high density (1011 g cm−3 ), electron captures also play an important role, due to the increasing electron Fermi energy that forbids the neutron decay: p + e− ↔ n + νe .

(5)

This reduces the number of free electrons therefore the pressure, again accelerating the collapse. Indeed, for MZAMS in the range of ∼8–10 M⊙ , the electron captures

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trigger the collapse of a degenerate ONeMg core. As a consequence of these processes, the core will evolve toward an increasingly dense and neutron-rich structure as the collapse proceeds. At some point, the density becomes sufficiently high so that the neutrinos are no more freely escaping from the core ( 1013 g cm−3 ). This proto-neutron star (NS) further collapses to reach to the nuclear density (∼1014 g cm−3 ), at which the collapse is suddenly stopped, forming the bounce shock on top of the proto-NS (Colgate and White 1966). The shock wave however finds it difficult to penetrate outward all the way against the ram pressure inserted by the infalling materials. In addition, the photodisintegration keeps extracting the energy from the shock wave. The shock is therefore stalled at ∼2×107 cm. Further energy deposition by neutrinos emitted from the newly formed, hot proto-NS is believed to be a key to reviving the shock wave, which then leads to the SN explosion by expelling all the materials above the NS. This is the standard CCSN mechanism, called the delayed neutrinoheating mechanism (Bethe and Wilson 1985). On the energetic ground, the energy source is the binding energy of the newly formed NS: ENS ∼

2 GMNS ∼ 5 × 1053 erg, RNS

(6)

if we use MNS ∼ 1.4M⊙ and RNS ∼ 106 cm for the mass and the radius of the newly formed NS. Most of this energy is emitted by neutrinos as confirmed by the detection of neutrinos from SN 1987A (Bionta et al. 1987; Hirata et al. 1987). Compared to this energy budget is the kinetic energy of the ejected material by an SN explosion; this is typically an order of ∼1051 erg (see section “Emissions from Supernovae”). Therefore, the conversion of ∼0.1–1% of the neutrino energy must be realized; this is a key problem in the CCSN explosion mechanism. It had been regarded to be a serious problem for several decades as virtually all the dedicated simulations (performed under the spherically symmetric assumption) failed to revive the stalled shock (Liebendörfer et al. 2001; Sumiyoshi et al. 2005). It is now believed that multidimensional effects are essentially important in the CCSN explosion mechanism, with an increasing number of reports for successful explosions in computer simulations. However, it is still a challenge to reproduce the explosions which look like what are observed as SNe; some key ingredients may still be missing, and the issue has been under further investigation intensively by various groups (see, e.g., the review articles introduced at the beginning of the section).

Core-Collapse Supernova Progenitors The evolution of the core as described in section “Core Evolution Toward the Iron-Core Formation” represents only a single face of the stellar evolution. The envelope is the other important ingredient characterizing the nature of a star,

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evolution of which is generally decoupled from the core evolution in the advanced stage. The key process here is a mass loss, either through a strong stellar wind or binary mass transfer (which can be either stable or unstable, including a common envelope phase), or both. A good review for the roles of the mass loss processes and the relation to SN progenitors can be found, e.g., in Langer (2012). If most of the mass is retained until the He core is well developed (as a reasonable assumption in many channels), the He core mass is basically determined by the ZAMS mass since the track of the evolution of the core properties is mainly controlled by the ZAMS mass (section “Massive Star Evolution and Core-Collapse Supernovae”) (but see, e.g., Laplace et al. 2021). The same argument applies for the C+O core mass. Figure 4 shows these relations. The relation has an important implication for several classes of SNe, called SNe IIb, Ib, or Ic, whose progenitors are believed to be a (nearly) bare He or C+O star with a large fraction of the envelope stripped away during the evolution (Fig. 1 and section “Emissions from Supernovae”). In most of the prescription used for the stellar-wind mass loss (Vink et al. 2001; van Loon et al. 2005), the mass-loss rate is generally stronger for a more massive star. This is a reason why the single-star evolution model sequence by Rauscher et al. (2002) (Fig. 4) has a peak in the final mass (i.e., the progenitor mass, including the H-rich envelope) around ∼20 M⊙ . For sufficiently large MZAMS , this effect

M=MZAMS MHe / MO / Mej [Mo· ]

15

Mfinal (single)

10

MHe Mej (He) MO Mej (O)

5 Mej (SNe IIb/Ib/Ic) 0 10

15

20

25 30 MZAMS [Mo· ]

35

40

Fig. 4 The relations between the ZAMS mass and the core mass of an evolved star (i.e., SN progenitor), for the He core (blue) and the O core (red). Two (single) stellar models are shown: Limongi and Chieffi (2003) shown by the solids lines and Rauscher et al. (2002) by the dashed lines. The final mass, with the mass loss given by a stellar wind (without a binary interaction), is also shown for the model by Rauscher et al. (2002). In addition, the expected ejecta masses are shown for bare He stars (MHe − MNS , gray line) and for C+O stars (MO − MNS , black line), based on the models by Limongi and Chieffi (2003), assuming MNS = 1.4M⊙ . A range of the ejecta masses for SNe IIb/Ib/Ic (which are believed to be explosions of either a He star or C+O star for which all or most of the H-rich envelope has been ejected before the SN explosion), as inferred by observational data, is shown by the gray area (Lyman et al. 2016) (see section “Emissions from Supernovae” for details)

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alone can remove all the H-rich envelope, leading to the formation of a bare He or even C+O star, i.e., a Wolf-Rayet (WR) star. The details depend on the massloss prescription, but this transition generally takes place at MZAMS ∼ 20–30 M⊙ in various models. We note that the strength of the stellar wind is also dependent on the metallicity; for lower metallicities, the amount of the stellar-wind mass loss decreases, and thus the ZAMS mass for the transition between an RSG and a WR moves upward (e.g., Heger et al. 2003). The binary interaction scenario predicts different behaviors. It is indeed believed that a large fraction of massive star binaries experience a phase of strong binary interaction during their evolution toward the SN explosion (Sana et al. 2012). Figure 5 shows, as an example for a case of stable mass transfer, an evolution model for a binary system with the initial masses of 18 M⊙ and 12 M⊙ . The initial orbital period is taken to be 5 days in this particular example. The primary starts experiencing the Roche lobe overflow (RLOF) after the hydrogen core exhaustion. When the primary’s mass decreases to ∼4.4 M⊙ , the binary once detaches. The primary expands again after the helium core exhaustion, and undergoes the final RLOF; the primary’s mass further decreases to ∼4.1 M⊙ . The companion’s mass increases through the mass accretion by the RLOF, reaching to the final mass of ∼18.4 M⊙ when the primary explodes as an SN. The SN progenitor in this model is essentially a He star but with a small amount of a H-rich envelope attached (∼0.06 M⊙ ), which brings it into a blue-supergiant dimension (∼40 R⊙ in its radius); it will thus explode as an SN IIb. In case the initial orbital period is shorter,

Fig. 5 An example of the binary evolution model (Folatelli et al. 2015); the evolutionary tracks of the primary and companion stars are shown in the Hertzsprung-Russell diagram

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then the primary will lose (nearly) an entire H-rich envelope and explode as an SN Ib. Further details on the binary evolution model toward SNe IIb/Ib/Ic (with stable mass transfer) can be found in, e.g., Yoon et al. (2010) and Ouchi and Maeda (2017) A common envelope also plays an important role, which can happen when the mass transfer rate is so high and the accreting star cannot react to it in thermal time scale. For example, when a donor is substantially more massive than the accreting companion (i.e., an extreme mass ratio), the orbital shrinks as the mass transfer proceeds, leading to a rapid and unstable mass transfer and to the common envelope phase, where the companion star is engulfed by the primary’s envelope. The details of the common envelope evolution have not yet been clarified despite intensive researches both in large simulations and observations (e.g., Iaconi et al. 2019, and references therein), and a phenomenological approach (Paczynski 1976) is frequently (almost always) used to treat this phase in binary evolution models (including the so-called binary population models); this is based on the energy balance between the envelope’s binding energy and (a fraction of) the (final) orbital energy. Namely, if there is a sufficient orbital energy exceeding the envelope’s binding energy before the two cores marge, the outcome is a close binary followed by successful ejection of the primary’s envelope (therefore the primary will become a He star for a massive-star binary, which is another possible progenitor channel for SNe Ib and Ic; Nomoto et al. 1995). Otherwise, the expected outcome is a merger of the cores of the two stars to become a (peculiar) single star (which can be a progenitor of some peculiar SNe, e.g., SN 1987A: Morris and Podsiadlowski 2007; Menon and Heger 2017). Yes another piece of potential importance is possible stellar activity toward the end of their lives. In the standard stellar evolution theory, it has been anticipated that the envelope reacts to the evolution of the core only slowly, despite the accelerated evolution of the core burning stages toward the end of the stellar life, i.e., the coreenvelope decoupling. In the standard picture, the minimal response time can be estimated by the thermal time scale of the envelope, i.e., tth ∼

GMc Menv RL

∼ 70 − 700 yrs

(7) 

Menv 10 M⊙



R 1013 cm

−1

,

(8)

where Mc is the core mass, Menv is the envelope mass, R is the radius and L is the core luminosity. The range here covers the core luminosity being 10–100% of the Eddington luminosity. The normalization here is given for an RSG progenitor. For a bare C+O or He star progenitor (∼ a few M⊙ and ∼1011 cm), the thermal time scale is even longer. Therefore, the thermal time scale is at least ∼100 years. This means that the properties of the envelope are virtually “frozen” at least in the final century; the properties of the star in the final century are thus not expected to show either a trace of a rapid core evolution or substantial variability. This simple picture, however, has been questioned in the last decade; there are mounting indications

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through observations of CCSNe that at least a fraction of SN progenitors show either the short-timescale variability or the rapid increase in the mass-loss rate in the final decades toward the SN. Section “SN Progenitors and Explosions as Seen in Observations” will provide further details on this topical issue.

White Dwarfs in a Binary and Thermonuclear Supernovae Thermonuclear Supernovae: Progenitors and Explosion Mechanisms Besides the CCSNe of a massive star, it has been widely accepted that type Ia SNe (and some variants) are the outcome of a thermonuclear explosion of a C+O WD. Roughly speaking, a (massive) C+O WD can be disrupted by thermonuclear runway for the following reasons: (1) Due to the dominance of electron degenerate pressure, increase in temperature is not canceled by the cooling due to the expansion. The increasing reaction rate of carbon burning can thus lead to drastic and rapid increase in temperature, further accelerating the energy generation by the nuclear burning, i.e., the thermonuclear runaway. (2) The binding energy of a WD is at most comparable to the nuclear energy generation once the thermonuclear runaway incinerates a non-negligible fraction of the WD. As an example, for even a WD near the Chandrasekhar-limiting mass, the binding energy is a few ×1050 erg. On the other hand, if ∼0.6 M⊙ of C+O materials are burnt to 56 Ni (section “Explosive Nucleosynthesis”), the nuclear energy generation exceeds 1051 erg. In this section, we will first overview the possible conditions and mechanisms triggering the thermonuclear runaway within a C+O WD (section “Thermonuclear Supernovae: Progenitors and Explosion Mechanisms”), and then summarize possible evolutionary channels toward such situations (section “Binary Evolution of a White Dwarf Toward Thermonuclear Runaway”). There are two popular scenarios for SN Ia progenitor(s) and explosion mechanism(s) (Fig. 6) (see, e.g., Hillebrandt and Niemeyer 2000, for a review): (1) the delayed-detonation mechanism on a C+O WD with nearly the Chandrasekharlimiting mass (MCh ) and (2) double-detonation mechanism on a C+O WD mainly considered for a sub-Chandrasekhar-limiting mass (sub-MCh ) C+O WD. The delayed-detonation model on a MCh C+O WD: As a C+O WD approaches to MCh in its mass, the central density and temperature increase in the highly degenerate central region (109 g cm−3 ), to the point where the rate of nuclear energy generation exceeds the cooling rates by neutrinos and convection. It is then likely that the thermonuclear runaway starts near the center of the WD. There are two modes in the nature of the frame propagation, as in the chemical combustion in laboratory experiments. Deflagration is a subsonic frame in which the frame is driven by heat conduction or diffusion process. Detonation is a supersonic frame in which the nuclear energy generation drives a shock wave, which keeps energized by the nuclear reactions behind it. Which mode is realized at the ignition is not completely clarified, but there are several arguments for the deflagration trigger

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Fig. 6 Thermonuclear SN explosion mechanisms

(e.g., Nomoto 1984; Niemeyer and Woosley 1997; Hillebrandt and Niemeyer 2000): (1) The degenerate (Fermi) energy per volume is scaled as ∝ ρ 4/3 in the relativistic regime, while the nuclear energy is so as ∝ ρ. As such, the ratio of the thermal energy added by the nuclear reaction to the degenerate energy is scaled as ∝ ρ −1/3 . Namely, excessive thermal energy to drive the pressure jump is less significant for higher density, preventing the formation of the detonation wave. (2) For typical conditions realized in the progenitor WD, the burning is likely in the flamelet regime at ∼109 g cm−3 (while in the distributed burning regime at ∼107 g cm−3 ). (3) Phenomenologically, prompt detonation deep inside a MCh WD produces too much 56 Ni, which contradicts to the luminosities of individual SNe Ia and the Galactic chemical evolution. However, deflagration alone is too weak to convert a good fraction of the C+O WD up to 56 Ni and Fe-peak elements (Röpke et al. 2007). The WD expands and the density decreases before the flame travels substantially, quenching the nuclear burning. The energy generation is thus limited, and it is possible that it would not disrupt a whole WD (e.g., Kromer et al. 2013). In the delayed-detonation model, it is hypothesized that the deflagration is turned into detonation (“deflagration-todetonation transition,” DDT) at the fuel density of ∼107 g cm−3 (Khokhlov 1991; Iwamoto et al. 1999). The detonation then burns a large fraction of the C+O WD up to 56 Ni. The double-detonation model on a Sub-MCh C+O WD: If the WD mass is substantially lower than MCh , the central density and temperature are far below those required by a spontaneous ignition of carbon burning runaway. However, if there is an additional process that can dynamically raise the temperature there, thermonuclear runaway can take place.

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Helium accumulated on the WD surface can potentially play an important role. If a sufficiently large amount of He is accumulated on the WD surface, it can induce a detonation wave caused by unstable triple-alpha reactions (Bildsten et al. 2007), as an analogy to a nova eruption due to accumulation of H-rich materials. The shock wave is inserted into the WD core. If the shock wave is sufficiently strong, it would initiate spontaneous carbon detonation near the center of the WD. This is the doubledetonation model (Nomoto 1982; Livne 1990; Woosley and Weaver 1994; Shen and Bildsten 2009). In both scenarios, multidimensional effects are critically important (see Fig. 7 as an example). In the delayed-detonation scenario, the deflagration phase is essentially asymmetric both in the trigger and flame propagation. The DDT then takes place at different spots, and the propagation of the detonation wave is affected by the asymmetrically distributed deflagration ash. In the double-detonation scenario, it is very likely that the He detonation is triggered on a spot rather than a shell. The subsequent He detonation, as well as the propagation of the shock wave into the C+O core, will be highly aspherical. Therefore, both scenarios have been intensively studied in terms of multidimensional simulations (e.g., Röpke et al. 2007; Kasen et al. 2009; Maeda et al. 2010; Fink et al. 2010; Seitenzahl et al. 2013; Tanikawa et al. 2019; Boos et al. 2021).

Fig. 7 An example of numerical (2D) simulations for the delayed-detonation scenario (Maeda et al. 2010). The upper and lower panels show the temperature and the mass fraction of the Fepeak elements, respectively. The temporal evolution is shown from the left to the right

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Binary Evolution of a White Dwarf Toward Thermonuclear Runaway One of the key issues related to the origin(s) of SNe Ia is which evolutionary channels lead to the formation of a (massive) C+O WD that satisfies conditions for thermonuclear runaway. In the delayed-detonation mechanism, the main question is how a C+O WD reaches (nearly) to MCh . In the double-detonation mechanism, the hurdle to create a massive C+O WD is lowered (∼1 M⊙ ), but there is another requirement that a sufficiently massive He envelope is formed (or a sufficiently high temperature is reached) to the point that it undergoes unstable He-burning. There are two major progenitor channels suggested for SNe Ia: single-degenerate (SD; Whelan and Iben 1973; Nomoto 1982) and double-degenerate (DD; Iben and Tutukov 1984; Webbink 1984) scenarios. The SD scenario considers a C+O WD as a mass accretor and a nondegenerate companion as a donor, while the DD scenario considers binary WDs including a merger of the two WDs. It should be emphasized that each explosion mechanism is not necessarily associated with each of the SD or DD channel; one may consider the delayed-detonation mechanism on a MCh C+O WD formed through a RLOF from a nondegenerate companion (SD) or as an outcome of merging WDs (DD). Similarly, the double-detonation mechanism may be realized by an accumulation of the He envelope through RLOF either from a nondegenerate companion (SD) or He-rich (or He) WD (DD), or even by a rapid accretion of He during a merging process of two WDs (DD). The SN Ia progenitor is a long-standing unresolved topic, for which a number of review articles can be found (e.g., Branch et al. 1995; Wang and Han 2012; Maoz et al. 2014; Postnov and Yungelson 2014; Maeda and Terada 2016; Livio and Mazzali 2018). An example of the binary evolution channels (potentially) leading to SNe Ia is the following, where the directions of the evolution and mass transfer are indicated by arrows with different symbols (“⇒” for the former and “→” for the latter). Note that it is for a demonstration purpose, and there are many variants in details (see the review articles mentioned above). (a) MS + MS ⇒ RG → MS ⇒ CE ⇒ C+O WD + MS: As the primary evolves and expands, it starts filling the RL (Roche lobe). As the primary is more massive than the secondary, a likely outcome is an unstable transfer leading to a common envelope (CE). Unless the CE leads to a core merger, it will leave a close binary of a C+O WD and a MS. (b) C+O WD ← MS/RG ⇒ SN (SD): As the nondegenerate secondary evolves, it starts filling the RL. The most plausible companion star in the SD scenario is either a MS (∼2 M⊙ ) or an RG (∼1 M⊙ ). The outcome of the RLOF depends on the mass-transfer rate ˙ (M): – M˙ ∼ 10−7 − 10−6 M⊙ yr−1 : The accretted materials are burnt to He and then to C in a steady-state manner. The WD mass thus increases, and can reach to MCh if the sufficient mass is provided by the donor (⇒ a MCh WD explosion in the SD, e.g., Nomoto 1984).

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– M˙  10−6 M⊙ yr−1 : Because of the rapid mass transfer, the WD cannot stably accrete the transferred mass in thermal time scale. The WD thus behaves like a giant with its envelope (formed by the accreted materials) inflating in its radius. The system thus undergoes a CE (then evolves to the point c below). However, it is also possible that the excessive mass in the accreted materials could be efficiently blown away from the system by a WD wind, with the effective accretion rate regulated to the steady-state limit. If this is realized, the system can lead to the thermonuclear explosion (⇒ a MCh WD explosion in the SD, e.g., Hachisu et al. 1996). – M˙  10−7 M⊙ yr−1 : The accreted materials are efficiently cooled and accumulated on the WD. When a critical mass is reached (which is lower for a more massive WD), the H-rich, accreted material undergoes thermonuclear runaway on the WD surface, i.e., a nova. It has not been clarified whether the WD mass indeed increases through the repeated accretion-nova evolution; it may become an SNe Ia (⇒ a MCh WD explosion in the SD, e.g., Hachisu and Kato 2001) or not. (c) C+O WD ← RG ⇒ CE: Following the expansion of the nondegenerate secondary, the system evolves into the CE phase. Further evolution may branch into different outcomes depending on the result of the CE interaction and the nature of the secondary. (c1) CE ⇒ Core merger ⇒ peculiar SN Ia? The core of the secondary may merge into the primary (C+O) WD. If the secondary’s core is a degenerate C+O core, it is essentially merging two C+O WDs as is similar to the DD system. If the secondary’s core is either a degenerate or nondegenerate He core, the system may suffer from a He-ignited double-detonation explosion. These channels are thus potential pathways to peculiar SNe Ia surrounded by a massive CSM (core-degenerate scenario or its variants; e.g., Sparks and Stecher 1974; Soker 2015; Jerkstrand et al. 2020). (c2) CE ⇒ C+O WD + C+O WD ⇒ SN (DD) The CE leaves a compact binary system of two C+O WDs. Following the angular momentum loss by gravitational waves, the two WDs may merge. If the sum of the two WD masses is far beyond MCh , a prompt carbon detonation may disrupt both WDs, which may lead to a peculiar SN Ia (⇒ a sub-MCh explosion in the DD, noting that it is essentially “sub-MCh ” in terms of the explosion condition, e.g., Pakmor et al. 2010). Otherwise, the outcome of the merger will be a massive WD surrounded by a hot envelope (formed by debris of the disrupted secondary). If the total mass is below MCh , the end product is likely a single massive WD. If the mass is above MCh , the WD core may eventually reach nearly to MCh by further accreting the C+O material from the envelope. If this is realized, it may explode as an SN Ia (a MCh explosion in the DD; Iben and Tutukov 1984; Webbink 1984). However, the C+O core may be converted to a ONeMg core by off-center carbon deflagration during the

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envelope accretion; in this case, the end product is a MCh ONeMg WD, which may collapse to a NS through electron capture reactions (Saio and Nomoto 1985; Schwab 2021). (c3) CE ⇒ C+O WD + He WD ⇒ SN (DD) In case the CE leaves a compact binary of a C+O WD and a He WD (or a C+O WD with a massive He envelope), further orbital shrink may lead to the He accretion to the primary WD, i.e., a potential AM CVn system (e.g., Bildsten et al. 2007). The outcome of the mass transfer is analogous to the SD case (point b above). For the high mass-transfer case, two WDs may merge, and the double detonation may result by the rapid He accretion during the merger process (⇒ a sub-MCh explosion in the DD; e.g., Pakmor et al. 2013; Shen et al. 2018; Tanikawa et al. 2019). For a moderate transfer rate, the He accretion may become steady state, leading to formation of a MCh C+O WD (⇒ a MCh explosion in the DD; e.g., Wang et al. 2009). For the low masstransfer case, the He envelope mass may reach to the condition for the He detonation (⇒ a sub-MCh explosion in the DD; e.g., Shen and Bildsten 2009). (c4) CE ⇒ C+O WD + He star ⇒ SN (SD) This is similar to the case c3. As the nondegenerate He companion evolves and expands, it will start experiencing the RLOF to the primary C+O WD. For the moderate mass-transfer rate, the primary WD may burn He steadily on its surface and reach to MCh (⇒ a MCh explosion in the SD). For a low masstransfer rate, the surface He detonation may result (⇒ a sub-MCh explosion in the SD). For the high mass transfer, the primary may reach to MCh if the WD wind stabilizes the mass accretion (⇒ a MCh explosion in the SD), or otherwise the system may undergo the merger, which is analogous to the point c1 above (⇒ a sub-MCh explosion or a peculiar SN).

Explosive Nucleosynthesis The initial configuration at the onset of the explosion is either an onion-like structure for CCSNe (with the Si layer at the base, as the Fe core has collapsed to become a compact object) or the C+O composition for SNe Ia. The shock wave or thermonuclear flame inserted by the explosion mechanism then induces the socalled explosive nucleosynthesis, following its propagation toward the outer layer of the progenitor star. The SN ejecta thus have a layered composition structure as an outcome of the explosive nucleosynthesis, for which an example is shown in Fig. 8. We refer to Arnett (1996), Woosley and Weaver (1995), and Thielemann et al. (1996) that provide valuable basis on this topic. To the zeroth-order approximation, we may assume that the region behind the shock wave forms a fireball dominated by the radiation pressure, with uniform temperature. The temperature (T ) behind the shock wave as a function of its radial location (R) can thus be estimated as follows (e.g., Maeda and Tominaga 2009):

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Fig. 8 An example of composition structure in the SN ejecta as an outcome of explosive nucleosynthesis in a CCSN (Maeda et al. 2002)

T ∼



3E 4π a

1/4

R −3/4 ∼ 1.3 × 1010 K



E 1051 erg

1/4 

R 108 cm

−3/4

,

(9)

where E is the explosion energy (which can be assumed to be roughly constant during the shock propagation for CCSNe, unless the explosion mechanism would be extremely “slow”; Sawada and Maeda 2019), and a is the radiation constant. The temperature thus decreases as a function of time, following the expansion of the shock wave toward the outer region. We thus see that the temperature inside the shock is higher than ∼109 K until the shock reaches to R ∼ 3 × 109 cm. Depending on the ZAMS mass, this can be comparable to the size of the C+O core. We therefore conclude that the explosive nucleosynthesis changes the composition in the substantial amount of materials in the innermost ejecta. The outcome of the explosive nucleosynthesis is roughly characterized by the peak temperature to which the material is heated behind the shock wave (T9 ≡ T /109 K) (e.g., Arnett 1996). • T9  5 (Complete Si-burning): At the high temperature, both forward and reverse reactions in main reaction channels through the strong force proceed much faster than the typical evolution time scale with which the thermal

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condition changes (i.e., expansion and cooling). The compositions thus basically follow the nuclear statistical equilibrium (NSE). Following the rapid temperature decrease, the reaction rates are becoming smaller and the abundance pattern “freezes out,” leaving the NSE abundance pattern at the high temperature as the final outcome. In a typical condition realized in CCSNe, weak interactions are much slower, and thus the electron fraction (Ye , i.e., the number of protons divided by that of nucleons) is conserved. For the materials with the (roughly) equal numbers of protons and neutrons (Ye ∼ 0.5, which applies to most part of the progenitor), the most abundant isotope is 56 Ni (due to the combination of its being at the peak in the binding energy and the equal numbers of protons and neutrons in it), followed by He and other Fe-peak elements. • T9 ∼ 4 − 5 (Incomplete Si burning): The relative abundances within Fe-peak elements, as well as those within intermediate-mass elements (IMEs), roughly follow the NSE abundance pattern within each cluster, but the ratio between the amounts of the Fe-peak elements and the IMEs is not necessarily described by the NSE; it is called quasi-NSE (QSE). This is (to the zeroth-order approximation) due to the bottleneck at Z = 20, i.e., Ca having a high stability with a magic proton number. The outcome is Si, S, 56 Ni, Ar, Ca, and Fe-peak elements, roughly in the decreasing order in the final mass fractions. • T9 ∼ 3 − 4 (Oxygen burning): The IMEs follow QSE, but the production of heavier elements is blocked by the Ca bottleneck. The abundant elements are O, Si, S, Ar, and Ca. • T9 ∼ 2−3 (Carbon and neon burning): In this temperature range, the explosive carbon and/or neon burning produces O, Mg, Si, and Ne. There are a few other processes especially in the high-temperature and/or highdensity regime that have to be taken into account, depending on the situation: • α-rich freeze out: The outcome of the Si-burning regime depends on the condition for the freeze out. Either for higher peak temperature or lower density, the triple α reaction freezes out earlier, leaving a larger amount of He. This enhances the α-capture reactions onto Fe-peak elements. As a result, the abundance pattern of Fe-peak elements is shifted, leaving a non-negligible amount of some specific isotopes that are difficult to produce in the usual Siburning. This includes the production of 44 Ti and 48 Ti (as a consequence of the chain of 40 Ca →44 Ti →48 Cr, which then decays to 48 Ti), and 64 Zn (through 56 Ni →60 Zn →64 Ge, which then decays to 64 Zn), and so on. This process is especially important in the innermost region of the CCSN ejecta. • ν-driven wind in CCSNe: In the standard picture, the CCSN explosion mechanism is driven by a hot bubble above the proto-NS that is continuously heated by neutrinos (section “Massive Star Evolution and Core-Collapse Supernovae”). This can also be regarded as a NS wind, which experiences distinctly higher temperature/entropy than the shock-heated material as discussed so far. It has been proposed as a candidate site for r-process nucleosynthesis (e.g., Qian and Woosley 1996), but recent state-of-the-art CCSN simulations show that the

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wind more likely becomes proton-rich and thus the r-process nucleosynthesis is limited (e.g., Wanajo et al. 2018). The nucleosynthesis outcome is therefore characterized by proton-rich Fe-peak elements/isotopes. • ν-process: As the neutrinos emitted from the proto-NS pass through the region that has experienced the Si-burning, the neutrinos can interact with Fe-peak elements through weak interactions. This can be an important process especially in the production of relatively minor isotopes. Examples include 56 Ni(ν, ν ′ p)55 Co, which eventually decays to 55 Fe and then to 55 Mn (e.g., Yoshida et al. 2008). • electron capture: The electron capture is important at high density. This is indeed one of the key processes in the formation of a proto-NS following a massive star collapse (section “Massive Star Evolution and Core-Collapse Supernovae”). While a large fraction of the material which has experienced the electron capture reactions is “locked” onto a NS, a small fraction of materials may participate in the explosive nucleosynthesis under the neutron-rich condition (which, however, will be altered to become proton-rich in recent CCSN simulations; see above). Indeed, electron capture is even more important in determining the ejecta composition in SNe Ia. If the progenitor WD is sufficiently massive (i.e., close to the Chandrasekhar mass), the central density reaches to ∼109 g cm−3 at which the electron capture reactions leads to a neutron-rich condition (i.e., lower Ye ). Unlike the CCSNe, this central region is ejected. Therefore, the innermost ejecta of SNe Ia are expected to have a large amount of neutron-rich Fe-peak elements such as 58 Ni, if the progenitor WD is sufficiently massive; this has been proposed as one powerful diagnostics to discriminate the MCh WD and sub-MCh WD progenitor scenarios (e.g., Maeda et al. 2010; Yamaguchi et al. 2015). The example shown in Fig. 8 (for a CCSN) can be qualitatively understood by the above summary. The innermost region with abundant He followed by 56 Ni is the region processes by the α-rich freeze out in the complete Si-burning regime. Toward the outer region, the most abundant isotopes change from 56 Ni to 28 Si, and then to 16 O; these regions have experienced the complete Si-burning (without α-rich freeze out), the incomplete Si-burning, and then the O-burning (with ineffective explosive nucleosynthesis toward the surface). Examples of the nucleosynthesis yields, as integrated over all the ejected materials, are shown in Fig. 9. It is seen that generally CCSNe are characterized by a large amount of IMEs (produced mainly through the hydrostatic evolution), while SNe Ia are so by Fe-peak elements (through the explosive burning). For CCSNe, the model in this figure is parameterized by the so-called mass cut, which determines the boundary between the NS/BH and the ejected materials; this has a direct link to the explosion mechanism (i.e., providing constraint on the explosion mechanism through the nucleosynthesis products; e.g., Sato et al. 2021). In the SN Ia model presented here, a large amount of stable Ni (58 Ni) is discerned, which is characteristic of the MCh WD scenario (see above).

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Fig. 9 Examples of nucleosynthesis yields for CCSNe (left panels; Maeda and Nomoto 2003) and SNe Ia (right panel; Maeda et al. 2010). In the left panels, the progenitor is a 16M⊙ He star (MZAMS = 40 M⊙ ), and the two panels are for models with different masses of ejected 56 Ni (larger for the lower panel; treated as the mass cut; see the text). The right panel is for the W7 model (Nomoto et al. 1984), which belongs to the MCh WD explosion scenario

Emissions from Supernovae Characteristic Behaviors The progenitor evolution, SN explosion mechanism, and nucleosynthesis products manifest themselves in the observational data of SNe. Studying the natures of SN remnants (mostly in the Milky Way but also in the local group) and extragalactic SNe provides complementary approaches. In this contribution, we focus on extragalactic SNe. As excellent textbooks on the emission processes and observational properties of SNe, we refer the readers to Arnett (1996) and Branch and Wheeler (2017) Figures 10 and 11 show typical light curves (LCs) and maximum-phase spectra for various types of SNe. In this chapter, we will overview how the natures of the progenitors and explosion mechanisms can be inferred and constrained based on these observational data. Once a progenitor star is fully disrupted by an underlying explosion mechanism, the resulting SN is regarded as metal-rich ejecta expanding into the ISM or circumstellar matter (CSM). The characteristic velocity, V , is roughly given as follows:   1/2   Mej −1/2 EK EK −1 V ∼ ∼ 7,000 km s , (10) Mej M⊙ 1051 erg

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Fig. 10 Examples of optical (R-band) light curves of SNe of different types. It is the compilation of the data from the following sources: Richmond et al. (1994), Leonard et al. (2002), Hsiao et al. (2007), Pastorello et al. (2007), Smith et al. (2007), Valenti et al. (2008, 2015), Clocchiatti et al. (2011), Zhang et al. (2012)

K. Maeda

−20 Ic−BL

IIn

Ia −18 IIP IIb

−16 Ic

IIL

Ibn −14 0

20

40

60

80 100 120 140

Days

Fig. 11 Examples of (near) maximum-light spectra of SNe of different types. It is the compilation of the data from the following sources: Barbon et al. (1995), Hamuy et al. (2001), Patat et al. (2001), Valenti et al. (2008), Anupama et al. (2009), Zhang et al. (2012), Pereira et al. (2013), and Srivastav et al. (2014). (The data are obtained from WISeREP (https://www.wiserep.org) (Yaron and GalYam 2012))

where EK is the kinetic energy associated with the expansion of the ejecta and Mej is the ejecta mass. The diffusion time scale is then given as follows (e.g., Arnett 1996): tdif ∼

κ βcR, Mej

(11)

where β is a scaling constant that depends on the distribution of the opacity (κ) and density. The characteristic radial extent of the ejecta is simply described as

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R = V t, where t is the time since the explosion (assuming V t is substantially larger the progenitor radius, R0 ). With β ∼ 13.8 which is applicable to a range of the density/opacity distribution, the diffusion time is described as follows:

tdif



κ ∼ 180 days 0.2 cm2 g−1



Mej M⊙

3/2 

E 1051 erg

−1/2 

t day

−1

.

(12)

The diffusion time scale decreases as a function of time. Therefore, it becomes shorter than the characteristic expansion time scale (∼R/V ) at some point, which roughly defines the time at the peak luminosity:

tpeak



κ ∼ 14 days 0.2 cm2 g−1

1/2 

Mej M⊙

3/4 

E 1051 erg

−1/4

.

(13)

This is, roughly speaking, the basic mechanism which determines the characteristic time scale in the rise and decay as seen in the light curves (Fig. 10). For example, if we take Mej ∼ 1.4 M⊙ and EK ∼ 1.3 × 1051 erg, which are appropriate for SNe Ia in the MCh WD scenario, we obtain V ∼ 7,000 km s−1 and tpeak ∼ 17 days. At the peak luminosity, the radius of the ejecta edge is R ∼ 1015 cm. In this phase, a large fraction of the ejecta must be opaque as is evident from the derivation above, so we can (roughly) approximate the SN emission as a blackbody with radius R. With the (observed) peak luminosity of L ∼ 1043 erg s−1 (for SNe Ia), the characteristic temperature (T ) can be estimated through the Stefan-Boltzmann law: T ∼ 11,000 K



1043

L erg s−1

1/4 

R 1015 cm

−1/2

.

(14)

Therefore, SNe emit most of the radiation power in the optical wavelengths. The spectral lines are formed above the photosphere, therefore in the outermost ejecta around the peak luminosity (see above). Therefore, the characteristic “spectral classification” (Fig. 1) reflects the composition in the outermost layer of the progenitor: type II for a progenitor with a H-rich envelope (e.g., an RSG), type Ib and Ic/Ic-BL for a He and C+O star, and type Ia for a WD progenitor. As the spectral lines are formed within the expanding medium above the photosphere, the characteristic line profile is the P-Cygni profile (e.g., Branch et al. 2005; Branch and Wheeler 2017), i.e., a combination of broad emission component and a blue-shifted absorption component (as seen in Fig. 11, except for SNe IIn and Ibn; see section “SN Progenitors and Explosions as Seen in Observations” for details). The line width and the amount of the blueshift reflect the velocity at the line-forming region, typically slightly above the photosphere. Following the expansion and the density decrease, the photosphere is receding in mass coordinate as a function of time; therefore, the photospheric velocity and line velocities usually decrease with time.

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Power Sources There are several options that can work as the sources of the SN luminosities. First option is the thermal energy deposited by the shock propagation through the progenitor star. From the equipartition, we expect that the thermal energy (Eth ) just after the shock breakout (i.e., the thermal energy at the initial radius of R0 for the expanding ejecta, where R0 is the progenitor radius) as follows: Eth (R0 ) ∼ EK . In the optically thick phase, we may neglect the energy loss by radiation; then, the thermal energy decreases as time goes by following the adiabatic expansion, i.e., Eth (R = R(t)) ∼ EK (R(t)/R0 )−1 (Arnett 1996). We can then estimate the characteristic luminosity by computing the following: L ∼ Eth (R = R(tpeak ))/tpeak . This expression reduces to the following; 41

L ∼ 10

ergs

−1



κ 0.2 cm2 g−1

−1 

R0 11 10 cm



EK 51 10 erg



Mej M⊙

−1

.

(15)

Given that the typical (observed) luminosity of SNe is 1042 erg s−1 , it is seen that this energy source is important for an RSG progenitor (SNe II) but not for a compact star (SNe Ia and Ib/c). Another important power source is the radioactive decay input, especially the decay chain of 56 Ni → Co → Fe, with the e-folding time of 8.8 days and 111.3 days, respectively (see ⊲ Chap. 98, “Radioactive Decay”). In the earliest phase, the input power is approximately described as follows:  L(56 Ni) ∼ 6.5 × 1043 exp −

t 8.8 days



M(56 Ni) erg s−1 , M⊙

(16)

where we neglect the contribution from the 56 Co decay and assume that all the γ rays from the 56 Ni decay are absorbed within the ejecta. The initial mass of 56 Ni is denoted by M(56 Ni). Later on, the contribution from the 56 Co decay dominates the energy input. The escape of the γ -ray should also be taken into account toward the later phase: 

t L( Co) ∼ 1.5 × 10 exp − 111.3 days 56

43



 M(56 Ni)  Dγ + fe+ erg s−1 , (17) M⊙

where fe+ ∼ 0.035 is the fraction of the decay energy channeled to the positron emission (which is assumed to be locally thermalized within the ejecta). The γ ray escape is described by Dγ , i.e., the fraction of the energy originally emitted as γ -rays but absorbed and thermalized within the ejecta: Dγ ∼ 1 − e−τγ ∼ τγ (for τγ → 0)

97 Stellar Evolution, SN Explosion, and Nucleosynthesis

τγ ∼ 1000 

 2 Mej /M⊙

EK /1051 erg



3413



t day

−2

.

(18)

By setting τγ ∼ 1, we can derive the date (tγ ) when the γ -ray escape becomes substantial: tγ ∼ 30 days



Mej M⊙



EK 51 10 erg

−1/2

.

(19)

By comparing the peak time as determined by the optical-photon diffusion and the characteristic time scale for the γ -ray escape, it is seen that the full trapping of the γ -ray power is a good approximation around the maximum-light phase. Then, the peak luminosity is roughly determined by the decay power at the peak date (usually dominated by the 56 Co decay for most of SNe); this is ∼1041 –1043 erg s−1 for M(56 Ni) ∼0.01 − 1 M⊙ . Yet another potential energy source is the ejecta-CSM interaction as shown schematically in Fig. 12, for which a good review can be found in, e.g., Chevalier and Fransson (2017). As the ejecta are expanding into the CSM, two shock waves are formed (Chevalier 1982): forward shock (FS) that defines the boundary between the shocked and unshoked CSM and the reverse shock (RS) that defines the boundary between the shocked and unshocked ejecta. The shocked CSM and ejecta are connected by the contact discontinuity (CD). The dissipation rate of the kinetic energy at the shocks is estimated as follows: Lint

 ˙  3 M/0.01 M⊙ yr−1 VSN ∼ 2 × 10 erg s−1 . vw /100 km s−1 4,000 km s−1 42

(20)

Here, VSN is the expansion velocity of the CD. As we see, the interaction power can dominate over the other energy sources (the initial thermal energy and/or the radioactive energy input) for an extremely high mass-loss rate of 0.01M⊙ yr−1 (assuming the mass-loss wind velocity of vw ∼ 100 km s−1 ). We note that the materials passing through the forward and reverse shocks are initially heated to

Fig. 12 Schematic picture of the SN-CSM interaction (Maeda and Moriya 2022)

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temperature emitting X-ray photons (Chevalier 1982; Chevalier and Fransson 2006, 2017; Maeda and Moriya 2022). For example, for the FS, the temperature will be ∼109 (VSN /10,000 km s−1 )2 K (see ⊲ Chap. 100, “Thermal Processes in Supernova Remnants”), with the corresponding photon energy of ∼100 keV. The temperature behind the RS is lower by one or two orders of magnitude, depending on the ejecta and CSM structures, leading to the corresponding photon energy of ∼ a few keV. The evolution of VSN depends on the properties of the ejecta and the CSM; if the density slopes of the ejecta and the CSM are both described by a single power −n law, n for the ejecta and s for the CSM (i.e., ρej ∝ vej and ρCSM ∝ r −s , noting that the unshocked ejecta follow the homologous expansion, vej ∝ r/t), it can be derived that VSN evolves as follows (Chevalier 1982; Moriya et al. 2013), from the dimensional analysis: s−3

(21)

VSN ∝ t n−s .

The value of n is described as a steep power law with n ∼ 7 − 13 for typical models, with a compact progenitor and extended progenitor resulting in shallow and steep gradient (Matzner and McKee 1999). For a steady-state mass-loss wind with a constant velocity, s = 2. If we take n = 10 and s = 2, VSN ∝ t −0.125 , and thus Lint ∼ t −0.375 . As a specific example, the following expression has been frequently applied for an explosion of a He or C+O progenitor, with n = 10.18 (Chevalier and Fransson 2006): 9

VSN ∼ 8 × 10 cm s

−1



EK 1051 erg

0.43 

Mej M⊙

−0.32

A∗−0.12



t day

−0.12

,

(22)

where A∗ is a normalization constant for the CSM density as defined by ρCSM = 5 × 1011 A∗ r −2 g cm−3 where r is in cm. Namely, A∗ ∼



 −1 vw M˙ , 10−5 M⊙ yr−1 1,000 km s−1

(23)

and A∗ ∼ 104 for M˙ ∼ 0.01M⊙ yr−1 and vw ∼ 100 km s−1 . We then have the following for the interaction power: 43

Lint ∼ 10

erg s

−1



EK 51 10 erg

1.29 

Mej 10M⊙

−0.96 

A∗ 104

0.64 

t 100 days

−0.36

.

(24)

SN Progenitors and Explosions as Seen in Observations With the basic properties of the SN emission as introduced in the previous sections, it is possible to connect different types of progenitors and explosion mechanisms to

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SN observables. In addition, there are other observational constraints placed on the nature of the progenitor and explosion, including the nature of progenitor candidates detected in pre-SN images (e.g., Smartt 2009). Type Ia SNe As mentioned in sections “Introduction” and “Characteristic Behaviors”, spectral properties of SNe Ia suggest a relation to a WD thermonuclear explosion. The typical velocity seen in spectral lines, e.g., Si II 6355, is ∼10,000 km s−1 , roughly consistent with the expected ejecta velocity for the WD thermonuclear explosions (Mej ∼ 1 − 1.4 M⊙ and EK ∼ (1 − 1.5) × 1051 erg) (note that the “average” velocity estimated by Equation 10 is underestimate for the spectral velocity in the “outermost” layer seen around the maximum light). The characteristic time scale in the light curve evolution is ∼15–20 days (depending on the band passes), which is again consistent with the range of Mej and EK expected in the WD thermonuclear explosions. The light curve evolution is well explained by the 56 Ni/Co/Fe decays as a main power source. The peak luminosity is ∼(1 − 2) × 1043 erg s−1 , i.e., M(56 Ni) ∼0.5 − 1 M⊙ . This is a range well explained by the delayed-detonation model and the double-detonation model (sections “White Dwarfs in a Binary and Thermonuclear Supernovae” and “Explosive Nucleosynthesis”). For a typical WD radius (∼109 cm), the thermal energy stored during the explosion will never be a dominant power as it is quickly gone as a result of the adiabatic cooling (Eq. 15). This indeed has led to several diagnostics proposed to discriminate between the SD and DD progenitor scenarios (e.g., Maeda and Terada 2016 for a review). An important difference in the SD scenario from the DD is the existence of a nondegenerate companion. The collision between the SN ejecta and a nondegenerate companion can generate and store the thermal energy (Kasen 2010); for an order-of-magnitude estimate, one can insert the binary separation (which is comparable to the radius of the companion, as it is filling the RL; ∼1011 –1013 cm) into Equation 15. The expected luminosity can overwhelm the 56 Ni power in the first few days, and it is a level that is detectable by recent high-cadence surveys. This is a topical issue with an increasing number of samples available for such investigation (i.e., those discovered soon after the explosion and then promptly and intensively followed-up) in the last few years. The latest observational results can be found in, e.g., Burke et al. (2022). Indeed, various methods have been proposed to discriminate between different progenitor scenarios (e.g., SD vs. DD) as well as different explosion mechanisms (e.g., delayed detonation vs. double detonation), including a search for a (surviving) companion star within SNRs in the MW and LMC as well as in pre-and post-SN images of nearby SNe. Covering all these topics is beyond the scope of this contribution, and we refer the readers to Maeda and Terada (2016) for a review. Last but not least, it must be emphasized that SNe Ia are a mixture of various subclasses and outliers (Taubenberger 2017). While their general observational features point to the thermonuclear WD explosion origin, the details differ. It has thus been suggested that SNe Ia may indeed originate through several evolution channels and explosion mechanisms. For example, there are a few peculiar SNe

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Ia for which the double detonation is a leading interpretation (Jiang et al. 2017; De et al. 2019). There is also a class of peculiar SNe Ia for which an explosion of a MCh C+O WD, but only by deflagration without the detonation, is a leading scenario (Jha 2017). It has not been clarified what evolutionary channel and explosion mechanism are responsible to the main population of SNe Ia (e.g., Maeda and Terada 2016, for a review) Type IIP/L SNe The expected RSG progenitors, with its large luminosity in the optical, make it practically possible to search for a progenitor star in pre-SN images mainly provided by Hubble Space Telescope archival data; it is called “the direct progenitor detection.” It is a challenging observation, but the progenitor candidates have been routinely detected for a handful of very nearby SNe IIP (e.g., Smartt 2009, 2015). In many cases, the expected RSG progenitors are recovered, and thus the RSG progenitors for SNe IIP have been solidly established. From statistical analyses, the range in MZAMS leading to SNe IIP as the final outcome has been derived to be ∼9–18 M⊙ . Within uncertainties, it shows a good match to the theoretical expectation from the standard stellar evolution models (section “Massive Star Evolution and Core-Collapse Supernovae”), while the relatively low value for the upper limit is puzzling; while we have RSGs in the MW with MZAMS  18 M⊙ , such stars do not explode as SNe IIP, against the standard expectation (∼25−30 M⊙ depending on details of the stellar evolution model; e.g., Fig. 4). This is called the RSG problem (Smartt 2009). The strong and long-lasting Balmer lines (with the P-cygni profile), as seen in Fig. 11, indicate that the photoshpere keeps being formed within a massive Hrich envelope, again suggesting an RSG progenitor. The typical mass of the H-rich envelope is ∼10 M⊙ (Fig. 4), and we may assume Mej ∼ 10 M⊙ together with EK ∼ 1051 erg. We then estimate that the typical timescale is ∼100 days, which matches to the “plateau” seen in SNe IIP (Fig. 10). While SNe IIL do not show the plateau as clearly as in SNe IIP, it is seen that the characteristic time scale is similar (or a bit shorter) (Fig. 10). The velocity in the spectral lines is smaller for SNe IIP/IIL than SNe Ia and II/Ib/Ic (see below), which is also in line with the small ratio of EK /Mej . We however note that this is a very simplified picture. For example, the opacity is never constant in space and time; the recombination of H, which drastically changes the opacity across the recombination front, is indeed a key in determining the LC properties of SNe IIP/L given its massive H-rich envelope, and this must be taken into account in comparing the model and data (Arnett 1996). In any case, the RSG progenitor has been shown to be largely consistent with observational properties of SNe IIP based on numerical radiation transfer simulations (e.g., Dessart et al. 2013). The origin of SNe IIL is less clear, with several possible interpretations for its rapidly declining LC evolution, e.g., it could be due to a relatively small amount of the H-rich envelope (Moriya et al. 2016) and/or the substantial contribution from the SN-CSM interaction (Morozova et al. 2017). SNe IIP/L experience the initial “cooling phase” with the time scale of 10– 20 days, before the onset of the recombination within the ejecta. This phase

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can also be modeled with a similar idea for the plateau phase but with the temperature evolution mainly determined by the adiabatic cooling rather than the recombination (Rabinak and Waxman 2011). This is a UV-bright emission given its high temperature, with rising optical LCs following the blackbody peak moving into the optical range due to the temperature decrease. This is a powerful diagnostics to derive the progenitor radius (see Eq. 15), and has been applied to a sample of SNe IIP/L. However, the increasing sample has shown discrepancy between the observed multiband LCs in the first 10–20 days and the model expectation based on the standard stellar evolution models (Morozova et al. 2015; Förster et al. 2019); the standard progenitor models predict a monotonically rising multiband optical LCs in this initial phase which then merge smoothly into the plateau phase, while the observed SNe IIP/L typically show a bump in the optical. A popular idea to explain this behavior is an existence of a confined and dense CSM within ∼1015 cm. The corresponding mass-loss rate in the last few decades (for v ∼ 10 km s−1 ) can reach to ∼10−3 –0.1 M⊙ yr−1 , far exceeding a conventional mass-loss rate adopted in standard stellar evolution models. This is further supported by the “flash spectra” (Gal-Yam et al. 2014; Yaron et al. 2017); a good fraction of SNe IIP/L show narrow (unresolved, 500 km s−1 ) emission lines of highly ionized ions superimposed on a blue continuum in infant spectra taken within a day or a few days since the explosion, which is totally different from typical SN IIP (and IIL) spectra with Balmer series seen as a broad (∼10,000 km s−1 ) P-cygni profile (e.g., Fig. 11). This flash spectrum is interpreted as an outcome of initial SN radiation producing UV ionizing photons (i.e., blue continuum) that passes through a dense CSM. This is followed by a quick recombination within the CSM (i.e., narrow emission lines from highly ionized ions). Its short duration limits the size of the dense CSM as ∼1015 cm (i.e., the light-travel time for the flash spectrum lasting only for ∼10 h). The discovery of the confined and dense CSM has led to a paradigm change in the stellar evolution study. The origin has not yet been clarified, but it is likely related to the rapid evolution of the stellar core in the final phase; some key processes in this “final phase” are probably still missing in our knowledge of the stellar evolution. This discovery has been driving further intensive study both by observational approaches (through infant SNe; e.g., Förster et al. 2019; Maeda et al. 2021) and theoretical approaches (through the interpretation of the infant SN observational data and stellar evolution simulations; e.g., Fuller 2017; Ouchi and Maeda 2019). Type IIb/Ib/Ic SNe The direct progenitor detection for SNe Ib and Ic has been very limited, with mostly upper limits derived for nearby objects (Smartt 2009). The upper limits sometimes go deeper than the expected magnitudes of Galactic WR stars, indicating that at least a fraction of SNe Ib/c progenitors are different from the Galactic WR population. There is one strong progenitor candidate detected for SN Ib (iPTF13bvn) (Cao et al. 2013; Folatelli et al. 2016): its properties favor the binary evolution scenario, but a massive single-star scenario has not been completely rejected. A key challenge is that the expected bare He or C+O progenitors are

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luminous in the UV, but relatively faint in the optical in which most of the preSN data are available. A recent detection of bright and red (i.e., extended) point source for SN Ib 2019yvr (Kilpatrick et al. 2021) adds further complication to this picture, which might indicate existence of a dense CSM around some SNe Ib, perhaps similar to the case for (some) SN IIP progenitors (see above). The direct progenitor investigation has turned out to be successful for SNe IIb (see Smartt 2015, for a review). Interestingly, the progenitors’ (or candidates’) radii show a large diversity, from a blue-supergiant (BSG) size (∼50R⊙ ) to an RSG (500R⊙ ), including a yellow-supergiant (YSG) dimension (∼200R⊙ ). This is interpreted to reflect the amount of the remained H-rich envelope, as the hydrostatic structure changes at the boundary of MH ∼ 0.1M⊙ ; the BSG for MH  0.1M⊙ , YSG for MH ∼ 0.1M⊙ , and RSG for MH  0.1 − 1M⊙ . For a more massive H-rich envelope, the SN will be observed as either SNe IIL or IIP. This sequence is consistent with the binary evolution scenario, in which the initial separation controls the final mass of the H-rich envelope and the radius of the progenitor (Ouchi and Maeda 2017). The SN properties (light curves and spectra) of SNe IIb/Ib/Ic favor a relatively low-mass He or C+O star (with no or thin H-rich envelope), over a massive WR progenitor expected in the single stellar evolution. The characteristic time scale and the spectral-line velocity are comparable to those of SNe Ia, and the typical ejected mass has been estimated to be Mej ∼ 1 − 3M⊙ (Lyman et al. 2016). As shown in Fig. 4, it corresponds to the mass range of MZAMS ∼ 10 − 20M⊙ , as is similar to SNe IIP. As such, it indicates that the major evolution channel toward SNe IIb/Ib/Ic is a binary evolution; they would become SNe IIP if they would not be in a close binary system. The bright initial cooling phase is expected for (some) SNe IIb with extended progenitors, with a typical time scale of a few days to a week, i.e., shorter than SNe IIP due to the smaller amount of the H-rich envelope. It has been used to infer the progenitor radius for the SN IIb progenitors, resulting in generally a consistent result with the direct progenitor detection (e.g., Bersten et al. 2012). The similar observational investigation is challenging for SNe Ib/Ic for their smaller radius, but the increasing examples of infant SN observations start producing meaningful upper limit for the radius of their progenitors (e.g., Stritzinger et al. 2020). Type IIn and Ibn/Icn SNe There are SNe showing signatures of strong interaction between the SN ejecta and dense CSM. The population of SNe IIn is a classical example, as characterized by strong Balmer series in emission lines (Fig. 11). When a high-dispersion spectroscopy is performed, a narrow component (∼100 km s−1 ) is frequently seen in the P-cygni profile overlapped on a broader component; it is interpreted that the narrow component originates in the unshoked dense CSM, while the broad component represents either the shocked region or unshocked ejecta (e.g., Smith 2017, for a review). Their LCs show diversity, with bright ones exceeding the peak luminosity of SNe Ia (Fig. 10). These bright SNe IIn typically show slowly evolving LCs; the total energy in the radiation thus can exceed 1050 erg, sometimes reaching to ∼1051 erg.

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This huge energy output, together with the spectral properties, suggests that they are fully powered by the SN-CSM interaction, where the energy budget is attributed to the kinetic energy of the ejecta dissipated through the interaction. It is seen in Equation 24 that the luminosity of 1043 erg s−1 can be explained by the CSM corresponding to the pre-SN mass-loss rate of 0.01 M⊙ yr−1 . This is confirmed by analyses of SN IIn LC in a more detailed manner (Moriya et al. 2013), with the estimated mass-loss rate in the range of ∼10−3 –1 M⊙ yr−1 . A caveat here is that such analysis might be biased toward bright objects (with high mass-loss rates). The progenitors of SNe IIn have not been clarified. With the huge mass budget, it is generally believed to be a massive star, perhaps those even more massive than other classes of CCSNe (see Gal-Yam and Leonard 2009 for a possible progenitor detection). However, the mechanism and origin of the huge mass-loss rate have not yet been understood, which might be either a luminous-blue variable like eruption, RL mass transfer in a binary, or even involve a CE evolution. SNe Ibn are a He-rich analog of SNe IIn. Instead of Balmer lines, a number of He lines are seen as emission lines (Fig. 11), pointing to the He-rich CSM (e.g., Pastorello et al. 2007). Therefore, the ejecta should also be H-poor, and thus they could also be considered as an analog of SNe Ib or Ic but with dense (He-rich) CSM. Interestingly, SNe Ibn show different characteristics from SNe IIn in their LC evolution (Hosseinzadeh et al. 2017; Maeda and Moriya 2022) (Fig. 10); they typically evolve much faster than SNe IIn, which indicates a rapidly increasing mass-loss rate toward the SN (Maeda and Moriya 2022). The progenitor origin of SNe Ibn, as well as its relation to SNe IIb/Ib/In, has not been clarified, but it is likely that the progenitors of SNe Ibn are intrinsically different from those of SNe IIb/Ib/Ic; for example, an idea has been proposed to associate SNe Ibn to a massive WR star (essentially through a single-star evolution), while a majority of SNe IIb/Ib/Ic are an outcome of a binary evolution of less massive stars (e.g., Pastorello et al. 2007; Maeda and Moriya 2022). Very recently, a carbon-rich analog of SNe Ibn has been discovered, coined SNe Icn (Gal-Yam et al. 2022); this newly found population will provide key information on the progenitor evolution of strongly interacting SNe. As a variant of SNe IIn showing signatures of strong SN-CSM interaction, the so-called SNe Ia-CSM have been suggested to be associated with a thermonuclear WD explosion rather than CCSNe; they show similarities with SNe Ia in their broad spectral features (Hamuy et al. 2003), and there is one example which showed clear transition from SN Ia to SN Ia-CSM with increasing strength of SN-CSM interaction in the late phase (Dilday et al. 2012). The origin of SNe Ia-CSM has not been clarified, with a major challenge in explaining how a large amount of CSM could be produced in relative low-mass systems involving a WD. At least for the most extreme cases, it may involve a CE phase to produce the dense CSM environment, and the thermonuclear WD explosion might be triggered even as an outcome of the core merger through the CE (Jerkstrand et al. 2020). Other variants Properties of SNe are indeed very diverse, and thus this review can cover only a fraction of SN subclasses. Here, we briefly mention on some peculiar

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and interesting subclasses; the readers are referred to Branch and Wheeler (2017) as a comprehensive review on this topic. In relation to SNe Ic, there is a class of SNe Ic but with much broader spectral lines in their spectra, called SNe Ic-BL (Fig. 11). The prototypical SN Ic-BL is SN 1998bw, which was discovered in association with a long/soft gamma-ray burst (GRB) 980425 (Galama et al. 1998). To explain a combination of broader spectral features (i.e., higher ejecta velocity) and longer time scale in its LC (i.e., longer diffusion time scale) than canonical SNe Ic, it has been argued that SN 1998bw has massive ejecta (∼10 M⊙ ) and a large kinetic energy (EK  1052 erg) (Iwamoto et al. 1998). A sample of SNe Ic-BL, some are associated with a GRB (GRB-SNe) but others are not, have been discovered, forming a class of SNe Ic-BL (Woosley and Bloom 2006, for a review). It turns out that GRB-SNe (including SN 1998bw) indeed represent the most extreme example in its ejecta mass and kinetic energy. These properties seem to be less extreme for SNe Ic-BL without associated GRBs, but still they are generally more energetic than canonical SNe Ic. The energy budget required for SNe Ic-BL (especially for GRB-SNe) is far beyond the expectation within the framework of the standard delayed neutrino explosion scenario for CCSNe (section “Core-Collapse Supernova (CCSN) Explosion Mechanism”), and thus different mechanisms have been proposed; two popular ideas are (1) formation of a black hole (BH) and an accretion disk inside a collapsing massive star (MacFadyen and Woosley 1999), which energize both relativistic jets (to explain GRBs) and energetic SN ejecta (to explain the SN component), and (2) formation of a highly magnetized NS (an analog of a magnetar but with rapid rotation) (Zhang and Mészáros 2001; Metzger et al. 2011). Both scenarios involve an efficient conversion of the gravitational binding energy to the final outflow energy, by storing the energy first in form of the rotational energy; the conversion of the rotation energy to the outflow energy is likely mediated by magnetic field. The progenitors have been suggested to be a rapidly rotating massive star (e.g., Paczy´nski 1998), the formation of which will require a special evolutionary channel either in a single or binary scenario (Yoon and Langer 2005). Another class of objects of interest is a population of super-luminous SNe (SLSNe) (e.g., Gal-Yam 2012, for a review). As in the classical classification scheme, they are divided into types II (H-rich; SLSNe-II) and I (H-poor; SLSNe-I). SLSNe-II are observationally a (even more) luminous variant of SNe IIn, and there is little doubt that they are mainly powered by the strong SN-CSM interaction. The required CSM is larger than SNe IIn, and the nature of the progenitor system has not been clarified yet. The nature of SLSNe-I is less clear; even the power source to keep thier high luminosities has not yet been robustly identified. A popular suggestion is that they might be powered by the spin-down energy of highly magnetized NS (or an actively accreting BH) in the center, produced by the core collapse and explosion (Maeda et al. 2007; Kasen and Bildsten 2010). The central engine therefore may be similar to the one for GRB-SNe, and they may be unified into a single scheme (Greiner et al. 2015; Nicholl et al. 2016; Suzuki and Maeda 2021). Rapidly evolving transients form a new class of transients that have been discovered recently, thanks to the new-generation, wide-field, and high-cadence

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surveys (e.g., Drout et al. 2014). Their short time scale, with characteristic time scale of 10 days, has been a hurdle for the real-time prompt follow-up observations, and thus the detailed information such as spectra had been largely missing until recently. The first systematic sample with the spectral classification has been recently reported for those discovered by Zwicky Transient Facility (ZTF) (Ho et al. 2021). It shows that the rapidly evolving transients are composed of different populations, mainly divided into three classes: relatively low-luminous SNe IIb/Ib, luminous SNe Ibn/IIn, and extremely rapid and luminous (and rare) AT 2018cowlike objects. AT 2018cow-like objects are very different from known SN populations in various observational properties (Perley et al. 2019) (Fig. 13); they are extremely rapid, raising to the luminous peak ( − 22 mag, as is comparable to SLSNe) at most in 5 days (or even less). The color in the UV/optical does not evolve much, unlike canonical SNe showing the blue-to-red evolution. The optical spectra are also different from SNe, with some similarity to tidal-disruption events. Interestingly, there is indication of a powerful central engine as seen in X-rays from AT 2018cow (Margutti et al. 2019), which might also be responsible to its special appearance in the UV/optical/NIR wavelengths. No consensus has been reached to its origin and even the power source, with various scenarios suggested so far, including, e.g., a BH formation following a failed SN explosion of a massive star (as is similar to a

Fig. 13 Observational properties of AT 2018cow (Perley et al. 2019). (Left:) Evolution of the bolometric luminosity, photospheric radius, and temperature as derived by a blackbody fit. (Right:) Spectral evolution

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model for a long GRB), a pulsational pair-instability SN originated in a very massive star, an electron-capture SN, a tidal disruption event by a supermassive BH, and an explosion following a CE, among others (e.g., Uno and Maeda 2020, and references therein).

High-Energy Emissions from Supernovae There are several mechanisms that are responsible to high-energy emissions from (young) SNe. We will list some of them in this section. Emission following decays of radioactive isotopes is one mechanism (see ⊲ Chap. 98, “Radioactive Decay” for details). In SNe, the most abundantly produced unstable isotope is 56 Ni (section “Explosive Nucleosynthesis”), which is also responsible to optical emissions (sections “Power Sources” and “SN Progenitors and Explosions as Seen in Observations”). Examples of the simulated high-energy emissions in the hard-X and MeV-γ rays are shown in Fig. 14 for a few SN Ia models. The decay chain 56 Ni → 56 Co → 56 Fe produces characteristic MeV γ -ray lines, which interact with gas in the expanding SN ejecta primary through Compton scattering. The degraded γ -rays through the Compton scattering create a continuum down to ∼100 keV below which the photons are absorbed through the photoelectric absorptions. Figure 14 shows strong lines from the 56 Ni decay on day 20 (e.g., 128 and 812 keV) and from the 56 Co decay on day 60 (e.g., 847 keV). As time goes by, a fraction of the escaping lines increases (see Equations 18 and 19), while the decay power decreases exponentially (Equations 16 and 17); the combination creates the peak in the flux evolution of the decay lines, e.g., ∼60–80 days for the 847 keV line in the case of SNe Ia.

Fig. 14 Examples of synthetic spectra for hard-X and γ rays as a result of radioactive decay chain → 56 Co → 56 Fe for a few SN Ia models (Maeda et al. 2012)

56 Ni

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These signals have been detected in SN II 1987A and SN Ia 2014J. For SN 1987A, the radioactive decay emission from the 44 Ti → 44 Sc → 44 Ca has additionally been robustly detected. Another example of the 44 Ti/Sc/Ca decay emission is the one from Cas A SN remnant. ⊲ Chapter 98, ”Radioactive Decay” provides a comprehensive description on these observations (see the descriptions and references therein). Given that synthesis of radioactive isotopes traces the innermost part of the exploding core (section “Explosive Nucleosynthesis”), these radioactive decay emissions serve as an irreplaceable probe to the explosion mechanism and the core properties of the progenitor stars. The SN-CSM interaction is another major emission process of high-energy photons from young SNe. As this originates in the FS and RS, this signal is an important probe to the natures of the CSM and the outermost layer of the progenitor star (Chevalier and Fransson 2017, for a review). If the shocks are in the adiabatic regime (i.e., with negligible cooling), the characteristic temperature is ∼100 keV at the FS and ∼1 keV at the RS; the most of the energy is thus emitted as thermal hardX and soft-X photons, for the FS and RS, respectively. However, the RS can easily be in the cooling regime and thus does not produce high-energy photons unless the CSM density is extremely low, and thus the X-ray emission is initially dominated by the one from the FS, essentially through free-free emission. Later on, the RS becomes adiabatic, and thermal emission from the RS can dominate in the soft X-ray photons. An additional mechanism is the inverse Compton (IC) scattering of the thermal optical photons from the ejecta by relativistic, nonthermal electrons produced at the FS. Further consideration must be provided for the absorption process; especially important is the photoelectric absorption in the soft X-ray band, mainly through the unshocked CSM (plus some contribution in the shocked FS and RS regions), the effect of which is highly dependent on the CSM density and composition. Figure 15 shows the evolution of the X-ray spectra for SN IIb 2011dh, given as a specific example. Its thermal nature at ∼500 days as originated in the RS is robustly identified (Maeda et al. 2014). The data at day 33 are also fit well by the RS thermal emission model. The X-ray emission on day 10 is probably contributed substantially by the FS component, either through the free-free emission or the IC (Sasaki and Ducci 2012). By identifying the thermal component, it is possible to robustly derive the CSM density, therefore the mass-loss rate. The result can further be combined with the radio synchrotron emission to infer the nature of the acceleration of relativistic, nonthermal electrons at the FS (Maeda 2012); the radio synchrotron model alone suffers from the degeneracy in the nature of the particle acceleration and the CSM density, but by adding the X-ray data, this can be at least partly solved. For SNe with extremely dense CSM, emissions from relativistic, nonthermal protons/ions accelerated at the FS can produce strong contributions across various wavelengths. Figure 16 shows such a model example, for SN IIn 2010jl; this is a very bright SN IIn and its CSM density is in the highest regime even for SNe IIn. The nonthermal protons produce γ -rays at the Gev and TeV ranges through the pion decay following the interaction with thermal protons. Secondary electrons thus

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Fig. 15 An example of X-ray emission (Maeda et al. 2014); it is for SN IIb 2011dh on day 12 (blue), 33 (green), and ∼500 (red). (The data shown here have been taken by the Chandra observatory)

Fig. 16 An example of synthetic multiwavelength emissions from an SN IIn, powered by a strong SN-CSM interaction (Murase et al. 2019)

produced can play an important role in the radio synchrotron emission together with the primary electrons directly accelerated at the FS. Even neutrinos at Gev and TeV ranges are produced; SNe with very strong SN-CSM interaction have thus been proposed as one of possible electromanetic counterparts for TeV neutrinos (e.g., those detected at the IceCube), i.e., a target in the multi-messenger astronomy (e.g., Murase et al. 2019). As mentioned above, the radio emission from SNe originates in the electrons accelerated at the FS in most cases (except for the extremely dense CSM in which

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the secondary electrons’ contribution becomes substantial; Fig. 16). As such, the observation and analysis of radio signals provide a powerful probe to the nature of the CSM (Chevalier and Fransson 2017, for a review). One of the recent highlights is investigation of the nature of the CSM in the very vicinity of the SN progenitor. Thanks to the new-generation (optical) transient surveys that routinely discover SNe soon after the explosion (within a few days), radio observations of infant SNe (within a week of the explosion) are now practically possible, which provide the nature of the CSM within ∼1015 cm. This is a powerful method to probe the nature of the mass loss just before the explosion; 1015 cm /vw ∼ 30 yrs for the RSG progenitor (vw ∼ 10 km s−1 ; SNe IIP) or even ∼0.3 yrs for the compact He or C+O progenitors (vw ∼ 1,000 km s−1 ; SNe Ib/c). Given the high CSM density toward the inner region even for a constant mass-loss rate and wind velocity, high-frequency (mm) observation is a key, thanks to its transparency (Matsuoka et al. 2019). Figure 17 shows such an example for SN Ic 2020oi; assuming vw ∼ 1,000 km s−1 , the analysis of the data allows to trace the mass-loss history down to the final ∼0.5 yr before the explosion. The ALMA data trace the optically thin regime, and the observed temporal evolution, the flat-steep-flat evolution, is interpreted as the CSM density having the same, flat-steep-flat distribution from the inner to the outer regions, i.e., it is not described by a steady-state mass-loss mechanism. The fluctuation seen for the final mass-loss properties in the sub-year time scale indicates that the origin of the final activity is related to the accelerated change in the core nuclear burning stage and that the envelope reacts to the core evolution dynamically; this finding further strengthens the argument for existence of the (yet-unclarified) final activity of (at least some of) massive stars in the final decades as has been probed by the optical emission (section “SN Progenitors and Explosions as Seen in Observations”), and pushes the investigation further down to the final months before the SN explosion.

Fig. 17 An example of radio emission, including the mm emission observed by the ALMA (Maeda et al. 2021) and the cm emission from VLA and other facilities (Horesh et al. 2020). SN Ic 2021oi shown here is a rare example for which multiband light curves including the mm wavelengths are obtained within a week after the explosion

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Conclusion The fields of stellar evolution and SN explosion, as well as the transient observations (including SNe), are quickly developing with inflating opportunities both in theoretical and observational approaches. In this chapter, we have provided an overview on the stellar evolution channels toward SNe, explosion mechanisms, and explosive nucleosynthesis. There are many unresolved issues in these fundamental processes in astronomy, and studying properties of SNe is a unique and powerful probe to study these issues which are otherwise difficult. Observational properties of SNe, covering the basic and classical pictures, as well as up-to-date recent findings, are also summarized in this chapter, with which we demonstrate how the natures of the progenitor stars and the explosion mechanisms can be constrained. The contents of this chapter aim at providing useful basis and guideline in this quickly developing field, and the readers are encouraged to access review articles and recent papers on individual subjects introduced in this chapter. Acknowledgments K.M. thanks Avinash Singh, Anjasha Gangopadhyay, and Kohki Uno for their assistance to produce Figs. 10 and 11. K.M. acknowledges support from the Japan Society for the Promotion of Science (JSPS) KAKENHI grant JP18H05223 and JP20H00174. Some data presented in this contribution are obtained from WISeREP (https://www.wiserep.org).

References G.C. Anupama, D.K. Sahu, U.K. Gurugubelli, T.P. Prabhu, N. Tominaga, M. Tanaka, K. Nomoto, MNRAS 392, 894 (2009) D. Arnett, Supernovae and Nucleosynthesis: An Investigation of the History of Matter, from the Big Bang to the Present (Princeton University Press, Princeton, 1996) R. Barbon, S. Benetti, E. Cappellaro, F. Patat, M. Turatto, T. Iijima, A&AS 110, 513 (1995) M.C. Bersten, O.G. Benvenuto, K. Nomoto et al., ApJ 757, 31 (2012) H.A. Bethe, J.R. Wilson, ApJ 295, 14 (1985) L. Bildsten, K.J. Shen, N.N. Weinberg, G. Nelemans, ApJ 662, L95 (2007) R.M. Bionta, G. Blewitt, C.B. Bratton et al., Phys. Rev. Lett. 58, 1494 (1987) S.J. Boos, D.M. Townsley, K.J. Shen, S. Caldwell, B.J. Miles, ApJ 919, 126 (2021) D. Branch, M. Livio, L.R. Yungelson, F.R. Boffi, E. Baron, PASP 107, 1019 (1995) D. Branch, E. Baron, N. Hall, M. Melakayil, J. Parrent, PASP 117, 545 (2005) D. Branch, J.C. Wheeler, Supernova Explosions. Astronomy and Astrophysics Library (Springer, Berlin/Heidelberg, 2017) S.W. Bruenn, E.J. Lentz, W.R. Hix et al., ApJ 818, 123 (2016) J. Burke, D.A. Howell, D.J. Sand et al., preprint, arXiv:2207.07681 (2022) A. Burrows, D. Vartanyan, Nature 589, 29 (2021) Y. Cao, M.M. Kasliwal, I. Arcavi et al., ApJ 775, L7 (2013) R.A. Chevalier, ApJ 258, 790 (1982) R.A. Chevalier, ApJ 259, 302 (1982) R.A. Chevalier, C. Fransson, ApJ 651, 381 (2006) R.A. Chevalier, C. Fransson, in Handbook of Supernovae, 875 (Springer, Cham, 2017) D.D. Clayton, Principles of Stellar Evolution and Nucleosynthesis (University of Chicago Press, 1984) A. Clocchiatti, N.B. Suntzeff, R. Covarrubias, P. Candia, AJ 141, 163 (2011)

97 Stellar Evolution, SN Explosion, and Nucleosynthesis

3427

S.A. Colgate, R.H. White, ApJ 143, 626 (1966) K. De, M.M. Kasliwal, A. Polin et al., ApJ 873, L18 (2019) L. Dessart, D.J. Hillier, R. Waldman, E. Livne, MNRAS 433, 1745 (2013) B. Dilday, D.A. Howell, S.B. Cenko et al., Science 337, 942 (2012) M.R. Drout, R. Chornock, A.M. Soderberg et al., ApJ 794, 23 (2014) A.V. Filippenko, ARA&A 35, 309 (1997) M. Fink, F.K. Röpke, W. Hillebrandt, I.R. Seitenzahl, S.A. Sim, M. Kromer, A&A 514, A53 (2010) G. Folatelli, M.C. Bersten, H. Kuncarayakti, O.G. Benvenuto, K. Maeda, K. Nomoto, ApJ 811, 147 (2015) G. Folatelli, S.D. Van Dyk, H. Kuncarayakti et al., ApJ 825, L22 (2016) F. Förster, T.J. Moriya, J.C. Maureira et al., Nat. Astron. 3, 107 (2019) J. Fuller, MNRAS 470, 1642 (2017) C.L. Fryer, Stellar Collapse. Astrophysics and Space Science Library, vol. 302 (Kluwer Academic Publishers, 2004) T.J. Galama, P.M. Vreeswijk, J. van Paradijs et al., Nature 395, 670 (1998) A. Gal-Yam, D.C. Leonard, Nature 458, 865 (2009) A. Gal-Yam, Science 337, 927 (2012) A. Gal-Yam, I. Arcavi, E.O. Ofek et al., Nature 509, 471 (2014) A. Gal-Yam, R. Bruch, S. Schulze et al., Nature 601, 201 (2022) J. Greiner, P.A. Mazzali, D.A. Kann et al., Nature 523, 189 (2015) I. Hachisu, M. Kato, K. Nomoto, ApJ 470, 97 (1996) I. Hachisu, M. Kato, ApJ 558, 323 (2001) M. Hamuy, P.A. Pinto, J. Maza et al., ApJ 558, 615 (2001) M. Hamuy, M.M. Phillips, N.B. Suntzeff et al., Nature 424, 651 (2003) A. Heger, C.L. Fryer, S.E. Woosley, N. Langer, D.H. Hartmann, ApJ 591, 288 (2003) W. Hillebrandt, J.C. Niemeyer, ARA&A 38, 191 (2000) K. Hirata, T. Kajita, M. Koshiba et al., Phys. Rev. Lett. 58, 1490 (1987) A.Y.Q. Ho, D.A. Perley, A. Gal-Yam et al., preprint (arXiv:2105.08811) (2021) A. Horesh, I. Sfaradi, M. Ergon et al., ApJ 903, 132 (2020) G. Hosseinzadeh, I. Arcavi, S. Valenti et al., ApJ 836, 158 (2017) E.Y. Hsiao, A. Conley, D.A. Howell et al., ApJ 663, 1187 (2007) R. Iaconi, K. Maeda, O. De Marco, T. Nozawa, T. Reichardt, MNRAS 489, 3334 (2019) I. Iben Jr., A.V. Tutukov, ApJ 284, 719 (1984) K. Iwamoto, P.A. Mazzali, K. Nomoto et al., Nature 395, 672 (1998) K. Iwamoto, F. Brachwitz, K. Nomoto, N. Kishimoto, H. Umeda, W.R. Hix, F.-K. Thielemann, ApJS 125, 439 (1999) H.-T. Janka, Ann. Rev. Nucl. Part. Sci. 62, 407 (2012) A. Jerkstrand, K. Maeda, K.S. Kawabata, Science 367, 415 (2020) S.W. Jha, in Handbook of Supernovae, 375 (Springer, Cham, 2017) J. Jiang, M. Doi, K. Maeda et al., Nature 550, 80 (2017) D. Kasen, F.K. Röpke, S.E. Woosley, Nature 460, 869 (2009) D. Kasen, ApJ 708, 1025 (2010) D. Kasen, L. Bildsten, ApJ 717, 245 (2010) A.M. Khokhlov, A&A 245, 114 (1991) C.D. Kilpatrick, M.R. Drout, K. Auchettl et al., MNRAS 504, 2073 (2021) R. Kippenhahn, A. Weigert, A. Weiss, Stellar Structure and Evolution. Astronomy and Astrophysics Library, 2nd edn. (Springer, Berlin/Heidelberg, 2012) K. Kotake, K. Sato, K. Takahashi, Rep. Progress Phys. 69, 971 (2006) A. Kovetz, O. Yaron, D. Prialnik, MNRAS. A new, efficient stellar evolution code for calculating complete evolutionary tracks, Oxford University Press, 395, 1857 (2009) M. Kromer, M. Fink, V. Stanishev et al., MNRAS 429, 2287 (2013) N. Langer, ARA&A 50, 107 (2012) E. Laplace, S. Justham, M. Renzo, Y. Götberg, R. Farmer, D. Vartanyan, S.E. de Mink, A&A 656, A58 (2021)

3428

K. Maeda

D.C. Leonard, A.V. Filippenko, E.L. Gates, PASP 114, 35 (2002) M. Liebendörfer, A. Mezzacappa, F.-K. Thielemann, O.E. Messer, W.R. Hix, S.W. Bruenn, Phys. Rev. D 63, 103004 (2001) M. Limongi, A. Chieffi, ApJ 592, 404 (2003) M. Livio, P.A. Mazzali, Phys. Rep. 736, 1 (2018) E. Livne, ApJ 354, 53 (1990) J.D. Lyman, D. Bersier, P.A. James, P.A. Mazzali, J.J. Eldridge, M. Fraser, E. Pian, MNRAS 457, 328 (2016) A.I. MacFadyen, S.E. Woosley, ApJ 524, 262 (1999) K. Maeda, T. Nakamura, K. Nomoto, P.A. Mazzali, F. Patat, I. Hachisu, ApJ 565, 405 (2002) K. Maeda, K. Nomoto, ApJ 598, 1163 (2003) K. Maeda, M. Tanaka, K. Nomoto et al., ApJ 666, 1069 (2007) K. Maeda, N. Tominaga, MNRAS 394, 1317 (2009) K. Maeda, F.K. Röpke, M. Fink, W. Hillebrandt, C. Travaglio, F.-K. Thielemann, ApJ 712, 624 (2010) K. Maeda, S. Benetti, M. Stritzinger et al., Nature 466, 82 (2010) K. Maeda, Y. Terada, D. Kasen et al., ApJ 760, 54 (2012) K. Maeda, ApJ 758, 81 (2012) K. Maeda, S. Katsuda, A. Bambda, Y. Terada, Y. Fukazawa, ApJ 785, 95 (2014) K. Maeda, Y. Terada, Int. J. Modern Phys. D 25, 1630024 (2016) K. Maeda, P. Chandra, T. Matsuoka et al., ApJ 918, 34 (2021) K. Maeda, T.J. Moriya, ApJ 927, 25 (2022) D. Maoz, F. Mannucci, G. Nelemans, ARA&A 52, 107 (2014) R. Margutti, B.D. Metzger, R. Chornock et al., ApJ 872, 18 (2019) T. Matsuoka, K. Maeda, S.-H. Lee, H. Yasuda, ApJ 885, 41 (2019) C.D. Matzner, C.F. McKee, ApJ 510, 379 (1999) A. Menon, A. Heger, MNRAS 469, 4649 (2017) B.D. Metzger, D. Giannios, T.A. Thompson, N. Bucciantini, E. Quataert, MNRAS 413, 2031 (2011) A. Mezzacappa, Ann. Rev. Nucl. Part. Sci. 55, 467 (2005) T.J. Moriya, K. Maeda, F. Taddia, J. Sollerman, S.I. Blinnikov, E.I. Sorokina, MNRAS 435, 1520 (2013) T.J. Moriya, M.V. Pruzhinskaya, M. Ergon, S.I. Blinnikov, MNRAS 455, 423 (2016) V. Morozova, A.L. Piro, M. Renzo et al., ApJ 814, 63 (2015) V. Morozova, A.L. Piro, S. Valenti, ApJ 838, 28 (2017) T. Morris, P. Podsiadlowski, Science 315, 1103 (2007) K. Murase, A. Franckowiak, K. Maeda, R. Margutti, J.F. Beacom, ApJ 874, 80 (2019) M. Nicholl, E. Berger, R. Margutti et al., ApJ 828, L18 (2016) J.C. Niemeyer, S.E. Woosley, ApJ 475, 740 (1997) K. Nomoto, ApJ 253, 798 (1982) K. Nomoto, ApJ 277, 791 (1984) K. Nomoto, F.-K. Thielemann, K. Yokoi, ApJ 286, 644 (1984) K. Nomoto, K. Iwamoto, T. Suzuki, Phys. Rep. 256, 173 (1995) R. Ouchi, K. Maeda, ApJ 840, 90 (2017) R. Ouchi, K. Maeda, ApJ 877, 92 (2019) B. Paczynski, Structure and evolution of close binary systems, in Proceedings of IAU Symposium, vol. 73, ed. by P. Eggleton, S. Mitton, J. Whelan (1976), p. 75 B. Paczy´nski, ApJ 494, L45 (1998) R. Pakmor, M. Kromer, F.K. Röpke, S.A. Sim, A.J. Ruiter, W. Hillebrandt, Nature 463, 61 (2010) R. Pakmor, M. Kromer, S. Taubenberger, V. Springel, ApJ 770, L8 (2013) A. Pastorello, S.J. Smartt, S. Mattila et al., Nature 447, 829 (2007) F. Patat, E. Cappellaro, J. Danziger, ApJ 555, 900 (2001) R. Pereira, R.C. Thomas, G. Aldering et al., A&A 554, 27 (2013) D.A. Perley, P.A. Mazzali, L. Yan et al., MNRAS 484, 1031 (2019)

97 Stellar Evolution, SN Explosion, and Nucleosynthesis

3429

K.A. Postnov, L.R. Yungelson, Liv. Rev. Relat. 17, 3 (2014) Y.-Z. Qian, S.E. Woosley, ApJ 471, 331 (1996) I. Rabinak, E. Waxman, ApJ 728, 63 (2011) T. Rauscher, A. Heger, R.D. Hoffman, S.E. Woosley, ApJ 576, 323 (2002) M.W. Richmond, R.R. Treffers, A.V. Filippenko et al., AJ 107, 1022 (1994) F.K. Röpke, W. Hillebrandt, W. Schmidt, J.C. Niemeyer, S.I. Blinnikov, P.A. Mazzali, ApJ 668, 1132 (2007) F.K. Röpke, S.E. Woosley, W. Hillebrandt, ApJ 660, 1344 (2007) H. Saio, K. Nomoto, A&A 150, L21 (1985) H. Sana, S.E. de Mink, A. de Koter et al., Science 337, 444 (2012) M. Sasaki, L. Ducci, A&A 546, 80 (2012) T. Sato, K. Maeda, S. Nagataki et al., Nature 592, 537 (2021) R. Sawada, K. Maeda, ApJ 886, 47 (2019) J. Schwab, ApJ 906, 53 (2021) I.R. Seitenzahl, F. Ciaraldi-Schoolmann, F.K. Röpke et al., MNRAS 429, 1156 (2013) K.J. Shen, L. Bildsten, MNRAS 699, 1365 (2009) K.J. Shen, D. Kasen, B.J. Miles, D.M. Townsley, ApJ 854, 52 (2018) S.J. Smartt, ARA&A 47, 63 (2009) S.J. Smartt, PASA 32, 16 (2015) N. Smith, W. Li, R.J. Foley et al., ApJ 666, 1116 (2007) N. Smith, in Handbook of Supernovae, 403 (Springer, Cham, 2017) N. Soker, MNRAS 450, 1333 (2015) W.M. Sparks, T.P. Stecher, ApJ 188, 149 (1974) S. Srivastav, G.C. Anupama, D.K. Sahu, MNRAS 445, 1932 (2014) M.D. Stritzinger, F. Taddia, S. Holmbo et al., A&A 634, A21 (2020) K. Sumiyoshi, S. Yamada, H. Suzuki, H. Shen, S. Chiba, H. Toki, ApJ 629, 922 (2005) Y. Suwa, T. Yoshida, M. Shibata, H. Umeda, K. Takahashi, MNRAS. Neutrino-driven explosions of ultra-stripped Type Ic supernovae generating binary neutron stars, Oxford University Press 454, 3073 (2015) A. Suzuki, K. Maeda, ApJ 908, 217 (2021) A. Tanikawa, K. Nomoto, N. Nakasato, K. Maeda, ApJ 885, 103 (2019) S. Taubenberger, in Handbook of Supernovae, 317 (Springer, Cham, 2017) F.-K. Thielemann, K. Nomoto, M. Hashimoto, ApJ 460, 408 (1996) K. Uno, K. Maeda, ApJ 897, 156 (2020) S. Valenti, N. Elias-Rosa, S. Taubenberger et al., ApJ 673, L155 (2008) S. Valenti, D. Sand, M. Stritzinger et al., MNRAS 448, 2608 (2015) J.T. van Loon, M.-R.L. Cioni, A.A. Zijlstra, C. Loup, A&A 438, 273 (2005) J.S. Vink, A. de Koter, H.J.G.L.M. Lamers, A&A 369, 574 (2001) S. Wanajo, B. Müller, H.-T. Janka, A. Heger, ApJ 852, 40 (2018) B. Wang, X. Meng, X. Chen, Z. Han, MNRAS 395, 847 (2009) B. Wang, Z. Han, New Astron. Rev. 56, 122 (2012) R.F. Webbink, ApJ 277, 355 (1984) J. Whelan, I. Iben Jr., ApJ 186, 1007 (1973) S.E. Woosley, T.A. Weaver, ApJ 423, 371 (1994) S.E. Woosley, T.A. Weaver, ApJS 101, 181 (1995) S.E. Woosley, J.S. Bloom, ARA&A 44, 507 (2006) H. Yamaguchi, C. Badenes, A.R. Foster et al., ApJ 801, L31 (2015) O. Yaron, A. Gal-Yam, PASP 124, 668 (2012) O. Yaron, D.A. Perley, A. Gal-Yam et al., Nat. Phys. 13, 510 (2017) S.-C. Yoon, N. Langer, A&A 443, 643 (2005) S.-C. Yoon, S.E. Woosley, N. Langer, ApJ 725, 940 (2010) T. Yoshida, H. Umeda, K. Nomoto, ApJ 672, 1043 (2008) B. Zhang, P. Mészáros, ApJ 552, L35 (2001) T. Zhang, X. Wang, C. Wu et al., AJ 144, 131 (2012)

Radioactive Decay

98

Roland Diehl

Contents Introduction: Basics of Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Discovery . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radioactivity in Astrophysics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . General Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Astrophysical Studies Using Radioactivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Radioactive decay of unstable atomic nuclei leads to liberation of nuclear binding energy in the forms of gamma-ray photons and secondary particles (electrons, positrons); their energy then energizes surrounding matter. Unstable nuclei are formed in nuclear reactions, which can occur either in hot and dense extremes of stellar interiors or explosions or from cosmic-ray collisions. In high-energy astronomy, direct observations of characteristic gamma-ray lines from the decay of radioactive isotopes are important tools to study the process of cosmic nucleosynthesis and its sources, as well as tracing the flows of ejecta from such sources of nucleosynthesis. These observations provide a valuable complement to indirect observations of radioactive energy deposits, such as the measurement of supernova light in the optical. Here we present basics of radioactive decay in astrophysical context, and how gamma-ray lines reveal details about stellar interiors, about explosions on stellar surfaces or of entire stars, and about the interstellar-medium processes that direct the flow and cooling of nucleosynthesis

R. Diehl () Max Planck Institut für extraterrestrische Physik, Garching, Germany e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_86

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ashes once having left their sources. We address radioisotopes such as 56 Ni, 44 Ti, 26 Al, 60 Fe, 22 Na, and 7 Be, and also how characteristic gamma-ray emission from the annihilation of positrons is connected to these. Keywords

Nucleosynthesis · Nuclear reactions · Massive stars · Supernovae · Interstellar medium · Abundances

Introduction: Basics of Radioactivity Discovery In the nineteenth century, various efforts aimed to bring order into the elements encountered in nature. The inventory of the elements assembled by the Russian chemist Dmitri Mendeleev in 1869 grouped elements according to their chemical properties as derived from the compounds they were able to form, at the same time sorting the elements by atomic weight. The ordering by Mendeleyev enforced gaps in the table, for expected but then unknown elements. In the second half of the nineteenth century, scientists were all excited about chemistry and the fascinating discoveries around elements with their properties and their apparent transformations in chemical reactions. Today, the existence of 118 elements is firmly established (IUPAC, the international union of chemistry, coordinates definitions, groupings, and naming; see www.IUPAC.org). Element 118, called oganesson (Og), is the most massive superheavy element which has been synthesized, and found to exist at least for short time intervals. More massive elements may still exist in an island of stability beyond. The latest additions, no. 113–118, all were discovered in the year 2016, which reflects the concerted experimental efforts. After Conrad Röntgen’s discovery in 1895 of X-rays as a type of penetrating electromagnetic radiation, Antoine Henri Becquerel discovered radioactivity in 1896, as he was engaged in chemical experiments in his research of photographicplate materials regarding phosphorescence. At the time, Becquerel had prepared some plates treated with uranium-carrying minerals, but did not get around to make the planned experiment. When he found the plates in their dark storage some time later, he accidentally processed them and was surprised to find an image of a coin which happened to have been stored with the plates. Excited about X-rays, he believed he had found yet another type of penetrating radiation. Within a few years, Becquerel with Marie and Pierre Curie and others recognized that the origin of the observed radiation was elemental transformations of the uranium minerals: The physical process of radioactivity had been found! But when subatomic particles and the atom were discovered at the beginning of the twentieth century, the revolutionary aspect of elements being able to spontaneously change their nature was drowned by such new excitement. Still, well before atomic and quantum physics began to unfold, the physics of weak interactions had already been discovered, in its form of radioactivity.

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162

126 184 Lead

82

number of protons

Tin

50

Nickel

82

28 20 50 8 2 number of neutrons

2

8

20

28

Fig. 1 The table of isotopes, showing the possible configurations of atomic nuclei in a chart of neutron number (abscissa) versus proton number (ordinate). Numbers identify the magic numbers of nucleons, which characterize the most tightly bound configurations. White arrows indicate the nuclear-reaction paths of specific processes of nucleosynthesis in cosmic sites. The stable isotopes are marked in black. All other isotopes (in color) are unstable, or radioactive; they will decay until a stable nucleus is obtained

The atomic nucleus is composed of hadrons, the protons and neutrons, which are subject to the strong nuclear force, which so binds an atomic nucleus. The landscape of nuclear configurations is illustrated in Fig. 1, showing numbers of neutrons as abscissa and number of protons as ordinate, with black symbols as the naturally existing stable isotopes, and colored symbols for unstable isotopes. The latter are subject to radioactive decay toward stable isotopes, with less total binding energy per nucleon. Often, the result of such inner transformations of the hadronic configuration produces a daughter nucleus in an excited state. The transition to the ground state then involves spin changes, emitting photons to carry away spin and energy. These are the characteristic photons that accompany most radioactive decays. The production of nonnatural isotopes and thus the generation of man-made radioactivity led to the Nobel Prize in Chemistry for Jean Frédéric Joliot-Curie and his wife Iréne in 1935 – the second Nobel Prize awarded for the subject of radioactivity after the 1903 prize went jointly to Pierre Curie, Marie Skłodowska Curie, and Henri Becquerel, also in the field of chemistry.

Characteristics The probability per unit time for a single radioactive nucleus to decay is independent of the age of that nucleus. Unlike our commonsense experience with living things,

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or with astrophysical objects that evolve, such as stars, radioactive decay does not become more likely as the nucleus ages. In β-decays, the transition is mediated by the weak interaction, transforming a neutron into a proton and vice versa. The mass difference of the neutron and the proton (plus an electron for charge neutrality) is (Patrignani 2016) 1.293332 MeV = 939.565413 − 938.272081 MeV for the mass of neutron and proton, respectively. Neutrons are unstable and decay from the weak interaction, with a mean life of 880 s, into a proton, an electron, and an anti-neutrino, releasing this mass difference in kinetic energy. This is the origin of radioactivity. When neutrons and protons transform through such weak interaction, the new configuration is unstable; the atomic nucleus can (and must) find a new stable configuration of its hadrons, lowering the total nuclear binding energy. The excess binding energy thus can be released. Depending on the direction of the transformation p ←→ n, β − or β + decays are characterized by emission of an electron or positron, respectively, for charge conservation: n −→ p + e− + νe

(1)

p −→ n + e+ + νe

(2)

If such a transformation occurs inside an atomic nucleus, the quantum state of the nucleus as a whole is altered. Depending on the variety of configurations in which this new state may be realized (i.e., the phase space available to the decaying nucleus), this transformation may be more or less likely, as the total energy of a composite system of nucleons aims at a minimum value. Beta decay is the most peculiar radioactive decay type, as it is caused by the nuclear weak interaction which converts neutrons into protons and vice versa. The neutrino ν carries energy and momentum to balance the dynamic quantities. There are three types (We ignore here two additional β decays which are possible from ν and ν captures, due to their small probabilities.) of β-decay: A Z XN

−→

A Z−1 XN +1

+ e+ + νe

(3)

A Z XN

−→

A Z+1 XN −1

+ e− + νe

(4)

A Z XN

+ e− −→

A Z−1 XN+1

+ νe

(5)

In addition to β − decay, these are the conversion of a proton into a neutron (β + decay), and electron capture. The weak interaction itself involves two different aspects with intrinsic and different strength, the vector and axial-vector couplings. These result in Fermi and Gamow-Teller transitions, respectively (see Langanke and Martínez-Pinedo 2003, for a review of weak interaction physics in nuclear astrophysics). 13 + An example of β decay is 13 7 N −→ 6 C + e + ν, having mean lifetime τ near 10 min. This contributes to the early light from nova explosions. The kinetic energy Q of the two leptons, as well as the created electron’s mass, must be provided by the

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radioactive nucleus having greater mass than the sum of the masses of the daughter nucleus and of an electron (neglecting the comparatively small neutrino mass): 13 2 Qβ = [M(13 7 N) − M(6 C) − me ]c

(6)

where these masses are nuclear masses, not atomic masses. A small fraction of the energy release Qβ appears as the recoil kinetic energy of the daughter nucleus, but the remainder appears as the kinetic energy of electron and of neutrino. Capture of an electron is a two-particle reaction, the bound atomic electron e− or a free electron in hot plasma being required for this type of β decay. Therefore, depending on availability of the electron, lifetimes in electron capture β decay can be very different for different environments. In the laboratory case, electron capture usually involves the 1s electrons of the atomic structure surrounding the radioactive nucleus, because those hold their largest density at the nucleus. The situation for electron capture processes differs significantly in the interiors of stars and supernovae: Nuclei are fully ionized in plasma at such high temperature. The capture lifetime of 7 Be, for example, which is 53 days against 1s electron capture in the laboratory, is lengthened to about 4 months in the central region of our Sun. The range of the β particle (its stopping length) in normal terrestrial materials is small, being a charged particle which undergoes Coulomb scattering. An MeV electron has a range of several meters in standard air, during which it loses energy by ionizations and inelastic scattering. In tenuous cosmic plasma such as in supernova remnants, or in interstellar gas, such collisions, however, become rare and may be unimportant compared to electromagnetic interactions of the magnetic field (collisionless plasma). Energy deposit or escape is a major issue in intermediate cases, such as in the expanding envelopes of stellar explosions, in supernovae (positrons from 56 Co and 44 Ti), and in novae (many β + decays such as 13 N). Even in small solids and dust grains, energy deposition from 26 Al β-decay, for example, injects 0.355 W kg−1 of heat. This is sufficient to result in melting signatures, which have been used to study condensation sequences of solids in the early solar system and are believed to control the water content in newly forming planets (Lichtenberg et al. 2019). Gamma decay is another expression for the de-excitation of a nucleus from its excited configuration of the nucleons to a lower-lying state of the same nucleons. We denote such electromagnetic transitions of an excited nucleus radioactive γ -decay when the decay time of the excited nucleus is considerably longer than what is typical for excited nuclei, and that nucleus thus may be considered a temporarily stable configuration of its own, a metastable nucleus. Typically, a nucleus relaxes in an intrinsically fast process, and lifetimes for excited states of an atomic nucleus are 10−9 s. The spin (angular momentum) is a conserved quantity of the system in such a transition. The spin of a nuclear state is a property of the nucleus as a whole and reflects how the states of protons and neutrons are distributed over the quantummechanically allowed shells or nucleon wave functions (as expressed in the shell

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model view of an atomic nucleus). The emitted photon (γ ray) carries a multipolarity that results from the spin differences of initial and final states of the nucleus. Dipole radiation is most common and has multipolarity 1, emitted when initial and final states have angular momentum difference ∆l = 1. Quadrupole radiation (multipolarity 2, from ∆l = 2) is ∼6 orders of magnitude more difficult to obtain, and likewise, higher multipolarity transitions are becoming less likely as probability decreases in this way. This explains why some excited states in atomic nuclei are much more long-lived (meta-stable) than others; their transitions to the ground state are also considered as radioactivity, and called γ decay. The range of a γ -ray (its stopping length) is typically about 5–10 g cm−2 in passing through matter of all types. Hence, except for dense stars and their explosions, radioactive energy from γ decay is of astronomical implication only. In radioactive decay, the number of decays at each time is proportional to the number of currently existing radioisotopes: dN = −λ · N dt

(7)

Here N is the number of isotopes, and the radioactive decay constant λ is the characteristic of a particular radioactive species. Therefore, in an ensemble consisting of a large number of identical and unstable isotopes, their number remaining after radioactive decay declines exponentially with time: t

N = N0 · e− τ

(8)

The decay time τ is the inverse of the radioactive decay constant, and τ characterizes the time after which the number of isotopes is reduced by decay to 1/e of the original number. Correspondingly, the radioactive half-life T1/2 is defined as the time after which the number of isotopes is reduced by decay to 1/2 of the original amount, with τ T1/2 = (9) ln(2) In the general laboratory situation, radioactive decay involves a transition from the ground state of the parent nucleus to the daughter nucleus in an excited state. But in cosmic environments, nuclei may be part of hot plasma, and temperatures exceeding millions of degrees lead to excited states of nuclei being populated. Thus, quantum mechanical transition rules may allow and even prefer other initial and final states, and the nuclear reactions involving a radioactive decay become more complex. Excess binding energy will be transferred to the end products, which are the daughter nucleus plus emitted (or absorbed, in the case of electron capture transitions) leptons (electrons, positrons, neutrinos) and γ -ray photons. In cosmic hot plasma, the occupancy of nuclear states may also be affected by the thermal excitation spectrum of the Boltzmann distribution of particles, populating states at different energies according to

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dN − E = Gj · e kB T dE

(10)

Here kB is Boltzmann’s constant, T the temperature of the particle population, E the energy, and Gj the statistical weight factor of all different possible states j which correspond to a specific energy (States may differ in their quantum numbers, such as spin, or orbital-momenta projections; if they obtain the same energy E, they are called degenerate.) E. Inside stars, and more so in explosive environments, temperatures can reach ranges which are typical for nuclear energy-level differences. Therefore, in cosmic sites, radioactive decay time scales may be significantly different from what we measure in terrestrial laboratories on cold nuclei. Also the atomic-shell environment of a nucleus may modify radioactive decay, if a decay involves capture or emission of an electron to transform a proton into a neutron, or vice versa. Electron capture decays are inhibited in fully ionized plasma, due to the nonavailability of electrons. Also β − -decays are affected, as the phase space for electrons close to the nucleus is influenced by the population of electron states in the atomic shell. An illustrative example of radioactive decay is the 26 Al nucleus, illustrated in Fig. 2. The ground state of 26 Al is a 5+ state. Lower-lying states of the neighboring isotope 26 Mg have states 2+ and 0+ , so that a rather large change of angular momentum ∆l must be carried by radioactive decay secondaries. This explains the large β-decay lifetime of 26 Al of τ ∼1.04×106 y. In the level scheme of 26 Al, excited states exist at energies 228, 417, and 1058 keV. The 0+ and 3+ states of these next excited states are more favorable for decay due to their smaller angular momentum differences to the 26 Mg states, although ∆l = 0 would not be allowed for the 228 keV state to decay to 26 Mg’s ground state. This explains its relatively long lifetime of 9.15 s, and it is called a metastable state of 26 Al. If thermally excited, which would occur in nucleosynthesis sites exceeding a few 108 K, 26 Al may decay through this state without γ -ray emission, while the ground state decay is predominantly a β + decay through excited 26 Mg states and thus including γ ray emission. Secondary products, lifetime, and radioactive energy available for deposits and observation depend on the environment.

Radioactivity in Astrophysics General Considerations Nuclear reactions in cosmic sites rearrange the basic constituents of atomic nuclei (neutrons and protons) among the different allowed configurations. Radioactive, i.e., unstable, isotopes are a result of such nuclear reactions, as a by-product. The existence of radioactive isotope reflects the previous occurrence of those nuclear reactions. The radioactive decay of isotopes provides energy input and compositional changes, leading to observable consequences. Hence, observations of radioactive decay provide a way to learn about astrophysical processes.

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Fig. 2 26 Al decay, with different states of the 26 Al and 26 Mg nuclei and the possible transitions between. Both electron capture and β + decay occur, and the latter leads to positron annihilation γ rays, in addition to the de-excitation γ rays from transitions within the 26 Mg nucleus. Note that decay from the first excited state of 26 Al does not lead to γ -ray emission (see text for details)

The composition of cosmic material in the current universe and its observable objects is the result of nuclear reactions throughout cosmic history from its beginnings to the isolation of an object from further nuclear processing. Big Bang Nucleosynthesis (BBN) about 13.8 Gyrs ago left behind a primordial composition where hydrogen (protons) and helium were the most abundant species; the total amount of nuclei heavier than He (the metals) was less than 10−9 (by number, relative to hydrogen) (Cyburt et al. 2016). Today, the total mass fraction of metals in matter with solar abundances is (Our local reference for cosmic material composition seems to be remarkably universal, and representative for the local universe. Note that the Sun formed 4.6 Gy ago; hence, this composition sample is from a time where the Galaxy was little more than half its current age. Solar composition is still debated: Earlier than ∼2005, the commonly used value for solar metallicity had been 2%.) Z = 0.0134 (Asplund et al. 2009), i.e., of order ∼percent, compared to a hydrogen mass fraction of X = 0.7381. This growth of metal abundances by about seven orders of magnitude is the effect of cosmic nucleosynthesis. Nuclear reactions in stars, supernovae, novae, and other places

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Fig. 3 The cycle of matter, with stars forming out of interstellar gas, evolving toward wind and explosions releasing newly formed isotopes, that are then fed back into the next generation of stars

where nuclear reactions may occur all contribute. But it also is essential that at least a fraction of the nuclear-reaction products inside those cosmic objects will eventually be made available to other cosmic gas and solids, and thus to latergeneration stars such as our solar system born 4.6 Gyrs ago. This cycling of material is illustrated in Fig. 3 and includes radioactive contributions in the ejecta from stellar nucleosynthesis. Throughout cosmic evolution, nuclear reactions occur in various sites with different characteristic environmental properties. Each reaction environment leads to rearrangements of the relative abundances of cosmic nuclei. Winds, explosions, and binary mass transfers can liberate some of those reaction products from the compact centers of stars and their explosions, while, however, a major fraction of reaction products is buried in compact remnants of stellar evolution, such as white dwarfs, neutron stars, and black holes. For some of those compact white dwarfs and neutron stars, interactions with a companion star within a binary system can lead some time later to ejections of material again, e.g., in the forms of novae or thermonuclear supernovae. The cumulative process of nuclear transformations and return of some of the products into the interstellar and stellar materials is called cosmic chemical evolution. Radioactivity is among the most directly related processes that can tell us about the astrophysical processes during cosmic chemical evolution.

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The phenomenon of radioactivity has impacts on astrophysical investigations in two fundamental aspects: 1. The presence of radioactive isotopes changes processes in astrophysical sites and objects from what is known from laboratories . 2. The presence of isotopes results in phenomena, the observations of which enable new and characteristic lessons on astrophysics.

Different Processes The existence of radioactive isotopes implies that high-energy processes which exceed the threshold of production for such isotopes will produce such output. Therefore, radioactivity presents a channel for absorbing energy in high-energy collisions, through incorporation of kinetic/external energy of the collision into internal nuclear binding or excitation energy. The nuclear reactions in nucleosynthesis environments that transform combinations of nucleons into others can be considered to mediate the thermal energy reservoir of a system with the cumulative nuclear binding energy that is represented by a particular composition of atomic nuclei (1a). The presence of radioactive material implies that the composition of that cosmic material will change over time, due to radioactive decay. Thus, for all physical and chemical processes which depend on composition, there will be a time-dependent component in such process (1b). The presence of radioactive material implies that radioactive decay will liberate nuclear binding energy, in the forms of γ -radiation and of energized daughter products. Both of these contribute to the heat of the respective environment, and thus to its thermal luminosity, as much as this energy is captured or absorbed by such environment (1c). Depending on the astrophysical objective, radioactive isotopes may be called short-lived, or long-lived, depending on how the radioactive lifetime compares to astrophysical time scales of interest. Examples are the utilization of 26 Al and 60 Fe (τ ∼My) to trace cumulative nucleosynthesis over a time interval of several million years (long-lived), or of 56 Ni and 44 Ti to trace how supernovae explode (shortlived). Note that in cosmic chemical evolution, on the other hand, 26 Al and 60 Fe would be called short-lived, because radioactive isotopes such as from Th and U with decay times of Gyrs are used for temporal evolution studies on cosmological time scales; 26 Al is also studied from meteorites with respect to the early solar system and measures the nucleosynthesis activity near the presolar nebula 4.6 Gyrs ago within a precision of Myrs.

New Astronomy Direct astronomical measurements of radioactivity use two main methods: Characteristic nuclear emission lines measured with gamma-ray telescopes and isotopic abundances in samples of cosmic matter captured within our solar system. Both of these methods are rather new and not so familiar disciplines of astronomy.

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They are complemented by less direct measurements of radioactivity, reflecting the differences in processes due to radioactivity as discussed above. The detection of the presence of radioactive nuclei in specific cosmic samples of material can be used to trace the past history and evolution of such sample: The amount of radioactivity reflects the time and intensity of energetic interactions, or exposure to a source of high energy; its characteristic drop in intensity verifies that this particular messenger is the source of information. Examples are the presence of Tc in spectra of giant stars, which is the astronomical proof of recent nuclear reactions within this star (Merrill 1952); then the anomalous isotopic ratio of Ne found in meteorites after they were heated to above 1000 K (see Clayton 2018, for more details of this route to the discovery of stardust); and the observed composition of cosmic rays near Earth which includes radio-isotopes resulting from interstellar spallation reactions, such as 10 Be, 36 Cl, and 26 Al (Mewaldt et al. 2001). A changing composition due to radioactive decay is best observed through the abundance of a daughter isotope which exceeds the isotope abundance ratios for the respective element. For example, excess 26 Mg in Al-rich inclusions of meteorites is interpreted as a result of decay of 26 Al and thus implies that an earlier time, radioactive 26 Al had been present in such material. This is the origin of a hypothesis that the early solar system had been enriched in some unexpected way with material carrying this radioactive isotope. Such changes in isotopic abundance ratios also provide a cosmic clock: From an initial abundance of radioactive material, decay enriches the daughter isotope and depletes the parent isotope, strictly following the exponential law of radioactive decay (see above). So, once an initial isotope abundance ratio is known, and material is isolated from any other influx or depletion of the specific isotopes, the time since isolation of such material can be calculated from the characteristic radioactive decay time that can be obtained from nuclear experiment or theory. We know 14 C dating from civilian life, e.g., conserving an atmospheric ratio 14 C/12 C of typically 1.2×10−12 in plants, which can be age-dated using the 14 C half-life of 5700 years, and counting the remaining 14 C and 12 C abundances with an AMS machine and single-ion detectors or current counters, respectively (Kutschera 2013). Section 1 of the following chapter below discusses specific astrophysical applications using tools of high-energy electromagnetic radiation as covered in this handbook. Nuclear reactions in the inner regions of stars release nuclear binding energy, some of this directly as part of the fusion reaction, but mostly through the fusion products and the radioactive processes therein, as discussed above. This energy release counterbalances the gravitational contraction, and thus can stabilize the star, as long as nuclear energy release is adjusted to gravitational pull and the energy loss due to radiation from the surface. Therefore, nuclear energy release stabilized the star as a long-lived object, and makes it shine, as it processes a fuel of lighter to more tightly bound nuclei (Eddington 1919). Exhaustion of a fuel terminates this inner energy source, and compression ensues and enables a next nuclear energy release process. Successive burning stages during the evolution of a star continue releasing nuclear energy and producing radioactivity; at each stage, they correspond to different nuclear fuels. At each stage, this energy release temporarily slows down

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the gravitational collapse of the star, with contraction and compressional heating in short transitional phases. Radiation transfer from γ -ray energies to thermal energies occurs in the large stellar envelope, so that the thermal emission of starlight from the surface has lost all information about the origin of the energy source and its shaping by radioactivity. In supernova explosions, the strive for most tightly bound nucleons near nuclear statistical equilibrium leads to a production of large amounts of radioactive 56 Ni (Arnett 1996): Of order 0.1 M⊙ are typically produced in core-collapse supernovae, as we know from SN1987A (0.07 M⊙ ) (Arnett et al. 1989; Fransson and Kozma 2002; McCray and Fransson 2016). Thermonuclear supernovae (type Ia) produce even more, typically 0.5 M⊙ (Scalzo et al. 2014; Seitenzahl and Townsley 2017). SN1987A was the first core-collapse supernova where gamma rays directly originating from the radioactive decay of 56 Ni could be seen: The Solar Maximum Mission (Simnett 1981) and its Gamma-Ray Spectrometer instrument (Ryan et al. 1979) showed the characteristic lines from decay of 56 Co at 847 and 1238 keV, respectively (Matz et al. 1988). SN2014J was the first such Type Ia supernova where those characteristic γ rays have been seen; this measurement and its implications is discussed in detail in the last section of the chapter below. The energy released from radioactive decay into its surroundings provides astronomical opportunities, observing high-energy photons (as covered in this handbook) from energized material, where other sources of energy are absent or implausible. The prominent case here is supernova explosions: Under explosive conditions in both physical types of supernova explosions, nuclear matter is processed in near-nuclear-reaction equilibrium. This equilibrium aims at a balance of number of particles (the phase space factor, according to Liouville’s theorem), and the minimization of kinetic energy as binding energies per nucleon are maximized. Under most conditions, this favors nucleon binding in the form of the radioactive nucleus 56 Ni, for matter composed of equal numbers of protons and neutrons (symmetric matter). 56 Ni decays first within 8.8 days to radioactive 56 Co, which again decays within 111 days to the end product, stable 56 Fe; this is illustrated in Fig. 4. The total energy released per 56 Ni nucleus in this decay chain is 6.7 MeV; for 1 M⊙ of 56 Ni, this corresponds to an energy of 2.3 ×1050 erg. The final section of the next chapter below discusses specific astrophysical applications. We note another prominent example where release of nuclear energy has important consequences: the decay of radioactive 26 Al embedded in planetesimals or dust grains of a protostellar nebula. Being formed out of cold interstellar matter at typical temperatures of order 10 K, these smallest solids contain all material that eventually may end up to form a planet. The decay of 26 Al liberates a heating power of 0.5 mW g−1 , which is sufficient under many conditions to heat a protostellar solid body to temperatures resulting in outgassing of volatile components, and in particular of water (Lichtenberg et al. 2019). This, however, is not within the scope of this handbook. Finally, the energy in radioactive decay is mostly released in the form of characteristic γ rays, from de-excitation of the daughter nucleus, in addition to kinetic energies of the daughter nucleus and leptons that result from the decay.

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Fig. 4 56 Ni decay, as an example of how the radioactive decay in supernova envelopes provides the power for subsequent thermal radiation, making supernovae being bright astronomical objects. Brightness is fading due to radioactive decay and dilution of the absorber for particles carrying the energy from radioactive decay

These γ rays are accessible to direct measurement and provide an astronomy of radioactive cosmic materials. Examples are the measurements of characteristic 56 Ni decay in supernova SN2014J, of 44 Ti decay in the young supernova remnants of Cas A and SN1987A, and the diffuse γ -ray glow of our Galaxy from 26 Al; all of these will be discussed in more detail below.

Astrophysical Studies Using Radioactivity Tracing Past Activity 26 Al was the first unstable isotope which was detected to decay in the interstellar medium (Mahoney et al. 1982). Its lifetime (1 My) is shorter than typical times of stellar evolution (Gyrs), and much shorter than the age of the Galaxy itself or older stars herein (>10 Gy). So it must have been produced recently. This observation of direct characteristic γ rays from radioactive decay of the 26 Al isotope demonstrated that nucleosynthesis, in some unknown mix of cosmic sources that include AGB (Iben and Renzini 1983) and WR stars (Meynet 1994), novae (Clayton and Hoyle 1974), core-collapse supernovae (Timmes et al. 1995), and cosmic-ray reactions (Kozlovsky et al. 1987), must have happened within the recent few Myrs of Galactic history.

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COMPTEL 1991−2000, ME 7 (Plüschke et al. 2001)

γ−Intensity [ph cm−2 sr−1 s−1] x 10−3 1

0

0.00

0.40

0.80

1.20

1.60

2.00

2.40

2.80

Fig. 5 The all-sky emission of γ rays from radioactive decay of 26 Al. This image (Plüschke et al. 2001) was obtained using a maximum-entropy regularization together with the maximumlikelihood method to iteratively fit a best image to the measured photon events

The diffuse emission from 26 Al decay (Fig. 5) was measured in detail during the first sky survey in γ rays toward the turn of the century, with the COMPTEL telescope (Schönfelder et al. 1993) on NASA’s Compton γ -ray Observatory (Gehrels et al. 1993), in its 1991–2000 mission. This measurement made a meaningful imaging analysis possible for the first time (Diehl 1995; Diehl et al. 1995; Knödlseder et al. 1999), and a sky map of the 26 Al emission with a resolution of about 4 degrees was derived through maximum-entropy analysis, shown in Fig. 5 (Plüschke et al. 2001). Apparently, 26 Al is of large-scale, Galactic origins. The theoretical considerations were put together with these observational results to conclude that massive stars and their core-collapse supernovae were believed to dominate the 26 Al production in the Galaxy (Prantzos and Diehl 1996). A main supporting argument for the Galaxy-wide contributions seen in 26 Al radioactivity was contributed from ESA’s INTEGRAL mission (Winkler et al. 2003) and its imaging gamma-ray spectrometer SPI (Vedrenne et al. 2003). SPI detectors with a high spectral resolution of about 3 keV enabled the observation of the characteristic signature of large-scale Galactic rotation in spectroscopy of the γ -ray line from 26 Al decay (Diehl et al. 2006; Kretschmer et al. 2013) that had been predicted already in 1978 (Lingenfelter and Ramaty 1978). Therefore, the observed gamma-ray flux can be translated into an observed total emitting mass of 26 Al within our Galaxy. This makes use of geometrical models of how sources are distributed within the Galaxy, such as double-exponential disks and spiral-arm models (see Diehl et al. 2006, for details). A first mass estimate of 2.8±0.8 M⊙

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(Diehl et al. 2006) was in line with theoretical expectations. Having this 26 Al mass value, one can now employ theoretical models for the dominating massive stars and their supernovae and their 26 Al yield, and in this way obtain the core-collapse supernova rate that is required to produce this much 26 Al. The value obtained in this way (Diehl et al. 2006) was a core-collapse supernova rate of 1.9±1.1 events per century for our Galaxy. The relatively large uncertainty quoted herein accounts for uncertainties both in the geometrical model (impacting on the 26 Al mass estimate) and in the core-collapse supernova modeling. Nevertheless, in this way, one had, for the first time, a supernova rate estimate that relied on observations encompassing the entire Galaxy, rather than inferences from other galaxies or from star counts near the solar system (see Diehl et al. 2006, for a discussion of these details and alternate methods). The supernova rate is key to driving turbulence within the interstellar medium (Krumholz et al. 2018; Koo et al. 2020), hence a key parameter to understand the dynamical state of interstellar medium. The 26 Al mass estimate was revised and refined, as better geometrical models for the assumed source distribution in the Galaxy could be developed, also to account for foreground emission from more-nearby massive-star groups, which reduces the estimated mass of 26 Al in the Galaxy. The total mass of 26 Al in the Galaxy is now estimated to be between 1.8 and 2 M⊙ (Diehl et al. 2018; Pleintinger 2020). The value of the Galactic core-collapse supernova rate therefore was updated with better estimates of the 26 Al mass and of model yields to 1.4±1.1 century−1 (Diehl et al. 2018; Pleintinger 2020), or one such supernova in our Galaxy every 71 years. At face value, the 294 supernova remnants observed in the Galaxy (Green 2019) thus present a tension with this value (see Chomiuk and Povich 2011, for a discussion of the astrophysical issue), as they would suggest a maximum sampling age of 21,000 y, while significantly larger ages have been inferred for some of these remnants. This, however, may be just another illustration of the dependence of the supernova remnant appearance on their surroundings. With 44 Ti, another radioactive isotope is attributed to supernovae, but it has a much shorter radioactive lifetime of just 86 years (Ahmad et al. 2006). Upon decay to 44 Sc, two lines are emitted at 69 and 78 keV as 44 Sc decays to its ground state; 44 Sc decays again within 5 h to 44 Ca, whose de-excitation emits a γ -ray line at 1156 keV energy. 44 Ti decay γ -rays have been observed from three supernovae, as discussed below in the section on “Diagnostics of Explosions.” But with this shorter lifetime, few sources across the Galaxy are expected to be found, even if one assumes that each supernova would eject radioactive 44 Ti. The connections between the rate of supernovae in our Galaxy and the number of sources that could be found through 44 Ti radioactivity have been analyzed (The et al. 2006; Dufour and Kaspi 2013), with the result that just a few 44 Ti sources are expected. The finding of the 360-year-old Cas A supernova remnant as the only such source in the Galaxy hence is remarkable. Searches have been made with γ -ray telescopes such as both COMPTEL (Dupraz et al. 1997) and both INTEGRAL main telescopes IBIS (Renaud et al. 2006; Tsygankov et al. 2016) and SPI (Weinberger et al. 2020). No new sources have been found by either of these, with ∼1–2 debated marginal

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candidates, such as Vela Junior (Iyudin et al. 1998; Schönfelder et al. 2000; Slane et al. 2001; Weinberger et al. 2020). In conclusion, it is asserted that 44 Ti ejection and γ -ray emission is attributed to a subclass of core-collapse supernovae only and requires special circumstances of the supernova explosion (as discussed below in the last section of the next chapter). Also 60 Fe γ -rays from its characteristic radioactive decay have been observed, from a cascade transition to the 60 Co ground state with γ rays at 1332 and 1173 keV. 60 Fe with τ = 3.6 Myrs is a second radio-isotope that is suited to trace accumulated past nucleosynthesis activity in the recent history of our Galaxy. A first signal from 60 Fe decay had been found with the scintillation detectors of the Reuven Ramaty High-Energy Solar Spectroscopic Imager (RHESSI) mission (Lin et al. 2002) that was aimed at the Sun for solar flare observations. Being pointed at the Sun, observations of celestial γ rays from the Galaxy, i.e., 26 Al and 60 Fe, were serendipitous, as the sky passes through the field of view of the unshielded detectors as a background varying over time (Smith 2003). Equipped with high-resolution Ge detectors, a clear signal from diffuse Galactic γ -ray emission from 26 Al and 60 Fe was found (Smith 2003). But spectral resolution was lost over the first few years of the 2002–2018 mission, so that it became more difficult to recognize the corresponding lines above background. The SPI spectrometer on INTEGRAL also collected data since 2002 and also found the signal from 60 Fe decay (Harris et al. 2005; Wang 2007). Unlike for RHESSI, SPI detectors were periodically heated to achieve an annealing of the degradation of spectral resolution from cosmicray bombardment in space. But it had been difficult for both instruments, with significances not exceeding the 5σ level, as spacecraft activation of 60 Co from cosmic rays occurs with time, and as the 60 Fe γ -ray brightness is much below that of 26 Al. The latter is quite in contrast to theoretical predictions (e.g., Timmes et al. 1995; Rauscher et al. 2002; Woosley and Heger 2007). The standard hypothesis is that both 26 Al and 60 Fe synthesis are dominated by massive stars, where 60 Fe is synthesized in the burning He and C shells from neutron capture on preexisting Fe nuclei, and released with the supernova explosion into the interstellar surroundings (Chieffi and Limongi 2002; Limongi and Chieffi 2006, 2018; Woosley and Heger 2007). But rare types of supernovae could be significant too (Woosley 1997). It was important, therefore, to exploit the 60 Fe γ -ray signal and discriminate potential single-source origins from diffuse emission, which was obtained by comparing sets of sky models fitting INTEGRAL/SPI data (Wang et al. 2020). This confirmed the diffuse nature of the 60 Fe γ rays, and also provided a best constraint on 60 Fe γ -ray intensity of below 0.4 of the 26 Al γ -ray brightness, considering also systematic uncertainties from model fitting and backgrounds at best (Wang et al. 2020). This ratio of two radioactivities both originating from massive stars is important, as it constrains the interior processes in such massive stars, independent of their number and locations as these cancel out in the ratio (e.g., see discussion in Woosley and Heger 2007). Understanding 60 Fe ejection from typical core-collapse supernovae then provides the background knowledge to interpret the 60 Fe nuclei that have been found in sediments on Earth, and also in lunar probes and in Antarctic

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snow (Wallner et al. 2021): These important findings of radioactive material deposits are proof of specific supernova activity near our solar system in the past few Myrs (Ellis et al. 1996). Exciting quantitative interpretations of this are the dating of such events and their relations to other known objects and their presumed historic evolution at distances of order 10 to 100 pc only (Wallner et al. 2016; Breitschwerdt et al. 2016). But these rely on the combination of theoretical modelings of the sources and their generic, Galaxy-wide confirmation, as provided by the diffuse 60 Fe γ -ray lines. Note that radioactivities are important tools for cosmic age-dating and for diagnostics of previous exposure of materials to high-energy reactions, in the fields of meteorites, of stardust, and of cosmic rays. These are not discussed in this handbook; see Clayton (1988), Clayton and Nittler (2004), Zinner (2008), and Israel et al. (2018) for reviews.

Tracing Flows of Nucleosynthesis Ejecta Some radioactive isotopes have a lifetime approaching the typical recycling time scale of interstellar gas into stars of 107 to 108 years. This offers a way to trace the flow of nucleosynthesis ejecta directly, i.e., through their radioactive afterglow. Note that other astronomical signatures of the release of newly produced cosmic material are of rather short duration, by comparison; supernova remnants, e.g., remain astronomically visible for times of order of several 10,000 years only (Koo et al. 2020; Vink 2012; Reynolds 2008). 26 Al with its lifetime of 1.04×106 y is on the short side of the recycling time of cosmic gas, but offers the brightest emission for this purpose. Its detection, measurements, and global Galactic interpretations in terms of massive-star feedback have been discussed in the previous section. In 1995, the GRIS balloon experiment (Tueller et al. 1988) had reported an indication that the 26 Al line was significantly broadened. A value of 6.4 keV (Naya et al. 1996) was obtained from a measurement with the high-resolution Ge detectors employed by this instrument. If interpreted as kinematic Doppler shifts of astrophysical origin, this translates into a 26 Al motion of 540 km s−1 (Naya et al. 1996). Considering the 1.04 × 106 y decay time of 26 Al, such a large velocity observed for averaged interstellar decay of 26 Al would naively translate into kpcsized cavities around 26 Al sources, so that velocities at the time of ejection would be maintained during the radioactive lifetime. An alternative hypothesis is that major fractions of 26 Al condensed onto grains, which would maintain ballistic trajectories in the tenuous interstellar medium (Chen et al. 1997; Sturner and Naya 1999). More recent high-quality spectroscopic data from INTEGRAL’s γ -ray spectrometer SPI have deepened and detailed these observations. SPI maintains a resolution of 3 keV at the energy of the 26 Al line (1809 keV) for multi-year data accumulation (Diehl et al. 2018); this corresponds to a Doppler velocity shift resolution of about 100 km s−1 for bright source regions (Kretschmer et al. 2013). Additionally, the INTEGRAL spectrometer SPI also is an imaging instrument, thus capable of mapping the spectral properties of 26 Al emission across the Galaxy. Already predicted in 1978 as a signature of large-scale Galactic rotation (Lingenfelter and Ramaty 1978), this signal was then seen in Galactic-plane survey data from

0.4 0.2 0.0 −0.2 0.6 0.4 0.2 0.0 −0.2 0.6 0.4 0.2 0.0 −0.2

l = −12° l = 0°

0.8 0.4 0.0 −0.4 0.6 0.4 0.2 0.0 −0.2

l = 12°

Flux / keV [rel. units]

Fig. 6 The 26 Al line as seen toward different directions (in Galactic longitude). This demonstrates kinematic line shifts from the Doppler effect, due to large-scale Galactic rotation (Kretschmer et al. 2013)

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1800 1805 1810 1815 1820 Energy [keV] Fig. 7 The line-of-sight velocity shifts seen in the 26 Al line versus Galactic longitude (data points with error bars), compared to measurements for molecular gas in CO (colors, intensity-coded from blue to red). The dashed line represents a model from 26 Al decay into cavities at the leading edge of spiral arms, as shown in Fig. 8 (Kretschmer et al. 2013)

INTEGRAL/SPI. In early INTEGRAL results (Diehl et al. 2006), it appears as a blue shift when viewing toward the fourth quadrant (objects on Galactic orbits approaching) and a red shift when viewing toward the first quadrant (receding objects, on average). The consolidated signature, with more years of exposure, is shown in Figs. 6 and 7). Comparison of the observed 26 Al velocity from large-scale Galactic rotation (Kretschmer et al. 2013) with the velocity of molecular gas exhibits a puzzling discrepancy (Fig. 7). The velocities seen for 26 Al throughout the plane of the Galaxy (Diehl et al. 2006; Kretschmer et al. 2013) exceed the velocities measured for

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molecular clouds, stars, and (the most precisely measured velocities of) maser sources by typically as much as 200 km s−1 (see Fig. 7). This high apparent bulk motion of decaying 26 Al means that the velocities of these radioactive nuclei remain higher than the velocities within typical interstellar gas for 106 years. Additionally, Fig. 7 shows that there is an apparent bias for this excess average velocity in the direction of Galactic rotation. This has been interpreted (Krause et al. 2015, 2021) as 26 Al decay occurring preferentially within large cavities (superbubbles), which are elongated into the direction of large-scale Galactic rotation (Fig. 8). If such cavities are interpreted as resulting from the early onset of stellar winds in massive-star groups, they characterize the source surroundings at times when stellar evolution terminates in core-collapse supernovae. Such wind-blown superbubbles around massive-star groups plausibly extend further in space in forward directions and away from spiral arms (that host the sources), as has been seen in images of interstellar gas from other galaxies (Schinnerer et al. 2019, and references therein). Such superbubbles can extend up to kpc (Krause et al. 2015) (see also Rodgers-Lee et al. 2019; Krause et al. 2021; Nath et al. 2020), which allows 26 Al to propagate at velocities similar to the sound speed within superbubbles. The dynamics of such superbubbles into the Galactic halo above the disk are unclear; this is perpendicular to the line of sight, so that measurements of 26 Al line Doppler velocities cannot provide an answer (see Krause et al. 2021, for a discussion of outflows into the halo). Nevertheless, these

Fig. 8 A model for the different longitude-velocity signature of 26 Al, assuming 26 Al blown into inter-arm cavities at the leading side of spiral arms (Krause et al. 2015)

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measurements underline the important consequences of massive-star clustering in shaping the interstellar medium, with connections to the astrophysics of stellar feedback in general (see Krause et al. 2020; Chevance et al. 2022, for recent theoretical considerations). One particular such superbubble has been identified near the solar system and toward the Orion region: The Eridanus cavity has been recognized in diffuse X-ray emission (Burrows et al. 1993), its boundaries are delineated in HI radio emission (Heiles et al. 1999), and γ rays from 26 Al have been detected (Siegert and Diehl 2017) (implications of these observations in terms of massive-star feedback have been discussed, a.o., by Fierlinger et al. 2016). Radioactive decay is often accompanied by the emission of positrons, if the decay is a β + decay; 26 Al decay as shown in Fig. 2 is an example. Once having escaped from the source, positrons will propagate through the interstellar medium as directed by magnetic fields, limited in time by interactions with particles and fields along the way. One of these interactions, in this case, is the annihilation of the positron with its antiparticle, the electron. This may occur in different ways, either directly, or through radiative captures, or through charge-exchange collisions with hydrogen atoms forming an intermediate positronium atom. As a result of positron annihilation, characteristic γ rays are generated, with a pair of photons at 511 keV energy for direct annihilations and for annihilation through the intermediate formation of para-positronium, and a spectrum rising in energy with an upper energy limit of 511 keV if through the intermediate formation of ortho-positronium, as spins of positronium and the annihilation γ -rays must be balanced. The study of positron propagation from their nucleosynthesis sources through interstellar surroundings (Alexis et al. 2014) suggests that propagation out to at most a few 100 pc may occur. The γ -ray emission from positron annihilation has been measured in detail and imaged across the entire sky with the INTEGRAL mission and data from the SPI instrument (Knödlseder et al. 2005; Jean et al. 2006; Siegert et al. 2016; Churazov et al. 2020). It is found that the emission morphology of positron annihilation γ rays is very different from those of any of the radioactivity candidates to produce the positrons, even if propagation is accounted for (see, e.g., Martin et al. 2010; Prantzos et al. 2011). Therefore, it is concluded that radioactivity only contributes a minority of positrons that are seen annihilating throughout the Galaxy; see Prantzos et al. (2011) for a review of positron astrophysics with lessons and remaining puzzles.

Diagnostics of Explosions Explosive nucleosynthesis occurs in complex networks of nuclear reactions. As the explosion is launched and proceeds, the environment and conditions for nuclear reactions vary due to the complex dynamics of material, and these are reflected in the products that result from a supernova explosion (Arnett 1996). Therefore, measurements of the radioactive ejecta of supernova explosions can be used directly as a diagnostics of the inner explosion, complementing sparsely available measurements from neutrinos and gravitational waves, which are the only messengers that directly escape from these inner regions of a supernova explosion. By comparison, all lowenergy radiation from X-rays down to infrared and radio are indirect, and shaped by processes outside of these inner regions.

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The gamma rays and positrons emitted from radioactive decay chain of 56 Ni through 56 Co (decay time τ = 8.8 days) to 56 Fe (τ = 111 days) energize the ejecta and envelope of the supernova from inside. The scattered and reprocessed radioactive energy is then responsible for the light that appears at the photosphere and makes supernovae to be bright sources. This photospheric emission has been key to many astrophysical studies of supernova explosions, in spite of its indirect origins far outside the explosion physics, because observations have been readily made available by the ensemble of telescopes worldwide and from infrared to UV wavelengths. For example, empirical laws have been used to estimate the amount of 56 Ni produced in the explosion (Arnett 1982), and spectroscopic measurements of elemental abundances have been used to infer the neutron to proton ratio in the explosion (Brachwitz et al. 2000; Mori et al. 2018; Yamaguchi et al. 2014). But if accessible, the radioactivity also provides a more direct diagnostic of the explosions themselves. The direct measurement of γ rays of 56 Ni decay had been predicted from supernova models (e.g., Colgate and McKee 1969; Clayton and Woosley 1974). But it took 40 years until, for the first time, the radioactive energy injection of 56 Ni decay could be measured directly as it powers the light from thermonuclear supernovae. INTEGRAL’s instruments in space orbit made this possible (Churazov et al. 2014), as SN2014J occurred on January 22, 2014 (Fossey et al. 2014), at a distance of only 3.3 Mpc in the nearby starburst galaxy M82 (Foley et al. 2014). INTEGRAL’s spectrometer SPI contributed γ -ray spectroscopy at fine resolution of the 56 Ni decay lines (see Fig. 4) (Diehl et al. 2014, 2015; Isern et al. 2016). This is a valuable complement, as it bypasses the uncertainties and complexities of radiation transport within the supernova, which downscatters MeV radiation by many orders of magnitude into optical light. Its diagnostic power had been emphasized by modeling work (e.g., Summa et al. 2013) long before SN2014J occurred. The amount of 56 Ni inferred from the γ -ray flux of 0.49±0.09 M⊙ (Diehl et al. 2015) is in agreement with the amount inferred from the optical brightness of the supernova, as based on the empirical peak-brightness/56 Ni heating-rate relation discussed above (Arnett’s rule (Arnett 1982)). The 56 Ni mass determination with infrared light curves (Dhawan et al. 2016) also is in agreement with this direct γ -ray-based 56 Ni mass determination in SN2014J. A key ingredient of modeling supernova light from thermonuclear supernovae in the broader electromagnetic spectrum from 56 Co radioactivity with its characteristic 111-day decay time has thus been measured by most direct messengers, as a reassuring confirmation of our standard understanding of the origins of supernova light. In details of the γ -ray spectroscopy, there had been indications of interesting irregularities that may be washed out by the processes of radiation transfer in a supernova envelope. The γ -ray line emission from decay of 56 Co was traced over 3 months with the INTEGRAL γ -ray spectrometer. Thus, the line centroid and width could be constrained in their evolution, as shown in Fig. 9. Naively, one would have expected a Doppler-broadened Gaussian line to appear and fade in its brightness, with some centroid shift from blue to red as the facing ejecta would shine early and receding ejecta from the distant part of the supernova would add later.

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Fig. 9 SN2014J signal intensity variations for the 847 keV line (center) and the 1238 keV line (right) as seen in four epochs of high-resolution γ -ray observations, in 10 keV energy bins. Clear and significant emission is seen in the lower energy band (left and center) through a dominating broad line attributed to 847 keV emission; the emission in the high-energy band in the 1238 keV line appears consistent and weaker, as expected from the branching ratio of 0.68 (right). For the 847 keV line, in addition a high-spectral resolution analysis is shown at 2 keV energy bin width (left), confirming an irregular appearance, i.e., not homogeneously in the form of a broad Gaussian (From Diehl et al. 2015)

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But, as shown in Fig. 9, the spectra rather show surprising spikes, which appear to come and go with time. Although statistical noise is a concern, it was asserted that a smooth appearance of the lines as suggested from a spherically symmetric gradual transparency to centrally located 56 Ni could be excluded (Diehl et al. 2015). Rather, it is indicated that individual clumps of 56 Co decay at different bulk velocities may have appeared at different times, signifying substantial deviations from spherical symmetry of explosion or 56 Co distribution (see Diehl et al. 2015, for more detail on the 56 Co γ -ray signal). Thus, γ -ray spectroscopy provides an additional indication that non-sphericity may be significant in type Ia explosions, and rather smoothed out in signals based on bolometric light reradiation from the entire supernova envelope. In SN2014J, even more spectacular was the detection of 56 Ni decay lines early on (Fig. 10): It was believed that 56 Ni would always be embedded so deeply within the supernova’s core that even γ rays could not leak out before 56 Ni was converted to 56 Co, due to its radioactive lifetime of about 9 days. Only some He cap models included the possibility of early γ -ray emission from 56 Ni decay (The and Burrows 2014), as helium deposition on the surface of the white dwarf could cause a helium surface explosion triggering the thermonuclear supernova. Thus, this discovery of early 56 Ni γ -ray lines was discussed as a support for such a double detonation (see Diehl et al. 2014, for more detail).

Fig. 10 Early γ -ray spectrum from SN2014J, finding the characteristic line at 158 keV from 56 Ni decay. Observed from a 3-day interval around day 17.5 after the explosion, this confirms an early visibility of 56 Ni, probably close to the surface, rather than embedded in the supernova center. The SPI instrumental background is shown as a scaled histogram, showing the SN2014J line offset from the centroid of a strong background line. The measured intensity corresponds to an initially synthesized 56 Ni mass of 0.06 M⊙ (From Diehl et al. 2015)

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We now turn to the case for core-collapse supernovae. Observations of supernova SN1987A with γ -ray telescopes had shown that the radioactive power source of supernova light was embedded within the massive envelope of such a supernova somewhat different than the standard onion shell picture of a massive star at the end of its stellar evolution would suggest: The SMM Gamma-Ray Spectrometer showed a surprisingly early appearance of the characteristic lines from decay of 56 Co at 847 and 1238 keV (Matz et al. 1988; Leising and Share 1990), only 6 months after the explosion. Detailed line spectroscopy of this signal suggests an early redshift of the line centroids (Leising and Share 1990), quite in contrast to expectations: Early inner radioactivity should be revealed from the near side of the supernova first. Follow-up spectroscopy with semiconductor detectors of higher spectral resolution than SMM’s scintillation detectors then showed an expected evolution from early blue-shifted lines to red shift of this early 56 Co line signal (Tueller et al. 1990). A detailed analysis of model ingredients that would be compatible with all γ -ray data on SN1987A 56 Co line emission suggests that a rather particular combination of bulk initial velocity of the 56 Ni produced, and some degree of nonspherical distribution with a suitable combination of envelope mass and explosion energy are needed (Jerkstrand et al. 2020). The bolometric light curve of SN1987A follows the predictions of fully trapping the energy from 56 Co decay for several hundred days. It can be modulated by standard envelope density models and changes in the escape fractions of γ -rays due to decreasing densities as the envelope expands. This radiation escape only becomes a significant effect beyond about 1000 days after the explosion. At later times, the change of slope in the bolometric light curve indicates that power now is delivered from radioactivities with longer decay times, first 57 Co and then 44 Ti (Seitenzahl et al. 2014). The 44 Ti radioactivity as a power source of SN1987A emission at this time was then beautifully confirmed through observations of the characteristic decay lines directly. 44 Ti decays to 44 Sc within τ ≃ 86 years (Ahmad et al. 2006), emitting characteristic γ -rays of 68.87 and 78.36 keV from de-excitation of 44 Sc. The subsequent decay of 44 Sc to 44 Ca occurs after τ ≃ 5.73 h only, producing a characteristic γ -ray line at 1157.02 keV from de-excitation of 44 Ca. Thus, for our purpose, we may characterize the decay of 44 Ti with a decay time of 86 y and three characteristic lines at 69, 78, and 1157 keV energy. The 67.9 and 78.4 keV lines of 44 Ti decay have been observed 25 years after explosion with INTEGRAL instruments (Grebenev et al. 2012), and more clearly (Boggs et al. 2015) with the NuSTAR hard X-ray telescope (Harrison et al. 2013). The NuSTAR hard Xray telescope provides a unique opportunity for observations of characteristic lines from radioactivity, as only up to energies of ∼80 keV it is possible to deflect and focus celestial photons with X-ray optics, thus increasing the collection area of a telescope beyond the detector surface area; this is common for standard telescopes, yet impossible at energies above 100 keV due to the penetrating nature of γ rays. Therefore, even at 55 kpc distance, the brightness of SN1987A was sufficient for a significant measurement of the 44 Ti radioactivity (Boggs et al. 2015). The measured line flux of 3.5×10−6 ph cm−2 s−1 translates into a 44 Ti amount of 1.5×10−4 M⊙ .

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By comparison, the INTEGRAL result is somewhat debated, in particular with a strikingly large inferred 44 Ti amount of (3.1±0.8)×10−4 M⊙ (Grebenev et al. 2012); subsequent analyses of data with INTEGRAL’s SPI instrument could not confirm a signal from SN1987A in these characteristic lines (Weinberger et al. 2020). The characteristic lines from 44 Ti decay in SN1987A are thus not bright enough for detailed spectroscopy. Therefore, a diagnostics is only provided by comparing measured fluxes to the yields of models of different types (e.g., Woosley and Hoffman 1991; Timmes et al. 1996; Nagataki et al. 1998; Magkotsios et al. 2008, 2010; Sukhbold et al. 2016; Wongwathanarat et al. 2017; Curtis et al. 2019). Note that these direct measurements all find 44 Ti amounts that fall on the high side of theoretical expectations, which are generally in the range of a few 10−5 M⊙ . The second case of a core-collapse supernova with interesting observational detail in high-energy emission for supernova explosion diagnostics is the rather young supernova remnant Cas A. At a distance of 3.4 kpc and an age of 360 years (Fesen et al. 2006), this remnant is close enough so that telescopes at X- and γ -ray energies can measure all characteristic lines from decay of radioactive 44 Ti at sufficient precision for supernova diagnostics. The Cas A supernova remnant was the first source where 44 Ti decay was directly observed through γ -rays with the COMPTEL instrument, and the characteristic line at 1157 keV (Iyudin et al. 1994). Later this signal was confirmed by several other high-energy astronomy instruments, i.e., OSSE and RXTE The et al. (1996), Rothschild et al. (1999), Vink et al. (2000), and Siegert et al. (2015). With its size, it was ideally suited for the NuSTAR imaging hard X-ray telescope (Harrison et al. 2013), to measure and image its radioactivity γ -rays from the radioactive 44 Ti that had been ejected with the supernova 360 years ago (Grefenstette et al. 2014). The image shown in Fig. 11 is an overlay of emission mapped with the Chandra X-ray telescope in characteristic lines from Fe and Si recombination lines, and emission from radioactive 44 Ti decay in the 69 and 78 keV lines imaged with the NuSTAR multilayer mirrors. The recombination line image had been puzzling for a while, as it shows Fe emission located outside of Si structures. This should not be, if a massive star’s iron core launches a core-collapse supernova with lighter elements further out. But the 44 Ti radioactivity should be co-produced with any iron that may be ejected from the inner regions of the supernova. The NuSTAR data clearly show its location, which is near the center of the explosion, as expected. The puzzle is resolved from the nature of the different line emissions: The recombination lines recorded with Chandra result as electron recombination occurs in highly ionized plasma, and the atomic shell reaches its ground state, emitting characteristic lines in X-rays for these highly ionized states. In contrast, radioactive decay is independent of ionization state and occurs as nuclei are present, independent of density or temperature. Therefore, the iron recombination line emission is sensitive to biases from ionization and is even absent for fully ionized plasma. Hence, the Chandra measurement shows iron recombining where it has been overrun by the reverse shock already, while iron in the interior of the remnant has not been ionized yet by the inward-moving reverse shock.

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Fig. 11 The image (Grefenstette et al. 2014) of the Cas A supernova remnant demonstrates how radioactivity complements our view: Characteristic lines from 44 Ti decay (blue) reveal the location of inner ejecta, while X-ray line emissions from iron (red) and silicon (green) atoms, which also are emitted from those inner ejecta, show a somewhat different brightness distribution, due to ionization emphasizing the parts of ejecta that have been shocked within the remnant

Moreover, the image in 44 Ti radioactivity lines spectacularly shows directly that radioactive ejecta appeared in several clumps, rather than as spherically symmetric shells. After SN1987A’s asphericity indicators (see above), this is another direct demonstration that sphericity is not common in core-collapse supernova explosions. The NuSTAR measurement allowed a decomposition of the 44 Ti signal through imaging spectroscopy, determining the spectra across the remnant for ∼ 20 independent positions (Grefenstette et al. 2017). These results show that there is kinematic diversity across the inner remnant and these nucleosynthesis ejecta, with remarkable redshift for a majority of the regions that could be discriminated (Fig. 12, left). A deeper analysis of cumulative data of INTEGRAL/SPI consistently finds that all 44 Ti decay lines are red-shifted by an amount that corresponds to a bulk velocity of (1800±800) km s−1 (Fig. 12, right), consistent with the NuSTAR findings; SPI cannot resolve regions within the remnant and only provide an integrated spectrum. Note that the Doppler shift scales with energy; therefore, the data from the 1157 keV line contribute most significantly to this bulk velocity determination with INTEGRAL. Again, as for SN1987A, a remarkable deviation from sphericity is found for this core-collapse supernova that created the Cas A remnant.

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Fig. 12 The spectra for 44 Ti emission from the Cas A supernova remnant show significant redshifts, indicating bulk motion away from the observer. The NuSTAR spectra for two different emission regions (left) (Grefenstette et al. 2017) show that different regions show different bulk velocities, preferentially however away from the observer. The INTEGRAL/SPI spectra for all three lines (right) (Weinberger 2021) for emission integrated across the entire remnant confirm this trend and show in particular a clear Doppler shift for the 1157 keV line (lower right)

Also fluorescent X-ray line emission at keV energies may be emitted from radioactive material, if decay occurs through electron capture and leads to such Xray emission as the atomic-shell vacancy is replenished (Seitenzahl et al. 2015); this may have added to the energization of the late SN1987A light curve, but direct detections remain ambiguous (Borkowski et al. 2010). Thus, observations of radioactive decay γ -ray lines provide an important complement to the rich archives of supernova light curves and spectra at other wavelengths; each of these is at an opposite end of the complex radiation transfer within a supernova, with γ -rays from primary radioactive decay within the supernova and detailed spectra with elemental lines from emission of optical/IR at the supernova photosphere.

Summary and Conclusions Radioactive decay occurs as unstable nuclei are created in nuclear reactions of cosmic nucleosynthesis. The decay is mediated by the weak interaction, and hence

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largely independent of thermodynamic parameters such as density or temperature. Therefore, radioactive decay is an interesting emission process for characteristic γ rays, which can provide new astronomical messages from sources of high-energy astrophysics. Mainly, the decay of radioactive isotopes signifies the past occurrence of such nuclear interactions to a sample of cosmic matter, also providing a clock which allows tracing back such history. The radioactive decay also provides a source of energy, which may be deposited to matter after typically a delay corresponding to the characteristic time of radioactive decay. This leads to interesting processes resulting from such energy input, in terms of heating and thermal radiation. The observation of a presence of radioactive material directly traces previous nucleosynthesis. It therefore can be used to locate cosmic nucleosynthesis events, and to measure their occurrence rates, depending if the radioactive decay time of a specific isotope is short or long, respectively. For isotopes with a radioactive decay time that is longer than the typical other radiative signatures of nucleosynthesis events such as stellar explosions, measuring the γ rays from radioactivity allows to trace the flow of freshly produced nucleosynthesis ejecta over millions of years, along their path to mix with material that may form a later generation of stars. This allows for estimations of recycling times in the cosmic cycle of matter that leads to enrichment of metals in cosmic times, also called cosmic (or Galactic Chemical Evolution (GCE)) chemical evolution. Radioactivity in and following supernova explosions and their γ rays also provide a new and different window into the processes that occur to launch and drive such explosions. In particular, relating γ -ray light curves and spectra to other observables characterizing the supernova explosions can unfold dynamical processes in inner supernova regions that otherwise are occulted from direct observations. Acknowledgments R.D. acknowledges support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under its Excellence Strategy with the Munich Clusters of Excellence Origin and Structure of the Universe and Origins (EXC-2094-390783311), and by the EU through COST action ChETEC CA160117.

References I. Ahmad, J.P. Greene, E.F. Moore, S. Ghelberg, A. Ofan, M. Paul, W. Kutschera, Improved measurement of the Ti44 half-life from a 14-year long study. Phys. Rev. C 74(6), 065803 (2006). https://doi.org/10.1103/PhysRevC.74.065803 A. Alexis, P. Jean, P. Martin, K. Ferrière, Monte Carlo modelling of the propagation and annihilation of nucleosynthesis positrons in the Galaxy. Astron. Astrophys. 564, A108 (2014). https://doi.org/10.1051/0004-6361/201322393 W.D. Arnett, Type I supernovae. I – Analytic solutions for the early part of the light curve. Astrophys. J. 253, 785 (1982). https://doi.org/10.1086/159681 D. Arnett, Supernovae and Nucleosynthesis. An Investigation of the History of Matter, from the Big Bang to the Present. Princeton Series in Astrophysics (Princeton University Press, New Jersey, 1996) W.D. Arnett, J.N. Bahcall, R.P. Kirshner, S.E. Woosley, Supernova 1987A. Ann. Rev. Astron. Astrophys. 27, 629 (1989). https://doi.org/10.1146/annurev.aa.27.090189.003213

98 Radioactive Decay

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M. Asplund, N. Grevesse, A.J. Sauval, P. Scott, The chemical composition of the sun. Ann. Rev. Astron. Astrophys. 47, 481 (2009). https://doi.org/10.1146/annurev.astro.46.060407.145222 S.E. Boggs, F.A. Harrison, H. Miyasaka, B.W. Grefenstette, A. Zoglauer et al., 44 Ti gamma-ray emission lines from SN1987A reveal an asymmetric explosion. Science 348, 670 (2015). https:// doi.org/10.1126/science.aaa2259 K.J. Borkowski, S.P. Reynolds, D.A. Green, U. Hwang, R. Petre et al., Radioactive scandium in the youngest galactic supernova remnant G1.9+0.3. Astrophys. J. Lett. 724, L161 (2010). https:// doi.org/10.1088/2041-8205/724/2/L161 F. Brachwitz, D.J. Dean, W.R. Hix, K. Iwamoto, K. Langanke, G. Martínez-Pinedo, K. Nomoto, M.R. Strayer, F.K. Thielemann, H. Umeda, The role of electron captures in Chandrasekharmass models for type IA supernovae. Astrophys. J. 536(2), 934 (2000). https://doi.org/10.1086/ 308968 D. Breitschwerdt, J. Feige, M.M. Schulreich, M.A.D. Avillez, C. Dettbarn, B. Fuchs, The locations of recent supernovae near the Sun from modelling 60 Fe transport. Nature 532, 73 (2016). https:// doi.org/10.1038/nature17424 D.N. Burrows, K.P. Singh, J.A. Nousek, G.P. Garmire, J. Good, A multiwavelength study of the Eridanus soft X-ray enhancement. Astrophys. J. 406, 97 (1993). https://doi.org/10.1086/172423 W. Chen, R. Diehl, N. Gehrels, D. Hartmann, M. Leising, J.E. Naya, N. Prantzos, J. Tueller, P. von Ballmoos, in The Transparent Universe, ed. by C. Winkler, T.J.L. Courvoisier, P. Durouchoux. ESA Special Publication, Noordwijk vol. 382 (1997), p. 105 M. Chevance, J.M.D. Kruijssen, M.R. Krumholz, B. Groves, B.W. Keller et al., Pre-supernova feedback mechanisms drive the destruction of molecular clouds in nearby star-forming disc galaxies. Mon. Not. R. Astron. Soc. 509(1), 272 (2022). https://doi.org/10.1093/mnras/stab2938 A. Chieffi, M. Limongi, The production of 26 Al, 60 Fe and 44 Ti in massive stars of solar metallicity. New Astron. Rev. 46, 459 (2002). https://doi.org/10.1016/S1387-6473(02)00183-5 L. Chomiuk, M.S. Povich, Toward a unification of star formation rate determinations in the Milky Way and other Galaxies. Astron. J. 142, 197 (2011). https://doi.org/10.1088/0004-6256/142/6/ 197 E. Churazov, R. Sunyaev, J. Isern, J. Knödlseder, P. Jean et al., Cobalt-56 γ -ray emission lines from the type Ia supernova 2014J. Nature 512, 406 (2014). https://doi.org/10.1038/nature13672 E. Churazov, L. Bouchet, P. Jean, E. Jourdain, J. Knödlseder et al., INTEGRAL results on the electron-positron annihilation radiation and X-ray & Gamma-ray diffuse emission of the Milky Way. New Astron. Rev. 90, 101548 (2020). https://doi.org/10.1016/j.newar.2020.101548 D.D. Clayton, Meteorites: studies of nucleosynthesis. Nature 332, 683 (1988). https://doi.org/10. 1038/332683a0 D.D. Clayton, in Astrophysics and Space Science Library, vol. 453, ed. by R. Diehl, D.H. Hartmann, N. Prantzos (2018), p. 29. https://doi.org/10.1007/978-3-319-91929-4_2 D.D. Clayton, F. Hoyle, Gamma-ray lines from novae. Astrophys. J. Lett. 187, L101 (1974). https:// doi.org/10.1086/181406 D.D. Clayton, L.R. Nittler, Astrophysics with presolar stardust. Ann. Rev. Astron. Astrophys. 42, 39 (2004). https://doi.org/10.1146/annurev.astro.42.053102.134022 D.D. Clayton, S.E. Woosley, Thermonuclear astrophysics. Rev. Mod. Phys. 46, 755 (1974). https:// doi.org/10.1103/RevModPhys.46.755 S.A. Colgate, C. McKee, Early supernova luminosity. Astrophys. J. 157, 623 (1969). https://doi. org/10.1086/150102 S. Curtis, K. Ebinger, C. Fröhlich, M. Hempel, A. Perego, M. Liebendörfer, F.K. Thielemann, PUSHing core-collapse supernovae to explosions in spherical symmetry. III. Nucleosynthesis yields. Astrophys. J. 870(1), 2 (2019). https://doi.org/10.3847/1538-4357/aae7d2 R.H. Cyburt, B.D. Fields, K.A. Olive, T.H. Yeh, Big bang nucleosynthesis: present status. Rev. Mod. Phys. 88(1), 015004 (2016). https://doi.org/10.1103/RevModPhys.88.015004 S. Dhawan, B. Leibundgut, J. Spyromilio, S. Blondin, A reddening-free method to estimate the 56 Ni mass of Type Ia supernovae. Astron. Astrophys. 588, A84 (2016). https://doi.org/10.1051/ 0004-6361/201527201 R. Diehl, Imaging diffuse emission with COMPTEL. Exp. Astron. 6, 103 (1995). https://doi.org/ 10.1007/BF00419264

3460

R. Diehl

R. Diehl, C. Dupraz, K. Bennett, H. Bloemen, W. Hermsen et al., COMPTEL observations of Galactic 26 Al emission. Astron. Astrophys. 298, 445 (1995) R. Diehl, H. Halloin, K. Kretschmer, G.G. Lichti, V. Schönfelder et al., Radioactive 26 Al from massive stars in the Galaxy. Nature 439, 45 (2006). https://doi.org/10.1038/nature04364 R. Diehl, T. Siegert, W. Hillebrandt, S.A. Grebenev, J. Greiner et al., Early 56 Ni decay gamma rays from SN2014J suggest an unusual explosion. Science 345(6201), 1162 (2014). https://doi.org/ 10.1126/science.1254738 R. Diehl, T. Siegert, W. Hillebrandt, M. Krause, J. Greiner, K. Maeda, F.K. Röpke, S.A. Sim, W. Wang, X. Zhang, SN2014J gamma rays from the 56 Ni decay chain. Astron. Astrophys. 574, A72 (2015). https://doi.org/10.1051/0004-6361/201424991 R. Diehl, D.H. Hartmann, N. Prantzos, Distributed Radioactivities, vol. 453, chap. 7 (Springer, Berlin/Heidelberg, 2018), pp. 427–500. https://doi.org/10.1007/978-3-319-91929-4_7 R. Diehl, T. Siegert, J. Greiner, M. Krause, K. Kretschmer et al., INTEGRAL/SPI γ -ray line spectroscopy. Response and background characteristics. Astron. Astrophys. 611, A12 (2018). https://doi.org/10.1051/0004-6361/201731815 F. Dufour, V.M. Kaspi, Limits on the number of galactic young supernova remnants emitting in the decay lines of 44 Ti. Astrophys. J. 775, 52 (2013). https://doi.org/10.1088/0004-637X/775/1/52 C. Dupraz, H. Bloemen, K. Bennett, R. Diehl, W. Hermsen, A.F. Iyudin, J. Ryan, V. Schoenfelder, COMPTEL three-year search for galactic sources of ˆ44ˆTi gamma-ray line emission at 1.157 MeV. Astron. Astrophys. 324, 683 (1997) A.S. Eddington, The sources of stellar energy. The Observatory 42, 371 (1919) J. Ellis, B.D. Fields, D.N. Schramm, Geological isotope anomalies as signatures of nearby supernovae. Astrophys. J. 470, 1227 (1996). https://doi.org/10.1086/177945 R.A. Fesen, M.C. Hammell, J. Morse, R.A. Chevalier, K.J. Borkowski et al., The expansion asymmetry and age of the Cassiopeia A supernova remnant. Astrophys. J. 645(1), 283 (2006). https://doi.org/10.1086/504254 K.M. Fierlinger, A. Burkert, E. Ntormousi, P. Fierlinger, M. Schartmann, A. Ballone, M.G.H. Krause, R. Diehl, Stellar feedback efficiencies: supernovae versus stellar winds. Mon. Not. R. Astron. Soc. 456, 710 (2016). https://doi.org/10.1093/mnras/stv2699 R.J. Foley, O.D. Fox, C. McCully, M.M. Phillips, D.J. Sand et al., Extensive HST ultraviolet spectra and multiwavelength observations of SN 2014J in M82 indicate reddening and circumstellar scattering by typical dust. Mon. Not. R. Astron. Soc. 443, 2887 (2014). https:// doi.org/10.1093/mnras/stu1378 J. Fossey, B. Cooke, G. Pollack, M. Wilde, T. Wright, Supernova 2014J in M82 = Psn J09554214+6940260. Central Bureau Electron. Telegrams 3792, 1 (2014) C. Fransson, C. Kozma, Radioactivities and nucleosynthesis in SN 1987A. New Astron. Rev. 46, 487 (2002). https://doi.org/10.1016/S1387-6473(02)00188-4 N. Gehrels, E. Chipman, D.A. Kniffen, The compton gamma ray observatory. Astron. Astrophys. Suppl. 97, 5 (1993) S.A. Grebenev, A.A. Lutovinov, S. Tsygankov, C. Winkler, Hard-x-ray emission lines from the decay of 44 ti in the remnant of supernova 1987a. Nature (tbd)((tbd)), (accepted for publication) (2012) D.A. Green, A revised catalogue of 294 Galactic supernova remnants. J. Astrophys. Astron. 40(4), 36 (2019). https://doi.org/10.1007/s12036-019-9601-6 B.W. Grefenstette, F.A. Harrison, S.E. Boggs, S.P. Reynolds, C.L. Fryer et al., Asymmetries in core-collapse supernovae from maps of radioactive 44 Ti in CassiopeiaA. Nature 506, 339 (2014). https://doi.org/10.1038/nature12997 B.W. Grefenstette, C.L. Fryer, F.A. Harrison, S.E. Boggs, T. DeLaney et al., The distribution of radioactive 44 Ti in Cassiopeia A. Astrophys. J. 834, 19 (2017). https://doi.org/10.3847/15384357/834/1/19 M.J. Harris, J. Knödlseder, P. Jean, E. Cisana, R. Diehl, G.G. Lichti, J.P. Roques, S. Schanne, G. Weidenspointner, Detection of γ -ray lines from interstellar 60 Fe by the high resolution spectrometer SPI. Astron. Astrophys. 433, L49 (2005). https://doi.org/10.1051/0004-6361: 200500093

98 Radioactive Decay

3461

F.A. Harrison, W.W. Craig, F.E. Christensen, C.J. Hailey, W.W. Zhang et al., The nuclear spectroscopic telescope array (NuSTAR) high-energy X-ray mission. Astrophys. J. 770, 103 (2013). https://doi.org/10.1088/0004-637X/770/2/103 C. Heiles, L.M. Haffner, R.J. Reynolds, in New Perspectives on the Interstellar Medium, ed. by A.R. Taylor, T.L. Landecker, G. Joncas. Astronomical Society of the Pacific Conference Series, San Francisco, vol. 168 (1999), p. 211 I. Iben, A. Renzini, Asymptotic giant branch evolution and beyond. Ann. Rev. Astron. Astroph. 21, 271 (1983). https://doi.org/10.1146/annurev.aa.21.090183.001415 J. Isern, P. Jean, E. Bravo, J. Knödlseder, F. Lebrun et al., Gamma-ray emission from SN2014J near maximum optical light. Astron. Astrophys. 588, A67 (2016). https://doi.org/10.1051/00046361/201526941 M.H. Israel, K.A. Lave, M.E. Wiedenbeck, W.R. Binns, E.R. Christian et al., Elemental composition at the cosmic-ray source derived from the ACE-CRIS instrument. I. 6 C to 28 Ni. Astrophys. J. 865(1), 69 (2018). https://doi.org/10.3847/1538-4357/aad867 A.F. Iyudin, R. Diehl, H. Bloemen, W. Hermsen, G.G. Lichti et al., COMPTEL observations of Ti-44 gamma-ray line emission from CAS A. Astron. Astrophys. 284, L1 (1994) A.F. Iyudin, V. Schönfelder, K. Bennett, H. Bloemen, R. Diehl, W. Hermsen, G.G. Lichti, R.D. van der Meulen, J. Ryan, C. Winkler, Emission from 44 Ti associated with a previously unknown Galactic supernova. Nature 396, 142 (1998). https://doi.org/10.1038/24106 P. Jean, J. Knödlseder, W. Gillard, N. Guessoum, K. Ferrière, A. Marcowith, V. Lonjou, J.P. Roques, Spectral analysis of the Galactic positron annihilation emission. Astron. Astrophys. 445, 579 (2006). https://doi.org/10.1051/0004-6361:20053765 A. Jerkstrand, A. Wongwathanarat, H.T. Janka, M. Gabler, D. Alp et al., Properties of gamma-ray decay lines in 3D core-collapse supernova models, with application to SN 1987A and Cas A. Mon. Not. R. Astron. Soc. 494(2), 2471 (2020). https://doi.org/10.1093/mnras/staa736 J. Knödlseder, D. Dixon, K. Bennett, H. Bloemen, R. Diehl, W. Hermsen, U. Oberlack, J. Ryan, V. Schönfelder, P. von Ballmoos, Image reconstruction of COMPTEL 1.8 MeV (26) Al line data. Astron. Astrophys. 345, 813 (1999) J. Knödlseder, P. Jean, V. Lonjou, G. Weidenspointner, N. Guessoum et al., The all-sky distribution of 511 keV electron-positron annihilation emission. Astron. Astrophys. 441, 513 (2005). https:// doi.org/10.1051/0004-6361:20042063 B.C. Koo, C.G. Kim, S. Park, E.C. Ostriker, Radiative supernova remnants and supernova feedback. Astrophys. J. 905(1), 35 (2020). https://doi.org/10.3847/1538-4357/abc1e7 B. Kozlovsky, R.E. Lingenfelter, R. Ramaty, Positrons from accelerated particle interactions. Astrophys. J. 316, 801 (1987). https://doi.org/10.1086/165244 M.G.H. Krause, R. Diehl, Y. Bagetakos, E. Brinks, A. Burkert, O. Gerhard, J. Greiner, K. Kretschmer, T. Siegert, 26 Al kinematics: superbubbles following the spiral arms? Constraints from the statistics of star clusters and HI supershells. Astron. Astrophys. 578, A113 (2015). https://doi.org/10.1051/0004-6361/201525847 M.G.H. Krause, S.S.R. Offner, C. Charbonnel, M. Gieles, R.S. Klessen et al., The physics of star cluster formation and evolution. Space Sci. Rev. 216(4), 64 (2020). https://doi.org/10.1007/ s11214-020-00689-4 M.G.H. Krause, D. Rodgers-Lee, J.E. Dale, R. Diehl, C. Kobayashi, Galactic 26 Al traces metal loss through hot chimneys. Mon. Not. R. Astron. Soc. 501(1), 210 (2021). https://doi.org/10. 1093/mnras/staa3612 K. Kretschmer, R. Diehl, M. Krause, A. Burkert, K. Fierlinger, O. Gerhard, J. Greiner, W. Wang, Kinematics of massive star ejecta in the Milky Way as traced by 26 Al. Astron. Astrophys. 559, A99 (2013). https://doi.org/10.1051/0004-6361/201322563 M.R. Krumholz, B. Burkhart, J.C. Forbes, R.M. Crocker, A unified model for galactic discs: star formation, turbulence driving, and mass transport. Mon. Not. R. Astron. Soc. 477(2), 2716 (2018). https://doi.org/10.1093/mnras/sty852 W. Kutschera, in European Physical Journal Web of Conferences, vol. 63 (2013), p. 03001. https:// doi.org/10.1051/epjconf/20136303001 K. Langanke, G. Martínez-Pinedo, Nuclear weak-interaction processes in stars. Rev. Modern Phys. 75, 819 (2003). https://doi.org/10.1103/RevModPhys.75.819

3462

R. Diehl

M.D. Leising, G.H. Share, The gamma-ray light curves of SN 1987A. Astrophys. J. 357, 638 (1990). https://doi.org/10.1086/168952 T. Lichtenberg, G.J. Golabek, R. Burn, M. Meyer, Y. Alibert, T. Gerya, C. Mordasini, in AAS/Division for Extreme Solar Systems Abstracts, vol. 51 (2019), p. 311.01 M. Limongi, A. Chieffi, Nucleosynthesis of 60 Fe in massive stars. New Astron. Rev. 50, 474 (2006). https://doi.org/10.1016/j.newar.2006.06.005 M. Limongi, A. Chieffi, Presupernova evolution and explosive nucleosynthesis of rotating massive stars in the metallicity range -3 ≤ [Fe/H] ≤ 0. Astrophys. J. Suppl. Ser. 237(1), 13 (2018). https://doi.org/10.3847/1538-4365/aacb24 R.P. Lin, B.R. Dennis, G.J. Hurford, D.M. Smith, A. Zehnder et al., The Reuven Ramaty HighEnergy Solar Spectroscopic Imager (RHESSI). Sol. Phys. 210, 3 (2002). https://doi.org/10. 1023/A:1022428818870 R.E. Lingenfelter, R. Ramaty, Gamma-ray lines – a new window to the Universe. Phys. Today 31, 40 (1978) G. Magkotsios, F.X. Timmes, M. Wiescher, C.L. Fryer, A. Hungerford et al., in Proceedings of the 10th Symposium on Nuclei in the Cosmos (NIC X), Mackinac Island, 27 July–1 Aug 2008. Available online at http://pos.sissa.it/cgi-bin/reader/conf.cgi?confid=53 (2008) G. Magkotsios, F.X. Timmes, A.L. Hungerford, C.L. Fryer, P.A. Young, M. Wiescher, Trends in 44 Ti and 56 Ni from core-collapse supernovae. Astrophys. J. Suppl. Ser. 191, 66 (2010). https:// doi.org/10.1088/0067-0049/191/1/66 W.A. Mahoney, J.C. Ling, A.S. Jacobson, R.E. Lingenfelter, Diffuse galactic gamma-ray line emission from nucleosynthetic Fe-60, Al-26, and Na-22 – preliminary limits from HEAO 3. Astrophys. J. 262, 742 (1982). https://doi.org/10.1086/160469 P. Martin, J. Vink, S. Jiraskova, P. Jean, R. Diehl, Annihilation emission from young supernova remnants. Astron. Astrophys. 519, A100 (2010). https://doi.org/10.1051/0004-6361/201014171 S.M. Matz, G.H. Share, M.D. Leising, E.L. Chupp, W.T. Vestrand, Gamma-ray line emission from SN1987A. Nature 331, 416 (1988). https://doi.org/10.1038/331416a0 R. McCray, C. Fransson, The remnant of supernova 1987A. Ann. Rev. Astron. Astrophys. 54, 19 (2016). https://doi.org/10.1146/annurev-astro-082615-105405 P.W. Merrill, Spectroscopic observations of stars of class S. Astrophys. J. 116, 21 (1952). https:// doi.org/10.1086/145589 R.A. Mewaldt, N.E. Yanasak, M.E. Wiedenbeck, A.J. Davis, W.R. Binns, E.R. Christian, A.C. Cummings, P.L. Hink, R.A. Leske, S.M. Niebur, E.C. Stone, T.T. Von Rosenvinge, Radioactive clocks and cosmic-ray transport in the galaxy. Space Sci. Rev. 99, 27 (2001) G. Meynet, Observation of the 1.8 MeV emission line from 26Al and the chemical evolution of the galaxy. Astrophys. J. Suppl. Ser. 92, 441 (1994). https://doi.org/10.1086/191992 K. Mori, M.A. Famiano, T. Kajino, T. Suzuki, P.M. Garnavich, G.J. Mathews, R. Diehl, S.C. Leung, K. Nomoto, Nucleosynthesis constraints on the explosion mechanism for type Ia supernovae. Astrophys. J. 863(2), 176 (2018). https://doi.org/10.3847/1538-4357/aad233 S. Nagataki, M.A. Hashimoto, K. Sato, S. Yamada, Y.S. Mochizuki, The high ratio of 44Ti/56Ni in cassiopeia A and the axisymmetric collapse-driven supernova explosion. Astrophys. J. Lett. 492, L45 (1998). https://doi.org/10.1086/311089 B.B. Nath, P. Das, M.S. Oey, Size distribution of superbubbles. Mon. Not. R. Astron. Soc. 493(1), 1034 (2020). https://doi.org/10.1093/mnras/staa336 J.E. Naya, S.D. Barthelmy, L.M. Bartlett, N. Gehrels, M. Leventhal, A. Parsons, B.J. Teegarden, J. Tueller, Detection of high-velocity 26 Al towards the Galactic Centre. Nature 384, 44 (1996). https://doi.org/10.1038/384044a0 C. Patrignani, e. (Particle Data Group), Review of particle physics. Chin. Phys. C 40(100001) (2016) M.M.M. Pleintinger, Star groups and their nucleosynthesis. Ph.D. thesis, Technische Universität München (2020) S. Plüschke, R. Diehl, V. Schönfelder, H. Bloemen, W. Hermsen et al., in Exploring the GammaRay Universe. ESA Special Publication, Noordwijk, vol. 459, ed. by A. Gimenez, V. Reglero, C. Winkler (2001), pp. 55–58

98 Radioactive Decay

3463

N. Prantzos, R. Diehl, Radioactive 26Al in the galaxy: observations versus theory. Phys. Rep. 267, 1 (1996). https://doi.org/10.1016/0370-1573(95)00055-0 N. Prantzos, C. Boehm, A.M. Bykov, R. Diehl, K. Ferrière et al., The 511 keV emission from positron annihilation in the Galaxy. Rev. Mod. Phys. 83, 1001 (2011). https://doi.org/10.1103/ RevModPhys.83.1001 T. Rauscher, A. Heger, R.D. Hoffman, S.E. Woosley, Nucleosynthesis in massive stars with improved nuclear and stellar physics. Astrophys. J. 576, 323 (2002). https://doi.org/10.1086/ 341728 M. Renaud, J. Vink, A. Decourchelle, F. Lebrun, R. Terrier, J. Ballet, An INTEGRAL/IBIS view of young Galactic SNRs through the 44 Ti gamma-ray lines. New Astron. Rev. 50, 540 (2006). https://doi.org/10.1016/j.newar.2006.06.061 S.P. Reynolds, Supernova remnants at high energy. Ann. Rev.Astron. Astrophys. 46, 89 (2008). https://doi.org/10.1146/annurev.astro.46.060407.145237 D. Rodgers-Lee, M.G.H. Krause, J. Dale, R. Diehl, Synthetic 26 Al emission from galactic-scale superbubble simulations. Mon. Not. R. Astron. Soc. 490(2), 1894 (2019). https://doi.org/10. 1093/mnras/stz2708 R.E. Rothschild, R.E. Lingenfelter, P.R. Blanco, D.E. Gruber, W.A. Heindl et al., RXTE observations of Cas A. Nucl. Phys. B Proc. Suppl. 69, 68 (1999). https://doi.org/10.1016/S09205632(98)00186-8 J.M. Ryan, L.L. Chupp, D.J. Forrest, M.L. Cherry, I.U. Gleske et al., in International Cosmic Ray Conference, vol. 5 (1979), p. 135 R. Scalzo, G. Aldering, P. Antilogus, C. Aragon, S. Bailey et al., Nearby Supernova Factory, Type Ia supernova bolometric light curves and ejected mass estimates from the Nearby Supernova Factory. Mon. Not. R. Astron. Soc. 440(2), 1498 (2014). https://doi.org/10.1093/mnras/stu350 E. Schinnerer, A. Hughes, A. Leroy, B. Groves, G.A. Blanc et al., The gas-star formation cycle in nearby star-forming galaxies. I. Assessment of multi-scale variations. Astrophys. J. 887(1), 49 (2019). https://doi.org/10.3847/1538-4357/ab50c2 V. Schönfelder, H. Aarts, K. Bennett, H. de Boer, J. Clear et al., Instrument description and performance of the Imaging Gamma-Ray Telescope COMPTEL aboard the Compton GammaRay Observatory. Astrophys. J. Suppl. Ser. 86, 657 (1993). https://doi.org/10.1086/191794 V. Schönfelder, H. Bloemen, W. Collmar, R. Diehl, W. Hermsen et al., in American Institute of Physics Conference Series, vol. 510, ed. by M.L. McConnell, J.M. Ryan (2000), p. 54. https:// doi.org/10.1063/1.1303173 I.R. Seitenzahl, D.M. Townsley, Nucleosynthesis in Thermonuclear Supernovae (Springer, Berlin/Heidelberg, 2017), p. 1955. https://doi.org/10.1007/978-3-319-21846-5.87 I.R. Seitenzahl, F.X. Timmes, G. Magkotsios, The light curve of SN 1987A revisited: constraining production masses of radioactive nuclides. Astrophys. J. 792(1), 10 (2014). https://doi.org/10. 1088/0004-637X/792/1/10 I.R. Seitenzahl, A. Summa, F. Krauß, S.A. Sim, R. Diehl et al., 5.9-keV Mn K-shell X-ray luminosity from the decay of 55 Fe in Type Ia supernova models. Mon. Not. R. Astron. Soc. 447(2), 1484 (2015). https://doi.org/10.1093/mnras/stu2537 T. Siegert, R. Diehl, in 14th International Symposium on Nuclei in the Cosmos (NIC2016), ed. by S. Kubono, T. Kajino, S. Nishimura, T. Isobe, S. Nagataki, T. Shima, Y. Takeda (2017), p. 020305. https://doi.org/10.7566/JPSCP.14.020305 T. Siegert, R. Diehl, M.G.H. Krause, J. Greiner, Revisiting INTEGRAL/SPI observations of 44 Ti from Cassiopeia A. Astron. Astrophys. 579, A124 (2015). https://doi.org/10.1051/0004-6361/ 201525877 T. Siegert, R. Diehl, G. Khachatryan, M.G.H. Krause, F. Guglielmetti, J. Greiner, A.W. Strong, X. Zhang, Gamma-ray spectroscopy of positron annihilation in the Milky Way. Astron. Astrophys. 586, A84 (2016). https://doi.org/10.1051/0004-6361/201527510 G.M. Simnett, in International Cosmic Ray Conference, vol. 12 (1981), pp. 205–227 P. Slane, J.P. Hughes, R.J. Edgar, P.P. Plucinsky, E. Miyata, H. Tsunemi, B. Aschenbach, RX J0852.0-4622: another nonthermal shell-type supernova remnant (G266.2-1.2). Astrophys. J. 548, 814 (2001). https://doi.org/10.1086/319033

3464

R. Diehl

D.M. Smith, The Reuven Ramaty High Energy Solar Spectroscopic Imager Observation of the 1809 keV Line from Galactic 26 Al. Astrophys. J. Lett. 589, L55 (2003). https://doi.org/10. 1086/375795 S.J. Sturner, J.E. Naya, On the nature of the high-velocity 26 Al near the galactic center. Astrophys. J. 526, 200 (1999). https://doi.org/10.1086/307979 T. Sukhbold, T. Ertl, S.E. Woosley, J.M. Brown, H.T. Janka, Core-collapse supernovae from 9 to 120 solar masses based on neutrino-powered explosions. Astrophys. J. 821, 38 (2016). https:// doi.org/10.3847/0004-637X/821/1/38 A. Summa, A. Ulyanov, M. Kromer, S. Boyer, F.K. Röpke et al., Gamma-ray diagnostics of Type Ia supernovae. Predictions of observables from three-dimensional modeling. Astron. Astrophys. 554, A67 (2013). https://doi.org/10.1051/0004-6361/201220972 L.S. The, A. Burrows, Expectations for the hard X-ray continuum and gamma-ray line fluxes from the type Ia supernova SN 2014J in M82. Astrophys. J. 786, 141 (2014). https://doi.org/10.1088/ 0004-637X/786/2/141 L.S. The, M.D. Leising, J.D. Kurfess, W.N. Johnson, D.H. Hartmann, N. Gehrels, J.E. Grove, W.R. Purcell, CGRO/OSSE observations of the Cassiopeia A SNR. Astron. Astrophys. Suppl. 120, C357+ (1996) L.S. The, D.D. Clayton, R. Diehl, D.H. Hartmann, A.F. Iyudin, M.D. Leising, B.S. Meyer, Y. Motizuki, V. Schönfelder, Are 44 Ti-producing supernovae exceptional? Astron. Astrophys. 450, 1037 (2006). https://doi.org/10.1051/0004-6361:20054626 F.X. Timmes, S.E. Woosley, D.H. Hartmann, R.D. Hoffman, T.A. Weaver, F. Matteucci, 26Al and 60Fe from supernova explosions. Astrophys. J. 449, 204 (1995). https://doi.org/10.1086/176046 F.X. Timmes, S.E. Woosley, D.H. Hartmann, R.D. Hoffman, The production of 44Ti and 60Co in supernovae. Astrophys. J. 464, 332 (1996). https://doi.org/10.1086/177323 S.S. Tsygankov, R.A. Krivonos, A.A. Lutovinov, M.G. Revnivtsev, E.M. Churazov, R.A. Sunyaev, S.A. Grebenev, Galactic survey of 44 Ti sources with the IBIS telescope onboard INTEGRAL. Mon. Not. R. Astron. Soc. 458, 3411 (2016). https://doi.org/10.1093/mnras/stw549 J. Tueller, S. Barthelmy, N. Gehrels, B.J. Teegarden, M. Leventhal, C.J. MacCallum, in Nuclear Spectroscopy of Astrophysical Sources, ed. by N. Gehrels, G.H. Share. American Institute of Physics Conference Series, vol. 170 (1988), pp. 439–443. https://doi.org/10.1063/1.37243 J. Tueller, S. Barthelmy, N. Gehrels, B.J. Teegarden, M. Leventhal, C.J. MacCallum, Observations of gamma-ray line profiles from SN 1987A. Astrophys. J. Lett. 351, L41 (1990). https://doi. org/10.1086/185675 G. Vedrenne, J.P. Roques, V. Schönfelder, P. Mandrou, G.G. Lichti et al., SPI: the spectrometer aboard INTEGRAL. Astron. Astrophys. 411, L63 (2003). https://doi.org/10.1051/0004-6361: 20031482 J. Vink, Supernova remnants: the X-ray perspective. Astron. Astrophys. Rev. 20, 49 (2012). https:// doi.org/10.1007/s00159-011-0049-1 J. Vink, J.S. Kaastra, J.A.M. Bleeker, H. Bloemen, The hard X-ray emission and 44ti emission of Cas A. Adv. Space Res. 25, 689 (2000). https://doi.org/10.1016/S0273-1177(99)00823-6 A. Wallner, J. Feige, N. Kinoshita, M. Paul, L.K. Fifield et al., Recent near-Earth supernovae probed by global deposition of interstellar radioactive 60 Fe. Nature 532, 69 (2016). https://doi. org/10.1038/nature17196 A. Wallner, M.B. Froehlich, M.A.C. Hotchkis, N. Kinoshita, M. Paul et al., 60 Fe and 244 Pu deposited on Earth constrain the r-process yields of recent nearby supernovae. Science 372(6543), 742 (2021). https://doi.org/10.1126/science.aax3972 W. Wang, Study of long-lived radioactive sources in the galaxy with integral/spi. Ph.D thesis, TU Munich, Munich (2007) W. Wang, T. Siegert, Z.G. Dai, R. Diehl, J. Greiner, A. Heger, M. Krause, M. Lang, M.M.M. Pleintinger, X.L. Zhang, Gamma-ray emission of 60 Fe and 26 Al radioactivity in our Galaxy. Astrophys. J. 889(2), 169 (2020). https://doi.org/10.3847/1538-4357/ab6336 C. Weinberger, Supernova diagnostics from gamma-ray lines in the young remnant phase. Ph.D. thesis, TU Munich (2021)

98 Radioactive Decay

3465

C. Weinberger, R. Diehl, M.M.M. Pleintinger, T. Siegert, J. Greiner, 44 Ti ejecta in young supernova remnants. Astron. Astrophys. 638, A83 (2020). https://doi.org/10.1051/0004-6361/202037536 C. Winkler, T.J.L. Courvoisier, G. Di Cocco, N. Gehrels, A. Giménez et al., The INTEGRAL mission. Astron. Astrophys. 411, L1 (2003). https://doi.org/10.1051/0004-6361:20031288 A. Wongwathanarat, H.T. Janka, E. Müller, E. Pllumbi, S. Wanajo, Production and distribution of 44 Ti and 56 Ni in a three-dimensional supernova model resembling cassiopeia A. Astrophys. J. 842(1), 13 (2017). https://doi.org/10.3847/1538-4357/aa72de S.E. Woosley, Neutron-rich nucleosynthesis in carbon deflagration supernovae. Astrophys. J. 476, 801 (1997). https://doi.org/10.1086/303650 S.E. Woosley, A. Heger, Nucleosynthesis and remnants in massive stars of solar metallicity. Phys. Rep. 442, 269 (2007). https://doi.org/10.1016/j.physrep.2007.02.009 S.E. Woosley, R.D. Hoffman, 57Co and 44Ti Production in SN 1987A. Astrophys. J. Lett. 368, L31 (1991). https://doi.org/10.1086/185941 H. Yamaguchi, C. Badenes, R. Petre, T. Nakano, D. Castro et al., Discriminating the progenitor type of supernova remnants with iron K-shell emission. Astrophys. J. Lett. 785(2), L27 (2014). https://doi.org/10.1088/2041-8205/785/2/L27 E. Zinner, Stardust in the laboratory. PASA 25, 7 (2008). https://doi.org/10.1071/AS07039

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Aya Bamba and Brian J. Williams

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evolution of Supernova Remnants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Free Expansion Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Adiabatic Expansion Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Snowplow Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dissipation Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Types of Supernova Remnants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shell-Type SNRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Plerion-Type SNRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mixed-Morphology SNRs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Although only a small fraction of stars end their lives as supernovae, all supernovae leave behind a supernova remnant (SNR), an expanding shock wave that interacts with the surrounding medium, heating the gas and seeding the cosmos with elements forged in the progenitor. In this chapter, we introduce the basic properties of galactic and extragalactic SNRs (section “Introduction”). We summarize how SNRs evolve throughout their life cycles over the course

A. Bamba () The University of Tokyo, Bunkyo-ku, Tokyo, Japan e-mail: [email protected] B. J. Williams X-Ray Astrophysics Laboratory, NASA Goddard Space Flight Center, Greenbelt, MD, USA e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_88

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of ∼106 years (section “Evolution of Supernova Remnants”). We discuss the various morphological types of SNRs and discuss the emission processes at various wavelengths (section “Types of Supernova Remnants”). Keywords

Supernova remnants (SNRs) · Free expansion phase · Adiabatic expansion phase · Shell-type SNR · Plerion-type SNR · Mixed morphology SNR

Introduction Supernova (SN) explosions are among the most energetic events in the universe since the Big Bang, releasing more energy (∼1051 –1053 ergs) than the Sun will release over its entire lifetime. They are the cataclysmic ends of certain types of stars and are responsible for seeding the universe with the material necessary to form other stars, planets, and life itself. We owe our very existence to generations of stars that lived and died billions of years ago, before the formation of our Sun and solar system. The processes of stellar evolution continue to occur today, with typical galaxies like the Milky Way hosting a few supernovae per century, on average. The study of supernovae and the role they play in shaping the evolution of star systems and galaxies is truly an exploration of our own origins. Supernova remnants (SNRs), the expanding clouds of material that remain after the explosion, spread elements over volumes of thousands of cubic light-years and heat the interstellar medium through fast shock waves generated by the ejecta from the star. There are currently ∼300 SNRs cataloged in our Galaxy (Green 2019), although radio surface brightness studies predict that only half of SNRs have been identified (Case and Bhattacharya 1998). Recent X-ray observations with good spatial resolution and large effective area allow us to detect many SNR samples in nearby galaxies as well, such as Magellanic Clouds (Maggi et al. 2016), M31 (Sasaki et al. 2012), and M33 (Garofali et al. 2017).

Evolution of Supernova Remnants The general picture of an SNR is that of a cloud of expanding material ejected from the star, rich in heavy elements like O, Si, and Fe, that drive a shock wave into the interstellar medium (ISM). This shock waves heat the interstellar gas it encounters to millions of degrees, creating a highly ionized plasma. Figure 1 shows Cassiopeia A in X-rays, an example of a young (∼350 yr) SNR in our own Galaxy. Although Cassiopeia A is known to have resulted from a core-collapse (CC) SN (see chapter on “SN”), it is generally difficult to tell the type of SN only by looking at the remnant. SNRs remain visible for thousands, often tens or hundreds of thousands, of years before dissipating their energy into the ISM. The life of an SNR can be thought of as consisting of four phases.

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Fig. 1 Cassiopeia A, a young remnant in our Galaxy, as seen at X-ray energies with Chandra. (Credit: NASA/CXC/SAO)

Free Expansion Phase The ejected gas mainly determines the evolution of SNRs in the initial phase. Since the pressure of surrounding matter is negligible in comparison, the exploded ejecta expands effectively without deceleration. As a result, this phase is called the “free expansion” phase. The characteristic (or typical) speed of the ejecta expansion, vs , is given by vs =



2E , Mej

(1)

where E and Mej are the kinetic energy of the explosion and the ejecta mass, respectively. With fiducial values of Ekin = 1 × 1051 erg and Mej = 1M⊙ , a typical velocity of the ejecta is ∼104 km s−1 . While this velocity for the ejecta is quite high, it is also a bulk velocity with very little randomization in the velocity of the various fluid elements without deceleration (this is the definition of “free expansion”). Thus, there is no heating, and the ejecta temperature is actually quite cold in the beginning, and the remnant is generally faint at all wavelengths. The exception is the radiation from nonthermal synchrotron emission from high-energy electrons accelerated in the shock (see chapter “Acceleration”). Virtually all SNRs emit radio waves, where the emission is entirely nonthermal in origin, resulting from synchrotron radiation from relativistic electrons spiraling around magnetic fields in the shock. Synchrotron emission is characterized by a featureless power-law spectrum, where the radio flux, Sν , is given by Sν ∝ ν −α , where ν is the frequency and α is the spectral index, which depends on the energy distribution of the electron population. For more detail, see chapter “Acceleration”. In Fig. 2, we show an example of a remnant, G1.9+0.3, which is still in the free expansion phase (Reynolds et al. 2008). The acceleration of electrons up to GeV energies is sufficient to produce radio synchrotron emission.

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Fig. 2 Left: SNR G1.9+0.3, the youngest remnant in the Galaxy, seen in radio waves from the VLA in 1985. Right: the remnant, in 2007, seen in X-rays with Chandra. In the 22 years between these images, the remnant expanded substantially, allowing the time since the original supernova explosion (about 140 years) to be estimated. (Credit: X-ray (NASA/CXC/NCSU/S.Reynolds et al.); radio (NSF/NRAO/VLA/Cambridge/D.Green et al.))

A small population of SNRs are apparently able to accelerate electrons to much higher energies (>10 TeV), sufficient to produce synchrotron radiation at X-ray energies (Koyama et al. 1995; Aharonian et al. 2004). G1.9+0.3 also falls into this category, and Fig. 2 also shows an image of the remnant that is essentially entirely from nonthermal synchrotron emission. For more details regarding the particle acceleration mechanisms, see the review by Reynolds (2008).

Adiabatic Expansion Phase At the end of the free expansion phase, the expansion begins to decelerate due to the forward shock sweeping up a non-negligible amount of material in the ISM. An estimate for when this transition occurs can be obtained by calculating the radius, RS0 , at which the swept-up mass equals the ejecta mass: 4 3 π Rs0 ρ0 = Mej , 3   −1/3 Mej 1/3  n0 0 Rs = 5.8 (pc), 10M⊙ 0.5 cm−3

(2) (3)

where ρ0 and n0 are mass and number densities in the cgs unit. Assuming typical values of supernova explosion and ISM, it generally takes a few hundred years for the radius of the SNR to reach Rs0 (though this can vary by orders of magnitude if the SN explodes into particularly low- or high-density regions of the ISM).

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This phase of deceleration of the forward shock wave also leads to the formation of a “reverse shock,” which propagates back into the ejecta towards the center of the SNR. Similarity solutions for the reverse shock are discussed in Hamilton and Sarazin (1984a, b). In this phase, the evolution of the SNR radius as a function of time can be written as R(t) ∝ t m ,

(4)

where m is the expansion parameter defined by Hughes (1999). At the end of the free expansion phase, m ≈ 1, by definition, but during this second phase, m gradually decreases to m = 0.4 (Sedov 1959). When the SNR shock starts decelerating, radiative cooling is still negligible, and the expansion is adiabatic. For the most simple case of a uniform ISM, the evolution can be written as the results of the similarity solution by Sedov (1959) (thus, this phase is often referred to as the “Sedov phase”). Assuming that a large amount of energy is instantaneously released in a small volume, expansion can be characterized by only two parameters, ρ0 (the mass density of the ISM) and Ekin (the kinetic energy of the explosion). We can define a nondimensional parameter ζ as ζ = Rs



Et 2 ρ0

−1/5

,

(5)

where Rs and t represent the radius and age of the SNR. Rs can be written as Rs = ζ0



Et 2 ρ0

1/5

(6)

,

where ζ0 is determined from the energy conservation equation. Using ζ0 = 1.17 for ideal gas (γ = 5/3) (Landau and Lifshitz 1959), Rs , the temperature T , and the shock velocity vs are written as   E51 1/5 2/5 t3 (pc), Rs = 5.0 n0   E51 Ts = 1.5 × 1010 Rs−3 (K) n0 = 1.2 × 108 ×

vs =



E51 n0

(7) (8)

2/5

t3 −6/5 (K),

(9)



1/5

(10)

dRs = 2.1 × 108 × dt

E51 n0

t3 −3/5 (cm s−1 ),

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Fig. 3 SNR DEM L71, located in the LMC. This X-ray image shows a clear separation between the forward shocked material in the ring on the outside and the reverse-shocked material in blue on the inside. (Credit: NASA/CXC/Rutgers/J.Hughes et al.)

where E51 , n0 , and t3 are the explosion energy in the unit of 1051 erg, the number density of the ambient gas in the unit of cm−3 , and the SNR age in the unit of 103 years. During the adiabatic expansion phase, ∼70% of the initial explosion energy is converted into thermal energy of swept-up matter (Chevalier 1974). Remnants in the adiabatic or Sedov expansion phase are typically bright at X-ray wavelengths, owing to both the hot ISM gas shocked by the forward shock and the hot ejecta shocked by the reverse shock. In Fig. 3, we show a canonical example of a remnant in this phase: DEM L71, a remnant in the LMC believed to be a few thousand years post-explosion (Hughes et al. 2002; Rakowski et al. 2003). High-mass stars typically eject mass as stellar winds before their explosions, forming a circumstellar medium (CSM). The winds make a density gradient around the progenitor star, making the deceleration of the shock slower. A modified similarity solution for this case is shown in Truelove and McKee (1999). These models introduced here ignored radiative cooling under the assumption of an ideal gas. In the case that the system is not truly adiabatic, energy is robbed from the shock, and vs becomes smaller. Such a case can be caused by efficient acceleration of cosmic rays at the shock front (Berezhko et al. 2002, for example).

Snowplow Phase When the shock velocity has decelerated to ∼200 km s−1 , the temperature of the gas drops below ∼106 K, and radiative cooling begins to affect the dynamics of the shock evolution. Cooling of the gas is a runaway process, as the more it cools, the more the cooling rate increases. The density of the shock front becomes highest

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Fig. 4 A portion of the Cygnus Loop SNR, seen with HST. Narrowband images of [O III], [S II], and Hα, plus V and I continuum bands combine to make this image. (Credit: NASA/ESA/Hubble Heritage Team)

where the timescale of radiative cooling becomes shortest; as a result, a cool, dense shell is formed just behind the shock front, whereas the inner gas still has high temperature and high pressure due to the low density. It is during this phase that the remnant becomes bright in optical emission from recombining atoms, most notably Hα, [S II], [N II], and [O III]. As an example of a remnant in this phase, we show an HST image of a portion of the Cygnus Loop in Fig. 4. The Cygnus Loop is the remains of a SN believed to be 10,000–20,000 years post-explosion. The cool shell continues the expansion further collecting ISM gas in a manner reminiscent of a snowplow (hence the name “snowplow phase”). At first, the gas expands adiabatically, then pV 5/3 becomes a constant. The shock expands with the time dependency of Rs ∝ t 2/7 . As the temperature cools down further, the pressure can be ignored, and the cool shell expands at a constant radial momentum with a time dependency of roughly Rs ∝ t 1/4 .

Dissipation Phase As the SNR gets even older, the expansion velocity becomes smaller. When the shock slows down to a velocity comparable to the sound velocity, the SNR blends into the interstellar medium. This is called the “dissipation phase” and marks the end of the SNR phase. The lifetime of typical SNRs is ∼106 years, during which time they will expand to radii of dozens to hundreds of parsecs, filling a volume large enough to encompass hundreds to thousands of star systems.

Types of Supernova Remnants Shell-Type SNRs The majority of remnants are classified as “shell-type” SNRs, where the forward shock is delineated by emission at wavelengths across the electromagnetic spectrum.

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The remnants shown in Figs. 1, 2, 3, and 4 are all shell-type SNRs. The physical processes responsible for emitting at various wavelengths differ. In radio regime, emission is dominated by synchrotron emission from energetic electrons (accelerated by the shock wave to GeV energies) spiraling around the turbulent magnetic field at the shock front. Historically, most SNRs have been discovered and categorized based on their radio emission (Green 2019). At infrared wavelengths, young SNRs (those in the free expansion or adiabatic expansion phases) are generally dominated by thermal emission from warm dust grains; see Dwek and Arendt (1992) for a review. Dust grains themselves do not generally feel the passage of the shock wave, but are suddenly immersed in the hot plasma behind the shock, where ion and electron temperatures can be tens of millions of degrees. Grains are collisionally heated by these particles and reach temperatures of 50–200 K. Dust at these temperatures radiates in the mid-IR, with thermal spectra peaking in the 20–100 µm range. Generally speaking, IR emission from young shell-type SNRs only shows up in emission from the shell of the remnant. This emission results from warmed interstellar grains; searches for dust associated with the ejecta in SNRs have turned up very little (Borkowski et al. 2006; Williams et al. 2006). As an example, in Fig. 5, we show the IR emission from DEM L71, the remnant whose X-ray emission is shown in Fig. 3. At optical wavelengths, emission from the shell of a shell-type remnant can be seen in one of two ways. If there is at least partially neutral material present ahead of the shock (often taken as an indication that the object is the remnant of a Type Ia SN; see Williams et al. 2011), then charge exchange can take place in the post-shock environment giving rise to a strong Hα component (Chevalier et al. 1980), as shown in the middle panel of Fig. 5. The temperatures in these remnants are too hot to allow recombination lines in other elements. In older remnants where the temperatures have cooled significantly, recombination lines from various elements begin to dominate (see section “Evolution of Supernova Remnants”).

Fig. 5 Left: the Spitzer 24 µm emission from DEM L71. Middle: the remnant in Hα. Right: the remnant in X-rays. (Figure modified from Figure 1 in Borkowski et al. 2006)

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At X-ray wavelengths, shell-type SNRs may show emission from either or both of the forward-shocked ISM/CSM and the reverse-shocked ejecta, depending on the evolutionary state of the remnant. The physical processes causing the X-ray emission can be either thermal, nonthermal, or both. The thermal emission is generally a combination of both bremsstrahlung continuum produced when hot ions and electrons interact, as well as line emission from highly ionized atoms of various metals, such as O, Fe, Ne, Si, and S. Nonthermal emission in SNRs arises from synchrotron emission identical to that seen in radio waves but from much more energetic (∼10 − 100 TeV) electrons. Because electrons can only be accelerated to energies this high very close to the blast wave, synchrotron emission is most often seen from the outer edges of the shell in shell-type SNRs (Bamba et al. 2003, 2005). Shell-type remnants with sufficient spatial extent can even be identified in gamma-rays. For example, Katagiri et al. (2011) used Fermi observations to show that the Cygnus Loop is spatially resolved into a shell in the 0.5–10 GeV energy range. The various physical processes involved in gamma-ray emission from SNRs is beyond the scope of this chapter; for a thorough review, see Reynolds (2008).

Plerion-Type SNRs Young neutron stars born in core-collapse SNe often form pulsar wind nebulae. Pulsar wind nebulae emit bright nonthermal emission from radio to very high energy gamma-rays, via synchrotron or inverse Compton processes. These are referred to as “plerion-type” or “plerionic” SNRs (Weiler and Panagia 1978). The typical plerion-type is the Crab nebula. It is the remnant of SN 1054 and is now one of the brightest celestial sources at most wavelengths. Figure 6 shows the X-ray image of the Crab nebula taken by Chandra. Jets extend out to the northwest and the southeast from the central source (the pulsar), while two torii are seen emanating outward from the center. The inner radius of the torus is 0.01–0.1 pc, which corresponds to the shock of the relativistic winds from the pulsar terminated Fig. 6 X-ray image of the Crab nebula taken with Chandra. (Credit: NASA/CXC/SAO)

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Fig. 7 X-ray image of the plerion-type SNR, G21.5−0.9 taken with Chandra. (Credit: (Credit: Heather Matheson Samar Safi-Harb (Univ. Manitoba), CXC, NASA))

by ambient material (Rees and Gunn 1974; Kennel and Coroniti 1984; Bamba et al. 2010). For more details, please see the chapter of this work concerning PWNe. Some plerion-type SNRs are surrounded by shells of emission resulting from the forward shock interacting with the surrounding medium. Such remnants are often called “composite type.” One of the typical composite-type SNRs is G21.5– 0.9 (Slane et al. 2000). Figure 7 is the X-ray image of G21.5–0.9. One can see both the central PWN and the outer shell. The Crab nebula is a case of a remnant without its shell; it is still an open issue why there is no detected shell surrounding the Crab nebula. Recent observations by the Hitomi satellite showed that the thermal X-ray emission around the Crab nebula is significantly fainter than other young SNRs (Hitomi Collaboration et al. 2018). The total ejecta mass is estimated to be less than ∼1 M⊙ , implying that the progenitor explosion was relatively low energy. One possibility is that the Crab nebula is a remnant of an electron capture supernova (Miyaji et al. 1980). More detailed observations for the Crab nebula and more samples are needed to understand the origin of plerion-type SNRs.

Mixed-Morphology SNRs Some relatively evolved SNRs show different morphologies in radio and X-ray bands: shell-like structure in radio, whereas the centrally filled in X-rays. They are called “mixed-morphology SNRs” or MM SNRs (Rho and Petre 1998). The X-rays are thermal; thus, it is not due to its central pulsar and/or pulsar wine nebula like plerion cases. The mechanism by which mixed-morphology remnants are formed is still unclear. Several hypotheses have been discussed to explain how a remnant with

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a radio shell can appear centrally filled in X-rays. The first possibility is “fossil emission” of the remnant (Seward 1985); the outer shell cools down due to the expansion and radiative cooling, and as a result, the shock temperature becomes too low to emit thermal X-rays. Synchrotron emission from the accelerated electrons in the shock disappears from the high-energy side due to the synchrotron cooling. Thus, the shells emitting synchrotron disappear within a few thousand years in the X-ray band, whereas they remain for more than ten thousand years in the radio band. Another possibility is due to “evaporated cloud”; the enhanced interior X-ray emission could arise from gas evaporated from clouds (White and Long 1991) in the cases that shocks of SNRs propagate through a cloudy interstellar medium. Dense and small-sized clouds can pass the shock and later evaporate and are heated and, as a result, make thermal X-ray emission inside the shells.

Conclusions Supernova remnants are an incredibly diverse class of objects. From simply a purely morphological standpoint, they are influenced by a number of factors, including mass loss from the progenitor system, the energy and isotropy of the explosion itself, and the structure of the surrounding ISM/CSM. The radiation they emit also varies from source to source: some remnants are bright in radio waves, some in optical, and some in X-rays. In general, the remnant’s state of dynamical evolution (which can be roughly thought of as the product of age and the density being encountered by the forward shock) is the most important factor for determining the spectral energy distribution for a particular SNR. Other chapters within this work will go into more detail on many aspects of SNR study.

References F.A. Aharonian, A.G. Akhperjanian, K.-M. Aye et al., Nature 432, 75 (2004) A. Bamba, R. Yamazaki, M. Ueno et al., ApJ 589, 827 (2003) A. Bamba, R. Yamazaki, T. Yoshida et al., ApJ 621, 793 (2005) A. Bamba, K. Mori, S. Shibata, ApJ 709, 507 (2010) E.G. Berezhko, S.I. Petukhov, S.N. Taneev, Astron. Lett. 28, 632 (2002). https://doi.org/10.1134/ 1.1505508 K. Borkowski et al., ApJ 642, 141 (2006) G.L. Case, D. Bhattacharya, Astrophys. J. 504, 761 (1998). https://doi.org/10.1086/306089 R.A. Chevalier, Astrophys. J. 188, 501 (1974). https://doi.org/10.1086/152740 R.A. Chevalier, R.P. Kirshner, J.C. Raymond, ApJ 235, 186 (1980) E. Dwek, R. Arendt, ARA&A 30, 11 (1992) K. Garofali, B.F. Williams, P.P. Plucinsky et al., MNRAS 472, 308 (2017). https://doi.org/10.1093/ mnras/stx1905 D.A. Green, J. Astrophys. Astron. 40, 36 (2019). https://doi.org/10.1007/s12036-019-9601-6 A.J.S. Hamilton, C.L. Sarazin, Astrophys. J. 287, 282 (1984a). https://doi.org/10.1086/162687 A.J.S. Hamilton, C.L. Sarazin, Astrophys. J. 281, 682 (1984b). https://doi.org/10.1086/162145 Hitomi Collaboration, F. Aharonian, H. Akamatsu et al., PASJ 70, 14 (2018) https://ui.adsabs. harvard.edu/abs/2018PASJ...70...14H/abstract

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J.P. Hughes, Astrophys. J. 527, 298 (1999). https://doi.org/10.1086/308082 J.P. Hughes, P. Ghavamian, C.E. Rakowski, P.O. Slane, ApJ 582, 95 (2002) H. Katagiri et al., ApJ 741, 44 (2011) C.F. Kennel, F.V. Coroniti, ApJ 283, 694 (1984) K. Koyama, R. Petre, E.V. Gotthelf et al., Nature 378, 255 (1995) L.D. Landau, E.M. Lifshitz, Course of Theoretical Physics (Pergamon Press, Oxford, 1959) P. Maggi, F. Haberl, P.J. Kavanagh et al., A&A 585, A162 (2016). https://doi.org/10.1051/00046361/201526932 S. Miyaji, K. Nomoto, K. Yokoi, D. Sugimoto, PASJ 32, 303 (1980) C.E. Rakowski, P. Ghavamian, J.P. Hughes, ApJ 590, 846 (2003) M.J. Rees, J.E. Gunn, MNRAS 167, 1 (1974) S.P. Reynolds, ARAA 46, 89 (2008) S.P. Reynolds et al., ApJ 680, 41 (2008) J. Rho, R. Petre, ApJL 503, L167 (1998). https://doi.org/10.1086/311538 M. Sasaki, W. Pietsch, F. Haberl et al., A&A 544, A144 (2012). https://doi.org/10.1051/00046361/201219025 L.I. Sedov, Similarity and Dimensional Methods in Mechanics (Academic, New York, 1959) F.D. Seward, Comments Astrophys. 11, 15 (1985) P. Slane, Y. Chen, N.S. Schulz et al., ApJL 533, L29 (2000) J.K. Truelove, C.F. McKee, Astrophys. J. Suppl. 120, 299 (1999). https://doi.org/10.1086/313176 K.W. Weiler, N. Panagia, A&A 70, 419 (1978) R.L. White, K.S. Long, ApJ 373, 543 (1991) B.J. Williams et al., ApJ 652, 33 (2006) B.J. Williams et al. ApJ 741, 96 (2011)

Thermal Processes in Supernova Remnants

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Hiroya Yamaguchi and Yuken Ohshiro

Contents Shock Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rankine–Hugoniot Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Collisionless Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Postshock Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Temperature Equilibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cooling and Recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal X-Ray Emission and Spectral Diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Short Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3480 3480 3482 3483 3483 3486 3488 3490 3494 3494

Abstract

This chapter provides a theoretical overview of thermal processes in supernova remnants (SNRs), which can be understood as a series of energy transfers. A part of the kinetic energy associated with expansion of SNRs is converted to the thermal energy of hot plasma via collisionless shock heating that occurs through collective interaction between particles and electromagnetic fields. An important consequence of this process is non-equilibration among the temperatures of different particle species; in the most extreme case, the ratio between the electron and proton temperatures can be as low as their mass ratio at the immediate postshock region. Subsequently, the thermal energy is transferred from the heavier particles (protons and ions) to the lighter ones (electrons) via Coulomb collisions in further downstream regions. Ionization of heavy elements also proceeds through collisions between ions and free electrons. Both processes H. Yamaguchi () · Y. Ohshiro Institute of Space and Astronautical Science/JAXA, Sagamihara, Japan e-mail: [email protected]; [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_89

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take several 10,000 years to achieve equilibrium under the typical density of the interstellar medium (ISM). Therefore, non-equilibrium of both temperatures and ionization are commonly expected for young, X-ray bright SNRs. The plasma properties can be investigated through spectral diagnostics of thermal X-ray emission, which is dominated by atomic emission lines, bremsstrahlung, and radiative recombination continua. Keywords

Supernova remnants · Shock waves · Thermal processes · Radiation mechanisms · X-rays

Shock Heating Rankine–Hugoniot Equations In supernova remnants (SNRs) expanding in the interstellar medium (ISM), the blast wave velocity of 1000 km s−1 is maintained for even thousands of years after the supernova explosion, which is substantially higher than the local sound speed, cs = (γ P /ρ)1/2 = (γ kT /μmp )1/2 (≈ 1 − 10 km s−1 for typical ISM), where γ , P , ρ, T , and μ are the specific heat ratio (γ = CP /CV ), pressure, mass density, temperature, and mean molecular weight of the local gas, respectively. Such supersonic flow colliding with another medium causes the formation of shock waves, where the thermodynamic properties (e.g., P , ρ, T , bulk velocity v) of the gas change abruptly. The relationships between the properties of the upstream and downstream fluids are expressed by the so-called Rankine–Hugoniot equations, which can be derived by considering the conservations of some fluid quantities across the shock. In high Mach number shocks, such as those found in young SNRs (M ≫ 10), the effect of magnetic fields is virtually negligible. Since the shock transition occurs in a sufficiently small length (which is however not infinitely small, as discussed later), the shock structure can be approximated as a plane parallel one that is steady in the shock rest frame (i.e., the coordinate comoving with the shock front). Therefore, the conservations of the mass, momentum, and energy (per unit mass) across the shock are, respectively, given as ρ1 v1 = ρ2 v2

(1)

ρ1 v12 + P1 = ρ2 v22 + P2

(2)

1 2 1 γ P1 γ P2 v + = v22 + , 2 1 γ − 1 ρ1 2 γ − 1 ρ2

(3)

where the subscripts 1 and 2 refer to the upstream and downstream, respectively. Note that |v1 | is equivalent to the shock velocity measured in the observer frame (Fig. 1).

100 Thermal Processes in Supernova Remnants

Observer frame Upstream (Unshocked)

Downstream (Shocked)

Vshock = |v1|

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Shock rest frame Upstream (Unshocked)

Downstream (Shocked)

v1

v2

Fig. 1 Schematic view of the shock front in the observer frame (left) and shock rest frame (right)

Then, the Rankine–Hugoniot equations are obtained as P2 (γ + 1)ρ2 − (γ − 1)ρ1 = P1 (γ + 1)ρ1 − (γ − 1)ρ2 χ≡

ρ2 v1 (γ − 1)P1 + (γ + 1)P2 = = . ρ1 v2 (γ + 1)P1 + (γ − 1)P2

(4) (5)

Here, χ is the compression ratio. These equations can also be expressed introducing the Mach number of the upstream fluid (M1 = v1 /cs1 ) as 2γ M12 − γ + 1 P2 = P1 γ +1 χ=

(γ + 1)M12 ρ2 v1 . = = ρ1 v2 (γ − 1)M12 + 2

(6) (7)

Equation 6 indicates that if the upstream Mach number is high enough (i.e., “strong shock”), the relation P2 ≫ P1 is expected. In this case, the compression ratio of χ = 4 is obtained from Equation 7 for a monoatomic ideal gas with γ = 5/3. These equations also predict M2 < 1 when M1 > 1, indicating that the fluid becomes subsonic when it flows across the shock front. Despite this drastic Mach number drop, the velocity changes only by a factor 4 during this transition. This is because the fluid becomes much hotter in the downstream than in the upstream due to the shock heating, and the Mach number is proportional to T −1/2. In fact, combining Equations 4 and 5 with the ideal gas law, we obtain the downstream temperature to be kT2 =

2(γ − 1) 3 μmp v12 , μmp v12 = 16 (γ + 1)2

(8)

which corresponds to ∼1.2 keV or ∼1.4×107 K for a shock velocity of 1000 km s−1 and the solar composition ISM (μ ≈ 0.6). It is worth noting that the right-hand side of Equation 8 is proportional to the bulk kinetic energy of the upstream fluid.

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Therefore, the strong shock heating can be interpreted as a process that converts a certain fraction of the kinetic energy to the internal (thermal) energy. It is observationally well known that cosmic-ray acceleration takes place at the fast shocks of young SNRs (next chapter), implying that a part of the kinetic energy is transferred to the nonthermal component as well. When the acceleration is efficient enough, the accelerated particles contribute to the downstream pressure significantly. Moreover, the highest energy particles may escape upstream, and thus the energy conservation given in Equation 3 becomes invalid. Consequently, the downstream temperature becomes lower than that predicted by Equation 8, and the compression ratio is modified as well. Such effect is observed in the fast shock in the northeast rim of the SNR RCW 86, where the postshock proton temperature (constrained using the Hα spectrum) is significantly lower than that inferred from its shock velocity (Helder et al. 2009) (but see also Yamaguchi et al. (2016) for the refined shock velocity measurement).

Collisionless Processes Although shock waves are observed both on Earth and in space, their microscopic characteristics are largely different from each other. In the terrestrial shocks that are formed in high-density environment, the shock heating and compression are achieved via direct interaction between particles. On the other hand, since the celestial shocks propagate in the low-density medium, where collisions between particles rarely happen, the shock transition takes place in a collisionless manner. The cross section for Coulomb collisions between two protons is approximated as σ ≈ π b2 =

4π e4 , m2p v 4

(9)

where b is an impact parameter that satisfies mp v 2 /2 = e2 /b (i.e., the kinetic energy at the infinity equals the Coulomb potential when the relative velocity between the particles is zero). Therefore, the mean free path for proton–proton interaction is obtained to be 4 −1   n v 1 p 20 cm. λ= ∼ 4 × 10 np σ 1 cm−3 1000 km s−1

(10)

This is substantially longer than the typical length of shock transition regions and even larger than the typical radius of SNRs (∼1019 cm). On the other hand, a gyro radius of a proton in the interstellar magnetic field is rg =

mp cv ∼ 1 × 1010 eB



v 1000 km s−1



B 1 µG

−1

cm,

(11)

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comparable to the thickness of the shock transition regions. This is why the shock transition in SNRs is thought to occur through collective interactions between particles and electromagnetic fields. In such “collisionless shocks,” it is not necessary that the temperature equilibration among different species is achieved immediately, and thus Equation 8 needs to be modified. This is because the preshock kinetic energy of each particle is proportional to its mass and the timescale for collisional equilibration between the different species is much longer than the time a particle spends in the shock transition zone. Therefore, in the most extreme case, the downstream temperature is expected to be independent among different species i as

kTi =

3 mi Vsh2 , 16

(12)

where Ti , mi , and Vsh are the temperature and mass of the species i and the shock velocity. This means that the ratio between electron and proton temperatures can be as low as β ≡ Te /Tp = me /mp ≈ 1/1836 at the immediate postshock region. However, a number of theoretical investigations have suggested that instantaneous energy transfer from protons (ions) to electrons can occur at shock fronts, resulting in a β value higher than their mass ratio (e.g., McKee 1974). This process is called “collisionless electron heating,” probably related to the formation of the collisionless shock itself. Detailed mechanism of this heating process is still poorly understood, although several scenarios have been proposed, such as lower hybrid wave heating in a cosmic-ray precursor (e.g., Rakowski et al. 2008), plasma wave heating due to Buneman instabilities (e.g., Cargill and Papadopoulos 1988), and cross-shock potential due to charge separation generated at the shock front (e.g., Balikhin et al. 1993). Observationally, collisionless electron heating is often confirmed in Balmer-dominated shocks in SNRs. It is suggested that the postshock temperature ratio is inversely correlated with the shock velocity, with me /mp  β  0.1 for fast shocks (Vsh  2000 km s−1 ) such as those observed in Tycho and SN 1006 and β ∼ 1 for slow shocks (Vsh  500 km s−1 ) such as those in Cygnus Loop (e.g., Rakowski 2005; Ghavamian et al. 2007). A more detailed review about the collisionless processes is found in, e.g., Rakowski (2005), Heng (2010), and Ghavamian et al. (2013).

Postshock Processes Temperature Equilibration We have seen in the previous section that the electron and proton temperatures are not necessarily equilibrated with each other at the collisionless shocks. If non-equilibrium plasma is formed, the electrons and protons slowly equilibrate to a common temperature via Coulomb collisions further downstream. With an

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assumption that a Maxwellian velocity distribution is achieved in each group of particle species, the energy equilibration rate can be described as kTp − kTe d(kTe ) = , dt teq

(13)

where teq is the equilibration timescale given by teq =

3me mp 8(2π )1/2 np e4 ln



kTp kTe + me mp

3/2

(14)

(Spitzer 1962). The term “ln ” is the Coulomb logarithm, where is given by 3

= 3 2e



k3T 3 π ne

1/2

(15)

,

obtaining ln ≈ 33.6 for Te ∼ 107 K and ne ∼ 1 cm−3 and similar values (difference less than 10%) for the plasma conditions of typical SNRs. From Equation 14, we obtain teq = 3.0 × 1011 α



np −1 1 cm−3



kT 1 keV

3/2 

ln

33.6

−1

s,

(16)

√ where α ≈ 1 for the case kTe ∼ kTp (i.e., near equipartition) and α = 2 2 for the case kTe /me = kTp /mp (i.e., both species have the same mean velocity, expected at the immediate postshock region). The dependence on the proton density and temperature given in Equation 16 can be explained as follows: The collision rate is given as np vσ and is anti-proportional to the equilibration timescale teq . Since 3/2 is obtained. σ ∝ v −4 (Equation 9) and v ∝ T 1/2 , the dependence teq ∝ n−1 p T It is indicated by Equations 13 and 16 that, although the electron temperature increases quickly when kTe ≪ kTp , it eventually takes long time for full equilibration. This timescale for the typical ISM density (np ∼ 1 cm−3 ) is about 10 kyr, longer than the age of young, X-ray bright SNRs, such as Cas A, Tycho, SN 1006, and W49B. In fact, the electron temperature observed in these SNRs is generally lower than the mean plasma temperature expected from their shock velocity (i.e., Equation 8), implying that the thermal equilibration has not been achieved in these objects. Figure 2 shows numerical calculations of the equilibration processes for different shock velocities and efficiency of the collisionless electron heating, confirming that the product of the proton density and elapsed time after the shock heating needs to be np t  1012 cm−3 s for full equilibration.

100 Thermal Processes in Supernova Remnants

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kTp

Temperature (keV)

1 kTe

0.1

(a) β = βmin 0.01 10

kTp

1 kTe

0.1 (b) β = 0.03 0.01 106

107

108

109 1010 npt (cm-3 s)

1011

1012

1013

Fig. 2 Equilibration between the proton temperature (solid lines) and electron temperature (dashed lines) via Coulomb collisions in postshock plasma. The shock velocities of 3000 km s−1 and 1000 km s−1 are assumed in the thick and thin lines, respectively. In panel (a), no collisionless electron heating is assumed, so the immediate postshock temperatures of protons and electrons are proportional to their mass. In panel (b), on the other hand, β = kTe /kTp = 0.03 is assumed at the immediate postshock region

In addition to the non-equilibration between electrons and protons, ion–proton non-equilibration is also expected in young SNRs. Equations 13 and 14 can be generalized into the equilibration timescale for arbitrary particle species i and j as d(kTi )  kTj − kTi = dt teq, ij

(17)

j

teq, ij =

3mi mj 8(2π )1/2 nj Zi2 Zj2 e4 ln



kTj kTi + mi mj

3/2

,

(18)

where Zi is the charge of the species i. This timescale is generally shorter for the ion–proton equilibration than for the electron–proton one, because of the smaller mass ratio in the former. Among heavy elements, on the other hand, heavier species may have a shorter timescale for the equilibration with protons despite the larger 2 . It should be noted, however, mass ratio, due to the dependence teq ∝ mion /Zion that the heavy elements are not always fully ionized, and their charge (Zi ) evolves

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with time in typical SNR plasma (see below). Therefore, to calculate the accurate temperature equilibration between heavy elements and protons (or electrons), timedependent ionization should be taken into account. More detailed calculations incorporating this effect are presented in Vink (2020).

Ionization In general, heavy elements in the immediate postshock plasma are at low charge state, because the electron temperature of preshock matters (both ISM and ejecta) is too low to produce highly charged ions, and ionization does not quickly proceed in collisionless plasma. Once free electrons in the shocked gas become energetic through the collisionless and/or Coulomb processes, heavy elements gradually get ionized by collisions with the hot electrons. Similar to the Coulomb collisions between free electrons and protons, the rate of the collisional ionization is extremely low in the rarefied environment. Figure 3 shows the ionization rate coefficients of representative Fe ions as a function of the electron temperature kTe , calculated using AtomDB (http://www.atomdb.org). Lower coefficient values are generally expected for more highly charged ions, because of their larger electron binding energy. In particular, there is a huge difference in the coefficients between Fe23+ and Fe24+ especially in the low-kTe regime. This is because K-shell electrons (both Fe23+ and Fe24+ ions hold) are much more strongly bound by the nuclei than L-shell ones (only Fe23+ ions hold) are. To calculate time-dependent ion population, both ionization and recombination should be considered. The rate equation for the atomic number Z element is given as 10−9 z = 12

Sz (Te) (cm3 s-1)

10−10

z = 16 z = 20

10−11

z = 23 −12

10

z = 24

−13

10

z = 25

10−14 10−15 0.2

0.5

1 2 kTe (keV)

5

Fig. 3 Ionization rate coefficients for selected Fe ions calculated using AtomDB

10

100 Thermal Processes in Supernova Remnants

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dfz = ne [Sz−1 (Te ) fz−1 − {Sz (Te ) + αz−1 (Te )} fz + αz (Te ) fz+1 ] , dt

(19)

1

 where fz is the fraction of the z-th ionized atom (thus Z z=0 fz = 1 is required), Sz (Te ) is the coefficient for the ionization from state z to state z + 1 and αz (Te ) is the coefficient for the recombination from state z + 1 to state z. In collisional ionization equilibrium (CIE) conditions, fractions of all the ions remain constant (i.e., dfz /dt = 0). Therefore, the ionization balance of CIE plasma depends solely on the electron temperature. In non-equilibrium ionization (NEI) plasma, on the other hand, dfz /dt = 0 is expected, and thus the ion population depends not only on the electron temperature but also on the ionization timescale ne t, where t is the time after the event that disturbs an equilibrium, such as shock heating. Figure 4 shows the ion fractions of (a) Fe for kTe = 5 keV and (b) Si for kTe = 2 keV as a function of ne t, indicating that ne t ≈ 1012 cm−3 s is required to reach CIE, comparable to the timescale for the temperature equilibration between different species (Fig. 2). Note, however, that the characteristic timescales for the CIE do depend on both atomic number and electron temperature, and an equilibrium could be achieved much earlier in some conditions (Smith and Hughes 2010). It is worth noting that the effect of innershell processes is not taken into account in Equation 19, despite its importance in high-kTe ionizing plasmas. If the innershell ionization or excitation takes place, either fluorescence or Auger process follows.

24+

16+

8+

Ion fraction 0.1

(a)

25+

0.01

26+

10 9

1010

1011

1012

1013

1

10 8

14+

4+

13+

12+

0.01

Ion fraction 0.1

(b)

10 8

10 9

1010 1011 net (cm-3 s)

1012

1013

Fig. 4 Ion populations expected for ionizing plasma: (a) Fe for kTe = 5 keV, (b) Si for kTe = 2 keV. Green, blue, red, magenta, and orange correspond to the bare, H-like, He-like, Ne-like, and Ar-like ions, respectively

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The former contributes to the photon emission via radiative deexcitation to the ground state, whereas the latter releases a few electrons at once (instead of a single photon) to deexcite. This means that the Auger process, triggered by the innershell ionization or excitation, leads to multiple ionization directly from state z to state z + i (i > 1), slightly modifying the ionization balance from the prediction of Equation 19.

Cooling and Recombination As SNRs evolve, thermal energy of the hot plasma is gradually lost via cooling processes such as radiation, thermal conduction, and adiabatic expansion. The radiative cooling is efficient in high-density, low-temperature (kTe < 0.1 keV) plasma, because free electrons recombine with heavy elements (e.g., C, O) efficiently at these temperatures. This effect is, therefore, essential in decelerated shocks, where the downstream temperature is relatively low from the beginning. Since the shocked plasma immediately loses its thermal energy in this case, the Rankine–Hugoniot relations (Equations 4, 5, 6, 7, and 8) may not be valid across such low-velocity, radiative shocks. The thermal conduction plays an important role when the hot plasma physically contacts with dense, cool materials such as neutral or molecular clouds (e.g., Slavin et al. 2017). In some SNRs evolving in dense environment, a negative correlation between the electron temperature and ambient cloud density is observed (e.g., Okon et al. 2020; Sano et al. 2021), implying that the thermal conduction indeed works in these objects. The adiabatic expansion is usually important in the late phase of SNR evolution but is also efficient in the early evolutionary phase if a progenitor explodes in dense circumstellar matter (CSM). In this case, rapid adiabatic expansion occurs after the breakout of the blast wave from the dense CSM to the low-density ISM, causing the drastic cooling of the shocked plasma (e.g., Itoh and Masai 1989). Once the plasma temperature decreases due to any of the cooling processes, recombination between free electrons and ions proceeds accordingly. Figure 5a shows the temperature-dependent recombination rate coefficients of some Fe ions, where the contributions of radiative recombination and dielectronic recombination are separately shown for z = 23 (i.e., recombination from Fe24+ to Fe23+ ). The difference in the rate coefficients among the charge states is relatively small, because, unlike the collisional ionization, the radiative recombination does not care about the ionization potential of target ions. The rate of the dielectronic recombination peaks at kTe ∼ 4 keV, since there are several resonant transitions with a free electron with the kinetic energy of ∼4.6 keV (KLL) and ∼5.7 keV (KLM). It is suggested by Fig. 5a that the typical recombination timescale ne t is of the order of 1011 –1012 cm−3 s, comparable to the ionization timescale. Therefore, if a plasma cools more rapidly than this timescale, an overionized state is realized. This is another type of NEI, where the recombination is dominant over the ionization

100 Thermal Processes in Supernova Remnants

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10−10

αz (Te) (cm3 s-1)

(a)

z = 16

10−11

z = 25 z = 23

(RR)

10−12

(DR)

10−13 0.2

0.5

5

10

1

(b)

1 2 kTe (keV)

Ion fraction 0.1

24+

16+

25+

0.01

26+

10 8

10 9

1010 1011 net (cm-3 s)

1012

1013

Fig. 5 (a) Recombination rate coefficients for selected Fe ions. The contributions of radiative recombination (RR) and dielectronic recombination (DR) are separately shown for z = 23 (i.e., recombination from He-like ions to Li-like ions). (b) Ion population of Fe expected for recombining plasma with kTinit = 5 keV and kTe = 0.5 keV. Green, blue, red, and magenta correspond to the bare, H-like, He-like, and Ne-like ions, respectively

in terms of reaction rates. Because of this, such NEI plasma is called “recombining plasma,” to be distinguished from ionizing plasma. Figure 5b shows the evolution of Fe ion fractions in a recombining plasma, expected after a sudden temperature drop from 5 to 0.5 keV (hereafter represented as kTinit and kTe , respectively). Its behavior is largely different from the case of ionizing plasma (Fig. 4); owing to the small charge dependence of the recombination rate, substantially wider ion population than in the ionizing plasma is expected. The recombining plasma generally exhibits spectral features characterized by enhanced continuum emission due to the radiative recombination (see next section). To date, presence of recombining plasma has been confirmed in more than a dozen SNRs that are categorized into the so-called mixedmorphology class (e.g., Yamaguchi 2020), implying that the rapid cooling is not unusual in the evolutionary channel of this class.

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Thermal X-Ray Emission and Spectral Diagnostics Since thermal plasmas in SNRs are optically thin, their spectrum is dominated by atomic lines and thermal continuum emission consisting mainly of bremsstrahlung and radiative recombination. Readers are referred to the literature on radiative processes for more details about the related physics (e.g., Rybicki and Lightman 1979). Analysis of such spectra determines the plasma properties (e.g., temperature, density, ionization state) and elemental abundances, which in turn constrain the physics of shock heating, supernova progenitors, and many more. As discussed in the previous sections, non-equilibration of both internal energies (i.e., temperatures) and ionization are commonly expected in SNRs. Therefore, unlike fully equilibrated plasmas (e.g., galaxy clusters), temperature of each species and ion populations are not tied with one another and thus must be measured nearly independently. Figure 6 shows a typical flow of spectral diagnostics (that can, in reality, be automatically performed by publicly available spectral analysis softwares, like Xspec and SPEX) and interpretation for SNR observations. Electron Temperature Firstly, electron temperature can be measured by either the continuum shape or flux ratios between certain emission lines. Coulomb interactions between free electrons and protons (or ions) produce a bremsstrahlung continuum, whose spectrum has an exponential cutoff that goes as exp[−hν/kTe ]. Therefore, the continuum slope at hν  kTe is particularly sensitive to the electron temperature.

Continuum Flux (brems)

Flux (RRC)

kTion

Line emission Width Heβ/Heα Lyα/Heα

Shape

kTe

Fe centroid

Absolute flux

Ion population net, kTinit

np, ne n ion

Thermal energy Shock velocity Nonthermal energy

Shock physics

Elemental abundance Reference abundance (ISM, SN yields)

Progenitor science ISM chemical composition

Fig. 6 Flowchart illustrating how the observables are converted to the physical quantities with spectral analysis of SNRs. Note that “Heα” and “Heβ,” indicating, respectively, the transitions from the n = 2 and n = 3 shells to the n = 1 shell, are not commonly used terms but valid only in this chapter

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In low-kTe and/or recombining plasma, radiative recombination of heavy elements may significantly contribute to the thermal continuum. Since its spectrum is also proportional to exp[−hν/kTe ] at hν ≥ I (where I is the ionization potential of the recombining ion), the electron temperature can be measured in a similar manner. However, if the continuum spectrum is dominated by a nonthermal component (e.g., synchrotron radiation from high-energy electrons), which is often the case in young SNRs, only emission lines are available for the electron temperature measurement. Usually, line intensity ratios between atomic transitions involving different quantum levels of identical ions provide useful diagnostics of electron temperature. This is because collisional excitation to higher quantum levels requires a larger kinetic energy (i.e., higher temperature) of free electrons. Figure 7a and b shows [n = 3 → 1]/[n = 2 → 1] flux ratios of He-like Fe and Si (hereafter “Heβ/Heα ratios”) as a function of kTe , where predictions for both CIE and NEI plasmas are presented. As expected, higher ratios are expected when the electron temperature is higher and difference between the CIE and NEI is relatively small. Although the “G-ratio,” defined as (f +i)/r (where f , i, and r denote forbidden, intercombination, and resonance transitions from n = 2 levels to n = 1 of He-like ions, respectively), is also sensitive to the electron temperature, this diagnostic is 0.2

0.2

Heβ/Heα ratio

(a) Fe

(b) Si 0.1

0.1 0.05

CIE NEI (2e+11) NEI (5e+11)

CIE NEI (2e+11) NEI (5e+11)

0.05 2

5 kTe (keV)

10

20

0.02

0.5

1 kTe (keV)

2

10

Lyα/Heα ratio

(c) Fe

10

(d) Si

1 1 0.1

0.1

5 keV 10 keV 20 keV

0.01

1011

1012 net (cm-3 s)

1 keV 2 keV 5 keV

0.01

1013

10−3 1010

1011

1012

1013

net (cm-3 s)

Fig. 7 Line intensity ratios expected for CIE or NEI (ionizing) plasma. (a) Fe Heβ/Heα ratios as a function of kTe . (b) Same as panel (a), but for Si. (c) Fe Lyα/Heα ratios as a function of ne t. (d) Same as panel (c), but for Si

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H. Yamaguchi and Y. Ohshiro

more often used to probe for other effects, such as charge exchange and resonance scattering (e.g., Katsuda et al. 2012; Amano et al. 2020). It should also be noted that these transitions can be resolved only by high-resolution spectrometers, such as the Reflective Grating Spectrometer on board XMM–Newton and the X-ray microcalorimeter Resolve on board XRISM. Ion Population (Ionization Timescale) Once the electron temperature is constrained, we can determine whether the plasma has reached ionization equilibrium by investigating the ionization population. If emission from both He-like and Hlike ions is present, Lyα-to-Heα flux ratios can be used to constrain the ionization timescale ne t (and kTinit for a recombining plasma). Figure 7c and d presents examples for the ionizing plasma case. In typical SNRs, the heavy elements lighter than Ca (Z  20) are dominated by the He-like and H-like ions, and thus this diagnostic can be applied. On the other hand, the Fe-group elements, such as Cr, Mn, Fe, and Ni, are often less ionized than the He-like state (e.g., Yamaguchi et al. 2014a). Therefore, collisional interactions between high-energy free electrons and low-ionized ions produce inner K-shell ionization, followed by fluorescence transitions (or Auger processes). The centroid energy of the Kα or Kβ fluorescence and their flux ratio offer excellent diagnostics of the ionization timescale as well as the electron temperature, as illustrated in Fig. 8. Notably, the Kβ/Kα ratio decreases as ionization proceeds until ne t ∼ 1010 cm−3 s. This is because Fe8+ and Fe16+ are the dominant charge states at ne t ∼ 109 cm−3 s and ne t ∼ 1010 cm−3 s, respectively (see Fig. 4), and thus the ions lose M-shell electrons (which are responsible for the Kβ fluorescence) in this regime (e.g., Yamaguchi et al. 2014b). If plasma is substantially overionized, prominent spectral features of radiative recombination continua (RRC) may be detected. The flux of the RRC offers

0.028

0.056

0.084

0.140

0.112

8.0

0.12 0.09

7.5

log (Te [K])

8.5

0.0

0.06 7.0

0.03 9.0

9.5

10.0

10.5

11.0

11.5

12.0

12.5

log (net [cm-3 s]) Fig. 8 Fe Kβ/Kα ratio as a function of the ionization timescale and electron temperature

13.0

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independent measures of the ion population. In particular, the radiative recombination into H-like ions provides unique information about the amount of bared ions. Ion Temperature When shock-heated ions have high temperature, a velocity dispersion due to their thermal motion becomes large. Therefore, emission lines originating from these ions are broadened due to the superposition of the Doppler shifts. The relationship between the full width at half maximum (FWHM) of the broadened line Δ(hν) and ion temperature kTi is given by   √ 2kTi 1/2 Δ(hν) , = 2 ln 2 hν0 mi c 2

(20)

where hν0 is the rest frame photon energy and mi is the ion mass. For instance, a broadening of only Δ(hν) ≈ 23 eV at hν0 = 7 keV (corresponding to the Lyα emission of Fe25+ ) is expected for kTFe = 100 keV and even narrower for lighter elements and/or lower temperature. Therefore, ion temperature measurement generally requires high spectral resolution, i.e., grating spectrometers or microcalorimeters. Note that, theoretically, heavy elements can have much higher temperature than protons and electrons if the collisionless shock heating follows Equation 12. In fact, the ion temperatures of SN 1987A are found to be proportional to the ion mass by detection of significant Doppler broadening of emission lines (Miceli et al. 2019). Elemental Abundances Since line emission is a consequence of collisional interaction between free electrons and ions, its intensity is proportional to ne nZ,z V , where nZ,z is the number density of the ion with the atomic number Z and charge number z and V is the plasma volume.  On the other hand, the intensity of thermal bremsstrahlung is proportional to Z z (z2 ne nZ,z V ). If the plasma has a typical ISM abundance, the bremsstrahlung is dominated by the interaction between protons and electrons, and its intensity is simply proportional to ∼ ne np V . Therefore, the line-to-continuum flux ratio, or the line equivalent width, gives a number ratio between the ion and proton, i.e., ne nZ,z V /(ne np V ) = nZ,z /np . Since the ion fraction nZ,z /nZ is uniquely determined by the combination of kTe , kTinit , and ne t, the elemental abundance nZ /np can also be determined if the plasma properties are well constrained. In the case of metal-rich plasma, on the other hand, contributions of the heavy elements to the bremsstrahlung become non-negligible because of the z2 dependence of the bremsstrahlung intensity. Therefore, the relationship between the line equivalent width and abundance departs from a linear correlation, so it is hard to constrain the absolute elemental abundance nZ /np . However, relative abundances among heavy elements (e.g., nFe /nSi ) can still be accurately constrained using the intensity ratios of the lines from different elements.

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H. Yamaguchi and Y. Ohshiro

Short Summary Thermal X-ray emission from SNRs is largely diverse among objects: e.g., low or high temperature, NEI or CIE, ionizing or recombining, and proton-rich (ISM) or metal-rich (ejecta). This diversity makes spectral analysis relatively complicated but also provides us plenty of information about the physics behind the origin and evolution of SNRs. High sensitivity and spectral resolution of X-ray observatories are essential to make the most of this advantage.

References Y. Amano, H. Uchida, T. Tanaka, L. Gu, T.G. Tsuru, Evidence for resonance scattering in the x-ray grating spectrum of the supernova remnant N49. Astrophys. J. 897, 12 (2020). https://doi.org/ 10.3847/1538-4357/ab90fc M. Balikhin, M. Gedalin, A. Petrukovich, New mechanism for electron heating in shocks. Phys. Rev. Lett. 70, 1259 (1993). https://doi.org/10.1103/PhysRevLett.70.1259 P.J. Cargill, K. Papadopoulos, A mechanism for strong shock electron heating in supernova remnants. Astrophys. J. 329, L29 (1988). https://doi.org/10.1086/185170 P. Ghavamian, J.M. Laming, C.E. Rakowski, A physical relationship between electron-proton temperature equilibration and mach number in fast collisionless shocks. Astrophys. J. 654, L69 (2007). https://doi.org/10.1086/510740 P. Ghavamian, S.J. Schwartz, J. Mitchell, A. Masters, J.M. Laming, Electron-Ion Temperature Equilibration in Collisionless Shocks: The Supernova Remnant-Solar Wind Connection Space Science Reviews 178, 633 (2013). https://doi.org/10.1007/s11214-013-9999-0 E.A. Helder, J. Vink, C.G. Bassa et al., Measuring the cosmic-ray acceleration efficiency of a supernova remnant. Science 325, 719 (2009). https://doi.org/10.1126/science.1173383 K. Heng, Balmer-dominated shocks: a concise review. Publ. Astron. Soc. Aust. 27, 23 (2010). https://doi.org/10.1071/AS09057 H. Itoh, K. Masai, The effect of a circumstellar medium on the X-ray emission of young remnants of Type II supernovae. Mon. Not. R. Astron. Soc. 236, 885 (1989). https://doi.org/10.1093/ mnras/236.4.885 S. Katsuda, H. Tsunemi, K. Mori et al., High-resolution x-ray spectroscopy of the galactic supernova remnant puppis A with XMM-Newton/RGS. Astrophys. J. 756, 49 (2012). https:// doi.org/10.1088/0004-637X/756/1/49 C.F. McKee, X-ray emission from an inward-propagating shock in young supernova remnants. Astrophys. J. 188, 335 (1974). https://doi.org/10.1086/152721 M. Miceli, S. Orlando, D.N. Burrows et al., Collisionless shock heating of heavy ions in SN 1987A. Nat. Astron. 3, 236 (2019). https://doi.org/10.1038/s41550-018-0677-8 H. Okon, T. Tanaka, H. Uchida et al., Deep XMM-newton observations reveal the origin of recombining plasma in the supernova remnant W44. Astrophys. J. 890, 62 (2020). https://doi. org/10.3847/1538-4357/ab6987 C.E. Rakowski, Electron ion temperature equilibration at collisionless shocks in supernova remnants. Adv. Space Res. 35, 1017 (2005). https://doi.org/10.1016/j.asr.2005.03.131 C.E. Rakowski, J.M. Laming, P. Ghavamian, The heating of thermal electrons in fast collisionless shocks: the integral role of cosmic rays, Astrophys. J. 684, 348 (2008). https://doi.org/10.1086/ 590245 G.B. Rybicki, A.P. Lightman, Radiative Processes in Astrophysics (Wiley-VCH, 1979)

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J.D. Slavin, R.K. Smith, A. Foster et al., Numerical simulations of supernova remnant evolution in a cloudy interstellar medium. Astrophys. J. 846, 77 (2017). https://doi.org/10.3847/1538-4357/ aa8552 H. Sano, H. Suzuki, K.K. Nobukawa et al., Discovery of a wind-blown bubble associated with the supernova remnant G346.6-0.2: a hint for the origin of recombining plasma. Astrophys. J. 923, 15 (2021). https://doi.org/10.3847/1538-4357/ac1c02 R.K. Smith, J.P. Hughes, Ionization equilibrium timescales in collisional plasmas. Astrophys. J. 718, 583 (2010). https://doi.org/10.1088/0004-637X/718/1/583 L. Spitzer, Physics of Fully Ionized Gases (Mineola, N.Y. USA, Dover Publications, 1962) ISBN: 0-486-44982-3 J. Vink, Physics and Evolution of Supernova Remnants (Gewerbestrasse, Cham, Switzerland Springer, 2020) ISBN: 978-3-030-55229-9 H. Yamaguchi, Recombining plasma in supernova remnants: discovery and progress in the last decade. Astron. Nachr. 341, 150 (2020). https://doi.org/10.1002/asna.202023771 H. Yamaguchi, C. Badenes, R. Petre et al., Discriminating the progenitor type of supernova remnants with iron K-shell emission. Astrophys. J. Lett. 785, L27 (2014a). https://doi.org/10. 1088/2041-8205/785/2/L27 H. Yamaguchi, K.A. Eriksen, C. Badenes et al., New evidence for efficient collisionless heating of electrons at the reverse shock of a young supernova remnant. Astrophys. J. 780, 136 (2014b). https://doi.org/10.1088/0004-637X/780/2/136 H. Yamaguchi, S. Katsuda, D. Castro et al., The refined shock velocity of the x-ray filaments in the RCW 86 northeast rim. Astrophys. J. Lett. 820, L3 (2016). https://doi.org/10.3847/2041-8205/ 820/1/L3

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . SNRs as the Origin of Galactic Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Cosmic-Ray Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Cosmic-Ray Composition and Leptonic Versus Hadronic Cosmic Rays . . . . . . . . . . The Galactic Cosmic-Ray Energy Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation from Leptonic and Hadronic Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Mechanism of Diffusive Shock Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Collisionless Shocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Diffusive Shock Acceleration Theory and Its Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . Acceleration Timescales and Maximum Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Effects of Radiative Losses and Cosmic-Ray Escape on the Maximum Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nonlinear Cosmic-Ray Acceleration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Injection Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray and Gamma-Ray Evidence for Cosmic-Ray Acceleration . . . . . . . . . . . . . . . . . . . . . Radio and X-Ray Synchrotron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . GeV-TeV Gamma Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Measurements of the Cosmic-Ray Acceleration Efficiency . . . . . . . . . . . . . . . . . . . . . . . . Evidence or Lack of Evidence for PeVatrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evidence for Low-Energy Cosmic Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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J. Vink () Anton Pannekoek Institute for Astronomy & GRAPPA, University of Amsterdam, Amsterdam, The Netherlands SRON National Institute for Space Research, Leiden, The Netherlands e-mail: [email protected] A. Bamba Research Center for the Early Universe, School of Science, The University of Tokyo, Bunkyo-ku, Tokyo, Japan e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_90

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Cosmic-Ray Escape from Acceleration Sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polarimetry and Magnetic-Field Turbulence and Topology . . . . . . . . . . . . . . . . . . . . . . . . Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Shocks of supernova remnants (SNRs) accelerate charged particles up to ∼100 TeV range via diffusive shock acceleration (DSA) mechanism. It is believed that shocks of SNRs are the main contributors to the pool of Galactic cosmic rays, although it is still under debate whether they can accelerate particles up to the “knee” energy (1015.5 eV) or not. In this chapter, we start with introducing SNRs as likely sources of cosmic rays and the radiation mechanisms associated with cosmic rays (Section “SNRs as the Origin of Galactic Cosmic Rays”). In Section “The Mechanism of Diffusive Shock Acceleration”, we summarize the mechanism for particle acceleration, including basic diffusive shock acceleration and nonlinear effects, as well as discussing the injection problem. Section “X-Ray and Gamma-Ray Evidence for Cosmic-Ray Acceleration” is devoted to the X-ray and gamma-ray observations of nonthermal emission from SNRs, and what these reveal about the cosmic-ray acceleration properties of SNRs. Keywords

Cosmic rays · Supernova remnants · Shocks · Diffusive shock acceleration (DSA) · Magnetic fields · Synchrotron · Inverse Compton scattering · Pion decay

Introduction In a series of seminal papers, Baade and Zwicky hypothesized that the most luminous novae – which they dubbed “supernovae” – marked the transition of a massive star into a neutron star. They also made the suggestion that supernovae (SNe) are responsible for accelerating the highly energetic particles that reach us from outside the solar system, the so-called cosmic rays (Baade and Zwicky 1934). Since the 1930s, our understanding of both SNe and cosmic rays have greatly expanded. We know now that there are both neutron star producing core-collapse SNe and thermonuclear SNe (Type Ia SNe). It has been established that cosmic rays consist of 99% of atomic nuclei, with sources in the Milky Way responsible for proton cosmic rays up to ≈3 × 1015 eV – below these energies, they are referred to as Galactic cosmic rays. And likely only above 1017 –1018 eV are cosmic rays originating from outside the Galaxy. But the idea that SNe are somehow responsible for most of the Galactic cosmic rays is still a leading hypothesis. The SN hypothesis for the origin of cosmic rays is supported by the match between SN energetics and the energy budget required for cosmic-ray production,

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which require that about 5–10% of SN explosion energy is used for acceleration cosmic rays. However, the main evidence for cosmic-ray acceleration powered by SNe has been the detection of nonthermal emission from SN remnants (SNRs). In this chapter, we will review the X-ray and gamma-ray evidence for this hypothesis. Initially the evidence consisted of the detection of synchrotron radio emission from SNRs, caused by the presence of relativistic electrons inside SNRs (Shklovsky 1954). Although electrons constitute ∼1% of the cosmic rays locally detected, the synchrotron radiation provided evidence that charged particles have somehow been accelerated to relativistic energies. The identification of synchrotron radiation from SNR shells also suggested that cosmic-ray acceleration may be powered by SN explosions, but that the acceleration itself is occurring around the shocks caused by the explosion in the first few hundreds to thousands of years after the SN explosion. A theory for how shocks accelerate charged particles was developed in the late 1970s (Axford et al. 1977; Krymskii 1977; Bell 1978; Blandford and Ostriker 1978) and is known as diffusive shock acceleration (DSA) or first-order Fermi acceleration (Malkov and Drury 2001). The idea that SNRs, rather than SNe, are accelerating cosmic rays received a major boost due to the discovery of nonthermal X-ray emission from SNRs in 1995 (Koyama et al. 1995) – later followed by the detection of TeV gamma-ray emission from SNRs (Aharonian et al. 2001, 2004) after some earlier hints at lower gammaray energies (Esposito et al. 1996). The nonthermal X-ray emission is caused by synchrotron emission from electrons with 10 TeV in energy, and it, therefore, testifies of the ability of shocks to accelerate charged particles to ultrarelativistic energies. Moreover, since these electrons radiatively lose their energies with the lifetime of young SNRs, it identifies the SNR stage, rather than the SN event itself, as the period in which cosmic rays are accelerated. The detection of gamma-ray emission in the very-high-energy (VHE) gammaray regime (100 GeV) confirms the presence of ultrarelativistic particles in SNRs. In addition, the broadband gamma-ray emission from ∼200 GeV to 100 TeV provides evidence that at least in some cases the gamma-ray emission is caused by relativistic ions. So gamma-ray emission currently provides the best evidence for the acceleration of atomic nuclei in SNRs – usually referred to as hadronic cosmic rays – which make up ∼99% of the cosmic rays detected locally. This is not to say that the case for a SNR origin for Galactic cosmic rays has been settled now. The current evidence does not support the idea that SNRs are capable of acceleration cosmic rays up to the cosmic-ray “knee” at ∼3 × 1015 eV. Solving this puzzle will be a challenge for the next two decades. Three leading ideas currently exist: (1) perhaps the interpretation of the cosmic-ray “knee” as being the maximum energy for proton cosmic-ray acceleration needs to be revised; (2) the highest energy cosmic rays are accelerated in the first year up to 10–100 yr after explosion of all supernovae; or (3) plasma turbulence in starforming regions powered by SNe and stellar winds collectively are responsible for the highest energy cosmic rays. In this chapter, we will focus on nonthermal X-ray and gamma-ray emission from SNRs and the implications for cosmic-ray acceleration by SNR shocks, but we will also discuss the need for some alternative ideas, which includes recent evidence

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for PeV cosmic rays in starforming regions (We note that some SNRs contain an energetic pulsar, which creates a pulsar wind nebula that also emits nonthermal radiation. Here we concentrate, however, solely on the nonthermal emission from SNRs shells).

SNRs as the Origin of Galactic Cosmic Rays Around 1911 Victor Hess (1912) established, using balloon flights, that ionizing radiation comes from outside the Earth atmosphere. Soon after this “penetrating radiation” was referred to as “cosmic rays,” a bit of a misnomer as in the 1930s it became clear that cosmic rays consist of energetic (0.1 GeV) charged particles that reach Earth from outside the solar system.

The Cosmic-Ray Spectrum The cosmic-ray energy spectrum is now well measured from ∼108 eV up to ∼1020 eV, and the distribution shows a power-law spectrum ∝ E −q , with q ≈ 2.7. However, the spectrum steepens around 3 × 1015 eV – a feature known as the “knee” – and flattens around 3 × 1018 eV (the “ankle”), around 5 × 1019 eV the steepens again. For this chapter, we are mainly concerned with the connection of cosmic rays with energies below the “knee,” as it is thought that the “knee” corresponds to the maximum energy protons are accelerated to in Galactic cosmicray sources. There is evidence from air-shower measurements that the cosmic-ray composition becomes heavier above the “knee” (Apel et al. 2011). The “ankle” then likely marks the division between Galactic cosmic rays and cosmic rays of extragalactic origin. So if indeed SNRs are the main sources of Galactic cosmic rays, they must be able to accelerate protons up to the “knee” at 3×1015 eV – 3 PeV – which is challenging from a theoretical point of view (Lagage and Cesarsky 1983). Sources of >PeV cosmic rays are often referred to as PeVatrons. So one of the leading unanswered questions is whether SNRs are indeed PeVatrons, and if not, what are the Galactic PeVatrons responsible for cosmic rays up to the “knee”?

The Cosmic-Ray Composition and Leptonic Versus Hadronic Cosmic Rays Most cosmic rays (∼99%) are protons or heavier atomic nuclei, collectively labeled as hadronic cosmic rays. Below ∼100 GeV, the composition of cosmic rays can be directly measured using detectors carried aboard balloon flight or satellites. This shows that the abundance pattern of cosmic-ray particles is similar to the solar system abundance pattern, except that the odd Z elements, such as boron (Z = 5), are more abundant than in the solar system, as a result of the breakup of cosmic-ray nuclei due to collisions with interstellar gas. The ratio between odd

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and even Z elements provides information on the typical path lengths of cosmicray particles from their sources of origin till detection. Moreover, the presence of radioactive nuclei, such as 10 Be, 26 Al, 36 Cl, and 54 Mn, can be used to estimate the amount of time that cosmic-ray particles spend on average in the Milky Way. From this it is inferred that cosmic rays with energies around 1 GeV spend about τesc ≈ 1.5×107 yr in the Milky Way, and that they must reside in low density regions for a large fraction of this time. Given that the cosmic rays are relativistic, the long escape time suggests that the particles move diffusively through the interstellar medium (ISM), characterized by a diffusion coefficient D ≈ 4 × 1028 cm2 s−1 . The diffusion coefficient is energy dependent, with a proportionality of ∝ E δ , with δ ∼ 0.3–0.7 (Strong et al. 2007). The abundance pattern, unfortunately, contains little information about the acceleration sites. However, there is evidence for an overabundance of 22 Ne (Binns et al. 2005), indicative of stellar-wind enriched material, and for a slight overabundance of volatile elements, perhaps indicative of dust particles injected preferentially into the acceleration process (Meyer et al. 1997). Only ∼1% of the Galactic cosmic rays are electrons, and even a smaller part are positrons – together often labeled “leptonic cosmic rays.” However, electrons, having a lower inertial mass than hadrons, are radiatively much more efficient than hadrons. As we will describe in Section “Radiation from Leptonic and Hadronic Cosmic Rays”, relativistic electrons produce radiation from the radio band to X-rays in the form of synchrotron radiation, but also produce gamma rays, mostly through inverse Compton scattering. Hadronic cosmic rays only significantly contribute to the gamma-ray part of the electromagnetic spectrum, making gamma-ray studies essential for studying the cosmic-ray acceleration efficiency of SNRs.

The Galactic Cosmic-Ray Energy Budget Although associating SNRs with Galactic PeVatrons is challenging from both a theoretical (Lagage and Cesarsky 1983) and observational point of view (as we will see), the main reason why SNRs and their associated energy source – SN explosions – are compellingly associated with Galactic cosmic rays is the available energy budget. The local energy density of cosmic rays is Ucr ∼ 1 eV cm−3 . If we approximate the volume of the Galaxy that is occupied by cosmic rays with a thick disc with radius of ∼10 kpc and thickness of 2 kpc, we have a total energy in cosmic rays of Ecr ≈ Ucr V ≈ 3 × 1055 erg. Since cosmic rays have a typical escape time from the Galaxy of 15 Myr, the power needed for maintaining the cosmic-ray energy density in the Galaxy is E˙ cr ≈ Ecr /τesc ≈ 6 × 1040 erg s−1 . This compares well with the total power provided by SN explosions. For two explosions per century, and 1051 erg of explosion energy, we find E˙ SN ≈ 6 × 1041 erg s−1 . So an cosmic-ray efficiency is needed for ≈10%. The total stellar wind power in the Galaxy is less, and also the rotational energy provided by pulsars is much less if they are born with initial spin periods P0 > 5 ms, as seems to be generally the case (e.g., Vink 2020, Chapter 12).

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Radiation from Leptonic and Hadronic Cosmic Rays So far we dealt with information about cosmic rays obtained by directly or indirectly measuring the properties of cosmic rays that reach the solar system. However, for measuring the properties of cosmic rays in cosmic accelerators, here SNRs, we rely on the radiation from cosmic rays while still being in their sources. Since the cosmic-ray spectrum is a nonthermal distribution, the ensuing radiation is often referred to as “nonthermal radiation.” But it should be noted that the radiation mechanisms responsible occur irrespective of whether the distribution is thermal or nonthermal; it is just that certain radiation types are predominantly associated with nonthermal distributions.

Synchrotron Radiation Historically the first type of emission that was associated with nonthermal particle distributions is synchrotron radiation, which was first identified in astrophysical context in the radio bands (Shklovsky 1954). Synchrotron radiation occurs when charged particles are forced to helical path following magnetic-field lines, due to the Lorentz force. The changing electric field associated with the nonlinear part of the path results in a radiation pattern that is mostly directed in the direction perpendicular to the magnetic-field direction. The power emitted by a single particle scales with its mass as m−2 , which makes that synchrotron radiation from electrons is 3 × 106 stronger than from protons. So synchrotron radiation is generally associated with either electrons or positrons, i.e., leptonic cosmic rays. The typical frequency at which an electron emits synchrotron radiation is 3 eB⊥ νsyn ≈0.29 × γ 2 = 1.8 × 1018 E 2 B⊥ Hz 2 me c  2   E B⊥ ≈0.47 × 109 Hz 1 GeV 100 µG

(1)

with γ and E respectively the Lorentz factor and energy (in erg, unless otherwise indicated) of the electron, and B⊥ the perpendicular component of the magneticfield strength. The factor 0.29 introduced corresponds to the peak of the broad spectral radiation distribution from a monoenergetic electron. This shows that radio synchrotron radiation around 1 GHz requires the presence of electrons with energies well in excess of a GeV, for magnetic fields that are typical for the interstellar medium of ∼5 µG. The radiated power from a single electron can be expressed as 

dE dt



=

4 σT cβ 2 γ 2 UB , 3

(2)

with σT = 6.65 × 10−25 cm2 the Thomson cross section, β = v/c (electron speed in units of the speed of light), and UB = B 2 /8π the magnetic-field energy density.

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This also sets the timescale for an electron to lose its energy due to synchrotron radiation:    −1  −2  E  9 (me c2 ) 634 ∼ E B = 1258 ≈ s τsyn ≈  yr. = dE/dt  4 e4 cB 2 E 1 TeV 100 µG B 2E (3)

The timescale suggests that for radio synchrotron emitting electrons around a few GeV, radiative losses are not important during typical lifetimes of SNRs (∼105 yr). However, for X-ray synchrotron emitting electrons, which are typically 10 TeV, radiative losses are important. See Section “Radio and X-Ray Synchrotron”. For SNRs synchrotron radiation from young SNRs has been detected up to ∼150 keV (e.g., The et al. 1996; Green 2015). For nonthermal distributions of electrons characterized by an energy distribution of the form N(E)dE ∝ E −q dE, the resulting synchrotron emissivity spectra have a power-law distribution of ǫsyn (ν)dν ∝ ν −α dν, with α = (q − 1)/2. (Note that in the radio astronomy literature, the minus sign is often included in the definition of α.) This relation follows from the factor γ 2 in (2). In high-energy astrophysics, it is more common to use the photon number emissivity (nν = ǫν / hν), resulting in a power-law index for the photon spectrum of Γ = α + 1 = (q + 1)/2. Synchrotron radiation is intrinsically polarized, with the electric vector of the polarization being perpendicular to the magnetic-field direction. The maximum possible polarization fraction from nonthermal electron distribution is Π=

α+1 , α + 5/3

(4)

corresponding to 69% for α = 0.5. In reality the polarization fraction is usually much lower, due to different magnetic-field orientations along the line of sight, or due to magnetic-field turbulence. Nevertheless, radio synchrotron polarization is often used to identify radio emission as synchrotron radiation.

Inverse Compton Scattering The same relativistic electrons that produce synchrotron radiation can also scatter background photons through inverse Compton scattering. Inverse Compton scattering can be thought of as Thomson scattering of a photon in the rest frame of the electron. In this frame, a background photon with energy hν0 has a Lorentz boosted energy of hν ′ ≈ γ (hν0 ) (with some angle dependence). Thomson scattering does not change the energy of the photon. However, transforming back to the observer frame results in an additional Lorentz boost, but with an energy distribution that depends on the scattering angle with respect to the motion of the electron. So the final scattered photon appears to have an energy of the order of hν ′′ ≈ γ 2 hν0 (see, e.g., Vink 2020, for details). As an example, an electron with energy of 1 TeV will upscatter a typical cosmic microwave background (CMB) photon of 0.0007 eV to an energy of 2.7 GeV.

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For a single electron, the radiation power is 

dE dt



=

4 σT γ 2 c 3



hν0 nrad (ν0 )dν0 =

4 σT γ 2 cUrad , 3

(5)

with Urad the radiation energy density. One recognizes here that σT cnrad (ν0 ) is the collision rate between electrons and background photons with a frequency ν0 . Note that the equation, as written on the right-hand side, is similar to that of synchrotron radiation, except that the magnetic-field energy density factor UB is replaced by the radiation energy density – c.f. Eq. 2. As the peaks of an spectral energy distribution (SED) indicate approximately how much flux or luminosity is produced as a function of frequency. Therefore, comparing the peaks in the SED of the synchrotron component (radio to X-rays) with the SED of gamma-ray inverse Compton scattering provides an estimate of the ratio of the energy density in background radiation and magnetic field: Psyn /PIC ≈ UB /Urad . An omnipresent component of the radiation energy density in the Universe is that associated with the cosmic microwave background (CMB), which is Urad,CMB ≈ 0.26 eV cm−3 . In addition, Galactic infrared emission and UV stellar light can have additional contributions that may be as large as the CMB, depending on the local environment of a source. The cross section for inverse Compton scattering is seriously reduced if the photon energy in the rest frame of the electron approaches or exceeds the rest mass energy, i.e., hν ′ = γ hν0  me c2 . For the scattered photon energy in the frame of the observer, this means that for hν ′′  (me c2 )2 / hν0 , the inverse Compton radiation component is strongly suppressed. This corresponds to hν ′′  400 TeV for the typical CMB photon energy of 0.0007 eV. However, for a typical optical or UV of around 1 eV, suppression starts already around upscattered photon energies of 0.2 TeV. This suppression of inverse Compton scattering and related effects are usually referred to as Klein-Nishina suppression/effects. Apart from Klein-Nishina effects, the spectral index of the photon spectrum is similar to that of synchrotron radiation: Γ = (q + 1)/2.

Nonthermal Bremsstrahlung Bremsstrahlung (or free-free emission) is the result of the (small) deflection of a charged particle when it passes close to another charged particle. Since the deflection depends on the mass of the particle, and electrons are light, usually the dominant form of bremsstrahlung is electron bremsstrahlung. Often bremsstrahlung from hot astrophysical plasmas are caused by electrons with a thermal (Maxwellian) velocity distribution, hence the name thermal bremsstrahlung. The total emissivity 1/2 of thermal bremsstrahlung scales as εff ∝ ne np Te . The differential emissivity (i.e., −1/2 per unit energy or frequency) scales as εff,ν ∝ ne np Te exp (−hν/kTe ). However, particle acceleration also results in a population of nonthermally distributed electrons. At high energies, these are referred to as leptonic cosmic

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rays. At lower energies, however, nonthermal bremsstrahlung may arise from the suprathermal electron population that constitutes the injection spectrum of the electron cosmic rays, or more in general, a nonthermal leftover from collisionless shock physics. Note that collisionless shocks may not immediately lead to a thermal distribution of particles. The suprathermal electrons should give rise to nonthermal, hard X-ray continuum radiation, best identified above 10 keV. The reason is that the X-ray below 10 keV SNRs is often dominated by thermal radiation processes, be it line emission, or thermal bremsstrahlung continuum and related processes, such as free-bound emission. Indeed, Asvarov et al. (1990) argued that the hints of hard X-ray continuum from young SNRs like Cas A and Tycho are formed by the low-energy tail of the electron cosmic-ray population. When hard X-ray emission from Cas A and other young SNRs was firmly established (The et al. 1996; Allen et al. 1997; Favata et al. 1997), there was a debate about the nature of this emission: was it nonthermal bremsstrahlung (e.g., Laming 2001) or synchrotron radiation (Allen et al. 1997; Reynolds 1998)? The latter caused by electrons from near the maximum of the electron cosmic-ray spectrum (∼10–100 TeV). Although the debate has not been completely settled, the general consensus is that for young SNRs the hard X-ray emission forms the high-energy tail of the synchrotron component. See, for example, the discussion on the NuSTAR imaging spectroscopy of the hard X-ray emission from Cas A (Grefenstette et al. 2015). One reason why a nonthermal bremsstrahlung interpretation has difficulties is that Coulomb collisions between the thermal plasma and the suprathermal electrons result in significant energy exchanges at low electron energies, and it leads to energy losses for suprathermal electrons. The energy-loss rates scale for nonrelativistic electrons as dEe /dt ∝ nH E −1/2 . This means that a nonthermal electron distribution at the shock front quickly starts losing its lower electron energy part, resulting in an inverted electron spectrum (Vink 2008). The timescale on which this happens for electrons below 100 keV is τ ≈ 1011 n−1 e s, which is the timescale applicable to Cas A. However, for SN1006, with its lower density plasma, nonthermal bremsstrahlung may be relevant. Although nonthermal X-ray bremsstrahlung is not discussed so often anymore for young SNRs, recently evidence based on NuSTAR observations shows that the hard X-ray emission from SNR W49B is relatively hard, with a power-law number index of Γ ≈ 1.4. It likely constitutes a case of nonthermal bremsstrahlung (Tanaka et al. 2018). This can be verified in the future, as a nonthermal electron population with energies in the 10–100 keV range leaves an imprint on Fe-K line ratios, which can be measured by the next-generation calorimetric X-ray detectors on board XRISM and Athena. Nonthermal bremsstrahlung as an ingredient for the (very) high-energy gammaray emission is less controversial than for the X-ray band. The responsible electrons (and possibly positrons) are part of the cosmic-ray population and will surely contribute to the gamma-ray emission. As the emission is caused by electrons, bremsstrahlung is labeled a leptonic emission component, together with inverse Compton scattering (Section “Inverse Compton Scattering”). Like the thermal

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bremsstrahlung component, nonthermal bremsstrahlung emissivity scales with density as ǫntb ne,cr np , with ne,cr referring to the relevant leptonic cosmic-ray density. This scaling is identical to pion decay emission; see Section “Pion Production and Decay”. Moreover, inverse Compton radiation is the dominant leptonic gammaray component for densities np  240 cm−3 (Hinton and Hofmann 2009), even when only considering the cosmic-microwave background as a source of seed photons. For modeling the SEDs of SNRs, it is usually assumed that the electron over proton cosmic-ray number ratio is ne /np ∼ 1/100. In that case, pion decay dominates the gamma-ray emission above ∼100 MeV over bremsstrahlung. For these reasons, nonbremsstrahlung is often neglected when modeling broad spectral energy distribution in gamma rays: for low densities, inverse Compton scattering dominates over bremsstrahlung, whereas for high densities, pion decay dominates over bremsstrahlung.

Pion Production and Decay The radiation mechanisms discussed above are mostly associated with leptonic cosmic rays (electrons/positrons). Only one mechanism is associated with hadronic cosmic rays: pion decay. Pions are the lightest mesons (hadrons with two quarks) and come in three flavors: π 0 ,π + , and π − . They are produced whenever a hadronic cosmic-ray particle (usually a proton) collides with target hadron, usually a proton in the local gas. For the lightest pion, π 0 (mπ 0 c2 = 135 MeV), a threshold energy of 280 MeV for the cosmic-ray proton is needed for the reaction p + p → p + p + π 0 . For a charged pion, a reaction like p + p → p + n + π + is needed. At sufficiently high energies, multiple pions, and even new protons and neutrons, can be created, provided nature’s conservation laws, such as energy, momentum, charge, and baryon number, are obeyed. Pions are unstable particles and decay into lighter particles and photons: π 0 →2γ , π + →μ+ + νμ ↓ e+ + νe + ν μ , π − →μ− + ν μ ↓ e− + ν e + νμ . So one of the outcomes of charged pion decay is electron and muon (anti)neutrinos, which are the particles of interest for high-energy neutrino detectors like IceCube and the future KM3NeT. No high-energy neutrino signals have yet been detected from SNRs.

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For this chapter, it is the neutral pion production that is of interest, as neutral pion decay leads to two photons each with an energy of 12 mπ 0 c2 = 67.5 MeV in the rest frame of the pion. However, a high-energy cosmic ray (E ≫ 280 meV) will lead to a pion with a considerable kinetic energy. So the gamma-ray photons from the decay will receive a Lorentz transformation, resulting in a photon energy of hν = 21 mπ 0 γπ 0 (1 ± βπ 0 cos θ ), with θ the angle between the pion direction and the direction of the two decay photons, which move in opposite directions in the frame of the pion. So each decay results in a low-energy photon – associated with the minus sign – and a high-energy photon, associated with the plus sign. Details of the relation between cosmic-ray energy and the expected probability distribution of the photon energies can be found in, for example, Kafexhiu et al. (2014). On average the higher energy photon has an energy that is about 10% of the energy of the cosmic-ray proton. See Fig. 1 for a typical SED for emission caused by hadronic cosmic rays, including the distribution in energy for protons with a give energy. For a proton cosmic-ray spectrum of N (E)dE ∝ E −q , the resulting photon spectrum has a similar spectral index, i.e., Γ ≈ q. We expect, therefore, that a gamma-ray spectrum dominated by pion decay has a spectral index of Γ ≈ 2.2 (for q = 2.2), whereas for the inverse Compton spectrum from a population of electrons with the same spectral index q, the photon spectrum is harder: Γ ≈ 1.6. A defining characteristic of a pion decay spectrum is that the spectrum is symmetric in logarithmic energies around half the rest mass energy of the pion, due to the ± sign in the Lorentz transformation of the two oppositely moving photons. In an SED, for which the spectrum is multiplied by E 2 , this results in a characteristic peak around 100–200 MeV and a sharp cutoff below these energies. This is referred to as the “pion bump” (see also Fig. 1).

The Mechanism of Diffusive Shock Acceleration Collisionless Shocks Particle acceleration appears to be a common byproduct of so-called collisionless shocks. In collisionless shocks, the changes in thermodynamic properties of the plasma across the shock boundary are not caused by particle-particle interactions through Coulomb interactions, but through collective effects – particles are randomly deflected by magnetic-field turbulence and/or electric fields. Collisionless shocks are common in many astrophysical situations as the densities are low, making Coulomb interactions rare. The absence of efficient Coulomb interactions does not allow charged particles that have velocities greatly in access of the local plasma velocity to redistribute their excess energy to other plasma particles, allowing them to acquire even more energy. In a collisionless shock, it is also not necessary for the electrons and ions to equilibrate their temperatures. Apart from these considerations, the standard Rankine-Hugoniot shock equations can be used, which state that mass, momentum, and enthalpy flux across the shock boundary are conserved. For a strong

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Fig. 1 A model SED for a pion decay gamma-ray spectrum based on the semi-analytical functions of Kafexhiu et al. (2014). The input proton spectrum is assumed to have a power-law distribution in momentum n(p)p 2 pdp ∝ p 2 p −q−2 , with q = 2.3. The colored lines show the results for monochromatic “beams” of protons with energies of 1 GeV (red), 1 TeV (green), 10 TeV (blue), and 1 PeV (cyan). The low-energy cutoff, together with the peak around 5×108 eV, is often referred to as the “pion bump.” (Based on a figure in Vink 2020.)

 shock – i.e., M = Vs /cs,1 = P1 /ρ1 Vs2  5 with cs the sound speed in the unshocked plasma – the post-shock plasma is characterized by χ≡

(γ + 1) ρ2 = = 4 (for γ = 5/3), ρ1 (γ − 1)

3 μV 2 , 16 s 1 1 v2 = Vs = Vs , χ 4   3 1 Vs = Vs , Δv = v1 − v2 = 1 − χ 4

< kT2 >=

(6) (7) (8) (9)

with subscript 1 and 2 indicating upstream (unshocked) and downstream (shocked) quantities, Vs the magnitude of the shock velocity, v1 and v2 the plasma velocities in the frame of the shock (i.e., |v1 | = Vs ), γ the plasma’s adiabatic index, χ ≡ ρ2 /ρ1 the shock compression ratio, and μ the average particle mass – μ ≈ 0.6 for solar system abundances.

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The strong shock approximation (M  5) is well justified for young SNRs, which have Vs ≈ 1000–7000 km s−1 , even if they are evolving in the hot part of the interstellar medium, where the typical sound speed is cs ∼ 10 km s−1 . However, once the shock velocity has dropped below ≈30 km s−1 , the strong shock approximation breaks down, also because the typical turbulent gas motions are characterized by similar velocities. Shock velocities below 50 km s−1 occur typically for SNRs that are several 10,000 years old. Note that for Vs  200 km s−1 – typically happening for SNR ages of 5000–20,000 yr – post-shock radiative cooling becomes important, due to strong optical/UV radiation. This results in very high shock compression ratios further downstream of the shock, as the plasma tries to maintain in pressure equilibrium, in the presence of energy losses. The high shock compression ratios lead to the optical narrow filaments that characterize the optical emission from middle-aged SNRs like the Cygnus Loop (Veil Nebula) or Spaghetti Nebula (Simeis 147). For more details on this topics, see this handbook in ⊲ Chap. 99, “Supernova Remnants: Types and Evolution” by A. Bamba and B. Williams.

Diffusive Shock Acceleration Theory and Its Extensions Efficient acceleration is likely mostly in young SNRs through the diffusive shock acceleration (DSA) mechanism (Bell 1978; Axford et al. 1977; Krymskii 1977). DSA operates on charged particles with energies well above kT2 . These particles have speeds greatly in access of Vs and are elastically scattering due to magneticfield irregularities. As a result, they diffusively wander through the plasma, which brings them every now and then across the shock front. The magnetic-field irregularities, probably associated with Alfvén or magneto-acoustic waves, are on average at rest with the local plasma, which moves with v1 in the unshocked plasma, and with v2 in the shock medium. The assumption is that for nonrelativistic shocks, the scattering of energetic charge particles makes the velocity distribution isotropic after a few scatterings. Every time a particle crosses the shock front, it has an excess velocity of Δv with respect to the new frame of reference, and the particle appears to have an excess energy given by a Lorentz boost (E → E ′ ). If we take the particle speed to be relativistic (v ≈ c), the Lorentz boost of E ′ = Γ (E − Δv/c cos θ ), with a nonrelativistic boost Γ ≈ 1, the gain in energy is       Δv 2 Vs 1 < ΔE >   ≈  cos θ  ≈ 1− . E c 3 c χ

(10)

A full cycle, in which the particle crosses from downstream to upstream and back, provides twice this energy. Since the energy gain is proportional to the energy itself, the energy of a charged particle grows exponentially with the number K of shock crossing cycles:

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1 K 4 Vs 1− , EK = E0 1 + 3 c χ

(11)

with E0 some initial energy. On the other hand, once particles are too far removed from the shock front downstream of the shock, they are unlikely to recross the shock front again. Once this is the case, the final energy is frozen in, and the particle is said to have escaped downstream – upstream escape is unlikely as the plasma will eventually be swept up by the shock. However, at very high energies, upstream escape can and probably does occur. The chance of escaping downstream during one shock cycle depends on the ratio between the plasma velocity v2 and the particle velocity (assumed to be c): Pesc = 4

v2 1 Vs =4 , c χ c

(12)

with the factor 4 arising from averaging over the angle of particle velocity with respect to the shock. So if inject N0 particles with energy E0 into the DSA process, after K full cycles, the number of particles has been reduced to N (E > EK ) = N0 (1 − Pesc )K ,

(13)

with EK given by (11) The combination of exponential growth in energy with an exponential decay in the number of particles that are still participating in the DSA process leads to a power-law distribution: N(> E) = CE −q+1 →

dN (E) = C ′ E −q , dE

(14)

with q=

χ +2 = 2 (for χ = 4). χ −1

(15)

Note that another way to derive this result is based on phase-space (momentumspace) conservation in the absence of collisions (Blandford and Ostriker 1978; Drury 1983), which gives a momentum distribution of N (p)4πp2 dp ∝ p−q+2 dp,

(16)

which is identical to N (E) ∝ E −q , but does not require the relativistic approximation E = |p|c and indicates that the expected cosmic ray is characterized by a power-law distribution in momentum. This means that a gradial flattening of the energy distribution is expected at particle energies E  mp,e c2 . The prediction of DSA of power-law distribution in energy with slope q = 2 – for E > mp,e c2 – matches well with the average radio spectral index of α = 0.5

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for SNRs, given that for synchrotron radiation, the relation between the particle index for the electron energy distribution and radio spectral index is α = (q − 1)/2. Moreover, the spectral index for cosmic rays in the galaxy is steeper than the source spectrum due to the energy-dependent diffusion coefficient for cosmic rays, leading to energy-dependent escape of cosmic rays from the galaxy. The relation is qcr = qsource + δ, with δ as defined above.

Acceleration Timescales and Maximum Energies It can be shown that for steady-state, plane parallel shock, the particle distribution as a function of space coordinate z is n(z, p) =n0 (p) exp[−|z|/ ldiff,1 (p)] for z > 0

(17)

n(z, p) =n0 (p) for z < 0,

(18)

with the shock moving in the positive z-direction, and with ldiff (p) = D1 (p)/v1 = D1 (p)/Vs . Here D1 (p) = 13 λmfp vcr is the diffusion coefficient in the unshocked (upstream) medium. Here vcr is the particle speed (for simplicity we take it to be c and assume particles are relativistic), and λmfp the typical scattering length scale of the particles (mean free path). This shows that there are always accelerated particles in front of the shock, with a length scale that depends on the momentum/energy of the particles. These particles are referred to as the cosmic-ray shock precursor. The shortest scattering length scale possible is of the order of the gyroradius of the particle λmfp  pc/eB, and is often parameterized as λmfp = ηpc/eB ≈ ηE/eZB, with η = 1 referred to as Bohm diffusion (Z is the charge). Also downstream there is a typical length scale over which particles are still able to diffusive back to the shock front: ldif,2 (p) = D2 (p)/v2 ≈ ηceE/v2 eB. The timescale in which particles are typically scattered back over the shock front on either side of the shock is τ1,2 = ldiff,1,2 /vcr . From this one can derive the time it takes for particle to perform a full acceleration cycle τ = τ1 + τ2 , and the acceleration rate can be derived from dE ΔE = = dt τ1 + τ2

4 c

4 Δv c E D1 D2 v1 + v2

3

≈

v1 − v2 E  D1 3 v1 +

D2 v2

.

(19)

The acceleration time to go from an energy E0 to E is then tacc

3 = v1 − v2



E

E0



D1 D2 + v1 v2



dE ′ . E′

(20)

The relation between v1 and v2 depends on the compression ratio χ , whereas the magnetic-field compression ratio, χB , depends on the orientation of the magnetic

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field and is one for parallel magnetic fields and χ for perpendicular magnetic fields. Ignoring that η may also differ at either side of the shock, but parametrizing the diffusion coefficient as D1 =

1 ηmax 3



E Emax

δ−1

cE , eZB1

(21)

one can derive the following approximation for the acceleration time scale to some maximum energy Emax :

tacc ≈ 1014

ηmax Zδ



Emax 1014 eV



Vs 5000 km s−1

−2 

B1 10 µG

 −1 1 +

χ χB



8/3

χ χ −1



yr.

(22)

−1 B V 2 t . The numerical values also show that it is This shows that Emax ∝ ηmax 1 s acc quite challenging for SNRs to accelerate particles up to the cosmic-ray “knee” at 3 × 1015 eV. First of all, at an age of ∼1000 yr, the shock velocity of most SNRs will have dropped to below 5000 km s−1 . One could also question how realistic it is that ηmax = 1, which is the minimum value possible (corresponding to Bohm diffusion). The only way to allow acceleration up to the “knee” is if the shock speeds can be higher, which happens in the very early phases of SNR evolution, or if B1 ≫ 10 µG, i.e., much higher than the typical interstellar magnetic-field strength. Amplification of the magnetic fields near SNR shocks is theoretically possible, and one often invoked process is the Bell mechanism (Bell 2004), in which the currents driven by cosmic-ray streaming in the upstream magnetic fields lead to a plasma instability that amplifies the magnetic field.

The Effects of Radiative Losses and Cosmic-Ray Escape on the Maximum Energy According to (22), the maximum energy particle can be accelerated to is limited by time. However, there are several other constraining elements. First of all, electrons radiate quite efficiently due to synchrotron radiation and inverse Compton scattering (Section “Radiation from Leptonic and Hadronic Cosmic Rays”). We can estimate the maximum energy of electrons in the presence of radiative losses by equating (22) with the synchrotron radiation loss time (2), which gives Ee,max ≈ 42η−1



B2 100 µG

−1/2 

Vs 5000 km s−1



T eV ,

(23)

where we used now the downstream magnetic-field B2 = χB χB . Interestingly, converting this maximum energy to the typical synchrotron photon energy gives a value that no longer depends on the magnetic-field strength (Aharonian and Atoyan 1999):

101 Nonthermal Processes and Particle Acceleration in Supernova Remnants

hνmax ≈ 3η−1



Vs 5000 km s−1

2

keV.

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(24)

Synchrotron spectra for which the cutoff energy is determined by radiative losses are called loss-limited spectra, whereas if it is determined by the available acceleration time, the spectra are called age-limited spectra. In general, it is now expected that most historical SNRs have loss-limited X-ray synchrotron spectra. But reality is more complex, as shown in a study of the X-ray synchrotron spectra from Tycho’s SNR (Lopez et al. 2015). Apart from available time and radiative losses, the maximum acceleration energy can also be limited by escape, i.e., at very high energies, the particles are no longer expected to return back from the upstream region to the shock. We can estimate the upstream escape by first calculating the maximum size of the cosmic-ray precursor length scale (Vink 2020), from the fact that tsnr > tacc : tsnr > tacc > 8

ldiff,1 D1 2 =8 . Vs Vs

(25)

The factor 8 incorporates the effects of magnetic-field compression at the shock in a conservative sense. Since we can generically approximate Vs = mRs /tsnr , with m = 1 indicating free-expansion and m = 2/5 the Sedov-Taylor expansion, we find that the precursor length scale is constraint to ldiff,1
1/2 the maximum energy will always increase with time for a constant or increasing B1 , whereas for m < 1/2 the maximum energy is in fact decreasing with time.

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Nonlinear Cosmic-Ray Acceleration In the standard theory of DSA, usually referred to as the test-particle approach, the shock structure is determined by the standard Rankine-Hugoniot shock equations. However, if a substantial fraction of the available shock energy flux ( 21 ρ0 Vs3 ) is used to accelerate particles, the shock structure itself will change, which in turn will change the particle acceleration properties (Eichler 1979). The theory describing this is nonlinear diffusive shock acceleration (non-linear DSA). The change itself comes about by the substantial pressure imposed by the shock precursor (Section “Acceleration Timescales and Maximum Energies”) on the plasma upstream of the shock, due to the fact that the cosmic-ray particles scatter off the magnetic-field irregularities thereby on average pushing the plasma away from the shock. This results in the plasma being forced to move before the shock arrives and is accompanied by a pre-compression of the plasma. This is a consequence of particle-flux conservation, which implies ρ0 v0 = ρ1 v1 , with ρ0 , v0 the plasma density and velocity (in the frame of the shock) far upstream of the precursor, and ρ1 , v1 the same quantities somewhere in the precursor. The length scale of the precursor depends on the energy of the particles under consideration (17), as ldiff,1 is energy-dependent: within the precursor, the cosmic-ray pressure increases toward the shock, and hence also the precursor compression builds up. The implication is that as the actual shock arrives (often called the subshock), the plasma is already moving with |v1 | = |v0 /χ1 < |Vs |, with χ1 = ρ1 /ρ0 = v0 /v1 the compression ratio in the precursor. Also the gas pressure is higher than far upstream due to adiabatic compression and perhaps additional heating mechanisms −γ (P1 > P0 χ1 ). Since the sonic Mach number is given by M 2 = ρv 2 /P , we have −γ +1 −γ +1 M12 = ρ1 v12 /P1 < ρ0 v02 χ1 /P0 = M02 χ1 , with γ the gas-adiabatic index. The lower Mach number at the (sub)shock or gas shock results in a lower plasma temperature. Another consequence is that the DSA process itself needs to be modified: the lowest energy cosmic rays do not diffuse far into the precursor and sample a lower contrast in shock difference across the shock (Δv = |v1 − v2 |), whereas only the highest energy particles sample the full velocity difference (Δv = |v0 − v2 |). The result is that the momentum distribution of accelerated particles is no longer a power-law distribution, as indicated by (15), but is concave (e.g., Ellison et al. 2000; Blasi et al. 2005). The total compression ratio of the shock (χtot = χ1 χ2 ) can in principle be much larger than the canonical value of 4, and the asymptotic value of q = 1.5 (Malkov and Drury 2001) rather than the canonical q = 2. Over the last decade, however, it has become clear that the effects of nonlinear DSA are not as extreme as once predicted. What appears to hold it in check is another cosmic-ray feedback effect (e.g., Vladimirov et al. 2008; Caprioli and Spitkovsky 2014): magnetic-field amplification. This prevents too much of the precursor compression.

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The Injection Problem The theory of DSA assumes a population of particles that are elastically scattering and moving fast enough to be able to scatter from the shocked medium, back upstream to the unshocked medium (or the precursor). The theory DSA does not explain how these particles acquired enough energy to start participating in the DSA process, i.e., it assumes there is a population of suprathermal particles which form the seed population of DSA accelerated particles. Early ideas on this “injection problem” assumed that the seed particles were just the high-velocity outliers from a thermal (Maxwellian) distribution (N (E) ∝ E 1/2 exp(−E/kT )), with E ≫ 3kT . However, SNR shocks are collisionless shocks, and it is not a priori clear whether the shock-heated particles even have a Maxwellian distribution. A more recent idea about the injection focuses on the phenomenology of collisionless shocks as seen in particle-in-cell (PIC) calculations, and in situ measurements of interplanetary shocks. These show that instead of immediately shock-heating the incoming particles, collisionless shocks reflect a fraction of the incoming particles back upstream, which interact with the unshocked particles. Some of these reflected particles may cross the shock and be reflected again. According to PIC simulations (Caprioli et al. 2015), these particles are the ones that form the seed particles for DSA. These seed particles are of observational interest as well, as suprathermal particles may have an effect on the Hα line width for non-radiative, or Balmerdominated, shocks (Nikoli´c et al. 2013), and they may give rise to measurable suprathermal bremsstrahlung (Asvarov et al. 1990). In fact, this was once taken as an alternative explanation for hard X-ray emission from young SNRs (Asvarov et al. 1990; Favata et al. 1997), and it is also thought to be the cause of hard Xray emission from W49B (Tanaka et al. 2018). Note, however, that due to Coulomb collisions, the initial spectrum of the seed particles may be substantially altered further downstream (Vink 2008). Hard X-ray emission from these seed particles is clearly a matter that needs further study, as it provides a glimpse into the initial stages of cosmic-ray acceleration by SNRs.

X-Ray and Gamma-Ray Evidence for Cosmic-Ray Acceleration Radio and X-Ray Synchrotron Traditionally SNRs are identified from other shell-type objects, such as HII regions, through their polarized radio emission and steep spectra in the 107 –1011 Hz band. These characteristics identify the emission as being caused by synchrotron radiation from nonthermal electrons with energies of around a few GeV. See Eq. (1). See Dubner and Giacani (2015) for a review on radio observations of SNRs.

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Since the typical radio spectral index is α ∼ 0.5 (Green 2019), the index of the particle distribution of accelerated electrons can be estimated as q ∼ 2, which is consistent with the DSA theory. The first discovery of synchrotron X-rays from shells of SNRs was found in shells of SN 1006 (Koyama et al. 1995), which provided the first evidence of accelerated electrons up to energies of several TeV. Currently around ten young SNRs with synchrotron X-rays are listed. Interestingly, many of these SNRs have faint or no thermal X-rays (Koyama et al. 1997; Tsunemi et al. 1999; Bamba et al. 2000, 2001, 2012; Yamaguchi et al. 2004; Reynolds et al. 2008), implying that the ambient density of these SNRs is lower than ordinal SNRs with thermal X-rays. The reason may be that X-ray synchrotron radiation requires a high shock speed (Eq. 24), which is more easily maintained over durations of a thousand year for low ambient densities. The steepening of the synchrotron spectrum corresponding to the cutoff energy of the nonthermal electron distribution is often occurring in the soft X-ray band (Bamba et al. 2008, for example). The cutoff photon energy is proportional to the square of the maximum electron energy and magnetic-field strength (see Eq. (1)), and measuring the cutoff leads us to understanding these physical parameters. Assuming the magnetic field of ∼10 µG, the maximum energy of electrons is derived to be ∼10–100 TeV, which is one or two orders below the “knee” energy. In the case of a loss-limited spectrum, the photon energy corresponding to the cutoff energy is independent of the magnetic field and only depends on the turbulence parameter η and shock velocity; see Eq. 24. Since for several young SNRs the shock velocity has been measured, one can infer from the detection of X-ray synchrotron radiation that the magnetic-field turbulence must be high, η  5, suggesting that the diffusion of 10–100 TeV electrons is close to the Bohm limit (Section “Acceleration Timescales and Maximum Energies”). In general it is assumed that the synchrotron emission originates from electron populations accelerated at the forward shock. The reason is that the forward shock velocity is a high Mach number shock for a relatively long time (∼104 yr) and that the plasma entering the shock should have typical magnetic-field strength of the order of the average Galactic magnetic field (B ∼ 5 µG). However, there is clear evidence that part of the plasma immediately downstream of the reverse shock of Cas A is emitting X-ray synchrotron radiation (Helder and Vink 2008; Uchiyama and Aharonian 2008). The implication is also that the bright radio shell of this remnant has electron populations likely accelerated by the reverse shock. Cas A is rather unique in this sense, perhaps because the reverse shock has an inward motion on the western side of Cas A (Sato et al. 2018; Vink et al. 2022a), which makes for a head-on collision between the inward motion of the reverse shock and expanding unshocked ejecta. However, for a few other SNRs, synchrotron emission from the reverse shock has also been suggested, such as G1.8+0.9 (Brose et al. 2019), RCW 86/SN 185 (Rho et al. 2002), and possibly RX J1713.7-3946 (Zirakashvili and Aharonian 2010).

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GeV-TeV Gamma Rays The first firm detection of gamma rays from the shells of SNRs was in 2004 by the atmospheric Cherenkov gamma-ray telescope H.E.S.S. (Aharonian et al. 2004) in the very-high-energy (VHE) gamma-ray band (Fig. 2). Later, Fermi detected several SNRs in the high-energy (HE) – or GeV – band. Currently more than 30 SNRs are detected in the GeV and/or VHE gamma-ray bands (Acero et al. 2016). In the HE and VHE bands, there are mainly two emission mechanisms from accelerated particles, inverse Compton scattering and π 0 decay emission (Section “Radiation from Leptonic and Hadronic Cosmic Rays”). Distinguishing between the leptonic (inverse Compton) and hadronic scenarios (π 0 decay) is mainly done with HE band spectra, since a simple leptonic scenario reproduces hard gamma-ray emission with photon index Γ ≈ 1.6 as described in Section “Radiation from Leptonic and Hadronic Cosmic Rays”, whereas the hadronic scenario requires rather flat spectra (Γ ≈ 2.2) with the low-energy cutoff around 100 MeV (the pion bump, Section “Pion Production and Decay”). A typical case for the leptonic scenario is SN 1006 (Acero et al. 2010), and for the hadronic scenario, W44 provide a good example (Abdo et al. 2010a; Giuliani et al. 2011). On the other hand, there are both leptonic and hadronic components in many SNR cases, and it makes difficult to resolve them. Molecular or atomic cloud

Fig. 2 TeV image of the supernova remnant RX J1713−3946 taken by H.E.S.S. (Aharonian et al. 2004)

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Fig. 3 Spectral energy diagram (SED) showing the spectral characteristics of various SNRs that are bright in gamma rays. Most of these SNRs have a spectral index around Γ ≈ 2 below 0.1 TeV, but an exception is RX J1713−3946. The relatively old SNR Puppis A shows a cutoff around 0.1 TeV, but the other SNRs have spectra steepening above ∼1 TeV. (Figure reproduced from H.E.S.S. Collaboration 2021)

observations are another key, since we can measure the density and total amount of target protons. RX J1713−3946, due its gamma-ray brightness a key target to study particle acceleration, shows a similar morphology in VHE gamma rays and proton column density, which is a strong evidence of hadronic origin (Fukui et al. 2012). However, its rather hard gamma-ray spectrum – Γ ≈ 1.5 (Abdo et al. 2011; H.E.S.S. Collaboration et al. 2018) – suggests a leptonic origin (Ellison et al. 2012), although more complex multi-zone hadronic models, which include dense clumps, can fit the spectrum as well (Inoue et al. 2012; Gabici and Aharonian 2014). See Fig. 3 for a comparison of several gamma-ray luminous SNRs. The future Cherenkov Telescope Array (CTA) will provide VHE gamma-ray maps of fainter SNRs with better spatial resolution and sensitivity. Comparing them with those in synchrotron X-rays (as the electron tracer) and proton column density, more detailed study will be available on leptonic and hadronic components (Acero et al. 2017). In addition, we may be able to observe haloes around SNRs from cosmic rays that have escape the vicinity of the SNR shocks.

Measurements of the Cosmic-Ray Acceleration Efficiency The total fraction of the supernova explosion energy that is transferred to cosmic rays is still an open issue. To explain the Galactic cosmic-ray energy budget,

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Fig. 4 Chandra view of SN1006. White and thin rim represents synchrotron X-rays, whereas red inside thermal plasma. (Credit: NASA/CXC/Middlebury College/F.Winkler)

5%–10% of the canonical 1051 erg explosion energy has to be channeled to hadronic cosmic rays. The first evidence for efficient electron acceleration comes from Chandra X-ray observations. Chandra discovered that synchrotron X-ray emission is confined to thin filaments – 1017 –5 × 1017 cm – near the shocks of young SNRs, such as Cas A and SN1006 as shown in Fig. 4 (Vink and Laming 2003; Bamba et al. 2003, 2005). Thin filaments imply that electrons are trapped near the shock fronts during a radiative loss timescale, due to strong and turbulent magnetic fields. The strong magnetic-field turbulence is probably a result of the interaction of cosmic rays with the plasma in the cosmic-ray shock precursor, as described in Section “Nonlinear Cosmic-Ray Acceleration”. So the magnetic fields are both an ingredient for and a result of efficient cosmic-ray acceleration. Chandra also discovered that some synchrotron filaments and knots are time variable with the timescale of ∼1 yr (Uchiyama et al. 2007; Uchiyama and Aharonian 2008; Okuno et al. 2020; Matsuda et al. 2020). The flux decline implies fast synchrotron losses, which also implies fast acceleration, in order for the electrons to reach these high energy in the presence of strong radiative losses. The expected magnetic-field strengths are up to a few 100 µG, although there is still many uncertainty on the topology of the magnetic fields. Efficient (nonlinear) acceleration results in deviation of the particle spectrum from a pure power law (Section “Nonlinear Cosmic-Ray Acceleration”), which should be reflected in thethe wide-band synchrotron spectrum. Vink et al. (2006) measured a spectral bending of the broad, radio-to-X-ray, synchrotron spectrum of the young SNR RCW 86, which implies that the acceleration in this SNR is efficient. Similar effects have been reported for SN1006 and Cas A (Allen et al. 2008; Domˇcek et al. 2021), which suggests that the efficient acceleration of electrons is common in young SNRs.

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The efficiency of hadronic cosmic-ray acceleration cannot be measured directly with X-rays. As discussed in Section “Pion Production and Decay”, protons interacting with the interstellar medium emit ∼GeV gamma-rays via pion decay. Thus, the luminosity in the gamma-ray band reflects the total energy of accelerated protons, although inverse Compton emission from accelerated electrons contaminates in some cases. Typical luminosities in the gamma-ray band are roughly 1033 –1036 erg s−1 (Acero et al. 2016), and the expected proton energy content is ∼1049 –1050 ergs, 1%–10% of the 1051 erg explosion energy. One of the most luminous SNRs in the GeV and TeV band is N 132D in the Large Magellanic Cloud (Ackermann et al. 2016; H.E.S.S. Collaboration et al. 2015), implying N 132D is one of the most efficient proton accelerators. Given the absence of synchrotron X-ray emission (Bamba et al. 2018) and the broadband spectral shape, the GeVTeV gamma-ray emission is best explained with a hadronic gamma-ray model, with an inferred energy in cosmic-ray protons of ∼1050 erg, which is 10% of the canonical SN explosion energy (Bamba et al. 2018; H.E.S.S. Collaboration 2021). This implies that N 132D is an efficient accelerator and/or the explosion energy is larger than 1051 erg.

Evidence or Lack of Evidence for PeVatrons Up to now there is no evidence that some SNRs are PeVatrons. The current maximum energy of accelerated particles can be estimated from the cutoff of gamma-ray emission. Considering particle escape, younger SNRs should have higher cutoff. Acero et al. (2016) showed that younger SNRs have harder emission in the GeV band (Figure 16 in Acero et al. 2016), although the scatter is very large. One of the youngest (∼2000 years old) and brightest gamma-ray SNRs, RX J1713.7−3946, has the cutoff of 3–17 TeV depending on the cutoff models (H.E.S.S. Collaboration et al. 2018). This leads the cutoff of proton energy of less than 100 TeV, indicating that RX J1713.7−3946 does not contain PeV protons, but it may have contained them in the past. The TeV gamma-ray emission extends significantly beyond the synchrotron X-ray emitting shell, implying that protons start escaping from the acceleration site, whereas electrons emitting synchrotron X-ray cannot escape due to the synchrotron cooling. Thus, we need even younger samples. Cas A is the best target with ∼400 years old, which is also bright in gamma rays. The spectral break is ∼0.2–3 TeV depending on the observations and spectral models (Ahnen et al. 2017; Abeysekara et al. 2020) – implying that Cas A does not contribute cosmic rays in the PeV range. Even younger samples, G1.9+0.3 (∼100 years old, Reynolds et al. 2008) or SN 1987A (∼40 years old), are too distant to detect high-energy gamma-rays with the present very high-energy gamma-ray telescopes. Future observations may conclude this problem with these objects. Interestingly, the aforementioned efficient accelerator, N 132D, shows no evidence for a break in its VHE gamma-ray spectrum – at least up to 8 TeV (H.E.S.S. Collaboration 2021) – implying a proton cutoff energy above 45 TeV; see the SED

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of N132D in Fig. 3. This is quite remarkable as N 132D is much older (2500 yr) than Cas A, which has a cutoff below 3 TeV. It is, therefore, likely that other than age, there are other factors determining the maximum acceleration energy, and subsequent escape of these highest energy cosmic rays. It has long been argued that the highest energy Galactic cosmic rays may come from a subset of SNRs, those interacting with the dense winds of their progenitors, and that the maximum energy is reached within a few years after the SN explosion (Ptuskin and Zirakashvili 2003; Cardillo et al. 2015; Marcowith et al. 2018). At the same time, there is evidence based on the cosmic-ray spectrum itself that protons may already deviate from a power-law distribution well before the “knee” (Lipari and Vernetto 2020). This could indicate that only a subset of SNe/SNRs are capable of accelerating up to the “knee.” Galactic PeVatrons do exist, as evidenced by the detection of PeV photons from Galactic plane regions by LHAASO (Aharonian et al. 2021). One of the PeVatrons is the Crab Nebula, likely a leptonic cosmic-ray source. Other PeVatrons are associated with star forming regions, but the LHAASO angular resolution is too low to identify individual sources within them. Alternatively, collective effects from fast stellar winds and SNe could create an environment sustained acceleration within superbubbles, i.e., the highly energetic, high pressure regions created by the collective effects of SN explosions and fast stellar winds. Superbubble acceleration provides an alternative model for the origin of PeV cosmic rays (Bykov and Fleishman 1992; Parizot et al. 2004).

Evidence for Low-Energy Cosmic Rays Synchrotron, inverse Compton, and pion decay emissions origin from particles accelerated well into the relativistic regime. On the other hand, there is only a little observation evidence for the low-energy particles that have just been injected into the DSA process. Nevertheless, these low-energy cosmic rays may be important for the overall nonthermal energy budget of SNRs. Low-energy protons with energies around ∼MeV interact with neutral iron in the interstellar medium and result in characteristic X-ray line emission at 6.4 keV (Lodders 2003; Dogiel et al. 2011; Tatischeff et al. 2012). Thus, 6.4 keV line emission should be a good indicator of ∼MeV protons, although the expected surface brightness is very low. XIS onboard Suzaku has a low and stable background level, and discovered the 6.4 keV line from shock-cloud interacting regions of several SNRs (Nobukawa et al. 2015, 2018; Bamba et al. 2018), which is the first observational clue for sub-relativistic protons. The proton energy density is estimated to be ≥10–100 eV cm−3 , which is more than ten times higher than that in the ambient interstellar medium. Electrons just injected have suprathermal energies. In the case that their density is high enough, they emit nonthermal bremsstrahlung in the hard X-ray band (Section “Nonthermal Bremsstrahlung”). W49B is the only target from which

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nonthermal bremsstrahlung from suprathermal electrons have been found (Tanaka et al. 2018), which is the first clue of electrons that have just been injected into the DSA process. More samples with better statistics will be needed to compare to cosmic-ray injection theories.

Cosmic-Ray Escape from Acceleration Sites Accelerated particles should escape from the shock front in order to become Galactic cosmic rays. Recent observations revealed some clues for particle escape. Accelerated electrons are trapped in the shock region; thus, synchrotron X-rays are a good indicator of the shock front. H.E.S.S. found that the VHE gamma rays in one region of RX J1713−3946 are also emitted from a region significantly outside the shock, as marked synchrotron X-rays (H.E.S.S. Collaboration et al. 2018), implying that the detected cosmic rays have already started to escape from the shock. GeV spectra of middle-aged SNRs are rather soft with the cutoff of around 10 GeV (Abdo et al. 2010a), which is much smaller than the “knee” energy. This is because that higher energy particles have already escaped from the acceleration site. The cutoff energy becomes smaller as SNRs ages older (Acero et al. 2016; Zeng et al. 2019; Suzuki et al. 2020). This means that particles with higher energies escape the shock earlier and low-energy particles still remain close to the acceleration sites. Among the bright GeV SNRs is the mixed-morphology SNR W28. This SNR is also detected in VHE gamma rays, but one of the surprises is that two VHE sources are not coincident with the SNR, but with nearby molecular clouds (Aharonian et al. 2008), which suggests that these clouds are illuminated by hadronic cosmic rays which escaped the SNR. Particles after the escape diffuse into the interstellar medium. When they encounter dense material, they emit gamma rays via π 0 decay. Such gamma-ray emitting clouds are found in the vicinity of several SNRs (Abdo et al. 2010b; Uchiyama et al. 2012).

Polarimetry and Magnetic-Field Turbulence and Topology As described in Section “The Effects of Radiative Losses and Cosmic-Ray Escape on the Maximum Energy”, the emission of X-ray synchrotron by young SNRs requires a turbulent magnetic field in the unshocked medium; see Eq. 24. Indeed, radio polarimetric observations of young SNRs show a low polarization fraction of 5–10% (Dickel and Jones 1990). Another characteristic of young SNRs, as revealed by radio polarimetry, is that the magnetic-field topology shows a preferentially radial direction of the magnetic field, whereas older SNRs show a preferentially tangential magnetic-field orientation (Milne and Dickel 1975). The latter can be easily understood, as shock compression of the magnetic field enhances the tangential component.

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The radial magnetic-field orientation is not well understood, but most theories invoke radial stretching of magnetic fields due to hydrodynamical instabilities such as Rayleigh-Taylor instabilities at the SNR contact discontinuity (Gull 1973; Jun and Norman 1996), or Richtmyer-Meshkov instabilities (Inoue et al. 2013) near the forward shock. The former should result in radial magnetic field further away from the shock front. Alternatively, the radial magnetic-field orientation may be an artifact of the acceleration process, if electrons are preferentially accelerated wherever the magnetic field is parallel to the shock normal, biasing the polarization measurements to certain pockets of plasma with a radial magnetic-field direction (West et al. 2017). Up to now, these polarimetric measurements were confined to radio synchrotron radiation, and a few cases in the infrared (e.g., Jones et al. 2003). With the launch of the NASA/ASI Imaging X-ray Polarimetric Explorer (IXPE Weisskopf et al. 2022), the magnetic-field topology in young SNRs can also be explored in X-rays. This is of interest because, as we explained above, X-ray synchrotron emission comes from a region very close to the shock front. Moreover, magnetic-field turbulence on a long length scale could leave pockets of plasma with a particular polarization mode, and a high (up to 40%) polarization fraction (Bykov et al. 2020). However, the presence of these high polarized regions depends on the spectrum of magnetic-field turbulence, and whether close to the shock the compression imparted a preferred magnetic-field orientation. At the time of this writing, observations of only one SNR, Cas A, have been reported (Vink et al. 2022b). Surprisingly, it shows a polarization fraction as low, or even lower, as in the radio (4%), and an overall radial magnetic-field structure. The latter implies that whatever is responsible for the overall radially oriented magneticfield structure in Cas A must already have created this pattern within the ∼1017 cm wide X-ray synchrotron rims. Planned, future observations by IXPE of other SNRs will tell whether Cas A is peculiar, or whether these findings also apply to Tycho’s SNR and SN 1006.

Concluding Remarks In this chapter, we introduced the basic X-ray and gamma-ray radiation processes related to the nonthermal particle distributions (i.e., cosmic rays) in SNRs. SNRs are the most plausibly the dominant sources of Galactic cosmic rays, from an energy budget point of view, but, as we showed, SNRs also show ample observational evidence for being sites of cosmic-ray acceleration, based on radio, X-ray, and gamma-ray observations. As we have shown, only gamma-ray radiation can be used to directly probe the hadronic cosmic-ray populations inside SNRs. On the other hand, X-ray synchrotron emission from electrons (leptonic cosmic rays) provides unequivocal proof that SNR shocks are the sites of active cosmic-ray acceleration. Despite the overwhelming evidence for cosmic-ray acceleration by SNRs, there is no evidence yet that SNRs are accelerating cosmic rays up to, or beyond, the

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“knee” at 3 × 1015 eV. In other words, SNRs do not seem to be PeVatrons. The highest energy cosmic rays leave SNRs, while SNRs are still relatively young (2000 yr), as is also evidence by gamma-ray observations. But even young SNRs contain cosmic-ray particles only with energies below ∼100 TeV. The escape of the highest energy particles at a young age suggests that perhaps the highest energy Galactic cosmic rays originate from the very early stages of SNR development, from a subset of SNRs. On the other hand, competing theories are that stellar superbubbles, or pulsars, are responsible for the acceleration of particles up to, or beyond, the “knee.” SNRs are still an important, or even dominant, contributor to the energization of superbubbles, but the highly turbulent plasma in superbubbles, confining cosmic rays for millions of years, may be a site for further acceleration of seed cosmic-ray particles originating from SNRs and colliding stellar winds. On the other hand, recent studies of the cosmic-ray spectrum at Earth itself suggest that the composition and spectral shape of the cosmic-ray spectrum around the “knee” is more complex than was assumed until recently, leaving room for cosmic-ray contributions from a mix of SNRs and other (related?) sources. A number of new X-ray and gamma-ray observing facilities will likely shed further light on the cosmic-ray acceleration properties of SNRs, their cosmic-ray energy budgets, and the role of SNRs in acceleration particles up to the “knee.” The recently launched IXPE satellite is carrying out a program to measure the polarization signatures of X-ray synchrotron radiation, which will inform us on the magnetic-field turbulence and magnetic-field topology near SNR shocks, both of which are important ingredients for the DSA process. XRISM (Tashiro et al. 2020) (to be launched in 2023) and Athena (Barret et al. 2018) (to be launched beyond 2032) will employ X-ray micro-calorimeters with high spectral resolution, which will enable us to precisely measure the plasma conditions (electron and ion temperatures) in the downstream regions of shock, which will lead to a better understanding of the energy fraction transferred to accelerated particles instead of to the heating of the plasma. Future gamma-ray facilities such as the next-generation imaging atmospheric telescope array CTA (Cherenkov Telescope Array Consortium et al. 2019) (operational sometime around 2027), and the water Cherenkov telescope LHAASO (di Sciascio and Lhaaso Collaboration 2016), will be able to make deeper probes of the gamma-ray source populations in the Milky Way and the Magellanic Clouds. LHAASO, which is already partially completed, is in particular very sensitive above 100 TeV, which is excellently suited to find Galactic PeVatrons. The first detections (Aharonian et al. 2021) show the association of the highest energy gamma-ray photons with pulsars and star forming regions. It is still being debated whether the pulsars are purely leptonic cosmic-ray sources, or also sites hadronic acceleration. As for the starforming regions, here LHAASO lacks the angular resolution to determine whether the region as a whole is a PeVatron – in accordance with the superbubble theory about the origin of cosmic rays – or whether there are PeVatrons located in these regions, which could include SNRs. CTA is a pointed observatory, and will be sensitive to photon energies of ∼200 TeV, but with an angular resolution of 1–3′ above 1 TeV. So it will be excellently suited to pinpoint the sources of

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hadronic cosmic rays, even in crowded starforming regions. Moreover, its large effective area is also well suited for transient gamma-ray sources, which can be used to search for gamma-ray emission from nearby extragalactic supernovae up to a year after explosion (c.f. H.E.S.S. Collaboration et al. 2019).

References A.A. Abdo et al., Fermi-lat discovery of GeV gamma-ray emission from the young supernova remnant Cassiopeia A. ApJ 710, L92–L97 (2010a) A.A. Abdo et al., Fermi large area telescope observations of the supernova remnant W28 (G6.40.1). ApJ 718(1), 348–356 (2010b) A.A. Abdo et al., Observations of the young supernova remnant RX J1713.7-3946 with the fermi large area telescope. ApJ 734(1), 28 (2011) A.U. Abeysekara et al., Evidence for proton acceleration up to TeV energies based on VERITAS and fermi-LAT observations of the Cas A SNR. ApJ 894(1), 51 (2020) F. Acero et al. (H.E.S.S. Collaboration), First detection of VHE γ -rays from SN 1006 by HESS. A&A 516, A62 (2010) F. Acero et al., The first fermi LAT supernova remnant catalog. ApJS 224, 8 (2016) F. Acero et al., Prospects for Cherenkov telescope array observations of the young supernova remnant RX J1713.7-3946. ApJ 840(2), 74 (2017) M. Ackermann et al., Deep view of the Large Magellanic Cloud with six years of Fermi-LAT observations. A&A 586, A71 (2016) F.A. Aharonian, A.M. Atoyan, On the origin of TeV radiation of SN 1006. A&A 351, 330–340 (1999) A. Aharonian, F. Akhperjanian, J. Barrio et al., Evidence for TeV gamma ray emission from Cassiopeia A. A&A 370, 112–120 (2001) F.A. Aharonian et al., High-energy particle acceleration in the shell of a supernova remnant. Nature 432, 75–77 (2004) F. Aharonian et al., Discovery of very high energy gamma-ray emission coincident with molecular clouds in the W 28 (G6.4-0.1) field. A&A 481, 401–410 (2008) F.A. Aharonian, Q. An, Z. Cao et al., Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 gamma-ray Galactic sources. Nature 594, 33–36 (2021) M.L. Ahnen et al., A cut-off in the TeV gamma-ray spectrum of the SNR Cassiopeia A. MNRAS 472(3), 2956–2962 (2017) G.E. Allen et al., Evidence of X-ray synchrotron emission from electrons accelerated to 40 TeV in the supernova remnant Cassiopeia A. ApJ 487, L97–L100 (1997) G.E. Allen, J.C. Houck, S.J. Sturner, Evidence of a curved synchrotron spectrum in the supernova remnant SN 1006. ApJ 683, 773–785 (2008) W.D. Apel, J.C. Arteaga-Velázquez, K. Bekk, M. Bertaina, J. Blümer et al., Kneelike structure in the spectrum of the heavy component of cosmic rays observed with KASCADE-Grande. Phys. Rev. Lett. 107(17), 171104 (2011) A.I. Asvarov, O.H. Guseinov, F.K. Kasumov, V.A. Dogel’, The hard X-ray emission of the young supernova remnants. A&A 229, 196–200 (1990) W.I. Axford, E. Leer, G. Skadron, The acceleration of cosmic rays by shock waves, in International Cosmic Ray Conference, vol. 11 (1977), pp. 132–+ W. Baade, F. Zwicky, Cosmic rays from super-novae. Proc. Natl. Acad. Sci. 20(5), 259–263 (1934) A. Bamba, K. Koyama, H. Tomida, Discovery of non-thermal X-rays from the shell of RCW 86. PASJ 52, 1157–1163 (2000) A. Bamba, M. Ueno, K. Koyama, S. Yamauchi, A diffuse X-ray source, AX J1843.8-0352: association with the radio complex G28.6-0.1 and identification of a new supernova remnant. PASJ 53(4), L21–L24 (2001)

3526

J. Vink and A. Bamba

A. Bamba, R. Yamazaki, M. Ueno, K. Koyama, Small-scale structure of the SN 1006 shock with Chandra observations. ApJ 589, 827–837 (2003) A. Bamba, R. Yamazaki, T. Yoshida, T. Terasawa, K. Koyama, A spatial and spectral study of nonthermal filaments in historical supernova remnants: observational results with Chandra. ApJ 621, 793–802 (2005) A. Bamba, Y. Fukazawa, J.S. Hiraga, J.P. Hughes, H. Katagiri et al., Suzaku wide-band observations of SN1006. PASJ 60, S153–S162 (2008) A. Bamba, G. Pühlhofer, F. Acero, D. Klochkov, W. Tian, R. Yamazaki, Z. Li, D. Horns, K. Kosack, N. Komin, Suzaku observations of the non-thermal supernova remnant HESS J1731-347. ApJ 756, 149 (2012) A. Bamba, Y. Ohira, R. Yamazaki, M. Sawada, Y. Terada et al., The transition from young to middle-aged supernova remnants: thermal and nonthermal aspects of SNR N132D. ApJ 854(1), 71 (2018) D. Barret, T. Lam Trong, J.-W. den Herder, L. Piro, M. Cappi, J. Houvelin, R. Kelley et al., The ATHENA X-ray integral field unit (X-IFU), in Space Telescopes and Instrumentation 2018: Ultraviolet to Gamma Ray, ed. by J.-W.A. den Herder, S. Nikzad, K. Nakazawa. Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 10699 (2018), p. 106991G A.R. Bell, The acceleration of cosmic rays in shock fronts. I. MNRAS 182, 147–156 (1978) A.R. Bell, Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays. MNRAS 353, 550–558 (2004) W.R. Binns, M.E. Wiedenbeck, M. Arnould, A.C. Cummings, J.S. George, S. Goriely, M.H. Israel, R.A. Leske, R.A. Mewaldt, G. Meynet, L.M. Scott, E.C. Stone, T.T. von Rosenvinge, Cosmicray neon, wolf-rayet stars, and the superbubble origin of galactic cosmic rays. ApJ 634, 351–364 (2005) R.D. Blandford, J.P. Ostriker, Particle acceleration by astrophysical shocks. ApJ 221, L29–L32 (1978) P. Blasi, S. Gabici, G. Vannoni, On the role of injection in kinetic approaches to non-linear particle acceleration at non-relativistic shock waves. MNRAS 361, 907–918 (2005) R. Brose, I. Sushch, M. Pohl, K.J. Luken, M.D. Filipovi´c, R. Lin, Nonthermal emission from the reverse shock of the youngest Galactic supernova remnant G1.9+0.3. A&A 627, A166 (2019) A.M. Bykov, G.D. Fleishman, On non-thermal particle generation in superbubbles. MNRAS 255, 269–275 (1992) A.M. Bykov, Y.A. Uvarov, P. Slane, D.C. Ellison, Uncovering magnetic turbulence in young supernova remnants with polarized X-ray imaging. ApJ 899(2), 142 (2020) D. Caprioli, A. Spitkovsky, Simulations of ion acceleration at non-relativistic shocks. I. Acceleration efficiency. ApJ 783(2), 91 (2014) D. Caprioli, A.-R. Pop, A. Spitkovsky, Simulations and theory of ion injection at non-relativistic collisionless shocks. ApJ 798, L28 (2015) M. Cardillo, E. Amato, P. Blasi, On the cosmic ray spectrum from type II supernovae expanding in their red giant presupernova wind. Astropart. Phys. 69, 1–10 (2015) Cherenkov Telescope Array Consortium, B.S. Acharya et al., Science with the Cherenkov Telescope Array (2019) J.R. Dickel, E.M. Jones, Magnetic fields in young supernova remnants, in Galactic and Intergalactic Magnetic Fields, ed. by R. Beck, R. Wielebinski, P.P. Kronberg. IAU Symposium, vol. 140 (1990), p. 81 G. di Sciascio, Lhaaso Collaboration, The LHAASO experiment: from gamma-ray astronomy to cosmic rays. Nucl. Part. Phys. Proc. 279–281, 166–173 (2016) V. Dogiel, D. Chernyshov, K. Koyama, M. Nobukawa, K.-S. Cheng, K-shell emission of neutral iron line from sagittarius B2 excited by subrelativistic protons. PASJ 63, 535 (2011) V. Domˇcek, J. Vink, J.V. Hernández Santisteban, T. DeLaney, P. Zhou, Mapping the spectral index of Cassiopeia A: evidence for flattening from radio to infrared. MNRAS 502(1), 1026–1040 (2021)

101 Nonthermal Processes and Particle Acceleration in Supernova Remnants

3527

L.O. Drury, An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas. Rep. Progress Phys. 46, 973–1027 (1983) G. Dubner, E. Giacani, Radio emission from supernova remnants. A&A Rev. 23, 3 (2015) D. Eichler, Particle acceleration in collisionless shocks – regulated injection and high efficiency. ApJ 229, 419–423 (1979) D.C. Ellison, E.G. Berezhko, M.G. Baring, Nonlinear shock acceleration and photon emission in supernova remnants. ApJ 540(1), 292–307 (2000) D.C. Ellison, P. Slane, D.J. Patnaude, A.M. Bykov, Core-collapse model of broadband emission from SNR RX J1713.7-3946 with thermal X-rays and gamma rays from escaping cosmic rays. ApJ 744(1), 39 (2012) J.A. Esposito, S.D. Hunter, G. Kanbach, P. Sreekumar, EGRET observations of radio-bright supernova remnants. ApJ 461, 820–+ (1996) F. Favata et al., The broad-band X-ray spectrum of the Cas A supernova remnant as seen by the BeppoSAX observatory. A&A 324, L49–L52 (1997) Y. Fukui, H. Sano, J. Sato, K. Torii, H. Horachi et al., A detailed study of the molecular and atomic gas toward the γ -ray supernova remnant RX J1713.7-3946: spatial TeV γ -ray and interstellar medium gas correspondence. ApJ 746, 82 (2012) S. Gabici, F.A. Aharonian, Hadronic gamma-rays from RX J1713.7-3946? MNRAS 445, L70–L73 (2014) A. Giuliani, M. Cardillo, M. Tavani, Y. Fukui, S. Yoshiike et al., Neutral pion emission from accelerated protons in the supernova remnant W44. ApJ 742, L30 (2011) D.A. Green, Constraints on the distribution of supernova remnants with Galactocentric radius. MNRAS 454, 1517–1524 (2015) D.A. Green, A revised catalogue of 294 Galactic supernova remnants. J. Astrophys. Astron. 40(4), 36 (2019) B.W. Grefenstette et al., Locating the most energetic electrons in Cassiopeia A. ApJ 802, 15 (2015) S.F. Gull, A numerical model of the structure and evolution of young supernovaremnants. MNRAS 161, 47–69 (1973) E.A. Helder, J. Vink, Characterizing the nonthermal emission of Cassiopeia A. ApJ 686, 1094– 1102 (2008) V.F. Hess, Über ber Beobachtungen der durchdringenden Strahlung bei sieben Freiballonfahrten. Physik. Zeitschr. 13, 1084 (1912) H.E.S.S. Collaboration, H. Abdalla et al., LMC N132D: A mature supernova remnant with a power-law spectrum extending beyond 8 TeV, A&A 655, 7 (2021) H.E.S.S. Collaboration, A. Abramowski et al., The exceptionally powerful TeV γ -ray emitters in the Large Magellanic Cloud. Science 347(6220), 406–412 (2015) H.E.S.S. Collaboration, H. Abdalla et al., H.E.S.S. observations of RX J1713.7-3946 with improved angular and spectral resolution: evidence for gamma-ray emission extending beyond the X-ray emitting shell. A&A 612, A6 (2018) H.E.S.S. Collaboration, H. Abdalla et al., Upper limits on very-high-energy gamma-ray emission from core-collapse supernovae observed with H.E.S.S. A&A 626, A57 (2019) J.A. Hinton, W. Hofmann, Teraelectronvolt astronomy. ARAA 47, 523–565 (2009) T. Inoue, R. Yamazaki, S.-I. Inutsuka, Y. Fukui, Toward understanding the cosmic-ray acceleration at young supernova remnants interacting with interstellar clouds: possible applications to RX J1713.7-3946. ApJ 744, 71 (2012) T. Inoue, J. Shimoda, Y. Ohira, R. Yamazaki, The origin of radially aligned magnetic fields in young supernova remnants. ApJ 772(2), L20 (2013) T.J. Jones, L. Rudnick, T. DeLaney, J. Bowden, The identification of infrared synchrotron radiation from Cassiopeia A. ApJ 587, 227 (2003) B.-I. Jun, M.L. Norman, On the origin of radial magnetic fields in young supernova remnants. ApJ 472, 245–+ (1996) E. Kafexhiu, F. Aharonian, A.M. Taylor, G.S. Vila, Parametrization of gamma-ray production cross sections for pp interactions in a broad proton energy range from the kinematic threshold to PeV energies. Phys. Rev. D 90(12), 123014 (2014)

3528

J. Vink and A. Bamba

K. Koyama et al., Evidence for shock acceleration of high-energy electrons in the supernova remnant SN 1006. Nature 378, 255–+ (1995) K. Koyama, K. Kinugasa, K. Matsuzaki, M. Nishiuchi, M. Sugizaki, K. Torii, S. Yamauchi, B. Aschenbach, Discovery of non-thermal X-rays from the northwest shell of the new SNR RX J1713.7-3946. PASJ 49, L7–L11 (1997) G.F. Krymskii, A regular mechanism for the acceleration of charged particles on the front of a shock wave. Akademiia Nauk SSSR Doklady 234, 1306–1308 (1977) P.O. Lagage, C.J. Cesarsky, The maximum energy of cosmic rays accelerated by supernova shocks. A&A 125, 249–257 (1983) J.M. Laming, Accelerated electrons in Cassiopeia A: an explanation for the hard X-ray tail. ApJ 546, 1149–1158 (2001) P. Lipari, S. Vernetto, The shape of the cosmic ray proton spectrum. Astropart. Phys. 120, 102441 (2020) K. Lodders, Solar system abundances and condensation temperatures of the elements. ApJ 591(2), 1220–1247 (2003) L.A. Lopez et al., A spatially resolved study of the synchrotron emission and titanium in Tycho’s supernova remnant using NuSTAR. ApJ 814, 132 (2015 M.A. Malkov, L. Drury, Nonlinear theory of diffusive acceleration of particles by shock waves . Rep. Prog. Phys. 64, 429–481 (2001) A. Marcowith, V.V. Dwarkadas, M. Renaud, V. Tatischeff, G. Giacinti, Core-collapse supernovae as cosmic ray sources. MNRAS 479(4), 4470–4485 (2018) M. Matsuda, T. Tanaka, H. Uchida, Y. Amano, T.G. Tsuru, Temporal and spatial variation of synchrotron X-ray stripes in Tycho’s supernova remnant. PASJ 72(5), 85 (2020) J.-P. Meyer, L.O. Drury, D.C. Ellison, Galactic cosmic rays from supernova remnants. I. A cosmicray composition controlled by volatility and mass-to-charge ratio. ApJ 487, 182–196 (1997) D.K. Milne, J.R. Dickel, 5 GHz polarization observations of 33 galactic radio sources. Aust. J. Phys. 28, 209–230 (1975) S. Nikoli´c, G. van de Ven, K. Heng, D. Kupko, B. Husemann, J.C. Raymond, J.P. Hughes, J. Falcón-Barroso, An integral view of fast shocks around supernova 1006. Science 340, 45–48 (2013) K.K. Nobukawa, M. Nobukawa, H. Uchiyama, T.G. Tsuru, K. Torii, T. Tanaka, D.O. Chernyshov, Y. Fukui, V.A. Dogiel, K. Koyama, Enhancement of the 6.4 keV line in the inner galactic ridge: proton-induced fluorescence? ApJ 807(1), L10 (2015) K.K. Nobukawa, M. Nobukawa, K. Koyama, S. Yamauchi, H. Uchiyama, H. Okon, T. Tanaka, H. Uchida, T.G. Tsuru, Evidence for a neutral iron line generated by MeV protons from supernova remnants interacting with molecular clouds. ApJ 854(2), 87 (2018) T. Okuno, T. Tanaka, H. Uchida, F.A. Aharonian, Y. Uchiyama, T.G. Tsuru, M. Matsuda, Time variability of nonthermal X-ray stripes in Tycho’s supernova remnant with Chandra. ApJ 894(1), 50 (2020) E. Parizot, A. Marcowith, E. van der Swaluw, A.M. Bykov, V. Tatischeff, Superbubbles and energetic particles in the Galaxy. I. Collective effects of particle acceleration. A&A 424, 747– 760 (2004) V.S. Ptuskin, V.N. Zirakashvili, Limits on diffusive shock acceleration in supernova remnants in the presence of cosmic-ray streaming instability and wave dissipation. A&A 403, 1–10 (2003) S.P. Reynolds, Models of synchrotron X-rays from shell supernova remnants. ApJ 493, 375–+ (1998) S.P. Reynolds, K.J. Borkowski, D.A. Green, U. Hwang, I. Harrus, R. Petre, The youngest galactic supernova remnant: G1.9+0.3. ApJ 680, L41–L44 (2008) J. Rho, K.K. Dyer, K.J. Borkowski, S.P. Reynolds, X-ray synchrotron-emitting Fe-rich ejecta in supernova remnant RCW 86. ApJ 581, 1116–1131 (2002) T. Sato, S. Katsuda, M. Morii et al., X-ray measurements of the particle acceleration properties at inward shocks in Cassiopeia A. ApJ 853(1), 46 (2018) J.S. Shklovsky, Supernovae as a Source of Cosmic Rays, in Liege International Astrophysical Colloquia, vol. 5. (1954), p. 515

101 Nonthermal Processes and Particle Acceleration in Supernova Remnants

3529

A.W. Strong, I.V. Moskalenko, V.S. Ptuskin, Cosmic-ray propagation and interactions in the galaxy. Annu. Rev. Nucl. Part. Sci. 57, 285–327 (2007) H. Suzuki, A. Bamba, R. Yamazaki, Y. Ohira, Study on the escape timescale of high-energy particles from supernova remnants through thermal X-ray properties. PASJ 72(5), 72 (2020) T. Tanaka, H. Yamaguchi, D.R. Wik, F.A. Aharonian, A. Bamba et al., NuSTAR detection of nonthermal bremsstrahlung from the supernova remnant W49B. ApJ 866(2), L26 (2018) M. Tashiro, H. Maejima, K. Toda, R. Kelley, L. Reichenthal et al., Status of x-ray imaging and spectroscopy mission (XRISM), in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 11444 (2020), p. 1144422 V. Tatischeff, A. Decourchelle, G. Maurin, Nonthermal X-rays from low-energy cosmic rays: application to the 6.4 keV line emission from the Arches cluster region. A&A 546, A88 (2012) L.-S. The et al., CGRO/OSSE observations of the Cassiopeia A SNR. A&AS 120, C357+ (1996) H. Tsunemi, E. Miyata, B. Aschenbach, Spectroscopic study of the Vela-Shrapnel. PASJ 51, 711–+ (1999) Y. Uchiyama, F.A. Aharonian, Fast variability of nonthermal X-ray emission in Cassiopeia A: probing electron acceleration in reverse-shocked ejecta. ApJ 677, L105–L108 (2008) Y. Uchiyama, F.A. Aharonian, T. Tanaka, T. Takahashi, Y. Maeda, Extremely fast acceleration of cosmic rays in a supernova remnant. Nature 449, 576–578 (2007) Y. Uchiyama, S. Funk, H. Katagiri, J. Katsuta, M. Lemoine-Goumard, H. Tajima, T. Tanaka, D.F. Torres, Fermi large area telescope discovery of GeV gamma-ray emission from the vicinity of SNR W44. ApJ 749(2), L35 (2012) J. Vink, Non-thermal bremsstrahlung from supernova remnants and the effect of Coulomb losses. A&A 486, 837–841 (2008) J. Vink, Physics and Evolution of Supernova Remnants. Astronomy and Astrophysics Library (Springer International Publishing, Springer Nature Switzerland (2020) J. Vink, J.M. Laming, On the magnetic fields and particle acceleration in Cassiopeia A. ApJ 584, 758–769 (2003) J. Vink, J. Bleeker, K. van der Heyden, A. Bykov, A. Bamba, R. Yamazaki, The X-ray synchrotron emission of RCW 86 and the implications for its age. ApJ 648, L33–L37 (2006) J. Vink, D.J. Patnaude, D. Castro, The forward and reverse shock dynamics of Cassiopeia A. ApJ 929(1), 57 (2022a) J. Vink, D. Prokhorov, R. Ferrazzoli, P. Slane, P. Zhou et al., X-ray polarization detection of Cassiopeia A with IXPE. ApJ, 938, 40 (2022) arXiv e-prints, arXiv:2206.06713 (2022b) A.E. Vladimirov, A.M. Bykov, D.C. Ellison, Turbulence dissipation and particle injection in nonlinear diffusive shock acceleration with magnetic field amplification. ApJ 688, 1084–1101 (2008) M.C. Weisskopf, P. Soffitta, L. Baldini, B.D. Ramsey, S.L. O’Dell et al., The imaging X-ray polarimetry explorer (IXPE): pre-launch. J. Astron. Telescopes Instrum. Syst. 8(2), 026002 (2022) J.L. West, T. Jaffe, G. Ferrand, S. Safi-Harb, B.M. Gaensler, When disorder looks like order: a new model to explain radial magnetic fields in young supernova remnants. ApJ 849, L22 (2017) H. Yamaguchi, M. Ueno, K. Koyama, A. Bamba, S. Yamauchi, XMM-newton observations of G32.45+0.1 and G38.55+0.0: diffuse hard X-ray sources found by the ASCA galactic plane survey. PASJ 56, 1059–1065 (2004) H. Zeng, Y. Xin, S. Liu, Evolution of high-energy particle distribution in supernova remnants. ApJ 874(1), 50 (2019) V.N. Zirakashvili, F.A. Aharonian, Nonthermal radiation of young supernova remnants: the case of RX J1713.7-3946. ApJ 708, 965–980 (2010)

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physical Description of a PWN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PWN Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observational Signatures and Notable PWNe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Infrared, Optical, and Ultraviolet . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma-Ray . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Young PWN: The Crab Nebula . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Stage 2”: Vela X . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Middle-Aged”: Geminga . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ultrahigh-Energy Gamma-Ray Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Recent Progress and Open Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . PWNe as PeVatrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . “Non-pulsar” Wind Nebulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Particle Transport (Diffusion and Advection) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A. M. W. Mitchell () Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen, Germany e-mail: [email protected] J. Gelfand NYU Abu Dhabi, Abu Dhabi, UAE e-mail: [email protected]; [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_157

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Abstract

Pulsar wind nebulae (PWNe), structures powered by energetic pulsars, are known for their detection across the entire electromagnetic spectrum, with diverse morphologies and spectral behavior between these bands. The temporal evolution of the morphology and spectrum of a PWN depends strongly on the properties of the associated neutron star, the relativistic outflow powered by its rotational energy, and surrounding medium, and thereby can vary markedly between objects. Due the continuous, but decreasing, injection of electrons and positrons into the PWN by the pulsar, the brightness and spectral variation within and among their wind nebulae reflect the magnetic field structure and particle transport within the PWN. This can include complex motions such as reverse flows or turbulence due to shock interactions and disruption to the nebula. During the last stage of the PWN’s evolution, when the neutron star moves supersonically with respect to its environment, the escape of accelerated particles into the surrounding medium creates an extensive halo evident in very-high-energy gamma-rays. This chapter describes some of the identifying characteristics and key aspects of pulsar wind nebulae through their several evolutionary stages. Keywords

Pulsar · Pulsar wind nebula · Acceleration · Magnetic field

Introduction Emission from pulsar wind nebulae (PWNe), the structures formed by the interaction between the highly relativistic outflow (“wind”) generated by a neutron star and the surrounding medium, has been detected across the electromagnetic spectrum – from the lowest-frequency ν  100 MHz radio waves (e.g., Driessen et al. 2018) to extremely high-energy γ -rays (photon energy Eγ ∼ 1015 eV; Lhaaso Collaboration et al. 2021). The detection of such high-energy photons from PWNe requires that particles are accelerated to at least PeV energies in these sources, and significant fraction of Galactic TeV sources associated with PWNe (e.g., Collaboration et al. 2018a, b) suggests these objects are an important source of cosmic ray leptons. However, the physical mechanisms responsible for producing these high-energy particles, and the physical conditions under which this acceleration occurs, remain unknown. This requires relating the observed properties of a PWN – e.g., its angular extent and broadband spectral energy distribution (SED) – to the physical properties of the emitting plasma. This entails understanding the evolution of a PWN, and the processes responsible for its emission described below. We first present a physical description of a PWN and then discuss how the properties of these sources are expected to evolve with time. We then describe the observed properties of PWNe in the framework of this physical description of their evolution and then discuss some of the open questions in this field.

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Physical Description of a PWN Even before their discovery, Pacini et al. (1968) speculated that neutron stars – the compact object created by the gravitational collapse of a massive star’s Fe core whose formation triggers a core-collapse supernova (e.g., Zwicky (1938) and reference thereafter) – were responsible for powering the sources now commonly referred to as PWN. (Historically, such sources were often referred to as “plerions” (Weiler and Panagia 1978; Weiler 1978), but usage of this term has diminished in recent years as our physical understanding of these objects has improved.) These neutron stars can often have extremely strong (B  1012 G) surface magnetic fields, whose field lines are anchored to locations on the neutron star’s outer crust. As a result, near the surface of the neutron star its magnetic field rotates with the same − → angular frequency ω, and around the same rotation axis Ω , as the neutron star’s surface. The co-rotation of the neutron star’s outer crust and magnetic field near the surface generates an extremely strong electric potential Φ along the magnetic poles, which creates a powerful current of charged particles (primarily electrons and positrons, e± , though ions are possibly an energetically important component as well; see Arons and Tavani (1994) for a review) who primarily travel along field lines in the magnetosphere (e.g., Goldreich and Julian (1969); see Fig. 1). Co-rotation with the neutron star surface at a distance R from the rotation axis − → Ω requires a speed vco−rot = ωR. Since particles and magnetic field lines cannot travel faster than the speed of light c, such co-rotation is only possible for distances where vco−rot < c, or R < RLC , where the radius of the light cylinder RLC is: RLC =

c . ω

(1)

Field lines which extend beyond R > RLC therefore can only be connected to the neutron star surface at one point and can extend R → ∞ far away. Particles produced along these “open” field lines will leave the magnetosphere, and the torque exerted on the neutron star surface, causing its rotational energy Erot to decrease with time. While the spin-down luminosity dEdtrot ≡ E˙ rot (t) of a pulsar is sensitive to the physical properties of its magnetosphere (e.g., Gruzinov 2005), it is typically approximated as (e.g., Goldreich and Julian 1969; Lorimer and Kramer 2012):   p+1 t − p−1 ˙ ˙ Erot (t) ≈ Erot,0 1 + τsd

(2)

where t is the age of the neutron star, E˙ rot,0 ≡ E˙ rot (t = 0) is its initial spin-down luminosity, τsd is the spin-down timescale for the neutron star, and p is the braking index, defined as ω˙ ∝ ωp . If the surface magnetic field of a pulsar is a pure dipole whose strength is constant with time (neither of which are true, e.g., Gruzinov 2005; Broderick and Narayan 2008), then E˙ rot can be associated with the magnetic dipole radiation of this field in which case:

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Fig. 1 Top: Schematic diagram of pulsar magnetosphere. (Reprinted with permission from Lorimer and Kramer 2012). Bottom: Schematic diagram of pulsar wind between light cylinder and termination shock. (Reprinted with permission from Mochol 2017; Sironi and Cerutti 2017)

• the braking index p ≡ 3, ˙ • the measured period P ≡ 2π ω and period-derivative P of the neutron star provide an estimate of its surface (dipolar) magnetic field strength Bsd (e.g., Lorimer and Kramer 2012; Condon and Ransom 2016 and references therein): Bsd = 3.2 × 1019



P P˙ G

(3)

as well as an approximation of its age, assuming an initial spin period P0 ≪ P , often referred to as the characteristic age tch (Lorimer and Kramer 2012; Condon and Ransom 2016):

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tch ≡

P P = . (p − 1)P˙ 2P˙

(4)

Under these assumptions, the spin-down timescale τsd and age t of the neutron star are related by: τsd =

2tch − t. p−1

(5)

When the plasma leaves the magnetosphere, it is initially in the form of a strongly magnetized (ratio of the magnetic to total power of this outflow ηB ≈ 1 or ratio of particle to magnetic power σ ≫ 1), equatorial wind composed of regions of alternating magnetic polarity, or “magnetic stripes” (Fig. 1; e.g., Coroniti 1990; Lyubarsky 2002; Mochol 2017; Sironi and Cerutti 2017 and references therein). The confinement of “pulsar wind” by the surrounding medium, whatever it may be, creates a “termination shock” (e.g., Kennel and Coroniti 1984; Slane 2017) where this initially highly relativistic (bulk Lorentz factors Γ0 ∼ 105 ), extremely low-pressure outflow is converted to a much lower (bulk) velocity, (relatively) high-pressure plasma. At this termination shock, a significant fraction of the initial magnetic energy of this wind is converted to the particle energy, such that the post-shock plasma is particle dominated (ηB ≪ 1, σ ∼ 1; e.g., Kennel and Coroniti 1984). While the physical mechanism responsible for this transformation is currently poorly understood, magnetic reconnection near the termination shock (e.g., Lyubarsky and Kirk 2001) and/or kink instabilities in the post-shock magnetic field (e.g., Porth et al. 2013) are believed to significantly contribute to this process. The dissipation of the magnetic energy of the pulsar wind will also accelerate particles to high energies. In addition to the “standard” Fermi acceleration mechanism thought to occur at strong shocks (e.g., Lu et al. 2021), magnetic reconnection at the termination shock is also expected to contribute significantly to the population of accelerated particles (e.g., Sironi and Spitkovsky 2011, 2014), with the maximum energy of these particles strongly depending on the properties (such as the width of magnetic stripes) and composition of the pre-shock wind (e.g., Arons 2012; Sironi et al. 2013; Lemoine et al. 2015). Measurements of the SED of PWNe suggest that the spectrum of particles accelerated at the termination shock, and injected into the PWN, is often well described by a broken power law (e.g., Bucciantini et al. 2011; Gelfand et al. 2015; Hattori et al. 2020; Tanaka and Takahara 2010, 2011; Torres et al. 2013 and references therein and citations thereafter): ⎧  −p1 E ⎨ ˙ ˙ N Emin ≤ E ≤ Ebreak break Ebreak dN −p2  = E ⎩ N˙ dE Ebreak ≤ E ≤ Emax break Ebreak

(6)

where typically p2 has a value comparable to that expected from Fermi acceleration at a strong shock (p2 ∼ 2.5; e.g., Berezhko and Ellison 1999; Keshet and

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Waxman 2005; Ellison et al. 2013, 2016), while p1 is often considerably smaller, with the harder particle spectrum injected at lower energies often interpreted as evidence for magnetic reconnection. While observational constraints on Emax are typically quite poor, for many PWNe, their SED suggests this quantity is of order ∼PeV (e.g., Bucciantini et al. 2011; Gelfand et al. 2015; Hattori et al. 2020; Kim and An 2020; Martín et al. 2012; Slane et al. 2012; Torres et al. 2013; Lhaaso Collaboration et al. 2021; Breuhaus et al. 2022; de Oña Wilhelmi et al. 2022). The content and emission from a PWN are dominated by this post-shock plasma. Since it is predominately composed of e± (particle creation or annihilation between the light cylinder and termination shock is thought to be negligible), the dominant emission mechanisms are synchrotron radiation from these leptons interacting with nebula’s magnetic field and the inverse Compton (IC) radiation from the interaction between these leptons and lower-energy photons. These lower-energy photons are believed to be dominated by external radiation fields – e.g., the cosmic microwave background (CMB), thermal emission from local dust, gas, and stars – with the synchrotron radiation from these leptons (which would result in synchrotron selfCompton or SSC emission) an important contributor for only the youngest, more energetic systems (e.g., Torres et al. 2013). Furthermore, the relativistic nature of this plasma means than it has a sound speed cs ≈ √c (Reynolds and Chevalier 3

1984) (for an adiabatic index γ = 43 ) and a comparable fast Alfvén speed (e.g., Zrake and Arons 2017). As a result, the pressure and magnetic field strength inside a PWN are expected to be roughly uniform (e.g., Reynolds and Chevalier 1984), broadly consistent with recent 3D MHD simulations of such objects (Figs. 2 and 3; Porth et al. 2014). The observed spatial properties of a PWN – defined to be the volume of space predominantly comprised of the shocked pulsar wind – depend on the flow of plasma

Fig. 2 Pressure distribution inside a (Stage 1) PWN as predicted by a 3D MHD simulation of such systems. (Figure reprinted from Porth et al. 2014)

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Fig. 3 Magnetic field lines (left), anisotropy (middle), and strength (right) in (Stage 1) PWN as predicted by a 3D MHD simulation of such systems. (Figure adapted from Porth et al. 2014)

between the termination shock and the PWN’s outer boundary, typically the location of the (“forward”) shock driven into the surrounding medium by the expanding plasma or, in the case of “bow-shock PWNe,” the supersonic motion of the neutron star itself. The primarily equatorial nature of the pre-shock pulsar wind results in the termination shock having a largely toroidal structure – believed to be responsible for the “inner ring” or torus of X-ray emission observed around some neutron stars (e.g., the Crab Nebula; Weisskopf et al. 2000). As a result, near the termination shock, the post-shock flow is primarily toroidal, though instabilities along the edge of the termination shock (often referred to as “high latitudes”) can redirect material inward. The inward material converges along the poles of the termination shock, and the increased pressure at this location results in a high bulk velocity polar outflow commonly referred to as a “jet” (Fig. 4; e.g., Lyubarsky 2002; Komissarov and Lyubarsky 2003; Del Zanna et al. 2004), though its characteristics are quite different than similar features observed in active Galactic nuclei and γ -ray bursts. On a microscopic level, as particles leave the termination shock, they rotate around a particular post-shock magnetic field line with a radius r ∼ rL , the Larmor radius of a particle with energy E in a magnetic field of strength B. As they propagate along a particular field line, a particle can transfer onto another one  1rL from the original. As a result, this flow is strongly dependent on the structure of the PWN’s magnetic field. The significant linear polarization of the radio emission detected from a large and diverse set of PWNe (e.g., Schmidt et al. 1979; Kothes et al. 2006, 2008; Lang et al. 2010; Ng et al. 2010; Ma et al. 2016; Ng et al. 2017; Kothes et al. 2020; Lai et al. 2022 and references therein) suggests that the magnetic fields in these sources are highly ordered throughout the evolutionary sequence described in the section above – though the geometry of this magnetic field can appear significantly different between systems in similar phases. The recent launch and successful deployment of the Imaging X-ray Polarimetry Explorer (IXPE; Weisskopf 2022) will result in measurement of the magnetic field structure traced by the highest-energy particles of the PWN – important for understanding the underlying acceleration of these particles. This mission has already produced such

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measurements for the Crab Nebula (e.g., Bucciantini et al. 2022). Recent models (e.g., Bucciantini 2018) and MHD simulations (Fig. 3; e.g., Porth et al. 2014) are able to qualitatively reproduce such ordered magnetic fields observed inside PWN, though the structure of these simulated magnetic fields is not necessarily consistent with the properties inferred from the polarized radio emission of such systems. On a macroscopic level, this flow can be treated as a combination of advection and diffusion (e.g., Tang and Chevalier 2012; Vorster and Moraal 2013), with a degree of turbulence (e.g., Porth et al. 2016; Zrake and Arons 2017) resulting from instabilities within the nebular magnetic field (e.g., Begelman 1998; Mizuno et al. 2011). Spatial variations in the strength and geometry of the PWN’s magnetic will likely lead to spatial variations in the dominant transport mechanism as well as in the diffusion coefficient (e.g., Figs. 4 and 5; Porth et al. 2016), which can be used to explain observed variations in the surface brightness and spectrum of PWN (e.g., Tang and Chevalier 2012; Ishizaki et al. 2017, 2018; Hu et al. 2022). Furthermore, the spectral evolution of the particles inside PWN – and their resultant emission – is strongly affected by the radiative losses of particles as they travel within the PWN, the adiabatic processes governing the overall interaction of the PWN with its surroundings, and the escape of particles from the PWN into the surrounding medium (e.g., Reynolds and Chevalier 1984; Gelfand et al. 2009; Bucciantini et al. 2011; Martín et al. 2012; Tanaka and Takahara 2011; Zhu et al. 2018, 2021). The escape of particles from the PWN is especially important for understanding the diffuse γ -ray emission observed around an increasing number of neutron stars. The rate and mechanism by which particles leave the PWN depends strongly on the stage of its evolution, as discussed in the next section.

PWN Evolution While the physical model of a PWN described above is expected to be applied throughout the lifetime of the neutron star, their physical characteristics will change significantly during this time. This evolution can be broadly attributed to two factors: • the decrease in energy deposited into the PWN by the central neutron star with time, as indicated in Equation 2, • and, more importantly, changes in the environment of the neutron star and its PWN. Below, we describe the expected changes in the environment of a neutron star, and how these changes impact the properties of the resultant PWN. Neutron stars have long been associated with core-collapse supernovae (e.g., Zwicky 1938; Zwicky et al. 1939) and are believed to be the remnant of the progenitor star’s Fe core whose gravitational collapse triggered this explosion. Therefore, initially, the neutron star is located in the “center” of the supernova remnant (SNR) formed by the expansion of the supernova ejecta into its surroundings

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Fig. 4 Results from a 3D MHD simulation of a “Stage 1” PWN. The top row shows the strength of the out-of-plane magnetic field (left), particle speed (middle), and magnitude of the radial diffusion coefficient (left). The second row shows the average magnetic field strength (left), fluctuation of magnetic field strength (middle), and relative change in magnetic field (right) resulting from turbulence inside this simulated PWN. The bottom row shows the average flux speed (left), fluctuations in flow speed (middle), and relative changes in flow speed (left) in this simulated PWN. Note the large-scale turbulence motions indicated by the white contours in the bottom-left panel. (All figures reprinted from Porth et al. 2016)

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Fig. 5 Radial diffusion coefficient associated with the turbulent motions observed in 3D MHD simulation of a PWN. (Figure reprinted from Porth et al. 2016)

Fig. 6 Schematic diagram of the structure of a PWN inside a SNR. This is the equivalent of Stage 1 in a later figure. Slane Handbook of Supernovae, ISBN 978-3-319-21845-8. Springer International Publishing AG, 2017, p. 2159

(Fig. 6; Gelfand et al. (2009) and many others). As a result, the PWN is initially surrounded by the slowest moving material produced in this explosion, and lowdensity ρ, high-pressure P plasma produced at the termination shock is expanding into the high-density, essentially pressure-less P ≈ 0, unshocked ejecta. The higher pressure inside the PWN causes it to expand within the SNR, sweeping up the surrounding material into a thin shell that confines the pulsar wind inside the PWN. The shock generated by the PWN’s expansion, as well as its emission, can heat dust created inside the SNR, resulting in infrared (e.g., Temim et al. 2012, 2017, 2019;

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Kim et al. 2013; Chawner et al. 2019) and (primarily near-infrared and optical) spectral line (e.g., Sankrit and Griffiths 1998; Zajczyk et al. 2012; Lee et al. 2019) emission. While this shell is expected to be very effective at confining the shocked pulsar wind inside the PWN, the extreme discrepancy in density between the pulsar wind and surrounding ejecta results in the formation of growth of Rayleigh-Taylor instabilities (Chandrasekhar 1961) which may assist in the escape of some particles from this source. The presence of such instabilities has been used to explain the observed filamentary structure observed around some PWN (e.g., Hester et al. 1996), and their development is believed to be sensitive to the rate the PWN expands within the SNR (e.g., Gelfand et al. 2009; Porth et al. 2014) and strength and orientation of the PWN’s magnetic field (Fig. 7; e.g., Bucciantini et al. 2004; Porth et al. 2014) – with a stronger tangential component to the nebular magnetic field believed to decrease the penetration of these instabilities into the PWN, and inhibit particle escape. During this phase, the radius of the PWN is expected to expand rapidly, increasing as Rpwn ∝ t 1.2 (Fig. 8; e.g., Reynolds and Chevalier 1984; Chevalier 2005; Gelfand et al. 2009), which results in a significant decrease in the strength its magnetic field strength (Fig. 8). The changing physical conditions drive the evolution of the PWN’s SED during this initial, free-expansion phase (e.g., Reynolds and Chevalier 1984; Gelfand et al. 2009; Tanaka and Takahara 2010; Bucciantini et al. 2011), with the decreasing magnetic field resulting in a decline in the synchrotron emission from the nebula, while the continuing injection of particles and energy by the central pulsar – which exceeds both the radiative and adiabatic losses of previously injected particles – into the PWN causes the inverse Compton emission from the PWN to increase with time (Fig. 9). The properties of the PWN during this stage are sensitive to the birth properties of the central neutron star and the characteristics of the progenitor supernova, and therefore observations of such PWN have been used to constrain these quantities (e.g., Hattori et al. 2020).

Fig. 7 Left: Simulation of the growth of a Stage 1 PWN with different values of the wind magnetization. As shown in this figure, the PWN is more elongated in higher magnetization wind, and in both Rayleigh-Taylor instabilities are observed to grow at the interface between the PWN and surrounding SNR. (Figure reprinted from Porth et al. 2014). Right: Radius Rpwn and penetration depth of Rayleigh-Taylor instabilities hRT in a PWN as calculated using the evolutionary model of Gelfand et al. (2009). The calculation of hRT in this model neglects the possible suppression of such instabilities by the nebula’s magnetic field. (Figure reproduced by permission of the AAS from Gelfand et al. 2009)

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Fig. 8 Left: Radius of the SNR, SNR reverse shock, PWN, termination shock, and location of the central neutron star with time for a PWN inside a SNR. Right: Strength of the PWN’s magnetic field with time. (Both figures reproduced by permission of the AAS from Gelfand et al. 2009)

Fig. 9 Theoretical evolution of the SED of a PWN inside a SNR for the four phases indicated by the vertical lines in the left panel of Fig. 8. The upper-left panel displays the SED during the initial free expansion of the PWN into the SNR, the upper right after the collision with the reverse shock until the end of the first compression, the lower left during the first re-expansion, and then the lower right during the second compression. (Figure adapted from Gelfand et al. (2009) by permission of AAS)

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The initial expansion of the PWN ends when it collides with the “reverse shock” driven into the supernova ejecta but interstellar medium shocked and heated at SNR forward shock (see Bandiera et al. (2021) for a recent calculation for its propagation inside a SNR). When this occurs, the pressure inside the PWN is much less than its surroundings, resulting in an inward force on the shell of material surrounding this PWN. This force first decelerates, and then eventually compresses, the PWN (Fig. 8; e.g., Reynolds and Chevalier 1984; van der Swaluw et al. 2001; Blondin et al. 2001; Bucciantini et al. 2003; Gelfand et al. 2009; Vorster and Moraal 2013) significantly impacting both the SED (Fig. 9) and morphology (Fig. 10) and SED of the PWN. While the exact impact of the reverse shock of a PWN depends on the particular properties of the system, the following generalities are believed to hold:

Fig. 10 “The Snail” – an example of a “Stage 2” system where the PWN is in the process of being disrupted by the SNR reverse shock. Slane Handbook of Supernovae, ISBN 978-3-319-21845-8. Springer International Publishing AG, 2017, p. 2159

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• This collision is likely to be asymmetric due to the space velocity of the pulsar, which causes it to move from the SN explosion site, and gradients in the surrounding medium. This asymmetry will likely displace the bulk of the PWN from the location of the pulsar (e.g., Fig. 10; Temim et al. 2013, 2015; Kolb et al. 2017) and can possibly physically separate the two (e.g., Gelfand et al. 2009). In this case, there would technically be two PWNe inside the SNR – a “relic” composed of particles injected into the PWN before this collision and a PWN powered by particles recently injected by the neutron star. • The compression of the PWN will increase the strength of the nebula’s magnetic field (Fig. 8; e.g., Bucciantini et al. 2003; Chevalier 2005; Gelfand et al. 2009). This significantly increases the synchrotron emission from the PWN, to the point that its luminosity can exceed the spin-down luminosity of the neutron star (Torres and Lin 2018; Bandiera et al. 2020). This increased luminosity results from the decreased synchrotron cooling time of particles within the nebula. As a result, particles injected into the PWN before it collides with the reverse shock will lose the bulk of their energy during this compression, creating a “relic population” of low-energy particles inside the PWN even if the PWN remains attached to the neutron star. However, the radiative losses of particles injected into the PWN during this compression will be much lower, and therefore such particles will dominate the observed high-energy emission. This resultant dichotomy in the particle spectrum introduces both spectral “breaks” into the SED of the PWN (top right panel of Fig. 9) and differences in the radio and X-ray morphology of the PWN (e.g., Fig. 10), since the lower-energy particles responsible for the radio emission will reflect the overall extent of the PWN, while the more recently injected higher-energy particles will be concentrated near the neutron star. The adiabatic compression of the PWN will cause its pressure to increase, until at some point, it will exceed that of the surrounding material. At this point, the low-density plasma inside the PWN will again accelerate its much higher density surroundings. In hydrodynamic models of such systems (e.g., Blondin et al. 2001; Gelfand et al. 2009), the rapid growth of Rayleigh-Taylor instabilities expected under these conditions will disrupt the PWN – injecting all of the particles into the surrounding SNR – though it is unclear if the strong magnetic field inside the PWN when this re-expansion begins (Fig. 8; Gelfand et al. 2009) prevents this disruption from occurring (e.g., Bucciantini et al. 2004). As the pulsar nears the outer boundary (e.g., van der Swaluw et al. 2004), and eventually exits, the SNR will be moving supersonically relative to its environment and will develop a bow-shock morphology due to the confinement of the pulsar wind by the ram pressure resulting from this motion (Fig. 11). By this time, the age of the neutron star t is expected to be much longer than its spin-down timescale, in which case the rate it injects energy into its surroundings E˙ psr is roughly constant with time. During this phase, high-energy particles accelerated at the termination shock

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Fig. 11 Schematic diagram of a “Stage 3”. Slane Handbook of Supernovae, ISBN 978-3-31921845-8. Springer International Publishing AG, 2017, p. 2159

are expected to propagate into the surrounding ISM through a variety of mechanisms mediated by the interaction between the PWN’s and interstellar magnetic fields (e.g., Bucciantini 2018; Barkov et al. 2019; Olmi and Bucciantini 2019). In summary, the evolution of a PWN can be described as consisting of three stages (Fig. 12): 1. Stage 1 – an initial expansion into the cold, slow-moving ejecta in the center of the SNR, where the shocked pulsar wind is confined by a shell of swept-up material. 2. Stage 2 – which begins when the PWN begins to interact with the material inside the SNR heated by the reverse shock, which initially compresses, and then possibly disrupts the PWN, at which point a significant fraction of the high-energy particles accelerated with the PWN are injected into the surrounding SNR. 3. Stage 3 – which begins when the neutron star begins to move supersonically with respect to its surroundings. High-energy particles within the resultant bow-shock PWN are expected to escape into the surrounding medium. As described above, in these latter stages, a higher fraction of the total highenergy particles accelerated inside a PWN will be found outside this structure and diffuse within the ISM. Therefore, their emission will extend well beyond the hydrodynamic boundaries of the PWN. This emission is likely to be most prominent in γ -rays, since the background photons needed to produce inverse Compton radiation are abundant, while the weak interstellar magnetic fields will likely result in the synchrotron radiation having a surface brightness too low to be observed by current facilities.

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Fig. 12 Schematic illustrating the evolutionary stages of a PWN environment. The pulsar velocity is toward the left and ISM density gradient upward in all three panels. The region producing highenergy (>1 TeV) gamma-rays through inverse Compton scattering is determined by the trajectories of the correspondingly energetic (>10 TeV) electrons and positrons. With increasing age, the physical size of the gamma-ray-emitting region also increases as indicated. X-ray emission is expected from the region bounded by the canonical pulsar wind nebula, shown in blue. (Credit: Giacinti et al. A&A, 636, A113, (2020), reproduced with permission ©ESO)

Observational Signatures and Notable PWNe The dominant emission mechanisms of synchrotron radiation and inverse Compton (IC) scattering lead to MWL SEDs that can be fairly well understood as a function of age of the responsible particle population. At X-ray energies, the synchrotron radiation is generated from young, high-energy particles recently released into the pulsar wind. The X-ray morphology traces the magnetic field structure around the pulsar, typically in tails or toroidal forms. At gamma-ray energies, the IC radiation can be generated by much older particles, with lower energy yet that continue to up-scatter photons from ambient radiation fields. Especially at gamma-ray energies, it is often challenging to distinguish the supernova remnant and plerionic components of a source. Composite supernova remnants “spp” for which this distinction has so far not been possible therefore form a subcategory of Galactic gamma-ray sources (Collaboration et al. 2018; Abdollahi et al. 2020).

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Figure 12 provides a sketch of PWN evolution, with a focus on the TeV emission, following well-understood stages yet incorporating the more recently established halo phenomenon (Gaensler and Slane 2006; Slane 2017; Giacinti et al. 2020). Although approximate age ranges are given, we note that the transition between evolutionary stages depends on the properties of the SN itself and of the surrounding ISM. Where density gradients are present in the surrounding ISM and/or the pulsar has a significant kick-velocity, the PWN-SNR system can become highly asymmetric with arbitrary morphology. At late evolutionary stages (e.g., third panel of Fig. 12), the remaining PWN is comprised only of the most recently accelerated energetic particles. The continuous acceleration of electrons and positrons maintains a small-scale PWN over long times, even after the pulsar has escaped the parent SNR. However, a much larger relic halo of escaped electrons and positrons forms around the pulsar in the ISM. Inverse Compton scattering of these leptons on ambient radiation fields produces a large-scale gamma-ray halo ∼10 − 100 pc in size. Extended, diffuse X-ray emission corresponding to mid-evolution PWNe (i.e., the second panel of Fig. 12) has been seen in several systems (Uchiyama et al. 2009; Bamba et al. 2010). Typically, the gamma-ray halo for late evolutionary stages extends out to sizes far in excess of the remaining PWN. Whether or not pulsar halos are also accompanied by large-scale diffuse X-ray emission remains to be investigated and verified. Although a strict classification based on the characteristic age of the pulsar is tempting, it is worth bearing in mind that the age is an inherently uncertain quantity. The age is determined from the measured pulsar period and period derivative from equation (4), where the characteristic age τc is obtained by crudely assuming that the braking index takes on a value of 3, such that τc = 2PP˙ . In fact, this assumption is only valid for a pure magnetic dipole radiation; a value of the braking index can ¨ be measured via n = ff˙f2 . For pulsars with a measured value of the braking index, this is typically 104 K are dominated by H II. The gas in these regions is either photoionized by nearby stars or heated by shock events in the medium. The majority of interstellar material production is due to stellar activity (Clayton 1978). Dense environments, like molecular clouds, may collapse due to their own gravity to eventually form a star. After the star has evolved along the main sequence of the Hertzprung-Russell diagram and turns into a giant star, the outer layers, containing gas from the recent dredge-up events, as well as gas from the pristine material (e.g., C, O, Si, and Mg), are ejected and returned to the surrounding medium (e.g., Whittet 2003). As the temperature decreases with distance from the star (Savage and Sembach 1996), gas may condense into solid grains (section “Interstellar Dust”).

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If a star has a sufficiently high initial mass (>8 M⊙ ), the giant-star phase will end into a core-collapse supernova (CCSN) explosion. In these conditions, iron can be formed either by the short-lived Si-burning or by decay of the 56 Ni. Actual dust formation is believed to take place in ejecta of CCSN (Dwek 2016; Slavin et al. 2020). The analysis of young remnants pointed out that the aftermath of the explosion can produce up to ∼0.4 M⊙ of dust (e.g., SN1987a, Matsuura et al. 2011). Similar values, summing the silicates and carbon contribution, were recently reported for the supernova remnant Cas A (0.4–0.6 M⊙ , De Looze et al. 2017), while ∼0.22 M⊙ was reported for the Crab nebula (Gomez et al. 2012). Type Ia SN should be also efficient producers of iron (Nozawa et al. 2011), formed in the innermost part of the explosion region of a white dwarf which exceeded the Chandrasekhar limit. However, iron dust from SN type Ia has been calculated to be readily destroyed by the SN reverse shock, therefore returning into gas phase (e.g., Gomez et al. 2012). In summary, the late stage of the star life is fundamental in the dust and gas cycle in the ISM, providing an efficient way to newly produce interstellar material. In the following, we describe the general properties of the cold ISM, in particular focusing on those aspects interesting for X-ray investigation. This will be necessarily concise. Then we illustrate the phenomenology of the ISM as seen by the current X-ray instrumentation. This is followed by a more quantitative description of the physical processes involved. A part of this chapter describes how new models for interstellar dust modeling are developed: from the laboratory measurements to the implementation into fitting routines. For clarity, we treat separately the ISM extinction as seen from high-resolution X-ray spectroscopy and dust scattering, studied with CCD imaging. At the end, the state of the art of our current understanding of the ISM from the X-ray point of view can be found, followed by an outlook on future missions.

The Cold ISM The spiral arms pattern in our Galaxy may be recovered from the study of the distribution and properties of the neutral hydrogen emission (Levine et al. 2006), the H II distinct regions, and molecular clouds, highlighted by H2 (Levine et al. 2006; Kalberla et al. 2007). The scale height of the disk occupied by diffuse emission changes considerably with distance from the center, going from 0.15 kpc in the central regions up to ∼2.2 kpc at the outer end of the Galactic profile traced by neutral hydrogen (∼35 kpc, Kalberla and Kerp 2009). The column density of the neutral hydrogen changes widely in the Galaxy and typically spans more than two orders of magnitudes, around the range ∼1020−22 cm−2 . Extreme values at both ends of this interval can be found. As soon as the H I column density exceeds ∼4 × 1020 cm−2 , the diffuse medium may superimpose with the colder, molecular medium, mainly traced by the CO molecule (Combes 1991; Dame et al. 2001). Contrary to the diffuse medium, the distribution of molecular material is clumpy. Often warm clumps lie at preferential longitudes, overlapping with the H II regions population, following the spiral structure (e.g., Solomon et al. 1985). The cold

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phases of hydrogen witness therefore both the star formation and the release of the interstellar material in the diffuse medium. Out of this reservoir comes the material for new stars and planets formation.

Interstellar Dust Intertwined with the cold gas is the dust phase, which constitutes about 1% of the total ISM (Whittet 2003; Boulanger et al. 2000). The presence of solid dust particles has been soon recognized, as the abundance of certain elements, measured from UV absorption lines, appeared significantly sub-solar (e.g., Savage and Sembach 1996). Abundant elements, like carbon, oxygen, and iron, appeared significantly depleted from the gas phase, indicating that they should be present in another form, for example in dust grains. The depletion of a given element x can be denoted as D(x), as (e.g., Whittet 2003): D(x) = log



Nx NH



− log



Nx NH



.

(1)

⊙

This can be simply transformed into the fractional depletion δ(x): δ(x) = 1 − 10D(x)

(2)

where δ(x) = 1 indicates that the element is totally included in dust, while if the element is only in gas form, δ(x) = 0. The depletion value is a function of temperature (Savage and Sembach 1996) and, as a consequence, of the environment where the element resides. In general, the denser and colder the environment, the more depleted an element Jenkins (2009). A large amount of observational multiwavelength (from radio to far-ultraviolet) evidence on dust has been collected in the last decades, allowing the determination of the general chemical composition of interstellar dust, its size, shape, and physical characteristics. The broadband spectral energy distribution (e.g., Compiègne et al. 2011), the extinction curve (section “The Extinction Curve”), and detailed infrared (IR) and far-infrared spectroscopy (e.g., Molster et al. 2010, and references therein) determined that carbon and silicates should dominate the chemical composition of dust. Carbon, produced in the aftermath of wind ejection from carbon-rich red-giant stars, has historically been assumed to be in the form of graphite. The prominent and ubiquitous extinction feature at 2175 Å (Fig. 1) can be interpreted as coming from small graphite grains, whose excitation energy would be consistent with the position of the observed feature (Stecher and Donn 1965). However, the line-of-sight broadening variations have been proposed to be due to the same type of excitation, but from the polycyclic-aromatic-hydrocarbon (PAH) molecules (Draine 2003). Graphite, in analogy with silicates, should also face a process of amorphization

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Fig. 1 Examples of observed extinction curves at different values of RV . The data are related to Herschel 36 (solid line), HD 48099 (dashed line) and BD+56 524 (dashed-dotted line) (Adapted from Cardelli et al. 1989)

in the ISM. Therefore, amorphous carbon or hydrogenated carbon (HAC) has been proposed as a possible candidate for the C reservoir (e.g., Compiègne et al. 2011; Duley et al. 1989). The inclusion of Mg, Si, Fe, and O into silicates has been proven through IR spectroscopy. The 9.7 and 18 µm absorption features, seen in the environment of oxygen rich stars, have been indeed interpreted as the stretching and bonding modes of Si–O and O–Si–O, respectively (e.g., Draine 2003; Molster et al. 2010). The amount of iron and magnesium inclusion in the silicate depends on the initial conditions in the giant-star winds where they were formed (Gail 2010, for a review). As the gas flows farther from the star and temperatures decrease with distance, the first dust particles can be formed by condensation, starting from Ti, at ∼1500 K. According to calculations assuming chemical equilibrium (Fig. 9 in Gail 2010), in a circumstellar envelope Mg and Si should bind into olivine first ([Mg,Fe]2 SiO4 ) at around 1100 K. Then, in rapid succession, pyroxene ([Mg,Fe]0.5 SiO3 at 1000 K) and metallic iron (at around 900 K) should form. This condensation sequence is indeed noticed in high mass-flow rate stars (Molster et al. 2010). In this case, the crystalline Mg-rich end of the olivine and pyroxene (Mg2 SiO4 and MgSiO3 , respectively) is observed. The fraction of crystalline dust in those environment is relatively small (10–15%, Molster et al. 2010). However, dust grains are often formed in a fast-

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cooling and evolving outflows, where the equilibrium conditions just described do not apply. In non-equilibrium, when the temperature becomes lower than 900 K, the dust forms preferentially amorphous aggregates, observed to be iron-rich (e.g., in protostars, Demyk et al. 1999). Both Mg and Si in solid form are almost completely included in silicates (Whittet 2003). However, the high depletion of iron (>90%) cannot be explained only in terms of silicate inclusion (Jenkins 2009; Dwek 2016; Poteet et al. 2015; Zhukovska et al. 2018). Iron can also exist in other stable forms, as metallic iron, iron oxides, and iron sulfides (e.g. Zhukovska et al. 2018). The presence of metallic iron cannot be directly observed at long wavelengths, as iron should not display any vibrational mode (Molster et al. 2010), making it difficult to directly test the presence of this iron form. It has been hypothesized that iron in FeS (with small inclusion of Ni) could exist as inclusion into larger silicate grains, mainly formed by amorphous enstatite. These aggregates are called Glasses with Embedded Metals and Sulfides (GEMS, Bradley 1994). They are commonly observed in comets, and they are a constituent of the interplanetary dust particle reservoir. Therefore, the majority (90– 99%) of GEMS particles should not have an ISM origin, but are believed to be formed in the solar nebula itself (Keller and Messenger 2011). However, GEMS-like grains may constitute a fraction of the amorphous silicate grains in the ISM. Indeed, GEMS with anomalous oxygen isotopic composition may have been processed in the ISM (Messenger et al. 2003). Recent detailed studies on cometary GEMS point out that some must have undergone more than one stage of processing, in a cold environment. The detected organic carbon in those GEMS would not indeed survive in the hot environment (>1300 K) of the solar nebula (Ishii et al. 2018). The Cassini mission, in orbit around Saturn, allowed the detection of dust grains consistent to be reprocessed multiple times in the ISM. The composition has been found to be dominated by magnesium-rich silicates with iron inclusion (Altobelli et al. 2016). Lower abundance metals are often highly depleted (e.g., Jenkins 2009). For example Al, Ca, and Ti, among the first elements to condense in the stellar envelope (at T = 1400–1600 K, Savage and Sembach 1996; Field 1974), are believed to form the first and innermost core of more complex silicate grains (Clayton 1978). This inclusion would provide a natural protection and would explain why the high depletion of these elements is almost insensitive to the environment temperature. Calcium carbonates have also been reported in spectra of envelopes of asymptoticgiant-branch stars (e.g., Kemper et al. 2002). Another low-abundance element, nickel, has a depletion pattern similar to the one of iron and a similar condensation temperature (1336 and 1354 K, for Fe and Ni, respectively) suggesting a common dust inclusion history. In equilibrium conditions, they should indeed condense into nickel-iron in the stellar envelope (Gail 2010). The temperature of the environments where dust resides has a profound impact on the grain internal structure. In the inner part of the stellar outflow, the newly formed dust is crystalline, thanks to the high temperatures (Gail 2010). However, any dust formed at temperatures E0 , by an “edge” function of the form exp(τ0 (E/E0 )−3 ), where E0 is the threshold X-ray energy at which the electrons can be expelled from the shell and τ0 is the absorption depth at energy E0 . Bound-bound transitions of neutral or mildly ionized ions in the ISM can also be present as well as absorption by highly ionized gas, described elsewhere in this volume. They clearly involve less energy than the absorption edge of the same ion; therefore, they appear in the spectrum generally at lower energies (or larger wavelength λ = 12.3985/E, if λ is expressed in Å and E in keV). In the ISM however, gas and dust always coexist in cold environments. The effect of dust in an X-ray spectrum can be noticed in three ways: (i) depletion of the gas phase into dust, resulting in an apparent underabundance of a given element, namely the ones locked in dust (section “Interstellar Dust”); (ii) the effect of X-rays interacting with solid particles, rather than gas, resulting in resonance effects (section “The X-Ray Fine Structure”); and (iii) the effect of scattering of the X-rays by the dust solid particles, which changes the overall cross section slope as a function of energy (Draine 2003, and section “Correcting X-ray Observations

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1.0

0.6 0.4

Transmission

0.8

0.2 0.0 19 20 30

21 10

22

3

Energy 1 [keV]

0.3

23 0.1

log

NH

−2 ]

[cm

24

Fig. 2 Transmitted X-ray spectrum as a function of energy and column density (Rogantini 2020)

for ISM Attenuation”). In Fig. 2, the effect of the cold ISM column density NH on a transmitted X-ray spectrum is shown. The smooth cut-off at lower energies is due to long tail of the hydrogen deep absorption edge at 13.6 eV. This curvature can be accurately measured, especially by broadband X-ray spectrometers, and the hydrogen column density determined (e.g., Kaastra et al. 2008). Albeit at a lower level, also He, H II and H2 contribute to the low-energy cut-off.

Dust Scattering from the ISM X-ray scattering has been used to study crystalline structures in different materials since the beginning of the twentieth century. The first time that this phenomenon was brought to attention regarding X-ray propagation through the interstellar medium was by Overbeck (1965), who noted that the apparent size of X-ray sources should increase due to the presence of interstellar dust. The source should then be surrounded by a round, diffuse halo. Hayakawa (1970) showed that this phenomenon could be used to measure the distance, size, and composition of interstellar dust grains. The first observation of a so-called dust scattering halo was not achieved until over a decade later, around the bright high mass X-ray binary GX 339-4, imaged with the Einstein Observatory (Rolf 1983). The first survey of dust scattering halos was enabled by the launch of the ROSAT satellite, which performed an all sky survey in the X-rays, revealing scattering halos around 25 bright point sources and providing benchmarks for scaling relations between optical and X-ray extinction properties of the ISM (Predehl and Schmitt 1995). Since then, dozens of dust scattering halos have been studied in detail, placing constraints on the dust grain size distributions in the ISM as well as the location

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Near Cloud

Far Cloud

Fig. 3 The 4–6 keV surface brightness profile of the dust scattering halo around Cygnus X-3. The radial profile can be fit with a model of dust that is distributed uniformly along the line of sight (gray solid line) or by assuming that the dust is concentrated in two dust clouds (dotted lines) at intermediate distance between the observer and the X-ray source (black dashed line). The data were gathered by the Chandra satellite (Modified from Corrales and Paerels 2015)

of dust clouds along the sight line to background Galactic X-ray binaries (see Smith et al. 2002; Draine and Tan 2003; Costantini et al. 2005; Smith 2008, for canonical examples). Dust scattering halos are typically on the order of 10 arcmin in angular extent, arise from dust approximately located at intermediate distances between the bright X-ray source and the observer, and probe ISM regions with physical sizes on the order of 1–30 pc along the line of sight. Figure 3 shows an example of the surface brightness profile of the scattering halo that originated from the high-mass X-ray binary Cygnus X-3. The theory of scattering by small particles is covered in detail by a several text books on the subject (van de Hulst 1957; Bohren and Huffman 1983). In the case of X-rays, interstellar dust is relatively transparent to the incident radiation (|m − 1| ≪ 1), where m denotes the complex index of refraction. Because the grains are typically much larger than the wavelength of incident radiation, there is a minimal phase shift when the light enters the particle (2π aλ−1 |m − 1| ≪ 1), where a is the radius of the dust grain. These are the conditions required to apply the RayleighGans approximation, yielding σsca

∼ = 2π a 2



2π a λ

2

|m − 1|2 .

By nature of the approximation, the differential cross section can be calculated by assuming that the electromagnetic wave inside the dust grain is the same as that incident upon it and integrating the scattered wave fronts from every part of

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the grain. For spherical dust grains, the differential scattering cross section can be approximated with a Gaussian function (Mauche and Gorenstein 1986), 4a 2 dσsca ≈ dΩ 9



2π a λ

4

 2  θ |m − 1| exp − sca . 2σ¯ 2

Here Ω is the solid angle and θsca is the scattering angle. Under the assumption of small scattering angles, σ¯ can be approximated as 

E σ¯ = 10.4 keV

−1 

a 0.1 µm

−1

arcmin.

This provides a sense of the halo angular extend for a single grain size (Mauche and Gorenstein 1986). An approximation for the dielectric response can be made by treating the dust grain as a collection of free electrons, the “Drude approximation” (Smith and Dwek 1998): |m − 1| ≈

ne re λ2 2π

where ne is the average density of electrons in the grain and re is the classical radius of an electron. Applying the Drude approximation yields the canonical Xray scattering cross section: −11

σsca ≈ 6.168 × 10

cm

2



ρ 3 g cm−3

2 

a 0.1 µm

4 

E keV

−2

where ρ is the material density of the dust grain and E is the energy of the incident light, and it is assumed that the material contains roughly equal numbers of protons and neutrons. In other words, this assumes ne ≈ ρ/2mp . The energy dependence of the cross section demonstrates that scattering is more important for soft X-rays. The strong dependence on particle radius (a 4 ) makes it so that the dust scattering phenomenon is particularly powerful for constraining the large end of the cosmic dust grain size distribution (Witt et al. 2001; Corrales and Paerels 2015; Valencic et al. 2019). An important caveat to this point is that the Rayleigh-Gans approximation breaks down as grains get larger (a ≥ 1 µm) or as we look towards very soft X-rays (E ≤ 0.3 keV). Smith and Dwek (1998) demonstrate that RayleighGans scattering can be applied as long as the energy of the incident X-ray photon, in keV, is significantly larger than the grain radius, in microns. When the RayleighGans approximation no longer applies, one can employ the more general anomalous diffraction theory or Mie scattering theory (section “Interaction of X-rays with Dust Grains”). Doing so demonstrates that the scattering cross section for X-rays is roughly flat for E(keV) ≤ a(µm), and no longer follows the canonical E −2 dependence (Smith and Dwek 1998; Corrales and Paerels 2015).

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Fig. 4 Illustration of the geometric principles used to compute the dust scattering halo intensity under the assumptions of single scattering. The positions of two dust clouds are represented by the blue and green planes along the line of sight between a telescope and an X-ray source, separated by a total distance D. The apparent angular distance between the point source and dust-scattered light is represented by θobs . In order for scattered light to reach the observer, it must fall onto the angle θsca , which equals θobs /(1 − x) under the small angle approximation. In the case that the X-ray source undergoes a bright outburst, the observer will see scattering from dust that lies along equal path lengths, represented by the ellipsoid in the illustration. Where the ellipsoid intersects the dust clouds, a ring pattern is observed, growing in angular size with time (Adapted from illustrations by S. Heinz)

To model the surface brightness profile of the resulting scattering halo image, one must integrate the differential scattering cross section over the interstellar dust grain size distribution while accounting for geometrical effects of the sight line. Figure 4 demonstrates the layout of the problem and defines fundamental parameters such as the dust fractional distance, x ≡ d/D, where d is the distance to the dust particle and D is the distance to the background X-ray source. Employing small angle approximations, the integral can be written as dI (E, θobs ) = dΩ



0

1  amax amin

Fa (E)

dσsca (E, a, θsca ) nd (a) ξ(x) da dx. dΩ

(6)

Here it is also assumed that the sight line is optically thin; therefore, only one scatter occurs before reaching the observer. In Eq. 6, Fa is the absorbed (apparent) flux of the background X-ray source after the effect of ISM absorption, nd is the grain size distribution (assumed to be the same everywhere along the sight line), ξ(x) represents the density distribution of dust along the sight line, and the differential scattering cross section must be evaluated for the appropriate scattering angle, θsca = θobs /(1 − x). Various approximations and semi-analytical solutions for the scattering halo intensity profile can be found in the literature (Mauche and Gorenstein 1986; Draine 2003; Corrales and Paerels 2015). The scattering halo integral above also assumes azimuthal symmetry of both the dust clouds

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(on 10s of pc scales) and the differential scattering cross section, the latter of which only holds true for spherical particles. For non-spherical particles, employment of anomalous diffraction theory demonstrates that the resulting dust scattering halo image can range from ellipsoidal to a nearly diamond shaped pattern, depending on the elongation and relative degrees of alignment among the dust grain population, induced by the presence of a magnetic field in the ISM (Draine and Allaf-Akbari 2006). Time Variable Scattering In the majority of cases, dust scattering halos are treated as static – a common approximation that reduces the complexity of the problem. However, in reality, dust scattering halo images are time variable because there is a path-length difference between the scattered light and non-scattered light. The image arising from a steady, unchanging point source can be referred to as a “static” or “quiescent” dust scattering halo. If the source of X-ray light undergoes a rapid high fluence outburst, ring images will be produced as the light from the flare propagates through interstellar clouds (Fig. 4). The surface of equal time delay as the X-ray wave front propagates through the interstellar medium is an ellipse, and each dust cloud intersecting that ellipse produces a separate ring. As the ellipsoidal surface grows with time, the angular sizes of the ring echoes also increase with time. This phenomenon is often referred to as a dust scattering echo or dust ring echo. The first dust scattering echoes were observed as a result of the X-ray afterglows from extragalactic gamma ray bursts, which scattered off of local Galactic dust, producing ring images that were resolvable by both XMM-Newton (Vaughan et al. 2004; Tiengo and Mereghetti 2006) and the Neil Gehrels Swift Observatory (Vaughan et al. 2006; Vianello et al. 2007). Dust scattering rings can be used to (i) measure the distance to the X-ray source, given the line-of-sight distribution of dust and knowledge of the X-ray light curve (Heinz et al. 2015); (ii) measure the line-of-sight dust abundance (ISM tomography), given full knowledge of the distance and X-ray light curve of the background source (Heinz et al. 2016); or (iii) estimate the time and fluence of an X-ray burst, given knowledge of the line-of-sight dust position and abundance. The interplay among all these parameters is described by the time delay (δt) associated with a particular observation angle (θobs , the angular distance between the central point source, and the observed scattering image) (Trümper and Schönfelder 1973): δt =

2 D xθobs , 2c (1 − x)

using the geometry described in Fig. 4. In the case of ring echoes originating from extragalactic sources, x ≪ 1, so the distance to the dust clouds can be measured directly from the angular size of the ring echoes. Following from the dust scattering halo integral above, the surface brightness profile for a dust ring echo is

104 Interstellar Absorption and Dust Scattering

dI (E, θobs , t) = dΩ



xmax  amax

xmin

amin

Fa (E, t − δt)

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dσsca nd (a) (E, a, θsca ) da dx, dΩ (xmax −xmin )

where δt and θsca are a function of x, and it is assumed that the dust cloud with an abundance and grain size distribution described by nd is uniformly distributed between xmin and xmax . Even slow changes in an X-ray light curve can lead to measurable differences in a dust scattering halo surface brightness profile as a function of time, which can be used to constrain the distance to the X-ray emitting source (or inversely, the position of the dust). The first distance measurement obtained in this way was for Cyg X-3 (Predehl et al. 2000). Data-driven methods of studying distances and lineof-sight positions of dust clouds include cross-correlation between light curves from an annulus centered on θobs and the light curve of a central point source (Ling et al. 2009) and de-convolution of the dust scattering halo image as a function of time using the predicted scattering halo intensity profile as a kernel (Heinz et al. 2016). Both methods can potentially be used to study dust scattering halo variability at a lower contrast than that typically seen for ring echoes.

The X-Ray Fine Structure The photoelectric effect describes the interaction of an incoming photon and the electrons in the atom. As the energy of the photon equals the binding energy of the electron, it is ejected from the atom with kinetic energy equal to E − E0 , where E is the incoming photon energy and E0 is the electron binding energy. The X-ray photon energy is sufficient to remove electrons from the innermost levels (K, L, M). The resulting spectroscopic feature displays first a sharp drop at the energy corresponding to the electron binding energy; then the probability of the effect to take place decreases exponentially, as the material becomes more transparent to photons with energy larger than the threshold one, creating a characteristic sawtooth feature. Absorption Fine Structure If the X-ray photons interact with solid particles, rather than gas, additional effects take place, creating the spectral features of EXAFS (extended X-ray absorption features) and XANES (X-ray absorption near edge structures), called collectively XAFS (X-ray absorption fine structure). The basic mechanism is illustrated in Fig. 5. The incoming photon interacts with the electron in the shell. The electron can be described as a wave that interacts with the neighboring ones, creating positive and negative interference. This diffraction pattern depends on the number of electrons and their distance to the nucleus, therefore revealing the chemical bonds in the grain. XANES appear as sharp features in the vicinity of the threshold energy, and they are the result of multiple backscattering from the neighboring atoms, while EXAFS,

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Fig. 5 Left panel: in a gas, the incoming X-ray photon will remove one of the inner orbit electrons to the continuum, without further interaction. The resulting cross section has a sawtooth shape, starting at E0 , the binding energy of the removed electron. Right panel: In a solid, the photoelectron wave of the removed electron interacts with the ones of the neighboring atoms, adding a characteristic interference pattern to the photoelectric cross section. The regime of features near E0 (pink shade and arrows in the insert) is called XANES, due to multiple scattering among the atoms, while the structures farther from E0 are dominated by single scattering (EXAFS, green shade and arrows in the insert) (Figure adapted from Zeegers 2018)

which are lower amplitude and broadened features, are visible at energies above 50–100 eV the threshold energy. They are the result of a single backscatter from the neighboring atoms. Scattering Fine Structure By the fundamental nature of dielectrics, an absorption resonance also yields a scattering resonance. As a consequence, the Rayleigh-Gans approximation also breaks down near the n = 1 (K shell) and n = 2 (L shell) photoabsorption features that are used to probe the metals comprising interstellar dust. More exact calculations for the scattering cross section, via either anomalous diffraction or Mie theory, demonstrate that every K and L shell absorption resonance has a complementary decrement in scattering efficiency (Martin 1970). This X-ray scattering fine structure (XSFS) signature affects the spectral shape of dust scattering halos as well as the apparent shape of photoabsorption, due to the contribution of dust scattering to the total extinction through the ISM (Hoffman and Draine 2016; Corrales et al. 2016). This fact makes it so that XSFS can also be investigated through direct high-resolution spectroscopy of point sources (section “Interaction of X-rays with Dust Grains” and Fig. 8). A dust scattering halo spectrum, when compared to the central point source, provides a direct measurement of the scattering opacity from dust in the ISM via the equation τsca



 Fh = ln +1 Fps

(7)

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where Fh is the spectrum of the halo and Fps is the point source spectrum after the effects of all sources of line-of-sight extinction. Using this method, the first detection of XSFS from a dust scattering halo was that around the low mass X-ray binary Cyg X-2, where the strength of the O K shell resonance is strong enough to become apparent in low-resolution spectra (Costantini et al. 2005). With sufficient resolution, XSFS may be used to discern the mineralogy of dust (Fig. 6, inset). As with dust scattering halos, the exact profile of XSFS depends on a variety of factors including grain size distributions, shape, and alignment (Hoffman and Draine 2016). The contribution of XSFS to apparent extinction is also dependent on the shape of the complementary scattering halo surface brightness profile and the spatial resolution of the X-ray spectrograph (Corrales et al. 2016). Finally, the broadband spectral energy distribution of a dust scattering halo is also affected by the dust grain size distribution. In the example shown in Fig. 6, extending the MRN distribution to a grain size of 0.5 µm enhances scattering and changes the shape of the dust scattering opacity curve so that it flattens at higher energies than the typical MRN distribution.

Fig. 6 A demonstration of X-ray scattering fine structure (XSFS) computed for a power-law distribution of spherical dust grains, using the optical properties for silicates produced by Draine (2003). Extending the MRN distribution to larger grains (dashed line) causes a departure from the E −2 dependence, characteristic of Rayleigh-Gans scattering, at a higher energy compared to the standard MRN distribution (solid line). The normalization for each curve has been scaled for ease of comparison The inset shows XSFS around Si K in more detail. The laboratory-derived optical constants from Zeegers et al. (2017) were used to compute the XSFS for several astrosilicate candidate materials

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Correcting X-ray Observations for ISM Attenuation When correcting X-ray observations for attenuation by the foreground ISM, it is important to separate the contributions from the gas phase (pure absorption) and the solid phase (dust absorption and scattering). It has been demonstrated that not including dust scattering in X-ray spectral models can yield different conclusions for the physical properties derived for the underlying source emission, such as the disk black-body temperatures in X-ray binaries, on the order of 30–50% (Smith et al. 2016). The modeling techniques for dust attenuation will depend on geometrical effects, including the relative distances between the dust and X-ray source, grain size distribution, and imaging resolution of the spectroscopic instrument (Corrales et al. 2016). Figure 7 describes the decision-making process for including dust scattering effects when evaluating an astronomical spectrum of interest.

Intermediate (ISM, IGM)

Is the angular size of the dust cloud less than 5 arcsec?

Yes

No

Where is the dust? Safely ignore dust scattering

Intrinsic to the source

No

Do you worry about clumpy dust clouds in your source?

Use idealized extinction models Yes

Yes Does your telescope have high imaging resolution (PSF width < 5'')?

No

Apply a partial covering factor

Do a full dust scattering calculation (Mie or ADT)

Fig. 7 Decision tree describing when and how to include dust scattering when fitting spectral models for a point source obscured by cool gas and dust, based on the scenarios described in Corrales et al. (2016). In each spectral model, the attenuation by gas and dust is broken down gas into three component: the opacity from gas absorption (τabs ), the absorption component from dust dust ), and the dust scattering optical depth (τ dust ). Dust that is intrinsic to the X-ray emitting (τabs sca system, but does not fully cover the X-ray source, contributes a fraction of the total dust scattering opacity towards extinction, according to the covering factor fcov . Dust that is intermediate along the line of sight may require a full dust scattering halo calculation if the telescope imaging resolution is worse than 5–10′′ . In this case, the user will need to determine what fraction of the scattering halo is enclosed by the image region used to extract a spectrum (fh ). Any modelers that wish to examine the effects of non-standard (e.g., MRN) dust grain size distributions that include a contribution from large >0.3 µm grains will need to do a full scattering halo calculation

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Laboratory Measurements of Solid Particles In order to interpret X-ray astronomical data, a comparison with reliable dust models is necessary. Thanks to experimental measurements campaigns, targeted specifically at analogues of interstellar dust materials, absorption profiles have been obtained of a number of X-ray edges: Fe L (Lee et al. 2009; Westphal et al. 2019), O K (Psaradaki et al. 2020), Al K (Costantini et al. 2019), Mg K (Rogantini et al. 2019), Si K (Zeegers et al. 2017, 2019), and Fe K (Lee and Ravel 2005; Rogantini et al. 2018). Depending on the edge energy and the measured sample thickness, different facilities and techniques are necessary in order to obtain the absorption profile. For the works cited here, the measurements were performed using synchrotron beamlines (with transmission and fluorescence techniques) as well as electron energy loss spectroscopy (EELS). Transmission A polychromatic synchrotron light beam is converted, through a monochromator, into a monochromatic energy beam (I0 ) that interacts with the specimen. The outcoming radiation (I ) is attenuated according to the Beer-Lambert law: I = I0 exp(−tμ),

(8)

where t is the thickness of the material and μ is the absorption coefficient, which depends on the atomic (Z) and mass number (A) of the sample as well as the incident ρZ 4 energy (E) and the density of the sample (ρ) according to μ ≈ AE 3 (Newville 2014). Fluorescence With this technique, the secondary effect of the photoelectric effect of fluorescence is measured (Newville 2014). As fluorescence photons are emitted at specific energies, this information can be used to recover the absorption profile. The absorption coefficient μ(E) can be approximated as I /IF , where I is again the incident intensity and IF is the measured intensity of the fluorescent emission. Electron Energy Loss Spectroscopy With this technique, the specimen is targeted by a beam of monochromatic electrons. The Coulomb interaction depends on whether the electrons interact with the nucleus, with peripheral electrons or with tightly bound electrons. In the last case, an inelastic scattering event occurs, which implies an exchange of energy. The incoming electron beam then loses energy depending on the binding energy of the atoms in the target, producing a spectral energy distribution, characteristic of the material. The outcoming kinetic energy of the electrons mirrors the absorbing part of the dielectric function (Egerton 2011).

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The attenuation of a beam through a medium can be described by Eq. 8. As the absorption profile of the material has been extracted, it will present as in Fig. 5 (right panel), with XANES features near the edge and EXAFS features at E > 50 − 100 eV from the inset of the edge. The latter can be expressed in analytical terms (e.g., Teo 1986). The function χ represents the superimposing sub-structures to the photoelectric edge shape: χ (E) =

μ(E) − μ0 (E) Δμ

(9)

where μ0 is the absorption coefficient of the smooth underlying continuum (Newville 2014). The function χ (E) is normalized by the edge jump at E0 (Fig. 5), through the term Δμ. The technique to analyzeEXAFS prescribes first 0) . Then, using a representation of χ into the wave number space k = 2m(E−E h¯ 2 the fact that the frequency of the EXAFS features depends on the distance of the absorbing atom and the neighboring scattering electrons, a Fourier transform of χ (k) would show a photoelectron scattering profile as a function of the distance. The detection of reliable EXAFS, which are shallow and broadened spectral features, is however strongly dependent on data quality. While at a synchrotron facility a detection may be achieved, in an astronomical context, EXAFS are not regularly observed. Signal-to-noise ratio of the data is the main limiting factor. In addition, a spectrum of an astronomical source may display many different features, from both intrinsic and intervening gas that would blend with the EXAFS, confusing the extraction of the signal. On the contrary, XANES, thanks to their sharpness and relatively high amplitude, can be well detected also in an astronomical X-ray spectrum (Fig. 5). The technique to treat the multiple scattering process in a material is not straightforward as for EXAFS and has been limited in the past by the heavy calculation required in following the scattering paths (Rehr and Albers 2000, for a review). Calculations are implemented in ab-initio codes, e.g., FEFF (Ankudinov et al. 1998) or Quantum Espresso (Giannozzi et al. 2009), among others, that provide comparable results with experimental data (e.g., Takahashi et al. 2018).

Implementation to Astrophysical Models Once the intensity profile of a material has been obtained, it needs to be postprocessed to be adapted to be part of an astrophysical model. Here we consider the case of a specimen observed in fluorescence by the LUCIA-beamline at the Soleil synchrotron facility. This description closely follows the procedure adopted in Zeegers et al. (2017, 2019), Rogantini et al. (2019), and Costantini et al. (2019). Some instrumental effects should be first taken into account. One of these effects is pile-up, which occurs when two or more photons are recorded at the same time, resulting as one photon with double the energy. The result is a spurious line feature that can be easily corrected for. If the sample is sufficiently thick, self-absorption

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in the sample will cause the fluorescence intensity to be visibly attenuated (Zeegers et al. 2017). Several empirical methods can be used to correct for this effect (Stern et al. 1995; Booth and Bridges 2005). Usually, multiple fluorescence observations are performed on the same specimen. If the data quality allows it, these are added to increase the signal-to-noise ratio of the measurement. These data are then inverted to mock a transmission profile. The pre- and post-edge are then fitted to a theoretical profile of known thickness (typically τ = 0.01 µm). The values tabulated starting from Henke et al. (1993) provide an excellent resource to compute, in first approximation, a transmission profile of a given material of known composition, density, and thickness. The obtained profile is related to the imaginary part k of the refraction index m = n + ik. The optical constants n and k are unique signatures of a material. Sometimes they are expressed with a different notation, e.g., as dielectric functions, ε1 and ε2 (Draine 2003), or as atomic scattering factors f1 and f2 . If the incident radiation has a wavelength λ larger than atomic dimension, or if the scattering angle is small, f1 and f2 are then not dependent from the scattering angle (Henke et al. 1993). Optical constants and scattering factors can be easily transformed into one another (see Rogantini et al. 2018): ρNA r0 2 λ f1 (E), 2π A ρNA r0 2 λ f2 (E). k(E) = 2π A

n(E) = 1 −

(10) (11)

Here ρ is the density of the material, NA the Avogadro number, r0 the electron radius, A the atomic mass, and λ the wavelength of the incoming radiation. The atomic scattering factors depend on one another according to the Kramers-Kroning relations (Kramers 1926; Kronig 1926). Therefore, the real part of the refraction index can be derived (Watts 2014; Henke et al. 1993): f1 (E) = Z ⋆ −

2 π



∞ 0

εf2 (ε) dε, ε2 − E 2

(12)

where Z ⋆ can be approximated as Z ⋆ ≈ Z − (Z/82.5)2.37 .

(13)

The factor Z ⋆ is a small relativistic modification of Z, in a high-energy photon limit (Cromer and Liberman 1970). This reduction in Z is only relevant for highZ elements. As observed for instance in Henke et al. (1993), Eq. 12 displays a discontinuity when ε = E. Furthermore, a true atomic scattering factor needs in principle to be defined at all energies, while experimental energy ranges are in fact limited. Recently, the use of a piecewise Laurent polynomial algorithm proved to offer an accurate description near the edge (Watts 2014), avoiding the requirement

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of an infinite coverage in energy or an homogeneous binning of the data. The real and imaginary parts of the refractive index are a necessary input to calculate the scattering and absorption efficiency in the interaction between the incoming X-rays and the dust particles.

Interaction of X-rays with Dust Grains The interaction of a set of plane parallel electromagnetic waves with a spherical particle is described by the Mie theory (Mie 1908), when the size parameter X = 2π a/λ does not exceed 2 × 104 (Bohren and Huffman 1983). In this relation, λ is the wavelength of the incident radiation and a the radius of the scattering sphere. The spherical shape of the target allows to separate the solution into the radial and angular dependence, in a form of infinite series of spherical multipole partial waves. The solutions are the scattering (Qs ) and extinction efficiency (Qe ). The absorption efficiency is simply given by Qa = Qe − Qs . The relative cross sections relate to the efficiency through the size of the particle C = Qπ a 2 . Conditions where the size parameter X was much larger were not initially foreseen in Mie theory codes (e.g., Wiscombe 1980). However, a large value of X can occur in various astrophysical contexts (Wolf and Voshchinnikov 2004, and references therein). Subsequent implementations allowed to include arbitrarily large values of X (MieX, Wolf and Voshchinnikov 2004), either to be able to model scattering from very large grains or take into account very short wavelengths. When the particle size is much larger than the wavelength, the van der Hulst’s Anomalous Diffraction Theory (ADT, van de Hulst 1957) provides an analytical approximation: Qs = 2 −

4 4 sin(p) + 2 (1 − cos(p)), p p

(14)

where p = 4π a(n˜ − 1)/λ and n˜ is the ratio between the refractive index inside and outside the sphere. This approximation is only valid if n˜ does not deviate significantly from unity, indicating that the refractive index in the sphere is not very different from the ambient space, causing only a small shift of the outcoming wave. In the X-ray range, both the Mie theory (especially the latest implementations) and the ADT can be used. In particular, Draine and Allaf-Akbari (2006) showed that for E ≥ 60 eV and a > 0.035 µm( 60EeV ), silicate grains can be safely treated using the ADT approximation. In the ISM, grains are not spherical, but rather porous and elongated. The effects of geometries different than spherical (e.g., spheroids) have been explored in Hoffman and Draine (2016), using an extension of ADT (GGADT, Hoffman et al. 2015). Different types of disordered aggregates (ballistic aggregates, BA) mimic different degrees of porosity, as defined in Shen et al. (2008). While the extinction cross section for spheroids does not undergo significant changes with respect to spheres, BA may show an increased absorption cross section near the edge features

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(Hoffman and Draine 2016). This effect appears more important for edges at low (E < 1.3 keV) energies and become less visible for, e.g., the Si K and Fe K edges. The extinction cross section can be calculated for a range of energies and grain radius, via the size parameter X. As in the ISM X-rays interact with a variety of grain sizes, rather than a single one, a grain size distribution should be applied (section “The Dust Size Distribution”). In Fig. 8 (left panel), a comparison between the MRN size distribution and a distribution with sizes ranging in the interval 0.05– 0.5 µm is shown. In this example, the large grain distribution follows the same power-law shape as prescribed in the MRN model. The modulation of the region at the longer wavelength side of E0 (XFSF, section “The X-Ray Fine Structure”), due to the scattering term n in the refraction index, is therefore sensitive to the grain size distribution, while the absorption pattern, at shorter wavelengths, is not significantly affected in shape. Absorption however is slightly less efficient as a function of grain size, as can be seen in the post-edge of Fig. 8 (left panel). When modeling the transmission of a smooth continuum source through interstellar dust, the characteristic dip in scattering efficiency near a photoabsorption feature can mimic the appearance of an emission feature, while it may be in fact the sign of large grain contribution to the extinction (Zeegers et al. 2017; Rogantini et al. 2019). The central panel of Fig. 8 shows the difference in the profile of the cross section between an amorphous and a crystalline material (olivine in this case). The XAFS of the amorphous material will appear smoother, depending on the degree of amorphization of the material (Zeegers et al. 2019). This smoothing is due to the disordered organization of the atoms in a glassy material. The XAFS near the absorption edges can provide direct information on the chemistry of the intervening matter (Fig. 8, right panel). Here the absorption profile of olivine (FeMgSiO4 ) is

Fig. 8 Impact of different grain properties on the shape of the absorption or extinction cross section. Left panel: the effect of large grains on the extinction cross section is to enhance the scattering peak. Here an MRN distribution (red line) is compared with a distribution shifted towards larger grains (blue line). Center Panel: the degree of crystallinity in a grain may be visible in the absorption cross section. The disordered organization in the lattice causes the absorption features to be smeared out (yellow line). Right panel: different electron configurations entail a different XAFS pattern (section “The X-Ray Fine Structure”). Here olivine (MgFeSiO4 , black line) is compared with a pyroxene (Mg0.75 Fe0.25 SiO3 , purple line) (Courtesy of S. Zeegers)

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compared with a pyroxene (Mg0.75 Fe0.25 SiO3 ). Both the amplitude and the position of the XAFS serve as a chemical composition diagnostics (see Zeegers et al. 2019, for more examples in the silicon region). Finally, once the extinction cross section has been calculated, it can be implemented in any spectral fitting program, such as XSPEC (Arnaud 1996) and SPEX (Kaastra et al. 1996).

Scattering and Absorption of X-rays: The State of Art Ever since the scientific investigation of the ISM began, gas and dust have been observed at all wavelengths. The study of ISM in the X-ray band has been hampered in the past by instrumental limitations, while at longer wavelengths a significantly better energy and spatial resolution allowed a deep understanding of the ISM properties. The X-ray band however offers several advantage points. In particular: (i) The broadband energy coverage (0.1–10 keV) of present X-ray observatories encompasses a variety of transitions, from neutral to highly ionized gas, of the fundamental metals in the Universe: C, N, O, Ne, and Fe, among others. On the dust observation side, the X-ray band covers all the features pertaining to the major dust constituents. The photoelectric edges of neutral C, O, Mg, Si, and Fe fall in the Xray band. While other elements can be relatively easily investigated, carbon can be at the moment only reached by the LETG spectrometer on board of Chandra. This spectral region however is complicated by instrumental effects that make the study of the astronomical carbon edge challenging (e.g., Schneider and Schmitt 2010). (ii) Transmission spectra in X-rays can be obtained from a large range of column densities (logNH (cm−2 ) = 20 − 23). Provided a bright X-ray source behind an ISM layer, the large penetrating power of X-rays allows the investigation of a variety of environments of our Galaxy, from the tenuous diffuse medium to molecular clouds (Fig. 2). The diffuse medium, from an X-ray point of view, includes a range of column densities, logNH (cm−2 ), of about 20–21.7. In this regime, the oxygen K and iron L edges are well visible at low energies. As the column density increases (logNH (cm−2 ) ∼21.7–22.7), the soft X-ray edges become more absorbed, and they are eventually lost into instrumental noise. At the same time, the Mg and Si K edges become prominent. At these column densities, a variety of environments can be sampled: from extended or low density molecular clouds to far away lines of sight that cross more than one Galactic arm, for example, towards the Galactic center. Finally, X-rays can also access highly absorbed lines of sight (logNH (cm−2 ) ∼23), corresponding to AV ∼50. At this moment however, the deep iron K edge at 7.1 keV (Fig. 2) cannot be characterized, due to the still moderate energy resolution and sensitivity of the current instruments in this spectral region (e.g., Rogantini et al. 2018). (iii) The gas and the dust components of the cold phase of the ISM can be studied along the same line of sight, giving a direct information on depletion and abundance of a given element. This is especially true for oxygen, whose O I 1s − 2p prominent transition at ∼23.5 Å, lies next to the O K photoelectric edge at ∼23.3 Å

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(Gatuzz et al. 2014; Psaradaki et al. 2020). For other elements included in both gas and dust, modeling can be more complicated, as the gas transitions may lie in the same energy range of the edge structure (e.g., the iron L edges at 17.1 Å, Costantini et al. 2012). In some situations, there may be no very prominent gas transitions (e.g., near the Si edge at 6.74 Å, Rogantini et al. 2019). (iv) The two components of extinction, i.e., scattering and absorption, may be investigated along the same line of sight. Both imaging and spectroscopy can indeed provide information on the dust chemistry, grain size distribution, and dust clumpiness along the line of sight (Corrales et al. 2016). (v) Finally, many of the bright X-ray sources in the Galaxy are located along the plane (|b| < 12 deg, Predehl and Schmitt 1995). This provides a very effective sampling along different lines of sight where most of the cold phase of the ISM resides. Low-mass X-ray binaries, thanks to their almost featureless intrinsic broadband spectrum, are the sources most suitable for dust studies. High-mass X-ray binaries and supernova remnants display a spectrum rich of emission lines over a broad energy interval. This hampers, in general, the detection of the dust fine structure close to the absorption edges. Dust modeling from the X-ray point of view aimed at first at confirming the findings obtained at long wavelengths. However, given the complementary and the advantages provided by the X-ray properties of the ISM, results have also challenged the common knowledge built up so far. Here we try to summarize our current understanding of dust from the X-ray side. Chemical Composition The strength of the X-ray band is to display, for a given column density, at least two visible absorption edges in an absorbed spectrum, potentially belonging to silicates. This allowed the study of these materials along lines of sight with different column densities. The studied sources, sometimes revisited with different instruments (namely, the XMM-Newton-RGS, Chandra-LETG and ChandraHETG grating spectrometers), are in general X-ray-bright low-mass X-ray binaries (F lux(2 − 10 keV) > 10−9 erg cm−2 s−1 ). From the study of both the individual edges and a simultaneous modeling of the O K and Fe L edges, prominent in the diffuse medium, it has been reported the presence of Mg-rich silicates both in absorption (Costantini et al. 2012; Psaradaki et al. 2020; Valencic and Smith 2013) and from scattering halos (Costantini et al. 2005). Amorphous olivine does not seem to play a major role towards those studied lines of sight. Valencic and Smith (2013) report, for example, a ratio of enstatite over olivine of about 3.4. As seen in section “Interstellar Dust,” Mg-rich silicates would be consistent with a chain of dust condensation events in equilibrium conditions in a stellar wind. However, even under these conditions, amorphous olivine should be present in significant amount. The GEMS-like particles, amorphous, and Mgrich silicates would be consistent with the X-ray results. In a dedicated experiment, however, the iron-L edge of one sight line has been compared with real GEMS, returned by the Stardust mission from the comet 81P/Wild 2 environment (Westphal et al. 2019). The iron profile of GEMS turned out to be incompatible with the

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astronomical data of the ISM, indicating that cometary fine-grained material might not be a proxy for interstellar dust. The iron edges provide in principle a direct view of iron in the ISM. Given the extreme depletion of this element, the edge shape is mostly determined by dust absorption. Along diffuse lines of sight, the iron L edge has been found to be dominated either by oxides (e.g., Fe2 O3 ) in a mixture of different silicates (Lee et al. 2009) or metallic iron (Costantini et al. 2012) or FeS mixed with metallic iron (Westphal et al. 2019). It must be noted however that different sets of dust models were used in different works, especially for iron compounds. Therefore, this apparent discordance in results may be still attributed to a difference in modeling and completeness of the data bases. Lines of sight characterized by a higher column density (logNH (cm−2 ) ∼22.1– 22.9) has been more consistently studied in the recent literature, using the same set of laboratory measurements for Mg and Si. The modeling of the Si K edge alone (Zeegers et al. 2019) and the combined Mg and Si K edges (Rogantini et al. 2020) pointed to a different scenario with respect to the more diffuse medium. The contribution of amorphous olivine has been reported to be dominant along these lines of sight. Considering the high signal-to-noise ratio data in the samples of source in Zeegers et al. (2019) and Rogantini et al. (2020, around 10 sources), olivine has been deemed to contribute more than 60%, and up to 80%, to the total dust budget for a given source. In Fig. 9 an example of Si absorption along the line of sight of GX 3+1 is given. The majority of absorption is attributed to amorphous olivine in this fit (Rogantini et al. 2020). Although the presence of olivine has been determined with high confidence, it has to be noted that for relatively large values of NH , the iron L edges are inaccessible. Therefore, the simultaneous presence of any metallic iron, iron sulfide, or iron oxides could not be tested.

Transmission

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Fig. 9 Chandra-HETG data around the Si edge along the line of sight of GX 3+1. The best fit (red line) is dominated by amorphous olivine (black line). Minor amounts of other types of dust and neutral gas were also detected. The data are normalized for the continuum emission intrinsic to the source (Adapted from Rogantini et al. 2020)

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Dust Size Distribution The MRN dust size distribution has been often preferred in the modeling, by virtue of its simple analytical form (section “The Dust Size Distribution”). By means of high-resolution X-ray spectroscopy, indications of a deviation from this distribution have been sometimes reported. Westphal et al. (2019) report a lower limit on the size of larger grain contribution of a > 245 nm along the line of sight of Cyg X-1. Zeegers et al. (2017) report an improvement of the fit towards GX 5-1 if a distribution with a size range of 0.05–0.5µm is adopted. Although the scattering feature in the pre-edge region can be a predictive tool for the dust distribution (Fig. 8), in practice, its use may be hampered by several factors. Low signal to noise in spectral regions that may be crowded with lines from the ISM may be a contributing factor (e.g., Psaradaki et al. 2020). Sometimes instrumental features may also confuse the picture (e.g., Rogantini et al. 2020). Finally, the scattering peak strength is energy dependent (Hoffman and Draine 2016; Draine 2003); therefore, some edges may not provide useful information. Results from scattering halos indicate that the dust size distribution may not be homogeneous from cloud to cloud. This can be quantified especially when bright and well-defined scattering rings are present (section “Dust Scattering from the ISM”). For instance, some intervening dust layers towards V404 Cyg, which displayed a series of time variable rings in 2015, have been found to have steeper dust size distributions with respect to MRN. A population of large grains was also reported along this line of sight (a > 0.15 µm, Heinz et al. 2016; Vasilopoulos and Petropoulou 2016; Beardmore et al. 2016). An upper limit of a < 0.4 µm has been found along the diffuse sight lines of sources within 5 kpc (Valencic and Smith 2015). Very large grains (with an upper limit of ∼0.6 µm) have been tentatively suggested for a line of sight near the Galactic center (Jin et al. 2017). However, given the variety of grain size distributions available in the literature, fitting 1-D surface brightness profiles of dust scattering halos often yields inconclusive results due to a degeneracy between the grain size and dust cloud location when modeling the intensity profile (Costantini et al. 2005; Xiang et al. 2005; Mao et al. 2014; Valencic and Smith 2015). Using other markers of dust in the ISM, such as the optical extinction properties AV or E(B − V ), can assist in constraining the dust grain population models (Valencic and Smith 2015). Comparing the dust scattering halo intensity profiles among different energy bands can also break this degeneracy (Corrales and Paerels 2015).

Crystallinity As seen above (Fig. 8, central panel), the sharpness of the XAFS near the edge may be an indicator, along side the edge shape and position, of absorption by dust in crystalline form. Recent modeling of the X-ray Si and Mg edges reports consistently the presence of crystalline dust, next to the amorphous component. Its contribution to the total dust was reported to be 4–35% when only the Si K edge was considered (Zeegers et al. 2019). A similar range of ∼7–27% was found for a different set of sources when a simultaneous Mg and Si fitting was performed

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(Rogantini et al. 2020). This is in apparent contradiction with studies in the IR (e.g., Kemper et al. 2004; Li et al. 2007, section “Interstellar Dust”). However, X-rays and IR may have different diagnostic power, as the X-rays reach the short range domain (atomic distances), while the IR tests the long range interaction (molecular distances). More studies are necessary to corroborate this findings; however, the presence of more crystalline structures than thought before may open new debate on crystalline dust formation and survival in the ISM. Abundance and Depletion As seen in section “Attenuation of X-Rays by the Interstellar Medium, the X-ray band does not host any distinctive hydrogen feature, but has to rely on the modeling of the soft energy cut off to determine the hydrogen column density. The evaluation of the metal abundances therefore depends on a reliable determination of the hydrogen along the line of sight and on the cosmic abundance chosen. In some circumstances (e.g., Lee et al. 2002; van Peet et al. 2009; Grinberg et al. 2015), additional cold material, possibly variable in time, may be associated to the immediate surrounding of the source, providing an apparent overabundance of metals along the line of sight. The metal abundances are determined using the depth of the respective edges and the strength of their gas transitions. The absorption edge includes both gas and dust total contributions, providing an immediate measure of the amount of a given element. Adopting Lodders and Palme (2009) as reference for solar abundances, the values recently reported do not differ dramatically from the solar ones. A deviation of 10–20% at most for iron and oxygen (Pinto et al. 2013; Costantini et al. 2012) and few percent for Mg and Si (e.g., Rogantini et al. 2020) has been found. The oxygen cold-gas content has been studied in detail in Nicastro et al. (2016) and Gatuzz et al. (2016). From the modeling of the O I absorption line in a sample of Galactic X-ray sources spectra, Nicastro et al. (2016) found the oxygen abundance for the cold medium, residing mainly in the Galactic disk, to be slightly super-solar, using the oxygen abundance prescribed in Wilms et al. −4 (2000) (A⊙ O = 4.9 × 10 ). Translating their result with the (Lodders and Palme −4 2009) oxygen abundance (A⊙ O = 6.0 × 10 ), for an easier comparison, a value of ⊙ AO /AO ∼ 1.3 is obtained. Using a similar approach, Gatuzz et al. (2016) report a wide range of abundance values, mostly sub-solar, along the line of sight of 24 X-ray binaries. It has to be noted that large uncertainties are associated to many of those measurements. Again, converting those values from the oxygen abundances used in that work (6.7 × 10−4 , Grevesse and Sauval 1998), to the value in Lodders and Palme (2009), a range AO /A⊙ O ∼ 0.25−1.5, with a median of ∼0.7, is obtained. The Fe abundance, derived from the Fe L edges, assuming gas as the only absorber, has been also studied in Gatuzz et al. (2016). With large associated uncertainties, the range reported is AFe /A⊙ Fe ∼ 0.17 − 1.55, with a median of ∼0.65. Note that the reference for the Fe solar abundance is very similar in this case for Grevesse and Sauval (1998) and Lodders and Palme (2009): 3.15 × 10−5 and 3.25 × 10−5 , respectively.

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Depletion values as measured in the X-rays generally confirm what hypothesized using longer wavelength techniques. In particular, when gas and dust components are used to model the Mg, Si, and Fe edges, it is systematically found that dust dominates the absorption. The Si inclusion in dust has been well constrained to be in the range 96–98% for all high-column density lines of sight (Rogantini et al. 2020). For magnesium, upper limits have been determined (>74–99% Rogantini et al. 2020). Iron has been also reported to be included almost totally in the dust phase (e.g., ∼87% Costantini et al. 2012). Oxygen has been studied along diffuse lines of sight, and its depletion has been found to be moderate. Around 7–20% is the amount of oxygen in dust necessary to fit the O K edge, the rest being in gas form (Pinto et al. 2013; Costantini et al. 2012; Psaradaki et al. 2020), consistently with what observed in optical/UV (Jenkins 2009). Dust Spatial Distribution Scattering halos offer a novel method to measure the spatial distribution of dust along the line of sight of a bright X-ray source. As described in section “Dust Scattering from the ISM,” quiescent dust scattering halo profiles are smooth and offer limited insight on the exact position of intervening dust (e.g., Smith et al. 2002). This is because the two parameters, distance of the background source and the distance of the scattering dust cloud, are degenerate with the dust grain size distribution (Predehl and Klose 1996), with resulting uncertainties that may reach hundreds of parsecs (e.g., Mao et al. 2014; Xiang et al. 2011). Nonetheless, the latest survey of 35 quiescent dust scattering halos imaged with the Chandra and XMM-Newton observatories finds that the majority of nearby (D < 5 kpc) ISM sight lines are well fit with single clouds (Valencic and Smith 2015), while more distant sources required multiple clouds or size distributions. More precise measurements of the foreground spatial distribution of dust can be determined from dust scattering echoes, especially when combined with other tracers of interstellar dust such as CO maps (Tiengo et al. 2010; Heinz et al. 2015) and stellar extinction studies (Heinz et al. 2016). It is anticipated that dozens more high contrast dust scattering echoes could be imaged with the next generation of X-ray telescopes, for this type of study (Corrales et al. 2019).

Future Outlook The X-ray observatories XMM-Newton and Chandra have enormously advanced the study of the ISM, thanks to the resolving power (R = E/ΔE ∼ 400 − 1000) of the grating instruments in the soft (∼0.5–2 keV) X-ray band. Future instruments, for example, the calorimeters on board XRISM (Tashiro et al. 2018) and Athena (Barret et al. 2016), will explore at higher resolution the energy range with energies >1–2 keV. This will make accessible different absorption edges (Al, S, Ca, Fe K edges Rogantini et al. 2018; Costantini et al. 2019), in addition to an even better

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view of the Mg and Si K edges. The energy resolution, ΔE, will be 5 and 2.5 eV for XRISM-Resolve and Athena-XIFU, respectively. This, combined with a high effective area in the 2–10 keV range, will allow the study of XAFS even for the shallower edges expected for, e.g., Ca and Al (Fig. 10, left panel). The new energy window will allow the X-ray exploration of very-high-column density molecular environments, near the Galactic center. In particular, the iron inclusion in those environments will be studied, by means of the Fe K edge at 7.1 keV (Rogantini et al. 2018). Absorption edges from Mg and Si will be explored into greater detail, allowing a deeper study on grain size distribution (XRISM Science Team 2020). A higher resolving power, as proposed for the concept mission Arcus (R ∼ 3800, Smith 2020), in the soft energy band would allow to study in detail, alongside the iron L edges, the oxygen K edge, rich in absorption features of gas and dust (e.g., Juett et al. 2004; Costantini et al. 2012; Psaradaki et al. 2020) and the carbon edge at 0.28 keV (Fig. 10, right panel). The study of this edge, with highresolution spectroscopy, would reveal the physical characteristics of one of the major components of ISM, as graphite would show distinctive features with respect to amorphous carbon or HAC (Costantini et al. 2019, and section “Interstellar Dust”). The high sensitivity provided by both future calorimeters and CCD-imaging instruments (Tashiro et al. 2018; Nandra et al. 2013) will allow to study many more, fainter scattering halos. Five Galactic X-ray sources have produced the brightest dust ring echoes to date (Tiengo et al. 2010; Heinz et al. 2015, 2016; Kalemci

Fig. 10 Left panel: Athena-XIFU simulation of the Ca K edge for an intervening column density of NH = 6.9 × 1022 cm−2 . The simulated data (adopting only gas) are compared with models with different types of dust. While different types of silicates will be difficult to distinguish using the Ca K edge alone, other compounds will be easily disentangled (adapted from Costantini et al. 2019). Right panel: Arcus simulation of the carbon region, for a source with a moderate column density. The simulated data (adopting only gas) are compared with models with different types of dust and gas mixture. Carbon in gas is assumed to be 40% of the total. The simulation shows that graphite and (hydrogenated) amorphous carbon can be disentangled (adapted from Costantini et al. 2019)

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et al. 2018; Nobukawa et al. 2020). The next generation of X-ray observatories, with 50–80 times the sensitivity of current instruments, are expected to capture high contrast dust ring echoes at about 30 times the frequency of current X-ray observatories (Corrales et al. 2019). The bright sources will offer to routinely perform spatially resolved halo spectroscopy, which reveals the chemical properties of dust alone (Decourchelle et al. 2013; XRISM Science Team 2020). In Fig. 11, an example of how spatially resolved scattering halo spectra will be observed is shown. Once the contribution of the central source spectrum has been divided out, the scattering halo spectrum will reveal the XSFS features (section “The X-Ray Fine Structure”). Those will allow us to determine both the chemistry (Fig. 11, upper panel) and the dust size distribution (lower panel) of virtually any line of sight displaying a scattering halo.

fh (Fh / Fps)

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Fig. 11 Simulated ratio, using the XRISM-resolve resolution, of scattering halo flux (Fh ) to point source flux (Fps ), accounting for the fraction of the scattering halo captured (fh ) by a small field-of-view. (Top) A zoom-in of the scattering features from silicate dust around the Si K edge, arising from an ISM column density of NH ≈ 4 × 1022 cm−2 and assuming an MRN (Mathis et al. 1977) power-law distribution of dust grains with particle sizes less than 0.3 µm. The simulated data and red curve follow the theoretical cross sections for silicate features from Draine (2003). The features modeled from laboratory data of Zeegers et al. (2017) are overlaid, for olivines (green) and amorphous pyroxenes (purple). (Bottom) Demonstration of the change in scattering halo flux from the contribution of large dust grains. The same ratio is plotted as in the top panel, for the MRN distribution of grains (solid curves). The same mass of dust, following a power-law slope of MRN but consisting of dust grains between 0.1 and 0.5 µm in radius, produces a much brighter scattering halo and XSFS features with a larger amplitude (dashed curves)

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Acknowledgments The authors wish to thank S. Zeegers, D. Rogantini, I. Psaradaki, R. Waters and S. Heinz for interesting discussions, help with the figures, and for their insightful comments on this manuscript.

References N. Altobelli et al., Flux and composition of interstellar dust at Saturn from Cassini’s Cosmic Dust Analyzer. Science 352, 312–318 (2016). https://doi.org/10.1126/science.aac6397 A.L. Ankudinov, B. Ravel, J.J. Rehr, S.D. Conradson, Real-space multiple-scattering calculation and interpretation of x-ray-absorption near-edge structure. Phys. Rev. B 58, 7565–7576 (1998). https://doi.org/10.1103/PhysRevB.58.7565 K.A. Arnaud, XSPEC: the first ten years. Astron. Data Anal. Softw. Syst. V 101, 17 (1996) F. Bacon, Sylva Sylvarum: Or a Natural History in Ten Centuries (1626). ISBN: 1497875498 I.M. Band, M.B. Trzhaskovskaia, D.A. Verner, D.G. Iakovlev, K-shell photoionization cross sections – calculations and simple fitting formulae. Astron. Astrophys. 237, 267–269 (1990) E.E. Barnard, On the dark markings of the sky, with a catalogue of 182 such objects. Astrophys. J. 49, 1–24 (1919). https://doi.org/10.1086/142439 D. Barret et al., The Athena X-ray Integral Field Unit (X-IFU). Space Telescopes and Instrumentation 2016: Ultraviolet to Gamma Ray 9905 (2016). https://doi.org/10.1117/12.2232432 A.P. Beardmore et al., Lord of the Rings – return of the King: Swift-XRT observations of dust scattering rings around V404 Cygni. Mon. Not. R. Astron. Soc. 462, 1847–1863 (2016). https:// doi.org/10.1093/mnras/stw1753 R.C. Bohlin, B.D. Savage, J.F. Drake, A survey of interstellar H I from Lalpha absorption measurements. II. Astrophys. J. 224, 132–142 (1978). https://doi.org/10.1086/156357 C.F. Bohren, D.R. Huffman, Absorption and Scattering of Light by Small Particles. (Wiley, New York, 1983) C.H. Booth, F. Bridges, Improved self absorption correction for fluorescence measurements of extended X-ray absorption fine structure. Phys. Scripta. 202 (2005). https://doi.org/10.1238/ physica.topical.115a00202 F. Boulanger, P. Cox, A.P. Jones, Course 7: dust in the interstellar medium. Infrared Space Astron. Today Tomorrow 70, 251 (2000). https://doi.org/10.1146/annurev.astro.34.1.279 J.P. Bradley, Chemically anomalous, preaccretionally irradiated grains in interplanetary dust from Comets. Science 265, 925–929 (1994). https://doi.org/10.1126/science.265.5174.925 J.A. Cardelli, G.C. Clayton, J.S. Mathis, The relationship between infrared, optical, and ultraviolet extinction. Astrophys. J. 345, 245 (1989). https://doi.org/10.1086/167900 P.A. Charles et al., The interstellar oxygen edge in the X-ray spectrum of the Crab Nebula. Astrophys. J. 230, L83–L86 (1979). https://doi.org/10.1086/182966 D.D. Clayton, Precondensed Matter: Key to the Early Solar System (Paper presesnted at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.). Moon Planets 19, 109–137 (1978). https://doi.org/10.1007/BF00896983 D.D. Clayton, Precondensed Matter: Key to the Early Solar System (Paper presesnted at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.). Moon Planets 19, 109–137 (1978). https://doi.org/10.1007/BF00896983 F. Combes, Distribution of CO in the milky way. Ann. Rev. Astron. Astrophys. 29, 195–237 (1991). https://doi.org/10.1146/annurev.aa.29.090191.001211 M. Compiègne et al., The global dust SED: tracing the nature and evolution of dust with DustEM. Astron. Astrophys. 525 (2011). https://doi.org/10.1051/0004-6361/201015292 L.R. Corrales, F. Paerels, The dust scattering halo of Cygnus X-3. Mon. Not. R. Astron. Soc. 453, 1121–1135 (2015). https://doi.org/10.1093/mnras/stv1704

104 Interstellar Absorption and Dust Scattering

3647

L.R. Corrales, J. García, J. Wilms, F. Baganoff, The dust-scattering component of X-ray extinction: effects on continuum fitting and high-resolution absorption edge structure. Mon. Not. R. Astron. Soc. 458, 1345–1351 (2016). https://doi.org/10.1093/mnras/stw376 L. Corrales, B.S. Mills, S. Heinz, G.M. Williger, The X-ray variable sky as seen by MAXI: the future of dust-echo tomography with bright galactic X-ray bursts. Astrophys. J. 874 (2019). https://doi.org/10.3847/1538-4357/ab0c9b E. Costantini, M.J. Freyberg, P. Predehl, Absorption and scattering by interstellar dust: an XMMNewton observation of Cyg X-2. Astron. Astrophys. 444, 187–200 (2005). https://doi.org/10.1051/0004-6361:20042562 E. Costantini et al., XMM-Newton observation of 4U 1820-30. Broad band spectrum and the contribution of the cold interstellar medium. Astron. Astrophys. 539 (2012). https://doi.org/ 10.1051/0004-6361/201117818 E. Costantini, S.T. Zeegers, D. Rogantini, C.P. de Vries, A.G.G.M. Tielens, L.B.F.M. Waters, X-ray extinction from interstellar dust. Prospects of observing carbon, sulfur, and other trace elements. Astron. Astrophys. 629 (2019). https://doi.org/10.1051/0004-6361/201833820 D.T. Cromer, D. Liberman, Relativistic calculation of anomalous scattering factors for X rays. J. Chem. Phys. 53, 1891–1898 (1970). https://doi.org/10.1063/1.1674266 T.M. Dame, D. Hartmann, P. Thaddeus, The milky way in molecular clouds: a new complete CO survey. Astrophys. J. 547, 792–813 (2001). https://doi.org/10.1086/318388 A. Decourchelle et al., The Hot and Energetic Universe: the astrophysics of supernova remnants and the interstellar medium. arXiv e-prints (2013) I. De Looze et al., The dust mass in Cassiopeia A from a spatially resolved Herschel analysis. Mon. Not. R. Astron. Soc. 465, 3309–3342 (2017). https://doi.org/10.1093/mnras/stw2837 K. Demyk, A.P. Jones, E. Dartois, P. Cox, L. D’Hendecourt, The chemical composition of the silicate dust around RAFGL7009S and IRAS 19110+1045. Astron. Astrophys. 349, 267–275 (1999) B.T. Draine, Interstellar dust grains. Ann. Rev. Astron. Astrophys. 41, 241–289 (2003). https://doi. org/10.1146/annurev.astro.41.011802.094840 B.T. Draine, Scattering by interstellar dust grains. II. X-rays. Astrophys. J. 598, 1026–1037 (2003). https://doi.org/10.1086/379123 B.T. Draine, Physics of the Interstellar and Intergalactic Medium, ed. by B.T. Draine (Princeton University Press, 2011). ISBN: 978-0-691-12214-4 B.T. Draine, K. Allaf-Akbari, X-ray scattering by nonspherical grains. I. Oblate spheroids. Astrophys. J. 652, 1318–1330 (2006). https://doi.org/10.1086/508133 B.T. Draine, A.A. Fraisse, Polarized far-infrared and submillimeter emission from interstellar dust. Astrophys. J. 696, 1–11 (2009). https://doi.org/10.1088/0004-637X/696/1/1 B.T. Draine, J.C. Tan, The scattered X-ray Halo around Nova Cygni 1992: testing a model for interstellar dust. Astrophys. J. 594, 347–362 (2003). https://doi.org/10.1086/376855 W.W. Duley, A.P. Jones, D.A. Williams, Hydrogenated amorphous carbon-coated silicate partcles as a source ofinterstellar extinction. Mon. Not. R. Astron. Soc. 236, 709–725 (1989). https:// doi.org/10.1093/mnras/236.4.709 E. Dwek, Iron: a key element for understanding the origin and evolution of interstellar dust. Astrophys. J. 825 (2016). https://doi.org/10.3847/0004-637X/825/2/136 H.M. Dyck, C.A. Beichman, Observations of infrared polarization in the Orion Nebula. Astrophys. J. 194, 57–64 (1974). https://doi.org/10.1086/153223 R.F. Egerton, Electron Energy-Loss Spectroscopy in the Electron Microscope, XII, 3rd edn. (Springer, New York, 2011), p. 491. https://doi.org/10.1007/978-1-4419-9583-4 K.M. Ferrière, The interstellar environment of our galaxy. Rev. Mod. Phys. 73, 1031–1066 (2001). https://doi.org/10.1103/RevModPhys.73.1031 G.B. Field, Interstellar abundances: gas and dust. Astrophys. J. 187, 453–459 (1974). https://doi. org/10.1086/152654 D.R. Foight, T. Güver, F. Özel, P.O. Slane, Probing X-ray absorption and optical extinction in the interstellar medium using Chandra observations of supernova remnants. Astrophys. J. 826 (2016). https://doi.org/10.3847/0004-637X/826/1/66

3648

E. Costantini and L. Corrales

H.-P. Gail, Formation and Evolution of Minerals in Accretion Disks and Stellar Outflows. Lecture Notes in Physics (Springer, Berlin, 2010), pp. 61–141. https://doi.org/10.1007/978-3-64213259-9_2 E. Gatuzz, J. García, C. Mendoza, T.R. Kallman, M.A. Bautista, T.W. Gorczyca, Physical properties of the interstellar medium using high-resolution Chandra spectra: O K-edge absorption. Astrophys. J. 790 (2014). https://doi.org/10.1088/0004-637X/790/2/131 E. Gatuzz, J.A. García, T.R. Kallman, C. Mendoza, Oxygen, neon, and iron X-ray absorption in the local interstellar medium. Astron. Astrophys. 588 (2016). https://doi.org/10.1051/00046361/201527752 P. Giannozzi et al., QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21 (2009). https://doi.org/10.1088/ 0953-8984/21/39/395502 H.L. Gomez et al., A cool dust factory in the Crab nebula: a herschel study of the filaments. Astrophys. J. 760 (2012). https://doi.org/10.1088/0004-637X/760/1/96 H.L. Gomez et al., Dust in historical Galactic Type Ia supernova remnants with Herschel. Mon. Not. R. Astron. Soc.420,3557–3573 (2012). https://doi.org/10.1111/j.1365-2966.2011.20272.x P. Gorenstein, Empirical relation between interstellar X-ray absorption and optical extinction. Astrophys. J. 198, 95–101 (1975). https://doi.org/10.1086/153579 N. Grevesse, A.J. Sauval, Standard solar composition. Space Sci. Rev. 85, 161–174 (1998). https:// doi.org/10.1023/A:1005161325181 V. Grinberg et al., Long term variability of Cygnus X-1. VII. Orbital variability of the focussed wind in Cyg X-1/HDE 226868 system. Astron. Astrophys. 576 (2015). https://doi.org/10.1051/ 0004-6361/201425418 T. Güver, F. Özel, The relation between optical extinction and hydrogen column density in the Galaxy. Mon. Not. R. Astron. Soc. 400, 2050–2053 (2009). https://doi.org/10.1111/j.13652966.2009.15598.x M.S. Hanner, M.E. Zolensky, The Mineralogy of Cometary Dust. Lecture Notes in Physics (Springer, Berlin, 2010), pp. 203–232. https://doi.org/10.1007/978-3-642-13259-9_4 S. Hayakawa, Scattering of cosmic X-rays by interstellar dust grains. Progress Theor. Phys. 43, 1224–1230 (1970). https://doi.org/10.1143/PTP.43.1224 S. Heinz et al., Lord of the rings: a kinematic distance to Circinus X-1 from a giant X-ray light echo. Astrophys. J. 806 (2015). https://doi.org/10.1088/0004-637X/806/2/265 S. Heinz et al., A joint Chandra and Swift view of the 2015 X-ray dust-scattering echo of V404 Cygni. Astrophys. J.825 (2016). https://doi.org/10.3847/0004-637X/825/1/15 B.L. Henke, E.M. Gullikson, J.C. Davis, X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92. At. Data Nucl. Data Tables 54, 181–342 (1993). https://doi.org/10.1006/adnd.1993.1013 H. Hirashita, N.V. Voshchinnikov, Effects of grain growth mechanisms on the extinction curve and the metal depletion in the interstellar medium. Mon. Not. R. Astron. Soc. 437, 1636–1645 (2014). https://doi.org/10.1093/mnras/stt1997 J. Hoffman, B.T. Draine, Accurate modeling of X-ray extinction by interstellar grains. Astrophys. J. 817 (2016). https://doi.org/10.3847/0004-637X/817/2/139 J. Hoffman, M. Tarczon, B.T. Draine, GGADT: Generalized Geometry Anomalous Diffraction Theory. Astrophysics Source Code Library. ascl:1510.001 (2015) H.A. Ishii et al., Multiple generations of grain aggregation in different environments preceded solar system body formation. Proc. Natl. Acad. Sci. 115, 6608–6613 (2018). https://doi.org/10.1073/ pnas.1720167115 F. Jansen et al., XMM-Newton observatory. I. The spacecraft and operations. Astron. Astrophys. 365, L1–L6 (2001). https://doi.org/10.1051/0004-6361:20000036 E.B. Jenkins, A unified representation of gas-phase element depletions in the interstellar medium. Astrophys. J. 700, 1299–1348 (2009). https://doi.org/10.1088/0004-637X/700/2/1299 C. Jin, G. Ponti, F. Haberl, R. Smith, Probing the interstellar dust towards the Galactic Centre: dustscattering halo around AX J1745.6-2901. Mon. Not. R. Astron. Soc. 468, 2532–2551 (2017). https://doi.org/10.1093/mnras/stx653

104 Interstellar Absorption and Dust Scattering

3649

A.M. Juett, N.S. Schulz, D. Chakrabarty, High-resolution X-ray spectroscopy of the interstellar medium: structure at the oxygen absorption edge. Astrophys. J. 612, 308–318 (2004). https:// doi.org/10.1086/422511 J.S. Kaastra, R. Mewe, H. Nieuwenhuijzen, SPEX: a new code for spectral analysis of X & UV spectra. UV and X-Ray Spectroscopy of Astrophysical and Laboratory Plasmas (1996), pp. 411–414 J.S. Kaastra, F.B.S. Paerels, F. Durret, S. Schindler, P. Richter, Thermal Radiat. Processes. Space Sci. Rev. 134, 155–190 (2008). https://doi.org/10.1007/s11214-008-9310-y P.M.W. Kalberla, J. Kerp, The Hi distribution of the milky way. Ann. Rev. Astron. Astrophys. 47, 27–61 (2009). https://doi.org/10.1146/annurev-astro-082708-101823 P.M.W. Kalberla, L. Dedes, J. Kerp, U. Haud, Dark matter in the Milky Way. II. The HI gas distribution as a tracer of the gravitational potential. Astron. Astrophys. 469, 511–527 (2007). https://doi.org/10.1051/0004-6361:20066362 E. Kalemci, T.J. Maccarone, J.A. Tomsick, A dust-scattering Halo of 4U 1630-47 observed with Chandra and Swift: new constraints on the source distance. Astrophys. J. 859 (2018). https:// doi.org/10.3847/1538-4357/aabcd3 L.P. Keller, S. Messenger, On the origins of GEMS grains. Geochimica et Cosmochimica Acta 75, 5336–5365 (2011). https://doi.org/10.1016/j.gca.2011.06.040 F. Kemper et al., Detection of carbonates in dust shells around evolved stars. Nature 415, 295–297 (2002). https://doi.org/10.1038/415295a F. Kemper, W.J. Vriend, A.G.G.M. Tielens, The absence of crystalline silicates in the diffuse interstellar medium. Astrophys. J. 609, 826–837 (2004). https://doi.org/10.1086/421339 H.A. Kramers, Wellenmechanik und halbzahlige Quantisierung. Zeitschrift fur Physik 39, 828–840 (1926). https://doi.org/10.1007/BF01451751 R.D.L. Kronig, On the theory of dispersion of x’rays. J. Opt. Soc. Am. (1917–1983) 12, 547 (1926) J.C. Lee, B. Ravel, Determining the grain composition of the interstellar medium with highresolution X-ray spectroscopy. Astrophys. J. 622, 970–976 (2005). https://doi.org/10.1086/ 428118 J.C. Lee, C.S. Reynolds, R. Remillard, N.S. Schulz, E.G. Blackman, A.C. Fabian, High-resolution Chandra HETGS and Rossi X-ray timing explorer observations of GRS 1915+105: a hot disk atmosphere and cold gas enriched in iron and silicon. Astrophys. J. 567, 1102–1111 (2002). https://doi.org/10.1086/338588 J.C. Lee, J. Xiang, B. Ravel, J. Kortright, K. Flanagan, Condensed matter astrophysics: a prescription for determining the species-specific composition and quantity of interstellar dust using X-rays. Astrophys. J. 702, 970–979 (2009). https://doi.org/10.1088/0004-637X/702/2/ 970 E.S. Levine, L. Blitz, C. Heiles, The spiral structure of the outer milky way in hydrogen. Science 312, 1773–1777 (2006). https://doi.org/10.1126/science.1128455 M.P. Li, G. Zhao, A. Li, On the crystallinity of silicate dust in the interstellar medium. Mon. Not. R. Astron. Soc. 382, L26–L29 (2007). https://doi.org/10.1111/j.1745-3933.2007.00382.x Z. Ling, S.N. Zhang, S. Tang, Determining the distance of Cyg X-3 with its X-ray dust scattering Halo. Astrophys. J. 695, 1111–1120 (2009). https://doi.org/10.1088/0004-637X/695/2/1111 H. Liszt, N(H I)/E(B – V). Astrophys. J. 780 (2014). https://doi.org/10.1088/0004-637X/780/1/10 K. Lodders, H. Palme, Solar system elemental abundances in 2009. Meteorit. Planet. Sci. Suppl. 72, 5154 (2009) J. Mao, Z. Ling, S.-N. Zhang, X-Ray Scattered Halo around IGR J17544-2619. Astrophys. J. 785 (2014). https://doi.org/10.1088/0004-637X/785/1/23. qui P.G. Martin, On the interaction of cosmic X-rays with interstellar grains. Mon. Not. R. Astron. Soc. 149, 221 (1970). https://doi.org/10.1093/mnras/149.3.221 J.S. Mathis, W. Rumpl, K.H. Nordsieck, The size distribution of interstellar grains. Astrophys. J. 217, 425–433 (1977). https://doi.org/10.1086/155591 M. Matsuura et al., Herschel detects a massive dust reservoir in supernova 1987A. Science 333, 1258 (2011). https://doi.org/10.1126/science.1205983 C.W. Mauche, P. Gorenstein, Measurements of X-ray scattering from interstellar grains. Astrophys. J. 302, 371 (1986). https://doi.org/10.1086/163996

3650

E. Costantini and L. Corrales

C.F. McKee, J.P. Ostriker, A theory of the interstellar medium: three components regulated by supernova explosions in an inhomogeneous substrate. Astrophys. J. 218, 148–169 (1977). https://doi.org/10.1086/155667 S. Messenger, L.P. Keller, F.J. Stadermann, R.M. Walker, E. Zinner, Samples of stars beyond the solar system: silicate grains in interplanetary dust. Science 300, 105–108 (2003). https://doi. org/10.1126/science.1080576 G. Mie, Beiträge zur Optik trüber Medien, speziell kolloidaler Metallösungen. Annalen der Physik 330, 377–445 (1908). https://doi.org/10.1002/andp.19083300302 F.J. Molster, L.B.F.M. Waters, F. Kemper, The Mineralogy of Interstellar and Circumstellar Dust in Galaxies. Lecture Notes in Physics (Springer, Berlin, 2010), pp. 143–201. https://doi.org/10. 1007/978-3-642-13259-9_3 K. Nandra et al., The Hot and Energetic Universe: A White Paper presenting the science theme motivating the Athena+ mission. arXiv e-prints (2013) M. Newville, Fundamentals of XAFS. Rev. Mineral. Geochem. 78, 33–74 (2014). https://doi.org/ 10.2138/rmg.2014.78.2 F. Nicastro et al., X-ray detection of warm ionized matter in the Galactic halo. Mon. Not. R. Astron. Soc. 457, 676–694 (2016). https://doi.org/10.1093/mnras/stv2923 K.K. Nobukawa, M. Nobukawa, S. Yamauchi, Discovery of annular X-ray emission centered on MAXI J1421-613: dust-scattering X-rays? Publ. Astron. Soc. Jpn. 72 (2020). https://doi.org/10. 1093/pasj/psaa007 T. Nozawa, K. Maeda, T. Kozasa, M. Tanaka, K. Nomoto, H. Umeda, Formation of dust in the ejecta of type Ia supernovae. Astrophys. J. 736 (2011). https://doi.org/10.1088/0004-637X/736/ 1/45 J.W. Overbeck, Small-angle scattering of celestial X-rays by interstellar grains. Astrophys. J. 141, 864 (1965). https://doi.org/10.1086/148180 C. Pinto, J.S. Kaastra, E. Costantini, C. de Vries, Interstellar medium composition through X-ray spectroscopy of low-mass X-ray binaries. Astron. Astrophys. 551 (2013). https://doi.org/10. 1051/0004-6361/201220481 C.A. Poteet, D.C.B. Whittet, B.T. Draine, The composition of interstellar grains toward ζ Ophiuchi: constraining the elemental budget near the diffuse-dense cloud transition. Astrophys. J. 801 (2015). https://doi.org/10.1088/0004-637X/801/2/110 P. Predehl, S. Klose, Dust scattered X-ray haloes as diagnostic tools: potential and current limitations. Astron. Astrophys. 306, 283 (1996) P. Predehl, J.H.M.M. Schmitt, X-raying the interstellar medium: ROSAT observations of dust scattering halos. Astron. Astrophys. 500, 459–475 (1995) P. Predehl, V. Burwitz, F. Paerels, J. Trümper, Chandra measurement of the geometrical distance to Cyg X-3 using its X-ray scattering halo. Astron. Astrophys. 357, L25–L28 (2000) I. Psaradaki et al., Interstellar oxygen along the line of sight of Cygnus X-2. Astron. Astrophys. 642 (2020). https://doi.org/10.1051/0004-6361/202038749 J.J. Rehr, R.C. Albers, Theoretical approaches to x-ray absorption fine structure. Rev. Mod. Phys. 72, 621–654 (2000). https://doi.org/10.1103/RevModPhys.72.621 S.K. Ride, A.B.C. Walker, Absorption of X-rays in the interstellar medium. Astron. Astrophys. 61, 339–346 (1977) D. Rogantini, The hot and dusty interstellar medium through X-ray spectroscopy. Ph.D. Thesis (2020) D. Rogantini et al., Investigating the interstellar dust through the Fe K-edge. Astron. Astrophys. 609 (2018). https://doi.org/10.1051/0004-6361/201731664 D. Rogantini et al., Interstellar dust along the line of sight of GX 3+1. Astron. Astrophys. 630 (2019). https://doi.org/10.1051/0004-6361/201935883 D. Rogantini et al., Magnesium and silicon in interstellar dust: X-ray (2020) D.P. Rolf, Evidence for the detection of X-ray scattering from interstellar dust grains. Nature 302, 46–48 (1983). https://doi.org/10.1038/302046a0 B.D. Savage, K.R. Sembach, Interstellar abundances from absorption-line observations with the hubble space telescope. Ann. Rev. Astron. Astrophys. 34, 279–330 (1996)

104 Interstellar Absorption and Dust Scattering

3651

M.L. Schattenburg, C.R. Canizares, High-resolution X-ray spectroscopy of the Crab Nebula and the oxygen abundance of the interstellar medium. Astrophys. J. 301, 759 (1986). https://doi.org/ 10.1086/163942 P.C. Schneider, J.H.M.M. Schmitt, X-raying the AU Microscopii debris disk. Astron. Astrophys. 516 (2010). https://doi.org/10.1051/0004-6361/201014038 Y. Shen, B.T. Draine, E.T. Johnson, Modeling porous dust grains with ballistic aggregates. I. Geometry and optical properties. Astrophys. J. 689, 260–275 (2008). https://doi.org/10.1086/ 592765 overview. Astron. Astrophys. 641. https://doi.org/10.1051/0004-6361/201936805 R. Siebenmorgen, N.V. Voshchinnikov, S. Bagnulo, N.L.J. Cox, J. Cami, C. Peest, Large interstellar polarisation survey. II. UV/optical study of cloud-to-cloud variations of dust in the diffuse ISM. Astron. Astrophys. 611 (2018). https://doi.org/10.1051/0004-6361/201731814 J.D. Slavin, E. Dwek, M.-M. Mac Low, A.S. Hill, The dynamics, destruction, and survival of supernova-formed dust grains. Astrophys. J. 902 (2020). https://doi.org/10.3847/1538-4357/ abb5a4 R.K. Smith, X-ray dust scattering at small angles: the complete Halo around GX13+1. Astrophys. J. 681, 343–349 (2008). https://doi.org/10.1086/588519 R.K. Smith, The Arcus soft x-ray grating spectrometer explorer. Soc. Photo-Opt. Instrum. Eng. (SPIE) Conf. Ser. 11444 (2020). https://doi.org/10.1117/12.2576047 R.K. Smith, E. Dwek, Soft X-ray scattering and Halos from dust. Astrophys. J. 503, 831–842 (1998). https://doi.org/10.1086/306018 R.K. Smith, R.J. Edgar, R.A. Shafer, The X-Ray Halo of GX 13+1. Astrophys. J. 581, 562–569 (2002). https://doi.org/10.1086/344151 R.K. Smith, L.A. Valencic, L. Corrales, The impact of accurate extinction measurements for X-ray spectral models. Astrophys. J. 818 (2016). https://doi.org/10.3847/0004-637X/818/2/143 P.M. Solomon, D.B. Sanders, A.R. Rivolo, The Massachusetts Stony Brook galactic plane CO survey – disk and spiral arm molecular cloud populations. Astrophys. J. 292, L19–L24 (1985). https://doi.org/10.1086/184465 T.P. Stecher, B. Donn, On graphite and interstellar extinction. Astrophys. J. 142, 1681 (1965). https://doi.org/10.1086/148461 E.A. Stern, M. Newville, B. Ravel, Y. Yacoby, D. Haskel, The UWXAFS analysis package: philosophy and details. Phys. B Condens. Matter 208, 117–120 (1995). https://doi.org/10.1016/ 0921-4526(94)00826-H O. Takahashi, Y. Tamenori, T. Suenaga, T. Ikeda-Fukazawa, J. Matsuno, A. Tsuchiyama, XANES spectra of forsterite in crystal, surface, and amorphous states. AIP Adv. 8 (2018). https://doi. org/10.1063/1.5017245 M. Tashiro et al., Concept of the X-ray Astronomy Recovery Mission. Space Telescopes and Instrumentation 2018: Ultraviolet to Gamma Ray 10699 (2018). https://doi.org/10.1117/12. 2309455 B.K. Teo, EXAFS: Basic Principles and Data Analysis, XVIII, 1st edn. (Springer, Berlin/Heidelberg, 1986), p. 349. https://doi.org/10.1007/978-3-642-50031-2 A.G.G.M. Tielens, Interstellar polycyclic aromatic hydrocarbon molecules. Ann. Rev. Astron. Astrophys. 46, 289–337 (2008). https://doi.org/10.1146/annurev.astro.46.060407.145211 A.G.G.M. Tielens, Interstellar PAHs and Dust. Planets, Stars and Stellar Systems. Volume 5: Galactic Structure and Stellar Populations, vol. 499 (2013). https://doi.org/10.1007/978-94007-5612-0_10 A. Tiengo, S. Mereghetti, Dust-scattered X-ray halos around gamma-ray bursts: GRB 031203 revisited and the new case of GRB 050713A. Astron. Astrophys. 449, 203–209 (2006). https:// doi.org/10.1051/0004-6361:20054162 A. Tiengo et al., The dust-scattering X-ray rings of the anomalous X-ray pulsar 1E 1547.0-5408. Astrophys. J. 710, 227–235 (2010). https://doi.org/10.1088/0004-637X/710/1/227 J. Trümper, V. Schönfelder, Distance determination of variable X-ray sources. Astron. Astrophys. 25, 445 (1973) R.J. Trumpler, Absorption of light in the galactic system. Publ. Astron. Soc. Pac. 42, 214 (1930). https://doi.org/10.1086/124039

3652

E. Costantini and L. Corrales

L.A. Valencic, R.K. Smith, Interstellar abundances toward X Per, Revisited. Astrophys. J. 770 (2013). https://doi.org/10.1088/0004-637X/770/1/22 L.A. Valencic, R.K. Smith, Interstellar dust properties from a survey of X-ray Halos. Astrophys. J. 809 (2015). https://doi.org/10.1088/0004-637X/809/1/66 L.A. Valencic, R.K. Smith, Interstellar dust properties from a survey of X-ray Halos. Astrophys. J. 809 (2015). https://doi.org/10.1088/0004-637X/809/1/66 L. Valencic et al., Astro2020 Science White Paper: Probing the Structure of Interstellar Dust from Micron to Kpc Scales with X-ray Imaging. arXiv e-prints (2019) H.C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957) J.C.A. van Peet, E. Costantini, M. Méndez, F.B.S. Paerels, J. Cottam, Properties of the ionised plasma in the vicinity of the neutron-star X-ray binary EXO 0748-676. Astron. Astrophys. 497, 805–813 (2009). https://doi.org/10.1051/0004-6361/200811181 G. Vasilopoulos, M. Petropoulou, The X-ray dust-scattered rings of the black hole low-mass binary V404 Cyg. Mon. Not. R. Astron. Soc. 455, 4426–4441 (2016). https://doi.org/10.1093/mnras/ stv2605 S. Vaughan et al., The discovery of an evolving dust-scattered X-ray Halo around GRB 031203. Astrophys. J. 603, L5–L8 (2004). https://doi.org/10.1086/382785 S. Vaughan et al., The Dust-scattered X-Ray Halo around Swift GRB 050724. Astrophys. J. 639, 323–330 (2006). https://doi.org/10.1086/499353 G. Vianello, A. Tiengo, S. Mereghetti, Dust-scattered X-ray halos around two Swift gamma-ray bursts: GRB 061019 and GRB 070129. Astron. Astrophys. 473, 423–427 (2007). https://doi. org/10.1051/0004-6361:20077968 D. Watson, The Galactic dust-to-metals ratio and metallicity using gamma-ray bursts. Astron. Astrophys. 533 (2011). https://doi.org/10.1051/0004-6361/201117120 D.M. Watson et al., Crystalline silicates and dust processing in the protoplanetary disks of the taurus young cluster. Astrophys. J. Suppl. Ser. 180, 84–101 (2009). https://doi.org/10.1088/ 0067-0049/180/1/84 B. Watts, Calculation of the Kramers-Kronig transform of X-ray spectra by a piecewise Laurent polynomial method. Opt. Express 22, 23628 (2014). https://doi.org/10.1364/OE.22.023628 J.C. Weingartner, B.T. Draine, Dust grain-size distributions and extinction in the milky way, large magellanic cloud, and small magellanic cloud. Astrophys. J. 548, 296–309 (2001). https://doi. org/10.1086/318651 M.C. Weisskopf, H.D. Tananbaum, L.P. Van Speybroeck, S.L. O’Dell, Chandra X-ray observatory (CXO): overview. X-Ray Opt. Instrum. Missions III 4012, 2–16 (2000). https://doi.org/10.1117/ 12.391545 A.J. Westphal, A.L. Butterworth, J.A. Tomsick, Z. Gainsforth, Measurement of the oxidation state of Fe in the ISM using X-ray absorption spectroscopy. Astrophys. J. 872 (2019). https://doi.org/ 10.3847/1538-4357/aafb3b D.C.B. Whittet, The gas-to-dust ratio in the Rho Ophiuchi cloud. Mon. Not. R. Astron. Soc. 196, 469–472 (1981). https://doi.org/10.1093/mnras/196.3.469 D.C.B. Whittet, Dust in the galactic environment. Dust in the galactic environment (2003) J. Wilms, A. Allen, R. McCray, On the absorption of X-rays in the interstellar medium. Astrophys. J. 542, 914–924 (2000). https://doi.org/10.1086/317016 W.J. Wiscombe, Improved Mie scattering algorithms. Appl. Opt. 19, 1505–1509 (1980). https:// doi.org/10.1364/AO.19.001505 A.N. Witt, R.K. Smith, E. Dwek, X-ray Halos and large grains in the diffuse interstellar medium. Astrophys. J. 550, L201–L205 (2001). https://doi.org/10.1086/319630 S. Wolf, N.V. Voshchinnikov, Mie scattering by ensembles of particles with very large size parameters. Comput. Phys. Commun. 162, 113–123 (2004). https://doi.org/10.1016/j.cpc.2004. 06.070 J. Xiang, S.N. Zhang, Y. Yao, Probing the spatial distribution of the interstellar dust medium by high angular resolution X-ray Halos of point sources. Astrophys. J. 628, 769–779 (2005). https://doi.org/10.1086/430848

104 Interstellar Absorption and Dust Scattering

3653

J. Xiang, J.C. Lee, M.A. Nowak, J. Wilms, Using the X-ray dust scattering Halo of Cygnus X-1 to determine distance and dust distributions. Astrophys. J. 738 (2011). https://doi.org/10.1088/ 0004-637X/738/1/78 XRISM Science Team, Science with the X-ray Imaging and Spectroscopy Mission (XRISM). arXiv e-prints (2020) S.T. Zeegers, X-ray spectroscopy of interstellar dust: from the laboratory to the Galaxy. Ph.D. Thesis (2018) S.T. Zeegers et al., Absorption and scattering by interstellar dust in the silicon K-edge of GX 5-1. Astron. Astrophys. 599 (2017). https://doi.org/10.1051/0004-6361/201628507 S.T. Zeegers et al., Dust absorption and scattering in the silicon K-edge. Astron. Astrophys. 627 (2019). https://doi.org/10.1051/0004-6361/201935050 H. Zhu, W. Tian, A. Li, M. Zhang, The gas-to-extinction ratio and the gas distribution in the Galaxy. Mon. Not. R. Astron. Soc. 471, 3494–3528 (2017). https://doi.org/10.1093/mnras/stx1580 S. Zhukovska, T. Henning, C. Dobbs, ApJ 857, 94 (2018). https://doi.org/10.3847/1538-4357/ aab438 V. Zubko, E. Dwek, R.G. Arendt, Interstellar dust models consistent with extinction, emission, and abundance constraints. Astrophys. J. Suppl. Ser. 152, 211–249 (2004). https://doi.org/10.1086/ 382351

Part XI Compact Objects Victor Doroshenko and Andrea Santangelo

Low-Mass X-ray Binaries

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Arash Bahramian and Nathalie Degenaar

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Nature of the Compact Primary in LMXBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Donors and Accretion Phenomenology in LMXBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Canonical Roche Lobe Overflow with Main Sequence or Giant Stars . . . . . . . . . . . . . . . . Ultracompact X-Ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Eclipsing LMXBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Wind-Fed Accretion in LMXBs: Symbiotic X-Ray Binaries . . . . . . . . . . . . . . . . . . . . . . . Magnetically Channeled Accretion in LMXBs: X-Ray Pulsars . . . . . . . . . . . . . . . . . . . . . Variability and Transient Outbursts in LMXBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Long-Term X-Ray Behavior: Transient and Persistent LMXBs . . . . . . . . . . . . . . . . . . . . . Short-Term X-Ray Behavior and Subclasses of NS LMXBs . . . . . . . . . . . . . . . . . . . . . . . Classification Based on X-Ray Luminosity: Two Extreme Ends . . . . . . . . . . . . . . . . . . . . Distribution and Demographics of LMXBs in the Galaxy . . . . . . . . . . . . . . . . . . . . . . . . . . . Galactic Center and Bulge . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Galactic Plane and Outer Parts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Globular Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Orbital Period Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A. Bahramian () International Centre for Radio Astronomy Research – Curtin University, Perth, WA, Australia e-mail: [email protected] N. Degenaar Anton Pannekoek Institute for Astronomy, University of Amsterdam, Amsterdam, The Netherlands e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_94

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Abstract

A large fraction of X-ray sources in our Galaxy are low-mass X-ray binaries, containing a black hole or a neutron star accreting from a gravitationally bound low-mass (1 M⊙ ) companion star. These systems are among the older population of stars and accreting systems in the Galaxy and typically have long accretion histories. Low-mass X-ray binaries are categorized into various subclasses based on their observed properties such as X-ray variability and brightness, nature of the companion star and/or the compact object, and binary configuration. In this chapter, we review the phenomenology of subclasses of these systems and summarize observational finding regarding their characteristics, populations, and their distribution in the Galaxy.

Keywords

Accretion discs · Black holes · Neutron stars · X-ray binaries

Introduction In this chapter we introduce and review basic properties of the low-mass X-ray binaries (LMXBs): binary star systems comprised of a compact object, either a black hole (BH) or neutron star (NS), that accretes gas from a companion star less massive than the compact primary (typically 1 M⊙ ) (X-ray binaries with massive companion stars (typically 10 M⊙ ) are called high-mass X-ray binaries (HMXBs)).The focus of this chapter is on the demographics of LMXBs (e.g., binary configurations and formation, companion and compact object types, Galactic numbers and distribution), as well as their phenomenological behavior, particularly in the X-ray band (e.g., luminosity and variability) (Other chapters in this book delve into the physics of accretion and compact objects. See section “Cross-References” for a list of these chapters). LMXBs are among the brightest X-ray point sources in the sky when they are actively accreting. This is therefore how they are typically discovered and identified. However, most LMXBs are not continuously accreting and are classified as transients, showing X-ray outbursts with high levels of accretion onto the compact object that typically only last for weeks to months. These accretion outbursts are separated by long intervals of quiescence, lasting months to tens of years, during which little or no accretion occurs. This transient behavior is commonly explained in terms of thermal-viscous instabilities in the accretion disk, the socalled disk instability model (DIM; Smak (1983), Lasota (2000), and Hameury (2020)) (See also ⊲ Chap. 108, “Formation and Evolution of Accreting Compact Objects” by Belloni et al). Despite their generally low duty cycles, enhancements in the sensitivity and monitoring capabilities of X-ray instruments have led to a steady increase in the discovery of transient LMXBs (see Fig. 1).

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Fig. 1 Growing population of BH LMXBs over the lifetime of X-ray observatories. Enhancements in observatories and analysis have increased the rate at which transient X-ray binaries have been discovered/confirmed. This figure was created in December 2021 by the BlackCAT team, based on the continuously updated and publicly available data from BlackCAT (Corral-Santana et al. 2016, https://www.astro.puc.cl/BlackCAT)

To date, there are ∼200 confirmed and candidate LMXBs identified in our Galaxy, through their X-ray properties (e.g., Liu 2007; Tetarenko et al. 2016a; Corral-Santana et al. 2016). For many LMXBs the nature of the compact primary remains to be identified, yet for several tens of systems, we know whether these contain BHs or NSs. Observationally, known NS-LMXB outnumber BH-LMXBs by a factor of ∼2, and this is consistent with theoretical predictions based on formation history of NSs and BHs (Kalogera and Webbink 1998). It is also worth noting that accreting BHs have been found more frequently in LMXBs, as opposed to HMXBs. This could either be a result of binary evolution (Belczynski and Ziolkowski 2009), or of observational biases (Casares et al. 2014). Around one fifth of the current observed NS-LMXBs sample is made up of accreting millisecond X-ray pulsars (AMXPs) and transitional millisecond radio pulsars (tMSRPs). In these systems, the accretion flow near the NS is shaped by the magnetic field of the NS and is directed toward the magnetic poles, producing X-ray pulsations (Bildsten et al. 1997; Wijnands and van der Klis 1998). AMXPs and tMSRPs are considered evolutionary links between (some) NS-LMXBs and recycled millisecond radio pulsars (MSRPs). In a large fraction of LMXBs, the compact object is accreting from a main sequence, subgiant or red giant star that is filling its Roche lobe, and thus mass transfer toward the compact object is primarily through Roche lobe overflow.

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However, other types of LMXBs, for example, consisting of a compact object accreting from a stripped remnant “core” of a star or winds of a low-mass giant that is not filling its Roche lobe (i.e., wind accretion) have also been observed. In this chapter we briefly go into common methods to determine the nature of the compact object in LMXBs (Section “The Nature of the Compact Primary in LMXBs”), after which we explore the dichotomy of LMXBs based on their companion type and accretion mechanism (Section “Donors and Accretion Phenomenology in LMXBs”), X-ray luminosity and (long-term) X-ray variability (Section “Variability and Transient Outbursts in LMXBs”) and their distribution throughout our Galaxy (Section “Distribution and Demographics of LMXBs in the Galaxy”). We close the chapter with a brief summary and prospects offered by future observatories and surveys (Section “Conclusion”).

The Nature of the Compact Primary in LMXBs Determining the nature of the compact object in a LMXB is generally an observationally challenging task. While there are phenomenological features in LMXB outbursts (either spectral or temporal) that sometimes allow distinguishing between NS- or BH-LMXB candidates (e.g., Belloni et al. 2005; Lin et al. 2007), these features are not sufficient to prove the nature of the compact object. Here we review some of the more widely used methods to determine the nature of the compact object in LMXBs. Bursts and Pulsations – The most robust method for confirming the presence of a NS in a LMXB is the detection of events that require a solid surface, like thermonuclear X-ray bursts (also called Type I X-ray bursts and arising from rapid runway fusion of accreted matter on the surface of the NS; Lewin et al. 1993; Strohmayer and Bildsten 2006), or coherent (X-ray) pulsations (caused by surface hotspots and modulated by the rotation of the NS; Alpar et al. 1982; Bildsten et al. 1997). NSs can be subclassified based on their magnetic field. In LMXBs we find primarily weakly magnetic NSs with B  108 G, though a handful of systems contain NSs with stronger magnetic fields of B  1011−13 G (Patruno and Watts 2012). However, NSs with strong magnetic fields are more commonly found in HMXBs (Bildsten et al. 1997). It is important to emphasize that the absence of coherent pulsations or thermonuclear X-ray bursts does not rule out a NS accretor in a LMXB, but there are other methods to investigate the nature of the compact primary. Radial velocity and estimation of the mass function One of the most robust methods for verifying BHs in LMXBs (and estimating their mass) is generally through radial velocity studies via optical or near-infrared spectroscopy – relying on Doppler displacement of spectral features that are confidently associated with the companion. While such radial velocity studies (and inferred mass estimates) have a strong dependence on systems’ inclination angle – a parameter difficult to constrain observationally – a lower limit of ≥3 M⊙ unambiguously identifies the

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compact object as a BH, since degeneracy pressure would not be able to prevent a star of such mass from collapsing (van Paradijs and McClintock 1995; Casares and Jonker 2014). Disk-Jet coupling Another diagnostic method assisting in determining the compact object in LMXBs is based on the observed coupling between jet outflow (observed in the radio bands) and accretion rate (associated with the X-ray luminosity). While both NS- and BH-LMXBs show evidence for jets, when at similar X-ray luminosity, BHs tend to be brighter in the radio than NSs by a factor of ∼5 to 20 (Fender et al. 2003; Migliari and Fender 2006; Tudor et al. 2017; Gallo et al. 2018). This correlation has shown to be promising in identifying candidates, but the scatter and overlap of NS and BH systems in this correlation are significant, and thus it is not sufficient for confirming nature of the compact object. Two notable examples of this scatter are IGR J17591−2342, a NS-LMXB that due to its bright radio emission was initially thought to harbor a BH (Russell et al. 2018; Gusinskaia et al. 2020), and the dynamically confirmed BH-LMXB Swift J1357.2−0933, for which its low radio luminosity initially led to speculations on the NS nature for the compact object (Sivakoff et al. 2011; Mata Sánchez et al. 2015). Quiescent X-ray properties The fact that NSs have a solid surface that, for typical temperatures of ∼106 K, should give rise to a black body-like thermal emission component in the quiescent X-ray spectrum of the LMXB. This diagnostic has often been used, for example, to identify NS-LMXBs in globular clusters (see section “Globular Clusters”). However, if the NS is very cold (causing its thermal emission peak to move out of the X-ray band), if residual accretion or magnetospheric processes play a role (giving rise to a bright, harder X-ray emission component), or if the extinction along the line of sight is very high (causing the soft thermal X-rays to be absorbed), this method may break down (Wijnands et al. 2005; Heinke et al. 2009a; Degenaar et al. 2012a). In other words, the absence of a thermal emission component in quiescent LMXBs is not evidence for a BH accretor. Other methods Apart from the detection of surface phenomena, dynamical mass measurements, radio/X-ray luminosity ratio, or quiescent properties, other methods used to gauge the nature of the compact object in LMXBs include the ratio of their optical/infrared over X-ray fluxes (Russell et al. 2006, 2007), approximation of mass ratio via properties of the hydrogen Hα emission line (Casares et al. 2016), or their X-ray spectral-timing behavior (Wijnands and van der Klis 1999a; van der Klis 2006; Wijnands et al. 2015). In exploring the nature of a compact object in a LMXB, it is important to note that detection of bursts or pulsations and radial velocity studies generally lead to relatively robust classification of the compact object, while methods relying on luminosity ratios, emission features, and quiescent properties generally provide valuable circumstantial evidence regarding the nature of the compact object, particularly when the former methods are unfeasible.

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Donors and Accretion Phenomenology in LMXBs Many physical and observational characteristics of LMXBs such as mass transfer rate, accretion mechanism, luminosity, and outburst duty cycle are largely – but not exclusively – linked with the binary configuration properties like binary separation/period, eccentricity, and nature of the donor star and, to a lesser extent, the nature of the compact object. For instance, all these factors play a role in the X-ray emission produced by a LMXB. The intrinsic brightness of a LMXB scales with the rate at which mass is accreted. There is a physical limit for the rate at which mass can be accreted hence on the brightness of LMXBs. This limit is the Eddington luminosity (above which radiation pressure prevents further accretion), which scales with the mass of the compact object as LEdd ≈ 1038 (M/M⊙ ) erg s−1 . It is often useful to express the brightness of LMXBs as a fraction of this Eddington luminosity. In this section, we discuss various subclasses of LMXBs based on binary configuration as determined through observations and their accretion properties. Figure 2 shows graphical impressions of some of the different types of LMXB systems discussed in the next sections.

Canonical Roche Lobe Overflow with Main Sequence or Giant Stars A large fraction of LMXBs consist of main sequence and subgiant or red giant branch stars filling their Roche lobe in a binary with a BH or a NS. Mass transfer from the companion then occurs through Roche lobe overflow onto an accretion disk. The orbital period in these systems is typically of order of hours for systems with a main sequence star and order of days/weeks for systems with giants (Liu 2007; Corral-Santana et al. 2016). Figure 2 shows schematic impressions of different Roche lobe overflow LMXBs (all but the bottom left image). Most of these canonical LMXBs are transient systems, identified in the X-rays by their outbursts that typically reach 0.01–0.5LEdd , while in quiescence their X-ray luminosity is ≤10−5 LEdd . When actively accreting, the emission of LMXBs at all wavelengths is typically dominated by that of the accretion flow and associated outflows. Direct and detailed studies of the donor star are therefore generally not possible when active accretion is occurring (i.e., in outbursting transients or persistent LMXBs). In quiescence, optical and infrared emission from LMXBs harboring main sequence stars and hydrogen-rich giants is generally dominated by the companion star, showing stellar atmospheric features like TiO features in the optical or CO bandheads in the near-infrared. These features are crucial for radial velocity measurements and thus dynamical mass measurements for compact objects in these systems. In addition to stellar features, many of these systems show strong hydrogen emission lines (hydrogen H-α in the optical, or Bracket-γ in the near-infrared),

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Fig. 2 Illustration of LMXBs in various configurations. Top-left: a transient eclipsing LMXB during outburst (e.g., GRS 1747−312), top-right: a persistent ultracompact X-ray binary with a low inclination angle (e.g., 2S 0918−549, Zhong and Wang 2011), middle-left: V404 Cyg during an outburst (as a well-known transient BH-LMXB), middle-right: Scorpius X-1 (as a well-known persistent NS-LMXB), bottom-left: GC 1+4 (as a symbiotic X-ray binary), bottomright: IGR J17062–6143 (as a very faint X-ray binary). These visualizations were produced using the publicly available BINSIM code (Hynes 2002, http://www.phys.lsu.edu/~rih/binsim/). Input for BINSIM includes parameters describing binary configuration (e.g., separation, inclination), companion properties (e.g., mass, Roche lobe overflow fraction, temperature), accretion flow and disk characteristic (disk inner and outer radii, temperature gradient), jet angle, and brightness, among other parameters. These visualizations prioritize simplification for clarity of impression over scientific accuracy. our aim here is to demonstrate relative size and brightness of some of the main components of LMXBs. Note that scales are not the same across the panels and vary from ∼10−2 AU (e.g., for an ultracompact X-ray binary) to ∼ a few AU (e.g., for a symbiotic X-ray binary)

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associated with the accretion disk. As these systems enter outburst, typically the optical and infrared emission gets dominated by the accretion disk continuum emission, sometimes with numerous hydrogen and helium emission features. The profile and strength of accretion emission lines H-α or Bracket-γ (in quiescent and/or outburst) are among key indirect indicators for accretion geometry (Steeghs 2004) and potential nature of the compact object (Casares et al. 2016).

Ultracompact X-Ray Binaries Ultracompact X-ray binaries (UCXBs) are primarily defined (and identified) by their very short orbital period of 80 min. At these orbital periods, only helium-burning subdwarf stars or white dwarfs are small enough to fit into the orbit and fill their Roche lobe (Paczynski and Sienkiewicz 1981; Rappaport et al. 1982; Savonije et al. 1986). We tabulate a list of currently known UCXBs and candidates in Table 1. A schematic impression of an UCXB is shown in Fig. 2 (top right and bottom right). Observationally, confirming the UCXB nature of a LMXB binary requires measurement of the orbital period. Thus, so far, only a few dozen UCXBs have been confirmed (e.g., Cartwright et al. 2013). While direct observation of orbital modulation has been the prime method for identifying UCXBs (e.g., Stella et al. 1987; Zurek et al. 2009; Galloway et al. 2010; Zhong and Wang 2011), in a significant fraction of these systems, discovery of an accreting millisecond X-ray pulsar (AMXP) has allowed estimation of orbital period through accurate timing of the X-ray pulsations (e.g., Wijnands and van der Klis 1998; Chakrabarty and Morgan 1998; Altamirano et al. 2010a; Sanna et al. 2016; Strohmayer et al. 2018). In addition to confirmed UCXBs, there are also candidate systems that are identified as such based on the X-ray evolution of their accretion outbursts (Heinke et al. 2015; Stoop et al. 2021), or their optical and X-ray spectral properties (Bassa et al. 2006; Armas Padilla et al. 2020; Coti Zelati et al. 2021). Furthermore, LMXBs that persistently accrete at very low rates are suspected to have small disks (since these are easier kept photoionized sustaining active accretion) and are hence considered good candidate UCXBs (in’t Zand et al. 2005, 2007). While most UCXBs discovered to date have been found to be persistently bright in the X-rays with the X-ray luminosity varying typically at LX > 1036 erg s−1 , a subset of UCXBs are transient systems, showing quiescent periods with LX < 1032 erg s−1 interspersed by outbursts. Additionally, some UCXBs are classified as very faint X-ray binaries (see section “Very-Faint X-Ray Binaries”), showing very faint (transient) accretion emission of LX ≃ 1034 − 1036 erg s−1 (van Haaften et al. 2012; Cartwright et al. 2013). Given the natures of both accretor and companion in UCXBs, these systems are extremely hydrogen-deficient, and abundance of elements is particularly unusual, typically dominated by He, C, O, and Ne (or less likely, by heavier elements). Thus the spectral continuum (particularly in the optical band) in these systems is generally void of stellar absorption features or any hydrogen emission or absorption lines.

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Table 1 A catalog of known Galactic UCXBs and candidates. Table partially based on in’t Zand et al. (2007) and Cartwright et al. (2013). “T/P” indicates whether the source is transient (T) or persistent (P). “NS/BH” indicates nature of the compact object (e.g., determined via detection of Type I X-ray bursts or pulsations). Currently, there are no confirmed BH-UCXB systems identified. Candidate UCXBs are generally identified based on their characteristics suc as signatures of hydrogen deficiency (e.g., long Type I X-ray bursts, featureless optical spectrum, or prominence of neon, carbon, or oxygen features) Distance Porb (kpc) (min) T/P

NS/BH

Reference

8.0 11.9 5.4 ∼6

11 17 17.4 18.2

P P P P

NS NS NS NS

4U 1850−087 M15 X−2 47Tuc X−9 IGR J17062−6143 XTE J1807−294 XTE J1751−305 4U 1626−67 XTE J0929−314 MAXI J0911−655 IGR J16597−3704 4U 1916−053 Swift J1756.9−2508 NGC 6440 X−2 IGR J17494−3030 2FGL J1653.6−0159

7.38 10.7 4.5 ∼7.3 ∼8 ∼8 ∼8 ∼8 10 7.2 ∼9.3 ∼8 8.2 ? ∼1

20.6 22.6 28 38 40.1 42 42 43.6 44.3 46.0 50 54.7 57.3 75 75

P P P T T T P T T T P T T T Qa

NS NS BH? NS NS NS NS NS NS NS NS NS NS NS NS

Stella et al. (1987) Zurek et al. (2009) Zhong and Wang (2011) Wang and Chakrabarty (2004); Wang et al. (2015) Homer et al. (1996) Dieball et al. (2005) Bahramian et al. (2017) Strohmayer et al. (2018) Markwardt et al. (2003) Markwardt et al. (2002) Chakrabarty et al. (1998) Galloway et al. (2002) Sanna et al. (2017) Sanna et al. (2018a) Walter et al. (1982) Krimm et al. (2007) Altamirano et al. (2010a) Ng et al. (2021a) Kong et al. (2014); Romani et al. (2014)

Candidate UCXBs 4U 1728−34 4U 0614+091 1A 1246−588 4U 1812−12

5.2 3.2 4.3 ∼4

10.8b 51c ? ?

P P P P

NS NS NS NS

Galloway et al. (2010) Shahbaz et al. (2008) in’t Zand et al. (2008) Bassa et al. (2006); Armas Padilla et al. (2020)

XMMU J181227.8−181234 1RXS J180408.9−342058 IGR J17285−2922 Swift J0840.7−3516 4U 1857+01

∼14 1 h. However, the authors note that the companion still appears to be hydrogen-deficient (thus still likely to be a UCXB) d An orbital period of 40 mins is indirectly inferred by Baglio et al. (2016) based on evolutionary tracks of a presumed He donor. However, this periodicity is not yet observationally confirmed, especially as Marino et al. (2019) note possible presence of H/He in the accreted material

Instead, emission lines from He, N, C, and O are prevalent in the optical (Nelemans et al. 2004, 2006), ultra-violet (Homer et al. 2002), and X-rays (Juett et al. 2001, 2003; Madej et al. 2010). To date, there have been no BHs confirmed in any UCXB system. However candidates have been identified based on X-ray and radio properties (Bahramian et al. 2016), X-ray outburst properties along with radio and X-ray properties (Stoop et al. 2021), or X-ray luminosity and optical spectroscopy (in an extragalactic system, Dage et al. 2019). There might be an observational bias against detecting BH-UCXB systems in the X-rays because the radiative efficiency and duration of the outbursts of BH LMXBs may drop sharply toward shorter orbital periods (Knevitt et al. 2014). Furthermore, confirming the presence of a BH in a UCXB system dynamically is particularly challenging, as traditional methods, like radial velocity measurements based on spectral features associated with the surface of the donor, are unfeasible. Galactic compact binaries like UCXBs are expected to be among the main sources of gravitational wave emission to be detected by future facilities like the Laser Interferometer Space Antenna (LISA) and TianQin (Amaro-Seoane et al. 2017; Luo et al. 2016). This includes the “dual-line” signal from the combination of NS spin and system orbit and the “chirp” signal from those of these systems that

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eventually go through coalescence (Nelemans et al. 2001; Tauris et al. 2018; Chen 2021; Suvorov et al. 2021). Therefore, it is highly desired to search for and find more UCXBs.

Eclipsing LMXBs Eclipsing LMXBs are not a characteristically separate class of LMXBs, as the eclipses are merely a result of high inclination angle (i ∼ 90◦ ) of the binary orbital plane from our point of view (see Fig. 2). However, our observational perspective of eclipsing binaries provides a unique direct method to study properties of accretion disk via eclipse mapping (Baptista et al. 2001) and evolution of orbital period in LMXBs on timescales of years/decades (e.g., Chou et al. 2014). It has also been suggested that study of eclipses in accreting systems in the radio band can prove powerful in understanding jet physics (Maccarone et al. 2020). Broadly speaking, the orbital period in X-ray binaries is expected to decay, as momentum is lost in accretion processes, outflows, gravitational radiation, and magnetic breaking (e.g., Paczy´nski et al. 1967; Verbunt and Zwaan 1981; Tavani et al. 1991). Studying the evolution of orbital period on timescale of years/decades in HMXBs has shown that such a decay is indeed present and can be generally described by a smooth linear or quadratic ephemeris model (e.g., Falanga et al. 2015). However, observations of LMXBs indicate while many of them show orbital decay, the changes in the orbital decay in some cases cannot be well described by linear or quadratic ephemeris models (Jain and Paul 2011; Wolff et al. 2009; Iaria et al. 2018; Ponti et al. 2017), and many of these systems exhibit multiple “epochs” of orbital decay with highly variable rates (Fig. 3), sometimes accompanied by period “jitters.” These anomalies demonstrate that evolution of orbital period in LMXBs on short timescales (years) is not fully understood (Detailed spectral/timing properties of eclipsing LMXBs are discussed in ⊲ Chap. 112, “Low-Magnetic-Field Neutron Stars in X-ray Binaries”). Currently there are ∼ a dozen eclipsing Galactic LMXBs identified (Table 2). Almost all of these systems have been identified as eclipsing LMXBs during bright outbursts. However, a select few have been identified in quiescence in deep observations (e.g., X5 in globular cluster 47 Tuc, which has been observed substantially by the Chandra X-ray observatory). In addition to the sources cataloged in Table 2, there are a handful of other eclipsing systems that either show only partial eclipses (e.g., see Chou et al. 2014, and references therein), or while eclipses have been observed period or nature of the system are uncertain (e.g., Maeda et al. 2013).

Wind-Fed Accretion in LMXBs: Symbiotic X-Ray Binaries In contrast with other classes of LMXBs, symbiotic X-ray binaries (SyXBs) stand out by the absence of Roche lobe overflow. These systems consist of a compact object (BH or NS) accreting from the winds of a low-mass late-type giant.

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1985

1990

1995

2000

2010 EXOSAT GINGA ROSAT ASCA RXTE

100 75 50

O−C (s)

2005

25 0 −25 −50 −75 46000

48000

50000

52000

54000

MJD (TDB, Days) Fig. 3 Evolution of orbital period in EXO 0748-676 (based on Wolff et al. 2009). The change in orbital period does not follow a single pattern and appears to show epochs, with different rates of change. EXO 0748-676 is among the best documented cases of such anomalous orbital changes in LMXBs; however, it is not the only eclipsing LMXB exhibiting irregular variations in orbital period evolution

It is important to clarify that we define symbiotic X-ray binaries distinctly from “symbiotic stars” (or symbiotic binaries), which are defined by a white dwarf accreting from winds of a late-type giant (In classification of symbiotic stars and systems based on their X-ray properties (e.g., the groups labeled as α, β, γ , δ, β/δ), symbiotic X-ray binaries are generally classified as the γ group (Murset et al. 1997; Luna et al. 2013)). GX 1+4 is the only SyXBs identified so far that has been observed to be persistently bright (≥1036 erg s−1 ) in the X-rays (Lewin et al. 1971; Serim et al. 2017; Iłkiewicz et al. 2017). However, most SyXBs show strong rapid variability, with quiescence luminosity LX ≤ 1033 erg s−1 and outburst LX ≥ 1034 erg s−1 within hours/days, and can decay as quickly (e.g., Patel et al. 2007; Masetti et al. 2007; Heinke et al. 2009b). Additionally, SyXBs tend to show rapid “faint” outbursts with peak luminosity 1034 erg s−1 ≤ LX ≤ 1036 erg s−1 (Masetti et al. 2006; Kaplan et al. 2007; Farrell et al. 2010; Kuranov and Postnov 2015). The sporadic nature of their variability makes SyXBs particularly difficult to detect and identify, thus characterizing their population and behavior requires sensitive frequent monitoring (e.g., with Swift/XRT or eROSITA; Bahramian et al. 2021a). To date, no BH SyXB system has been identified. In a large fraction of SyXBs, discovery of spin periods (in the 100 s to 1000 s of seconds range) have led to identification of the NS accretor (Patel et al. 2004; Bodaghee et al. 2006; Thompson et al. 2006; Corbel et al. 2008, see also Table 3). Companion stars in SyXBs are typically K-M III giants (Chakrabarty and Roche 1997; Masetti et al. 2002; Bozzo et al. 2013; Bahramian et al. 2014a; Shaw et al. 2001). However, in rare cases the

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Table 2 A catalog of known Galactic LMXBs exhibiting clear total eclipses (for the purpose of this catalog we omit LMXBs with suggestive or partial eclipses). “NS/BH” indicates nature of the compact object (via detection of Type I X-ray bursts or pulsations, or deep X-ray spectroscopy in case of quiescent systems like 47 Tuc X5). No eclipsing BH-LMXB has been confirmed as of this writing Porb P˙orb System XTE J1710−281a

(hour) 3.281063218(7)

(10−12 s s−1 ) −1.6 ≤ P˙orb ≤ 0.2

NS/BH NS

EXO 0748−676b 4U 2129+47c IGR J17451−3022 H 1658−298d

3.824088(1) 5.238220(2) 6.2834(5) 7.1161099(3)

– 103(±13) – −8.5(±1.2)

NS NS ? NS

CXOGC J174540.0 −290031

7.767(2)

–

?

AX J1745.6−2901 47 Tuc X5

8.3510081(2) 8.67(1)

−40.3(±2.7) –

? NS

3FGL J0427.9−6704 Swift J1749.4−2807

8.80128(2) 8.816866(2)

– –

NS NS

GRS J1747−312

12.3595273(2)

–

NS

Swift J1858.6−0814

21.3448(4)

–

NS

Her X-1e

40.80402216(5)

−48.5(±1.3)

NS

Reference Jain and Paul (2011) Wolff et al. (2009) Bozzo et al. (2007) Bozzo et al. (2016) Wachter et al. (2000) and Iaria et al. (2018) Muno et al. (2005a); Porquet et al. (2005) Ponti et al. (2017) Heinke et al. (2003a) Strader et al. (2016) Markwardt and Strohmayer (2010) in’t Zand et al. (2003) Buisson et al. (2021) (Staubert et al. 2009)

a Jain

and Paul (2011) demonstrate that XTE J1710-281 shows irregular variations and find the best-fit ephemeris solution is a piece-wise linear model b EXO 0748-676 shows strong variations in ephemeris and Wolff et al. (2009) indicate no simple linear or quadratic solution describes all data c Bozzo et al. (2007) speculate that the ephemeris of 4U 2129+47 indicates that it could be in fact part of a hierarchical triplet system d The best-fit ephemeris solution suggested by Iaria et al. (2018) contained linear, quadratic, and a sinusoidal term with a period of 2.31 yr. The authors suggest such a modulation could be produced by the gravitation coupling of the orbit with changes in the shape of the magnetically active companion star e We note that Her X-1 is not strictly a LMXB as the companion is estimated to be ∼2 M ⊙

companions have been identified as carbon stars (Masetti et al. 2011; Hynes et al. 2014). Owing to the detached nature of SyXBs and the size of the companion, these systems typically have long orbital periods ranging from tens to thousands of days and in many cases difficult to constrain with current available coverage of these systems (Hinkle et al. 2006; Nespoli et al. 2010; Kuranov and Postnov 2015).

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Table 3 A catalog of identified Galactic SyXBs and SyXB candidates. Table partially based on Yungelson et al. (2019), see also Kuranov and Postnov (2015) and Merc et al. (2019). “NS/BH” indicates nature of the compact object (via detection of Type I X-ray bursts or pulsations). No symbiotic BH-LMXB has been confirmed as of this writing. It is worth noting that Peak LX is the reported peak luminosity; SyXBs can have short-lived flares (minutes long) reaching higher luminosities that may have been missed in pointed observations too short to be noticed in X-ray monitors. SyXB candidates not listed in this table include 4U 1954+31 (proposed to be a SyXB by Corbel et al. (2008) and Masetti et al. (2006), recent works indicate it is likely an HMXB (Hinkle et al. 2020)), IRXS J180431.1–273932 (suggested as SyXB by Nucita et al. (2007), disputed by Masetti et al. (2012)), IGR J16393–4643 (suggested as a SyXB by Nespoli et al. (2010), disputed by Bodaghee et al. (2012a)), 2XMM J174016.0–290337 (suggested as a SyXB by Farrell et al. (2010) and disputed by Thorstensen and Halpern (2013)), Swift J175233.3–293944 (suggested as symbiotic by Wevers et al. (2017), a white dwarf compact object is favored by Bahramian et al. (2021a)) Pspin s 140

Porbit d 1161

Peak Lx erg s−1 1036

Distance kpc 4.3

Sct X−1 3XMM J181923.7−170616 IGR J16358−4726

113 408

? ?

2 × 1034 ?

≥4 ?

NS/BH Reference NS Chakrabarty and Roche (1997), Hinkle et al. (2006), Ferrigno et al. (2007), and González-Galán et al. (2012) NS Kaplan et al. (2007) NS Qiu et al. (2017)

5850

?

3 × 1036

5–13

NS

IGR J17329−2731 CGCS 5926 4U 1700+24

6680 ? ?

? ∼151 4391b

3 × 1035 3 × 1032 1034

∼ 2.7 6(±1)a 0.544

NS ? NS

IGR J16194−2810 CXOGBS J173620.2 −293338 XTE J1743−363

? ?

? ?

≤1035 1033

2.1(±0.2)a ? ∼8a,c ?

?

?

?

∼8a,c

?

IGR J17445−2747

?

?

?

1.1–7.6

NS

System GX 1+4

Patel et al. (2004), Patel et al. (2007), Nespoli et al. (2010), and Lutovinov et al. (2005) Bozzo et al. (2018) Masetti et al. (2011) Masetti et al. (2002), Masetti et al. (2006), and Hinkle et al. (2019) Masetti et al. (2007) Hynes et al. (2014) Smith et al. (2012) and Bozzo et al. (2013) Mereminskiy et al. (2017) and Shaw et al. (2001) (continued)

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Table 3 (continued) System XMMU J174445.5 −295044 IGR J17197−3010 CXOGBS J174614.3 −321949 CXOGBS J173620.2 −293338 IGR J17597−2201

Swift J2037.2+4151

Pspin s ?

Porbit d ?

Peak Lx erg s−1 1035

Distance kpc 3.1

? ?

? ?

≤2 × 1035 6–17 1034 ∼8a,c

NS/BH Reference ? Bahramian et al. (2014a) ? Masetti et al. (2012) ? Wetuski et al. (2021)

?

?

≤1033

∼8a,c

?

Wetuski et al. (2021)

?

?

?

15?

NS

?

?

1036

∼10

?

Chaty et al. (2008), Ratti et al. (2010) and Zolotukhin and Revnivtsev (2015) Molina et al. (2021)

a Indicates the distance (and luminosity) has been updated based on Gaia EDR3 (Gaia Collaboration

et al. 2021). This includes applying parallax zero-point correction based on Lindegren et al. (2021) and considering a Galactic prior based on distribution of LMXBs (Atri et al. 2019) b An alternative period of 404 days is also discussed by Galloway et al. (2002) and Hinkle et al. (2019) c Indicates that while a parallax value is reported EDR3 for the source, it is not significant and thus distance estimation is dominated by prior assumptions

The spectrum of SyXBs in the optical and NIR regimes is typically dominated (almost completely) by the companion star. In some cases, strong hydrogen emission lines like H-α or Br-γ (sometimes broad and/or double-peaked) are also observed, particularly during enhanced X-ray activity (Chakrabarty and Roche 1997; Nespoli et al. 2010). Furthermore, during enhanced activity, contribution from the accretion continuum can be noticed at shorter wavelengths (Fig. 4; Bozzo et al. 2018). Study of accretion and outflows in SyXBs in the radio frequencies is also challenging due to their rapid variability. However, radio observations of GX 1+4 – the only persistent SyXB – have allowed study of these mechanisms in SyXBs. While earlier radio observations of this system reported non-detections or marginal detections (Seaquist et al. 1993; Fender et al. 1997; Martí et al. 1997), later observations by the Karl G. Jansky Very Large Array showed significant detection of emission, which perhaps could be caused by the outflow (van den Eijnden et al. 2018a).

Magnetically Channeled Accretion in LMXBs: X-Ray Pulsars In a sub-group of NS-LMXBs, material from the inner part of the accretion disk is funneled along the magnetic field lines of the NS onto its magnetic poles. This localized accretion causes hotspots that give rise to X-ray pulsations modulated at the spin period of the NS (Bildsten et al. 1997; Wijnands and van der Klis

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10−12 Observed spectrum Companion + Disk

Companion star (M giant) Accretion disk continuum

Hα

Flux (erg/s/cm2)

10−13 10−14 10−15 10−16 10−17

8500

8000

7500

7000 A) Wavelength (˚

6500

6000

5500

Fig. 4 Optical spectrum of a typical symbiotic X-ray binary (IGR J17329-2731) during an outburst. While generally, the optical and infrared continua are dominated by the companion, strong accretion features like broad or double-peaked H-α lines can sometimes be visible. During outbursts, the continuum emission from the accretion disk (i.e., multicolor blackbody) can also be observed in some cases at shorter wavelengths. (Figure based on Bozzo et al. 2018)

1998). Roughly 20% of NS-LMXBs display rapid X-ray pulsations, in a range of ∼1–10 ms and are called accreting millisecond X-ray pulsars (AMXPs; see Campana and Di Salvo (2018) for an overview until 2018 and Sanna et al. (2018a,b) and Ng et al. (2021a) for three new AMXPs discovered since). The NSs in AMXPs have relatively weak magnetic field strengths of B < 109 G (Mukherjee et al. 2015). Furthermore, these NSs are thought to have acquired their rapid spin by angular momentum transfer in the accretion process and are likely the progenitors of millisecond radio pulsars (MSRPs) (Bhattacharya and van den Heuvel 1991; Alpar et al. 1982). The connection between AMXPs and MSRPs seems to be supported by the discovery of the so-called transitional millisecond radio pulsars (tMSRPs); these are NSs in binary systems that are sometimes observable as regular millisecond radio pulsars but at other times look more like a LMXB with an accretion disk present and no observable radio pulsations (Campana and Di Salvo 2018). Currently, there are three systems showing clear evidence for switches between these two manifestations, which occur on a timescale of years (IGR J18245–2452 in the globular cluster M28, PSR J1023+0038, and XSS J12270–4859; Archibald et al. (2009),Papitto et al. (2013), and Bassa et al. (2014)). Given the scientific interest of studying systems that appear to bridge different NS populations, there has been much effort in finding more tMSRPs. This has resulted in several good candidate systems (see Papitto and de Martino (2010) for a recent overview), but so far no new confirmed ones have emerged yet. The binary parameters of AMXPs (and tMSRPs) are well-known through accurate timing of their (X-ray) pulsations. In a handful of systems, for which

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the orbital period is ∼2 h, the companion is thought to be a brown dwarf. The remaining AMXPs are split into roughly equal groups of systems with white dwarf or helium donor stars in tight orbits (∼0.25–1.25 h, i.e., UCXBs) and systems with main sequence donor stars and longer orbital periods (nearly all ∼3–11 h) (Campana and Di Salvo 2018). The three confirmed tMSRPs all fall in the latter group. Apart from the rapidly spinning AMXPs, a very small subgroup (10%) of NS LMXBs displays much slower pulsations (seconds to hours). In addition to slower spin, the NSs in these systems also have stronger magnetic fields (B ∼ 1010−12 G) than the rapidly spinning AMXPs. There are four slow pulsars in Roche lobe overflow LMXBs (2A 1822–371, 4U 1626–67, GRO 1744–28, and Her X-1) (Her X-1 formally classifies as an intermediate-mass X-ray binary (IMXB).), and their spin periods are in the range of ∼0.1–2 s. In addition, there are five slow pulsars found in the wind-fed SyXBs which have spin periods of ∼10 min to ∼5 h (see Table 3). For the wind-accreting systems, the accretion efficiency is likely too low to transfer significant amounts of angular momentum that spin up the NS. However, for the slow pulsars in Roche lobe overflow systems, it is not yet clear why these NSs have not been spinned up. The explanation likely lies in the prior evolution of the binary (Verbunt et al. 1990; Rappaport and Joss 1997; van Paradijs et al. 1997). In terms of binary parameters, the slow LMXB pulsars are a heterogeneous group with orbital periods from 11 days and white dwarf, main sequence or giant companions.

Variability and Transient Outbursts in LMXBs In addition to the physical classification based on compact object type, donor type and mode of mass transfer discussed in the previous sections, LMXBs can be phenomenologically categorized based on their X-ray behavior. In the following sections, we provide an overview of classifications based on their long-term X-ray variability (on ∼months/year timescales), short-term X-ray variability (on ∼ days/weeks timescales), and X-ray (peak) luminosity. As we will see, the dynamic range in X-ray luminosity traced out by the population of LMXBs as a whole covers many orders of magnitude, from LX ≃ 1039 erg s−1 for sources accreting around the Eddington luminosity to LX ≃ 1030 erg s−1 for quiescent systems in which little or no accretion occurs. It is important to remind the reader that with these various ways to (physically or phenomenologically) classify LMXBs, there is overlap between different categories. For instance, several AMXPs are UCXBs, and the broad distinctions of persistent and transient sources contain basically all other subclasses. Furthermore, NS-LMXBs can be divided into different categories based on their X-ray properties (AMXPs, slow pulsars, non-pulsating systems, atolls, Z-sources), as briefly discussed in section “Classification Based on X-Ray Luminosity: Two Extreme Ends.”

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Long-Term X-Ray Behavior: Transient and Persistent LMXBs One of the primary classifications of LMXBs is based on their long-term X-ray behavior, which separates the persistent systems from the transient ones. Persistent LMXBs are always actively accreting but can still show (in some cases quite strong) X-ray variability (e.g., Fig. 5 bottom). Transient LMXBs, on the other hand, exhibit large swings in their X-ray luminosity that separate outbursts of active accretion with periods of quiescence (an example is shown in Fig. 5 top). Whereas there is no strict definition of what level of X-ray luminosity variability defines a transient, generally LMXBs are considered transient if their X-ray luminosity changes by a factor of 1000. The long-term light curves shown in Fig. 5 are examples of the differences in long-term X-ray behavior observed among LMXBs. These light curves are based on publicly available data from the all-sky X-ray monitoring of MAXI (2–20 keV; Matsuoka et al. 2009).

01 1-0 20 20

20

18

16

-0

-0

1-

1-

01

01

01 14

-0

1-

20

0.5

20

20

20

12

10

-0

-0

1-

1-

01

01

Extended Outbursts: Quasi-persistent LMXBs Typically, the outbursts of transient LMXBs last for a few weeks up to ∼ a year, while their inactive quiescent phases may extend for many years or even decades.

GX 339-4 (transient) MAXI Count rate 4-10 keV (Crab)

0.4 0.3 0.2 0.1 3.0 2.5

GRS 1915+105 (quasi-persistent)

2.0 1.5 1.0 0.5 55500

56000

56500 57000 57500 Modified Julian Date (Day)

58000

58500

Fig. 5 Light curves of LMXBs and their variability over the past decade based on monitoring data from MAXI/GSC (Matsuoka et al. 2009). Top: the transient black hole LMXB GX339-4, showing several distinct accretion outbursts of different brightness. Bottom: the quasi-persistent black hole LMXB GRS 1915+105, illustrating that large variations in brightness can also occur in systems that are continuously active

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A more detailed overview of this follows in section “Outburst Statistics of Transient LMXBs,” but here we note that a small subclass of LMXBs falls more or less in between the two categories defined above: these systems are formally transient (i.e., clearly switching between active and inactive periods) but exhibit extended outburst episodes that last for years or even decades. An extreme example is the (eclipsing) NS-LMXB EXO 0748–676, which exhibited an outburst of 24 years between the early 1980s and 2009 (Degenaar et al. 2011b). Systems with extended outbursts of 1 yr have been dubbed “quasi-persistent” LMXBs. It is worth noting that the quasi-persistent LMXBs include a handful of systems that were observed to switch on at some point in time but have never returned to quiescence since. Examples are the BH-LMXB GRS 1915+105, which has been active since 1992 (e.g., Motta et al. 2021), and the NS system IGR J17062–6143, which has been accreting actively since 2006 (Hernández Santisteban et al. 2019). On the other hand, there are also LMXBs that were once thought to be persistent because they continued to be detected for years following their original discovery but then suddenly dimmed into quiescence. One example is the NS-LMXB X1732– 304 in the globular cluster Terzan 1, which was discovered in 1980 and suddenly disappeared in the late 1990s (Guainazzi et al. 1999). The cause of the extended outbursts is not fully clear but may lie in mass-transfer variations from the donor star, e.g., due to irradiation or moving sun spots (King and Cannizzo 1998; Shaw et al. 2019) (The standstill observed for Z Cam stars (Hameury 2020) could be the white-dwarf analogues of the extended outbursts of quasi-persistent LMXBs (Shaw et al. 2019)). Table 4 lists LMXBs known to display quasi-persistent outbursts.

Outburst Statistics of Transient LMXBs Systematically studying samples of transient LMXBs has provided insight into their luminosity distribution, outburst duration, and duty cycles (Chen et al. 1997; Yan and Yu 2015; Lin et al. 2019; Tetarenko et al. 2016a). Many of these studies made use of RXTE, which provided more regular and much denser coverage than any of the earlier X-ray satellites, while providing a baseline longer than that of current X-ray monitoring missions (15 years). Yan and Yu (2015) performed a systematic analysis of 110 transient outbursts from 36 sources, consisting of 22 (c)BHs and 14 NSs, observed with RXTE between 1996 and 2011. This study was limited to fluxes above ≈2 × 10−9 erg s−1 cm−2 (2–12 keV), which translates into a luminosity of LX ≈ 2 × 1037 (D/8 kpc)2 erg s−1 at the distance of the Galactic center. The full range of (peak) X-ray luminosities covered by this sample ranged from LX ≈ 2 × 1037 to 3 × 1038 erg s−1 , with an average peak luminosity of LX ≈ 5 × 1037 erg s−1 . This distribution is shown in Fig. 6. Furthermore, the range in outburst duration in this sample spanned ≈2 weeks to 2 years, with an average duration of ≈50 days. The sample under study showed that the duty cycle of transient LMXBs (i.e., the ratio of the time spend in outburst versus that in quiescence) is generally low: on average ≈2.5%, though with a wide spread of ≈1–50%. Figure 7 shows the distribution of outburst duration (left) and duty cycle (right) for this large sample of LMXBs studied with RXTE.

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Table 4 List of (confirmed) LMXBs that are quasi-persistent, i.e., transient systems but exhibiting prolonged outbursts of >1 yr System GRS 1915+105

Current state Subclass Activea BH

Swift J1753.5−0127 IGR J17098−3628 IGR J17091−3624 EXO 0748−676 MXB 1659−298 KS 1731−260 HETE J1900.1−2455 MAXI J0556−332b XTE J1701−462 XTE J1701−407 IGR J17062−6143

Quiescent Quiescent Quiescent Quiescent Quiescent Quiescent Quiescent Quiescent Quiescent Activec Activec

Swift J0911.9−6452 (NGC 2808) Swift J1858.6−0814

Active

1M 1716−315 1H 1905+000 AX J1745.6−2901b (Galactic center) AX J1754.2−2754 XMMU J174716.1−281048 4U 2129+47 2S 1711−339

Quiescent Quiescent Active

Reference Miller et al. (2020) and Motta et al. (2021) BH Zhang et al. (2019) BHC Capitanio et al. (2009) BHC Pereyra et al. (2020) NS, eclipsing Degenaar et al. (2011b) NS, eclipsing Wijnands et al. (2003) NS Wijnands et al. (2001) NS, AMXP Degenaar et al. (2017a) NS, transient Z-source Homan et al. (2014) NS, transient Z-source Fridriksson et al. (2010) NS Degenaar et al. (2011c) NS, VFXB, AMXP Hernández Santisteban et al. (2019) NS, AMXP, UCXB Ng et al. (2021b); Sanna et al. (2017) NS, accreting near Eddington Buisson et al. (2020) and Parikh et al. (2020) NS Jonker et al. (2007) NS Jonker et al. (2006) NS, eclipsing Degenaar et al. (2015)

Activec Quiescent

NS, VFXB NS, VFXB

Degenaar et al. (2012b) Del Santo et al. (2007)

Quiescent Quiescent

NS NS

XB 1733−30 (Terzan 1) Quiescent

NS

Nowak et al. (2002) Swank and Markwardt (2001) Guainazzi et al. (1999)

Quiescent

a The

X-ray emission from GRS 1915+105 suddenly dropped in 2018 and has remained low since, but this is likely caused by local obscuration and not by ceasing accretion activity (Motta et al. 2021) b These quasi-persistent LMXBs are known to also exhibit regular (i.e., shorter) outbursts c These (NS) LMXBs accrete at relatively low X-ray luminosity and are therefore not detected by all-sky X-ray monitors such as Swift/BAT and MAXI. Therefore, the status of these sources can only be verified via pointed X-ray observations (e.g., with Swift/XRT); since these generally do not occur regularly, the status of these sources is not accurately known at present

When comparing the BHs in the sample to the NSs, Yan and Yu (2015) found that the BHs peak at higher X-ray luminosity than NSs in absolute numbers. However, when scaled to the mass-dependent Eddington luminosity, the NS peak at higher ratios (see Fig. 6). Furthermore, it was found in this work that the outbursts of BHs generally decay slower and last longer (88 days on average) than for the NSs (39

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NS BH ALL

25

Number of Outbursts

3677

NS BH ALL

NS BH ALL

20

15

10

5

0.1

1037 1038 0.01 0.10 1.00 Peak Luminosity (ergs s-1, 2-12 keV) Peak Luminosity (LEdd, 2-12 keV)

1.0 10.0 Peak Flux (crab, 2-12 keV)

Fig. 6 Peak X-ray luminosity distribution of NS and BH LMXB outbursts observed with RXTE between 1996 and 2011. (Figure from Yan and Yu 2015) 14

NS BH ALL Numbers of Outbursts

Numbers of Sources

12 10 8 6 4

NS BH ALL

25

20

15

10

5 2 0.01

0.10 Duty Cycle

10

100 Duration (days)

Fig. 7 Distribution of the duty cycle (left) and duration (right) of outbursts observed from transient NS and BH LMXBs with RXTE between 1996 and 2011. (Figure from Yan and Yu 2015)

days), while the NSs appear to have higher-duty cycles. This is shown in Fig. 7. However, see below for an important caveat about these average numbers. A number of other, recent works performed similar systematic analyses of large samples of LMXBs but then focusing specifically on the BH systems. For instance, Dunn et al. (2010) studied the behavior of 25 BHs using 13 years of RXTE data, and Reynolds and Miller (2013) studied 21 BH LMXBs using 5 years of Swift/XRT data. Furthermore, Tetarenko et al. (2016a) collected RXTE, MAXI and INTEGRAL data to study 132 outbursts from 57 BH LMXBs (compiled in the WATCHDOG database) (A complementary BH catalog, called BLACKCAT, has been drawn up by Corral-Santana et al. 2016). The average outburst statistics inferred from these BH-targeted studies are broadly consistent with the NS/BH sample analyzed by Yan and Yu (2015).

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It is important to note that the above discussed systematic studies do not include (i) LMXBs located within a few tens of arminutes (few tens of pc) of the Galactic center and (ii) transient LMXBs with peak luminosities LX  1037 (D/8 kpc)2 erg s−1 . This is both because of the limitations in spatial resolution and sensitivity of the instrument that accumulated the large amount of data used in these studies. It is not a priory clear that LMXBs with fainter peak luminosities would behave similar to the brighter systems. In section “Very-Faint X-Ray Binaries” we discuss previous and ongoing efforts to characterize the outburst properties of very faint LMXBs, which have peak outburst luminosities as low as LX ≃ 1034−36 (D/8 kpc)2 erg s−1 , including those located in crowded regions like the Galactic center. An important word of caution is that the above discussed outburst statistics of LMXBs is typically driven by a small group of sources that have high recurrence rates. For instance, in the work of Yan and Yu (2015), the outburst statistics of the NS sample, containing 14 sources in total, is largely driven by the behavior of the 3 most active systems that exhibit outbursts every few (50% exhibited only a single outburst.

The Role of the Orbital Period in the Long-Term X-Ray Behavior The distribution in observed (peak) luminosities among the LMXBs is in part due to the range of orbital periods. Based on theoretical arguments, the peak outburst luminosity is expected to scale with the size of the accretion disk, hence the orbital period of the binary (King and Ritter 1998; Portegies Zwart et al. 2004; van Haaften et al. 2012). Although the number of LMXBs with known orbital periods is modest, this theoretical expectation seems to be borne out by observations of samples of NS and BH LMXBs (Shahbaz et al. 1998; Wu et al. 2010; van Haaften et al. 2012). However, a recent study focusing only on BH LMXBs and applying rigorous statistical tests did not find a clear correlation between the peak X-ray luminosity and orbital period (Tetarenko et al. 2016a). Other factors that may play a role in setting the outburst peak luminosity, reducing it from the value that could be achieved based on the mass-transfer rate, are mass loss (e.g., via disk winds; Tetarenko et al. 2018) and local obscuration (e.g., as for BH LMXB V404 Cyg; Koljonen and Tomsick 2020). Apart from the peak outburst luminosity, the recurrence time of LMXBs may also depend on the orbital period. Mass transfer in LMXBs can be driven by expansion of the donor star, which happens during different evolutionary stages. Systems with long orbital periods (12 h) harbor (sub)giant donor stars that may drive larger mass accretion rates than the main sequence or evolved donor stars in short-period (12 h) LMXBs. This again appears to be largely borne out by observations (Lin et al. 2019). Finally, the orbital period of the binary also has impact on whether or not a source is transient or persistent. This distinction depends on the mass accretion rate and size

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of the disk, i.e., whether the generated accretion luminosity is sufficient to keep the entire disk ionized hence allowing for continuous accretion (Coriat et al. 2012; in’t Zand et al. 2007; Tetarenko et al. 2016a).

Short-Term X-Ray Behavior and Subclasses of NS LMXBs In addition to long-term X-ray variations, both persistent and transient LMXBs vary in X-rays on short timescales: from weeks to days to second and even sub-second variability. Such short-term variability in X-ray luminosity is often associated with changes in the X-ray spectrum of LMXBs. This gives rise to several distinct X-ray spectral-timing states, which are thought to be related to changes in the accretion morphology (Hasinger and van der Klis 1989; Remillard and McClintock 2006; Done et al. 2007). Among the NS LMXBs, several sub-groups with distinct short-term X-ray variability have been defined. For instance, a small group of the brightest NS LMXBs trace out a very distinct “Z”-shaped pattern when their intensity in different energy bands is plotted in a so-called color-color diagram (CCD). These Z-sources are thought to be accreting around LX ≃ LEdd (see section “Accretion Around the Eddington Luminosity in LMXBs”). Other bright NSs, accreting at one to several tens of percent of the Eddington limit, instead trace out an “C”-shaped pattern in the CCD and are commonly referred to as atoll sources.

Classification Based on X-Ray Luminosity: Two Extreme Ends Wijnands et al. (2006) laid out a classification of LMXBs in terms of their peak X-ray luminosity measured in the 2–10 keV band, making the distinction between bright to very bright (LX ∼ 1037−39 erg s−1 ), faint (LX ∼ 1036−37 erg s−1 ), and very faint (LX  1036 erg s−1 ) systems. This classification is largely driven by the sensitivity limits of historic X-ray instruments and does not necessarily reflect significant physical differences (Wijnands et al. 2006). This is reinforced by the fact that many transient LMXBs display outbursts with different peak luminosity that fall into different luminosity categories (Degenaar and Wijnands 2010; Campana et al. 2013; Wijnands and Degenaar 2013). Nevertheless, different subpopulations of LMXBs are more likely (or exclusively) found in particular (2–10 keV) luminosity ranges. As already touched upon in previous sections, the X-ray luminosity is expected to scale with the system properties of the LMXB, such as the size of the accretion disk (hence binary orbit) and mode of mass transfer. So there is a physical motivation for a making a distinction based on the peak X-ray luminosity. To illustrate this, we discuss in more detail the two extreme ends of the luminosity classification of LMXBs: veryfaint X-ray binaries (VFXBs) and sources that accrete around the Eddington limit. In either of the luminosity classes, we find both persistent and transient systems.

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X-ray Luminosity (erg s−1)

Very-Faint X-Ray Binaries By definition, VFXBs have (peak) accretion luminosities of LX  1036 erg s−1 . Figure 8 shows an example of how the outburst of a transient VFXB compares to that of a bright LMXB. For sources located at distances of several kpc and beyond, historic X-ray missions and current all-sky X-ray monitors like Swift/BAT and MAXI do not have the required sensitivity to detect the accretion emission of VFXBs. This class of LMXBs has therefore long remained hidden. Over the past two decades, however, VFXBs have been found in increasing numbers by various means. At present, a few tens of VFXBs have been identified in the Milky Way. Similar to the bright LMXBs, the VFXBs can be either be classified as (quasi-)persistent or transient based on their long-term X-ray behavior. In Table 5 we list currently known VFXBs. A significant number of VFXBs harbor NSs and have been discovered through their thermonuclear X-ray bursts, since this makes them shine close to the Eddington limit for a brief moment of time. In particular, the BeppoSAX satellite picked up a number of thermonuclear X-ray bursts without detecting any persistent X-ray counterpart. These objects were hence dubbed “burst-only sources” (Cornelisse et al. 2002a,b). We now know that these concern NSs that accrete at very low X-ray luminosity, either persistently or transiently. Other X-ray instruments such as INTEGRAL and Swift/BAT have also discovered VFXBs through the detection (and follow-up) of thermonuclear X-ray bursts (Chelovekov and Grebenev 2010; Degenaar et al. 2010, 2012c).

1038

Aql X-1 XMM J174457

1037 1036 1035 1034 1033 0

20

40

60

80

100

120

Time (days) Fig. 8 Example light curves that illustrate the differences in outburst properties between VFXBs and bright LMXBs. Shown are two frequently two frequently active transient systems that both harbor a neutron star primary: the VFXB XMM J174457 and bright LMXB Aql X-1. For both sources, Swift/XRT data of outbursts occurring in 2016 were used. It is worth noting that while many transient VFXB outbursts are often short, as in this example, some can last for weeks/months

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The increased sensitivity and improved spatial resolution of X-ray instruments have also allowed for the discovery of a growing number of VFXBs through X-ray surveys, primarily of the Galactic center and bulge, with missions such as ASCA, Chandra ,and XMM-Newton (Sakano et al. 2005; Muno et al. 2005b; Wijnands et al. 2006; Jonker et al. 2011; Degenaar et al. 2012a). However, a detailed characterization of the outburst properties of VFXBs, such as their outburst duration and recurrence time, requires monitoring surveys in regular (at least weekly) visits with sensitive X-ray instruments to be performed (Degenaar et al. 2015; Carbone and Wijnands 2019; Bahramian et al. 2021a). Such programs have been carried out mostly with RXTE/PCA and Swift/XRT. The RXTE/PCA bulge monitoring project ran between 1999 and 2011 (Swank and Markwardt 2001) and pushed to a factor of a few lower X-ray luminosities than typical all-sky X-ray monitors (LX of a few times 1035 erg s−1 ). This allowed to study the behavior of the brightest VFXBs and provided a first picture of their outburst durations and recurrence times. In more recent years, this has been complemented by monitoring campaigns that exploit the flexibility of the Swift mission and push down a further order of magnitude fainter X-ray luminosity (Degenaar et al. 2015; Bahramian et al. 2021a). Statistics on the outburst properties of VFXBs has been steadily accumulated through Swift’s Galactic Center monitoring program, which has provided nearly daily X-ray monitoring of about a dozen transient VFXBs since 2006 (Kennea et al. 2006; Degenaar et al. 2015). Initial studies using the first few years of monitoring data showed that the outbursts of the transient VFXBs are often short (1 month) but that the outburst recurrence times are not very different from that of bright LMXBs: typical duty cycles are ≃1–30% (Degenaar and Wijnands 2009, 2010). As the Swift Galactic center monitoring program is reaching a ≃15 yr baseline, it is starting to provide similar outburst statistics on transient VFXBs as has been available for bright transient LMXBs. Apart from providing valuable statistics on the X-ray outburst behavior, determining the system parameters of VFXBs (i.e., donor types and orbital periods) in the Galactic center is largely hampered by the very high extinction and crowding. Based on what has been learned from the outburst behavior of VFXBs in the Galactic center, a dedicated monitoring program was therefore designed to effectively find such systems with Swift/XRT in less obscured regions of the Galactic bulge (Shaw et al. 2001; Bahramian et al. 2021a). This Swift bulge survey is ongoing and are expected to provide more insight into the (distribution of) system parameters of the faintest accreting LMXBs (see section “Galactic Center and Bulge”). Despite the observational challenges, system parameters are known for a number of VFXBs. Nearly half of the VFXBs listed in Table 5 have NS primaries, as evidenced by the detection of thermonuclear X-ray bursts or coherent X-ray pulsations. In absence of such features, it is often difficult to probe the nature of the compact object. However, dynamical mass estimates reveal BHs in Swift J1357.2– 0933 (Corral-Santana et al. 2013) and XTE J1118+480 (McClintock et al. 2001; Wagner et al. 2001). Furthermore, the X-ray spectral properties of XTE J1728– 295 point to a BH accretor (Sidoli et al. 2011; Stoop et al. 2021) and the bright

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Table 5 List of VFXBs in our Galaxy. The letters P, QP, and T refer to persistent, quasi-persistent and transient, respectively. cBH and cNS refer to candidate BHs and candidate NSs, respectively. The indication “burster” implies that the source displays thermonuclear X-ray bursts (hence must harbor a NS) System T/P/QP NS/BH Comments Persistent and quasi-persistent VFXBs IGR J17254−3257 P NS Burster 1RXS J171824.2−402934 1RXH J173523.7−354013 M15 X−3

P

NS

cUCXB, burster

P

NS

P

cNS

IGR J17062−6143

QP

NS

Burster, H-rich donor Main sequence donor UCXB, AMXP, buster

AX J1754.2−2754

QP

NS

cUCXB, burster

XMMU J174716.1−281048 SAX J1806.5−2215

QP

NS

cUCXB, burster

QP

NS

Burster

IGR J17597−2201

QP

NS

AX J1538.3−5541

QP

?

XTE J1744−230 Transient VFXBs IGR J17379−3747a

QP

?

Buster, XTE J1759−220 LMXB-like spectrum RXTE bulge scan

T

NS

burster, AMXP

IGR J17591−2342

T

NS

Burster, AMXP

Swift J185003.2−005627 Swift J1734.5−3027 MAXI J1807+132

T

NS

Burster

T T

NS NS

Burster Burster

MAXI J1957+032

T

cNS

IGR J17494−3030

T

cNS

XTE J1719−29 XTE J1118+480

T T

cNS BH

Porb = 4.1 h

Swift J1357.2−0933

T

BH

Porb = 2.6 h

Reference Chenevez et al. (2007) and Ratti et al. (2010) in’t Zand et al. (2005) and in’t Zand et al. (2009) Degenaar et al. (2010) Heinke et al. (2009c) and Arnason et al. (2015) Strohmayer et al. (2018) and Hernández Santisteban et al. (2019) Chelovekov and Grebenev (2007) and Shaw et al. (2017b) Del Santo et al. (2007) and Kaur et al. (2017) Cornelisse et al. (2002a) and Shaw et al. (2017b) Brandt et al. (2007) and Fortin et al. (2018) Sugizaki et al. (2001) and Degenaar et al. (2012b) Swank and Markwardt (2001) Chelovekov and Grebenev (2010) and Sanna et al. (2018b) Sanna et al. (2018c) and Kuiper et al. (2020) Degenaar et al. (2012c) Bozzo et al. (2015) Shidatsu et al. (2017) and Jiménez-Ibarra et al. (2019) Mata Sánchez et al. (2017) and Beri et al. (2019) Armas Padilla et al. (2013c) and Ng et al. (2021a) Armas Padilla et al. (2011) Wagner et al. (2001) and McClintock et al. (2001) Armas Padilla et al. (2013c), Corral-Santana et al. (2013) and Mata Sánchez et al. (2015) (continued)

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Table 5 (continued) System XTE J1728−295

T/P/QP NS/BH Comments T cBH IGR J17285−2922

IGR J18175−1530 XMMSL1 J171900.4−353217 XTE J1734−234 WGA J1715.3−2635 XTE J1637−498 Swift J175233.9−290952 Swift J174038.1−273712 SRGt J071522.1−191609

T T

? ?

T T T T

? ? ? ?

T

?

T

?

IGR J17445−2747

T

NS

XTE J1817−155 XTE J1719−356

Reference Swank and Markwardt (2001), Sidoli et al. (2011) and Stoop et al. (2021) Markwardt et al. (2007) Read et al. (2010) and Markwardt et al. (2010) Swank and Markwardt (2001) Swank and Markwardt (2001) Markwardt et al. (2008) Shaw et al. (2001) and Bahramian et al. (2021a) Bahramian et al. (2021b) and Rivera Sandoval et al. (2021)

Gokus et al. (2020), van den Eijnden et al. (2020) and Bahramian et al. (2020) SyXB

Mereminskiy et al. (2017), Shaw et al. (2001) and Bahramian et al. (2021a) XMMU J174445.5 T ? SyXB Heinke et al. (2009b) and −295044 Bahramian et al. (2014a) VFXBs covered by Swift’s Galactic Center monitoring campaign XMM J174457−2850.3 T NS Burster Sakano et al. (2005) Swift T ? Degenaar and Wijnands (2009) J174622.1−290634 Swift T ? CXOGC Degenaar and Wijnands (2009) J174553.7−290347 J174553.8−290346 CXOGC T ? Muno et al. (2005b), Degenaar J174540.0−290005 and Wijnands (2009), Koch et al. (2014) and Heinke et al. (2015) CXOGC T ? Muno et al. (2005b) and J174538.0−290022 Degenaar et al. (2015) CXOGC T ? Muno et al. (2005b), Degenaar J174535.5−290124 and Wijnands (2009, 2010) CXOGC T ? Muno et al. (2005b) J174541.0−290014 CXOGC T cBH Porb =7.9 h, Muno et al. J174540.0−290031 eclipser, obscured? (2005b,a) and Porquet et al. (2005) CXOGCJ174554.3 T ? XMMU Muno et al. (2005b) −285454 J174554.4−285456 XMM J174544−2913.0 T ? Sakano et al. (2005) Swift T ? Degenaar et al. (2015) J174535.5−285921 a This

is the same source as IGR J17364−2711, IGR J17380−3749 and XTE J1737−376

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radio emission of the Galactic center transient CXOGC J174540.0–290031 seem to argue in favor of a BH as well (Muno et al. 2005a; Porquet et al. 2005). The latter is, however, a high inclination system that while appearing as a VFXB might be intrinsically bright. At present, the compact object has not yet been classified for nearly half of VFXBs. The challenge arises from the fact that thermonuclear X-ray bursts are rare at low accretion rates (i.e., it takes a long time to accumulate sufficient fuel to ignite a burst; Degenaar et al. 2010, 2011a), and X-ray pulsations are difficult to detect at low X-ray fluxes (Patruno 2010; Strohmayer and Keek 2017; van den Eijnden et al. 2018b; Bult et al. 2019, 2021). Furthermore, the donor stars are often too faint or too highly absorbed for optical mass measurements in quiescence (Shaw et al. 2017a). Similarly, indirect methods such as studying their rapid incoherent X-ray variability are hampered by their faint emission (Armas Padilla et al. 2014). Therefore, other methods have been explored to classify VFXBs. When the outburst of a transient VFXBs is densely monitored (e.g., using Swift) or high-quality X-ray spectra are obtained (e.g., with XMM-Newton), a tentative identification of the compact object may be made based on the presence of a soft spectral component (Armas Padilla et al. 2011) (albeit see Armas Padilla et al. (2013a,b)) or the X-ray spectral evolution along the decay of an accretion outburst (Wijnands et al. 2015). At least one transient VFXB identified as NS based on this method (IGR J17494–3030; Armas Padilla et al. (2013c) and Wijnands et al. (2015)) was later found to be an AMXP (Ng et al. 2021a). Spectral shape and its evolution can thus be a diagnostic to identify the compact object in VFXBs (though see Parikh et al. (2017) for NSs with unusually hard spectra that do not confirm the general trends). For several VFXBs the detection of coherent (millisecond) X-ray pulsations has allowed to measure orbital period through pulsar timing (Sanna et al. 2018c; Strohmayer et al. 2018), and for a handful of others, such information is available from X-ray or multiwavelength studies (Bahramian et al. 2014b; Shaw et al. 2001). This suggests that VFXBs are an inhomogenous class in terms of donor stars and mass-transfer mode. The population of VFXBs includes systems with evolved dwarf donors in short orbits, main sequence and giant donors in wider orbits, Roche lobe overflow and wind-fed systems, as well as various subclasses of LMXBs such as UCXBs and tMSRPs (We note that other classes of compact objects such as HMXBs, magnetars, and bright accreting white dwarfs (cataclysmic variables) can show up as X-ray transients with similar luminosities as that of transient VFXBs. The X-ray spectral-timing properties of multiwavelength properties of such objects would be different from LMXBs, which are the focus here). So far, many of the known VFXBs have (X-ray) characteristics consistent with Roche lobe overflow LMXBs, so this appears to the dominant subclass. Since the accretion luminosity of LMXBs scales (among other factors) with the orbital period (see section “Orbital Period Distribution”), it is not surprising that several VFXBs have been found to have short orbital periods. For instance, the few BH systems among the VFXBs all have orbital periods shorter than BHs in bright LMXBs (see section “Orbital Period Distribution”). Furthermore, several VFXBs have been

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identified as (candidate) UCXBs (see Table 5). Binary evolution considerations predict that VFXBs should present short-period systems with evolved donor stars (King and Wijnands 2006). There are also a few (transient or persistent) VFXBs that are SyXBs, e.g., accreting from the wind of a giant companion (Shaw et al. 2001; Bahramian et al. 2021a). This is also not unexpected based on binary evolution arguments (Maccarone and Patruno 2013). Finally, we note that a number of VFXBs may be intrinsically bright LMXBs that only appear subluminous because we are viewing the system at high inclination. One example is the eclipsing Galactic center transient VFXB CXOGC J174540.0–290031 (Muno et al. 2005a; Porquet et al. 2005). However, only a small fraction of the full VFXB population is expected to appear faint due to such inclination effects (Wijnands et al. 2006). Summarizing, separating VFXBs as a class is mostly phenomenological, but there might be actual physical differences with respect to brighter systems; e.g., they might be less X-ray luminous because their accretion disks are small overall, or because their inner accretion disk is evaporated into a radiatively inefficient flow or pushed out by the NS magnetic field. Moreover, at the low accretion rates associated with VFXBs, we can probe different physics than with bright LMXBs in terms of accretion and outflows (Degenaar et al. 2017b; van den Eijnden et al. 2021), NS physics (Wijnands 2008), thermonuclear burning (Cooper and Narayan 2007; Peng et al. 2007), and binary evolution (Maccarone et al. 2015).

Accretion Around the Eddington Luminosity in LMXBs At the other extreme end of VFXBs in terms of X-ray output, there are a modest number of LMXBs that accrete around (slightly below and above) the Eddington luminosity. Table 6 lists some of the basic characteristics of LMXBs that are known to accrete at these high rates. Most of these harbor (confirmed or expected) NS primaries; there are only two BH-LMXBs listed. These are the well-known quasi-persistent BH GRS 1915+105 (see Fig. 5 bottom) and the transient system V404 Cyg (see Fig. 2 middle left). The latter is not observed to be particularly luminous but is thought to be heavily obscured and intrinsically accreting around the Eddington limit during (some of) its outbursts (Tetarenko et al. 2016a; Motta et al. 2017; Koljonen and Tomsick 2020). The group of Eddington-accreting LMXBs includes the six persistent Z-sources (see also section “Short-Term X-Ray Behavior and Subclasses of NS LMXBs”), which have been known and extensively studied since the dawn of X-ray astronomy (Hasinger and van der Klis 1989). These sources are expected to harbor NS primaries, although only GX 17+1 and Cyg X-2 show conclusive evidence for this by the detection of thermonuclear bursts (Kahn and Grindlay 1984). Identifying the donor stars in the Z-sources is not straightforward, because they are persistently accreting, and their accretion disks and jets are so bright that these contribute significantly to the optical/infrared emission (Bandyopadhyay et al. 2003). A schematic impression from one of the Z-sources, Sco X-1, is shown in Fig. 2 (middle right). Furthermore, Cir X-1 and GX 13+1 are two persistent sources that exhibit variations in their X-ray luminosity but during some epochs behave similar to the

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Z-sources (Oosterbroek et al. 1995). Both Cir X-1 and GX 13+1 are known to harbor a NS through the detection of thermonuclear bursts (Matsuba et al. 1995; Linares et al. 2010). In the case of Cir X-1, it is debated whether it is a LMXB or a HMXB system (Johnston et al. 2016). There are also four transient LMXBs, confirmed to harbor NSs through the detection of thermonuclear bursts or quiescent thermal emission, that showed similar behavior as the Z-sources during the peak of their outbursts (see Table 6). These are, therefore, thought to have reach accretion rates around the Eddington limit (despite their distances being poorly constrained in some cases) and are referred to as transient Z-sources (Wijnands and van der Klis 1999b; Altamirano et al. 2010b; Homan et al. 2010, 2014). Furthermore, GRO J1744–28 is a transient LMXB that harbors a slowly pulsating neutron star (Finger et al. 1996) which accretes around the Eddington limit at the peak of its outbursts (Mönkkönen et al. 2019). Finally, there are a handful of other LMXBs that, like V404 Cyg, are not observed to be particularly luminous but are suspected to be intrinsically accreting around the Eddington limit. Evidence pointing in this direction comes, e.g., from their orbital period evolution (Bak Nielsen et al. 2017) or their strong jets and disk winds (Panurach et al. 2021). For these sources it appears that the most luminous inner part of the binary is obscured, e.g., due to a high inclination or because of strong disk winds. As can be seen in Table 6, several of the high-accretion rate LMXBs have long orbital periods and evolved donor stars. Indeed, their orbital periods are typically too long for a main sequence star to fill its Roche lobe and drive the observed high mass accretion rates. As discussed in section “The Role of the Orbital Period in the Long-Term X-Ray Behavior”, finding that bright LMXBs have relatively long orbital periods is theoretically not surprising. Indeed, it was already suggested early on that the mass donors in Z-sources are evolved stars that are ascending on the giant branch and that high mass-transfer rates could be driven by the associated expansion of the donor star (Taam et al. 1983; Webbink et al. 1983; Hasinger and van der Klis 1989). However, at least one Z-source likely cannot harbor an evolved donor; the infrared counterpart of GX 17+1 is far too faint to allow a giant donor unless the source distance is wrong (Jonker et al. 2000; Callanan et al. 2002). It should also be noted that large orbital period and evolved companion star do not necessarily imply that mass accretion can be driven up to the Eddington limit. For instance, 4U 1624–49 likely hosts an evolved star and has an orbital period of ≈21 h (Jones and Watson 1989) but is a luminous atoll instead of a Z-source. We note that similarly high accretion rates as encountered in these LMXBs are also reached in some HMXBs. Well-known examples are the (c)BH systems SS443, V4641 Sgr, and Cyg X-3 (Koljonen and Tomsick 2020). Furthermore, (super)Eddington accretion rates are a defining property of the population of ultraluminous X-ray sources (ULXs). These are extra-Galactic BHs or NSs that appear to be accreting at super-Eddington rates and of which there are many hundreds known to date (Walton et al. 2022). However, a large fraction of ULXs may be HMXBs instead of LMXBs (see Kuranov et al. (2021) and references therein).

T/P/QP P P

P

P P P T

T T T P

P

T QP T P

T P

System Cyg X−2 GX 349+2

Sco X−1

GX 5−1 GX 17+1 GX 340+0 IGR J17480−2446

XTE J1701−462 MAXI J0556−332 2S 1803−245 GX 13+1

Cir X−1

GRO J1744−28 GRS 1915+105 V404 Cyg 2A 1822−371

Swift J1858.6−0814 AC 211 (X2127+119)

NS NS?

NS BH BH NS

NS

NS NS NS NS

NS NS NS NS

NS

NS/BH NS NS

0.9 0.7

11.8 33.5 6.5 0.23

16.7

? ? ? 24.5

? ? ? 0.9

0.8

? ?

G/K giant K giant K subgiant Main sequence

Debated

? ? ? K giant

Subgiant (K or later) Early-type giant? ? ? Subgiant

Porb (d) Donor 9.8 A giant 0.9 Sub-giant?

Z-source Z-source Z-source Transient Z-source, AMXP Transient Z-source Transient Z-source Transient Z-source Hybrid atoll/Z-source Often in low-flux state Slow pulsar Sometimes obscured Obscured Obscured, slow pulsar Obscured Obscured

Z-source

Comments Z-source Z-source

Buisson et al. (2020, 2021) van Zyl et al. (2004) and Panurach et al. (2021)

Finger et al. (1996) and Gosling et al. (2007) Tetarenko et al. (2016a) Koljonen and Tomsick (2020) Jonker et al. (2003) and Bak Nielsen et al. (2017)

Shirey et al. (1999) and Johnston et al. (2016)

Homan et al. (2010) Homan et al. (2014) Wijnands and van der Klis (1999b) Garcia et al. (1992)

Reference Cowley et al. (1979) and Casares et al. (1998) Wachter and Margon (1996) and Bandyopadhyay et al. (1999) LaSala and Thorstensen (1985) and Mata Sanchez et al. (2015) Jonker et al. (2000) and Bandyopadhyay et al. (2003) Jonker et al. (2000) and Callanan et al. (2002) van der Klis (2006) Altamirano et al. (2010b) and Patruno et al. (2012)

Table 6 List of Galactic LMXBs accreting around the Eddington limit. The letters P, QP, and T refer to persistent, quasi-persistent and transient, respectively. We note that in the case of Cir X-1, it is debated whether the system is a LMXB or a HMXB system (Johnston et al. 2016)

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Distribution and Demographics of LMXBs in the Galaxy LMXBs are found all around us in the Galaxy (Fig. 9); however, their formation channel, population density, and demographic vary depending on the environment. Formation of the compact object in X-ray binaries inflicts a kick on the binary. This kick adds a peculiar motion to the X-ray binary’s Galactocentric orbit and can displace it substantially from where the binary was formed. Despite this, given the large mass and short life span of the companion, HMXBs are not generally expected to be displaced substantially from their original birthplace. Observations indicating HMXBs trace star formation and young star associations support these expectations (Grimm et al. 2003; Bodaghee et al. 2012b). In contrast, the low mass and long life span of companions in LMXBs allows them to achieve significant displacement from their birthplace in present day observations (e.g., Repetto et al. 2012) or be found in regions associated with old star populations (e.g., Galactic center, Galactic bulge, globular clusters, e.g., Arnason et al. 2021). Observed spatial distribution of LMXBs also shows a strong concentration of these systems in the central 2 kpc of the Galaxy, with the overall population showing a larger scale height compared to HMXBs (410 pc for LMXBs, compared to 150 pc for HMXBs Grimm et al. 2002). Consequently, Grimm et al. (2002) also note that around ∼50% of LMXBs are in the Galactic disk, compared to ∼25% in the Galactic bulge.

Fig. 9 Distribution of a subset of known LMXBs in the sky overlaid on the Gaia all-sky image. Pink circles represent BH-LMXBs from Tetarenko et al. (2016a), and blue circles are all other LMXBs as cataloged by Liu (2007). Given discovery of new LMXBs over the past decade and new revelations on classification of some previously known LMXBs, this plot is not representing the entire currently known sample of LMXBs, and it serves only as an example demonstrating the Galactic distribution of LMXBs. (Background image from the Gaia mission (A. Moitinho; ESA/Gaia/DPAC). Figure made using MW-PLOT (https://pypi.org/project/mw-plot/))

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Over the past few decades, monitoring and survey programs with various X-ray observatories have provided a more complete picture of distribution of LMXBs in our Galaxy. These include all-sky monitoring programs (e.g., with ROSAT, Swift/BAT, MAXI, INTEGRAL, Voges et al. 1999; Baumgartner et al. 2013; Kawamuro et al. 2018; Hori et al. 2018; Krivonos et al. 2013) and survey programs targeting the Galactic center (Muno et al. 2006; Heard and Warwick 2013; Degenaar et al. 2015; Sazonov et al. 2020), Galactic bulge (Jonker et al. 2014; Kuulkers et al. 2007; Grebenev and Mereminskiy 2015; Bahramian et al. 2021a), Galactic plane (Giacconi et al. 1971; Grindlay et al. 2003; Motch et al. 2010), and globular clusters (Clark et al. 1975; Verbunt et al. 2001; Grindlay et al. 2001a; Pooley et al. 2003). These surveys have substantially pushed our understanding of LMXB population and distribution in the Galaxy. However, it is important to note that our current view is still heavily impacted by selection effects caused by telescope sensitivity and survey cadence limitations and interstellar absorption (Jonker et al. 2021), among other effects such as uneven coverage. Current and future survey efforts (e.g., eROSITA) will improve on some of these limits. In the following sections, we briefly discuss a subset of surveys and monitoring programs targeting different parts of the Galaxy in the context of LMXBs.

Galactic Center and Bulge The Galactic center has been heavily observed by various X-ray observatories including Chandra, XMM-Newton, Swift, and INTEGRAL. Using Chandra (Wang et al. 2002; Muno et al. 2006) reported and cataloged hundreds of X-ray sources in the central part of the Galaxy, identifying numerous X-ray sources associated with old stellar populations, thus classifying a large fraction of them as old cataclysmic variables, and a smaller group (∼10) as likely LMXBs. Swift/XRT has been observing the Galactic center on a ∼weekly basis since 2006. These observations have led to identification of multiple transient LMXBs and outbursts within 25′ of the Galactic center (Degenaar et al. 2015). A large fraction of these transients were also identified as VFXBs, showing outbursts with peak LX < 1036 erg s−1 (see section “Very-Faint X-Ray Binaries”). Identification of dozens of faint and transient likely LMXBs (and hundreds of other unclassified X-ray sources) in the Galactic center motivated theoretical exploration of the origin and nature of these energetic systems in the region. Population synthesis work by Liu and Li (2006) suggested that NS-LMXBs are likely to dominate the population of X-ray sources in the Galactic center. However, later work by Ruiter et al. (2006) suggested that a majority of these sources may be intermediate polars (a subclass of cataclysmic variables) and that the population of LMXBs is likely to be comparatively small (∼dozens). This was found to be consistent with further observations of the Galactic center by Chandra (Zhu et al. 2018) suggesting number of quiescent LMXBs in the Galactic center cannot be substantially larger than ∼150.

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Muno et al. (2005b) noted an overabundance of transients (particularly transient VFXBs) in the central parsec of the Galaxy – suggesting these systems could be LMXBs that have formed dynamically (similar to globular clusters; see section “Globular Clusters”), or alternatively HMXBs associated with the young star population in the central region. However, this overabundance has not been observed in the Swift/XRT monitoring of the Galactic center out to 25 pc (running since 2006; Degenaar et al. 2015). Extending X-ray surveys to the Galactic bulge, the Chandra Galactic Bulge Survey identified ∼170 candidate cataclysmic variables and quiescent LMXBs (Jonker et al. 2011, 2014; Wevers et al. 2016, 2017). Swift/XRT monitoring of the Galactic bulge led to identification of ∼7 new VXFBs, most of which appear to be symbiotic in nature (Shaw et al. 2001; Bahramian et al. 2021a), leading them to conclude that a large fraction of VFXBs are perhaps SyXBs. At higher luminosities, INTEGRAL surveys of the Galactic bulge have identified dozens of bright LMXB candidates (Kuulkers et al. 2007; Grebenev and Mereminskiy 2015). Exploring characteristics of the X-ray luminosity function of persistent versus transient LMXBs detected by INTEGRAL (Revnivtsev et al. 2008) concluded that the distribution of transient LMXBs is comparatively more focused around the Galactic center.

Galactic Plane and Outer Parts Survey and monitoring coverage of the Galactic plane and halo in the X-rays is substantially shallower and less complete than the Galactic center and bulge. Nevertheless, surveys such as the XMM-Newton and Swift Galactic Plane surveys (Motch et al. 2010; Gorgone et al. 2019) have discovered a handful of LMXBs and LMXB candidates. However, the overwhelming majority of LMXBs identified in the Galactic plane and halo are discovered while exhibiting bright outbursts detected by all-sky monitors such as MAXI or Swift/BAT. Most LMXBs (outside globular clusters) are expected to have formed in the Galactic plane (e.g., following the mass distribution of low-mass stars in the Galaxy (Gilfanov et al. 2004)). However, a small number of LMXBs are found at high Galactic latitudes (e.g., see Jonker and Nelemans 2004; Shaw et al. 2013; Arnason et al. 2021). While it is possible that a nonzero fraction of LMXBs has formed in the halo, a more likely explanation is receiving high natal kicks when the BH or NS is formed through supernova. Given the relatively old age of LMXBs, a high binary natal kick can displace the LMXB significantly from where the compact object in the binary was originally formed (Assuming the binary is not disrupted as a result of the supernova kick) (Repetto et al. 2012). While both BH-LMXBs and NS-LMXBs have been found with high Galactic scale heights, indicating evidence for large kicks in both classes (Repetto and Nelemans 2015), NS-LMXBs are found to reach higher scale heights compared to BH-LMXBs with similar binary natal kicks (Repetto et al. 2017). Furthermore,

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comparing observation-based distribution of binary natal kicks of BH-LMXBs and NS-LMXBS indicates that the kick velocities are smaller for BH-LMXBs compared to NS-LMXBs (Atri et al. 2019).

Globular Clusters Observationally, an overabundance of X-ray binaries in Milky Way globular clusters was noticed soon after the emergence of X-ray astronomy (Clark et al. 1975). Globular clusters contain ∼10−4 fraction of Galactic mass, while containing ∼10–20% of the total population of Galactic LMXBs. In the Galactic field, LMXBs are thought to have predominantly formed through “primordial” binary evolution (e.g., Paczynski et al. 1976; Tauris and van den Heuvel 2006) (however, challenges remain in explaining formation of LMXBs with heavy compact objects – e.g., see Podsiadlowski et al. (2003)). In contrast, the high density of globular clusters (which can reach up to 106 times the solar neighborhood) leads to frequent encounters between members of the cluster. These encounters are expected to open multiple channels for formation of LMXBs in globular clusters, including collision of red giants with a compact object (Sutantyo et al. 1975), tidal capture of a compact object by a companion star (Fabian et al. 1975), or exchange encounters during which a compact object replaces the lower mass member of an existing binary (Hills et al. 1976). Observational evidence supporting this link was first discussed in Verbunt and Hut (1987). Detailed follow-up studies with the Chandra observatory allowed highresolution imaging of faint X-ray sources and provided clear evidence of this link in the Milky Way (Pooley et al. 2003; Heinke et al. 2003b) and other galaxies (Sarazin et al. 2003; Kundu et al. 2007; Kundu and Zepf 2007). Focused studies of individual globular clusters over the past two decades have led to identification and classification of dozens of X-ray binaries (e.g., Grindlay et al. 2001b; Heinke et al. 2006a; Servillat et al. 2008; Maxwell et al. 2012) and X-ray emission from radio millisecond pulsars (Bogdán and Gilfanov 2010; Bhattacharya et al. 2017). Furthermore, a non-negligible fraction of transient and persistent LMXBs (with peak LX > 1035 erg s−1 ) discovered in the Milky Way have been localized to globular clusters (see Table 7, Bahramian et al. 2014b). A large fraction of these systems have been determined to be NS-LMXBs based on detection of type I X-ray bursts or of X-ray pulsations. There are also numerous quiescent LMXBs identified in globular clusters which have not exhibited bright outbursts yet. These systems are identified through X-ray spectroscopy, generally showing a spectrum well described by NS atmospheric models (e.g., Rutledge et al. 2002; Gendre et al. 2003; Becker et al. 2003; Heinke et al. 2006b; Guillot et al. 2009; Walsh et al. 2015; Bahramian et al. 2015). Quiescent and transient NS-LMXBs in globular clusters provide unique opportunities for study of accretion and NS equation of state. These opportunities are largely thanks to the independent constraints on distance that is achieved for

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globular clusters (e.g., see Harris et al. (1996) and references therein for distance measurements) and in some cases existence of pre-outburst observations of the LMXB as the globular cluster was targeted for other studies. Observations of quiescent NS-LMXBs have allowed detailed study of the equation of state in NSs based on constraints on mass and radius obtained via X-ray spectral modeling of the NS atmosphere, which is the dominant emitting region in the X-rays with little or no contamination from the accretion flow in quiescence (Guillot et al. 2013; Heinke et al. 2014; Steiner et al. 2018). Detailed study of transient systems during and after their outburst decay has provided insights about thermal processes in the crust of NSs, for example, showing that internal heating of NSs occurs significantly closer to the surface than previously thought (e.g., Degenaar et al. 2011d; Degenaar and Wijnands 2012; Wijnands et al. 2017; Vats et al. 2018). Multiwavelength observations of transient LMXBs in globular clusters during their outbursts have led to the first confirmation of a transitional millisecond pulsar (Papitto et al. 2013) and strong constraints on the disk-jet coupling in NS-LMXBs (Tetarenko et al. 2016b). In contrast with the Galactic field, where there are dozens of strong BH-LMXB candidates with ∼20 dynamically confirmed (Tetarenko et al. 2016a; Corral-Santana et al. 2016), there are currently no dynamically confirmed BH-LMXBs identified in globular clusters (Galactic or otherwise), and almost all transient LMXBs in globular clusters so far have been identified to be NS-LMXBs (Table 7, Verbunt and Lewin 2006). Historically, it was thought that while globular clusters produce thousands of BHs through their evolution, a large fraction of these BHs decouple from the rest of the cluster in form of a subcluster, segregate toward the cluster core, and eventually get ejected from the cluster (e.g. Sigurdsson and Hernquist 1993). However, detection of strong BH-LMXB candidates in Galactic (Strader et al. 2012; Chomiuk et al. 2013) and extra-Galactic clusters (Maccarone et al. 2007; Dage et al. 2020), along with identification of detached dynamically confirmed BHs (Giesers et al. 2018, 2019), changed these assertions.

Orbital Period Distribution For a limited fraction of (transient and persistent) LMXBs, the orbital period has been measured (via eclipses, radial velocity studies, pulsar timing). There are ∼21 confirmed BH LMXBs with orbital periods measured, which vary from a few hours to several weeks; see Fig. 10. Almost all of these systems show orbital periods of Rco , the rotational velocity of the magnetosphere is supersonic relative to the infalling material, resulting in a centrifugal barrier to accretion often referred to as the propeller effect. In this case, since the accreting material has a lower rotational velocity than the magnetosphere,

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it exerts a torque on the magnetosphere, dissipating some of the neutron star’s rotational energy, thus causing a spindown of the star. Direct accretion occurring when Ra > Rco > RM can spin-up the NS, especially if an accretion disk is formed. Magnetospheric barriers to accretion seem required to explain the behavior of supergiant fast X-ray transients, a class of HMXBs described in section “Supergiant Fast X-Ray Transients,” and may contribute to the variability of other HMXBs as well. For more details on the effects of the magnetosphere on wind accretion, see Bozzo et al. (2008), Kretschmar et al. (2019), and Mushtukov and Tsygankov (2022).

Classes of High-Mass X-Ray Binaries Since the compact objects in the majority of HMXBs accrete matter from the stellar wind of their binary companions, their X-ray properties strongly depend on the properties of the donor stellar wind. Therefore, HMXBs are often classified based on the spectral type of the donor star, as well as the type of compact object they host. While hard X-ray telescopes (i.e., INTEGRAL, NuSTAR) have been very effective at discovering HMXBs, classifying HMXBs requires identifying their optical/infrared counterparts. Since the angular resolution of hard X-ray telescopes (∼0.5–5 arcminutes) is often insufficient for identifying unique optical/infrared counterparts, it is often necessary to first more precisely determine the source position using a soft-X-ray telescope (i.e., XMM-Newton, Chandra), as exemplified in Fig. 3. For HMXBs in crowded Galactic fields or in external galaxies that have many possible optical counterparts even after being localized with Chandra, the chance coincidence probability of all possible counterparts identified within a search radius based on the X-ray positional uncertainty can be calculated to identify the most likely counterpart. The spectral type of the optical/infrared counterpart can then be determined via optical/infrared spectroscopy, or in cases when spectroscopy is not feasible, color-magnitude and/or color-color diagrams can be used for an approximate classification. The donor stars in most HMXBs have been determined to be either supergiant (Sg) O/B stars or Be stars. The properties of these two primary classes of HMXBs, Sg XBs and Be XBs, are described first. Wolf-Rayet X-ray binaries and two additional classes of X-ray sources with possible connections to HMXBs, ultraluminous X-ray sources and gamma-ray binaries, are also presented. Finally, methods for distinguishing between NS and BH HMXBs are discussed.

Supergiant X-Ray Binaries Supergiant (Sg) XBs are primarily wind-fed systems with supergiant O- or Btype (luminosity class I–II) stars. The winds of these high-mass stars are driven by the absorption of ultraviolet resonance lines, and the extent of the acceleration depends on the ionization, excitation, and chemical composition of the stellar

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Fig. 3 Example of the multi-wavelength process required to classify new hard X-ray sources. In each optical image, the error circle of a source discovered by NuSTAR near the Galactic plane is shown in red, and the error circles of soft X-ray sources detected in follow-up Chandra observations are shown in blue, numbered from brightest to faintest. The i-band images come from (a) the Sloan Digitized Sky Survey and (b) the IPHAS survey. The red + symbols mark the positions of the most likely optical counterparts determined by a previous study based on available soft X-ray and optical catalogs; the soft X-ray catalogs tend to have larger positional uncertainties compared to the on-axis follow-up Chandra observations. As can be seen, for hard X-ray sources in crowded Galactic fields, Chandra’s positional accuracy is crucial for identifying the correct optical counterpart. (Credit: Taken from Figure 4 in Tomsick et al. (2018), reproduced with permission ©AAS)

wind (Kudritzki and Puls 2000). The ionization of the wind material is affected both by the effective temperature of the star and the X-ray emission from the accreting compact object (Kretschmar et al. 2019). The wind mass loss rates of OB supergiants are typically in the range of 10−6 –10−5 M⊙ yr−1 , several orders of magnitude higher, compared to the 10−10 –10−7 M⊙ yr−1 mass loss rates of main sequence O and B stars (Smith 2014). Our census of Sg XBs in the Milky Way Galaxy and our understanding of their properties changed substantially with the launch of INTEGRAL in 2002. Due to its improved sensitivity at hard X-ray energies (17–100 keV) and its repeated surveys of the Galactic plane, INTEGRAL has discovered 40 new confirmed HMXBs (Krivonos et al. 2012, 2022), more than half of which are Sg XBs located in our Galaxy (Walter et al. 2015). Prior to INTEGRAL, only about 10% of the roughly 130 HMXBs known were classified as Sg XBs (Liu et al. 2000), so the prevalence of Sg XBs among the new INTEGRAL HMXBs was a surprise. Most of the INTEGRAL Sg XBs are either highly obscured or extremely variable, explaining their late discovery through monitoring and hard X-ray observations. About one third of the HMXBs detected in the Milky Way Galaxy are now classified as Sg XBs (Walter et al. 2015; Fortin et al. 2023), but the vast majority (>80%) of HMXBs in the LMC and SMC are Be HMXBs (Haberl and Sturm 2016; Antoniou and Zezas 2016), which are described in section “Be X-Ray Binaries.”

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Persistent “Classical” HMXBs Classical Sg XBs are persistent sources with luminosities consistently above ∼1035 erg s−1 . However, their luminosity is not constant with time; their flux typically varies by a factor of 10–100 (Walter et al. 2015; Kretschmar et al. 2019). Most Sg XBs are wind-fed systems, with typical orbital periods of 3–60 days, and most host NSs with spin periods 100 s. Some of their variability may be due to the clumpy nature of the winds of massive stars. While there is observational evidence of clumping in the winds of massive stars, the sizes and masses of the clumps are not well constrained (Smith 2014). The fact that line-driven winds are likely to be unstable was recognized by analytical studies in the 1970s, and, more recently, numerical hydrodynamical simulations have found that the line-driven instability can result in density variations up to a factor of 104 (Kretschmar et al. 2019). As detailed in Martínez-Núñez et al. (2017), the line-driven instability can account for a lot of the variability observed in classical HMXBs. However, the clump masses required to explain some of the X-ray flares seen in some classical Sg XBs, including Vela X-1, 4U 1700-37, and IGR J16418-4532, are a factor of 10–1000 above the maximum clump mass of ∼1018 g predicted by simulations of the line-driven instability. This may be due to the limitations of current simulations, or it may indicate that some of the X-ray variability of these sources cannot be solely attributed to variations in the stellar wind density but may result from the centrifugal or magnetic barriers to accretion due to the magnetosphere described in section “Interactions Between the Accretion Flow and the Magnetosphere”. An additional factor that can impact the X-ray variability of Sg XBs is the influence of the accreting compact object on the stellar wind structure. The X-ray emission is expected to photoionize the gas in the vicinity of the compact object, decelerating the wind due to the decreased availability of resonance lines (Walter et al. 2015). This effect has been observed in some Sg XBs, including Vela X-1, GX 301-2, 4U 1907+09, and EXO 1722-363, in which the terminal wind velocities are measured to be lower than expected based on the luminosities of the donor stars. As shown in Fig. 1, at high X-ray luminosities, a photoionization wake of highdensity material is expected to be produced as the higher velocity wind from the stellar surface runs into the slower wind that has been photoionized by the compact object (e.g., Blondin et al. 1990). Furthermore, the orbital motion of the accreting object can lead to the formation of a bow shock and a trailing accretion wake of low-density, highly-ionized gas, which can also be seen in Fig. 1. These impacts on the stellar wind depend on the X-ray luminosity of the compact object and can introduce additional X-ray variability. At least six Sg XBs show persistent levels of high obscuration, with hydrogen column densities NH  1023 cm−2 (Walter et al. 2015). The X-ray spectra of three of these HMXBs are shown in Fig. 4; the dearth of X-ray photons below about 4 keV in these spectra is the result of the high obscuring column densities in these systems. Most of these highly obscured HMXBs remained undetected until INTEGRAL’s sensitive hard X-ray surveys. Some obscured HMXBs (IGR J16393-4611, IGR J16418-4532, IGR J18027-2016) have short orbital period (Porb < 5 days); such

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Fig. 4 X-ray spectra of three highly obscured HMXBs. Data from INTEGRAL ISGRI (>20 keV) and XMM-Newton EPIC ( 5 × 1040 erg s−1 ), whose X-ray spectra and variability more closely resemble those of BHs accreting at sub-Eddington rates. One of the most compelling IMBH candidates discovered to date is ESO 243-49 HLX-1, a ULX classified as a hyperluminous X-ray source (HLX) due to its extreme luminosity, which can reach 1.1 × 1042 erg s−1 . Combined with evidence indicating that most ULXs host stellar-mass black holes or neutron stars, studies of the stellar populations in the vicinity of ULXs have led to the consensus view that most ULXs can be considered the high-luminosity end of the HMXB population. ULXs are found primarily in star-forming galaxies. In starburst galaxies, they tend to be located near star clusters with ages of ∼6 Myr, and in galaxies with moderate star formation rates, ULXs tend to be found near OB associations with ages of 10–20 Myr (Kaaret et al. 2017). The donor stars in ULXs are thus likely to be high-mass stars. Although most ULXs are located in such crowded fields that unambiguous counterpart identification is not possible, in some cases, it has been possible to identify and study the individual optical counterparts of ULXs. For about 20 ULXs, the SEDs of their optical counterparts have been wellsampled. The optical SEDs of bright optical counterparts are very blue, consistent with the SEDs expected for the winds of super-Eddington accretion disks, whose

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optical emission dominates over that of the donor star (Fabrika et al. 2015). Fainter optical counterparts instead have SEDs consistent with those of supergiant A-G stars, so in these ULXs, the donor star may be able to outshine the hot accretion disk wind due to lower accretion rates (Fabrika et al. 2021). The optical spectra of only about 10 ULXs have been well-studied to date; they exhibit broad emission lines with FWHM ≈300–1600 km s−1 indicative of strong disk winds (Fabrika et al. 2015). The donor stars of 9 ULXs have been spectroscopically classified: M101 ULX-1 has a Wolf-Rayet donor, ULXP NGC 7793 P13 has a B9 Ia supergiant donor, the ULX candidate SS 433 has an A 3-7 I supergiant donor, and 6 other ULXs appear to be red supergiants, although five of these require additional confirmation (Fabrika et al. 2021). Even though most ULXs are thought to be high-luminosity HMXBs, their X-ray spectral properties differ in significant ways from those of most HMXBs (see section “NS HMXB X-Ray Spectra”) due to having super-Eddington accretion disks. ULX X-ray spectra often show a double-peaked shape and an exponential cutoff above 10 keV (Kaaret et al. 2017); the low energy peak is associated with the thermal temperature of the disk (kTdisk ∼ 0.2 keV), while the second is due to the Comptonization of soft photons by free electrons with kTe ∼ 1–2 keV and high optical depth (τ ≥ 6). For comparison, typical values for black hole HMXBs are kTdisk ∼ 1 keV, kTe ∼ 100 keV, and τ ≤ 1 (McClintock and Remillard 2006), although it should be noted that it is not currently possible to constrain the very hard X-ray spectrum of ULXs well due to their low observed fluxes compared to Galactic HMXBs. Depending on the relative contributions of the different spectral components, ULX spectra can appear softer or harder, and ULXs can transition between different spectral states, which are shown in Fig. 8. These different spectral states may result from the observer’s line-of-sight relative to the central conical funnel formed by the disk wind; this angle can vary with the precession of the disk, thought to occur on

Fig. 8 Example energy X-ray spectra from XMM EPIN PN observations of different ULXs exhibiting three different spectral states. From left to right they are the following: broadened disk, NGC 1313 X-2; hard ultraluminous, Ho IX X-1; soft ultraluminous, NGC 5408 X-1. The contributions from each of the components of the best-fitting absorbed multicolor disk (blue dotted line) plus power-law (red dashed line) model are shown. (Credit: Figure 1 in Sutton et al. (2013), “The ultraluminous state revisited: fractional variability and spectral shape as diagnostics of superEddington accretion,” MNRAS, 435, 2)

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timescales of 2–200 days based on the detection of superorbital periods, and the accretion rate, which affects the disk geometry (Kaaret et al. 2017; Fabrika et al. 2021). The greatest variability is observed when ULXs are in the soft spectral state, but the majority of the variability is associated with the hard component (Fabrika et al. 2021). This variability is consistent with the soft state being associated with a greater inclination between the line of sight and the wind funnel axis, which results in the inner accretion disk being more likely to occasionally be obscured by optically thick clumps of wind.

Gamma-Ray Binaries While X-ray emission generally dominates the spectral energy distribution of HXMBs, gamma-ray binaries radiate more power in gamma rays above 1 MeV than in X-rays. Such systems can be inconspicuous in X-rays yet stand out in the gamma-ray sky. Emission at such high energies is necessarily from non-thermal particles: in these systems, particle acceleration dominates how energy is channelled into radiation. Like HMXBs, gamma-ray binaries consist of a compact object and a high-mass stellar companion, but a significant difference between these two classes of sources is that some (or all) gamma-ray binaries may be rotation-powered rather than accretion powered. While differing in terms of energy production mechanisms, there may be an evolutionary link between gamma-ray binaries and HMXBs. Table 1 lists confirmed gamma-ray binaries as of early 2022 (see Dubus 2013; Paredes and Bordas 2019; Chernyakova and Malyshev 2020 for reviews and references). Gamma-ray binaries emit from radio to TeV energies, as shown in Fig. 9. Their radio emission is generally optically thin with an intensity Sν ∼ ν −1/2 and is observed on a scale larger than the binary orbit. VLBI observations have resolved the radio emission of several binaries into a collimated flow whose position angle rotates with orbital phase, as expected if the non-thermal particles were collimated by the stellar wind of the companion. The optical-UV is dominated by radiation from the massive star. In X-rays, gamma-ray binaries typically show hard powerlaw spectra with photon indices Ŵ ≈ 1.5 extending well beyond 10 keV, whereas typical X-ray binaries show cutoffs (see section “NS HMXB X-Ray Spectra”). The spectral energy distribution of gamma-ray binaries peaks in the 0.1 to 10 MeV range. Table 1 Confirmed gamma-ray binaries (Dubus 2013; Paredes and Bordas 2019; Chernyakova and Malyshev 2020)

Name PSR J2032+4127 PSR B1259-63 HESS J0632+057 LS I +61◦ 303 1FGL J1018.6-5856 4FGL J1405.1-6119 LMC P3 LS 5039

Binary components Pulsar B0Ve Pulsar O9.5Ve ? B0Vpe Pulsar ? B0Ve ? O6V(f) ? O6.5III ? O5III(f) Pulsar ? O6.5V(f)

Porb (d) ∼17000 1237 315 26.5 16.6 13.7 10.3 3.9

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Fig. 9 Spectral energy distribution νFν of the gamma-ray binary LSI +61◦ 303 showing emission from radio to TeV gamma rays, peaking around 10 MeV. (Data from Dubus 2013; VERITAS Collaboration et al. 2016; Chernyakova et al. 2017; Xing et al. 2017)

In the higher 0.1 to 30 GeV range, the Fermi-Large Area Telescope (LAT) spectra of these sources are usually well-fit by a power-law with an exponential cutoff at a few GeV. Above 100 GeV, the typical spectrum is a power-law with a photon index of Ŵ ≈ −2.5. Several particle acceleration sites and/or radiative processes must be involved given the clearly distinct spectral components from X-ray to TeV energies. Two of the gamma-ray binaries, PSR B1259-63 and PSR J2032+4127, host radio pulsars with pulse periods of 48 ms and 143 ms, respectively, a much faster rotation rate than that of HMXB X-ray pulsars (see section “X-Ray Pulsations”). Radio pulsar timing indicates that the neutron star in these two systems is steadily spinning down on timescales of 105 years, consistent with “normal” radio pulsars. Normal radio pulsars are rotation-powered: the combination of their fast rotation and high magnetic field (∼1012 G) generates a tenuous relativistic wind that extracts the rotational energy of the neutron star and accelerates particles to very high energies. Part of this spindown power is radiated in pulsed radio to gamma-ray emission in the vicinity of the neutron star or further away in a pulsar wind nebula (PWN) where the relativistic wind interacts with the interstellar medium. The general understanding is that PSR B1259-63 and PSR J2032+4127 are scaled-down PWN, with the relativistic wind interacting with the companion’s stellar wind on AU scales rather than the parsec scales of typical PWN. In most HMXBs, the neutron star accretes material from the stellar wind forming X-ray pulsations as the material is channelled toward the magnetic poles of the neutron star. The mechanism responsible for radio pulsations is not expected to occur in HMXB X-ray pulsars because electric fields are shorted out in this high-density environment. Inversely, accretion is quenched if the pressure from a

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rotation-powered pulsar relativistic wind exceeds the ram pressure of the stellar wind at the Bondi-Hoyle-Littleton capture radius. This occurs when ˙ w c ≈ 1035 E˙ > 4Mv



  M˙ vw erg s−1 1016 g s−1 1000 km s−1

(10)

where M˙ is the accretion rate and vw is the stellar wind velocity. In PSR B1259-63 and PSR J2032+4127, the pulsar relativistic wind is powerful enough to quench the accretion flow and turn on the radio pulsar mechanism. As the pulsar spins down, its E˙ decreases, and its wind cannot hold off accretion. Thus, these pulsars are expected to switch from rotation-powered radio pulsars to accretion-powered X-ray pulsars on their spindown timescale of ≈105 yr. All the gamma-ray binaries could be rotation-powered by young pulsars, like PSR B1259-63 and PSR J2032+4127. In this scenario, gamma-ray binaries represent a short-lived (105 yr) phase between the supernova birth of a fast-rotating neutron star and the longer-lived HMXB phase triggered by the onset of accretion. This is supported by the scarcity of gamma-ray binaries compared to HMXBs and by observational similarities between all gamma-ray binaries (Dubus et al. 2017). Radio pulsations may be very difficult or impossible to detect in most gamma-ray binaries: the dense environment due to the stellar wind or circumstellar disk scatters and attenuates radio pulsations, as happens for PSR B1259-63 over part of its eccentric orbit. Indeed, PSR B1259-63 and PSR J2032+4127 have the longest orbits among gamma-ray binaries, corresponding to the widest separations with their highmass stellar companion. Pulsations can also be searched for at X-ray or gamma-ray energies, but the low photon count rates require integrating over tens to hundreds of orbits to build up sufficient signal-to-noise, so the pulsar orbital motion must be taken into account in the analysis. Despite these hurdles, intermittent 269 ms radio pulsations have been attributed to LS I+61◦ 303 (Weng et al. 2022), and a tentative 9s gamma-ray pulsation has been reported for LS 5039 (Yoneda et al. 2020). Alternatively, gamma-ray binaries have also been interpreted as microquasars, with the non-thermal emission arising from particle acceleration in a relativistic jet, in a scaled-down version of the high-energy emission observed from AGN jets (Bosch-Ramon and Khangulyan 2009; Massi et al. 2020). The microquasar scenario would be supported if the compact object mass in some gamma-ray binaries turned out ≥3 M⊙ , pointing to a BH rather than a pulsar. In fact, three BH candidates with high-mass stellar companions are firmly detected at gamma-ray energies: Cyg X-1, Cyg X-3, and SS 433, all of which are accreting and launch relativistic jets. However, the gamma-ray luminosities of Cyg X-1 and Cyg X-3 are only a few percent of their X-ray luminosities, so unlike gamma-ray binaries, these sources are not dominated by non-thermal emission. Their gamma-ray emission is also correlated with changes in their radio/X-ray spectral state, clearly linking particle acceleration to the accretion/ejection process in these sources. Gamma-ray binaries do not show these spectral state changes typical of accreting BH X-ray binaries. In the specific case of SS 433, the gamma-ray emission region is not the binary itself but a region where the jet-inflated bubble interacts with the ISM.

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Gamma-ray surveys and radio pulsar surveys are the prime tools to discover new gamma-ray binaries. In gamma-rays, point sources in the Galactic Plane make good candidates, triggering follow-up observations in the radio, X-ray, and optical bands to search for a possible HMXB association. The angular resolution is not always sufficient to rule out a chance superposition with another type of source, so variability is key to establish the association of the gamma-ray emission with the binary. Searching for periodic emission in unidentified gamma-ray sources of the Fermi-LAT catalog has proven fruitful to discover new gamma-ray binaries. PSR B1259-63 and PSR J2032+4127 were instead discovered in radio pulsar searches, where they stood out because of their massive stellar companion. Their powerful gamma-ray emission was only detected later, identifying them as gammaray binaries. Future radio surveys with the SKA can be expected to increase the number of known pulsars with massive companions, providing a new path to identifying gamma-ray binary candidates.

Black Hole Versus Neutron Star X-Ray Binaries There are several observational signatures that can help determine whether the compact object in an HMXB is a NS or a BH. The detection of X-ray pulsations (see section “X-Ray Pulsations”) is considered definitive evidence of the presence of a NS, and such objects are referred to as pulsars. These X-ray pulsations result from the X-ray emission produced near the star’s magnetic poles coming into and out of the observer’s view as the NS rotates. Since the accretion flow around BHs is not collimated by magnetic fields, no X-ray pulsations are expected from BH HMXBs. However, the lack of pulsations does not necessarily mean that an HMXB harbors a BH since a neutron star’s magnetic field geometry, the degree of misalignment between its magnetic and rotation axes, the orientation of its magnetic poles relative to our line-of-sight, or a very long spin period can make X-ray pulsations difficult to detect. X-ray spectral features of HMXBs, described in section “NS HMXB X-Ray Spectra”, can also help differentiate between NSs and BHs (see section “NS HMXB X-Ray Spectra”), although many of these diagnostics require fairly high-quality X-ray spectra. Some NS HMXBs exhibit cyclotron resonance scattering features in their X-ray spectra, which are produced as a result of their strong magnetic fields and thus provide clear evidence of the presence of a NS. NS HMXBs tend to exhibit exponential cutoffs to their power-law spectra at lower energies than BH HMXBs, so the detection of an exponential cutoff at 40 keV is indicative, but not definitive, evidence of a NS. Furthermore, accreting BHs undergo spectral state transitions, while most NS HMXBs do not. In the high/soft state, the spectra of BH XBs exhibit relativistic reflection features from the inner edge of the accretion disk, including a relativistically broadened iron line whose width depends on the BH spin. In the low/hard state, BH XBs exhibit a tight correlation between their X-ray and radio emission (Gallo et al. 2003), the latter of which is associated with relativistic jets. Thus, observing that an HMXB undergoes spectral state transitions, possesses the

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aforementioned spectral features, or obeys the X-ray radio correlation provides a strong, but not definitive, indication of the presence of a BH.

Mass Measurements of Compact Objects in HMXBs Measuring a compact object mass that exceeds 2–3 M⊙ currently provides the most definitive observational proof of a BH since NS masses cannot theoretically exceed such values. However, even this method is imperfect in that it cannot reliably differentiate between massive NSs and low-mass BHs. The masses of compact objects in HMXBs can be constrained in two primary ways: (i) using the X-ray lightcurves of eclipsing binaries, which have a sufficiently high inclination that the compact object is eclipsed by its companion, or (ii) measuring the radial velocity curve of the donor star. Using more than ten years of monitoring observations by the Integral Soft Gamma-Ray Imager (ISGRI) on the INTEGRAL satellite and the All-Sky Monitor (ASM) on RXTE, Falanga et al. (2015) measured the masses of ten eclipsing HMXBs. The masses were constrained by determining the binary orbital parameters and then measuring the duration of X-ray eclipses in the 17–40 keV lightcurves, folded on the orbital period. Most of the HMXB eclipsing sample consisted of supergiant HMXBs with orbital periods ≤10 days, since it easier to discover and accurately measure eclipses for short-period systems. As shown in Fig. 10, the mass range of the compact objects in these HMXBs was found to be 1.02–2.12 M⊙ with the majority of the masses clustering between values of 1.4 and 1.7 M⊙ as expected for neutron stars. Fig. 10 Masses of the ten eclipsing HMXBs. The neutron star masses determined by Falanga et al. (2015) are shown with solid lines, while values from prior literature are represented with dashed lines. The error bars correspond to uncertainties at 1σ confidence level. The dashed vertical line indicates the canonical neutron star mass of 1.4 M⊙ . (Credit: Figure 4 from Falanga, M., et al., A&A, 577, A130, 2015, reproduced with permission © ESO)

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Radial velocity measurements of the donor star in an HMXB can provide a lower limit on the compact object mass, if the mass of the donor can be estimated based on its spectral type. If the inclination angle of the binary can be constrained, then this lower limit on the compact object mass can be tightened. Xray polarization measurements, which can be made with unprecedented sensitivity with the Imaging X-ray Polarimetry Explorer (IXPE), can help determine the inclination of X-ray emitting regions and piece together the geometric orientations of the binary components. If an accretion disk is present around the compact object and the radial velocity of emission lines originating from the disk can be measured or if changes in the timing of X-ray pulsations can be measured, then the compact object mass can be measured. The black hole mass constraints determined from radial velocity measurements for six HMXBs were compiled by Özel et al. (2010). The orbital periods of these HMXBs range from 1 to 5 days, and the donor stars include two Wolf-Rayet stars, two OB supergiants, and two OB giants/subgiants. More recently, the mass of the compact object in MWC 656 was measured to be 3.8–6.9 M⊙ (Casares et al. 2014) based on the radial velocity curves of the Be donor star and the accretion disk; this mass measurement confirmed this source as the only currently known Be-BH XB. This binary, originally identified through its uncertain association with a gammaray source, was found to be in an X-ray quiescent state (LX ∼ 10−8 LEdd ) and confirmed to follow the X-ray/radio correlation (Ribó et al. 2017). The masses of the black holes in HMXBs tend to be higher than those of black holes in LMXBs (Özel et al. 2010). This trend may result from the fact that mass transfer in LMXBs requires close binary separations that can likely only be produced if the system underwent a common envelope phase when the primary expanded; the ejection of the hydrogen envelope during this phase results in a naked helium core, which can experience further substantial mass loss during the WolfRayet phase. Thus, such a star would likely only be able to leave behind a black hole with mass 500 s) may host magnetars as well. A soft X-ray excess is observed in some NS HMXB spectra, which is often modeled with a blackbody component (Mushtukov and Tsygankov 2022). In diskfed HMXBs, this soft excess likely results from the reprocessing of hard X-rays by the inner edge of the accretion disk. In wind-fed HMXBs, the soft excess may arise from the photoionized stellar wind in the vicinity of the NS or thermal emission from the NS surface. Both NS and BH HMXB spectra can display iron (Fe) fluorescent emission lines. This fluorescent emission is produced when an X-ray photon ejects an inner shell electron, and then an electron from an upper energy level falls down to a lower energy level. The most common Fe fluorescent line observed in HMXB spectra is Fe Kα, which is produced when an electron falls down to the lowest energy level (n = 1) from the second energy level (n = 2). In NS HMXBs, Fe Kα emission lines have typical equivalent widths of ∼100 eV and a central line energy of 6.4 keV, corresponding to neutral or low-ionization Fe (Coburn et al. 2002). This iron emission can provide insights into the geometric structure of material around the neutron star (Mushtukov and Tsygankov 2022).

Cyclotron Resonance Scattering Features Some NS HMXB spectra exhibit cyclotron resonance scattering features (CRSFs) in their spectra (Coburn et al. 2002). CRSFs are absorption line-like features arising from the resonant scattering of photons by electrons whose energies are quantized into Landau levels by a strong magnetic field. The quantized energy levels are approximately harmonically spaced, with the fundamental line energy begin equal to: Ec = 11.6

B (1 + z)−1 keV 1012 G

(11)

where B is the magnetic field strength and z is the gravitational redshift of the NS. Since the sizes and masses of neutron stars span a narrow range, the fundamental cyclotron line energy can be used to estimate the strength of the NS magnetic field. One complication in the measurement of the fundamental line energy is that in hard sources with multiple strong harmonic lines, the fundamental line can be difficult to detect due to photon spawning, when an electron remains in an excited Landau level after scattering and emits a photon of similar energy to the fundamental line energy when it de-excites.

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Using cyclotron line measurements of ten accreting neutron stars, Coburn et al. (2002) found a positive correlation between the magnetic field strength and the power-law cutoff energy of the NS X-ray spectra up to CRSF energies of 35 keV. This trend suggests that the spectral cutoff energy is connected to the NS magnetic field, possibly via an intermediate quantity, the most likely of which is the electron temperature, which depends on B up to a saturation point. In individual NS HMXBs, it has been observed that the CRSF line energy varies with the source X-ray flux. As shown in Fig. 12, both positive correlations and negative correlations between the CRSF line energy and X-ray lumionosity have been observed (Staubert et al. 2019); in some cases, both trends can be observed in the same source. Positive CRSF energy-luminosity correlations tend to be associated with lower luminosities than negative correlations. It has also been found that the power-law photon index (Ŵ) of the spectral continuum follows the opposite trend with X-ray flux as the CRSF line energy (the spectra of sources with a positive CRSF energy-flux correlation become harder with increasing flux, and vice versa). Different explanations have been suggested to explain these trends. The positive correlation between CRSF energy and X-ray luminosity is explained either by the formation of a collisionless shock above the neutron star surface, the height of which is anti-correlated with the mass accretion rate, or by radiation pressure slowing down the relativistic plasma near the NS surface, decreasing the observed redshift of the CRSF energy as the luminosity increases. The negative correlation observed at high luminosities is thought to be associated with a radiation-dominated shock, whose height above the NS surface increases with mass accretion rate and the radiation

70

ECRSF [keV]

60

GX 304−1

50

A 0535+26

40

Her X-1

Cep X-4

SMC X-2

30

V 0332+53 Vela X-1

20

4U 1538−522

0.1

1

10 Luminosity [1037 erg s−1 ]

Fig. 12 Compilation of correlations between cyclotron line energy ECRSF and X-ray luminosity. Both correlations and anti-correlations can be seen. The luminosities are calculated using the distances measured by Gaia. (Credit: Staubert et al. (2019), A&A, 622, A61, 2019, reproduced with permission © ESO)

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from this taller accretion column illuminating a greater portion of the NS surface. See Mushtukov and Tsygankov (2022) for more details about these models.

Spectral States of Be XBs While most NS HMXBs do not exhibit substantial spectral variability, recently, some systematic studies were performed to study the spectral states in Be XB pulsars that exhibit Type II outbursts. Studies of the CD, HID, and power spectra of Be XB pulsars found their correlated spectral-timing behavior shares a number of similarities with LMXBs and BH-XRBs and identified two different branches in the HID during Type II outbursts (e.g., Reig and Nespoli 2013). This behavior has been attributed to two different accretion modes, which depend on whether or not the source luminosity exceeds a critical value, which is mainly determined by the magnetic field strength and is equal to ∼(1−4)×1037 erg s−1 for the studied sources. Given that the spectral state transitions in BH XRBs and NS LMXBs are associated with changes in their accretion disks, it is worth noting that the spectral states exhibited by these Be XBs occur during Type II outbursts, during which a transient accretion disk is expected to form around the NS. Other examples of spectral state changes in Be XBs include GRO J1008-57 transitioning to a cold (low-ionization) disk state in between Type I outbursts and Swift J0243.6+6124, the first Galactic ULX pulsar transitioning from a gas-supported to a radiation-supported accretion disk while experiencing a super-Eddington outburst (Mushtukov and Tsygankov 2022).

Spectral States of BH Systems While the spectra of most NS HMXBs do not tend to show large spectral changes, BH HMXBs (e.g., Cyg X-1, Cyg X-3) transition between different spectral states, as shown on the left side of Fig. 13. The spectrum of accreting BHs, including BH HMXBs, consists of three primary components, shown on the right side of Fig. 13: a blackbody component associated with the accretion disk, a power-law component arising from Compton up-scattering of the disk emission by non-thermal electrons in the corona, and the reflected spectrum of the coronal emission by the inner parts of the disk, which exhibits an iron line and Compton hump. Different BH spectral states are thought to result from changes to the geometry of the disk and corona associated with variations of the mass accretion rate (McClintock and Remillard 2006). Accreting BHs exhibit two primary spectral states referred to as the high/soft state and the low/hard state. The high/soft state occurs at high accretion rates ˙ ). During this between about 0.1 and 0.5 of the Eddington accretion rate (MEdd state, the X-ray spectrum is dominated by the thermal blackbody emission from the accretion disk, with typical temperatures of kTdisk ∼ 1 keV; in this state, the powerlaw component associated with the corona has a photon index of Ŵ ∼ 2–3 extending to MeV energies (Zdziarski 2000). Iron line emission arising from the inner edge of the accretion disk is especially prominent in the high/soft state. Spectral fitting of

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Fig. 13 Left: Energy spectra of the BH HMXB Cyg X-1 in the soft, intermediate, and hard states measured by ASCA, RXTE, and CGRO/OSSE. Right: Soft-state spectrum of Cyg X-1 from ASCA-RXTE. Lines show the total best-fit spectral model (solid), as well as the individual model components: disk blackbody photons (long dashes), Comptonization by nonthermal electrons (dominating the short-dashed curve above the break at 15 keV) and by thermal ones (dominating the short-dashed curve below the break), and Compton reflection from the disk (dots). (Credit: Figures 1 & 7 from Zdziarski (2000), reproduced by permission the author)

the continuum disk emission or the relativistically broadened iron line can be used to estimate the spin of the BH (McClintock and Remillard 2006). The low/hard ˙ . In state occurs at low accretion rates between approximately 0.01 and 0.1 MEdd the low/hard state, the X-ray spectrum is dominated by the Comptonized continuum from the corona of electrons with a typical temperature of kTe ∼ 100 keV and optical depth τ ≤ 1, which exhibits a cutoff at 50–100 keV (Zdziarski 2000); it is thought that in this state, the accretion disk is truncated farther away from the black hole (McClintock and Remillard 2006). Radio jet emission appears in the low/hard state and disappears during the transition to the high/soft state. For more details about the spectral states of accreting BHs, see Black holes: accretion processes.

Variability HMXBs exhibit X-ray variability on a wide range of timescales. Some HMXBs display periodic variability. Both orbital and super-orbital modulations in HMXB lightcurves have been observed, and NS HMXBs can exhibit X-ray pulsations associated with the rotation period of the NS. Aperiodic variability occurs on a variety of timescales in HMXBs, from milliseconds to years. While some HMXBs are persistent and have fairly constant luminosities that only vary a factor of a few, about 40% of Galactic HMXBs are considered transient sources due to their large variability (Neumann et al. 2023), reaching faint luminosities that make them undetectable in typical surveys. The percentage of HMXBs in the Magellanic Clouds that are transient is even higher since they are dominated by Be XBs, and the majority of Be XBs are transient sources (Coe and Kirk 2015; Antoniou and Zezas 2016).

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Periodic Variability X-Ray Pulsations As discussed in section “NS HMXB X-Ray Spectra”, material accreting onto a NS in an HMXB is channeled toward the magnetic poles due to its strong magnetic field. Therefore, as the NS rotates, X-ray pulsations from emission regions near the magnetic poles can be observed, and the accreting compact object is referred to as a “pulsar.” The detection of X-ray pulsations and measurement of the NS spin period is performed through a periodogram or power spectrum analysis of the X-ray lightcurve. At least half of the HMXBs in the Milky Way and the SMC have been found to be pulsars (Coe and Kirk 2015; Haberl and Sturm 2016; Fortin et al. 2023). Analysis of the Chandra X-ray Visionary Program (XVP) observations of the SMC revealed that actually all Chandra sources with LX  4 × 1035 erg s−1 exhibited X-ray pulsations (Hong et al. 2017). The spin periods of NSs in HMXBs span a wide range from ∼1 to 104 s (Corbet 1986; Reig et al. 2012; Townsend et al. 2011). It has been observed that the NS spin period is anti-correlated with both the maximum soft X-ray luminosity and the average hard X-ray luminosity of the HMXB (Sidoli and Paizis 2018). Thus, HMXBs with low NS spin periods tends to have the highest X-ray luminosities, which can be explained by the onset of the propeller effect (Illarionov and Sunyaev 1975); the faster the NS rotates, the greater the mass accretion rate needed to overcome the centrifugal barrier to accretion. Once the spin period is determined, the lightcurve can be folded on the period to measure the X-ray pulse profile. Pulse profiles often vary as a function of energy and source luminosity (Kretschmar et al. 2019). For example, Lutovinov and Tsygankov (2009) found that some bright HMXBs exhibit double-peaked pulse profiles in the 20–40 keV band, but one of the peaks tends to decrease in relative intensity as the energy increases, making the profiles appear more single-peaked at higher energies (see left side of Fig. 14). A feature of pulse profiles that is commonly measured is the pulse fraction, defined as P F = (Imax − Imin )/(Imax + Imin ) where Imax and Imin are the background-corrected count rates at the pulse profile maximum and minimum, respectively. While the exact value of the pulse fraction varies from source to source, it can be as low as 10–20% at soft X-ray energies (3–10 keV) and is typically >50% above 40 keV (e.g., Tsygankov et al. 2007; Lutovinov and Tsygankov 2009). As shown in the bottom panels of Fig. 14, in bright HMXBs, the pulse fraction tends to increase with energy, although its behavior as a function of energy is often more peculiar near the cyclotron line energy harmonics (Lutovinov and Tsygankov 2009). In most cases, the pulse fraction decreases with increasing luminosity (e.g., Tsygankov et al. 2007; Yang et al. 2018). Variations of the pulse profile and pulse fraction are thought to be related to the geometry of the accretion flow and its changes with mass accretion rate. At low accretion rates, the X-ray emission originates in hot spots on the NS surface and is expected to produce a “pencil” beam of emission, as sketched in Fig. 1. As the accretion rate increases, a collisionless shock forms above the NS surface, and at

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Fig. 14 Pulse profile for the X-ray pulsars A0535+262 and Her X-1 (in a high state) in the (a) 20–30, (b) 30–40, (c) 40–50, (d) 50–70, and (e) 70–100 keV energy bands from IBIS/INTEGRAL data. Panel (f) shows the energy dependence of the pulse profile. The vertical dashed line indicates the cyclotron line energy of the source. (Credit: Taken from Figures 7 & 12 from Lutovinov and Tsygankov 2009)

even higher rates, a radiative shock results in the formation of an accretion column; in both of these scenarios, the chance that photons in the column will scatter off of in-falling electrons increases, causing more emission to escape out the side of the column in a “fan” beam of emission (Mushtukov and Tsygankov 2022). Different beam patterns result in different pulse profiles. The aforementioned observed trends of the pulse fraction and pulse profiles with energy and luminosity in bright HMXBs are consistent with the presence of accretion columns in which the temperature decreases with height, resulting in hard X-rays forming in smaller regions closer to the NS surface (Lutovinov and Tsygankov 2009). Eclipses of parts of the accretion column, which can explain the fact that some pulse profiles of bright HMXBs

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transition from being double-peaked to single-peaked at higher energies (Lutovinov and Tsygankov 2009), can be used to estimate the NS radius and constrain the NS equation of state (Mushtukov et al. 2018). par However, pulse formation is a complex process, and detailed models describing X-ray pulse profiles over a wide range of luminosity are still not fully developed. Such models must account for gravitational light bending and for reflected emission off the NS surface from fan beam emission arising from the accretion column (Mushtukov and Tsygankov 2022). The reflected emission off the NS surface also impacts the formation of CRSF, as discussed in section “Cyclotron Resonance Scattering Features”, so selfconsistent models should be able to explain both the CRSF and pulse profiles. At the super-Eddington accretion rates of ULX pulsars, the presence of an outflow can also impact the X-ray beaming and the pulse profiles (Mushtukov and Portegies Zwart 2023).

Orbital Periods and Variability As discussed in section “Be X-Ray Binaries”, many Be XBs exhibit orbital variability, undergoing Type I outbursts periodically at or near periastron. In these systems, the Type I outburst periodicity, as measured from X-ray or optical light curves, provides a way of determining the orbital period. A small number of HMXBs exhibit X-ray eclipses in their lightcurves, providing a different way of measuring the orbital period. Orbital motion can introduce modulations in the timing of X-ray pulsations, as the pulsar moves periodically toward and away from the observer, just as orbital motion produces Doppler shifts in the optical/infrared spectra of the donor stars. Either pulsar timing or radial velocity curves measured via spectroscopic observations provide a way of measuring both the orbital period and eccentricity of the binary system. Most HMXBs follow a similar positive correlation between orbital period and eccentricity (Sidoli and Paizis 2018). The exceptions to this trend are a few Be XBs with low eccentricity and orbital periods longer than 20 days; it is thought that these may be systems in which the NS experiences a lower natal kick (Townsend et al. 2011). More eccentric systems tend to exhibit greater dynamic range in their luminosities, consistent with the fact that the compact objects in these systems experience a wider range of donor wind parameters over their orbit (Sidoli and Paizis 2018), although eccentricity is not the only factor that can result in a high dynamic range. Different classes of HMXBs occupy different parts of the spin-orbital period parameter space (e.g., Corbet 1986; Townsend et al. 2011; Sidoli and Paizis 2018), which is often referred to as the Corbet diagram. A compilation of the spin and orbital periods of different types of HMXBs is shown in Fig. 15. Disk-fed HMXBs, including some ULXs (Townsend and Charles 2020), have the shortest orbital periods (3 days) and fast spins; their spin and orbital periods may be anticorrelated, but there are too few such sources with spin and orbit measurements to make a definitive conclusion. The fast rotations of the NSs in these systems are thought to result from efficient spin-up by the accretion disk.

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Spin Period (seconds)

10000 1000 100 10 Sg, disk−fed Sg, wind−fed SFXT Be, MW Be, SMC ULX, Sg ULX, Be ULX, unknown

1 0.1 1

10

100

1000

Orbital Period (days) Fig. 15 The spin period versus orbital period of different groups of HMXBs is shown with different symbols, as indicated in the legend. (Data is compiled from Corbet 1986; Grebenev 2009; Townsend et al. 2011; Reig et al. 2012; Klus et al. 2014; Coe and Kirk 2015; Martínez-Núñez et al. 2017; King and Lasota 2019; Townsend and Charles 2020)

Classical wind-fed Sg XBs have high spin periods and orbital periods of 3–60 days, in between those of disk-fed HMXBs and Be XBs. No clear correlation is seen between the spin and orbital periods of wind-fed Sg XBs. This has often been interpreted as a result of inefficient angular momentum transfer by wind accretion. The orbital periods of SFXTs span a wide range, overlapping with both Sg and Be HMXBs, although they tend to have higher eccentricities at a given orbital period than other HMXBs (Sidoli and Paizis 2018). The vast majority of Be XBs have longer orbital periods than Sg XBs and lower-average spin periods. The spin and orbital periods of Be XBs are positively correlated, with slower spinning pulsars residing in longer period orbits, suggesting that the NSs in Be XBs evolve toward an equilibrium period (Corbet 1986). Angular momentum can be efficiently transferred from the Be equatorial decretion disk to the compact object during periastron passage (Waters and van Kerkwijk 1989); if the angular velocity of the infalling material is greater than that of the magnetosphere, it is accreted and spins up the NS; otherwise, the propeller effect flings the infalling material away, spinning down the NS in the process (Illarionov and Sunyaev 1975). Using the latest census of Be XBs in the Milky Way and the Magellanic Clouds, two subpopulations with different characteristic spin and orbital periods and orbital eccentricities have been identified (Knigge et al. 2011). The bimodality is more prominent in the logPspin distribution (than in the logPorb ), with the two peaks shown at Pspin ∼ 10 s (Porb ∼ 40 d) and Pspin ∼ 200 s (Porb ∼ 100 d), respectively. Be XB pulsars with Pspin < 40 s were found to more likely experience type II outbursts and exhibit greater long-term X-ray variability compared with those with

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Pspin > 40 s (Haberl and Sturm 2016); these trends suggest that the Pspin bimodal distribution is likely due to different accretion modes in Be XBs (Haberl and Sturm 2016), although it has also been attributed to the two types of NS-forming supernovae, electron-capture versus iron-core-collapse supernovae (Knigge et al. 2011).

Superorbital Modulations Superorbital modulations have been observed in the X-ray lightcurves of several HMXBs. These modulations are periodic or quasi-periodic luminosity variations on timescales longer than the orbital period, typically by a factor of 3–10 (e.g., Kotze and Charles 2012 and references therein). The origins of superorbital modulations vary for different types of HMXBs. In disk-fed HMXBs, such as SMC X-1, these modulations are thought to result from the precession of a tilted or warped accretion disk periodically obscuring the X-ray source or varying the geometry of hot spots in the accretion flow (Kretschmar et al. 2019). Be XBs exhibit both X-ray and optical superorbital variability. The optical modulations are likely associated with the formation and depletion of the Be star’s circumstellar disks or with the neutron star’s orbit impacting the precession or warping of this circumstellar disk (Rajoelimanana et al. 2011). These variations in the circumstellar disk can modulate the accretion onto the compact object, resulting in X-ray superorbital periods. ULXs and disk-fed HMXBs both follow the same correlation between superorbital and orbital periods, so it has been suggested that the superorbital periods in ULXs may similarly be attributed to the modulation of precessing hot spots or density waves in the accretion or circumstellar disk by the binary motion of the system (Townsend and Charles 2020). Several theories for the origin of superorbital modulations in wind-fed HMXBs have been proposed (see Kretschmar et al. (2019) and references therein). This variability may be driven by tidally regulated oscillations of the outer layers of the supergiant donor resulting in a variable accretion rate onto the compact object. Another possibility is that these variations in the accretion rate may result from interaction between the neutron star and co-rotating interaction regions (CIRs) of the supergiant, which are spiral-shaped density and velocity perturbations in the stellar wind. In some cases, for example, in 4U 1820-30, the superorbital period may be caused by the presence of a third stellar companion inducing an eccentricity in the inner binary, which in turn modulates the mass transfer rate. More observations spanning many superorbital cycles are required for more wind-fed SgHMXBs to better understand the origin of their superorbital modulations.

Aperiodic Variability Short-Timescale Variability On timescales of milliseconds to hours, HMXBs exhibit aperiodic variability which produces a red noise power-law continuum in power spectra of their X-ray lightcurves (Belloni and Hasinger 1990). The power spectrum of some HMXBs

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demonstrates a break in their power-law continuum. For most accreting X-ray pulsars as well as accreting black holes, the red noise power-law index is α ≈ 1.4– 2.0 at frequencies above the break and α ≈ 0–1 at frequencies below the break (Hoshino and Takeshima 1993); for accreting pulsars, this break frequency is close or equal to the pulsation frequency, and for Roche-lobe overflow systems, it is close to the orbital frequency (Içdem and Baykal 2011). Several other hydrodynamics processes have also been suggested to contribute to the aperiodic variability, including (1) density fluctuations due to magnetohydrodynamic turbulence in the accreting plasma (Hoshino and Takeshima 1993), (2) stochastic perturbations in the accretion disk being advected to the magnetospheric radius (Revnivtsev et al. 2009), (3) Rayleigh-Taylor instabilities occurring at the magnetospheric boundary when the accretion rate is low and the flow is subsonic (Shakura et al. 2013), and (4) wind inhomogeneities or instabilities in the shock front resulting from the photoionization of the stellar wind by the NS (Manousakis and Walter 2015). The power spectra of HMXBs can exhibit quasi-periodic oscillations (QPOs), which tend to be well fit by Lorentzian functions and whose physical origin, although still not completely understood, is thought to be associated with processes or inhomogeneities in the inner accretion disk (e.g., Kaur et al. 2008; Ingram and Motta 2019). QPOs have been observed in both BH and NS HMXBs; QPOs in NS HMXBs can provide constraints on the magnetic field strength of the NS since the accretion disks in NS HMXBs, if they are present, are truncated at the magnetosphere. Finally, in the case of NS HMXBs, pulsations of the X-ray emission originating in the vicinity of the magnetic poles of the NS can introduce peaks in the power spectrum at the NS spin frequency and its harmonics (Belloni and Hasinger 1990). Thus, the power spectra of HMXBs can be used to probe important properties of the compact objects and the accretion flow.

Long-Timescale Variability On longer timescales of days to years, different classes of HMXBs can exhibit different types of variability, including the periodic variability described in the previous section and aperiodic variability including the “off-states” and the flaring behavior of some Sg XBs discussed in section “Supergiant X-Ray Binaries”. A useful way to encapsulate and visualize the variety of long-term behavior displayed by HMXBs is with cumulative luminosity distributions (CLDs), which measure the fraction of time that a source is observed above a given luminosity. The biggest challenge in measuring CLDs that provide an accurate representation of the source variability is that they require monitoring over long timescales. Even when based on long monitoring campaigns, it is important to be mindful of the fact that CLDs can be uncertain at the high luminosity end due to potentially missing rare, high-luminosity events, and uncertain at the low luminosity end due to the incompleteness of detections when the source flux nears the sensitivity of the instrument. From a CLD diagram, it is straightforward to determine key variability metrics. The maximum value along the y-axis that a source reaches in a CLD diagram is referred to as the duty cycle, the fraction of the observed time that

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the source is detected above the minimum luminosity set by the sensitivity of the instrument. The variability amplitude of the source is shown by the spread of values along the x-axis. The most comprehensive studies of HMXB CLDs to date are reported in Bozzo et al. (2015) and Sidoli and Paizis (2018), which focus on the soft and hard X-ray bands, respectively. Bozzo et al. (2015) present the 2–10 keV CLDs of 11 HMXBs based on monitoring campaigns lasting from approximately 2 weeks to 2 years with Swift XRT; three of the sources studied were classical Sg XBs, six were SFXTs, and two were “intermediate” SFXTs, with X-ray properties in between those of classical HMXBs and SFXTs. The 18–50 keV CLDs studied in Sidoli and Paizis (2018) are based on 14 years of monitoring observations by INTEGRAL IBIS/ISGRI; this work includes 58 HMXBs, the vast majority of which reside in the Milky Way and include both Sg and Be HMXBs. A representative sample of the 18–50 keV CLDs from Sidoli and Paizis (2018) is shown in Fig. 16. At both soft and hard X-ray energies, the CLDs of classical Sg XBs exhibit a single knee (Bozzo et al. 2015; Sidoli and Paizis 2018). Compared to classical systems, the soft and hard X-ray CLDs of SFXTs are shifted to lower luminosities by factors of 10–100 at comparable duty cycles, and they exhibit large variability amplitudes of >100 compared to LX)

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Fig. 16 Cumulative 18–50 keV luminosity functions of a representative set of HMXBs measured from INTEGRAL observations divided into 2 kilosecond bins. Different classes of HMXBs are shown in different color shades as indicated in the legend. The HMXB names are written next to the curves in the corresponding color. (Credit: Adapted from Figures 1–4 of Sidoli and Paizis (2018), “An INTEGRAL overview of High-Mass X-ray Binaries: classes or transitions?”, MNRAS, 481, 2)

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if they are real features possibly related to the triggering mechanisms responsible for the highest accretion rates in SFXTs (Bozzo et al. 2015). Given the larger HMXB sample in the study by Sidoli and Paizis (2018), some additional trends can be noted for the hard X-ray CLDs. The CLDs of classical Sg XBs follow a log-normal distribution, while those of SFXTs are power-law distributions with a power-law slope of ≈2. Among the classical Sg XBs, the RLO systems reach the highest luminosities, and the CLDs of sources with higher median luminosities and lower spin periods tend to be steeper with a lower variability amplitude than those of sources with lower median luminosities. The 18–50 keV CLDs of Be XBs have high variability amplitude (>100), higher average hard X-ray luminosity in outburst than SFXTs, and duty cycles that are intermediate between those of classical Sg XBs and SFXTs. They also exhibit much more complex shapes than any of the Sg XBs, often with multiple knees, indicative of the different types of outbursts (Type I and Type II) that they can experience or different accretion regimes. CLDs thus provide a way of distinguishing between different classes of HMXBs and of identifying HMXBs with intermediate properties based on their long-term variability.

HMXB Populations in the Milky Way and Magellanic Clouds Due to the Milky Way’s large footprint on the sky and the transient nature of many HMXBs, our understanding of the Galactic HMXB population has largely depended upon the identification of HMXBs among the X-ray sources detected and monitored over time by all-sky surveys and other large-scale surveys. Due to the high levels of obscuration that exist near the Galactic plane, hard X-ray surveys have been critical for gathering as complete a census as possible of the Milky Way’s HMXB population. INTEGRAL’s dedicated monitoring survey of the Galactic Plane has made particularly significant contributions to our understanding of Galactic HMXBs, reaching sensitivity of 7 × 10−12 erg s−1 cm−2 in the 17–60 keV band over half of the Plane at latitude |b| < 17.5◦ (Krivonos et al. 2012) and discovering highly obscured HMXBs as well as SFXTs. The most recent catalogs of HMXBs in the Milky Way can be found in Liu et al. (2006), Walter et al. (2015), Fortin et al. (2023), and Neumann et al. (2023) and contain approximately 150 unique confirmed and candidate HMXBs. About a third of Galactic HMXBs are classified as Sg XBs (including SFXTs), ≈50% are Be HMXBs, and the donor star remains unclassified in about 20% (Fortin et al. 2023). The Magellanic Clouds have been excellent targets for studies of young XRB populations at a depth similar to that of Galactic studies, but without the limitations of distance uncertainties and high obscuration. The Small Magellanic Cloud (SMC), our second nearest star-forming galaxy at a distance of 62 kpc, harbors an HMXB population comparable to the observed population in the Milky Way (e.g., Liu et al. 2005; Antoniou et al. 2010; Coe and Kirk 2015; Haberl and Sturm 2016). By combining data from Haberl and Sturm (2016) and Antoniou et al. (2019), 137 confirmed and highly likely HMXBs have been identified. The spectroscopic properties of these sources (or, when not available, their multi-wavelength photometric

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properties) have allowed the classification of the vast majority as Be XBs (e.g., Antoniou et al. 2009; Coe and Kirk 2015). In contrast, due mainly to its large extent on the sky and large-scale diffuse X-ray emission from the hot ISM, our nearest neighbor at 50 kpc, the Large Magellanic Cloud (LMC) has been surveyed in the X-rays less extensively and to lower sensitivity limits than the SMC. Thus, the number of known HMXBs in the LMC remains significantly smaller than that of the SMC. Antoniou and Zezas (2016) compiled a list of 40 confirmed and candidate HMXBs and classified them based on their optical photometric properties. Subsequently, two additional studies (van Jaarsveld et al. 2018; Haberl et al. 2022) increased the known HMXB population of the LMC to ∼60 members (25 XRB pulsars and ∼35 candidate HMXBs from the literature). The bulk of the LMC HMXBs have been classified as Be or candidate Be HMXBs, with only four LMC HMBs being Sg or candidate Sg XBs (Antoniou and Zezas 2016; van Jaarsveld et al. 2018). In the recent future, deeper X-ray observations from the Chandra Very Large Program survey of the LMC will reach comparable sensitivities to X-ray surveys of the SMC, enabling the discovery of fainter HMXBs in this galaxy. Furthermore, eRosita’s all-sky surveys, given their high cadence and sensitivity, are likely to discover new HMXBs in both the Galaxy and Magellanic Clouds.

HMXB Luminosity Function X-ray binaries are the primary sources of X-ray emission in “normal” galaxies without an active galactic nucleus (AGN), with HMXBs being the dominant source in star-forming galaxies (e.g., Mineo et al. 2012). In addition to being a key ingredient to the X-ray emission of galaxies, the X-ray luminosity function (XLF) of HMXBs also can provide some insights into the accretion processes occurring in these systems. The XLF of Galactic HMXBs is challenging to measure. It requires X-ray surveys of fairly uniform sensitivity along the Galactic plane and accurate distance measurements to individual HMXBs. Furthermore, it is necessary to correct for the fraction of the HMXB population residing in regions of the Milky Way (MW) that are not observable given the sensitivity limit of the X-ray survey, which requires modeling the mass distribution of the Galaxy and its relationship to the spatial distribution of HMXBs. Despite these challenges, the Galactic HMXB XLF measurements made by different studies are in general agreement with one another, as shown in Fig. 17. Between X-ray luminosities of LX ∼ 1035 and 1037 erg s−1 , the XLF is well fit by a power-law (dN/dL ∝ L−α ) with best-fitting index α ≈ 1.3–1.7 (see Lutovinov et al. (2013) and references therein). The Galactic XLF exhibits a break or cutoff around LX ∼ 1037 erg s−1 , and its power-law slope at higher luminosities is α > 2. Such high luminosities would require near Eddington or super Eddington accretion rates, which likely can only be reached as HMXBs approach RLO; thus, the relative scarcity of high luminosity sources is consistent with the fact that

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Fig. 17 The shaded area represents the cumulative HMXB luminosity function (1–200 keV) as reconstructed by Doroshenko et al. (2014) through modeling the observed flux distribution of HMXBs detected by the INTEGRAL Galactic survey. Best fits of the HMXB luminosity function from previous studies converted to the 1–200 keV are also shown. (Credit: Taken from Figure 2 from Doroshenko et al. (2014), A&A, 567, A7, 2014, reproduced with permission © ESO)

RLO is unstable in HMXBs and therefore short-lived (see section “Accretion in HMXBs”). The Galactic XLF measurements extending to the faintest luminosities (LX ∼ 1034 erg s−1 ) show a hint of flattening below 1034 –1035 erg s−1 (Lutovinov et al. 2013; Doroshenko et al. 2014). A faint-end flattening of the HMXB XLF also seems to be supported by recent results (Tomsick et al. 2017; Clavel et al. 2019) based on NuSTAR observations that find a dearth of low-luminosity HMXBs compared to expectations based on the XLF measured by Lutovinov et al. (2013). This flattening can, at least partly, be attributed to the propeller effect, the centrifugal inhibition of accretion due to the interaction of the accretion flow with the pulsar’s magnetic field (Illarionov and Sunyaev 1975). Both the number of known MW HMXBs and the number of HMXB distance measurements have increased by ≈50% since these studies of the Galactic HMXB XLF were carried out, thanks in large part to INTEGRAL’s ongoing Galactic Plane survey and parallax measurements from Gaia, so tighter constraints on the Galactic HMXB XLF are possible in the near future. The shape of the XLF of MW HMXBs is consistent with the universal XLF of HMXBs in the range L2−10 keV ≈ 1035 –1037 erg s−1 . In the 2–10 keV band, the XLF of HMXBs in other star-forming galaxies exhibits a consistent power-law slope of α ≈ 1.6 between 1035 and 1040 erg s−1 and a cutoff at LX ∼ 1040 erg s−1 (e.g., Mineo et al. 2012). Thus, the MW XLF appears to have a lower-luminosity cutoff compared to other star-forming galaxies, but its power-law slope below that cutoff is consistent with the universal XLF. Unlike the slope, the normalization of the HMXB XLF varies from galaxy to galaxy because it depends on the galaxy’s star formation rate (SFR) (e.g., Mineo et al. 2012).

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The XLFs of HMXBs in the LMC and SMC are also consistent with the powerlaw slope of the universal XLF between LX ≈ 1035 –1037 erg s−1 , although these XLFs were based on small numbers of sources (Shtykovskiy and Gilfanov 2005b; Shtykovskiy and Gilfanov 2005a). Both of these XLFs appear to flatten below ∼1035 erg s−1 , similar to the observed hint of flattening in the MW XLF that may be due to the propeller effect (Tomsick et al. 2017; Clavel et al. 2019). Tighter constraints on the LMC and SMC XLFs can now be made using the larger HMXB samples provided in the most recent catalogs.

Spatial Distribution and Ages Our position within the Milky Way’s spiral disk gives us an edge-on view of our Galaxy that allows us to measure the vertical scale height of HMXBs but makes it more challenging to measure their radial distribution as it is more difficult to detect and determine accurate distances to HMXBs on the far side of the Galaxy due to obscuration by dust and smaller parallexes. The HMXB scale height has been found to be ≈100 pc, which is larger than the scale heights of massive stars (Lutovinov et al. 2013). This result suggests that HMXBs have traveled farther from the Galactic plane than their parent stellar populations due to supernova kicks imparted to the binary systems when the compact object is formed. Using a value of 100 km s−1 for the typical systemic velocity of HMXBs (e.g., Bodaghee et al. 2012), the typical vertical distance traveled by HMXBs from their parent populations can be used to place a lower limit on their kinematic ages of ≈1 Myr. Kinematic ages provide an estimate of the typical time lag between the formation of the first compact object when the more massive star explodes as a supernova and the onset of the X-ray bright, accretion phase. The radial distribution of HMXBs in the Milky Way is found to be similar to the distribution of giant HII regions and CO gas associated with the spiral arms (e.g., Lutovinov et al. 2013), a result consistent with the expected young ages (few to tens of Myr) of HMXBs (e.g., Linden et al. 2010). Correcting the observed distribution of HMXBs for INTEGRAL’s survey sensitivity, Lutovinov et al. (2013) found that it peaks between 2 and 8 kpc from the Galactic Center and is consistent with the star formation rate surface density. Other works (including Bodaghee et al. (2012) shown in Fig. 18), using larger samples of HMXBs, calculated the spatial cross-correlation function between HMXBs and OB associations or star forming complexes, finding significant clustering and average offsets of 0.4±0.2 kpc (Bodaghee et al. 2012) and 0.3 ± 0.05 kpc (Coleiro and Chaty 2013). The observed pattern of offsets in these studies cannot be explained by Galactic rotation alone but are consistent with natal kick velocities of 100 ± 50 km s−1 and kinematic ages of ≈4 Myr. The total ages of HMXBs, not just their kinematic ages, can be determined by associating HMXBs with their birthplaces, which requires accurate distances. Coleiro and Chaty (2013) estimated the ages of a small sample of 13 HMXBs by first obtaining more precise distance estimates through the fitting of their optical to near-infrared spectral energy distribution; they then compared the HMXB positions

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Fig. 18 Galactic distribution of HMXBs with known distances as of 2012 (79, filled triangles) and the locations of OB associations (458, circles). The symbol size of the latter is proportional to the amount of activity in the association (amount of ionizing photons as determined from the radio continuum flux). Galactic spiral arm model is overlaid with the Sun situated at 7.6 kpc from the Galactic center (GC). HMXBs whose distances are not known have been placed at 7.6 kpc (23, empty triangles), i.e., the Sun-GC distance. The shaded histogram represents the number of HMXBs in each 15 deg bin of galactic longitude as viewed from the Sun. (Credit: Figure 2 from Bodaghee et al. (2012), reproduced with permission ©AAS)

to the locations of the Galactic spiral arms and modeled the rotation of the arms and the motion of HMXBs due to Galactic rotation alone to determine the point in time when the position of each HMXB most closely coincided with one of the spiral arms. With this method, they found mean ages of ∼45 Myr for Sg XBs and ∼51 Myr for Be HMXBs. While these estimates are consistent with the different evolutionary timescales expected for these two classes of HMXBs, these results are not conclusive due to the small sample size. With new parallax distance estimates to many HMXBs from Gaia (Fortin et al. 2023), it should be possible to improve measurements of Galactic HMXB ages.

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Studies of the spatial distribution and ages of HMXB can be more easily carried out in the Magellanic Clouds. By comparing the positions of HMXBs in the SMC and LMC with spatially resolved star formation history (SFH) maps, it has been determined that the Be XBs in the SMC are associated with bursts of star formation that occurred ∼20–60 Myr ago (e.g., Antoniou et al. 2010), while LMC HMXBs are associated with a more recent star formation episode (∼6–40 Myr ago) (e.g., Antoniou and Zezas 2016). The spatial cross-correlation function between HMXBs and OB associations in the SMC reveals strong clustering (Bodaghee et al. 2021). The average distance between an HMXB and its nearest OB association in the SMC is 150 pc; this offset is lower in the SMC Bar (120 ± 90 pc) than in the SMC Wing (450 ± 180 pc), which faces the LMC. Since a large fraction of the Be XBs in the SMC are connected with a burst of star formation ≈40 Myr ago, and stellar evolution models predict it takes ≈5–20 Myr for a high-mass star to undergo a supernova explosion and collapse into a compact object, the period of time that the HMXBs have had to migrate away from their OB associations of origin as a result of supernova kicks is ≈20–35 Myr. From this estimate, it can be calculated that the kick velocities received by SMC HMXBs are typically 2–34 km s−1 (Bodaghee et al. 2021), much lower than those of their Milky Way counterparts, in agreement with previous studies. While the transverse velocities of Galactic Be HMXBs are lower by a factor of ≈3 compared to Galactic Sg XBs (which can be explained by differences in their evolution van den Heuvel et al. 2000), the difference between the Galactic and SMC HMXB space velocities cannot be fully ascribed to the overabundance of Be HMXBs in the SMC (Bodaghee et al. 2021). Similar studies of the spatial distribution of HMXBs in the LMC have yet to be carried out.

Comparing the Milky Way and Magellanic HMXB Populations As mentioned in previous sections, there are significant differences between the observed HMXB populations in the Milky Way and Magellanic Clouds. While roughly a third of MW HMXBs are now known to host supergiant donors and 50% host Be stars (Fortin et al. 2023), in the SMC, only two HMXBs, SMC X-1 and CXOU J005409.57-724143.5, have been classified as Sg XBs compared to the ≈70 that have been classified as Be HXMBs (Coe and Kirk 2015; Haberl and Sturm 2016). While the LMC HMXB population has not been as thoroughly studied as that of the SMC, of the ≈30 HMXBs that have been classified, only four are confirmed or candidate Sg XBs (Antoniou and Zezas 2016; van Jaarsveld et al. 2018). Thus, the HMXB populations of both Magellanic Clouds, especially the SMC, appear to have a greater ratio of Be/Sg XBs than the Milky Way. It is unlikely that a significant population of Sg XBs in the Magellanic Clouds remain undetected due to obscuration given their low dust content; furthermore, INTEGRAL surveys of the SMC and LMC have not uncovered highly obscured Sg XBs as they did in the Milky Way (Coe et al. 2010; Grebenev et al. 2013), and monitoring campaigns of the SMC have discovered transient Be XBs but no SFXTs (Kennea et al. 2018).

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The overabundance of Be XBs in the SMC has been noted and investigated by several studies. The Be XB population of the SMC was estimated to be larger than that of the Milky Way by a factor of ≈1.5 after accounting for differences in their star formation rates (Antoniou et al. 2009; Shtykovskiy and Gilfanov 2005b). The HMXB formation efficiency of the SMC was found to increase as a function of time following a burst of star formation up to ∼40–60 Myr, reaching a peak efficiency that is higher than that of the LMC by a factor of ≈17 (Antoniou and Zezas 2016; Antoniou et al. 2019). One factor that is thought to contribute to the abundance of HMXBs in the SMC is its low metallicity (Z∼0.2Z⊙ ); lower metallicity stars have weaker stellar winds, which impact their evolution and is predicted to result in more numerous and more luminous HMXB populations (e.g., Linden et al. 2010). The first theoretical study that addressed the effect of metallicity on the formation and evolution of HMXBs and compared its results to the HMXB populations of the Milky Way and Magellanic Clouds was that of Dray (2006). This study performed extensive Monte Carlo simulations of binary systems that were able to reproduce the orbital properties and X-ray luminosities of Galactic HMXBs and found that the number of HMXBs increased with decreasing metallicity. The simulation results for half solar metallicity were in decent agreement with the properties of LMC HMXBs, although the LMC comparison sample was small. However, while the predicted increase in the number of HMXBs by a factor of 3 for the subsolar metallicity environment of the SMC could be consistent with the observed number of SMC HMXBs, the orbital period of the distribution of the simulated binaries was skewed to much lower orbital periods than the observed distribution. This study showed that metallicity alone cannot explain the observed SMC HMXB population; in this work, the orbital period distribution of the SMC HMXBs could only be reproduced by an HMXB population associated with a very large burst of star formation ∼30–100 Myr ago, consistent with the estimated ages of the SMC HMXBs by observational studies (e.g., Antoniou et al. 2010). Recently, it has been shown that the shape of the high-luminosity end of the HMXB XLF depends on the metallicity of the young stellar population, while the HMXB XLF has the same power-law slope independent of metallicity at LX < (3 − 10) × 1037 erg s−1 , but above 1038 erg s−1 , the XLF gradually flattens and extends to higher luminosities with decreasing metallicities (Lehmer et al. 2021). This trend results from formation of a greater number of luminous HMXBs, including ULXs, at lower metallicities (e.g., Dray 2006; Linden et al. 2010; Fragos et al. 2013). The bright end of the SMC XLF above 1037 erg s−1 appears to flatten in a way that is consistent with the XLFs of other low-metallicity galaxies (Lehmer et al. 2021). Studies of HMXBs in the Milky Way and Magellanic Clouds have thus demonstrated that both metallicity and age impact the properties of HMXB populations. These effects are being investigated in more detail by both theoretical simulations (e.g.,Linden et al. 2010; Fragos et al. 2013) and observational studies of HMXBs in other galaxies (e.g., Lehmer et al. 2021). Studying the impact of both metallicity and age on HMXB properties is relevant to understanding the gravitational wave sources that may evolve from HMXBs as well as the contribution of the first generations of HMXBs in the Universe to the heating of intergalactic gas during the Epoch of Reionization.

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Cross-References ⊲ Basics of Fourier Analysis for High-Energy Astronomy ⊲ Black Holes: Accretion Processes in X-ray Binaries ⊲ Low-Magnetic-Field Neutron Stars in X-ray Binaries ⊲ Low-Mass X-ray Binaries ⊲ Modeling and Simulating X-ray Spectra ⊲ Time Domain Methods for X-ray and Gamma-ray Astronomy ⊲ X-ray Binaries in External Galaxies

References V. Antoniou, A. Zezas, Star formation history and X-ray binary populations: the case of the Large Magellanic Cloud. MNRAS 459(1), 528–553 (2016). https://doi.org/10.1093/mnras/stw167 V. Antoniou, A. Zezas, D. Hatzidimitriou, J.C. McDowell, The Chandra survey of the Small Magellanic Cloud “Bar”. II. Optical counterparts of X-ray sources. ApJ 697(2), 1695–1716 (2009). https://doi.org/10.1088/0004-637X/697/2/1695 V. Antoniou, A. Zezas, D. Hatzidimitriou, V. Kalogera, Star formation history and X-ray binary populations: the case of the Small Magellanic Cloud. ApJL 716(2), 140–145 (2010). https://doi. org/10.1088/2041-8205/716/2/L140 V. Antoniou, A. Zezas, J.J. Drake, C. Badenes, F. Haberl, N.J. Wright, J. Hong, R. Di Stefano, T.J. Gaetz, K.S. Long, P.P. Plucinsky, M. Sasaki, B.F. Williams, P.F. Winkler, SMC XVP Collaboration, Deep Chandra survey of the Small Magellanic Cloud. III. Formation efficiency of high-mass X-ray binaries. ApJ 887(1), 20 (2019). https://doi.org/10.3847/1538-4357/ab4a7a E.S. Bartlett, J.S. Clark, M.J. Coe, M.R. Garcia, P. Uttley, Timing and spectral analysis of the unusual X-ray transient XTE J0421+560/CI Camelopardalis. MNRAS 429(2), 1213–1220 (2013). https://doi.org/10.1093/mnras/sts411 P.A. Becker, M.T. Wolff, Thermal and bulk comptonization in accretion-powered X-ray pulsars. ApJ 654(1), 435–457 (2007). https://doi.org/10.1086/509108 K. Belczynski, J. Ziolkowski, On the apparent lack of Be X-ray binaries with black holes. ApJ 707(2), 870–877 (2009). https://doi.org/10.1088/0004-637X/707/2/870 K. Belczynski, V. Kalogera, T. Bulik, A comprehensive study of binary compact objects as gravitational wave sources: evolutionary channels, rates, and physical properties. ApJ 572(1), 407–431 (2002). https://doi.org/10.1086/340304 T. Belloni, G. Hasinger, An atlas of aperiodic variability in HMXB. A&A 230, 103–119 (1990) J.M. Blondin, T.R. Kallman, B.A. Fryxell, R.E. Taam, Hydrodynamic simulations of stellar wind disruption by a compact X-ray source. ApJ 356, 591 (1990). https://doi.org/10.1086/168865 A. Bodaghee, J.A. Tomsick, J. Rodriguez, J.B. James, Clustering between high-mass X-ray binaries and OB associations in the Milky Way. ApJ 744(2), 108 (2012). https://doi.org/10. 1088/0004-637X/744/2/108 A. Bodaghee, V. Antoniou, A. Zezas, J.A. Tomsick, Z. Jordan, B. Jackson, R. Agnew, E. Frechette, A.E. Hornschemeier, J. Rodriguez, Evidence for low kick velocities among high-mass x-ray binaries in the Small Magellanic Cloud from the spatial correlation function. ApJ 919(2), 81 (2021). https://doi.org/10.3847/1538-4357/ac11f4 A.Z. Bonanos, D.L. Massa, M. Sewilo, D.J. Lennon, N. Panagia, L.J. Smith, M. Meixner, B.L. Babler, S. Bracker, M.R. Meade, K.D. Gordon, J.L. Hora, R. Indebetouw, B.A. Whitney, Spitzer SAGE infrared photometry of massive stars in the large magellanic cloud. AJ 138(4), 1003– 1021 (2009). https://doi.org/10.1088/0004-6256/138/4/1003 H. Bondi, F. Hoyle, On the mechanism of accretion by stars. MNRAS 104, 273 (1944). https://doi. org/10.1093/mnras/104.5.273

106 High-Mass X-ray Binaries

3767

V. Bosch-Ramon, D. Khangulyan, Understanding the very-high emission from microquasars. Int. J. Mod. Phys. D 18(3), 347–387 (2009). https://doi.org/10.1142/S0218271809014601 E. Bozzo, M. Falanga, L. Stella, Are there magnetars in high-mass X-ray binaries? The case of supergiant fast X-ray transients. ApJ 683(2), 1031–1044 (2008). https://doi.org/10.1086/589990 E. Bozzo, P. Romano, L. Ducci, F. Bernardini, M. Falanga, Supergiant fast X-ray transients as an under-luminous class of supergiant X-ray binaries. Adv. Space Res. 55(4), 1255–1263 (2015). https://doi.org/10.1016/j.asr.2014.11.012 R.O. Brown, W.C.G. Ho, M.J. Coe, A.T. Okazaki, Simulating the X-ray luminosity of Be X-ray binaries: the case for black holes versus neutron stars. MNRAS 477(4), 4810–4816 (2018). https://doi.org/10.1093/mnras/sty973 A. Camero-Arranz, M.H. Finger, C.A. Wilson-Hodge, P. Jenke, I. Steele, M.J. Coe, J. GutierrezSoto, P. Kretschmar, I. Caballero, J. Yan, J. Rodríguez, J. Suso, G. Case, M.L. Cherry, S. Guiriec, V.A. McBride, X-ray and optical observations of A 0535+26. ApJ 754(1), 20 (2012). https://doi.org/10.1088/0004-637X/754/1/20 J. Casares, I. Negueruela, M. Ribó, I. Ribas, J.M. Paredes, A. Herrero, S. Simón-Díaz, A Be-type star with a black-hole companion. Nature 505(7483), 378–381 (2014). https://doi.org/10.1038/ nature12916 J.I. Castor, D.C. Abbott, R.I. Klein, Radiation-driven winds in Of stars. ApJ 195, 157–174 (1975). https://doi.org/10.1086/153315 S. Chaty, A. LeReun, I. Negueruela, A. Coleiro, N. Castro, S. Simón-Díaz, J.A. Zurita Heras, P. Goldoni, A. Goldwurm, Multiwavelength study of the fast rotating supergiant high-mass X-ray binary IGR J16465-4507. A&A 591, 87 (2016). https://doi.org/10.1051/0004-6361/201628110 M. Chernyakova, D. Malyshev, Gamma-ray binaries, in Multifrequency Behaviour of High Energy Cosmic Sources – XIII, 3–8 June 2019, Palermo (2020), p. 45 M. Chernyakova, I. Babyk, D. Malyshev, I. Vovk, S. Tsygankov, H. Takahashi, Y. Fukazawa, Study of orbital and superorbital variability of LSI +61◦ 303 with X-ray data. MNRAS 470(2), 1718–1728 (2017). https://doi.org/10.1093/mnras/stx1335 M. Clavel, J.A. Tomsick, J. Hare, R. Krivonos, K. Mori, D. Stern, NuSTAR observations of the unidentified INTEGRAL Sources: constraints on the Galactic population of HMXBs. ApJ 887(1), 32 (2019). https://doi.org/10.3847/1538-4357/ab4b55 W. Coburn, W.A. Heindl, R.E. Rothschild, D.E. Gruber, I. Kreykenbohm, J. Wilms, P. Kretschmar, R. Staubert, Magnetic fields of accreting X-ray pulsars with the Rossi X-ray timing explorer. ApJ 580(1), 394–412 (2002). https://doi.org/10.1086/343033 M.J. Coe, J. Kirk, Catalogue of Be/X-ray binary systems in the Small Magellanic Cloud: Xray, optical and IR properties. MNRAS 452(1), 969–977 (2015). https://doi.org/10.1093/mnras/ stv1283 M.J. Coe, A.J. Bird, D.A.H. Buckley, R.H.D. Corbet, A.J. Dean, M. Finger, J.L. Galache, F. Haberl, V.A. McBride, I. Negueruela, M. Schurch, L.J. Townsend, A. Udalski, J. Wilms, A. Zezas, INTEGRAL deep observations of the Small Magellanic Cloud. MNRAS 406(4), 2533–2539 (2010). https://doi.org/10.1111/j.1365-2966.2010.16844.x A. Coleiro, S. Chaty, Distribution of high-mass X-ray binaries in the Milky Way. ApJ 764(2), 185 (2013). https://doi.org/10.1088/0004-637X/764/2/185 R.H.D. Corbet, The three types of high-mass X-ray pulsator. MNRAS 220, 1047–1056 (1986). https://doi.org/10.1093/mnras/220.4.1047 V. Doroshenko, A. Santangelo, L. Ducci, D. Klochkov, Supergiant, fast, but not so transient 4U 1907+09. A&A 548, 19 (2012). https://doi.org/10.1051/0004-6361/201220085 V. Doroshenko, L. Ducci, A. Santangelo, M. Sasaki, Population of the Galactic X-ray binaries and eRosita. A&A 567, 7 (2014). https://doi.org/10.1051/0004-6361/201423766 L.M. Dray, On the metallicity dependence of high-mass X-ray binaries. MNRAS 370(4), 2079– 2090 (2006). https://doi.org/10.1111/j.1365-2966.2006.10635.x G. Dubus, Gamma-ray binaries and related systems. Astron. Astrophys. Rev. 21, 64 (2013). https:// doi.org/10.1007/s00159-013-0064-5 G. Dubus, N. Guillard, P.-O. Petrucci, P. Martin, Sizing up the population of gamma-ray binaries. A&A 608, 59 (2017). https://doi.org/10.1051/0004-6361/201731084

3768

F. Fornasini et al.

I. El Mellah, J.O. Sundqvist, R. Keppens, Wind Roche lobe overflow in high-mass X-ray binaries. A possible mass-transfer mechanism for ultraluminous X-ray sources. A&A 622, 3 (2019). https://doi.org/10.1051/0004-6361/201834543 P. Esposito, G.L. Israel, D. Milisavljevic, M. Mapelli, L. Zampieri, L. Sidoli, G. Fabbiano, G.A. Rodríguez Castillo, Periodic signals from the Circinus region: two new cataclysmic variables and the ultraluminous X-ray source candidate GC X-1. MNRAS 452(2), 1112–1127 (2015). https://doi.org/10.1093/mnras/stv1379 S. Fabrika, The jets and supercritical accretion disk in SS433. Astrophys. Space Phys. Rev. 12, 1–152 (2004) S.N. Fabrika, K.E. Atapin, A.S. Vinokurov, O.N. Sholukhova, Ultraluminous X-ray sources. Astrophys. Bull. 76(1), 6–38 (2021). https://doi.org/10.1134/S1990341321010077 S. Fabrika, Y. Ueda, A. Vinokurov, O. Sholukhova, M. Shidatsu, Supercritical accretion disks in ultraluminous X-ray sources and SS 433. Nat. Phys. 11(7), 551–553 (2015). https://doi.org/10. 1038/nphys3348 M. Falanga, E. Bozzo, A. Lutovinov, J.M. Bonnet-Bidaud, Y. Fetisova, J. Puls, Ephemeris, orbital decay, and masses of ten eclipsing high-mass X-ray binaries. A&A 577, 130 (2015). https://doi. org/10.1051/0004-6361/201425191 F. Fortin, F. García, A. Simaz Bunzel, S. Chaty, A catalogue of high-mass X-ray binaries in the Galaxy: from the INTEGRAL to the Gaia era. A&A 671, 149 (2023). https://doi.org/10.1051/ 0004-6361/202245236 T. Fragos, B. Lehmer, M. Tremmel, P. Tzanavaris, A. Basu-Zych, K. Belczynski, A. Hornschemeier, L. Jenkins, V. Kalogera, A. Ptak, A. Zezas, X-ray binary evolution across cosmic time. ApJ 764(1), 41 (2013). https://doi.org/10.1088/0004-637X/764/1/41 D.B. Friend, J.I. Castor, Radiation driven winds in X-ray binaries. ApJ 261, 293–300 (1982). https://doi.org/10.1086/160340 E. Gallo, R.P. Fender, G.G. Pooley, A universal radio-X-ray correlation in low/hard state black hole binaries. MNRAS 344(1), 60–72 (2003). https://doi.org/10.1046/j.1365-8711.2003. 06791.x R. Giacconi, S. Murray, H. Gursky, E. Kellogg, E. Schreier, T. Matilsky, D. Koch, H. Tananbaum, The third UHURU catalog of X-ray sources. ApJS 27, 37 (1974). https://doi.org/10.1086/ 190288 R. Giacconi, H. Gursky, F.K.R. Paolini, B.B. Rossi, Evidence for X-rays from sources outside the Solar System. Phys. Rev. Lett. 9(11), 439–443 (1962). https://doi.org/10.1103/PhysRevLett.9. 439 S. Grebenev, Supergiant fast X-ray transients observed by INTEGRAL, in The Extreme Sky: Sampling the Universe Above 10 keV (2009), p. 60. https://doi.org/10.22323/1.096.0060 S.A. Grebenev, A.A. Lutovinov, S.S. Tsygankov, I.A. Mereminskiy, Deep hard X-ray survey of the Large Magellanic Cloud. MNRAS 428(1), 50–57 (2013). https://doi.org/10.1093/mnras/sts008 M. Grudzinska, K. Belczynski, J. Casares, S.E. de Mink, J. Ziolkowski, I. Negueruela, M. Ribó, I. Ribas, J.M. Paredes, A. Herrero, M. Benacquista, On the formation and evolution of the first Be star in a black hole binary MWC 656. MNRAS 452(3), 2773–2787 (2015). https://doi.org/10. 1093/mnras/stv1419 F. Haberl, R. Sturm, High-mass X-ray binaries in the Small Magellanic Cloud. A&A 586, 81 (2016). https://doi.org/10.1051/0004-6361/201527326 F. Haberl, C. Maitra, G. Vasilopoulos, P. Maggi, A. Udalski, I.M. Monageng, D.A.H. Buckley, Three new high-mass X-ray binaries in the Large Magellanic Cloud. A&A 662, 22 (2022). https://doi.org/10.1051/0004-6361/202243301 J. Hong, V. Antoniou, A. Zezas, F. Haberl, M. Sasaki, J.J. Drake, P.P. Plucinsky, S. Laycock, Deep Chandra survey of the Small Magellanic Cloud. II. Timing analysis of X-ray pulsars. ApJ 847(1), 26 (2017). https://doi.org/10.3847/1538-4357/aa8953 M. Hoshino, T. Takeshima, A turbulent model of time variability in X-ray binary pulsars. ApJL 411, 79 (1993). https://doi.org/10.1086/186917 J.B. Hutchings, D. Crampton, A.P. Cowley, P.S. Osmer, The spectroscopic orbit and masses of SK 160/SMC X-1. ApJ 217, 186–196 (1977). https://doi.org/10.1086/155569

106 High-Mass X-ray Binaries

3769

B. Iç, A. Baykal, Viscous timescale in high mass X-ray binaries. A&A 529, 7 (2011). https://doi. org/10.1051/0004-6361/201015810 A.F. Illarionov, R.A. Sunyaev, Why the number of galactic X-ray stars is so small? A&A 39, 185 (1975) A.R. Ingram, S.E. Motta, A review of quasi-periodic oscillations from black hole X-ray binaries: observation and theory. New Astron. Rev. 85, 101524 (2019). https://doi.org/10.1016/j.newar. 2020.101524 P.A. Jenke, M.H. Finger, C.A. Wilson-Hodge, A. Camero-Arranz, Orbital decay and evidence of disk formation in the X-Ray Binary pulsar OAO 1657-415. ApJ 759(2), 124 (2012). https://doi. org/10.1088/0004-637X/759/2/124 M. Jeon, A.H. Pawlik, V. Bromm, M. Milosavljevi´c, Radiative feedback from high-mass X-ray binaries on the formation of the first galaxies and early reionization. MNRAS 440(4), 3778– 3796 (2014). https://doi.org/10.1093/mnras/stu444 P. Kaaret, H. Feng, T.P. Roberts, Ultraluminous X-ray sources. Annu. Rev. Astron. Astrophys. 55(1), 303–341 (2017). https://doi.org/10.1146/annurev-astro-091916-055259 R. Kaur, B. Paul, B. Kumar, R. Sagar, A study of the long-term evolution of quasi-periodic oscillations in the accretion-powered X-ray pulsar 4U 1626-67. ApJ 676(2), 1184–1188 (2008). https://doi.org/10.1086/529130 J.A. Kennea, M.J. Coe, P.A. Evans, J. Waters, R.E. Jasko, The first year of S-CUBED: the swift Small Magellanic Cloud survey. ApJ 868(1), 47 (2018). https://doi.org/10.3847/1538-4357/ aae839 A. King, J.-P. Lasota, No magnetars in ULXs. MNRAS 485(3), 3588–3594 (2019). https://doi.org/ 10.1093/mnras/stz720 H. Klus, W.C.G. Ho, M.J. Coe, R.H.D. Corbet, L.J. Townsend, Spin period change and the magnetic fields of neutron stars in Be X-ray binaries in the Small Magellanic Cloud. MNRAS 437(4), 3863–3882 (2014). https://doi.org/10.1093/mnras/stt2192 C. Knigge, M.J. Coe, P. Podsiadlowski, Two populations of X-ray pulsars produced by two types of supernova. Nature 479(7373), 372–375 (2011). https://doi.org/10.1038/nature10529 M.M. Kotze, P.A. Charles, Characterizing X-ray binary long-term variability. MNRAS 420(2), 1575–1589 (2012). https://doi.org/10.1111/j.1365-2966.2011.20146.x P. Kretschmar, F. Fürst, L. Sidoli, E. Bozzo, J. Alfonso-Garzón, A. Bodaghee, S. Chaty, M. Chernyakova, C. Ferrigno, A. Manousakis, I. Negueruela, K. Postnov, A. Paizis, P. Reig, J.J. Rodes-Roca, S. Tsygankov, A.J. Bird, M. Bissinger né Kühnel, P. Blay, I. Caballero, M.J. Coe, A. Domingo, V. Doroshenko, L. Ducci, M. Falanga, S.A. Grebenev, V. Grinberg, P. Hemphill, I. Kreykenbohm, S. Kreykenbohm né Fritz, J. Li, A.A. Lutovinov, S. Martínez-Núñez, J.M. Mas-Hesse, N. Masetti, V.A. McBride, A. Neronov, K. Pottschmidt, J.a. Rodriguez, Advances in understanding high-mass X-ray binaries with INTEGRAL and future directions. New Astron. Rev. 86, 101546 (2019). https://doi.org/10.1016/j.newar.2020.101546 I. Kreykenbohm, J. Wilms, P. Kretschmar, J.M. Torrejón, K. Pottschmidt, M. Hanke, A. Santangelo, C. Ferrigno, R. Staubert, High variability in Vela X-1: giant flares and off states. A&A 492(2), 511–525 (2008). https://doi.org/10.1051/0004-6361:200809956 R. Krivonos, S. Tsygankov, A. Lutovinov, M. Revnivtsev, E. Churazov, R. Sunyaev, INTEGRAL/IBIS nine-year Galactic hard X-ray survey. A&A 545, 27 (2012). https://doi.org/10. 1051/0004-6361/201219617 R.A. Krivonos, S.Y. Sazonov, E.A. Kuznetsova, A.A. Lutovinov, I.A. Mereminskiy, S.S. Tsygankov, INTEGRAL/IBIS 17-yr hard X-ray all-sky survey. MNRAS 510(4), 4796–4807 (2022). https://doi.org/10.1093/mnras/stab3751 R.-P. Kudritzki, J. Puls, Winds from hot stars. Annu. Rev. Astron. Astrophys. 38, 613–666 (2000). https://doi.org/10.1146/annurev.astro.38.1.613 U. Lee, Y. Osaki, H. Saio, Viscous excretion discs around Be stars. MNRAS 250, 432–437 (1991). https://doi.org/10.1093/mnras/250.2.432 B.D. Lehmer, A.R. Basu-Zych, S. Mineo, W.N. Brandt, R.T. Eufrasio, T. Fragos, A.E. Hornschemeier, B. Luo, Y.Q. Xue, F.E. Bauer, M. Gilfanov, P. Ranalli, D.P. Schneider, O. Shemmer, P. Tozzi, J.R. Trump, C. Vignali, J.-X. Wang, M. Yukita, A. Zezas, The evolution of normal

3770

F. Fornasini et al.

galaxy X-ray emission through cosmic history: constraints from the 6 MS Chandra deep fieldsouth. ApJ 825(1), 7 (2016). https://doi.org/10.3847/0004-637X/825/1/7 B.D. Lehmer, R.T. Eufrasio, A. Basu-Zych, K. Doore, T. Fragos, K. Garofali, K. Kovlakas, B.F. Williams, A. Zezas, L. Santana-Silva, The metallicity dependence of the high-mass X-ray binary luminosity function. ApJ 907(1), 17 (2021). https://doi.org/10.3847/1538-4357/abcec1 Z. Liao, J. Liu, X. Zheng, L. Gou, Spectral evidence of an accretion disc in wind-fed X-ray pulsar Vela X-1 during an unusual spin-up period. MNRAS 492(4), 5922–5929 (2020). https://doi.org/ 10.1093/mnras/staa162 T. Linden, V. Kalogera, J.F. Sepinsky, A. Prestwich, A. Zezas, J.S. Gallagher, The effect of starburst metallicity on bright X-ray binary formation pathways. ApJ 725(2), 1984–1994 (2010). https:// doi.org/10.1088/0004-637X/725/2/1984 J.-F. Liu, J.N. Bregman, Y. Bai, S. Justham, P. Crowther, Puzzling accretion onto a black hole in the ultraluminous X-ray source M 101 ULX-1. Nature 503(7477), 500–503 (2013). https://doi. org/10.1038/nature12762 Q.Z. Liu, J. van Paradijs, E.P.J. van den Heuvel, A catalogue of high-mass X-ray binaries. A&AS 147, 25–49 (2000). https://doi.org/10.1051/aas:2000288 Q.Z. Liu, J. van Paradijs, E.P.J. van den Heuvel, High-mass X-ray binaries in the Magellanic Clouds. A&A 442(3), 1135–1138 (2005). https://doi.org/10.1051/0004-6361:20053718 Q.Z. Liu, J. van Paradijs, E.P.J. van den Heuvel, Catalogue of high-mass X-ray binaries in the Galaxy (4th edn.). A&A 455(3), 1165–1168 (2006). https://doi.org/10.1051/0004-6361: 20064987 A.A. Lutovinov, S.S. Tsygankov, Timing characteristics of the hard X-ray emission from bright X-ray pulsars based on INTEGRAL data. Astron. Lett. 35(7), 433–456 (2009). https://doi.org/ 10.1134/S1063773709070019 A.A. Lutovinov, M.G. Revnivtsev, S.S. Tsygankov, R.A. Krivonos, Population of persistent highmass X-ray binaries in the Milky Way. MNRAS 431(1), 327–341 (2013). https://doi.org/10. 1093/mnras/stt168 R.K.D. MacDonald, C.D. Bailyn, M. Buxton, A.G. Cantrell, R. Chatterjee, R. Kennedy-Shaffer, J.A. Orosz, C.B. Markwardt, J.H. Swank, The black hole binary V4641 Sagitarii: activity in quiescence and improved mass determinations. ApJ 784(1), 2 (2014). https://doi.org/10.1088/ 0004-637X/784/1/2 A. Manousakis, R. Walter, Origin of the X-ray off-states in Vela X-1. A&A 575, 58 (2015). https:// doi.org/10.1051/0004-6361/201321414 G. Maravelias, A. Zezas, V. Antoniou, D. Hatzidimitriou, F. Haberl, Hα imaging for BeXRBs in the Small Magellanic Cloud, in The Lives and Death-Throes of Massive Stars, vol. 329, ed. by J.J. Eldridge, J.C. Bray, L.A.S. McClelland, L. Xiao (2017), pp. 373–375. https://doi.org/10. 1017/S1743921317002757 S. Martínez-Núñez, P. Kretschmar, E. Bozzo, L.M. Oskinova, J. Puls, L. Sidoli, J.O. Sundqvist, P. Blay, M. Falanga, F. Fürst, A. Gímenez-García, I. Kreykenbohm, M. Kühnel, A. Sander, J.M. Torrejón, J. Wilms, Towards a unified view of inhomogeneous stellar winds in isolated supergiant stars and supergiant high mass X-ray binaries. Space Sci. Rev. 212(1–2), 59–150 (2017). https://doi.org/10.1007/s11214-017-0340-1 N. Masetti, M.L. Pretorius, E. Palazzi, L. Bassani, A. Bazzano, A.J. Bird, P.A. Charles, A.J. Dean, A. Malizia, P. Nkundabakura, J.B. Stephen, P. Ubertini, Unveiling the nature of INTEGRAL objects through optical spectroscopy. III. Observations of seven southern sources. A&A 449(3), 1139–1149 (2006). https://doi.org/10.1051/0004-6361:20054332 M. Massi, M. Chernyakova, A. Kraus, D. Malyshev, F. Jaron, S. Kiehlmann, S.A. Dzib, R. Sharma, S. Migliari, A.C.S. Readhead, Evidence for periodic accretion-ejection in LS I +61◦ 303. MNRAS 498(3), 3592–3600 (2020). https://doi.org/10.1093/mnras/staa2623 J.E. McClintock, R.A. Remillard, Black hole binaries, in Compact Stellar X-ray Sources, vol. 39 (2006), Cambridge University Press, Cambridge, pp. 157–213 S. Mineo, M. Gilfanov, R. Sunyaev, X-ray emission from star-forming galaxies – I. High-mass X-ray binaries. MNRAS 419(3), 2095–2115 (2012). https://doi.org/10.1111/j.1365-2966.2011. 19862.x

106 High-Mass X-ray Binaries

3771

I.M. Monageng, V.A. McBride, M.J. Coe, I.A. Steele, P. Reig, On the relationship between circumstellar disc size and X-ray outbursts in Be/X-ray binaries. MNRAS 464(1), 572–585 (2017). https://doi.org/10.1093/mnras/stw2354 A. Mushtukov, S. Tsygankov, Accreting strongly magnetised neutron stars: X-ray Pulsars (2022). arXiv e-prints 2204–14185, https://doi.org/10.48550/arXiv.2204.14185 A.A. Mushtukov, S. Portegies Zwart, Bright X-ray pulsars: how outflows influence beaming, pulsations and pulse phase lags. MNRAS 518(4), 5457–5464 (2023). https://doi.org/10.1093/ mnras/stac3431 A.A. Mushtukov, P.A. Verhagen, S.S. Tsygankov, M. van der Klis, A.A. Lutovinov, T.I. Larchenkova, On the radiation beaming of bright X-ray pulsars and constraints on neutron star mass-radius relation. MNRAS 474(4), 5425–5436 (2018). https://doi.org/10.1093/mnras/ stx2905 M. Neumann, A. Avakyan, V. Doroshenko, A. Santangelo, XRBcats: Galactic high mass Xray binary catalogue (2023). arXiv e-prints 2303–16137, https://doi.org/10.48550/arXiv.2303. 16137 F. Özel, D. Psaltis, R. Narayan, J.E. McClintock, The black hole mass distribution in the Galaxy. ApJ 725(2), 1918–1927 (2010). https://doi.org/10.1088/0004-637X/725/2/1918 J.M. Paredes, P. Bordas, Broad-band emission from gamma-ray binaries, in Frontier Research in Astrophysics – III. 28 May–2 June, 2018. Mondello (Palermo) (2019), p. 44 K.A. Postnov, L.R. Yungelson, The evolution of compact binary star systems. Liv. Rev. Relativ. 17(1), 3 (2014). https://doi.org/10.12942/lrr-2014-3 A.F. Rajoelimanana, P.A. Charles, A. Udalski, Very long-term optical variability of high-mass Xray binaries in the Small Magellanic Cloud. MNRAS 413(3), 1600–1622 (2011). https://doi. org/10.1111/j.1365-2966.2011.18243.x P. Reig, E. Nespoli, Patterns of variability in Be/X-ray pulsars during giant outbursts. A&A 551, 1 (2013). https://doi.org/10.1051/0004-6361/201219806 P. Reig, J.M. Torrejón, P. Blay, Accreting magnetars: a new type of high-mass X-ray binaries? MNRAS 425(1), 595–604 (2012). https://doi.org/10.1111/j.1365-2966.2012.21509.x P. Reig, On the neutron star-disc interaction in Be/X-ray binaries. MNRAS 377(2), 867–873 (2007). https://doi.org/10.1111/j.1365-2966.2007.11657.x P. Reig, Be/X-ray binaries. Astrophys. Space Sci. 332(1), 1–29 (2011). https://doi.org/10.1007/ s10509-010-0575-8 M. Revnivtsev, E. Churazov, K. Postnov, S. Tsygankov, Quenching of the strong aperiodic accretion disk variability at the magnetospheric boundary. A&A 507(3), 1211–1215 (2009). https://doi.org/10.1051/0004-6361/200912317 M. Ribó, P. Munar-Adrover, J.M. Paredes, B. Marcote, K. Iwasawa, J. Moldón, J. Casares, S. Migliari, X. Paredes-Fortuny, The first simultaneous X-ray/radio detection of the first Be/BH system MWC 656. ApJL 835(2), 33 (2017). https://doi.org/10.3847/2041-8213/835/2/L33 T. Rivinius, A.C. Carciofi, C. Martayan, Classical Be stars. Rapidly rotating B stars with viscous Keplerian decretion disks. Astron. Astrophys. Rev. 21, 69 (2013). https://doi.org/10.1007/ s00159-013-0069-0 N.I. Shakura, K.A. Postnov, A.Y. Kochetkova, L. Hjalmarsdotter, Quasispherical subsonic accretion in X-ray pulsars. Phys. Usp. 56(4), 321–346 (2013). https://doi.org/10.3367/UFNe.0183. 201304a.0337 P. Shtykovskiy, M. Gilfanov, High mass X-ray binaries in the LMC: dependence on the stellar population age and the “propeller” effect. A&A 431, 597–614 (2005a). https://doi.org/10.1051/ 0004-6361:20041074 P. Shtykovskiy, M. Gilfanov, High-mass X-ray binaries in the Small Magellanic Cloud: the luminosity function. MNRAS 362(3), 879–890 (2005b). https://doi.org/10.1111/j.1365-2966. 2005.09320.x L. Sidoli, A. Paizis, An INTEGRAL overview of high-mass X-ray binaries: classes or transitions?. MNRAS 481(2), 2779–2803 (2018). https://doi.org/10.1093/mnras/sty2428 N. Smith, Mass loss: its effect on the evolution and fate of high-mass stars. Annu. Rev. Astron. Astrophys. 52, 487–528 (2014). https://doi.org/10.1146/annurev-astro-081913-040025

3772

F. Fornasini et al.

R. Staubert, J. Trümper, E. Kendziorra, D. Klochkov, K. Postnov, P. Kretschmar, K. Pottschmidt, F. Haberl, R.E. Rothschild, A. Santangelo, J. Wilms, I. Kreykenbohm, F. Fürst, Cyclotron lines in highly magnetized neutron stars. A&A 622, 61 (2019). https://doi.org/10.1051/0004-6361/ 201834479 A.D. Sutton, T.P. Roberts, M.J. Middleton, The ultraluminous state revisited: fractional variability and spectral shape as diagnostics of super-Eddington accretion. MNRAS 435(2), 1758–1775 (2013). https://doi.org/10.1093/mnras/stt1419 S.A. Tjemkes, E.J. Zuiderwijk, J. van Paradijs, Optical light curves of massive X-ray binaries. A&A 154, 77–91 (1986) J.A. Tomsick, S. Chaty, J. Rodriguez, R. Walter, P. Kaaret, Chandra localizations and spectra of INTEGRAL sources in the Galactic plane. ApJ 685(2), 1143–1156 (2008). https://doi.org/10. 1086/591040 J.A. Tomsick, G.B. Lansbury, F. Rahoui, M. Clavel, F.M. Fornasini, J. Hong, J. Aird, D.M. Alexander, A. Bodaghee, J.-L. Chiu, J.E. Grindlay, C.J. Hailey, F.A. Harrison, R.A. Krivonos, K. Mori, D. Stern, Galactic sources detected in the NuSTAR Serendipitous Survey. ApJS 230(2), 25 (2017). https://doi.org/10.3847/1538-4365/aa7517 J.A. Tomsick, G.B. Lansbury, F. Rahoui, J. Aird, D.M. Alexander, M. Clavel, A. Cuturilo, F.M. Fornasini, J. Hong, L. Klindt, D. Stern, Chandra observations of NuSTAR Serendipitous Sources near the Galactic plane. ApJ 869(2), 171 (2018). https://doi.org/10.3847/1538-4357/ aaf007 L.J. Townsend, P.A. Charles, Orbital and superorbital periods in ULX pulsars, disc-fed HMXBs, Be/X-ray binaries, and double-periodic variables. MNRAS 495(1), 139–143 (2020). https://doi. org/10.1093/mnrasl/slaa078 L.J. Townsend, M.J. Coe, R.H.D. Corbet, A.B. Hill, On the orbital parameters of Be/X-ray binaries in the Small Magellanic Cloud. MNRAS 416(2), 1556–1565 (2011). https://doi.org/10.1111/j. 1365-2966.2011.19153.x S.S. Tsygankov, A.A. Lutovinov, E.M. Churazov, R.A. Sunyaev, 4U 0115+63 from RXTE and INTEGRAL data: pulse profile and cyclotron line energy. Astron. Lett. 33(6), 368–384 (2007). https://doi.org/10.1134/S1063773707060023 E.P.J. van den Heuvel, S.F. Portegies Zwart, S.E. de Mink, Forming short-period Wolf-Rayet Xray binaries and double black holes through stable mass transfer. MNRAS 471(4), 4256–4264 (2017). https://doi.org/10.1093/mnras/stx1430 E.P.J. van den Heuvel, S.F. Portegies Zwart, D. Bhattacharya, L. Kaper, On the origin of the difference between the runaway velocities of the OB-supergiant X-ray binaries and the Be/X-ray binaries. A&A 364, 563–572 (2000) N. van Jaarsveld, D.A.H. Buckley, V.A. McBride, F. Haberl, G. Vasilopoulos, C. Maitra, A. Udalski, B. Miszalski, Identification of high-mass X-ray binaries selected from XMM-Newton observations of the LMC. MNRAS 475(3), 3253–3261 (2018). https://doi.org/10.1093/mnras/ stx3270 VERITAS Collaboration, S. Archambault, A. Archer, T. Aune, A. Barnacka, W. Benbow, R. Bird, M. Buchovecky, J.H. Buckley, V. Bugaev, K. Byrum, J.V. Cardenzana, M. Cerruti, X. Chen, L. Ciupik, E. Collins-Hughes, M.P. Connolly, W. Cui, H.J. Dickinson, J. Dumm, J.D. Eisch, A. Falcone, Q. Feng, J.P. Finley, H. Fleischhack, A. Flinders, P. Fortin, L. Fortson, A. Furniss, G.H. Gillanders, S. Griffin, J. Grube, G. Gyuk, M. Hütten, N. Hå, D. Hanna, J. Holder, T.B. Humensky, C.A. Johnson, P. Kaaret, P. Kar, N. Kelley-Hoskins, M. Kertzman, Y. Khassen, D. Kieda, M. Krause, F. Krennrich, S. Kumar, M.J. Lang, G.a. Maier, Exceptionally bright TeV flares from the binary LS I +61◦ 303. ApJL 817(1), 7 (2016). https://doi.org/10.3847/2041-8205/ 817/1/L7 E.A. Vitrichenko, D.K. Nadyozhin, T.L. Razinkova, Mass-luminosity relation for massive stars. Astron. Lett. 33(4), 251–258 (2007). https://doi.org/10.1134/S1063773707040044 R. Walter, J. Zurita Heras, L. Bassani, A. Bazzano, A. Bodaghee, A. Dean, P. Dubath, A.N. Parmar, M. Renaud, P. Ubertini, XMM-Newton and INTEGRAL observations of new absorbed supergiant high-mass X-ray binaries. A&A 453(1), 133–143 (2006). https://doi.org/10.1051/ 0004-6361:20053719

106 High-Mass X-ray Binaries

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R. Walter, A.A. Lutovinov, E. Bozzo, S.S. Tsygankov, High-mass X-ray binaries in the Milky Way. A closer look with INTEGRAL. Astron. Astrophys. Rev. 23, 2 (2015). https://doi.org/10.1007/ s00159-015-0082-6 L.B.F.M. Waters, M.H. van Kerkwijk, The relation between orbital and spin periods in massive X-ray binaries. A&A 223, 196–206 (1989) S.-S. Weng, L. Qian, B.-J. Wang, D.F. Torres, A. Papitto, P. Jiang, R. Xu, J. Li, J.-Z. Yan, Q.-Z. Liu, M.-Y. Ge, Q.-R. Yuan, Radio pulsations from a neutron star within the gamma-ray binary LS I +61o 303. Nat. Astron. (2022). https://doi.org/10.1038/s41550-022-01630-1 Y. Xing, Z. Wang, J. Takata, Superorbital modulation at GeV energies in the γ -ray binary LS I + 61◦ 303. ApJ 851(2), 92 (2017). https://doi.org/10.3847/1538-4357/aa9b36 J. Yang, A. Zezas, M.J. Coe, J.J. Drake, J. Hong, S.G.T. Laycock, D.R. Wik, Anticorrelation between X-ray luminosity and pulsed fraction in the Small Magellanic Cloud pulsar SXP 1323. MNRAS 479(1), 1–6 (2018). https://doi.org/10.1093/mnrasl/sly085 H. Yoneda, K. Makishima, T. Enoto, D. Khangulyan, T. Matsumoto, T. Takahashi, Sign of hard-Xray pulsation from the γ -ray binary system LS 5039. Phys. Rev. Lett. 125(11), 111103 (2020). https://doi.org/10.1103/PhysRevLett.125.111103 A.A. Zdziarski, Radiative processes and geometry of spectral states of black-hole binaries, in Highly Energetic Physical Processes and Mechanisms for Emission from Astrophysical Plasmas, vol. 195, ed. by P.C.H. Martens, S. Tsuruta, M.A. Weber (2000), Astronomical Society of the Pacific, San Francisco, p. 153 A.A. Zdziarski, J. Mikolajewska, K. Belczynski, Cyg X-3: a low-mass black hole or a neutron star. MNRAS 429, 104–108 (2013). https://doi.org/10.1093/mnrasl/sls035 J. Ziolkowski, Be/X-ray binaries. Mem. della Soc. Astron. Ital. 73, 1038–1038 (2002). https://doi. org/10.48550/arXiv.astro-ph/0208455

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . What Is a White Dwarf? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Electron Degeneracy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Equation of State of Electron-Degenerate Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Chandrasekhar Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . White Dwarf Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . White Dwarf Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accreting White Dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Roche Lobe Overflow and Accretion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Outflows and Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Binary Components and the Diversity in Accreting White Dwarfs . . . . . . . . . . . . . . . . . . Cataclysmic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accreting White Dwarfs in the Broader Astrophysical Context . . . . . . . . . . . . . . . . . . . . . Discovering Accreting White Dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accreting White Dwarfs Found in Optical Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accreting White Dwarfs Found in X-Ray Surveys . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Surveys That Will Detect Accreting White Dwarfs . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

White dwarfs are the most common endpoints of stellar evolution. They are often found in close binary systems in which the white dwarf is accreting matter from a companion star, either via an accretion disc or channelled along the white dwarf magnetic field lines. The nature of this binary depends on the masses and the

N. A. Webb () Institute de Recherche en Astrophysique et Planétologie, Toulouse, France e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_96

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separation of the two stellar components, as well as other parameters such as the white dwarf magnetic field and the nature of the stars. This chapter looks at the formation of white dwarfs and intrinsic properties, before looking at the different populations of accreting white dwarf binary systems that exist. The chapter covers the characteristics of the various sub-populations and looks at how they evolve. The means to discover and study various sub-classes of accreting white dwarfs in the optical and other bands is discussed, and the role of these systems in the broader astrophysical context are considered. Future missions that will find new systems and new populations are also reviewed. Finally some of the current open questions regarding accreting white dwarfs are presented. Keywords

Close binaries · Novae · Cataclysmic variables · White dwarfs · Accretion discs · Surveys · Globular clusters · Supernovae Ia

Introduction White dwarfs are formed at the end of the lives of the least massive stars and are thus the most common endpoints of stellar evolution. White dwarfs were the first type of compact object to be discovered. William Herschel made the first detection of a white dwarf, 40 Eridani B in 1783 (Herschel 1785). However, it wasn’t until 1915 when Adams (1915) demonstrated that Sirius’ companion had a mass of around a solar mass. However, it had a low luminosity similar to that of 40 Eridani B (Adams 1914), revealing that these stars were different from the general population of stars observed. The approximately flat optical spectrum (∼4000–7000 Å), along with the low luminosity, which indicates a small radius, caused Luyten (1922) to refer to these stars as white dwarfs. By 1924, it was clear that white dwarfs were very different to other stars known (Eddington 1924), but it was only in 1931 that Chandrasekhar (1931) understood the nature of the dense degenerate matter constituting these objects. Today, around a hundred thousand white dwarfs are known. Many are found in the solar neighbourhood (e.g. Jiménez-Esteban et al. 2018), and some are young enough and therefore bright enough to be visible through a pair of binoculars (e.g. 40 Eridani B, magnitude ∼9.5). White dwarfs are characterised by small radii, typically similar to the radius of the Earth, but with masses reaching 1.4 M⊙ (Chandrasekhar 1931). This implies high densities and therefore strong gravitational fields, which become stronger as the mass increases (and the radius decreases; see section “White Dwarf Characteristics”), so that it becomes necessary to use general relativity to understand their nature and their environment. If a white dwarf is in a close binary system, matter from the companion star may be lost through the inner Lagrangian point of the binary (see chapter “Overall Accretion Disk Theory”) and become trapped in the gravitational field of the white dwarf, allowing it to fall onto the white dwarf, rendering it hotter and brighter than an isolated white dwarf of a similar age.

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Studying the evolution of these systems can give an insight into the white dwarf nature and help to understand the accretion phenomenon which is found throughout the universe, in stellar and planetary formation, as well as around supermassive black holes in the hearts of galaxies. This chapter covers white dwarfs and the nature of the different binary systems containing these compact objects, as well as the different populations of these systems, where and how they are found and how they can be used to understand different phenomena in the universe.

What Is a White Dwarf? In main-sequence stars, i.e. stars burning hydrogen in their core, the hydrostatic equilibrium is achieved thanks to the gas pressure opposing the pressure due to the mass of the star. However, white dwarfs are no longer undergoing fusion. For white dwarfs to find a stable equilibrium, a different pressure is required, and this is through electron degeneracy. The physics of the electron degeneracy dictate the white dwarf characteristics and properties, including the maximum mass allowed and how the white dwarf responds to accreted matter. The electron degeneracy and its implications for the nature of the white dwarf are described in the following subsections.

Electron Degeneracy The pressure, Pe , that electrons (e− ) can exert is a function of their density (ρe ), i.e. Pe = f (ρe ). To determine this pressure, the number of free-electron states in a volume, V , are calculated. For simplicity, a cube with the length of the side, L, is considered. This means V = L3 . Duplicating this cube to fill all the space available and allowing the wave vectors of the free-electron quantum states to take only discrete values, the electron wave function is given by ψ ∝ e(ikx) , when considering the three dimensions, x, y, z, k = (kx ,ky ,kz ), so that the replication of the cube leads to: kx = nx

2π L

where

nx = 1, 2, . . .

(1)

The allowed states are separated by 2π/L, so the density of the states in k space (N ) is dN = g

L3 3 d k (2π )3

(d 3 k ≡ dkx dky dkz )

(2)

where g is the degeneracy factor for spin (spin can be either up (↑) or down (↓)).

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Taking the de Broglie relationship for the electron’s momentum, p, associated with its wave vector: p = h¯ k, where h¯ is the Planck constant divided by 2π , the density of the states in k space is converted to momentum space using: dN = g

L3 d 3p (2π h) ¯ 3

(3)

The number density of particles per unit volume (n) with momentum states in d 3 p is then dn = g

1 f (p)d 3 p (2π h) ¯ 3

(4)

where f (p) is the mode occupation number, i.e. the number of particles in the cube with a particular wave function. For bosons (e.g. photons), f (p) is not restricted, but fermions (i.e. electrons with spin angular momentum h/2) must obey the Pauli ¯ exclusion principle. This states that f (p) ≤ 1

(5)

The electron gas is thus different to a classical gas, and the Pauli exclusion principle limits the density of the electron gas.

The Equation of State of Electron-Degenerate Matter Treating the particle momenta as a Maxwellian distribution, where each velocity (v) component has a Gaussian distribution with a standard deviation, gives the following equation Ψ (v) =

1 2 2 e(−v /2σ ) d 3 v (2π σ 2 )3/2

(6)

The velocity dispersion (σ ) is a function of the temperature, T , through the equipartition of energy: σ 2 = kB T /m (where kB is the Boltzmann constant and m the particle mass). Writing Eq. 6 in terms of the number density of particles in a given momentum range and then multiplying by the total number density of particles and using the momentum equation p = mv gives, dn =

n 2 e(−p /2mkB T ) d 3 p 3/2 (2π mkB T )

(7)

Comparing Eqs. 6 and 4 implies a critical density (ncrit ) where the classical description would violate the Pauli exclusion principle (Eq. 5) for p = 0.

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ncrit =

g (mkB T )3/2 (2π )3/2 h¯ 3

(8)

The gas will then be in the classical regime at high temperatures and fixed density, but quantum effects become important as T → 0. Integrating Eq. 4 over all momentum states leads to the total number density of particles: n=



g (2π h) ¯ 3

f (p)d 3 p

(9)

Then as T → 0, the states are occupied only up to the Fermi momentum (pF ). Hence:  pF g 4π 3 g pF (10) d 3p = n= 3 (2π h) (2π h) ¯ ¯ 3 3 0 The Fermi momentum is then correlated with the particle density as shown in Eq. 11, 3 pF = 2π h¯ 4πg 

1/3

n1/3

(11)

If the gas density increases, the Fermi momentum will also increase. The additional particles are forced to fill the higher momentum states because the lower momentum states have already been occupied. The pressure from the electrons can be determined by considering the pressure as a momentum flux, and therefore the flux of electrons in the x-direction is just the number of electrons crossing a unit area per unit time, or ne vx . The pressure is then approximated by P ∼ px ne vx . Using Eq. 4, the pressure in the x-direction (which by isotropy must be equal to the pressure in any direction) is P = Px =

g (2π h) ¯ 3



px vx f (p)d 3 p

(12)

Using spherical polar coordinates in momentum space 

1 px vx dpx dpy dpz = 3



1 (px vx + py vy + pz vz )dpx dpy dpz = 3



pv4πp2 dp (13)

so g 1 P = 3 (2π h) ¯ 3



∞ 0

pvf (p)4πp2 dp

(14)

As T → 0 (Eq. 10), electron speeds do not achieve relativistic values so that pv = p2 /me , and

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Pe =

4πg 3(2π h) ¯ 3



g p2 2 p dp = pF5 2 me 30π h¯ 3 me

pF

0

(15)

Rewriting the pressure as a function of density ρe = me ne using Eq. 11

pF =



6π hρ ¯ e gme

1/3

(16)

and substituting into Eq. 15, the pressure for non-relativistic electrons can be determined as follows:

Pe =

g 30π 2 h¯ 3



6π 2 h¯ 3 g

5/3

where K1 =

ρ 5/3 me

−8/3

π 2 h¯ 2 8/3

5me



6 gπ

5/3

= K1 ρe

2/3

(17)

(18)

As before, as the densities increase (Eq. 11), the Fermi momentum increases until it reaches relativistic values. Some particles may be compelled into momentum states with velocities approaching the speed of light, c. Replacing v with c gives the relativistic expression 4πg Pe = 3(2π h) ¯ 3



pF

pcp2 dp =

0

gc 24π 2 h¯ 3

pF4

(19)

or

Pe =

gc 24π 2 h3 ¯



6π h¯ 3 ρe gme

where K2 =

4/3

π h¯ c 4/3

4me



4/3

= K2 ρe

(20)

1/3

(21)

6 gπ

Equations 17 and 20 reveal that, in a degenerate gas, the pressure depends on the density alone and is thus independent of temperature. In a partially degenerate gas, a residual temperature dependence remains. Only the electrons are considered in determining the pressure. In Eqs. 17 and 20, it can be seen that the particle mass is in the denominator. As the proton is 1836 times more massive than the electron, its contribution to the pressure is therefore negligible.

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The Chandrasekhar Mass As the white dwarf is supported by electron degeneracy, there must be a limit to the pressure that can be provided, simply because there is a limit to the phase space density of the electrons. Therefore, it is intuitive that there is a maximum mass for the white dwarf. This mass can be deduced by estimating the energy density, U , of the degenerate gas in a similar way to that which was done for the pressure. Integrating over momentum space and incorporating a term, ε(p), to convey the energy per mode, the energy density is given by g U= (2π h) ¯ 3



∞

ε(p)f (p)4πp2 dp

0

(22)

As T → 0, f (p) = 1 but is zero otherwise. In the relativistic case, ε(p) = pc. Using this in Eq. 22 and integrating gives rise to the electron energy density (Ue ) Ue =

g 1 4π cpF4 34 (2π h) ¯

(23)

Using Eq. 11 to express Ue as a function of the electron number density gives Ue =

3 4



6π 2 g

1/3

4/3

hcn ¯ e

(24)

The non-relativistic case for ε(p) = p2 /2me then gives 3h¯ 2 Ue = 10me



6π 2 g

2/3

5/3

ne .

(25)

The total kinetic energy (EK ) of the degenerate electrons is proportional to their energy density multiplied by the volume. In the relativistic case, EK ∝ Ue V ∝ 4/3 ne V ∝ M 4/3 /R, where M is the mass and R is the radius of the white dwarf. The gravitational energy (Ep ) is proportional to M 2 /R. The total energy (Etot ) is then the sum of both terms, Etot = (AM 4/3 − BM 2 )/R, where A and B are constants. For a set of masses, the total energy must be positive. The total energy is reduced as the radius increases (the star expands) at which point the electrons become only mildly relativistic. The star then exists as a stable white dwarf. If, however, the mass increases, the total energy becomes negative, and the radius decreases until gravitational collapse is inevitable; see section “Exceeding the Chandrasekhar Mass” for more discussion on this point. To determine the mass at which the electron degeneracy pressure is no longer sufficient to support the white dwarf, A and B must be determined (Chandrasekhar 1931). These values depend on the molecular weight per electron of the material inside the white dwarf and the density profile. The critical mass at which the

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electron pressure is overcome was first determined by Subrahmanyan Chandrasekhar (Chandrasekhar 1931) and is named after him, the Chandrasekhar mass. This was subsequently determined to be ∼1.4 M⊙ (Ostriker et al. 1966).

White Dwarf Formation Stars with masses up to ∼8–10.6 M⊙ , depending on the initial stellar metallicity (Maeder and Meynet 1989; Meynet 1991; Ibeling and Heger 2013; Doherty et al. 2015; Woosley and Heger 2015), leave behind white dwarfs at the end of their lives. There are different types of white dwarf (see section “White Dwarf Characteristics”), and their nature is often related to the initial mass of the progenitor. Stars on the main sequence of the Hertzsprung Russell diagram undergo hydrogen fusion in their core, providing a force that counteracts the gravitational force due to the mass of the star, so that the star remains in hydrostatic equilibrium. Hydrogen fusion produces helium. When insufficient hydrogen remains in the core to continue the fusion process, the star leaves the main sequence with a helium flash. For the lowest mass stars, there is insufficient pressure, and the temperature is too low for the helium to undergo fusion. These stars leave behind remnants that are constituted mainly of hydrogen or helium. Stars with a mass 1.85 M⊙ (Meynet 1991) can continue to burn helium in a stable fashion and produce carbon-oxygen cores. Once insufficient matter remains for the fusion process to continue, the gravitational force due to the mass of the star dominates. The outer parts of the star are blown away during the planetary nebula phase, and the core will then collapse due to gravity.

White Dwarf Characteristics Rotation Rates In non-degenerate, i.e. normal matter, the volume increases with the mass. For degenerate matter, the opposite occurs, so as the mass of the white dwarf increases, the radius decreases (see also section “The Chandrasekhar Mass”). This was described by Nauenberg (1972), 8

R = 7.8 × 10 cm



1.44 M

2/3

−



M 1.44

2/3 1/2

(26)

The radius of a solar mass white dwarf is approximately the same as the radius of the Earth (∼6000 km). Less massive white dwarfs have larger radii, for example, a 0.7 M⊙ white dwarf would have a radius of ∼7500 km. Chandrasekhar mass white dwarfs have smaller radii, ∼1200 km. The compact nature of white dwarfs implies that the gravitational force responsible for holding it together (GMm/R 2 ), where m is the mass of a particle on the surface of the white dwarf, is extremely high. This means that white dwarfs can rotate extremely rapidly without flying apart

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due to the centripetal force (mv 2 /R). The velocity (v) at the surface of the star is (2π r)/P , where P is the period of the rotation of the star, and therefore the theoretical minimum rotational period of a white dwarf can be calculated: GMm m4π 2 R > R2 P2

⇒

P > 2π



R3 GM

(27)

From Eq. 27, the minimum period is for a minimum radius, which corresponds to a white dwarf with the Chandrasekhar mass. This implies a minimum rotation period of ∼0.5 s. Without energy injected into the system to maintain this high rotation rate, the white dwarf will rapidly spin down. Indeed, no white dwarf with such a short period has been detected to date, where the shortest rotation period of a white dwarf is 24.93 s for the white dwarf in the cataclysmic variable LAMOST J024048.51+195226.9 (Pelisoli et al. 2021), as mass transfer in such a binary can transfer angular momentum to the white dwarf, spinning it up; see section “Dwarf Novae and Novalikes”.

Magnetic Field As angular momentum should be conserved as the star evolves to a white dwarf, so the magnetic flux may also be conserved. Some main-sequence stars can show magnetic fields as high as 3 × 102 –3 × 104 G (1 G (Gauss) is the CGS unit for magnetic fields and corresponds to 10−4 T (Tesla).) (Wickramasinghe and Ferrario 2010). The magnetic flux, B, is proportional to the inverse of the radius squared, and therefore magnetic fields of the order 108 G can be generated when the mainsequence star collapses to the white dwarf (Wickramasinghe and Ferrario 2010). White dwarfs with lower magnetic fields of 103 –104 G may have had their fields generated by convective dynamos during stellar evolution to the white dwarf state or for fields of 105 –106 G, through contemporary dynamos in cooling white dwarfs that develop extensive convective envelopes. Temperature and Cooling White dwarfs are born with high temperatures. The initial temperature can be estimated using the contraction of the thermally unsupported stellar core down to the radius at which degeneracy pressure will halt the contraction. The virial theorem states that just before reaching the final point of equilibrium, the thermal energy (Eth = 23 N kB T ) will equal half of the potential energy (GM 2 /R). For a pure helium composition, the number of nuclei in the core is M/4mp , and the number of electrons is M/2mp , so Eth

3 M = 2 mp

Using the virial theorem,



 1 1 9 M + kB T kB T = 2 4 8 mp

(28)

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kB T ∼

4 GMmp 9 R

(29)

for a solar mass white dwarf, its temperature at birth is ∼1 × 109 K. This hot temperature implies that the emission peaks in the X-ray range. Once the core becomes an exposed white dwarf, its radiation ionises the gas blown off during the asymptotic giant branch (AGB) phase, giving rise to the planetary nebula discussed above. The white dwarf will start to cool. Neglecting the envelope around the white dwarf and assuming a uniform temperature throughout, the maximum cooling rate can be determined. The radiative energy loss is obtained by equating the luminosity, L, of the blackbody, given by the Stefan-Boltzmann law, to the rate of change of thermal energy (Eq. 28): L = 4π R 2 σ T 4 ∼

3 MkB dT dEth = dt 8 mp dt

(30)

where σ is the Stefan-Boltzmann constant. Separating the variables T and t and integrating, the cooling time to reach a temperature T is τcool ∼

−3  1 3 MkB 1 1 T 9 ∼ 3 × 10 yr 8 mp 4π R 2 σ 3 T 3 103 K

(31)

In reality this is too rapid. The outer, non-degenerate envelope acts as an insulator, and the inner regions crystallise, modifying the cooling with time (e.g. Wood 1992). One of the interests in understanding exactly how white dwarfs cool is that they have cooling times comparable to the age of the universe. It may therefore be possible to use these objects to determine the history of star formation in our galaxy by modelling their luminosity function. Studying these systems in binary systems in which accretion onto the surface of the white dwarf occurs (see section “Accreting White Dwarfs”) can help understand how white dwarfs cool as the white dwarf is constantly being heated and cooled due to increasing and decreasing accretion.

Composition Most white dwarfs are composed of carbon and oxygen, but the atmosphere is usually observed to be predominantly hydrogen (∼83% of spectroscopically confirmed white dwarfs). White dwarfs with hydrogen atmospheres are called DA white dwarfs. Seven percent of white dwarfs (e.g. Ourique et al. 2019) show helium spectra and are known as DO white dwarfs if they are hot enough to show He II lines (from singly ionised helium) and DB if they only show He I lines (from neutral helium). DC white dwarfs are too cool to show absorption lines in their optical spectra (∼5% of white dwarfs) and are believed to have helium atmospheres which explains why hydrogen lines are not seen (e.g. Ourique et al. 2019). DQ white dwarfs, showing carbon lines or bands, count for only 1% of white dwarfs. White dwarfs with other types of metal lines in their optical spectra are known as DZ

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white dwarfs and make up about 4% of the population (e.g. Ourique et al. 2019). The atmosphere is always dominated by the lightest element present, as the high surface gravity leads to a stratification of the atmosphere. Due to the high density of white dwarfs, the atmosphere also has a high pressure. In the optical and ultra-violet spectra, broad line wings are observed due to pressure broadening (or collisional broadening, Foley 1946), as collisions between atmospheric atoms reduce the effective lifetime of a state, leading to broader lines. This is most notable in the Balmer lines seen in the optical spectra of DA white dwarfs, but as white dwarfs are hot and therefore also emit strongly at shorter wavelengths, the effect is also seen in the Lyman lines in the ultra-violet, for example Barstow et al. (2003). Isolated white dwarfs can be detected in soft (low energy) X-rays, but the spectra are thermal in nature and do not usually show any lines. X-ray emission is stronger when the white dwarf is in a binary system accreting from a companion star (see section “Accreting White Dwarfs”).

Observed Masses and Radii The Montreal White Dwarf Database (Dufour et al. 2017) provides data for ∼56,000 spectroscopically confirmed white dwarfs. The average temperature for the white dwarfs in this database is ∼7500 K but with a large range spanning ∼3000– 180,000 K. The mean mass of the sample is 0.57 M⊙ but with the range spanning very low (∼0.01 M⊙ ) masses up to masses in slight excess of the Chandrasekhar mass, ∼1.49 M⊙ . The average surface gravity is log(g) ∼8, with the range spanning 3.1–10. The magnetic fields are in the range 1 ×105 –9 ×108 G. These values are similar to the almost complete sample of white dwarfs detected out to 100 pc with Gaia (Jiménez-Esteban et al. 2018). This survey also gives an average white dwarf radius of ∼0.012 R⊙ (8346 km), with a range 0.002–0.02 R⊙ (1391–13,910 km), but with a possible bimodal distribution with maxima at 0.01 R⊙ (6955 km) and at 0.0125 R⊙ (8694 km), which remains to be explained.

Accreting White Dwarfs The majority of stars are found in binary systems, where the two stars orbit about their common centre of mass. The orbital period, or the time it takes for the two stars to orbit each other, can be thousands of years (Porb ). These systems will evolve as described in the chapter “Overall Binary Evolution Theory”, and one or both of the stars can evolve to become a white dwarf, depending on its initial mass; see section “White Dwarf Formation”. Due to the compact nature of the white dwarf (see section “Electron Degeneracy”), the orbital period can become very short (see section “Observed Orbital Period Distribution”), as little as tens of minutes, so that the stars are very close, and they will have a strong influence on one another. The different types of close binary systems containing white dwarfs are discussed here.

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Roche Lobe Overflow and Accretion A full account of accretion and ejection is beyond the scope of this chapter which are discussed in chapters “Accretion Process” and “The Extreme of SMBH Accretion/Ejection”; however, several notions concerning these topics are necessary to understand some of the aspects covered in this chapter. To understand a binary system and the mutual influence of the two stars, the total potential (gravitational and centripetal forces) should be considered. This is approximated by the Roche potential, ΦR and assumes point-like stars in circular orbits. Considering Cartesian coordinates (x, y, z) that rotate with the binary, the x-axis is described by the line traversing the stellar centres (separated by a distance a and of masses M1 and M2 ), the y-axis is in the direction of orbital motion of the primary, and the z-axis is perpendicular to the orbital plane. The gravitational potential ΦG is then defined as: ΦG = −

(x 2

GM1 GM2 − 2 2 0.5 2 +y +z ) [(x − a) + y 2 + z2 ]0.5

(32)

and the centripetal potential ΦC is written as 1 ΦC = − Ω 2 [(x − µa)2 + y 2 ] 2

(33)

where µ is the mass of the second star (M2 ) with respect to their combined masses (M1 + M2 ), also known as the mass function and Ω is 2π/Porb . The Roche potential can be written as: ΦR = −

GM2 1 GM1 − − Ω 2 [(x − µa)2 + y 2 ] 2 (x 2 + y 2 + z2 )0.5 [(x − a)2 + y 2 + z2 ]0.5 (34)

Close to the star, the potential is dominated by its gravitational potential, so the stellar surfaces are almost spherical. Further from the stellar centre, both effects become important: the tidal effect, which causes an elongation in the direction of the companion star and flattening due to the centripetal force. The surfaces are then distorted so that their major axis is along the line connecting the stellar centres. The innermost equipotential surface encompassing both stars defines the Roche lobe of each star. Matter inside a Roche lobe is gravitationally bound to that star. The topology of the surfaces can be determined by the Lagrange points, the point at which the gradient of the potential becomes zero. There are five such points where the effective gravity from the two stars and the centrifugal force cancel. The inner Lagrangian point, L1 (also called the ‘saddle point’), forms a pass between the two Roche lobes. L1 , L2 (situated behind the Roche lobe corresponding to M2 ) and L3 (behind the Roche lobe corresponding to M1 ) are unstable, i.e. a small perturbation will displace a body placed at these points. However, L4 (situated above L1 in the

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rotation plane) and L5 (situated below L1 in the rotation plane) are stable, i.e. resist gravitational perturbations. If one star fills its Roche lobe exactly, e.g. M2 , whilst the other, here the white dwarf, is still smaller than its Roche lobe, the binary is said to be semi-detached, or an interacting binary. If the star M2 expands, it will encounter a hole in its surface, near L1 . Here, hydrostatic equilibrium is no longer possible and matter will flow through the nozzle around L1 into the Roche lobe of the white dwarf. This is known as Roche-lobe overflow. The matter that arrives in the white dwarf Roche lobe is gravitationally bound to it. The matter has angular momentum, due to the rotation of the binary system, and so it will circle around the white dwarf, eventually forming a ring. Due to friction in the ring, the material will spread into a disc shape, known as an accretion disc. The matter forms a thin disc around the white dwarf if the mass transfer rate is low. In this case, the height of the disc is much smaller than the radius (typically 0.1–3%). The matter loses angular momentum due to frictional forces within the disc, allowing matter to fall onto the white dwarf, heating it up and causing it to become brighter, either over the whole surface or at the poles, depending on the magnetic field configuration; see section “Magnetic CVs”. The accretion disc is cool towards the exterior, mainly emitting in the infrared but becomes hotter towards the centre where it achieves high enough temperatures that result in X-ray emission. Each disc annulus emits a blackbody spectrum that corresponds to the temperature of that annulus. The accretion disc then emits the totality of the annuli, called a disc blackbody. The lowest frequencies ν are the Rayleigh-Jeans tail emission from the outer regions of the disc, where the intensity Iν ∝ ν 2 . The middle part of the spectrum results from the sum of the blackbodies (Iν ∝ ν 1/3 ), and the highest frequencies emanate from the inner edge of the accretion disc with a temperature Tin that has an exponential cutoff, Iν ∝ e−hν/kTin . Spectral lines may be superposed on this emission. Accretion is an efficient way of producing energy. As particles with mass m fall from infinity onto the compact white dwarf, they lose their gravitational potential energy, and the change in energy ∆Eacc is given by: ∆Eacc =

GMm R

(35)

where M and R are the mass and the radius of the white dwarf. Outbursts occur as matter builds up in the disc, so that the density and therefore the temperature increase. At a critical density, the matter, essentially hydrogen if accreting from a hydrogen-rich star, ionises and thus becomes more viscous, allowing matter to pass through the disc and fall onto the white dwarf. This results in an important increase in the luminosity until sufficient matter is evacuated from the disc, so that it becomes less dense and cooler, thus ending the outburst. Theory predicts that the outbursts start either in the outer regions of the disc and move inwards through the disc and are termed as outside-in, or they start in the inner regions of the disc and move outwards and are called inside-out outbursts

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(Smak 1984). It is unclear prior to an outburst whether the outburst is going to be outside-in or inside-out. It is likely that the type of outburst that takes place is due to the amount and location of material left in the disc after the previous outburst (Smak 1984). For a detailed treatment, see chapter “Overall Accretion Disk Theory”.

Outflows and Jets Momentum can be extracted from the radiation field of the accretion disc through line opacity (Castor et al. 1975), driving a wind (or outflow) from the accretion disc surface. However, magnetic fields threading the accretion disc can also play a role in launching the wind. Broad, blue-shifted, high-excitation absorption lines, along with P Cygni line profiles observed from cataclysmic variables (novalikes and dwarf novae in outburst) seen face on, are evidence for winds from the accretion discs in these systems. These winds are not thought to be completely radiatively driven, as wind line strengths are not directly correlated with the strength of the photo-ionising continuum, e.g. Froning (2005). Jets, collimated beams of high-velocity material, often emitted perpendicular to the accretion disc have been detected in some accreting white dwarf systems. The energy to launch jets is thought to come either from the rotation of the compact object (Blandford and Znajek 1977) or from differential rotation in the accretion disc (Blandford and Payne 1982). Therefore, it is logical to expect that jets may be launched from accreting white dwarfs if the magnetic field is not so strong that it disrupts the central regions of the disc. Indeed, jets have been detected from a wide range of accreting white dwarfs, including supersoft sources, e.g. Tomov et al. (1998), and in symbiotic systems, e.g. Taylor et al. (1986). Alternative models also exist. Observational evidence shows that the jets are often brightest in the radio domain, with spectra indicating that the emission mechanism is synchrotron, supporting these theories. Evidence for jet emission from a cataclysmic variable, outside a nova eruption, was first detected from SS Cyg (Körding et al. 2008). These jets appear to be similar to jets detected in X-ray binaries (stellar mass black holes or neutron stars accreting from a companion star), as radio flares best explained by transient jets were detected as SS Cyg moved from quiescence to outburst in the same way as X-ray binaries. The power associated with these jets was analogous to X-ray binary jets. However, Hameury et al. (2017) state that the evolution throughout the outburst observed in cataclysmic variables and that in X-ray binaries may be somewhat different. Indeed, although the flaring/jet emission observed is generally similar to that observed in X-ray binaries, there are a number of differences, notably the persistence of radio emission in the plateau phase (peak of outburst) of dwarf novae outbursts. Further, novalikes, which have persistently high accretion rates have also been shown to have jet emission, e.g. Coppejans and Knigge (2020). Emission corresponding to jets has also been detected from several other cataclysmic variables; see Coppejans and Knigge (2020) for a review. However, one

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system, VW Hyi, has not shown evidence for jets, even though it is very nearby (∼54 pc (Pala 2019)), and the reason for this is unclear. It may be that the jet emission, which is transient, was simply missed. Alternatively, it may be due to the mass of the white dwarf in this system which is significantly less massive than the white dwarfs in the other systems exhibiting jet emission, where the white dwarf in VW Hyi is 0.67 M⊙ and those in the other systems have masses >0.8 M⊙ with the white dwarf in U Gem measuring 1.2 M⊙ (Ritter and Kolb 2011). This lower mass and thus larger radius (see section “The Chandrasekhar Mass”) will influence the accretion rate, where a lower accretion rate implies less accretion power, which could lead to weaker jets or even no jets. Magnetic cataclysmic variables have also been seen to show radio emission reminiscent of jets, but it is not yet clear if this radio emission is coming from a jet or from somewhere else within the system (secondary star, interacting matter between the two stars, etc.) (Coppejans and Knigge 2020).

Binary Components and the Diversity in Accreting White Dwarfs The diversity in the white dwarf masses and magnetic fields, as well as the diversity in the companion star mass and nature (main-sequence or evolved star or compact object) along with the evolutionary stage of the binary, gives rise to a very wide range of accreting white dwarf systems. This diversity is covered in the following sections.

Cataclysmic Variables The term Cataclysmic Variable (CV) describes a wide variety of semi-detached close binary systems, where the primary is a white dwarf, accreting matter from a companion (secondary) star via Roche Lobe overflow (see section “Roche Lobe Overflow and Accretion” and ⊲ Chap. 109, “Black Holes: Accretion Processes in X-ray Binaries”). A block diagram showing the different classes and sub-classes of accreting white dwarfs is given in Fig. 1. CVs are considered non-magnetic when the field is not strong enough to alter the accretion flow, often taken to mean that the accretion disc extends all the way down to the surface of the white dwarf. The sub-classes of CVs were originally defined from the shape of the optical photometric light curves. Nowadays, spectroscopic and polarimetric observations are used to classify the various CVs into sub-classes. Many of the sub-classes can be categorised simply by the mass transfer rate and the type (if any) of outbursts that they exhibit. By plotting the mass transfer rate against the orbital period, CVs can be shown to fall roughly into different categories (Osaki 1996) and shown in Fig. 2. The main features of each category are further described in the following subsections.

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Fig. 1 Different classes of accreting white dwarfs and their sub-classes Fig. 2 Different classes of dwarf novae shown with respect to their approximate mass transfer rate as a function of orbital period. The period gap is indicated as a grey vertical bar and the critical mass transfer rate (see section “Dwarf Novae and Novalikes”) is indicated as a dotted line

Classical Novae Classical novae have been known for hundreds (or maybe thousands) of years as they can be so bright; they were initially mistaken for new (nova) stars appearing in the universe, which explains the origin of their name. Classical novae are now known to be luminous transients, brightening in the optical by up to 9 magnitudes in a few days. This occurs when degenerate shells of accreted material burn explosively (thermonuclear runaway) on the surface of white dwarfs. The speed of the decline phase gives the nova class. These are usually expressed as either t2 or t3 , indicating the time to decay by either two or three magnitudes from the peak magnitude. The classification is then given by very f ast 0. Otherwise, the sudden increase in |M˙ d | will result in further increase of |M˙ d |, which leads then to dynamically unstable mass transfer. Even though realistic and detailed binary calculations must be performed to investigate the stability of mass transfer (e.g., Chen and Han 2008; Woods et al. 2012; Pavlovskii and Ivanova 2015; Ge et al. 2020), polytropes can shed some light on this process in a very simple way and provide a reasonable first-order approach to the problem in some cases (e.g., Hjellming and Webbink 1987; Soberman et al. 1997). More specifically, composite polytropes, which are supposed to reproduce rather well the structure of fully convective low-mass MS stars, provide ζad in very good agreement with those computed from detailed stellar models (Ge et al. 2020). On the other hand, condensed polytropes, which are approximations of red giants, are unable to reproduce the non-ideal gas effect and inefficient convection occurring in detailed stellar models, which implies that condensed polytropes likely underestimated ζad of red giants (Ge et al. 2020). If simple stellar models do not provide realistic estimates, the adiabatic radius–mass exponent needs to be calculated by solving the differential equations for stellar structure. Once ζad has been obtained, it needs to be compared to ζRL in order to evaluate whether mass transfer is dynamically stable or not. The Roche lobe radius–mass exponent ζRL can be expressed as ζRL

∂ ln a = + ∂ ln Md



∂ ln(RRL /a) ∂ ln q



∂ ln q ∂ ln Md

 ,

(11)

where a is the semimajor axis. The three terms in Equation 11 can be written as (Eggleton 1983; Soberman et al. 1997; Woods et al. 2012)

108 Formation and Evolution of Accreting Compact Objects

∂ ln a = ( 1 − αml ) ∂ ln Md ∂ ln(RRL /a) 2 = − ∂ ln q 3

2 q 2 − 2 + q (1 − βml ) q +1



q 1/3 3



3831



−

q , q +1

 1.2q 1/3 + 1/(1 + q 1/3 ) , 0.6q 2/3 + ln(1 + q 1/3 )

(12)

(13)

and ∂ ln q = 1 + ( 1 − αml − βml ) q, ∂ ln Md

(14)

where 0 ≤ αml ≤ 1 corresponds to the fraction of mass lost from the vicinity of the donor in the form of fast isotropic winds, and 0 ≤ βml ≤ 1 corresponds to the fraction of mass lost from the vicinity of the accretor due to isotropic re-emission. Given that the fraction of mass leaving the donor that is effectively accreted is 1 − αml − βml , the fully conservative case corresponds to αml = βml = 0, while αml + βml = 1 represents the fully non-conservative case. In a more general situation, ζRL depends on several other processes, which are related to orbital AML and mass loss from the system (Soberman et al. 1997), such as emission of gravitational waves, magnetic wind braking, tidal interactions, and torques exerted by circumbinary disks. The most important dependencies of ζRL with respect to the stability of mass transfer are those on the mass ratio as well as on the fraction of mass lost from the binary. The relation between ζad and ζRL for a binary composed of a red giant donor with initial mass 1.2 M⊙ and a companion of mass 1.1 M⊙ is illustrated in the lefthand panel of Fig. 1 (taken from a binary model Woods et al. 2012). As mentioned before, the limit for dynamical stability strongly depends on βml . In particular, the greater βml , the smaller ζRL . This means that the greater βml , the better the chances for the red giant donor to remain in hydrostatic equilibrium. If wind mass loss is included in the simulations, ζRL decreases even further for more evolved red giants (i.e., red giants with larges core masses), for a given βml . For instance, when mass loss through winds is not considered, fully conservative mass transfer is dynamically stable only for core masses 0.63 M⊙ , but this limit becomes 0.46 M⊙ , if wind mass loss is included. Even though the fundamental principles related to dynamical stability of mass transfer are well-understood, outcomes of binary models are strongly dependent on the physical assumptions. As mentioned earlier, for a given binary at the onset of mass transfer, ζRL strongly depends on the mass ratio and on the assumed mass loss and orbital AML prescriptions. While ζad depends entirely on the donor mass and its evolutionary status. Thus, for a given binary, it is possible to derive a critical mass ratio separating dynamically stable from unstable mass transfer, as a function of the evolutionary status of the donor. This critical mass ratio is plotted as a function of the donor radius on the right-hand side of Fig. 1, for a donor with mass 5 M⊙ , taken from three different binary models (Chen and Han 2008; Pavlovskii and Ivanova 2015;

βml = 0.0 0.6 βml = 0.2

ζad , ζRL

0.4

βml = 0.4 βml = 0.6

0.2

βml = 0.8

0.0

βml = 1.0 −0.2 Woods et al. (2012) −0.4

1.2 M + 1.1 M 0.2

0.3

0.4

wind mass loss taken into account 0.5

Md,c ( M )

0.6

0.7

4.0

Ge et al. (2020) Pavlovskii & Ivanova (2015)

3.5

Chen & Han (2008)

5M

onset of AGB phase

dynamically unstable

critical mass ratio for dynamical time-scale mass transfer

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D. Belloni and M. R. Schreiber

ζad

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3.0 2.5 2.0 1.5 1.0 1.4

1.6

1.8

2.0

2.2

2.4

2.6

log10 (Rd /R )

Fig. 1 Adiabatic (ζad ) and Roche lobe (ζRL ) mass–radius exponents for a red giant donor of initial mass 1.2 M⊙ with a companion of mass 1.1 M⊙ , as a function of the red giant core mass (Md,c ), taken from a binary model (left-hand panel Woods et al. 2012), and the critical mass ratio separating dynamically stable from unstable mass transfer for a donor of mass 5 M⊙ , as function of its radius (Rd ) during its evolution, taken from three different binary models (right-hand panel Chen and Han 2008; Pavlovskii and Ivanova 2015; Ge et al. 2020). In the computation of ζRL in the left-hand panel, for six different fractions of mass lost due to isotropic re-emission from the vicinity of the accretor (βml ), mass loss through stellar winds is considered (red lines) or not (blue horizontal lines). In the right-hand panel, wind mass loss is not considered in either binary model and fully conservative mass transfer is assumed. It is clear from the left-hand panel that non-conservative (βml > 0) mass transfer is more easily dynamically stable in comparison with the fully conservative case (βml = 0), regardless of whether wind mass loss is taken into account or not. This happens because ζRL becomes smaller as βml increases, which allows mass transfer to be dynamically stable for smaller core mass, i.e., the more mass loss through isotropic re-emission is allowed, the more extended the range of stability. The inclusion of wind mass loss enhances this effect, by decreasing even further ζRL , for core masses greater than ∼0.3 M⊙ , extending in turn even further the range of stability. The right-hand panel, on the other hand, clearly illustrates how the assumptions made in binary models can drastically change the boundary separating dynamically stable from unstable mass transfer. For instance, the solid critical mass ratio strongly increases during the AGB evolution, which is not seen in the other two models. In addition, the dashed critical mass ratio is on average much greater than the other two models

Ge et al. 2020). Even though all binary models show the initial decrease in the critical mass ratio as the donor evolves along the first giant branch (FGB), it is clear from the figure that these models provide qualitative and quantitative different results. In particular, one of them delivers on average a much higher critical mass ratio, in comparison with the other two. In addition, while in two models the critical mass ratio slowly decreases as the donor climbs the asymptotic giant branch (AGB), the other model predicts a rapid increase of the critical mass ratio. The main

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differences in the three works are connected with the mass transfer rate equation (whether it is limited by the local sound speed or not), the radius used to quantify ζad (surface or inner) and the Lagrangian radius adopted to quantify ζRL (inner or outer). Therefore, despite significant progress during the last decade, the limiting mass ratio for the onset of dynamically unstable mass transfer remains quite uncertain. This has significant implications for our general understanding of the formation of close binaries hosting compact objects, as dynamically unstable mass transfer is considered a crucial ingredient in most formation scenarios proposed for these objects. If mass transfer is dynamically unstable, there are mainly two outcomes. If the donor is either an MS star or a degenerate object, then most likely the binary will merge on the dynamical timescale of the donor, with a non-null fraction of the total mass being eventually lost in such an energetic event. On the other hand, if the donor has evolved beyond the MS, common-envelope (CE) evolution will be triggered, resulting in a strong decrease of the orbital period. In fact, CE evolution triggered by dynamically unstable mass transfer represents the standard scenario for the formation of close binaries containing a compact object. Without a proper understanding of the conditions for dynamically unstable mass transfer, it will be impossible to reliably predict the relative numbers of objects as important as SN Ia progenitors and binaries that are main gravitational wave sources.

Thermal Timescale Mass Transfer If the Roche lobe filling donor in a binary can maintain hydrostatic equilibrium, the natural follow-up question is whether it must sacrifice its own thermal equilibrium or not to restrain its surface within its Roche lobe. The thermal equilibrium of a star, i.e., the balance between the nuclear energy production and the atmospheric radiation losses, is disturbed as a response to mass loss. However, as in the case of hydrostatic equilibrium, the donor may be able to re-establish thermal equilibrium, if mass transfer proceeds on a timescale slower than its thermal timescale, i.e., if the donor interior has enough time to relax to thermal equilibrium. Otherwise, mass transfer will be thermally unstable, i.e., it will proceed on the thermal timescale of the donor. In order to verify whether this happens or not, we use the thermal equilibrium radius–mass exponent ζeq , defined by ζeq ≡

d ln Rd

. d ln Md th

(15)

In order to calculate ζeq , the mass–radius relation for stars in thermal equilibrium must be known. If mass transfer is dynamically stable, it will also be thermally stable if ζeq > ζRL . In this case, mass transfer needs to be driven by an external process and proceeds on a timescale different from the dynamical and thermal timescales. On the other hand, if ζad > ζRL > ζeq , mass transfer will be driven by thermal readjustment and proceed on the donor thermal timescale.

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Nuclear or Orbital Angular Momentum Loss Timescale Mass Transfer If mass transfer is dynamically and thermally stable, continuous mass transfer can still be generated by either stellar or binary evolutionary processes. In this case, mass transfer is not self-stimulated as in the previous cases, since mass transfer does not proceed by the virtue of the inability of the donor to remain in either dynamical or thermal equilibrium. Dynamically and thermally stable mass transfer is driven by either nuclear expansion of the Roche lobe filling star or orbital AML. In the former case, the donor keeps filling its expanding Roche lobe, while in the latter case, the Roche lobe and the donor shrink as a response to mass loss. In case mass transfer is driven by nuclear expansion of the donor, mass transfer proceeds at a rate such that Rd ∼ RRL . On the other hand, if mass transfer is driven by orbital AML, then the mass transfer rate is entirely dependent on the strength of orbital AML. The main orbital AML mechanisms driving the evolution of binaries are gravitational wave radiation (GR, e.g., Paczy´nski 1967) and magnetic wind braking (MB, e.g., Huang 1966; Mestel 1968). Using the weak-field approximation of general relativity, it is possible to derive the orbital angular momentum changes due to emission of gravitational waves from two point masses as (Hurley et al. 2002) 

 7 2 e 1 + M M ( M + M ) J˙GR 1 2 1 2 8 = −8.315 × 10−10 yr−1 , (16)  5/2 Jorb a4 1 − e2

where a is the semimajor axis in R⊙ , M1 and M2 are the binary component masses in M⊙ , e is the eccentricity, and Jorb is the orbital angular momentum given by Jorb = a 2



M1 M2 M 1 + M2



2π Porb



1 − e2 ,

(17)

where Porb is the orbital period in years. Emission of gravitational waves acts all the time in every binary. However, from the strong dependence on the orbital separation, only for very close binaries, it will have any impact on the orbital angular momentum evolution. Of course, how close a given binary must be so that GR is non-negligible depends on the component masses and on the eccentricity. While Equation 16 is well-established and gravitational wave radiation is wellunderstood, the same can unfortunately not be said about MB. The main physical processes that drive MB are quite easy to understand, but as usual the devil is in the details. It is clear that a highly ionized wind leaving the star is forced to corotate with the magnetic field of the star out to the Alfvén radius, thereby taking away more angular momentum than the specific angular momentum of the star that consequently spins down. If the star is tidally locked to the orbit, i.e., if the star is synchronized with the orbital motion, the mass loss through winds removes significant amounts of orbital angular momentum, even if the wind mass-loss rate is relatively small. The torques produced by the magnetized winds depend on the

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strength of the magnetic field, the Alfvén radius, the wind mass-loss rate, and the stiffness of the magnetic field at large distances from the star. However, the details of these dependencies are very uncertain and neither observationally nor theoretically well-constrained. Consequently, in the last decades, several attempts to formulate empirical laws or recipes that are applicable to particular cases have been developed, and a large number of MB prescriptions is available on the market (Knigge et al. 2011). Unfortunately, as we will see, for a given fixed star mass, these MB prescriptions provide dramatically different orbital AML rates spanning easily several orders of magnitude. In what follows, we briefly mention some important MB prescriptions but discuss later in more detail their impact on the evolution of accreting compact objects. A MB prescription that is widely used for stars in open star clusters and based on several simplifying assumptions for the winds, magnetic field geometry, and flow acceleration profile was developed by Kawaler (1988) as J˙MB,Kaw = − KW 

M M⊙



Ω s−1

−n/3

1 + 4aK n/3 

1 − 2n/3   M˙ wind R 2−n R⊙ − 10−14 M⊙ yr−1

dyn cm ,

(18)

where aK depends on the scaling between the secondary magnetic field and spin, n depends on the secondary magnetic field geometry, M˙ wind < 0 is the star mass-loss rate through winds, and Ω, R, and M are the star spin, radius, and mass, respectively. Even though the parameter KW depends on the ratio of the wind speed to the escape speed at the Alfvén radius and how the star magnetic field scales with the star radius and spin, it is usually approximated by ∼2.035×1033 (24.93n )(6.63×105 )4n/3 . With aK = 1 and n = 1.5, Equation 18 describes the standard Skumanich law (Verbunt and Zwaan 1981), as orbital AML due to MB becomes proportional to Ω 3 . On the other hand, in the context of accreting compact objects driven by orbital AML, usually the so-called RVJ prescription (Rappaport et al. 1983) is adopted, which is given by J˙MB,RVJ = − 3.8 × 10−30



M g



R⊙ cm

4 

Ω s−1

3 

R R⊙

γMB

dyn cm , (19)

where 0 ≤ γMB ≤ 4 is a free parameter that largely affects how J˙MB varies during the binary evolution. With γMB = 4, Equation 19 describes the standard Skumanich law. Despite the fact that the RVJ prescription can explain several observations of accreting objects, it has serious problems in different contexts, mainly connected with the mass transfer rates it provides and the corresponding evolutionary timescales during CV and LMXB evolution (e.g., Podsiadlowski et al. 2002; González Hernández et al. 2017; Belloni et al. 2020a; Pala et al. 2022). In order to

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overcome part of these difficulties, recently a new convection and rotation boosted (CARB) prescription that enhances orbital AML due to MB was proposed (Van et al. 2019; Van and Ivanova 2019). The CARB prescription can be expressed as (Van and Ivanova 2019)

−1/3 14/3 2  8/3 R Ω⊙ B⊙ J˙MB,CARB = − −M˙ wind 3  −2/3 2 Ω 2 R2 2 , vesc + K22



Ω Ω⊙

11/3 

τconv τ⊙,conv

8/3 (20)

where vesc is the surface escape velocity, τconv is the convective turnover time, B is the surface magnetic field strength, and K2 = 0.07. The main difference between the RVJ and the CARB prescription is that the former is the result of an empirical fitting scheme, while the latter was obtained in a self-consistent physical way, considering wind mass loss, the dependence of the magnetic field strength on the outer convective zone, and the dependence of the Alfvén radius on the donor spin. We illustrate in Fig. 2 the orbital AML rates provided by the three MB prescriptions mentioned above. The evolutionary sequences have been computed by us using the Modules for Experiments in Stellar Astrophysics (MESA) code (Paxton et al. 2011, 2013, 2015, 2018, 2019), in which we evolved a Roche lobe filling star with initial mass of 1 M⊙ , orbiting a point-mass companion of mass 1.4 M⊙ . In the simulations, we take into account stellar wind mass loss, adopting the Reimers (1975) prescription with the scaling factor equal to 1, and assume βml = 0.8 and αml = 0. For MS masses 0.4 M⊙ , the CARB prescription clearly provides higher orbital AML rates than the RVJ and the Kawaler prescriptions. For MS masses greater than that, the CARB, RVJ, and Kawaler prescriptions provide comparable orbital AML rates if nK = 1.5 and γMB = 0. Finally, GR is typically much weaker than any of these prescriptions, expect for the Kawaler recipe with n  1. In addition to GR and MB, there are other sources of orbital AML acting on interacting binaries that arise as a consequence of mass transfer. For this reason, this type of orbital AML is called consequential AML. Among the several mechanisms proposed for consequential AML, the most important are a fast isotropic wind from the vicinity of the donor, isotropic re-emission from the vicinity of the accretor (King and Kolb 1995), a circumbinary disk (Spruit and Taam 2001), and winds from the accretion disk (Cannizzo and Pudritz 1988). Consequential AML is by definition an orbital AML mechanism that is mass-transfer-dependent, i.e., it is null in the absence of mass transfer. It is usually written in a simple parameterized form as J˙CAML M˙ d = ν , Jorb Md

(21)

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1038

−J˙ (dyn cm )

36

10

CARB (subgiant) u

CARB (M S)

1037

K waler Ka ((n = 1.5)

= 0)) RVJ (γMB

B= RVJ (γγM

35

10

RVJ (γMB = 2) Kawaler (n n = 1.25)

4)

1034 1033 Gravitational Wave Radiation

1032 0.1

0.2

0.3

0.4

0.5 0.6 M (M )

0.7

0.8

0.9

1.0

Fig. 2 Comparison of the orbital AML rates (−J˙) due to GR and due to some MB prescriptions, during the evolution of a low-mass Roche lobe filling star, as a function of its mass (M). All tracks have been computed by us with the MESA code, assuming solar metallicity, wind mass loss (Reimers parameter equals to 1), βml = 0.8, αml = 0, a point-mass accretor with initial mass of 1.4 M⊙ , and the initial mass of the donor is 1.0 M⊙ . Each track represents the evolution from the onset of Roche lobe filling to the moment when the star becomes fully convective (when MB is supposed to cease or at least significantly decrease). The dot-dashed red lines correspond to the CARB prescription (Van and Ivanova 2019), for which we chose two different initial orbital periods, namely 12 h to illustrate the case of an unevolved MS star (helium-core mass equals to zero), and 4 days to illustrate the subgiant case (helium-core mass ∼0.1 M⊙ ). The solid blue lines show the RVJ prescription (Rappaport et al. 1983), for three different values of γMB , and in all these cases, we chose an initial orbital period of 12 h, corresponding in turn to unevolved MS stars. The Kawaler (1988) prescription is marked by the long-dashed green lines, for three different values of n, assuming in all three sequences aK = 1, for which we also chose an initial orbital period of 12 h, corresponding to the unevolved MS star case. Finally, the short-dashed black lines correspond to the strength of GR in each of the evolutionary sequences, which can be easily associated with them by comparing the mass at which the MB becomes inefficient, i.e., the lowest mass in each track. It is clear that the CARB recipe provides on average higher orbital AML rates than the RVJ and the Kawaler prescriptions, the latter for n  1.5, especially for masses 0.4 M⊙ . On the other hand, the CARB, RVJ, and Kawaler prescriptions provide comparable orbital AML rates for larger masses, if nK = 1.5 and γMB = 0. In addition, the Kawaler prescription is much more sensitive to the chosen parameters, in comparison with the RVJ prescription, as it provides much more different orbital AML rates, for small variations of nK . Moreover, except for the Kawaler prescription with n  1, GR in all evolutionary sequences contributes only negligibly to the total orbital AML. Finally, regarding the type of the star in the CARB tracks, we can see that the orbital AML rate is initially higher for a more evolved star but decreases as the star mass decreases, resulting in a weaker MB at masses 0.4 M⊙ , in comparison with an unevolved MS star

where ν depends on the binary properties, including perhaps the mass transfer rate itself, and is the parameter characterizing the strength of consequential AML. Its form depends entirely on the mechanism driving orbital AML.

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In the case of a circumbinary disk, ν is given by (Spruit and Taam 2001) νCB = γ δml ( 1 + q ),

(22)

where δml is the fraction of the mass lost from the binary components that feeds the circumbinary disk, and the parameter γ takes into account the characteristics of the circumbinary disk as a function of time and depends on the inner edge of the circumbinary disk, the binary semimajor axis, the viscous timescale at the inner edge of the circumbinary disk, and the mass of the circumbinary disk. In the case of mass loss from the binary, ν may correspond to the specific angular momentum of the accretor (isotropic re-emission) or the donor (fast isotropic wind), given by (King and Kolb 1995) νml,a = βml



q2 1+q



,

νml,d = αml



1 1+q



.

(23)

Fast isotropic winds and isotropic re-emission may also generate additional orbital AML due to friction arising from the interaction of the ejected material and the accretor/donor. This frictional AML then strongly depends on the velocity of the ejected material and on the orbital velocity of the accretor/donor as well as on the geometrical cross-section of the accretor/donor (Shara et al. 1986; Schenker et al. 1998; Schreiber et al. 2016; Sparks and Sion 2021). We have already illustrated in Fig. 2 that MB typically provides orbital AML rates several orders of magnitude higher than those expected from GR. The rates predicted by consequential AML may be higher or lower in comparison with MB, depending on the form of the two types of orbital AML. For instance, frictional AML due to isotropic winds and/or isotropic re-emission is typically negligible, unless the expansion velocity of the ejected material is very small (Liu and Li 2019). The same also occurs for consequential AML due to mass loss (isotropic winds or isotropic re-emission), which typically provides rates smaller than those related to either MB or GR alone. On the other hand, consequential AML due to a circumbinary disk can be the dominant source of orbital AML depending on the parameters of the disk and the rate at which it is fed (Willems et al. 2005; Ma and Li 2009). So far we have briefly described the current understanding of the different processes that can drive mass transfer in binaries. This included the stability of a given binary against mass transfer on the dynamical and thermal timescales of the donor as well as mass transfer driven by the nuclear evolution of the donor and orbital AML. The largest uncertainties in current models are probably related to the conditions separating dynamically stable from dynamically unstable mass transfer, the strength and parameter dependencies of orbital AML through magnetic braking, and the processes that drive consequential AML. On the basis of the above-described knowledge of mass transfer in binaries, formation channels for the different types of accreting compact binaries have been developed in the last decades which we will review in the following section.

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Formation Channels Most accreting compact objects form from the evolution of zero-age MS–MS binaries. Some may form from stellar mergers in hierarchical systems, i.e., from triples, quadruples and, eventually, higher-order systems. Dynamical interactions, which are common in high-density environments such as the central parts of dense star clusters, could also lead to the formation of a sufficiently important fraction of accreting compact objects, especially for those originating from highmass stars. While for some specific systems, and some particular types of accreting compact objects, the triple and/or the dynamical scenario is required to explain their properties, in most cases the contribution from these two scenarios is expected to be much smaller than that of binary evolution. This is simply because of the lower frequency of triples and higher-order hierarchical systems in comparison to binaries (e.g., Moe and Di Stefano 2017) and because strong dynamical interactions only occur frequently in dense star clusters. In what follows, we therefore mainly focus on accreting compact objects formed through binary evolution but add a few comments on additional formation channels through dynamical interactions at the end of this section. The current small orbital separations of close binaries in which a compact object accretes from a non-degenerate low-mass companion, i.e., CVs and LMXBs, imply that these systems are currently much smaller than the progenitor of the compact object was as a giant. Consequently, the orbit of the binary must have been significantly reduced during the formation of the compact object, most likely through CE evolution generated by dynamically unstable mass transfer (Webbink 1975; Paczy´nski 1976). The current orbital periods of most wide binaries in which a WD accretes from the winds of an evolved low-mass red giant, i.e., most S-type SySts, are significantly longer than those of post-CE binaries but short enough that mass transfer must have occurred when the WD was formed. Therefore, in these cases, the most likely scenario is that the orbit expanded during the formation of the WD, which happens when the mass transfer is dynamically stable and most likely non-conservative (Webbink 1988). SyXBs are similar to SySts, in the sense that they are also wide-orbit binaries in which the compact object accretes from the wind of an evolved low-mass red giant. However, their compact objects are NSs, which implies that stable non-conservative mass transfer cannot be the formation channel, because the required mass ratio of the zero-age MS–MS binary implies that the non-degenerate companions should be high-mass stars, which is not the case. A possible formation scenario for these systems could be the formation of a long-period post-CE binary, hosting a helium star paired with a low-mass star, followed by either electron-capture or core-collapse supernova leading to the NS (Lü et al. 2012; Yungelson et al. 2019). Regarding compact objects accreting from high-mass non-degenerate stars, i.e., HMXBs, those in wide orbits (e.g., Be-HMXBs) are most likely formed through an episode of dynamically stable non-conservative mass transfer, while those having orbital periods of only a few days (e.g., sg-HMXBs) seem to have formed through

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CE evolution (Tauris et al. 2017). On the other hand, NSs/BHs accreting from the strong and dense winds of Wolf–Rayet stars, i.e., WR-HMXBs, require two episodes of mass transfer, one to form the accreting compact object and the other one to form the Wolf–Rayet star. Even though the first episode of mass transfer is most likely dynamically stable non-conservative mass transfer (Qin et al. 2019), there is evidence that in some WR-HMXBs the second episode of mass transfer was CE evolution, while others can be more easily explained when the second episode was dynamically stable non-conservative mass transfer (van den Heuvel et al. 2017). Finally, in those very close binaries in which the compact object is accreting from a Roche lobe filling WD or semi-degenerate helium-rich star, i.e., AM CVns and UCXBs, two episodes of mass transfer are needed, and at least one of these episodes must have been CE evolution. More specifically, these systems may form either through two CE phases, or through dynamically stable non-conservative mass transfer followed by CE evolution, or finally through CE evolution followed by dynamically stable non-conservative mass transfer (Solheim 2010; Nelemans et al. 2010). In what follows, we will in more detail address the main formation channels of accreting compact objects, which are illustrated in Fig. 3.

Common-Envelope Evolution When the more massive star of a zero-age MS–MS binary evolves off the MS and fills its Roche lobe, it will give rise to dynamically unstable mass transfer, if ζad < ζRL . In this case, the mass-loss timescale becomes so short that the donor cannot remain within its Roche lobe, which leads to the formation of a CE around the dense giant core and the MS star. Even though a CE event in many situations is triggered by dynamically unstable mass transfer, there are also other mechanisms able to do that, such as the Darwin instability (e.g., Hut 1980), which occurs if the future donor angular momentum at synchronism exceeds one-third of that of the orbit. The Darwin instability corresponds to a tidal instability. It occurs when not enough orbital angular momentum is extracted from the orbit to maintain the star synchronized as it evolves. Tidal forces will spin up the star by removing orbital angular momentum, resulting in a binary with smaller orbital separation and in turn even less orbital angular momentum. This implies that the star will need even more orbital angular momentum to stay synchronized with the orbital motion. This leads to a runaway process of orbital decay and ultimately a CE event. Because of drag forces during CE evolution, the MS star and the core spiral in toward their common center of mass and the CE is expelled. In this process, a large fraction of the initial orbital energy and orbital angular momentum is lost with the envelope, which leads to a post-CE binary with an orbital period orders of magnitude shorter than that of the initial MS–MS binary. In case dynamically unstable mass transfer was generated from a massive star to its companion, the post-CE binary hosts a helium star, which is the progenitor of the compact object, and the binary separation may increase due to a natal kick during the collapse of the helium star.

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zero-age main-sequence–main-sequence binary Roche lobe overflow when the more massive star expands

ζad < ζRL dynamically unstable

αml

common-envelope evolution

nuclear/thermal time-scale

ζad > ζRL dynamically stable

βml

increase Porb s/decre

δml

ases

envelope vanishes

P orb de

αCE αth αrec

creases

helium star white dwarf

core-collapse or electron-capture supernova Porb and e increase secondary evolves to a red giant

secondary evolves to a red giant

symbiotic star angular momentum loss and/or nuclear evolution of the secondary

high-mass companion

black hole or neutron star low-/intermediate-mass companion

angular momentum loss and/or nuclear evolution of the secondary

accretion from the circumstellar disk of a Be secondary or secondary evolves to a supergiant

symbiotic X-ray binary

Be/supergiant high-mass X-ray binary

low-mass X-ray binary

cataclysmic variable

Porb decreases detached millisecond pulsar binary

dynamically stable/unstable Roche lobe overflow

Wolf-Rayet high-mass X-ray binary white dwarf + helium star or white dwarf + white dwarf angular momentum loss

AM CVn

ultra-compact X-ray binary neutron star/black hole binary

Fig. 3 Main formation channels leading to accreting compact objects. Starting from a zeroage MS–MS binary, when the more massive MS star evolves and fills its Roche lobe, mass transfer stars. Mass transfer is dynamically stable if the adiabatic radius–mass exponent (ζad ) is greater than the Roche lobe radius–mass exponent (ζad ), and unstable otherwise, leading to CE evolution. During dynamically stable mass transfer, the orbital period increases or decreases as a response to mass transfer, and the orbital period at the end of mass transfer depends on the binary properties at the onset of Roche lobe filling and on the fraction of the transferred mass that is lost (αml + βml + δml ) during the event. On the other hand, if CE evolution happens, drag forces remove orbital energy, which is used with a certain efficiency (αCE ) to eject the envelope, potentially together with a fraction of other sources of energy, such as recombination energy (αrec ) and/or thermal energy (αth ). The outcome of CE evolution is a binary with a much shorter orbital period. Compact objects in close orbits accreting from a Roche lobe filling nondegenerate low-mass companion (i.e., CVs and LMXBs) are believed to form during one episode of CE evolution. NSs accreting from the winds of low-mass red giants in wide orbits (i.e., SyXBs) are also expected to form in an episode of CE evolution. On the other hand, WDs in wide orbits accreting from the winds of low-mass red giants (i.e., SySt) are expected to form through an episode of dynamically stable non-conservative mass transfer. Regarding NSs or BHs accreting from high-mass companions (i.e., HMXBs), they can be formed through dynamically stable nonconservative mass transfer or CE evolution. Finally, compact objects accreting from Roche lobe filling WDs or semi-degenerate helium-rich stars (i.e., AM CVns and UCXBs) are formed through two episodes of mass transfer, at least one of them being CE evolution

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Despite a lot of effort and (computational) resources that are spent toward a better understanding of CE evolution, we still struggle to identify and describe some of the main physical processes involved in this crucial evolutionary phase. The main reason for this failure lies in the fact that modeling CE evolution is very demanding from a computational point of view, since it involves a complex mix of physical processes operating over a huge range of scales (Ivanova et al. 2013). In the absence of reliable simulations that cover the full complexity of CE evolution, a very simplistic approach is frequently used to overcome this problem and to make predictions for populations of post-CE binary characteristics. These simple equations based on energy and angular momentum conservation provide useful constraints on the outcome of CE evolution.

The Energy Budget of Common-Envelope Evolution In the so-called energy formalism, the outcome of CE evolution is usually approximated by the balance between the change in the orbital energy and the envelope binding energy. This energy conservation equation is parameterized with a parameter 0 ≤ αCE ≤ 1, which corresponds to the efficiency with which orbital energy is used to eject the envelope. In other words, αCE represents the fraction of the difference in orbital energy (before and after the CE phase) that unbinds the envelope, i.e., Ebind = αCE ∆Eorb = − αCE



G Md,c Ma G Md M a − 2 af 2 ai



,

(24)

where Ebind is the envelope binding energy, Eorb is the orbital energy, Md,c is the core mass of the donor, ai is the semimajor axis at onset of CE evolution, and af is the semimajor axis after CE ejection. The binding energy is usually approximated by Ebind = −

G Md (Md − Md,c ) , λ Rd

(25)

where λ is the binding energy parameter, which depends on the structure of the donor (Dewi and Tauris 2000; Claeys et al. 2014). In case thermal and/or recombination energies stored inside the envelope are assumed to help in ejecting the envelope, the binding energy equation is usually written as Ebind = −



Md Md,c

Gm dm + αth r(m)



Md Md,c

εth (m) dm + αrec



Md

εrec (m) dm, (26)

Md,c

where εth and εrec are the specific thermal and recombination energies and αth and αrec are the fractions of the thermal and recombination energies that are assumed to contribute to unbinding the envelope. Thermal energy is the thermodynamic internal energy of the CE, which is constrained by the virial theorem, and can be

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released and partially used to help in the CE ejection. Recombination energy is stored in ionized helium or hydrogen within the CE. These ions can recombine in the expanding layers of the gaseous CE, once it has sufficiently cooled and expanded, thereby releasing energy (Lucy 1967) that can contribute to unbinding the CE. The binding energy parameter λ can be computed by equating Equations 25 and 26. When αth > 0 and/or αrec > 0, additional sources of energy contribute to the ejection of the CE, which implies that less orbital energy is needed to unbind the envelope. Deriving constraints on the values of αCE , αth , and αrec has been a focus of close compact binary research in the last decades. Unfortunately, several slightly different CE prescriptions are available, which needs to be taken into account when comparing the results of different studies. In what follows, we briefly describe the constraints obtained so far for binaries hosting WDs, for which the progenitors are intermediate-mass MS stars, and for those hosting NSs or BHs, which originate from the evolution of high-mass MS stars. Regarding low-/intermediate-mass stars, the best way for constraining the CE evolution is by using samples of detached WD–MS post-CE binaries because of the large number of known systems and because it is relatively easy to characterize them (Nebot Gómez-Morán et al. 2011). Reconstruction of the evolution of observationally characterized post-CE binaries consisting of WDs with M-type companions suggests that CE ejection is rather inefficient, with αCE ∼ 0.2 − 0.3 (Zorotovic et al. 2010). Comparisons between predictions from binary population synthesis with observations reached similar conclusions for this type of post-CE binary (Toonen and Nelemans 2013; Camacho et al. 2014; Cojocaru et al. 2017). Recently, observational surveys have become capable of identifying close WD binaries with MS companions more massive than M-type MS stars (spectral types A, F, G, and K), and early results indicate the existence of a population of postCE binaries that can be reproduced with the same small CE efficiency (Parsons et al. 2015; Hernandez et al. 2021). However, for some of these systems, a small fraction of recombination energy seems to be required to contribute to CE ejection (Zorotovic et al. 2014). Close binaries hosting hot subdwarf B stars (i.e., helium-core-burning stars with very thin hydrogen-rich envelopes), mostly paired with WDs but some also with M-type MS stars, are also reasonably good targets for estimating the efficiency of CE ejection, as CE evolution is certainly involved in their formation. Contrary to WD–MS post-CE binaries, results from binary population synthesis of hot subdwarf B stars indicate that the observations are better reproduced with αCE ∼ 0.75 and a large fraction (∼0.75) of the internal energy (thermal plus recombination) contributing to expelling the envelope (Han et al. 2002, 2003), which indicates that both CE ejection and the conversion of thermal and recombination energies into kinetic energy are efficient processes. However, given that the sample of WD–MS binaries is cleaner in the sense that only one phase of mass transfer is involved, the observational constraints indicating a small value for the CE efficiency should be considered as being stronger. In addition, we have to be aware that the energy prescription for CE evolution is too simplistic, and several unknown physical

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processes are not properly taken into account, which might affect the constraints derived from observations of different systems on the CE efficiency. With respect to progenitors of accreting compact objects hosting NSs and BHs, the situation is more complicated because we know less about CE evolution in this mass range (Ivanova et al. 2013), and the situation might be quite different from the previous case. The main reason for these expected differences is that CE evolution leading to WD–MS post-CE binaries is generated by dynamically unstable mass transfer from red giant donors with a convective envelope (Taam and Sandquist 2000), while for high-mass stars with solar metallicity the onset of Roche lobe filling usually happens when the donor is in the Hertzsprung gap and has a radiative envelope. In addition, metallicity has a strong impact on the evolution of high-mass stars prior to the onset of Roche lobe overflow, which is independent of the effect of metallicity-dependent winds, thereby altering the evolutionary stage at which Roche lobe filling occurs (Klencki et al. 2020). In most cases, this causes λ to be far lower for high-mass stars than for intermediate-mass stars (Kruckow et al. 2016), implying that in several situations, there would be apparently not enough energy available to eject the CE. For a long time, this has been believed to be the case for BH-LMXBs, which would require an abnormally high efficiency for the envelope ejection in binary models (e.g., Yungelson and Lasota 2008), since it is very difficult for the binary hosting a Roche lobe filling high-mass star paired with a much less massive companion to eject the CE at the expense of only orbital energy. However, more recent calculations have shown that this is not an actual issue in the formation of BH-LMXBs, since they could be produced without invoking unrealistically high CE efficiencies (Wiktorowicz et al. 2014). The real problem arises when trying to reproduce the donor mass distribution in this population. Despite the fact that it is possible to reproduce individual BH-LMXBs in binary models, we cannot yet reproduce the properties of the entire population with just one model (Wiktorowicz et al. 2014). We will come back to this issue later. Regarding SyXBs, in the absence of other sources of energies, in population synthesis aiming at explaining their observational properties, αCE needs to be as high as 4 (Yungelson et al. 2019), which is unrealistically high. This result could suggest that there are other sources of energy that are required to help to expel the envelope or that these X-ray binaries do not form through standard CE evolution. For instance, they could instead be preferentially formed from accretion-induced collapses of a massive oxygen–neon–magnesium WD (e.g., Hinkle et al. 2006). Another possibility, perhaps more realistic, is that the uncertainties and simplifications involved in stellar and binary evolution calculations, for example mixing in stellar interiors, core-collapse/electron-capture supernova, and CE evolution, are the main reason for the problems in reproducing these systems, as well as BH-LMXBs (e.g., Belczynski et al. 2021).

Common-Envelope Evolution from Hydro-dynamical Simulations Despite the above-described attempts to constrain αCE , αth , and αrec , it seems unlikely that there is a universal recipe within the simplistic energy formalism

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able to account for all types of accreting compact objects. In the case of low-/intermediate-mass stars, evidence is growing evidence that the efficiency of expelling common envelopes is rather low, and overall the energy formalism delivers reasonable results. In contrast, it is very difficult to explain the properties of accreting compact objects coming from high-mass stars based on the energy balance of CE evolution, regardless of the assumed values for the CE evolution parameters. This difficulty must to some degree arise from our inability to understand the role played by other sources of energies acting together with orbital energy, as well as correctly computing the CE binding energy in an unbiased way. CE evolution can be divided into several subsequent phases, which helps to better understand why this event is so complicated to be modeled. Most of the problems arise from the fact that each of these phases occurs at a particular timescale, involving a particular physical process (e.g., Podsiadlowski 2001). The first phase is the loss of co-rotation, which can last hundreds of years, and corresponds to very small changes in the orbital separation in comparison with the orbital period. During this phase, the accretor orbits either outside the future CE or inside the CE outer layers (e.g., Ivanova and Nandez 2016). The second phase is called plunge-in, which corresponds to the rapid spiral-in with huge changes in the orbital separation. During this phase, the accretor plunges inside the CE, and the orbital energy is transferred to the CE, driving its expansion, in case there is enough energy available for that. At the end of this phase, most of the CE mass is outside the orbit of accretor and the core of the donor (e.g., Ivanova and Nandez 2016). During the third phase, when the CE is well-extended, a self-regulating spiral-in occurs on the thermal timescale of the CE, during which energy released due to the spiral-in is transported to the CE surface and subsequently radiated away. This phase corresponds to small changes in the orbital energy (e.g., Ivanova and Nandez 2016). CE evolution terminates at the end of the self-regulating spiral-in phase with either the ejection of the CE or the accretor or the core of the donor filling its Roche lobe. The latter most likely result is a merger but could also provide another pathway for CE ejection (e.g., Podsiadlowski et al. 2010). We illustrate CE evolution in the left-hand panel of Fig. 4, where we show the evolution of the orbital separation from just before the plunge-in phase until just after the self-regulating spiral-in, for two models taken from a study based on a three-dimensional smoothed particle hydrodynamics code (Ivanova and Nandez 2016). In these simulations, the authors chose a low-mass red giant donor with a mass of 1.8 M⊙ , a core mass of 0.318 M⊙ , and a radius of 16.3 R⊙, and several companion masses. The figure clearly illustrates that there is a huge orbital shrinkage during the plunge-in phase until the onset of the self-regulating spiral-in phase, which is precisely what the energy formalism tries to reproduce. However, in those cases that avoid merger, the CE is not always effectively ejected, which represents a long-standing problem in numerical simulations of CE evolution (e.g., Ohlmann et al. 2016; Soker 2017). Given the above-mentioned inefficient ejection of the CE predicted in simulations, there should exist at least one energy source, perhaps more, in addition to orbital energy, that would be able to expel the remaining bound matter (e.g.,

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end of the plunge-in phase

0.0

−0.5

onset of the self-regulating spiral-in phase

0.6

0.4

ation e nergies recomb in

log10 (a/R )

0.2 M

onset of the plunge-in phase 0.5

0.8

p

l plus

0.1 M

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fraction of the CE mass that is ejected

Ivanova & Nandez (2016)

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y erg en l a nti ote

Sand et al. (2020) AGB donor: 0.97 M point-mass companion: 0.49 M

0.2

−1.0 540

560

580

600

620

time ( days )

640

660

0.0 0

500

1000

1500

2000

2500

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Fig. 4 Change in the orbital separation (left-hand panel Ivanova and Nandez 2016) and envelope mass (right-hand panel Sand et al. 2020) through time during CE evolution, taken from two different CE evolution models. In the left-hand panel, the onset of the plunge-in phase (when ( | a˙ | Porb ) / a becomes greater than 0.1), the end of the plunge-in phase (when ( | a˙ | Porb ) / a becomes smaller than 0.1), and the onset of the self-regulating spiral-in (when | ( E˙ orb Porb ) / Eorb | becomes smaller than 0.01) are indicated with crosses. The transition between the end of the plunge-in phase and the onset of the self-regulating spiral-in is not sudden in these simulations, although it lasts for only a few days. In the model with companion mass of 0.1 M⊙ , there is not enough orbital energy available to expel the CE, and the binary is expected to merge during the selfregulating spiral-in phase. However, in the model with companion mass of 0.2 M⊙ , even though orbital energy is transferred to the CE, it is not enough to entirely eject the CE during the selfregulating spiral-in phase. Despite the fact that a strong reduction in the orbital separation occurs, like in the 0.2 M⊙ model, in most numerical simulations, the CE is not entirely ejected, which indicates that other sources should contribute to the CE ejection together with orbital energy. In the right-hand panel, there is a comparison between the case without internal energy and the case with internal energy (thermal plus recombination), which has been widely proposed as the key source of energy usually missing in the simulations. It is clear in this simulation that the CE can be ejected with the help from internal energy. However, there are strong physical arguments suggesting that this energy would be simply radiated way, not actually contributing to the CE ejection. If confirmed beyond doubts, other sources of energy or transfer mechanisms must be playing a role and should be further explored as alternatives to recombination energy

Soker 2017). It has been argued for a long time that thermal energy and mainly hydrogen and helium recombination energy could solve this problem (e.g., Webbink 2008; Nandez et al. 2015; Ivanova 2018). The impact of including thermal and recombination energies is illustrated in the right-hand panel of Fig. 4, which shows the evolution of the unbound mass fraction through time, taken from a numerical simulation with a moving-mesh hydrodynamics code (Sand et al. 2020). In this simulation, the donor is on the AGB undergoing helium-shell burning and no thermal pulses, with a mass of 0.97 M⊙ and a core mass of 0.545 M⊙ . Almost the

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entire CE mass is unbound when the stored internal (thermal plus recombination) energy is used, most of which is only released at rather late times, when the expanding CE sufficiently cools down. This is not the case when only the potential energy contributes to the binding energy, since ∼10% of the CE mass is still inside the orbit of the donor core and the companion, after the plunge-in phase. No further dynamical spiral-in is expected, because of the low density of the remaining envelope and the co-rotation of the material, avoiding in turn any drag force. The example above, together with other simulations, provides support to the claim that internal (mainly recombination) energy might be a key ingredient in CE evolution. On the other hand, most of the available recombination energy could be simply radiated away (e.g., Soker et al. 2018; Grichener et al. 2018), since the optical depth is expected to be low when recombination occurs, allowing radiation to more easily escape. In addition, despite the fact that the amount of available recombination energy depends on the core definition, it is expected to be smaller in high-mass stars than in intermediate-mass stars. Therefore, some simulations suggest that recombination energy is unlikely to help in the removal of the CE in this mass range (Ricker et al. 2019). In any event, it is widely accepted by now that only dynamical spiral-in is most likely not enough to completely remove the CE. In case recombination energy is not significantly helping, other sources of energy would be needed (e.g., Soker 2017). These additional contributions could come from nuclear energy (Podsiadlowski et al. 2010), accretion energy (Voss and Tauris 2003), dust-driven winds (Glanz and Perets 2018), interaction of the binary (core of the donor + companion) with a circumbinary disk (Kashi and Soker 2011), large-amplitude pulsations (Clayton et al. 2017), or jets launched by the companion as it accretes mass from the circumbinary envelope when it is about to exit the CE from inside (Soker 2017; Moreno Méndez et al. 2017; López-Cámara et al. 2019, 2020, 2022). Even though there are several mechanisms available, they have been poorly explored in hydrodynamical simulations, and it is still not clear which one is dominant, if any at all, and under which conditions. This means that CE evolution is a subject far from being well-understood, and, hopefully, in the next years, further hydro-dynamical simulations will shed more light on this extremely important phase for the formation of accreting compact objects.

Dynamically Stable Non-conservative Mass Transfer Even though the energy formalism is successful to some extent in avoiding the messy physics involved in the several phases of CE evolution, it fails to reproduce some observed systems, in particular double-helium WD binaries. Explaining these systems with two consecutive CE events requires that energy is generated during CE (which implies that the energy conservation law is violated), or at best, that an unknown source of energy, much greater than the orbital energy, is contributing to expelling the envelope (which can be considered unrealistic). To solve this problem, an alternative but similarly simplistic formalism was invented based on conservation of angular momentum, which is usually called

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angular momentum (or γ ) formalism (Nelemans et al. 2000; Nelemans and Tout 2005). Although this new approach could somehow work mathematically, it does not provide a physical explanation for the required CE phases without spiral-in (e.g., Webbink 2008; Ivanova et al. 2013). We believe that most systems for which no reasonable solutions in the framework of CE energy balance exist are actually not formed through CE evolution, but rather dynamically stable non-conservative mass transfer. Indeed, there is strong theoretical evidence that an increase in the orbital separation can be reached during an episode of dynamically stable non-conservative mass transfer on a thermal and/or nuclear timescale, which can potentially reproduce otherwise inexplicable systems. In what follows, we discuss in more detail systems that may form through this dynamically stable non-conservative mass transfer channel.

Low-/Intermediate-Mass Stars There are several types of binaries hosting (proto) WDs with orbital periods longer than ∼100 days. In some of them, it is clear that some sort of interaction in their history must have occurred, because of observed chemical anomalies. For instance, barium stars, which are paired with WDs, are F-/G-type MS stars or G-/K-type red giants exhibiting strong absorption lines of ionized barium in their spectrum as well as of other s-process elements (e.g., Jorissen et al. 2019; Escorza et al. 2019), which could not have been synthesized by them. In a similar way, carbon-enhanced metalpoor stars show abundances of s-process elements (e.g., Jorissen et al. 2016; Hansen et al. 2016) that cannot be explained in the context of single star evolution. S-process elements are produced during the thermally pulsing AGB phase (e.g., Käppeler et al. 2011), and it is therefore widely accepted that these elements were transferred to the barium stars and carbon-enhanced metal-poor stars via stellar winds or dynamically stable Roche lobe overflow, when the WD progenitor was at this evolutionary stage. Other types of binaries having comparable orbital periods include post-AGB binaries, with orbital periods in the range of ∼100–2500 days (Oomen et al. 2018). In addition, some blue stragglers, which are typically found in old star clusters and correspond to MS stars bluer, brighter, and more massive than those around the cluster turnoff point, are in binaries with orbital periods between ∼100 and ∼3000 days. While some hot subdwarf B stars are members of close binaries, a certain fraction of these stars are members of binaries with rather wide orbits. Hot subdwarf B stars are post-FGB binaries that must have formed when their progenitors filled their Roche lobe just before reaching the tip of the FGB. The typical orbital periods for wide binaries containing hot subdwarf B stars range from ∼700 to ∼1300 days. Moreover, most S-type SySts have orbital periods between ∼200 and ∼1500 days. In some cases, there is evidence for negligible mass accretion during these episodes of mass transfer, such as for hot subdwarf B stars (Vos et al. 2018), while in other cases, such as for barium stars and carbon-enhanced metal-poor stars, only a non-negligible amount of mass accretion can explain their chemical properties (e.g., Miszalski et al. 2013; Abate et al. 2015a,b). All these binaries, in addition to having orbital periods usually longer than ∼100 days, have in many cases non-null eccentricities. We show the orbital period

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Fig. 5 Diagram depicting the orbital period (Porb ) versus eccentricity for several types of low-/intermediate-mass post-mass-transfer binaries with orbital period longer than ∼100 day, namely barium star binaries (Van der Swaelmen et al. 2017), blue straggler binaries (Carney et al. 2001; Mathieu and Geller 2009), post-AGB binaries (Oomen et al. 2018), s-process-polluted carbon-enhanced metal-poor star (CEMP-s) binaries (Jorissen et al. 2016; Hansen et al. 2016), wide-orbit hot subdwarf B binaries (Vos et al. 2015; Otani et al. 2018), S-type SySts (Mikołajewska 2003; Brandi et al. 2009; Fekel et al. 2007, 2008; Hinkle et al. 2009; Fekel et al. 2010), and R Aqr, which is the only D-type SySt with radial velocity data suitable for orbital determination (Gromadzki and Mikołajewska 2009). The hatched regions correspond to the location of postCE binaries (Porb  100 days) and of systems formed without Roche lobe filling (Porb  2000 days), taken from a binary model (Belloni et al. 2020b). It is clear from the diagram that there is a significant fraction of systems in eccentric binaries with orbital periods between ∼100 and ∼2000 days, which is precisely between the region occupied by post-CE binaries and the region occupied by systems formed without Roche lobe filling. Therefore, most of these systems apparently cannot be explained by CE evolution, nor by the lack of Roche lobe filling. Indeed, the overwhelming majority of these systems are most likely formed during dynamically stable non-conservative mass transfer, accompanied by an eccentricity pumping mechanism that would efficiently work against tidal circularization for some system, but not for all of them, as it must also account for those systems in circular orbits

versus eccentricity diagram for them in Fig. 5, where we also added a hatched region indicating the location of the post-FGB and post-AGB binaries formed without Roche lobe overflow (taken from a binary model Belloni et al. 2020b). We can see from the figure that those systems with orbital periods longer than ∼2000 days fit reasonably well within the expected region for WD binaries where the WD progenitor never filled its Roche lobe. The same certainly holds for most D-type SySts, which have long orbital periods (40 years), although only for one system the orbital period has been accurately measured. The mass exchange that is required to explain the formation of barium stars and s-process-polluted carbon-enhanced

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metal-poor stars with periods exceeding ∼2000 days has likely been driven by efficient wind accretion, instead of Roche lobe overflow. In contrast, systems with orbital periods shorter than ∼2000 days must have experienced Roche lobe overflow. Given their current orbital period, the progenitors of the WD (or hot subdwarf B stars) in these systems must have filled their Roche lobes at some point along their evolution. It is difficult to explain the periods of these systems as a result of CE evolution, since orbital periods of post-CE binaries are usually shorter than ∼100 days (Nie et al. 2012; Zorotovic et al. 2014) and often just a few hours (Nebot Gómez-Morán et al. 2011). In addition, even though some of these binaries are on circular orbits, many others have eccentric orbits, which is not expected for post-CE binaries, since tidal forces during CE evolution would clearly have managed to circularize their orbits. Consequently, Fig. 5 indicates that a different mode of mass transfer has to be considered to understand these systems. For orbital periods longer than the typical outcome of CE evolution, but shorter than those that might avoid Roche lobe overflow, i.e., 100 and 2000 days, dynamically stable and non-conservative mass transfer represents a reasonable alternative. Indeed, several theoretical studies show that dynamically stable non-conservative mass transfer can explain these systems (e.g., Webbink 1988; Chen and Han 2008; Chen et al. 2013; Gosnell et al. 2019; Vos et al. 2020). Depending on the combination of initial masses, metallicity, and orbital period of the low/intermediate-mass zero-age MS–MS binaries, the more massive star could fill its Roche lobe while on the FGB (having or not a degenerate core) or on the AGB. The properties of post-stable mass transfer binaries then depend on the above-mentioned combination of initial masses, initial orbital period, and metallicity as well as on the fraction of mass and orbital angular momentum lost by the binary during the process. We show evolutionary tracks for dynamically stable non-conservative mass transfer in Fig. 6. It is clear that orbital periods between a few hundreds and a few thousands days can be achieved during dynamically stable non-conservative mass transfer. Extrapolating the results shown in the figure toward smaller initial periods, one can easily imagine that stable mass transfer may also lead to orbital periods 100 days. According to Figs. 5 and 6, formation through dynamically stable but nonconservative mass transfer therefore represents a reasonable scenario for most blue stragglers, post-AGB binaries, long-period binaries hosting subdwarf B stars, and a significant fraction of barium stars and s-process-polluted carbon-enhanced metalpoor stars. Also most S-type SySts, which correspond to ∼80% of known SySts (Mikołajewska 2003, 2007; Mikolajewska 2010; Mikołajewska 2012), should be formed through an episode of dynamically stable non-conservative mass transfer. Their WD and red giant masses are mostly in the range ∼0.4–0.6 M⊙ and ∼1.2–2.2 M⊙ (Mikołajewska 2003), which does not seem difficult to obtain with dynamically stable non-conservative mass transfer, especially when taking into account a potential WD mass growth during SySt evolution. Following the episode of mass transfer, the WD companion will eventually evolve beyond the MS and

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Fig. 6 Evolution toward a post-FGB binary with the donor mass (Md ) of the orbital period (Porb ), in the left-hand panel, and the mass transfer rate (M˙ d ), in the right-hand panel, during dynamically stable non-conservative mass transfer using the MESA code. We chose two different initial orbital periods (100 and 300 days) and seven different values for the transferred mass-loss fraction from the vicinity of the accretor due to isotropic re-emission (βml ), from 0.1 to 0.7 in steps of 0.1, which are indicated in the figure (the upper curve in each set of tracks in the left-hand panel corresponds to βml = 0.1). The simulations start with a zero-age MS–MS circular binary, with stars of masses 1.50 and 1.43 M⊙ , with negligible rotation. In addition, we considered solar metallicity, changes in the rotation of the stars, tidal synchronization as well as wind mass loss (Reimers parameter equals to 0.5). Furthermore, except for stellar winds, we assumed that any mass loss in the form of fast isotropic wind from the donor is negligible (αml = 0), and ignored mass loss and orbital AML due to a circumbinary disk (δml = 0). We can see some nice correlations in the left-hand panel of this figure, in which the colors indicate the evolution of the accretor mass (Ma ) along each track. In particular, the smaller βml , the longer Porb at the end of mass transfer, which occurs because the increase in the orbital period due to mass transfer is much stronger than the increase due to mass loss from the binary. In addition, as expected, the smaller βml , the larger the fraction of mass effectively accreted by accretor, and in turn, the greater Ma at the end of the mass transfer episode. Finally, the longer the initial Porb , the longer Porb at the end of mass transfer. The right-hand panel of the figure illustrates the typical behavior in such episodes of dynamically stable mass transfer (e.g., Woods et al. 2012), namely the transition from a thermally unstable to a thermally stable phase of mass transfer, the latter being driven then by the nuclear evolution. The mass transfer starts thermally unstable because the equilibrium radius–mass exponent (ζeq ) is smaller than the Roche lobe radius–mass exponent (ζRL ), which means that it is driven by the thermal readjustment of the donor, and proceeds initially on the donor thermal timescale. However, as the donor loses mass and changes its structure, ζeq eventually becomes larger than ζRL , and mass transfer proceeds on the donor nuclear timescale. We can also see a nice correlation in this panel, the smaller βml , the greater the peak of M˙ d during thermally unstable mass transfer. This happens because the donor is increasingly driven out of thermal equilibrium, as mass transfer tends to be more conservative. On the other hand, the smaller βml , the lower the mass transfer rate during thermally stable mass transfer, i.e., the slower the mass transfer, which has an impact on the post-FGB mass. In particular, the smaller βml , the larger Md at the end of mass transfer, which can also be seen in the left-hand panel and happens because the overall evolution is slower when mass transfer tends to be more conservative, allowing in turn the core mass to grow more as βml decreases

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become an evolved red giant, either close to the tip of the FGB, or on the AGB. In most cases, the mass transfer from the red giant to the WD is enhanced due to gravitationally focused wind accretion (Mohamed and Podsiadlowski 2007, 2012; Abate et al. 2013; de Val-Borro et al. 2009; Skopal and Cariková 2015; de Val-Borro et al. 2017). If the accretion rate onto the WD is sufficiently high, the binary will become a SySt. Despite the general agreement between predictions and observed systems, there are three S-type SySts that have very different WD and red giant masses, and their red giants are nearly filling their Roche lobe, namely T CrB (Stanishev et al. 2004), RS Oph (Brandi et al. 2009; Mikołajewska et al. 2017), and V3890 Sgr (Mikołajewska et al. 2021). In these three systems, the compact objects are massive carbon–oxygen WDs with masses in the range ∼1.2–1.4 M⊙ , and their Roche lobe filling red giants have relatively low masses (∼0.7–1.2 M⊙ ). These characteristics exclude that these systems formed through stable mass transfer as the mass of the donor star (i.e., WD progenitor) in the progenitor system was far more massive than the accretor (i.e., red giant progenitor). It is therefore very likely that these three SySts have formed through CE evolution (Liu et al. 2019), and their WD/red giant masses have substantially increased/decreased during their evolution. Why CE evolution resulted in exceptionally long orbital periods in these cases (∼200– 600 days) remains unclear. However, if additional energy (e.g., recombination energy) is efficiently contributing to expelling the envelope, such long post-CE periods seem possible (Rebassa-Mansergas et al. 2012; Zorotovic et al. 2014). Following the CE evolution, the WD companion becomes an evolved red giant, its extended atmosphere eventually fills its Roche lobe, and mass transfer proceeds similarly to what is illustrated in Fig. 6. We will discuss in more detail the secular evolution of the different types of SySts later. Even though dynamically stable non-conservative mass transfer is a very good candidate to explain the orbital periods of a large fraction of systems with orbital periods ranging from ∼100 to ∼2000 days, the observed eccentricities remain to be explained. In order to have orbital periods consistent with observations at the end of mass transfer, the initial orbital periods cannot be too short, nor too long. This would imply then that, even for an initially eccentric orbit, tidal interaction should be strong enough to circularize the orbit before the onset of mass transfer. However, it is clear from Fig. 5 that many systems have eccentric orbits at the end of mass transfer. This leads then to three possibilities, either we still do not fully understand the tidal interaction phenomenon, specially the circularization timescales, or there is an eccentricity pumping mechanism operating during mass transfer, or both effects are acting together. Concerning the first possibility, i.e., tidal forces, recent observational efforts on ellipsoidal red giant binaries in the Large Magellanic Cloud suggest that tidal interaction should be much weaker than expected from theoretical considerations (Nie et al. 2017). Among the 81 binaries that were investigated, 20% have eccentric orbits, which should not exist according to our understanding on tidal dissipation in convective stars. In order to explain such systems, the circularization efficiency needs to be two orders of magnitude smaller than predicted.

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Regarding the possibility that the large eccentricities are generated by some kind of eccentricity pumping, we note that there are currently several mechanisms proposed that could at least help to explain the non-circular orbits of the post-stable mass transfer binaries. First, the eccentricity can increase if the mass-loss rate from the donor is higher near periastron than near apastron. The required enhanced mass loss occurs during periastron passages can be caused by either wind accretion or Roche lobe overflow or even a combination of both, in which there is a smooth transition between wind accretion and Roche lobe filling (Bonaˇci´c Marinovi´c et al. 2008; Soker 2000; Vos et al. 2015). Second, in the circumbinary disk scenario, eccentricity pumping occurs due to the resonances in the interaction of the binary with a circumbinary disk (Dermine et al. 2013; Vos et al. 2015). Since circumbinary disks are most likely created only from mass lost from the outer Lagrangian point, the eccentricity pumping due to circumbinary disks should actually work together with the phase-dependent Roche lobe overflow scenario, by enhancing even further the eccentricity. A third possibility is that the proto WD receives a natal kick after the mass transfer episode, similarly to natal kicks in the formation of NSs, although not that strong. The final possibility is the triple scenario, in which dynamical and stellar evolution with a tertiary companion would be responsible for creating eccentric binaries hosting compact objects, via chaotic orbital evolution of the stars, which can trigger close encounters, collisions, and exchanges between the stellar components (e.g., Perets and Kratter 2012). Even though all these scenarios are promising and provide reasonable results for particular systems, they all fail to some extent to explain the overall properties of the systems, and further investigations are needed (e.g., Vos et al. 2015; Rafikov 2016; Oomen et al. 2020; Escorza et al. 2020). There is an important question to be answered regarding the picture we described above. If the accretion efficiency during dynamically stable non-conservative mass transfer is high, what happens with the accretor spin? This issue has been addressed in binary models (Matrozis et al. 2017), which suggest that only ∼0.05 M⊙ of accreted material is usually enough to drive the accretor to critical rotation. This is a major problem to explain barium stars and s-process-polluted carbon-enhanced metal-poor stars unless there exists a mechanism allowing the accretor to transfer its spin angular momentum back to the orbit with the help of tidal torques from the donor (Matrozis et al. 2017). However, it is not yet clear what kind of mechanism could do this job.

High-Mass Stars After discussing dynamically stable non-conservative mass transfer among low-/intermediate-mass stars, we now turn to the implication of this mass transfer mode for the formation of HMXBs. We start by discussing the eclipsing sg-HMXB M33 X–7, which hosts a rapidly spinning, 15.65 M⊙ BH orbiting a close to Roche lobe filling underluminous, ∼70 M⊙ O-type supergiant in a slightly eccentric orbit with a short orbital period of 3.45 days (Orosz et al. 2007). The existence of this HMXB can neither be explained by CE evolution nor rotational mixing, but dynamically stable non-conservative mass transfer offers a solution (Valsecchi et al.

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2010). Starting with a zero-age MS–MS binary with stellar masses of ∼90 M⊙ and ∼30 M⊙ and an orbital period of ∼3 days, the more massive MS star fills its Roche lobe and dynamically stable mass transfer occurs. A fraction of the mass leaving the donor escapes the binary as strong isotropic winds, and part is effectively accreted by the accretor. After mass transfer finishes, due to the strong winds when the initially more massive star becomes a Wolf–Rayet star, the binary hosts a Wolf–Rayet star synchronized with the orbital motion, due to tidal interaction, and a massive O-type MS star. The Wolf–Rayet star with an iron–nickel core later collapses to a BH, leading to rapidly spinning BH in a slightly eccentric short-period orbit with a high-mass O-type MS star. When the O-type MS star becomes an O-type supergiant almost filling its Roche lobe, the binary becomes a BH-HMXB and wind accretion explains its X-ray luminosity. This formation picture is also consistent with other sg-HMXBs hosting rapidly rotating BHs and O-type supergiants almost filling their Roche lobes, such as Cyg X–1 (Miller-Jones et al. 2021) and LMC X–1 (Orosz et al. 2009), in which dynamically stable non-conservative mass transfer cannot only explain their masses and orbital periods, but also their BH spins (Qin et al. 2019). Even though the initial orbital periods in such models are very short (only a few days), they are neither odd nor rare, when compared with observations. The orbital period distribution of binaries hosting O-type MS stars, the so-called Sana distribution (Sana et al. 2012), although extending until ∼106 days, is dominated by systems with orbital periods shorter than ∼10 days. According to the described formation channel, the orbital period does not significantly increase after the onset of mass transfer, which explains why sg-HMXBs can be formed through dynamically stable non-conservative mass transfer and still have current orbital periods shorter than ∼10 days. In most known HMXBs, a NS accretes from the circumstellar decretion disk of a rapidly rotating Be star (e.g., Reig 2011), and their orbital periods are predominantly in range from ∼10 to ∼400 days (e.g., Karino 2021). According to the wind compression disk model (Bjorkman and Cassinelli 1993), an equatorial disk is formed around a rapidly rotating star due to ram pressure confinement by the stellar wind. The disk is formed because the supersonic wind leaving the star surface at high latitudes travels along paths that move it down to the equatorial plane, where the material passes through a standing oblique shock on the top of the disk. The ram pressure of the polar wind thus confines and compresses the disk. The emission lines typically observed in an active Be star are attributed to this equatorial disk (Porter and Rivinius 2003). As mass from this outflowing disk is transferred to the compact object via the accretion gate mechanism (Ziolkowski 2002), preferentially during periastron passages or enhanced activity of the Be star, the system becomes bright in X-rays and observable as a Be-HMXB. The typical age of a Be-HMXB is ∼40–50 Myr (e.g., Williams et al. 2013; Garofali et al. 2018), which is believed to be a direct consequence of the NS formation and B star mass-loss activity timescales. Given their properties, specially their relatively long orbital periods and their rapidly rotating Be stars, they have most likely formed through an episode of stable non-conservative mass transfer

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(e.g., Rappaport and van den Heuvel 1982; Tauris et al. 2017), during which the B star spins up. Despite the fact that there is only one known Be-HMXB in which the compact object is a BH (MWC 656 Casares et al. 2014), it seems more likely that Be-HMXBs hosting BHs are formed during CE evolution (Grudzinska et al. 2015), although given the uncertainties in the stability criterion (Olejak et al. 2021; Belczynski et al. 2021), dynamically stable non-conservative mass transfer is not necessarily ruled out. The main problem with having Be-HMXBs hosting BHs formed through CE evolution is that the existence of the Be star cannot be easily explained, since a mechanism different from Roche lobe overflow would be needed to spin up the B star. Gravitationally focused wind accretion prior CE evolution seems to be a good candidate for that (Grudzinska et al. 2015; El Mellah et al. 2019a). In the Corbet’s diagram (Corbet 1986), i.e., the orbital period versus NS spin period diagram, Be-HMXBs exhibit a clear correlation, which is explained in terms of the equilibrium period, defined as the period at which the rotation velocity at the magnetospheric radius equals the Keplerian velocity (e.g., Waters and van Kerkwijk 1989). If the NS spin period is shorter than the equilibrium period, then matter is efficiently ejected from the vicinity of the NS due to the propeller mechanism (Illarionov and Sunyaev 1975), and the NS spin decreases. On the other hand, if the NS spin period is longer than the equilibrium period, then mass and angular momentum is transferred onto the NS thereby increasing its rotational velocity. The correlation comes from the fact that the equilibrium period depends on the accretion rate, and in turn, on the orbital period. In addition, Be-HMXBs can be separated into two groups in the orbital period versus eccentricity diagram, one being those in low-eccentricity orbits (0.2) and the other one composed of high-eccentricity orbits (0.2) (Pfahl et al. 2002; Townsend et al. 2011). This could then indicate two distinct formation channels, with (core-collapse supernova) and without (electron-capture supernova) strong natal kicks during the helium star collapse into the NS.

Combination of Dynamically Stable Non-conservative Mass Transfer and Common-Envelope Evolution The orbits of AM CVns and UCXBs are so close that two episodes of mass transfer must occur to explain their orbital periods, at least one of them being CE evolution. Similarly, WR-HMXBs, which are compact objects accreting part of the winds from massive helium stars, are also expected to be formed through two episodes of mass transfer, given their short orbital periods. However, unlike the previous case, these systems can be formed in two episodes of dynamically stable non-conservative mass transfer. There are then three possible combinations for AM CVns and UCXBs: (i) double CE evolution, (ii) CE evolution followed by dynamically stable nonconservative mass transfer, and (iii) dynamically stable non-conservative mass transfer followed by CE evolution; and there is another possible combination for WR-HMXBs, in addition to stable non-conservative mass transfer followed by CE

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evolution, which is (iv) double dynamically stable non-conservative mass transfer. In what follows, we will discuss in more detail these formation channels, based on results from binary models.

Evolution Through Two Episodes of Common-Envelope Evolution Starting with a zero-age MS–MS binary, if the initial orbital period is not too short nor too long, the initially more massive star will fill its Roche lobe after evolving beyond the MS. If the initially more massive star is much more massive than its companion, then mass transfer will be dynamically unstable and CE evolution commences. The result of such an interaction will be a helium star or a WD, depending on the mass and core mass of the donor at the onset of CE evolution, orbiting the initially less massive MS star with an orbital period orders of magnitude shorter than initially. In case of a helium star, depending on its mass and composition, it will quickly collapse into a WD, NS, or BH, and in the latter cases, this collapse will produce a core-collapse or electron-capture supernova. If the orbital period of the post-CE binary is not too short, the initially less massive MS will have room to grow and evolve off the MS before filling its Roche lobe. If the compact object is much less massive than its companion, then another CE will be triggered and the orbital period is shortened even further. In case the companion of the compact object is initially a low-/intermediate-mass MS star and if it fills its Roche lobe on the FGB, then it will become a helium WD after CE evolution, if its mass is initially smaller than ∼2 M⊙ , or a helium star if its mass is initially larger than that. On the other hand, if the low or intermediate-mass star fills its Roche lobe on the AGB, then the compact object companion will likely become a carbon–oxygen WD. After the second CE evolution, the post-CE binary will be brought into contact due to emission of gravitational waves, becoming in turn an AM CVn or an UCXB, depending on the nature of the compact object, accreting from either a helium/carbon–oxygen WD or a helium star, or even a hybrid WD, in case the helium star becomes a WD before filling its Roche lobe. This is a standard formation channel for AM CVns and UCXBs (e.g., Solheim 2010) in which the accreting compact object is formed first during the binary evolution. However, even if this scenario ends up having a non-negligible contribution to these populations, it cannot account for the existence of some particular types of binaries related to AM CVns and UCXBs, such as close detached double-helium WDs in which the younger WD is more massive than the older WD (e.g., Nelemans et al. 2000), or millisecond pulsars in close detached binaries with helium WDs (e.g., Tauris et al. 2011). Therefore, alternative scenarios involving dynamically stable non-conservative mass transfer are needed. Dynamically Stable Non-conservative Mass Transfer Followed by Common-Envelope Evolution Starting from a zero-age MS–MS binary, if the orbital period is sufficiently short, the initially more massive star will fill its Roche lobe on the Hertzsprung gap, or

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when it is an unevolved giant. If the initial masses of the stars are comparable, or at least the initially more massive star is not much more massive than its companion, then mass transfer will be dynamically stable. The orbital period in this case may increase, as illustrated in Fig. 6, leading then to a binary with an orbital period longer than the orbital period the zero-age binary had initially, hosting a (proto) WD and a companion that is more massive than the zero-age MS stars. This companion can still be on the MS or already slightly evolved, since it could have started its evolution off the MS, in case the initial masses are comparable. The companion of the (proto) WD then keeps evolving until it fills its Roche lobe, leading to dynamically unstable mass transfer, since it is much more massive than the WD. The post-CE binary will have an orbital period orders of magnitude shorter than at the onset of CE evolution, hosting a WD paired with a WD or helium star, which will later collapse into a WD, NS, or BH, depending on its mass. If the post-CE binary orbital period is sufficiently short, the (proto) WD will fill its Roche lobe, giving rise to an AM CVn or UCXBs, depending on the nature of the accreting compact object. Unlike the double CE evolution scenario, in the scenario in which dynamically stable non-conservative mass transfer is followed by CE evolution, the accreting compact object is formed second. This scenario has been invoked to explain the existence of double-helium WDs in which the younger WD is more massive than the older WD (Woods et al. 2012), which is a natural consequence of this scenario. Most importantly, this scenario can solve the energy budget problem we mentioned earlier (e.g., Webbink 2008; Ivanova et al. 2013), suggesting that the importance of dynamically stable non-conservative mass transfer for binary evolution has been underestimated in several contexts. However, the existence of millisecond pulsars in close detached binaries with helium WDs cannot be explained within this formation channel, which means that another channel most likely plays a key role in formation of UCXBs. Regarding WR-HMXBs, they are believed to be the direct progenitors of merging binary BHs, which means that these merger events can also be used to further constrain WR-HMXBs (e.g., Kalogera et al. 2007). We have already discussed that the properties of sg-HMXBs hosting BHs can be reasonably well explained by an episode of dynamically stable non-conservative mass transfer. This is also the most common outcome for the first episode of mass transfer in merging BH binary models (e.g., Belczynski et al. 2016, 2020). In these binaries, the BH is accreting from the winds of an O-type supergiant that is almost filling its Roche lobe. When it effectively fills its Roche lobe, depending on the binary properties, mass transfer can be dynamically unstable or not. A CE evolution is the most common scenario for the formation of merging binary BHs, specially those mergers with massive stellar-mass BHs, such as GW190521 (e.g., Belczynski 2020). The sg-HMXB M33 X–7 will apparently undergo CE evolution, given that its O-type supergiant is much more massive than its BH companion (Orosz et al. 2007). On the other hand, in the sg-HMXB Cyg X–1, the O-type supergiant is more massive than its BH companion only by a factor of two (Miller-Jones et al.

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2021), which implies that mass transfer will be most likely dynamically stable when the O-type supergiant fills its Roche lobe. Finally, the mass of the O-type supergiant in sg-HMXB LMC X–1 is around three times its BH companion mass (Orosz et al. 2009), and it is much less clear whether mass transfer could be dynamically stable or unstable in this case. Now regarding the current population of confirmed WR-HMXBs, there are two systems that have very short orbital periods, namely Cyg X–3, in the Milky Way (4.8 h, Zdziarski et al. 2013), and CG X–1, in the Circinus galaxy (7.8 h, Qiu et al. 2019), which mostly implies that the BHs orbit within the Wolf–Rayet photospheres. These extremely short orbital periods suggest that there was a strong orbital shrinkage, mostly likely only possible during CE evolution. For the remaining confirmed WR-HMXBs, the orbital periods are longer than a day, and these systems could be explained by a weak spiral-in during dynamically stable non-conservative mass transfer (van den Heuvel et al. 2017), as we will discuss later.

Common-Envelope Evolution Followed by Dynamically Stable Non-conservative Mass Transfer The situation here is initially similar to the double CE evolution scenario, i.e., from a zero-age MS–MS binary, the initially more massive star fills its Roche lobe when it evolves off the MS, leading to dynamically unstable mass transfer, because it is much more massive than its companion. However, unlike in the double CE evolution scenario, the post-CE binary orbital period is shorter, and the compact object companion is not allowed to significantly grow before filling its Roche lobe. Therefore, in this case, the zero-age MS–MS binary orbital period must be shorter than that in double CE scenario. When the companion of the compact object fills its Roche lobe, depending on its mass and the mass of the compact object, mass transfer can be either dynamically unstable or dynamically stable. If the donor is much more massive than the compact object, mass transfer will be dynamically unstable, which implies that the compact object and its companion will most likely merge on the dynamical timescale of the donor. In case the donor is an MS star, this is the natural outcome of dynamically unstable mass transfer. On the other hand, if the donor is a Hertzsprung gap star, or an unevolved FGB star, then a merger is also expected, since there would not be enough orbital energy available to eject the CE, due to the short orbital period of the binary. If the donor is a low-mass star, then mass transfer will most likely be dynamically stable and non-conservative. The beginning of the evolution can be thermally stable or not, depending on the masses of the accreting compact object and the donor, and on the properties of the donor. In any event, the binary will become a CV or a LMXB, depending on the nature of the compact object. If the donor is an M-/Ktype MS star, i.e., an MS star with mass 0.8 M⊙ , then it will eventually become a hydrogen-rich degenerate star, i.e., a brown dwarf, when enough mass is lost. However, if the donor is an evolved MS star of an earlier type or a Hertzsprung

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gap star, then it has already or will develop a growing degenerate helium core. In these cases, when the donor hydrogen envelope is entirely consumed, it becomes a semi-degenerate helium-rich star. At this moment, the CV/LMXB becomes an AM CVn/UCXB. The donor transition from a non-generate to a semi-degenerate configuration may be preceded by a short detached phase, depending on the post-CE binary properties (e.g., Chen et al. 2021; Soethe and Kepler 2021). Alternatively, if the post-CE binary properties are such that this detached phase happens at longer orbital periods (1 day), then emission of gravitational waves will not be strong enough to bring the binary close enough so that the compact object companion could fill again its Roche lobe within a Hubble time. The existence of millisecond pulsars in close detached binaries is essentially explained in such a way, since the NS becomes a millisecond pulsar during the LMXB evolution (the so-called recycling scenario (e.g., Bhattacharya and van den Heuvel 1991; Di Salvo and Sanna 2020)), and the close detached population are those systems observed in the transition from LMXB to UCXB. Those systems that directly become UCXBs, or effectively manage to become UCXBs after the detached phase, are then UCXBs hosting accreting millisecond pulsars.

Evolution Through Two Episodes of Dynamically Stable Non-conservative Mass Transfer We have argued before that WR-HMXBs with extremely short orbital periods can most likely only be explained with CE evolution. However, the remaining confirmed WR-HMXBs have orbital periods longer than ∼1 day, namely X–1 in the IC 10 galaxy (34.9 h, Silverman and Filippenko 2008), X–1 in the NGC 300 galaxy (32.8 h, Crowther et al. 2010), and ULX–1 in the galaxy M101 (196.8 h, Liu et al. 2013). Despite their short orbital periods, they could have formed through dynamically stable non-conservative mass transfer, since it is possible in such cases to avoid CE evolution during the formation of the Wolf–Rayet stars, due to the high masses of the Wolf–Rayet progenitors. A slow spiral-in during dynamically stable non-conservative mass transfer is possible if the Wolf–Rayet progenitor has a radiative envelope and if it is at most ∼3–4 times the BH mass (van den Heuvel et al. 2017; Neijssel et al. 2019), although the exact critical mass ratio depends on the several model assumptions (e.g., Olejak et al. 2021; Belczynski et al. 2021). This seems to be the fate of several WR-HMXB progenitors. Based on an analysis of the small sample of Wolf–Rayet + O-type MS binaries, with orbital periods clustering at around one week (van der Hucht 2001), it has been recently suggested that, after the Wolf–Rayet star becomes a BH and its O-type companion fills its Roche lobe, they are expected to become WR-HMXBs with orbital periods as short as ∼1 day (van den Heuvel et al. 2017). These WRHMXBs will then evolve to binary BHs, when the Wolf–Rayet donors collapse to BHs. This then suggests that not only the formation of WR-HMXBs can avoid CE, but also the formation of merging BHs (Olejak et al. 2021; Belczynski et al. 2021).

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Further Considerations on the Formation of Ultra-Compact X-Ray Binaries The first three scenarios highlighted above correspond to the most traditional scenarios for the formation of AM CVns and UCXBs. Regarding UCXBs, there is an additional channel, via accretion-induced collapse of an oxygen–neon–magnesium WD (e.g., Belczynski and Taam 2004). If such a WD triggers electron-capture reactions at its center upon reaching the Chandrasekhar mass limit, then the burning that propagates outward makes central temperatures and pressures high enough to cause a collapse of the WD into a NS (e.g., Nomoto and Kondo 1991). Binary models, in which different types of donors have been considered, mainly MS stars and helium star donors, have shown that this is indeed possible (e.g., Tauris et al. 2013), leading to the formation of millisecond pulsar binaries. In the case of MS stars, after the accretion-induced collapse, the binary temporarily detaches (for 103 –105 years), due to the small kicks, but, due to orbital AML, it soon becomes an LMXB. And the subsequent formation of the UCXB is similar to that already discussed. The UCXB progenitors in this case are SSXBs with MS donors with masses of ∼2.0–2.6 M⊙ , for a metallicity of 0.02, and of ∼1.4–2.2 M⊙ , for a metallicity of 0.001. It is worth mentioning that this formation channel may also help to explain the existence of millisecond pulsars in eccentric detached binaries (e.g., Freire and Tauris 2014). In the case of helium stars, the binary also temporarily detaches and soon becomes an UCXB, due to orbital AML through emission of gravitational waves. Unlike the previous case, the helium stars quickly (1 Myr) become carbon–oxygen WDs with masses of ∼0.6–0.9, causing the binary to detach. Further orbital AML could eventually make the binary semidetached again, and the UCXB would host a millisecond pulsar accreting from a carbon–oxygen WD donor. This happens for AM CVns with helium star donors with masses of ∼1.1–1.5 M⊙ . Even though possible, the contribution from this channel is most likely small. This is because of the narrow range in the parameter space of the accreting WD that allows it to eventually exceed the Chandrasekhar mass limit. In particular, during the accreting WD evolution, there is a very narrow range of mass transfer rates such that the WD mass can effectively increase (e.g., Nomoto et al. 2007; Shen and Bildsten 2007; Wolf et al. 2013). In addition, given that a typical mass of an oxygen–neon– magnesium WD is ∼1.2 M⊙ , the donor cannot be much more massive than that, since otherwise mass transfer becomes dynamically unstable, which restricts even more the parameter space of the UCXB progenitors.

Additional Channels Through Dynamical Interactions in High-Density Environments In addition to the formation channels highlighted above, dynamical interactions in crowded regions of star clusters, specially globular clusters, can create conditions to form accreting compact objects from systems that would otherwise not evolve

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into them. A way of addressing whether a type of X-ray sources is predominantly dynamically formed in globular clusters is by means of the cluster stellar encounter rate, which depends on the central density, the core radius, and the central velocity dispersion (Verbunt and Hut 1987; Pooley et al. 2003). If dynamical interactions are supposed to play any significant role in the formation of X-ray sources, a correlation between the number of sources of a particular type within a cluster and its stellar encounter rate could indicate that dynamical interactions played a significant role in their formation, despite the several potential problems with this interpretation (Belloni and Rivera 2021). For a long time, this has been believed to happen for LMXBs and UCXBs, which correspond to the brightest X-ray sources found in Milky Way globular clusters, as there is continuously growing strong evidence for such a correlation (Pooley and Hut 2006; Ivanova et al. 2008). There are currently 21 bright X-ray sources in 15 Milky Way globular clusters, being 8 persistent and 13 transients (van den Berg 2020), and they are still consistent with being dynamically formed, especially considering their mass density, which is much higher than that of systems in the Milky Way disk. Given the problem with reproducing the properties of BH-LMXBs in binary models (Wiktorowicz et al. 2014) and the above-mentioned over-abundance of LMXBs in the Milky Way globular cluster population in comparison with the Milky Way disk population, a natural solution to the problem could be a dynamical origin for the field population (i.e., those LMXBs not belonging to stellar aggregates). Recent Monte Carlo numerical simulations of evolving globular clusters (Kremer et al. 2018) show that progenitors of LMXBs are ejected from their host clusters over a wide range of ejection times, contributing to ∼300 NS-LMXBs and ∼180 BHLMXBs to the Milky Way field population, not all of them being indeed observable due to observational selection effects. More than 20 galaxies within ∼25 Mpc have been deeply investigated with Chandra and Hubble Space Telescope (Lehmer et al. 2020). These observations have revealed that, in order to properly describe the X-ray luminosity function of the field population of LMXB, a component that scales with the globular cluster specific frequency is needed. In addition, it has a shape consistent with that found for the globular cluster population of LMXBs. This then indicates that most, if not all, LMXBs in the fields of these galaxies are formed similarly to those in globular clusters and in turn could have origin in globular clusters. These binaries could be ejected from the globular clusters due to energetic dynamical interaction leading to their formation, or the cluster itself could dissolve due to strong tidal interaction. However, for galaxies with low globular cluster specific frequency, the X-ray luminosity function has a component that scales with stellar mass, suggesting then that a substantial population of LMXBs in these galaxies are formed through binary evolution, without invoking dynamics. These findings may alleviate quite a bit the problems of reproducing the proprieties of BH-LMXBs in the Milky Way field. However, it is not clear whether enough systems are predicted to form through this channel, nor whether their positions in the Milky Way as well as their kinematic properties, nor their numbers could be explained as ejected from globular clusters, or from dissolving star clusters. For instance, while the observed systems are almost entirely concentrated in the

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Milky Way disk (Corral-Santana et al. 2016), those predicted to form in globular clusters and latter ejected to the field are spherically distributed around the Milky Way disk, reflecting the observed distribution of globular clusters in the Milky Way. In addition, the number of systems predicted by this channel seems too low to account for the large number of BH-LMXBs inferred from observations (∼104 –108 Tetarenko et al. 2016). Therefore, the current theoretical and observational evidence indicates that a dynamical origin in star cluster is unlikely to be the dominant formation channel for these systems. A more promising alternative to bring into agreement predicted and observed properties seems to be the standard CE evolution, coupled with a revision of the strength of orbital AML during their evolution, as we will see later. Regarding the fainter X-ray sources such as CVs, the situation is much more difficult to be addressed, due to the several biases and selection effects (Belloni and Rivera 2021), e.g., the photometric incompleteness in the more crowded central parts of the clusters is most likely playing a key role in the characterization of these sources (e.g., Cohn et al. 2021). Therefore, any conclusions drawn from a comparison between the numerical simulations and observations of faint X-ray sources should be taken with a grain of salt. Despite that, it is still possible to infer the impact of dynamics on this population, if observational selection effects are somehow addressed. Recent numerical simulations suggest that fewer CVs should be expected in dense globular clusters relative to the Milky Way field, due to the fact that dynamical destruction of CV progenitors is more important in globular clusters than dynamical formation of CVs (Belloni et al. 2019). This is consistent with observations (Cheng et al. 2018), because the faint X-ray populations, primarily composed of CVs and chromospherically active binaries, are under-abundant in globular clusters with respect to the solar neighborhood and local group dwarf elliptical galaxies. Regarding the dynamical formation of CVs in globular clusters, these simulations show that the detectable CV population is predominantly composed of CVs formed via standard CE evolution (70%). This happens because the main dynamical scenarios have a very low probability of occurring, which resulted in (or very weak, if at all) correlation between the predicted number of detectable CVs and the predicted globular cluster stellar encounter rate. Despite the fact that these results are consistent with recent observations (Cheng et al. 2018), we shall mention that, even though it is not expected to be dominant, dynamics should play a sufficiently important role to explain the relatively larger fraction of bright CVs (i.e., those close to the MS in the color-magnitude diagram) observed in denser clusters. Regarding SySts and SyXBs, despite a few reasonable candidates have been proposed over the years, none so far has been confirmed in the entire Milky Way globular cluster population. This issue has been partially addressed in Monte Carlo numerical simulations of evolving globular clusters (Belloni et al. 2020b), in which SySts with WDs formed without Roche lobe overflow have been investigated. These simulations show that their orbital periods are typically sufficiently long (103 days) so that dynamical disruption of their progenitors is virtually unavoidable in very dense clusters. On the other hand, in less dense clusters, some of these SySts are still predicted to exist, although their identification should be rather

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difficult in observational campaigns, mainly due to their locations within the clusters and rareness. Despite these simulations aimed at explaining the lack of SySts in globular clusters, they do not necessarily correspond to definite answers to the issue, since most known SySts have orbital period between ∼200 and ∼103 days, which means that most SySts were not addressed in the simulations. Further simulations are still missing, in which the formation of SySts through dynamically stable nonconservative mass transfer is consistently taken into account and the impact of dynamics on their progenitors is evaluated. So far, we have discussed the population of accreting compact objects in old star clusters. These star clusters cannot harbor HMXBs, since at their present-day ages, the entire population of HMXBs have already become single NSs/BHs or binaries hosting either NSs and/or BHs. However, in very young starburst galaxies (only a few Myr old), HMXBs are expected to be the dominant source of X-rays. Given that high-mass stars, and potentially all stars (Kroupa 1995; Lada and Lada 2003), are most likely formed in binaries (e.g., Sana et al. 2012) in embedded clusters (e.g., Marks and Kroupa 2012), it is not surprising that observations suggest that the HMXBs in starburst galaxies are consistent with being formed in star clusters (e.g., Kaaret et al. 2004). Even though young star clusters are most likely HMXB factories, these HMXBs are not necessarily formed dynamically. The analysis of the X-ray sources in the merging Antennae galaxies and in the dwarf starburst NGC 4449 suggests that high stellar density and in turn dynamical interactions are not a primary driver of HMXB formation (Johns Mulia et al. 2019), which is consistent with star cluster direct N-body simulations (Garofali et al. 2012). Therefore, despite being rather frequent in starburst galaxies and likely formed in compact star clusters, there is evidence supporting that HMXBs form directly from primordial high-mass binaries, without any significant influence of dynamics.

Secular Evolution The mass transfer in accreting compact objects is dynamically stable and can be separated into three main modes: (i) Roche lobe overflow (if Rd ∼ RRL ), (ii) atmospheric Roche lobe overflow (if 0.9 RRL  Rd  RRL ), and (iii) wind accretion (if Rd  0.9 RRL ). In CVs, LMXBs, AM CVns, and UCXBs, the donor is filling its Roche lobe. Therefore, mass transfer in these systems can be driven by orbital AML or by nuclear expansion of the donor, with or without an initial phase of thermally unstable mass transfer. On the other hand, despite the fact that in most SySts, SyXBs, sg-HMXBs, and WR-HMXBs, the donor is under-filling its Roche lobe, mass transfer still occurs, mainly when the extended atmosphere of the donor fills its Roche lobe, or due to accretion of a significant part of the winds from the donor. Among the observational properties, the donor mass and the mass transfer rate deserve special attention, as these two quantities are somewhat tied to the secular evolution of accreting compact objects. We show these properties of accreting compact objects in Figs. 7 and 8, against their orbital periods, together with

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Fig. 7 Comparison between observed and predicted properties of accreting compact objects in the plane donor mass (Md ) versus orbital period (Porb ). The observational data correspond to BHLMXBs (Wiktorowicz et al. 2014; Shao and Li 2020), BH-HMXBs (Crowther et al. 2010; Orosz et al. 2009, 2007; Casares et al. 2014; Zdziarski et al. 2013; Silverman and Filippenko 2008; Liu et al. 2013; Miller-Jones et al. 2021), NS-LMXBs (Bassa et al. 2009; Van et al. 2019), UCXBs (Van et al. 2019), eclipsing sg-HMXBs (Clark et al. 2002; Quaintrell et al. 2003; van der Meer et al. 2007; Mason et al. 2010, 2011, 2012; Bhalerao et al. 2012; Falanga et al. 2015; Pearlman et al. 2019), eclipsing AM CVns (Copperwheat et al. 2011; Green et al. 2018; van Roestel et al. 2021), eclipsing CVs (McAllister et al. 2019), S-type SySts (most of which are eclipsing, Mikołajewska 2003; Stanishev et al. 2004; Brandi et al. 2009; Mikołajewska et al. 2021; Hinkle et al. 2009), SyXBs (Hinkle et al. 2006, 2019), and SSXBs (Kalomeni et al. 2016). In particular, we labeled the only known Be-HMXB hosting a BH (MWC 656 Casares et al. 2014), a WR-HMXB with an extremely short orbital period (Cyg X–3 Zdziarski et al. 2013), and the two SySts T CrB (Stanishev et al. 2004) and RS Oph (Brandi et al. 2009), which are among the few SySts in which the red giant is nearly filling its Roche lobe, and in addition, given their high carbon–oxygen WD masses, they will most likely evolve toward Type Ia supernovae (Liu et al. 2019). The theoretical evolutionary tracks correspond to the lines, of which all colored tracks were computed by us using the MESA code, adopting solar metallicity, assuming the RVJ prescription (Rappaport et al. 1983) (Equation 19, with γMB = 3), for the MB, and considering tidal interaction (Hurley et al. 2002) and stellar wind mass loss, with the Reimers parameter equals to 0.5 for FGB stars and the Blöcker parameters equal to 0.02 for AGB stars. In all these colored tracks, we chose several different initial orbital periods and initial masses for the point-mass compact object and its zero-age MS star companion. The black tracks correspond to previous binary evolution models, in which the donor is initially a helium WD (Wong and Bildsten 2021), a helium star (Heinke et al. 2013; Wang et al. 2021), or a MS star (Kalomeni et al. 2016; Chen et al. 2021). Given that the evolutionary tracks pass through most observational points, we could naively conclude that our current knowledge on how accreting compact objects evolve is not bad. However, major problems arise when we take into account the entire populations of different types of accreting compact objects, and confront results from population synthesis with observations. These problems are most likely connected with our poor understanding of the mechanisms driving the evolution of accreting compact objects. Despite that, there has been important progress in the last couple of years, which can definitely guide us toward a solution to these problems

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Fig. 8 Comparison between observed and predicted properties of accreting compact objects in the plane mass transfer rate (M˙ d ) versus orbital period (Porb ). We only considered in the plot those systems in which the donor is a Roche lobe filling low-mass star, i.e., BH-LMXBs (Coriat et al. 2012), NS-LMXBs (Van et al. 2019), UCXBs (Van et al. 2019), AM CVns (Ramsay et al. 2018), and CVs (Pala et al. 2022). Some of the colored evolutionary tracks in Fig. 7 are shown, which were computed by us with the MESA code. The black lines correspond to evolutionary tracks from previous binary models, in which the donor is initially either a WD (Wong and Bildsten 2021), or a helium star (Heinke et al. 2013; Wang et al. 2021), or a MS star (Goliasch and Nelson 2015; Chen et al. 2021), the latter having an initial phase of thermally unstable mass transfer. We also included in the figure, as gray thick lines, the critical mass transfer rates (Coriat et al. 2012), above which the accretion disks are stable and the systems are persistent sources, and transient otherwise, considering irradiated accretion disks or not. By comparing the observational data with these critical mass transfer rates, we can see that the disk instability model reasonably well explains persistent and transient sources, except perhaps in the case of Cyg X–2 (but see Coriat et al. 2012) and some AM CVns. There are two representative tracks for CVs, the solid red line computed by us and the long-dashed black line (Goliasch and Nelson 2015), which were both computed with the RVJ prescription (Rappaport et al. 1983) (Equation 19, with γMB = 3). We can clearly see that this MB prescription is not adequate to explain the persistent and transient sources with orbital periods longer than ∼3 h. In addition, CVs hosting fully convective M-type MS stars, at orbital periods shorter than ∼2 h, exhibit a spread in the mass transfer rates that cannot be explained by only gravitational wave radiation. With respect to NS-LMXBs, it is also clear that the RVJ prescription (dashed red lines) is not able to account for the persistent sources, which has been a long-standing problem of LMXB evolution. However, when a MB law (Van et al. 2019) similar to the recently developed CARB prescription (Van and Ivanova 2019) is adopted (dot-dashed black lines Chen et al. 2021), mass transfer rates are great enough so that they can be explained. The persistent UCXBs with long orbital periods (40 min) can apparently only be explained if the donor is initially a helium star, which is consistent with observations (e.g., Heinke et al. 2013). There are two particular systems, one AM CVn (SDSS J1908+3940) and one CV (SDSS J1538+5123), that are very interesting, since they apparently cannot be explained by any of the tracks we included in the figure. While it has been proposed that this CV might be either a newly born system or a post-nova system, it is not clear what might be happening with this AM CVn

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evolutionary tracks computed by us with the MESA code and other tracks from previous binary models. In what follows, we will describe the dynamically stable evolution of accreting compact objects as well as the up-to-date observational information that can be used to constrain evolutionary models, which includes their orbital periods, their mass transfer rates, and their donor and compact object masses, but without being exclusively limited to them.

Cataclysmic Variables and Low-Mass X-Ray Binaries As mentioned earlier, CVs and LMXBs are formed through an episode of CE evolution. More specifically, after CE evolution, a post-CE binary is formed in a detached binary hosting a compact object and a non-degenerate star. Because of orbital AML and/or nuclear evolution of the future donor, the orbital separation decreases up to the formation of the accreting compact binary, when the nondegenerate companion starts filling its Roche lobe and becomes a donor. The donors in CVs and LMXBs are usually MS stars, subgiants, or unevolved red giants.

Low-Mass Unevolved M-/K-Type Main-Sequence Star Donors Let us start with the case in which the donor is initially a low-mass unevolved MS star, corresponding to post-CE binaries hosting MS stars with types M and K (0.8 M⊙ ), which do not significantly evolve within the Hubble time. This case is illustrated in Figs. 7 and 8 by the solid red track, for which the point-mass compact object and zero-age MS star have both the same initial mass of 0.8 M⊙ , and the initial orbital period is 12 h. In this case, the MS donor has a radiative core, which implies that MB is the main orbital AML mechanism driving the binary evolution. MB causes mass transfer rates high enough so that the MS donor is only able to maintain thermal equilibrium if it is slightly bloated, which means that MS donors are somewhat oversized in comparison with isolated MS stars (Knigge et al. 2011). When the MS donor becomes fully convective, MB is expected to cease or, at least, become much less efficient (disrupted MB scenario), most likely as a consequence of a rise in the secondary star magnetic complexity (Taam and Spruit 1989; Garraffo et al. 2018), rather than the originally proposed demise of the dynamo (Rappaport et al. 1983; Spruit and Ritter 1983). From this point on, the main driving mechanism becomes GR. This leads to a significant drop in the mass transfer rate and a slowdown of the evolution, as AML through GR is in general orders of magnitude weaker than MB. Such a drop in the mass transfer rate allows the MS donor to re-establish thermal equilibrium at its normal size (i.e., decrease in size), and the system becomes a detached binary since the companion of the compact object is no longer filling its Roche lobe. This detachment occurs at the upper edge of the so-called orbital period gap (a paucity of observed accreting systems in the orbital period range of 2–3 h). Even though the system is now detached, it keeps losing angular momentum due to GR and continues to evolve toward shorter orbital periods. When the orbital

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period is sufficiently short, the MS donor fills its Roche lobe again, and mass transfer restarts, i.e., the system is again a CV evolving now with lower mass transfer rates toward shorter orbital periods, which happens at the lower edge of the orbital period gap. When the donor mass becomes too low to sustain hydrogen burning, it becomes a hydrogen-rich degenerate object, i.e., a brown dwarf. From this point on, the donor expands in response to the mass loss, leading to an increase in the orbital period. The so-called orbital period minimum is then a natural consequence of the transition from a fully convective MS star to a brown dwarf. The edges of the orbital period gap, and consequently its width, as well as the orbital period minimum depend on the metallicity (Stehle et al. 1997; Kalomeni et al. 2016), the accreting compact object mass, and the orbital AML rate (Knigge et al. 2011; Belloni et al. 2020a). For instance, regarding the impact of the metallicity, the higher the central helium fraction, the shorter the orbital period minimum, and the orbital period minimum can be as short as ∼10–40 min, when the central helium fraction is nearly unity (Kalomeni et al. 2016). The orbital period minimum is also affected by orbital AML in the following way. For systems having fully convective donors at a given orbital period, the stronger/weaker the orbital AML, the higher/lower the mass transfer rate, and in turn the smaller/greater the donor mass, which allows the donor to reach the mass limit for hydrogen burning at longer/shorter orbital periods. Orbital AML is also expected to have a strong impact on the orbital period gap, due to variations in the MB strength for systems with donors having convective cores. The stronger/weaker MB, the more/less bloated the donor is, which means that it becomes fully convective at a lower/higher mass (see Fig. 2), having in turn a smaller/greater radius. This implies that system will become semi-detached again at a shorter/longer orbital period, i.e., the lower edge of the orbital period gap is located at shorter/longer orbital periods. For a sufficiently weak MB, such as the RVJ prescription with γMB ≥ 5, the donor bloating is negligible, especially near fully convective boundary, and the system evolves virtually without detaching. On the other hand, for a very strong MB, such as that provided by the CARB prescription or by the Kawaler prescription with n  1.5, the donor becomes fully convective at a mass as small as ∼0.18 M⊙ , and the orbital period gap can start at an orbital period as long as ∼7–8 h. This happens because, as the donor approaches the fully convective boundary, it is increasingly driven out of thermal equilibrium, leading to an increase in its radius by a factor of 2 in comparison with isolated M-type MS stars with similar masses. Then, as a response of the donor to mass loss, the orbit expands. The above outlined evolution successfully describes several features of the evolution of LMXBs and CVs. However, it is clearly not complete. For instance, it does not include the impact of the magnetic field of the compact object on the evolutionary picture for CV and LMXB, which can be significant as we will explain in what follows. If the compact object magnetic moment, which is proportional to its magnetic field strength and to the cube of its radius, is sufficiently large (1033 G cm3 ), then a coupling of the donor magnetic field lines and the compact object magnetic field lines may lead to an increase of the portion of the donor winds that remains trapped to the binary (Li et al. 1994; Webbink and

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Wickramasinghe 2002). This effect would make winds to carry away less angular momentum, resulting in reduced orbital AML via MB and, in turn, diminished mass transfer rates. While NS magnetic fields seem to considerably decay during LMXB evolution (Zhang and Kojima 2006), the magnetic field strength in most accreting WDs is expected to change only negligibly, which is a consequence of mass loss due to nova eruptions (Zhang et al. 2009). Given the small sizes of NSs (only ∼10–20 kilometers) and their relatively weak magnetic fields (∼108 –109 G) due to accretion-induced field decay, their magnetic moments are usually not strong enough to cause an important impact on LMXB evolution. The situation is different for WDs, as they are much bigger (∼5000–10000 kilometers), which implies that, if they host sufficiently strong magnetic fields (107 G), the CV evolution is most likely different from the remaining CVs hosting WDs with weaker magnetic fields (Belloni et al. 2020a). In case the WD magnetic moment is higher than ∼1034 –1035 G cm3 , MB is completely suppressed and the CV evolution is driven by only GR, i.e., at a much lower orbital AML rate, without detaching. Recent binary models provide strong support to this magnetic evolutionary picture for such CVs, as the predicted mass transfer rates are in agreement with the observations and the orbital period gap is absent in this population, which reasonably well agrees with observations (Belloni et al. 2020a). It even seems that CV evolution in general cannot be understood ignoring the origin of WD magnetic fields and its impact on orbital AML and exchange between the stellar components and the orbit. Including magnetic field generation due to a rotationand crystallization-driven dynamo (Isern et al. 2017; Schreiber et al. 2021) and the impact of the generated field on the evolution of CVs can reproduce several observational facts that remain otherwise inexplicable, such as the existence of AR Sco, which hosts a radio-pulsing WD (Marsh et al. 2016), the relative numbers of magnetic and non-magnetic CVs (Pala et al. 2020), and the absence of strong magnetic WDs among young detached post-CE binaries (Liebert et al. 2005).

Subgiant or A-/F-/G-Type Main-Sequence Star Donors Let us now consider the case in which the donor is a nuclear-evolved MS star (i.e., near the end of the MS) or a subgiant at the onset of mass transfer to the compact object. In other words, we are now looking at post-CE binaries hosting MS stars of spectral type G or earlier (1 M⊙ ). If the orbital period of the post-CE binary is sufficiently long, the future donor star will have enough time to evolve on the MS, or even become a subgiant, before filling its Roche lobe. For stars having convective envelopes, the onset of mass transfer occurs due to a combination of orbital AML due to MB and nuclear evolution of the future donor, while for stars having radiative envelopes, it is triggered only by nuclear evolution of the future donor. The evolution for these two types of donors is illustrated in Figs. 7 and 8 by the long-dashed and dot-dashed black tracks, which were taken from different binary models (Goliasch and Nelson 2015; Kalomeni et al. 2016; Chen et al. 2021), by the two dashed red and green tracks with shortest initial orbital periods (1 day), and by the two yellow tracks (initial orbital periods set as 1 and 3 days). The difference between the three sets of colored tracks is the initial mass of the compact

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object, which is 0.8 M⊙ in the red tracks, 1.2 M⊙ in the green tracks, 1.4 M⊙ in the yellow tracks, and the zero-age MS mass, which is 1.2 M⊙ for the green and red tracks, and 3.0 M⊙ in the yellow tracks. Depending on the mass and structure of the donor as well as on the mass of the compact object, the mass transfer can be thermally unstable at the very beginning of the evolution. Thermally unstable mass transfer typically occurs when the nuclearevolved MS or subgiant donor is significantly more massive than the compact object at the onset of Roche lobe overflow, as in the case of the yellow tracks in Figs. 7 and 8. More generally, for a given donor evolutionary state, the higher the mass ratio at the onset of Roche lobe overflow, the greater the chances that the mass transfer will be thermally unstable. The mass transfer rates during this phase are typically larger than those provided by thermally stable mass transfer and can exceed ∼10−7 –10−6 M⊙ yr−1 , which is high enough to completely drive the donor out of thermal equilibrium. In case the compact object is a WD, systems observed at this phase appear typically as SSXBs. The orbital period during this thermally unstable phase decreases as a consequence of the donor response to thermal timescale mass loss. However, when mass transfer stabilizes, the donor re-establishes thermal equilibrium and the orbital period can further decrease or reverse and increase. Let us now discuss the evolution following the onset of thermally stable mass transfer. For stars with radiative envelopes, orbital AML due to MB does not take place, and the orbital period should increase as a response to mass transfer. For stars with convective envelopes, there are two possibilities. In case the nuclear timescale of the donor is shorter than its MB-driven mass-loss timescale, then the binary evolution will be driven by the donor nuclear evolution. Mass transfer then proceeds on the nuclear timescale of the donor, the orbital period increases, and the evolution is usually called divergent. On the other hand, in case MB is sufficiently strong, such that the MB-driven mass-loss timescale becomes shorter than nuclear timescale, the evolution will be driven by orbital AML and the orbital period will decrease. In this case, the evolution is called convergent, and the system will evolve to either a CV or LMXB with a hydrogen-rich degenerate donor (in case the MS donor did not have time to start developing a degenerate helium core) or an AM CVn or UCXB with helium-rich degenerate donors (in case the donor is initially a subgiant or in case the MS donor managed to develop a degenerate helium core). The evolution toward a hydrogen-rich degenerate donor is similar to the case in which the donor is an unevolved low-mass MS star (compare long-dashed black and solid red tracks in Fig. 8). However, the evolution toward AM CVns and UCXBs is rather different from that of the previous cases, which can be seen by comparing the long-dashed and dot-dashed black tracks with the solid red track in Fig. 7, and the dot-dashed black track with the long-dashed black and solid red tracks in Fig. 8. For instance, the orbital period minimum becomes much shorter for donors that were more evolved at the onset of Roche lobe overflow. This happens because the donors have helium cores that are partially degenerate, with masses that are too low to trigger helium burning. This allows their radii to considerably shrink as the binary evolves, so that the binary can reach orbital periods as short as ∼6 min, before

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the donor becomes degenerate and the orbital period subsequently increases as a response to mass transfer. More generally, whether convergent or divergent evolution takes place depends on the strength of orbital AML due to MB, on the fraction of mass loss from the binary, on the metallicity, and on the binary properties at onset of Roche lobe overflow, most importantly the orbital period, donor structure, and compact object and donor masses (e.g., Nelson et al. 2004; Deng et al. 2021). For instance, the impact of the compact object mass can be seen in Figs. 7 and 8 by comparing the dashed red and green tracks with the shortest initial orbital period, in which the RVJ prescription with γMB = 3 was adopted. We can see that the red track in which the point-mass compact object mass is 0.8 M⊙ is convergent, while the green track in which the point-mass compact object mass is 1.2 M⊙ is divergent. In addition, when the RVJ prescription is compared with the CARB prescription, the bifurcation period obtained with the latter is much longer (Istrate et al. 2014; Deng et al. 2021; Chen et al. 2021; Soethe and Kepler 2021). This is a natural consequence of the orbital AML rates provided by the CARB prescription being much larger than those obtained with the RVJ prescription.

Comparison with Observations Let us start our comparison between theory and observations discussing how good the disk instability model (e.g., Lasota 2001) is to explain persistent and transient systems. By inspecting Fig. 8, we can see that in general this model successfully explains why some CVs and LMXBs exhibit outbursts, while others do not. Irradiation heating of the accretion disk is usually negligible for the stability of disks in CVs (Dubus et al. 2018), while in the case of LMXBs X-ray irradiation needs to be taken into account (Coriat et al. 2012). The net effect of including irradiation is that a system at a given orbital period can be persistent for lower mass transfer rates in comparison with non-irradiated accretion disks, which is in general the case (compare CVs and LMXBs in Fig. 8). However, the disk instability model apparently fails to explain two systems in Fig. 8, namely the CV SDSS J1538+5123 and the NS-LMXB Cyg X–2. The time-averaged mass transfer rates in CVs can be estimated with the disk instability model itself (Dubus et al. 2018) or by analyzing the ultraviolet emission from the WD during quiescence (Townsley and Gänsicke 2009), the latter being used for SDSS J1538+5123. From the ultraviolet spectra, the WD effective temperature can be estimated, and this is considered a good indicator of the mass transfer rate, since the WD is compressionally heated due to the accretion process, and the higher the mass transfer rate, the higher the WD effective temperature (Townsley and Bildsten 2003, 2004). SDSS J1538+5123 is a dwarf nova (i.e., transient) located below the orbital period gap and therefore should according to the disk instability model have mass transfer rates much lower than the ∼1.8 ± 0.7 × 10−9 M⊙ yr−1 inferred from its high WD effective temperature. However, there is no problem with the disk instability model here, and this high WD effective temperature is most likely related to a recent nova eruption (Pala et al. 2017), and therefore, the temperature is not a good indicator of the time-averaged mass transfer rate in this particular case.

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The persistent system Cyg X–2 is the only NS-LMXB that does not agree with the predictions of the disk instability model, which clearly indicates that this system should be transient. One possibility for this disagreement would be that Cyg X–2 is in fact a transient source undergoing a very long outburst (Coriat et al. 2012), similarly to what happens with the well-known BH-LMXB GRS 1915+105, which is a transient source and has the longest orbital period (33.85 days) of this population. Given that the longer the orbital period, the larger the accretion disk, the disks in these wider systems can accumulate enough mass to fuel an outburst for decades. The accretion disk in Cyg X–2 is estimated to have a mass of ∼2.5×1028 g, which is massive enough to sustain outbursts lasting up to 80 years(Coriat et al. 2012). Let us move now to compare expected secular evolution of CVs and LMXBs with observations. When we compare the tracks with the observational data in these figures, we can see that most CVs are consistent with having initially unevolved low-mass MS donors (solid red track). However, some CVs clearly reveal abnormal (non-solar) abundances in their spectra, indicating that the material has undergone thermonuclear processing by the CNO cycle (see Sparks and Sion 2021 for a list of systems). These CVs contribute to ∼5–15% of the entire CV population (Gänsicke et al. 2003; Pala et al. 2020), and given that their donors are not expected to possess this material, two scenarios have been proposed to explain them. As a first possibility, they are descendants of SSXBs, i.e., they are systems hosting initially nuclear-evolved MS stars that underwent a short phase of thermally unstable mass transfer before reaching their present-day configurations (Schenker et al. 2002; Podsiadlowski et al. 2003). In this way, the donor has its outer layers stripped during this phase, revealing CNO-processed material. The other possibility would be donor contamination by the accretion of CNO-processed material from ejected by the WD during nova eruptions (Stehle and Ritter 1999). Even though the first scenario over predicts the number of such CVs by a factor of 2–6 (Schenker et al. 2002), it has been for a long time accepted as most likely. This is because it is apparently rather difficulty for the donor to capture enough nova-processed material (Sparks and Sion 2021), e.g., because its geometrical crosssection is small and the high-velocity material that the secondary geometrically intercepts is not highly nuclear-processed. However, it has been recently suggested that these problems can be overcome if a significant part of the ejected material leaves the WD with velocities smaller than the escape velocity (Sparks and Sion 2021). This is possible because the thermonuclear runaway on the WD causes a strong propagating shock wave, which leaves behind a large velocity gradient in the expanding shell. This implies that part of this shell will reach escape velocity, but the remaining material will be gravitationally bound to the binary, leading to a nonrotating CE-like structure surrounding the CV. This nova-induced CE-like structure will then contain a large amount of non-solar metallicity material, which can be efficiently accreted by the donor, creating a significant non-solar convective region. However, given that virtually all CVs are supposed to undergo nova cycles and that only ∼10–15% of them exhibit peculiar abundances, it remains unclear under which conditions this sort of pollution can efficiently work, and whether it can explain

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why most CV donors fail in to efficiently accrete. These questions could and should be addressed in future detailed binary models, since their answers are potentially related to major problems connected with CV secular evolution, as we will see later. Before moving to LMXBs, we just mention a few interesting long period (∼14–48 h) CVs that host subgiant donors, i.e., BV Cen (Gilliland 1982) and GK Per (Álvarez-Hernández et al. 2021) in the Milky Way field, and AKO 9 in the globular cluster 47 Tuc (Knigge et al. 2003). Interestingly, the masses of the WDs in BV Cen (∼1.02–1.44 M⊙ Watson et al. 2007) and GK Per (∼0.92– 1.19 M⊙ Álvarez-Hernández et al. 2021) are significantly higher than the average among CVs (∼0.8 ± 0.2 M⊙ Zorotovic et al. 2011; McAllister et al. 2019; Pala et al. 2022), which is consistent with the evolutionary picture in which the WD mass has grown due to the high mass transfer rates expected when the donor is initially an evolved MS star or a subgiant. This makes this type of CVs very good candidates for being Type Ia supernova progenitors, under certain conditions, although they correspond to a negligible fraction of the entire CV population. When we compare the distribution of LMXBs and CVs in Fig. 7, together with the evolutionary tracks, it is very likely that the contribution of systems with initially evolved donors is much larger for LMXBs in comparison to CVs, as they have on average significantly longer orbital periods for the same range of donor masses. While the evolutionary sequence given by solid red line in this figure seems to nicely explain at least around half of NS-LMXBs, a lot of them can only be explained if the donor is initially an evolved MS star or a subgiant. The situation is even more dramatic for BH-LMXBs, since only two systems host M-type MS donors, and the majority of systems with orbital periods shorter than ∼1 day have K-type MS donors (Shao and Li 2020). In addition, it seems that a significant fraction of LMXBs start their evolution having initially intermediate-mass donors (Podsiadlowski and Rappaport 2000), especially in the case of BH-LMXBs. Similarly to CVs, the LMXBs with longest orbital periods (1 days) most likely have subgiant or red giant donors, such as Cyg X–2 (Casares et al. 1998), GRO J1744–28 (Doroshenko et al. 2020), GX 13+1 (Bandyopadhyay et al. 1999), XTE J1550–564 (Orosz et al. 2011), GX 339–4 (Muñoz-Darias et al. 2008), GS 1354–64 (Casares et al. 2009), GRO J1655–40 (Israelian et al. 1999), V4641 Sgr (MacDonald et al. 2014), GS 2023+338 (Khargharia et al. 2010), and GRS 1915+105 (Harlaftis and Greiner 2004). These systems are then evolving toward longer orbital periods, as mass transfer is driven by the nuclear expansion of the donor. Even though the evolutionary picture that we have discussed reasonably well explains the main observational features of individual CVs and LMXBs, as illustrated in Figs. 7 and 8, there are still major problems when we take into account the entire populations and compare observed properties with those predicted by population synthesis that are most likely intrinsically connected with the orbital AML mechanisms driving the binary evolution. In particular, the standard RVJ prescription (Equation 19) for MB usually assumed for models of CVs and LMXBs is probably the origin of most of the problems we are currently facing. For instance, the predicted fraction of CVs hosting brown dwarfs is much higher than observed (Belloni et al. 2020a; Pala et al. 2020), which suggests that the overall

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evolutionary timescale should be much longer than predicted by models using the RVJ prescription. In addition, the predicted mass transfer rates of CVs above the orbital period gap are typically much higher than those inferred from observations, except for systems near the upper edge of the orbital period gap, for which predicted rates are much smaller than those inferred from observations (Belloni et al. 2020a; Pala et al. 2022). This suggests that the dependence of MB with the orbital period should be the opposite of what is predicted by the RVJ prescription. While this recipe leads to a decreasing orbital AML rate as the CV evolves (see Fig. 2), observations suggest that the overall rate should increase as the CV evolves. Moreover, the predicted mass transfer rates for NS-LMXB are so low that they cannot explain the persistent sources (Podsiadlowski et al. 2002), which suggests that MB should be much stronger in these systems than predicted by the RVJ prescription. Furthermore, the predicted donor mass distribution of BH-LMXBs peaks at a much higher value than the observed distribution (Wiktorowicz et al. 2014), which suggests that MB should also be stronger in these systems. Finally, when the RVJ prescription is adopted, a well-known fine-tuning problem arises when trying to reproduce millisecond pulsars in close detached binaries (orbital periods in the range ∼2–9 h) with helium WD companions of mass 0.2 M⊙ , Istrate et al. (2014), and Chen et al. (2021), which represents a big problem in the formation of these binaries. Regarding LMXBs and their descendants, recent binary models (Van et al. 2019; Van and Ivanova 2019), in which the CARB prescription has been proposed, indicate that the problem with the persistent NS-LMXBs can be solved with this recipe that provides much higher orbital AML rates (see Fig. 2) and therefore higher mass transfer rates, especially for persistent systems with shorter orbital periods. For this reason, the CARB prescription might also solve the problem with BH-LMXBs, since it could shift the predicted donor mass distribution toward lower values and hopefully reproduce the observed distribution. In addition, this new prescription might also be consistent with the fast orbital decay observed in some BH-LMXBs, such as XTE J1118+480 (González Hernández et al. 2012), A0620–00 (González Hernández et al. 2014), and GRS 1124–68 (González Hernández et al. 2017), which cannot be explained with the RVJ prescription. When applied to close detached millisecond pulsar binaries, the CARB prescription also provides a solution to the fine-tuning problem (Soethe and Kepler 2021). In addition, not only compact binaries are well-reproduced by this prescription but also wide-orbit binaries can be explained, and in general, the relation between the helium WD mass and the orbital period predicted by this prescription is in agreement with observations (Soethe and Kepler 2021). Regarding CVs, it has been proposed that not only the problem with the mass transfer rates but also the problem with the fraction of post-orbital period minimum could be solved with another MB prescription (Belloni et al. 2020a; Pala et al. 2020). A reasonable candidate to solve both problems is the Kawaler prescription with n ∼ 1.25, which is shown in Fig. 2. This prescription predicts an overall evolutionary timescale substantially longer than that obtained with the RVJ prescription, which may perhaps contribute significantly to reduce the predicted number of CVs that manage to reach the orbital period minimum. Moreover, given that the orbital AML

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rates provided by this prescription are around one order of magnitude higher than GR, the constraints provided by detached WD–MS post-CE binaries (Schreiber et al. 2010) are not expected to be violated, which strengthens even more the potential of solving CV problems with this prescription. In addition to the problems most likely connected with the standard RVJ prescription for MB, there are other problems that are probably associated with another orbital AML mechanism, i.e., consequential AML, which is not included in the standard evolutionary picture. For instance, the observed CV WD mass distribution has a peak at ∼0.8 M⊙ (Zorotovic et al. 2011; McAllister et al. 2019; Pala et al. 2022), while most predicted CV WD masses are on average smaller than that (Zorotovic et al. 2011; McAllister et al. 2019; Pala et al. 2022; Zorotovic and Schreiber 2020). In addition, for CVs hosting fully convective MS donors, there is a clear spread in their mass transfer rates inferred from observation that is definitely not predicted when GR is taken as the only driver of their evolution (Pala et al. 2022). Moreover, still when only GR is considered, the predicted mass transfer rates among post-orbital-period-minimum CVs are much lower than those inferred from observations (Pala et al. 2022), and the predicted orbital period minimum is significantly shorter than observed (Howell et al. 2001; Gänsicke et al. 2009; Knigge et al. 2011). These problems might be solved if the total AML for these systems is stronger than predicted by GR (Knigge et al. 2011; Schreiber et al. 2016; Nelemans et al. 2016). In case there is another orbital AML mechanism driving the evolution together with GR for CVs with fully convective MS donors and brown dwarf donors, then the predicted mass transfer rates might be significantly enhanced, which would cause the CVs to evolve faster so that their donors become degenerate at longer orbital periods. The problem with the WD masses can be solved if the strength of this additional orbital AML is inversely proportional to the WD mass, such that most CVs with low-mass WDs would become dynamically unstable at the onset of mass transfer (Schreiber et al. 2016). Similarly, the spread in the mass transfer rates for CVs with fully convective MS donors might also be solved with this dependence on the WD mass, if perhaps the additional orbital AML also depends on the age of the CV. The most natural choice of additional orbital AML to enhance the mass transfer rates would be consequential AML, and there are very good candidates for the above-highlighted dependence on the WD mass, and eventually on the time since the onset of mass transfer(Schenker et al. 1998; Schreiber et al. 2016; Nelemans et al. 2016). The frictional orbital AML produced by novae depends strongly on the expansion velocity of the shell (Schenker et al. 1998). For low-mass WDs (0.55 M⊙ ), the expansion velocity is small (Yaron et al. 2005), and this may lead to strong orbital AML by friction that makes most CVs with low-mass WDs dynamically unstable. In particular, given the velocity gradient in the nova shell we mentioned earlier, it is reasonable to expect that a nova-induced CE-like structure surrounding the binary will be formed after the eruption. This idea has been tested in binary models (Nelemans et al. 2016), which confirms that such a configuration drastically affects the stability of mass transfer in CVs with low-mass WDs. As we mentioned earlier, this form of consequential AML could also explain the existence of CVs with non-solar abundance, as an alternative to the post-SSXB scenario,

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which predicts more such CVs (a factor of 2–6) than observed. Other promising mechanisms are circumbinary disks (Spruit and Taam 2001; Willems et al. 2005), or a combination of both, e.g., if the circumbinary disk is fed by a fraction of the accreted matter that is re-emitted by WD due to the nova eruptions.

AM CVns and Ultra-Compact X-Ray Binaries As we mentioned earlier, AM CVns and UCXBs can be formed in three ways, either through two CE evolution, or through dynamically stable non-conservative mass transfer followed by CE evolution, or through CE evolution followed by dynamically stable non-conservative mass transfer. Since the later channel from CVs/LMXBs has just been addressed, we focus on the other two, which have always a CE evolution for the second episode of mass transfer. Similarly to CVs and LMXBs, after CE evolution, a detached post-CE binary is formed and evolves toward shorter orbital periods due to orbital AML, leading to the onset of mass transfer, when the donor fills its Roche lobe. However, unlike these systems, the main mechanism driving the evolution of AM CVns and UCXBs is always GR, since typically their donors are initially helium WDs or helium stars.

Helium White Dwarf or Helium Star Donors Let us start with the case in which the donor is initially a helium WD. This case is illustrated in Fig. 7 and 8 by the dotted black track in each figure, which were taken from a binary model (Wong and Bildsten 2021). Even though the orbital period corresponding to the onset of mass transfer depends on the mass ratio and on helium WD properties, mainly its radius, and in turn its mass, it is of order of a few minutes. After that, the further binary evolution depends on the initial entropy and the subsequent thermal evolution of the donor and is usually separated into three phases (e.g., Deloye et al. 2007; Solheim 2010; Kaplan et al. 2012; Wong and Bildsten 2021). In the very beginning, the donor contracts in response to mass loss as the outermost radiative layer is stripped off, leading to an increase in the mass transfer rate. The mass transfer rate then grows from zero to its maximum, which can be up to ∼10−8 –10−6 M⊙ yr−1 , depending the donor properties, while the donor radius decreases to a minimum value. During this phase, the mass-loss timescale becomes much shorter than the donor thermal timescale, and the orbital period decreases as a response to mass transfer. After this quick phase, which lasts 106 years, the donor radius evolution reverses and the donor expands in response to mass loss. This happens because, during the first phase, the entropy profile eventually becomes sufficiently shallow that the expansion of the underlying layers starts to dominate. The binary then evolves toward longer orbital periods driven by GR, with decreasing mass transfer rates. During this second phase, which can last ∼1 Gyr, the mass-loss timescale is much shorter than the donor timescale, and the donor responds adiabatically to the mass loss. The third phase starts when the mass-loss timescale becomes comparable to or shorter than the donor thermal timescale in the underlying layers. This allows the donor to cool down and contract, although

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the contraction ends when the donor has shed sufficient entropy to reach its fully degenerate configuration. This phase starts at an orbital period of ∼40 min. Let us now address the case in which the companion of the compact object was very close to the tip of the FGB just before CE evolution, resulting in turn in a post-CE binary hosting the compact object and a helium star. In case the post-CE binary orbital period is sufficiently short, the compact object companion will still be a helium star, i.e., still burning helium, at the onset of mass transfer. The binary evolution for this case is illustrated in Figs. 7 and 8 by the solid and short-dashed black tracks taken from two binary models (Heinke et al. 2013; Wang et al. 2021). Depending on the mass, the lifetime of a helium star is typically ∼10–103 Myr, more massive stars having shorter lifetimes, and its radius can increase up to ∼30% during its life (Yungelson 2008), and how large it can become strongly depends on the amount of hydrogen left after CE evolution (Bauer and Kupfer 2021). Thus, unlike the previous case, the onset of Roche lobe filling is driven by a combination of orbital AML due to GR and nuclear expansion of the donor. Therefore, the orbital period at which the onset of mass transfer occurs depends on the masses of the compact object and helium star as well as on the evolutionary status of the helium star. In particular, the longer the post-CE binary orbital period, the more time the helium star has to evolve, becoming larger, and in turn the longer the orbital period at the onset of mass transfer. Given the orbital AML rates provided by GR and the helium star lifetimes, to have a helium star at onset of mass transfer, the post-CE binary orbital must be typically shorter than ∼2 h (Yungelson 2008). After mass transfer starts, the further evolution for systems hosting helium star donors is different from those having helium WDs (Savonije et al. 1986; Yungelson 2008; Solheim 2010; Wang et al. 2021). During the Roche lobe overflow, the mass-loss timescale is typically shorter than the thermal timescale of the donor, which makes the donor slightly bloated as a response to mass loss. This causes a rapid increase in the mass transfer rate, reaching values of a few 10−8 M⊙ yr−1 , after the residual hydrogen is entirely consumed. In a more realistic situation, a non-negligible residual outer hydrogen envelope is left in the helium star after CE evolution, which plays a significant role during the early evolution (Bauer and Kupfer 2021). The donors can spend tens of Myr transferring this small amount of hydrogen-rich material at low rates (−10−10 − ∼10−9 M⊙ yr−1 ), before finally transitioning to a phase where helium is transferred at much higher rates (≥10−8 M⊙ yr−1 ). Since the donor should be modestly evolving and expanding, in the absence of orbital AML, the orbital period should increase in response to mass loss. However, since GR is sufficiently strong, the donor nuclear evolution timescale is longer than the GR-driven mass-loss timescale, which leads to convergent evolution, and the orbital period decreases. A significant fraction of the energy released through nuclear burning is absorbed in the donor envelope, which leads to a decrease in its luminosity and an increase of its thermal timescale. As the binary evolves and the donor mass drops, nuclear burning quickly becomes less important, which makes the convective core to be replaced by an outer convection zone that penetrates inward. At the same time, as the orbital period decreases, the mass-loss timescale also decreases, causing the mass transfer rate to slightly increase. Toward the end of this initial phase, the donor thermal timescale becomes

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much longer than the mass-loss timescale, and the thermal structure of the donor is severely perturbed. The mass transfer rate then increases faster, as the donor tries to remain within its Roche lobe. At some point, helium burning in the center of the donor virtually vanishes and the donor is driven far out of thermal equilibrium. The mass transfer rate then reaches its maximum and the orbital period its minimum. This typically occurs when the donor mass is ∼0.20–0.26 M⊙ , at an orbital period of ∼8–11 min. Since the star becomes more degenerate, its radius starts to increase and the further evolution resembles that of systems hosting helium WD donors, in which the donor is evolving adiabatically in response to mass loss. The mass transfer rate drops, while the binary evolves toward longer orbital periods. In case the compact object is a WD, some interesting features are expected in the first phases of AM CVn evolution hosting initially helium star donors. It has been shown by binary models (Fink et al. 2007; Brooks et al. 2015) that, if the initial mass of the helium star is 0.4 M⊙ and the accreting WD mass is initially 0.8 M⊙ , enough mass is accumulated onto the accreting WD, leading to a first thermonuclear flash that is likely vigorous enough to trigger a detonation in the helium layer. This thermonuclear runaway originated from the detonation in the helium layer of the accreting WD may create converging shock waves that reach the core. If the carbon in the core is also detonated, the thermonuclear runaway is seen as a Type Ia supernova. Those that survive the first flash and eject mass will have a temporary increase in orbital separation, but orbital AML through GR drives the donor back into contact, resuming mass transfer and triggering several subsequent weaker flashes. Despite the fact that the three evolutionary channels leading to AM CVns and UCXBs are in principle viable, there are theoretical arguments against two of them. It has been argued that most, if not all, WDs accreting initially from helium WDs merge at the beginning of the evolution (Shen 2015). This would happen due to nova eruptions during the initial phases of accretion that would trigger dynamical friction within the expanding nova shell, shrinking the orbit and causing the mass transfer rate to become dynamically unstable. If that is true, most, if not all, AM CVns would come from WDs initially accreting from helium stars or from CVs with subgiant or nuclear-evolved MS donors. It has been argued, based on the RVJ prescription for orbital AML due to MB, that only a negligible fraction of AM CVns could have originated from CVs (Goliasch and Nelson 2015; Liu et al. 2021). The reason for that is the narrow range of CV properties from which AM CVns originate. However, the situation here is very similar to the fine-tuning problem related to the formation of close detached millisecond pulsar binaries. As the CARB prescription, which predicts higher orbital AML rates than the standard RVJ prescription, can solve the millisecond pulsar fine-tune problem, it would not be surprising if it can also increase the probability of forming AM CVns from CVs.

Comparison with Observations After describing the main features of AM CVn and UCXB evolution, we can confront prediction with observations. Let us start with a brief discussion of the persistent and transient sources with respect to what the disk instability model predicts. By inspecting Fig. 8, we can see that this model provides quite convincing

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results, similarly to the case of CVs and LMXBs, especially for UCXBs (Heinke et al. 2013). However, some AM CVns deserve attention, like ASASSN-14cc and ASASSN-14mv. The disk instability model predicts that these two systems should be persistent, but they have undergone outbursts (Ramsay et al. 2018). In addition, SDSS J1525+3600 and GP Com have never shown outbursts (Ramsay et al. 2018), although the model predicts that they should be transient. Finally, despite their very low mass transfer rates (10−11 M⊙ yr−1 ), SDSS J1208+3550, SDSS J1137+4054, V396 Hya and SDSS J1319+5915 are marked in the figure as persistent, since they have never been observed in outburst. Even though it is very likely that the lack of outbursts related to the last four systems is due to the fact that their accretion disks are stable and cold, it is not clear what might be happening with the other systems. When we compare the evolutionary tracks for the three channels leading to AM CVns and UCXBs in Figs. 7 and 8, we can see that they can reasonably well explain observations, and some particular systems can be better described by particular channels. For instance, as noted in previous studies (Heinke et al. 2013), UCXBs can be separated into three groups: (i) transients with orbital periods longer than ∼40 min, (ii) persistent with orbital periods shorter than ∼25 min, and (iii) transient with orbital period longer than that. Since the mass transfer rate drops as an UCXB evolves with a WD donor, sources in the groups (i) and (ii) could in principle be explained by any scenario. However, those in the group (iii), i.e., the long-period persistent UCXBs 4U 1626–67, 4U 1916–053, and 4U 0614+091, can apparently only be explained if the donor is initially a helium star or perhaps if they are descendants of LMXBs. This is because if the donor is initially a helium WD, mass transfer rates in this orbital period range are expected to be similar to those in group (i), i.e., orders of magnitude lower than those inferred for the group (iii). This could have important implications when comparing the population of UCXBs in the Milky Way field with those belonging to globular clusters. As already noted before (Zurek et al. 2009; Heinke et al. 2013), the persistent UCXBs in globular clusters have orbital periods much shorter than those of 4U 1626– 67, 4U 1916–053, and 4U 0614+091 (the longest orbital period is 22.58 min for M15 X–2, Dieball et al. 2005). According to Heinke et al. (2013), this fact could be naturally explained if long-period persistent UCXBs have initially helium star donors that ignite helium under non-degenerate conditions in the center. This is because UCXBs in globular clusters cannot form in such a way, and the reason for that is twofold. First, the typical evolutionary time-scale for an UCXB to be seen as persistent is only a few tens of Myr (Wang et al. 2021). Second, for low metallicities, only MS stars with masses ≥ 1.85 M⊙ will evolve without developing a degenerate helium core on the FGB (Han et al. 2002), which is a much higher mass than that of MS stars close to the turn-off point in globular clusters (∼0.8–0.9 M⊙ , e.g. Cohn et al. 2010; Lugger et al. 2017; Rivera Sandoval et al. 2018; Cohn et al. 2021). This would then explain the lack of long-period persistent UCXBs in globular clusters. However, helium stars can also originate from less massive stars, which undergo the helium core flash to ignite helium off-centre (e.g. Han et al. 2002; Bauer and Kupfer 2021), and it is not clear why such helium stars should behave in a different way than those formed under non-degenerate conditions. In addition,

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there is an over-abundance of bright Xray sources in globular clusters in comparison to the Milky Way field, which indicates that dynamics are playing a significant role in their formation. Furthermore, it has been shown that strong MB can lead to mass transfer rates high enough to explain long-period persistent UCXBs (Van et al. 2019; Van and Ivanova 2019). Therefore, the difference in the orbital period distribution of persistent UCXBs in the two environments most likely arises from a more complex interplay between dynamics and binary evolution than previously thought by Heinke et al. (2013). There is one AM CVn (SDSS J1908+3940) that seems challenging to be explained by any evolutionary channel. This system has an orbital period of ∼18 min and an inferred mass transfer rate of ∼4 × 10−7 –10−6 M⊙ yr−1 (Ramsay et al. 2018). For its orbital period, this mass transfer rate is orders of magnitude higher than expected from any type of initial donor, which is 10−8 M⊙ yr−1 . Future observational efforts and binary models with focus on this system could help to understand whether any of these formation channels could explain its properties. If not, perhaps something atypical is occurring with this system that pushed its inferred mass transfer rate to such a high value. Unfortunately, except for a few particular systems, we still do not know which of these three formation channels is the dominant among AM CVns and UCXBs, if any is dominating at all, which compromises studies of their intrinsic populations. It seems clear as well that, for the overwhelming majority of systems, having only the orbital period, donor mass and mass transfer rate are not enough to distinguish between the different evolutionary scenarios, and more information is needed. There are a few ways to better evaluate the contribution of each channel, by gathering more information about these systems. For instance, by identifying and studying the properties of potential progenitors, such as the system LAMOST J0140355+392651 (ElBadry et al. 2021). This system has an orbital period of 3.81 h and hosts a bloated, relatively cool, low-mass (∼0.15 M⊙ ) proto WD and a massive (∼0.95 M⊙ ) WD companion. Its properties can be well-explained as a CV entering the detached phase, when the donor envelope has been entirely consumed. In this case, the proto WD was a nuclear-evolved MS star before the onset of mass transfer. The system will evolve through this detached phase due to GR, and mass transfer will eventually resume, after a few Gyr. This sort of investigation provides key information to understand binary evolution leading to AM CVns, and UCXBs. However, the number of these systems is far too low to provide conclusive evidences for a particular channel being dominant or not. Another possibility is by constraining the properties of their donors with detailed analyses of their chemical composition, which allows us to investigate in more detail their evolutionary history (Nelemans et al. 2010). Those formed through CV/LMXB evolution are expected to retain a greater fraction of their hydrogen in comparison with systems formed in the other two channels. This would imply that the presence of hydrogen in their spectra is needed to rule out the other channels as well as systems not exhibiting hydrogen in their spectra are most likely not formed in such a way. In both helium WD and helium star channels, the transferred material is expected to be mainly composed of helium with CNO-processed material, mainly

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nitrogen, and abundance ratios of these elements are believed to be an effective discriminant between these two channels. A third possibility is by means of the donor mass–radius measurements obtained from precise analyses of eclipsing systems, since each evolutionary channel predicts on average different radii for the same mass (Deloye et al. 2007; Yungelson 2008; Goliasch and Nelson 2015), although some overlap is also expected depending on the initial properties of the donor as well as how the WD donor cooling is treated. In general, systems having initially helium WD donors evolve with smaller radii than systems having initially helium star donors, and these evolve with smaller radii than those originated from CVs/LMXBs. The last option we discuss is applicable to UCXBs and consists of investigating the existence/lack of thermonuclear explosions that occur on the surface of the NS as well as their features. It has been proposed that there is a strong correlation between the iron Kα line strength in their X-ray spectra and the abundance of carbon–oxygen in the accretion disc (Koliopanos et al. 2013). This line occurs at ∼6.4–6.9 keV and is a result of the reflection of the radiation by the accretion disk and the surface of the WD facing the NS, and for this reason, it can provide clues on the disk chemical composition. This correlation coupled with the fact that UCXBs with prominent and persistent iron Kα emission also show bursting activity, it has been proposed that UCXBs with persistent iron emission have helium-rich donors, while those that do not, likely have carbon–oxygen or oxygen–neon–magnesiumrich donors (Koliopanos et al. 2021). This possibility can be further explored, but more elaborated X-ray reflection models will be eventually needed. Having in mind these possibilities, we illustrate with eclipsing AM CVns how they may help to disentangle the formation channels. Thus far, there are seven eclipsing AM CVns with accurate measurements of the masses and radii of their donors (Copperwheat et al. 2011; Green et al. 2018; van Roestel et al. 2021). When considering only the radii and masses, YZ LMi can be easily explained by either the helium WD or the helium star channels, ZTF J0407–0007 by the helium WD channel, and ZTF J2252–0519 by the helium star channel. The remaining (Gaia14aae, ZTF J1637+4917, ZTF J0003+1404 and ZTF J0220+2141) have very large radii, which could be only explained by the CV channel. However, when the chemical properties of these seven systems are taken into account, the situation becomes much more complicated. Regarding those systems apparently formed through the CV channel, since no hydrogen was detected in the spectra of any of them, it seems more likely that they have formed in a different way. Therefore, the situation for these systems apparently seems rather challenging. A possibility to bring into agreement predicted and observed WD donor radii and chemical properties is by avoiding the phase in which the donor can contract and cool down. This phase is predicted to exist because, at some point, the donor thermal timescale becomes comparable or shorter than the mass-loss timescale, since the orbital AML rate is continuously dropping as the AM CVn evolves. If there is an additional source of orbital AML, e.g., consequential AML, such that the donor cooling is significantly delayed, then the donors could keep their large sizes, even when the orbital period is longer than ∼40 min. However, this possibility at the moment is very speculative, and future detailed binary models could verify whether

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consequential AML is able to do that, and if so, for which mechanisms and under which conditions. After describing compact objects accreting from Roche lobe filling donors, we can turn to a discussion of other modes of transfer, in which the donor is not filling the Roche lobe and is either a low-/intermediate-mass-evolved red giant, or a supergiant, or a Wolf–Rayet star.

Symbiotic Stars and Symbiotic X-Ray Binaries We have argued before that, in order to explain their orbital periods (∼200– 103 days), most S-type SySts should form through an episode of dynamically stable non-conservative mass transfer. After this event, the resulting post-stable mass transfer binary, with an orbital period longer than ∼100 days, hosts a WD orbiting a low-mass MS star or perhaps a subgiant or red giant, depending on the mass ratio of the zero-age MS–MS binary. On the other hand, those S-type SySts hosting massive WDs as well as SyXBs are most likely formed through CE evolution, leading to long-period post-CE binaries, since dynamically stable nonconservative mass transfer cannot explain their properties. Finally, given the very long orbital periods of D-type SySts (40 years), their WD progenitors are not expected to form during an episode of Roche lobe filling, i.e., their WDs are formed similarly to single WDs. In the three situations, given the relatively long orbital period of the binary, the WD companion has enough room to evolve and expand, and the binary will become a SySt or a SyXB under certain conditions. Even though in what follows we discuss the evolution of these systems with focus on SySts, the case of SyXBs is very similar, except from the fact that the compact object is a NS. The donors in SySts are either located near the tip of the FGB or on the AGB (e.g., Gromadzki et al. 2013; Mikołajewska 2007). The typical luminosity of accreting WDs in SySts is ∼102 –104 L⊙ (Mikolajewska 2010), and in most cases, these are powered by nuclear burning due to the very high accretion rates, which are typically ∼10−8 –10−7 M⊙ yr−1 . In addition, in most SySts, the red giant is under-filling its Roche lobe filling (Mikołajewska 2012; Boffin et al. 2014), but in some cases it is nearly filling its Roche lobe, as evidenced by the clear signature of ellipsoidal variations in their light curve (Gromadzki et al. 2013). Therefore, in what follows, we discuss two promising modes of mass transfer for these systems, which are: (i) atmospheric Roche lobe overflow (Ritter 1988), if 0.9 RRL  Rd  RRL , or (ii) gravitationally focused wind accretion (Mohamed and Podsiadlowski 2007, 2012; Abate et al. 2013; de Val-Borro et al. 2009; Skopal and Cariková 2015; de Val-Borro et al. 2017), if Rd  0.9 RRL .

Atmospheric Roche Lobe Overflow As the red giant evolves, its radius approaches its Roche lobe, and at some point the mass transfer rate provided by Equation 1 will become relevant. If the red giant mass is not much higher than the compact object mass, ζad > ζRL , and mass transfer is dynamically stable. We show in Fig. 7, as dashed green lines, several evolutionary tracks in which the initial point-mass compact object mass is 1.2 M⊙ ,

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and the zero-age MS mass is 1.25. For those with initial orbital periods longer than ∼5 days but shorter than ∼100 days, the onset of mass transfer occurs when the donor is an unevolved red giant on the FGB. The mass transfer in this case is similar to what is depicted in Fig. 6, and it is characterized by an initial phase of thermally unstable mass transfer, until the donor mass is sufficiently low such that the mass transfer stabilizes. After that, mass transfer proceeds on the nuclear timescale of the donor. The mass transfer rates nicely correlate with the evolutionary status of the donor. First, the longer the initial orbital period, the more evolved the donor at the onset of mass transfer. Consequently, the more evolved the donor, the higher the mass transfer rates. For instance, during thermally unstable mass transfer, the rates for the binaries with shortest and longest initial orbital period are ∼3 × 10−8 and ∼6 × 10−6 M⊙ yr−1 , respectively. During nuclear timescale mass transfer, the rates for the same binaries are ∼5 × 10−9 and ∼7 × 10−8 M⊙ yr−1 , respectively. There are at least three SySts in which their red giant donors are very close to filling their Roche lobes and their WDs are massive enough so that mass transfer can be regarded as dynamically stable. T CrB is a well-studied SySt with a relatively short orbital period (227 days), hosting a massive carbon–oxygen WD (1.37 ± 0.13 M⊙ ) and a red giant with mass 1.12 ± 0.23 M⊙ (Stanishev et al. 2004). RS Oph is another well-known SySt, which also hosts a massive carbon– oxygen WD (1.2–1.4 M⊙ ). However, its orbital period (453 days) is longer than that of T CrB, and it hosts a less massive red giant donor (0.68–0.80 M⊙ , Brandi et al. 2009). This likely indicates that both SySts could share similar evolutionary sequences, in which the orbital period is expanding as the red giant is consumed. The last SySt we know in which the red giant donor is nearly filling its Roche lobe is V3890 Sgr (Mikołajewska et al. 2021). Similarly to the other two systems, this SySt also hosts a massive carbon–oxygen WD (1.35 ± 0.13 M⊙ ). However, its longer orbital period (747 days) combined with the mass of its red giant donor (1.05 ± 0.11 M⊙ ) suggests that the evolutionary pathway of V3890 Sgr is slightly different from those of T CrB and RS Oph, starting at a longer orbital period. The properties of T CrB and RS Oph can be nicely reproduced if the post-CE binary hosts a WD with mass ∼1.15 M⊙ , and a MS star companion with mass ∼1.4 M⊙ , as illustrated in Fig. 7 by the solid green track passing through these two systems. As mentioned earlier, T CrB and RS Oph could indeed be explained with the same evolutionary sequence, if the WD mass in the former is smaller, which would imply that T CrB may evolve to something similar to RS Oph. In order to reproduce the properties of these two systems with the same evolutionary sequence, the post-CE binary orbital period needs to be as long as ∼200 days, and the fraction of mass lost from the vicinity of the WD due to isotropic re-emission needs to be βml ∼ 0.6. The predicted masses of the WD and red giant during the T CrB stage are ∼1.25 and ∼1.07 M⊙ , and during the RS Oph stage, they are ∼1.38 and ∼0.67 M⊙ . The WD will exceed the Chandrasekhar limit and explode in a Type Ia supernova when the orbital period is ∼500–800 days, depending on the assumed Chandrasekhar limit. After the onset of mass transfer, the binary reaches the T CrB stage after ∼0.2 Myr. The transition from the T CrB stage to the RS Oph stage takes

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∼1 Myr, and from RS Oph stage to the Type Ia supernova 1–4 Myr, depending on the assumed Chandrasekhar limit. The properties of V3890 Sgr can also be reproduced with similar WD and companion masses after CE evolution, as well as the same mass-loss fraction during SySt evolution. However, the post-CE binary orbital period must be much longer (∼600 days) than in the previous case. An example of evolutionary sequence (rightmost solid green track) is shown in Fig. 7. The predicted masses of the WD and red giant at the orbital period of V3890 Sgr are ∼1.25 and ∼0.96 M⊙ . Similarly to the previous case, the evolution will terminate when the WD exceeds the Chandrasekhar limit. As mentioned earlier, mass transfer will be dynamically stable only if the red giant mass is comparable to or only slightly more massive than the compact object mass. This condition is usually not satisfied in SySts (Mikołajewska 2003), since their WD masses are typically 0.6 M⊙ , while their red giant donors usually have masses of ∼1.2–2.2 M⊙ , implying mass ratios 2.5. Such mass ratios are likely high enough to cause mass transfer to be dynamically unstable. In this case, as the red giant radius approaches the Roche lobe radius, the mass transfer rates provided by Equation 1 always increase, leading to CE evolution. This behavior is illustrated in Fig. 9 by the solid lines. The evolutionary tracks in this figure correspond to some of the blue tracks in Fig. 7, and they all start with a zero-age MS star with mass 1.6 M⊙ orbiting a point-mass WD with mass 0.53 M⊙ , but each one of them starts at a different orbital period. Before the onset of CE evolution, the atmospheric Roche lobe overflow model provides accretion rates that can only explain SySts that are close filling their Roche lobe, i.e., Rd  0.90 RRL . Moreover, the SySt lifetime predicted by this model is ∼0.01–0.1 Myr. This is orders of magnitude shorter than those typically assumed in studies that try to estimate the expected number of SySts in the Milky Way (e.g., Kenyon et al. 1993). In general, regardless of the assumptions, these investigations predict much more Milky Way SySts than observed. This problem could be partially/completely overcome with the atmospheric Roche lobe overflow model, if the intrinsic population of S-type SySts in the Milky Way hosts red giants close to Roche lobe filling. However, if only a small fraction in the intrinsic population shows evidence for ellipsoidal variability, like currently observed (Gromadzki et al. 2013), then this model most likely does not correspond to the dominant mode of mass transfer for these systems. In what follows, we discuss the case in which the red giant is strongly under-filling its Roche lobe.

Gravitationally Focused Wind Accretion In the case of low-mass red giants, the mass transfer rates provided by Equation 1 in the atmospheric Roche lobe overflow model are only relevant if Rd  0.85– 0.9 RRL . If this condition is not satisfied, then the accretion rates onto the WD are negligible, and in turn this model cannot explain the observed WD luminosities in SySts. This implies that mass transfer must be associated with accretion of part of the stellar winds from the red giant, i.e.,

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red: AGB donor

−17

10

100

200

300

500 1000 Porb ( days )

ηwind,wRLOF ∼ 0

ηwind,wRLOF ∼ 0

ηwind,wRLOF ∼ 0

ηwind,wRLOF ∼ 0

ηwind,wRLOF ∼ 0.09

blue: FGB donor

10−15

08

10

5 ≤ (ρc /ρsph ) ≤ 15 (τ ∼ 0.1 − 1 Myr)

ηwind,BHL

−13

yr τ ∼1M

ηwind,wRLOF ∼ 0.08

10−11

ηwind,BHL ∼

M˙ a (M yr−1 )

10−9

rough lower limit to trigger the symbiotic phenomenon

atmospheric Roche lobe overflow Bondi-Hoyle-Lyttleton wind Roche lobe overflow wind compression

Myr

10−7

τ ∼ 0.1 Myr

10−5

Rd = RRL Rd = 0.9 RRL Rd = 0.8 RRL

τ ∼ 0.01

10−3

2000

Fig. 9 Predicted accretion rate (M˙ a ) onto the WD during pre-SySt and SySt evolution, as a function of the orbital period Porb , according to the atmospheric Roche lobe overflow model (Equation 1), the Bondi–Hoyle–Lyttleton model (Equations 27 and 28, with αwind = 1.5), the wind Roche lobe overflow model (Equations 27, 29, and 30, with Tdust = 1 500 K and p = 1), and the wind compression model (Equation 31, assuming 5 ≤ ρ c /ρ sph ≤ 15). The gray thick horizontal line marks the minimum accretion rate such that the system can be considered a SySt, which is ∼10−8 M⊙ yr−1 . The evolutionary tracks were computed by us using the MESA code and correspond to some of those shown in Fig. 7. For these selected tracks, we start the simulations with a zero-age MS star of mass 1.6 M⊙ orbiting a point-mass WD with mass 0.53 M⊙ , which are consistent with the average values for the red giant and WD in SySts (Mikołajewska 2003). We chose nine different initial orbital periods, from left to right: 300, 450, 600, 800, 1000, 1700, 2400, 3100, and 3800 days, and evolve each one of them until the onset of CE evolution. In all tracks, the orbital period increases/decreases as the SySt evolves mainly as a response to red giant donor spin evolution, since it quickly becomes synchronized with the orbit while ascending the FGB. For the three binaries with shortest initial orbital period, Roche lobe filling occurs when the donor is on the FGB, while for the remaining binaries it takes place when the donor is on the AGB. In case the orbital period during the SySt phase is shorter than 103 days, we computed the accretion rates provided by the atmospheric Roche lobe overflow model (solid lines) and those obtained with gravitationally focused wind accretion, for which we assumed either the Bondi– Hoyle–Lyttleton model, if the donor is on the FGB (dashed blue lines), or the wind Roche lobe overflow model, if the donor is on the AGB (dashed red lines), or the wind compression model (green areas). Furthermore, we only show the accretion rates provided by the wind Roche lobe overflow model when the orbital periods are longer than 103 days. The average Bondi–Hoyle– Lyttleton and wind Roche lobe overflow accretion rate efficiencies (ηwind,BHL and ηwind,wRLOF ) are indicated in the figure, while those for the compression wind model are given by (5–15)×ηwind,BHL . Also indicated is the typical SySt lifetime (τ ), based on the atmospheric Roche lobe overflow and wind compression model, for orbital periods shorter than 103 days, and based on the wind Roche lobe overflow model, for orbital periods longer than that. SySts with orbital periods shorter than 103 days cannot be easily explained by the Bondi–Hoyle–Lyttleton model, nor the wind Roche lobe overflow model, as these mass transfer modes do not provide accretion rates high enough to trigger the symbiotic phenomenon. However, the required rates in this period range can be obtained with the wind compression model, if the accretion efficiency is  5 times higher than that from the Bondi–Hoyle–Lyttleton model. On the other hand, the wind Roche lobe overflow model is clearly able to explain SySts with AGB donors at orbital periods longer than 103 days. Finally, the atmospheric Roche lobe overflow model always provides sufficiently high accretion rates, when Rd  0.85–0.9 RRL

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M˙ a = − ηwind M˙ wind ,

(27)

where ηwind is the orbit-averaged wind accretion rate efficiency. Observations suggest that the wind mass-loss rate from a typical red giant donor in SySts is 10−7 M⊙ yr−1 (e.g., Skopal 2005), implying that ηwind  0.1 to reach the accretion rates of 10−8 –10−7 M⊙ yr−1 needed to explain the hydrogen nuclear burning. The most simple case of wind accretion occurs when we assume that stellar winds are supersonic and spherically symmetric, which is the so-called Bondi–Hoyle– Lyttleton model (Hoyle and Lyttleton 1939; Bondi and Hoyle 1944; Edgar 2004). In this case, the WD can accrete part of the stellar wind as it orbits through it and the accretion rate efficiency, i.e., the fraction of the stellar winds that is effectively accreted by the WD, can be estimated as

ηwind,BHL

αwind = √ 2 1 − e2



G Ma 2 a vwind

2 

1+



vorb vwind

2 −3/2

≤ 1,

(28)

where vwind and vorb are the wind and orbital velocities, respectively, and αwind is a parameter to be adjusted based on observations. Depending on the properties of the red giant and the orbital separation, the winds can be gravitationally focused toward the orbital plane and more easily accreted by the WD. Even though there are a few models available to estimate gravitationally focused wind accretion rates (e.g., Abate et al. 2013; Skopal and Cariková 2015; Saladino et al. 2019), we will only consider two models to illustrate how this mechanism can lead to accretion efficiencies much higher than those obtained with the Bondi–Hoyle–Lyttleton model. These two models are: (i) the wind Roche lobe overflow model (Mohamed and Podsiadlowski 2007, 2012; Abate et al. 2013) and (ii) the wind compression model (Bjorkman and Cassinelli 1993; Skopal and Cariková 2015), and they look very promising in the context of SySts. Let us start with the wind Roche lobe overflow model. During the AGB phase, winds are most likely driven by a combination of pulsation-induced shock waves and radiation pressure on dust grains Höfner and Olofsson (2018). Stellar pulsation and convection induce strong shock waves in the extended atmosphere, pushing the gas outward, which reaches cooler regions. Since most of the gas in a cool AGB star is in molecular form, some species may condense into dust grains, giving rise to a dusty shell around the star. These dust grains are then accelerated outward by radiation pressure and the gas is dragged along. In the presence of a companion, the gas can remain within the AGB Roche lobe, if the wind acceleration radius is larger than the AGB Roche lobe radius (Abate et al. 2013). When this happens, instead of having the red giant effectively filling its Roche lobe due to nuclear evolutionary processes, the slow winds fill its Roche lobe, enhancing in turn the wind accretion onto the WD (Mohamed and Podsiadlowski 2007, 2012; de Val-Borro et al. 2009, 2017; Saladino et al. 2019). This implies that the accretion rates predicted by the wind Roche lobe overflow model are expected to be higher than those provided

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by the Bondi–Hoyle–Lyttleton model, but smaller than those obtained with the atmospheric Roche lobe overflow model. The accretion rate efficiency in the wind Roche lobe overflow model can be expressed as (Abate et al. 2013) ηwind,wRLOF = q

2



25 9

      Rdust Rdust 2 + 0.918 − 0.234 ≤ 0.5, −0.284 RRL RRL (29)

where the maximum value 0.5 comes from the results of hydro-dynamical simulations (Mohamed and Podsiadlowski 2007, 2012), and Rdust is the dust condensation radius, corresponding to the radius of the wind acceleration zone, given by (Höfner 2007) Rdust =



Rd 2



Tdust Teff

−(4+p)/2

,

(30)

where Tdust is the dust condensation temperature and p is a parameter characterizing wavelength dependence of the dust opacity. Another way to enhance wind accretion is by means of asymmetric radiationdriven winds from rotating red giants. Based on the wind compression disk model (Bjorkman and Cassinelli 1993), which explains the equatorial circumstellar disks in rapidly rotating Be stars, it has been proposed that gravitational focusing in SySts can be achieved if the radiation-driven wind from the red giant donor is not spherically symmetric and is partially confined to the equatorial plane around the donor (Skopal and Cariková 2015). Compared to Be stars, normal red giants are slow rotators. Despite that, red giants in SySts rotate faster than isolated stars with comparable spectral type (Zamanov et al. 2007, 2008), and this mechanism can still work, leading to the formation of a circumstellar gaseous disklike component around the red giant donor. Therefore, part of the wind leaving the red giant can be compressed to its equatorial plane, which increases the mass loss around the equatorial plane, proving then accretion rate efficiencies that are enhanced in comparison with the spherically symmetric case, i.e., the Bondi–Hoyle– Lyttleton model. The required assumption that winds are asymmetric seems to be consistent with observations. For instance, based on the velocity profile of the wind from the giant near the orbital plane of the eclipsing SySts EG And and SY Mus, it was possible to conclude that their winds are not spherically symmetric (Shagatova et al. 2016). In addition, the properties of the nebular [O III] λ5007 line in EG And provide further support for the wind being focusing toward the orbital plane (Shagatova et al. 2021). The accretion rate efficiency in the wind compression model can be expressed as (Skopal and Cariková 2015) ηwind,WC = ηwind,BHL



ρ c (r) ρ sph (r)



,

(31)

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where r is the distance between the center of the red giant and the WD, ρ sph (r) is the density of the spherically symmetric wind at a distance r, and ρ c (r) is the local density of the compressed wind at a distance r in the equatorial plane. The quantity ρ c (r)/ρ sph (r) also depends on the radius and rotational velocity of the red giant, on the initial and terminal wind velocities, and on how the wind is accelerated. For typical rotational velocities of red giants in SySts (∼6–10 km s−1 Zamanov et al. 2008) and wind terminal velocities (∼20–50 km s−1 ), the accretion rate efficiencies obtained with the wind compressional model, in comparison with those from the Bondi–Hoyle–Lyttleton model, can be enhanced by a factor of ∼5–15 (Skopal and Cariková 2015). We compare in Fig. 9 the accretion rates onto the WDs in SySts predicted by the atmospheric Roche lobe overflow model, the Bondi–Hoyle–Lyttleton model, the wind Roche lobe overflow model, and the wind compression model. It is clear from the figure that the Bondi–Hoyle–Lyttleton model cannot account for the accretion rates in SySts. On the other hand, the wind Roche lobe overflow model can reasonably well explain the SySts with orbital periods longer than a few thousand days. However, for those systems with orbital periods shorter than ∼103 days, this model is most likely unable to provide the required accretion rates, since in this orbital period range it provides accretion rate efficiencies comparable to the Bondi–Hoyle–Lyttleton model (Abate et al. 2013). The wind compression model is a good candidate to explain SySts in this range, as it provides accretion rates 10−8 M⊙ yr−1 . As final comment, the SySt lifetimes predicted by these gravitationally focused wind accretion models (∼0.1–1 Myr) may also help to bring into agreement predicted and observed numbers of Milky Way SySts, although further and more detailed calculations are needed to better address this issue.

Supergiant and Wolf–Rayet High-Mass X-Ray Binaries We have just described the modes of mass transfer in SySts and SyXBs. Given that sg-HMXBs and WR-HMXBs are the massive counterparts of these systems, the same modes could be in principle directly applicable to sg-HMXBs and WRHMXBs. Let us start with sg-HMXBs hosting NSs in which the supergiants are nearly filling their Roche lobes, such as Cen X–3, SMC X–1, LMC X–4 (van der Meer et al. 2007), and XMMU J013236.7+303228 (Bhalerao et al. 2012). The mass transfer in these systems can be described by the atmospheric Roche lobe overflow mode in which the extended photosphere of the supergiant is in contact with the Roche radius. In this case, matter flows to the compact object through the inner Lagrangian point, and an accretion disk around the NS is formed. Given that the donor masses in these systems are several times higher than the masses of their NS companions, mass transfer will quickly become dynamically unstable mass transfer, triggering CE evolution. The most likely outcome of this situation is a complete coalescence ˙ of the system, leading to the formation of a Thorne–Zytkow object (Thorne and

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Zytkow 1975), which would be a very cool red supergiant with a degenerate neutron core, although these objects remain thus far hypothetical. In other sg-HMXBs and WR-HMXBs, their donors are under-filling their Roche lobes, and the most likely mode of mass transfer for them is gravitationally focused wind accretion. An important implication of this mass transfer mode is that it can naturally explain wind-fed ultraluminous X-ray sources (ULXs Kaaret et al. 2017), such as the WR-HMXB M101 ULX–1 (El Mellah et al. 2019a). In addition, it also offers an explanation for the existence of accretion disks in the WR-HMXBs IC 10 X–1 and NGC 300 X–1, since this model is consistent with the formation of a wind-captured disk (El Mellah et al. 2019b). Moreover, results from recent binary models indicate that the contribution of wind-fed ULXs to the overall ULX population is up to ∼75–96% for young ( 1, which is sufficient in most cases. In addition, the hot electrons can also Compton up-scatter the soft photons from bremsstrahlung and synchrotron radiation. The formulae for these are (Narayan and Yi 1995; Abramowicz and Fragile 2013)

fbr,C = fbr



  3η1 3−(η3 +1) − (3θe )−(θ3 +1) η1 xc η1 − − 3θe η3 + 1

  fsynch,C = fsynch η1 − η2 (xc /θe )η3 .

(26)

(27)

Here η = 1 + η1 + η2 (x/θe )η3 is the Compton energy enhancement factor, and x=

hν hνc , xc = , me c 2 me c 2

x1 = 1 + 4θe + 16θe2 , x2 = 1 − exp(−τes ), η1 =

(28)

−eta1 lnx2 x2 (x1 − 1) , η3 = −1 − , η2 = , η 3 1 − x1 x2 3 lnx1

where h is Planck’s constant and νc is the critical frequency, below which it is assumed that the emission is completely self-absorbed and above which the emission is assumed to be optically thin.

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Links to Observations in XRBs X-ray binaries (XRBs) are the brightest compact sources in galaxies and have been used as unique tools to study not only the accretion onto a compact object but also the General Relativity in the strong gravitational field regime (see reviews from Zhang 2013; Belloni and Motta 2016). Moreover, galactic black hole binaries (BHBs) provide prototypes for the supermassive black holes in AGNs, with the advantages that stellar-mass BHs have much higher flux and much shorter characteristic timescales than AGNs. In this section, we will introduce the observational signatures that make contact to black hole accretion in X-ray binaries.

Spectral Components and Identifications The contributions from the optically thick and optically thin emission mechanisms can be easily identified in the observed spectra of X-ray binaries (BHBs) as soft and hard spectral components. During an outburst, the relative strengths of these components change frequently in concert with the changes in luminosity, thereby developing a set of empirical spectral classification states that can be used to broadly characterize the underlying physical state of accretion flow.

Accretion Disk The soft component is believed to originate from the radiation of the SSD, which is indeed confirmed by the observed Ldisk ∝ Td4 relation between the disk luminosity and disk temperature in BHBs (Davis et al. 2006; Dunn et al. 2011). The theoretical spectrum of SSD in the optically thick limit is a sum of blackbody spectra of different temperatures (section “Shakura–Sunyaev Disks,” Eqs. 10–11). In realistic situations, a widely applied model to interpret observations of BHBs is the so-called multicolor disk blackbody model (known as diskbb in XSPEC) (Mitsuda et al. 1984), assuming that the viscous torque vanishes at the ISCO, thereby allowing easy integration of the total flux. The disk temperature Eqs. 10 at the inner disk radius rin is given at

Tin = K

⎡

˙ ⎣ 3GM m 3 8π σ rin

(1 −



⎤1/4 6Rg )⎦ , rin

(29)

while the peak of the energy spectrum can be found at ∼fc 2.36Tin , where fc is the color correction factor. To improve the accuracy of the spectral fittings, a number of modified blackbody models have been proposed to include different inner viscous torque boundary conditions, Doppler effect due to the rotation of the matter in the disk, Thomson scatterings in the upper layer and in the atmosphere of the disk, etc. (Ebisawa et al. 1991; Shimura and Takahara 1995; Ross and Fabian 1996; Davis et al. 2006).

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Therefore, in principle, a well-described spectral energy distribution for the emission produced by an SSD around a black hole of known mass could put constraints on the overall radiative efficiency of the accretion process. More importantly, it puts constraints on the inner boundary condition of the accretion disk and therefore on the black hole spin (Zhang et al. 1997). Particularly, the BH spin changes the location of ISCO and hence changes the effective inner edge of the disk, which ultimately changes the Tin . The higher the spin is, the smaller the ISCO is, and the higher the inner disk temperature is. Note the observed thermal spectrum also depends on the disk inclination, and thus this parameter must be determined before BH spin can be extracted from the thermal spectrum (see Reynolds 2021).

Corona The hard component is generally thought to originate in corona through Compton up-scatterings of the soft photons from accretion disk or the synchrotron emission of the electrons (Galeev et al. 1979; Poutanen et al. 2018). Despite decades of numerous studies, there is still no consensus on the detailed geometry of the corona. For example, the “lamppost” model assumes that the corona locates on the rotation axis of the BH, above a standard thin disk that extends to the ISCO, which may also correspond to the base of the jet (Markoff et al. 2005; Markoff 2010); the “sandwich” model proposes that the corona is the atmosphere above the inner part of an optically thick accretion disk (Beloborodov 1998); the ADAF configuration (spherical corona) assumes that corona is the inner hot flow that lies between the inner radius of accretion disk and the BH, meaning that the accretion disk has to be truncated at a certain radius, etc. Figure 3 shows examples from some plausible configurations of the corona. Moreover, recent studies have suggested that the geometry of corona evolves with time (Kara et al. 2019) and could be inhomogeneous (Mahmoud and Done 2018a, b; García et al. 2021; Yang et al. 2022). Nevertheless, it is clear that the electrons in the corona cannot be uniformly thermal due to the heating of the accretion disk, which consequently affects the shape of the observed hard spectrum (i.e., the value of the photon index Ŵ) (Poutanen and Veledina 2013). The photon index Ŵ of the Comptonized spectrum depends on the parameters of the Comptonizing matter, primarily on the electron temperature, Te , and the Thompson optical depth τe (Sunyaev and Titarchuk 1980; Poutanen and Svensson 1996)

Ŵ=



9 π 2 me c 2 − 1/2. + 4 3κB Te (τe + 2/3)2

(30)

The Comptonized spectrum cuts off exponentially at higher energies when the electrons reach an approximate equipartition with the up-scattered photons. Sometimes, in the soft state of BHBs, the electron in the corona also contains a high-energy non-thermal tail beyond the thermal distribution (Poutanen and Veledina 2013; Gierli´nski and Done 2003; Zdziarski et al. 2017).

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Fig. 3 Examples of possible corona geometries: lamppost geometry (top left), sandwich geometry (top right), spherical geometry (bottom left), and toroidal geometry (bottom right). (Figure reproduced from Bambi 2017)

Reflection Besides the thermal and Comptonized components, the other commonly observed component in the X-ray spectra of accreting BHs is the reflection emission. The typical features of X-ray reflection component are the relativistic broadened Fe-Kα emission line at ∼6.4 keV and the Compton hump peaked around 20–30 keV. X-ray hard photons from the corona can be down-scattered by the accretion disk and further reprocessed to produce a reflection component. The Compton hump results from the combination of photo-electric absorption of low-energy photons and multiple electron down-scattering of the hard photons. Since the reflection mainly comes from the innermost regions of the accretion disk, the reflection spectra studies of XRBs can be a powerful tool to study the region close to BHs. The observed X-ray reflection spectrum is distorted by the Doppler effect and the gravitational redshift of the black hole potential. Both effects become stronger as accretion disk approaching the BH. The X-ray reflection spectra have been widely used to measure the spin of the BH. This method assumes that the X-ray reflection spectrum is truncated by the ISCO, and thus both the ISCO and spin can be measured via the strength of the Doppler and gravitational broadening. The application of the X-ray reflection spectroscopy (RS) method works on black hole X-ray binaries in their luminous hard states, with typical accretion rates of m ˙ ∼ 0.01–0.3 mEdd ˙ . However, the difficulties lie in properly estimating the extent of the “red” wing, which is most directly related to the spin of the black hole, and in modeling the hard X-ray source photons and the disk ionization, both of which strongly affect the reflection spectrum (Reynolds 2021).

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Spectral States Conversely, the spectrum of XRBs is a combination of the emissions from the disk, corona, and the reflection. During an outburst of a BHB, the source exhibits different spectral states and transitions, in particular, the X-ray spectral state transitions between the historical high/soft state (HSS) and low/hard state (LHS, see Belloni and Motta (2016) for a review). Typically, in the LHS, the spectrum of BHBs is dominated by a power-law component (Ŵ ∼ 1.5–2.1) in hard X-rays, which is thought to be produced by the Compton scattering of soft photons of the hot electrons in the corona. In the HSS, the spectrum is characterized by a multicolor blackbody component that dominates at about 1 keV, which is believed to arise from a geometrically thin, optically thick accretion disk, covered by a weak/hot corona. The typical accretion geometry is shown in the left panel of Fig. 4. Recently, the observations of BHBs have shown more complicated spectral features, suggesting a combination of various accretion flows (Kara et al. 2019; You et al. 2021; Ruan et al. 2019), accompanied by wind/outflows in some cases (see Yuan et al. 2015; Bu et al. 2016; Bu and Gan 2018 and the references therein). Nevertheless, a common accepted scenario of the accretion geometry in all these observations is the co-existence of hot and cold accretion flows, of which the systems have either an inner ADAF connecting to a truncated disk or a “lamppost" corona lying above a standard thin disk which extends inward to the ISCO. Most BHBs are transients, spending most of their lifetimes in the quiescent state (QS), and occasionally go into an outburst that could last from a few days to several months (except for one peculiar source, GRS 1915+105, has been active since the discovery). Despite that the outbursts of different systems have variant spectral-timing properties, these systems generally show similar behaviors in a Hardness-Intensity Diagram (HID) and a Hardness-rms Diagram (HRD) (Belloni and Motta 2016), with the hardness defined as the ratio of count rates between a soft band and a hard band. From the HID (Fig. 4, left panel), one can easily identify the

hard state strong corona

hard photons

weak corona

soft photons

soft state

Fig. 4 Left panel: description of the accretion flow structures in the historical hard and soft states. Right panel: a schematic description of HID and HRD of a BHB outburst. The letters refer to main locations described in the text. (Figure reproduced from Belloni and Motta 2016)

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two states as the two “vertical” branches. The right branch corresponds to the LHS, which is observed at the start and at the end of an outburst only, with relatively low accretion rate. The left branch corresponds to the HSS, with relatively high accretion rate. In addition, there are two intermediate states in the central part of the diagram, recognized as the Hard Intermediate State (HIMS) and Soft Intermediate State (SIMS). The precise transition between these four states needs additional information on the properties of the fast variability and/or changes in the multiwavelength relations (Belloni 2020). Despite various accretion solutions have been proposed to explain the accretion flow of BHBs, the “truncated disk model” might be the most popular one in explaining the disk truncation and spectral states transition. This model pictures the hard state as a truncated SSD thin disk adjoined with an inner ADAF flow (or corona) that lies between the truncated disk and the ISCO. At this stage, the disk is truncated at very large radii, only a few photons from the disk illuminate the flow, and the spectra show typical shape of a thermal Comptonization distribution. As the disk moves inward, it extends further underneath the flow, so that there are more seed photons intercepted by the flow, leading to a softer spectra. This scenario gives us a spectrum that is a combination of both hard and soft components and a thin disk with a progressively smaller inner radius. These are the typical features of the spectra observed during the (usually) short-lived HIMS and SIMS. When the truncated disk reaches the ISCO, the hot flow collapses into an SSD, where the spectrum is characterized by a multicolor blackbody component. However, the physical mechanism triggering the truncation of disk is still under discussion (see the review from Liu and Qiao 2022). Among various possibilities, the disk and corona coupling model seems to be a promising scenario (section “Disk-Corona and Jets”). Specifically, the interaction between the disk and corona causes disk gas evaporating to the corona or coronal gas condensing to the disk, depending on the gas supply rate and how the gas feeds to the accretion. The evolution of accretion geometry during an outburst of BHBs is illustrated in Fig. 5.

Timing Perspectives on Accretion Besides the spectral properties, the fast variability is also an important characteristic of accreting BHs and a key ingredient for understanding the accretion processes in these systems (Motta 2016; Ingram and Motta 2019; Belloni 2020). The fast variability is believed to be produced by the inhomogeneity in the inner accretion flow. For a given radius, if the timescale of the inhomogeneities is longer than the orbital timescale, this could lead to a signal concentrated around the frequencies corresponding to that radius. Hence the inhomogeneity could be used as a “test particle” to probe the geometry of accretion flow. BHXBRs typically show fast X-ray variability on a wide range of timescales. Fast variability is usually studied through the power density spectra (PDS) that is composed of broadband noise and peak components called Quasi-Periodic Oscillations (QPOs). The strength of the fast variability is quantified as the fractional

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Fig. 5 A schematic description of the accretion flow structures in different spectral states as consequences of disk-corona interaction, driven by mass accretion rate m. ˙ (Figure reproduced from Liu and Qiao 2022)

rms of the PDS. It is observed to have a very strong connection with the spectral state of BHBs, i.e., the accretion geometries of these systems. Generally, the PDS is dominated by the noise component during the LHS and HSS and is characterized with QPOs during the intermediate states. In some cases, the type of QPOs can even help to distinguish the intermediates states.

Noise and Propagation In the LHS, PDS of BHBs is dominated by strong band-limited noise with fractional rms values up to 40–50%, with usually no QPOs. At this state, the energy spectrum is dominated by the corona, which is high variable. The PDS can be described with a sum of Lorentzian functions that measure the characteristic frequencies of the main components seen on the PDS. Generally, there are four components that have been observed in a BHB: a low-frequency flat-top breaks at a certain value, a lowfrequency bump (could evolve to a QPO), a broader bump at higher frequency, and a highest frequency break. During an outburst, as source flux (and accretion rate) increases, the total rms decreases slightly, all characteristic frequencies increase, and the energy spectrum softens. One of the most well recognized models proposed to incorporate these frequencies is the propagating fluctuation models (Lyubarskii 1997; Kotov 2001). In this model, the band-limited noise components are proposed to break down at local viscous frequency fvisc ∝ 1/R 2 . Fluctuation can be generated at any radius in the hot flow, but the fluctuation from the outer region will modulate the inner region because the inward motion of accretion flow. The outer and inner radii of this hot

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flow were suggested as the origins of the low and high frequency breaks (or broad Lorentzians) in the PDS. Generally, numerical models combining the propagating fluctuations process with a hot flow show widely agreement with the variability properties observed in XRBs. However, when considering only the variability in the hot flow, it turned out to be difficult to accurately reproduce all the observed timing properties with the model. Several improved propagating fluctuation models have been proposed by considering: a considerably variable disk that propagates variability into the hot flow (Rapisarda et al. 2016); an extra variability in the hot flow and different propagation speeds of the fluctuations (Rapisarda et al. 2017); an additional backward propagation from the hot flow (Mushtukov et al. 2018); or a spectrally in-homogeneous hot flow (Mahmoud and Done 2018a, b; Kawamura et al. 2022), in order to match the power spectral shape and width observed in BHs. However, these improved models recently have been challenged by the high energy variability observed at 30–200 keV (Yang et al. 2022; Kawamura et al. 2023), which encourages further investigation of the fundamental hypotheses of the propagating fluctuations model. On the contrary to LHS, in the HSS, the variability is very weak and limited to a few percentages, and the PDS typically has a pure power-law shape. The energy spectrum is dominated by the thermal disk component, which is not much variable. However, this conclusion is restricted by the instrument capability, since most of the instruments are not sensitive to photons below 0.5 keV. XMM-Newton studies on BHBs have shown that the disk variability is not only strong in the hard state but also precede the hot flow variability (Uttley et al. 2014). They proposed that the disk variations could even drive the harder X-ray variability at lower frequencies. At higher frequencies, where are closer to the BH, the hot flow variability dominates over the disk variability.

QPOs QPOs are not only a common characteristic in BHBs but also observed from cataclysmic variables, through neutron star XRBs and enigmatic ultra-luminous X-ray sources, to AGNs (see the review from Belloni (2020). In addition, universal characteristic frequency correlations found in these systems suggest that the QPOs probably have a similar origin, independent of the nature of the compact object (Wijnands and van der Klis 1999; Psaltis et al. 1999; Bu et al. 2015, 2017). Low-frequency (LF) QPOs are commonly observed in the intermediate states of the BHBs, when both considerable emissions from disk and corona are observed in the energy spectrum. The frequency of LFQPOs varies over a range of frequencies from ∼0.01 to 30 Hz and can be much higher in neutron star systems. LFQPOs are defined in three types (type-A, -B, and -C) and their appearances generally relate to the spectral state, for instance, type-C QPOs in the HIMS, type-B QPOs in the SIMS, and type-A QPOs in the HSS. These three types of QPO have been shown not to be the same signal, based on, in particular, the simultaneous detection of a type-B and a type-C QPO (Belloni and Motta 2016).

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Several models have been proposed to explain the origin of type-C QPOs, which are generally based on two different mechanisms: instabilities in the accretion flow and geometric effects under general relativity (see the review by Ingram 2019). While it seems no doubt that type-C QPOs are caused by an azimuthally asymmetric geometric effect that favours a precession origin, there still no unified paradigm has been confirmed (see the review by Ingram and Motta 2019). Among various proposed models, the Lense-Thirring (LT) precession from either a hot flow or small-scaled jet is widely accepted in explaining the type-C QPOs observed in BHBs (Ingram et al. 2009; Motta et al. 2014; Ma et al. 2021). Specifically, the hot flow model assumes a truncated disk geometry, of which the BH spin axis is assumed to be moderately misaligned with the rotational axis of the binary system. The QPO frequency is determined by the LT precession of the inner hot flow. The observed flux is modulated by Doppler boosting and solid angle effects, and the broadband noise associated with QPOs would arise from variations in mass accretion rate from the outer regions of the accretion flow that propagate toward the BH, modulating the variations from the inner regions and, consequently, modulating also the radiation in an inclination-independent manner (Ingram and Klis 2013). On the other hand, the jet-precession model assumes the LT precession comes from a small-scaled jet instead of the hot flow, which does not necessarily require a truncated disk (Ma et al. 2021). While the LT precession can in principle explain the type-C QPO properties upon the source inclination, recent results appear to challenge the model, at least in its current form (Marcel and Neilsen 2021; Nathan et al. 2022), which further arises fundamental questions on whether the LT precession radius is the inner disc radius or whether the LT precession is the “right” precession for type-C QPOs. Recently, several improved disc–corona coupling models have been proposed to explain the radiative properties of the variability (Karpouzas et al. 2020; Bellavita et al. 2022; Zdziarski et al. 2021; Kawamura et al. 2022). Among these models, the VKOMPTH model, assuming the QPO arises from the coupled oscillation between the corona and the disc, has been tested to be very promising in explaining the QPOs observed in XRBs, including the kilohertz (kHz) QPOs in neutron star system and type-A, -B, -C QPOs in BHBs (Zhang et al. 2023; García et al. 2021). Type-B QPOs appear only in the SIMS and are found in narrow range of frequencies, i.e., around 6 Hz or 1–3 Hz. Their PDS also shows very weak red noise, which distinguishes them directly from type-C QPOs. It is widely accepted that type-B QPOs are associated with the relativist jet (Fender et al. 2009), however, not clear how. Some work has suggested that type-B could also originate from the LT precession of the jet (Liu et al. 2022). Type-A QPOs are the least studied type of QPO because of their small numbers (∼10). They are observed in the HSS, right after the hard to soft transition when the overall variability is already very low. One plausible model for this signal is based on the “accretion ejection instability” (AEI), according to which this instability could form low azimuthal wave numbers driven by magnetic stresses, standing spiral patterns which would be the origin of LFQPOs (see Motta (2016) for a review).

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Compared to LFQPOs, the high-frequency (HF) QPOs in BHBs are much less studied due to much fewer detection and thus make the tests of model difficult. They appear only when the accretion rate is high and can sometimes be seen in pairs. Because of their higher frequency, it is assumed to come from the innermost region of the disk, closer than where the LFQPOs are produced. They are proposed to be produced by the nonlinear resonance between orbital and radial epicyclic motion (Belloni and Motta 2016). These resonance models have successfully explained HFQPOs with frequency ratio consistent with 2:3 or 1:2.

Conclusion There is no doubt that “α-prescription” will continue to be the pillar of black hole accretion theory, not only because it allows one to build models that couple the dynamics and thermodynamics of the accretion flow phenomenologically just by an α but also it enables decades of theoretical work achieved valuable insights within this paradigm without addressing much fundamental physics. Decades of efforts have focused on the dynamics of the MRI turbulence, but very few on the thermodynamics that connects directly to the observations. For instance, it is still not clear what is the true nature of the thin disk transition radius that links to the observational characteristics of XRBs, i.e., the hard to soft transitions, the high-frequency break noise, or the quasi-periodic oscillations. How do viscous instabilities affect the variability. What makes the accretion power distribute into various forms (jet, ejection, and outflow). And most importantly, what is the nature of corona? From the observational perspective, for the last decade, thanks to the availability of several new missions (Insight-HXMT, NICER, and IXPE), our understandings on the BH accretion has enhanced significantly. These instruments provide an enormous amount of data to test the growing number of theoretical models attempting to explain the spectra, timing, and polarization of accreting compact objects. We are allowed to study the fast variability in much higher X-ray band, which directly puts new constraints on the structures of the disk/corona of XRBs. More interestingly, spectro-polarimetric studies seem very insightful in constraining the coronal geometry. Nevertheless, there are still many open questions (the origin and propagation of disk variability, the origin of HFQPOs, degeneracy in the spectral modeling, the location and structure of corona, etc.), waiting for new instruments capable of collecting more photons and reaching a much higher sensitivity for fast variations. Acknowledgments Q.C.B. acknowledges the support from the National Program on Key Research and Development Project (Grant No. 2021YFA0718500) and the National Natural Science Foundation of China (Grant Nos. U1838201, U1838202, 11733009, 11673023, U1838111, U1838108, and U1938102).

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References M.A. Abramowicz, P.C. Fragile, Foundations of black hole accretion disk theory. Liv. Rev. Relativ. 16(1), 1–88 (2013). https://doi.org/10.12942/lrr-2013-1 M.A. Abramowicz, B. Czerny, J.P. Lasota, E. Szuszkiewicz, Slim accretion disks ApJ 332, 646– 658 (1988). https://doi.org/10.1086/166683 M.A. Abramowicz, M. Calvani, L. Nobili, Thick accretion disk with super-Eddington luminosities. ApJ 242(2), 772–788 (1989). https://doi.org/10.1086/158512 M.A. Abramowicz, X.M. Chen, M. Granath, J.P. Lasota, Advection-dominated accretion flows around Kerr black holes. ApJ 471(2), 762 (1996). https://doi.org/10.1086/178004 S.A. Balbus, Numerical simulations of the MRI and real disks, in Astrophysics of Cataclysmic Variables and Related Objects, vol. 330, (2004), pp. 185–196. arXiv preprint astro-ph/0411281 S.A. Balbus, J.F. Hawley, Instability, turbulence, and enhanced transport in accretion disks. Rev. Mod. Phys. 70(1), 1–53 (1998). https://doi.org/10.1103/RevModPhys.70.1 C. Bambi, Black Holes: A Laboratory for Testing Strong Gravity, vol. 10 (Springer, Singapore, 2017), pp. 978–981. https://doi.org/10.1007/978-981-10-4524-0 C. Bellavita, F. García, M. Méndez, K. Karpouzas, vKompth: a variable Comptonization model for low-frequency quasi-periodic oscillations in black hole X-ray binaries. Monthly Notices of the Royal Astronomical Society 515(2), 2099–2109 (2022). https://doi.org/10.1093/mnras/ stac1922 T.M. Belloni, Probing the spacetime around a black hole with X-ray variability, in Topics on Strong Gravity: A Modern View on Theories and Experiments (2020), pp. 153–176. https://doi.org/10. 1142/9789813277342_0005 T.M. Belloni, S.E. Motta, Transient black hole binaries, in Astrophysics of Black Holes (Springer, Berlin/Heidelberg, 2016), pp. 61–97. https://doi.org/10.1007/978-3-662-52859-4_2 A.M. Beloborodov, Plasma ejection from magnetic flares and the X-ray spectrum of Cygnus X-1. ApJ 510(2), L123 (1998). https://doi.org/10.1086/311810 R.D. Blandford, M.C. Begelman, On the fate of gas accreting at a low rate on to a black hole. Mon. Not. R. Astron. Soc. 303(1), L1–L5 (1999). https://doi.org/10.1046/j.1365-8711.1999.02358.x R.D. Blandford, R.L. Znajek, Electromagnetic extraction of energy from Kerr black holes. Mon. Not. R. Astron. Soc. 79, 433–456 (1977). https://doi.org/10.1093/mnras/179.3.433 R. Blandford, D. Meier, A. Readhead, Relativistic jets from active galactic nuclei. Annu. Rev. Astron. Astrophys. 57, 467–509 (2019). https://doi.org/10.1146/annurev-astro-081817-051948 A. Brandenburg, A. Nordlund, R.F. Stein, U. Torkelsson, Dynamo-generated turbulence and largescale magnetic fields in a Keplerian shear flow. ApJ 446, 741–754 (1995). https://doi.org/10. 1086/175831 D.F. Bu, Z.M. Gan, On the wind production from hot accretion flows with different accretion rates. Mon. Not. R. Astron. Soc. 474, 1206–1213 (2018). https://doi.org/10.1093/mnras/stx2894 Q.C. Bu, L. Chen, Z.S. Li et al., Correlations in horizontal branch oscillations and break components in XTE J1701–462 and GX 17+2. ApJ 799(1), 2 (2015). https://doi.org/10.1088/ 0004-637X/799/1/2 D.F. Bu, F. Yuan, Z.M. Gan et al., Hydrodynamical numerical simulation of wind production from black hole hot accretion flows at very large radii. ApJ 818, 83 (2016). https://doi.org/10.3847/ 0004-637X/818/1/83 Q. Bu, T.M. Belloni, L. Chen, J. Qu, Low frequency quasi-periodic oscillations in the higheccentric LMXB Cir X-1: extending the WK correlation for Z sources. ApJ 841(2), 122 (2017). https://doi.org/10.3847/1538-4357/aa7068 B. Czerny, Slim accretion disks: theory and observational consequences. Universe 5(5), 131 (2019). https://doi.org/10.3390/universe5050131 S.W. Davis, C. Done, O.M. Blaes, Testing accretion disk theory in black hole X-ray binaries. ApJ 647(1), 525 (2006). https://doi.org/10.1086/505386 C. Done, M. Gierli´nski, A. Kubota, Modelling the behaviour of accretion flows in X-ray binaries. Astron. Astrophys. Rev. 15(1), 1–66 (2007). https://doi.org/10.1007/s00159-007-0006-1

109 Black Holes: Accretion Processes in X-ray Binaries

3935

R.J.H. Dunn, R.P. Fender, E.G. K˙ording, T. Belloni, A. Merloni, A global study of the behaviour of black hole X-ray binary discs. MNRAS 411(1), 337–348 (2011). https://doi.org/10.1111/j. 1365-2966.2010.17687.x K. Ebisawa, K. Mitsuda, T. Hanawa, Application of a general relativistic accretion disk model to LMC X-1, LMC X-3, X1608–522, and X1636–536. ApJ 367, 213–220 (1991). https://doi.org/ 10.1086/169620 M. Falanga, T. Belloni, P. Casella, M. Gilfanov, P. Jonker, A. King, (eds.) The Physics of Accretion onto Black Holes (Springer, New York, 2015). https://doi.org/10.1007/978-1-4939-2227-7 R.P. Fender, J. Homan, T.M. Belloni, Jets from black hole X–ray binaries: testing, refining and extending empirical models for the coupling to X-rays. Mon. Not. R. Astron. Soc. 396(3), 1370– 1382 (2009). https://doi.org/doi.org/10.1111/j.1365-2966.2009.14841.x L. Foschini, M. Berton, A. Caccianiga et al., Properties of flat-spectrum radio-loud narrow-line Seyfert 1 galaxies. A& A 575, A13 (2015). https://doi.org/10.1051/0004-6361/201424972 A.A. Galeev, R. Rosner, G.S. Vaiana, Structured coronae of accretion disks. ApJ 229, 318–326 (1979). https://doi.org/10.1086/156957 C.F. Gammie, R. Popham, Advection-dominated accretion flows in the Kerr metric. I. Basic equations. ApJ 498(1), 313 (1998). https://doi.org/10.1086/305521 F. García, M. Méndez, K. Karpouzas, T. Belloni, L. Zhang, D. Altamirano, A two-component Comptonization model for the type-B QPO in MAXI J1348–630. Monthly Notices of the Royal Astronomical Society 501(3), 3173–3182 (2021). https://doi.org/10.1093/mnras/staa3944 M. Gierli´nski, C. Done, The X-ray/γ -ray spectrum of XTE J1550–564 in the very high state. Mon. Not. R. Astron. Soc. 342(4), 1083–1092 (2003). https://doi.org/10.1046/j.1365-8711. 2003.06591.x J.F. Hawley, X. Guan, J.H. Krolik, Assessing quantitative results in accretion simulations: from local to global. ApJ 738(1), 84 (2011). https://doi.org/10.1088/0004-637x/738/1/84 A. Ingram, M.V.D. Klis, An exact analytic treatment of propagating mass accretion rate fluctuations in X-ray binaries. Mon. Not. R. Astron. Soc. 434(2), 1476–1485 (2013). https://doi.org/10.1093/ mnras/stt1107 A.R. Ingram, S.E. Motta, A review of quasi-periodic oscillations from black hole X-ray binaries: observation and theory. New Astron. Rev. 85, 101524 (2019). https://doi.org/10.1016/j.newar. 2020.101524 A. Ingram, C. Done, P.C. Fragile et al., Low-frequency quasi-periodic oscillations spectra and Lense-Thirring precession. Mon. Not. R. Astron. Soc. 397, L101–L105 (2009). https://doi.org/ 10.1111/j.1745-3933.2009.00693.x E. Kara, J.F. Steiner, A.C. Fabian et al., The corona contracts in a black-hole transient. Nature 565(7738), 198–201 (2019). https://doi.org/10.1038/s41586-018-0803-x K. Karpouzas, M. Méndez, E.M. Ribeiro, D. Altamirano, O. Blaes, F. García, The Comptonizing medium of the neutron star in 4U 1636 – 53 through its lower kilohertz quasi-periodic oscillations. Monthly Notices of the Royal Astronomical Society 492(1), 1399–1415 (2020). https://doi.org/10.1093/mnras/stz3502 T. Kawamura, M. Axelsson, C. Done, T. Takahashi, A full spectral-timing model to map the accretion flow in black hole binaries: the low/hard state of MAXI J1820+070. Monthly Notices of the Royal Astronomical Society 511(1), 536–552 (2022). https://doi.org/10.1093/mnras/ stac045 T. Kawamura, C. Done, M. Axelsson, T. Takahashi, MAXI J1820+070 X-ray spectral-timing reveals the nature of the accretion flow in black hole binaries. Monthly Notices of the Royal Astronomical Society 519(3), 4434–4453 (2023). https://doi.org/10.1093/mnras/stad014 A.R. King, J.E. Pringle, M. Livio, Accretion disc viscosity: how big is alpha?. MNRAS 376(4), 1740–1746 (2007). https://doi.org/10.1111/j.1365-2966.2007.11556.x O. Kotov, E. Churazov, M. Gilfanov, On the X-ray time-lags in the black hole candidates. Monthly Notices of the Royal Astronomical Society 327, 799–807 (2001). https://doi.org/10.1046/j. 1365-8711.2001.04769.x B.F. Liu, E. Qiao, Accretion around black holes: the geometry and spectra. iScience 25(1) (2022). https://doi.org/103544.10.1016/j.isci.2021.103544

3936

Q. Bu and S.-N. Zhang

H. Liu, Q. Wu, Possible origin of radio emission from non-thermal electrons in hot accretion flows for low-luminosity active galactic nuclei. ApJ 764(1), 17 (2013). https://doi.org/10.1088/0004637X/764/1/17 H.X. Liu, Y. Huang, Q.C. Bu et al., Transitions and origin of the type-B quasi-periodic oscillations in the black hole X-ray binary MAXI J1348–630. Astrophys. J. 938(2), 108 (2022). https://doi. org/10.3847/1538-4357/ac88c6 Y.E. Lyubarskii, Flicker noise in accretion discs. Mon. Not. R. Astron. Soc. 292, 679–685 (1997). https://doi.org/10.1093/mnras/292.3.679 X. Ma, L. Tao, S.N. Zhang et al., Discovery of oscillations above 200 keV in a black hole X-ray binary with Insight-HXMT. Nat. Astron. 5(1), 94–102 (2021). https://doi.org/10.1038/s41550020-1192-2 R. Mahmoud, C. Done, Modelling the energy dependence of black hole binary flows. Mon. Not. R. Astron. Soc. 473, 2084–2097 (2018). https://doi.org/10.1093/mnras/stx2359 R.A.D. Mahmoud, C. Done, Modelling the energy dependence of black hole binary flows. Mon. Not. R. Astron. Soc. 473(2), 2084–2097 (2018a). https://doi.org/10.1093/mnras/stx2359 R.A.D. Mahmoud, C. Done, A physical model for the spectral-timing properties of accreting black holes. Mon. Not. R. Astron. Soc. 480(3), 4040–4059 (2018b). https://doi.org/10.1093/mnras/ sty2133 T. Manmoto, Advection-dominated accretion flow around a Kerr black hole. ApJ 534(2), 734 (2000). https://doi.org/10.1086/308768 G. Marcel, J. Neilsen, Can Lense–Thirring precession produce QPOs in supersonic accretion flows? ApJ 906(2), 106 (2021). https://doi.org/10.3847/1538-4357/abcbf9 S. Markoff, From multiwavelength to mass scaling: accretion and ejection in microquasars and AGN. Jet Paradigm 143–172 (2010). https://doi.org/10.1007/978-3-540-76937-8_6 S. Markoff, M.A. Nowak, J. Wilms, Going with the flow: can the base of jets subsume the role of compact accretion disk coronae?. ApJ 635(2), 1203 (2005). https://doi.org/10.1086/497628 J.C. McKinney, R.D. Blandford, Stability of relativistic jets from rotating, accreting black holes via fully three-dimensional magnetohydrodynamic simulations. Mon. Not. R. Astron. Soc. 394, L126–L130 (2009). https://doi.org/10.1093/mnras/179.3.433 F. Meyer, E. Meyer-Hofmeister, Accretion disk evaporation by a coronal siphon flow. Astron. Astrophys. 288, 175–182 (1994) K. Mitsuda, H. Inoue, K. Koyama et al., Energy spectra of low-mass binary X-ray sources observed from TENMA. Publ. Astron. Soc. Jpn. 36, 741–759 (1984) S.E. Motta, Quasi periodic oscillations in black hole binaries. Astron. Nachr. 337(4–5), 398–403 (2016). https://doi.org/10.1002/asna.201612320 S.E. Motta, T. Munoz-Darias, A. Sanna et al., Black hole spin measurements through the relativistic precession model: XTE J1550–564. Mon. Not. R. Astron. Soc.: Lett. 439(1), L65–L69 (2014). https://doi.org/10.1093/mnrasl/slt181 A.A. Mushtukov, A. Ingram, M. van der Klis, Propagating mass accretion rate fluctuations in X-ray binaries under the influence of viscous diffusion. Monthly Notices of the Royal Astronomical Society 474(2), 2259–2276 (2018). https://doi.org/10.1093/mnras/stx2872 K.E. Nakamura, M. Kusunose, R. Matsumoto, S. Kato, Optically thin, advection-dominated twotemperature disks. Publ. Astron. Soc. Jpn. 49(4), 503–512 (1997). https://doi.org/10.1093/pasj/ 49.4.503 E. Nathan, A. Ingram, J. Homan, D. Huppenkothen, P. Uttley, M. van der Klis, S. Motta, D. Altamirano, M. Middleton, Phase-resolved spectroscopy of a quasi-periodic oscillation in the black hole X-ray binary GRS 1915+105 with NICER and NuSTAR. Monthly Notices of the Royal Astronomical Society 511(1) 255–279 (2022). https://doi.org/10.1093/mnras/stab3803 R. Narayan, J.E. McClintock, Advection-dominated accretion and the black hole event horizon. New Astron. Rev. 51, 733–751 (2008). https://doi.org/10.1016/j.newar.2008.03.002 R. Narayan, I. Yi, Advection-dominated accretion: a self-similar solution. ApJL 428, 13–16 (1994). https://doi.org/10.1086/187381 R. Narayan, I. Yi, Advection-dominated accretion: underfed black holes and neutron stars. ApJ 452, 710–735 (1995). https://doi.org/10.1086/176343

109 Black Holes: Accretion Processes in X-ray Binaries

3937

R. Narayan, R. Mahadevan, E. Quataert, Accretion discs, in Theory of Black Hole Accretion Disks, ed. by M.A. Abramowicz, G. Björnsson, J.E. Pringle (Cambridge University Press, Cambridge, 1998), pp. 148–182 I.D. Novikov, K.S. Thorne, Astrophysics of Black Holes, in Black Holes, Based on lectures given at the 23rd session of the Summer School of Les Houches, ed. by C. DeWitt, B.S. DeWitt (1973), pp. 343–450, Gordon and Breach, New York B. Paczy´nsky, P.J. Wiita, Thick accretion disks and supercritical luminosities. Astron. Astrophys. 88, 23–31 (1980) J. Peitz, S. Appl, Viscous accretion discs around rotating black holes. Mon. Not. R. Astron. Soc. 286(3), 681–695 (1997). https://doi.org/10.1093/mnras/286.3.681 J. Poutanen, R. Svensson, The two-phase pair corona model for active galactic nuclei and X-ray binaries: how to obtain exact solutions. ApJ 470, 249 (1996). https://doi.org/10.1086/177865 J. Poutanen, A. Veledina, Modelling spectral and timing properties of accreting black holes: the hybrid hot flow paradigm, in The Physics of Accretion onto Black Holes (Springer, New York, NY, 2013), pp. 61–85 J. Poutanen, G. Lipunova, S. Fabrika, A.G. Butkevich, P. Abolmasov, Supercritically accreting stellar mass black holes as ultraluminous X-ray sources. MNRAS 377(3), 1187–1194 (2007). https://doi.org/10.1111/j.1365-2966.2007.11668.x J. Poutanen, A. Veledina, A.A. Zdziarski, Doughnut strikes sandwich: the geometry of hot medium in accreting black hole X-ray binaries. Astron. Astrophys. 614, A79 (2018). https://doi.org/10. 1051/0004-6361/201732345 D. Psaltis, T. Belloni, M. van der Klis, Correlations in quasi-periodic oscillation and noise frequencies among neutron star and black hole X-ray binaries. ApJ 520, 262 (1999). https:// doi.org/10.1086/307436 E. Quataert, R. Narayan, On the energetics of advection-dominated accretion flows. ApJ 516(1), 399 (1999). https://doi.org/10.1086/307097 E. Quataert, R. Narayan, Spectral models of advection-dominated accretion flows with winds. ApJ 520(1), 298 (1999a). https://doi.org/10.1086/307439 S. Rapisarda, A. Ingram, M. Kalamkar, M. van der Klis, Modelling the cross-spectral variability of the black hole binary MAXI J1659–152 with propagating accretion rate fluctuations. Monthly Notices of the Royal Astronomical Society 462(4), 4078–4093 (2016). https://doi.org/10.1093/ mnras/stw1878 S. Rapisarda, A. Ingram, M. van der Klis, Modelling hard and soft states of Cygnus X-1 with propagating mass accretion rate fluctuations. Mon. Not. R. Astron. Soc. 472, 3821–3832 (2017). https://doi.org/10.1093/mnras/stx2110 C.S. Reynolds, Observational constraints on black hole spin. Annu. Rev. Astron. Astrophys. 59, 117–154 (2021). https://doi.org/10.1146/annurev-astro-112420-035022 R.R. Ross, A.C. Fabian, The spectra of accretion discs in low-mass X-ray binaries. Mon. Not. R. Astron. Soc. 281(2), 637–643 (1996). https://doi.org/10.1093/mnras/281.2.637 J.J. Ruan, S.F. Anderson, M. Eracleous et al., The analogous structure of accretion flows in supermassive and stellar mass black holes: new insights from faded changing-look quasars. ApJ 883, 76 (2019). https://doi.org/10.3847/1538-4357/ab3c1a N.I. Shakura, R.A. Sunyaev, Black holes in binary systems. Observational appearance. Astron. Astrophys. 24(3), 337–355 (1973) S.L. Shapiro, S.A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (A Wiley-Interscience Publication, New York, 2008). https://doi.org/10.1002/ 9783527617661 T. Shimura, F. Takahara, On the spectral hardening factor of the X-ray emission from accretion disks in black hole candidates. ApJ 445, 780–788 (1995) A. Sadowski, ˛ Slim disks around Kerr black holes revisited. ApJS 183(2), 171 (2009). https://doi. org/10.1088/0067-0049/183/2/171 A. Sadowski, ˛ M. Bursa, M. Abramowicz et al., Spinning up black holes with super-critical accretion flows. Astron. Astrophys. 532, A41 (2011). https://doi.org/10.1051/0004-6361/201116702

3938

Q. Bu and S.-N. Zhang

R.A. Sunyaev, L.G. Titarchuk, Comptonization of X-rays in plasma clouds-Typical radiation spectra. Astron. Astrophys. 86, 121–138 (1980) P. Uttley, E.M. Cackett, A.C. Fabian et al., X-ray reverberation around accreting black holes. Astron. Astrophys. Rev. 22(1), 1–66 (2014). https://doi.org/10.1007/s00159-014-0072-0 K.Y. Watarai, T. Mizuno, S. Mineshige, Slim-disk model for ultraluminous X-ray sources. ApJ 549(1), L77 (2001). https://doi.org/10.1086/319125 G.R. Werner, D.A. Uzdensky, Nonthermal particle acceleration in 3D relativistic magnetic reconnection in pair plasma. Astrophys. J. Lett. 843(2), L27 (2017). https://doi.org/10.3847/ 2041-8213/aa7892 R. Wijnands, M. van der Klis, The broadband power spectra of X-ray binaries ApJ 514, 939 (1999). https://doi.org/10.1086/306993 F.G. Xie, F. Yuan, The influences of outflow on the dynamics of inflow. ApJ 681(1), 499 (2008). https://doi.org/10.1086/588522 F.G. Xie, F. Yuan, Interpreting the radio/X-ray correlation of black hole X-ray binaries based on the accretion – jet model. Mon. Not. R. Astron. Soc. 456(4), 4377–4383 (2016). https://doi.org/ 10.1093/mnras/stv2956 Q.X. Yang, F.G. Xie, F. Yuan et al., Correlation between the photon index and X-ray luminosity of black hole X-ray binaries and active galactic nuclei: observations and interpretation. Mon. Not. R. Astron. Soc. 447(2), 1692–1704 (2015). https://doi.org/10.1093/mnras/stu2571 Z.X. Yang, L. Zhang, Q.C. Bu et al., The accretion flow geometry of MAXI J1820+ 070 through broadband noise research with insight hard X-ray modulation telescope. Astrophys. J. 932(1), 7 (2022). https://doi.org/10.3847/1538-4357/ac63af B. You, Y. Tuo, C. Li et al. Insight-HXMT observations of jet-like corona in a black hole X-ray binary MAXI J1820+070. Nat. Commun. 12, 1025 (2021). https://doi.org/10.1038/s41467-02121169-5 F. Yuan, Luminous hot accretion flows: thermal equilibrium curve and thermal stability. ApJ 594(2), L99–102 (2003). https://doi.org/10.1086/378666 F. Yuan, R. Narayan, Hot accretion flows around black holes. Annu. Rev. Astron. Astrophys. 52, 529–588 (2014). https://doi.org/10.1146/annurev-astro-082812-141003 F. Yuan, Z. Gan, R. Narayan et al., Numerical simulation of hot accretion flows. III. Revisiting wind properties using the trajectory approach. ApJ 804, 101 (2015). https://doi.org/10.1088/ 0004-637X/804/2/101 Z. Yu, F. Yuan, L.C. Ho, On the origin of ultraviolet emission and the accretion model of lowluminosity active galactic nuclei. ApJ 726(2), 87 (2010). https://doi.org/10.1088/0004-637X/ 726/2/87 A.A. Zdziarski, D. Malyshev, M. Chernyakova, G.G. Pooley, High-energy gamma-rays from Cyg X-1. Mon. Not. R. Astron. Soc. 471(3), 3657–3667 (2017). https://doi.org/10.1093/mnras/ stx1846 A.A. Zdziarski, M.A. Dziełak, B. De Marco, M. Szanecki, A. Nied´zwiecki, Accretion geometry in the hard state of the black hole X-ray binary MAXI J1820+070. ApJL 909(1), L9 (2021). https://doi.org/10.3847/2041-8213/abe7ef S.N. Zhang, Black hole binaries and microquasars. Front. Phys. 8(6), 630–660 (2013). https://doi. org/10.1007/s11467-013-0306-z S.N. Zhang, W. Cui, W. Chen, Black hole spin in X-ray binaries: observational consequences. ApJ 482(2), L155 (1997). https://doi.org/10.1086/310705 L. Zhang, M. Méndez, F. García, Y. Zhang, R. Ma, D. Altamirano, Z.-X. Yang, X. Ma, L. Tao, Y. Huang, S. Jia, S.-N. Zhang, J. Qu, L. Song, S. Zhang, Type-A quasi-periodic oscillation in the black hole transient MAXI J1348–630. Monthly Notices of the Royal Astronomical Society 526(3), 3944–3950 (2023). https://doi.org/10.1093/mnras/stad3062

Black Holes: Timing and Spectral Properties and Evolution

110

Emrah Kalemci, Erin Kara, and John A. Tomsick

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Galactic Black Holes: An Observational View . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Iron Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Absorption Lines and Winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radio- and Near-Infrared Emission and Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Quasi-periodic Oscillations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Lags and Reverberation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Soft γ -Rays and Polarization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Outliers in Hardness Intensity Diagram Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Modeling and Interpretation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal Disc Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Origin of Winds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Hard State Accretion Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Corona Origin/Jet Connection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Origin of Gamma-Ray Tail . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Origin of QPOs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future of Black Hole Research in X-ray and Gamma-Ray Domain . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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E. Kalemci () Faculty of Engineering and Natural Sciences, Sabancı University, Istanbul, Turkey e-mail: [email protected] E. Kara MIT Kavli Institute for Astrophysics and Space Research, Cambridge, MA, USA e-mail: [email protected] J. A. Tomsick Space Sciences Laboratory, University of California, Berkeley, CA, USA e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_100

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Abstract

We review the timing and spectral evolution of black hole X-ray binary systems, with emphasis on the current accretion-ejection paradigm. When in outburst, stellar mass black hole binaries may become the brightest X-ray sources in the sky. Analysis of high signal-to-noise data has resulted in a general framework of correlated X-ray spectral and fast timing behavior during an outburst. We utilize recent data from small but powerful observatories launched in the last decade supported by multi-wavelength ground-based observations. Coordinated observations showed that outflows (in the form of jets and winds) are an integral part of this evolution, providing a coherent phenomenological picture that we discuss in terms of the hardness-intensity diagram and spectral states. We pay particular attention to the evolution of broad and narrow emission and absorption lines and hard tails in the energy spectrum, quasi-periodic oscillations, lags, and reverberation from fast timing studies, making the connections with multi-wavelength observations when relevant. We use the bright outburst of MAXI J1820+070 as a recent test case to discuss different aspects of spectral and timing evolution, but the data and results are not limited to this source. In the second part of the review, we discuss competing theoretical models that can explain different aspects of the rich phenomenology. Data from future missions and simulation results will have the power to resolve discrepancies in these models, and black hole binary research will continue to be an exciting field that allows for tests of fundamental physics and studies of the properties of matter in strong gravitational fields. Keywords

Black hole physics · Accretion · Accretion disks · X-rays: binaries · Jets

Introduction Galactic black hole (BH) research is in the midst of an era of frequent discoveries, thanks to the maturation of data from small, yet powerful space observatories launched in the last decade, as well as flurry of activity from bright transients lighting up the X-ray and γ -ray sky (see Fig. 1). These new observatories, namely, Nuclear Spectroscopic Telescope Array (NuSTAR (Harrison et al. 2013)), Neutron Star Interior Composition Explorer (NICER (Gendreau et al. 2016)), and Hard Xray Modulation Telescope (Insight-HXMT (Zhang et al. 2014)), provided exciting new results over those presented in the seminal review of timing and spectral evolution in X-rays by Remillard and McClintock (2006) and subsequent reviews of different aspects of the subject (Belloni 2010; Gilfanov 2010; Belloni and Motta 2016; Bambi 2018; Bambi et al. 2020). Multi-wavelength campaigns have become the norm, with unprecedented cooperation between groups all over the world to coordinate ground- and space-based

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MAXI J1820+070

6 4 2 0 5

MAXI J1638+471

4 MAXI 2-20 keV rate

3 2 1 0 10

MAXI J1248-632

8 6 4 2 0 8

MAXI J1535-572

6 4 2 0 600

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1200 1400 1600 Time (MJD-57000 days)

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Fig. 1 MAXI light curves of four bright outbursts observed between MJD 57600 and MJD 59000

observations to probe the physics of accretion and ejection around BHs. One of these campaigns for transient source MAXI J1820+070 utilized all the active X-ray observatories at the time with multi-wavelength support. This source was not only extremely bright but also extremely rich in terms of phenomenology observed in other sources which resulted in the publication of many interesting articles. We used MAXI J1820+070 as a case study here for the discussion of different aspects of spectral and timing evolution of BHs to highlight contributions of the new observatories on top of the established framework based on the pioneering research done in the Rossi X-ray Timing Explorer (RXTE (Bradt et al. 1993)) era.

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The review starts with an overview of spectral and timing observational results in section “Galactic Black Holes: An Observational View” that provides the rich phenomenology of black hole research. Next, deeper information is provided on the important aspects of the phenomenology on the observational level, leaving the discussion of the underlying models in section “Modeling and Interpretation”. The review finishes with a discussion of what we can expect in the future with the future observatories in section “Future of Black Hole Research in X-ray and Gamma-Ray Domain”.

Galactic Black Holes: An Observational View Black hole binary (BHB) systems consist of a black hole and an ordinary star. Together with neutron star binaries, they form a larger class of objects called Xray binaries (XRB) in which matter accreted from the companion star may form an accretion disk around the compact object. The inner parts of the accretion disk heat up to millions of degrees in the deep gravitational potential well of the compact object resulting in X-ray emission. XRBs, especially the BHBs, provide natural laboratories where one can, among other things, study the effects of General Relativity in strong gravitational field through spectral and timing studies. In this review, BHB denotes systems with stellar mass black holes; intermediate mass black hole candidates are not considered. The first ever discovered BHB is Cyg X−1, which is a persistent system and has a high mass companion (therefore, it is a high mass X-ray binary). Since then, many other BHBs have been discovered. Currently, the number of BHBs reported is close to 70 (see https://www.astro.puc.cl/BlackCAT/ (Corral-Santana et al. 2016) for an up to date list and references). Most BHBs turned out to include low mass companions (hence most are low mass X-ray binaries). Moreover, most BHBs are transients, normally their luminosities are very low (Lx < 1033 erg/s), and they can only be detected for a limited amount of time (typically weeks to months) when the mass accretion rate increases (see Fig. 1). One can compare this luminosity with the Eddington Luminosity LEdd , which is the maximum luminosity for which the radiation pressure balances the gravitational force towards the compact object. The Eddington Luminosity is proportional to mass of the object, and for one solar mass (M⊙ ), it is 1.26 ×1038 erg s−1 (Bambi 2018). Note that dynamically measured masses of BHBs are typically between 5–10 M⊙ (Corral-Santana et al. 2016). A full historical account of the discoveries regarding BHBs and their main properties is out of scope of this review; interested readers can consult (Remillard and McClintock 2006; Belloni and Motta 2016), and references therein. The launch of RXTE in 1995 deserves a special mention, as it revolutionized the field, thanks to the large effective area detectors with unprecedented time resolution, and an all sky monitor (ASM) that allowed many new outbursts to be detected. Its scheduling flexibility, together with improved signal-to-noise ratio, led to many discoveries and established a phenomenological landscape that is used in this review as well. In the RXTE era, one of the most important discoveries about the BHBs has been

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the overall accretion – ejection paradigm; relativistic outflows detected as jets in the radio band (section “Radio- and Near-Infrared Emission and Jets”), and winds detected in X-rays (section “Absorption Lines and Winds”) were found to be closely related to X-ray spectral and temporal behavior in an outburst. The fast timing properties of BHBs are studied in the Fourier domain through the power spectral density (PSD), frequency-dependent lags, and coherence techniques (sections “Quasi-periodic Oscillations” and “Lags and Reverberation”). The PSD shows both broad and narrow features, and the narrow features are called quasiperiodic oscillations (QPOs). Most of the time, BHBs are in a very low mass accretion regime called the quiescence, or the quiescenct state. However, in an outburst, they may span eight orders of magnitude in luminosity, with typical quiescence levels of below 10−5 LEdd (Plotkin et al. 2013) to maximum levels of a few LEdd (Motta et al. 2017). This places them among the brightest X-ray emitters in the sky. During outbursts, BHBs often follow a well-known track when the intensity is plotted against the X-ray hardness called the “Hardness Intensity Diagram” (HID) (Belloni and Motta 2016) as shown in Fig. 2. In this track, sources show distinct and correlated X-ray spectral and fast timing properties called states. Moreover, the behavior in other wavelengths (especially in radio and near infrared) is also closely related to the X-ray spectral states. Galactic BHs tend to travel counterclockwise in the HID, from the bottom right, completing a sequence of states before fading into quiescence (see section “Outliers in Hardness Intensity Diagram Evolution” for a discussion of sources not following the usual sequence). The outbursts start in the hard state in which the X-ray spectrum (the navy blue curve in Fig. 3) is dominated by a hard component

1 3 4

Hard State Hardest corona, weak disk Compact radio jet Iron line and Compton hump Highest RMS: Type C QPOs, Reverberation lags

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Hard Intermediate State (HIMS) Softening corona, stronger disk Compact radio jet shuts down Iron line and Compton hump High RMS: Type C QPOs, Reverberation lags

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Soft Intermediate State (SIMS) Still softer corona, stronger disk Ballistic radio jet Iron line and Compton hump Low RMS: Transition from Type C to B QPOs

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Soft State Weak corona, strong disk No radio jet, equatorial winds Less prominent iron line and Compton hump Low RMS: Rarely Type A QPOs, no lags

Fig. 2 The hardness intensity diagram of MAXI J1820+070, illustrating the four main accretion states of a low mass X-ray binary outburst. For each state, we provide a short description of the key observables. (Figure credit: Jingyi Wang and authors)

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Fig. 3 The X-ray and γ -ray spectra of MAXI J1820+070 at two times during its 2018 outburst shown in log-log scale. The red and blue points show the spectrum of the source in the soft and hard states, respectively

associated with inverse Comptonization of seed photons from inner parts of the disk in a hot electron corona (see sections “Corona Origin/Jet Connection” and “Hard State Accretion Geometry” for a discussion of the origin and geometry) with a distinct break at tens to hundreds of keV (section “Soft γ -Rays and Polarization”). While a softer component associated with blackbody emission from the disk may exist (section “Thermal Disc Modeling”), its contribution to the X-ray luminosity is low. A component due to the reflection of hard photons by the disk is often present, and part of this component is an emission line due to fluorescence of iron. The shape of the line provides a means to study the effects of strong gravity on the inner accretion disk material. A broad and often asymmetric iron line from reflection of disk material close to the black hole is often seen at higher luminosities but can turn into a narrow iron line at low luminosities (section “Iron Lines”). The power spectral density (PSD) reveals strong broadband noise (tens of % RMS) and quasi-periodic oscillations (QPOs, see section “Quasi-periodic Oscillations” for details). The observations in the hard state for MAXI J1820+070 are shown in navy blue color in the HID (Fig. 2). The radio spectrum in this state is consistent with compact, self-absorbing jets (Fender 2001) (section “Radio- and Near-Infrared Emission and Jets”). As the outburst evolves with increasing accretion rate, the soft emission associated with the disk increases, and a transition to the hard intermediate state (HIMS) is observed. The emission from the corona becomes softer as well (if modeled with a power-law spectrum, the spectral index increases compared to those in the hard state). Type C QPOs are still present, and the overall root mean square variability (RMS) is still high, but the RMS drops with increasing disk flux (see Fig. 6). In some sources, there is a sudden transition to a softer state called the soft intermediate state (SIMS) manifested with a radio flare, a decreased continuum RMS amplitude of variability, and appearance of a Type B QPO (see Fig. 6, sections “Radio- and Near-Infrared Emission and Jets”, and “Quasi-periodic Oscillations”). Some sources show rapid transition back and forth between the HIMS and the SIMS (Belloni et al. 2011). The observations in HIMS and SIMS for MAXI J1820+070 are shown in blue and orange, respectively, in the HID (Fig. 2)

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As the disk emission becomes more dominant, another transition takes place to the soft state. In this state, the emission from the corona is very weak (the contrast can be seen in Fig. 3). The soft γ -ray spectrum extends without a break up to a few MeVs (Grove et al. 1998). The RMS variability is very low (a few % RMS, see Fig. 6) and QPOs are absent. The observations in the soft state for MAXI J1820+070 are shown in red in the HID (Fig. 2). Radio emission is quenched by 3.5 orders of magnitude (Russell et al. 2019), indicating that the jets are absent; however, high-resolution X-ray spectral observations indicate presence of an equatorial wind in high inclination sources (Ponti et al. 2012) (section “Absorption Lines and Winds”). As the disk flux starts to decrease, the source may go through the SIMS and HIMS and eventually ends up at the hard state again (Belloni and Motta 2016). The transition back to the hard state takes place at a much lower flux compared to the transition to the softer states during the outburst rise (sometimes this behavior is called “hysteresis”). There are also indications that the transition back to the hard state occurs at a fixed bolometric luminosity (Maccarone 2003; Vahdat Motlagh et al. 2019). As the luminosity goes even lower, some sources show a softening in their spectrum before they fade to quiescence (Kalemci et al. 2013; Plotkin et al. 2013). A few important additional items should be noted at this point. For papers before and in the early RXTE era, the hard state and the soft state were denoted as the low state and the high state, respectively. While using “high/low” instead of “soft/hard” state could be justified if only the soft X-rays are considered, when X-ray bolometric luminosities are used, the hard state rise luminosities can exceed the soft state luminosities (Dunn et al. 2010). This is also evident in Fig. 3. Sometimes terms like high soft state and low hard state are used as well (Belloni and Motta 2016). A few sources divert to a very luminous (close to or exceeding the Eddington Luminosity) and soft state called the ultra-luminous, hyper-soft, or anomalous state (Belloni 2010). For in-depth discussion of different definitions of states, see Belloni (2010). While the hardness intensity diagram is extremely useful to see the big picture in terms of spectral states, it does not provide the details that may be very important to characterize the source behavior. For example, it is not clear how fast the evolution takes place in different states; while the intermediate states span a wide range in hardness in MAXI J1820+070 (see Fig. 2), they lasted for 20 days. In contrast, the source spent more than 100 days in the initial hard state (Shidatsu et al. 2019). For other useful diagrams utilized in describing especially the timing properties of states, see references in Belloni and Motta (2016).

Iron Lines The X-ray spectra of accreting BHs often show a reflection component that is formed when hard X-rays irradiate the disk. This component includes a fluorescent iron emission line, an iron absorption edge, and a broad excess peaking at tens of

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keV (Lightman and White 1988; Fabian et al. 1989). Relativistic velocities of the disk material and a redshift from the BH’s gravitational field distort the reflection component (Laor 1991). Although the entire reflection component is affected, the distortion is most apparent in the iron Kα emission line, and this is clearly seen in both active galactic nuclei (Tanaka et al. 1995) and stellar mass black holes (Miller 2007). Although sources do not show reflection components at all times, and some sources do not show them at all, the presence of reflection is common. The majority of sources have reflection components, and they can occur in a variety of spectral states. For example, Cyg X−1 exhibits a strong reflection component in its hard state (Nowak et al. 2011; Parker et al. 2015), its soft state (Walton et al. 2016), and its intermediate state (Tomsick et al. 2018). GX 339−4 is an active BH transient with a well-studied reflection component in multiple spectral states (e.g., Zdziarski et al. 1998; Parker et al. 2016). The velocities in the inner portions of the disk can exceed 10% of the speed of light, producing a symmetric distortion of close to 1 keV at the 6.4 keV energy of the iron emission line. The gravitational effect produces an asymmetric distortion, which leads to a red wing of the emission line. A main goal of modeling the iron line and reflection component is to measure the location of the inner edge of the accretion disk (Rin ). If the disk extends to the innermost stable circular orbit (the ISCO), then measuring Rin provides a measurement of the BH spin. Even if the disk is slightly truncated and does not reach the ISCO, the Rin measurement still provides a lower limit on the BH spin. Some spectral and timing measurements can be interpreted as the disk becoming highly truncated for sources in the hard state (Tomsick et al. 2009; Plant et al. 2015; De Marco and Ponti 2016; Xu et al. 2020), while other measurements are not indicative of truncation (Miller et al. 2015). Most observations that suggest a high level of truncation have occurred for sources that are at low luminosities near 0.1% Eddington. At these low luminosities, the iron line profile changes from having a relativistic profile to a relatively narrow line, which provides a low limit on Rin (Tomsick et al. 2009; Plant et al. 2015; Xu et al. 2020). However, the relativistic iron line seen at high luminosities in the hard state leaves it unclear precisely when the disk becomes truncated. Determining the location of Rin and characterizing its evolution in the hard state is an active area of research (e.g., Wang-Ji et al. 2018). The iron line and other spectral components are illustrated in Fig. 4. The spectrum shown of MAXI J1820+070 in the hard state is based on modeling of a NICER and NuSTAR spectrum. The two direct components are the thermal disk emission at low energies and the coronal emission, which is modeled as being produced by Comptonization by high-energy electrons in the jet with a thermal distribution. Figure 4 illustrates the source geometry used in work by Buisson et al. (2019). We discuss possible source geometries, which are likely state-dependent, in section “Hard State Accretion Geometry”. The properties of the reflection component provide motivation for the double-lamppost since many sources have reflection components that combine relativistic reflection from the inner disk and non-relativistic reflection from the outer disk.

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Fig. 4 A possible physical scenario for the X-ray production based on the model used to fit hard state spectra of MAXI J1820+070 in Buisson et al. (2019). We thank Dr. Javier Garcia for providing a first version of this figure

NuSTAR has enabled advances in reflection and iron line studies for a number of reasons. NuSTAR’s 3–79 keV bandpass is very well-matched to measuring the reflection component. Its advantages over RXTE are its much better energy resolution as well as improved sensitivity (especially at the high-energy part of the bandpass) due to lower background. NuSTAR also provides advances over CCD instruments like those on XMM-Newton and Suzaku by providing sensitive measurements at higher energies. In addition, photon pile-up can lead to spectral distortion in CCD instruments (Done and Diaz Trigo 2010; Miller et al. 2010) which is not trivial to account for. Although pile-up can often be mitigated by using certain detector modes or by modeling the pile-up effects, it is a significant source of systematic uncertainty for bright sources. However, NuSTAR has a triggered readout system that is not susceptible to pile-up. The NuSTAR advances in bandpass and avoiding pile-up have occurred along with advances in reflection modeling by making the models more physically realistic (García et al. 2014). These advances have increased the reliability of the modeling technique as a tool to measure the properties in the inner accretion disk, including the inner disk radius and the spins of black holes.

Absorption Lines and Winds High resolution spectral observations of BHBs revealed the presence of absorption lines (see Fig. 5, Left) blue shifted by up to a few thousand km s−1 , showing that these sources not only produce collimated jets but can also drive winds. The lines are mainly hydrogen- and helium-like iron Kα, indicating material that is strongly photoionized by the X-ray illumination from the central source (see reviews by Ponti et al. 2012, 2016; Díaz Trigo and Boirin 2016). The wind is an important component in the accretion flow as the mass outflow rate in this component can exceed the mass accretion rate through the disk (Ponti et al. 2012; King et al. 2012). It is also one of the determining factors in the general

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High inclination-dipping LMXB

Fig. 5 Left: Chandra grating spectrum of GRO J1655−40 in the soft state. (Figure credit: Adapted, NASA/CXC/U.Michigan/Miller et al. 2006). Right: The hardness luminosity diagram of high inclination LMXBs, combined with detection (circles) and upper limits (triangles) of key wind absorption feature. Gray circles show all observations from all sources, and colored circles and triangles are from high inclination BHBs. (Figure credit: Ponti et al. 2012)

outburst profile and duration (Dubus et al. 2019; Tetarenko et al. 2020). Winds are observed across the black hole mass scale (King et al. 2013, and references therein), and a comparison of their properties in supermassive BHs and Galactic BHs can provide clues about the driving mechanisms of the winds. Whether we can observe evidence of winds in X-rays depends on the spectral state and disk inclination: wind signatures are preferentially detected in soft states for high inclination sources (see Fig. 5, Done et al. 2007; Ponti et al. 2012). The inclination effect indicates that the plasma has a flat, equatorial geometry above the disk providing large amount of material in the line of sight. Wind signatures are also imprinted in the optical emission lines of He and H as P Cygni profiles and broad emission line wings (Muñoz-Darias et al. 2019, and references therein). These “cold winds” are detected in the hard state. In fact, similar near infrared line features obtained by VLT/X-Shooter indicate that the cold winds are present throughout the outburst in both soft and hard states (Sánchez-Sierras and Muñoz-Darias 2020). See section “Origin of Winds” for a discussion of competing models to explain the origin of winds in BHBs.

Radio- and Near-Infrared Emission and Jets In addition to the accretion disk, corona and winds observed in the X-ray band, XRBs are also known to launch powerful jets that are most clearly observed through synchrotron emission in the radio to infrared (IR). These jets are capable of carrying away a significant amount of the accretion energy and depositing large amounts of energy into their surrounding environments (Gallo et al. 2005; Russell et al. 2007; Tetarenko et al. 2017). Radio emission is only detected in the hard state

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and during the state transition. Thus, it is clear that the launching mechanism is somehow related to the accretion process, but the causal connection between accretion and ejection and how these relativistic jets are launched, collimated and accelerated remain open questions. Here we describe the properties of the radio and IR emission during the black hole outburst, and observational efforts to probe the disk-jet connection. At the beginning of an outburst, when the X-ray emission is spectrally hard, the radio and IR show a steady, compact (AU-sized) jet (Dhawan et al. 2000; Corbel et al. 2000; Fender 2001; Stirling et al. 2001; Fender et al. 2004). The radio-to-mm spectral energy distribution (SED) shows a flat or inverted spectrum that extends up to ∼1013 Hz, beyond which the jet becomes optically thin and the spectrum steepens. This frequency of the spectral break is thought to be set by the location in the jet where particle acceleration begins: higher frequencies correspond to an acceleration zone that is closer to the black hole. In a typical outburst, as the accretion rate increases throughout the hard state, the spectral break is observed to evolve to lower frequencies (down to the radio band), which has been interpreted as being due to the particle-acceleration region moving further from the black hole. During the transition from hard to soft state, the steady, compact jet turns off, but that is not the end of the story for the jet. In several cases where high-cadence radio monitoring was possible, the end of the state transition was marked by rapid flaring in radio before completely shutting down in the soft state. The flares have been associated with the ejection of discrete knots of plasma moving away from the black hole at relativistic velocities (e.g., Mirabel and Rodríguez 1994; Fender and Belloni 2004; Bright et al. 2020). No compact radio core is observed in the soft state, but one can observe residual and spatially extended radio emission from ejecta launched during the state transition. In some cases, these knots can reach separations of tens of thousands of times farther than the jet core. In the remarkable case of MAXI J1820+070, Bright et al. (2020) discovered that during the state transition, an isolated radio flare from the compact core expanded to a spatially extended, bi-polar, relativistic outflow that was also detected in the X-rays, likely due to shocks from the jet ejecta interacting with the interstellar medium (Corbel et al. 2002; Espinasse et al. 2020). The dramatic change in both the jet (as observed in radio) and the inner accretion flow (as probed in X-rays) during an outburst motivated studies correlating these two wavelengths in order to better understand their connection. Indeed, the strong correlation between X-ray and radio luminosity suggests that an increase in the mass accretion rate onto the black hole results in an increase in mass loading in the jet (Hannikainen et al. 1998; Corbel et al. 2002; Gallo et al. 2003). This same correlation is even seen in supermassive black holes when scaled properly for black hole mass (Merloni et al. 2003; Falcke et al. 2004). While early studies suggested ∼0.7 (Corbel X-ray binaries in outburst exist on a single track, such that Lradio ∝ LX et al. 2002), in a large population study, Gallo et al. (2012) showed that there were two populations: one that is “radio-loud” and another “radio-quiet”, which may be related to changes in the radiative efficiency of the accretion flow throughout the outburst (Casella and Pe’er 2009; Koljonen et al. 2018; Espinasse and Fender 2018)

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and/or variations in observed luminosity due to inclination affects (Zdziarski et al. 2016; Motta et al. 2015, 2018; Muñoz-Darias et al. 2013; Heil et al. 2015). Beyond correlations in population studies, cross-correlation between the X-ray band and radio/IR/optical bands on timescales as short as milliseconds, have revealed insights into the causal connection between these emitting regions. Several systems show a rapid IR/optical lag of ∼0.1 s behind the X-rays (Gandhi et al. 2008, 2017; Vincentelli et al. 2019; Paice et al. 2019), which has been interpreted as being due to the propagation delay between the X-ray corona and the first IR/optical emission zone in the jet and thus constrains the physical scale over which plasma is accelerated and collimated in the inner jet (Jamil et al. 2010; Malzac 2013, 2014). This model can also explain the observed lag on a timescale of ∼minutes between radio and sub-mm bands, as the propagation front moves outwards in the jet. In addition to these lags, other tantalizing broadband timing properties are observed in several sources, but their origins remain a topic of debate, including an anticorrelation of the X-ray and optical/IR at zero-lag (e.g., Veledina et al. 2011; Paice et al. 2021) and quasi periodic oscillations (QPOs) at the same temporal frequency in both X-ray and optical/IR (Vincentelli et al. 2021). Simultaneous, fast photometry observations in X-rays and longer wavelengths are challenging to coordinate, and the field is relatively young. Future coordinated campaigns at several points in the outburst have the potential to be a powerful tool for probing disk-jet connection in X-ray binaries.

Quasi-periodic Oscillations QPOs are a tantalizing phenomenology commonly observed during black hole outbursts, where variability power is concentrated in a narrow frequency range (Fig. 6). Their origin is still debated, but much progress has been made in the last decade to understand the physics behind these striking features. QPOs broadly take the form of “low-frequency QPOs” (LFQPO, in the temporal frequency range of ∼0.005 − 40 Hz) and “high frequency QPOs” (HFQPO, observed at ∼40 − 450 Hz). There is a rich phenomenology and an admittedly confusing nomenclature, which we attempt to distill below. We refer readers to more thorough descriptions of QPOs in Casella et al. (2005), Belloni (2010), and Ingram and Motta (2019).

Low-Frequency QPOs As the source emerges in the hard state (dominated by the hard Comptonization component), the variability is very strong over a wide range of timescales (resulting in a broadband noise PSD that is often phenomenologically modeled as several broad Lorentzian components with fractional RMS of ∼30%). Just as the spectra are observed to change dramatically, so too do the variability properties. As the source flux increases in the hard state, the variability becomes more rapid, resulting in a shifting of the broad Lorentzians to higher frequencies. Often the variability becomes more concentrated at particular frequencies, resulting in the appearance of coherent QPOs. These particular hard and HIMS state QPOs are known as “Type C

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Fig. 6 The power spectral density of MAXI J1820+070 in four spectral states. The colors match the spectral types in Fig. 2. (Figure credit: Jingyi Wang)

QPOs” and are by far the most common type of QPO observed in black hole XRBs. They occur in a frequency range of ∼0.05–30 Hz, often accompanied by their higher-order harmonics. Type C QPOs have been known for decades (first seen with Ariel 6 observations of GX 339−4; Motch et al. 1983), and their origin remains elusive, but a major breakthrough came in 2015 when Motta et al. (2015) and Heil et al. (2015) discovered that the strength of the Type C QPO is dependent on the inclination of the binary orbit. More edge-on systems show stronger Type C QPO amplitudes. This suggests that the origin of Type C QPOs is geometric rather than due to intrinsic resonances in the accretion flow. Moreover, Ingram et al. (2016) found in one source, H1743-322, that the iron line centroid energy shifts with QPO phase, which gives stronger credence to geometric models. Possible origins of Type C QPOs are discussed in detail in section “Origin of QPOs”. Entering the HIMS, more power is concentrated in the QPOs, and the broadband noise level diminishes to a fractional RMS value of ∼10%. The frequency of the Type C QPOs continues to increase throughout the HIMS, until suddenly the Type C QPO vanishes and is replaced by a Type B QPO, which typically occurs in a narrower frequency range (1–6 Hz) and generally has a lower variability amplitude than Type C QPOs. The presence of the Type B QPO marks the transition to the

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SIMS. Type B QPOs are less commonly observed than Type C QPOs, but this may simply be due to the fact that they are short-lived. In MAXI J1820+070 the Type C QPO (and harmonics) were observed for ∼100 days, while the Type B QPO was seen in half of one observation for just a few hundred seconds. The Type B QPO has long been suspected to be associated with the transient ballistic jet seen in the SIMS, and in MAXI J1820+070 Homan et al. (2020) showed the clearest connection to date between these phenomena. The Type B QPO was detected 1.5–2.5 hours before the radio jet flare. Type B QPOs also show an inclination dependence (again suggesting a geometric origin), but unlike Type C QPOs, they are stronger in face-on systems. The soft state, when the accretion disk dominates the spectrum, shows very little variability on the ∼hour timescale of a typical observation (i.e., a fractional RMS of 1010 K (when the iron-group nuclei in the core separate in α particles, free nucleons, etc.). In the course of hours, much of the heat of the proto-neutron star is radiated away by neutrinos emitted through a variety of processes, while the temperature decreases to ≈ 109 –1010 K. After ≈10–100 yr (the time-scale of the thermal relaxation), the internal layers are expected to have become isothermal. At this point, the thermal evolution of the neutron star essentially depends on its heat capacity and the balance between the energy losses (mainly due to the emission of neutrinos from the interior and of photons from the surface) and heating mechanisms, such as the decay of the magnetic field, frictional heating, and (exothermal) nuclear reactions. The cooling is dominated by neutrino emission until the central temperature decreases to ≈ 105 –107 K, which may take ≈ 103 –106 yr. While most cooling curves agree that neutron stars reach a temperature of ≈ 105 K in 107 yr, the path changes dramatically between the minimal (or standard) cooling, in which the temperature decreases gradually (via modified Urca reactions), and enhanced (or accelerated cooling), where direct Urca processes still take place (owing to very high central density and/or exotic composition). In the latter scenario, the temperature drops abruptly by a factor ≈10 during the first ≈50–100 yr. In general, a large number of different cooling curves can be found, as the thermal evolution of the neutron stars critically depends on a number of poorly known physical conditions, including the neutron star mass, composition, equation of state, the impact of superfluidity and superconductivity, and the magnetic field on the various processes, as well as the processes themselves (a comprehensive overview of the neutron star cooling is given in Potekhin et al. 2015). Therefore, the importance of constraining models with measurements of the thermal component is clear. The thermal component can be observed in high-quality spectra from the extreme ultraviolet to soft X-rays (roughly below 0.5 keV).

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Naively, thermal emission can be expected to be isotropic. For RPPs, however, the situation is more complicated. For instance, heating of polar areas by the relativistic particles accelerated in strong magnetic field, influence of the magnetic field on thermal conductivity of the crust, and/or propagation of energy through magnetized atmosphere might lead to apparently non-uniform surface temperature distribution. As a result, isolated neutron stars are often observed to exhibit pulsed X-ray emission, typically with sinusoidal profiles with small pulsed fraction. In general, the presence of an atmosphere (0.1–10 cm thick, with density  102 g cm−3 , gaseous or condensed, depending on the chemical composition, temperature, and magnetic field strength – in general, low temperatures and high magnetic fields favor a condensed atmosphere.) is expected to significantly alter the emerging spectrum (see Potekhin et al. 2015 for a review). Heavy-element atmospheres should result in the presence of many spectral features, due to cyclotron and absorption lines by ions in different ionization states. However, if observed at low spectral resolutions, such a spectrum appears similar to a blackbody of comparable effective temperature. Light elements accreted from the interstellar medium or from the fallback of supernova debris have a significant impact on the spectral continuum, resulting in a highenergy tail and producing few absorption features (only cyclotron lines in the case of complete ionization). It has been estimated that even a tiny amount of hydrogen (10−20 M⊙ ) makes the emerging spectrum virtually identical to that of a pure hydrogen atmosphere. Essentially, this is due to the fact that the opacity of light elements decreases rapidly with the energy, so that at high energies, only hotter deeper layers of the neutron star can be observed. Because of this, the spectral parameters derived by a fit with a simple blackbody model can be wrong: the temperature can be overestimated by a factor up to ≈3, and the blackbody radius can be substantially overvalued (a number of different neutron star atmosphere models are available in the main fitting packages for X-ray spectral analysis). The magnetic field substantially changes the opacities for the different polarizations of the photons, thus making the emerging flux dependent on the direction of the magnetic field and producing a flux modulation with the spin in non-aligned rotating neutron stars even in the unlikely case of perfectly uniform surface temperature. Thermal emission may also result from the presence of hot spots on the neutron star surface due to currents of relativistic pairs of electrons and positrons from the materialization of gamma-rays produced in the polar-cap or outer-gap acceleration sites in the magnetosphere. This thermal emission is generally rather hard (0.1– 0.2 keV) and traceable to a blackbody radius much smaller than the stellar radius (from just a few meters to 1–2 km). It is often the dominating thermal component, especially in old objects, such as the recycled millisecond pulsars, which have already lost much of their initial heat. Unless the system geometry and the viewing angle are unfavorable, these hot spots obviously produce a flux modulation, and thus their emission can be disentangled from the other components via phase-resolved spectroscopic studies (e.g., De Luca et al. 2005).

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Pulsar electrodynamics is an immense topic, and we refer the readers to Harding (2022) and references therein for an overview. As anticipated in the introduction, there is a general agreement on the fact that rotating and magnetized neutron stars act as unipolar inductors, creating very high electric potentials. The acceleration of charged particles to very high relativistic energies is at the basis of the nonthermal pulsed radiation (and of the hot spots from backflowing particles that we have just seen). The details of the mechanisms, as well as the sites of the acceleration, however, are still uncertain. The particle acceleration may occur near the surface or in the outer magnetosphere. Goldreich and Julian (1969) first observed that neutron stars are unlikely to be surrounded by vacuum, as the induced electric force has a component parallel to the magnetic field that wins over the gravitational force at the

Fig. 2 Scheme of the magnetosphere of a pulsar

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star surface (by many orders of magnitude). The charge density in the neutron-star   · B/(2π magnetosphere has a maximum value of ρGJ ≈ −Ω c) (Goldreich–Julian charge density), which screens the electric field parallel to the magnetic field; the particle and the magnetic field corotate with the neutron star possibly up to the socalled light cylinder, with radius RLC = cPspin /(2π ), the imaginary surface where the azimuthal velocity of the (co-rotating) magnetic field reaches the speed of light (Fig. 2). Therefore, there are magnetic field lines that close within RLC and open field lines that cross the light cylinder. The regions of the star where the open field lines start are the polar gaps. The induced potential drop along the open field lines is 2 V, and the lines and particles that flow along them become ∆V ≈ 6 × 1012 B12 /Pspin the pulsar wind. The particle moving along the field lines emit via synchrotron and curvature radiation (the latter is believed to be the main radiation mechanism at GeV energies) and may Compton-scatter the soft thermal photons from the neutron star at higher energies. Photons >1 GeV may materialize in the strong field near the surface of the star producing pairs (γ + B → e+ + e− ) or starting cascades of pairs. The surviving pairs may be responsible for the hot spots and/or contribute to the coherent radio emission process. The existence of bright gamma-ray pulsars and the fact that their gamma-ray peaks are often not in phase with the radio pulses led the astrophysicists to consider other acceleration sites in the magnetosphere, near the light cylinder where the magnetic field decreases as r −3 . Here, the magnetic field is much fainter, and therefore less high-energy photons are lost in the pair production; these emission models are called outer-gap models. Other possible acceleration sites are the slot gaps along the last open magnetic field lines (the edges of the polar gaps). Moreover, reconnection in the striped wind outside the light cylinder has been envisioned as an additional feasible mechanism; for an oblique rotator, the asymptotic wind magnetic field near the rotational equator should consist of stripes of a toroidal field with alternating polarity. In general, these different models may co-exist in the same pulsar or in pulsars at different evolutionary states. The spectrum of magnetospheric emission is generally a power law with a cutoff, dN/dE = K(E/E0 )−γ exp −(E/Ec )ζ with γ ≈ 2; in the case of outer or slot gap models, the cutoff is expected to be exponential (ζ = 1) with Ec in the range between 1 and 10 GeV, while for the polar gap, the cutoff should be superexponential (ζ > 1). The high-quality spectra of many pulsars collected with Fermi favor the outer magnetosphere as the main site of production of gammaray emission, while it is believed that radio emission is connected to the polar gap and the magnetic pair production. Because the geometry of the polar gap models entails a small beam size, these models have troubles explaining the broad pulsations observed at gamma-rays. Most pulsars show two peaks separated by 0.1–0.5 cycles trailing the radio peak; the larger the gamma-ray peak separation, the smaller the lag (see Fig. 3). In the case of the recycled millisecond pulsars, all models have difficulty in explaining their radio emission, since their magnetic fields are so weak that the magnetic-induced electron-positron pair production for most of them should not occur even close to the surface in the polar gaps. A possible solution is a multipolar structure of the magnetic field as such a field would have a surface strength much higher than what is inferred from the spin period and its derivative.

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Fig. 3 Gamma-ray (black, Fermi/LAT data) and radio (red, Parkes or Green Bank telescopes data) pulse profiles for the pulsars J1747–2958 (top), J1509–5850 (middle), J1709–4429 (bottom). (From Abdo et al. 2013)

Magnetars Among the isolated neutron stars, magnetars are certainly the most variable with their unpredictable bursting activities observed in the X-rays and γ -rays on different timescales, ranging from milliseconds to hundreds of seconds, and longliving enhancements of their X-ray persistent luminosity, commonly referred to as outbursts (see, e.g., Esposito et al. (2021) for a review and references therein). These transient events trigger the all-sky monitors, such as the Burst Alert Telescope on board the Neil Gehrels Swift Observatory and the Gamma-ray Burst Monitor on the Fermi mission, allowing the discovery of new magnetars and the detection of bursting activity from known magnetars. At the time of writing (2023 August), the magnetar family comprises about 30 members, residing in our galaxy at low latitudes in the galactic plane, with the exception of two sources located in the Magellanic Clouds, SGR 0526–66 and CXOU J0100–7211. An updated list is

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maintained at http://www.physics.mcgill.ca/~pulsar/magnetar/main.html; Olausen and Kaspi (2014). Magnetars show pulsations at relatively long periods (P ∼ 1–12 s), which slow down on timescales of a few thousand years (P˙ ∼ 10−13 –10−11 s s−1 ). The timing parameters imply characteristic ages of τc ∼ 103 –105 yr and external dipolar magnetic fields of Bdip ∼ 1014 –1015 G, making them the strongest magnets we know of in the universe. There is a growing evidence that a stronger field might be present inside the neutron star and in non-dipolar components in the magnetosphere. The persistent X-ray luminosity of LX ∼ 1032 –1036 erg s−1 is generally higher than ˙ pointing to an extra source of power. For this reason, their spin-down luminosity E, it is believed that magnetar emission is fed by the instabilities and decay of their superstrong magnetic field.

Magnetar History in a Nutshell The dawn of the neutron star class of magnetars dates back to March 5, 1979, when an intense burst of hard X-/soft γ -rays was detected in the direction of the Large Magellanic Cloud, from the source currently known as SGR 0526–66 (Mazets et al. 1979). This giant flare showed features different from those of gamma-ray bursts (GRBs): it was much brighter than a usual GRB, and the emission decayed over a timescale of about 200 s with a tail modulated at a period of 8.1 s, suggesting a neutron-star origin for this event. The source was found to be recurrent, with emission of short soft γ -ray bursts in the following months. Meanwhile, more and more of such bursts were observed and initially classified as GRBs. However, they were coming repeatedly from the same direction in the sky and exhibited a softer spectrum than those of most GRBs, hence the source designation as Soft Gammaray Repeaters (SGRs). For instance, the source of GRB 790107 was observed to repeat more than 100 times between 1979 and 1986 and nowadays is recognized as SGR 1806–20. In the same years, an unusual 7 s X-ray pulsar, 1E 2259+586, was discovered as a bright persistent source (LX ∼ 1035 erg s−1 ) at the center of the supernova remnant G109.1–1.0 (Fahlman and Gregory 1981). Originally thought to be in a binary system with an elusive low-mass companion star, this object shared similar characteristics with a handful of other sources, such as 1E 1048.1–5937 and 4U 0142+614: bright X-ray pulsations at few-second periods, an X-ray luminosity exceeding the spin-down energy loss rate, and no apparent companion from which to accrete matter. Owing to these traits, these new sources were awarded the epithet of Anomalous X-ray Pulsar (AXP). Following the discovery of SGRs as a peculiar group of bursting isolated neutron stars, a variety of models were put forward. The most successful explanation is provided in terms of a highly magnetized neutron star, hence the name magnetar, with Bdip ∼ 1014 –1015 G (Duncan and Thompson 1992). According to the magnetar model, the dominant energy reservoir in these sources is magnetic: giant flares are caused by a large-scale reconnection of the magnetic field, and the short

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fainter bursts are triggered when magnetic stresses build up in a portion of the crust sufficiently to crack it (Thompson and Duncan 1995, 1996). Thompson and Duncan (1996) further pointed out similarities between the AXPs and SGRs in their quiescent state, arguing that AXPs are also magnetars with a decaying field powering the high X-ray luminosity. Alternative scenarios considered isolated neutron stars with ∼1012 G magnetic fields accreting from a fallback disk formed after the supernova explosion (see, e.g., Alpar 2001); however, these models fail to explain the powerful flaring activity observed in these sources. The confirmation of the magnetar picture was brought by the measurement of the period derivative of an SGR for the first time. Using Rossi X-Ray Timing Explorer data, Kouveliotou et al. (1998) discovered pulsations in the persistent X-ray flux of SGR 1806−20 at a period of 7.47 s and a spin-down rate of 2.6 × 10−3 s yr−1 , implying Bdip = 8 × 1014 G and τc = 1.5 kyr. Moreover, the observed X-ray luminosity was two orders of magnitude higher than the rotational energy loss rate. Therefore, only the magnetar model could account for these observed properties. A few years later, the detection of SGR-like bursts from two AXPs (1E 2259+586 and 1E 1048.1−5937) blurred the boundary between SGRs and AXPs, observationally unifying the two groups as predicted by Thompson and Duncan (1996). Since then, it is clear that both SGRs and AXPs host magnetars, which can show a continuous spectrum of behaviors, from long periods in quiescence to strong bursting activity and major flares.

Persistent Emission The primary manifestations of this group of highly magnetized neutron stars occur in the X-ray energy range. All confirmed magnetars display pulsations in the soft X-ray band ( S) ∝ S −α ) with indexes in the range ∼0.6–0.9. SGR 1935+2154 is one of the most burst prolific magnetars. Since its discovery in 2014, it emitted about 300 bursts, as solitary events or associated with outbursts,

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and a burst forest (i.e., emission of a plethora of short bursts clustered in time) on April 27–28, 2020. The average burst energy increased during the four episodes registered between 2014 and 2016, suggesting that the next bursting activity would have likely been more intense. Contrary to this expectation, the burst energies of the 2019 and 2020 episodes (excluding the burst forest for the latter) indicate a flattening of the average burst energy curve. Moreover, the bursts detected during the latest two activations were slightly longer and softer than those observed at earlier epochs (see, e.g., Lin et al. 2020). On April 27, 2020, SGR 1935+2154 entered a new exceptional active phase, whose onset was marked by a storm of highly energetic bursts detected with the Swift Burst Alert Telescope and the Fermi Gamma-ray Burst Monitor. NICER observed the source ∼6 hours after the initial trigger and caught the tail of the burst forest (see Fig. 7, top panel; Younes et al. 2020). During the first ∼20 minutes of the pointing, more than 220 bursts were identified translating into a burst rate of >0.2 burst s−1 , to be compared with the rate of 0.008 burst s−1 derived 3 hours later. The majority of the bursts exhibited multi-peaked profiles with shorter rise than fall times, in agreement with the bulk of short magnetar bursts, and the 1–10 keV spectra are well modelled by an absorbed blackbody with an average temperature of 1.7 keV. However, what made this new active phase really unique is the detection of a bright, millisecond-duration radio burst, with properties reminiscent those of fast radio bursts. This was the first time to observe such an event from a known magnetar. A day after the initial trigger, the Canadian Hydrogen Intensity Mapping Experiment (CHIME) and the Survey for Transient Astronomical Radio Emission 2 (STARE2) independently observed the radio burst (Andersen et al. 2020; Bochenek et al. 2020). The energy released Eradio ∼ 1034 – 1035 erg is about three orders of magnitude greater than that of any radio pulse from the Crab pulsar, previously the source of the brightest Galactic radio bursts, and 30 times less energetic than the weakest extragalactic fast radio burst observed so far. Remarkably, the radio burst was temporally coincident with a hard X-ray burst (see, e.g., Mereghetti et al. 2020), showing for the first time that magnetar bursts can have a bright radio counterpart. The bottom panel of Fig. 7 shows the light curves of the hard X-ray burst as observed by INTEGRAL and of the doublepeaked radio burst detected by CHIME. The X-ray light curve consists of a broad pulse with three narrow peaks separated by ∼30 ms. The X-ray peaks lag the radio ones by ∼6.5 ms; this short delay implies that both components arise from a small region of the neutron star magnetosphere. The X-ray burst spectrum was harder than any other extracted from bursts emitted by the same source, while the energy output EX ∼ 1039 erg is in the range of energies expected from magnetar bursts, resulting in Eradio /EX ∼ 10−5 . This discovery motivated the search for bright radio bursts in archival radio and X-ray simultaneous data of magnetar outbursts. Another detection was reported during the 2009 outburst of the magnetar 1E 1547.0–5408 (Israel et al. 2021). Two radio bursts were observed, and one of them was anticipated by a short X-ray burst by ∼1 s, implying Eradio /EX ∼ 10−9 . These two detections strengthened the hypothesis that at least a sub-group of fast radio bursts can be powered by magnetars at cosmological distances. Furthermore, the wide range of the radio-to-X-ray energy ratios suggests that magnetar radio bursts can resemble

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Fig. 7 Top panel: NICER light curve of the burst forest emitted by SGR 1935+2154 in 2020 April. The light curve was extracted from the first ∼1200 seconds of the observation acquired on 2020 April 28, starting at 00:40:58 UTC, in the 1–10 keV energy range. More than ∼220 bursts were detected. The inset is a zoom-in at the area delimited with a dotted gray box, representing the most intense bursting period. (From Younes et al. 2020). Bottom panel: Light curves of the simultaneous X-ray (blue) and radio (red) burst, as observed with the INTEGRAL IBIS/ISGRI instrument and CHIME respectively, emitted by SGR 1935+2154 on 2020 April 28. (Adapted from Mereghetti et al. 2020)

both the powerful fast radio burst and the typical singles pulses from ordinary radio pulsars, bridging the two populations. Outbursts Short bursts are often accompanied by large enhancements of the persistent X-ray flux that can increase up to three orders of magnitude higher than the pre-outburst level. Then, the flux usually relaxes back to the quiescent level on timescales ranging from weeks to months/years. The decay pattern varies from outburst to outburst but in most cases is characterized by a very rapid initial decay within minutes to hours, followed by a slower fading modelled by a power-law or exponential function. Sometimes, the flux decrease might be interrupted by a period

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Fig. 8 Temporal evolution of the bolometric (0.01–100 keV) luminosities for the major outbursts occurred up to the end of 2016 and with intended and long coverage. (From Coti Zelati et al. 2018)

of stability or can drop suddenly. Figure 8 shows the long-term light curves of all the outbursts detected up to the end of 2016 and monitored intensively in X-rays. During an outburst, the X-ray spectrum undergoes an overall initial hardening and then slowly softens on the timescale of the flux relaxation. For instance, for a soft X-ray spectrum modelled with an absorbed blackbody and a power law, the hardening may correspond to an increase in the blackbody temperature and a decrease in the photon index, while if only one thermal component is required for the quiescent spectrum, a second hotter blackbody may appear during an outburst. The emission area, temperature, and luminosity associated with this new component typically decline as the outburst progresses until becoming undetectable again. In some cases, a hard non-thermal tail is detected at the outburst peak and observed to fade on faster timescales than the softening of the 0.3–10 keV X-ray spectrum. It is believed that outbursts are caused by heat deposition in a restricted area of the magnetar surface; however, the responsible heating mechanism is still poorly understood. The energy is injected into the crust and then conducted up to the surface because of magnetic stresses, resulting in displacements/fractures of the crust itself (see, e.g., Gourgouliatos and Lander 2021). The energy should be injected into the outer crust; otherwise, most of it would be radiated in the form of neutrinos. Moreover, a minimum value of energy is required to yield an observable effect. For energy 1043 erg, a saturation effect occurs, meaning that a larger amount of energy does not change the observable result. The surface photon luminosity reaches a limiting value of ∼1036 erg s−1 since the crust becomes so hot that nearly all the energy is released via neutrinos before it reaches the surface (Pons and Rea 2012). Moreover, the crustal displacements induce a strong twist on the magnetic field lines outside in the magnetosphere (Beloborodov 2009). Additional heating of the surface layers is then produced by the currents flowing in the bundle as they hit the star. The twist must decay in order to supply its own currents; the gradual untwisting induces a reduction of the area impacted by the magnetospheric charges and the luminosity decreases. Both mechanisms are most likely at work during an outburst. In these terms, it is worthy to mention the case of the magnetar 1E 1547–5408 (Coti Zelati et al. 2020). About 1 year after the latest outburst in 2009, the source settled in a relatively high-flux state, which was observed to be steady over the last 10 years. During these 10 years, the soft X-ray flux attained a value ∼30 times higher than its historical minimum measured in 2006. Moreover, hard X-ray observations carried out in 2016 and 2019 revealed a faint emission up to ∼70 keV, described by a flat power law component with a 10–70 keV flux ∼20 times smaller than that at the peak of the 2009 outburst. These properties are at variance with the typical overall softening observed in an ordinary magnetar outburst and can be naturally accounted for by invoking the untwisting bundle scenario as the only mechanism driving the outburst. The source has reached a new persistent magnetospheric state, different from that observed during the pre-outburst epoch. A magnetospheric reconnection can lead to a local reorganization of the magnetic field, leaving a new pattern of twisted lines associated to current bundles that could dissipate over decades. The flowing currents are responsible for both the non-thermal X-ray emission, via resonant Compton scattering of photons from the surface by the charged particles, and the thermal X-ray emission, via the current dissipation in localized regions close to the stellar surface. The 2009 outburst and the new persistent state of 1E 1547– 5408 provide compelling evidence that a small sample of magnetar outbursts can be entirely powered by the dissipation of magnetospheric currents. Moreover, the source underwent a new outburst in 2022 April, its first since its major 2009 outburst, and the flux decayed back to the same pre-outburst new persistent level. Changes in the timing properties have been reported several times along with outburst episodes. In some cases, the pulse profiles become more complex in shape with a multi-peaked configuration, and accordingly, the pulsed fraction varies (see Fig. 4, left panel). Glitches, i.e., sudden increases in the rotational frequency of the star, are very common during outbursts with amplitude in the range δν/ν ∼ 10−9 –10−5 . Note that many glitches are also observed in the absence of measurable change in the X-ray flux. A statistical study of these timing anomalies in magnetars and rotation-powered was performed (Fuentes 2017). The glitch activity, defined as the time-averaged change of the rotation frequency due to glitches, of magnetars with the smallest characteristic ages τc is lower than that of pulsars with similar τc . However, their activity is larger than that of pulsars of equal spin-down power.

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The only parameter for which the glitch activity of magnetars appears to follow the same relation as for rotation-powered pulsars is the spin-down rate. An interesting aspect of magnetar glitches is the over-recovery following the timing event, often resulting in a net spin-down or anti-glitches. The most famous anti-glitch candidate was reported for the magnetar 1E 2259+586, whose spin frequency changed by a factor of ∼ − 5 × 10−8 Hz in less than 4 days (Archibald 2013). This event was accompanied by multiple X-ray radiative episodes, such as the emission of a short hard X-ray burst and an increase of the persistent flux by a factor of 2. The extreme and rapid variability in the spin-down torque appears to be another common feature following magnetar outbursts. Several magnetars have been intensively monitored after a flaring episode, and when torque variations are observed, they can dominate the long-term evolution of these sources. Radio transient pulsed emission has been detected in a handful of magnetars, associated with an X-ray outburst. XTE J1810–197, which briefly became the brightest radio pulsar at the time of this discovery, was the first radio-loud magnetar to be discovered (Camilo et al. 2006). The radio emission was observed 1 year after the onset of the X-ray outburst in 2003. The X-ray flux reached the pre-outburst level in early 2007, although the source remained radio loud until late 2008. Radio pulsations were then caught from 1E 1547–5408 (Camilo et al. 2007), PSR 1622– 4950, the only magnetar discovered in the radio band so far (Levin et al. 2010), and SGR J1745–2900, found at an angular separation of 0.1 pc from Sgr A∗ (Eatough et al. 2013). The most recent additions to this small group are Swift J1818.0–1607 (see, e.g., Lower et al. 2020), discovered in 2020 March, and SGR 1935+2154, whose radio pulsed emission was detected after the emission of a few clustered short radio bursts (Zhu et al. 2023). The spectrum of the pulsating radio emission of magnetars is flatter than that of rotation-powered pulsars: S ∝ ν −0.5 for the former and S ∝ ν −1.8 for the latter, where S is the flux density and ν is the frequency. The only exception is Swift J1818.0–1607, which shows a steeper spectrum (S ∝ ν −2.3 ) compared with the other radio-loud magnetars. Moreover, the radio emission displays large pulse-to-pulse variability with pulse shapes that can vary considerably on timescales of minutes. The single pulses are usually comprised of narrow, spiky sub-pulses with a high degree of linear polarization. A systematic study of all outbursts detected in the X-rays up to the end of 2016 was performed by Coti Zelati et al. (2018) who reanalysed about 1100 X-ray observations in a consistent way, focusing on the temporal evolution of the soft X-ray spectral parameters (This study is complemented by the Magnetar Outburst Online Catalog, http://magnetars.ice.csic.es/.). This work highlighted some common trends in all the outbursts by investigating possible (anti-)correlations between different parameters, e.g., peak and quiescent luminosity, decay timescale, energy released during the outburst, τc , and Bdip . For instance, they found that a larger luminosity at the outburst onset corresponds to a larger amount of energy released during the outburst, and the outbursts with a longer overall duration are also the more energetic ones. An anti-correlation between the quiescent luminosity and the outburst luminosity increase was discovered, suggesting a limiting luminosity of

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∼1036 erg s−1 for the outbursts regardless of the quiescent luminosity level (see Pons and Rea (2012) and above). The energy released in an outburst linearly depends on Bdip , and a sort of limiting energy as a function of age is observed. In other words, the young magnetars undergo more energetic outbursts than older ones. These characteristics are naturally explained in terms of field decay.

Low-Magnetic Field Magnetars The picture according to which magnetar activity is driven by a super-strong magnetic field has been challenged by the discovery of three magnetars with a magnetic field within the range of those of ordinary radio pulsars, Bdip ∼ (0.6–4) × 1013 G (see Turolla and Esposito (2013) for a review and reference therein). We should bear in mind that we are referring to the strength of the large-scale, dipolar component of the magnetic field estimated from the spin parameters far away from the stellar surface (see Eq. 3) and that magnetar activity (i.e., bursts and outbursts) is driven by ultrastrong magnetic fields, “hidden” in the star interior and/or at the surface. On June 5, 2009, the detection of a couple of short hard X-ray bursts heralded the existence of a new magnetar, SGR 0418+5729. Follow-up observations in the soft X-ray band disclosed a bright persistent counterpart with an observed flux of a few 10−11 erg s−1 cm−2 and a spin period of ∼9.1 s. The first 5 months of monitoring yielded only an upper limit on the spin-down rate, |P˙ | < 1.1 × 10−13 s s−1 (at 3σ confidence level), which corresponds to an upper limit on Bdip of 3 × 1013 G. This value was the lowest spin-inferred magnetic field among the magnetar population at that time. An unambiguous measure of P˙ required more than 3 years of continuous monitoring. A coherent timing analysis with a baseline of ∼1200 days gave P˙ = 4(1) × 10−15 s s−1 , implying Bdip ∼ 6 × 1012 G and τc ∼ 36 Myr, giving confirmation that SGR 0418+5729 was a low-B magnetar. Swift J1822.3– 1606 was discovered through the detection of a series of magnetar-like bursts on July 14, 2011. The fast slew of the Swift X-ray Telescope promptly detected a bright source at an observed flux level of ∼2 × 10−10 erg s−1 cm−2 and pulsating at ∼8.4 s. ROSAT serendipitously observed the region of the sky covering the magnetar position in September 1993. A reanalysis of these observations unveiled a source at a location consistent with that of Swift J1822.3–1606 at a flux level of ∼4 × 10−14 erg s−1 cm−2 , most likely being the magnetar in its quiescent state. A campaign lasting 1.3 years allowed for the determination of the period derivative, equal to P˙ = 1.34(1) × 10−13 s s−1 (Rodríguez Castillo et al. 2016). Therefore, from the timing parameters, Bdip ∼ 3 × 1013 G and τc ∼ 1 Myr. Swift J1822.3– 1606 is thus the magnetar with the second lowest magnetic field. The last member of this small group is 3XMM J185246.6+003317 (3XMM J1852; (see, e.g., Zhou et al. 2014)). It was serendipitously discovered while undergoing an outburst in 2008 during an XMM-Newton campaign of the supernova remnant Kes 79. The magnetar rotates at a period P ∼ 11.6 s. No spin-down was detected during the

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seven months of the outburst decay. The 3σ upper limit for the period derivative |P˙ | < 1.4 × 10−13 s s−1 translates to τc > 1.3 Myr and Bdip < 4 × 1013 G, defining 3XMM J1852 as the third low-B magnetar. The smallness of the period derivative is mirrored in the spin-inferred Bdip and τc , which is two or three orders of magnitudes larger than the typical values for magnetars (103 –105 yr). These two properties are suggestive that these three sources might be old magnetars that have already experienced a substantial field decay over their lifetime. Further features, such as the small number of detected bursts and the low quiescent luminosity, corroborate this interpretation. These discoveries showed how neutron stars with dipolar magnetic fields lower than those of ordinary magnetars can emit bursts and outbursts. Actually, one of the key ingredients to power magnetar bursting activity is the internal magnetic field, its toroidal component in particular. Therefore, the low-B magnetars should retain a strongenough (∼1014 G) internal toroidal field to seldomly produce crustal displacements, resulting in a much lower burst rate compared to younger objects. Indeed, magnetothermal evolutionary models support this scenario: the evolution of an initial Bdip ∼ 2 × 1014 G provides the observed characteristics for SGR 0418+5729 and Swift J1822.3–1606 at an age of ∼1 Myr and 0.5 Myr, respectively, if the initial toroidal field is high enough, ∼1016 G for the former and ∼5 × 1015 G for the latter. An observational gauge of the magnetic field strength in neutron stars is provided by cyclotron features in their X-ray spectra. Such a feature was reported in the lowB magnetar SGR 0418+5729 during its 2009 outburst (Tiengo et al. 2013). The most striking property of the absorption line is its strong dependence on the star rotational phase: the line energy is in the 1–5 keV range and varies strongly with the spin phase, roughly by a factor of 5 in one-tenth of a spin cycle (see Fig. 9). The most plausible explanation for the feature variability is given if the line is due to cyclotron resonant scattering. The cyclotron energy for a particle of charge e and mass m is Ecycl =

11.6  me  B12 keV, 1+z m

(6)

where z ∼ 0.8 is the gravitational redshift, me is the electron mass, and B12 is the magnetic field in units of 1012 G. In this scenario, the strong dependence of the line energy with phase arises from the different fields experienced by the charged particles interacting with the photons emitted from the surface. If protons are the particles responsible for the scattering, the feature energy implies a magnetic field spanning from 2 × 1014 G to > 1015 G, much higher than Bdip . According to the simplest model, the scattering may take place in a small localized magnetic loop close to the surface of the neutron star. If this interpretation is correct, this result provides evidence for a complex topology of the magnetosphere, with strong nondipolar magnetic field components. A similar phase-dependent absorption feature was detected in another low-B magnetar, Swift J1822.3–1606 (Rodríguez Castillo et al. 2016). The energy of the feature varies between ∼5 and ∼12 keV, and the resulting strength of the magnetic field in the small magnetic coronal loop is in the

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Fig. 9 Normalized energy versus phase image of SGR 0418+5729 extracted from the XMMNewton observation carried out on August 12, 2009, about 2 months after the outburst onset. The image was obtained by binning the source counts into 100 phase bins and 100-eV-wide energy channels and then by normalizing the counts to the phase-averaged spectrum and pulse profile. The red line indicates the expected phase dependence of the features in the proton cyclotron scattering model developed by Tiengo et al. (2013). (From Tiengo et al. 2013)

(6–25) ×1014 G range. Two additional detections were reported in two X-ray dim isolated neutron stars (see section “Overview of the Observational Properties”).

Magnetar-Like Activity from High-B Rotation-Powered Pulsars As there are magnetars having rather low dipolar magnetic fields, there exists a small group of rotation-powered pulsars with magnetar field strengths. Since the strong magnetic field is the source of instabilities in magnetars, magnetar-like bursts and outbursts might also be expected from high-B pulsars and, indeed, have been observed in two such sources. PSR J1846−0258 is the neutron star associated with the supernova remnant Kes 75. With a rotation period of 326 ms, it is one of the youngest known pulsars in the galaxy and has a Bdip ∼ 5 × 1013 G. PSR J1846−0258 behaved as a typical rotation-powered pulsar for the majority of its observed lifetime, with an X-ray luminosity lower than its spin-down luminosity and powering a bright pulsar wind nebula. However, it has no detectable radio emission, although this may be due to unfavorable beaming. Data collected with the Rossi X-Ray Timing Explorer between 2000 and 2006 allowed us to measure the braking index equal to n = 2.65 ± 0.01 (Livingstone et al. 2006). This value is less than 3, which is expected

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from magnetic dipole radiation, implying that another physical mechanism must affect the pulsar rotational evolution (e.g., a time-varying magnetic moment or the effects of magnetospheric plasma on the spin-down torque). Remarkably, this pulsar emitted a few short (∼0.1 s) magnetar-like bursts in May 2006 coincident with an enhancement of the pulsed flux that lasted about 2 months (Gavriil et al. 2008). This event recalled a typical magnetar outburst. Its quiescent spectrum is like that of other young rotation-powered pulsars, well described by a simple power law with photon index Γ ∼ 1.2. During the outburst, the spectrum softened (Γ ∼ 1.9) significantly and called for an extra component, a blackbody with kT ∼ 0.9 keV, resembling the spectra of magnetars. Due to the softening, the 0.5–2 keV flux showed the largest increase (a factor of ∼20), whereas the 2–10 keV flux increased only by a factor of ∼6. The onset of the outburst was accompanied by a large glitch and an increase in the timing noise of the pulsar. The glitch recovery was unusual for a rotation-powered pulsar but was reminiscent of timing behavior observed from magnetars: the glitch decayed over ∼130 days resulting in a net decrease of the pulse frequency. A 7-year post-outburst monitoring campaign revealed a change in the braking index. The post-outburst value, n = 2.19 ± 0.03, is discrepant at the 14.5σ level from the pre-outburst braking index. A change in n might be due to a change in the configuration of the pulsar magnetosphere (Archibald et al. 2015). After 14 years of quiescence, PSR J1846−0258 entered again in outburst on August 1, 2020 (see, e.g., Blumer et al. 2021). The spectral evolution was similar to what was observed previously in 2006. Radio magnetars are generally characterized by spin-down luminosity E˙ larger than their X-ray luminosity LX , in line with the rotation-powered pulsars, and radio pulsations had been detected within a few days of the outburst onset. For PSR J1846−0258, the X-ray efficiency LX /E˙ 160 was registered, and the spectrum underwent a hardening with kT increasing from ∼0.2 keV to ∼1.1 keV. These two sources belong to a small yet growing class of objects that straddle the boundary between rotationally and magnetically powered neutron stars. In the coming years, additional high-B pulsars might undergo a magnetar-like transition, strengthening the link between radio pulsars and magnetars and, thus, providing observational evidence for a grand unification of the isolated neutron star population.

Central Compact Objects Central Compact Objects (CCOs) form a small, heterogeneous group of isolated X-ray emitting neutron stars, observed close to the geometrical center of young (0.3–7 kyr) supernova remnants and characterized by the absence of emission at other wavelengths (see De Luca et al. (2017) for a review and references therein). This class consists of a dozen confirmed sources (See the complete catalog at http:// www.iasf-milano.inaf.it/~deluca/cco/main.htm.) that only show thermal soft X-ray emission (0.2–5 keV), with no evidence for a non-thermal component. Their spectra are well modelled by the sum of two blackbodies with temperatures kT ∼ 0.2– 0.5 keV and small emitting radii ranging from 0.1 to a few km. Their luminosity, of the order of 1033 erg s−1 , is generally steady, and in most cases, pulsations are not detected (see Table 1). The name CCO was used for the first time by Pavlov et al. (2000) to refer to the point-like source at the centre of the supernova remnant Cassiopeia A. Since then, it had become the label for objects that share the abovementioned properties, although it could be misleading. The Crab pulsar is located at the center of its nebula and is a compact object; however, it is not classified as a CCO because of its emission at other wavelengths apart from X-rays. The first observed CCO, 1E 161348–5055 in the supernova remnant RCW 103, turned out to be a unique source, exhibiting a magnetar-like outburst in 2016 and possibly another one in 1999–2000 (see section “1E 161348–5055: A Hidden Magnetar”).

Fun Facts About CCOs The proof that CCOs are indeed neutron stars came with the detection of pulsations from three objects: PSR J1852+0040 in Kes 79 (P ∼ 105 ms; Gotthelf et al. 2005), PSR J0821–4300 in Puppis A (P ∼ 112 ms; Gotthelf and Halpern 2009), and 1E 1207.4–5209 in G296.5+10.0 (P ∼ 424 ms; Zavlin et al. 2000). Observational

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Table 1 Properties of the well-established central compact objects (first table) and two candidates (second table). (Modified from Gotthelf et al. 2013)

CCO CCO PSR J0821–4300 CXOU J085201.4–461753 1E 1207.4–5209 CXOU J160103.1–513353 1WGA J1713.4–3949 XMMU J172054.5–372652 XMMU J173203.3–344518 PSR J1852+0040 CXOU J232327.9+584842 CXOU J181852.0–150213 1E 161348–5055b 2XMMi J115836.1–623516 XMMU J173203.3–344518 a The

SNR SNR Puppis A G266.1–1.2 G296.5+10.0 G330.2+1.0 G347.3–0.5 G350.1–0.3 G353.6–0.7 Kes 79 Cas A G15.9+0.2 RCW 103 G296.8–0.3 G353.6–0.7

Agea (kyr) 4.5 1 7 ≤3 1.6 0.9 ∼ 27 7 0.33 1–3 ∼2 10 ∼ 27

d (kpc) 2.2 1 2.2 5 1.3 4.5 3.2 7 3.4 8.5 3.3 9.6 3.2

P Bdip (s) (1010 G) 0.112 2.9 ... ... 0.424 9.8 ... ... ... ... ... ... ... ... 0.105 ... ... 24 × 103 ... ...

3.1 ... ... ... ... ...

Lx,bol (erg s−1 ) 5.6 × 1033 2.5 × 1032 2.5 × 1033 1.5 × 1033 ∼ 1 × 1033 3.9 × 1033 1.3 × 1034 5.3 × 1033 4.7 × 1033 ∼ 1 × 1033 1.1−80 × 1033 1.1 × 1033 1.3 × 1034

age refers to the supernova remnant age. has shown magnetar-like behaviour.

b 1E 161348–5055

campaigns spanning several years made it possible to measure the corresponding period derivatives of the order of 10−18 –10−17 s s−1 (see, e.g., Gotthelf et al. 2013). From the derived timing solutions, we can infer that (1) the spin-down luminosity is about a factor of 10 lower than the X-ray luminosity; (2) the characteristic age τc is 4–5 orders of magnitude larger than the age of the host supernova remnants, indicating that CCOs were either born spinning at nearly their present periods or had an atypical magnetic field evolution; and (3) the inferred dipolar magnetic field Bdip is 1010 –1011 G, remarkably smaller than that of the bulk of the radio pulsars. Given these low B-field strengths, CCOs were labelled as “anti-magnetars”: neutron stars born with weak magnetic fields that have not been effectively amplified trough dynamo effects, due to their slow rotation at birth. The “anti-magnetars” scenario does not, however, account for several observational aspects. In the following, we focus on the properties of the three pulsating CCOs. Model fitting of the X-ray spectrum of PSR J1852+0040 with two blackbodies yields small emitting radii (R1 = 1.9 km and R2 = 0.45 km, for components with temperatures of kT1 = 0.30 keV and kT2 = 0.52 keV, respectively; Halpern and Gotthelf 2010). The thermal emission is highly modulated with a pulsed fraction of ∼64% and is characterized by a single broad pulse, whose shape does not appear to be a function of energy. These properties also suggest that the emitting area is small. Such tiny, hot spots are at odds with the inferred magnetic field value since surface temperature anisotropies are associated with the effects of much stronger magnetic fields. For PSR J0821–4300, the spectrum is well described by two blackbodies with the addition of a spectral feature, which can be modelled by either an emission line at ∼0.75 keV or two absorption lines at ∼0.46 keV and ∼0.92 keV. The pulse profile of PSR J0821–4300 shows a sinusoidal shape with a 180◦ phase reversal at ∼1.2 keV

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(see, e.g., Gotthelf et al. 2013). A pair of antipodal hot spots of different areas and temperatures on the neutron star surface is able to reproduce the thermal spectrum and the energy-dependent pulse profile. As for the case of the CCO in Kes 79, explaining the non-uniform temperature distribution of the source may require a crustal field that is stronger than the external dipole field. Finally, the X-ray spectral energy distribution of 1E 1207.4–5209 exhibits a continuum emission of thermal origin defined by the sum of two blackbodies. A satisfactory fit is achieved by including four absorption lines with simple Gaussian profiles centered at ∼0.7, 1.4, 2.1, and 2.8 keV (see Fig. 10, left panel; Bignami et al. 2003; De Luca et al. 2004). The harmonically spaced spectral features are naturally explained by electron cyclotron absorption from the fundamental and three harmonics. This interpretation allows a direct measurement of the magnetic field: the fundamental cyclotron energy of ∼0.7 keV yields a magnetic field strength of Bcyc ∼ 8 × 1010 G, assuming a 25% gravitational redshift. This result is consistent with the magnetic field inferred from the spin-down parameters, Bdip ∼ 9.8 × 1010 G. The X-ray pulsation is dominated by the complicated modulation of the spectral features as a function of the rotational phase, while the continuum is almost unpulsed. Twenty years of timing observations performed between 2000 and 2019 revealed that 1E 1207.4–5209 had two small glitches (see Fig. 10, right panel; Gotthelf and Halpern 2020). This is the first time to detect such phenomenon in a CCO and in an isolated neutron star with a period derivative as small as that of this source. The phase ephemeris can be well modelled

Fig. 10 Left: Residuals in units of sigma obtained from a comparison between the data with the best fit thermal continuum model (i.e., the sum of two blackbodies) for 1E 1207.4–5209. The presence of four absorption spectral features at ∼0.7, 1.4, 2.1, and 2.8 keV is evident. (From De Luca et al. 2004). Right:Phase residuals from the pre-glitch timing solution, modeled as two successive glitch-like changes in frequency. Glitch epochs of 2010 November 09 and May 23, 2014, are estimated from the intersection of the respective pre- and post-glitch fits. (From Gotthelf and Halpern 2020)

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including two glitches that took place at the estimated epochs of November 9, 2010, and May 23, 2014. Alternative timing models, which do not consider glitches, can also fit the data; however, the resulting timing residuals and second frequency derivative are orders of magnitude larger than in isolated neutron stars with similar spin-down parameters. No changes were observed in the spectrum and the central energies of the spectral features, meaning that the surface magnetic field strength was constant before and after the glitches. Therefore, it is interesting to consider that the glitches might be triggered by the motion of an internal field, as strong as those of canonical young pulsars that show glitches. Beside the three pulsed CCOs, this group includes about ten more sources without detected pulsations. These objects have similar spectral properties as the CCO pulsars, making it reasonable to assume that they are also isolated neutron stars born with weak dipole magnetic fields. The most studied CCO is the X-ray point source at the center of the supernova remnant Cassiopeia A. Discovered in the first-light observations of Chandra, it is among the youngest-known neutron stars, as the supernova remnant age is estimated at ∼350 yr. Its spectrum is well described by different models. A blackbody, a magnetic, or non-magnetic hydrogen atmosphere models are consistent with the emission coming from small hot spots, similar to what has been observed for other CCOs. However, timing investigations were unsuccessful in identifying pulsations down to a pulsed fraction limit of 12%. These apparently contradictory results are reconciled by the discovery that a low magnetized (Bdip < 1011 G) carbon atmosphere model gives a satisfactory spectral fit with the emission arising from the entire neutron star surface, which would not necessarily vary with the star rotation (Heinke and Ho 2010). A decrease of the surface temperature by 4% and a 21% change of the flux were reported over a time span of 10 years (from 2000 to 2009) by using multi-epoch Chandra observations. Such direct measurement of the cooling of an isolated neutron star would have profound theoretical implications for our understanding of the internal composition and structure of these compact objects. By applying cooling models, it would be possible to constrain neutrino emission mechanisms and envelope compositions (Heinke and Ho 2010). However, it was noted that these Chandra observations suffered from several instrumental effects that can cause time-dependent spectral distortions. Therefore, additional Chandra pointings were carried out in such a setup to minimize the instrument effects in four epochs (2006, 2013, 2015, and 2020; Posselt and Pavlov 2022). An apparent increase in the cooling rate between 2015 and 2020 and the variations of the inferred hydrogen column densities between the different epochs were reported. The authors note that these changes could indicate systematic effects such as caused by, for instance, an imperfect calibration of the increasing contamination of the optical-blocking filter. The carbon atmosphere model with low magnetic field provides a good spectral fit not only for the CCO in Cassiopeia A but also for a few more sources (see, e.g., Klochkov et al. 2015). These models assume homogeneous temperature distribution on the entire neutron star surface, naturally explaining the absence of detected pulsations within the current limit. Moreover, they make it possible to reconcile thermal luminosities with the known or estimated distances and to constrain the

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neutron star equation of state. Mass and radius are used to estimate the surface gravity and gravitational redshift affecting the atmosphere model, and they are two of the four free fit parameters of the model. For instance, for the CCO in the supernova remnant G353.6–0.7 (as well-known as HESS J1731–347), the obtained best-fit neutron star mass and radius are 1.55 M⊙ and 12.4 km for the preferred distance of 3.2 kpc. These values are compatible with the most commonly used nuclear equations of state (Klochkov et al. 2015). To combine these results with cooling theories has a potential to put more stringent constraints (see for more details, Ofengeim et al. 2015). Observational results, such as the presence of hot spots in the pulsed CCOs and the occurrence of a glitch, hint at a stronger magnetic field in the interior of CCOs. Alternative explanations to the “anti-magnetar” hypothesis have been discussed. CCOs might be magnetars in quiescence characterized by a weak dipole field and a strong crustal magnetic field that emerges locally in confined areas. However, this scenario seems unlikely owing to the lack of variability in CCOs, at variance with what seen in magnetars, even if it could be correct for a sub-group of the sample. Another theory regarding the CCO nature posits that they are born with a canonical neutron star magnetic field that was buried by the fallback of the debris of the supernova explosion, the so-called “hidden magnetic field” interpretation. Several models proposed that a typical magnetic field in the range of 1012 –1014 G can be pushed deep inside the crust by accreting a mass of ∼10−4 –10−2 M⊙ . The result is an external magnetic field lower than the internal hidden one, which might re-emerge on a timescale of 103 –105 yr once the accretion stops. After this stage, the magnetic field at the surface is restored close to its value at birth (see, e.g., Torres-Forné et al. 2016). The thermal evolution during the re-emergence phase can produce different degrees of anisotropy in the surface temperature, explaining the large pulsed fraction measured for the CCO in Kes 79 and the antipodal hot spots of PSR J0821–4300 in Puppis A. Furthermore, these models predict that weak dipolar magnetic fields could be common in very young (< few kyr) neutron stars, and CCOs might be ancestors of old radio pulsars as long as their surface field grows to the critical limit required for radio emission. An observational test to prove the “hidden magnetic field” scenario is to measure the braking index n. In case of a constant magnetic field and magneto dipolar braking mechanism, n is equal to 3, while values smaller than 3 translate into a growing field. Estimates of n have not been achieved so far for CCOs; their low period derivatives make this task extremely challenging. Interestingly, all reported values for young rotation-powered pulsar (τc ∼ 103 − 104 yr) are in agreement with n < 3, providing support for this picture (see, e.g., Marshall et al. 2016).

1E 161348–5055: A Hidden Magnetar 1E 161348−5055 (1E 1613) was discovered in 1980 when the Einstein Observatory detected a point-like source lying close to the center of the 2-kyr-old supernova

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remnant RCW 103. It was the first candidate radio-quiet isolated neutron star discovered in a supernova remnant. It has been one of the prototypes of the CCO class. However, in the last two decades, observations revealed remarkable features that make 1E 1613 stand out from the other CCOs. Firstly, unlike the other members of this class that generally have a steady emission, it displays a strong flux variability on a month/year timescale, undergoing an outburst at the end of 1999 with a flux increase by a factor of ∼100. Secondly, a long periodicity of 6.7 hr was detected with a strong nearly sinusoidal modulation (De Luca et al. 2006). Although the 6.7-hr periodicity could be recognized in all the data sets that were long enough, the corresponding pulse profile changed according to the source flux level: from a sine-like shape when the source is in a low state (observed soft X-ray flux ∼10−12 erg s−1 cm−2 ) to a more complex, multi-peak configuration in a high state (∼10−11 erg s−1 cm−2 ). The long-term variability, the unusual periodicity, and the pulse profile changes have contributed to build an intriguing phenomenology in the neutron star scenario. Based on these characteristics, two main interpretations were put forward: 1E 1613 could be either the first low-mass X-ray binary in a supernova remnant with an orbital period of 6.7 hr or a peculiar isolated compact object with a rotational spin period of 6.7 hr, invoking the magnetar scenario that naturally accounts for the flux and pulse shape variations. In 2016, a new event shed light on the nature of this source: on June 22, the Swift Burst Alert Telescope triggered on a short (∼10 ms) hard X-ray magnetar-like burst from the direction of RCW 103 (see, e.g., Rea et al. 2016), with a spectrum described by a blackbody (kT ∼ 9 keV) and a luminosity of ∼2 × 1039 erg s−1 in the 15–150 keV energy range for a distance of 3.3 kpc. Meanwhile, the Swift X-Ray Telescope detected an enhancement of the 0.5–10 keV flux by a factor of ∼100 with respect to the quiescent level that persisted for years and was observed up to 1 month before (see Fig. 11). Follow-up observations with Chandra and NuSTAR confirmed that the burst marked the onset of a magnetar-like outburst. For the first time, a hard X-ray, non-thermal spectral component was detected up to ∼30 keV, modelled by a power law with photon index Γ ∼ 1.2, while the soft X-ray spectrum was well described by the sum of two blackbodies. The light curve displayed two broad peaks per cycle, in contrast with the sinusoidal shape observed since 2005. In the first year from the onset of the outburst, the overall energy emitted was ∼2 × 1042 erg (Borghese et al. 2018). This event prompted searches for an infrared counterpart. The Hubble Space Telescope and the Very Large Telescope observed the field of view few weeks after the onset (see, e.g., Esposito et al. 2019). The images disclose a new object at the position of the source, not detected in previous observations. The counterpart properties ruled out the binary scenario; however, it is not clear whether the infrared emission comes from the neutron star magnetosphere or a fallback disk. While all the aspects caught by these observations – the appearance of a hard power-law tail at the outburst peak, the variability of the pulse profile in time, and the infrared counterpart – point toward a magnetar interpretation of 1E 1613, its long periodicity is puzzling; a very efficient braking mechanism is required to slow down the source from a fast birth period (< 0.5 s) at the currently measured value of

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Fig. 11 Swift-BAT 15–150 keV image of the burst detected on June 22, 2016, from the direction of the supernova remnant RCW 103 (bottom). Two Swift-XRT co-added 1–10 keV images of RCW 103 during the quiescent state of 1E 161348−5055 (from April 18, 2011, to May 16, 2016; exposure time of 66 ks; top left) and in outburst (from June 22 to July 20, 2016; exposure time of 67 ks; top right). The white circle marks the positional accuracy of the detected burst, which has a radius of 1.5 arcmin. (From Rea et al. 2016)

6.7 hr in ∼2 kyr. Most models consider a propeller interaction with a fallback disk that can provide an additional spin-down torque besides that due to dipole radiation. Ho and Andersson (2017) predict a remnant disk of ∼10−9 M⊙ around a rapidly rotating neutron star that is initially in an ejector phase, and after hundreds of years, its rotation period slows down enough to allow the onset of a propeller phase. By matching its observed spin period and young age, 1E 1613 is found to have a slightly higher dipolar magnetic field than all known magnetars, Bdip ∼ 5 × 1015 G.

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X-Ray Dim Isolated Neutron Stars Thanks to its high sensitivity in the soft X-ray band (0.1 − 2.5 keV), the ROSAT satellite led to the discovery of seven thermally emitting soft X-ray pulsars, labelled the X-ray Dim Isolated Neutron Stars (XDINSs), and commonly nicknamed “The Magnificent Seven” (see Turolla (2009) for a review and references therein). Radio emission from these sources has not been detected so far despite deep searches, while all of them have confirmed optical and/or ultraviolet counterparts. XDINSs are hotter than they ought to be, considering their ages and the available energy reservoir provided by the loss of rotational energy. They are among the closest neutron stars we know of, with distances ≤ 500 pc as derived from the modelling of the distribution of the hydrogen column density NH . Parallax measurements are available for only two sources, RX J1856.5–3754 and RX J0720.4–3125, yielding a +210 distance of 123+11 −15 pc and 280−85 pc, respectively, in agreement with estimations obtained from the spectrum and NH . Unlike CCOs, XDINSs have strong magnetic field (∼1013 G), similar to those of the high-B pulsars, are old objects (τc ∼ a few Myr), and are not found at the center of supernova remnants. Table 2 reports the overall properties of this class of isolated neutron stars.

Overview of the Observational Properties Timing studies of the XDINSs disclosed X-ray pulsations at spin periods in the range of 3–12 s with period derivatives of the order of 10−14 –10−13 s s−1 , implying dipolar magnetic fields Bdip ∼ (1–4) ×1013 G and characteristic ages τc ∼ 1–4 Myr.

Table 2 Overall properties of the X-ray dim isolated neutron stars. E0 refers to the central energies of the broad absorption line. Bdip corresponds to the surface, dipolar strength of the magnetic field measured at the equator, and Bcyc is the magnetic field strength evaluated assuming that the spectral features in the phase-averaged spectra are proton cyclotron resonances. L indicates the bolometric luminosity radiated from the surface. (Adapted from Pires et al. 2014) kT P log P˙ τc E0 Bdip Bcyc log L Source RX J1856.5–3754 RX J0720.4–3125a RX J1605.3+3249b RX J1308.6+2127 RX J2143.0+0654 RX J0806.4–4123 RX J0420.0–5022c a

(eV) 61 84–94 100 100 104 95 48

(s) 7.06 8.39 ... 10.31 9.43 11.37 3.45

(ß) −13.527 −13.156 ... −12.951 −13.398 −13.260 −13.553

(106 yr) 3.8 1.9 ... 1.4 3.7 3.2 1.9

(eV) – 311 400 390 750 486 ...

(1013 G) 1.47 2.45 ... 3.48 1.95 2.51 1.00

(1013 G) – 5.62 8.32 3.98 1.41 9.12 ...

(erg s−1 ) 31.5–31.7 32.2–32.4 31.9–32.2 32.1–32.2 31.8–31.9 31.2–31.4 30.9–31.0

Hambaryan et al. (2017) claimed that the most likely genuine period is 16.78 s, twice that reported in the literature b A period of 3.39 s was claimed but not confirmed by later observations c An absorption line at ∼0.3 keV was reported, but not confirmed

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These properties place the XDINSs at the end of the rotation-powered radio pulsar toward long periods and below the magnetars in the P − P˙ diagram (Fig. 1). RX J1605.3+3249 is the only member of this neutron star group that still lacks a coherent timing solution. A possible candidate spin period of 3.39 s and spindown derivative of ∼1.6 × 10−12 s s−1 were proposed with a significance level of ∼4σ , making RX J1605.3+3249 the XDINS with the highest magnetic field (Bdip ∼ 7.5×1012 G, Pires et al. 2014). Targeted monitoring campaigns with XMMNewton and NICER ruled out this candidate with stringent upper limits on the pulsed fraction equal to 1.5% and 2.6% for periods above 150 ms and 2 ms, respectively (see, e.g., Malacaria et al. 2019). Moreover, for RX J0720.4-3125, Hambaryan et al. (2017) claimed that the most likely genuine period is twice that reported in the literature, 16.78 s instead of 8.39 s. A second peak was identified in the periodogram of all pointed XMM-Newton observations in different energy bands, and for some energy intervals, the timing series showed a more significant peak corresponding to P = 16.78 s. The light curves folded at the new claimed period display a markedly double-peaked shape that depends on time and energy. XDINSs are characterized by very soft X-ray spectra described by an absorbed blackbody with low values for the absorption column density (NH ∼ 1020 cm−2 ) and temperatures in the range 50–100 eV, with no evidence for a power-law tail extending at higher energies (see Fig. 12 and text below). The emission is purely

Fig. 12 Phase-averaged spectra of the X-ray dim isolated neutron stars extracted from the highest-counting statistic XMM-Newton observations. Solid lines represent the best-fitting models, consisting of an absorbed blackbody for RX J1856.5–3754 and an absorbed blackbody with the inclusion of a broad Gaussian line in absorption for all the other sources. Dashed lines indicate the blackbody components. (Image credit: A. Borghese)

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thermal, with little contamination from magnetospheric activity or surrounding supernova remnant and is believed to come directly from the neutron star surface. This trait makes “The Magnificent Seven” ideal targets for probing atmosphere models, and they can be used to constrain the mass-to-radius ratio neutron stars. For instance, fitting the phase-resolved spectra of RX J1308.6+2127 with a model consisting of a condensed iron surface and a partially ionized hydrogen-thin atmosphere above gives a true radius of 16 ± 1 km for a standard neutron star mass 1.4 M⊙ . The determined mass-to-radius ratio (M/M⊙ )/(R/km) = 0.087±0.004 implies a very stiff equation of state for this source (Hambaryan et al. 2011). Applying the same procedure and model, the mass-to-radius ratio was derived for another XDINS, RX J0720.4–3125. Its (M/M⊙ )/(R/km) is equal to 0.105 ± 0.002, assuming a mass of 1.4 M⊙ and radius of 13.3 ± 0.5 km, inferred from spectral fitting. As in the previous measurement, this value points to a stiff equation of state (Hambaryan et al. 2017). All the XDINSs have detected weak optical and ultraviolet counterparts, thanks to Hubble Space Telescope observations (Kaplan 2011). The extrapolation at lower energies of the best-fit model inferred from the X-rays underestimates the actual observed flux. This phenomenon is known as optical excess and is witnessed in all seven objects. Its origin is still an open issue. If the X-ray and optical radiation arise from different regions on the neutron star surface, variations in the excess are expected to correlate with changes in the X-ray pulsed fraction. However, such correlations have not been observed, suggesting that this picture is incomplete. Other alternative scenarios should be considered: the optical excess might be due to magnetospheric emission, atmospheric effects, or the presence of a nebula. Recently, an extended near-infrared emission was discovered around RX J0806.4– 4123, having flux in excess with respect to the expected value from the extrapolation of its ultraviolet-optical flux. It can be interpreted as coming from a pulsar wind nebula fed by shocked pulsar wind particles of relatively low energy or a disk with a favorable viewing geometry (Posselt et al. 2018). The spectral signature of the two scenarios is different and can be investigated with future high-resolution observations with the James Webb Space Telescope. Moreover, deep near-infrared surveys are required to understand whether such extended emission is a common property among some types of isolated neutron stars or if RX J0806.4–4123 is a special case. XDINSs were considered to be steady sources, hence RX J0720.4–3125 was included in the calibration targets for the EPIC and RGS instruments on board XMM-Newton. However, the monitoring campaign revealed long-term variations in its timing and spectral parameters. In the period between 2001 and 2003, while the total flux stayed constant, the blackbody temperature increased from ∼84 eV to ∼94 eV, and the pulse profile changed as well, with an increase of the pulsed fraction. In the following years, this trend reversed with a decrease of the surface temperature, hinting at a cyclic behavior. The temperature evolution covering the time span between 2000 and 2005 could be described by a sinusoidal function with a period of ∼7 yr. The most likely explanation involved a freely processing neutron star with two hot spots with different temperature and size,

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not located in antipodal positions. The observed blackbody temperature variations are produced by the changes in the viewing geometry of the two spots as the star processes (Haberl et al. 2006). RX J0720.4–3125 continued to be monitored with XMM-Newton and Chandra until 2012. The new observations from 2005 to 2012 disclosed a monotonic decrease in the temperature, excluding a cyclic pattern with a 7-year period. Moreover, a 14-year period seemed unlikely because the extrapolated temperature value at the end of the cycle was different from the initial one. On the other hand, the timing behavior favored the interpretation in terms of a single sudden event, such as a glitch, with the spectral parameters changing remarkably around the proposed glitch date (Hohle et al. 2012). RX J0720.4–3125 is the only XDINS to have undergone a glitch so far. As stated above, the hallmark of the XDINSs is their thermal spectrum detected in the soft X-rays without any need to include a power law at higher energies. Although a blackbody model provides an overall good description of their spectral energy distribution, broad absorption features had been found in most of the XDINSs (see Fig. 12 and Table 2). The brightest XDINS, RX J1856.5–3754, exhibits a featureless spectrum, compatible with a blackbody with hints of a second colder thermal component detected also in optical and ultraviolet bands (Sartore et al. 2012). The presence of a spectral line at ∼0.3 keV was initially claimed but not confirmed by later, deeper observations for the faintest member, RX J0420.0– 5022 (Kaplan and van Kerkwijk 2011). For the remaining sources, the properties of the spectral features are similar: the central energies range from ∼300 eV to ∼800 eV, they are quite broad with widths generally in the range of ∼70–170 eV, the equivalent widths are several tens of eV (30–150 eV), and they vary with the spin phase. Note that the two XDINSs with no apparent spectral features are the coldest, with kT ∼ 45–60 eV, while the other five objects with claimed lines have similar temperatures (kT ∼ 80–100 eV). Deviations from a pure blackbody can be explained by several physical mechanisms. One hypothesis is that the spectral lines can be produced by proton cyclotron resonances in a hot ionized layer near the surface. The line energies imply a magnetic field strengths of the order of 1013 G, in rough agreement with the values inferred from the timing. An alternative hypothesis would rest upon atomic transitions in a magnetized atmosphere. The energies of the absorption features can be matched with transitions in a hydrogen atmosphere in most cases, apart from one: for RX J2143.0+0654, the line energy of ∼0.7 keV is substantially higher than what is observed for all the other sources and for any transition in hydrogen; therefore, a helium or heavier element atmosphere is required. Finally, an inhomogeneous surface temperature distribution can induce spectral distortions in the form of spectral features (Viganò et al. 2014). Temperature anisotropies can be inferred from the measurements of small blackbody emitting areas and are theoretically expected, e.g., by magnetospheric particle bombardments or anisotropic thermal conductivity caused by a strong magnetic field. Predicting the temperature distribution on the neutron star surface is hard due to many theoretical uncertainties, such as the magnetic field geometry. Therefore, the easiest approach is to explore a wide variety of temperature profiles that differ in crustal temperature, magnetic field strength, and number of hotspots and to compare them with the

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observations. Viganò et al. (2014) concluded that two requirements are needed to produce a spectral line: one or more hot, small regions should have a temperature larger by at least a factor of ∼2 than the average temperature of the rest of the neutron star surface, and the hot spot(s) and the colder part should contribute equally to the total flux. Temperature inhomogeneities can play an important role in the emission processes and should be taken into account in combination with more sophisticated emission models (e.g., atmospheric/condensed surface models). The discovery of a phase-dependent absorption feature in two low-magnetic field magnetars (see section “Low-Magnetic Field Magnetars”) and the fact that XDINSs are believed to be descendants of magnetars, according to magneto-thermal evolutionary models (Viganò et al. 2013), motivated the search for such features in “The Magnificent Seven.” Only in two sources, RX J0720.4–3125 and RX J1308.6+2127, was a phase-variable absorption feature found with properties similar to those of the line reported in the magnetars SGR 0418+5729 and Swift J1822.3–1606, strengthening the evolutionary link between these two groups of isolated neutron stars (Borghese et al. 2015, 2017). In both detections, the line energy is about ∼0.75 keV with an equivalent width of ∼15 − 30 eV. The features are significantly detected in only 20% of the star rotational phase and appear to be stable over the time interval covered by the observations (∼12 yr and 7 yr for RX J0720.4–3125 and RX J1308.6+2127, respectively). In light of the similarities with SGR 0418+5729, the feature might be explained invoking by the same physical mechanism: proton cyclotron resonant scattering. In this scenario, the sharp variation with phase is ascribed to the presence of small-scale (∼100 m) magnetic structures close to the neutron star surface. The implied magnetic field in the loop is about a factor of ∼5 higher than the dipolar component for both sources. These findings are supportive of a picture in which the magnetic field of highly magnetized neutron stars is more complex than a pure dipole with deviations on a small scale, such as localized high B-field bundles.

Rotating Radio Transients To conclude the gallery tour of the non-accreting neutron stars, we briefly discuss the Rotating Radio Transients (RRATs), which were discovered only a few years ago through the detection of sporadic single radio pulses. The largest common denominator between the arrival times of these pulses made it possible to figure out an underlying periodicity pointing to neutron stars for these sources. The known population of RRATs tallies to about 100 sources, and for one-fifth of them, it has been possible to also estimate the spin-down rate. Even though there is evidence of RRATs with longer periods, older ages and higher magnetic fields than the average in RPPs, they are not tightly clustered or located in unusual areas in the P –P˙ diagram. The current consensus is that RRATs are radio-emitting RPPs that for some reason display an extreme form of the more common nulling observed in several radio pulsars.

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Only one RRAT, J1819–1458 (P = 4.3 s, τc = 0.1 Myr, B ∼ 5 × 1013 G), has been observed as an X-ray pulsar. Its X-ray spectrum is thermal, with a blackbody temperature of 140 eV, similar to that of some middle-age pulsars and of the XDINs, and a possible absorption feature at 0.5 keV. Interestingly, the distance to the source inferred from the radio dispersion measure implies an X-ray luminosity of ≈ 4 × 1033 erg s−1 , ten times larger than the spin-down power.

Conclusion Although we have been observing neutron stars and pulsars at all wavelengths for more than 50 years, they are still delivering striking surprises, such as the recent discovery of powerful millisecond-long radio bursts from the magnetar SGR J1935+2154. This is largely due to the arrival of ever more powerful groundbased and space-borne observatories, but it is fair to say that the neutron star phenomenology exceeded the expectations of the astronomers. Indeed, at first glance, they appear to be simple objects: they are gravitationally collapsed bodies made predominantly of neutrons (and chances are that they are all ruled by the same – yet elusive – equation of state), nearly collapsing into a black hole, being just a few times their Schwarzschild radius. More than 30 years after Baade and Zwicky (1934) suggested that a supernova is the transition of an ordinary star to a neutron star was it realized that neutron stars might have been observable for attributes other than the tremendous heat with which they emerge from the explosion (Tsuruta and Cameron 1966). Pacini (1967) was probably the first to note that if neutron stars were endowed with strong magnetic fields (as could be expected from some considerations on the retainment of the magnetic moment of the progenitor star, but see, e.g., Gourgouliatos and Esposito (2018) and references therein), then they should have been powerful emitters of electromagnetic waves owing to their fast rotation (Eq. 2). However, there is increasing evidence that the magnetic field is not simply a mean for pulsars to convert their rotational kinetic energy in radiation and particles. Magnetars in particular have been of paramount importance in suggesting that it is the magnetic field that drives the amazing observational diversity of the different classes of neutron stars, not only the external poloidal component, which is responsible for the rotation braking, but also the toroidal internal component (which may store much more energy), their balance, and their (co)evolution. The existence of this component in any kind of neutron star is necessary because purely poloidal configurations are intrinsically unstable on short scales (as well as the purely toroidal ones), as is suggested by the model of dynamo formation of the magnetic field in the proto-neutron star, and it is tempting to invoke it to answer, for instance, the unusual behavior of some pulsars or the plentiful puzzling radio emission of the recycled millisecond pulsars. Furthermore, observational evidence of surface magnetic fields more complex than dipoles is emerging. This hidden factor in the P –P˙ diagram may be the fil rouge connecting the various groups of

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neutron stars and explaining their diversity together with a few other fundamental characteristics, such as the age, the mass, and the envelope composition. Huge theoretical efforts are ongoing on neutron stars. Moreover, upcoming new instruments will help define their equation of state, characterize their emission properties, unveil the existence of new mysterious objects, and, finally, constrain the census of slippery objects, such as the magnetars, the RRATs, transient radio pulsars in general, and, thus, the galactic and nearby extragalactic population. However, another awesome aspect of pulsars is that even if we still have to figure out a lot about them, we can nonetheless use them to investigate many problems of physics. As they are clocks with extreme properties in extreme environments, they can be used to test general relativity and alternative theories (e.g., Stairs 2003), to probe the interstellar medium and magnetic field, and to explore the low-frequency gravitational background. Though we do not understand them well, pulsars are going to bring us gifts and keep us busy for many more decades to come!

References A.A. Abdo, M. Ajello, A. Allafort, L. Baldini, J. Ballet, G. Barbiellini, M.G. Baring, D. Bastieri, A. Belfiore, R. Bellazzini, B. Bhattacharyya, E. Bissaldi, E.D. Bloom, E. Bonamente, E. Bottacini, T.J. Brandt, J. Bregeon, M. Brigida, P. Bruel, R. Buehler, M. Burgay, T.H. Burnett, G. Busetto, S. Buson, G.A. Caliandro, R.A. Cameron, F. Camilo, P.A. Caraveo, J.M. Casandjian, C. Cecchi, Ö. Çelik, E. Charles, S. Chaty, R.C.G. Chaves, A. Chekhtman, A.W. Chen, J. Chiang, G. Chiaro, S. Ciprini, R. Claus, I. Cognard, J. Cohen-Tanugi, L.R. Cominsky, J. Conrad, S. Cutini, F. D’Ammando, A. de Angelis, M.E. DeCesar, A. De Luca, P.R. den Hartog, F. de Palma, C.D. Dermer, G. Desvignes, S.W. Digel, L. Di Venere, P.S. Drell, A. DrlicaWagner, R. Dubois, D. Dumora, C.M. Espinoza, L. Falletti, C. Favuzzi, E.C. Ferrara, W.B. Focke, A. Franckowiak, P.C.C. Freire, S. Funk, P. Fusco, F. Gargano, D. Gasparrini, S. Germani, N. Giglietto, P. Giommi, F. Giordano, M. Giroletti, T. Glanzman, G. Godfrey, E. V. Gotthelf, I.A. Grenier, M.H. Grondin, J.E. Grove, L. Guillemot, S. Guiriec, D. Hadasch, Y. Hanabata, A.K. Harding, M. Hayashida, E. Hays, J. Hessels, J. Hewitt, A.B. Hill, D. Horan, X. Hou, R.E. Hughes, M.S. Jackson, G.H. Janssen, T. Jogler, G. Jóhannesson, R.P. Johnson, A.S. Johnson, T.J. Johnson, W.N. Johnson, S. Johnston, T. Kamae, J. Kataoka, M. Keith, M. Kerr, J. Knödlseder, M. Kramer, M. Kuss, J. Lande, S. Larsson, L. Latronico, M. Lemoine-Goumard, F. Longo, F. Loparco, M.N. Lovellette, P. Lubrano, A.G. Lyne, R.N. Manchester, M. Marelli, F. Massaro, M. Mayer, M.N. Mazziotta, J.E. McEnery, M.A. McLaughlin, J. Mehault, P.F. Michelson, R.P. Mignani, W. Mitthumsiri, T. Mizuno, A.A. Moiseev, M.E. Monzani, A. Morselli, I.V. Moskalenko, S. Murgia, T. Nakamori, R. Nemmen, E. Nuss, M. Ohno, T. Ohsugi, M. Orienti, E. Orlando, J.F. Ormes, D. Paneque, J.H. Panetta, D. Parent, J.S. Perkins, M. Pesce-Rollins, M. Pierbattista, F. Piron, G. Pivato, H.J. Pletsch, T.A. Porter, A. Possenti, S. Rainò, R. Rando, S.M. Ransom, P.S. Ray, M. Razzano, N. Rea, A. Reimer, O. Reimer, N. Renault, T. Reposeur, S. Ritz, R.W. Romani, M. Roth, R. Rousseau, J. Roy, J. Ruan, A. Sartori, P.M. Saz Parkinson, J.D. Scargle, A. Schulz, C. Sgrò, R. Shannon, E.J. Siskind, D.A. Smith, G. Spandre, P. Spinelli, B.W. Stappers, A.W. Strong, D.J. Suson, H. Takahashi, J.G. Thayer, J.B. Thayer, G. Theureau, D.J. Thompson, S.E. Thorsett, L. Tibaldo, O. Tibolla, M. Tinivella, D.F. Torres, G. Tosti, E. Troja, Y. Uchiyama, T.L. Usher, J. Vandenbroucke, V. Vasileiou, C. Venter, G. Vianello, V. Vitale, N. Wang, P. Weltevrede, B.L. Winer, M.T. Wolff, D.L.Wood, K.S. Wood, M. Wood, Z. Yang, The second Fermi Large Area Telescope catalog of gamma-ray pulsars. ApJS 208, 17 (2013)

4024

A. Borghese and P. Esposito

M.A. Alpar, On young neutron stars as propellers and accretors with conventional magnetic fields. ApJ 554, 1245–1254 (2001) B.C. Andersen, K.M. Bandura, M. Bhardwaj, A. Bij, M.M. Boyce, P.J. Boyle, C. Brar, T. Cassanelli, P. Chawla, T. Chen, J.F. Cliche, A. Cook, D. Cubranic, A.P. Curtin, N.T. Denman, M. Dobbs, F.Q. Dong, M. Fandino, E. Fonseca, B.M. Gaensler, U. Giri, D.C. Good, M. Halpern, A.S. Hill, G.F. Hinshaw, C. Höfer, A. Josephy, J.W. Kania, V.M. Kaspi, T.L. Landecker, C. Leung, D.Z. Li, H.H. Lin, K.W. Masui, R. Mckinven, J. Mena-Parra, M. Merryfield, B.W. Meyers, D. Michilli, N. Milutinovic, A. Mirhosseini, M. Münchmeyer, A. Naidu, L.B. Newburgh, C. Ng, C. Patel, U.L. Pen, T. Pinsonneault-Marotte, Z. Pleunis, B.M. Quine, M. Rafiei-Ravandi, M. Rahman, S.M. Ransom, A. Renard, P. Sanghavi, P. Scholz, J.R. Shaw, K. Shin, S.R. Siegel, S. Singh, R.J. Smegal, K.M. Smith, I.H. Stairs, C.M. Tan, S.P. Tendulkar, I. Tretyakov, K. Vanderlinde, H. Wang, D. Wulf, A.V. Zwaniga, T.C. Collaboration, A bright millisecond-duration radio burst from a Galactic magnetar. Nature 587(7832), 54–58 (2020) R.F. Archibald, V.M. Kaspi, C.Y. Ng, K.N. Gourgouliatos, D. Tsang, P. Scholz, A.P. Beardmore, N. Gehrels, J.A. Kennea, An anti-glitch in a magnetar. Nature 497, 591–593 (2013) R.F. Archibald, V.M. Kaspi, A.P. Beardmore, N. Gehrels, J.A. Kennea, On the braking index of the unusual High-B rotation-powered pulsar PSR J1846-0258. ApJ 810, 67 (2015) R.F. Archibald, V.M. Kaspi, S.P. Tendulkar, P. Scholz, A magnetar-like outburst from a High-B radio pulsar. ApJ 829, L21 (2016) W. Baade, F. Zwicky, Cosmic rays from super-novae, in Proceedings of the National Academy of Science, vol. 20 (1934), pp. 259–263 A.M. Beloborodov, Untwisting magnetospheres of neutron stars. ApJ 703, 1044–1060 (2009) G.F. Bignami, P.A. Caraveo, A. De Luca, S. Mereghetti, The magnetic field of an isolated neutron star from X-ray cyclotron absorption lines. Nature 423, 725–727 (2003) H. Blumer, S. Safi-Harb, M.A. McLaughlin, W. Fiore, Reactivation of the high magnetic field pulsar PSR J1846-0258 with magnetar-like bursts. ApJ 911, L6 (2021) C.D. Bochenek, V. Ravi, K.V. Belov, G. Hallinan, J. Kocz, S.R. Kulkarni, D.L. McKenna, A fast radio burst associated with a Galactic magnetar. Nature 587(7832), 59–62 (2020) A. Borghese, N. Rea, F. Coti Zelati, A. Tiengo, R. Turolla, Discovery of a strongly phase-variable spectral feature in the isolated neutron star RX J0720.4-3125. ApJ 807, L20 (2015) A. Borghese, N. Rea, F. Coti Zelati, A. Tiengo, R. Turolla, S. Zane, Narrow phase-dependent features in X-ray Dim Isolated Neutron Stars: a new detection and upper limits. MNRAS 468, 2975–2983 (2017) A. Borghese, F. Coti Zelati, P. Esposito, N. Rea, A. De Luca, M. Bachetti, G.L. Israel, R. Perna, J.A. Pons, Gazing at the ultraslow magnetar in RCW 103 with NuSTAR and Swift. MNRAS 478, 741–748 (2018) E. Burns, D. Svinkin, K. Hurley, Z. Wadiasingh, M. Negro, G. Younes, R. Hamburg, A. Ridnaia, D. Cook, S.B. Cenko, R. Aloisi, G. Ashton, M. Baring, M.S. Briggs, N. Christensen, D. Frederiks, A. Goldstein, C.M. Hui, D.L. Kaplan, M.M. Kasliwal, D. Kocevski, O.J. Roberts, V. Savchenko, A. Tohuvavohu, P. Veres, C.A. Wilson-Hodge, Identification of a local sample of gamma-ray bursts consistent with a magnetar giant flare origin. ApJ 907, L28 (2021) F. Camilo, S.M. Ransom, J.P. Halpern, J. Reynolds, D.J. Helfand, N. Zimmerman, J. Sarkissian, Transient pulsed radio emission from a magnetar. Nature 442, 892–895 (2006) F. Camilo, S.M. Ransom, J.P. Halpern, J. Reynolds, 1E 1547.0-5408: a radio-emitting magnetar with a rotation period of 2 seconds. ApJ 666, L93–L96 (2007) A.J. Castro-Tirado, N. Østgaard, E. Göˇgü¸s, C. Sánchez-Gil, J. Pascual-Granado, V. Reglero, A. Mezentsev, M. Gabler, M. Marisaldi, T. Neubert, C. Budtz-Jørgensen, A. Lindanger, D. Sarria, I. Kuvvetli, P. Cerdá-Durán, J. Navarro-González, J.A. Font, B.B. Zhang, N. Lund, C.A. Oxborrow, S. Brandt, M.D. Caballero-García, I.M. Carrasco-García, A. Castellón, M.A. Castro Tirado, F. Christiansen, C.J. Eyles, E. Fernández-García, G. Genov, S. Guziy, Y.D. Hu, A. Nicuesa Guelbenzu, S.B. Pandey, Z.K. Peng, C. Pérez del Pulgar, A.J. Reina Terol, E. Rodríguez, R. Sánchez-Ramírez, T. Sun, K. Ullaland, S. Yang, Very-high-frequency oscillations in the main peak of a magnetar giant flare. Nature 600, 621–624 (2021) J. Chadwick, Possible existence of a neutron. Nature 129, 312 (1932)

111 Isolated Neutron Stars

4025

S. Chandrasekhar, The maximum mass of ideal white dwarfs. ApJ 74, 81 (1931) A.C. Collazzi, C. Kouveliotou, A.J. van der Horst, G.A. Younes, Y. Kaneko, E. Gö˘gü¸s, L. Lin, J. Granot, M.H. Finger, V.L. Chaplin, D. Huppenkothen, A.L. Watts, A. von Kienlin, M.G. Baring, D. Gruber, P.N. Bhat, M.H. Gibby, N. Gehrels, J. McEnery, M. van der Klis, R.A.M.J. Wijers, The five year Fermi/GBM magnetar burst catalog. ApJS 218, 11 (2015) F. Coti Zelati, N. Rea, J.A. Pons, S. Campana, P. Esposito, Systematic study of magnetar outbursts. MNRAS 474, 961–1017 (2018) F. Coti Zelati, A. Borghese, N. Rea, D. Viganò, T. Enoto, P. Esposito, J.A. Pons, S. Campana, G.L. Israel, The long-term enhanced brightness of the magnetar 1E 1547.0-5408. A&A 633, A31 (2020) F. Coti Zelati, A. Borghese, G.L. Israel, N. Rea, P. Esposito, M. Pilia, M. Burgay, A. Possenti, A. Corongiu, A. Ridolfi, C. Dehman, D. Viganò, R. Turolla, S. Zane, A. Tiengo, E.F. Keane, The new magnetar SGR J1830-0645 in outburst. ApJ 907, L34 (2021) A. De Luca, S. Mereghetti, P.A. Caraveo, M. Moroni, R.P. Mignani, G.F. Bignami, XMM-Newton and VLT observations of the isolated neutron star 1E 1207.4-5209. A&A 418, 625–637 (2004) A. De Luca, P.A. Caraveo, S. Mereghetti, M. Negroni, G.F. Bignami, On the polar caps of the three musketeers. ApJ 623, 1051–1069 (2005) A. De Luca, P.A. Caraveo, S. Mereghetti, A. Tiengo, G.F. Bignami, A long-period, violently variable X-ray source in a young supernova remnant. Science 313, 814–817 (2006) A. De Luca, Central compact objects in supernova remnants. J. Phys. Conf. Ser. 932, 012006 (2017) V.S. Dhillon, T.R. Marsh, S.P. Littlefair, C.M. Copperwheat, R.D.G. Hickman, P. Kerry, A.J. Levan, N. Rea, C.D.J. Savoury, N.R. Tanvir, R. Turolla, K. Wiersema, The first observation of optical pulsations from a soft gamma repeater: SGR 0501+4516. MNRAS 416, L16–L20 (2011) R.C. Duncan, C. Thompson, Formation of very strongly magnetized neutron stars: implications for gamma-ray bursts. ApJ 392, L9 (1992) R.P. Eatough, H. Falcke, R. Karuppusamy, K.J. Lee, D.J. Champion, E.F. Keane, G. Desvignes, D.H.F.M. Schnitzeler, L.G. Spitler, M. Kramer, B. Klein, C. Bassa, G.C. Bower, A. Brunthaler, I. Cognard, A.T. Deller, P.B. Demorest, P.C.C. Freire, A. Kraus, A.G. Lyne, A. Noutsos, B. Stappers, N. Wex, A strong magnetic field around the supermassive black hole at the centre of the Galaxy. Nature 501, 391–394 (2013) P. Esposito, A. De Luca, R. Turolla, F. Coti Zelati, W. Hummel, A. Tiengo, G.L. Israel, N. Rea, R.P. Mignani, A. Borghese, Long X-ray flares from the central source in RCW 103. XMM-Newton and VLT observations in the aftermath of the 2016 outburst. A&A 626, A19 (2019) P. Esposito, N. Rea, G.L. Israel, Magnetars: a short review and some sparse considerations, in Astrophysics and Space Science Library, ed. by T.M. Belloni, M. Méndez, C. Zhang. Astrophysics and Space Science Library, vol. 461 (2021), pp. 97–142 G.G. Fahlman, P.C. Gregory, An X-ray pulsar in SNR G109.1-1.0. Nature 293, 202–204 (1981) Fermi-Lat Collaboration, High-energy emission from a magnetar giant flare in the Sculptor galaxy. Nat. Astron. 5, 385 (2021) D.A. Frail, S.R. Kulkarni, J.S. Bloom, An outburst of relativistic particles from the soft γ -ray repeater SGR1900+14. Nature 398, 127–129 (1999) J.R. Fuentes, C.M. Espinoza, A. Reisenegger, B. Shaw, B.W. Stappers, A.G. Lyne, The glitch activity of neutron stars. A&A 608, A131 (2017) B.M. Gaensler, C. Kouveliotou, J.D. Gelfand, G.B. Taylor, D. Eichler, R.A.M.J. Wijers, J. Granot, E. Ramirez-Ruiz, Y.E. Lyubarsky, R.W. Hunstead, D. Campbell-Wilson, A.J. van der Horst, M.A. McLaughlin, R.P. Fender, M.A. Garrett, K.J. Newton-McGee, D.M. Palmer, N. Gehrels, P.M. Woods, An expanding radio nebula produced by a giant flare from the magnetar SGR 1806-20. Nature 434, 1104–1106 (2005) F.P. Gavriil, M.E. Gonzalez, E.V. Gotthelf, V.M. Kaspi, M.A. Livingstone, P.M. Woods, Magnetarlike emission from the young pulsar in Kes 75. Science 319, 1802 (2008) R. Giacconi, H. Gursky, F.R. Paolini, B.B. Rossi, Evidence for X-rays from sources outside the solar system. Phys. Rev. Lett. 9, 439–443 (1962)

4026

A. Borghese and P. Esposito

P. Goldreich, W.H. Julian, Pulsar electrodynamics. ApJ 157, 869 (1969) E.V. Gotthelf, J.P. Halpern, Discovery of a 112 ms X-ray pulsar in Puppis A: further evidence of neutron stars weakly magnetized at birth. ApJ 695, L35–L39 (2009) E.V. Gotthelf, J.P. Halpern, The timing behavior of the central compact object pulsar 1E 1207.45209. ApJ 900, 159 (2020) E.V. Gotthelf, J.P. Halpern, F.D. Seward, Discovery of a 105 ms X-ray pulsar in Kesteven 79: on the nature of compact central objects in supernova remnants. ApJ 627, 390–396 (2005) E.V. Gotthelf, J.P. Halpern, J. Alford, The Spin-down of PSR J0821-4300 and PSR J1210-5226: confirmation of central compact objects as anti-magnetars. ApJ 765, 58 (2013) D. Götz, S. Mereghetti, A. Tiengo, P. Esposito, Magnetars as persistent hard X-ray sources: INTEGRAL discovery of a hard tail in SGR 1900+14. A&A 449, L31–L34 (2006) K.N. Gourgouliatos, P. Esposito, Strongly magnetized pulsars: explosive events and evolution, in The Physics and Astrophysics of Neutron Stars, vol. 457, ed. by L. Rezzolla, P.M. Pizzochero, D.I. Jones, N. Rea, I. Vidaña (Springer Nature Switzerland, Basel, 2018), pp. 57–93 K.N. Gourgouliatos, S.K. Lander, Axisymmetric magneto-plastic evolution of neutron-star crusts. MNRAS 506, 3578–3587 (2021) F. Haberl, R. Turolla, C.P. de Vries, S. Zane, J. Vink, M. Méndez, F. Verbunt, Evidence for precession of the isolated neutron star RX J0720.4-3125. A&A 451, L17–L21 (2006) J.P. Halpern, E.V. Gotthelf, Spin-Down Measurement of PSR J1852+0040 in Kesteven 79: central compact objects as anti-magnetars. ApJ 709, 436–446 (2010) V. Hambaryan, V. Suleimanov, A.D. Schwope, R. Neuhäuser, K. Werner, A.Y. Potekhin, Phaseresolved spectroscopic study of the isolated neutron star RBS 1223 (1RXS J130848.6+212708). A&A 534, A74 (2011) V. Hambaryan, V. Suleimanov, F. Haberl, A.D. Schwope, R. Neuhäuser, M. Hohle, K. Werner, The compactness of the isolated neutron star RX J0720.4-3125. A&A 601, A108 (2017) K. Harding, The emission physics of millisecond pulsars, in As-trophysics and Space Science Library (S. Bhattacharyya, A. Papitto, and D. Bhattacharya, eds.), vol. 465 of Astrophysics and Space Science Library, pp. 57–85, Jan. 2022 C.O. Heinke, W.C.G. Ho, Direct observation of the cooling of the Cassiopeia A neutron star. ApJ 719, L167–L171 (2010) A. Hewish, S.J. Bell, J.D.H. Pilkington, P.F. Scott, R.A. Collins, Observation of a rapidly pulsating radio source. Nature 217, 709–713 (1968) W.C.G. Ho, N. Andersson, Ejector and propeller spin-down: how might a superluminous supernova millisecond magnetar become the 6.67 h pulsar in RCW 103. MNRAS 464, L65–L69 (2017) M.M. Hohle, F. Haberl, J. Vink, C.P. de Vries, R. Turolla, S. Zane, M. Méndez, The continued spectral and temporal evolution of RX J0720.4-3125. MNRAS 423 1194–1199 (2012) K. Hurley, T. Cline, E. Mazets, S. Barthelmy, P. Butterworth, F. Marshall, D. Palmer, R. Aptekar, S. Golenetskii, V. Il’Inskii, D. Frederiks, J. McTiernan, R. Gold, J. Trombka, A giant periodic flare from the soft γ -ray repeater SGR1900+14. Nature 397, 41–43 (1999) K. Hurley, S.E. Boggs, D.M. Smith, R.C. Duncan, R. Lin, A. Zoglauer, S. Krucker, G. Hurford, H. Hudson, C. Wigger, W. Hajdas, C. Thompson, I. Mitrofanov, A. Sanin, W. Boynton, C. Fellows, A. von Kienlin, G. Lichti, A. Rau, T. Cline, An exceptionally bright flare from SGR 1806-20 and the origins of short-duration γ -ray bursts. Nature 434, 1098–1103 (2005) G.L. Israel, T. Belloni, L. Stella, Y. Rephaeli, D.E. Gruber, P. Casella, S. Dall’Osso, N. Rea, M. Persic, R.E. Rothschild, The discovery of rapid X-ray oscillations in the tail of the SGR 1806-20 hyperflare. ApJ 628, L53–L56 (2005) G.L. Israel, M. Burgay, N. Rea, P. Esposito, A. Possenti, S. Dall’Osso, L. Stella, M. Pilia, A. Tiengo, A. Ridnaia, A.Y. Lien, D.D. Frederiks, F. Bernardini, X-ray and radio bursts from the magnetar 1E 1547.0-5408. ApJ 907, 7 (2021) L. Jaeger, Women of Genius in Science: Whose Frequently Overlooked Contributions Changed the World (Springer International Publishing, Switzerland, Cham, 2023) D.L. Kaplan, A. Kamble, M.H. van Kerkwijk, W.C.G. Ho, New optical/ultraviolet counterparts and the spectral energy distributions of nearby, thermally emitting, isolated neutron stars. ApJ 736, 117 (2011)

111 Isolated Neutron Stars

4027

D.L. Kaplan, M.H. van Kerkwijk, A coherent timing solution for the nearby, thermally emitting isolated neutron star RX J0420.0-5022. ApJ 740, L30 (2011) D. Klochkov, V. Suleimanov, G. Pühlhofer, D.G. Yakovlev, A. Santangelo, K. Werner, The neutron star in HESS J1731-347: central compact objects as laboratories to study the equation of state of superdense matter. A&A 573, A53 (2015) C. Kouveliotou, S. Dieters, T. Strohmayer, J. van Paradijs, G.J. Fishman, C.A. Meegan, K. Hurley, J. Kommers, I. Smith, D. Frail, T. Murakami, An X-ray pulsar with a superstrong magnetic field in the soft γ -ray repeater SGR1806–20. Nature 393, 235–237 (1998) L. Kuiper, W. Hermsen, P.R. den Hartog, W. Collmar, Discovery of luminous pulsed hard X-ray emission from anomalous X-ray pulsars 1RXS J1708-4009, 4U 0142+61, and 1E 2259+586 by INTEGRAL and RXTE. ApJ 645, 556–575 (2006) L. Levin, M. Bailes, S. Bates, N.D.R. Bhat, M. Burgay, S. Burke-Spolaor, N. D’Amico, S. Johnston, M. Keith, M. Kramer, S. Milia, A. Possenti, N. Rea, B. Stappers, W. van Straten, A radio-loud magnetar in X-ray quiescence. ApJ 721, L33–L37 (2010) L. Lin, E. Gö˘gü¸s, O.J. Roberts, M.G. Baring, C. Kouveliotou, Y. Kaneko, A.J. van der Horst, G. Younes, Fermi/GBM view of the 2019 and 2020 burst active episodes of SGR J1935+2154. ApJ 902, L43 (2020) M.A. Livingstone, V.M. Kaspi, E.V. Gotthelf, L. Kuiper, A braking index for the young, high magnetic field, rotation-powered pulsar in Kesteven 75. ApJ 647, 1286–1292 (2006) M.E. Lower, R.M. Shannon, S. Johnston, M. Bailes, Spectropolarimetric properties of swift J1818.0-1607: a 1.4 s radio magnetar. ApJ 896, L37 (2020) C. Malacaria, S. Bogdanov, W.C.G. Ho, T. Enoto, P.S. Ray, Z. Arzoumanian, T. Cazeau, K.C. Gendreau, S. Guillot, T. Güver, G.K. Jaisawal, M.T. Wolff, NICER Magnetar, Magnetospheres Team, A joint NICER and XMM-Newton view of the “Magnificent” thermally emitting X-ray isolated neutron star RX J1605.3+3249. ApJ 880, 74 (2019) R.N. Manchester, G.B. Hobbs, A. Teoh, M. Hobbs, The Australia telescope national facility pulsar catalogue. AJ 129, 1993–2006 (2005) F.E. Marshall, L. Guillemot, A.K. Harding, P. Martin, D.A. Smith, A new, low braking index for the LMC pulsar B0540-69. ApJ 827, L39 (2016) E.P. Mazets, S.V. Golentskii, V.N. Ilinskii, R.L. Aptekar, I.A. Guryan, Observations of a flaring X-ray pulsar in Dorado. Nature 282, 587–589 (1979) S. Mereghetti, V. Savchenko, C. Ferrigno, D. Götz, M. Rigoselli, A. Tiengo, A. Bazzano, E. Bozzo, A. Coleiro, T.J.L. Courvoisier, M. Doyle, A. Goldwurm, L. Hanlon, E. Jourdain, A. von Kienlin, A. Lutovinov, A. Martin-Carrillo, S. Molkov, L. Natalucci, F. Onori, F. Panessa, J. Rodi, J. Rodriguez, C. Sánchez-Fernández, R. Sunyaev, P. Ubertini, INTEGRAL discovery of a burst with associated radio emission from the magnetar SGR 1935+2154. ApJ 898, L29 (2020) D.D. Ofengeim, A.D. Kaminker, D. Klochkov, V. Suleimanov, D.G. Yakovlev, Analysing neutron star in HESS J1731-347 from thermal emission and cooling theory. MNRAS 454, 2668–2676 (2015) S.A. Olausen, V.M. Kaspi, The McGill magnetar catalog. ApJS 212, 6 (2014) F. Pacini, Energy emission from a neutron star. Nature 216, 567–568 (1967) G.G. Pavlov, V.E. Zavlin, B. Aschenbach, J. Trümper, D. Sanwal, The compact central object in Cassiopeia A: a neutron star with hot polar caps or a black hole?. ApJ 531, L53–L56 (2000) A.M. Pires, F. Haberl, V.E. Zavlin, C. Motch, S. Zane, M.M. Hohle, XMM-Newton reveals a candidate period for the spin of the “Magnificent Seven” neutron star RX J1605.3+3249. A&A 563, A50 (2014) J.A. Pons, N. Rea, Modeling magnetar outbursts: flux enhancements and the connection with short bursts and glitches. ApJ 750, L6 (2012) B. Posselt, G.G. Pavlov, The cooling of the central compact object in Cas A from 2006 to 2020. ApJ 932, 83 (2022) B. Posselt, G.G. Pavlov, Ü. Ertan, S. Çalı¸skan, K.L. Luhman, C.C. Williams, Discovery of extended infrared emission around the neutron star RXJ0806.4-4123. ApJ 865, 1 (2018) A.Y. Potekhin, J.A. Pons, D. Page, Neutron stars – cooling and transport. Space Sci. Rev. 191, 239–291 (2015)

4028

A. Borghese and P. Esposito

A.Y. Potekhin, A. De Luca, J.A. Pons, Neutron stars – thermal emitters. Space Sci. Rev. 191, 171–206 (2015) N. Rea, A. Borghese, P. Esposito, F. Coti Zelati, M. Bachetti, G.L. Israel, A. De Luca, Magnetarlike activity from the central compact object in the SNR RCW103. ApJ 828, L13 (2016) D.W. Richards, J.M. Comella, The period of pulsar NP 0532. Nature 222, 551–552 (1969) G.A. Rodríguez Castillo, G.L. Israel, P. Esposito, J.A. Pons, N. Rea, R. Turolla, D. Viganò, S. Zane, Pulse phase-coherent timing and spectroscopy of CXOU J164710.2-45521 outbursts. MNRAS 441, 1305–1316 (2014) G.A. Rodríguez Castillo, G.L. Israel, A. Tiengo, D. Salvetti, R. Turolla, S. Zane, N. Rea, P. Esposito, S. Mereghetti, R. Perna, L. Stella, J.A. Pons, S. Campana, D. Götz, S. Motta, The outburst decay of the low magnetic field magnetar SWIFT J1822.3-1606: phase-resolved analysis and evidence for a variable cyclotron feature. MNRAS 456, 4145–4155 (2016) S. Safi-Harb, H.S. Kumar, Using Chandra to unveil the high-energy properties of the high magnetic field radio pulsar J1119-6127. ApJ 684, 532–541 (2008) N. Sartore, A. Tiengo, S. Mereghetti, A. De Luca, R. Turolla, F. Haberl, Spectral monitoring of RX J1856.5-3754 with XMM-Newton. Analysis of EPIC-pn data. A&A 541, A66 (2012) I.S. Shklovsky, On the nature of the source of x-ray emission of Sco XR-1. ApJ 148, L1 (1967) I.H. Stairs, Testing general relativity with pulsar timing. Liv. Rev. Relativ. 6, 5 (2003) C. Thompson, A.M. Beloborodov, High-energy emission from magnetars. ApJ 634, 565–569 (2005) C. Thompson, R.C. Duncan, The soft gamma repeaters as very strongly magnetized neutron stars – I. Radiative mechanism for outbursts. MNRAS 275, 255–300 (1995) C. Thompson, R.C. Duncan, The soft gamma repeaters as very strongly magnetized neutron stars. II. Quiescent neutrino, X-ray, and Alfven wave emission. ApJ 473, 322 (1996) A. Tiengo, P. Esposito, S. Mereghetti, XMM-Newton observations of CXOU J010043.1-721134: the first deep look at the soft x-ray emission of a magnetar. ApJ 680, L133 (2008) A. Tiengo, P. Esposito, S. Mereghetti, R. Turolla, L. Nobili, F. Gastaldello, D. Götz, G.L. Israel, N. Rea, L. Stella, S. Zane, G.F. Bignami, A variable absorption feature in the X-ray spectrum of a magnetar. Nature 500, 312–314 (2013) A. Torres-Forné, P. Cerdá-Durán, J.A. Pons, J.A. Font, Are pulsars born with a hidden magnetic field?. MNRAS 456, 3813–3826 (2016) S. Tsuruta, A.G.W. Cameron, Cooling and detectability of neutron stars. Can. J. Phys. 44, 1863 (1966) R. Turolla, Isolated neutron stars: the challenge of simplicity, in Astrophysics and Space Science Library, vol. 357, ed. by W. Becker (2009), p. 141 R. Turolla, P. Esposito, Low-magnetic magnetars. Int. J. Mod. Phys. D 22, 1330024–1330163 (2013) R. Turolla, S. Zane, A.L. Watts, Magnetars: the physics behind observations. A review. Rep. Prog. Phys. 78, 116901 (2015) D. Viganò, N. Rea, J.A. Pons, R. Perna, D.N. Aguilera, J.A. Miralles, Unifying the observational diversity of isolated neutron stars via magneto-thermal evolution models. MNRAS 434, 123– 141 (2013) D. Viganò, R. Perna, N. Rea, J.A. Pons, Spectral features in isolated neutron stars induced by inhomogeneous surface temperatures. MNRAS 443, 31–40 (2014) Z. Wadiasingh, M.G. Baring, P.L. Gonthier, A.K. Harding, Resonant inverse compton scattering spectra from highly magnetized neutron stars. ApJ 854, 98 (2018) G. Younes, T. Güver, C. Kouveliotou, M.G. Baring, C.-P. Hu, Z. Wadiasingh, B. Begiçarslan, T. Enoto, E. Gö˘gü¸s, L. Lin, A.K. Harding, A.J. van der Horst, W.A. Majid, S. Guillot, C. Malacaria, NICER view of the 2020 burst storm and persistent emission of SGR 1935+2154. ApJ 904, L21 (2020) S. Zane, L. Nobili, R. Turolla, The magnetar emission in the IR band: the role of magnetospheric currents, in High-Energy Emission from Pulsars and Their Systems, ed. by D.F. Torres, N. Rea. Proceedings of the First Session of the Sant Cugat Forum on Astrophysics, Astrophysics and Space Science Proceedings (2011), pp. 329–335

111 Isolated Neutron Stars

4029

V.E. Zavlin, G.G. Pavlov, D. Sanwal, J. Trümper, Discovery of 424 millisecond pulsations from the radio-quiet neutron star in the supernova remnant PKS 1209-51/52. ApJ 540, L25–L28 (2000) P. Zhou, Y. Chen, X.-D. Li, S. Safi-Harb, M. Mendez, Y. Terada, W. Sun, M.-Y. Ge, Discovery of the transient magnetar 3XMM J185246.6+003317 near supernova remnant Kesteven 79 with XMM-Newton. ApJ 781, L16 (2014) W. Zhu, H. Xu, D. Zhou, L. Lin, B. Wang, P. Wang, C. Zhang, J. Niu, Y. Chen, C. Li, L. Meng, K. Lee, B. Zhang, Y. Feng, M. Ge, E. Gogus, X. Guan, J. Han, J. Jiang, P. Jiang, C. Kouveliotou, D. Li, C. Miao, X. Miao, Y. Men, C. Niu, W. Wang, Z. Wang, J. Xu, R. Xu, M. Xue, Y. Yang, W. Yu, M. Yuan, Y. Yue, S. Zhang, Y. Zhang, A radio pulsar phase from SGR J1935+2154 provides clues to the magnetar FRB mechanism, Science Advances 9, 30 (2023)

Low-Magnetic-Field Neutron Stars in X-ray Binaries

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Tiziana Di Salvo, Alessandro Papitto, Alessio Marino, Rosario Iaria, and Luciano Burderi

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Zoo of Low-Magnetic-Field Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transient and Persistent Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Classical LMXBs: Z-Sources and Atolls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fast X-ray Variability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-ray Spectral Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Bursting Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High-Inclinations Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accreting Millisecond Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Transitional Millisecond Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Faint and Very Faint Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiwavelength Observations of NS LMXBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Facts (and Peculiarities) of NS LMXBs Jets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions and Future Perspectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4032 4034 4034 4037 4039 4045 4057 4065 4073 4086 4089 4091 4092 4093 4095

T. Di Salvo () · R. Iaria Dipartimento di Fisica e Chimica – Emilio Segré, Universitá di Palermo, Palermo, Italy e-mail: [email protected] A. Papitto INAF—Osservatorio Astronomico di Roma, Monteporzio Catone, Roma, Italy e-mail: [email protected] A. Marino Dipartimento di Fisica e Chimica – Emilio Segré, Universitá di Palermo, Palermo, Italy Astrophysics & Planetary Sciences, Institute of Space Sciences (ICE, CSIC), Barcelona, Spain e-mail: [email protected] L. Burderi Dipartimento di Fisica, Universitá degli Studi di Cagliari, Monserrato, Italy e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_103

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Abstract

We give an overview of the properties of X-ray binary systems containing a weakly magnetized neutron star. These are old (Giga-years lifetime) semidetached binary systems containing a neutron star with a relatively weak magnetic field (less than ∼1010 Gauss) and a low-mass (less than 1 M⊙ ) companion star orbiting around the common center of mass in a tight system, with orbital period usually less than 1 day. The companion star usually fills its Roche lobe and transfers mass to the neutron star through an accretion disk, where most of the initial potential energy of the in-falling matter is released, reaching temperatures of tens of million Kelvin degrees, and therefore emitting most of the energy in the X-ray band. Their emission is characterized by a fast-time variability, possibly related to the short time scales in the innermost part of the system. Because of the weak magnetic field, the accretion flow can approach the neutron star until it is accreted onto its surface sometimes producing spectacular explosions known as type-I X-ray bursts. In some sources, the weak magnetic field of the neutron star (∼108 –109 Gauss) is strong enough to channel the accretion flow onto the polar caps, modulating the X-ray emission and revealing the fast rotation of the neutron star at millisecond periods. These systems are important for studies of fundamental physics, and in particular for test of General Relativity and alternative theories of gravity and for studies of the equation of state of ultra-dense matter, which are among the most important goals of modern physics and astrophysics. Keywords

Neutron stars · Low magnetic field · X-ray binaries · X-ray pulsars · Millisecond X-ray pulsars · Transitional pulsars · Fast variability · Type-I bursts · Burst oscillations · X-ray spectra · High-inclination sources · Very faint X-ray sources

Introduction In this chapter, we deal with weakly magnetized neutron stars (hereafter NSs) in low-mass X-ray binaries (hereafter LMXBs). In an LMXB, the compact object interacts, through its gravitational field, with the other component, named the donor, which is usually less massive than the compact object. The donor is therefore a low-mass (usually less than 1 solar mass, M⊙ ) normal main sequence star, or a degenerate dwarf (white dwarf), or an evolved star (red giant). These are therefore old systems with typical lifetime of the order of billions of years, long enough to dissipate most of the original NS magnetic field, resulting in fields of the order of 108−10 Gauss. The donor star, which is typically not a strong wind emitter, fills its Roche lobe and hence transfers mass to the compact object through the inner Lagrangian point. The transferred matter has a high-specific angular momentum

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and forms an accretion disk before reaching the NS surface. More than two hundred of these systems have been detected in the Milky Way. Since these are old systems, they are mostly found in the Galactic bulge and disk and 2–3 dozen of these systems are found in Globular Clusters (see Liu et al. 2007, and the more recent catalogue by Avakyan et al. 2023). Few of them have also been discovered in nearby galaxies. LMXBs are among the brightest sources of the X-ray sky, suffice to say that the discovery in 1962 of the brightest of these sources, Scorpius X-1, using rocket-borne instruments, earned Riccardo Giacconi the Nobel prize in 2002 for the discovery of the first cosmic X-ray sources and marked the beginning of X-ray astronomy. A typical LMXB emits almost all of its radiation in X-rays, and typically less than one percent in visible light, so they are among the brightest objects in the X-ray sky, but relatively faint in visible light. The apparent magnitude is typically around 15 to 20. The brightest part of the system in this band is the accretion disk around the compact object, usually brighter than the donor star. Orbital periods of LMXBs range from ten minutes to days, with typical values below 1 day. In NS LMXBs, the matter transferred from the companion star eventually hits the NS surface generating electromagnetic radiation and making the accreting object a powerful source of energy (Frank et al. 2002). The accretion disk also emits radiation produced via viscous dissipation, and hence, the large majority of the emission from these systems is powered by gravitational potential energy release. Typically, about 10% of the rest-mass energy of the accreted matter is released and emitted mostly in the X-ray band (reaching temperatures from 0.1 to 1 keV up to more than a hundred keV). The apparent luminosity of these systems depends on different parameters, such as the mass accretion rate and the geometry of the system, and can range from few 1031 erg/s up to few times the Eddington limit for an NS: LEdd = 4π GMmp c/σT = 1.26 × 1038 M/M⊙ erg/s,

(1)

where M is the mass of the central object, mp the proton mass, σT the Thomson cross-section, and M⊙ ≃ 2 × 1033 g the mass of the Sun. Although the geometry of the innermost part of the system is still unclear, the low magnetic field of NSs in LMXBs in principle allows the accretion disk to approach the NS surface. The region connecting the inner edge of the disk to the NS, where the azimuthal (Keplerian) velocity of matter in the disk smoothly approaches the velocity at the NS surface, is dubbed boundary layer and is an important source of radiation as well. The NS magnetosphere can affect the accretion process depending on the mass accretion rate and the magnetic field strength (see, e.g., Ghosh et al. 1977; Ghosh and Lamb 1978). The accreting matter transfers its angular momentum to the NS; when the inner disk is sufficiently close to the NS surface, the interaction of the NS magnetic field with the accreting matter can spin the star up, bringing the NS rotation  to very short spin periods, close to the Keplerian frequency (given by ΩK = GMNS /r 3 , where r is the distance from the NS center) at the inner edge of the disk (spin equilibrium). This is consistent with the observed stellar spin frequencies, typically in the range 200–700 Hz.

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Many LMXBs show type-I X-ray bursts, a spectacular eruption in X-rays every few hours to days. During these bursts, the observed X-ray intensity goes up sharply in ∼0.5−5 s and decays relatively slowly in ∼10−100 s. The typical energy emitted in a few seconds during such a burst is ∼1039 ergs (the energy our Sun releases in more than a week). These are interpreted as thermonuclear flashes on the NS surface, caused by material freshly accreted onto the surface that reaches densities and temperatures sufficient for nuclear ignition (see Section “Bursting Sources” for details). The burning is unstable and propagates around the star, resulting in an X-ray burst typically characterized by a fast rise and an exponential decay (FRED). Type-I bursts provide a rare opportunity for the observer to measure the radius of a NS that 2 σ T 4 = f 4πD 2 , radiates like a spherical blackbody of luminosity Lburst = 4πRNS X where D is the distance to the source, fX the flux during the burst, T the temperature from the peak wavelength of the (blackbody) spectrum during the burst, and σ the Stefan–Boltzmann constant. The fact that X-rays can be detected from both the NS and the inner part of the disk for many LMXBs provides an excellent opportunity to study the extreme physics of and around NSs, where special and general relativistic effects can play a role (see, e.g., Bhattacharyya 2010 as a review). Moreover, constraining mass and radius of NSs is important in order to infer constraints on the Equation of State (EoS) of matter at ultra-nuclear density (see Özel and Freire 2016 as a review), which is one of the major goals of modern physics and astrophysics. The EoS relates the pressure of a gas to its density and also determines the equilibrium relation between the mass and radius of a NS. However, the central X-ray emission from these sources cannot be spatially resolved with current X-ray facilities because of the large distances of these sources. Therefore, in order to investigate the properties of the accretion flow close to a NS, we have to rely on the study of their spectral and timing properties. In the following, we will describe some of these properties as well as the information they provide.

The Zoo of Low-Magnetic-Field Neutron Stars Low-magnetic-field NSs can be classified in several ways according to their phenomenology that in turn depends on the mass accretion rate, NS magnetic field strength, geometry of the inner disk region and its inclination with respect to our line of sight, orbital period, chemical composition, companion-star type, and so on. In the following, we will explore the zoo of X-ray emitting low-magnetic-field NSs.

Transient and Persistent Sources One of these classifications is based on the long-term X-ray variability, according to which NS LMXBs can be classified as transient or persistent sources. In persistent sources, the X-ray emission remains stable, although with variations of

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the luminosity up to one order of magnitude, whereas in transient sources (X-ray Transient, XRT) bright outburst phases (with luminosity up to the Eddington limit) are alternated with long-lasting quiescence phases (with luminosity down to a few 1031 erg/s). The large majority of NS LMXBs show a transient behavior, whereas only a couple of dozen of these sources are persistent at different luminosity levels: from faint and very faint sources (typical luminosity below ∼1035 erg/s, see section “Faint and Very Faint Sources”) to the brightest sources (emitting at, or close to, the Eddington limit). X-ray outbursts often are accompanied by a brightening of the optical counterpart by 2–5 magnitudes, usually interpreted as reprocessing of high energy radiation from the accretion disk. The transient nature of these LMXBs is normally attributed to an accretion disk instability (see, e.g., King 2001 as a review) that causes high accretion rate for certain periods of time and almost no accretion during other times. However, recurrence times and duration of X-ray outbursts are highly variable from source to source, even for very similar sources. Indeed, some sources show regular outbursts every few years—this is the case for instance of Aql X-1 or SAX J1808.4-3658. Other sources show very long (tens of years) periods of X-ray quiescence and rarely go into outburst. Many LMXBs showing coherent pulsations at millisecond periods, the so-called accreting millisecond pulsars (AMSPs, see Section “Accreting Millisecond Pulsars”), have shown just one X-ray outburst in the last 25 years. Other sources show years-long periods of X-ray activity before starting similarly long periods of quiescence. This is the case of EXO 0748-676 that has been observed for more than 20 years as a persistent X-ray source before going into quiescence in 2008. Similarly, HETE J1900.1-2455 returned to quiescence in late 2015, after a prolonged accretion outburst of about 10 year (e.g., Di Salvo and Sanna 2022 and references therein). Some sources have also shown close-in-time outbursts (about a month or so apart), e.g., the 2008 outburst of IGR J00291+5934. This variegated phenomenology, together with other observational facts (mainly related to the observed orbital period evolution), led some authors to propose that other parameters may play a role in determining recurrence times and duration of X-ray outbursts, such as the magnetic field of a fast rotating NS (e.g., Burderi et al. 2001) or strong outflows and winds driving large mass loss from these systems (Ziółkowski and Zdziarski 2018). During the X-ray outburst, usually characterized by a fast rising phase, a peak or plateau where the maximum luminosity is reached, and a slower decay of the X-ray flux, the source undergoes variation of its spectral properties. Typically, the source transits from a hard/low-luminosity state to a soft/high-luminosity state and then back again to the hard/low-luminosity state. In the hard state, most of the flux is emitted in the hard X-ray band, above 10 keV, and the X-ray spectrum is dominated by a Comptonized continuum due to soft photons Compton upscattered off a hot, optically thin, electron cloud, named the corona. In the soft state, most of the flux is emitted in the soft X-ray band, below 10 keV, and the X-ray spectrum is dominated by low-temperature blackbody-like components. This spectral evolution is probably caused by the (Compton) cooling of the hot electron corona that becomes denser and more compact around the NS, making the luminous inner accretion disk more

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visible. Hard-to-soft and soft-to-hard state transitions do not usually occur at the same X-ray luminosity, but often an hysteresis is observed, such that the transition back to the hard state occurs at a luminosity several times lower than the hard-to-soft transition (Muñoz-Darias et al. 2014). Because of this spectral evolution toward soft states during the outburst, these sources are named soft X-ray transients (SXTs). However, some transients do not show a transition to the soft sate, their spectra remaining in the hard state even at the peak of the outburst. This is the case of the majority of AMSPs that are therefore named hard X-ray transients (HXTs). It is unclear whether this feature may be related to the presence of a relevant magnetosphere in these sources that could prevent the accretion disk from significantly approaching the star, or to the mass accretion rate that remains relatively low (peak X-ray luminosity of ∼1036 − 1037 erg/s) even during the outburst. These sources are often not detected during quiescent states due to their low luminosity, and for many scientific purposes, it is preferable to observe them during their outbursts to maximize the statistics. Also, new transients are typically discovered during the outburst states. However, these outbursts are normally unpredictable, and therefore, large field-of-view instruments (such as the ASM onboard RXTE, MAXI onboard the International Space Station, ISS, the ESA high-energy-observatory INTEGRAL, and BAT onboard Swift) are required to continuously monitor the X-ray sky. However, there are scientific reasons that motivate observations of transient NS LMXBs in their quiescent states. For example, during the quiescence, the NS surface, heated up by previous outburst episodes, should be the primary X-ray emitting component, and this can be modeled to constrain the stellar radius. Also the study of the cooling history of the NS may give information on the microphysics of the stellar interior and of the dense matter present in the crust (e.g., Cackett et al. 2008; Wijnands et al. 2017). In this case, high-sensitivity imaging instruments (e.g., Chandra and XMM-Newton) are used to observe the sources in quiescence. The observed X-ray emission from a transient NS LMXB during X-ray quiescence is expected to primarily originate from the NS surface/atmosphere (with sometimes some residual accretion). This atmosphere should be composed of pure hydrogen, and devoid of any X-ray spectral line; in fact, the composition of the atmosphere is likely to be affected by rapid gravitational settling, which may cause the accreted heavy elements to sink below the NS photosphere. Moreover, the relatively low magnetic field of NSs in LMXBs (unlike isolated NSs) makes the modeling simpler. Assuming a blackbody emission from the NS surface in a quiescent LMXB, the inferred radius at infinity, R∞ , can be obtained from the 4 )1/2 D, where F relation: R∞ = (F∞ /σ T∞ ∞ is the observed bolometric flux, and T∞ is the best-fit blackbody temperature. Correcting for the hardening factor, f (due to scattering of photons by the electrons and the frequency dependence of the opacity in the NS atmosphere), and for the effects of the gravitational redshift, we can write the actual radius as: RBB = R∞ f 2 /(1 + z), where 1 + z = (1 − 2GM/c2 R)−1/2 is the surface gravitational redshift for a non-spinning NS.

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Classical LMXBs: Z-Sources and Atolls Another widely used classification of LMXBs is based on their correlated spectral and timing behavior (see, e.g., Bhattacharyya 2009 as a review). A convenient way to study how the X-ray spectrum of an LMXB changes with time and how it is correlated with changes in timing features is to compute a color–color diagram (hereafter CD). In this case, the available energy range is divided into four (or three) contiguous energy bands that we can indicate with numbers from 1 to 4 for increasing energy. The photon counts in each band in a given time interval (seconds or minutes or hours depending on the statistics) are used to define the soft and hard colors, with the ratio of the counts in the band 2 with respect to the band 1 indicated as soft color (SC) and the ratio of the counts in the band 4 with respect to the band 3 indicated as hard color (HC). In a CD the HC is plotted versus the SC for a given source at different times, and it is used to track changes of the spectral hardness of the source. The SC or HC can also be plotted versus the total source photon counts, and in this way we get what is called a hardness–intensity diagram (HID). NS LMXBs can be divided into two classes based on the shape of their CD: (i) the so-called Z-sources that show a Z-like track in the CD (see Fig. 1, right panel), which are sources persistently emitting at high luminosity, close to the Eddington limit for a NS, and (ii) the so-called atoll sources that show a C-like track in the CD (see Fig. 1, left panel), which are persistent and transient sources that can become rather bright but typically show luminosities of few tenths of the Eddington limit. These two classes of sources, not only follow a different spectral evolution as traced by their CD, but also show spectral changes that are correlated with distinctly different timing properties (see van der Klis 2006 as a review). The three branches of the Z track are called horizontal (HB), normal (NB), and flaring (FB) branches, respectively. The source moves along the Z track on time scale ranging from hours to a couple of days, performing a random walk and not jumping from a branch to another. The lower part of the CD of a typical atoll is called the banana state (BS, because of its shape), while the upper part is called the island state (IS). Like in Z-sources, atolls move along the BS back and forth with no hysteresis on timescales of hours to a day or so, while the motion on the IS is much slower (days to weeks). Observational windowing can cause isolated patches to form, which is why this state is called island state. A group of four sources (that are GX 13+1, GX 3+1, GX 9+1, GX 9+9), called bright atolls or GX-atoll sources, are persistently bright sources and are nearly always in the BS (see van der Klis 2006 and references therein). The Z and atoll tracks may show slow drifts (i.e., a secular motion on time scales of months to years), usually more visible in the HID, that do not much affect the variability and its strong correlation with the position along the track, originating a phenomenon known as parallel tracks (see Section “Fast X-ray Variability”). What drives the spectral evolution of these sources in the CD is not clear yet. Interestingly, in both atoll and Z-sources, most of the X-ray spectral and timing properties depend only on the position of a source in the diagram.

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Atoll sources

Z sources IS

HB

. m

. m

NB FB LB

UB

~0.01

~0.1

Luminosity / Eddington Fig. 1 Typical CD of Atoll (left) and Z (right) sources. The (inferred) increasing mass accretion rate is indicated by the arrows. Two states are clearly defined for atoll sources, the island state, and the banana state (LB lower banana, UB upper banana), corresponding to hard and soft states, respectively. As for Z-sources, three branches are distinguishable: the horizontal branch (HB), the normal branch (NB), and the flaring branch (FB) (from Migliari and Fender 2006)

The main parameter that determines these properties, and thus the evolution on the diagram, is probably the mass accretion rate m, ˙ which is linked to the accretion luminosity as Lacc = ηmc ˙ 2 , where η is the accretion efficiency (∼10–15% for a NS). Note, however, that the X-ray luminosity of the source is not clearly correlated with the position in the CD, especially in the NB of Z-sources, where the X-ray luminosity decreases, while the mass accretion rate should increase instead. Given the complexity of these paths, it is thought that more than one parameter must be involved. It is also not well understood what, apart from the luminosity, distinguishes between Z and atoll sources. It has been proposed that Z-sources may have a higher accretion rate and a higher magnetic field strength (B > 109 Gauss, see, e.g., Gierlinski and Done 2002). However, the discovery of the first transient Z-source, XTE J1701–462 (Homan et al. 2007), provided new important information on the nature of Z and atoll sources. This transient source started its outburst as a Z-source, exhibiting both the typical Z-shaped track in the X-ray CD and the X-ray timing phenomenology normally observed in Z-sources. However, as its overall luminosity decreased, a transition from Z-source to atoll source behavior was observed. This transition manifested itself both as changes in the shapes of the track in X-ray CD and HID and as changes in the fast time variability, X-ray burst behavior, and X-ray spectra (Homan et al. 2010). This strongly suggests that the variety in behavior observed in NS LXMBs with a different luminosity can be linked to

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changes in a single variable parameter, namely the mass accretion rate, without the need for additional differences in the NS parameters or viewing angle. Furthermore, the evolution of XTE J1701–462 along the outburst is at odd with the hypothesis that the position along the CD of Z-sources is determined by the instantaneous mass accretion rate, since m ˙ variations along individual Z tracks appear to be quite small. On the other hand, variation in m ˙ seems to drive the evolution of the source in the atoll track. The motion along Z track may instead be the result of instabilities, whose presence does depend on the mass accretion rate, or may be determined by the instantaneous mass accretion rate through the disk normalized by its own long-term average, that has also been proposed to explain the parallel-tracks phenomenon. Thanks to the extensive monitoring provided by the instruments onboard RXTE, we know that both atoll and Z-sources can show superorbital modulation, which are quasi-periodic variations on long time scales (5–15 years) with substantial modulation amplitudes for atoll sources and lower modulation amplitudes for Z-sources (see, e.g., Charles 2011 and references therein). The different behavior between Z and atoll sources is attributed to variations in the accretion rate that are less pronounced in Z-sources since they are accreting close to the Eddington limit. The possible causes of these modulations are many; warping/tilting and/or precession of the accretion disc may lead to periodic/quasi-periodic superorbital modulation of the X-ray flux (see, e.g., Kotze and Charles 2012). Other possible mechanisms are long-term modulation of the mass transfer rate, as the one that induces spectral state transitions, or the presence in the system of a third body that can modulate the mass transfer rate, or magnetic-activity variations in the donor convection zone, similar to the solar cycle, leading to changes in the angular momentum of the donor, and hence to changes in the orbital period and the Rochelobe size that, in turn, will modulate the mass transfer rate.

Fast X-ray Variability NS LMXBs show a variety of timing features in their power spectral density (PSD), many of which are not well understood yet. Continuum power, in excess of the mean random power, is often observed at frequencies less than ∼10–100 Hz. The nature of this power, and the corresponding shape of the power spectral component, depends on the source state as determined by its position in the CD. For example, a power-law-like continuum (∝ ν −α , called very low frequency noise, VLFN) is usually observed below ∼1 Hz in the softest states: for atoll sources in the end part of the BS (upper banana) and for Z-sources on the FB. It has been variously ascribed to accretion rate variations and unsteady nuclear burning. The detection of broad Lorentzian curves at 1034 erg/s) at least ten time larger than values typically found for AMSPs (Marino et al. 2019b), since this fits the magnetic screening scenario described above. However, quasi-persistent accretion is perhaps not enough to explain alone the pulse disappearance. X-ray emission from IGR J17062–6143 has persisted during the last ≈15 years, and pulsations have never disappeared so far (Bult et al. 2021). On the other hand, the prolific transient Aql X-1 was an even more extreme case as it showed coherent X-ray pulsations for just 120 s over a couple of Ms of data collected over the years (Casella et al. 2008). In this case, the time scale of the magnetic field re-emergence would be way faster than expected according to the magnetic screening scenario. Therefore, it seems clear that the problem of understanding what determines the lack of pulsations from most LMXBs remains open.

Accretion Torques The possibility of observing a pulsar actually spinning-up due to accretion makes observations of AMSPs most  appealing. Matter in the accretion disk rotates at a Keplerian rate ωK (r) = GM∗ /r 3 and yields its angular momentum to the NS when the magnetosphere drives its motion at r = Rin √. The torque acting ˙ K (Rin )R 2 = M˙ GM∗ Rin . Accreting on the pulsar is expressed as Nmat ≃ Mω in mass at a rate of 1017 g/s (i.e., roughly ten per cent of the Eddington rate) would spin up a 1.4 M⊙ NS with a moment of inertia of I = 1045 g cm2 at a rate 17 g/s)(R /20 km)1/2 Hz/s. Making the ˙ ν˙ mat = Nmat /(2π I ) ≃ 3 × 10−13 (M/10 in dependence of the truncation radius on the mass accretion rate explicit using Eq. 4 shows that the dependence of the material torque on the mass accretion rate is almost

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linear (ν˙ mat ∝ M˙ 6/7 ). In principle, measuring the variation of the spin-up torque during an outburst gives a dynamical estimate of the mass accretion rate onto the ˙ 2 is assumed, of the accretion NS, and once the efficiency of the process LX /Mc luminosity. The proximity of the co-rotation radius of AMSPs to the NS radius also means that spin-down torques due to the field lines that thread the disk beyond the co-rotation surface are likely important (Ghosh and Lamb 1979). The degree of diffusivity of magnetic field lines through the disk and the radial extent of the field/disk interaction set the magnitude of the magnetic spin-down torque. Klu´zniak and Rappaport (2007) considered the interaction over a large radial extent and expressed such a torque as Nmag = −µ2 /9R0 [3 − 2(Rco /R0 )3/2 ], where R0 is the 3 for radius at which the total torque vanished. This expression reduces to ≃µ2 /9Rco a disk truncated near the co-rotation radius. D’Angelo and Spruit (2012) considered that a lower field diffusivity made the interaction region much narrower ∆r/r < 0.1. A disk truncated near the co-rotation takes the angular momentum yielded by the NS and increases its density to redistribute it outward. The truncation radius of the disk stays close to co-rotation even if the accretion rate further decreases (a so-called trapped state), and the NS spins down at a rate of the same order than 3 )(∆r/R ). The spin-down rate due the expression given above, Nmag ≃ −(µ2 /Rin in 3 ≃ to the field/disk interaction is of the order of ν˙ mag ≃ −(1/2π I ) × µ2 /9Rco −15 8 2 2 6 × 10 (B/10 G) (P /2.5 ms) Hz/s. This expression can become comparable to the spin-up term as soon as the magnetic field approaches 109 G, and the pulsar is not an extremely fast one. To measure such tiny rates of changes of the spin frequency, one generally needs to apply timing techniques based on the coherent phase connection of the pulse observed at different times during an outburst. RXTE and later NICER performed high-cadence monitoring of the outbursts of AMSPs to measure their timing solution. However, finding accurate solutions was often troublesome. Only a few AMSPs showed a regular evolution of the phase of their X-ray pulse profiles during an outburst. The pulse phases measured by RXTE during the discovery outburst of IGR J00291+5934 followed a parabolic evolution compatible with a constant spinup rate of (5.1 ± 0.3) × 10−13 Hz/s (see, e.g., Burderi et al. 2007). Considering the expected dependence of the accretion torque on the mass accretion rate indicated a spin-up rate roughly ten times larger than expected from the observed flux (at a distance of 4 kpc). Unfortunately, RXTE ended its operations in 2012 and could not monitor the subsequent outburst shown by the source in 2015. A similar spin-up rate characterized data observed from other three AMSPs (XTE J1751-305, XTE J1807-294 and IGR J17511-3057; see Di Salvo and Sanna 2022, and references therein) even if irregular variations of the phase complicated the interpretation and required considering the pulse phase computed on higher-order harmonics to recover a cleaner pattern. The opposite curvature of the roughly parabolic trend of the pulse phases of four other AMSPs (XTE J0929-314, XTE J1814-338, IGR J17498–2921, IGR J17591-2342, see Di Salvo and Sanna 2022, and references therein) indicated a spin-down compatible with a slightly larger intensity of the magnetic field (≃ a few ×108 − 109 G) compared to other AMSPs. In all cases, the

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limitations set by outbursts lasting a few weeks and the intrinsic tiny spin frequency derivatives reduced the statistical significance of the measurements. Most importantly, a correlation between the phase and the X-ray flux variations was present in a few cases. Patruno et al. (2009a) attributed much of the phase variations to a correlation with the X-ray flux, likely due to corresponding movements of the hot spots on the NS surface. Under this hypothesis, the significance of many measurements of the spin frequency derivative would decrease to the point that even determining the sign would be out of reach. However, why AMSPs would show spin frequency derivatives lower by at least one order of magnitude than those predicted by accretion theories, with torques balancing out to a high degree of precision, would remain unexplained. However, Bult et al. (2021) have recently managed to measure a spin-up rate of (3.77 ± 0.09) × 10−15 Hz/s for the quasi-persistent AMSP IGR J17062-6143 over 12 years of observations. The spin-up was directly visible in the frequency space and did not suffer from possible biases related to the pulse phase timing noise. Indeed, the low spin-up rate supports a scenario in which the magnetic torque exerted by a B ≃ 5 × 108 G on a disk truncated near the co-rotation radius balances almost perfectly the accretion torque. In this complicated picture, the pulse phase timing noise of SAX J1808.4–3658 even defies an easy correlation with the X-ray flux. Irregular movements of the phase computed on the first harmonic of the pulse prevented any meaningful measurement of the torques acting on the NS. However, Burderi et al. (2006) noted that the second harmonic phases behaved more orderly and did not show the abrupt jumps seen for the first harmonic. A smoother evolution of even higher-order harmonics than odd ones could result from slight variations of the ratio between the fluxes received from the two almost antipodal hot spots on the surface of AMSPs (Riggio et al. 2011). De-occultation of the antipodal spot as the disk recedes during an outburst is an intriguing alternative explanation of the observed behavior (Ibragimov and Poutanen 2009).

Spin Frequency Distribution Accretion of mass in an LMXB is very efficient in spinning up an NS. A major question is understanding how far it can go in accelerating the rotation of an NS. Spotting an NS spinning at a period close or below a millisecond would directly set constraints on the EoS of NS matter. Mass shedding at the equator for the maximum mass allowed by an EoS sets the minimum spin period accessible, Pmin ≃ 0.96(M/M⊙ )−1/2 (R/10 km)3/2 ms (see, e.g., Lattimer 2012, and references therein). Given a certain mass, a stiffer EoS describes large stars that could not spin faster than a thousand times per second. Accretion of mass increases the angular momentum of an NS as far as the Keplerian velocity of the inflowing plasma is faster than the rotation of the NS field lines at the disk truncation radius Rin . The accretion torque is assumed to vanish as soon as Rin equals the co-rotation radius. A spinning-up 1.4 M⊙ NS subject only to accretion torques approaches an equilibrium period defined by this condition:

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  −3/7 3/2 6/7  M˙ 2π Rin µ ξ 3/2  = ≃ 0.87 ms, (5) 0.5 (GM∗ )1/2 1026 G cm3 1016 g/s

obtained by making use of Eq. 4. Regardless of the details on the expression of Rin , it is clear that a combination of a higher accretion rate and a lower magnetic field strength brings the truncation radius down to the NS surface. The equilibrium period obtained in that case is as low as ≃0.5 ms for a 1.4 M⊙ NS. However, we have not yet found a sub-millisecond pulsar despite decades of searches and improvements in the detectors and the computing power. The fastest accreting millisecond pulsar known has a period of 1.6 ms (IGR J00291+5934; Galloway et al. 2005), just slightly slower than the quickest radio pulsar PSR J1748– 2446ad (1.4 ms; Hessels et al. 2006). Chakrabarty (2008) estimated the distribution of spin frequencies of AMSPs to be cutoff at ≃730 Hz. Burderi et al. (2001) attributed the absence of sub-millisecond pulsars to the switch on of a rotationpowered pulsar as soon as the mass transfer rate decreased below a given value. The pulsar wind would then efficiently eject the mass transferred by the donor star from the system (the so-called radio ejection phase) and complicate any further accretion. Several works subsequently analyzed the distribution of the spin frequency of AMSPs and suggested they were on average faster than their assumed descendancy of rotation-powered radio MSPs. Spin-down torques act on the NS as the companion star detaches from its Roche lobe and the mass transfer rate declines, possibly explaining this difference. Tauris (2012) used evolutionary calculations to show that the magnetic spin-down torque applied on the NS when Rin equals and exceeds the co-rotation radius at the end of the secular mass transfer phase can dissipate more than half of the rotational energy of the pulsar. Papitto et al. (2014a) argued that the number of AMSPs was still too low to single out a significant difference compared to radio MSPs but showed that LMXBs that show coherent oscillations only during type-I X-ray bursts were indeed faster than radio MSPs. Patruno et al. (2017a) considered the spin distribution of all LMXBs and found statistical evidence for two sub-populations with distributions peaking at ≈300 Hz (i.e., 3.3 ms, similar to radio MSPs) and ≈575 Hz (i.e., 1.7 ms). The very narrow (σ ≈ 30 Hz) distribution of the faster population of LMXBs suggested the existence of a very efficient mechanism to cut off the accretion-driven spin-up. A spin-down torque related to the emission of gravitational waves from a rotating object with mass quadrupole Q becomes very effective at high spin frequencies (Ngw ∝ Q2 ν 5 ) compared to torques related to the rotation of a NS dipolar magnetic field µ (Nsd ∝ µ2 ν 3 ) and represents an intriguing option to cut off the NS spin-up (Bildsten 1998). Either unstable modes of oscillation, crustal, or magnetic strains can support the formation of asymmetries in the NS mass distribution (Lasky 2015). Although Patruno et al. (2012) showed that the spin equilibrium set by the disk/field interaction was alone enough to explain the observed properties of AMSPs, Bhattacharyya and Chakrabarty (2017) have recently highlighted the effect of transient accretion. They found that at a given average mass accretion rate, the spin equilibrium period of transients is much smaller than for persistent LMXBs. These calculations highlighted the requirement

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Fig. 20 Left: Secular evolution of the spin frequency of SAX J1808.4–3658 calculated relatively to the value observed in 1998. Black points represent measurements obtained with RXTE, while colored squared represent the NICER measurements obtained for the 2019 outburst of the source for three different models. The solid line indicates the spin evolution best-fit model. Right: Orbital evolution of SAXJ1808.4–3658. The dashed (blue), dashed–dot (red), and solid (green) curves are the best-fit parabola between the orbital phases measured in the intervals 1998–2008, 2008–2019, and 1998–2019, respectively. (Credit: Bult et al. (2020), ©AAS. Reproduced with permission)

of an additional effect to explain the observed distribution of spin frequencies. Gravitational radiation stands out as the most intriguing option. The observed long-term spin behavior of AMSPs is a valuable testbed for theories of spin evolution. A direct comparison of the spin frequency measured in different consecutive outbursts allowed for a measurement of the spin evolution of AMSPs almost not impacted by the pulse phase timing noise affecting outbursts (see Di Salvo and Sanna 2022, and references therein for a list of the available measurements). Between 1998 and 2019, SAX J1808.4-3658 has spun down at an average rate of ν˙ = −1.01(7) × 10−15 Hz/s (see the left panel of Fig. 20, Bult et al. 2021 and references therein). The spin-down rate of IGR J00291+5934 was harder to estimate since the accretion-driven spin-up taking place during outbursts introduced a sawtooth-like behavior of the spin frequency. The spin-down between the first two outbursts recorded (see, e.g. Papitto et al. 2011) was of the same order as in SAX J1808.4-3658 (= (−4.1 ± 1.2) × 10−15 Hz/s), while the 2015 accretion episode only allowed to set a coarser upper limit (|˙ν | < 6 × 10−15 Hz/s). XTE J175–305, SWIFT J1756.9–2508, and IGR J17494–3030 also showed a long-term spin-down ranging from −5 × 10−16 to −2 × 10−14 Hz/s. The observed spin-down rates of AMSPs are compatible with magnetic fields in 3, the range a few ×108 − 109 G at the magnetic poles (˙νsd = −(1/2π I ) × µ2 /Rlc where Rlc = cP /2π = 119(P /2.5 ms) km). On the other hand, assuming that the spin-down was due to gravitational radiation led to a relatively small measurement of the average NS mass quadrupole, Q < 2 × 1036 g cm2 . Under the hypothesis that the emission of gravitational radiation governs the spin-down of AMSPs, the fastest spinning AMSP IGR J00291+5934 would decelerate at a rate (599/401)5 ≃ 7.5 times larger than SAX J1808.4-3658. The measurements obtained so far indicate a smaller ratio ≃4 ± 1. This ratio is of the order of the value expected if magnetodipole rotation is instead the dominant effect (≃(599/401)3 ≃ 3). Monitoring the

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future outbursts shown by these AMSPs and widening the sample of AMSPs with a measured long-term ν˙ will allow discriminating between the different models proposed to explain the long-term spin-down of AMSPs.

X-ray Spectra The X-ray spectra of AMSPs are typically hard throughout their outbursts. The spectra are dominated by a power-law dN/dE ∝ E −Γ with a photon index Γ ≃ 2 that extends up to 100 keV or even beyond (Poutanen 2006). The commonly accepted model locates the origin of these hard X-ray photons in the accretion columns that develop above the NS polar caps. The freely falling plasma moving along the magnetospheric field lines decelerates in a shock just above the NS surface. The electrons energized at the shock upscatter the soft thermal photons emerging from the underlying surface yielding a spectrum extending up to their equilibrium temperature (Gierli´nski et al. 2002; Gierli´nski and Poutanen 2005). Modeling this hard component with a thermal Comptonization model in a slab geometry assumed for accretion columns indicated a moderately optically thick medium (τ ≈ 1 − 3) with electrons characterized by a temperature of kTe ≃ 25 − 50 keV, upscattering a seed blackbody spectrum with temperature kTbb ≃ 0.3 − 1.0 keV emitted by a surface with a size Abb ≃ 20 km2 compatible with the expectations for a hot spot (see, e.g. Papitto et al. 2020, and references therein). One or two thermal components characterize the softer X-ray energies (kT ≃ 0.1−1 keV). The normalization of the colder one (A > 100 km2 ) is compatible with emission from the inner rings of the truncated accretion disk, whereas the hotter one comes from the fraction of the NS surface that feeds the accretion columns with soft photons. In addition, broad (σ ∼ a few keV) emission lines emerged at the energies of the Iron K-α transition (6.4–7 keV; Papitto et al. 2009; Cackett et al. 2010) and sometimes also of ionized species of Sulfur, Argon, and Calcium at lower energies (Di Salvo et al. 2019). The estimates of the inner disk radius given by modeling these lines with relativistic disk reflection models were compatible with the tight range expected for the observations of pulsations (R∗ < Rin < Rco ). Fitting simultaneously the line profile and the spectral continuum measured at soft and hard X-rays by different telescopes (e.g., XMM-Newton and NuSTAR, see Fig. 21 for details) further confirmed the presence of a disk reflection component that might play an important role to constrain the geometry of the system (e.g., by allowing a measurement of the system’s inclination; see, e.g., Di Salvo et al. 2019).

Pulse Profiles Two harmonic components are generally sufficient to model the pulse shapes of AMSPs. The fractional amplitude of the fundamental is typically lower than ten per cent and shows a dependence on the photon energy, even though different trends characterized the various sources. Some showed a marked increase going from a few to 10 keV, whereas other AMSPs showed a drop of the amplitude in the same energy range (see Patruno and Watts 2021, and references therein). The two components contributing to the pulsed emission of AMSPs (thermal photons

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Fig. 21 Left: XMM-Newton RGS and pn spectra of SAX J1808.4–3658 in the energy range 0.6–10 keV (top) and residuals in units of σ (bottom) with respect to the best-fit model. The model consists of a blackbody, the Comptonization component nthComp, and four disk lines describing the reflection component. Right: NuSTAR spectrum in the energy range 3–70 keV (top) and residuals in units of σ (bottom) with respect to the continuum model of SAX J1808.4–3658 when the Fe line normalization is set to 0. (see Di Salvo et al. 2019 for further details)

from the hot spots on the surface and harder photons upscattered in the accretion columns) served to interpret the latter behavior. Photons upscattered in the accretion columns have a wider angular distribution than the soft thermal photons and yield a weaker modulation at the spin period (Poutanen and Gierli´nski 2003). The times of arrival of pulsed photons also showed a dependence on their energy. Photons of a few keV generally arrive later than harder photons by 100–200 µs. The broader emission pattern of photons upscattered in the accretion columns than soft photons emitted from the hot spots possibly explains why an observer would see the former arrive earlier (Poutanen and Gierli´nski 2003). Phase lags generally saturate around 8–10 keV. On the other hand, IGR J00291+5934 showed a reversal of the lags above 6 keV. The higher number of scatterings required to reach energies of 50–100 keV could explain the longer time they take to reach the observer (see, e.g., Papitto et al. 2020, and references therein). Modeling the X-ray pulse profiles produced from the surface of MSPs is one of the most powerful techniques to measure simultaneously the mass and the equatorial radius of an NS to constrain its EoS.The gravitational field of an NS bends the trajectory and energy of the photons emitted by hot spots on its surface in a way proportional to the ratio M∗ /Req . This effect causes a drop in the pulse amplitude compared to the non-relativistic case and introduces a characteristic energy dependence. The relativistic motion of the hot spots on the NS surface skews the pulse shape depending on the size of its equator Req . The X-ray pulse shape of MSPs thus encodes the desired information on the mass and radius of the NS (Poutanen and Gierli´nski 2003). Recently, this technique led to the first measurements of the mass and radius of two isolated rotation-powered MSPs and highlighted the complex multipolar structure of their magnetic field (Riley et al. 2019; Miller et al. 2019). AMSPs are much brighter than isolated rotation-powered MSPs and represent a

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viable alternative. However, the pulse phase timing noise observed from a few AMSPs and the degeneracy between the geometrical parameters M and Req and the spot geometrical parameters, such as the binary inclination i, the spot co-latitude θ , prevented getting meaningful constraints from RXTE data (see, e.g., Poutanen and Gierli´nski 2003). The re-opening of the polarimetric X-ray window with the Imaging X-ray Polarimetry Explorer (IXPE) and later with the planned enhanced Xray Timing and Polarimetry mission (eXTP) might be a game-changer. The expected degree of polarization of the hard X-ray emission produced in the hot shocked regions above the NS surface is ∼10–20% (Poutanen 2020). IXPE observations could be already enough to constrain i and θ within a few degrees (Salmi et al. 2021). Such estimates would allow to measure the mass and the radius of AMSPs with a relative uncertainty of a few per cent, comparable or slightly smaller than rotation-powered MSPs. X-ray polarimetry could then revive the prospects of using AMSPs to measure the EoS of NS.

X-ray Quiescence From the peak of an outburst to the quiescence, the X-ray luminosity of AMSPs drops by more than four orders of magnitude (e.g., from a few ×1036 to ≃1032 erg/s). Following Eq. 4, the truncation radius will expand from a few tens of km to a few hundred. First, it will exceed the co-rotation radius (31 km for a 1.4 M⊙ NS spinning at 2.5 ms, such as SAX J1808.4-3658). When this happens, the disk matter cannot provide angular momentum anymore to the NS, and rather it is the rotating magnetosphere that speeds up the rotating disk plasma. Illarionov and Sunyaev (1975) first considered this situation and argued that the magnetospheric centrifugal barrier would quench accretion on the NS altogether. Actually, the disk matter would be flung out of the system only if the angular momentum deposited by the magnetosphere in the disk exceeds the escape velocity (Rin > 21/3 Rco , Spruit and Taam 1993). For Rin ≃ Rco , the disk readjusts itself to redistribute the excess angular momentum outward, allowing accretion to proceed albeit at a reduced rate (D’Angelo and Spruit 2010, 2012). 3D magneto-hydrodynamic simulations confirmed that accretion and ejection of plasma coexist in the propeller state (see Romanova et al. 2018, and references therein). It is a non-stationary cycle made of matter building up beyond the magnetospheric radius, pushing the inner radius of the disk inward, opening and inflating the field lines of the magnetosphere (with both accretion and ejection taking place), which expands and re-starts the cycle. The efficiency of mass ejection is minimal in the weak propeller conditions (Rin ≥ Rco ) and is maximal in the strong propeller state (Rin > 5Rco ), in which conical jets and a strong wind are launched. The persistence of accretion during the propeller state would explain why pulsations of SAX J1808.4–3658 are detected down to a luminosity of at least a few 1034 erg/s (the sensitivity limit of RXTE), roughly a hundred times weaker than the peak luminosity. Radial oscillations of the magnetospheric boundary located close to or just beyond the co-rotation boundary are the most likely explanation of the ∼1 Hz quasi-periodic oscillation appeared in the later stages of some of the outbursts of SAX J1808.4–3658 (Patruno et al. 2009c). Transitions between a weak and a strong propeller occurring on a time

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scale shorter than a second also provided a satisfactory explanation of the bimodal magnitude and spectral variability of the transitional millisecond pulsar IGR J18245–2452 in outburst (Ferrigno et al. 2014). In quiescence, the X-ray luminosity of AMSPs is much lower (LX ≃ 5 × 1031 erg/s for SAX J1808.4–3658). A Γ ≃ 1.4 power law described the quiescent X-ray spectrum of SAX J1808.4–3658 (e.g. Campana et al. 2002). The NS atmosphere had a temperature of at most ≈30 eV already a couple of years after the last X-ray outburst, requiring a fast atmospheric cooling likely related to URCA neutrino emission processes involving protons, hyperons, or deconfined quarks (Heinke et al. 2007). IGR J00291+5934 is the other AMSP with well-defined quiescent properties (e.g., Campana et al. 2008). A thermal component with a temperature of 50–100 eV (depending on the assumed model) coexisted with the power-law component, indicating a slower cooling that could be related to a lower NS mass. Even assuming that residual accretion powers the emission of AMSPs in quiescence, the low X-ray luminosity indicates that the inner disk radius would also exceed the light-cylinder radius (RLC = cP /2π = 120 (P /2.5 ms) km). According to conventional wisdom, the presence of high-density plasma inside the light cylinder prevents the rotation-powered pulsar, or at least the radio-emission mechanism, from working. Emptying the light cylinder would instead allow the switch-on of a rotation-powered pulsar whose relativistic wind would then eject the plasma transferred by the companion from the system (Burderi et al. 2001). Expectations were that a radio pulsar would be active during the quiescent states of transient LMXBs (Stella et al. 1994). Some pieces of evidence indirectly support this scenario. The X-ray luminosity observed in quiescence from SAX J1808.4–3658 was not high enough to irradiate the companion star up to the magnitude observed in the optical band; the spin-down luminosity of a rotation-powered pulsar with a magnetic field of a few ×108 G represented an intriguing solution to the problem (Burderi et al. 2003). The orbit of SAX J1808.4–3658 expanded at a rate much faster than conservative mass transfer can explain, whereas ejection of the mass transferred by the companion from the vicinity of the inner Lagrangian point that connects the binary Roche lobes would remove enough angular momentum (Di Salvo et al. 2008). Lastly, the emission of a rotationpowered pulsar would explain the detection of a gamma-ray counterpart to SAX J1808.4–3658 (de Oña Wilhelmi et al. 2016). However, deep searches for pulsations in the radio band did not succeed (see Patruno et al. 2017b, and references therein). Absorption or scattering of radio waves by matter enshrouding the system could explain such a non-detection. Discovering an AMSP that behaves as a radio pulsar during the X-ray quiescence changed the picture (Papitto et al. 2013). IGR J18245-2452, with a relatively long orbital period of ∼11 h, is the only transitional millisecond pulsar (see Section “Transitional Millisecond Pulsars”) observed in a bright X-ray outburst. Long eclipses of the radio pulsations observed in quiescence proved the presence of matter ejected by the pulsar wind and partly enshrouding the binary system. Undetected during the accretion outburst, it took less than a couple of weeks for

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radio pulsations to reappear after it had ended. Observations of IGR J18245-2452 eventually proved that variations of the mass accretion rate make a pulsar swing from a rotation to an accretion-powered regime and vice versa. The optical and ultraviolet pulsations detected from SAX J1808.4-3658 gave further indication of emission powered by the rotation of the NS magnetic field (Ambrosino et al. 2021). Strikingly, the detection took place during the rising and the declining phases of an accretion outburst. Self-absorbed cyclotron emission in accretion columns entrained by a ≈108 G magnetic field is a viable mechanism to explain the pulsed emission observed from cataclysmic variables at those wavelengths. However, the optical/UV pulsed luminosity of SAX J1808.4–3658 exceeded by two orders of magnitudes what this process can produce. Similar reasoning rules out reprocessed emission from the irradiated disk. In addition, the sinusoidal shape of the pulse profiles argues against a substantial beaming of the radiation. A mechanism related to the acceleration of electrons and positrons to relativistic energies by the pulsar rotating electromagnetic field seems in order. Enveloping a significant fraction of the pulsar wind by the disk surrounding the pulsar would help attain the high efficiency in converting the spin-down power into radiation required by the observed pulsed optical/UV luminosity. Similar considerations hold for the case of the transitional millisecond pulsar PSR J1023+0038 (see Section “Transitional Millisecond Pulsars”). Strikingly, magnetospheric particle acceleration in SAX J1808.4–3658 would coexist with accretion onto the polar caps, a possibility generally excluded for pulsars.

Binary Evolution The transitional millisecond pulsar IGR J18245-2452 bridged the population of AMSPs and irregularly eclipsed rotation-powered MSPs. The phenomenology of the latter class of pulsars descends from the interaction between the relativistic pulsar wind and the matter lost by the companion star and ejected from the system. These eclipsed pulsars belong to close binary systems (Porb < day) and are called redbacks or black widows depending on the nature of the companion star. A nondegenerate hydrogen-rich star with Md ≃ 0.1 − 1 M⊙ is the companion of redback pulsars, whereas a low-mass (Md < 0.06 M⊙ ) degenerate star is the companion of black widows. The existence of a link between AMSPs, redbacks, and black widows is not surprising. They all belong to binary systems with a donor that is losing mass and close enough that the energy densities of the accretion flow and the pulsar wind are comparable over the typical binary scale. Slight variations of the accretion rate might then push a system into either the accretion or the rotation-powered regime. Observing the variations in the orbital period of AMSPs is a powerful tool to investigate the binary evolution. The fast expansion of the orbit of SAX J1808.4–3658 (P˙orb ≃ a few ×10−12 ; see the right panel of Fig. 20) is reminiscent of the evolution observed from black widow pulsars and strongly suggests a nonconservative evolution in which a large fraction of the matter transferred by the donor is ejected by the system (Di Salvo et al. 2008). In addition, the expected values of the average X-ray luminosity of AMSPs obtained assuming a conservative binary evolution governed by magnetic braking and emission of gravitational waves

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are much larger than the values obtained by averaging the X-ray emission observed during the outbursts with the much longer quiescence intervals (Marino et al. 2019b). This finding further strengthened the hypothesis that non-conservative mass transfer characterizes the class of AMSPs as a whole. However, the similarity between SAX J1808.4–3658 and black widows also extended to the quasi-cyclic variations of the orbital phase observed during its last few outbursts (see, e.g., Bult et al. 2020; Illiano et al. 2023b). An intense short-term angular momentum exchange between the mass donor and the orbit caused by the gravitational quadrupole coupling with the variable oblateness of the companion might explain such quasicyclic variations of the orbital period (Applegate and Shaham 1994). Monitoring the future outbursts of SAX J1808.4–3658 will help understand if the observed variations of the orbital phase are a good tracer of the secular expansion of the orbit or they rather reflect shorter-term variations. Interestingly, the orbital evolution of IGR J00291+5934 is much slower (P˙orb < 5 × 10−13 ) and is compatible with the evolution driven by the emission of gravitational radiation (see, e.g., Sanna et al. 2017b). Tailo et al. (2018) performed binary evolution calculations and showed the significant role that irradiation of the companion star by the pulsar emission has to play to reproduce the current characteristics of these AMSPs. Irradiation induces cycles of expansion of the donor star followed by mass ejection and contraction on a thermal time scale. SAX J1808.4–3658 and IGR J00291+5934 might be at different stages of this evolution; the former would evolve rapidly by losing mass at high rates, the latter would experience mass transfer mass at much lower rates and evolve much more slowly.

Transitional Millisecond Pulsars Transitional millisecond pulsars (TMSPs) are a small subset of LMXBs, observed at different times either in an accretion disk state or a rotation-powered radio pulsar regime (see the recent review by Papitto and de Martino 2022). Variations in the mass accretion rate are the driver of the state transitions observed so far from three systems (see Table 3). TMSPs allowed us to witness the possible outcomes of the interaction between the electromagnetic field of an MSP and the matter lost by the companion star. When rotation-powered, TMSPs behave as redback pulsars (see, e.g., Strader et al. 2019), matter ejected by the pulsar wind from the inner Lagrangian Point irregularly eclipses radio pulsations. The pulsar wind/plasma interaction creates an intrabinary shock where particles are accelerated to relativistic energies and radiate synchrotron photons (Bogdanov et al. 2011). Viewing the intrabinary shock at different angles along the orbit yields a distinctive orbital modulation of the X-ray emission so produced. Irradiation of the companion star by the high energy emission of the pulsar also determines an orbital sinusoidal modulation of the optical emission (see, e.g., de Martino et al. 2015). The behavior of TMSPs surrounded by an accretion disk is much more peculiar. Only IGR J18245–2452 showed a relatively bright outburst with properties typical

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Fig. 22 Left: XMM-Newton 0.3–10 keV EPIC light curve of PSR J1023+0038 in the subluminous disk state, binned every 10 s (top) and optical monitor light curve, binned every 30 s (bottom). Blue, red, and green points indicate high-, low-, and flaring-mode intervals. Right: X-ray pulse profile observed during the high mode (blue points) and the optical pulse profiles in the high (red points) and flares (green points) detected by SiFAP2 at the INAF TNG Galileo Telescope. (Credit: Papitto et al. (2019), ©AAS. Reproduced with permission)

of AMSPs (see Section “X-ray Quiescence”). When accretion-powered, the other two TMSPs PSR J1023+0038 (Archibald et al. 2009) and XSS J12270-4859 (Bassa et al. 2014) stayed for years in a very faint state (LX ≃ a few × 1033 erg/s) with peculiar multiwavelength properties. Note that IGR J18245-2452 also featured this sub-luminous disk state, although for a shorter interval. What determines whether a source shows a bright outburst or a much fainter state remains unexplained. PSR J1023+0038 is the best-studied case of a TMSP in the sub-luminous disk state, although the others show similar phenomenology. The X-ray light curve of TMSPs in this state shows rapid (∼10 s) switching between two roughly constant flux levels usually dubbed as high and low modes (Bogdanov et al. 2015) (an example is shown in the left panel of Fig. 22). The ratio between the flux in the high and low modes is ≈5–10. Simultaneous transitions show up in the ultraviolet, optical, and near-infrared bands. However, for the latter two, the sign of the correlation with the X-ray/UV band is uncertain. X-ray (Archibald et al. 2015) and optical (in the case of PSR J1023+0038, Ambrosino et al. 2017) pulsations appear during the high mode and disappear in the low modes. Optical pulsations of PSR J1023+0038 lag X-ray ones by ∼100–200 µs and maintain such a delay over the years (Papitto et al. 2019; Illiano et al. 2023a, see the right panel of Fig. 22). The pulsar spins down at almost the same rate shown during the radio pulsar state (Jaodand et al. 2016). In addition, the gamma-ray emission of TMSPs increases by a factor of a few when an accretion disk appears in the system (see, e.g., Torres et al. 2017, and references therein). The flat-spectrum radio emission is compatible with the presence of a jet, while the brightening observed simultaneously to X-ray low modes suggests the ejection of plasmoids (Bogdanov et al. 2018). The properties of TMSPs in the sub-luminous disk state (e.g., a gamma-ray counterpart with a 0.1– 100 GeV flux a few times larger than the 0.1–10 keV X-ray flux) are so peculiar that they have been used to identify at least five strong candidates TMSPs (see Papitto et al. 2020, and references therein).

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Table 3 Main properties of the TMSPs discovered so far. Information taken from Papitto and de Martino (2022). The median mass of the companion star M˜ d is evaluated for i = 60◦ and an NS mass of 1.4 M⊙ . Companion type can be either a main sequence (MS), a white dwarf (WD), or a brown dwarf (BD). Observed states are labeled as radio pulsar (RP), sub-luminous disk state (SLD), and accretion outburst (OUT). Candidates identified on the basis of the similarities of the multiwavelength emission with that observed from TMSPs in the sub-luminous disk state are listed in the lower part of the table TMSPs ν (Hz) Porb (h) M˜ d (M⊙ ) Donor type Obs. states PSR J1023+0038 XSS J12270–4859 IGR J18245–2452

592 592 254

4.75 6.91 11.0

0.16 0.25 0.21

MS MS MS

RP,SLD RP,SLD RP,SLD,OUT

Candidate TMSPs RXS J154439.4–112820 CXOU J110926.4–650224 4FGL J0407.7–5702 3FGL J0427.9–6704 4FGL J0540.0-7552

ν (Hz) – – – – –

Porb (h) 5.8

Modes Yes Yes ? Flares Flares

Gamma rays Yes Yes Yes Yes Yes

Obs. states SLD SLD SLD SLD RP(?),SLD

– 8.8 –

The observation of characteristics typical of either accreting LMXBs (a disk, enhanced X-ray emission although fainter than bright LMXBs, X-ray pulsations) or rotation-powered pulsars (enhanced gamma-ray emission, spin-down rate, optical pulses) complicates the identification of the nature of the sub-luminous state. This duplicity is understood considering that the accretion luminosity of TMSPs in the sub-luminous disk state is of the same order of the pulsar spin-down power (≈ a few × 1034 erg/s), and both processes must be relevant. Earlier models argued that TMSPs were rotation-powered pulsars enshrouded by plasma of the intrabinary shock located far (∼109 −1010 cm) from the pulsar (see, e.g., Coti Zelati et al. 2014). The observation of X-ray pulsations and fast switching between X-ray modes hardly fitted this scenario, suggesting that the accretion flow reached the NS surface, albeit at a low rate. Locking of the disk in a trapped low-M˙ state (D’Angelo and Spruit 2012) or the ejection of most of the disk matter through the propeller effect could explain the low X-ray luminosity observed (Papitto et al. 2014b). More recently, Papitto et al. (2019) and Veledina et al. (2019) reconsidered the hypothesis of an enshrouded rotation-powered pulsar after the discovery of optical pulsations from PSR J1023+0038. Similar problems arise in explaining such a phenomenon in terms of accretion to those mentioned for SAX J1808.4–3658 (see Section “X-ray Quiescence”), only exacerbated by the phase lags of optical pulse compared to X-ray ones. Emission of pulsed X-ray and optical synchrotron emission from the termination shock of the pulsar wind by the disk just outside the light cylinder would provide a satisfactory explanation in which the rotation of the magnetic field and mass accretion coexist. In all the mentioned scenarios, the transitions between high and low modes could reflect the movement of the disk truncation radius related to changes of the physical mechanism powering the emission (e.g., from the propeller to the rotation-powered state, Campana et al. (2016), or vice versa, Veledina et al.

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(2019), or from the light-cylinder radius to outward (Baglio et al. 2023; Papitto et al. 2019)). Reconnection of the magnetic field lines threading the disk (or the donor star) could instead explain the flares observed from the X-rays to the nearinfrared band (Campana et al. 2019).

Faint and Very Faint Sources As already discussed in Section “Transient and Persistent Sources,” transient X-ray binaries spend most of their lifetime in quiescence (at very low X-ray luminosities, 100 Rg (Degenaar et al. 2017). Magnetic inhibition may trigger the onset of a propeller phase, with following outflows as an observational signature (Degenaar et al. 2017), as in the sub-luminous X-ray state of the TMSPs (see Section “Transitional Millisecond Pulsars”). Indeed, it was proposed that the majority of the VFXTs may be TMSPs undergoing their “active” X-ray state (Heinke et al. 2015). Other possibilities invoke: (i) a brown dwarf or even a planet as donors in VFXTs (King and Wijnands 2006), already present as companion stars at the formation of the binary system, (ii) low (King and Wijnands 2006) or (iii) high (e.g., Muno et al. 2005) inclination angles; (iv) the existence of a “period gap,” as in Cataclysmic Variables (CVs), where accretion via Roche-lobes overflow is inactive, but a lowlevel accretion via stellar wind is present (Maccarone and Patruno 2013). Due to

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the heterogeneous phenomenology displayed by these puzzling sources, a single explanation for all the systems is unlikely to exist, and these enlisted mechanisms may be at play in different objects.

Multiwavelength Observations of NS LMXBs So far, we have been focusing on the rich and variegated phenomenology of mainly the X-ray emission from NS LMXBs across different classes. However, these objects are bright all over the electromagnetic spectrum, from radio up to γ -ray frequencies. First of all, in the X-ray window, we only see part of the accretion disk multicolor blackbody spectrum, the one corresponding to the innermost regions of the disk. The outer regions of the disk are bright especially in the UV and optical realm and usually dominate these realms, especially if the contribution from the donor star is negligible, i.e., for UCXBs. At longer wavelengths, the disk emission becomes negligible and the spectral contribution from the jet becomes dominant. Jets are collimated outflows of ionized, relativistic particles that are almost ubiquitous in accretion-powered sources (see Belloni 2010 for a review), including low-magnetized NSs in X-ray binaries. Jets are observed in both Z and atolls sources. Sources in the former class, in addition to be brighter in X-rays, are usually more radio-loud than atoll sources (with the exception of the bright atoll GX 13+1). Radiation from jets extends from radio to mid-IR, and it is ascribed to the superposition of self-absorbed synchrotron spectra emitted at different wavelengths by the different portions of the jet. With only a few exceptions, such as Sco X-1 (Fomalont et al. 2001), jets in LMXBs are typically not resolved and are only visible as point-like radio sources; hence, they are often called compact jets. Spectra from compact jets, i.e., which can be described as Sν ∝ ν α , are typically flat (The flatness of these spectra is actually not expected, and it witnesses the existence of some internal energy replenishment mechanisms, such as magnetic reconnection or internal shocks (see, e.g., Malzac 2014 and references therein).) (α ≈ 0) or inverted (α > 0) at low energies, i.e., where the jet is opaque, up to a spectral break typically located at IR frequencies, after which the jet becomes optically thin and the spectrum is steep, well described by a power law. A representative Spectral Energy Distribution is shown in Fig. 23 (left), where the separate contributions from jet and accretion flow are highlighted. Two physical processes are universally accepted to produce jet: the Blandford– Znajek (B-Z) mechanism for rotation-powered jets and the Blandford–Payne (B-P) mechanism for disk-driven jets, although the former mechanism is only plausible for jets in BH systems (see, however, Migliari et al. (2011) for a discussion on rotationpowered jets in NS binaries). On the contrary, the B-P mechanism is applicable to NS LMXBs, but it ignores completely the role, if any, played by the NS own magnetic field in producing the jet, recently included instead in the models by, e.g., Parfrey and Tchekhovskoy (2017).

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Fig. 23 Spectral Energy Distribution of the NS LMXB 4U 0614+091 modeled with the Internal Shocks ishem model for the jet, an irradiated disk model diskir, and a blackbody model for the emission from the NS surface/boundary layer (Marino et al. 2020)

Facts (and Peculiarities) of NS LMXBs Jets Despite being apparently different phenomena, several observational evidences firmly indicate that matter accretion and jets are inextricably intertwined. Decades of radio and X-rays observations of BH X-ray binaries have indeed shown that the physical properties of the jet change drastically depending on whether the system is in hard, intermediate, or soft spectral state. In hard state, steady compact jets with typical radio-flat spectra are produced. While systems evolve through the intermediate states, radio emission becomes flared and variable and the jet becomes “transient,” i.e., composed of discrete, radio bright, knots. Finally, in soft state, radio emission is suppressed and jets are quenched. Furthermore, in hard state, radio and X-rays emission are clearly correlated (see, e.g., Tetarenko et al. 2016). The emerging picture points out the existence of a solid disk-jet interconnection, at least in systems harboring BHs. The patterns of behavior showed by jets in atolls, which have spectral and timing characteristics similar to BH systems, on the other hand, seem to be less clear (see Migliari and Fender 2006; den Eijnden et al. 2021 for comprehensive studies). When

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Fig. 24 Radio/X-ray correlation for the full sample of accreting stellar mass BHs (black circles) and NSs (blue squares), subdivided by classes. (Data taken from https://doi.org/10.5281/zenodo. 1252036 (Bahramian et al. 2018))

observed, jets are systematically fainter in systems hosting NSs, i.e., typically of a factor ∼20, when compared to jets in BH systems (Gallo et al. 2018). Jet suppression in soft state is observed, but it is not the norm in NS LMXBs, with several systems not showing quenching at all (Migliari and Fender 2006). Interestingly, Russell et al. (2021) showed that jet quenching in the persistent UCXB 4U 1820-303 was triggered not when the system transitioned to the soft state, as in BH systems, but when the flux exceeded a certain threshold, shedding light on the possibility that jets may be more responsive to the accretion rate rather than the spectral state in NS LMXBs. As shown in Fig. 24, radio and X-rays luminosities in hard state are correlated in NS LMXBs as well, but their distribution on a radio–X-rays diagram is scattered and harder to interpret when compared to BH systems (see, e.g., Tetarenko et al. 2016). It has been suggested that jets in NS LMXBs may also have different geometries or couplings with the disk (Marino et al. 2020). It is still unclear whether the presence of a magnetic field and/or a stellar surface, the mass and spin of the accretor or a different structure of the accretion flow may account for these differences between BH and NS systems.

Conclusions and Future Perspectives NSs with low magnetic fields are important as they provide us with a unique opportunity to study several aspects of the extreme physics of these objects and of the accretion flow around them. As we have discussed in this chapter, these systems

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are in fact useful for obtaining information on: (i) the constraints on the EoS models of matter at supra-nuclear density in the nuclei of NS through the measurement of stellar parameters, such as mass and radius; (ii) the physics of the atmosphere of NS as well as the physical characteristics of the crust and nucleus; (iii) the geometry and physical properties of the accretion flow in a strong gravitational field regime around these objects; (iv) general relativity tests and alternative theories of gravity. In principle, LMXBs may be useful to put constraints on alternative theories of gravity, if their orbital periods can be measured with high accuracy. Since the difference in the orbital period evolution of binaries interpreted with General Relativity (GR) and other theories of Gravity (e.g., Brans–Dicke gravity) is related to the mass difference of the two members of the binary system, these sources provide prime candidates for constraining deviations from GR (see Psaltis 2008 and references therein). Despite more than 50 years of research and observations of systems containing NS with low magnetic fields, to date there are still several questions to be clarified regarding these systems, many of which have been briefly discussed in this review. Trying to understand these still unclear issues is, however, of capital importance to obtain information on several aspects of the fundamental physics of these objects and the surrounding environment. The understanding of the complex long-term orbital residuals in these systems is of fundamental importance to constrain the orbital period evolution in these systems, which will provide a way to study the evolutionary path leading to the formation of MSPs. Also, the precise determination of the orbital period derivative caused by mass transfer will give in perspective the possibility to constrain alternative theories of gravity. Other astrophysical issues that the observation of these systems could clarify concern the possibility that these systems can form and contain exoplanets; the study of the long-term accretion process and of the structures formed by the material transferred from the companion star and/or accreting onto the compact object; the search for an observational way to distinguish systems containing a BH from those containing NS which has the potential to unveil the signature indicating the presence or absence of a solid surface for the compact object. This can be done with future more sensitive instruments/observers with large collecting area, and good spectral and temporal resolution, using simultaneous multiwavelength observations, and with the use of large monitors capable of frequently scanning the entire X-ray sky with sufficient sensitivity to discover and characterize new transients during their X-ray outbursts and to spot peculiar behaviors of these sources. In this regard, space missions planned for the future, such as Athena, eXTP, XRISM, will certainly be important. The detailed spectral and spectroscopic analysis that the next generation telescopes such as Athena and XRISM will allow could provide strong constraints on the radius and mass of NS, and hence on the EoS of ultra-dense matter, as well as on the geometry of the accretion flow. Furthermore, the combination of the good timing and polarimetry capabilities of eXTP will enable parallel ways to constrain the accretion geometry, e.g., by studying time lags between the different spectral components or the polarization of the incoming radiation. It is also noteworthy that analogous polarimetry studies are now possible with IXPE, launched in December 2021. Finally, the improved sensitivity of these

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instruments might also allow the discovery and characterization of similar sources in other Galaxies, allowing a comparison with the behavior of known Galactic sources.

References M.A. Alpar, A.F. Cheng, M.A. Ruderman et al., A new class of radio pulsar. Nature 300, 728–730 (1982) D. Altamirano, P. Casella, A. Patruno et al., Intermittent millisecond X-ray pulsations from the neutron star X-ray transient SAX J1748.9-2021 in the globular cluster NGC 6440. Astrophys. J. 674, L45 (2008) F. Ambrosino, A. Papitto, L. Stella et al., Optical pulsations from a transitional millisecond pulsar. Nat. Astron. 1, 854–858 (2017) F. Ambrosino, A. Miraval Zanon, A. Papitto et al., Optical and ultraviolet pulsed emission from an accreting millisecond pulsar. Nat. Astron. 5, 552–559 (2021) A. Anitra, T. Di Salvo, R. Iaria et al., Spectral analysis of the low-mass X-ray pulsar 4U 1822-371: reflection component in a high-inclination system. Astron. Astrophys. (2021). https://doi.org/ 10.1051/0004-6361/202140557 J.H. Applegate, J. Shaham, Orbital period variability in the eclipsing pulsar binary PSR B1957+20: evidence for a tidally powered star. Astrophys. J. 436, 312 (1994) A.M. Archibald, I.H. Stairs, S.M. Ransom et al., A radio pulsar/X-ray binary link. Science 324, 1411 (2009) A.M. Archibald, S. Bogdanov, A. Patruno et al., Accretion-powered pulsations in an apparently quiescent neutron star binary. Astrophys. J. 807, 62 (2015) A. Avakyan, M. Nuemann, A. Zainab et al., XRBcats: Galactic low-mass X-ray binary catalogue. A&A 675, 14 (2023) D.C. Backer, S.R. Kulkarni, C. Heiles et al., A millisecond pulsar. Nature 300, 615–618 (1982) A. Bahramian, J. Miller-Jones, J. Strader, A. Tetarenko, R. Plotkin, A. Rushton, V. Tudor, S. Motta, L. Shishkovsky, Radio/X-ray correlation database for X-ray binaries (v0.1) [Data set]. Zenodo (2018). https://doi.org/10.5281/zenodo.1252036 A. Bahramian, C.O. Heinke, J.A. Kennea, T.J. Maccarone, P.A. Evans et al., The Swift bulge survey: motivation, strategy, and first X-ray results. MNRAS 501(2), 2790 (2021) D.R. Ballantyne, T.E. Strohmayer, The evolution of the accretion disk around 4U 1820-30 during a Superburst. ApJ 602(2), L105 (2004) D. Barret, The broad band x-ray/hard x-ray spectra of accreting neutron stars. AdSpR 28: 307–321 (2001) D. Barret, Accretion flows around stellar mass black holes and neutron stars. AIPC 703, 238–249 (2004) C.G. Bassa, A. Patruno, J.W.T. Hessels et al., A state change in the low-mass X-ray binary XSS J12270-4859. Mon. Not. R. Astron. Soc. 441, 1825–1830 (2014) M.C. Baglio, F. Coti Zelati, S. Campana et al., Matter ejections behind the highs and lows of the transitional millisecond pulsar PSR J1023+0038. A&A 677, A30 (2023) T. Belloni, The jet paradigm. In: The Jet Paradigm: From Microquasars to Quasars. Lecture Notes in Physics, vol. 794. ISBN 978-3-540-76936-1. Springer-Verlag Berlin Heidelberg (2010) S. Bhattacharyya, X-ray views of neutron star low-mass X-ray binaries. Curr. Sci. 97, 6 (2009) S. Bhattacharyya, Measurement of neutron star parameters: a review of methods for low-mass X-ray binaries. AdSpR 45, 949 (2010) S. Bhattacharyya, D. Chakrabarty, The effect of transient accretion on the spin-up of millisecond pulsars.ì. Astrophys. J. 835, 4 (2017)

4096

T. Di Salvo et al.

L. Bildsten, Propagation of nuclear burning fronts on accreting neutron stars: X-ray bursts and sub-Hertz noise. ApJ 438, 852 (1995) L. Bildsten, Gravitational radiation and rotation of accreting neutron stars. Astrophys. J. 501, L89–L93 (1998) G.S. Bisnovatyi-Kogan, B.V. Komberg, Possible evolution of a binary-system radio pulsar as an old object with a weak magnetic field. Sov. Astr. Lett. 2, 130–132 (1976) S. Bogdanov, A.M. Archibald, J.W.T. Hessels et al., A Chandra X-ray observation of the binary millisecond pulsar PSR J1023+0038. Astrophys. J. 742, 97 (2011) S. Bogdanov, A.M. Archibald, C. Bassa et al., Coordinated X-ray, ultraviolet, optical, and radio observations of the PSR J1023+0038 system in a low-mass X-ray binary state. Astrophys. J. 806, 148 (2015) S. Bogdanov, A.T. Deller, J.C.A. Miller-Jones et al., Simultaneous Chandra and VLA observations of the transitional millisecond pulsar PSR J1023+0038: anti-correlated X-ray and radio variability. Astrophys. J. 856, 54 (2018) S. Bogdanov, S. Guillot, P.S. Ray, M.T. Wolff, D. Chakrabarty et al., Constraining the neutron star mass-radius relation and dense matter equation of state with NICER. I. The millisecond pulsar X-ray data set. ApJL 887(1), L25 (2019) P.M. Bult, K.C. Gendreau, T.E. Strohmayer et al., NICER follow-up observations of the accreting millisecond X-ray pulsar MAXI J0911-655. Astr. Tel. 1, 12869 (2019) P. Bult, D. Chakrabarty, Z. Arzoumanian et al., Timing the pulsations of the accreting millisecond pulsar SAX J1808.4-3658 during its 2019 outburst. Astrophys. J. 898, 38 (2020) P. Bult, T.E. Strohmayer, C. Malacaria et al., Long-term coherent timing of the accreting millisecond pulsar IGR J17062-6143. Astrophys. J. 912, 120 (2021) L. Burderi, A. Possenti, F. D’Antona et al., Where may ultrafast rotating neutron stars be hidden? ApJ 560, L71–L74 (2001) L. Burderi, T. Di Salvo, F. D’Antona et al., The optical counterpart to SAX J1808.4-3658 in quiescence: evidence of an active radio pulsar? Astron. Astrophys. 404, L43–L46 (2003) L. Burderi, T. Di Salvo, M.T. Menna et al., Order in the chaos: spin-up and spin-down during the 2002 outburst of SAX J1808.4-3658. Astrophys. J. 653, L133–L136 (2006) L. Burderi, T. Di Salvo, G. Lavagetto et al., Timing an accreting millisecond pulsar: measuring the accretion torque in IGR J00291+5934. Astrophys. J. 657, 961–966 (2007) L. Burderi, T. Di Salvo, A. Riggio et al., New ephemeris of the ADC source 2A 1822-371: a stable orbital-period derivative over 30 years. Astron. Astrophys. (2010). https://doi.org/10. 1051/0004-6361/200912881 E.M. Cackett, R. Wijnands, J.M.B. Miller, N. Degenaar, Cooling of the crust in the Neutron star Low Mass X-ray Binary MXB 1659-29. ApJ 687, L87–L90 (2008) E.M. Cackett, J.M. Miller, D.R. Ballantyne et al., Relativistic lines and reflection from the inner accretion disks around neutron stars. ApJ 720, 205–225 (2010) S. Campana, T. Di Salvo, Accreting pulsars: mixing-up accretion phases in transitional systems. Astrophys. Space Sci. Library 457, 149 (2018) S. Campana, L. Stella, F. Gastaldello et al., An XMM-Newton study of the 401 Hz accreting pulsar SAX J1808.4-3658 in quiescence. Astrophys. J. 575, L15–L19 (2002) S. Campana, L. Stella, G. Israel et al., XMM-Newton observations of IGR J00291+5934: signs of a thermal spectral component during quiescence. Astrophys. J. 689, L129 (2008). https://doi. org/10.1086/595867 S. Campana, F. Coti Zelati, A. Papitto et al., A physical scenario for the high and low X-ray luminosity states in the transitional pulsar PSR J1023+0038. Astron. Astrophys. 594, A31 (2016) S. Campana, A. Miraval Zanon, F. Coti Zelati et al., Probing X-ray emission in different modes of PSR J1023+0038 with a radio pulsar scenario. Astron. Astrophys. 629, L8 (2019) P. Casella, D. Altamirano, A. Patruno et al., Discovery of coherent millisecond X-ray pulsations in Aquila X-1. Astrophys. J. 674, L41 (2008)

112 Low-Magnetic-Field Neutron Stars in X-ray Binaries

4097

D. Chakrabarty, The spin distribution of millisecond X-ray pulsars. Decade Accreting MilliSecond X-ray Pulsars 1068, 67–74 (2008) D. Chakrabarty, E.H. Morgan, M.P. Muno, D.K. Galloway, R. Wijnands et al., Nuclear-powered millisecond pulsars and the maximum spin frequency of neutron stars. Nature 424(6944), 42 (2003) P. Charles, LMXBs: an overview. ASPC 447, 19 (2011) J. Chetana, P. Biswajit, Eclipse timings of the LMXB XTE J1710-281: orbital period glitches. MNRAS (2011). https://doi.org/10.1111/j.1365-2966.2010.18110.x M.J. Church, M. Bałuci´nska-Church, A complex continuum model for the low-mass X-ray binary dipping sources: application to X 1624-49. A&A 300, 441 (1995) M.J. Church, M. Bałuci´nska-Church, Measurements of accretion disc corona size in LMXB: consequences for Comptonization and LMXB models. MNRAS 348, 955–963 (2004). https:// doi.org/10.1111/j.1365-2966.2004.07162.x R. Cornelisse, F. Verbunt, J.J.M. in’t Zand, E. Kuulkers, J. Heise, BeppoSAX Wide Field Cameras observations of six type I X-ray bursters. A&A 392, 885 (2002) F. Coti Zelati, M.C. Baglio, S. Campana et al., Engulfing a radio pulsar: the case of PSR J1023+0038. Mon. Not. R. Astron. Soc. 444, 1783–1792 (2014) A. Cumming, L. Bildsten, Carbon flashes in the heavy-element ocean on accreting neutron stars. ApJ 559(2), L127 (2001) A. Cumming, E. Zweibel, L. Bildsten, Magnetic screening in accreting neutron stars. ApJ 557, 958–966 (2001) ˙ A. D’Aí, P. Zycki, T. Di Salvo, R. Iaria, G. Lavagetto, N.R. Robba, Broadband spectral evolution of Scorpius X-1 along its color-color diagram. ApJ 667, 411–426 (2007) A. D’Aì, R. Iaria, T. Di Salvo et al., Chandra X-ray spectroscopy of a clear dip in GX 13+1. Astron. Astrophys. (2014). https://doi.org/10.1051/0004-6361/201322044 C.R. D’Angelo, H.C. Spruit, Episodic accretion on to strongly magnetic stars. MNRAS 406, 1208– 1219 (2010) C.R. D’Angelo, H.C. Spruit, Accretion discs trapped near corotation. Mon. Not. R. Astron. Soc. 420, 416–429 (2012) N. Degenaar, V.F. Suleimanov, Testing the equation of state with electromagnetic observations, in: The Physics and Astrophysics of Neutron Stars. Astrophysics and Space Science Library, vol 457, p. 185. ISBN 978-3-319-97615-0. Springer Nature Switzerland AG (2018) N. Degenaar, J.M. Miller, R. Wijnands, D. Altamirano, A.C. Fabian, X-ray emission and absorption features during an energetic thermonuclear X-ray burst from IGR J17062-6143. ApJL 767(2), L37 (2013) N. Degenaar, C. Pinto, J.M. Miller, R. Wijnands, D. Altamirano et al., An in-depth study of a neutron star accreting at low Eddington rate: on the possibility of a truncated disc and an outflow. MNRAS 464(1), 398–409 (2017) N. Degenaar, D.R. Ballantyne, T. Belloni, M. Chakraborty, Y.-P. Chen et al., Accretion disks and coronae in the X-ray flashlight. Space Sci. Rev. 214(1), article id. 15, 61pp. (2018) M. Del Santo, L. Sidoli, S. Mereghetti, A. Bazzano, A. Tarana, P. Ubertini, XMMU J174716.1281048: a “quasi-persistent” very faint X-ray transient? Astron. Astrophys. 468(1), L17 (2007) D. de Martino, A. Papitto, T. Belloni et al., Multiwavelength observations of the transitional millisecond pulsar binary XSS J12270-4859. Mon. Not. R. Astron. Soc. 454, 2190–2198 (2015) J. van den Eijnden, N. Degenaar, T.D. Russell, R. Wijnands, A. Bahramian et al., A new radio census of neutron star X-ray binaries. MNRAS 507(3), 3899 (2021) E. de Oña Wilhelmi, A. Papitto, J. Li et al., SAX J1808.4-3658, an accreting millisecond pulsar shining in gamma rays? Mon. Not. R. Astron. Soc. 456, 2647–2653 (2016) M. Díaz Trigo, A.N. Parmar, L. Boirin et al., Spectral changes during dipping in low-mass X-ray binaries due to highly-ionized absorbers. Astron. Astrophys. (2006). https://doi.org/10.1051/ 0004-6361:20053586 M. Díaz Trigo, L. Sidoli, L. Boirin et al., XMM-Newton observations of GX 13 + 1: correlation between photoionised absorption and broad line emission. Astron. Astrophys. (2012). https:// doi.org/10.1051/0004-6361/201219049

4098

T. Di Salvo et al.

T. Di Salvo, A. Sanna, Accretion powered X-ray millisecond pulsars, in Millisecond Pulsars, ed. by S. Bhattacharyya, A. Papitto, D. Bhattacharya. Astrophysics and Space Science Library (ASSL) Springer, 465, 87–124 (2022) T. Di Salvo, L. Stella, High energy radiation from neutron star binaries, in The Gamma-Ray Universe, ed. by A. Goldwurm, D. Neumann, J. Tran Thanh Van. Proceedings of the XXII Moriond Astrophysics Meeting, The Gioi Publishers (Vietnam) (2002), arXiv:astro-ph/0207219 T. Di Salvo, R. Iaria, N. Robba, L. Burderi, High resolution and broad band spectra of low mass X-ray binaries: a comparison between black holes and neutron stars. ChJAS 6a, 183–191 (2006) T. Di Salvo, L. Burderi, A. Riggio, A. Papitto, M.T. Menna, Orbital evolution of an accreting millisecond pulsar: witnessing the banquet of a hidden black widow? MNRAS 389(4), 1851– 1857 (2008) T. Di Salvo, A. D’Aí, R. Iaria et al., A relativistically smeared spectrum in the neutron star X-ray binary 4U 1705-44: looking at the inner accretion disc with X-ray spectroscopy. MNRAS 398, 2022–2027 (2009) T. Di Salvo, A. Sanna, L. Burderi et al., NuSTAR and XMM-Newton broad-band spectrum of SAX J1808.4-3658 during its latest outburst in 2015. Mon. Not. R. Astron. Soc. 483, 767–779 (2019) E. Egron, T. Di Salvo, S. Motta et al., Testing reflection features in 4U 1705-44 with XMMNewton, BeppoSAX, and RXTE in the hard and soft states. A&A 550, A5 (2013) A.C. Fabian, M.J. Rees, L. Stella, N.E. White, X-ray fluorescence from the inner disc in Cygnus X-1. MNRAS 238, 729–736 (1989) C. Ferrigno, E. Bozzo, A. Papitto et al., Hiccup accretion in the swinging pulsar IGR J18245-2452. Astron. Astrophys. 567, A77 (2014) C. Ferrigno, E. Bozzo, A. Sanna et al., Discovery of a soft X-ray 8 mHz QPO from the accreting millisecond pulsar IGR J00291+5934. MNRAS 466, 3450–3459 (2017) E.B. Fomalont, B.J. Geldzahler, C.F. Bradshaw, Scorpius X-1: the evolution and nature of the twin compact radio lobes. ApJ 558, 283 (2001) P.C. Fragile, D.R. Ballantyne, A. Blankenship, Interactions of type I X-ray bursts with thin accretion disks. Nat. Astron. 4, 541 (2020) J. Frank, A.R. King, J.P. Lasota, The light curves of low-mass X-ray binaries. Astron. Astrophys. 178, 137–142 (1987) J. Frank, A. King, D.J. Raine, Accretion Power in Astrophysics, 3rd edn. (Cambridge University Press, Cambridge, 2002) E. Gallo, N. Degenaar, J. van den Eijnden, Hard state neutron star and black hole X-ray binaries in the radio:X-ray luminosity plane. MNRAS 478(1), L132 (2018) D.K. Galloway, L. Keek, Thermonuclear X-ray bursts. In: Timing Neutron Stars: Pulsations, Oscillations and Explosions, ed. by T.M. Belloni, M. Méndez, C. Zhang. Astrophysics and Space Science Library, vol. 461, pp. 209–262. ISBN: 978-3-662-62110-3. Springer Berlin Heidelberg, Berlin, Heidelberg (2021) D.K. Galloway, C.B. Markwardt, E.H. Morgan et al., Discovery of the accretion-powered millisecond X-ray pulsar IGR J00291+5934. Astrophys. J. 622, L45–L48 (2005) D.K. Galloway, E.H. Morgan, M.I. Krauss et al., Intermittent pulsations in an accretion-powered millisecond pulsar. ApJ 654, L73–L76 (2007) D.K. Galloway, M.P. Muno, J.M. Hartman, D. Psaltis, D. Chakrabarty, Thermonuclear (type I) X-ray bursts observed by the Rossi X-ray timing explorer. ApJSS 179(2), 360-422 (2008) D.K. Galloway, J. in’t Zand, J. Chenevez, H. Worpel, L. Keek et al., The Multi-INstrument Burst ARchive (MINBAR). ApJSS 249(2), 32 (2020) P. Ghosh, F.K. Lamb, Disk accretion by magnetic neutron stars. ApJ 223, L83 (1978) P. Ghosh, F.K. Lamb, Accretion by rotating magnetic neutron stars. III. Accretion torques and period changes in pulsating X-ray sources. ApJ 234, 296–316 (1979) P. Ghosh, C.J. Pethick, F.K. Lamb, Accretion by rotating magnetic neutron stars. I. Flow of matter inside the magnetosphere and its implications for spin-up and spin-down of the star. ApJ 217, 578 (1977)

112 Low-Magnetic-Field Neutron Stars in X-ray Binaries

4099

M. Gierlinski, C. Done, A comment on the colour-colour diagrams of low-mass X-ray binaries. MNRAS 331, L47—L50 (2002) M. Gierli´nski, J. Poutanen, Physics of accretion in the millisecond pulsar XTE J1751-305. Mon. Not. R. Astron. Soc. 359, 1261–1276 (2005) M. Gierli´nski, C. Done, D. Barret, Phase-resolved X-ray spectroscopy of the millisecond pulsar SAX J1808.4-3658. Mon. Not. R. Astron. Soc. 331, 141–153 (2002) C.O. Heinke, P.G. Jonker, R. Wijnands et al., Constraints on thermal X-ray radiation from SAX J1808.4-3658 and implications for neutron star neutrino emission. Astrophys. J. 660, 1424– 1427 (2007) C.O. Heinke, A. Bahramian, N. Degenaar, R. Wijnands, The nature of very faint X-ray binaries: hints from light curves. MNRAS 447(4), 3034 (2015) J.W.T. Hessels, S.M. Ransom, I.H. Stairs et al., A radio pulsar spinning at 716 Hz. Science 311, 1901–1904 (2006) J.S. Heyl, r-modes on rapidly rotating, relativistic stars. I. Do type I bursts excite modes in the neutron star ocean? ApJ 600(2), 939 (2004) J. Homan, M. van der Klis, R. Wijnands et al., Rossi X-ray timing explorer observations of the first transient Z source XTE J1701–462: shedding new light on mass accretion in luminous neutron star X-ray binaries. ApJ 65, 420–430 (2007) J. Homan, M. van der Klis, J.K. Fridriksson et al., XTE J1701–462 and its implications for the nature of subclasses in low-magnetic-field neutron star low-mass X-ray binaries. ApJ 719, 201– 212 (2010) C. Hu, Y. Chou, Y. Chung, A parameterization study of the properties of the X-ray dips in the low-mass X-ray binary X1916-053. Astrophys. J. (2008). https://doi.org/10.1086/527549 R. Iaria, T. Di Salvo, A. D’Aì et al., X-ray spectroscopy of the ADC source X1822-371 with Chandra and XMM-Newton. Astrophys. J. (2013). https://doi.org/10.1051/0004-6361/ 201015305 R. Iaria, A.F. Gambino, T. Di Salvo et al., A possible solution of the puzzling variation of the orbital period of MXB 1659-298. MNRAS (2018). https://doi.org/10.1093/mnras/stx2529 R. Iaria, S.M. Mazzola, T. Bassi et al., Broadband spectral analysis of MXB 1659-298 in its soft and hard state. Astron. Astrophys. (2019). https://doi.org/10.1051/0004-6361/201833982 R. Iaria, A. Sanna, T. Di Salvo et al., Evidence of a non-conservative mass transfer in the ultracompact X-ray source XB 1916-053. Astron. Astrophys. (2021). https://doi.org/10.1051/00046361/202039225 A. Ibragimov, J. Poutanen, Accreting millisecond pulsar SAX J1808.4-3658 during its 2002 outburst: evidence for a receding disc. Mon. Not. R. Astron. Soc. 400, 492–508 (2009) A.F. Illarionov, R.A. Sunyaev, Why the number of galactic X-ray stars is so small? A&A 39, 185 (1975) G. Illiano, A. Papitto, F. Ambrosino et al., Investigating the origin of optical and X-ray pulsations of the transitional millisecond pulsar PSR J1023+0038. A&A 669, A26 (2023a) G. Illiano, A. Papitto, A. Sanna et al., Timing analysis of the 2022 outburst of the accreting millisecond X-ray pulsar SAX J1808.4-3658: hints of an orbital shrinking. Astrophys. J. Lett. 942, L40 (2023b) J.J.M. in’t Zand, F. Verbunt, T.E. Strohmayer, A new X-ray outburst in the globular cluster NGC 6440: SAX J1748.9-2021. A&A 345, 100–108 (1999) J.J.M. in’t Zand, D.K. Galloway, H.L. Marshall, D.R. Ballantyne, P.G. Jonker et al., A bright thermonuclear X-ray burst simultaneously observed with Chandra and RXTE. A&A 553(11), A83 (2013) A. Jaodand, A.M. Archibald, J.W.T. Hessels et al., Timing observations of PSR J1023+0038 during a low-mass X-ray binary state. Astrophys. J. 830, 122 (2016) A.R. King, Disc instabilities in soft X-ray transients, in Proceedings of the van Paradijs Memorial Symposium (2001) A.R. King, R. Wijnands, The faintest accretors. MNRAS 366(1), L31 (2006) W. Klu´zniak, S. Rappaport, Magnetically torqued thin accretion disks. Astrophys. J. 671, 1990– 2005 (2007)

4100

T. Di Salvo et al.

M.M. Kotze, P.A. Charles, Characterizing X-ray binary long-term variability. MNRAS 420, 1575– 1589 (2012) E. Kuulkers, P.R. den Hartog, J.J.M. in’t Zand, F.W.M. Verbunt, W.E. Harris, M. Cocchi, Photospheric radius expansion X-ray bursts as standard candles. A&A 399, 663 (2003) P.D. Lasky, Gravitational waves from neutron stars: a review. PASA 32, e034 (2015) J.M. Lattimer, The nuclear equation of state and neutron star masses. Ann. Rev. Nucl. Part. Sci. 62, 485–515 (2012) J.M. Lattimer, M. Prakash, The equation of state of hot, dense matter and neutron stars. Phys. Rep. 621, 127 (2016) Q.Z. Liu, J. van Paradijs, E.P.J. van den Heuvel, A catalogue of low-mass X-ray binaries in the Galaxy, LMC, and SMC (Fourth edition). A&A 469, 8 (2007) R.M. Ludlam, J.M. Miller, M. Bachetti et al., A hard look at the neutron stars and accretion disks in 4U 1636-53, GX 17+2, and 4U 1705-44 with NuStar. ApJ 836, 140 (2017) T.J. Maccarone, A. Patruno, Are the very faint X-ray transients period gap systems? MNRAS 428(2), 1335 (2013) J. Malzac, The spectral energy distribution of compact jets powered by internal shocks. MNRAS 443(1), 299 (2014) A. Marino, M. Del Santo, M. Cocchi, A. D’Aí, C. Ferrigno et al., New insights on the puzzling LMXB 1RXS J180408.9-342058: the intermediate state, the clocked type-I X-ray bursts, and much more. MNRAS 490(2), 2300 (2019a) A. Marino, T. Di Salvo, L. Burderi et al., Indications of non-conservative mass transfer in AMXPs. Astron. Astrophys. 627, A125 (2019b) A. Marino, J. Malzac, M. Del Santo, S. Migliari, R. Belmont et al., Testing jet geometries and discjet coupling in the neutron star LMXB 4U 0614 + 091 with the internal shocks model. MNRAS 498(3), 3351 (2020) M. Méndez, On the maximum amplitude and coherence of the kilohertz quasi-periodic oscillations in low-mass X-ray binaries. MNRAS 371, 1925–1938 (2006) M. Méndez, T. Belloni, Is there a link between the neutron-star spin and the frequency of the kilohertz quasi-periodic oscillations? MNRAS 381, 790–796 (2007) M. Méndez, T.M. Belloni, High-frequency variability in neutron-star low-mass X-ray binaries. ASSL 461, 263–331 (2021) A. Merloni, A.C. Fabian, R.R. Ross, On the interpretation of the multicolour disc model for black hole candidates. MNRAS 313, 193–197 (2000) S. Migliari, R.P. Fender, Jets in neutron star X-ray binaries: a comparison with black holes. MNRAS 366, 79–91 (2006) S. Migliari, J.C.A. Miller-Jones, R.P. Fender et al., Linking jet emission, X-ray states, and hard X-ray tails in the neutron star X-ray binary GX 17+2. ApJ 671, 706–712 (2007) S. Migliari, J.C.A. Miller-Jones, D.M. Russell, The influence of spin on jet power in neutron star X-ray binaries. MNRAS 415(3), 2407 (2011) M.C. Miller, F.K. Lamb, D. Psaltis, Sonic-point model of kilohertz quasi-periodic brightness oscillations in low-mass X-ray binaries. ApJ 508, 791–830 (1998) M.C. Miller, F.K. Lamb, A.J. Dittmann et al., PSR J0030+0451 mass and radius from NICER data and implications for the properties of neutron star matter. Astrophys. J. 887, L24 (2019) S. Motta, D’Aí, A. Papitto, A. Riggio, T. Di Salvo et al., X-ray bursts and burst oscillations from the slowly spinning X-ray pulsar IGR J17480-2446 (Terzan 5). MNRAS 414(2), 1508 (2011) M.P. Muno, E. Pfahl, F.K. Baganoff, W.N. Brandt, A. Ghez et al., An overabundance of transient X-ray binaries within 1 parsec of the galactic center. ApJ 622(2), L113 (2005) T. Muñoz-Darias, R.P. Fender, S.E. Motta, T. Belloni, Black hole-like hysteresis and accretion states in neutron star low-mass X-ray binaries. MNRAS 443(4), 3270 (2014) J. Nättilä, A.W. Steiner, J.J.E. Kajava, V.F. Suleimanov, J. Poutanen, Equation of state constraints for the cold dense matter inside neutron stars using the cooling tail method. A&A 591, A25 (2016) F. Özel, P. Freire, Masses, radii, and the equation of state of neutron stars. ARA&A 54, 401–440 (2016)

112 Low-Magnetic-Field Neutron Stars in X-ray Binaries

4101

A. Papitto, D. de Martino, Transitional millisecond pulsars, in Millisecond Pulsars, ed. by S. Bhattacharyya, A. Papitto, D. Bhattacharya. Astrophysics and Space Science Library (ASSL) Springer, 465, 157–200 (2022) A. Papitto, T. Di Salvo, A. D’Aì et al., XMM-Newton detects a relativistically broadened iron line in the spectrum of the ms X-ray pulsar SAX J1808.4-3658. Astron. Astrophys. 493, L39–L43 (2009) A. Papitto, A. Riggio, L. Burderi et al., Spin down during quiescence of the fastest known accretion-powered pulsar. Astron. Astrophys. 528, A55 (2011) A. Papitto, C. Ferrigno, E. Bozzo et al., Swings between rotation and accretion power in a binary millisecond pulsar. Nature 501, 517–520 (2013) A. Papitto, D.F. Torres, N. Rea et al., Spin frequency distributions of binary millisecond pulsars. Astron. Astrophys. 566, A64 (2014a) A. Papitto, D.F. Torres, J. Li, A propeller scenario for the gamma-ray emission of low-mass X-ray binaries: the case of XSS J12270-4859. Mon. Not. R. Astron. Soc. 438, 2105–2116 (2014b) A. Papitto, F. Ambrosino, L. Stella et al., Pulsating in unison at optical and X-ray energies: simultaneous high time resolution observations of the transitional millisecond pulsar PSR J1023+0038. Astrophys. J. 882, 104 (2019) A. Papitto, M. Falanga, W. Hermsen et al., The INTEGRAL view of the pulsating hard X-ray sky: from accreting and transitional millisecond pulsars to rotation-powered pulsars and magnetars. New Astron. Rev. 91, 101544 (2020) K. Parfrey, A. Tchekhovskoy, General-relativistic simulations of four states of accretion onto millisecond pulsars (2017) A. Patruno, Evidence of fast magnetic field evolution in an accreting millisecond pulsar. Astrophys. J. 753, L12 (2012) A. Patruno, A.L. Watts, Accreting millisecond X-ray pulsars. Astrophys. Space Sci. Library 461, 143–208 (2021) A. Patruno, R. Wijnands, M. van der Klis, An alternative interpretation of the timing noise in accreting millisecond pulsar. Astrophys. J. 698, L60–L63 (2009a) A. Patruno, A. Watts, M. Klein Wolt et al., 1 Hz flaring in SAX J1808.4-3658: flow instabilities near the propeller stage. Astrophys. J. 707, 1296–1309 (2009c) A. Patruno, B. Haskell, C. D’Angelo, Gravitational waves and the maximum spin frequency of neutron stars. Astrophys. J. 746, 9 (2012) A. Patruno, B. Haskell, N. Andersson, The spin distribution of fast-spinning neutron stars in lowmass X-ray binaries: evidence for two subpopulations. Astrophys. J. 850, 106 (2017a) A. Patruno, A. Jaodand, L. Kuiper et al., Radio pulse search and X-ray monitoring of SAX J1808.4-3658: what causes its orbital evolution? Astrophys. J. 841, 98 (2017b) A. Patruno, K. Wette, C. Messenger, A deep pulse search in 11 low mass X-ray binaries. ApJ 859, 112 (2018) F. Pintore, A. Sanna, T. Di Salvo et al., Broad-band spectral analysis of the accreting millisecond X-ray pulsar SAX J1748.9–2021. MNRAS 457, 2988–2998 (2016) J. Poutanen, Accretion-powered millisecond pulsars. AdSpR 38, 2697–2703 (2006) J. Poutanen, Relativistic rotating vector model for X-ray millisecond pulsars. Astron. Astrophys. 641, A166 (2020) J. Poutanen, M. Gierli´nski, On the nature of the X-ray emission from the accreting millisecond pulsar SAX J1808.4-3658. Mon. Not. R. Astron. Soc. 343, 1301–1311 (2003) D. Psaltis, Probes and tests of strong-field gravity with observations in the electromagnetic spectrum. LRR 11, 9 (2008) D. Psaltis, D. Chakrabarty, The disk-magnetosphere interaction in the accretion-powered millisecond pulsar SAX J1808.4-3658. ApJ 521, 332–340 (1999) V. Radhakrishnan, G. Srinivasan, On the origin of the recently discovered ultra-rapid pulsar. Curr. Sci. 51, 1096–1099 (1982) A. Riggio, A. Papitto, L. Burderi et al., A model to interpret pulse phase shifts in AMXPs: SAX J1808.4-3658 as a proof of concept. Radio Pulsars: Astrophys. Key Unlock Secrets Universe 1357, 151–154 (2011)

4102

T. Di Salvo et al.

T.E. Riley, A.L. Watts, S. Bogdanov et al., A NICER view of PSR J0030+0451: millisecond pulsar parameter estimation. Astrophys. J. 887, L21 (2019) M.M. Romanova, A.A. Blinova, G.V. Ustyugova et al., Properties of strong and weak propellers from MHD simulations. New Astron. 62, 94–114 (2018) T.D. Russell, N. Degenaar, J. van den Eijnden, M. Del Santo, A. Segreto et al., The evolving radio jet from the neutron star X-ray binary 4U 1820-30. MNRAS 508(1), L6 (2021) T. Salmi, V. Loktev, K. Korsman et al., Neutron star parameter constraints for accretion-powered millisecond pulsars from the simulated IXPE data. Astron. Astrophys. 646, A23 (2021) A. Sanna, A. Papitto, L. Burderi et al., Discovery of a new accreting millisecond X-ray pulsar in the globular cluster NGC 2808. Astron. Astrophys. 598, A34 (2017a) A. Sanna, F. Pintore, E. Bozzo et al., Spectral and timing properties of IGR J00291+5934 during its 2015 outburst. Mon. Not. R. Astron. Soc. 466, 2910–2917 (2017b) J. Speicher, D.R. Ballantyne, J. Malzac, Cooling of accretion disc coronae by Type I X-ray bursts. MNRAS 499(3), 4479 (2020) H.C. Spruit, R.E. Taam, An instability associated with a magnetosphere-disk interaction. ApJ 402, 593 (1993) L. Stella, M. Vietri, Lense-thirring precession and quasi-periodic oscillations in low-mass X-ray binaries. ApJ 492, L59–L62 (1998) L. Stella, M. Vietri, kHz quasiperiodic oscillations in low-mass X-ray binaries as probes of general relativity in the strong-field regime. PhRvL 82, 17–20 (1999) L. Stella, S. Campana, M. Colpi et al., Do quiescent soft X-ray transients contain millisecond radio pulsars? Astrophys. J. 423, L47 (1994) J. Strader, S. Swihart, L. Chomiuk et al., Optical spectroscopy and demographics of redback millisecond pulsar binaries. Astrophys. J. 872, 42 (2019) T.E. Strohmayer, C.B. Markwardt, Evidence for a millisecond pulsar in 4U 1636-53 during a Superburst. ApJ 577(1), 337 (2002) T.E. Strohmayer, W. Zhang, J.H. Swank, A. Smale, L. Titarchuk et al., Millisecond X-ray variability from an accreting neutron star system. ApJL 469, L9 (1996) M. Tailo, F. D’Antona, L. Burderi et al., Evolutionary paths of binaries with a neutron star – I. The case of SAX J1808.4 – 3658. Mon. Not. R. Astron. Soc. 479, 817–828 (2018) T.M. Tauris, Spin-down of radio millisecond pulsars at genesis. Science 335, 561 (2012) A.J. Tetarenko, A. Bahramian, G.R. Sivakoff, E. Tremou, M. Linares et al., Disc-jet coupling in the Terzan 5 neutron star X-ray binary EXO 1745-248. MNRAS 460(1), 345 (2016) D.F. Torres, L. Ji, J. Li et al., A search for transitions between states in redbacks and black widows using seven years of fermi-LAT observations. Astrophys. J. 836, 68 (2017) N. Trueba, J.M. Miller, A.C. Fabian et al., A redshifted inner disk atmosphere and transient absorbers in the ultracompact neutron star X-ray binary 4U 1916-053. Astrophys. J. Lett. (2020). https://doi.org/10.3847/2041-8213/aba9de P. Ubertini, A. Bazzano, M. Cocchi, L. Natalucci, J. Heise, J.M. Muller, J.J.M. in’t Zand, Bursts from GS 1826-238: a clocked thermonuclear flashes generator. ApJ 514(1), L27 (1999) Y. Ueda, H. Murakami, K. Yamaoka et al., Chandra high-resolution spectroscopy of the absorptionline features in the low-mass X-ray binary GX 13+1. Astrophys. J. (2004). https://doi.org/10. 1086/420973 M. van der Klis, Rapid X-ray variability, in Compact Stellar X-ray Sources, ed. by W.H.G. Lewin, M. van der Klis (Cambridge University Press, Cambridge, 2006), pp. 39–112 M. van der Klis, J.H. Swank, W. Zhang et al., Discovery of submillisecond quasi-periodic oscillations in the X-ray flux of Scorpius X–1. ApJ 469, L1 (1996) J. van Paradijs, M. van der Klis, Luminosity dependence of the hardness of the 13–80 keV X-ray spectra of low-mass X-ray binaries. A&A 281, L17–L20 (1994) A. Veledina, J. Nättilä, A.M. Beloborodov, Pulsar wind-heated accretion disk and the origin of modes in transitional millisecond pulsar PSR J1023+0038. Astrophys. J. 884, 144 (2019) F.M. Vincentelli, Y. Cavecchi, P. Casella, S. Migliari, D. Altamirano et al., Discovery of a thermonuclear Type I X-ray burst in infrared: new limits on the orbital period of 4U 1728-34. MNRAS 495(1), L37 (2020)

112 Low-Magnetic-Field Neutron Stars in X-ray Binaries

4103

A.L. Watts, Thermonuclear burst oscillations. ARAA 50, 609 (2012) N.E. White, J.H. Swank, The periodic absorption events from 4U 1915-05. Astrophys. J. (1982). https://doi.org/10.1086/183737 R. Wijnands, Quasi-periodic oscillations and noise in neutron star and black-hole X-ray binaries. AdSpR 28, 469–479 (2001) R. Wijnands, M. van der Klis, A millisecond pulsar in an X-ray binary system. Nature 394, 344– 346 (1998) R. Wijnands, N. Degenaar, M. Armas Padilla, D. Altamirano, Y. Cavecchi et al., Low-level accretion in neutron star X-ray binaries. MNRAS 454(2), 1371 (2015) R. Wijnands, N. Degenaar, D. Page, Cooling of accretion-heated neutron stars. JApA 38, 49 (2017) M.T. Wolff, P.S. Ray, K.S. Wood et al., Eclipse timings of the transient low-mass X-ray binary EXO 0748-676. IV. The Rossi X-ray timing explorer eclipses. Astrophys. J. Suppl. (2009). https://doi.org/10.1088/0067-0049/183/1/156 H. Worpel, D.K. Galloway, D.J. Price, Evidence for enhanced persistent emission during subEddington thermonuclear bursts. ApJ 801(1), 60 (2015) C. Yi, Measuring the orbital periods of low mass X-ray binaries in the X-ray band. Res. Astron. Astrophys. (2014). https://doi.org/10.1088/1674-4527/14/11/001 A.A. Zdziarski, W.N. Johnson, P. Magdziarz, Broad-band γ -ray and X-ray spectra of NGC 4151 and their implications for physical processes and geometry. MNRAS 283, 193–206 (1996) A.A. Zdziarski, P. Lubi´nski, D.A. Smith, Correlation between Compton reflection and X-ray slope in Seyferts and X-ray binaries. MNRAS 303, L11–L15 (1999) J. Ziółkowski, A.A. Zdziarski, Non-conservative mass transfer in stellar evolution and the case of V404 Cyg/GS 2023+338. MNRAS 480, 1580–1586 (2018)

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Alexander Mushtukov and Sergey Tsygankov

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic Field: The Reason for the XRP Uniqueness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observational Appearance of X-ray Pulsars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Coherent Pulsations: The Definitive Feature of XRPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . How Bright Are They? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aperiodic Variability or Flickering XRPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Energy Spectrum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Polarization Properties of XRPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Optical Companions in XRPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Physics and Geometry of Accretion in XRPs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mass Transfer in the Binary System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accretion Flow Interacting with the NS Magnetosphere . . . . . . . . . . . . . . . . . . . . . . . . . . Geometry and Physics of the Emitting Region at the NS Surface . . . . . . . . . . . . . . . . . . . Spectra Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Open Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Key Points to Have in Mind . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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A. Mushtukov () Astrophysics, Department of Physics, University of Oxford, Oxford, UK Leiden Observatory, Leiden, The Netherlands e-mail: [email protected] S. Tsygankov Department of Physics and Astronomy, University of Turku, Turku, Finland e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_104

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Abstract

X-ray pulsars (XRPs) are accreting strongly magnetized neutron stars (NSs) in binary systems with, as a rule, massive optical companions. Very reach phenomenology and high observed flux put them into the focus of observational and theoretical studies since the first X-ray instruments were launched into space. The main attracting characteristic of NSs in this kind of systems is the magnetic field strength at their surface, about or even higher than 1012 G, that is about six orders of magnitude stronger than what is attainable in terrestrial laboratories. Although accreting XRPs were discovered about 50 years ago, the details of the physical mechanisms responsible for their properties are still under debate. Here, we review recent progress in observational and theoretical investigations of XRPs as a unique laboratory for studies of fundamental physics (plasma physics, QED, and radiative processes) under extreme conditions of ultra-strong magnetic field, high temperature, and enormous mass density. Keywords

X-ray pulsars · Neutron stars · Accretion · Accretion discs · Strong magnetic fields · Radiative transfer · Neutrinos · X-rays

Introduction The first coherent pulsations of the X-ray flux from the cosmic source Cen X-3 were discovered back in the early 1970s by the first X-ray space observatory UHURU (Fig. 1, Giacconi et al. 1971) and almost immediately recognized as a result of accretion of matter onto a strongly magnetized NS (Lamb et al. 1973; Davidson and Ostriker 1973). The strong magnetic field (B-field) of the NS in XRP (typically 1012 G at the surface) affects both the global geometry of accretion flow in the system and physical processes in close proximity to the NS surface. As a result, the primary observational features of XRPs (temporal variability at different scales and spectral properties) bear information about interaction of matter and radiation with extremely strong magnetic fields. The matter in the form of plasma from the optical companion can be accreted by a compact object via the stellar wind, accretion disc, or their combination. In the case of XRPs, at a certain distance from an NS, the flow cannot move toward the compact object without being disturbed by the magnetic field and is stopped forming the boundary at the NS magnetosphere (see Fig. 2). The material penetrates into the magnetosphere due to various instability mechanisms and then follows the magnetic field lines toward small regions (∼1010 cm2 ) at the stellar surface close around the magnetic poles. Here, the kinetic energy of accreting matter is released predominantly in the form of X-rays. Due to the misalignment of the NS magnetic and rotation axes, the emission detected by a distant observer exhibits pulsations

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Fig. 1 2002 Noble Prize for Physics Riccardo Giacconi, the X-ray observatory UHURU, and Xray pulsations detected from Cen X-3 (Giacconi et al. 1971)

with the NS period of rotation. Pulsation periods in XRPs lie in the range from ∼0.1 s to thousands of seconds and show complex evolution with time (Bildsten et al. 1997). About one hundred XRPs in our Galaxy and the Magellanic Clouds are known up to date (Walter et al. 2015). Conventionally, they can be divided into persistent and transient sources, with the latter ones covering more than five orders of magnitude in luminosity during outbursts (Doroshenko et al. 2020b). The apparent X-ray luminosity of XRPs may vary from 1032 up to 1041 erg s−1 , with the brightest sources belonging to the recently discovered class of pulsating ultraluminous X-ray sources (see Bachetti et al. 2014, Israel et al. 2017, and Fabrika et al. 2021 for a review). Accreting XRPs can be studied observationally not only in X-rays but also in the radio band (van den Eijnden et al. 2018a, b). It is also expected that the brightest members of this family can be equally bright in neutrinos being the socalled neutrino pulsars (Mushtukov et al. 2018b). In the nearest future, we will have a chance to measure X-ray polarization in XRPs thanks to the upcoming dedicated X-ray polarimeters. The basic phenomenological interpretation of the main observational features of XRPs has remained essentially unchanged since their discovery. At the same

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Fig. 2 Schematic illustration of accretion geometry in X-ray pulsars. Companion star provides material for the accretion process. Accreting material forms an accretion disc or accretes via the stellar wind. At a certain distance from a central object called the magnetospheric radius, the accretion flow experiences a strong pressure of NS magnetic field and cannot move across magnetic field lines anymore. Due to the instabilities at the magnetospheric radius, the flow settles magnetic field lines and follows them toward the NS surface. Finally, the accretion flow reaches NS in small regions located close to the magnetic poles of a star, where it loses its energy emitting it predominantly in the form of X-rays. (From Tsygankov et al. 2022a)

time, a number of exciting details and complications related to questions of stellar evolution, accretion flow dynamics, and radiation physics have emerged thanks to the unprecedented quality of the data collected by modern X-ray instruments. Below, we review a recent progress in both observational and theoretical studies of XRPs in a broad range of physical parameters.

Magnetic Field: The Reason for the XRP Uniqueness NSs are born as a result of a core collapse in massive supergiant O or B stars with initial mass greater than 8 − 10 solar masses during the supernova explosion. The earliest and simplest predictions for the NS magnetic field were based on the assumption that the magnetic flux of a progenitor star is conserved (Ginzburg 1964). Indeed, the typical radius of the NS progenitor is ROB ∼ 1011 cm, while the NS radius is R ∼ 106 cm. If magnetic flux is conserved during supernova explosion, the field is amplified by a factor of (ROB /R)2 ∼ 1010 . These simple calculations predict magnetic field strengths on the NS surface of the order of ∼1012 G, in good agreement with estimates obtained from the energy of the cyclotron resonant

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scattering spectral features in XRPs (Staubert et al. 2019) and spin periods and spin period derivatives in radio pulsars (Gold 1968). However, since the NS is formed from the progenitor’s core comprising only ∼15% of its total original mass, it is not correct to use the whole stellar radius to estimate the magnetic field amplification due to the flux conservation (Spruit 2008). More realistic scenarios for the formation of extremely strong magnetic field in NSs involve dynamo amplification of magnetic fields at the proto-NS stage (Thompson and Duncan 1993). Overall, it is expected that NSs are born with a range of magnetic field strength covering a few orders of magnitude from 1011 and up to 1015 G. The extremely strong magnetic field of NSs in XRPs is one of the key features causing a keen interest in this class of objects. Indeed, the typical strength of the magnetic fields we are dealing in the everyday life is less than 1 G. The field strength in the active regions of normal stars can be of the order of 103 G. The strongest magnetic field available in terrestrial laboratories is about 106 G (Hahn et al. 2019), which can be generated for a few seconds only and used by experimental physicists to probe plasma physics under extreme conditions. Unfortunately, the magnetic field of a few million gauss is the maximum of our experimental abilities. A magnetic field of strength B>

m2e e3 c = 2.35 × 109 G ℏ3

(1)

destroys the basic laws of “school chemistry.” In this field, the Lorentzian force of interaction between electrons and the external magnetic field becomes stronger than the electric force of interaction between electrons and atomic nuclei. Thus, the magnetic field becomes strong enough to change the structure of the energy levels in atoms and their chemical properties (Lai 2001). A magnetic field exceeding 1011 G affects the wave functions of charged elementary particles and influences the properties of the magnetized vacuum and of photon propagation in the medium itself. In particular, the electron motion becomes quantized in the direction perpendicular to the magnetic field with electrons occupying the so-called Landau energy levels. The characteristic scale of the extreme magnetic field is given by the critical field value: BQ ≡

m2e c3 ≃ 4.414 × 1013 G. eℏ

(2)

At this field strength, the transverse motion of electrons becomes relativistic, and the linear scale of electron de Broglie wave becomes equal to the scale of electron’s gyroradius. In such a strong magnetic field, one can expect processes, which are impossible in a weak field limit: photon splitting (Mentzel et al. 1994) and onephoton pair production and annihilation (Daugherty and Harding 1983). Equating the magnetic energy (∼R 3 B 2 /6) and the gravitational binding energy (∼0.6GM 2 /R), we can estimate the maximal “virial” value of the magnetic field for an NS (Broderick et al. 2000):

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Bmax ≈ 1018



M 1.4M



R 10 km

−2

G.

(3)

A stronger magnetic field would induce a dynamical instability of a hydrostatic configuration and cannot be sustained in a considerable fraction of the star (Chandrasekhar and Fermi 1953). The initial structure of the NS magnetic field can be different depending on the details of magnetic field formation during the dynamo process. Further evolution of the NS magnetic field is regulated by many factors, including Ohmic decay, Hall effect, and accretion process (see Igoshev et al. (2021) for a review). These processes influence both magnetic field strength and structure. Typically, the largescale magnetic field in XRPs is assumed to be dominated by the dipole component because of its slow weakening with distance (∝ r −3 ). In spherical coordinates (r, θ, ϕ), the dipole magnetic field B is given by Br(d) =

2µd cos θB , r3

(d)

Bθ

=

µd sin θB , r3

(4)

where µd is a dipole magnetic moment, and θB is the colatitude related to the dipole magnetic axis. In the case of pure dipole magnetic field, the dipole magnetic moment µd ≡ B20 r 3 , where B0 is the field strength at the magnetic pole, i.e., at θB = 0. At a small distance from an NS surface, higher multipoles, like the quadrupole component (q)

(q)

Br

=

µq (3 cos2 θB − 1) , r4

(q)

(q)

Bθ

=

µq sin 2θB , r4

(5)

(q)

where µq is the quadrupole magnetic moment and θB is the colatitude related to the quadrupole magnetic axis, can come into play (Long et al. 2007). In the case of pure quadrupole field, the quadrupole magnetic moment is given by µq ≡

B0 4 r , 2

(q)

where B0 is the field strength θB = 0. Some XRPs already provide evidence of possibly strong non-dipole components of their magnetic field (Israel et al. 2017; Tsygankov et al. 2017a; Mönkkönen et al. 2022).

Observational Appearance of X-ray Pulsars XRPs are among the brightest sources on the X-ray sky that allowed many observatories to collect rich datasets covering several decades. In this section, we will discuss the observational appearance of XRPs at different timescales and

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energy bands. This is a complicated task considering the richness of phenomenology available nowadays. We will consider only the basic features here with the choice of topics being inevitably subjective. We will start with a discussion of the coherent flux pulsations, the definitive feature of the XRPs. It will be shown that the analysis of pulsations and their temporal evolution can tell us a lot about a system and the accretion process in it. Then, we will talk about the luminosity of XRPs, which is directly related to the mass accretion rate in a system, and its variability. Estimates of the mass accretion rate, in turn, help to identify the place of XRPs among other classes of accreting compact objects and figure out which physical processes come into play. We will see that different sub-classes of XRPs exhibit various types of luminosity variation patterns opening a door into a world of unstable processes in XRPs developing on different timescales and involving various aspects of physics. Even stochastic flickering of XRPs can tell us a lot about the geometry of accretion flows and physical conditions there. The spectral analysis of XRPs emission gives us an opportunity to go further in the understanding of accretion onto magnetized NSs. Spectral features bear fingerprints of elementary processes shaping radiation and matter interaction in the emitting regions of an NS. XRPs are binary systems, and the properties of the NS companions make it possible to estimate the age of a system and understand the place of XRPs in the global evolution of binaries.

Coherent Pulsations: The Definitive Feature of XRPs Coherent pulsations of the flux observed from XRPs, naturally explained by a misalignment between the rotation and magnetic axes of an NS, are characterized by phase light curves (aka pulse profiles) of very different shapes (see examples in Figs. 3, 4, and 5). In contrast to radio pulsars, typical pulsations of XRPs have a large duty cycle (50%), and emission never drops to zero intensity at the pulse minimum. The convenient way to characterized pulsation amplitude in a given energy band is the so-called pulsed fraction (PF), which can be calculated as PF ≡

Fmax − Fmin , Fmax + Fmin

(6)

where Fmin and Fmax are minimum and maximum X-ray flux detected within the pulse period, respectively. The pulsed fraction of XRPs may depend on the source luminosity and energy band and can be as high as 100% at high energies. The pulse profile shape in XRPs may have complex morphology and, similarly to the pulsed fraction, vary with the energy band (see Figs. 3 and 4) and accretion luminosity (compare the upper and lower panels in Fig. 3). Variations of pulse profiles with the energy band can be caused by the dependence of the beam pattern on photon energy and/or local absorption due to not spherically symmetric distribution of matter in the system. Changes in the pulse profiles with accretion luminosity indicate the dependence of the geometry of the emission forming region and, therefore, of the beam pattern on the mass accretion rate (see the basic model

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Fig. 3 Dependence of the pulse profile of SMC X-3 on energy in two NuSTAR observations with different X-ray luminosities: (panel a) Lbol = 10.2 × 1038 erg s−1 and (panel b) Lbol = 1.9 × 1038 erg s−1 . Different energy bands are shown with different colors (shown in the bottom panel). The profiles are normalized by the mean flux in each energy band and plotted twice for clarity. One can see that the pulse profiles tend to be dependent on both the energy band and the accretion luminosity, which reflects the dependence of the beam pattern on energy and mass accretion rate. (From Tsygankov et al. 2017a)

types of beam patterns in Fig. 30, Gnedin and Sunyaev 1973; Lutovinov et al. 2015). Remarkably, the pulse profiles can also demonstrate a strong short-term variability on a pulse period timescale (see Fig. 5). In practice, the average observed X-ray energy flux over the pulse profile is used to estimate the accretion luminosity of XRP. The relative stability of the NS rotation rate can be used to determine the orbital parameters of the binary system. Indeed, the observed pulse period in XRPs is affected by the Doppler effect due to the NS orbital motion. Thanks to that, periodic variations of the pulse period are widely used to establish orbital parameters in a binary system. From another side, strong variations of pulse period due to the

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Fig. 4 Pulse profiles of V 0332+53 at different energies obtained by the RXTE observatory during the brightening phase of the 2004–2005 outburst at the luminosity L ≃ 16 × 1037 erg s−1 . The cyclotron line in the source spectrum during this observation is Ecycl ≃ 27.2 keV (shown with the red dashed line). (From Tsygankov et al. 2010)

orbital motion may preclude from the discovery of pulsations from some sources, e.g., as it was in the case of pulsating ULXs (Israel et al. 2017). The long-term variations of the pulse period (see Fig. 21) are related to the physics of the accretion

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Fig. 5 Light curve of 4U 0115+63 in the 17–20.3 keV energy band obtained with the RXTE/PCA instrument at a luminosity of ∼6.6 × 1037 erg s−1 (gray curve). The solid black line indicates the average pulse profile shape in this energy band for the entire observing session. One can clearly see the pulse-to-pulse variability of the pulse profile shape with the second peak being much more variable than the main one. (From Tsygankov et al. 2007)

process, in particular angular momentum exchange between the accretion flow and NS. Simultaneous measurements of the spin-up/-down trends and the corresponding luminosity are typically used to probe the NS magnetic field and physical features of the accretion flow. In addition to the long-term steady evolution of the NS spin period, sudden changes of rotation frequency called “glitches” (in the case of frequency increase) and “anti-glitches” (in the case of frequency decrease) were detected in XRPs and pulsating ULXs (see Bachetti et al. (2020) and the references therein). Although the details of physics standing behind glitches are not very well known, it is thought that the sudden changes of spin frequency can be related to a transfer of angular momentum between superfluid and non-superfluid components of an NS (see the discussion and the references in Ray et al. 2019). It is remarkable that glitches are known to be typical events for isolated radio pulsars, whereas anti-glitches seem to be a specific feature of the accretion process. Indeed, the phenomenon of antiglitch can be caused by prolonged rapid spin-up of the NS due to the accretion process. In this case, the sudden transfer of angular momentum from NS outer crust to superfluid inner crust (and possibly core) leads to the drop of the pulsation frequency (Ducci et al. 2015).

How Bright Are They? The actual luminosity of an XRP can be estimated from the observed X-ray energy flux if one knows the distance to the source, beaming factor, and spectral distribution in the broad energy band. For normal XRPs, the distances remain the largest uncertainty, being often known with errors as large as 50 per cent. At the same time, thanks to the Gaia observatory, the distance to a substantial number of the

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NGC 5907 X-1 M82 X-2 NGC 1313 X-2 M51 X-7 NGC 7793 P13 NGC 300 X-1 Swift J0243.6+6124 SMC X-3 V 0332+53 4U 0115+63 A 0535+26 Vela X-1 X Persei

10

32

10

34

10

36

38

40

10

10

42

10

Apparent Luminosity, erg s-1 Fig. 6 Apparent luminosity and luminosity range observed in some X-ray transients powered by accretion onto magnetized NSs. Gray segments correspond to “normal” X-ray transients, while the red ones correspond to ULX pulsars. The dashed line represents the Eddington luminosity for an NS

Galactic XRPs is known with an accuracy of about 10 per cent. For the bright XRPs, unknown beaming factor due to the geometry of accretion flow results in an additional contribution to the uncertainty (King et al. 2017; Mushtukov et al. 2021a). The apparent luminosity of XRPs covers many orders of magnitude from ∼1032 erg s−1 up to ∼1041 erg s−1 (see Fig. 6 for several representative examples). At the low end of this range, we see either accreting systems at very low mass accretion rates (Tsygankov et al. 2017c) or XRPs in the propeller state (Illarionov and Sunyaev 1975; Ustyugova et al. 2006), where accretion is stopped by a strong magnetic field and X-rays emission is produced by cooling of the NS surface heated during the episodes of intensive accretion (Tsygankov et al. 2016; Wijnands and Degenaar 2016). The upper limit in the luminosity range is provided by the recently discovered XRPs in ultra-luminous X-ray sources (ULXs, Bachetti et al. 2014; Israel et al. 2017), where the apparent luminosity can exceed the Eddington luminosity LEdd

4π GMmp c = ≈ 1.26 × 1038 σT



M M⊙



erg s−1 ,

(7)

where M is a mass of an NS, mp is a mass of a proton, and σT = 6.65 × 10−25 cm2 is the Thomson scattering cross section, by a factor of hundreds.

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Fig. 7 Variations of accretion disc geometry and geometry of the emitting region expected at different mass accretion rates (left) and the observed light curve during the giant outburst in XRP Swift J0243.6+6124 (right). At relatively low mass accretion rates, accretion disc is expected to be gas pressure dominated and geometrically thin, and accretion process results in hot spots located close to the NS magnetic poles (III). The increase of the mass accretion rate leads to an increase of X-ray luminosity. The radiative force starts to affect dynamics of accretion flow in the vicinity of the NS surface and leads to appearance of radiation dominated shock and accretion columns above stellar surface (II). Further increase of the mass accretion rate turns accretion disc into geometrically thick radiation pressure-dominated mode (I). At extremely high mass accretion rates, the disc can be even advection dominated when the photons are confined in the flow and participate in accretion process. (From Doroshenko et al. 2020b)

The vast majority of known XRPs are transient sources and demonstrate dramatic variations of X-ray luminosity on timescales from weeks and months during the outbursts (see Figs. 7, 18 and 22) down to seconds (see Fig. 8 right, Lewin et al. 1996). The transient nature can be caused by variations of mass accretion rate from the companion in a binary system, processes in accretion flow in between NS and its companion, and processes happening in close proximity to the NS. One of the most numerous classes of the transient XRPs is systems with Be optical companions (BeXRBs). Such systems are characterized by the variability of two types. Type I outbursts, related to the enhanced mass accretion rate near the periastron passage, have short duration (about 10–20% of the orbital period) and relatively low peak luminosity (L  1037 erg s−1 ). On the contrary, type II (giant) outbursts, caused by the formation of the circumstellar disc around the companion, are rare events. They last for several orbital periods, during which NS luminosity may exceed the Eddington limit. An example of a giant outburst from BeXRB Swift J0243.6+6124 discovered in 2017 is presented in Fig. 7. Another sub-class of strongly variable high-mass X-ray binaries (HMXBs) is Super-giant Fast X-ray Transients (SFXTs), discovered with the INTEGRAL observatory (Sguera et al. 2005). In these binaries, a strongly magnetized NS accretes matter via wind from the OB super-giant companion. However, in contrast

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Fig. 8 Light curve of Supergiant Fast X-ray Transient IGR J18410−0535 (left, from Bozzo et al. 2011) and short-term brightening observed in bursting XRP GRO J1744−28 at the peak of its outburst (right, from Mönkkönen et al. 2019). These kinds of short-term transient activity in XRPs can be caused by the development of various instabilities in the accretion flow. In particular, the activity observed in the SFXT can be a result of sudden matter penetration through the centrifugal barrier of an NS in a propeller state or stellar wind clumpiness. The fast (tens of seconds) brightening in GRO J1744−28 can be explained by the development of instability in the radiation pressure-dominated disc when the inner disc parts suddenly fall onto the NS (in this scenario, the deeps following the brightening correspond to accretion disc recovery)

to the classical wind-fed supergiant HMXBs, which exhibit themselves as persistent and relatively bright sources with luminosity around 1036 erg s−1 , SFXTs have very low quiescence luminosity and produce short and bright flares with typical duration of a few hours. This class of objects is not homogeneous in terms of the observed properties. To explain the variety of variability patterns, several models were proposed, including clumpy stellar wind (Walter and Zurita Heras 2007), propeller mechanism (Grebenev and Sunyaev 2007), and quasi-spherical settling accretion (Shakura et al. 2014). An example of a powerful flare from SFXT IGR J18410−0535 is shown in Fig. 8 (left). Apart from the discussed types of variability, a unique behavior is demonstrated by GRO J1744−28, Galactic XRP in low-mass X-ray binary. Namely, in the peak of very rare and bright outbursts, it exhibits extremely bright flares with duration of only several (∼10) seconds. This variability pattern appears due to transition of the inner accretion disc into the radiation-dominated regime when the LightmanEardley instability can be developed with subsequent decrease of the inner disc mass, reflected in the flux drop right after the burst (see Fig. 8 right, Cannizzo 1996). The brightest X-ray pulsars belong to the recently discovered class of pulsating ULXs. ULXs are off-nuclear, extragalactic X-ray sources with isotropic luminosities exceeding the Eddington limit for a stellar-mass black hole, i.e., L  1039 erg s−1 (see Fabrika et al. (2021) for a review). ULXs were discovered back in the 1980s by the Einstein space observatory (Long and van Speybroeck 1983) and considered for decades as accreting black holes with intermediate (Colbert and Mushotzky 1999) or stellar masses (Poutanen et al. 2007). Nowadays, there are several hundred

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Table 1 The basic properties of detected ULX pulsars: their maximal apparent luminosity, spin period, spin period derivative, a pulsed fraction (PF), orbital period, and the estimation of companion mass in a binary. Two ULX pulsars show significant changes in their pulse periods on the timescale of ten years. For these objects, we represent parameters corresponding to different epochs LX (max) P PF Porb M2 P˙ Name M82 X-2 NGC 7793 P13 NGC 5907 X-1

[erg s−1 ] 1.8 × 1040 5 × 1039 2 × 1041

NGC 300 X-1

4.7 × 1039

M51 X-7 NGC 1313 X-2

7 × 1039 2 × 1040

[s] 1.37 0.42 1.42 1.13 125 31.5 20 2.8 1.5

[10−10 s s−1 ] ∼2 ∼0.35 115 47 1.4 × 105 5.5 × 103 1.7 × 103 1.6 − 9.4 ?

% >20 ∼20 ∼15 ∼15 ? ∼90 ∼90 5–20 5–6.5

[d] 2.52 64 5.3

[M⊙ ] >5.2 18–23 ?

?

–

∼2 ?

? 10 Hz. The nature of strong additional variability at high frequency is still under debates. Different authors relate it to various phenomena from the photon bubble instability in accretion column (Klein et al. 1996b) to the rapidly propagating mass accretion rate fluctuation in the inner radiation pressure-dominated parts of a disc (Mönkkönen et al. 2019). The plot represents data published in Mönkkönen et al. (2019)

McHardy et al. 2004). Strong aperiodic variability can be considered as a typical feature of the accretion process and sometimes used as an argument confirming or ruling out accretion in X-ray sources (Doroshenko et al. 2020a). At a short timescale, aperiodic variability in XRPs sometimes extends down to milliseconds. In addition to the peak related to the coherent pulsations, the observed power density spectrum (PDS) typically includes a broad continuum component, which can be approximated by a broken (or double broken) power law, and narrow features that are classified as quasi-periodic oscillations (QPOs). Both components in accreting compact objects, including XRPs, are known to evolve with the observed luminosity (see Revnivtsev et al. (2009) and Fig. 9). A typical feature of PDS in XRP is a high-frequency break (f  10−2 Hz). The break frequency can depend on the accretion luminosity. In some sources, the break frequency depends on luminosity as f ∝ L3/7 , which is similar to the expected dependence of the Keplerian frequency at the inner disc radius on the luminosity (see Fig. 10). Fluctuations of the X-ray flux are largely caused by fluctuations of the mass accretion rate onto the NS surface. The latter carries information about geometry and physical condition of the accretion flow: wind/disc accretion, inner and outer radii of accretion disc, gas or radiation pressure-dominated accretion flow, development

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Fig. 10 The dependence of the break frequency in the PDS of A 0535+26 on the observed flux (circles with error bars). The dependence of the QPO frequency observed in A 0535+26 is shown by open dotted circles. The solid circles show the results of the QPO frequency multiplied by 2.5 to match the break frequency trend. The dashed line shows frequency dependence f ∝ L3/7 (similar to the dependence of the expected Keplerian frequency at the inner disc radius). The dotted line shows the observed spin frequency of the pulsar. The plot represents the data published in Revnivtsev et al. (2009)

of instabilities in the accretion flow, etc. Fluctuations of the flux, however, do not exactly replicate fluctuations of the mass accretion rate due to several reasons: • Superposition between fluctuating mass accretion rate and NS rotation can strongly distort the PDS (Lazzati and Stella 1997). • Fluctuations of the X-ray flux can be affected by variations of the beam pattern formed in the emitting regions (Klein et al. 1996b). • Fluctuations of the X-ray flux can be disturbed by the accretion flow in between the inner disc radius and NS surface (Mushtukov et al. 2019a).

Energy Spectrum The effective temperature in XRPs can be estimated from the accretion luminosity L and the expected area S of the emitting region at the NS surface (We define Q = Qx 10x in cgs units if not mentioned otherwise.):

113 Accreting Strongly Magnetized Neutron Stars: X-ray Pulsars

Teff =



L σSB S

1/4

1/4 −1/4

≃ 5.6 L37 S10

4121

keV,

(8)

where σSB is the Stefan-Boltzmann constant. The estimation (8) gives Teff ∼ 1 keV for L37 = 1 even if one takes the total area to an NS. It explains why most of the radiation in XRPs is emitted in the X-ray band. However, one has to keep in mind that the energy spectra of XRPs cannot be approximated with a simple blackbody. Spectra of all bright XRPs (L  1035 erg s−1 ) are quite similar to one other and can be roughly described with a cutoff power law continuum (Nagase 1989). In a few dozens of sources, on top of continuum spectra, one can detect cyclotron absorption scattering feature (for the details, see a review Staubert et al. (2019) and Table 2). In some sources, the scattering feature can be accompanied by several (up to five) higher harmonics (see Fig. 11). Because the accretion flow reaches the NS surface with a velocity comparable to the speed of light and temperature near the NS surface is about a few keV (or higher), bulk and thermal comptonization play a key role in the formation of non-thermal X-ray emission and define the observed shape of its spectrum (Becker and Wolff 2007) (Fig. 12). Recently, it has been discovered that the spectra of some XRPs experience dramatic spectral changes when the mass accretion rate drops below ∼1035 erg s−1 : instead of a classical single-component shape, the spectra show two distinct components with the one peaked at a few keV and the other peaked at a few tens of keV (see Fig. 13, Tsygankov et al. 2019a, b; Lutovinov et al. 2021). In some cases, the cyclotron absorption scattering feature is detected on top of the high-energy component (Tsygankov et al. 2019a). However, these spectral changes at low luminosity are not a general trend for all XRPs, and

Table 2 Cyclotron line sources discovered after Staubert et al. (2019) System Type Swift Be trans. J0243.6+6124 Cen X-3 HMXB

Pspin (s) 9.8

Porb (days) 28

Ecl. no

Ecyc (keV) 120–146

Instr. of detection Insight-HXMT

4.8

2.09

yes

28, 47a

Insight-HXMT

Swift J1626.6−5156 GRO J1750−27 Swift J1808.4−1754 XTE J1858+034

Be trans.

15.3

132.9

no

5,9,13,17

NuSTAR

Be trans.

4.45

29.8

no

43

NuSTAR

Be trans.

910

−

no

21

NuSTAR

SyB

220

81?,380?

no

48

NuSTAR

GRO J2058+42

Be trans.

195

110

no

10,20,30

NuSTAR

a Second

harmonic. The fundamental one at ∼28 keV was known before

Reference Kong et al. (2022) Yang et al. (2023) Molkov et al. (2021) Malacaria et al. (2022b) Salganik et al. (2022) Tsygankov et al. (2021) and Malacaria et al. (2021) Molkov et al. (2019)

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Fig. 11 Energy spectra of two XRPs: V 0332+53 (red squares) with three harmonics of the cyclotron absorption line and LMC X-4 (blue circles) without cyclotron features in the spectrum. (From Walter et al. 2015)

some sources conserve the classical spectral shape down to very low mass accretion rates (see Fig. 14). At the same time, if an XRP demonstrates a two-component spectrum, it can be misinterpreted as a classical pulsar spectrum with CRSF. This can be a reason why some sources with known CRSF do not show higher harmonics of the line. This effect can potentially significantly reduce the number of XRPs with known cyclotron features. Cyclotron scattering features appear in spectra of XRPs due to the resonant Compton scattering in a strong magnetic field (Herold 1979; Daugherty and Harding 1986) in a line forming region, which is located in close proximity to the NS surface. Cyclotron lines were predicted in the 1970s (Gnedin and Sunyaev 1974) and discovered shortly after that Truemper et al. (1978). The fundamental cyclotron line (corresponding to the electron transition between the first excited and the ground Landau levels) appears at Ecyc

ℏeB ≈ 11.6 ≃ me c



B 1012 G



keV.

(9)

Because of a simple relation between the cyclotron energy and magnetic field strength, the detection of the cyclotron scattering feature in the source spectrum can be used as a direct probe of the NS magnetic field strength. Since the discovery of the cyclotron lines in XRPs (Truemper et al. 1978), it has been found that the

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Fig. 12 Top left: Positive correlation of cyclotron line centroid energy with accretion luminosity in XRP GX 304−1. The plot reproduces results reported in Rothschild et al. (2017). Top right: Negative correlation of the cyclotron energy with the luminosity in V 0332+53. The plot reproduces results reported in Doroshenko et al. (2017). Note that XRPs V 0332+53 and A 0535+26 show both positive and negative correlations, which can be considered as an evidence of the emitting region geometry dependence on the mass accretion rate, i.e., transition through the critical luminosity. Bottom: Cyclotron energy variations with the accretion luminosity observed in a set of variable XRPs. Blue circles and diamonds represent the data for the subcritical XRPs (i.e., demonstrating the positive correlation), and black circles and diamonds show pulsars with supercritical behavior (i.e., the negative correlation). For Vela X-1, the energy of the first harmonic divided by two is used. We used the data points used in Mushtukov et al. (2015b) for 4U 0115+63, Vela X-1, Her X1, the data reported for GX 304−1 in Rothschild et al. (2017), for V 0332+53 in Doroshenko et al. (2017), and for XRP A 0535+26 in Kong et al. (2021). Red solid line represents predictions for the critical luminosity calculated according to Mushtukov et al. (2015b)

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Fig. 13 Variations of the X-ray energy spectrum of A 0535+262 with accretion luminosity (left) and spectra of three XRPs at low mass accretion rates (right): GX 304−1 (gray points), A 0535+262 (blue and red points), and X Persei (green points) (Tsygankov et al. 2019a, b; Doroshenko et al. 2012). It appears that the broadband energy spectrum of some XRPs experiences dramatic changes at low mass accretion rates, which indicates changes in the physical structure of the emitting regions at the NS surface. Note, however, that such spectral changes are not a general feature of XRPs, and several sources do not show dramatic spectral changes at low mass accretion rates (see, for example, Fig. 14) Fig. 14 Unfolded energy spectra of transient XRP MAXI J0903−531 at different states with luminosity varying by a factor of ∼30. Remarkably, the energy spectrum conserves its shape over the wide range of accretion luminosity. (From Tsygankov et al. 2022b)

centroid energy of the cyclotron features could vary with the accretion luminosity, pulsation phase, and on long (years) timescales. In particular, the long-timescale reduction and evolution of the line centroid energy were found in Her X-1 (Staubert et al. 2017; Xiao et al. 2019). The variations of cyclotron line energy with accretion luminosity have been detected in a number of XRPs including V 0332+53 (Tsygankov et al. 2006, 2010), Her X-1 (Staubert et al. 2007, 2014), A 0535+26 (Caballero et al. 2007), Vela X-1 (Fürst et al. 2014; Wang 2014), GX 304−1 (Klochkov et al. 2012; Rothschild et al. 2017), Cep X-4 (Vybornov et al. 2017), 4U 0115+63 (Mihara et al. 2004; Tsygankov et al. 2007), GRO J1008−57 (Chen et al. 2021), and 2S 1553-542 (Malacaria et al. 2022a). Moreover, sources with relatively low mass accretion rates show a positive correlation between the line centroid energy and luminosity, while sources with relatively high mass accretion rates show a negative correlation (see Fig. 12). In two

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sources – V0332+53 (Doroshenko et al. 2017) and A 0535+26 (Kong et al. 2021) – both correlations were observed with the critical luminosity dividing positive and negative dependencies robustly measured. In the same two sources, it was also shown that the relation between the line centroid energy and accretion luminosity is not the same during the raising and fading parts of the outburst, i.e., the same source can have different line centroid energies at the same apparent luminosity (Cusumano et al. 2016; Kong et al. 2021). Cyclotron lines were shown to be variable with the pulse phase in several XRPs (Lutovinov et al. 2015, 2017). Recently, it has also been found that the cyclotron line can be pulse phase-transient and appear only in a narrow range of the pulse phases (Molkov et al. 2019). The variability of the cyclotron line energy in the spectra of XRPs is considered to be related to the geometry of accretion flow in close proximity to the NS surface. The geometry of the emitting region, in turn, is related to the mass accretion rate and magnetic field strength and structure (Basko and Sunyaev 1976; Mushtukov et al. 2015a). In addition to the main continuum components discussed above, some XRPs demonstrate the appearance of the soft emission component (aka soft excess) and fluorescent iron line in their spectra. The former is often modelled as a blackbody with a temperature of about 0.1 keV. It was shown by Hickox et al. (2004) that reprocessing of hard X-rays from the NS by the inner region of the accretion disc is the most probable process that can explain the soft excess in the brightest pulsars (with L > 1038 erg s−1 ). In less bright XRPs, the soft excess may be explained by diffuse gas or thermal emission from the NS surface. The fluorescent Kα iron line is another emission component frequently detected in the XRPs spectra and can be utilized to study the spatial distribution and ionization state of the cold matter around the X-ray sources (see, e.g., Basko et al. 1974; Inoue 1985; Gilfanov 2010; Aftab et al. 2019). In accreting XRPs, the fluorescent emission may be produced at any point from the surface of the massive donor star itself or stellar wind/accretion disc, down to the Alfvén surface and accretion stream/column (see, e.g., Inoue 1985). Some XRPs exhibit the variability of the equivalent width of the iron line with the rotational phase of the neutron star. For instance, the pulsating iron line was detected in LMC X-4 (Shtykovsky et al. 2017), Cen X-3 (Day et al. 1993), GX 301−2 (Liu et al. 2018; Zheng et al. 2020), Her X-1 (Choi et al. 1994), and 4U 1538−522 (Hemphill et al. 2014). Most recently, the variability of iron line equivalent width and iron K-edge at ∼7.1 keV with NS spin and orbital period were discovered in the transient XRP V 0332+53 (Tsygankov and Lutovinov 2010; Bykov et al. 2021). X-ray energy spectra of pulsating ULXs are softer than the spectra of normal XRPs. They do not show a significant difference with the spectra of ULXs, where pulsations were not detected (Walton et al. 2018b and Fabrika et al. 2021 for a review). Recently, the discovery of a cyclotron scattering feature at 4.5 keV in the spectrum of ULX-8 in galaxy M51 (Brightman et al. 2018) (note that pulsations were not detected in this particular ULX so far) and potential cyclotron scattering feature around 13 keV in pulsating ULX-1 in the galaxy NGC300 (Walton et al. 2018a) were reported.

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Due to the complexity of the problem of the emission formation in XRPs, no selfconsistent physical model able to describe the observed spectra from these objects in a broad range of mass accretion rates has been proposed yet. Therefore, in the vast majority of the observational studies, the easily parameterized phenomenological models are used in order to characterize spectral shape and to obtain some physical parameters in the emission regions of an NS. The list of the most commonly applied models available in the spectral fitting package XSPEC (Arnaud 1996) is presented in Table 3. A detailed description of these models can be found in the XSPEC manual (https://heasarc.gsfc.nasa.gov/xanadu/xspec/manual/Models. html). It is worth mentioning, however, that physical interpretation of the best-fit parameters obtained from such phenomenological models should be taken with great caution. A typical example of such over-interpretation is a discussion of the emission region properties obtained from the physical blackbody component, added to compensate residuals in the fit with absolutely nonphysical power law component.

Polarization Properties of XRPs Polarization can be considered as the most direct way to probe geometrical configuration of highly magnetized NSs: the inclination of their rotation axis, the Table 3 List of the phenomenological models utilized for the approximation of different components of emission from XRPs Model Power law with high-energy exponential cutoff A high energy cutoff

XSPEC

notation

A blackbody spectrum

BBODYRAD

Cyclotron absorption line

CYCLABS

Gaussian absorption line

GABS

Gaussian line profile

GAU

A photoelectric absorption

TBABS , PHABS

CUTOFFPL HIGHECUT

Description Additive model for the continuum emission from XRPs Multiplicative model for the continuum emission. It is used in combination with a power law component Additive blackbody component with normalization proportional to the surface area. It is used to account for the soft excess Multiplicative model for the cyclotron absorption line component Another version of a multiplicative model for the cyclotron absorption line component Additive model component in the form of gaussian line profile. It is used, e.g., to approximate iron fluorescent line emission Multiplicative model used to account for the photoelectric absorption

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angle between the rotation axis and magnetic field axis, possible asymmetries of dipole magnetic field configuration, the presence of a non-dipole component in the magnetic field structure, etc. Until recently, the emission of XRPs was expected to be strongly polarized (up to 80%) with specific behavior of the polarization degree over the pulse phase expected for different accretion geometries (see, e.g., Meszaros et al. 1988; Caiazzo and Heyl 2021). The reason for that is a strong dependence of cross section of processes of interaction between radiation and matter (Compton scattering, free– free magnetic absorption/emission and cyclotron scattering/absorption, in the first place) on photon energy and momentum direction in respect to magnetic field (see Harding and Lai (2006) for a review). Unfortunately, sensitive enough polarimeters able to operate in the X-ray band were not available for astronomers until recently. This situation has changed with the launch of the Imaging X-ray Polarimeter Explorer (IXPE, Weisskopf et al. 2022) on 2021 December 9. Already, the first observations of XRPs performed with this instrument led to the completely unexpected results. Namely, it was found that even bright XRPs (with luminosities exceeding 1037 erg s−1 ) show polarization degree (PD) well below 20% even in the phase-resolved data (Fig. 15 and Doroshenko et al. 2022; Marshall et al. 2022; Tsygankov et al. 2022a). To some extent, this

Fig. 15 Top: The dependence of the normalized flux of Cen X-3 in the 2–8 keV energy band on the pulse phase. Middle: The dependence of the polarization degree on phase from the spectro-polarimetric analysis. Bottom: The dependence of the polarization angle on the pulse phase. The orange line corresponds to the best-fit rotating vector model (RVM). (Adopted from Tsygankov et al. 2022a)

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result can be explained by the structure of the atmosphere of an NS, where the upper layers are expected to the hotter than the underling ones due to the accretion process. Nevertheless, the problem about the reasons for the low PD remains open and awaits a solution. Consideration of low polarization degree requires analyses of additional to the intrinsic polarization from the hot spot scenarios and mechanisms influencing X-ray polarization. In particular, polarization on the level of percents can be due to (i) X-ray reflection from the atmosphere of an NS, (ii) reflection/reprocessing of photons by the accretion flow covering magnetosphere of an NS, (iii) X-ray reflection from accretion disc in a system, (iv) scattering by the stellar wind, and (v) reflection of X-ray by the companion star (see the discussion and the references in Tsygankov et al. 2022a). Parameters of NS rotation in XRPs can be obtained from the variations of the polarization angle during the pulse period on the base of the rotating vector model (RVM, see, e.g., Radhakrishnan and Cooke 1969; Poutanen 2020), which is a standard method in determination of NS rotation geometry in radio astronomy for years and applicable for decoding the data on X-ray polarization. RVM, however, assumes the dipole configuration of NS magnetic field in XRP, which is not necessarily a case, and the possibility on non-dipole field structure was already discussed in the literature (Israel et al. 2017; Tsygankov et al. 2017a; Mönkkönen et al. 2022). Nonetheless, applying RVM to the data on a few XRPs obtained by IXPE, it was possible to get the position angles of NS spin axis, NS inclinations, and a magnetic obliquity (the angle between the spin and magnetic field axis, see details in Doroshenko et al. 2022 and Tsygankov et al. 2022a).

Optical Companions in XRPs Observational appearances and properties of XRPs, like orbital variability and parameters of a binary system, its age, NS magnetic field strength, and the mechanism of the mass transfer, are related to the type of a companion star and orbital separation in a system. Schematic view on geometry (including companion star size, orbital separation, and eccentricity) of some XRPs of different types is represented in Fig. 16. Accreting highly magnetized NSs are hosted both in HMXBs, where companion stars are young and have masses 8 M⊙ (e.g., V 0332+53, 4U 0115+63, Vela X-1), and in low-mass X-ray binaries (LMXBs), where the companions are older and have masses 2 M⊙ (e.g., GRO J1744−28, Her X-1, GX 1+4). In the HMXBs, it is possible to distinguish two sub-classes of companions: massive early type stars (Cen X-3, Vela X-1, etc.) and Be-stars (BeXRBs, e.g., V 0332+53, A0535+26, GRO J1008−57, etc.). In contrast to white dwarfs or black holes binaries, the contribution of the accretion disc to the total optical emission of a HMXB is negligibly small. In the non-Be HMXBs, the companions are typically a massive giant with mass 20 M⊙ and orbital periods Porb ∼ 1.5 − 10 days. Such companions are near to filling their Roche lobe, and the mass loss occurs either via atmospheric Roche lobe overflow or via the stellar wind. These systems

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Fig. 16 The schematic view of the geometry of some XRPs, including LMXBs (Her X-1 and GX 1+4), wind-fed sources (Vela X-1, Cen X-3 and GX 301−2), BeXRBs (V 0332+53, 4U 0115+63 and Swift J0243.6+6124), and ULX pulsars (M82 X-2 and NGC 7793 P13). The black section illustrates the linear scale corresponding to 100 light seconds. The geometry of XRPs is reproduced from the orbital parameters reported by Fermi/GBM Accreting Pulsars Program (http://gammaray.nsstc.nasa. gov/gbm/science/pulsars/) and a review (Walter et al. 2015). Note that due to the unknown orbital inclination of the binary systems, the represented sizes of the orbits can be underestimated

show eclipses, and the orbits are generally circular. BeXRBs host a Be star of mass ∼10–20 M⊙ lying deep inside its Roche lobe and demonstrating emission lines in its spectrum, originating from the circumstellar disc arising as a result of a rapid rotation of the star. Orbits in Be systems have long periods (Porb  15 days) and large eccentricity, resulting in strong flux variability in BeXRBs. Several BeXRBs belong to the small class of persistent sources and are characterized by circular orbits and relatively low luminosity (e.g., X Persei, RX J0440.9+4431). The detailed review of BeXRBs properties can be found in Reig (2011). There are few HMXB XRPs associated with supernova remnants (Heinz et al. 2013; Maitra et al. 2019), which indicate extreme youth (few × 104 yrs) of NSs in these particular binaries. XRPs in the LMXBs are very rare, which is related to the typical ages of LMXBs (109 years) and the fact that strong magnetic field tends to decay with time due to Ohmic processes, Hall evolution, and accretion onto the NS surface. There are two types of LMXBs hosting XRPs: (i) Type I LMXBs (age 109 years), where companions are represented by moderate-age main-sequence star or an evolved companion and orbital periods Porb ≃ 0.2–10 days (example: Her X-1) and (ii) Type II LMXBs are represented by older systems (age 5 × 109 years) with companions represented by low-luminous main-sequence or dwarf star and orbital periods of the order of a few hours (e.g., 4U 1626−67).

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Optical companions in pulsating ULXs are poorly studied because ULXs, in general, are extragalactic sources, and their multiwavelength counterparts are often faint. It was reported about blue supergiant as a donor star pulsating ULX NGC 7793 P13 (Motch et al. 2011) and about red supergiant in NGC 300 X-1 (Heida et al. 2019). In other pulsating ULXs, companions are unknown. However, it remains possible to estimate companion mass on the base of measured orbital periods in systems.

Physics and Geometry of Accretion in XRPs XRPs are powered by the accretion of matter ejected from the companion star and accelerated by the gravitational field of an NS. The velocity of accreting material in the vicinity of the NS surface is close to the free-fall velocity vff and can be estimated as   RSh m ≃ 0.54 c , (10) v ≈ vff ≈ c R R6 where c is a speed of light, RSh = 2GM/c2 ≃ 2.95×105 m cm is the Schwarzschild radius, R is the radius of an NS, and m ≡ M/M⊙ is the NS mass in units of solar masses. The kinetic energy of matter accreting onto the NS surface with free-fall velocity is comparable to the rest mass energy Ekin ≈ macc c

2



1



 − 1 ∼ 0.2 macc c2 . 1 − (vff /c)2

(11)

As soon as matter reaches the surface of an NS, its kinetic energy is released and emitted mostly in the X-ray energy band. The total luminosity is related to the mass accretion rate as   m M˙ GM M˙ Ltot = erg s−1 . (12) ≈ 1.33 × 1037 R 1017 g s−1 R6 If the mass accretion rate per unit area of the NS surface is m ˙ ≡

M˙  3×104 g s−1 cm−2 , S

(13)

the temperature and pressure of matter funneled by a strong magnetic field to the relatively small polar areas of the NS are sufficient for stable thermonuclear burning, precluding the appearance of thermonuclear bursts in XRPs (Bildsten and Brown 1997). But still, the energy release due to thermonuclear burning is negligible compared to the one from the conversion of kinetic energy: nuclear fusion yields only

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Enuc ≈ 0.007 macc c2 ,

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(14)

which is ∼20 times smaller than the energy release due to the accretion onto an NS (11). The phenomenon of XRP requires directional motion of accreting material toward small regions onto the NS surface. The key factor defining accretion flow geometry in XRPs is the strong magnetic field of an NS. The accreting material in XRPs is represented by highly ionized plasma, which becomes subject to the Lorentz force in the magnetic field of an NS. At large distances from the compact object, the accretion flow is unaffected by the NS magnetic field, and one can use well-known solutions describing disc or spherical accretion processes. However, in the vicinity of an NS, the magnetic field becomes strong enough to shape entirely the geometry of the flow directing it toward NS magnetic poles. Thus, we already have the basic physical picture of XRP powered by the accretion of matter onto strongly magnetized NS. Now, we will go into more detail and closely consider the processes developing on different spatial scales. We will start with large scales, comparable to the size of the entire binary system and see how the material can be captured from the companion star. Then, we will discuss the geometry of accretion flow forming within the Roche lobe of an NS, the region where the gravity of the compact object dominates. We will figure out how and where the strong magnetic field of an NS becomes important and what kind of observational phenomenon arises because of that. Finally, we will see what happens at the polar regions of an NS, where material lands and loses its kinetic energy.

Mass Transfer in the Binary System The geometry of accretion inside the Roche lobe of an NS is determined by the characteristic distance at which matter becomes gravitationally captured by the compact object and by the mean specific angular momentum carried by the matter at this distance. Thus, the geometry is largely determined by the way how the companion star losses its mass. We would mention three basic mass loss mechanisms typical to XRPs: (i) Roche lobe overflow (e.g., Her X-1, GRO J1744-28) (ii) Capture of matter from the decretion disc in Be-system (e.g., V 0332+53, 4U 0115+63) (iii) Mass loss due to stellar wind (e.g., Vela X-1, Cen X-3) Both geometrical size of the companion star and orbital separation in a binary system evolve due to mass exchange and physical processes in stars (Rappaport et al. 1982). Roche lobe overflow starts when the companion star during the evolution of a binary becomes large enough and starts to lose its mass through the inner Lagrangian point. The rate of mass transfer through the inner Lagrangian point is determined by the stellar evolution of the companion and variations of the distance

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between companions in a system due to the mass exchange and energy losses due to gravitational waves. The specific angular momentum of the matter captured by the NS can be estimated as l0 ∼ η0 a 2 Ωorb ,

(15)

where a is orbital separation, Ωorb is the angular velocity in a system, and η0 is a dimensionless parameter of the order of unity. The specific angular momentum given by (15) is much larger than that in the Keplerian rotation near the NSs. As a result, the Roche lobe overflow in a system results in the formation of an accretion disc around the compact object. The capture of matter from the decretion disc in BeXRBs is a much more complicated mechanism, whose analysis requires detailed numerical simulations. BeXRBs contain a Be star in a relatively wide orbit (typical orbital periods are tens or hundreds of days) of significant eccentricity (e  0.1) with compact object (often, it is an NS, see, e.g., Reig (2011), but BHs are also represented in BeXRBs, see, e.g., Munar-Adrover et al. 2014). The orbital angular momentum of BeXRB is typically misaligned to the spin of the Be star, which is likely a result of kick experienced during the supernova explosion (Martin et al. 2009). The capture of material from the decretion disc results in formation of accretion disc of complicated dynamics around a compact objects (Martin et al. 2014). The wind is the major source of accretion in a binary system if the companion star does not fill its Roche lobe. The accretion fed by the stellar wind is particularly relevant for systems containing an early type (O or B) star or red giant and a compact object in a close orbit. The mass loss rate in early type stars can be as high as 10−6 − 10−5 M⊙ yr−1 ∼ 6 × (1019 − 1020 ) g s−1 and the velocity of the wind is highly supersonic and typically estimated as vw ∼ 108 cm s−1 . The mass accretion rate from the wind is determined by the mass losses from the companion star, the velocity of the stellar wind, and the velocity of an NS in respect to the companion. Equating the gravitational energy of wind material to its kinetic energy, one can estimate the typical radius of gravitational capture or socalled accretion radius: Racc =

2GM −2 ≈ 2.6 × 1010 mvrel,8 cm, 2 vrel

(16)

where vrel is the relative velocity of an NS in respect to the wind. The capture of the material from supersonic stellar wind results in the formation of a bow shock with a cone-shaped cavity around an NS (see Fig. 17, Bisnovatyi-Kogan et al. 1979; Wilkin 1996). The relative velocity of a stellar wind vrel in a binary system is determined by the orbital velocity of an NS vorb and the velocity of a stellar wind vw . In the case of spherically symmetric mass loss from the companion and vw ≫ vorb , the companion mass loss is M˙ c = 4π r 2 ρvw

(17)

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Fig. 17 XRP accreting from the stellar wind. The wind is captured at the accretion radius, and a bow shock with a cone-shaped cavity forms around an NS in the case of supersonic wind flow

and the mass accretion rate onto a compact object is 2 M˙ 0 ≈ π Racc ρvw ,

(18)

where r is the orbital separation between companions in a binary and ρ is a mass density of a wind at the orbit of an NS. Combining (16), (17), and (18), we get an estimation of the mass accretion rate from the stellar wind:   m2 M˙ c Racc 2 ≈ 1.7 × 10−4 M˙ c 4 2 M˙ 0 ≈ 4 r vw,8 r12   m M˙ c 16 g s−1 . ≈ 10 −6 −1 4 2 10 M⊙ yr vw,8 r12

(19)

In the case of vw ∼ vorb , one has to account for the influence of orbital motion on the relative velocity of the wind and the rough estimation given by (19) turns into M˙ 0 = M˙ c q 2 (1 + q)2

ξ tan4 β , π(1 + tan2 β)3/2

(20)

where q = M/Mc is a mass ratio in a binary, parameter ξ ∼ 1 and tan β = vorb /vw (see Fig. 17, and Davidson and Ostriker 1973; Lipunov 1992 for details).

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In very close binary systems, one has to account for the motion of a companion star around the mass center, which leads to the wind collimation in the orbital plane. Under this condition and in the case of relatively slow wind, the mass accretion rate onto the compact object from the stellar wind can be higher and even comparable to the mass accretion rates typical for ULX pulsars (El Mellah et al. 2019).

Accretion Flow Interacting with the NS Magnetosphere Magnetospheric Boundary Because the accreting material in XRPs is highly ionized and affected by the Lorentz force, the strong magnetic field of an NS shapes the geometry of the accretion flow in XPRs to a great extent. In XRPs, the magnetic field of an NS is strong enough to disrupt the accretion flow at the magnetospheric boundary that is located at a large distance (∼108 cm) from the central object. The distance where the accretion flow is disrupted by the field is called the magnetospheric radius Rm . Accreting material from the magnetospheric boundary is funneled toward the polar cups of an NS, stopped at the magnetospheric boundary or ejected to infinity. The physics of the interaction between the accretion flow and NS magnetic field is exceedingly complex (see Lai 2014 for a review). Still, some useful estimations can be obtained even from a simplified physical picture. The magnetic field pressure is given by Pmag = B 2 /(8π ) and increases rapidly toward the NS. In the case of B-field dominated by the dipole component (see Eq. 4), Pmag =

1 µ2d , 8π r 6

(21)

where µd = B0 R 3 /2 is a dipole magnetic moment, B0 is magnetic field strength at the NS magnetic poles, and r is a distance from an NS center. Equating the magnetic field pressure and the ram pressure of accreting material, which is Pram = ρv 2 ∼

1 (2GM)1/2 M˙ 4π r 5/2

(22)

in the case of spherically symmetric accretion with free-fall velocity, we estimate the radius from the NS where the magnetic field disrupts the accretion flow 4/7 −2/7 RA = 2.7 × 108 µ30 M˙ 17 m−1/7 cm

(23)

4/7 −2/7 12/7 = 1.8 × 108 B12 M˙ 17 m−1/7 R6 cm,

the so-called Alfvén radius. A similar estimate assuming the quadrupole magnetic field configuration (see Eq. 5) is given by (q) 4/11 −2/11 16/11 RA = 3.44 × 107 B12 M˙ 17 m1/11 R6 cm.

(24)

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The actual magnetospheric radius is of the order of the Alfvén radius but depends on the exact accretion flow geometry interacting with the NS magnetic field. It is useful to introduce the coefficient of proportionality Λ between the radius of the magnetosphere and Alfvén radius: Rm = ΛRA .

(25)

In the particular case of disc accretion, the inner disc radius is typically assumed to be by a factor of 2 smaller than the Alfvén radius (Λ = 0.5), while in the case of spherical accretion Λ ≈ 1 (Ghosh and Lamb 1978, 1979a). However, this picture is oversimplified, and one has to keep in mind that the inner disc radius can be affected by the disc inclination with respect to the magnetic dipole of an NS, magnetic field structure (Lipunov 1978; Scharlemann 1978; Aly 1980), and by physical conditions in the accretion flow (Psaltis and Chakrabarty 1999; Chashkina et al. 2017), which can be geometrically thin or thick, gas or radiation pressure dominated, advective or non-advective. In wind-fed XRPs, accretion onto the NS is possible under the condition Rm < Racc ,

(26)

1/2 −7/2 B  6 × 1015 M˙ 17 m2 R6−3 vrel,8 G

(27)

i.e., in the case of

at the surface of an NS, or 2 7 M˙ > 2.8 × 109 B12 m−4 R66 vrel,8 g s−1 .

(28)

Otherwise, the magnetic barrier sets in, and the flow from the donor star cannot be captured properly and is deflected away. For practical application, it is useful to have rough estimates of some physical conditions at Rm . Particularly, in the case of magnetic field dominated by the dipole component, the field strength at the magnetospheric radius is −5/7 6/7 B(Rm ) ∼ 105 Λ−3 µd,30 M˙ 17 m3/7 G,

(29)

and the Keplerian angular velocity is ΩK (Rm ) =



GM 3 Rm

1/2

−6/7 3/7 ≈ 2.6 Λ−3/2 µd,30 M˙ 17 m5/7 rad s−1 .

(30)

Note that the stronger the magnetic field is at the NS surface, the weaker it is at the magnetospheric boundary. Because accreting material at Rm is expected to be hot and ionized, the penetration of the flow into the NS magnetosphere is problematic but possible

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due to the development of various instabilities, including magnetic Rayleigh– Taylor (Arons and Lea 1976; Kulkarni and Romanova 2008), Kelvin–Helmholtz instabilities (Burnard et al. 1983), and reconnection. Extremely hot plasma is known to be stable relative to the Rayleigh–Taylor instability, which is the main mechanism of plasma penetration into the magnetosphere of an NS (Elsner and Lamb 1977). Thus, for the effective matter penetration into the magnetosphere, the temperature of the accretion flow has to be below a certain critical value. This condition is typically satisfied in disc-fed XRPs but can be violated in wind-fed sources. If so, the accretion flow onto the magnetized NS is below the value estimated by (19) and is determined by the ability of matter to cool below the critical temperature. If the luminosity of wind-fed XRPs is 4 × 1036 erg s−1 , the material captured at Racc cannot cool rapidly enough, which results in the formation of an extended quasistatic shell (Shakura et al. 2012) around the NS magnetosphere. The mass accretion rate through the shell is driven by the cooling processes and the ability of plasma to enter the magnetosphere.

Influence of the Magnetospheric Rotation Another important linear scale for the accreting compact object is the corotation (or centrifugal) radius, where the gravity is in balance with the centrifugal force acting on matter which is in corotation with the NS. In other words, this is the radius where the magnetic field lines rotate with the same (Keplerian) velocity of matter in the accretion disc: Rcor =



GMP 2 4π 2

1/3

≃ 1.5 × 108 m1/3 P 2/3 cm.

(31)

As follows from Eqs. (23) and (24), the Alfvén radius, i.e., inner radius of accretion flow unaffected by the field, depends on the mass accretion rate: the larger the mass accretion rate, the smaller the inner radius. If the accretion flow penetrates into the corotation radius (Rm < Rcor ), the matter is not dynamically inhibited from falling onto the NS. In the opposite case, when Rm > Rcor , the centrifugal barrier will prevent direct accretion onto the central object, which results in the appearance of the propeller effect (Illarionov and Sunyaev 1975; Ustyugova et al. 2006). Equating the magnetospheric and corotation radii, one can estimate the limiting mass accretion rate, which separates regimes of accretion and propeller state: M˙ prop ≈ 7.4 × 1017 Λ7/2 µ2d,30 P −7/3 m−5/3 g s−1

(32)

2 = 2 × 1017 Λ7/2 B12 P −7/3 m−5/3 R66 g s−1 .

The corresponding accretion luminosity is Lprop = Llim (R) =

GM M˙ prop 2 ≈ 2.7×1037 Λ7/2 B12 P −7/3 m−2/3 R65 erg s−1 . (33) R

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As soon as XRP switches into the propeller state, accretion flow stops at Rm = Rcor and does not reach the NS surface. Because Rm ≫ R in XRPs, the accretion efficiency in propeller regime is much lower. As a result, the decrease of mass accretion rate below M˙ prop leads to the drop of luminosity to the value expected for so-called magnetospheric accretion case, when kinetic energy of matter is released at the magnetospheric radius (Corbet 1996; Raguzova and Lipunov 1998): Llim (Rcor ) =

GM M˙ prop R = Llim (R) . Rcor Rcor

(34)

In the absence of other sources of emission (such as, for example, NS surface heated up by accretion), the dramatic drop of accretion luminosity (about 102 for a typical XRP) should be accompanied by significant spectral changes. The effective temperature of accretion disc at radial coordinate r can be estimated as 1/4 −3/4 Teff ≃ 3.5 × 10−2 M˙ 17 m1/4 r8 keV,

(35)

which gives a rough estimation of the effective temperature at the magnetospheric boundary −3/7 13/28 Teff (Rm ) ∼ 0.02 Λ−3/4 µd,30 M˙ 17 m5/14 keV.

(36)

Thus, the accretion disc at the magnetospheric radius typical for XRPs hardly produces valuable amount of photons in the X-ray energy band (Fig. 18). However, leakage of matter through the centrifugal barrier or/and cooling of NS polar cups can provide noticeable X-ray emission (Tsygankov et al. 2016; Wijnands and Degenaar

Fig. 18 Light curves obtained at the end of the outbursts observed from XRPs 4U 0115+63 (left) and V 0332+53 (right) and transition to the propeller state at the luminosity marked by red dashed lines. Both sources were detected in the quiescent state and demonstrated brightening near the periastron passages (see the vertical blue dashed lines). (From Tsygankov et al. 2016)

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Fig. 19 Dramatic spectral changes observed during transition into the propeller state in XRPs 4U 0115+63 (top) and V 0332+53 (bottom). In both cases, the spectra in the propeller state (blue points) can be well fitted with the absorbed blackbody model with the temperature ∼0.5 keV and radius of the emitting area ∼0.6−0.8 km. The observed soft blackbody-like spectra in the propeller state can be a sign of cooling of the NS polar regions after their heating during the outburst. (From Tsygankov et al. 2016)

2016). This kind of emission with soft X-ray energy spectra was observed in two XRPs in the propeller state (see Fig. 19, Tsygankov et al. 2016, and Wijnands and Degenaar 2016). The timescale of transition from the accretion to the propeller regime strongly depends on the structure of the disc-magnetosphere interaction region. Even in the case of pure disc accretion, when the sharpest onset of centrifugal barrier is expected, the material can only enter the magnetosphere due to instabilities arising in their interaction. These instabilities may drive the dramatic variability of X-ray flux at different timescales and make the transition essentially non-instant. Unfortunately, the difficulty of predicting the exact time of the transition did not allow us to observe such events “in real time” so far. The constraints on the transition timescale in the available data are limited mainly by the observations cadence. For instance, in the case of the pulsating ULX NGC 5907, such a transition

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happened faster than in 6 days (Israel et al. 2017), in the transient XRPs 4U 0115+63 and V 0332+53 faster than ∼1.5 day (Tsygankov et al. 2016). However, the most detailed observation of the transition between the quiescent and accretion states was obtained fortuitously for 4U 0115+63 with the BeppoSAX satellite (Campana et al. 2001). Namely, during the observation close to periastron, a huge luminosity increase by a factor of ∼250 in less than 15 h was revealed. This was interpreted as the opening of the centrifugal barrier during the onset of accretion state. Accreting plasma in the state of magnetospheric accretion is accumulated at the magnetospheric boundary and forms a dead disc (Siuniaev and Shakura 1977). If the magnetospheric radius remains to be close to the corotation radius, the accumulation of material should lead to the events of episodic accretion onto the NS surface (see Fig. 20, D’Angelo and Spruit 2010). The episodes of accretion are expected to be quasi-periodic with periods determined by the viscous timescale in the disc.

Spin-Ups and Spin-Downs of NS in XRPs The accretion process and interaction of accretion disc/wind with the magnetosphere of an NS results in angular momentum exchange and corresponding variations in the NS spin period (Parfrey et al. 2016) and direction of its rotation axis (Biryukov and Abolmasov 2021). The rate of change of the NS angular momentum J is determined by the total accretion torque K tot dJ = K tot . dt

16

1.06

12

1.04

8

1.02 4 1

Rm/Rcor

12 10 8 6 4 2

b

1.06 1.04 1.02 1 0

1

2 Time [tv]

3

4

mass accretion rate

1.08

mass accretion rate

a

1.08 Rm/Rcor

(37)

5

Fig. 20 Accumulation of matter in the accretion disc during the propeller state can result in events of episodic accretion onto the NS surface. Variations of the inner disc radius (black dashed lines) and mass accretion rate (in relative units) onto the NS surface (red solid lines) are shown for different average mass accretion rates: (a) M˙ = 4.6 × 1017 g s−1 and (b) M˙ = 7.6 × 1017 g s−1 . (The curves are reproduced from D’Angelo and Spruit 2010)

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Fig. 21 Binary motion corrected spin frequency evolution of three XRPs with different accretion mechanisms: disc accretion for A 0535+26, wind accretion for Vela X-1, and transient disc formation in the wind-fed GX 301−2 (top panels). The corresponding pulsed flux in the 12–50 keV energy band is shown in the bottom panels. From the Fermi/GBM Accreting Pulsars Program (http://gammaray.nsstc.nasa.gov/gbm/science/pulsars/)

In the case of accretion from stellar wind, the sign and magnitude of the torque are rather uncertain because of the stochastic fluctuations of the sign and magnitude of the specific angular momentum of the clumpy matter captured by the NS. It is nicely seen in the variation of NS spin frequency observed in XRP Vela X-1 presented in Fig. 21. In the case of accretion from the disc, the material is expected to move with nearly Keplerian velocity. In general, it is expected that XRPs, accreting at high

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mass accretion rates, spin up due to the interaction between the NS magnetosphere and the accretion flow. Indeed, in this case, the inner disc radius locates within the corotation radius (Rm < Rcor ), and the angular velocity of accretion flow at the inner disc edge exceeds the angular velocity of the NS magnetosphere. On the contrary, in the propeller mode, when the inner disc radius is located outside the corotation radius (Rm > Rcor ), a gradual spin down is expected. This kind of behavior is seen in XRP A 0535+26 (see Fig. 21), where the accretion process occurs through the disc and the outbursts are correlated with spin-up phases, while the off-states are accompanied by a decrease of the NS spin frequency. In some XRPs, like in GX 301−2, the accretion onto the central object may proceed from both the disc and the stellar wind. In this case, the spin frequency behavior inherits traits from both accretion channels. The quantitative approach requires a bit more detailed analysis. Let us consider the case of accretion from the disc. Assuming an alignment between accretion disc axis, NS spin axis, and dipole magnetic axis, it is possible to make estimations of the torques. Furthermore, we will focus on this particular case. The torque applied to the NS has two contributions: the one associated with mass accretion (Pringle and Rees 1972) 2 ˙ m K0 = MR ΩK (Rm )

(38)

and the other related to the disc–star coupling Km . As a result, the total torque is given by (39)

Ktot = K0 + Km .

Magnetic torque Km can be either positive or negative depending on the location of the interaction zone relative to the corotation radius. Several models have been proposed for estimating magnetic torque (Parfrey et al. 2016). These are often expressed in the form (40)

Ktot = n(ωs )K0 , where n is a dimensionless function and ωs ≡



Ωs ΩK,m



=



Rm Rcor

3/2

(41)

is the “fastness” parameter. There are two simple analytical models proposed for the case of slowly rotating NSs: • In Ghosh and Lamb (1979b) was proposed n(GL) (ωs ) ≃ 1.39

1 − ωs [4.03(1 − ωs )0.173 − 0.878] . 1 − ωs

(42)

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• If the magnetic stress communicated by the magnetosphere is limited by its susceptibility to field line opening and reconnection, the torque is given by (Wang 1995) n(W ) (ωs ) ≃

(7/6) − (4/3)ωs + (1/9)ωs2 . 1 − ωs

(43)

Note that these models are only applicable when Rm < Rcor . The corresponding changes of the NS spin period P can be estimated as 2/7 6/7 −1 −3/7 6/7 P˙ ≈ −2 × 10−12 n(ωs )P 2 µ30 L37 I45 m R6 s s−1 .

(44)

The spin period derivative P˙ turns to zero at some specific combination of the inner disc radius and the corotation radius, which means that the pulsar is in equilibrium. The corresponding spin period is called the equilibrium spin period Peq . The equilibrium period is different in different torque models. In Ghosh and Lamb model described by (42), it is reached at ωs = 0.35 and equals 6/7 −3/7

15/7

(GL) = 5.7 Λ3/2 B12 L37 m−2/7 R6 Peq

s.

(45)

In Wang’s model described by (43), equilibrium corresponds to ωs = 0.95 and the equilibrium period is 6/7 −3/7

15/7

(W ) Peq = 2.1 Λ3/2 B12 L37 m−2/7 R6

s.

(46)

The propeller state arising under the condition of Rm > Rcor affects the torque applied to the NS. When the accretion flow gets attached to the stellar field lines, the matter starts to corotate with the NS. If 2π Rm /P exceeds the escape velocity at the magnetospheric radius vesc = (2GM/Rm )1/2 , i.e., if Rm > 21/3 Rcor ,

(47)

the accreting matter may be ejected due to the centrifugal force. Ejection of matter modifies the total torque: 2 Ktot = K0 + Km − M˙ eject Rm Ω,

(48)

where M˙ eject is the mass ejection rate. Misalignment of the NS dipole and its rotation axis (that is required for the pulsations appearance) makes the problem of interaction between NS and accretion flow more complex, resulting in at least two additional effects: (i) the plasma in the magnetosphere can flow to the polar cup more easily and (ii) misaligned stellar dipole can excite non-axisymmetric waves in the disc (Lai and Zhang 2008). Note that the estimations of the inner disc radius are strongly model dependent for the

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Fig. 22 Light curve observed from BeXRB GRO J1008−57. The source shows outbursts every periastron passage. In the end of the outburst, the source does not reach the luminosity level where one can expect transition into the propeller state (red dashed line). Instead of that, at some luminosity, shown with the blue dotted line, the fast fading of the source is stopped and accretion process turns into a stable mode lasting until the next outburst. The stable mode in between the outbursts corresponds to the accretion from the cold recombined disc of low viscosity. (From Tsygankov et al. 2017b)

case of accretion onto inclined magnetic dipoles (Lipunov 1978; Bozzo et al. 2018). Because inclination is usually not known for particular XRPs, estimates of NS magnetic field strength based on measurements of P˙ or spin equilibrium period remain quite uncertain (Figs. 22 and 23).

Different Physical Conditions in Accretion Discs Around XRPs The picture of accretion disc interaction with the NS magnetosphere becomes even more complex if one takes into account physical conditions in the accretion disc (Spruit 2010). We would highlight a few states of accretion disc appearing at different mass accretion rates (see Fig. 24): • At very low mass accretion rates (M˙  1014 g s−1 ), the mass density of accreting material is too low to cause sufficiently intensive cooling of accreting plasma. As a result, accretion flow reaches the virial temperature and turns into a state of geometrically thick advection dominated accretion flow (ADAF) (Narayan and Yi 1995). This condition of accretion flow was not detected in XRPs so far. • Gas pressure-dominated geometrically thin accretion disc composed of cold recombined material or relatively hot ionized gas (aka C-zone). • At sufficiently large mass accretion rates (M˙  few × 1017 g s−1 , see the red zone in Fig. 24), the inner regions of accretion disc become radiation pressure dominated and geometrically thick (aka A-zone, see, e.g., Shakura and Sunyaev 1973). Because of large optical thickness of accretion flow, it can be advective (Lipunova 1999). Energy release in the disc leads to mass losses due to the radiation-driven outflows (Mushtukov et al. 2019a; Chashkina et al. 2019). Gas pressure-dominated accretion discs are most common under the observed conditions in the majority of XRPs (see Fig. 24). Under these conditions, the disc is geometrically thin. Its relative scaleheight Hm at radial coordinate r can be approximated by

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Fig. 23 Collection of some known BeXRBs (shown in black), as well as the accreting millisecond pulsar SAX J1808.4−3658, the intermediate pulsar GRO J1744−28, and the accreting magnetar M82 X-2 (all three shown in blue) on the B−P plane. The dashed line corresponds to the prediction of P ∗ (B) for parameter Λ = 0.5. This line separates sources with different final states of an outburst: the propeller regime (below the line) and stable accretion from the cold disc (above the line). Persistent low-luminous BeXRBs are shown in green



Hm r



C

3/20

1/8

≈ 0.03 α −1/10 M˙ 17 m−3/8 r8 ,

(49)

where α is the dimensionless viscosity parameter of order of 0.1 (Suleimanov et al. 2007). The phase transition of an accreting material between cold recombined state and hot ionized state causes development of thermal instability in the accretion flow. Recombination of matter in the accretion flow leads to a decrease of the opacity, fast local cooling of accretion disc, reduction of its geometrical thickness, and corresponding reduction of viscosity (similarly, ionization of matter in the accretion flow leads to an increase of local viscosity). Additionally, the phase transition between the ionized and recombined states can cause change of the dimensionless viscosity parameter α (see, e.g., Hameury 2020), which is expected to be higher in ionized hot state than in recombined cold by a factor of αhot /αcold ∼ 5 − 10. The development of thermal instability leads to the appearance of cooling and heating waves propagating inside-out or outside-in in the accretion disc. Stable accretion

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19

10

zo n

K gas ra pr m es er su op re ac ity

e

11

0 4K

12

0

0

G)

G)

14

M˙ hot ≃ 1016 αhot m



rout 2.68 g s−1 , 1010 cm

(50)

where rout is the effective outer disc radius, or when the mass accretion rate is so low that the temperature is low enough to keep the accreting material recombined even at the inner radius −0.004 −0.88 M˙ < M˙ cold ≃ 4 × 1015 αcold m



rin 2.65 −1 gs , 108 cm

(51)

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where rin = Rm is the inner disc radius. Note that expressions (50) and (51) imply that accreting material has solar chemical composition and is dominated by hydrogen. A different chemical composition results in different conditions for the critical mass accretion rates. The transition between the ionization states can be significantly affected by accretion disc irradiation by the NS (King and Ritter 1998; Lipunova et al. 2022). The irradiation can keep the inner regions of accretion disc in a hot state and prevent propagation of the cooling wave. To clarify the influence of the irradiation, it is useful to estimate local irradiating flux Qirr = Cirr

L , 4π r 2

(52)

where Cirr

z0 = (1 − A)Ψ (θ ) q, r

q=



 d ln z0 −1 d ln r

(53)

is a dimensionless irradiation parameter (Suleimanov et al. 2007; Lipunova et al. 2022), (1 − A) ≤ 1 is the fraction of absorbed incident flux, z0 is the semithickness of accretion disc, and Ψ (θ ) is the angular distribution of the irradiating flux (for the case of isotropic central source of radiation, Ψ (θ ) = 1). Taking q ≃ 1/8, which is valid for the C-zone of accretion disc (Shakura and Sunyaev 1973), assuming isotropic emission from the central source, and using (1−A) ≃ 0.1 (Suleimanov et al. 1999), one gets Qirr ≈ 5 × 1016 L37 r8−2 erg s−1 cm−2 . Therefore, the irradiation can potentially keep the effective temperature in accretion disc above 1/2 104 K within the radial coordinate r ∼ 2 × 1010 L37 cm. Note, however, that the internal temperature of accretion disc is affected by the illumination insignificantly (in the case of optically thick accretion disc, see, e.g., Suleimanov et al. 1999), and therefore the influence of irradiation on the disc transition between hot and cold states is still questionable. Transitions between different ionization states of an accretion disc are commonly considered to be responsible for bright outbursts in dwarf novae and soft X-ray transients (Lasota 2001). Recently, transitions were proposed to explain variations of the observed mass accretion rate in the end of X-ray outbursts in transient XRPs (Tsygankov et al. 2017b). In this case, the outburst decay in transient XRP should be accompanied by two processes: (i) transition of accretion disc to the cold recombined state, when the cooling front moves outside-in and (ii) simultaneous expansion on the inner disc radius Rm due to reduction of mass accretion rate at the inner edge of the accretion disc (see expressions 23 and 25). At some point, the cooling front reaches the inner disc radius, and depending on the radial coordinate where it happens, one would expect different outcomes of the mass accretion rate decay: if the cooling front meets the inner disc radius outside the corotation radius, the outburst ends up with transition to the propeller state (Illarionov and Sunyaev 1975) (see Fig. 18); in the opposite case, accretion

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disc becomes entirely recombined and stable (Tsygankov et al. 2017b), i.e., further fast drop of the mass accretion rate stops (see Fig. 22). Interestingly, the final state of the source after an outburst is determined by two fundamental parameters of the NS: its magnetic field and spin period. Equating the expressions for luminosities Lcold = GM M˙ cold /R and Lprop (33), one can derive the critical value of the spin period, determining the source behavior after an outburst, as a function of the NS magnetic field: 0.49 −0.17 1.22 P ∗ ≈ 38 Λ6/7 B12 m R6 s.

(54)

If the spin period P < P ∗ , an XRP will end up in the propeller regime. Otherwise, the source will start to accrete steadily from the cold disc (see Fig. 23). Some variations of the luminosity are possible even in the state of accretion from the cold disc, but because of low viscosity and correspondingly long viscose timescales the variations are expected to be slow. It is still not known quite well how cold and largely recombined accretion disc interacts with the NS magnetic field. Larger mass density of a cold disc (due to the low viscosity) and peculiarities of its interaction with the B-field may lead to a dependence on the mass accretion rate different from that given by (23). Radiation pressure-dominated accretion discs are typical for the brightest XRPs 6/11 (L > 3.4 × 1038 Λ21/22 B12 m6/11 erg s−1 ). Accretion disc is expected to be radiation pressure-dominated at radial coordinates (Suleimanov et al. 2007) 16/21

r < Rrad ≈ 2.2 × 108 L39

16/21

m−3/7 R6

cm.

(55)

Geometrical scaleheight of such a disc is independent of radial coordinate: Hd,rad ≈ 107 L39 m−1 R6 cm.

(56)

At sufficiently high mass accretion rates, the radiation pressure gradient in the inner parts of accretion disc becomes high enough to compensate gravitational attraction in the direction perpendicular to the disc plane. Then, the accretion disc generates winds driven by radiation force, spending a fraction εw ∈ [0; 1] of viscously dissipated energy to launch the outflows. As a result, only a fraction of the mass accretion rate from the donor star reaches the boundary of NS magnetosphere and accretes onto the central object. Outflows launched by radiation pressure come into play within the spherization radius Rsp (see Fig. 25), inside of which the radiation force due to the energy release in the disc is no longer balanced by gravity. This radius can be roughly estimated as (Lipunova 1999; Poutanen et al. 2007) 

−2/3 2 cm, − (1.1 − 0.7εw )m ˙0 Rsp ≈ 9 × 105 m ˙ 0 1.34 − 0.4εw + 0.1εw

(57)

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Fig. 25 Schematic structure of accretion flow at extremely high mass accretion rates onto strongly magnetized NS. If the spherization radius Rsp exceeds the magnetospheric radius Rm , accretion disc starts to lose matter via wind. At sufficiently high mass accretion rates, the accretion flow covering magnetosphere becomes optically thick. (From Mushtukov et al. 2019a)

where m ˙ 0 = M˙ 0 /M˙ Edd is the dimensionless mass accretion rate from the donor star in units of Eddington mass accretion rate at the NS surface: LEdd R ≈ 1.9 × 1018 R6 g s−1 . M˙ Edd = GM

(58)

In the case of accreting BHs with an accretion disc extends down to the innermost stable orbit (ISCO), and NS with low magnetic field, the outflow can carry out a significant amount of material from the accretion flow. In the case of XRPs, the inner disc radius is much larger than the radius of the ISCO and the fraction of material carried out by the outflow is dependent on both the mass accretion rate and the magnetic field strength of the NS. The mass accretion rate at a given radial coordinate r can be estimated as r ˙ M(r) = M˙ ISCO + (M˙ 0 − M˙ ISCO ) , Rsp

(59)

where M˙ 0 is the mass accretion rate outside the spherization radius, and M˙ ISCO = M˙ 0

1−A 1 − A (0.4 m ˙ 0 )−1/2

(60)

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is the expected mass accretion rate at ISCO, where A ≈ εw (0.83 − 0.25εw ). Combining (23), (25), and (59), one can get the dependence of the inner disc radius on the mass accretion rate from the companion star Rm (M˙ 0 ) and the mass accretion rate at the inner disc radius (i.e., onto the NS surface) for the case of advective accretion discs. The mass loss from the disc due to the wind requires that accretion flow penetrates deeper into the magnetosphere of an NS (Mushtukov et al. 2019a; Chashkina et al. 2019). Note, however, that at high mass accretion rates, when the inner parts of the disc become geometrically thick, one additional ingredient starts to affect the displacement of the inner disc radius. Because thick accretion disc intercepts a large fraction of X-ray radiation from the central source, the inner disc radius is determined by the balance between ram pressure, magnetic field pressure, and, additionally, radiative force acting on its inner edge (Chashkina et al. 2017). Effectively, it can be considered as dependence of Λ parameter in relation (25) on the mass accretion rate at the inner disc radius. Detailed analyses show that the inner disc radius tends to decrease with the increase of the mass accretion rate till the disc is gas pressure dominated (as it is predicted by equations 23 and 25), and then the inner disc radius is almost independent of the mass accretion rate and starts to decrease with the mass accretion rate again as soon as advection comes into play (see, e.g., Chashkina et al. (2019) and Fig. 26). Strong outflows from accretion discs, expected at high mass accretion rates, can cause beaming of X-ray radiation in the direction orthogonal to the disc plane (King and Lasota 2019). The effectiveness of beaming due to the wind launch is still discussed. At the same time, there is no doubt that the winds are launched at high mass accretion rates and their evidence were already found in observations (Kosec et al. 2018).

Stochastic Fluctuations of the Mass Accretion Rate As we have already seen, the X-ray flux in XRPs shows strong aperiodic fluctuations observed in a wide range of Fourier frequencies (see examples of PDS in Fig. 9). The aperiodic variability is a natural feature of accretion process through the wind, where one would expect variability due to the clumpiness of accretion flow, or through the disc, where the variability is a result of propagating fluctuations of the mass accretion rate (Lyubarskii 1997). Let us focus on the accretion disc case as prevalent among known XRPs. The inward mass transfer in the accretion disc is possible thanks to viscosity and friction between the adjacent rings in the disc, which helps to transfer the angular momentum of accreting material outward (see, e.g., Spruit 2010). The viscosity in the accretion disc is likely caused by the magnetic dynamo that generates a poloidal magnetic field component in a random fashion (Balbus and Hawley 1991; Hawley et al. 1995). The initial fluctuations of the mass accretion rate arise all over the disc and then propagate inwards and outward (Mushtukov et al. 2018a), modulating the fluctuations arising at other radial coordinates. The timescale of the magnetic dynamo is close to the local Keplerian timescale (Tout and Pringle 1992; Stone et al. 1996):

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Rm [108 cm]

0 .5

1 Λ=

Λ=

0.8

0.6

wind

advection

advection > radiation

1

0.4

0.2 1017

gas pressure

1018

radiation pressure

1019

. Min, g/s

1020

1021

Fig. 26 Magnetospheric radius Rm as a function of the mass accretion rate at the inner disc radius for an NS with dipole magnetic moment µ = 1030 G cm3 . Segments of the red solid curve correspond to the different regimes of accretion near the magnetospheric boundary. One can see that Λ ≈ 0.5 in the case of gas pressure-dominated inner parts of the accretion disc. The inner disc radius is weakly dependent on the mass accretion rate in the case of radiation pressure-dominated non-advective regime of accretion. At higher mass accretion rates, when the inner disc parts are under the influence of advection, the dependence of the inner disc radius on the mass accretion rate becomes stronger, but Λ ≈ 1. (The red curve is reproduced from Chashkina et al. 2019)

tdyn ∼ tK =

2π ∝ r 3/2 . ΩK

(61)

Therefore, different timescales are introduced into the accretion flow at different distances from an NS, while the observed variability of X-ray flux reflects the variability of the mass accretion rate at the inner parts of accretion disc (Kotov et al. 2001; Ingram 2016; Mushtukov et al. 2018a). The shortest timescale of the aperiodic variability corresponds to the inner disc radius and is expected to be close to the Keplerian frequency at Rm (30). The detailed models of propagating fluctuations of the mass accretion rate predict broadband PDS with a break at the dynamo frequency corresponding to Rm . Because the inner disc radius depends on the NS magnetic field and mass accretion rate, the displacement of breaks in PDS is variable from one source to another. In transient XRPs, the break frequency depends on the accretion luminosity reflecting the variability of the magnetospheric radius (Fig. 27), as observed in some XRPs (for example, A 0535+26, Figs. 9 left and 10). This schematic picture of the aperiodic variability in XRPs is not the ultimate truth. On top of variability caused by propagating fluctuations of the mass accretion

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Fig. 27 Structure of the disc-magnetosphere interaction as a function of mass accretion rate in XRPs and the corresponding changes in the observed PDS. The PDS shows break at Fourier frequency corresponding to the dynamo frequency at the inner disc radius. The frequency of the magnetic dynamo is expected to be proportional to the local Keplerian frequency. Thus, the increase of the mass accretion rate and corresponding decrease of the inner disc radius result in the break’s shift toward higher frequencies. Measurement of the break frequency in PDS of XRP can be used to estimate geometrical size of the NS magnetosphere

rate, one would expect several other phenomena affecting broadband PDS. Among them are (i) variability of the geometry of the emitting region at the NS surface, (ii) appearance of the photon bubbles at extremely high accretion luminosity (see the next section, Klein et al. 1996a, b), (iii) partial reprocessing of X-ray emission by the accretion flow in between the inner disc radius and NS surface (see Fig. 25 and Mushtukov et al. 2019a for details), and (iv) development of instabilities in radiation pressure dominated part of an accretion disc (Cannizzo 1996).

Geometry and Physics of the Emitting Region at the NS Surface If the source is in accretion mode, plasma penetrates into the NS magnetosphere at Rm and following magnetic field lines reaches NS surface in a small region located close to the magnetic poles of a star. The size of the landing region could be roughly estimated as

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rpol ≈ R



R Rm

1/2

−2/7

≈ 7 × 104 Λ−1/2 B12

1/7 9/14 M˙ 17 m1/14 R6 cm,

(62)

which gives rpol  1 km for typical XRPs parameters. The shape of the landing regions is determined by the geometry of accretion funnel above the NS surface. The accretion funnel is filled and the landing region can be close to the filled circle of area −4/7

2 Sspot = π rpol ≈ 5 × 109 Λ−1 B12 (w)

2/7 9/7 M˙ 17 m1/7 R6 cm2

(63)

in the case of accretion from the stellar wind. In the case of disc accretion, the accretion funnel is hollow, and the landing region can form ring-like structures around the NS magnetic poles. The geometrical thickness of the rings is determined by the inner disc radius and the width of the transition zone in it. Assuming that the transition zone at the magnetospheric boundary has a typical scale similar to the accretion disc scaleheight Hm at the inner disc radius, we can estimate the geometrical thickness of accretion channel in close proximity to the NS surface: d0 ≈ R



R Rm

1/2

Hm Rm

(64)

R 3 Hm . 2 Rm

(65)

and the area of accretion channel base (d)

Sspot = 2π rpol d0 ≈ 2π

This is a reasonable approximation in the case of accretion disc truncated in a Czone (see Fig. 24), where the disc is geometrically thick and gas pressure dominated. Then, using approximate disc scaleheight in a C-zone (49), we can rewrite (64) as −3/14

d0,C ≈ 2.3 × 103 α −1/10 Λ−3/8 B12

9/35 3/4 M˙ 17 m−9/28 R6 cm,

(66)

and (65) as −1/2

(d) Sspot,C ≈ 109 α −1/10 Λ−7/8 B12

2/5 39/28 M˙ 17 m−1/4 R6 cm2 .

(67)

In the case of accretion disc truncated in the radiation pressure-dominated zone (A-zone in Fig. 24), the thickness of the transition region can be smaller than the accretion disc scaleheight, and estimates require additional analyses. Development of instabilities inside an accretion channel can result in a filled funnel even in the case of accretion from the disc. Inclination of the dipole magnetic axis to the disc plane can result in asymmetric accretion funnel and fractionally filled ringlike structures at the NS surface (see numerical simulations performed in Kulkarni and Romanova 2013). Moreover, possible exchange instability in the accretion flow

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above the stellar surface can result in a stochastic shape of the landing region (Hameury et al. 1980). Before the inevitable deceleration in the vicinity of the NS surface, the velocity of accreting material is expected to be close to the free-fall velocity (even if one accounts for matter motion along dipole magnetic filed lines). The temperature of accreting plasma is determined by synchrotron emission and inverse Compton (Siuniaev 1976). We have already seen that the effective temperature in the emitting region is expected to be 1 keV (see equation 8). Using the estimates for the hot spot area (63) and (67), we can improve the estimate of the effective temperature and obtain (w) Teff

=



L (w) 2σSB Sspot

1/4

1/7 5/28

11/28

≃ 5.7 Λ1/4 B12 L37 m1/28 R6

keV

(68)

for the case of accretion from the wind and (d) Teff

=



L (d) 2σSB Sspot

1/4

1/8 3/20

≃ 8.6 α 1/40 Λ7/32 B12 L37 m13/80 R6−0.45 keV

(69)

for the case of accretion from the gas pressure-dominated disc. At the polar regions of the NS, accretion flow is decelerated via different mechanisms depending on the mass accretion rate. At low mass accretion rates, when the radiation pressure is insignificant, the flow is stopped either by Coulomb collisions in the atmosphere of an NS (Zel’dovich and Shakura 1969; Basko and Sunyaev 1975; Pavlov and Yakovlev 1976) or in the collisionless shock above the NS surface (Langer and Rappaport 1982; Bykov and Krasil’Shchikov 2004). At high mass accretion rates, radiation pressure affects dynamics of accretion flow and material can be stopped above the NS surface in a radiation-dominated shock (Basko and Sunyaev 1976). Let us consider each of these possibilities: • Coulomb collisions and hot spots at the NS surface In this case, the deceleration of the accretion flow happens on a short stopping length in the top layer of the NS atmosphere (Kirk and Galloway 1981; Harding et al. 1984; Miller et al. 1989) and accretion process results in hot spots at the stellar surface. Most of the kinetic energy of the accretion flow is carried by ions, which lose their kinetic energy in ion-electron Coulomb collisions occurring with or without electron excitation to high Landau levels. The stopping power of the plasma and the stopping length are also affected by the generation of the collective plasma oscillations. Typical stopping length in the atmosphere of an NS can be estimated as a few tens of g cm−2 (Harding et al. 1984; Nelson et al. 1993). Accounting for the material spreading over the NS surface leads to the conclusion that the emitting region may have more complex geometry with accretion mound forming at the base of the accretion channel (see Fig. 28, Mukherjee et al. 2013).

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Fig. 28 The structure of the accretion mound in the case of filled (left) and hollow (right) accretion channel. The horizontal axis corresponds to the distance from the NS magnetic pole, and the vertical axis represents the height above the NS surface. Magnetic field lines distorted by plasma spreading over the NS surface are shown as black solid lines. The red dash-dotted line denotes the top of the mound. Magnetic field at the NS surface is taken to be ∼1012 G. (The curves are reproduced from Mukherjee et al. 2013)

• Collisionless shock Collisionless shock may arise due to the development of instabilities in plasma moving along magnetic field lines toward NS magnetic poles. To the best of our knowledge, no quantitative studies of such instabilities have been performed up to date. However, some models of collisionless shocks were developed based on the assumption that such shock does develop (Langer and Rappaport 1982). The temperature of plasma right after the shock region can be estimated under the assumption that the process of plasma heating is adiabatic. Then, the electron gas is cooling rapidly due to the inverse Compton effect and synchrotron emission. The cooling process of ions is much slower, and the ion gas loses its energy mostly due to interaction with the cooler gas of electrons. As a result, one would expect two-temperature plasma below the shock region. • Radiation-dominated shock and accretion columns The increase of the mass accretion rate leads to the increase of accretion luminosity and strengthening of the radiative force applied to the accretion flow above the surface. At certain accretion luminosity, the radiation pressure becomes strong enough to stop accretion flow above the NS surface (Basko and Sunyaev 1976): 36

Lcrit ≈ 4 × 10



σT σeff



l0 2 × 105 [cm]



m erg s−1 , R6

(70)

where σT is the non-magnetic Thomson scattering cross section, σeff is the effective cross section in accretion channel above NS surface, and l0 is the length of accretion channel base. This luminosity is called “critical.” Note that it is not enough to compensate the gravitational force by the radiative one in

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Fig. 29 Schematic structure of hollow accretion column confined by a strong magnetic field and supported by radiation pressure above the surface of an NS. The height of the column can be comparable to the NS radius. At extreme mass accretion rates, the column can potentially turn in the advective regime, when X-ray photons are confined within the accretion flow. The photons originated from the region marked in blue on the plot cannot leave accretion channel because the diffusion timescale for them is larger than the dynamic timescale. There is possibly a small region on the bottom of the column (marked in red), where the mass density is so high that the gas pressure dominates over the radiation pressure. (From Mushtukov et al. 2018b)

order to stop accretion flow above the NS surface (which moves with freefall velocity). Because the scattering cross section in a strong magnetic field depends on the photon energy and B-field strength, an effective scattering cross section σeff and the critical luminosity (70) depend on the field strength at the NS surface (Mushtukov et al. 2015b). The critical luminosity was determined observationally in two transient XRPs up to now: V 0332+53 (Doroshenko et al. 2017) and A 0535+262 (Kong et al. 2021). Luminosity higher than the critical one results in the appearance of radiationdominated shock and accretion columns above the polar regions of accreting NS (Inoue 1975; Basko and Sunyaev 1976; Wang and Frank 1981; Mushtukov et al. 2015a; Gornostaev 2021) (Fig. 29). Accretion columns are confined by a strong magnetic field and supported by radiation pressure. The theory of the accretion column structure is one of the key unsolved problems in the physics of XRPs. The problem is highly complex, especially at high accretion rates when there is a strong coupling between matter and radiation in the accretion channel. Even accounting for non-magnetic radiative transfer requires the usage of advanced numerical calculations and huge computational resources (Kawashima et al. 2016). Order of magnitude estimations show that accretion columns can provide

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luminosity as high as 1040 erg s−1 and, therefore, can explain the observed luminosity of recently discovered ULX pulsars (Bachetti et al. 2014; Israel et al. 2017). At the same time, it is known that the accretion column structure and maximal luminosity depend on the geometry of the accretion channel (in particular, on its geometrical thickness, determined by accretion flow interaction with the NS magnetosphere at Rm , see Mushtukov et al. 2015a) and magnetic field structure in the vicinity of the NS surface (Brice et al. 2021). Additionally, at very high mass accretion rates, photon diffusion from accretion column becomes inefficient. It leads to the development of the photon bubble instability (Klein and Arons 1989; Arons 1992; Klein et al. 1996a), which causes strong time-dependent density fluctuations inside the accretion column. The presence of these fluctuations may alter the time-averaged structure of the column. Because photons will tend to preferentially escape along low-density channels, photon bubbles may ultimately determine the angular distribution of X-ray photon emission, reduce the efficacy of radiation pressure, and affect the estimates of the mass accretion rates above which photons can be trapped by advection process. It was predicted that photon bubble instability can be observed as quasi-periodic oscillations at Fourier frequencies from ∼102 to 104 Hz (Klein et al. 1996a). The signs of photon bubble instability were not detected solidly so far (Revnivtsev et al. 2015), but the excess of aperiodic variability detected in some sources at high mass accretion rates (see, for example, Fig. 9 right) was interpreted by some authors as an evidence of photon bubbles (Klein et al. 1996b). Recent studies have shown that accretion columns can be strongly influenced by advection (Mushtukov et al. 2018b), when photons are locked inside the accretion column, at extremely high mass accretion rates (>1020 g s−1 ) typical for the brightest XRPs. In this case, the opacity in accretion channel and, therefore, the dynamics of accretion flow can be affected by the production of electron–positron pairs (Mushtukov et al. 2019c) and possibly a strong neutrino emission (Mushtukov et al. 2018b; Kaminker et al. 1992). Different geometries of emitting regions above the NS surface imply different scenarios of spectra formation and different beam patterns (Gnedin and Sunyaev 1973). In particular, it is natural to expect a pencil beam diagram from the accretion with hot spots at the NS surface (see case A in Fig. 30), while collisionless shocks and radiation-dominated accretion columns would cause fan beam diagram (see case B1 in Fig. 30). The beam pattern naturally determines the pulse profiles in XRPs. Therefore, observations of XRPs and variations of their pulse profiles over a wide range of accretion luminosity can provide an evidence of changes in geometry of emitting region caused by changes of the mass accretion rate. In particular, switch from the hot spot geometry to accretion column and corresponding change of a beam pattern can cause phase shift in the observed pulse profile. In fact, the process of pulse profile formation is far more complicated than it might seem on the base of simplified models. There are at least two features to be taken into account in the models. One of them is the influence of gravitational light bending on the

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Fig. 30 Beaming of X-ray radiation from the NS in XRP at sub-critical mass accretion rates, when the accretion process results in hot spots at the NS surface (A), and at super-critical mass accretion rates, when the accretion columns arise above the stellar surface (B1 and B2 ). The B2 case implies beaming of accretion column radiation toward the NS surface. In this case, the X-ray flux detected by a distant observer is composed of the direct radiation from the columns (red pieces of the beam pattern) and the radiation intercepted and reflected by the NS atmosphere (blue pieces of the beam pattern)

pulse profiles formation (Riffert and Meszaros 1988; Kraus 2001; Poutanen and Beloborodov 2006), which, in the case of bright XRPs with accretion columns, can cause significant increase of the observed pulsed fraction and might affect the relation between the apparent and actual luminosity (Mushtukov et al. 2018c; Inoue et al. 2020). The second feature that complicates the pulse profile modelling is the inclusion of additional sources of X-ray emission. In the case of accretion column

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formation in bright XRPs, a fraction of X-rays emitted by the column is intercepted by the NS surface and reprocessed by its atmosphere (see case B2 Fig. 30, Poutanen et al. 2013). This process influences both spectra (Postnov et al. 2015) and pulse profile formation (Lutovinov et al. 2015; Mushtukov et al. 2018c).

Spectra Formation Challenges and Complications We have to confess that there is still no self-consistent model of spectra formation in XRPs that would cover a wide range of accretion luminosities. Observational data tell us that over a wide luminosity range the broadband energy spectra of XRPs can be described by an absorbed power law model modified with an exponential cutoff at high energies. Some sources show significant deviations at low luminosity, but this is not a general trend. The basic ingredients of the spectra formation modelling in XRPs are (i) geometry of the emitting region (which can be dependent on the mass accretion rate), (ii) the details of energy release mechanism and production of seed photons, and (iii) all major processes influencing radiative transfer. The set of possible geometries of the emitting region can be reduced to two general configurations: the case of a plane-parallel atmosphere (implying sub-critical mass accretion rates) and the case of a cylindrical emitting region (implying super-critical mass accretion rates or formation of collisionless shock in the low-luminosity state). The major processes determining spectral formation in XRPs are magnetic Compton scattering (Daugherty and Harding 1986), cyclotron emission/absorption (Harding and Daugherty 1991), and magnetic bremsstrahlung (see Meszaros 1992 for a review). At extreme mass accretion rates, electron–positron pair creation and annihilation can come into play. In strongly magnetized plasma, the cross section of all of these processes shows dramatic dependence on the photon polarization state, photon energy, and momentum direction. All these make the calculation of radiative transfer very complicated task, especially in the case of its strong coupling with the dynamical structure of the emitting region. Because cross sections of the major processes responsible for the radiative transfer are polarization dependent (Meszaros 1992; Harding and Lai 2006), the radiation leaving the emitting regions in XRPs is expected to be highly polarized. Models predicting polarization in XRPs should account for both radiative transfer in the emitting regions and influence of an extended NS magnetosphere on polarization of X-ray photons. The latter is due to the QED vacuum polarization (Gnedin et al. 1978; Pavlov and Gnedin 1984), which effectively results in the rotation of photon polarization plane while the photons propagate in the NS magnetosphere. Rotation of the polarization plane due to the photon interaction with NS magnetic field is noticeable within the so-called adiabatic radius Rad . For the case of the dipole magnetic field configuration, the adiabatic radius can be estimated as

113 Accreting Strongly Magnetized Neutron Stars: X-ray Pulsars 0.4 0.2 Rad ≃ 7.6 × 106 B12 EkeV R6 cm,

4159

(71)

where EkeV is the photon energy in keV (González Caniulef et al. 2016). Outside the adiabatic radius, the effects of vacuum polarization can be neglected.

Broadband Energy Spectra The first attempts to model spectral formation in XRPs were based on the Feautrier numerical scheme (Mihalas 1978) and performed by Nagel (1981a, b), who studied radiative transfer in two specific geometries: the slab and the cylinder. The calculations were performed either taking into account angular redistribution of photons but assuming coherent scattering (Nagel 1981a) or allowing the energy exchange in scattering events but neglecting angular redistribution (Nagel 1981b). These calculations were improved later by taking into account both energy exchange and angular redistribution of X-ray photons due to the scattering, as well as the vacuum polarization effects (Meszaros and Nagel 1985a, b). These works, however, have solved the radiative transfer problem under the assumptions of constant temperature, constant mass density in the atmosphere, non-relativistic Maxwellian distribution of electrons, and the electron gas being at rest. It has been shown that the classical power law spectra with the cutoff at high energies can be produced in the accretion shock due to bulk and thermal Comptonization of soft seed photons (Lyubarskii and Syunyaev 1982; Becker and Wolff 2007). In Becker and Wolff (2007), it was possible to get analytical solutions for cylindrical geometry in the form of Green functions. The analytical solutions, however, do not account for coupling between hydrodynamical and radiative transfer parts of the problem, which can result in solution violating energy conservation (Thalhammer et al. 2021). Recently, the model by Becker and Wolff (2007) was generalized by accounting for an X-ray polarization in the radiative transfer part (Caiazzo and Heyl 2021). Under the condition of high mass accretion rate, additional ingredients can influence the process of broadband spectra formation: • X-ray reflection from the atmosphere of an NS Super-critical mass accretion rates result in the appearance of accretion column above magnetic poles of an NS. Because the radiation from the walls of accretion column can be beamed toward the NS surface (Kaminker et al. 1976; Lyubarskii and Syunyaev 1988), a large fraction of X-ray luminosity can be intercepted by the atmosphere of an NS (Poutanen et al. 2013). Reprocessing and reflection of X-rays can influence spectra making it harder (Postnov et al. 2015). • Reprocessing of X-rays by accretion flow within the magnetospheric radius A fraction of X-ray photons can be reprocessed by accretion flow in between the inner disc radius and NS surface. Such a reprocessing becomes especially important at accretion luminosity >few × 1038 erg s−1 , when the flow can turn in optically thick state due to the Compton scattering (Mushtukov et al. 2017).

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• Reprocessing of X-rays by the outflows launched from the disc Extreme mass accretion rates onto the NS surface lead to radiation driven outflows from accretion disc. Strong outflows cause geometrical collimation of X-ray photons. Multiple reflections and reprocessing of the photons due to their interaction with the outflow can influence X-ray spectra making it softer. In contrast to the standard pulsar spectra observed at high luminosities, the transition of some XRP to the state with low mass accretion rate results in very different spectral shape, consisting of two broad components (see Fig. 13, Tsygankov et al. 2019a, b; Lutovinov et al. 2021). Such spectral distribution can be explained by models where the upper layers of NS atmosphere are overheated by the accretion process, and seed photons are produced by magnetic free–free emission and cyclotron de-excitation of electrons from high Landau levels (see Fig. 31, Mushtukov et al. 2021b; Sokolova-Lapa et al. 2021). According to these models, accretion flow is stopped in the atmosphere by Coulomb collisions with some fraction of kinetic energy going into heat, while another going into the excitation of electrons to the upper Landau levels. Excited electrons almost immediately transfer to the ground Landau level emitting one or several cyclotron photons. The lowenergy component in X-ray spectra is formed due to the thermal emission of strongly magnetized plasma, while the high-energy component is a result of cyclotron

Fig. 31 Schematic picture of the theoretical model explaining spectra formation at extremely low mass accretion rates. The X-ray energy spectrum is originated from the atmosphere of an NS with the upper layer overheated by low-level accretion. The accretion flow is stopped in the atmosphere due to collisions. Collisions result in excitation of electrons to upper Landau levels. The following radiative de-excitation of electrons produces cyclotron photons. The cyclotron photons are partly reprocessed by magnetic Compton scattering and partially absorbed in the atmosphere. The reprocessed photons form a high-energy component of the spectrum, while the absorbed energy is released in thermal emission and forms a low-energy part of the spectrum. (From Mushtukov et al. 2021b)

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Fig. 32 (Left:) XRP energy spectra in two polarization modes at low mass accretion rates. Solid line describes the total flux, while the dotted and the dashed lines correspond to extraordinary and ordinary modes, respectively. (Right:) Atmospheric structure: electron temperature (solid) and electron number density (dashed–dotted). The major spectral components and associated formation regions are indicated in both panels. The plots are reproduced on the base of Sokolova-Lapa et al. (2021)

emission. Both components experience magnetic absorption in the atmosphere and comptonization. Resonant Compton scattering at the cyclotron energy forces cyclotron photons to leave the atmosphere in the wings of a cyclotron line. It results in the broadening of high-energy component and the appearance of a cyclotron scattering feature on top of it (see Figs. 31 and 32). Current models of spectra formation at a low-luminosity state require the upper layers of the NS atmosphere to be overheated up to temperatures T  40 keV. This result is aligned with earlier calculations of the atmospheric structure under conditions of its heating by the accretion process (Zel’dovich and Shakura 1969). Under the condition of high temperatures, a large fraction (if not the major) of seed cyclotron photons is produced due to the magnetic bremsstrahlung in the atmosphere. One of the significant parameters in the models is the typical depth of accretion flow brake in the atmosphere. In that sense, accurate theoretical models of spectra formation at a low mass accretion rate can shed light on the aspects of plasma physics in a strong field regime. Note also that the models developed here (Mushtukov et al. 2021b; Sokolova-Lapa et al. 2021) do not require the formation of collisionless shock (at least, at the luminosity range and at magnetic field strength, where two-component spectra are observed). The problems of the models describing spectra formation at low luminosity are related to the lack of their self-consistency. In particular, there are still no self-consistent calculations of the temperature structure in the atmosphere, and it is still not explained how the spectra composed of two component at low state transforms to “classical” spectra observed at higher mass accretion rates. In a couple of transient XRPs in the propeller state (Tsygankov et al. 2016), soft spectra composed of one blackbody-like component were detected (see Fig. 19). In both cases, the spectra in the propeller state were well fitted by the absorbed blackbody model with the temperature ∼0.5 keV and radius of the emitting area ∼0.6–0.8 km. Because the centrifugal barrier largely prevents matter penetration to

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the NS surface in the propeller state, the observed blackbody-like emission can be due to cooling of accretion heated NS crust. The accretion-induced heating of the NS crust and its subsequent cooling has been studied extensively for NSs with low surface magnetic field (B  108 G), but not for strongly magnetized sources (B  1012 G). The strong magnetic field could alter both heating and cooling processes due to magnetic field influence on the heat transfer and details of energy release during the accretion state (Potekhin et al. 2015; Wijnands and Degenaar 2016). The models involving cooling of the NS crust predict slow reduction of X-ray flux from the NS surface and gradual decrease of blackbody temperature. The observational data available up to date are largely consistent with the cooling hypothesis (see, however, Rouco Escorial et al. 2017).

Cyclotron Lines: The Fingerprints of a Strong Magnetic Field In addition to the continuum emission, in the spectra of some XRPs, a narrow absorption feature, a cyclotron resonant scattering feature (aka cyclotron line), may be observed. Photons experience resonant Compton scattering by the electron in rest at energies (n) Eres (b) = 511 keV

⎧ ⎨ 1 + 2nb sin2 θ − 1 ⎩ B,

sin2 θ

, for θ = 0, n = 1, 2, ,

(72)

for θ = 0,

Where the Landau level number n ∈ {0, 1, 2, 3, }, and θ is the angle between the photon momentum and local direction of magnetic field. Expression (72) naturally results in the approximate relation between the magnetic field strength and the energy of the fundamental cyclotron line (9). Currently, cyclotron lines are known in a few dozens of XRPs (Staubert et al. 2019) providing an important (and sometimes the only) tool to measure magnetic field strength in accreting strongly magnetized NSs (see expression 9 relating cyclotron energy and local magnetic field strength). It is great luck if the cyclotron line is observed in X-ray energy spectra with its harmonics because, in this case, one can be more confident that the feature in the spectra is nothing else but the cyclotron line. Photons can be scattered resonantly by any charged particles including protons and ions. However, the scattering cross section is significantly smaller due to the larger mass of ions. The energy of the fundamental line in the case of scattering by ion is relatively small and given by −3

Eres,ion ≃ 6.3 × 10

  Z keV, B12 A

(73)

where Z is the atomic number and A is the mass number of the ion. The proton resonant scattering feature was discussed in interpretation of X-ray spectra in ULX NGC M51 X-8 (Brightman et al. 2018). Variations of mass accretion rate and luminosity in XRPs result in changes of dynamics and geometry of the emitting regions in the vicinity of the NS surface.

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These changes can cause variations in the cyclotron line properties. The most investigated phenomenon here is variations of the cyclotron line centroid energy with the accretion luminosity. As we have already mentioned, there are sources showing a positive correlation between the line centroid energy and luminosity (Staubert et al. 2007; Klochkov et al. 2012; Rothschild et al. 2017; Chen et al. 2021) and sources, where the correlation is negative (Mihara et al. 2004; Tsygankov et al. 2006). The first ones show systematically lower accretion luminosity (see Fig. 12). The explanation of observed cyclotron line behavior is based on expected variations of geometry of the line forming regions with changes in a mass accretion rate. In particular, the positive correlation is considered as evidence for the sub-critical accretion regime, when the accretion process results in hot spots at the magnetic poles of an NS or in collisionless shock above them. The negative correlation, on the contrary, can be considered as evidence for super-critical accretion when radiationdominated shock appears above the stellar surface. Let us consider some theoretical models explaining the variation of cyclotron line centroid energy: • Positive correlation There are two models explaining the positive correlation between observed cyclotron line energy and accretion luminosity: one is based on the assumption that collisionless shock is formed above the NS surface, and another is assuming that the energy of accreting material is released in hot spots at the surface. (A) The models based on the assumption of collisionless shock formation (Staubert et al. 2007; Rothschild et al. 2017) use the fact that the shock height above NS surface is anticorrelated with the mass accretion rate: the higher the mass accretion rate, the closer collisionless shock locates to the stellar surface (Langer and Rappaport 1982; Bykov and Krasil’Shchikov 2004). Thus, at higher mass accretion rates, the typical field strength in a line forming region is higher, which results in a positive correlation between the line centroid energy and luminosity (see Fig. 33A). (B) The alternative model explaining the positive correlation assumes that the broadband X-ray energy spectrum forms in the hot spots at the NS surface (see Fig. 33B, Mushtukov et al. 2015c). Because of the relatively low mass accretion rate, the accretion regime is sub-critical and the accretion flow above NS surface is optically thin for continuum X-ray radiation. The flow, however, remains optically thick for X-ray photons at energies close to the cyclotron one. Variations in mass accretion rate and luminosity cause variations in the dynamics of accreting material: the higher the luminosity, the larger the radiative force acting on the accretion flow, and the smaller the velocity of the flow just above the surface of an NS. The resonant scattering of X-ray photons by the accretion flow is affected by the Doppler effect in accretion channel: the resonant scattering by slower accretion flow results in the appearance of cyclotron feature at higher energies. Thus, the model naturally predicts the positive correlation. Note that the displacement of the cyclotron centroid energy is affected by both bulk velocity of accreting

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Fig. 33 Schematic illustration of the models explaining positive (A,B) and negative (C,D) correlations between accretion luminosity and cyclotron line centroid energy in XRPs: (A) according to the models accounting for the collisionless shock, the cyclotron centroid energy increase with the luminosity is associated with the decrease of collisionless shock height. (B) In the model accounting for the Doppler effect in the accretion channel, radiation pressure affects the velocity of the accreting matter: the higher the luminosity, the lower the velocity in the vicinity of the NS surface, the lower the redshift, and the higher the cyclotron line centroid energy. (C) The most straightforward model explaining the negative correlation associates the decay of the cyclotron line centroid energy with the growth of accretion column and a corresponding shift of a line forming region to a larger height, where the B-fields is weaker. (D) According to the reflection model, the cyclotron features form due to the reflection/reprocessing of X-rays by the atmosphere of an NS. Magnetic field strength decreases toward the equator of an NS. Thus, the larger is the luminosity, the higher is the accretion column, the larger the illuminated fraction of an NS surface, the weaker the average magnetic field, and the lower the cyclotron line energy

material and direction of photon propagation. Therefore, correlation properties are influenced by the beam pattern as well (Nishimura 2014). We would speculate that precise accounting for the MHD structure of a line forming region can provide additional hypothesis on the nature of the positive correlation. In particular, hot spots have more complex structure than we usually assume in the models. Finite timescale of matter spreading over the NS surface from the polar regions results in the appearance of accretion mounds at the polar

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cups of an NS (Mukherjee et al. 2013). The spreading process results in magnetic field distortion in the line forming regions (unless there is some mechanism that allows mass to slip through the magnetic field lines, see, e.g., Kulsrud and Sunyaev 2020). Such distortions can cause variations of typical magnetic field strength in a line forming region and affect variations of the line centroid energy with the luminosity. • Negative correlation The negative correlation is expected in super-critical XRPs and all models explaining the correlation involve radiation dominated accretion columns. (C) The most straightforward model explaining the negative correlation assumes that the cyclotron line is formed in radiation dominated shock, which height above the NS surface depends on the mass accretion rate: the higher the mass accretion rate, the higher the shock above the NS surface (see Fig. 33C). Because the field strength B ∝ r −3 , the higher mass accretion rate places the line forming region in the area of lower magnetic field strength, which naturally leads to the negative correlation. This model, however, has a couple of problematic points: (i) in the case of high accretion columns, the range of magnetic field strength represented in the line forming region is so broad that the cyclotron lines are expected to be very wide or even disappear from the spectra (Nishimura 2008) and (ii) because B ∝ r −3 , even small variations of accretion column height have to result in a significant variations of cyclotron line centroid energy, while observations demonstrate ∆Ecyc /Ecyc  0.1 (see top right panel in Fig. 12, Tsygankov et al. 2006; Cusumano et al. 2016; Doroshenko et al. 2017). (D) Another possible explanation of the negative correlation is related to the specific features of accretion column. Radiation leaving accretion column from its sides is expected to be beamed toward the NS surface due to the relativistic effects (Kaminker et al. 1976; Lyubarskii and Syunyaev 1988). Because of that, a large fraction of X-ray luminosity produced by accretion columns is intercepted by the atmosphere of an NS. Reprocessing of X-ray radiation by the atmosphere results in the appearance of an absorption-like feature at the cyclotron energy corresponding to the local magnetic field strength (Ivanov 1973; Grigoryev et al. 2019). In the case of magnetic field dominated by dipole component, the field strength at the NS surface is given √ by B = 0.5 B0 1 + 3 cos2 θ, where B0 is the field strength at the magnetic pole, and θ is the co-latitude at the stellar surface. Then, the variations of the accretion column height with luminosity naturally results in the appearance of the negative correlation: the higher the mass accretion rate, the larger the accretion column height, the larger the area illuminated by accretion column around the magnetic poles of an NS, the smaller the average magnetic field strength over the illuminated part of a star, and the smaller the cyclotron line centroid energy in X-ray spectrum (see Fig. 33D and Poutanen et al. (2013) for details). The reflection model naturally explains small amplitudes of observed variations of the cyclotron line energy: magnetic field strength

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varies by a factor of 2 only over the NS surface and possibly large changes of accretion column height result in a small variations of line displacement. Recent Monte Carlo simulations (Kylafis et al. 2021) show that observed variations of cyclotron line energy might be too large to be explained by the model. However, the final conclusions on the model applicability can be done only after detailed simulations of the reflection process. Note that the discussed theoretical models explaining the negative correlation do not exclude each other, and the cyclotron lines can appear in X-ray energy spectra due to combination of all these mechanisms of cyclotron line formation.

Open Issues In this section, we highlight key open issues in physics and astrophysics of XRPs. 1. Advanced spin-up/-down theory in XRPs in the view of super-fluidity of NS inner crust and core 2. Detailed theory and numerical model of accretion from a cold disc. Quantitative description of XRP transition into cold disc mode. Inner disc radius in the state of accretion from the cold disc 3. First principal simulations of plasma (with different physical properties) penetration into the magnetosphere of an NS 4. Detailed theoretical model of disc accretion onto inclined magnetic dipoles and NS with a more complicated geometry of NS magnetic field 5. Detailed theory and numerical simulations of plasma deceleration in the atmosphere of magnetized NS 6. Theoretical models of NS crustal heating induced by accretion and the crustal cooling under conditions of a strong magnetic fields (B  1012 G) 7. Existence of collisionless shocks above NS surface at low mass accretion rates. Accurate numerical simulations of collisionless shock formation 8. Self-consistent theoretical and numerical model of accretion column accounting for radiative transfer in a strongly magnetized accreting plasma, appearance of the photon bubble instability, nuclear reactions in accretion channel, neutrino emission and possible deviations of accreting material from the condition of local thermodynamic equilibrium 9. Unified theory explaining spectra, polarization and pulse profile formation in XRPs over a wide range of accretion luminosity (1033 –1041 erg s−1 ) 10. Explanation of unexpectedly low polarization degree observed in sub-critical X-ray pulsars by IXPE 11. Numerical model reproducing formation, shape and variability (i.e., phaseresolved variability and variability with accretion luminosity) of cyclotron scattering features in spectra of XRPs over a wide range of accretion luminosity 12. Theory of magnetic field evolution under the influence of accretion

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13. Fraction of accreting NSs and BHs in ULXs. Magnetic field strength and structure in ULXs powered by accretion onto NSs 14. Influence of ULXs powered by accretion onto NSs on global evolution of highmass X-ray binaries and production of gravitational wave sources

Key Points to Have in Mind 1. XRPs are accreting strongly magnetized NSs in close binary systems. The strong magnetic field of the order of 1012 G in XRPs affects both geometry of accretion flow on the spatial scales of ∼108 cm and physical processes in close proximity to the NS surface. The magnetic field at the NS surface in XRPs is orders of magnitude stronger than the magnetic field achievable in labs. 2. Luminosity of XRPs is powered by accretion process. Nuclear burning in XRPs is going in a stable regime, and its contribution to the luminosity is insignificant. 3. Strong magnetic field in XRPs disrupts accretion flow toward an NS at Rm ∼ 108 cm and forces accreting material to land NS surface in small regions located close to magnetic poles of a star. The energy release occurs predominantly in these regions. Observed pulsations of the X-ray flux, thus, are a result of misalignment between the rotational and magnetic axes of an NS. 4. XRPs provide a rich phenomenology. Spin periods of NSs in XRPs cover a few orders of magnitude from a fraction of a second up to thousands of seconds. The apparent X-ray luminosity of some sources covers more than 7 orders of magnitude on the timescales from minutes to months. Many XRPs properties, including their X-ray energy spectra, power density spectra, and pulse profiles, are known to be variable with the luminosity. 5. There are three primary mechanisms of the mass transfer between NS and its companion in XRPs: (i) Roche lobe overflow, (ii) capture of matter from the decretion disc in Be-system, and (iii) companion mass loss due to the stellar wind. 6. Rotation of an NS sets up a centrifugal barrier for the accreting material. The accretion flow can penetrate through the barrier in the case of a sufficiently high mass accretion rate. At low mass accretion rates, the centrifugal barrier stops accretion flow at the magnetospheric boundary and largely prevents accretion into an NS surface (propeller effect). 7. On the other hand, interaction of accretion flow with the NS magnetosphere affects rotation of a compact object and spin periods are known to be variable in XRPs. Analyses of spin period variability allow estimating magnetic field strength. However, the interaction of accretion flow with NS magnetosphere is affected by many parameters (inclination of a magnetic dipole in respect to the accretion flow, the exact structure of NS magnetic field, etc.), which influence is not investigated sufficiently. 8. Because of the wide range of mass accretion rates represented in XRPs, accretion discs show a great variety of possible physical conditions there. The

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physical conditions in the discs largely affect the observational manifestation of XRPs. Depending on the mass accretion rate onto the NS surface, one would expect different geometry of the emitting regions at the poles of a star. Relatively low mass accretion rates (1017 g s−1 ) lead to the hot spot geometry. Large mass accretion rates (1017 g s−1 ) result in the appearance of radiationdominated shock above the surface and a sinking region below it – the structure called “accretion column.” Accretion columns, supported by radiation pressure and confined by a strong magnetic field, allow luminosity well above the Eddington limit. At extreme mass accretion rates, accretion columns might be advective. In this case, the internal condition can be sufficient to provide strong neutrino emission with luminosity comparable to the photon luminosity of XRPs. On the other hand, large mass accretion rates can lead to the development of the photon bubble instability. Geometry of the emitting region affects spectra and beam pattern formation in XRPs. Cyclotron absorption features often observed in the XRPs spectra arise due to the resonant Compton scattering of X-ray photons in a strong magnetic field. The cyclotron features serve as the only direct method of measuring the NS magnetic field strength. The dependence of the emission region structure at the NS surface on the mass accretion rate is reflected in the variations of the cyclotron energy with the source luminosity.

Cross-References ⊲ Fundamental Physics with Neutron Stars ⊲ High-Mass X-ray Binaries ⊲ Low-Mass X-ray Binaries

References N. Aftab, B. Paul, P. Kretschmar, ApJS 243(2), 29 (2019). https://doi.org/10.3847/1538-4365/ ab2a77, 1906.07739 J.J. Aly, A&A 86, 192–197 (1980) K.A. Arnaud, XSPEC: the first ten years, in Astronomical Data Analysis Software and Systems V, ed. by G.H. Jacoby, J. Barnes. Astronomical Society of the Pacific Conference Series, vol. 101 (1996), p 17 J. Arons, ApJ 388, 561 (1992). https://doi.org/10.1086/171174 J. Arons, S.M. Lea, ApJ 207, 914–936 (1976). https://doi.org/10.1086/154562 M. Bachetti et al., Nature 514(7521), 202–204 (2014). https://doi.org/10.1038/nature13791, 1410.3590 M. Bachetti et al., ApJ 891(1), 44 (2020). https://doi.org/10.3847/1538-4357/ab6d00, 1905.06423 S.A. Balbus, J.F. Hawley, ApJ 376, 214 (1991). https://doi.org/10.1086/170270

113 Accreting Strongly Magnetized Neutron Stars: X-ray Pulsars

4169

M.M. Basko, R.A. Sunyaev, A&A 42(3), 311–321 (1975) M.M. Basko, R.A. Sunyaev, MNRAS 175, 395–417 (1976). https://doi.org/10.1093/mnras/175.2. 395 M.M. Basko et al., A&A 31, 249–263 (1974) P.A. Becker, M.T. Wolff, ApJ 654(1), 435–457 (2007). https://doi.org/10.1086/509108, astroph/0609035 L. Bildsten, E.F. Brown, ApJ 477(2), 897–904 (1997). https://doi.org/10.1086/303752, astroph/9609155 L. Bildsten et al., ApJS 113(2), 367–408 (1997). https://doi.org/10.1086/313060, astro-ph/9707125 A. Biryukov, P. Abolmasov, MNRAS 505(2), 1775–1786 (2021). https://doi.org/10.1093/mnras/ stab1378, 2105.00754 G.S. Bisnovatyi-Kogan, Y.M. Kazhdan, A.A. Klypin, A.E. Lutskii, N.I. Shakura, Sov. Ast. 23, 201–205 (1979) E. Bozzo et al., A&A 531, A130 (2011). https://doi.org/10.1051/0004-6361/201116726, 1106.5125 E. Bozzo, S. Ascenzi, L. Ducci, A. Papitto, L. Burderi, L. Stella, A&A 617, A126 (2018). https:// doi.org/10.1051/0004-6361/201732004, 1806.11516 N. Brice, S. Zane, R. Turolla, K. Wu, MNRAS 504(1), 701–715 (2021). https://doi.org/10.1093/ mnras/stab915, 2104.06138 M. Brightman et al., Nat. Astron. 2, 312–316 (2018). https://doi.org/10.1038/s41550-018-0391-6, 1803.02376 A. Broderick, M. Prakash, J.M. Lattimer, ApJ 537(1), 351–367 (2000) https://doi.org/10.1086/ 309010, astro-ph/0001537 D.J. Burnard, J. Arons, S.M. Lea, ApJ 266, 175–187 (1983). https://doi.org/10.1086/160768 A.M. Bykov, A.M. Krasil’Shchikov, Astron. Lett. 30, 309–318 (2004). https://doi.org/10.1134/1. 1738153, astro-ph/0412319 S.D. Bykov, E.V. Filippova, M.R. Gilfanov, S.S. Tsygankov, A.A. Lutovinov, S.V. Molkov, MNRAS 506(2), 2156–2169 (2021). https://doi.org/10.1093/mnras/stab1852, 2106.14261 I. Caballero et al., A&A 465(2), L21–L24 (2007). https://doi.org/10.1051/0004-6361:20067032, astro-ph/0702536 I. Caiazzo, J. Heyl, MNRAS 501(1), 109–128 (2021). https://doi.org/10.1093/mnras/staa3428, 2009.00631 S. Campana, F. Gastaldello, L. Stella, G.L. Israel, M. Colpi, F. Pizzolato, M. Orlandini, D. Dal Fiume, ApJ 561(2), 924–929 (2001). https://doi.org/10.1086/323317, astro-ph/0107236 J.K. Cannizzo, ApJLett 466, L31 (1996). https://doi.org/10.1086/310167, astro-ph/9605127 S. Chandrasekhar, E. Fermi, ApJ 118, 116 (1953). https://doi.org/10.1086/145732 A. Chashkina, P. Abolmasov, J. Poutanen, MNRAS 470(3), 2799–2813 (2017). https://doi.org/10. 1093/mnras/stx1372, 1703.07005 A. Chashkina, G. Lipunova, P. Abolmasov, J. Poutanen, Super-Eddington accretion discs with advection and outflows around magnetized neutron stars. A&A 626, A18 (2019). https://doi. org/10.1051/0004-6361/201834414, 1902.04609 X. Chen et al., ApJ 919(1), 33 (2021). https://doi.org/10.3847/1538-4357/ac1268, 2107.03267 C.S. Choi, F. Nagase, F. Makino, T. Dotani, S. Kitamoto, S. Takahama, ApJ 437, 449 (1994). https://doi.org/10.1086/175008 E.J.M. Colbert, R.F. Mushotzky, ApJ 519(1), 89–107 (1999). https://doi.org/10.1086/307356, astro-ph/9901023 R.H.D. Corbet, ApJLett 457, L31 (1996). https://doi.org/10.1086/309890 G. Cusumano, V. La Parola, A. D’Aì, A. Segreto, G. Tagliaferri, S.D. Barthelmy, N. Gehrels, MNRAS 460(1), L99–L103 (2016). https://doi.org/10.1093/mnrasl/slw084, 1604.07831 C.R. D’Angelo, H.C. Spruit, MNRAS 406(2), 1208–1219 (2010). https://doi.org/10.1111/j.13652966.2010.16749.x, 1001.1742 J.K. Daugherty, A.K. Harding, ApJ 273, 761–773 (1983). https://doi.org/10.1086/161411 J.K. Daugherty, A.K. Harding, ApJ 309, 362 (1986). https://doi.org/10.1086/164608 K. Davidson, J.P. Ostriker, ApJ 179, 585–598 (1973). https://doi.org/10.1086/151897

4170

A. Mushtukov and S. Tsygankov

C.S.R. Day, F. Nagase, K. Asai, T. Takeshima, ApJ 408, 656 (1993). https://doi.org/10.1086/ 172625 V. Doroshenko, A. Santangelo, I. Kreykenbohm, R. Doroshenko, A&A 540, L1 (2012). https://doi. org/10.1051/0004-6361/201218878, 1202.6271 V. Doroshenko, S.S. Tsygankov, A.A. Mushtukov, A.A. Lutovinov, A. Santangelo, V.F. Suleimanov, J. Poutanen, MNRAS 466(2), 2143–2150 (2017). https://doi.org/10.1093/mnras/ stw3236, 1607.03933 V. Doroshenko, A. Santangelo, V.F. Suleimanov, S.S. Tsygankov, A&A 643, A173 (2020a). https:// doi.org/10.1051/0004-6361/202038948, 2009.14064 V. Doroshenko et al., MNRAS 491(2), 1857–1867 (2020b). https://doi.org/10.1093/mnras/stz2879, 1909.12614 V. Doroshenko et al., Nat. Astron. 6, 1433–1443 (2022). https://doi.org/10.1038/s41550-02201799-5, 2206.07138 L. Ducci, P.M. Pizzochero, V. Doroshenko, A. Santangelo, S. Mereghetti, C. Ferrigno, A&A 578, A52 (2015). https://doi.org/10.1051/0004-6361/201525667, 1505.00548 H.P. Earnshaw, T.P. Roberts, M.J. Middleton, D.J. Walton, S. Mateos, MNRAS 483(4), 5554–5573 (2019). https://doi.org/10.1093/mnras/sty3403, 1812.04684 I. El Mellah, J.O. Sundqvist, R. Keppens, A&A 622, L3 (2019). https://doi.org/10.1051/00046361/201834543, 1810.12937 R.F. Elsner, F.K. Lamb, ApJ 215, 897–913 (1977). https://doi.org/10.1086/155427 S.N. Fabrika, K.E. Atapin, A.S. Vinokurov, O.N. Sholukhova, Astrophys. Bull. 76(1), 6–38 (2021). https://doi.org/10.1134/S1990341321010077, 2105.10537 F. Fürst et al., ApJ 780(2), 133 (2014). https://doi.org/10.1088/0004-637X/780/2/133, 1311.5514 P. Ghosh, F.K. Lamb, ApJLett 223, L83–L87 (1978). https://doi.org/10.1086/182734 P. Ghosh, F.K. Lamb, ApJ 232, 259–276 (1979a). https://doi.org/10.1086/157285 P. Ghosh, F.K. Lamb, ApJ 234, 296–316 (1979b). https://doi.org/10.1086/157498 R. Giacconi, H. Gursky, E. Kellogg, E. Schreier, H. Tananbaum, ApJLett 167, L67 (1971). https:// doi.org/10.1086/180762 M. Gilfanov, X-ray Emission from Black-Hole Binaries, vol. 794 (2010), p 17. https://doi.org/10. 1007/978-3-540-76937-8_2 M. Gilfanov, H.J. Grimm, R. Sunyaev, Nucl. Phys. B Proc. Suppl. 132, 369–375 (2004). https:// doi.org/10.1016/j.nuclphysbps.2004.04.065, astro-ph/0309725 V.L. Ginzburg, Sov. Phys. Doklady 9, 329 (1964) I.N. Gnedin, R.A. Sunyaev, A&A 36, 379–394 (1974) Y.N. Gnedin, R.A. Sunyaev, A&A 25, 233 (1973) Y.N. Gnedin, G.G. Pavlov, Y.A. Shibanov, Sov. Astron. Lett. 4, 117–119 (1978) T. Gold, Nature 218(5143), 731–732 (1968). https://doi.org/10.1038/218731a0 D. González Caniulef, S. Zane, R. Taverna, R. Turolla, K. Wu, MNRAS 459(4), 3585–3595 (2016). https://doi.org/10.1093/mnras/stw804, 1604.01552 M.I. Gornostaev, MNRAS 501(1), 564–575 (2021). https://doi.org/10.1093/mnras/staa3560, 2012.10501 S.A. Grebenev, R.A. Sunyaev, Astron. Lett. 33(3), 149–158 (2007). https://doi.org/10.1134/ S1063773707030024 V.V. Grigoryev, D.I. Nagirner, S.I. Grachev, Astrophysics 62(1), 129–146 (2019). https://doi.org/ 10.1007/s10511-019-09569-4 S. Hahn et al., Nature 570, 496–499 (2019) J.M. Hameury, Adv. Space Res. 66(5), 1004–1024 (2020). https://doi.org/10.1016/j.asr.2019.10. 022, 1910.01852 J.M. Hameury, S. Bonazzola, J. Heyvaerts, A&A 90(3), 359–365 (1980) A.K. Harding, J.K. Daugherty, ApJ 374, 687 (1991). https://doi.org/10.1086/170153 A.K. Harding, D. Lai, Rep. Progress Phys. 69(9), 2631–2708 (2006). https://doi.org/10.1088/00344885/69/9/R03, astro-ph/0606674 A.K. Harding, P. Meszaros, J.G. Kirk, D.J. Galloway, ApJ 278, 369–381 (1984). https://doi.org/10. 1086/161801

113 Accreting Strongly Magnetized Neutron Stars: X-ray Pulsars

4171

J.F. Hawley, C.F. Gammie, S.A. Balbus, ApJ 440, 742 (1995). https://doi.org/10.1086/175311 M. Heida et al., ApJLett 883(2), L34 (2019). https://doi.org/10.3847/2041-8213/ab4139, 1909.02171 S. Heinz et al., ApJ 779(2), 171 (2013). https://doi.org/10.1088/0004-637X/779/2/171, 1312.0632 P.B. Hemphill, R.E. Rothschild, A. Markowitz, F. Fürst, K. Pottschmidt, J. Wilms, ApJ 792(1), 14 (2014). https://doi.org/10.1088/0004-637X/792/1/14, 1407.1028 H. Herold, Phys. Rev. D 19(10), 2868–2875 (1979). https://doi.org/10.1103/PhysRevD.19.2868 R.C. Hickox, R. Narayan, T.R. Kallman, ApJ 614(2), 881–896 (2004). https://doi.org/10.1086/ 423928, astro-ph/0407115 A.P. Igoshev, S.B. Popov, R. Hollerbach, Universe 7(9), 351 (2021). https://doi.org/10.3390/ universe7090351, 2109.05584 A.F. Illarionov, R.A. Sunyaev, A&A 39, 185 (1975) A.R. Ingram, Astronomische Nachrichten 337(4–5), 385 (2016). https://doi.org/10.1002/asna. 201612318, 1511.07181 A. Inoue, K. Ohsuga, T. Kawashima, PASJ 72(2), 34 (2020). https://doi.org/10.1093/pasj/psaa010, 2003.07569 H. Inoue, PASJ 27(2), 311–323 (1975) H. Inoue, Space Sci. Rev. 40(1–2), 317–338 (1985). https://doi.org/10.1007/BF00212905 G.L. Israel et al., Science 355(6327), 817–819 (2017). https://doi.org/10.1126/science.aai8635, 1609.07375 V.V. Ivanov, Transfer of radiation in spectral lines (1973) A.D. Kaminker, V.N. Fedorenko, A.I. Tsygan, Soviet Ast. 20, 436 (1976) A.D. Kaminker, O.Y. Gnedin, D.G. Yakovlev, P. Amsterdamski, P. Haensel, Phys. Rev. D 46(10), 4133–4139 (1992). https://doi.org/10.1103/PhysRevD.46.4133 T. Kawashima, S. Mineshige, K. Ohsuga, T. Ogawa, PASJ 68(5), 83 (2016). https://doi.org/10. 1093/pasj/psw075, 1608.04211 A. King, J.P. Lasota, MNRAS 485(3), 3588–3594 (2019). https://doi.org/10.1093/mnras/stz720, 1903.03624 A. King, J.P. Lasota, MNRAS 494(3), 3611–3615 (2020). https://doi.org/10.1093/mnras/staa930, 2003.14019 A. King, J.P. Lasota, W. Klu´zniak, MNRAS 468(1), L59–L62 (2017). https://doi.org/10.1093/ mnrasl/slx020, 1702.00808 A.R. King, H. Ritter, MNRAS 293(1), L42–L48 (1998). https://doi.org/10.1046/j.1365-8711.1998. 01295.x J.G. Kirk, D.J. Galloway, MNRAS 195, 45P–50P (1981). https://doi.org/10.1093/mnras/195.1.45P R.I. Klein, J. Arons, Time-dependent two dimensional radiation hydrodynamics of accreting matter onto highly magnetised neutron stars, in Two Topics in X-Ray Astronomy, Volume 1: X Ray Binaries. Volume 2: AGN and the X Ray Background, ed. by J. Hunt, B. Battrick. ESA Special Publication, vol 1 (1989), p. 89 R.I. Klein, J. Arons, G. Jernigan, J.J.L. Hsu, ApJLett 457, L85 (1996a). https://doi.org/10.1086/ 309897 R.I. Klein, J.G. Jernigan, J. Arons, E.H. Morgan, W. Zhang, ApJLett 469, L119 (1996b). https:// doi.org/10.1086/310277 D. Klochkov et al., A&A 542, L28 (2012). https://doi.org/10.1051/0004-6361/201219385, 1205.5475 L.D. Kong et al., ApJLett 917(2), L38 (2021). https://doi.org/10.3847/2041-8213/ac1ad3, 2108.02485 L.D. Kong et al., ApJLett 933(1), L3 (2022). https://doi.org/10.3847/2041-8213/ac7711, 2206.04283 P. Kosec, C. Pinto, D.J. Walton, A.C. Fabian, M. Bachetti, M. Brightman, F. Fürst, B.W. Grefenstette, MNRAS 479(3), 3978–3986 (2018). https://doi.org/10.1093/mnras/sty1626, 1803.02367 O. Kotov, E. Churazov, M. Gilfanov, MNRAS 327(3), 799–807 (2001). https://doi.org/10.1046/j. 1365-8711.2001.04769.x, astro-ph/0103115 U. Kraus, ApJ 563(1), 289–300 (2001). https://doi.org/10.1086/323791

4172

A. Mushtukov and S. Tsygankov

A.K. Kulkarni, M.M. Romanova, MNRAS 386(2), 673–687 (2008). https://doi.org/10.1111/j. 1365-2966.2008.13094.x, 0802.1759 A.K. Kulkarni, M.M. Romanova, MNRAS 433(4), 3048–3061 (2013). https://doi.org/10.1093/ mnras/stt945, 1303.4681 R.M. Kulsrud, R. Sunyaev, J. Plasma Phys. 86(6), 905860602 (2020). https://doi.org/10.1017/ S0022377820001026 A.G. Kuranov, K.A. Postnov, L.R. Yungelson, Astron. Lett. 46(10), 658–676 (2020). https://doi. org/10.1134/S1063773720100084, 2010.03488 N.D. Kylafis, J.E. Trümper, N.A. Loudas, A&A 655, A39 (2021). https://doi.org/10.1051/00046361/202039361, 2108.07573 D. Lai, Rev. Modern Phys. 73(3), 629 (2001). https://doi.org/10.1103/RevModPhys.73.629, astroph/0009333 D. Lai, Theory of disk accretion onto magnetic stars, in European Physical Journal Web of Conferences, vol. 64 (2014), p. 01001. https://doi.org/10.1051/epjconf/20136401001, 1402.1903 D. Lai, H. Zhang, ApJ 683(2), 949–956 (2008). https://doi.org/10.1086/589822, 0709.3086 F.K. Lamb, C.J. Pethick, D. Pines, ApJ 184, 271–290 (1973). https://doi.org/10.1086/152325 S.H. Langer, S. Rappaport, ApJ 257, 733–751 (1982). https://doi.org/10.1086/160028 J.P. Lasota, New Astron. Rev. 45(7):449–508 (2001). https://doi.org/10.1016/S13876473(01)00112-9, astro-ph/0102072 D. Lazzati, L. Stella, ApJ 476(1), 267–277 (1997). https://doi.org/10.1086/303611, astroph/9609026 W.H. LewinG, R.E. Rutledge, J.M. Kommers, J. van Paradijs, C. Kouveliotou, ApJLett 462, L39 (1996). https://doi.org/10.1086/310022 V.M. Lipunov, Sov. Ast. 22, 702–706 (1978) V.M. Lipunov, Astrophysics of neutron stars (1992) G. Lipunova, K. Malanchev, S. Tsygankov, N. Shakura, A. Tavleev, D. Kolesnikov, MNRAS 510(2), 1837–1856 (2022). https://doi.org/10.1093/mnras/stab3343, 2110.08076 G.V. Lipunova, Astron. Lett. 25(8), 508–517 (1999). astro-ph/9906324 J. Liu, R. Soria, E. Qiao, J. Liu, MNRAS 480(4), 4746–4753 (2018). https://doi.org/10.1093/ mnras/sty2180, 1808.03036 K.S. Long, L.P. van Speybroeck, X-ray emission from normal galaxies, in Accretion-Driven Stellar X-ray Sources, ed. by W.H.G. Lewin, E.P.J. van den Heuvel (1983), pp. 117–146 M. Long, M.M. Romanova, R.V.E. Lovelace, MNRAS 374(2), 436–444 (2007) https://doi.org/10. 1111/j.1365-2966.2006.11192.x, astro-ph/0610487 A. Lutovinov et al., ApJ 912(1), 17 (2021). https://doi.org/10.3847/1538-4357/abec43, 2103.05728 A.A. Lutovinov, S.S. Tsygankov, V.F. Suleimanov, A.A. Mushtukov, V. Doroshenko, D.I. Nagirner, J. Poutanen, MNRAS 448(3), 2175–2186 (2015). https://doi.org/10.1093/mnras/ stv125, 1502.03783 A.A. Lutovinov, S.S. Tsygankov, K.A. Postnov, R.A. Krivonos, S.V. Molkov, J.A. Tomsick, MNRAS 466(1), 593–599 (2017). https://doi.org/10.1093/mnras/stw3058, 1609.02942 Y.E. Lyubarskii, MNRAS 292(3), 679–685 (1997). https://doi.org/10.1093/mnras/292.3.679 Y.E. Lyubarskii, R.A. Syunyaev, Sov. Astron. Lett. 8, 330–335 (1982) Y.E. Lyubarskii, R.A. Syunyaev, Sov. Astron. Lett. 14, 390 (1988) C. Maitra et al., MNRAS 490(4), 5494–5502 (2019). https://doi.org/10.1093/mnras/stz2831, 1910.02792 C. Malacaria et al., ApJ 909(2), 153 (2021). https://doi.org/10.3847/1538-4357/abddbc, 2101.07020 C. Malacaria et al., ApJ 927(2), 194 (2022a). https://doi.org/10.3847/1538-4357/ac524f, 2201.11376 C. Malacaria et al., Astron Telegram 15241, 1 (2022b) H.L. Marshall et al., ApJ 940(1), 70 (2022). https://doi.org/10.3847/1538-4357/ac98c2, 2210.03194 R.G. Martin, C.A. Tout, J.E. Pringle, MNRAS 397(3), 1563–1576 (2009). https://doi.org/10.1111/ j.1365-2966.2009.15031.x, 0905.2362

113 Accreting Strongly Magnetized Neutron Stars: X-ray Pulsars

4173

R.G. Martin, C. Nixon, P.J. Armitage, S.H. Lubow, D.J. Price, ApJLett 790(2), L34 (2014). https:// doi.org/10.1088/2041-8205/790/2/L34, 1407.5676 I.M. McHardy, I.E. Papadakis, P. Uttley, M.J. Page, K.O. Mason, MNRAS 348(3), 783–801 (2004). https://doi.org/10.1111/j.1365-2966.2004.07376.x, astro-ph/0311220 M. Mentzel, D. Berg, G. Wunner, Phys. Rev. D 50(2), 1125–1139 (1994). https://doi.org/10.1103/ PhysRevD.50.1125 P. Meszaros, High-energy radiation from magnetized neutron stars (1992) P. Meszaros, W. Nagel, ApJ 298, 147–160 (1985a). https://doi.org/10.1086/163594 P. Meszaros, W. Nagel, ApJ 299, 138–153 (1985b). https://doi.org/10.1086/163687 P. Meszaros, R. Novick, A. Szentgyorgyi, G.A. Chanan, M.C. Weisskopf, ApJ 324, 1056 (1988). https://doi.org/10.1086/165962 D. Mihalas, Stellar atmospheres (W. H. Freeman & Co., San Francisco, 1978) T. Mihara, K. Makishima, F. Nagase, ApJ 610(1), 390–401 (2004). https://doi.org/10.1086/421543 G. Miller, I. Wasserman, E.E. Salpeter, ApJ 346, 405 (1989). https://doi.org/10.1086/168020 S. Molkov, A. Lutovinov, S. Tsygankov, I. Mereminskiy, A. Mushtukov, ApJLett 883(1), L11 (2019). https://doi.org/10.3847/2041-8213/ab3e4d, 1909.09159 S. Molkov, V. Doroshenko, A. Lutovinov, S. Tsygankov, A. Santangelo, I. Mereminskiy, A. Semena, ApJLett 915(2), L27 (2021). https://doi.org/10.3847/2041-8213/ac0c15, 2106.09514 J. Mönkkönen, S.S. Tsygankov, A.A. Mushtukov, V. Doroshenko, V.F. Suleimanov, J. Poutanen, A&A 626, A106 (2019). https://doi.org/10.1051/0004-6361/201935507, 1905.05593 J. Mönkkönen, S.S. Tsygankov, A.A. Mushtukov, V. Doroshenko, V.F. Suleimanov, J. Poutanen, MNRAS 515(1), 571–580 (2022). https://doi.org/10.1093/mnras/stac1828, 2206.01502 C. Motch, M.W. Pakull, F. Grisé, R. Soria, Astronomische Nachrichten 332(4), 367 (2011). https:// doi.org/10.1002/asna.201011501, 1011.4215 D. Mukherjee, D. Bhattacharya, A. Mignone, MNRAS 430(3), 1976–1987 (2013). https://doi.org/ 10.1093/mnras/stt020, 1212.3897 P. Munar-Adrover, J.M. Paredes, M. Ribó, K. Iwasawa, V. Zabalza, J. Casares, ApJLett 786(2), L11 (2014). https://doi.org/10.1088/2041-8205/786/2/L11, 1404.0901 A.A. Mushtukov, V.F. Suleimanov, S.S. Tsygankov, J. Poutanen, MNRAS 454(3), 2539–2548 (2015a). https://doi.org/10.1093/mnras/stv2087, 1506.03600 A.A. Mushtukov, V.F. Suleimanov, S.S. Tsygankov, J. Poutanen, MNRAS 447(2), 1847–1856 (2015b). https://doi.org/10.1093/mnras/stu2484, 1409.6457 A.A. Mushtukov, S.S. Tsygankov, A.V. Serber, V.F. Suleimanov, J. Poutanen, MNRAS 454(3), 2714–2721 (2015c). https://doi.org/10.1093/mnras/stv2182, 1509.05628 A.A. Mushtukov, V.F. Suleimanov, S.S. Tsygankov, A. Ingram, MNRAS 467(1), 1202–1208 (2017). https://doi.org/10.1093/mnras/stx141, 1612.00964 A.A. Mushtukov, A. Ingram, M. van der Klis, MNRAS 474(2), 2259–2276 (2018a). https://doi. org/10.1093/mnras/stx2872, 1707.07578 A.A. Mushtukov, S.S. Tsygankov, V.F. Suleimanov, J. Poutanen, MNRAS 476(3), 2867–2873 (2018b). https://doi.org/10.1093/mnras/sty379, 1801.04810 A.A. Mushtukov, P.A. Verhagen, S.S. Tsygankov, M. van der Klis, A.A. Lutovinov, T.I. Larchenkova, MNRAS 474(4), 5425–5436 (2018c). https://doi.org/10.1093/mnras/stx2905, 1707.09822 A.A. Mushtukov, A. Ingram, M. Middleton, D.I. Nagirner, M. van der Klis, MNRAS 484(1), 687– 697 (2019a). https://doi.org/10.1093/mnras/sty3525, 1811.02049 A.A. Mushtukov, G.V. Lipunova, A. Ingram, S.S. Tsygankov, J. Mönkkönen, M. van der Klis, MNRAS 486(3), 4061–4074 (2019b). https://doi.org/10.1093/mnras/stz948, 1904.01132 A.A. Mushtukov, I.S. Ognev, D.I. Nagirner, MNRAS 485(1), L131–L135 (2019c). https://doi.org/ 10.1093/mnrasl/slz047, 1904.04604 A.A. Mushtukov, S. Portegies Zwart, S.S. Tsygankov, D.I. Nagirner, J. Poutanen, MNRAS 501(2), 2424–2429 (2021a). https://doi.org/10.1093/mnras/staa3809, 2011.09710 A.A. Mushtukov, V.F. Suleimanov, S.S. Tsygankov, S. Portegies Zwart, MNRAS 503(4), 5193– 5203 (2021b). https://doi.org/10.1093/mnras/stab811, 2006.13596 F. Nagase, Accretion-powered X-ray pulsars. PASJ 41, 1 (1989)

4174

A. Mushtukov and S. Tsygankov

W. Nagel, ApJ 251, 288 (1981a). https://doi.org/10.1086/159464 W. Nagel, ApJ 251, 278–296 (1981b). https://doi.org/10.1086/159463 R. Narayan, I. Yi, ApJ 452, 710 (1995). https://doi.org/10.1086/176343, astro-ph/9411059 R.W. Nelson, E.E. Salpeter, I. Wasserman, ApJ 418, 874 (1993). https://doi.org/10.1086/173445 O. Nishimura, ApJ 672(2), 1127–1136 (2008). https://doi.org/10.1086/523782 O. Nishimura, ApJ 781(1), 30 (2014). https://doi.org/10.1088/0004-637X/781/1/30 K. Parfrey, A. Spitkovsky, A.M. Beloborodov, ApJ 822(1), 33 (2016). https://doi.org/10.3847/ 0004-637X/822/1/33, 1507.08627 G.G. Pavlov, Y.N. Gnedin, Astrophys. Space Phys. Res. 3, 197 (1984) G.G. Pavlov, D.G. Yakovlev, Sov. J. Exp. Theor. Phys. 43, 389 (1976) K.A. Postnov, M.I. Gornostaev, D. Klochkov, E. Laplace, V.V. Lukin, N.I. Shakura, MNRAS 452(2), 1601–1611 (2015). https://doi.org/10.1093/mnras/stv1393, 1506.07082 A.Y. Potekhin, A. De Luca, J.A. Pons, Space Sci. Rev. 191(1–4), 171–206 (2015). https://doi.org/ 10.1007/s11214-014-0102-2, 1409.7666 J. Poutanen, A&A 641, A166 (2020). https://doi.org/10.1051/0004-6361/202038689, 2006.10448 J. Poutanen, A.M. Beloborodov, MNRAS 373(2), 836–844 (2006). https://doi.org/10.1111/j.13652966.2006.11088.x, astro-ph/0608663 J. Poutanen, G. Lipunova, S. Fabrika, A.G. Butkevich, P. Abolmasov, MNRAS 377(3), 1187–1194 (2007). https://doi.org/10.1111/j.1365-2966.2007.11668.x, astro-ph/0609274 J. Poutanen, A.A. Mushtukov, V.F. Suleimanov, S.S. Tsygankov, D.I. Nagirner, V. Doroshenko, A.A. Lutovinov, ApJ 777(2), 115 (2013). https://doi.org/10.1088/0004-637X/777/2/115, 1304.2633 J.E. Pringle, M.J. Rees, A&A 21, 1 (1972) D. Psaltis, D. Chakrabarty, ApJ 521(1), 332–340 (1999). https://doi.org/10.1086/307525, astroph/9809335 V. Radhakrishnan, D.J. Cooke, ApLett 3, 225 (1969) N.V. Raguzova, V.M. Lipunov, A&A 340, 85–102 (1998) S. Rappaport, P.C. Joss, R.F. Webbink, ApJ 254, 616–640 (1982). https://doi.org/10.1086/159772 P.S. Ray et al., ApJ 879(2), 130 (2019). https://doi.org/10.3847/1538-4357/ab24d8, 1811.09218 P. Reig, Astroph. Sp. Sci. 332(1), 1–29 (2011). https://doi.org/10.1007/s10509-010-0575-8, 1101.5036 M. Revnivtsev, M. Gilfanov, E. Churazov, A&A 363, 1013–1018 (2000). astro-ph/0007092 M. Revnivtsev, E. Churazov, K. Postnov, S. Tsygankov, A&A 507(3), 1211–1215 (2009). https:// doi.org/10.1051/0004-6361/200912317, 0909.2996 M.G. Revnivtsev, S.V. Molkov, M.N. Pavlinsky, MNRAS 451(4), 4253–4258 (2015). https://doi. org/10.1093/mnras/stv1263, 1506.01568 H. Riffert, P. Meszaros, ApJ 325, 207 (1988). https://doi.org/10.1086/165996 G.A. Rodríguez Castillo et al., ApJ 895(1), 60 (2020). https://doi.org/10.3847/1538-4357/ab8a44, 1906.04791 R.E. Rothschild et al., MNRAS 466(3), 2752–2779 (2017). https://doi.org/10.1093/mnras/ stw3222, 1610.08944 A. Rouco Escorial, A.S. Bak Nielsen, R. Wijnands, Y. Cavecchi, N. Degenaar, A. Patruno, MNRAS 472(2), 1802–1808 (2017). https://doi.org/10.1093/mnras/stx2111, 1704.00284 A. Salganik, S.S. Tsygankov, A.A. Lutovinov, A.A. Djupvik, D.I. Karasev, S.V. Molkov, MNRAS 514(2), 2707–2715 (2022). https://doi.org/10.1093/mnras/stac1462, 2205.12140 E.T. Scharlemann, ApJ 219, 617–628 (1978). https://doi.org/10.1086/155823 V. Sguera et al., A&A 444(1), 221–231 (2005). https://doi.org/10.1051/0004-6361:20053103, astro-ph/0509018 N. Shakura, K. Postnov, A. Kochetkova, L. Hjalmarsdotter, MNRAS 420(1), 216–236 (2012). https://doi.org/10.1111/j.1365-2966.2011.20026.x, 1110.3701 N. Shakura, K. Postnov, L. Sidoli, A. Paizis, MNRAS 442(3), 2325–2330 (2014). https://doi.org/ 10.1093/mnras/stu1027, 1405.5707 N.I. Shakura, R.A. Sunyaev, A&A 500, 33–51 (1973)

113 Accreting Strongly Magnetized Neutron Stars: X-ray Pulsars

4175

A.E. Shtykovsky, A.A. Lutovinov, V.A. Arefiev, S.V. Molkov, S.S. Tsygankov, M.G. Revnivtsev, Astron. Lett. 43(3), 175–185 (2017). https://doi.org/10.1134/S1063773717030069, 1610.08092 R.A. Siuniaev, Sov. Astron. Lett. 2, 111–114 (1976) R.A. Siuniaev, N.I. Shakura, Pisma v Astronomicheskii Zhurnal 3, 262–266 (1977) E. Sokolova-Lapa et al., A&A 651, A12 (2021). https://doi.org/10.1051/0004-6361/202040228, 2104.06802 H.C. Spruit, Origin of neutron star magnetic fields, in 40 Years of Pulsars: Millisecond Pulsars, Magnetars and More, ed. by C. Bassa, Z. Wang, A. Cumming, V.M. Kaspi. American Institute of Physics Conference Series, vol. 983 (2008), pp. 391–398. https://doi.org/10.1063/1.2900262, 0711.3650 H.C. Spruit, Accretion disks (2010). arXiv e-prints arXiv:1005.5279, 1005.5279 R. Staubert, N.I. Shakura, K. Postnov, J. Wilms, R.E. Rothschild, W. Coburn, L. Rodina, D. Klochkov, A&A 465(2), L25–L28 (2007). https://doi.org/10.1051/0004-6361:20077098, astroph/0702490 R. Staubert, D. Klochkov, J. Wilms, K. Postnov, N.I. Shakura, R.E. Rothschild, F. Fürst, F.A. Harrison, A&A 572, A119 (2014). https://doi.org/10.1051/0004-6361/201424203, 1410.3647 R. Staubert, D. Klochkov, F. Fürst, J. Wilms, R.E. Rothschild, F. Harrison, A&A 606, L13 (2017). https://doi.org/10.1051/0004-6361/201731927, 1710.05150 R. Staubert et al., A&A 622, A61 (2019). https://doi.org/10.1051/0004-6361/201834479, 1812.03461 J.M. Stone, J.F. Hawley, C.F. Gammie, S.A. Balbus, ApJ 463, 656 (1996). https://doi.org/10.1086/ 177280 V. Suleimanov, F. Meyer, E. Meyer-Hofmeister, A&A 350, 63–72 (1999) V.F. Suleimanov, G.V. Lipunova, N.I. Shakura, Astron. Rep. 51(7), 549–562 (2007). https://doi. org/10.1134/S1063772907070049 P. Thalhammer et al., A&A 656, A105 (2021). https://doi.org/10.1051/0004-6361/202140582, 2109.14565 C. Thompson, R.C. Duncan, ApJ 408, 194 (1993). https://doi.org/10.1086/172580 C.A. Tout, J.E. Pringle, MNRAS 259, 604–612 (1992). https://doi.org/10.1093/mnras/259.4.604 J. Truemper, W. Pietsch, C. Reppin, W. Voges, R. Staubert, E. Kendziorra, ApJLett 219, L105– L110 (1978). https://doi.org/10.1086/182617 S. Tsygankov, A. Lutovinov, (2010). arXiv e-prints arXiv:1002.1898, 1002.1898 S.S. Tsygankov, A.A. Lutovinov, E.M. Churazov, R.A. Sunyaev, MNRAS 371(1), 19–28 (2006). https://doi.org/10.1111/j.1365-2966.2006.10610.x, astro-ph/0511237 S.S. Tsygankov, A.A. Lutovinov, E.M. Churazov, R.A. Sunyaev, Astron. Lett. 33(6), 368–384 (2007). https://doi.org/10.1134/S1063773707060023, 0704.2874 S.S. Tsygankov, A.A. Lutovinov, A.V. Serber, MNRAS 401(3), 1628–1635 (2010). https://doi.org/ 10.1111/j.1365-2966.2009.15791.x, 0909.5379 S.S. Tsygankov, A.A. Lutovinov, V. Doroshenko, A.A. Mushtukov, V. Suleimanov, J. Poutanen, A&A 593, A16 (2016). https://doi.org/10.1051/0004-6361/201628236, 1602.03177 S.S. Tsygankov, V. Doroshenko, A.A. Lutovinov, A.A. Mushtukov, J. Poutanen, A&A 605, A39 (2017a). https://doi.org/10.1051/0004-6361/201730553, 1702.00966 S.S. Tsygankov, A.A. Mushtukov, V.F. Suleimanov, V. Doroshenko, P.K. Abolmasov, A.A. Lutovinov, J. Poutanen, A&A 608, A17 (2017b). https://doi.org/10.1051/0004-6361/201630248, 1703.04528 S.S. Tsygankov, R. Wijnands, A.A. Lutovinov, N. Degenaar, J. Poutanen, MNRAS 470(1), 126– 141 (2017c). https://doi.org/10.1093/mnras/stx1255, 1703.04634 S.S. Tsygankov, V. Doroshenko, A.A. Mushtukov, V.F. Suleimanov, A.A. Lutovinov, J. Poutanen, MNRAS 487(1), L30–L34 (2019a). https://doi.org/10.1093/mnrasl/slz079, 1905.09496 S.S. Tsygankov, A. Rouco Escorial, V.F. Suleimanov, A.A. Mushtukov, V. Doroshenko, A.A. Lutovinov, R. Wijnands, J. Poutanen, MNRAS 483(1), L144–L148 (2019b). https://doi.org/10. 1093/mnrasl/sly236, 1810.13307 S.S. Tsygankov et al., ApJ 909(2), 154 (2021). https://doi.org/10.3847/1538-4357/abddbd, 2101.07030

4176

A. Mushtukov and S. Tsygankov

S.S. Tsygankov et al., ApJLett 941(1), L14 (2022a). https://doi.org/10.3847/2041-8213/aca486, 2209.02447 S.S. Tsygankov et al., A&A 661, A45 (2022b). https://doi.org/10.1051/0004-6361/202141821, 2108.06365 G.V. Ustyugova, A.V. Koldoba, M.M. Romanova, R.V.E. Lovelace, ApJ 646(1), 304–318 (2006). https://doi.org/10.1086/503379, astro-ph/0603249 J. van den Eijnden, N. Degenaar, T.D. Russell, J.C.A. Miller-Jones, R. Wijnands, J.M. Miller, A.L. King, M.P. Rupen, MNRAS 473(1), L141–L145 (2018a). https://doi.org/10.1093/mnrasl/ slx180, 1711.01971 J. van den Eijnden, N. Degenaar, T.D. Russell, R. Wijnands, J.C.A. Miller-Jones, G.R. Sivakoff, J.V. Hernández Santisteban, Nature 562(7726), 233–235 (2018b). https://doi.org/10.1038/ s41586-018-0524-1, 1809.10204 G. Vasilopoulos, M. Petropoulou, F. Koliopanos, P.S. Ray, C.B. Bailyn, F. Haberl, K. Gendreau, MNRAS 488(4), 5225–5231 (2019). https://doi.org/10.1093/mnras/stz2045, 1905.03740 V. Vybornov, D. Klochkov, M. Gornostaev, K. Postnov, E. Sokolova-Lapa, R. Staubert, K. Pottschmidt, A. Santangelo, A&A 601, A126 (2017). https://doi.org/10.1051/0004-6361/ 201630275, 1702.06361 R. Walter, J. Zurita Heras, A&A 476(1), 335–340 (2007). https://doi.org/10.1051/0004-6361: 20078353, 0710.2542 R. Walter, A.A. Lutovinov, E. Bozzo, S.S. Tsygankov, A&ARv 23, 2 (2015). https://doi.org/10. 1007/s00159-015-0082-6, 1505.03651 D.J. Walton et al., ApJLett 857(1), L3 (2018a). https://doi.org/10.3847/2041-8213/aabadc, 1803.07571 D.J. Walton et al., ApJ 856(2), 128 (2018b). https://doi.org/10.3847/1538-4357/aab610, 1803.04424 W. Wang, MNRAS 440(2), 1114–1124 (2014). https://doi.org/10.1093/mnras/stu210, 1401.7421 Y.M. Wang, ApJLett 449, L153 (1995). https://doi.org/10.1086/309649 Y.M. Wang, J. Frank, A&A 93, 255–268 (1981) M.C. Weisskopf et al., J. Astron. Telesc. Instrum. Syst. 8(2), 026002 (2022). https://doi.org/10. 1117/1.JATIS.8.2.026002, 2112.01269 R. Wijnands, N. Degenaar, MNRAS 463(1), L46–L50 (2016). https://doi.org/10.1093/mnrasl/ slw096, 1602.02275 F.P. Wilkin, ApJLett 459, L31 (1996). https://doi.org/10.1086/309939 G.C. Xiao et al., J. High Energy Astrophys. 23, 29–32 (2019). https://doi.org/10.1016/j.jheap.2019. 09.002, 1910.02393 W. Yang, W. Wang, Q. Liu, X. Chen, H.J. Wu, P.F. Tian, J.S. Chen, MNRAS 519(4), 5402–5409 (2023). https://doi.org/10.1093/mnras/stad048 Y.B. Zel’dovich, N.I. Shakura, Sov. Ast. 13, 175 (1969) X. Zheng, J. Liu, L. Gou, MNRAS 491(4), 4802–4806 (2020). https://doi.org/10.1093/mnras/ stz3327, 1911.02284

Fundamental Physics with Neutron Stars

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Joonas Nättilä and Jari J. E. Kajava

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Formation of Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . First Observation of a Neutron Star . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theoretical Arguments for the Existence of Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . Rotating Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic Fields of Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gamma Ray Blasts from the Past . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Many Observational Faces of Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratories of Gravitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Space-Time Deformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Rotating Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Radiation from the Star’s Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pulse Profile Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gravitational Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Interpretation of Gravitational Waveforms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratories of Nuclear Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dense Matter Inside Compact Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Degeneracy Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermal-Like Emission from Isolated Neutron Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermonuclear X-ray Bursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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J. Nättilä () Center for Computational Astrophysics, Flatiron Institute, New York, NY, USA Physics Department and Columbia Astrophysics Laboratory, Columbia University, New York, NY, USA e-mail: [email protected] J. J. E. Kajava Serco for ESA, ESA/ESAC, Madrid, Spain Department of Physics and Astronomy, University of Turku, Turku, Finland e-mail: [email protected]; [email protected]

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Laboratories of Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spindown Power of Magnetized Balls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Charges in the Magnetosphere . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Force-Free and Magnetohydrodynamic Solutions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Evolving Magnetic Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mysterious Pulsar Radio Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pulsar Wind Nebulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Laboratories of Plasma Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Standard Quantum Electrodynamic Interactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Pair Cascades . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vacuum Birefringence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Superfluid and Superconducting Interiors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Gliches and Quakes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Giant Bursts and Fast Radio Bursts from Magnetars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Extreme Particles: Cosmic Rays, Neutrinos, and More . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

Neutron stars are rich laboratories of multiple branches of modern physics. These include gravitational physics, nuclear and particle physics, (quantum) electrodynamics, and plasma astrophysics. In this chapter, we present the pioneering theoretical studies and the pivotal historical observations on which our understanding of neutron stars is based on. Then, we discuss the usage of neutron stars as probes of fundamental theories of physics. Keywords

Neutron stars · Pulsars · Magnetars · Mergers · Dense matter · Gravitational physics · Particle physics · Nuclear physics · Electrodynamics · Plasma physics

Introduction Neutron stars are extremely dense, rapidly rotating, superfluid magnets. They shine to us across a broad electromagnetic spectrum from low-frequency radio bands to high-energy X-rays and gamma rays. Some of them produce continuous radiation, some show pulsations, and some explode in flares. This activity is powered by their huge gravitational, magnetic, rotational, and chemical energy. These enormous reservoirs of energy, in turn, drive exotic phenomena encompassing many fields of modern physics, from the quantum realm to space-time-deforming general relativity. Most of the observed phenomena from neutron stars are so extreme that they cannot be studied in contemporary terrestrial laboratories. This makes neutron stars the cosmic laboratories of extreme physics.

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A canonical neutron star has a radius of R ≈ 12 km and a mass of M ≈ 1.5 M⊙ ; the observed masses range from about 1.1 to 2.1 M⊙ , and theoretically supported radii range from about 10 to 15 km. This makes them extremely dense astrophysical objects capable of significantly distorting the local space-time – hence, general relativity is needed when describing the physical laws around them. Neutron stars are also observed to rotate with spin periods ranging from P ∼ 0.001 to 10 s. When such a tightly compressed object is rapidly rotating, it stores massive amounts of angular momentum that will result in additional “twisting” of the space-time “fabric,” in addition to the more usual curving effect caused by the concentrated mass. The first section of this chapter describes the gravitational physics of neutron stars. The large density means that the matter inside neutron stars is under tremendous pressure. The mean density inside the star, ρ¯ ∼ 1015 g cm−3 , is comparable to the density inside the atomic nuclei. The matter is compressed into such a small volume that quantum mechanical effects define its behavior. How the matter responds to this squeezing, as the particles try to counter the compressing force, is encapsulated in the – still unknown – equation of state (EOS) of the cold, dense matter. The nuclear and particle physics of neutron stars are described in the second section of this chapter. Neutron stars have strong magnetic fields, ranging from B ∼ 108 to 1015 G. As the star spins, the topology of this dynamic magnetosphere changes. The physics of the magnetosphere is governed by both electromagnetism, describing the dynamical evolution of the electric and magnetic fields, and quantum electrodynamics (QED), describing the coupling of the electromagnetic fields and particles. The electrodynamics, QED phenomena, and plasma physics of neutron stars are discussed in the third and fourth sections of this chapter.

Formation of Neutron Stars The idea of stars composed of neutrons originates from Lev Landau (Landau 1932; Yakovlev et al. 2013); he was the first to speculate on the possibility of squeezing the matter inside regular stars so tightly that quantum effects would start to dominate: “. . . the density of the matter becomes so great that atomic nuclei come in close contact, forming one gigantic nucleus.” Interestingly, this idea was coined even before the existence of neutrons was known. (Existence of electrically neutral particles with a mass mn ≈ mp ≈ 5 × 10−25 g was proven by Chadwick in 1932a, 1932b.) Similar ideas were later proposed also by Baade and Zwicky (1934) – they were even bold enough to suggest that neutron stars might form in supernovae. This turned out to be exactly right! Neutron stars are now known to be born from a collapse of a main sequence star, slightly more massive than our own Sun, with a mass M⋆ ∼ 10 M⊙ , where M⊙ ≈ 1.99 × 1033 g (Shapiro and Teukolsky 1983). Such a star has a radius of approximately 5× that of our own Sun, R⋆ ∼ 5R⊙ where R⊙ ≈ 6.96 × 1010 cm. (In reality, the massive star evolves off the main sequence before the supernova

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explosion and can expand in its radius. However, the discussed values are good “first guesses” to perform the order-of-magnitude estimates presented in this section.) Then, the resulting (very approximate) estimate for the mean density of the matter 1 inside the progenitor star is ρ⋆ ≈ 0.1 g cm−3 , roughly 10 of the density of liquid water. Such stars fuse lighter elements into heavier metals, all the way up to iron. Eventually, the heavy iron elements accumulate and sink to the bottom of the gravitational potential, forming an iron core for the star. This core has a theoretically known maximum mass of about 1.4 M⊙ . Once this limit is exceeded, the core collapses, and the outer layers explode as a bright supernova. The remnant core consists of roughly M/mp ∼ M⊙ /mp ∼ 1057 atoms, where mp ≈ 1.67 × 10−24 g is the mass of a proton. Suppose those atoms shed their electrons and form a giant blob of neutrons. In that case, the resulting remnant will 1 have a characteristic size ℓ ∼ (1057 ) 3 rn ∼ 10 km, where rn ∼ 10−13 cm is the approximate size of an atomic nucleon. A compact object with a mass ∼ M⊙ and radius ∼10 km is hence left behind – a neutron star! Even though these values are approximate and based on very naive conservation laws, they are not far from the actual observed values for neutron stars; here we adopt the canonical values of a neutron star mass MNS = 1.4 M⊙ and radius RNS = 12 km. A canonical neutron star has an extraordinarily high mean density, ρ¯ ∼ 3 ∼ 1015 g cm−3 , and surface gravity, g ∼ 1014 cm s−2 . The central MNS /RNS density of such an object, ρc ∼ ρ, ¯ far exceeds the typical density of a nucleon, ρn ∼ mp /rn3 ∼ 1014 g cm−3 ≪ ρc . This implies that the matter is compressed so densely that there is no empty space between the atomic core and the electrons; instead, individual atomic nuclei are packed side by side, forming a macroscopic “quantum ball” of neutrons.

First Observation of a Neutron Star While the theoretical existence of neutron stars was speculated already in the 1920s, conclusive observational evidence came only at the end of the 1960s. Neutron stars were first detected using a radio antenna in the pastures of Cambridge (Hewish et al. 1968). The primitive antennas were originally designed for monitoring the radio emission from quasars; they were, however, sensitive enough to detect all kinds of human-made noise signals (arc welders, sparking thermostats, etc.) Among many such noise signals, Jocelyn Bell, a student of Tony Hewis, noticed a signal that did not seem to have a direct connection to anything happening on Earth; instead, the signal – that was sometimes on, sometimes off – seemed to originate from a specific location in the sky. The mystery deepened when they were able to resolve the signal, using a high-speed recorder, into a regular set of pulses with a stable period of P ≈ 1.337 s. The source was initially (and jokingly?) named LGM-1, standing for Little Green Men, since they did not know of any astrophysical engine capable of powering this periodic extraterrestrial signal.

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By 1968, the radio observers had detected multiple pulsing signals with periods varying from P ≈ 0.25 to 3.3 s. The sub-structure of the pulses themselves could be even shorter, Δt < 0.01 s. The sources were also found to be extremely stable. There was, however, a small systematic decrease detected in many of them, on a timescale of P /P˙ ∼ 103 to 106 yr, where P˙ ≡ dP /dt is the so-called period derivative, quantifying the change of the period. (Such highly accurate measurements were possible because the signals were very stable and could be accumulated over long time intervals of many years.)

Theoretical Arguments for the Existence of Neutron Stars So what can we conclude from these observational facts? The following reasoning was laid out by an American astrophysicist Thomas Gold (1968). Firstly, the short duration of the pulses implies a tiny object; light crosses a distance of ∼3000 km in a duration of the sub-pulse, Δt ∼ 0.01 s. This means that the emitting region must be smaller than that. In practice, only black holes, neutron stars, or white dwarfs are small enough astrophysical objects so that their radius R < 3000 km. This was the first clue: the culprit has to be some type of compact object. Secondly, how to produce a stable pulsation from such sources? The usual suspects that could introduce such highly periodic signals include rotation, vibration, or orbital motions. Orbital motions are, however, ruled out because the observed periods of the signal were not increasing (corresponding to inspiral) but were found to be decreasing (i.e., negative period derivatives). In addition, a binary system with an orbital period of Porb ∼ 1 s would merge in a few years as it loses angular momentum via gravitational radiation. Therefore, orbital motions could not be the source of the pulsations. The shortest timescale out of the proposed emission mechanisms results from vibrations; here, the gravity of the object√is a natural candidate for the restoring force. The timescale for this is t ∼ 2π/ Gρ, which, for the densities of white dwarfs, ρ ∼ 108 g cm−3 , is ∼1 s, borderline too slow to explain the fastest observed pulse periods. Conversely, for neutron stars, corresponding to characteristic densities ρ ∼ 1014 g cm−3 , the vibration timescale would be milliseconds, borderline too fast to explain the slowest observed pulses. Black holes do not have a surface capable of emitting vibrations, so they do not need to be considered for this mechanism. These conflicting timescales were used to argue against vibration as a source of the pulsations. Furthermore, it is also quite unlikely that any surface vibration could go on for years and years without damping. This left the contemporary researchers only with rotation. A maximum rotation rate that a star can support  before being ruptured will be close to its Keplerian frequency, fK = (1/2π ) GM/R 3 ; it is fK ∼ 1700 Hz for a neutron star and fK ∼ 0.1 Hz for a white dwarf (with MWD ∼ M⊙ and RWD ∼ 7 × 108 cm). This, in the end, helped rule out white dwarfs from the possible list of sources because they

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would have a hard time sticking together under such a rapid rotation. Any surface emission from rotating black holes was also naturally ruled out because black holes do not have a surface. This reasoning led contemporary scientists to believe that the Little Green Men observed in the Cambridge pasture originated from rotating neutron stars.

Rotating Neutron Stars So, what rotation rates can we expect neutron stars to have? The magnitude of the spin can be estimated from the conservation of angular momentum during the formation of the proto-neutron star. Our own Sun rotates around itself with a period of P⊙ ∼ 25.5 days or ν⊙ ≈ 4.5 × 10−7 Hz. If such a star is compressed into a neutron star, and the angular momentum is conserved during the process, (A realistic formation of a proto-neutron star in a supernova collapse might not conserve angular momentum; for example, suppose there is an off-axis stream of material falling toward the center. In that case, it can result in a seeming over-accumulation of net angular momentum in the core parts. Hence, estimates of the initial angular momentum of a proto-neutron star are very uncertain.) the new spin would be ν ∼ (R⊙ /RN S )2 ν⊙ ∼ 2000 Hz. This value is a bit high, but it does get us to the right ballpark. Observed spin frequencies of neutron stars vary from ∼0.01 Hz up to ∼700 Hz (Caleb et al. 2022). Some X-ray pulsars have been argued to rotate as slowly as ∼10−5 Hz (Sidoli et al. 2017). The spin period of neutron stars is not constant; even the first pioneering observations of pulsars could detect a slow downward drift in the spin period. This spindown of pulsars is slow and continuous with P˙ /P ∼ 10−12 s s−1 , and it results from magnetic dipole losses as the magnetosphere rotates and generates electromagnetic radiation which, in turn, carries a fraction of the star’s angular momentum away. This kind of spindown is, therefore, naturally expected for isolated pulsars. In addition, many pulsars show abrupt spindown events, called glitches, where the spin suddenly changes in seconds. There are also observations of neutron stars in binary systems – in fact, a big fraction of stars in any galaxy is expected to reside in systems with multiple stars; exotic multiples up to seven stars are known (Tokovinin 2018). These binary systems are evolving, and the stars commonly exchange mass. When the mass is transferred onto the neutron star, it can be spun up: as the in-falling material streams in, hits the star off center, and exerts a torque, it can transfer some of the binary system’s angular momentum into the central object. Alternatively, the torque can be transferred to the star via the magnetic field lines that are attached to the inner disk. This angular momentum transfer generates a sub-population of neutron stars called “recycled millisecond pulsars” – neutron stars spun up by accretion to spin periods of up to P ∼ 0.001 s. This also highlights the importance of understanding the surroundings of neutron stars when trying to explain their physics. In many cases, the evolution and physics of the neutron stars in binary systems are intimately influenced by the companion star.

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Magnetic Fields of Neutron Stars The remaining fundamental quantity of a neutron star is its magnetic field. The neutron star’s magnetic field strength can be estimated from the conservation of magnetic flux during its birth (Woltjer 1964). A typical progenitor of a neutron star has a magnetic field of B⊙ ∼ 1 G; for comparison, a typical fridge magnet has a magnetic field of ∼10 G. The stellar magnetic fields are powered by dynamo processes in which the differential rotation and convective circulations inside the star amplify the magnetic field. The field can be highly tangled and irregular due to the turbulent motions of the stellar interiors. When such a star collapses into a neutron star, the dynamo process is thought to halt and the internal magnetic field to be squeezed into a smaller volume. The resulting strength of the new field can be estimated from the conservation of the  magnetic flux through the surface (ΦB = S B · dS, where dS is an infinitesimal area element); alternatively, we can think that the number of magnetic field lines penetrating the star’s surface is conserved. Thus, by conservation of magnetic flux, we end up with BNS ∼ B⊙ (R⊙ /RNS )2 ∼ 1010 G. The resulting field is enormous; the largest continuously operating human-made magnets on Earth can sustain “only” ∼106 G. Observed magnetic fields of regular neutron stars range from 108 to 1012 G. Some neutron stars are observed to house an even stronger magnetic field of ∼1014 to 1016 G – these are known as magnetars (Thompson and Duncan 1995). The atypical magnetic field is thought to originate from a dynamo process that occurs during the progenitor star’s collapse, amplifying the star’s regular magnetic field by an unknown factor of ∼100 to 1000 to super-high strengths. Additionally, these magnetars are thought to be so young, t ≪ 106 yr, that the enormous field has not yet had time to (resistively) decay away. These magnetars were discovered because of the most violent astrophysical events ever observed by humankind.

Gamma Ray Blasts from the Past At 10:51 am EST on March 5th, 1979, two unmanned Soviet space probes, Venera 11 and Venera 12, suddenly became overloaded with an unprecedented gamma ray shower. (See https://solomon.as.utexas.edu/magnetar.html for more details.) The gamma rays first hit Venera 11 and then, 5 seconds later, Venera 12. The onboard detectors observed a sudden jump from a regular background gamma ray count rates of ∼100 up to ∼40,000 counts per second and then a level entirely off the scale, all during a Δt ∼ m s. After this, 11 seconds later, the gamma rays reached an American space probe Helios 2 orbiting the Sun, also knocking it out. None of the detectors were designed to withstand such intense emission, which saturated the internal photon counters. On that day, an unprecedented gamma ray wavefront continued to sweep through our solar system. After the Helios 2 probe, it reached the planet Venus, where the Pioneer Venus spacecraft detected a burst of gamma rays and quickly saturated. After 7 more seconds, the wavefront reached Earth and was detected by Vela satellite

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and Soviet Prognoz 7, again knocking their internal detectors out. Even the Einstein X-ray observatory, orbiting Earth, detected a strong signal, even though it was not pointing in the direction of the blast – the gamma rays were diffusing through its back metal shield and still overloading the detector. A similar thing happened to the international Sun-Earth Explorer (ISEE) that was pointing in another direction, but the gamma rays penetrating through its solid metal body were still energetic enough to ramp up the detector to the maximum. Fourteen and half hours later, another fainter burst arrived from the same spot, lasting 1.5 s. Then, a month later, on April 5th and again on April 24th, two more gamma ray bursts were detected. Humankind was registering its first giant flares from what became known as soft gamma ray repeaters. Tracking of the March 5th wavefront that swept through our solar system enabled contemporary researchers to pinpoint the origin of the blast to a nearby supernova remnant, SNR N49. However, this supernova remnant was not even in our galaxy but ≈50 kpc away in one of our satellite galaxies, Large Magellanic Cloud. The intense blast had traveled almost 160,000 years to us and was still powerful enough to knock out our space-borne detectors. The nature of the soft gamma ray repeaters and these giant flares remained a mystery for years as no plausible energy source was established to explain the production of the immense gamma rays observed. Many years later, Robert Duncan and Chris Thompson, both at Princeton University, started investigating the implications of hot and messy proto-neutron stars right after they were born in supernova explosions (Duncan and Thompson 1992). Recent simulations seemed to indicate that the dense fluid in the core had strong convective motions that helped to carry the heat out from the hot remnant. The ultra-dense matter at the interior would also carry electric currents; hence, a dynamo process similar to Earth’s core could, in theory, be possible. If the neutron star would collapse fast enough, rotate rapidly, and have strong convective motions, it could house a magnetic dynamo inside of it, which could amplify any existing magnetic field by twisting and folding it to anywhere from 10 to 1000 times of its original strength. Therefore, if typical pulsars with B ∼ 1012 G were the outcome of a failed dynamo, what would happen if the dynamo succeeded? They hypothesized that a successful dynamo process would result in a neutron star with an enormous magnetic field up to B ∼ 1016 G field. These monsters they, later on, dubbed “magnetars.” The first observational implication of such a field would be that if the star’s internal stresses twisted and shook the magnetosphere, it could exhibit spectacular flares similar to our own Sun. Therefore, in the case of a magnetar, the flare could turn a fraction of that immense magnetic field into radiation and, in theory, power intense blasts of gamma rays with luminosities L  1043 erg s−1 , capable of explaining the observed giant flares saturating our X-ray and gamma ray detectors. Eventually, this became the accepted explanation for the giant flares, rendering magnetars the kings of the magnetic fields in the known Universe.

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Many Observational Faces of Neutron Stars As we have seen, neutron stars have multiple observational “faces.” We have detected both isolated neutron stars and neutron stars in binary systems. The types of companion stars in the binary systems vary from low-mass stars to other neutron stars (or even black holes). Some neutron stars are powered by rotation (pulsars) and some only by their internal heat (e.g., central compact objects found in supernova remnants). There is a distinct dichotomy in the observed spin distribution: regular pulsars, identified typically as relatively young neutron stars, are slowly spinning (P ∼ 1 s), whereas older neutron stars in binary systems have been spun up by accretion, giving rise to what we know as recycled millisecond pulsars. These recycled millisecond pulsars can be further divided into rotation-powered (i.e., radio millisecond pulsars, thought to operate similarly to regular pulsars but to spin faster) and accretionpowered (i.e., pulsating on X-ray frequencies due to the in-falling material that is channeled to the magnetic poles, creating hot spots onto the surface) sources. A few stars, known as transitional millisecond pulsars, are observed to transition between these two states. Some of the rotation-powered millisecond pulsars are also identified as “spiders” (named so because these stars are acting nasty on their companion stars). Spiders generally have irregular radio eclipses due to intra-binary material driven off the donor by a pulsar wind. They can be further divided into black widows (characterized by very low-mass companions of Mc < 0.06 M⊙ ) and redbacks (characterized by hydrogen-rich companions of Mc  0.1 M⊙ ). Various classes of neutron stars and their observational phenomena are listed in Table 1.

Laboratories of Gravitation The extreme density of the matter that is concentrated inside neutron stars makes them ideal laboratories of gravitation at the extreme limit because they can strongly deform the space-time metric (Misner et al. 1973; Shapiro and Teukolsky 1983; Paschalidis and Stergioulas 2017): the high compactness of the star will curve the space-time, whereas the rapid rotation can twist it. These effects create complex space-time metric deformations, which modify the visual appearance of neutron stars. Detailed modeling of these effects allows us to estimate the radius and mass of neutron stars from observations. Another frontier in the gravitational physics of neutron stars is the gravitational wave observations from merging neutron star binaries (Baiotti 2019). Modeling these systems relies on understanding and exploiting the dynamical, time-dependent side of gravity: as the coalescing, space-time-deforming neutron stars merge, they will simultaneously vibrate space-time itself. The resulting gravitational waves can

Pulsating radio emission, pulsating X-rays, gamma ray emission SGRs: hard X-ray flares, giant bursts. AXPs: persistent and pulsating X-ray emission, transient radio emission. Additionally: fast radio bursts Type I thermonuclear X-ray bursts, burst oscillations

Millisecond-period radio pulsations, X-ray, and gamma ray emission X-ray pulsations. Sometimes also thermonuclear bursts X-ray pulsations, X-ray flaring, transient optical emission X-ray emission, radio emission, optical measurements of the companion X-ray emission, radio emission, optical measurements of the companion

3320b 30c

118d

472e

38e

Magnetars

22e

18e 3f

Constant thermal-like soft X-ray emission

≈10a

Very young neutron stars with extremely strong magnetic fields. Divided into soft gamma repeaters (SGRs) and anomalous X-ray pulsars (AXPs) Low-mass X-ray binary systems (Mc  M⊙ ) Bursters Accreting neutron stars, which depict thermonuclear X-ray bursts Recycled millisecond pulsars RMSPs Rotation-powered millisecond pulsars. Like regular pulsars but spun up by angular momentum gain from the accretion AMSP Accretion-powered millisecond pulsars TrMSPs Transitional millisecond pulsars. MSPs transitioning between accretion-powered and rotation-powered states Spider binaries Black widows RMSPs with irregular radio pulsations. Very low companion masses of Mc < 0.06 M⊙ Redbacks RMSPs with irregular radio pulsations. Hydrogen-rich companion with Mc  0.1 M⊙

Observed phenomena

#

Class Description Isolated neutron stars CCOs Weakly magnetized young neutron stars in centers of supernova remnants Pulsars Spinning, magnetized, young neutron stars

Table 1 Different observational classes of neutron stars

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Accreting neutron stars with high-mass (Mc  10 M⊙ ) companions

≈294i

33 + 28h

Mushtukov and Tsygankov (2022) 4g

Broadband emission from radio to X-rays and gamma rays. Cosmic rays Multi-band electromagnetic emission, cosmic rays

precursor emission (?), gravitational waves, short gamma ray bursts, kilonova (seen in IR, optical, UV)

constant X-ray emission, X-ray pulsations

Notes: a http://www.iasf-milano.inaf.it/~deluca/cco/main.htm (list of observed CCOs) b https://www.atnf.csiro.au/research/pulsar/psrcat/ (pulsars catalog; (Manchester et al. 2005)) c http://www.physics.mcgill.ca/~pulsar/magnetar/main.html (list of observed magnetars) d https://personal.sron.nl/~jeanz/bursterlist.html (list of observed type-I bursters) e https://blacksidus.com/millisecond-pulsar-catalogue/ (millisecond pulsar catalog) f Patruno et al. 2022 (Papitto and de Martino 2022) g GW170817, GW190425, GW200105, GW200115 h PWN + PWN w/o coinciding pulsar http://www.physics.mcgill.ca/~pulsar/pwncat.html (PWN catalog; (Kaspi et al. 2006)) i https://www.mrao.cam.ac.uk/surveys/snrs/snrs.data.html (list of SNRs; (Green 2019))

Merging Coalescing binary systems composed of a neutron star and compact binaries another compact object (NS-WD, NS-NS, or NS-BH). These systems can also be observed when they coalesce and merge Environments PWNs Pulsar wind nebulae. The region inside a supernova remnant powered by a wind from a central pulsar SNRs Supernova remnants. Large-scale structures that are the result of supernova explosions. The region is bounded by an expanding shock wave

HMXBs

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then be detected and compared to general relativistic hydrodynamic simulations to constrain the properties of the neutron star matter. In practice, this allows measuring the tidal deformability of the ultra-dense matter of the coalescing neutron stars.

Space-Time Deformations The high density of the neutron star leads to strong space-time distortions. The exterior space-time metric of a static, non-rotating spherical object is given by the Schwarzschild metric (Misner et al. 1973) (We follow the Misner et al. 1973 sign convention and use a metric signature of (−, +, +, +).), ds 2 = −(1 − u)dt 2 +

dr 2 + r 2 dθ 2 + r 2 sin2 θ dφ 2 , 1−u

(1)

where t is the coordinate time, r is the radial coordinate (defined so that the area at a time fixed time is 4π r 2 ), θ is the latitudinal angle, φ is the longitudinal angle, and u is the compactness parameter, u≡

2GMNS RS , = RNS RNS c2

(2)

G is the gravitational constant, and RS ≈ 2.95(M/ M⊙ ) km is the Schwarzschild radius.(Sometimes it can be more convenient to use the isotropic Schwarzschild metric of the form 2

ds = −



1−

1+

u¯ 2 u¯ 2

2

  u¯ 4 dt + 1 + (d¯r 2 + r¯ 2 (dθ 2 + sin2 θ dφ 2 )), 2 2

(3)

where r¯ is the isotropic radial coordinate and u¯ ≡ M/¯r is the isotropic compactness. Surfaces of constant time in this metric are conformally flat; therefore, all the angles are represented without distortion. However, in this case, the measured distances depend on the location. See Nättilä and Pihajoki 2018.) A neutron star is so compact that the corresponding Schwarzschild radius, RS ≈ 4.1 km, is slightly smaller than the star’s physical radius, RNS /RS ≈ 3. Hence, the star is on the brink of collapsing into a black hole. The neutron star compactness parameter, u, measures the severity of space-time distortions. Its value is somewhere between u ≈ 0.3 − 0.5, leading to strong dilation √ effects of the coordinate time t (∝ 1 − u ≈ 0.8) and stretching of the radial √ coordinate (∝ 1/ 1 − u ≈ 1.2) of the space-time close to the star’s √ surface. Escape velocity from on top of such an object is very large, vesc = 2GMNS /RNS ∼ 1.93 × 1010 cm s−1 , and is comparable to the speed of light, ∼c/2.

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Rotating Stars Rotation of the compact star, and hence the large angular momentum, will lead to additional shear-like distortions of the space-time metric (Paschalidis and Stergioulas 2017). In this case, we need to specify the exact latitude where the effect is studied; a typical choice is an equator with the corresponding equatorial radius Re , defined such that the circumference of a star (using the Schwarzschild metric radial coordinate) is 4π Re , as measured in the local static frame. The radius at the pole is smaller, Rp < Re . For a star rotating with an angular velocity Ω, the moment of inertia is INS ∼ 1045 g cm2 . Angular momentum is then J = I Ω. The dimensionless angular velocity is Ω Ω¯ ≡ = ΩK



Ω 2 Re3 , GMNS

(4)

 where the Newtonian mass shedding limit (Kepler limit) is ΩK = GM/Re3 . Observed neutron stars have Ω¯ ∼ 0.01–0.1 resulting in strong rotational space-time effects. Rotation can be incorporated into the space-time metric by expanding around the ¯ The first-order expansion corresponds formally to the Kerr-like small parameter Ω. metric, where an extra angular velocity term of a local inertial frame appears. This is known as the frame-dragging effect, where the space-time is rotating together with the star (i.e., in practice, velocity ν → (ν − νfd ), where νfd is the frame-dragging velocity). Second-order expansion is formally related to Hartle-Thorne-like metric (Hartle and Thorne 1968), which, in addition to the frame-dragging effects, has (two) quadrupole moments entering into the metric description(These are the multipole moments of the energy density and pressure. Their value depends on the coordinate system, whereas a single coordinate-invariant quadrupole moment can be obtained as a combination of the two (Pappas and Apostolatos 2012). ) (Braje et al. 2000; Cadeau et al. 2007; Bauböck et al. 2013; AlGendy and Morsink 2014; Nättilä and Pihajoki 2018). The rotation will also modify the actual shape of the star, making it oblate – the rotating star develops a bulge on the equator. The shape is numerically found to be close to an oblate spheroid (Morsink et al. 2007; AlGendy and Morsink 2014; Nättilä and Pihajoki 2018; Suleimanov et al. 2020),

R(θ ) ≈ Re 1 −



Ω Ω¯

2

2



(0.788 − 2.06u) cos θ ,

(5)

where R(θ ) is the radius at a colatitude θ (angle from the pole toward the equator).

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Radiation from the Star’s Surface The strong stretching of the metric in the radial direction modifies the apparent visual look of neutron stars for distant observers. The most prominent effect is the gravitational light bending around the star that increases the apparent radius (that we would measure by looking at the star from a distance) to be R R∞ = √ . 1−u

(6)

Similarly, the dilation of the time component modifies the energy of the emanating photons. This effect, gravitational redshift, is also connected to u and is given as 1 . 1+z= √ 1−u

(7)

It is a measure of how much, for example, the frequency changes, νf /νi = (1 + z)−1 (where νf is the observed and νi initial photon frequency), as a photon climbs out from the gravitational well created by the neutron star. The typical effect is a redshift, νi > νf , where the frequency is reduced during the climb. The photon energy is also modified by the Doppler-like boosting factor, δ=

1 − β2 , 1 − β cos ζ 

(8)

where RΩ β(θ ) = √ sin θ, c 1−u

(9)

is the surface velocity of the rotating star and ζ is the angle between the photon momentum and the surface velocity vector, β = β(− sin φ, cos(φ), 0) at the emission point. The Doppler boosting of the radiation can lead to a blue shifting of the radiation, νf > νi , causing an increase in the frequency, as photons are “slingshot” away from the surface like being thrown out from a rapidly rotating cartwheel. The total frequency (or energy) change is the product of the gravitational and Doppler boosting factors, νf /νi = δ/(1+z). Observed flux scales as FE ∝ (νf /νi )3 and energy-integrated flux as F ∝ (νf /νi )4 . The emergent flux is visualized in Fig. 1 for two different example cases. Finally, we note that all the radiative processes should be defined in the co-rotating frame of the star (i.e., for an observer located at the surface).

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Fig. 1 Example images of rapidly rotating neutron stars. The colormap shows the radiation flux, F ∝ (1 + z)−4 , from rotationally distorted neutron stars as a function of the non-redshifted, nonboosted flux, F0 (z = 0). Left panel shows an image of a typical massive neutron star (MN S = 2 M⊙ , RN S = 13 km) spinning with a frequency f = 600 Hz being observed with an inclination angle (w.r.t. to the spin axis) of i = 60◦ . Right panel shows the visual appearance of the same neutron star with an extreme spin frequency of f = 1400 Hz close to the mass-shedding limit. The ray-tracing is performed with the general relativistic ray-tracing code Arcmancer (Pihajoki et al. 2018)

To summarize, the emission calculations typically take into account space-time deformation effects up to second order in rotation, which are composed of the following: (i) Gravitational potential (and hence gravitational redshift) (ii) Doppler boosting, which originates from the rotating surface (iii) Change in the local emission angle (affecting the limb darkening and brightening effects) (iv) Time transformations (because the integration of finite-sized areas needs to take place simultaneously) (v) Oblate shape of the star To a lesser extent, we also need to take into account the following: (vi) Quadrupole deformations of the space-time (modifying the gravitational redshift term) (vii) Frame-dragging effect (reducing the angular velocity close to the equator) (viii) Quadrupole deformations which modify the differential emission area element (dS = R 2 d cos θ dφ for a flat space-time metric)

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Typical neutron star images are constructed using the so-called S+D approximation (Schwarzschild metric and Doppler boosting) (Pechenick et al. 1983; Poutanen and Gierli´nski 2003; Poutanen and Beloborodov 2006), where the observer’s polar coordinates are connected to the star’s co-rotating spherical coordinates (algebraically) and quantities computed at the surface of the star are Lorentzboosted into the static non-rotating observer’s frame. The method can be refined by taking into account the oblate shape of the star (Cadeau et al. 2007; Morsink et al. 2007; Lo et al. 2013; Nättilä and Pihajoki 2018; Salmi et al. 2018; Bogdanov et al. 2019; Loktev et al. 2020).

Pulse Profile Modeling If the surface of the neutron star has a spot that is located off the rotational axis (in comparison to the whole surface just emitting uniformly), it produces periodic pulsations with the spin frequency of the star. Information in these pulse profiles can be used to constrain the geometry of the rotating system together with the mass and radius of the neutron star. Creation of such spots requires some physical effect that breaks the axisymmetry (along the azimuthal direction) on the surface and makes an azimuthal patch of the surface brighter (or, in theory, dimmer, corresponding to cold spots that produce flux deficit as a function of the phase). Three mechanisms for spot creation are typically considered: heated magnetic polar caps in isolated pulsars, accretion-heated spots in binary systems, and dynamic thermonuclear burning regions. Heated magnetic polar caps of isolated pulsars In isolated pulsars, the magnetospheric activity above the surface leads to acceleration of charged particles that are launched toward the surface (e.g., Ruderman and Beloborodov 2007). The infalling “rain” of charged particles leads to heating the star’s surface – a hot spot. The opposite magnetic pole of the star can house a second antipodal spot. There are observational implications that some of such polar caps might not be circular but resemble more arc-like structures (banana-shaped spots) (Riley et al. 2019; Miller et al. 2019). Such complex structures can be created, for example, if the magnetic field of the neutron star is not a dipole but has higher-order multipole components due to a more tangled internal field. Accretion-heated spots of neutron stars in (low-mass X-ray) binary systems Accretion-heated spots are generally labeled as originating from accreting millisecond pulsars. In these systems, the surface is heated by the material from the companion star, which falls into the neutron star. The spot is formed as the magnetic field of the neutron star channels the material into a stream that hits the surface and heats it. Thermonuclear burning fronts The thermonuclear burning of accumulated material on top of accreting neutron stars (in low-mass X-ray binary systems) can sustain

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a coherent burning region, similar to hurricanes on Earth’s weather layer. The dynamics of these storms are still not very well understood: the burning fronts can lead to spots that drift (i.e., the spot is slowly moving on the surface) and expand (i.e., the burning front propagates into the fresh fuel), making their modeling very complicated. Irrespective of the origin of the spots, the information in the observed pulsating emission – pulse profile – can be used to measure the radius and mass of the neutron star housing the spot. The simplest assumption for an emitting spot is a circular emission region at a colatitude θs with a half-angular size ρ (measured in degrees using great-circle distances). During one rotation of the star, the spot first becomes visible to the observer, then crosses the visible surface, and finally disappears behind the star. This leads to a phase-resolved pulse profile where the detected emission increases, peaks, and decays. Depending on the observer’s inclination angle i and on the spot’s colatitude, the spot can disappear behind the star, experience a partial occultation, or always remain visible. As an example, NASA’s NICER (Neutron Star Interior Composition Explorer) mission has used the pulse profile analysis to constrain the radius and mass of the rotation-powered millisecond pulsar PSR J0030+0451 to be R ≈ 12.7 ± 1.2 km +1.3 km and M ≈ 1.34 ± 0.16 M⊙ , as measured by Riley et al. (2019), or R ≈ 13.0−1.1 and M ≈ 1.44 ± 0.15 M⊙ , as measured by Miller et al. (2019). These NICER observations also indicated that emission areas were, in fact, more consistent with three elongated arcs instead of just two antipodal circular spots. This might imply that the magnetic field structure is more complex than the regularly assumed dipole field. Similarly, the NICER collaboration has constrained the radius of a massive pulsar PSR J0740+6620 with a known mass of M ≈ 2.08 ± 0.07 M⊙ to be +1.3 +2.6 km, as measured by Riley et al. (2021), or R ≈ 13.7−1.5 km, as R ≈ 12.4−1.0 measured by Miller et al. (2021). For comparison, a similar pulse profile analysis was performed with RXTE (Rossi X-ray Timing Explorer) data to constrain the radius of the accretion-powered millisecond pulsar SAX J1808.4−3658 to be R ≈ 11.9 ± 0.5 km (assuming mass M = 1.7 M⊙ ) (Salmi et al. 2018). These measurements agree with neutron stars with a radius of R ≈ 12 km.

Gravitational Waves So far, we have discussed static gravitational effects like the gravitational bending of light rays or the redshift of photon energy. Recent pioneering observations of gravitational waves from neutron star mergers are a good example of dynamic gravitational phenomena where space-time changes as a function of time (Baiotti 2019). A typical toy picture of a gravitational wave depicts the wave on a vibrating elastic membrane with a surface wave-like perturbation moving on it. This conforms to the geometric interpretation of gravity as a space-time curvature, i.e., general relativity. Alternatively, we can imagine the gravitational waves as a consequence of special relativity in which a change in the gravitational field takes time to be felt

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at a distance; any perturbation (even of space-time) will propagate with a maximum velocity of c. Imagine a general field with strength decreasing as an inverse square of the distance, ∝ r −2 . Such a field can be visualized by a familiar picture of radial field lines originating from the source of the field. If such a source is uniformly moving, the field lines will still have the same radial form. However, if the source is accelerating, there will be a propagating “dividing zone” between a moving radial field line region close to the source (expanding with a maximum velocity of c) and a further-away exterior region still depicting a field of a non-moving source. The discontinuous zone dividing the interior and exterior regions has a width cΔt, where Δt is the duration of the acceleration. The discontinuity can be understood as a wave traveling away from the accelerating source. This forms an alternative basis for understanding the nature of gravitational waves. Mathematically, the simplest object that can launch such a pulse is a time-varying monopole, X˙ ≡ dX/dt = 0, where X is, for example, the electric charge (X → q, where q is an electric charge; relevant for theories of electromagnetism) or mass (X → M, where M is mass; appropriate for theories of gravitation). However, the conservation of electric charge and conservation of mass prevent the existence of time-varying monopoles. So any perturbation traveling on a field generated by any kind of “change of a monopole” is forbidden. Let us next consider dipoles, the second-most simple mathematical object in line. In electromagnetism, an electric  dipole (i.e., a pair of balanced positive and negative charges) is given as Pq = qi si , where si is the distance of the charge from the center of the charge cloud. Acceleration (e.g., a rotating  motion) corresponds to a non-zero second-time derivative: P¨q ≡ ∂ 2 Pq /∂t 2 = qi ai = 0, where ai = 0 is the acceleration of the ith charge. As is well known, this leads to electromagnetic dipole radiation. We return to this form of energy loss in the electromagnetism section. Gravitation turns out to be more complex since momentum is always conserved (in a closed system), and so P¨M ≡ ∂ 2 PM /∂t 2 = Mi ai = 0. To make a system emit gravitational radiation, time-varying higher-order moments are required. The subsequent mathematical entity in the multipole expansion after the dipole moment is the quadrupole moment (e.g., four balanced charges arranged in the corners of a square). The quadrupole moment of mass distribution is defined as IM =  Mi si ⊗ si , where ⊗ denotes the tensor product of two vectors, resulting in a quadrupole moment being a rank-2 tensor that is described with a 3 × 3 matrix. The corresponding physical quantity is the gravitational tidal field, g ′ = Δg/Δd, which represents an observable relative acceleration (i.e., a force) between two displaced particles within a small displacement of Δd (i.e., the gradient of gravity). The dominant gravitational .... radiation originates from the fourth-time derivative of the quadrupole moment, I , which produces a change in the gravitational (tidal) field g per displacement s of g ′ = ∂g/∂s .... (∼ Δg/Δd, where ∂g ∼ Δg and s ∼ Δd). from the source. This change is proportional to g ′ ∼ I /r, where r is the distance ... Other, weaker modes scale as g ′ ∼ I /r 5 , I˙/r 4 , I¨/r 3 , and I /r 2 , all falling off more

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.... rapidly than the dominant I /r term. The dominating mode contains terms of the form Ms a, ¨ Mv a, ˙ and Ma 2 ; for oscillatory motion, relevant for rotating systems with equal masses M moving over distance s with frequency f , all of these scale as ∝ Mf 4 s 2 . The amplitude of the gravitational radiation then scales as GM f 4 s 2 s2 1 ∼ GM 4 , 4 r c λ r

g′ ∼

(10)

where λ is the wavelength. In gravitational wave physics, the most commonly used parameter characterizing the amplitude of the wave is not g ′ (i.e., change in gravity per displacement) but the dimensionless strain, h≡2



g ′ dt 2 ∼ 2

Δ[Δd] , Δd

(11)

(i.e., change in displacement per displacement). The two integrals in the strain formula represent an instantaneous change in displacement as a function of time. Therefore, h is twice the fractional change in the displacement between two nearby masses due to the gravitational waves. This can be understood geometrically as follows. Similar to electromagnetic radiation, this displacement is on a plane transverse to the direction of the motion of the waves; i.e., the wave is a shear wave. It stretches the space-time along one axis and squeezes the other axis orthogonal to it. The net distortion is twice as large as what the stretching or squeezing would independently give. Note also that h itself is not observable; only the second derivatives and higher of h (that produce acceleration) are detectable. The final scaling of the strain is h∼

GM 1 v 2 . c2 r c

(12)

In the most standard, already observed scenario of two in-spiraling neutron stars, the rotating binary system corresponds to a non-zero quadrupole moment that acts as a cyclic source of gravitational waves. A neutron star with a mass M ∼ 2 M⊙ , inspiral velocity v ∼ c (just before the merger), and at a distance r ∼ 6 × 1025 cm (≈ 20 megaparsecs) would result in a peak dimensionless strain of 10−20 . This kind of fluctuation in the strain was indeed observed in the GW170817 event (Abbott et al. 2017). Other possible mechanisms for generating gravitational wave radiation from neutron stars are, e.g., breaking of axisymmetry in rotating pulsars; here a small mountain on top of the neutron star (corresponding to some defect of the crust) would also lead to non-zero gravitational quadrupole moment and hence emission of gravitational waves. The perturbation amplitude from rotating mountains is much weaker, and these signals have not yet been detected.

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Interpretation of Gravitational Waveforms Latest observations of gravitational waves from merging double neutron star binary systems offer a powerful way for constraining the properties of the ultra-dense matter inside the stars (Baiotti 2019). The gravitational wave emission observed from neutron stars is often split into the chirp and ringdown phases. The chirp phase occurs at the beginning of the inspiral as the two stars begin to coalesce toward each other but are not yet touching. In this case, the gravitational wave frequency is just twice the orbital frequency of the binary, fGW ≈ 2fK , where fK is the Keplerian orbital frequency. The contact frequency, the frequency reached at the contact between the two objects, is well-approximated as fc =

c3 c¯3/2 , 2G M

(13)

where c¯ = GM/Rc2 is the average compactness, assuming identical stars with M1 = M2 = M and R1 = R2 = R. The chirp frequency is observable for tens of seconds and peaks at fGW ∼ 1 kHz. During the chirp phase, the equation of state can be probed by measuring the dimensionless quadrupole tidal deformability (polarizability coefficient), Λ=

2 k2 3



Rc2 GM

5

,

(14)

where k2 is the quadrupole Love number. Its measured posterior distribution is currently consistent with Λ = 0 (corresponding to two black holes merging). However, since the system is a known double neutron star binary (and, in addition, because a gamma ray burst was detected), we are confident that the GW170817 event measured the tidal deformability of the ultra-dense matter inside neutron stars. This measurement rules out the softest equations of states that require large Λ ≫ 0. As the two stars merge, they will either collapse directly into a black hole or remain, for a while, as a “joint” neutron star. The resulting star can be either a stable neutron star supported by the standard pressure of the matter or a quasi-stable supra massive/hyper massive neutron star, supported (at least partially) by the centrifugal acceleration from the rotation of the object. Supramassive neutron star remnants assume a uniform rotation profile, Ω(r) ∝ r (where r is the radius from the center of the remnant), whereas hypermassive remnants have differentially rotating interiors. The cores of the two merging stars continue to rotate inside a common envelope for a while, resulting in a ringdown gravitational wave emission. The ringdown phase is short (the system loses angular momentum rapidly due to efficient dissipation caused by the dense surrounding cloud) and emits gravitational waves at high frequencies. The ringdown phase has three characteristic frequencies,

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Ω1 < Ω2 < Ω3 , with a distinct physical origin. The physical origin of the frequencies can be understood by a toy model describing a rotation of two balls connected by a spring. The balls mimic the cores of the initial neutron stars, which rotate in a common envelope. Such a system can have three characteristic configurations if the system is rotating and the spring is vibrating. When the balls are at their maximum separation, the system has the largest moment of inertia and, conversely, the smallest rotation frequency, Ω1 . At their closest separation, the system has the smallest moment of inertia and, conversely, the highest rotation frequency, Ω3 . If there is no dissipation, the angular frequency of the system will ˙ oscillate between these two states. Time spent at a given frequency is ∝ Ω/Ω, ˙ and so most time is spent at Ω ≈ 0, i.e., at the two extreme states, resulting in power-spectrum peaks at frequencies corresponding to Ω1 and Ω3 . If the spring is dissipative, the system asymptotes to an average frequency, Ω2 ≈ (Ω1 + Ω3 )/2. This leads to a time-growing third peak at a frequency of Ω2 . Realistic merger simulations confirm that the initial few oscillations of the ringdown show a gravitational wave spectrum with two frequency peaks at f = Ω1 /π and Ω3 /π . Realistic merger remnant configurations are highly dissipative, so they quickly develop a strong peak at f ≈ Ω2 /π , with weaker sidebands at f1 and f3 . Especially the f1 frequency correlates with the compactness, u ≡ 2GM/Rc2 , enabling a more accurate equation of state constraints in the future when observations of the ringdown phase become possible. Finally, we note that the (short) gamma ray bursts occurring shortly after the neutron star mergers are also an important new avenue of research (Fernández and Metzger 2016). They are sources of electromagnetic radiation (so-called kilonova) and possible neutrinos. They are also speculated to be responsible for the heavy element production in our universe since the merger fuses extremely heavy elements, and the gamma ray burst expels them to the surrounding interstellar medium.

Laboratories of Nuclear Physics The density inside neutron stars is so high, and the particles are packed together so tightly that quantum effects play an essential role in controlling the behavior of the matter (Haensel et al. 2007). This makes neutron stars exciting laboratories of nuclear physics. Furthermore, since the interiors of neutron stars are the densest form of observable matter known in the universe, they provide a pathway into new studies exploring particle physics and quantum chromodynamics – something previously thought possible only with particle colliders. This line of research of the neutron star interiors is encapsulated into the unknown equation of state of the matter, P (ρ, T , . . .), describing a pressure P as a function of thermodynamic properties of the matter like density, ρ, temperature, T , and so on.

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Dense Matter Inside Compact Objects When the matter is compressed from ordinary matter toward the ultra-dense states inside neutron stars, different forces play a role hierarchically. First, the pressure is supported by the thermal motions of the gas. When compressed further, the charge repulsion between negatively charged electrons and positively charged protons becomes important. Both of these effects are explainable by classical physics and are used to describe the matter and equation of state inside regular stars. For compact objects, like neutron stars and white dwarfs, quantum mechanics is involved when explaining the behavior of matter. First, for dense enough matter (such as those found inside white dwarfs or outer layers of neutron stars), the electrons start to be packed so densely that quantum mechanics influences their motions via the so-called degeneracy pressure. When the compression is continued, the protons and neutrons will follow, providing a degeneracy pressure (such as in the core of neutron stars). The equation of state at these densities is still unknown. Beyond even the densities reachable in the interiors of neutron stars, we know that the final support of an ultra-dense matter is given by quarks via their degeneracy pressure (such conditions could perhaps exist inside the most massive neutron stars) (Annala et al. 2020, 2022).

Degeneracy Pressure Nuclear matter behaves in a somewhat analogous manner to liquids: the particles composing the liquid experience attraction between their neighbors but strongly resist compression when tightly packed. This resistance originates from zero-point motions of electrons (electron degeneracy pressure) and later on from zero-point motions and mutual interactions of neutrons (neutron degeneracy pressure). The degeneracy pressure is based on Pauli’s exclusion principle that forbids two identical fermions (spin- 12 particles) from occupying the same quantum state. This introduces a quantum mechanical pressure as fermions repel their neighbors with similar quantum states. We can derive the resulting pressure from Heisenberg’s uncertainty principle, which asserts that position and momentum cannot be simultaneously determined to be better than ΔxΔyΔzΔpx Δpy Δpz = h3 ,

(15)

where h is the Planck’s constant and Δx3 Δp3 is the 6D phase-space volume of the particles, where location vector x = (x, y, z) and momentum vector p = (px , py , pz ). This means that there exists a zero-point momentum, called Fermimomentum, pF . The Fermi-momentum can be associated with a Fermi-energy, EF . For nonrelativistic case (p ≪ mc), it is EF = pF2 /2m. Here we consider Fermi energy for a (cold) 3D space with N fermions filling the available energy states from the

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lowest up to the Fermi energy. It can be approximated similar to the energy in a square-well potential of size L, EF =

π 2 h¯ 2 2 π 2 h¯ 2 2 2 2 (n r + n + n ) = x y z 2mL2 2mL2 n

(16)

where rn is the radius in n-space and ni are the principle quantum numbers in 3D. The total energy is obtained by integrating all states inside the Fermi sphere, Etot = 2

π 2 h¯ 2 16mL2



rn 0

4π rn2 drn rn2 =

π 3 h¯ 2 5 r 10mL2 n

(17)

Here the factor of 2 comes from the fact that we have two different spin states for fermions. Finally, the pressure is obtained from the standard thermodynamic relation (assuming a volume of V = L3 ), P =−



∂Etot ∂V



S,N

=

π 3 h¯ 2 15m



3N πV

5/3

(18)

assuming constant entropy (S) and particle number (N ). We can generalize the expression into a form (Haensel et al. 2007),  3γ xr AD Pr xr5 P = Pr ∼ γAD Pr xr4

(xr ≪ 1)

(xr ≫ 1),

(19)

where Pr = me c2 /9π 2 λ¯ 3C ∼ 1.5 × 1023 dyn cm−2 is a typical pressure, λ¯ C = h/m ¯ e c = 3.86 × 10−11 cm is the (reduced) Compton wavelength, xr = pF /me c is the dimensionless Fermi-momentum, and γAD = 53 or γAD = 34 is the polytropic index for non-relativistic (xr ≪ 1) or ultra-relativistic (xr ≫ 1) gas. Note that 1/3 xr ∝ ne ∝ ρ 1/3 . The transition between non-relativistic and ultra-relativistic regimes occurs at xr ∼ 1 corresponding to ρ ∼ 106 g cm−3 . This theoretical treatment provides a pathway to understanding the nuclear physics of the cores of neutron stars. It is easy to see that degenerate neutron gas will behave similarly to degenerate electron gas since we can replace the mass me → mn . Repulsive nuclear interaction, however, also contributes to the pressure at very high densities, rendering the equation of state in the neutron star core, ρ > 1014 g cm−3 , unknown. Multiple competing nuclear equations of state models exist at these densities (see Fig. 2). Structure of a neutron star with one of these models, SLy (Skyrme Lyon model; Douchin and Haensel 2001), is demonstrated in Fig. 3. Most models assume fully nucleonic material (i.e., interactions between the neutrons). Some models also assume that the material is enriched with hyperons,

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Fig. 2 Examples of the different equation of state models and the corresponding neutron star mass-radius relations. Each EOS has a one-to-one mapping between the density-pressure and massradius planes

Fig. 3 Equation of state, P (ρ), of the dense matter inside neutron stars. The upper horizontal axis gives the same relation as a function of radius, P (RSLy,1.4 ), for a M = 1.4 M⊙ star with the SLy equation of state. Different regions inside the star are highlighted, including atmosphere, for which the equation of state is given by the ideal gas law (various temperatures of T = 106 , green curve; 5 × 106 , blue curve; and 107 K, black curve are shown); ocean, where the plasma is Coulomb liquid; outer crust, where the equation of state is split between non-relativistic degenerate electron gas (P ∝ ρ 5/3 ; magenta dashed line) and relativistic degenerate electron gas (P ∝ ρ 4/3 ; dashed blue line), and inner crust and the core where the P (ρ) is still uncertain (various models are shown with different colored curves). Location of the neutron drip, ρND (where neutrons start to leak out from the atomic cores) and saturation density, ρn (corresponding roughly to densities inside nucleons), are also shown with red dotted vertical lines

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nucleons containing strange quarks, or that the stars are composed entirely of strange-quark matter (mixture of up and down and strange quarks), making them, in fact, strange stars, in comparison to neutron stars. The strange star models produce very soft equations of states which are generally disfavored by current observations of the heaviest neutron stars of M ≈ 2M⊙ (e.g., Demorest et al. 2010). In summary, the state of ultra-dense matter is still open at the densities corresponding to the interiors of neutron stars. Eventually, for high enough densities, the material will decompose into quarks, with an equation of state given by the perturbative quantum chromodynamics. The equation of state in different density intervals is then composed of the following: (i) Ideal gas law (P = N kT /V , where kT is the gas temperature) for ρ  103 g cm−3 (ii) Non-relativistic degenerate electron gas (P ∝ ρ 5/3 ) up to ρ ∼ 106 g cm−3 (iii) Relativistic degenerate electron gas (P ∝ ρ 4/3 ) up to ρ ∼ 1011 g cm−3 (iv) Degenerate neutron gas with additional, unknown, nuclear interactions (v) Quark matter with pressure given by quantum chromodynamics, at ρ  40ρn (where ρn is the saturation density). The equation of state is also visualized in Fig. 3. Especially the unknown equation of the state of the matter inside the core is under active research. Observations of neutron stars allow an unrivaled opportunity to put definite constraints on the state of the ultra-dense matter. Various methods exist for constraining the mass, both mass and radius, and in some cases the state of the matter indirectly. For recent reviews, see Özel and Freire (2016), Suleimanov et al. (2016), Miller and Lamb (2016), and Lattimer (2019) and especially Degenaar and Suleimanov (2018) that focuses specifically on the various methods for mass and radius measurements. We have already discussed the possibility of using the pulse profiles (and their dependency on the gravitational potential) to provide constraints for the equation of state. Other promising methods include constraining the size of the emission directly from the X-ray emission emanating from the surface. Various methods used to constrain the equation of state of ultra-dense matter inside neutron stars are listed and described in Table .

Thermal-Like Emission from Isolated Neutron Stars The most important part of interpreting the electromagnetic emission from neutron stars is understanding the physics of the atmosphere that reprocesses all the radiation going through it. The atmosphere of a neutron star is a thin, ∼1 to 10 cm height, slab of hot plasma. To model it, equations of radiative transfer are solved, and the atmosphere is (typically) assumed to be in a radiative and hydrostatic equilibrium. This kind of modeling bears a great similarity to modeling regular stellar atmospheres.

4202 Table 2

J. Nättilä and J. J. E. Kajava Methods for constraining the neutron star equation of state

Method Description Mass measurements Radio pulsars Accurate timing of radio pulsars allows the in binary determination of orbital parameters (orbital systems period Porb , inclination angle sin i, the mass of the companion Mc , and total mass of binary MT = MN S + Mc ) for neutron stars in binary systems. For nearly edge-on systems, the propagation of the signal through the gravitational potential of the companion allows breaking the degeneracy in the mass (Shapiro delay) Optical Optical measurements of a companion star measurements rotating around a neutron star allow the of binary determination of orbital parameters (Porb , systems sin i, Mc , and MT = MN S + Mc ) of the system. Additional information via i) Shapiro delay, ii) observations of spectral lines of the companion star, or iii) modeling of eclipses (black widow systems) can be used to break the degeneracy between the mass and inclination Simultaneous mass and radius measurements Thermonuclear Time-resolved X-ray observations of X-ray bursts cooling of neutron star atmosphere after thermonuclear X-ray bursts allow determination of R, M, distance D, hydrogen mass fraction X, and other system parameters by comparing the cooling track to theoretical model calculations. Distance measurements help narrow the constraints X-ray pulse Modeling of phase-folded X-ray pulse profile profiles allows constraining the parameters modeling of the gravitational potential (compactness GM/Rc2 ). Higher-order effects like Doppler boosting and relativistic aberration of angles allow breaking of the degeneracy between R, M, and observer inclination angle sin i and spot colatitude cos θs

Thermally emitting qLMXBs

Modeling of X-ray spectral observations of quiescent (non-accreting) X-ray binary systems allows constraining the size of the emitting region (∝ R 2 /D 2 ), and relativistic effects carry additional information about compactness which allows weak constraints on the mass M too. Distance measurements help narrow the constraints

Notable measurements PSR J161-2230: M = 1.908 ± 0.016 M⊙ (Demorest et al. 2010; Fonseca et al. 2016; Arzoumanian et al. 2018), PSR J0348+0432: M = 2.01 ± 0.03 M⊙ (Antoniadis et al. 2013), PSR J0740+6620: M = 2.08 ± 0.07 M⊙ (Fonseca et al. 2021) Black widow system PSR J0952-0607 M = 2.35 ± 0.17 M⊙ (Romani et al. 2022)

Burster 4U 1702−429 R = 12.4 ± 0.4 km and M = 1.9 ± 0.3 M⊙ (Nättilä et al. 2017)

PSR J0030+0451 R ≈ 12.7 ± 1.2 km and M ≈ 1.34 ± 0.16 M⊙ (Riley et al. 2019) or R ≈ 13.0+1.3 −1.1 km and M ≈ 1.44 ± 0.15 M⊙ (Miller et al. 2019). PSR J0740+6620 with mass M ≈ 2.08 ± 0.07 M⊙ and +1.3 R ≈ 12.4−1.0 km (Riley et al. 2021) or R ≈ 13.7+2.6 −1.5 km (Miller et al. 2021) Statistical combination of five sources yielded R = 9.1+1.3 −1.5 km for M = 1.4 M⊙ (90% confidence) (Guillot et al. 2013). Similar analysis of 8 sources yielded R = 10 − 14 km for M = 1.4 M⊙ (Steiner et al. 2018) (continued)

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(continued)

Thermally emitting isolated neutron stars

Modeling of X-ray spectra observations of isolated neutron stars allows constraining the size of the emitting region (∝ R 2 /D 2 ), and relativistic effects carry additional information about the compactness, which allows weak constraints on the mass M too. Distance measurements help narrow the constraints Other constraints Constraints Measurements of neutron stars with fast from fast spin spin allow constraining the maximum possible values of M and R by requiring the star not to break up (mass shedding limit) Tidal Modeling of gravitational wave signals deformability from mergers carries information on the measurements tidal deformability of the material that can be translated to M and R constraints

CCO HESS J1731−347 +0.9 R = 12.4−2.2 km and M = 1.55 ± 0.3 M⊙ (Klochkov et al. 2015)

PSR J1748−2446a rotating f = 716.356 Hz (Hessels et al. 2006) limits R < 16 km (for M = 2 M⊙ ) GW170817 allowed constraining the tidal deformability (Abbott et al. 2017), which in turn translates to R  14 km for M = 1.4 M⊙

The atmosphere is thought to be composed of light elements. It is typically assumed to be in a local thermodynamical equilibrium (LTE) so that the equation of state follows an ideal gas law, P = nkT , and Saha equation can be used to calculate the ionization levels. Heavier elements are expected to sink to the bottom due to the large gravitational potential (i.e., the atmosphere has a very short sedimentation timescale); hence the atmosphere is often taken to be composed of the lightest elements only, such as hydrogen or helium. For accreting systems, the composition is often taken to coincide with the elements in the companion star’s outer envelope. The most direct application of the atmosphere models is the interpretation of the thermal-like emission from central compact objects (CCOs), point-like X-ray sources in supernova remnants, using the atmosphere model spectra. These CCOs are young (t < 104 yr) neutron stars with modest X-ray luminosities of Lx ∼ 1033 erg s−1 . They have thermal spectra consistent with temperatures of kT ∼ 0.1 to 0.5 keV. Interestingly, recent observations indicate that some CCOs are better explained by the carbon composition of the atmosphere. Using carbon atmosphere models, Ho and Heinke (2009) constrained the radius of a neutron star in Cas A to be between R ≈ 10 − 14 km. Similar measurement was done for HESS J1731-347 by Klochkov et al. (Suleimanov et al. 2014; Klochkov et al. 2015) who constrained the mass and radius to be M = 1.55 ± 0.3 M⊙ and R = 12.4+0.9 −2.2 km, respectively.

Thermonuclear X-ray Bursts Thermonuclear (type-I) X-ray bursts are a phenomenon unique to neutron stars (for a recent review, see Galloway and Keek 2021). They offer a more complex alternative for measuring the neutron star radius by comparing the time-resolved

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X-ray spectra to theoretical atmosphere models. In addition, thermonuclear burning on top of neutron stars is a rich phenomenon with many unknown physical features. The bursts are triggered by unstable thermonuclear burning of matter accumulated onto the neutron star envelope from a binary companion. During the burning, hydrogen and helium fuse into heavier elements through the hot CNO cycle and triple alpha reactions, sometimes triggering the rp-process (rapid proton captures) that can generate elements up to tellurium (Schatz et al. 2001). Enormous amounts of energy are released quickly, particularly for helium-rich fuel: triple alpha reactions are not limited by beta decays that limit the CNO hydrogen burning. The most energetic bursts can have rise times that are less than an ms (in’t Zand et al. 2014), suggesting that on rare occasions, the neutron star envelope can also detonate rather than deflagrate (i.e., the burning front can expand both super- and sub-sonically) and cause a relativistic outflow that drives the outer neutron star envelope into the interstellar space. Observations of X-ray bursts probe several key fundamental physics problems. In bursts where the rp-process is important, the (often poorly known) nuclear reaction rates of various proton-rich isotopes play a key role in the morphology of the X-ray light curves (Cyburt et al. 2016). This has the potential to make the thermonuclear bursts also laboratories of nuclear physics, rivaling any Earthly nuclear burning physics experiment on nuclear reaction rates. The extreme parameter regime also enables studies of more exotic proton-rich isotopes that can be present during the burning. The burning ashes generated during the X-ray burst – in addition to the possible, stable nuclear burning (Schatz et al. 1999) – settle down to the neutron star ocean. At the bottom of the ocean, chemical separation occurs, wherein heavier elements crystallize into a solid crust and lighter elements such as oxygen and carbon preferably remain in the liquid ocean (Horowitz et al. 2007). This transitional layer of the star is where so-called super-bursts are triggered, which are powered by nuclear burning of carbon (Cornelisse et al. 2000; Cumming and Bildsten 2001; Strohmayer and Brown 2002). In the accreted crust (Lau et al. 2018), the chemical composition is further altered through pycnonuclear reactions that also heat the crust (Haensel and Zdunik 2008). However, the neutron-rich nuclei in the outer crust undergo repeated cycles of electron captures and beta decay. The resulting neutrino losses effectively thermally decouple the ocean/atmosphere from the hotter inner crust (Schatz et al. 2014). Also, very recently, a new type of nuclear burning regime has been proposed, the so-called hyper bursts that are triggered possibly by unstable burning of oxygen or neon at densities of ρ ∼ 1011 g cm−3 near the neutron drip (Page et al. 2022). It is practically impossible to obtain direct observational constraints deeper down from these densities. Therefore, to probe the properties of the inner crust and the ultra-dense neutron star core, we must place constraints on the macroscopic properties of the star: their masses and the radii. We can place constraints on the neutron star masses and radii by analyzing quasi-thermal light emitted by their photospheres. During X-ray bursts, the entire

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atmosphere heats up, such that the photospheric temperatures can reach almost 3 keV, and then it rapidly cools down as the fusion reactions start waning down at the burning depths. The most energetic bursts reach the Eddington limit, which results in photospheric expansion, and they act as standard distance candles (Kuulkers et al. 2003). Moreover, these photospheric radius expansion bursts are expected to launch radiatively driven winds (Paczynski and Proszynski 1986; Guichandut et al. 2021), which may enrich the interstellar medium with the burning ashes (Weinberg et al. 2006; in’t Zand and Weinberg 2010; Kajava et al. 2017b). Multiple techniques have been used to constrain neutron star masses and radii. The majority of them – such as the touchdown method (Damen et al. 1990; Özel 2006) or the cooling tail methods (Suleimanov et al. 2011, 2017; Nättilä et al. 2016) – rely on the fact that their X-ray spectra can be adequately modeled with a simple black body model. Another approach is modeling X-ray bursts using sophisticated atmosphere models, whose properties depend on the neutron star mass and radius, among many other variables (Nättilä et al. 2017). All of these techniques, however, have relied upon the assumption that the environment where the X-ray bursts occur remains unaltered by the explosion of light and mechanical energy exerted by the burst-driven winds. Recent observational data indicate clearly that this is not the case the majority of times; the X-ray bursts alter the properties of the accretion disks surrounding the neutron stars (Worpel et al. 2013, 2015; Zhang et al. 2016; Kajava et al. 2017c; Degenaar et al. 2018). The accretion flow in the disk conversely seems to influence the spectral properties of the bursts (Kajava et al. 2014, 2017a). The burst-disk interactions severely limit the use of X-ray bursts in making precise mass-radius measurements. Typically, their impact can only be inferred from studying large numbers of bursts rather than seeing clear imprints in individual bursts. In addition, the atmosphere models that have been used so far ignore many important factors, such as rapid stellar rotation that can cause the star to become oblate and modify the energy distribution of the radiation via strong Doppler boosting. But the potential of constraining dense matter equations of state models using X-ray bursts is enormous. For example, Nättilä et al. (2017) constrained the neutron star’s radius in one X-ray burster to within 400 meters. This target was, however, ideal in many ways: the mass accretion rate was uncharacteristically low, and the source was in the hard spectral state, facilitating optimal measurement conditions for the radius. Unfortunately, most of the other observed bursts/bursters are less optimal in their behavior.

Laboratories of Electrodynamics Understanding the physics of neutron star magnetospheres requires the usage of both classical electromagnetism and quantum electrodynamics (QED) (Arons 1979, 2007; Cerutti and Beloborodov 2017; Beskin 2018). From the perspective of electromagnetism, the neutron star is just a rotating magnetized ball in a vacuum.

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This kind of simplification, however, only gets us so far because the strong magnetic field also means that electromagnetic radiation (photons) and plasma particles start to a couple in the framework of QED.

Spindown Power of Magnetized Balls What can we expect from a dense ball of plasma (R ∼ 106 cm) that is rotating rapidly (P ∼ 1 s) and spinning a huge magnetic field (B ∼ 1012 G) around? The rotational energy of such a star is given by E=

1 I Ω 2, 2

(20)

where the moment of inertia I = 25 MR 2 ∼ 1045 g cm2 . Since isolated pulsars are observed to slow down, the corresponding spindown power is E˙ = I Ω Ω˙ ∼ 1032 erg s−1 .

(21)

for an angular velocity of Ω = 2π/P ≈ 6 s−1 and spindown rate of Ω˙ ∼ 10−13 . The simplest physical model for this slow-down is an electromagnetic torque acting on a rotating dipole. The angular momentum is carried away from the system by electromagnetic radiation, Poynting flux. The corresponding magnetic dipole energy loss rate is ¨ ⊥ )2 2 (m 2 B 2Ω 4R6 2 P0−4 erg s−1 , = sin2 χ ∼ 1032 B12 E˙ = 3 c3 3 c3

(22)

where m⊥ = m sin χ , m = BR 3 is the magnetic moment, B is the star’s polar magnetic field, and χ is the magnetic dipole inclination angle with respect to the spin axis. The period and angular velocity are related simply as P = 2π/Ω. In the last expression, the quantities are scaled as Qx ≡ 10x Q. Equating the spindown power and the magnetic dipole losses allows us to estimate the magnetic field. We obtain B ≈ 1012



P 1s



P˙ G, 10−15

(23)

that agrees with our previous estimate of the strength of the magnetic field for characteristic pulsar parameters.

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Charges in the Magnetosphere The above estimates demonstrate that the basic arguments based on electrodynamics lead to quantitative agreement. The standard pulsar model, therefore, consists of a rotating magnetized ball with a dipole field. Let us now refine this model to include charge carriers – plasma. From the perspective of our “rotating ball model,” the magnetic field is spun by an excellent conductor. This rotation induces electric fields in the conductor. We can model the pulsar as a Faraday disk dynamo to estimate the order of magnitude of these electric fields. In this picture, we have a disk of radius R, rotating with an angular velocity Ω. The disk is penetrated by magnetic fields of strength B ∼ 1012 G. The rotating conductor experiences the moving magnetic field as an electric field, |E| = | −

v ΩBR × B| ∼ , c c

(24)

where v = Rˆr×Ω is the tangential velocity of the outer disk rim. The corresponding voltage induced by the rotating disk (for a Faraday disk generator) is V ∼ 1015 V. There is also a large current flowing in the “circuit,” I = P /V ∼ 1014 A (assuming spindown power of P ∼ 1038 erg s−1 ). The large electric field can lift charges from the star’s surface. Goldreich and Julian (1969) showed that this induces a (minimum) charge density of ρGJ =

Ω ·B ∇ ·E ≈− . 4π 2π c

(25)

These charges are pulled from the surface because the electromagnetic forces far exceed gravity. The corresponding number density of plasma is nGJ = ρGJ /e ∼ 1012 cm−3 . An actual number density can be even higher, n = MnGJ , where M ≫ 1 is the so-called multiplicity parameter. The charge density in the magnetosphere leads to a formation of a (minimum) conduction current of J = nev,

(26)

where ne = ρR is the charge density required to screen the parallel electric E =

E·B → 0; B

(27)

in the opposite case, the electric field would lift the charges until it would become screened.

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The minimum Goldreich-Julian charge density (Goldreich and Julian 1969) also has higher-order relativistic corrections so that ρGJ → ρGJ + additional relativistic terms (Muslimov and Tsygan 1992). They modify the Goldreich-Julian charge density, ρGJ ≈ −

(Ω − ω)B , 2π c

(28)

where ω ≈ c2GI 2 r 3 Ω is the angular velocity of the space-time drag at a distance r from a rotating body. These corrections are, in reality, important to fully explain the plasma feeding into the magnetosphere.

Force-Free and Magnetohydrodynamic Solutions Much of the further progress in understanding the structure of the magnetospheres originates from numerical studies (Fig. 4). This is understandable because the related equations are nonlinear and often require numerical tools to probe the solutions. The subsequent structure of the magnetosphere depends on how dense the plasma is, that is, if M ≫ 1. Goldreich and Julian (1969) introduced the idea of a force-free magnetosphere where the parallel electric fields are always screened. Here, the electromagnetic energy density is so large that all inertial, pressure, and dissipative forces can be neglected. This means that the pulsar can be considered immersed in a massless conducting fluid instead of a vacuum. Similarly, Michel (1969) introduced a magnetohydrodynamical counterpart; this also assumes a large density, compared to nGJ .

Fig. 4 Schematic view of the pulsar magnetosphere. The neutron star in the center has an inclined dipole magnetic field w.r.t. to the spin axis of χ = π/12. Open and closed magnetic field lines are shown with solid black curves; magnetic field lines forming the Y-point are depicted with dotted curves. The light cylinder is shown with blue dashed curves

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In both systems, the plasma starts to rotate rigidly together with the star. This rigid rotation becomes impossible at a sufficiently large radius. This is known as the light cylinder, where the magnetic field moves with the speed of light, and the plasma can no longer co-rotate. Therefore, the light cylinder radius is RLC =

c . Ω

(29)

It is RLC ∼ 109 to 1010 cm (i.e., 103 R⋆ ) for P ∼ 0.1 − 1 s. Inside this region, r < RLC , the magnetic field is primarily dipolar (higher-order moments decrease faster with r than dipole moment). Outside of it, r > RLC , all the field lines are open, and the flux is conserved so that Br 2 = const.; then, B ∝ r −1 . The problem of magnetospheric structure can be formulated in a type of Grad-Shafranov equation that encapsulates the aligned rotator; the equation is familiar from magnetic confinement (Bateman 1978) with Grad-Shafranov equation being its relativistic counterpart (Scharlemann and Wagoner 1973; Michel 1973). Contopoulos et al. (1999) solved this equation by iterative technique assuming E · B = 0 and E 2 − B 2 < 0 (implying subluminal E × B drift velocity). The important outcome of this exercise was that the last closed field at the equator has a Y-type neutral point. This means that the return current flows in a current sheet at the boundary of the closed zone where the magnetic field flips sign. The result has since then been produced by others confirming its universal nature (Gruzinov 2005; McKinney 2006; Timokhin 2006; Spitkovsky 2006). The corresponding spindown energy losses of the aligned rotator were numerically confirmed to be 4 2

Ω μ E˙ = k 3 , c

(30)

with k = 1 ± 0.1.

Evolving Magnetic Topology Important progress came when Spitkovsky (2006) numerically solved the magnetospheric structure with time-dependent force-free simulations. This confirmed the presence of the current sheet at the equator and allowed the solution with an arbitrary (magnetic) inclination angle χ > 0 (angle between the magnetic moment and rotation axis). Then, the generalized spindown is μ2 Ω 4 E˙ = k 3 (1 + sin2 χ ) c

(31)

with k = 1 ± 0.1. This expression introduces the E˙ ∝ (1 + sin2 χ ) dependency on the inclination angle, χ . The magnetic topology of an oblique rotator, χ > 0, is just a rotationally distorted version of the simpler aligned rotator geometry, χ = 0. Note that the solution still assumes a magnetosphere filled with the plasma of density sufficient to short out the parallel electric fields.

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This generalized spindown power formula suggests an increase in the losses with increasing χ . Therefore, the inclination angle should decrease with time for old pulsars. Since RLC increases as the pulsar spin downs, there must be a net conversion of open field lines to closed field lines on the spindown timescale. This topological change requires the violation of the ideal MHD. This will then necessarily lead to reconnection (Lyubarsky and Kirk 2001). The most likely location is at the Y-point and in the current sheet. The importance of reconnection was later confirmed with fully kinetic simulations that do not require us to impose the assumption of dense plasma background (Philippov et al. 2014, 2015a, b; Philippov and Spitkovsky 2014; Chen and Beloborodov 2014; Cerutti et al. 2015, 2016).

Mysterious Pulsar Radio Emission The spindown luminosity, ∼1038 erg s−1 , leaks out from the pulsar magnetosphere and can act as free energy to produce observable emission. However, only a tiny fraction, 10−6 to 10−4 , of that energy is known to end up in the radio band to generate the actual pulsar emission (see Philippov and Kramer 2022, for a recent review). Quoting J. Arons, this makes pulsars dogs that don’t bark (Arons 1979). The origin of this emission is still unknown, but it is thought to be connected to the pair avalanches (see next section) regulating the electric circuit of the magnetosphere. The radio emission is broadband, extending to as low as tens of MHz and up to 150 GHz. The energy output peaks at a frequency of a few hundred MHz with a specific energy flux of a few Jansky (Philippov and Kramer 2022). (Jansky is a unit of energy flux used primarily in radio astronomy. It is 10−23 erg s−1 cm−2 Hz−1 .) The emission is elliptically polarized with a high degree of polarization, reaching ≈100%. The linearly polarized component dominates the emission. Circular polarization degree can reach up to ≈10%. The polarization angle of many pulsars has a canonical swing, where the angle evolves as a function of the pulsar phase, tracing a (tilted) S-shaped trajectory. This angle sweep takes place independently of frequency, pointing to geometric effects that are well explained with a rotating vector model (Radhakrishnan and Cooke 1969; Poutanen 2020b). Observations averaging over multiple pulses of radio emission have given the pulsars their status as the most accurate clocks in the universe. Individual pulses, however, vary significantly from pulse to pulse, and many show high sub-pulse variability. Some pulsars have individual pulses that drift in phase, others sometimes switch off (nulling), and others abruptly flip between various states (moding). The origin and nature of these sub-pulse variabilities are still unknown.

Pulsar Wind Nebulae So where does the rest of the large spindown energy go? Most of that energy is carried away by electromagnetic Poynting flux and by the charged particle outflow

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streaming out from the pulsar. But all that energy and charged particles are not just freely flowing into a vacuum; the neutron stars are surrounded by gas from their old stellar remnants. The interaction of that electromagnetic energy and charged particles generates a hazy, glowing turbulent blob of gas around the neutron star known as a pulsar wind nebula. This makes the nebulae huge calorimeters in the sky that trap, reprocess, and weigh the energy output of pulsars. As an example, the Crab nebula is probably the most well-studied nebula (and neutron star) of all time. Crab has a spin period of P ≈ 33 ms and a period derivative of P˙ ≈ 420 × 10−15 . Its age can be estimated from P /2P˙ ≈ 1000 yr (dynamical age), matching well with the historical supernova in 1054AD. The nebula emits in a broad range of spectrum from radio to optical to X-rays to gamma rays; injected power of E˙ = 5 × 1038 erg s−1 is required to be channeled into the surrounding plasma to explain the observed luminosity of the nebula. These estimates are well in line with the spindown power of a magnetized ball with B ∼ 1012 G, corresponding to a power of ∼1038 erg s−1 . To better understand the interaction of energy and the charged particles, the radiation, and its generation, we need an understanding also of plasma physics. This is the focus of our next section.

Laboratories of Plasma Physics The magnetospheres of neutron stars are composed of charged particles – plasma. As the magnetospheric plasma cools down, it radiates its energy away and populates the medium with photons. The nonlinear dynamics of this plasma and radiation are governed by radiative plasma physics. In this section, we introduce the basic concepts of such systems.

Standard Quantum Electrodynamic Interactions The magnetospheres of regular radio pulsars are composed of a large magnetic field of B⋆ ∼ 1012 G. Rapid rotation of this field leads to a generation of large electric fields, as well; these electric fields can open large potential gaps in the magnetosphere. The resulting voltage accelerates particles to relativistic energies, and these high-energy particles produce luminous radiation. The interaction of the charged particles and the radiation field requires the coupling of radiative physics and electrodynamics. Therefore, the pulsar magnetospheres are prime laboratories of quantum electrodynamics (Jauch and Rohrlich 1976; Berestetskii et al. 1982). In practice, quantum electrodynamics describes the interaction of photons (electromagnetic radiation) and charged particles. The simplest two-body interactions between photons and electrons are (We give a schematic description of these interactions by denoting electrons with e− , positrons with e+ , and photons with γ . Pairs are succinctly given as e± . Altered (or often energized) end-products are

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denoted with a prime, x → x ′ . The passive magnetic field (or virtual photons) is expressed with [B]. ): (i) Pair creation (photons interacting with photons to create pairs), γ + γ ′ → e− + e+ (ii) Pair annihilation (electrons interacting with positrons to create photons), e− + e+ → γ + γ ′ (iii) Compton scattering (photons interacting with pairs to exchange energy), e± + ′ γ → e± + γ ′ (iv) Coulomb scattering (pairs interacting with pairs to exchange energy), e± + e± → e±′ + e±′′ and e± + e∓ → e±′ + e∓′′ Magnetic field adds an extra flavor to these (lowest-order) interactions because it can be thought of as consisting of virtual photons. This enables single-body interactions (or, alternatively, two-body interactions composed of “real” against “virtual” species) such as (v) Synchrotron radiation (pairs upscattering virtual photons), e± + [B] → e± + γ + [B] (vi) Single-photon (magnetic) pair creation (photons pair-creating with virtual photons), γ + [B] → e± + [B] All of these processes are important in the neutron star magnetospheres.

Pair Cascades The magnetosphere of pulsars is prone to avalanches of pair creation (Sturrock 1971). They evolve as follows (Beskin 2018). The twisting electric field (from the rotation of the star) induces a longitudinal electric field to the magnetosphere, E ∼ (ΩR/c)B. Any (primary) particle in this region is accelerated to ultrarelativistic energies, εe ≫ 1, where εe ≡ Ee /me c2 is the particle’s energy, Ee , in the units of electron-rest mass me c2 . The strong magnetic field of the environment, however, renders the synchrotron cooling time to be very short, τs ∼

1 c ∼ 10−15 s, ωB ωB re

(32)

where ωB = eB/me c is the particle’s gyro-frequency and re = e2 /me c2 classical electron radius. Since the synchrotron emission power depends on the perpendicular component of the particle’s velocity, Psynch ∝ εe2 sin α, where sin α is the angle between the particle’s momenta and the magnetic field. This forces the particles to move along the magnetic field lines; pairs in the magnetosphere can be imagined as beads sliding on a wire.

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The synchrotron cooling and the curvature of the magnetic field cause these electrons (or positrons) to emit gamma ray photons, εγ ∼ 1, as they slide along the B field lines. Here εγ ≡ Eγ /me c2 is the energy of the photon in the units of electron 2 rest mass. The energy losses from the curvature radiation, Pc = 23 Re 2 εe4 , depend on c the curvature radius, Rc ∼ RN S , and the energy of the electron, εe , and impose an upper bound on the particle’s energy. Balancing acceleration, eE , and the curvature losses, Pc , results in εmax ∼ (Rc2 E /e)1/4 (i.e., emax me c2 ∼ 107 MeV). Therefore, the magnetosphere is expected to be full of high-energy gamma rays. The gamma rays, corresponding to energies εγ ∼ 1, single-photon pair-produce with the magnetic field, resulting in low-energy secondary pairs, εe ∼ 1. The required magnetic field strength can be estimated by considering the energy gap between the adjacent Landau levels, hω ¯ B , and comparing it to the electron rest m2 c 3

mass energy, hω ¯ B = me c2 . This results in BQED = eeh¯ ≈ 4.4 × 1013 G. Before pair-producing, the mean free path of photons in the magnetosphere is (Omitting a logarithmic function that weakly depends on the neutron star parameters) lγ ∼

Rc BQED 1 . 10 B εγ

(33)

This is ∼Rc ∼ R⋆ for MeV photons. As a result, the neutron star magnetosphere is quickly filled with e± that screens the initial voltage. The creation of secondary pairs is halted when the longitudinal electric field, E , is screened. Therefore, considering a rotating magnetized ball in a vacuum is not enough since the magnetosphere is dynamic and capable of generating its own plasma. This nonlinear feedback mechanism causes cyclic bursts of pair creation where a single seed electron can trigger a generation of a huge number of pairs. The resulting charges are blown out relativistically into the surrounding space. After the magnetosphere has cleared from the pairs, the voltage starts to grow again. This leads to cyclic generation of bursts.

Vacuum Birefringence For extremely large magnetic fields, especially those of magnetars with B ∼ 1015 G, even the properties of the surrounding vacuum itself become modified. This happens because of another quantum electrodynamic phenomenon called vacuum birefringence. Birefringence, in general, is a property of, for example, crystals in which the speed of light inside the crystal is dependent on the direction of the light with respect to the axis of the crystal. In crystals, this breaking of isotropicity can happen even if the crystal lattice is, for example, more tightly packed in one direction. This causes the crystal to have different refractive indices of light depending on the direction; birefringence means that instead of one regular, isotropic refractive index, n1 , the medium has two indices, n1 and n2 .

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The vacuum around strongly magnetized neutron stars can become birefringent and develop a differing refractive index along and perpendicular to the local magnetic field direction, n , and n⊥ . The effect is caused by virtual electron-positron pairs of the vacuum background spontaneously appearing and annihilating. Like any charged particle, these virtual pairs also gyrate in the strong magnetic field. This creates an imaginary crystal lattice in the vacuum that modifies the propagation of electromagnetic waves through it. Most notably, the polarization of the radiation is forced to align with the ambient magnetic field. The strength of the effect can be quantified as (Heyl et al. 2003), αF n − n⊥ = 30π



B BQED

2

sin2 α,

(34)

where αF ≈ 1/137 is the fine structure constants and α is the angle between the direction of propagation and the external field. The magnetic field remains strong enough to a distance known as the polarization limiting radius, rpl ∼ 107



B 1012 G

2/5 

Eγ 0.5 keV

1/5

(sin α)2/5 cm.

(35)

This renders the radiation in the inner regions, r < rpl , strongly birefringent and, therefore, also modifies the polarization of the radiation. If the inner field is coherent, like a dipole field, the ordered magnetic field means that the polarization direction of the radiation is also coherent. An observer integrating the polarized radiation over a large solid angle containing the face of the star will hence detect a large net polarization. Therefore, a high degree of polarization is expected for radiation from magnetars.

Superfluid and Superconducting Interiors The material at the core of the neutron star is thought to be in a superfluid state (Baym et al. 1969). The strong interaction force between the nucleons renders the charge-neutral neutrons into a superfluid state and the electrically charged protons into a superconducting state. The electrons are expected to remain in their regular state because the corresponding superconducting transition temperature is very small compared to the temperatures relevant for neutron stars. The superconductivity can lead to drastic changes in the magnetic properties of the object. Most crucially, superconductors exhibit the Meissner effect, where magnetic flux is expelled from the superconducting regions. However, the diffusion timescale of flux repulsion from macroscopic regions for the core material is very

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long (tD ∼ 1022 s) owing to the enormous electrical conductivity (large density enables easy transport of charges). The protons in the core are thought to form a type-II superconductor. This state is characterized by a periodic array of quantized vortices of super-current, which is aligned parallel to the local magnetic field. ( On the other hand, type-I superconductors have fine-scale, alternative regions of normal material encapsulating magnetic flux and superconducting regions exhibiting the Meissner effect. The state of the superconductor depends on the ratio of proton coherence length to the penetration depth. ) The magnetic flux associated with an individual proton vortex is φ0 ≈

hc ≈ 2 × 10−7 G cm2 , 2e

(36)

and the number of vortices per area is, therefore, B/φ0 , meaning that billions of super-current vortices can thread the core. For B ∼ 1012 G, the vortex lattice has a lattice separation of roughly 5 × 10−10 cm. This is large compared to the interparticle distance, meaning that the vortices are mesoscale in size. The neutrons in the core are also in a superfluid state. A salient feature of the superfluid state is that the angular momentum of the superfluid becomes quantized into vortices that carry the angular momentum. Therefore, the core is expected to be composed of multiple vortices carrying the angular momentum of the rotating star. These superfluid vortex lines are parallel to the rotation axis. Each neutron pair vortex supports h¯ of angular momentum; multiple vortices are, therefore, required to support the total angular momentum. The existence of a superfluid component and the possibility of a superconducting core make neutron stars the largest blobs of superfluid material in the universe. They allow us to study superfluidity and superconductivity at the extreme limit since the core can remain superfluid even up to temperatures of millions of Kelvin due to the immense pressure.

Gliches and Quakes The high accuracy of pulsar timing measurements makes it possible to measure even the tiniest change in the star’s rotation rate. These high-precision measurements have revealed a phenomenon called glitches. Glitches are a rare, short-duration pulsar timing phenomenon. They are seen as sudden positive jumps of rotational frequency, Δν > 0 (determined as the difference between the frequency after and before the glitch), in the pulsar timing data, followed by a negative change of the slope, ν˙ < 0. The glitch magnitudes vary from Δν/ν ≈ 10−12 to 10−5 , and they have been detected in over 100 rotation-powered pulsars and magnetars (Espinoza et al. 2011).

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Most glitches are followed by a recovery phase, where the spindown rate increases and tends toward the pre-glitch value. The recovery phase can be modeled with an exponential function, ∝ e−t/tr , with a typical relaxation time of ∼100 days together with a longer timescale component with a relaxation timescale of ∼1000 days. Physically, the glitches are thought to occur because of a rapid transfer of angular momentum between the superfluid interior and the outer crust of the neutron star, driven by catastrophic unpinning of the superfluid vortices (Anderson and Itoh 1975; Haskell and Melatos 2015). The angular momentum mismatch is created by slowing down the star’s crust with electromagnetic torques. The rotation of the superfluid interior of the star, on the other hand, remains unchanged because the quantized vortices remain pinned. After the rotation mismatch exceeds an unknown threshold value, the vortices are unpinned and begin to slide along the lattice plane. Migration of the vortices away from the axis of rotation results in a spindown of the superfluid component, bringing the two components closer to co-rotation. Magnetars are observed to also anti-glitch, where sudden negative, Δν < 0, rotation rate changes, i.e., spindowns (rather than conventional spin-ups) of the star are observed (Archibald et al. 2013). These events are speculated to occur due to magnetospheric reconfiguration. Something needs to trigger the catastrophic unpinning of the superfluid vortices. The most plausible candidates are starquakes and catastrophic readjustments of the crust (Ruderman 1976). The quakes are expected to occur when the crust accumulates stress beyond a critical strain that it can sustain, leading to a mechanical failure of the crystal lattice (Horowitz and Kadau 2009). Why or how such large stress can build up in the crust lattice is still unknown. Seismic motions of the crust will also couple the pulsar interior and the magnetosphere. The quake is expected to launch an elastic shear wave into the crust lattice, and since the magnetic field is frozen in the crust and liquid core, it also leads to perturbation of the magnetosphere. The resulting crustal oscillations deform the magnetic field lines and excite Alfvén waves on the magnetosphere (e.g., Bransgrove et al. 2020). These waves can also interact with each other and heat the magnetospheric plasma (e.g., Li et al. 2019; Nättilä and Beloborodov 2022).

Giant Bursts and Fast Radio Bursts from Magnetars A similar kind of star quake event, only more extreme, is thought to also power magnetar flaring phenomena. In this case, super-strong crustal quakes are proposed as triggers of giant bursts (Duncan and Thompson 1992). Similarly, smaller quakes could produce fast radio bursts as a side product of magnetospheric activity. Giant bursts Giant bursts are massively energetic blasts of radiation. A typical giant burst consists of a short, ∼0.2 s sharp pulse of hard X-rays and soft gamma rays of energies E ∼ 100 keV to MeV. The initial pulse is followed by a fainter,

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slowly fading tail lasting minutes. In the case of the famous March 5th, 1979 event, the tail also varied in intensity with a sinusoidal perturbation (with two differing peaks per cycle) and a period of 8 s. These oscillations were seen for more than 20 cycles. The leading model that could power these flares is a large-scale magnetospheric reconfiguration – these models rely on the large magnetic energy reservoir of the magnetar and on the fact that energy stored in the magnetic field can be quickly released to explain the extremely short duration of the pulses. In this picture, a strong crustal quake launches Alfvén waves into the magnetosphere. The waves twist the field lines, causing them to inflate and expand. The inflated bundle overtwists and undergoes rapid magnetic reconnection. The magnetic reconnection leads to the creation of strong non-ideal electric fields and turbulent plasma motions that can energize and heat the local plasma (e.g., Nättilä and Beloborodov 2021). The mechanism resembles the energization mechanism observed behind solar flares. The twisted, evolving bundle carries a strong electric current and a relativistic stream of particles along the arched magnetic line loop. The streaming charged particles quickly radiate their energy as synchrotron radiation and can furthermore Compton upscatter the photons up to relativistic energies. These high-energy photons will pair-create, forming a trapped pair-plasma cloud. Cooling of this pair plasma in the strong magnetic field provides a mechanism for generating the ultra-luminous soft gamma ray burst seen from the soft gamma ray repeaters. Furthermore, the streaming plasma will also fall back to the star, heating the magnetic footprints. Self-consistent modeling of the giant bursts requires detailed plasma physics models in strong magnetic fields and large radiation densities (Beloborodov 2021). Fast radio bursts Similar plasma physics-related phenomena to giant bursts are the recently found fast radio bursts (FRBs) (Cordes and Chatterjee 2019; Petroff et al. 2019, 2022). FRBs are short ∼1 ms duration radio pulses with energies ∼1035 to 1043 erg s−1 (translating to 50 mJy to 100 Jy) observed between radio frequencies from 400 Mhz to 8 GHz. The emission is strongly polarized, exhibiting linear polarization degrees up to 100%. FRBs are the biggest radio emission-based enigma since the discovery of pulsars. The latest coincident observation of FRB, together with a flaring magnetar, undeniably established a connection between the two (at least for some sub-class of FRBs). The extremely high brightness temperature required to explain the FRB emission requires a coherent electromagnetic emission mechanism. The high coherence means that many particles are required to emit in phase rendering the problem automatically into a plasma physics problem. Current leading coherent emission mechanisms are the synchrotron maser instability from magnetized collisionless shocks (Sironi et al. 2021) and plasma waves (magnetosonic fast modes) from collapsing, reconnecting current sheets beyond the light cylinder of the magnetars (Lyubarsky 2020; Mahlmann et al. 2022). These and other emission mechanisms are reviewed in Lyubarsky (2021).

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Extreme Particles: Cosmic Rays, Neutrinos, and More Finally, it should be mentioned that neutron stars are thought to be the origin of many high-energy particle events like cosmic rays and neutrinos and, more speculatively, even sources of dark matter candidates like axions. Observations of all of these can be used to probe fundamental symmetries in physical laws because their energies are unreachable by Earthly laboratories. In addition, they help us better understand the nature of particle acceleration in our universe. Cosmic rays Cosmic rays are relativistic protons or heavier atomic nuclei moving with velocities near the speed of light. The flux of cosmic rays is constantly raining down on us on Earth. They are typically detected when they slam into the upper layers of Earth’s atmosphere and dissipate their energy in showers of secondary high-energy particles (like X-rays, protons, electrons, alpha particles, pions, muons, neutrinos, and neutrons). The secondary particles have been first observed decades ago and are now routinely monitored. In the most extreme case, a dim fluorescent light from a cosmic ray exciting atmospheric nitrogen can be detected if the night is dark and moonless. On a more regular basis, they are detected by space-borne observatories such Fermi Gamma-Ray Space Telescope (detecting the secondary gamma rays from the showers) or ground-based observatories such as HESS or HAWCK (detecting Cerenkov radiation from the cosmic rays entering the Earth’s atmosphere). The cosmic ray energy spectrum peaks at ∼109 eV and extends into a broad power-law tail. The power-law tail has two breaks: first one, (named “knee”) at ∼1015 eV and another (named “ankle”) at ∼1018 eV. The lowest energy particles, 1010 eV, are thought to originate mostly from our own Sun (due to solar flares accelerating particles), while the intermediate energies, 1010 eV  ECR  1015 eV, are galactic cosmic rays, accelerated by shocks in supernova remnants (Giuliani et al. 2011; Ackermann et al. 2013) – neutron stars in action! Other more distant sources of high-energy cosmic rays could include, for example, active galactic nuclei (supermassive black holes at the centers of galaxies). The most energetic cosmic rays, named ultra-high-energy cosmic rays (UHECRs), can have kinetic energies up to 1020 eV. In comparison, the LHC (Large Hadron Collider) on Earth can only probe energies up to ∼1017 eV. These extreme particles are composed of the lightest elements, most likely pure protons or light nuclei like helium cores. However, each carries a kinetic energy equivalent to a baseball (mb ∼ 150 g) traveling with a velocity of vb ≈ 100 km h−1 ∼ 2800 cm s−1 , Ekin =

1 1 mb vb2 ∼ 150 g × (2800 cm s−1 )2 ∼ 6 × 108 erg ∼ 4 × 1020 eV. (37) 2 2

The UHECR particle is extremely relativistic since its energy is EUCR = γUCR mp c2 , so that γUCR ∼ 1010 for EUCR ∼ 109 erg. Their energy is so high that they are theoretically expected to quickly lose it by scattering against the low-energy photons

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of the cosmic microwave background (Greisen-Zatsepin-Kuzmin limit; GZK limit). This means that they cannot be produced by, for example, the most distant quasars or active galactic nuclei but must instead originate from somewhere nearby. The big question is what mechanism can accelerate protons to such extreme Lorentz factors in our neighborhood? This mystery is complemented by the latest observation of PeV photons from the Crab (Lhaaso Collaboration et al. 2021) that also strongly challenges our picture of the particle acceleration and its limits. Neutron stars are plausible engines for powering the particle acceleration in many cosmic ray generation models. Neutrinos Another class of extreme particle is the neutrinos – light-weight (mν  0.120 eV) subatomic particles that interact only via weak interaction and gravity. Neutrinos come in three leptonic flavors: electron neutrinos (νe ), muon neutrinos (νμ ), and tau neutrinos (ντ ). They oscillate between the different flavors; a neutrino with a specific flavor is composed of a quantum superposition of all three flavors and can randomly change its appearance via flavor oscillations. They are produced in radioactive decay, nuclear reactions, or as secondary particles by cosmic rays interacting with Earth’s atmosphere. Most of the neutrinos detected on Earth come from the Sun. However, some neutrinos are confirmed to have a cosmic origin. These “cosmic neutrinos” have been directly observed from a core-collapse supernova explosion SN 1987A (Hirata et al. 1987), making supernovae and neutron stars prime candidates for neutrino sources. The primary mechanism for neutrino emission in the supernova explosions (i.e., non-degenerate matter with density ρ < 107 g cm−3 ) is the annihilation of electron-positron pairs into neutrino-antineutrino pairs, e− + e+ → ν + ν¯ (where ν is the neutrino and ν¯ is anti-neutrino) (Beaudet et al. 1967). At high temperatures, T  109 K, the volumetric energy loss rate from the pair annihilation is (see Mushtukov et al. (2018) for discussion) 24

Qν ≈ 4 × 10



T 1010 K

9

erg cm−3 s−1 .

(38)

Similar mechanisms could be at play in ultraluminous X-ray sources if they are interpreted as systems with super-Eddington accretion channeled onto magnetized neutron stars (Basko and Sunyaev 1976; Bachetti et al. 2014); the high mass flux, production of an accretion shock, and the resulting shock-heated high temperatures would render the accretion columns on top of these neutron stars into efficient sources of neutrinos – neutrino pulsars (Mushtukov et al. 2018)! Detection of astrophysical neutrinos holds great promise for probing fundamental physics. In the event of a close-by galactic supernova, there is hope that we could accurately measure the neutrino energies and flavor spectrum. This would help us better constrain the core-collapse supernova physics and any high-energy nonstandard interactions beyond the standard model of particle physics.

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Axions Neutron stars are also speculated to work as probes of various dark matter candidate particles (Tinyakov et al. 2021). The most intriguing of these is the axion, an extremely light (ma < 1 eV) elementary particle, postulated to resolve the strong CP symmetry problem in quantum chromodynamics. Axions couple to the electromagnetic fields and can change the behavior of the electrodynamic processes in the magnetosphere. Most notable of these couplings is the alteration of the physics at the magnetospheric gap region, E · B = 0, which is associated with a strong voltage, efficient production of gamma rays, and therefore also the possible origin of axions (Prabhu 2021).

Summary Research of neutron stars encompasses many branches of modern physics, from gravitational physics to nuclear and particle physics, from electrodynamics to plasma physics. What makes neutron stars unique is that they exhibit extreme behavior in each one of these fields, often offering novel insight into the limits of our physical theories. We started by presenting a (short) history of neutron stars and their discovery. For a more thorough historical discussion on neutron stars, we refer the reader to Yakovlev et al. (2013). We then reviewed the basic arguments behind the studies of gravitation, nuclear and particle physics, electromagnetism and quantum electrodynamics, and plasma physics in the context of neutron stars. Each of these fields is still full of mysteries and unexplained phenomena that need to be solved to understand the physics and astrophysics of neutron stars better. In this chapter we have provided a quick precursor to the field of fundamental physics of neutron stars, and for the interested reader, more thorough reviews of these topics can be found from the following studies. Excellent sources of more information for studies of gravity include (Misner et al. 1973; Paschalidis and Stergioulas 2017). The physics of emergent radiation is discussed in Potekhin (2014) and the effects of light-bending in Nättilä and Pihajoki (2018) and Suleimanov et al. (2020). Notably, a simple model of light bending in curved space-time is developed in Beloborodov (2002) and Poutanen (2020a). Studies of the neutron star equation of states are reviewed in Özel and Freire (2016) and Lattimer (2019). Measurements of neutron star radii are discussed in Miller and Lamb (2016), Suleimanov et al. (2016), and Degenaar and Suleimanov (2018). The recent gravitational wave observations are presented, for example, in Baiotti (2019). Studies of neutron stars and pulsar magnetospheres are reviewed in Cerutti and Beloborodov (2017) and Beskin (2018). Pair cascades and quantum electrodynamic effects are discussed in Svensson (1982a, b). Magnetars and their observations are reviewed in Kaspi and Beloborodov (2017), and plasma physics of fast radio bursts are well-discussed in Lyubarsky (2021).

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Cross-References ⊲ Isolated Neutron Stars ⊲ Low-Magnetic-Field Neutron Stars in X-ray Binaries ⊲ Low-Mass X-ray Binaries

References B.P. Abbott et al. in LIGO Scientific Collaboration and Virgo Collaboration, GW170817: observation of gravitational waves from a binary neutron star inspiral. Phys. Rev. Lett. 119(16), 161101 (2017). https://doi.org/10.1103/PhysRevLett.119.161101, 1710.05832 M. Ackermann et al., Detection of the characteristic pion-decay signature in supernova remnants. Science 339(6121), 807–811 (2013). https://doi.org/10.1126/science.1231160, 1302.3307 M. AlGendy, S.M. Morsink, Universality of the acceleration due to gravity on the surface of a rapidly rotating neutron star. ApJ 791(2), 78 (2014). https://doi.org/10.1088/0004-637X/791/2/ 78, 1404.0609 P.W. Anderson, N. Itoh, Pulsar glitches and restlessness as a hard superfluidity phenomenon. Nature 256(5512), 25–27 (1975). https://doi.org/10.1038/256025a0 E. Annala, T. Gorda, A. Kurkela, J. Nättilä, A. Vuorinen, Evidence for quark-matter cores in massive neutron stars. Nat. Phys. 16(9), 907–910 (2020). https://doi.org/10.1038/s41567-0200914-9, 1903.09121 E. Annala, T. Gorda, E. Katerini, A. Kurkela, J. Nättilä, V. Paschalidis, A. Vuorinen, Multimessenger constraints for ultradense matter. Phys. Rev. X 12(1), 011058 (2022). https://doi.org/10. 1103/PhysRevX.12.011058, 2105.05132 J. Antoniadis, P.C.C. Freire, N. Wex, T.M. Tauris, R.S. Lynch, M.H. van Kerkwijk, M. Kramer, C. Bassa, V.S. Dhillon, T. Driebe, J.W.T. Hessels, V.M. Kaspi, V.I. Kondratiev, N. Langer, T.R. Marsh, M.A. McLaughlin, T.T. Pennucci, S.M. Ransom, I.H. Stairs, J. van Leeuwen, J.P.W. Verbiest, D.G. Whelan, A massive pulsar in a compact relativistic binary. Science 340(6131), 448 (2013). https://doi.org/10.1126/science.1233232, 1304.6875 R.F. Archibald, V.M. Kaspi, C.Y. Ng, K.N. Gourgouliatos, D. Tsang, P. Scholz, A.P. Beardmore, N. Gehrels, J.A. Kennea, An anti-glitch in a magnetar. Nature 497(7451), 591–593 (2013). https:// doi.org/10.1038/nature12159, 1305.6894 J. Arons, Some problems of pulsar physics or I’m madly in love with electricity. Space Sci. Rev. 24(4), 437–510 (1979). https://doi.org/10.1007/BF00172212 J. Arons, Pulsars: progress, problems and prospects (2007). arXiv e-prints arXiv:0708.1050, 0708.1050 B. Arzoumanian et al. in NANOGrav Collaboration, The NANOGrav 11-year Data Set: highprecision timing of 45 millisecond pulsars. ApJS 235(2), 37 (2018). https://doi.org/10.3847/ 1538-4365/aab5b0, 1801.01837 W. Baade, F. Zwicky, Cosmic rays from super-novae. Proc. Natl. Acad. Sci. 20, 259–263 (1934). https://doi.org/10.1073/pnas.20.5.259 M. Bachetti, F.A. Harrison, D.J. Walton, B.W. Grefenstette, D. Chakrabarty, Fürst F, D. Barret, A. Beloborodov, S.E. Boggs, F.E. Christensen, W.W. Craig, A.C. Fabian, C.J. Hailey, A. Hornschemeier, V. Kaspi, S.R. Kulkarni, T. Maccarone, J.M. Miller, V. Rana, D. Stern, S.P. Tendulkar, J. Tomsick, N.A. Webb, W.W. Zhang, An ultraluminous X-ray source powered by an accreting neutron star. Nature 514(7521), 202–204 (2014). https://doi.org/10.1038/ nature13791, 1410.3590

4222

J. Nättilä and J. J. E. Kajava

L. Baiotti, Gravitational waves from neutron star mergers and their relation to the nuclear equation of state. Prog. Part. Nucl. Phys. 109, 103714 (2019). https://doi.org/10.1016/j.ppnp.2019. 103714, 1907.08534 M.M. Basko, R.A. Sunyaev, The limiting luminosity of accreting neutron stars with magnetic fields. MNRAS 175, 395–417 (1976). https://doi.org/10.1093/mnras/175.2.395 G. Bateman, MHD Instabilities (MIT Press, Cambridge, 1978) M. Bauböck, E. Berti, D. Psaltis, F. Özel, Relations between neutron-star parameters in the HartleThorne approximation. ApJ 777(1), 68 (2013). https://doi.org/10.1088/0004-637X/777/1/68, 1306.0569 G. Baym, C. Pethick, D. Pines, Superfluidity in neutron stars. Nature 224(5220), 673–674 (1969). https://doi.org/10.1038/224673a0 G. Beaudet, V. Petrosian, E.E. Salpeter, Energy losses due to neutrino processes. ApJ 150, 979 (1967). https://doi.org/10.1086/149398 A.M. Beloborodov, Gravitational bending of light near compact objects. ApJ 566, L85–L88 (2002). https://doi.org/10.1086/339511 A.M. Beloborodov, Emission of magnetar bursts and precursors of neutron star mergers. ApJ 921(1), 92 (2021). https://doi.org/10.3847/1538-4357/ac17e7, 2011.07310 V.B. Berestetskii, E.M. Lifshits, L.P. Pitaevskii, Quantum electrodynamics (2nd revised edn.) (1982). https://doi.org/10.1016/C2009-0-24486-2 V.S. Beskin, Radio pulsars: already fifty years! Phys. Usp. 61(4), 353–380 (2018). https://doi.org/ 10.3367/UFNe.2017.10.038216, 1807.08528 S. Bogdanov, F.K. Lamb, S. Mahmoodifar, M.C. Miller, S.M. Morsink, T.E. Riley, T.E. Strohmayer, A.K. Tung, A.L. Watts, A.J. Dittmann, D. Chakrabarty, S. Guillot, Z. Arzoumanian, K.C. Gendreau,Constraining the neutron star mass-radius relation and dense matter equation of state with NICER. II. Emission from hot spots on a rapidly rotating neutron star. ApJ 887(1), L26 (2019). https://doi.org/10.3847/2041-8213/ab5968, 1912.05707 T.M. Braje, R.W. Romani, K.P. Rauch, Light curves of rapidly rotating neutron stars. ApJ 531, 447–452 (2000). https://doi.org/10.1086/308448 A. Bransgrove, A.M. Beloborodov, Y. Levin, A quake quenching the vela pulsar. ApJ 897(2), 173 (2020). https://doi.org/10.3847/1538-4357/ab93b7, 2001.08658 C. Cadeau, S.M. Morsink, D. Leahy, S.S. Campbell, Light curves for rapidly rotating neutron stars. ApJ 654, 458–469 (2007). https://doi.org/10.1086/509103, astro-ph/0609325 M. Caleb, I. Heywood, K. Rajwade, M. Malenta, B. Willem Stappers, E. Barr, W. Chen, V. Morello, S. Sanidas, J. van den Eijnden, M. Kramer, D. Buckley, J. Brink, S.E. Motta, P. Woudt, P. Weltevrede, F. Jankowski, M. Surnis, S. Buchner, M.C. Bezuidenhout, L.N. Driessen, R. Fender, Discovery of a radio-emitting neutron star with an ultra-long spin period of 76 s. Nat. Astron. 6, 828–836 (2022). https://doi.org/10.1038/s41550-022-01688-x, 2206.01346 B. Cerutti, A.M. Beloborodov, Electrodynamics of pulsar magnetospheres. Space Sci. Rev. 207(1– 4), 111–136 (2017). https://doi.org/10.1007/s11214-016-0315-7, 1611.04331 B. Cerutti, A. Philippov, K. Parfrey, A. Spitkovsky, Particle acceleration in axisymmetric pulsar current sheets. MNRAS 448(1), 606–619 (2015). https://doi.org/10.1093/mnras/stv042, 1410.3757 B. Cerutti, A.A. Philippov, A. Spitkovsky, Modelling high-energy pulsar light curves from first principles. MNRAS 457(3), 2401–2414 (2016). https://doi.org/10.1093/mnras/stw124, 1511.01785 J. Chadwick, Possible existence of a neutron. Nature 129, 312 (1932a). https://doi.org/10.1038/ 129312a0 J. Chadwick, The existence of a neutron. Proc. R. Soc. Lond. Ser. A 136, 692–708 (1932b). https:// doi.org/10.1098/rspa.1932.0112 A.Y. Chen, A.M. Beloborodov, Electrodynamics of axisymmetric pulsar magnetosphere with electron-positron discharge: a numerical experiment. ApJ 795(1), L22 (2014). https://doi.org/ 10.1088/2041-8205/795/1/L22, 1406.7834 I. Contopoulos, D. Kazanas, C. Fendt, The axisymmetric pulsar magnetosphere. ApJ 511(1), 351–358 (1999). https://doi.org/10.1086/306652, astro-ph/9903049

114 Fundamental Physics with Neutron Stars

4223

J.M. Cordes, S. Chatterjee, Fast radio bursts: an extragalactic enigma. ARA&A 57, 417–465 (2019). https://doi.org/10.1146/annurev-astro-091918-104501, 1906.05878 R. Cornelisse, J. Heise, E. Kuulkers, F. Verbunt, J.J.M. in’t Zand, The longest thermonuclear X-ray burst ever observed? A BeppoSAX wide field camera observation of 4U 1735-44. A&A 357, L21–L24 (2000). astro-ph/0003454 A. Cumming, L. Bildsten, Carbon flashes in the heavy-element ocean on accreting neutron stars. ApJ 559(2), L127–L130 (2001). https://doi.org/10.1086/323937, astro-ph/0107213 R.H. Cyburt, A.M. Amthor, A. Heger, E. Johnson, L. Keek, Z. Meisel, H. Schatz, K. Smith, Dependence of x-ray burst models on nuclear reaction rates. ApJ 830(2), 55 (2016). https:// doi.org/10.3847/0004-637X/830/2/55, 1607.03416 E. Damen, E. Magnier, W.H.G. Lewin, J. Tan, W. Penninx, J. van Paradijs, X-ray bursts with photospheric radius expansion and the gravitational redshift of neutron stars. A&A 237, 103 (1990) N. Degenaar, V.F. Suleimanov, Testing the equation of state with electromagnetic observations, in The Physics and Astro-physics of Neutron Stars, Astrophysics and Space Science Library, vol. 457, ed. by L. Rezzolla, P. Pizzochero, D.I. Jones, N. Rea, I. Vidaña (2018), p. 185. https:// doi.org/10.1007/978-3-319-97616-7_5 N. Degenaar, D.R. Ballantyne, T. Belloni, M. Chakraborty, Y.P. Chen, L. Ji, P. Kretschmar, E. Kuulkers, J. Li, T.J. Maccarone, J. Malzac, S. Zhang, S.N. Zhang, Accretion disks and coronae in the x-ray flashlight. Space Sci. Rev. 214(1), 15 (2018). https://doi.org/10.1007/s11214-0170448-3, 1711.06272 P.B. Demorest, T. Pennucci, S.M. Ransom, M.S.E. Roberts, J.W.T. Hessels, A two-solar-mass neutron star measured using Shapiro delay. Nature 467(7319), 1081–1083 (2010). https://doi. org/10.1038/nature09466, 1010.5788 F. Douchin, P. Haensel, A unified equation of state of dense matter and neutron star structure. A&A 380, 151–167 (2001). https://doi.org/10.1051/0004-6361:20011402, astro-ph/0111092 R.C. Duncan, C. Thompson, Formation of very strongly magnetized neutron stars: implications for gamma-ray bursts. ApJ 392, L9 (1992). https://doi.org/10.1086/186413 C.M. Espinoza, A.G. Lyne, B.W. Stappers, M. Kramer, A study of 315 glitches in the rotation of 102 pulsars. MNRAS 414(2), 1679–1704 (2011). https://doi.org/10.1111/j.1365-2966.2011. 18503.x, 1102.1743 R. Fernández, B.D. Metzger, Electromagnetic signatures of neutron star mergers in the advanced LIGO Era. Ann. Rev. Nucl. Part. Sci. 66(1), 23–45 (2016). https://doi.org/10.1146/annurevnucl-102115-044819, 1512.05435 E. Fonseca, T.T. Pennucci, J.A. Ellis, I.H. Stairs, D.J. Nice, S.M. Ransom, P.B. Demorest, Z. Arzoumanian, K. Crowter, T. Dolch, R.D. Ferdman, M.E. Gonzalez, G. Jones, M.L. Jones, M.T. Lam, L. Levin, M.A. McLaughlin, K. Stovall, J.K. Swiggum, W. Zhu, The NANOGrav nineyear data set: mass and geometric measurements of binary millisecond pulsars. ApJ 832(2), 167 (2016). https://doi.org/10.3847/0004-637X/832/2/167, 1603.00545 E. Fonseca, H.T. Cromartie, T.T. Pennucci, P.S. Ray, A.Y. Kirichenko, S.M. Ransom, P.B. Demorest, I.H. Stairs, Z. Arzoumanian, L. Guillemot, A. Parthasarathy, M. Kerr, I. Cognard, P.T. Baker, H. Blumer, P.R. Brook, M. DeCesar, T. Dolch, F.A. Dong, E.C. Ferrara, W. Fiore, N. Garver-Daniels, D.C. Good, R. Jennings, M.L. Jones, V.M. Kaspi, M.T. Lam, D.R. Lorimer, J. Luo, A. McEwen, J.W. McKee, M.A. McLaughlin, N. McMann, B.W. Meyers, A. Naidu, C. Ng, D.J. Nice, N. Pol, H.A. Radovan, B. Shapiro-Albert, C.M. Tan, S.P. Tendulkar, J.K. Swiggum, H.M. Wahl, W.W. Zhu, Refined mass and geometric measurements of the highmass PSR J0740+6620. ApJ 915(1), L12 (2021). https://doi.org/10.3847/2041-8213/ac03b8, 2104.00880 D.K. Galloway, L. Keek, Thermonuclear X-ray Bursts, in Timing Neutron Stars: Pulsations, Oscillations and Explosions, Astrophysics and Space Science Library, vol. 461, ed. by T.M. Belloni, M. Méndez, C. Zhang (2021), pp. 209–262. https://doi.org/10.1007/978-3-662-621103_5, 1712.06227 A. Giuliani, M. Cardillo, M. Tavani, Y. Fukui, S. Yoshiike, K. Torii, G. Dubner, G. Castelletti, G. Barbiellini, A. Bulgarelli, P. Caraveo, E. Costa, P.W. Cattaneo, A. Chen, T. Contessi, E. Del

4224

J. Nättilä and J. J. E. Kajava

Monte, I. Donnarumma, Y. Evangelista, M. Feroci, F. Gianotti, F. Lazzarotto, F. Lucarelli, F. Longo, M. Marisaldi, S. Mereghetti, L. Pacciani, A. Pellizzoni, G. Piano, P. Picozza, C. Pittori, G. Pucella, M. Rapisarda, A. Rappoldi, S. Sabatini, P. Soffitta, E. Striani, M. Trifoglio, A. Trois, S. Vercellone, F. Verrecchia, V. Vittorini, S. Colafrancesco, P. Giommi, G. Bignami, Neutral pion emission from accelerated protons in the supernova remnant W44. ApJ 742(2), L30 (2011). https://doi.org/10.1088/2041-8205/742/2/L30, 1111.4868 T. Gold, Rotating neutron stars as the origin of the pulsating radio sources. Nature 218(5143), 731–732 (1968). https://doi.org/10.1038/218731a0 P. Goldreich, W.H. Julian, Pulsar electrodynamics. ApJ 157, 869 (1969). https://doi.org/10.1086/ 150119 D.A. Green, A revised catalogue of 294 Galactic supernova remnants. J. Astrophys. Astron. 40(4), 36 (2019). https://doi.org/10.1007/s12036-019-9601-6, 1907.02638 A. Gruzinov, Power of an axisymmetric pulsar. Phys. Rev. Lett. 94(2), 021101 (2005). https://doi. org/10.1103/PhysRevLett.94.021101, astro-ph/0407279 S. Guichandut, A. Cumming, M. Falanga, Z. Li, M. Zamfir, Expanded atmospheres and winds in type I x-ray bursts from accreting neutron stars. ApJ 914(1), 49 (2021). https://doi.org/10.3847/ 1538-4357/abfa13, 2103.08476 S. Guillot, M. Servillat, N.A. Webb, R.E. Rutledge, Measurement of the radius of neutron stars with high signal-to-noise quiescent low-mass x-ray binaries in globular clusters. ApJ 772(1), 7 (2013). https://doi.org/10.1088/0004-637X/772/1/7, 1302.0023 P. Haensel, J.L. Zdunik, Models of crustal heating in accreting neutron stars. A&A 480(2), 459– 464 (2008). https://doi.org/10.1051/0004-6361:20078578, 0708.3996 P. Haensel, A.Y. Potekhin, D.G. Yakovlev, Neutron Stars 1: Equation of State and Structure. Astrophysics and Space Science Library, vol. 326 (Springer, New York, 2007) J.B. Hartle, K.S. Thorne, Slowly rotating relativistic stars. II. Models for neutron stars and supermassive stars. ApJ 153, 807 (1968). https://doi.org/10.1086/149707 B. Haskell, A. Melatos, Models of pulsar glitches. Int. J. Mod. Phys. D 24(3), 1530008 (2015). https://doi.org/10.1142/S0218271815300086, 1502.07062 J.W.T. Hessels, S.M. Ransom, I.H. Stairs, P.C.C. Freire, V.M. Kaspi, F. Camilo, A radio pulsar spinning at 716 Hz. Science 311(5769), 1901–1904 (2006). https://doi.org/10.1126/science. 1123430, astro-ph/0601337 A. Hewish, S.J. Bell, J.D.H. Pilkington, P.F. Scott, R.A. Collins, Observation of a rapidly pulsating radio source. Nature 217(5130), 709–713 (1968). https://doi.org/10.1038/217709a0 J.S. Heyl, N.J. Shaviv, D. Lloyd, The high-energy polarization-limiting radius of neutron star magnetospheres – I. Slowly rotating neutron stars. MNRAS 342(1), 134–144 (2003). https:// doi.org/10.1046/j.1365-8711.2003.06521.x, astro-ph/0302118 K. Hirata, T. Kajita, M. Koshiba, M. Nakahata, Y. Oyama, N. Sato, A. Suzuki, M. Takita, Y. Totsuka, T. Kifune, T. Suda, K. Takahashi, T. Tanimori, K. Miyano, M. Yamada, E.W. Beier, L.R. Feldscher, S.B. Kim, A.K. Mann, F.M. Newcomer, R. van, W. Zhang, B.G. Cortez, Observation of a neutrino burst from the supernova SN1987A. Phys. Rev. Lett. 58(14), 1490– 1493 (1987). https://doi.org/10.1103/PhysRevLett.58.1490 W.C.G. Ho, C.O. Heinke, A neutron star with a carbon atmosphere in the Cassiopeia A supernova remnant. Nature 462(7269), 71–73 (2009). https://doi.org/10.1038/nature08525, 0911.0672 C.J. Horowitz, K. Kadau, Breaking strain of neutron star crust and gravitational waves. Phys. Rev. Lett. 102(19), 191102 (2009). https://doi.org/10.1103/PhysRevLett.102.191102, 0904.1986 C.J. Horowitz, D.K. Berry, E.F. Brown, Phase separation in the crust of accreting neutron stars. Phys. Rev. E 75(6), 066101 (2007). https://doi.org/10.1103/PhysRevE.75.066101, astroph/0703062 J.J.M. in’t Zand, N.N. Weinberg, Evidence of heavy-element ashes in thermonuclear x-ray bursts with photospheric superexpansion. A&A 520, A81 (2010). https://doi.org/10.1051/0004-6361/ 200913952, 1001.0900 J.J.M. in’t Zand, L. Keek, Y. Cavecchi, Relativistic outflow from two thermonuclear shell flashes on neutron stars. A&A 568, A69 (2014). https://doi.org/10.1051/0004-6361/201424044, 1407.0300

114 Fundamental Physics with Neutron Stars

4225

J.M. Jauch, F. Rohrlich, The Theory of Photons and Electrons. The Relativistic Quantum Field Theory of Charged Particles with Spin One-Half (Springer Nature, 1976). https://doi.org/10. 1007/978-3-642-80951-4 J.J.E. Kajava, J. Nättilä, O.M. Latvala, M. Pursiainen, J. Poutanen, V.F. Suleimanov, M.G. Revnivtsev, E. Kuulkers, D.K. Galloway, The influence of accretion geometry on the spectral evolution during thermonuclear (type I) X-ray bursts. MNRAS 445(4), 4218–4234 (2014). https://doi.org/10.1093/mnras/stu2073, 1406.0322 J.J.E. Kajava, K.I.I. Koljonen, J. Nättilä, V. Suleimanov, J. Poutanen, Variable spreading layer in 4U 1608-52 during thermonuclear X-ray bursts in the soft state. MNRAS 472(1), 78–89 (2017a). https://doi.org/10.1093/mnras/stx1963, 1707.09479 J.J.E. Kajava, J. Nättilä, J. Poutanen, A. Cumming, V. Suleimanov, E. Kuulkers, Detection of burning ashes from thermonuclear X-ray bursts. MNRAS 464(1), L6–L10 (2017b). https://doi. org/10.1093/mnrasl/slw167, 1608.06801 J.J.E. Kajava, C. Sánchez-Fernández, E. Kuulkers, J. Poutanen, X-ray burst-induced spectral variability in 4U 1728-34. A&A 599, A89 (2017c). https://doi.org/10.1051/0004-6361/201629542, 1611.03976 V.M. Kaspi, A.M. Beloborodov, Magnetars. ARA&A 55(1), 261–301 (2017). https://doi.org/10. 1146/annurev-astro-081915-023329, 1703.00068 V.M. Kaspi, M.S.E. Roberts, A.K. Harding, Isolated neutron stars: from the Surface to the Interior. in Compact stellar X-ray sources, vol. 39, ed. by Z. Silvia, T. Roberto, P. Dany, Cambridge University Press, Cambridge, (2006), pp. 279–339 D. Klochkov, V. Suleimanov, G. Pühlhofer, D.G. Yakovlev, A. Santangelo, K. Werner, The neutron star in HESS J1731-347: central compact objects as laboratories to study the equation of state of superdense matter. A&A 573, A53 (2015). https://doi.org/10.1051/0004-6361/201424683, 1410.1055 E. Kuulkers, P.R. den Hartog, J.J.M. in’t Zand, F.W.M. Verbunt, W.E. Harris, M. Cocchi, Photospheric radius expansion x-ray bursts as standard candles. A&A 399, 663–680 (2003). https://doi.org/10.1051/0004-6361:20021781, astro-ph/0212028 L.D. Landau, On the theory of stars. Phys. Z. Sowjetunion 1, 285–288 (1932) J.M. Lattimer, Neutron star mass and radius measurements. Universe 5(7), 159 (2019). https://doi. org/10.3390/universe5070159 R. Lau, M. Beard, S.S. Gupta, H. Schatz, A.V. Afanasjev, E.F. Brown, A. Deibel, L.R. Gasques, G.W. Hitt, W.R. Hix, L. Keek, P. Möller, P.S. Shternin, A.W. Steiner, M. Wiescher, Y. Xu, Nuclear reactions in the crusts of accreting neutron stars. ApJ 859(1), 62 (2018). https://doi.org/ 10.3847/1538-4357/aabfe0, 1803.03818 Lhaaso Collaboration, Z. Cao et al., Peta-electron volt gamma-ray emission from the crab nebula. Science 373, 425–430 (2021). https://doi.org/10.1126/science.abg5137, 2111.06545 X. Li, J. Zrake, A.M. Beloborodov, Dissipation of Alfvén waves in relativistic magnetospheres of magnetars. ApJ 881(1), 13 (2019). https://doi.org/10.3847/1538-4357/ab2a03, 1810.10493 K.H. Lo, M.C. Miller, S. Bhattacharyya, F.K. Lamb, Determining neutron star masses and radii using energy-resolved waveforms of x-ray burst oscillations. ApJ 776, 19 (2013). https://doi. org/10.1088/0004-637X/776/1/19, 1304.2330 V. Loktev, T. Salmi, J. Nättilä, J. Poutanen, Oblate Schwarzschild approximation for polarized radiation from rapidly rotating neutron stars. A&A 643, A84 (2020). https://doi.org/10.1051/ 0004-6361/202039134, 2009.08852 Y. Lyubarsky, Fast radio bursts from reconnection in a magnetar magnetosphere. ApJ 897(1), 1 (2020). https://doi.org/10.3847/1538-4357/ab97b5, 2001.02007 Y. Lyubarsky, Emission mechanisms of fast radio bursts. Universe 7(3), 56 (2021). https://doi.org/ 10.3390/universe7030056, 2103.00470 Y. Lyubarsky, J.G. Kirk, Reconnection in a striped pulsar wind. ApJ 547(1), 437–448 (2001). https://doi.org/10.1086/318354, astro-ph/0009270 J.F. Mahlmann, A.A. Philippov, A. Levinson, A. Spitkovsky, H. Hakobyan, Electromagnetic fireworks: fast radio bursts from rapid reconnection in the compressed magnetar wind. ApJ 932(2), L20 (2022). https://doi.org/10.3847/2041-8213/ac7156, 2203.04320

4226

J. Nättilä and J. J. E. Kajava

R.N. Manchester, G.B. Hobbs, A. Teoh, M. Hobbs, VizieR Online Data Catalog: ATNF Pulsar Catalog (Manchester+, 2005) (VizieR Online Data Catalog VII/245, 2005) J.C. McKinney, Relativistic force-free electrodynamic simulations of neutron star magnetospheres. MNRAS 368(1), L30–L34 (2006). https://doi.org/10.1111/j.1745-3933.2006.00150.x, astroph/0601411 F.C. Michel, Relativistic stellar-wind torques. ApJ 158, 727 (1969). https://doi.org/10.1086/150233 F.C. Michel, Rotating magnetospheres: an exact 3-D solution. ApJ 180, L133 (1973). https://doi. org/10.1086/181169 M.C. Miller, F.K. Lamb, Observational constraints on neutron star masses and radii. Eur. Phys. J. A 52, 63 (2016). https://doi.org/10.1140/epja/i2016-16063-8, 1604.03894 M.C. Miller, F.K. Lamb, A.J. Dittmann, S. Bogdanov, Z. Arzoumanian, K.C. Gendreau, S. Guillot, A.K. Harding, W.C.G. Ho, J.M. Lattimer, R.M. Ludlam, S. Mahmoodifar, S.M. Morsink, P.S. Ray, T.E. Strohmayer, K.S. Wood, T. Enoto, R. Foster, T. Okajima, G. Prigozhin, Y. Soong, PSR J0030+0451 mass and radius from NICER data and implications for the properties of neutron star matter. ApJ 887(1), L24 (2019). https://doi.org/10.3847/2041-8213/ab50c5, 1912.05705 M.C. Miller, F.K. Lamb, A.J. Dittmann, S. Bogdanov, Z. Arzoumanian, K.C. Gendreau, S. Guillot, W.C.G. Ho, J.M. Lattimer, M. Loewenstein, S.M. Morsink, P.S. Ray, M.T. Wolff, C.L. Baker, T. Cazeau, S. Manthripragada, C.B. Markwardt, T. Okajima, S. Pollard, I. Cognard, H.T. Cromartie, E. Fonseca, L. Guillemot, M. Kerr, A. Parthasarathy, T.T. Pennucci, S. Ransom, I. Stairs, The radius of PSR J0740+6620 from NICER and XMM-Newton data. ApJ 918(2), L28 (2021). https://doi.org/10.3847/2041-8213/ac089b, 2105.06979 C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W.H. Freeman, San Francisco, 1973) S.M. Morsink, D.A. Leahy, C. Cadeau, J. Braga, The oblate schwarzschild approximation for light curves of rapidly rotating neutron stars. ApJ 663, 1244–1251 (2007). https://doi.org/10.1086/ 518648, arXiv:astro-ph/0703123 A. Mushtukov, S. Tsygankov, Accreting strongly magnetised neutron stars: x-ray pulsars (2022). arXiv e-prints arXiv:2204.14185, 2204.14185 A.A. Mushtukov, S.S. Tsygankov, V.F. Suleimanov, J. Poutanen, Ultraluminous x-ray sources as neutrino pulsars. MNRAS 476(3), 2867–2873 (2018). https://doi.org/10.1093/mnras/sty379, 1801.04810 A.G. Muslimov, A.I. Tsygan, General relativistic electric potential drops above pulsar polar caps. MNRAS 255, 61–70 (1992). https://doi.org/10.1093/mnras/255.1.61 J. Nättilä, A.M. Beloborodov, Radiative turbulent flares in magnetically dominated plasmas. ApJ 921(1), 87 (2021). https://doi.org/10.3847/1538-4357/ac1c76, 2012.03043 J. Nättilä, A.M. Beloborodov, Heating of magnetically dominated plasma by Alfvén-wave turbulence. Phys. Rev. Lett. 128(7), 075101 (2022). https://doi.org/10.1103/PhysRevLett.128. 075101, 2111.15578 J. Nättilä, P. Pihajoki, Radiation from rapidly rotating oblate neutron stars. A&A 615, A50 (2018). https://doi.org/10.1051/0004-6361/201630261, 1709.07292 J. Nättilä, A.W. Steiner, J.J.E. Kajava, V.F. Suleimanov, J. Poutanen, Equation of state constraints for the cold dense matter inside neutron stars using the cooling tail method. A&A 591, A25 (2016). https://doi.org/10.1051/0004-6361/201527416, http://adsabs.harvard.edu/abs/ 2016A%26A...591A..25N, 1509.06561 J. Nättilä, M.C. Miller, A.W. Steiner, J.J.E. Kajava, V.F. Suleimanov, J. Poutanen, Neutron star mass and radius measurements from atmospheric model fits to x-ray burst cooling tail spectra. A&A 608, A31 (2017). https://doi.org/10.1051/0004-6361/201731082, http://adsabs.harvard. edu/abs/2017A%26A...608A..31N, 1709.09120 F. Özel, Soft equations of state for neutron-star matter ruled out by EXO 0748 - 676. Nature 441(7097), 1115–1117 (2006). https://doi.org/10.1038/nature04858, astro-ph/0605106 F. Özel, P. Freire, Masses, radii, and the equation of state of neutron stars. ARA&A 54, 401–440 (2016). https://doi.org/10.1146/annurev-astro-081915-023322, 1603.02698 B. Paczynski, M. Proszynski, Models of radiation-driven winds from general relativistic neutron stars. ApJ 302, 519 (1986). https://doi.org/10.1086/164012

114 Fundamental Physics with Neutron Stars

4227

D. Page, J. Homan, M. Nava-Callejas, Y. Cavecchi, M.V. Beznogov, N. Degenaar, R. Wijnands, A.S. Parikh, A “Hyperburst” in the MAXI J0556-332 neutron star: evidence for a new type of thermonuclear explosion (2022). arXiv e-prints arXiv:2202.03962, 2202.03962 A. Papitto, D. de Martino, Transitional millisecond pulsars, in Millisecond Pulsars, Astrophysics and Space Science Library, vol. 465, ed. by S. Bhattacharyya, A. Papitto, D. Bhattacharya (2022), pp. 157–200. https://doi.org/10.1007/978-3-030-85198-9_6, 2010.09060 G. Pappas, T.A. Apostolatos, Revising the multipole moments of numerical spacetimes and its consequences. Phys. Rev. Lett. 108(23), 231104 (2012). https://doi.org/10.1103/PhysRevLett. 108.231104, 1201.6067 V. Paschalidis, N. Stergioulas, Rotating stars in relativity. Living Rev. Relativ. 20(1), 7 (2017). https://doi.org/10.1007/s41114-017-0008-x, 1612.03050 K.R. Pechenick, C. Ftaclas, J.M. Cohen, Hot spots on neutron stars – the near-field gravitational lens. ApJ 274, 846–857 (1983). https://doi.org/10.1086/161498 E. Petroff, J.W.T. Hessels, D.R. Lorimer, Fast radio bursts. A&A Rev. 27(1), 4 (2019). https://doi. org/10.1007/s00159-019-0116-6, 1904.07947 E. Petroff, J.W.T. Hessels, D.R. Lorimer, Fast radio bursts at the dawn of the 2020s. A&A Rev. 30(1), 2 (2022). https://doi.org/10.1007/s00159-022-00139-w, 2107.10113 A. Philippov, M. Kramer, Pulsar magnetospheres and their radiation. Ann. Rev. Astron. Astrophys. 60(1), 495–558 (2022). https://doi.org/10.1146/annurev-astro-052920-112338 A. Philippov, A. Tchekhovskoy, J.G. Li, Time evolution of pulsar obliquity angle from 3D simulations of magnetospheres. MNRAS 441(3), 1879–1887 (2014). https://doi.org/10.1093/ mnras/stu591, 1311.1513 A.A. Philippov, A. Spitkovsky, Ab initio pulsar magnetosphere: three-dimensional particle-in-cell simulations of axisymmetric pulsars. ApJ 785(2), L33 (2014). https://doi.org/10.1088/20418205/785/2/L33, 1312.4970 A.A. Philippov, B. Cerutti, A. Tchekhovskoy, A. Spitkovsky, Ab initio pulsar magnetosphere: the role of general relativity. ApJ 815(2), L19 (2015a). https://doi.org/10.1088/2041-8205/815/2/ L19, 1510.01734 A.A. Philippov, A. Spitkovsky, B. Cerutti, Ab initio pulsar magnetosphere: three-dimensional particle-in-cell simulations of oblique pulsars. ApJ 801(1), L19 (2015b). https://doi.org/10. 1088/2041-8205/801/1/L19, 1412.0673 P. Pihajoki, M. Mannerkoski, J. Nättilä, P.H. Johansson, General purpose ray tracing and polarized radiative transfer in general relativity. ApJ 863(1), 8 (2018). https://doi.org/10.3847/1538-4357/ aacea0, 1804.04670 A.Y. Potekhin, Atmospheres and radiating surfaces of neutron stars. Phys. Usp. 57(8), 735–770 (2014). https://doi.org/10.3367/UFNe.0184.201408a.0793, 1403.0074 J. Poutanen, Accurate analytic formula for light bending in Schwarzschild metric. A&A 640, A24 (2020a). https://doi.org/10.1051/0004-6361/202037471, 1909.05732 J. Poutanen, Relativistic rotating vector model for x-ray millisecond pulsars. A&A 641, A166 (2020b). https://doi.org/10.1051/0004-6361/202038689, 2006.10448 J. Poutanen, A.M. Beloborodov, Pulse profiles of millisecond pulsars and their Fourier amplitudes. MNRAS 373, 836–844 (2006). https://doi.org/10.1111/j.1365-2966.2006.11088.x, arXiv:astroph/0608663 J. Poutanen, M. Gierli´nski, On the nature of the x-ray emission from the accreting millisecond pulsar SAX J1808.4-3658. MNRAS 343, 1301–1311 (2003). https://doi.org/10.1046/j.13658711.2003.06773.x A. Prabhu, Axion production in pulsar magnetosphere gaps. Phys. Rev. D 104(5), 055038 (2021). https://doi.org/10.1103/PhysRevD.104.055038, 2104.14569 V. Radhakrishnan, D.J. Cooke, Magnetic poles and the polarization structure of pulsar radiation. Astrophys. Lett. 3, 225 (1969) T.E. Riley, A.L. Watts, S. Bogdanov, P.S. Ray, R.M. Ludlam, S. Guillot, Z. Arzoumanian, C.L. Baker, A.V. Bilous, D. Chakrabarty, K.C. Gendreau, A.K. Harding, W.C.G. Ho, J.M. Lattimer, S.M. Morsink, T.E. Strohmayer, A NICER view of PSR J0030+0451: millisecond pulsar

4228

J. Nättilä and J. J. E. Kajava

parameter estimation. ApJ 887(1), L21 (2019). https://doi.org/10.3847/2041-8213/ab481c, 1912.05702 T.E. Riley, A.L. Watts, P.S. Ray, S. Bogdanov, S. Guillot, S.M. Morsink, A.V. Bilous, Z. Arzoumanian, D. Choudhury, J.S. Deneva, K.C. Gendreau, A.K. Harding, W.C.G. Ho, J.M. Lattimer, M. Loewenstein, R.M. Ludlam, C.B. Markwardt, T. Okajima, C. Prescod-Weinstein, R.A. Remillard, M.T. Wolff, E. Fonseca, H.T. Cromartie, M. Kerr, T.T. Pennucci, A. Parthasarathy, S. Ransom, I. Stairs, L. Guillemot, I. Cognard, A NICER view of the massive pulsar PSR J0740+6620 informed by radio timing and XMM-Newton spectroscopy. ApJ 918(2), L27 (2021). https://doi.org/10.3847/2041-8213/ac0a81, 2105.06980 R.W. Romani, D. Kandel, A.V. Filippenko, T.G. Brink, W. Zheng, PSR J0952-0607: the fastest and heaviest known galactic neutron star. ApJ 934(2), L18 (2022). https://doi.org/10.3847/20418213/ac8007, 2207.05124 M. Ruderman, Crust-breaking by neutron superfluids and the Vela pulsar glitches. ApJ 203, 213– 222 (1976). https://doi.org/10.1086/154069 M. Ruderman, A.M. Beloborodov, Thermal emission areas of heated neutron star polar caps. Ap&SS 308(1–4), 419–422 (2007). https://doi.org/10.1007/s10509-007-9332-z T. Salmi, J. Nättilä, J. Poutanen, Bayesian parameter constraints for neutron star masses and radii using x-ray timing observations of accretion-powered millisecond pulsars. A&A 618, A161 (2018). https://doi.org/10.1051/0004-6361/201833348, 1805.01149 E.T. Scharlemann, R.V. Wagoner, Aligned rotating magnetospheres. General analysis. ApJ 182, 951–960 (1973). https://doi.org/10.1086/152195 H. Schatz, L. Bildsten, A. Cumming, M. Wiescher, The rapid proton process ashes from stable nuclear burning on an accreting neutron star. ApJ 524(2), 1014–1029 (1999). https://doi.org/10. 1086/307837, astro-ph/9905274 H. Schatz, A. Aprahamian, V. Barnard, L. Bildsten, A. Cumming, M. Ouellette, T. Rauscher, F.K. Thielemann, M. Wiescher, End point of the rp process on accreting neutron stars. Phys. Rev. Lett. 86(16), 3471–3474 (2001). https://doi.org/10.1103/PhysRevLett.86.3471, astro-ph/0102418 H. Schatz, S. Gupta, P. Möller, M. Beard, E.F. Brown, A.T. Deibel, L.R. Gasques, W.R. Hix, L. Keek, R. Lau, A.W. Steiner, M. Wiescher, Strong neutrino cooling by cycles of electron capture and β − decay in neutron star crusts. Nature 505(7481), 62–65 (2014). https://doi.org/10.1038/ nature12757, 1312.2513 S.L. Shapiro, S.A. Teukolsky, Black Holes, White Dwarfs, and Neutron Stars: The Physics of Compact Objects (Wiley, New York, 1983) L. Sidoli, G.L. Israel, P. Esposito, G.A. Rodríguez Castillo, K. Postnov,) AX J1910.7+0917: the slowest x-ray pulsar. MNRAS 469(3), 3056–3061 (2017). https://doi.org/10.1093/mnras/ stx1105, 1705.01791 L. Sironi, I. Plotnikov, J. Nättilä, A.M. Beloborodov, Coherent electromagnetic emission from relativistic magnetized shocks. Phys. Rev. Lett. 127(3), 035101 (2021). https://doi.org/10.1103/ PhysRevLett.127.035101, 2107.01211 A. Spitkovsky, Time-dependent force-free pulsar magnetospheres: axisymmetric and oblique rotators. ApJ 648(1), L51–L54 (2006). https://doi.org/10.1086/507518, astro-ph/0603147 A.W. Steiner, C.O. Heinke, S. Bogdanov, C.K. Li, W.C.G. Ho, A. Bahramian, S. Han, Constraining the mass and radius of neutron stars in globular clusters. MNRAS 476(1), 421–435 (2018). https://doi.org/10.1093/mnras/sty215, 1709.05013 T.E. Strohmayer, E.F. Brown, A remarkable 3 hour thermonuclear burst from 4U 1820-30. ApJ 566(2), 1045–1059 (2002). https://doi.org/10.1086/338337, astro-ph/0108420 P.A. Sturrock, A model of pulsars. ApJ 164, 529 (1971). https://doi.org/10.1086/150865 V. Suleimanov, J. Poutanen, M. Revnivtsev, K. Werner, A neutron star stiff equation of state derived from cooling phases of the x-ray burster 4U 1724-307. ApJ 742(2), 122 (2011). https://doi.org/ 10.1088/0004-637X/742/2/122, 1004.4871 V.F. Suleimanov, D. Klochkov, G.G. Pavlov, K. Werner, Carbon neutron star atmospheres. ApJS 210(1), 13 (2014). https://doi.org/10.1088/0067-0049/210/1/13, 1311.6037

114 Fundamental Physics with Neutron Stars

4229

V.F. Suleimanov, J. Poutanen, D. Klochkov, K. Werner, Measuring the basic parameters of neutron stars using model atmospheres. Eur. Phys. J. A 52, 20 (2016). https://doi.org/10.1140/epja/ i2016-16020-7, 1510.06962 V.F. Suleimanov, J. Poutanen, J. Nättilä, J.J.E. Kajava, M.G. Revnivtsev, K. Werner, The direct cooling tail method for x-ray burst analysis to constrain neutron star masses and radii. MNRAS 466(1), 906–913 (2017). https://doi.org/10.1093/mnras/stw3132, 1611.09885 V.F. Suleimanov, J. Poutanen, K. Werner, Observational appearance of rapidly rotating neutron stars. X-ray bursts, cooling tail method, and radius determination. A&A 639, A33 (2020). https://doi.org/10.1051/0004-6361/202037502, 2005.09759 R. Svensson, Electron-positron pair equilibria in relativistic plasmas. ApJ 258, 335–348 (1982a). https://doi.org/10.1086/160082 R. Svensson, The pair annihilation process in relativistic plasmas. ApJ 258, 321–334 (1982b). https://doi.org/10.1086/160081 C. Thompson, R.C. Duncan, The soft gamma repeaters as very strongly magnetized neutron stars – I. Radiative mechanism for outbursts. MNRAS 275(2), 255–300 (1995). https://doi.org/10. 1093/mnras/275.2.255 A.N. Timokhin, On the force-free magnetosphere of an aligned rotator. MNRAS 368(3), 1055– 1072 (2006). https://doi.org/10.1111/j.1365-2966.2006.10192.x, astro-ph/0511817 P. Tinyakov, M. Pshirkov, S. Popov, Astroparticle physics with compact objects. Universe 7(11), 401 (2021). https://doi.org/10.3390/universe7110401, 2110.12298 A. Tokovinin, The updated multiple star catalog. ApJS 235(1), 6 (2018). https://doi.org/10.3847/ 1538-4365/aaa1a5, 1712.04750 N.N. Weinberg, L. Bildsten, H. Schatz, Exposing the nuclear burning ashes of radius expansion type I x-ray bursts. ApJ 639(2), 1018–1032 (2006). https://doi.org/10.1086/499426, astroph/0511247 L. Woltjer, X-rays and type I supernova remnants. ApJ 140, 1309–1313 (1964). https://doi.org/10. 1086/148028 H. Worpel, D.K. Galloway, D.J. Price, Evidence for accretion rate change during type I x-ray bursts. ApJ 772(2), 94 (2013). https://doi.org/10.1088/0004-637X/772/2/94, 1303.4824 H. Worpel, D.K. Galloway, D.J. Price, Evidence for enhanced persistent emission during subeddington thermonuclear bursts. ApJ 801(1), 60 (2015). https://doi.org/10.1088/0004-637X/ 801/1/60, 1501.02070 D.G. Yakovlev, P. Haensel, G. Baym, C. Pethick, Lev Landau and the concept of neutron stars. Phys. Usp. 56(3), 289–295 (2013). https://doi.org/10.3367/UFNe.0183.201303f.0307, 1210.0682 G. Zhang, M. Méndez, M. Zamfir, A. Cumming, The link between coherent burst oscillations, burst spectral evolution and accretion state in 4U 1728-34. MNRAS 455(2), 2004–2017 (2016). https://doi.org/10.1093/mnras/stv2482, 1510.07213

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Novae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Light Curves of Novae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Spectra of Novae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Higher Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Dwarf Novae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Combination Novae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nova-Like Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Persistent Super-Soft Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . BeWD Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Symbiotic Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Oddballs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Magnetic Cataclysmic Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Spectra of mCVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Masses of White Dwarfs in mCVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Light Curves of mCVs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AM CVn Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HM Cnc and V407 Vul: Direct Impact Accretion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

In this chapter, we consider the processes which can lead to X-ray emission from different types of cataclysmic variable stars (CVs). CVs are semidetached, binary star systems where material is transferred from the donor star (also known as the companion or secondary star) onto the white dwarf primary. CVs are divided into several subclasses based on the observed phenomenology in the optical and X-ray bands, which, in turn, is largely defined by the magnetic field strength of the accretor. In nonmagnetic systems, a variety of observed behaviors are identified, depending on the accretion rate: novae, dwarf novae, nova-like variables, symbiotic binaries, and super-soft sources are all examples of nonmagnetic CVs. In magnetic systems (polars and intermediate polars, or DQ Her and AM Her systems, respectively), the accretion flow is channeled to polar regions, and the observational appearance is different. X-rays are typically produced through hot or energetic processes, and in CVs they are formed via shocks (within a boundary layer or accretion column, or through interactions either internal to the nova ejecta or between the ejecta and a stellar wind) or from hydrogen burning (either steady fusion or a thermonuclear runaway). All of these different types of accreting white dwarfs are discussed here, considering both spectral and temporal variability in the different populations. Keywords

Cataclysmic variable stars · X-ray binary stars · Novae · Dwarf novae · Nova-like variables · Persistent super-soft sources · Symbiotic binary stars · Polars · Intermediate Polars · AM Canum Venaticorum stars

Introduction As discussed in ⊲ Chap. 107, “Accreting White Dwarfs”, there are many different types of accreting white dwarfs (WDs); this classification is historically based predominantly on phenomenology observed in the optical band. Here we consider the mechanisms through which these systems may produce X-rays. We emphasize that the physical processes responsible for both the X-ray and optical emission are tightly interconnected, so it is important to understand both of them. As such, use of the commonly used CV classification is still justified. In general, the energetic X-rays are formed on, or very close to, the WD itself (determined via observations of eclipsing systems; e.g. Mukai et al. 1997), whereas the optical emission comes from further out in the binary system, and more than one mechanism for forming X-rays may be active in any given type of cataclysmic variable (CV) system. Both optically thin and optically thick X-ray emission is possible, depending on the processes occurring. Continuum and line emission (or absorption) is measured, and this can be frequently absorbed – totally or partially – by the surrounding environment. Accreting WDs can be split into nonmagnetic and magnetic sources, with the cut being a field strength of around 106 G. In this chapter, we will first cover the

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nonmagnetic population, before progressing to the sources with significant magnetic fields. There is, of course, no hard start or end point for the X-ray bandpass within the electromagnetic spectrum. Here we consider energies from around 0.3 keV up to ∼150 keV, which can be observed by current missions such as Swift (XRT – X-Ray Telescope – and BAT – Burst Alert Telescope), MAXI (Monitor of All-sky X-ray Image), NuSTAR (Nuclear Spectroscopic Telescope Array), and NICER, (Neutron star Interior Composition Explorer) for example. In addition to the information in this chapter, Mukai (2017) provides an excellent review on the subject of X-rays from accreting WDs.

Novae As accreting WDs go, novae are the most explosive type. Mass transfer from the secondary star to the WD leads to the formation of a layer of hydrogen on the WD surface. Eventually, when enough material has been transferred, nuclear burning will ignite at the base of this envelope; the pressure will then increase, until it reaches a sufficient level to trigger a thermonuclear runaway (TNR; see review articles in Bode and Evans 2008). Following this TNR explosion, material is flung outward, obscuring the WD surface. To date, this point is usually the first sign of a nova eruption, when a new optical source is detected: the optical peak occurs at the point of maximum expansion of the photosphere. (While most novae are first discovered as new optical sources, V959 Mon was initially detected in γ -rays by the Fermi-LAT, when too close to the Sun for ground-based telescopes to observe; an optical counterpart was later discovered, and the two detections identified as being one and the same source (Cheung et al. 2012).) However, models of nova outbursts predict that there should be a brief (0.5+ day), soft X-ray flash shortly after hydrogen ignition, but before the optical discovery, known as the “fireball phase” (e.g., Starrfield et al. 1990). While several searches have previously been attempted (e.g., Kato et al. 2016; Morii et al. 2016), it is only recently that such an X-ray flash has been detected – by eROSITA (extended Roentgen Survey with an Imaging Telescope Array) during its second all-sky survey (König et al. 2022), for the nova YZ Ret (Nova Ret 2020). In this case, a very soft flash of X-rays was detected 11 hr before its optical brightening, lasting no more than 8 hr. The softness of the spectrum is likely the reason why MAXI failed to find any similar flashes (Morii et al. 2016). While there are many ground-based telescopes – both large facilities and the far-reaching community of amateur astronomers – constantly scanning for new optical transients, we are currently lacking in all-sky X-ray monitors to provide the same level of prompt transient location. In the future, missions such as Einstein Probe (currently planned for launch at the end of 2022) will observe the entire sky at X-ray energies with a high cadence, hopefully allowing us to identify more such X-ray flashes. As the nova ejecta expand, they become optically thin, usually allowing the surface nuclear burning to become visible. (If the nuclear burning only lasts for a very short interval, it may switch off before the ejecta thin out enough to allow

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the soft X-rays to become visible. In the case of V745 Sco (Page et al. 2015), it is postulated that the active nuclear burning had ended before the ejecta had fully cleared, meaning that only the cooling emission was later detected, so placing it close to this “invisibility zone” where the SSS emission would be entirely missed.) This optically thick radiation peaks in the soft X-ray band and is thus termed the “super-soft source” (SSS) phase (Krautter 2008). This soft emission continues for as long as there is sufficient hydrogen for nuclear burning and can sometimes be extended longer than expected if accretion resumes early on (e.g., Aydi et al. 2018). A cooling and fading soft spectral component may still be seen for a while after the burning has come to an end; when the nuclear reactions can no longer be sustained, the nova returns to quiescence. Once accretion resumes, hydrogen again builds up on the WD surface; thus, the nova cycle begins anew. Classical novae do not tend to be detectable X-ray emitters during quiescence. Recurrent novae (Classical novae are those which have only been seen to erupt once; a small number of systems have been detected in outburst multiple times, and these are known as recurrent novae. All novae are expected to erupt more than once, but over timescales of typically thousands of years.), on the other hand, have higher accretion rates (Schaefer 2010) and can often be detected in X-rays between eruptions (e.g., Orio 1993).

X-Ray Light Curves of Novae The onset of the SSS phase is often found to be chaotic when monitored at a sufficiently high frequency (at least several times a day); this is demonstrated in the top panel of Fig. 1. Such variability is not always the case, though, and Page et al. (2015) discusses a clear counterexample; see also the bottom panel of Fig. 2. This high-amplitude flux variability was first identified in the Swift observations of the 2006 eruption of RS Oph (Osborne et al. 2011), but subsequently found in many other novae (see Page et al. (2020) for a review). While the exact details of the mechanism leading to this variability are uncertain, it appears to be at least partly due to variable visibility of the WD (e.g., Osborne et al. 2011; Page and Osborne 2014). Following the nova eruption, the material ejected may well be clumpy. Should these clumps pass through the observer’s line of sight, soft X-rays (which dominate the spectrum of the source at this time) will be blocked, and the measured count rate will drop. Spectral fits also show variations in the photospheric temperature; measurements of 100 eV are found when fitting Swift X-ray spectra (e.g., Page and Osborne 2014), with the lowest temperatures leading to some – possibly most – of the SSS emission occurring outside the XRT bandpass, and thus a decreased observed count rate over 0.3–10 keV. Figure 2 presents a selection of X-ray light curves of novae well-monitored by Swift, demonstrating the range of variability detected; see Page et al. (2020) for a large sample. In addition to this impressive high-amplitude variability in X-ray brightness, the RS Oph data showed a strong, smaller-scale quasiperiodic oscillation (QPO) of around 35 s during much of the bright SSS phase (Osborne et al. 2011);

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Fig. 1 Top: The beginning of the super-soft X-ray emission frequently shows large-scale flux variability. This was first identified in the Swift observations of RS Oph following its 2006 eruption, shown here. Bottom: A sample of SSS X-ray spectra for RS Oph, showing a variety of temperatures and brightnesses. The legend gives the days after the 2006 eruption when the spectra were obtained

Fig. 3 highlights one of the intervals of interest. Following this initial discovery, transient QPOs of up to ∼100 s were subsequently identified in other X-ray bright, SSS phases of novae, as well (e.g., Ness et al. 2015). It is not yet certain what drives these oscillations, with explanations ranging from rotation to non-radial g-mode pulsations (that is, low-frequency non-radial, gravity mode – or buoyancy – pulsations, driven by temperature-sensitive nuclear burning; Kawaler 1988); see discussion in Ness et al. (2015). All the suggestions present certain problems, however. If the modulation is related to rotation, then some form of differentiation of the emission is required, rather than the nuclear burning being constant over the entire WD surface, possible examples being occultation of a magnetic hotspot, or

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variable absorption. However, the oscillations sometimes appear multi-periodic, and the fractional amplitude varies, which cannot be explained by a simple WD rotation model (Beardmore et al. 2008). While the g-mode pulsations were suggested as an explanation by Osborne et al. (2011), more recent work by Wolf et al. (2018) predicts that pulsations would only be stable under ∼10 s, shorter than the QPOs which have been measured in novae.

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X-Ray Spectra of Novae The SSS emission appears, to first order, similar to a blackbody (BB; lower panel of Fig. 1), possibly with superimposed absorption edges, particularly when using lowresolution spectra from an instrument such as the XRT onboard Swift. Grating data, from the Reflection Grating Spectrometer (RGS) on XMM-Newton or the Chandra Low/High Energy Transmission Gratings (LETG, HETG), show a much more complicated situation with multiple emission and/or absorption lines superimposed on the continuum (Fig. 4). It is clear that a BB is a vast oversimplification of the actual emission, which must be more akin to a stellar atmosphere. Indeed, using a BB approximation can potentially underestimate the temperature and overestimate the luminosity (Krautter et al. 1996), although, as shown by Osborne et al. (2011), this is not always the case. However, as of 2022 the available idealized stellar atmosphere models tend to provide worse fits from a statistical standpoint than a simple BB, and the complex results from high-resolution X-ray spectra indicate further development of atmosphere models is needed before conclusive, physically motivated modeling of nova X-ray spectra can be performed (Ness 2020). While the soft, optically thick emission discussed above dominates the spectra during the SSS phase, harder X-rays arising from shock interactions can also be observed before, during, and after this interval (e.g., Brecher et al. 1977). As reviewed by Chomiuk et al. (2021), shocked X-ray emission in classical novae can be caused by collisions between outflows moving at different velocities. In the case of recurrent novae, the evolved companions will be losing material in the form of a wind. The material ejected from the WD during the nova eruption should collide with this wind, leading to shocked emission. Bode et al. (2006) demonstrated that the data collected for the 1985 and 2006 eruptions of RS Oph were consistent with shocks propagating through the wind from the red giant (RG) companion. This shocked emission can typically be parameterized in X-ray spectra by a small number

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Fig. 4 A sample of X-ray grating spectra obtained with Chandra and XMM-Newton following the 2006 eruption of RS Oph, showing a variety of emission and absorption features – clearly more complex than a simple BB continuum as low-resolution spectra can suggest. (Reproduced from Ness et al. 2009)

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of discrete temperature optically thin components, though this is a simplification of a much more complex situation (e.g., Vaytet et al. 2011). In some systems, the signatures of shocks in novae are seen to extend beyond the X-ray range considered in this chapter, and up to GeV energies. This is discussed in the next section. We also note that novae can occur in magnetic systems (polars and intermediate polars – IPs; see the section entitled “Magnetic Cataclysmic Variables” for a detailed discussion on X-rays from these sources), which may lead to differences in the observed X-ray emission, with V407 Lup (Nova Lupi 2016) being a well-monitored example (Aydi et al. 2018). There is an indication in this nova that harder X-rays may “turn on” at late times, whereas shock emission would be expected to be present from the start. This, together with the detection of two distinct periodicities in the optical, UV and X-ray data, was taken as evidence of the likely magnetic nature of the system.

Higher Energies Since the 2008 launch of the Fermi Gamma-ray Space Telescope, with its Large Area Telescope (LAT) covering energies from ∼20 MeV to >300 GeV, more and more novae have been detected at GeV energies. Gordon et al. (2021) consider Fermi-LAT-detected novae which were also observed by Swift-XRT, finding that, somewhat surprisingly, the X-rays expected from shocks are not usually visible concurrently with the GeV emission, but rather appear after the γ -rays have faded away. V407 Cyg, with its RG companion, was the exception (though V745 Sco and V1535 Sco – each with giant companions – were both also clearly detected in X-rays at early times, but only had marginal LAT detections); all other novae in the sample were systems with dwarf secondary stars. The authors suggest a scenario whereby the GeV emission in recurrent systems with giant stars is related to external shocks between the WD ejecta and the dense wind from the companion, while the novae with Main Sequence companions produce γ -rays via internal shocks between multiple ejection events (Chomiuk et al. 2014); these latter shocks are embedded within the high-density ejecta, and thus initially hidden from view. Alternatively, the X-rays may be suppressed early on by corrugated shock fronts (Metzger et al. 2015; Steinberg and Metzger 2018). Harder X-rays (>10 keV) are less likely to be absorbed, however, and observations by NuSTAR have, indeed, identified X-ray emission concurrent with GeV γ -rays (e.g., Nelson et al. 2019), though fainter than might be expected from the corresponding γ -ray luminosities (Gordon et al. 2021).

Dwarf Novae Despite the similar names, dwarf novae (DNe) and novae are very different beasts. While a nova eruption is related to processes on the WD itself (see the section entitled “Novae”), the preferred explanation for DNe is the so-called disk instability

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model (DIM), where the outburst is caused by changes in the state of the accretion disk. In short, material transferred from the secondary star builds up in the disk more rapidly than it can be accreted onto the WD; this continues until the density and temperature reach critical levels corresponding to partial hydrogen ionization in the inner disk region. This leads to an increase in the viscosity, and hence a disk instability, which causes much of the excess material to be rapidly accreted, releasing a burst of gravitational potential energy. There is also an alternative proposed model, wherein the outburst is caused by a sudden increase in the mass transfer rate from the companion star to the disk (i.e., an instability in the secondary star itself leads to the DN outburst); however, a physical mechanism leading to this stellar instability is not altogether obvious. See Chap. “Overall accretion disk theory” for more details on DN optical outbursts and the DIM. It is interesting to note that the DIM has also been applied to explain some parts of X-ray pulsar phenomenology (Tsygankov et al. 2017) with the only difference being that the inner disk radius is defined by the magnetosphere of the neutron star rather than the WD surface. “Dwarf nova” is an umbrella term, covering systems with similar, yet subtly different, outbursts as observed at optical wavelengths (U Gem, SU UMa, ER UMa and Z Cam; see ⊲ Chap. 107, “Accreting White Dwarfs”). However, the X-rays (in the nonmagnetic systems) are always produced in the same way, namely, through shocks within the boundary layer (BL) between the accretion disk and WD surface (Patterson and Raymond 1985a, b). The Keplerian velocity of the inner disk is much faster than the rotation of the WD (in the range of ∼3000 km s−1 , compared with ∼300 km s−1 for the WD surface velocity), so the accreting material has to slow down over a short distance. This lost kinetic energy heats the BL to X-ray temperatures, leading to it emitting up to half the total luminosity of the system, with the remaining part released in the disk (e.g., Lynden-Bell and Pringle 1974). The type of X-ray emission from the BL is dependent on the accretion rate. During quiescence, the rate of mass transfer through the BL is relatively low. In this case, optically thin emission occurs, as the in-falling material collides with the WD surface forming hard X-ray shocks (Patterson and Raymond 1985a). However, this is not the end of the story. Hot, relatively low-density gas such as this does not radiate efficiently: cooling should mainly occur through bremsstrahlung (free-free) radiation, which relies on interactions between charged particles, of which there are few in this rarefied material. In the case of particularly low density, the hot gas therefore expands, leading to even fewer opportunities for collisions/radiation, and hence expanding even further. This process leads to the BL puffing up into a diffuse, hot, X-ray-emitting corona (e.g., Meyer and Meyer-Hofmeister 1994). As material flows toward the WD, it releases gravitational potential energy, continuing to heat the corona, which itself conducts energy into the accretion disk. Evaporation from the disk serves to replenish gas lost from the corona – and so the cycle repeats. Harder X-rays of up to 20 keV [see, e.g., Warner (1995) for relevant calculations] will be formed in such a hot corona, whereas shocks with kT around a few keV will occur within the gas collapsing directly onto the WD surface, generated when the accretion rate, and hence density, is somewhat higher (Pringle and Savonije 1979).

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During the DN outburst, however, the accretion rate, and therefore the amount of material in the BL, increases significantly. Thus, there are more particles to experience more collisions, and the BL can cool more readily. Under these conditions, no corona is formed, and the BL becomes optically thick to X-rays. The shocked photons are absorbed and thermalized within the layer (Patterson and Raymond 1985b). Because of this, the harder X-ray emission during outburst is usually strongly suppressed in comparison to quiescence, with a corresponding increase in the extreme UV (EUV) and/or soft X-rays. This was first observed in detail for SS Cyg in 1996 by Wheatley et al. (2003), combining data from RXTE (Rossi X-ray Timing Explorer) and EUVE (Extreme Ultraviolet Explorer), where the hard X-rays (RXTE was only sensitive to photons above 1.5 keV; no simultaneous soft X-ray data were collected) were seen to rise shortly after the start of the optical outburst, and then abruptly quench as the EUV emission took over. Toward the end of the optical outburst, the X-rays (and, slightly delayed again, the EUV) undergo another temporary rebrightening. The lag between the start of the rises at optical and X-ray energies is attributed to the propagation time of the heating wave moving through the disk to reach the BL, before being accreted, while the delay between the X-ray and UV increases implies the UV photons are the soft tail of the optically thin, hard X-ray component. Despite these plausible explanations for the temporary X-ray flares at the start and end of the outburst, Fertig et al. (2011) point out that most DNe do not actually show these features, though Byckling et al. (2009) and Neustroev et al. (2018) provide two other examples where such brief X-ray increases at either end of the outburst are indeed seen. Figure 5 shows long-term X-ray observations of SS Cyg in the top plot, covering 2009–2021; SS Cyg undergoes a DN outburst approximately every 50 d. Interestingly, since 2019 the hard X-rays (>10 keV) have mainly shown a brightening trend. The bottom plot shows the outburst of SS Cyg in 2010 April, observed in X-rays (light curves produced using the online Swift XRT product generator at https:// www.swift.ac.uk/user_objects) and optical (data taken from AAVSO: American Association of Variable Star Observers; see also Russell et al. 2016). The UV source was too bright for the Swift UVOT (UV/Optical Telescope) to observe usefully. The rise and rapid switch-off of the X-rays shortly following the start of the optical outburst, and again, toward the end, can be seen, with the majority of the increase above 1 keV. During the main body of the optical outburst, the X-ray spectrum is softer. While the majority of DNe are X-ray fainter during the outburst, some instead show an increase in X-ray luminosity during this time, with an appearance, or strengthening, of a harder X-ray component. This is still not fully understood – and neither, indeed, is the reason why there are residual harder, optically thin X-rays detected during outburst, when the BL is expected to be completely optically thick (see further discussion in Mukai 2017). An example of a DN exhibiting unexplained phenomena is SSS J122221.7311525, a WZ Sge-type DN (the subset of the SU UMa DNe which show only superoutbursts), which was followed in detail throughout one such superoutburst by Swift (Neustroev et al. 2018). This source showed a significantly higher X-ray

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Fig. 5 Top: X-ray observations of SS Cyg from 2009 to 2021. The upper panel shows data from pointed observations with the narrow-field XRT onboard Swift, which is why there are large gaps in the coverage; the middle and lower panels show data from MAXI and Swift-BAT, which constantly survey areas of the sky. Bottom: The 2010 April outburst of SS Cyg observed over the X-ray and optical bands. The upper panel shows the soft (0.3–1 keV) and hard (1–10 keV) X-ray light curves overplotted. The time axis is Modified Julian Date

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luminosity during outburst than at quiescence (displaying an optically thin spectrum, with no sign of the expected soft component; as mentioned by Byckling et al. (2009), however, even a small spectral change could lead to the soft emission falling below the XRT bandpass, emerging in the EUV band instead), and, interestingly, the X-ray flux varied abruptly at the same time as the optical superhump behavior changed (an effect also seen in observations of GW Lib presented in the same paper). This suggests a link between the inner region (from where the X-rays are emitted) and further out in the disk (from where the superhumps arise), indicating that the accretion disk models for such systems are incomplete. Note that, while the majority of DNe are nonmagnetic systems, as considered in this section, some magnetic CVs (such as GK Per; Evans et al. 2009) also show this kind of outburst. However, as discussed in the section entitled “Magnetic Cataclysmic Variables”, there is no boundary layer in magnetic CV systems, since the inner part of the accretion disk is disrupted. In such cases, most of the energy is released in the stand-off shock close to the polar regions, in the form of optically thin plasma. This emission is likely only weakly dependent on the accretion rate (Hameury and Lasota 2017) and can be used to constrain the magnetic field in these objects (Suleimanov et al. 2016).

Combination Novae As an aside, we note that there are also “combination novae”: sources which show both dwarf and classical nova characteristics. As for the other populations of accreting WDs discussed in this chapter, the classification of the sources is not based on the X-ray characteristics, but rather the optical wavelengths. Combination novae undergo an event which starts off as an accretion disk instability, leading to enough of the disk material being accreted onto the WD to trigger the thermonuclear shell burning and mass ejection typically expected in a classical nova. Such an outburst was first reported by Sokoloski et al. (2006) in the symbiotic star Z And, where the authors established that, while the start of the event resembled a DN-like disk instability, the total eruption was too energetic to be purely accretion driven. X-ray observations by Chandra and XMM-Newton showed soft spectra, with the majority of the photons below 2 keV, although there were relatively few source counts collected in two of the three observations. Sokoloski et al. (2006) suggest that many classical symbiotic outbursts may actually fall under this heading of combination novae and Bollimpalli et al. (2018) consider that the recurrent nova eruptions in RS Oph could be triggered by disk instabilities (though they believe that the Z And combination nova event is more likely to have been triggered by increased mass transfer from the giant companion, rather than a disk instability).

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Nova-Like Variables Nova-like systems are nonmagnetic CVs in which the mass-transfer rate is high enough (M˙ ≥ 10−9 M⊙ yr−1 ) to sustain the disk in a perpetually hot state. Because the disk is stable, they will not show dwarf nova outbursts (i.e., they are termed noneruptive systems), instead maintaining an outburst-like steady state. ˙ one would expect the emission mechanisms to be similar to At such a high M, DNe in outburst, i.e., a BL with an optically thick, soft X-ray emitting component. In the VY Scl systems – nova-likes that transition between high and low states due to varying mass accretion rate; they are also known as anti-dwarf novae – at ˙ the BL is expected to be optically thin and emit hard X-rays. However, lower M, there are few high-quality X-ray observations of nova-likes that allow us truly to determine the nature of the X-rays. Deep XMM-Newton observations of the highinclination nova-like UX UMa found an X-ray spectrum with two components. The soft X-ray emission was uneclipsed, suggesting an extended origin. The hard component, conversely, was eclipsed, such that it must originate close to the WD surface within the BL (Pratt et al. 2004), questioning the notion that high M˙ BLs are strong soft X-ray emitters. Similarly, Balman et al. (2014) found that, in three high-state nova-like systems, the X-ray spectra were dominated by optically thin emission with maximum temperatures in the range 21–50 keV, and postulated that the BL may be merged with an advection dominated accretion flow (ADAF) and/or an X-ray emitting “corona” as in X-ray binaries. (Note that, while accreting binary systems containing WDs are referred to as CVs, those with neutron stars or black holes are termed X-ray binaries.) The few deep X-ray observations of nova-likes seem to point to multiple origins for the X-ray emission and appear to have posed more questions about the emission mechanisms than they have answered.

Persistent Super-Soft Sources Besides novae which may pass through a transient super-soft phase, there is also a population of persistent (or, at least, very long-lived) luminous super-soft sources. A number of strong X-ray sources in the Large Magellanic Cloud (LMC) were analyzed by van den Heuvel et al. (1992), who found that the emission could be explained by (quasi-) steady hydrogen burning on WDs when the accretion rate is sufficiently high (∼10−7 M⊙ yr−1 ) – the so-called close binary super-soft source (CBSS) model (see also Kahabka and van den Heuvel 1997). The high accretion rate in such systems is thought to arise due to the mass-losing companion star being more massive than the WD (whereas, in the case of a nova, the WD has the larger mass). Alternatively, in some steady super-soft systems, the WD may accrete via wind-driven mass transfer from a low-mass companion which is being irradiated by the WD itself (van Teeseling and King 1998). Despite the “persistent” in the name, these sources do pass through X-ray faint states. It has been speculated (Reinsch et al. 2000) that these “off” intervals are

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Fig. 6 Swift-XRT spectrum of persistent super-soft source CAL 87. Almost all the detected counts are soft, and, as for novae in their SSS phase, the spectrum can be parameterized with either a BB plus edges (as shown here) or a stellar atmosphere model

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caused by the accretion rate increasing, causing the WD photosphere to expand, thus shifting the peak of the emission out of the X-ray band and into the EUV. When the photosphere shrinks back down, the source will rebrighten in the X-rays. This is similar to the changes measured in the SSS temperatures in novae described in the section entitled “X-Ray Light Curves of Novae”, which may help to explain the high-amplitude flux variability sometimes seen. Figure 6 plots the Swift-XRT spectrum of CAL 87, one of the persistent SSS in the LMC, highlighting the softness of the emission, with very few counts above 1 keV; it looks very similar to the RS Oph SSS spectra shown in Fig. 1. Figure 7 shows an eROSITA image of the LMC. In RGB false color images such as this, softer sources (e.g., persistent SSS or novae passing through a super-soft phase) appear redder, while harder sources are bluer.

BeWD Systems Be X-ray binaries are a type of high-mass X-ray binary (HMXB) comprising a Betype star (i.e., a B-star which shows emission lines) and (usually) a neutron star; a large number of these systems are known. BeWD systems, where the compact object is, instead, a WD, have been predicted to be even more numerous than their higher mass BeNS counterparts (Raguzova 2001), though, to date, only a handful have been detected (see summary in Coe et al. 2020). The Swift Small Magellanic Cloud Survey (known as S-CUBED; Kennea et al. 2018) is starting to discover more of these objects (Coe et al. 2020; Kennea et al. 2021) when they undergo an outburst and flare up in X-rays, due to enhanced accretion. The X-ray emission of a BeWD system is soft, showing a spectrum similar to the SSS discussed above, although the X-rays are produced through shocked radial accretion, not nuclear burning (Kennea et al. 2021).

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Fig. 7 eROSITA false color image of the Large Magellanic Cloud. Soft sources appear red, and harder ones blue. (Credit: Frank Haberl, Chandreyee Maitra, MPE.)

Symbiotic Stars Symbiotic binaries are those where a WD accretes from an RG companion; there are also some neutron star symbiotic systems, but we do not consider those here. accretes from an RG companion. In some cases, where the WD mass is high enough and sufficient mass transferred, these systems can erupt as recurrent novae – RS Oph, for example, as mentioned above. As discussed by Luna et al. (2013), when modifying and expanding an original classification scheme based on ROSAT (Röntgensatellit) data from Mürset et al. (1997), WD symbiotics can be split into groups which show only super-soft emission (i.e., 107 G), and their specific accretion rates are low. In this regime, cyclotron cooling suppresses the bremsstrahlung cooling (Woelk and Beuermann 1996), though bremsstrahlung losses can never be completely ignored (Wu et al. 1994). Cyclotron emission causes the shock height to reduce by one to two orders of magnitude and reduces the electron temperature of the PSR by an order of magnitude (Wu et al. 1994; Woelk and Beuermann 1996) compared to the IP case. Reflection With X-rays being produced so close to the surface of the WD in mCVs, one might expect ∼half of the emitted radiation to be directed toward the WD and reflected back to the observer. X-ray reflection in accreting compact objects manifests in the X-ray spectrum as a broad Compton “hump” in the 10–30 keV range, and a neutral Fe Kα line at 6.4 keV (George and Fabian 1991), and is often detected in X-ray binaries and AGN as a result of photons being reflected from the accretion disk. In the case of mCVs, the importance of reflection has been implied due to the presence of the Fe Kα line (Ezuka and Ishida 1999). However, with the exception of the prototypical polar AM Her (Rothschild et al. 1981) and EF Eri (Done et al. 1995), detections of the Compton hump were originally difficult to come by. However, Mukai et al. (2015) utilized the hard X-ray capabilities of the then-newly launched NuSTAR observatory unambiguously to detect the reflection continuum in IPs for the first time (see Fig. 10). Mukai et al. (2015) were also able to measure the amplitude of the reflection component, which provides a way of estimating the height of the shock. For reference, a reflection amplitude of unity implies that the X-ray emitter (i.e., the shock) is just above the surface of the reflector (the WD). A deviation from 1 would therefore imply a non-negligible shock height. This was found to be the case for V709 Cas, where the measured reflection amplitude 50 eV) would be locally superEddington if the soft component originates from the surface of the WD. Further adding to the puzzle is the fact that spectral fits do not support an alternative hypothesis that the soft component occurs in the coolest part of the PSR (Bernardini et al. 2017). de Martino et al. (2020) theorize that perhaps there is a temperature gradient over the polar cap, and we are only measuring the innermost, hottest regions. In addition, the shape of the accretion region in IPs may play a role in how we interpret the soft component.

Masses of White Dwarfs in mCVs CVs are binary systems, which paves the way for dynamical mass determination, via Kepler’s third law, of WDs through optical spectroscopy. However, for the subclass of mCVs in particular, there is an alternative way to measure the mass of the WD through modeling of their X-ray spectra. This method requires no knowledge of the binary parameters, and bypasses the need for a measurement of the binary inclination, something which is extremely rare in non-eclipsing binaries. We showed in Equation 3 that the temperature of the shock can be directly related to the mass and radius of the WD. We show that, for a reasonable value of MWD , we might expect kTshock  20 keV. This implies that, if we are in fact able to measure directly kTshock itself, we could turn Equation 3 around and measure MWD .

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The power of the X-ray spectrum as a mass diagnostic was discussed as early as the 1980s in the context of AM Her, the prototypical polar (Rothschild et al. 1981). Cropper et al. (1998) presented an early mass survey of mCVs, modeling the PSR continuum spectra of five polars and eight IPs using data from the Ginga satellite. They reported an average M¯ WD = 0.96 M⊙ for polars and M¯ WD = 0.93 M⊙ for IPs, while noting their model was limited by not including viewing-angle dependence on the absorption, or any variation in m. ˙ Spectral modeling of mCVs prior to 2000 was also limited to energies 20 keV, as were probed by X-ray observatories of the time, despite the expected values of kTshock implying a spectral turnover at much higher energies. As a result, some early studies focused instead on deriving MWD through the measurement of the intensity ratios of H-like and He-like Fe lines, which are also a diagnostic of kTshock (Ezuka and Ishida 1999). With the inclusion of hard X-ray instruments onboard X-ray telescopes such as RXTE and Suzaku, measurements of MWD via the hard X-ray continuum became much more reliable. Suleimanov et al. (2005) developed their own PSR model, applying it to the RXTE 3–100 keV spectra of 14 IPs and finding generally good agreement with the few IPs with independent optical measurements of MWD . Yuasa et al. (2010) applied the same model to 3–50 keV Suzaku spectra of 17 IPs, while also including the (resolved) 6–7 keV Fe emission complex in the model – something of a hybrid of the continuum and emission line methods. (We note here that recent mass studies of mCVs have tended to focus mostly on IPs, not polars, as their spectra are relatively uncomplicated by cyclotron cooling; see the section entitled “Cyclotron Cooling in Polars”.) However, though the rapid advancement of X-ray detectors heralded a significant improvement in mCV mass determination through the measurement of the hard X-ray continuum, the above studies still suffered from uncertain background. The hard X-ray instruments carried by Suzaku and RXTE (and all other X-ray missions prior to 2012) were non-imaging telescopes, meaning that the background had to be modeled rather than measured. Despite being strong hard X-ray emitters, IPs are still relatively faint in the hard X-ray band (10 keV light curves. In this model, the slightly elevated shock means that, as the WD spins, there are a variety of viewing angles during which both X-ray emitting poles are simultaneously visible to the observer, hence the modulation (Mukai 1999). The finite shock height model can also be used to explain the properties of EX Hya, for which there is no evidence for absorption effects in the X-ray light curves (Mukai 1999; Luna et al. 2018). Mukai et al. (2015) showed that combining knowledge of the reflection properties of the X-ray spectra of IPs with the spin-resolved X-ray light curves can provide strong constraints on shock height.

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Though the X-ray light curves for the vast majority of IPs show strong modulations on Pspin , the asynchronous nature of the systems means there can be complex interactions between the spin of the WD and the orbital motion of the binary. Thus, we often see modulations not just at Pspin and Porb , but also Pbeat = (Pspin −1 − Porb −1 )−1 and its harmonics. The relative strengths of the various modulations present in the power spectra of IP light curves (at both X-ray and optical wavelengths) are in fact an important diagnostic of the dominant mode of accretion in IPs (Wynn and King 1992; Ferrario and Wickramasinghe 1999). The classic picture of an IP, as discussed at the very beginning the section entitled “Magnetic Cataclysmic Variables”, assumes that the WD is accreting from at least a partial accretion disk that terminates at Rm . At Rm , material then flows along the magnetic field lines on to the magnetic poles of the WD; hence, we see a modulation on Pspin . An optical observer might also see modulations on Pbeat due to reprocessing of X-rays by parts of the system that are outside of the WD co-rotation frame (e.g., in the binary rest frame; Warner 1986). However, what would we see if there were no partial accretion disk, and matter flowed directly from the donor on to the WD? The idea of a diskless IP was first explored by Hameury et al. (1986), who drew comparisons to Algol systems. In many short-period Algols, the distance of closest approach of the ballistic gas stream that travels from L1 (Rmin ) is less than the radius of the accreting star, such that no disk can form (see also direct impact AM CVn systems in the section entitled “HM Cnc and V407 Vul: Direct Impact Accretion”). Similarly, for some IPs, an orbital configuration might arise in which Rmin < Rm , in which case no disk would form and matter instead flows along magnetic field lines in a similar fashion to polars, though still highly asynchronous. This is known as “stream-fed” accretion. Hameury et al. (1986) estimated that the Rmin < Rm inequality would be satisfied for IPs with Porb < 5 h. A re-examination of the conditions required for disks in IPs concluded that if Pspin  0.1 Porb then a partial disk can form (King and Lasota 1991, see also Fig. 8). If this inequality is broken, then either the system is severely out of spin equilibrium (theorized to be the case for EX Hya; Hellier 2014), or the accretion flow is unlike the standard Keplerian disk we assume for IPs, hence the stream-fed model. (However, Norton et al. (2004) find that, for IPs where Pspin /Porb  0.5, accretion may instead be fed from a non-Keplerian ringlike structure at the edge of the WD’s Roche lobe.) Furthermore, there is also a theorized hybrid between the stream- and disk-fed models known as the “disk-overflow” model in which a partial disk does form, but some of the ballistic stream is also able to overflow the disk at the same time and flow along the field lines (e.g., Hellier 1993). For disk-overflow accretion to occur, the ballistic stream needs to approach the inner edge of the disk, which is the case when Rmin ∼ Rm . Thus, we might expect disk-overflow accretion to take place in systems where Pspin ∼ 0.1Porb (such as FO Aqr; see below). Wynn and King (1992) developed a number of diskless IP models and calculated theoretical X-ray power spectra. They found that for a simple stream-fed IP at low inclination (i.e., no eclipses), the majority of the X-rays are modulated on Pbeat rather than Pspin . This is due to the phenomenon of “pole-switching” where a given field line (fixed in the WD spin frame) will sweep up material from the accretion

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stream (fixed in the orbital frame), but the material is preferentially directed onto the nearest pole, which switches every half a beat cycle. Ferrario and Wickramasinghe (1999) explored the concept further, finding that one can also use the optical light curves and spectra to distinguish between dominant accretion models. V2400 Oph is widely regarded to be the first known diskless IP, showing strong X-ray variations on Pbeat (Buckley et al. 1997). FO Aqr is the prototypical “disk-overflow” system – essentially a hybrid accretion geometry – as it often shows a strong X-ray modulation at both Pspin and Pbeat (Hellier 1993). However, the relative strength of the spin and beat components in the X-ray power spectrum has been known to change between observations, suggesting that the accretion geometry of the system, and perhaps other IPs, may be somewhat fluid. In 2016 FO Aqr showed a drastic drop in flux at both optical and X-ray energies (Kennedy et al. 2017). The X-ray power spectra suggested that this socalled low state was linked to a transition to a stream-fed geometry. Upon returning to its typical flux, the WD spin began to dominate once more, suggesting a return to a typical disk-fed geometry. FO Aqr showed two more low states in 2017 and 2018, with each drop in flux associated with a change in the dominant accretion mode (Littlefield et al. 2020), suggesting a fundamental link between mass-transfer rate and accretion geometry. Several IPs have historically shown low states that have been reported after the fact (e.g., Garnavich and Szkody 1988; Shaw et al. 2020) so it has been difficult to study the X-ray timing properties of these systems. However, the decreases in flux in these sources may also be linked to a changing accretion geometry (Covington et al. 2022). Though the light curves of IPs are typically dominated by the periodic variability discussed above, it is important to note that IPs do also show aperiodic variability. The aperiodic power spectra of IPs (the aperiodic power spectrum, or noise power spectrum, refers to the power spectrum of a light curve that has had known periodic variability removed) often show a broken power law shape, with a characteristic break frequency νb . The value of νb is thought to be associated with the Keplerian frequency of the disk at its inner edge (Revnivtsev et al. 2009, 2011), i.e., for a typical disk-fed IP, at Rm . If this is the case, then one can measure νb to constrain Rm : 1 νb = 2π



GMWD 3 Rm

(4)

Recalling, from the  section entitled “X-Ray Spectra of mCVs”, that Equation 1

−1 can be modified by a 1 − rm term for matter not falling from ∞, one finds that the value of kTshock decreases with decreasing Rm . If the inner disk is particularly close to the WD (4RWD ; see, e.g., Suleimanov et al. 2019), then failing to take this into account can result in an underestimate in MWD . Thus, in some recent mass surveys of IPs, the aperiodic power spectra have been used to constrain Rm and account for non-infinite fall heights in the subsequent calculations of MWD (Suleimanov et al. 2016, 2019; Shaw et al. 2020).

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AE Aqr and the Propeller Systems For fast spinning and strongly magnetized mCVs, another interesting phenomenon can be observed. AE Aqr is an IP with Pspin = 33 s, and the WD is spinning down at a rate of P˙spin = 5.64 × 10−14 s s−1 (de Jager et al. 1994). A magnetized WD spinning at such a high rate should eject matter from the system as the rapidly rotating magnetosphere acts as a centrifugal barrier to any material flowing from the donor star (Wynn et al. 1997). This “propeller effect” is something which is often seen in other accreting systems such as those containing neutron stars (e.g., Tsygankov et al. 2016), but for a long time, AE Aqr was the only confirmed example of a CV in a propeller mode. Though the majority of matter is being flung away from the system by the magnetosphere, AE Aqr is still an X-ray source, and the X-ray emission is seen to be pulsed on the WD Pspin , suggesting that some material is managing to penetrate the barrier and accrete onto the WD (e.g., Kitaguchi et al. 2014). There are other IPs that appear to show rapidly rotating WDs similar to AE Aqr, but these show no signatures of the propeller effect and are entirely consistent with being accretion powered. However, in 2020, LAMOST J024048.51+195226.9 was seen to exhibit similar flaring and spectral properties to AE Aqr, raising the possibility of it being an AE Aqr twin (Garnavich et al. 2021). The initially elusive WD spin was detected at optical wavelengths with Pspin = 24.93 s (Pelisoli et al. 2022) and firmly established LAMOST J024048.51+195226.9 as only the second IP seen in a propeller mode. Both AE Aqr and LAMOST J024048.51+195226.9 are also persistent radio sources (Bookbinder and Lamb 1987; Pretorius et al. 2021), which is rare for IPs (Barrett et al. 2020). However, the origins of the radio emission are believed to be different for each source, with the radio emission in AE Aqr consistent with synchrotron emitting material, while the emission from LAMOST J024048.51+195226.9 is characteristic of magnetic plasma radiation or electron cyclotron maser emission, possibly from the magnetically active donor star (Barrett 2022). Similar to AE Aqr and LAMOST J024048.51+195226.9, AR Sco is a WD binary with Pspin = 1.95 min and Porb = 3.56 h (Marsh et al. 2016). However, despite having very similar broadband and temporal properties to the two propeller systems, AR Sco cannot be considered an IP as there is no evidence for accretion in the system. Instead, AR Sco is thought to be a WD analogue to pulsars, with all nonstellar emission powered by the spin-down of the WD (Buckley et al. 2017).

AM CVn Systems As discussed in ⊲ Chap. 107, “Accreting White Dwarfs”, AM CVn stars are a subclass of CVs that consist of a WD accreting matter from a hydrogen-poor companion – often another WD or a nondegenerate helium donor (see Solheim (2010) for a review). They have short orbital periods (Porb as low as 5 minutes in the case of HM Cnc; Israel et al. 1999). Historically, AM CVn systems have been

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relatively poorly studied in X-rays compared to other accreting WDs – only three were detected in the ROSAT All Sky Survey, with one being AM CVn itself (Ulla 1995). However, the launch of XMM-Newton at the end of the twentieth century prompted a number of multiwavelength studies. As with all CVs, AM CVn systems accrete via Roche lobe overflow and all but two systems (discussed below) form an accretion disk. As a result, the X-ray emission mechanisms are similar to “normal” (i.e., hydrogen-rich) CVs; that is, the disk is never hot enough to emit X-rays, but they are instead produced through shocks at the BL between the inner disk and the WD accretor. The X-ray spectra of the AM CVn stars (with disks, at least) are well fit with a multi-temperature thermal plasma model (see, e.g., Ramsay et al. 2005). However, unlike hydrogen-rich CVs, the elemental abundances deviate significantly from a solar composition. Some systems (e.g., Strohmayer 2004; Ramsay et al. 2005) show significant nitrogen and neon overabundance in addition to the expected hydrogen deficiency. A nitrogen overabundance can be explained by CNO processes in the donor (Marsh et al. 1991). However, a neon overabundance can only be explained through the helium burning process, where nitrogen is burned into carbon and oxygen, so an excess of both nitrogen and neon is puzzling. Kupfer et al. (2016) postulate that, in the case of GP Com, a short phase of He burning may have occurred in the donor, but stopped before N was depleted and C/O became too abundant. Alternate scenarios involve crystallization processes in the core of the donor that enhance neon abundances. However, ultimately the authors found no satisfactory solution to the observed high neon and nitrogen abundances in GP Com, so it remains an open question. The X-ray light curves of AM CVn systems generally show no coherent modulations (e.g., Ramsay et al. 2005), typical of systems with low magnetic field strengths. However, ROSAT observations of GP Com did reveal flux and hardness ratio modulations on the Porb of the system (e.g., van Teeseling and Verbunt 1994) which may indicate variable absorption due to the rotating accretion stream. The temporal properties of GP Com in X-rays remain an outlier in terms of AM CVn systems with disks, however.

HM Cnc and V407 Vul: Direct Impact Accretion HM Cnc and V407 Vul are a special case in the context of the AM CVn systems. They are the two shortest period binaries, with Porb = 321 and 569 s for HM Cnc and V407 Vul, respectively. Their X-ray spectra are very similar, exhibiting a soft, relatively featureless, BB-like spectrum, with enhanced neon (relative to solar) in V407 Vul (Strohmayer 2008; Ramsay 2008). The short orbital periods of these two systems means that Rmin (the distance of closest approach of the ballistic gas stream from the accretor; see the section entitled “X-Ray Light Curves of Intermediate Polars”) is smaller than the radius of the accretor itself, and the matter flowing from the L1 point directly impacts the photosphere of the primary before it can form a disk (see Marsh and Steeghs 2002;

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Fig. 15 Schematic of the direct-impact model in the case of V407 Vul, assuming a primary mass M1 = 0.5 M⊙ and a donor mass M2 = 0.1 M⊙ . The donor (center of mass at X = 1) fills its Roche lobe, and material flows through the L1 point but impacts the surface of the primary before being able to form a disk. The dashed line is tangent to the impact point, showing that impact is hidden from the donor in this particular scenario. (Reproduced with permission from Marsh and Steeghs 2002)

Ramsay et al. 2002, and Fig. 15). This “direct-impact” accretion model explains the majority of the observed properties of HM Cnc and V407 Vul with the fewest assumptions. (ES Cet (Porb = 620s) is sometimes classified as a direct-impact accretor (see, e.g., discussion by Solheim 2010), but the detection of double-peaked emission lines in the optical spectrum suggests that there is at least a small disk in the system.) In the direct-impact model, the narrow accretion stream will impact an area smaller than a fraction f = 8.5 × 10−5 of the surface area of the primary (Dolence et al. 2008). The density and ram pressure of the stream is high enough to penetrate ∼100 km (Wood 2009) into the photosphere of the accretor where it will thermalize, mix, and well up to the surface to produce the observed soft X-rays (similar to the blob accretion model for soft X-ray emission in polars discussed in the section entitled “The Soft Component of mCVs”). Unlike disk-fed AM CVn stars, the two direct impact systems do show strong coherent modulations (Strohmayer 2002, 2005). The light curves are characterized by an “on/off” pattern in the X-rays that lag the optical light curves by ∼0.2 phase. Wood (2009) showed that the X-ray light curves of HM Cnc and V407 Vul can be reproduced if there are two X-ray hot spots on the surface of the accretor, one for the impacting material and a second downstream of the impact point for the upwelling material. The slight phase offset of the X-ray light curves with respect to the optical emission is thought to be due to a temperature gradient around the impact/upwelling regions, with temperature decreasing as a function of distance from the hotspots (Marsh and Steeghs 2002; Wood 2009).

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Conclusions Cataclysmic variables are binary star systems, each of which consists of a WD accreting from a companion star, yet, despite the similar constituents, they form a diverse group. As the name suggests, CVs vary, both in the optical and X-ray wavebands. Soft X-rays are emitted through nuclear burning on the surfaces of some WDs, while other systems show harder X-ray emission arising from shock interactions; some CVs show both lower- and higher-energy X-ray photons. The WD mass, accretion rate, and magnetic field strength are defining characteristics of CV evolution and lead to the range of observed properties. This chapter has provided an introduction to the X-ray emission from accreting WDs. This is a broad field, with an ever-increasing population, as X-ray missions become more sensitive, and further all-sky surveys are performed. The “Living Swift X-ray Point Source” (LSXPS) Catalogue (released in 2022) expands upon the previous static Swift catalogues updating constantly with every new Swift observation, with a corresponding list of transients serendipitously (and automatically) discovered in the data – some of which will be new CV outbursts (Evans et al. 2023). In addition, upcoming missions such as XRISM (X-Ray Imaging Spectroscopy Mission) and Athena (Advanced Telescope for High Energy Astrophysics) will offer high-resolution spectroscopy of CVs and symbiotic stars, opening up a new parameter space for research.

References K. Aizu, X-ray emission region of a white dwarf with accretion. Prog. Theor. Phys. 49, 1184–1194 (1973). https://doi.org/10.1143/PTP.49.1184 E. Aydi, M. Orio, A.P. Beardmore, J.U. Ness, K.L. Page, N.P.M. Kuin, F.M. Walter, D.A.H. Buckley, S. Mohamed, P. Whitelock, J.P. Osborne, J. Strader, L. Chomiuk, M.J. Darnley, A. Dobrotka, A. Kniazev, B. Miszalski, G. Myers, N. Ospina, M. Henze, S. Starrfield, C.E. Woodward, Multiwavelength observations of V407 Lupi (ASASSN-16kt) – a very fast nova erupting in an intermediate polar. MNRAS 480(1), 572–609 (2018). https://doi.org/10. 1093/mnras/sty1759, 1807.00706 S. ¸ Balman, P. Godon, E.M. Sion, Swift X-ray telescope observations of the nova-like cataclysmic variables MV Lyr, BZ Cam, and V592 Cas. ApJ 794(1), 84 (2014). https://doi.org/10.1088/ 0004-637X/794/1/84, 1408.1996 P. Barrett, C. Dieck, A.J. Beasley, P.A. Mason, K.P. Singh, Radio observations of magnetic cataclysmic variables. Adv. Space Res. 66(5), 1226–1234 (2020). https://doi.org/10.1016/j.asr. 2020.04.007, 2004.11418 P.E. Barrett, VLA observations of the AE Aqr-type cataclysmic variable LAMOST J024048.51+195226.9. AJ 163(2), 58 (2022). https://doi.org/10.3847/1538-3881/ac3ed9, 2111.14949 A.P. Beardmore, J.P. Osborne, K.L. Page, M.R. Goad, M.F. Bode, S. Starrfield, Swift-XRT discovery of a 35s periodicity in the 2006 outburst of R.S. Ophiuchi, in R.S. Ophiuchi (2006) and the Recurrent Nova Phenomenon, ed. by A. Evans, M.F. Bode, T.J. O’Brien, M.J. Darnley. Astronomical Society of the Pacific Conference Series, vol. 401 (2008), p. 296 F. Bernardini, D. de Martino, K. Mukai, D.M. Russell, M. Falanga, N. Masetti, C. Ferrigno, G. Israel, Broad-band characteristics of seven new hard X-ray selected cataclysmic variables. MNRAS 470(4), 4815–4837 (2017). https://doi.org/10.1093/mnras/stx1494, 1706.04005

4266

K. L. Page and A. W. Shaw

K. Beuermann, V. Burwitz, AM Herculis binaries in the ROSAT ERA, in Magnetic Cataclysmic Variables, ed. by D.A.H. Buckley, B. Warner. Astronomical Society of the Pacific Conference Series, vol. 85 (1985), p. 99 K. Bakowska, ˛ T.R. Marsh, D. Steeghs, G. Nelemans, P.J. Groot, Spectroscopy of the helium-rich binary ES Ceti reveals accretion via a disc and evidence of eclipses. A&A 645, A114 (2021). https://doi.org/10.1051/0004-6361/202039266, 2011.09213 M.F. Bode, A. Evans, Classical Novae. Cambridge University Press, Cambridge, UK (2008), vol. 43 M.F. Bode, T.J. O’Brien, J.P. Osborne, K.L. Page, F. Senziani, G.K. Skinner, S. Starrfield, J.U. Ness, J.J. Drake, G. Schwarz, A.P. Beardmore, M.J. Darnley, S.P.S. Eyres, A. Evans, N. Gehrels, M.R. Goad, P. Jean, J. Krautter, G. Novara, Swift observations of the 2006 outburst of the recurrent nova RS Ophiuchi. I. Early X-ray emission from the shocked ejecta and red giant wind. ApJ 652(1), 629–635 (2006). https://doi.org/10.1086/507980, astro-ph/0604618 D.A. Bollimpalli, J.M. Hameury, J.P. Lasota, Disc instabilities and nova eruptions in symbiotic systems: RS Ophiuchi and Z Andromedae. MNRAS 481(4), 5422–5435 (2018). https://doi.org/ 10.1093/mnras/sty2555, 1804.07916 J.A. Bookbinder, D.Q. Lamb, Discovery of radio emission from AE Aquarii. ApJL 323, L131 (1987). https://doi.org/10.1086/185072 K. Brecher, W.H. Ingham, P. Morrison, On transient thermal X-ray emission from novae. ApJ 213, 492–496 (1977). https://doi.org/10.1086/155180 D.A.H. Buckley, F. Haberl, C. Motch, K. Pollard, A. Schwarzenberg-Czerny, K. Sekiguchi, ROSAT observations of RX J1712.6-2414: a discless intermediate polar? MNRAS 287(1), 117– 123 (1997). https://doi.org/10.1093/mnras/287.1.117 D.A.H. Buckley, P.J. Meintjes, S.B. Potter, T.R. Marsh, B.T. Gänsicke, Polarimetric evidence of a white dwarf pulsar in the binary system AR Scorpii. Nat. Astron. 1, 0029 (2017). https://doi. org/10.1038/s41550-016-0029, 1612.03185 K. Byckling, J.P. Osborne, P.J. Wheatley, G.A. Wynn, A. Beardmore, V. Braito, K. Mukai, R.G. West, Swift observations of GW Lib: a unique insight into a rare outburst. MNRAS 399(3), 1576–1586 (2009). https://doi.org/10.1111/j.1365-2966.2009.15378.x, 0907.2659 C.G. Campbell, A.D. Schwope, Asynchronous rotation in the polars. A&A 343, 132–136 (1999) C.C. Cheung, S.N. Shore, I. De Gennaro Aquino, S. Charbonnel, J. Edlin, E. Hays, R.H.D. Corbet, D.L. Wood, Possible association of the gamma-ray transient Fermi J0639+0548 with Nova Mon 2012. Astron. Telegram 4310, 1 (2012) L. Chomiuk, J.D. Linford, J. Yang, T.J. O’Brien, Z. Paragi, A.J. Mioduszewski, R.J. Beswick, C.C. Cheung, K. Mukai, T. Nelson, V.A.R.M. Ribeiro, M.P. Rupen, J.L. Sokoloski, J. Weston, Y. Zheng, M.F. Bode, S. Eyres, N. Roy, G.B. Taylor, Binary orbits as the driver of γ -ray emission and mass ejection in classical novae. Nature 514(7522), 339–342 (2014). https://doi. org/10.1038/nature13773, 1410.3473 L. Chomiuk, B.D. Metzger, K.J. Shen, New insights into classical novae. ARA&A 59(1), 391–444 (2021). https://doi.org/10.1146/annurev-astro-112420-114502, 2011.08751 M.J. Coe, J.A. Kennea, P.A. Evans, A. Udalski, Swift J004427.3-734801 – a probable Be/white dwarf system in the Small Magellanic Cloud. MNRAS 497(1), L50–L55 (2020). https://doi. org/10.1093/mnrasl/slaa112, 2005.02891 A.E. Covington, A.W. Shaw, K. Mukai, C. Littlefield, C.O. Heinke, R.M. Plotkin, D. Barrett, J. Boardman, D. Boyd, S.M. Brincat, R. Carstens, D.F. Collins, L.M. Cook, W.R. Cooney, D.C. Fernández, S. Dufoer, S. Dvorak, C. Galdies, W. Goff, F.-Z. Hambsch, S. Johnston, J. Jones, K. Menzies, L.A.G Monard, E. Morelle, P. Nelson, Y. Ögmen, J.W Rock, R. Sabo, J. Seargeant, G. Stone, J. Ulowetz, T. Vanmunster, Investigating the low-flux states in six intermediate polars. ApJ 928(2), 164 (2022). https://doi.org/10.3847/1538-4357/ac5682. arXiv, e-prints arXiv:2202.08365. https://ui.adsabs.harvard.edu/abs/2022ApJ...928..164C M. Cropper, The Polars. Space Sci. Rev. 54(3–4), 195–295 (1990). https://doi.org/10.1007/ BF00177799 M. Cropper, G. Ramsay, K. Wu, White dwarf masses in magnetic cataclysmic variables – multitemperature fits to GINGA data. MNRAS 293, 222 (1998). https://doi.org/10.1046/j.1365-8711. 1998.00610.x

115 X-ray Emission Mechanisms in Accreting White Dwarfs

4267

M. Cropper, K. Wu, G. Ramsay, A. Kocabiyik, Effects of gravity on the structure of post-shock accretion flows in magnetic cataclysmic variables. MNRAS 306, 684–690 (1999). https://doi. org/10.1046/j.1365-8711.1999.02570.x, astro-ph/9902355 O.C. de Jager, P.J. Meintjes, D. O’Donoghue, E.L. Robinson, The discovery of a brake on the white dwarf in AE Aquarii. MNRAS 267, 577–588 (1994). https://doi.org/10.1093/mnras/267.3.577 D. de Martino, F. Bernardini, K. Mukai, M. Falanga, N. Masetti, Hard X-ray cataclysmic variables. Adv. Space Res. 66(5), 1209–1225 (2020). https://doi.org/10.1016/j.asr.2019.09.006, 1909.06306 J. Dolence, M.A. Wood, I. Silver, SPH simulations of direct impact accretion in the ultracompact AM CVn binaries. ApJ 683(1), 375–382 (2008). https://doi.org/10.1086/589817, 0805.0338 C. Done, P. Magdziarz, Complex absorption and reflection of a multitemperature cyclotronbremsstrahlung X-ray cooling shock in BY Cam. MNRAS 298, 737–746 (1998). https://doi. org/10.1046/j.1365-8711.1998.01636.x, astro-ph/9712226 C. Done, J.P. Osborne, A.P. Beardmore, The EF ERI GINGA data and physical models for the Xray spectra of AM Herculis systems. MNRAS 276(2), 483–494 (1995). https://doi.org/10.1093/ mnras/276.2.483 P.A. Evans, C. Hellier, Why do some intermediate polars show soft X-ray emission? A survey of XMM-newton spectra. ApJ 663, 1277–1284 (2007). https://doi.org/10.1086/518552, 0704.1388 P.A. Evans, A.P. Beardmore, J.P. Osborne, G.A. Wynn, The unusual 2006 dwarf nova outburst of GK Persei. MNRAS 399(3), 1167–1174 (2009). https://doi.org/10.1111/j.1365-2966.2009. 15376.x, 0907.1407 P.A. Evans, K.L. Page, A.P. Bearmore, R.A.J. Eyles-Ferris, J.P. Osborne, S. Campana, J.A. Kennea, S.B. Cenko, A real-time transient detector and the living Swift-XRT point source catalogue. MNRAS 518(1), 174–184 (2023). https://doi.org/10.1093/mnras/stac2937, 2208.14478. https:// ui.adsabs.harvard.edu/abs/2023MNRAS.518..174E H. Ezuka, M. Ishida, Iron line diagnostics of the postshock hot plasma in magnetic Cataclysmic variables observed with ASCA. ApJS 120, 277–298 (1999). https://doi.org/10.1086/313181 A.C. Fabian, J.E. Pringle, M.J. Rees, X-ray emission from accretion on to white dwarfs. MNRAS 175, 43–60 (1976). https://doi.org/10.1093/mnras/175.1.43 L. Ferrario, D.T. Wickramasinghe, The power of intermediate polars. MNRAS 309(2), 517–527 (1999). https://doi.org/10.1046/j.1365-8711.1999.02860.x D. Fertig, K. Mukai, T. Nelson, J.K. Cannizzo, The fall and the rise of X-rays from dwarf novae in outburst: RXTE observations of VW Hydri and WW Ceti. PASP 123(907), 1054 (2011). https:// doi.org/10.1086/661949, 1107.3142 A. Fischer, K. Beuermann, Accretion physics of AM Herculis binaries. I. Results from onedimensional stationary radiation hydrodynamics. A&A 373, 211–221 (2001). https://doi.org/ 10.1051/0004-6361:20010600, astro-ph/0105190 P. Garnavich, P. Szkody, Observed low states in DQ Herculis systems. PASP 100, 1522, (1988). https://doi.org/10.1086/132358 P. Garnavich, C. Littlefield, R.M. Wagner, J. van Roestel, A.D. Jaodand, P. Szkody, J.R. Thorstensen Confirmation of a second propeller: a high-inclination twin of AE Aquarii. ApJ 917(1), 22 (2021). https://doi.org/10.3847/1538-4357/ac0339, 2102.08377 I.M. George, A.C. Fabian, X-ray reflection from cold matter in active galactic nuclei and X-ray binaries. MNRAS 249, 352–367 (1991) A.C. Gordon, E. Aydi, K.L. Page, K.L. Li, L. Chomiuk, K.V. Sokolovsky, K. Mukai, J. Seitz, Surveying the X-ray behavior of novae as they emit γ -rays. ApJ 910(2), 134 (2021). https://doi. org/10.3847/1538-4357/abe547, 2010.15930 C.J. Hailey, K. Mori, K. Perez, A.M. Canipe, J. Hong, J.A. Tomsick, S.E. Boggs, F.E. Christensen, W.W. Craig, F. Fornasini, J.E. Grindlay, F.A. Harrison, M. Nynka, F. Rahoui, D. Stern, S. Zhang, W.W. Zhang, Evidence for intermediate polars as the origin of the Galactic center hard X-ray emission. ApJ 826, 160 (2016). https://doi.org/10.3847/0004-637X/826/2/160, 1605.06066 J.M. Hameury, A.R. King, The X-ray light curves of AM Herculis systems. Mon. Not. R. Astron. Soc. 235(2), 433–439 (1988). https://doi.org/10.1093/mnras/235.2.433 J.M. Hameury, J.P. Lasota, Dwarf nova outbursts in intermediate polars. A&A 602, A102 (2017). https://doi.org/10.1051/0004-6361/201730760, 1703.03563

4268

K. L. Page and A. W. Shaw

J.M. Hameury, A.R. King, J.P. Lasota, Accretion flows in the non-synchronous magnetic cataclysmic variables. MNRAS 218, 695–710 (1986). https://doi.org/10.1093/mnras/218.4.695 J. Heise, A.C. Brinkman, E. Gronenschild, M. Watson, A.R. King, L. Stella, K. Kieboom, An X-ray study of AM Herculis. I. Discovery of a new mode of soft X-ray emission. A&A 148, L14–L16 (1985). C. Hellier, Disc-overflow accretion in the intermediate polar FO Aquarii. MNRAS 265, L35–L39 (1993). https://doi.org/10.1093/mnras/265.1.L35 C. Hellier, The magnetospheric boundary in cataclysmic variables. Eur. Phys. J. Web Conf. 64, 07001 (2014). https://doi.org/10.1051/epjconf/20136407001, 1312.4779 Y. Hillman, D. Prialnik, A. Kovetz, M.M. Shara, Growing white dwarfs to the Chandrasekhar limit: the parameter space of the single degenerate SNIa channel. ApJ 819(2), 168 (2016). https://doi. org/10.3847/0004-637X/819/2/168, 1508.03141 Y. Hillman, M. Orio, D. Prialnik, M. Shara, P. Bezák, A. Dobrotka, The supersoft X-ray transient ASASSN-16oh as a thermonuclear runaway without mass ejection. ApJ 879(1), L5 (2019). https://doi.org/10.3847/2041-8213/ab2887, 1906.11464 M. Ishida, K. Mukai, J.P. Osborne, Observation of EX Hydrae with ASCA. PASJ 46, L81–L85 (1994) G.L. Israel, M.R. Panzera, S. Campana, D. Lazzati, S. Covino, G. Tagliaferri, L. Stella, The discovery of 321 S pulsations in the ROSAT HRI light curves of 1BMW J080622.8+152732 = RX J0806.3+1527. A&A 349, L1–L4 (1999) O. König, J. Wilms, R. Arcodia, T. Dauser, K. Dennerl, V. Doroshenko, F. Haberl, S. Hämmerich, C. Kirsh, I. Kreykenbohm, M. Lorenz, A. Malyali, A. Merloni, A. Rau, T. Rauch, G. Sala, A. Schwope, V. Suleimanov, P. Weber, K. Werner, X-ray detection of a nova in the fireball phase. Nature 605, 248–250 (2022). https://doi.org/10.1038/s41586-022-04635-y P. Kahabka, E.P.J. van den Heuvel, Luminous supersoft X-ray sources. ARA&A 35, 69–100 (1997). https://doi.org/10.1146/annurev.astro.35.1.69 M. Kato, H. Saio, M. Henze, J.U. Ness, J.P. Osborne, K.L. Page, M.J. Darnley, M.F. Bode, A.W. Shafter, M. Hernanz, N. Gehrels, J. Kennea, I. Hachisu, X-ray flashes in recurrent novae: M31N 2008-12a and the implications of the Swift nondetection. ApJ 830(1), 40 (2016). https:// doi.org/10.3847/0004-637X/830/1/40, 1607.07985 S.D. Kawaler, The hydrogen shell game: pulsational instabilities in hydrogen shell–burning planetary nebula nuclei. ApJ 334, 220 (1988). https://doi.org/10.1086/166832 J.A. Kennea, K. Mukai, J.L. Sokoloski, G.J.M. Luna, J. Tueller, C.B. Markwardt, D.N. Burrows, Swift observations of hard X-ray emitting white dwarfs in symbiotic stars. ApJ 701(2), 1992– 2001 (2009). https://doi.org/10.1088/0004-637X/701/2/1992, 0907.0764 J.A. Kennea, M.J. Coe, P.A. Evans, J. Waters, R.E. Jasko, The first year of S-CUBED: the Swift Small Magellanic Cloud Survey. ApJ 868(1), 47 (2018). https://doi.org/10.3847/1538-4357/ aae839, 1810.05481 J.A. Kennea, M.J. Coe, P.A. Evans, L.J. Townsend, Z.A. Campbell, A. Udalski, Swift J011511.0725611: discovery of a rare Be star/white dwarf binary system in the SMC. MNRAS 508(1), 781–788 (2021). https://doi.org/10.1093/mnras/stab2632, 2109.05307 M.R. Kennedy, P.M. Garnavich, C. Littlefield, P. Callanan, K. Mukai, E. Aadland, M.M. Kotze, E.J. Kotze, X-ray observations of FO Aqr during the 2016 low state. MNRAS 469(1), 956–967 (2017). https://doi.org/10.1093/mnras/stx880, 1704.01909 A.R. King, J.P. Lasota, Spin evolution and magnetic fields in cataclysmic variables. ApJ 378, 674– 681 (1991). https://doi.org/10.1086/170467 A.R. King, G.A. Williams, Absorption dips and the geometry of the AM Herculis systems. MNRAS 215, 1P–4 (1985). https://doi.org/10.1093/mnras/215.1.1P R. Kippenhahn, H.C. Thomas, Accretion belts on white dwarfs. A&A 63(1–2), 265–272 (1978). T. Kitaguchi, H. An, A.M. Beloborodov, E.V. Gotthelf, T. Hayashi, V.M. Kaspi, V.R. Rana, S.E. Boggs, F.E. Christensen, W.W. Craig, C.J. Hailey, F.A. Harrison, D. Stern, W.W. Zhang, NuSTAR and Swift observations of the fast rotating magnetized white dwarf AE Aquarii. ApJ 782(1), 3 (2014). https://doi.org/10.1088/0004-637X/782/1/3, 1312.5039 J. Krautter, X-ray emission from classical novae in outburst. in Eds. by M.F. Bode, A. Evans, Classical Novae, 2nd edn. Cambridge University Press, Cambridge, UK (2008), vol. 43, p. 232

115 X-ray Emission Mechanisms in Accreting White Dwarfs

4269

J. Krautter, H. Oegelman, S. Starrfield, R. Wichmann, E. Pfeffermann, ROSAT X-Ray Observations of Nova V1974 Cygni: The Rise and Fall of the Brightest Supersoft X-Ray Source. ApJ 456, 788 (1996). https://doi.org/10.1086/176697 J. Kuijpers, J.E. Pringle, Comments on radial white dwarf accretion. A&A 114(1), L4–L6 (1982) T. Kupfer, D. Steeghs, P.J. Groot, T.R. Marsh, G. Nelemans, G.H.A. Roelofs, UVES and X-Shooter spectroscopy of the emission line AM CVn systems GP Com and V396 Hya. Mon. Not. R. Astron. Soc. 457(2), 1828–1841 (2016). https://doi.org/10.1093/mnras/stw126 D.Q. Lamb, A.R. Masters, X and UV radiation from accreting magnetic degenerate dwarfs. ApJL 234, L117–L122 (1979). https://doi.org/10.1086/183121 C. Littlefield, P. Garnavich, M.R. Kennedy, J. Patterson, J. Kemp, R.A. Stiller, F.J. Hambsch, T.A. Heras, G. Myers, G. Stone, G. Sjöberg, S. Dvorak, P. Nelson, V. Popov, M. Bonnardeau, T. Vanmunster, E. de Miguel, K.B. Alton, B. Harris, L.M. Cook, k.A. Graham, S.M. Brincat, D.J. Lane, J. Foster, R. Pickard, R. Sabo, B. Vietje, D. Lemay, J. Briol, N. Krumm, M. Dadighat, W. Goff, R. Solomon, S. Padovan, G. Bolt, E. Kardasis, A. Debackère, J. Thrush, W. Stein, B. Walter, D. Coulter, V. Tsehmeystrenko, J.F. Gout, P. Lewin, C. Galdies, D.C. Fernandez, G. Walker, J.J. Boardman, E. Pellett, The rise and fall of the king: the correlation between FO Aquarii’s low states and the white dwarf’s spin-down. ApJ 896(2), 116 (2020). https://doi.org/ 10.3847/1538-4357/ab9197, 1904.11505 M. Livio, J.E. Pringle, Star spots and the period gap in cataclysmic variables. ApJ 427, 956 (1994). https://doi.org/10.1086/174202 G.J.M. Luna, J.L. Sokoloski, K. Mukai, T. Nelson, Symbiotic stars in X-rays. A&A 559, A6 (2013). https://doi.org/10.1051/0004-6361/201220792, 1211.6082 G.J.M. Luna, K. Mukai, M. Orio, P. Zemko, Constraining the accretion geometry of the intermediate polar EX Hya using NuSTAR, Swift, and Chandra observations. ApJL 852(1), L8 (2018). https://doi.org/10.3847/2041-8213/aaa28f, 1711.03942 D. Lynden-Bell, J.E. Pringle, The evolution of viscous discs and the origin of the nebular variables. MNRAS 168, 603–637 (1974). https://doi.org/10.1093/mnras/168.3.603 T.J. Maccarone, T.J. Nelson, P.J. Brown, K. Mukai, P.A. Charles, A. Rajoelimanana, D.A.H. Buckley, J. Strader, L. Chomiuk, C.T. Britt, S.W. Jha, P. Mróz, A. Udalski, M.K. Szyma´nski, I. Soszy´nski, R. Poleski, S. Kozłowski, P. Pietrukowicz, J. Skowron, K. Ulaczyk, Unconventional origin of supersoft X-ray emission from a white dwarf binary. NatAs 3, 173–177 (2019). https://doi.org/10.1038/s41550-018-0639-1, 1907.02130 T.R. Marsh, D. Steeghs, V407 Vul: a direct impact accretor. MNRAS 331(1), L7–L11 (2002). https://doi.org/10.1046/j.1365-8711.2002.05346.x, astro-ph/0201309 T.R. Marsh, K. Horne, S. Rosen, Evidence for CNO processed material in the accretion disk of GP Comae. ApJ 366, 535 (1991). https://doi.org/10.1086/169588 T.R. Marsh, B.T. Gänsicke, S. Hümmerich, F.J. Hambsch, K. Bernhard, C. Lloyd, E. Breedt, E.R. Stanway, D.T. Steeghs, S.G. Parsons, O. Toloza, M.R. Schreiber, P.G. Jonker, J. van Roestel, T. Kupfer, A.F. Pala, V.S. Dhillon, L.K. Hardy, S.P. Littlefair, A. Aungwerojwit, S. Arjyotha, D. Koester, J.J. Bochinski, C.A. Haswell, P. Frank, P.J. Wheatley, A radiopulsing white dwarf binary star. Nature 537(7620), 374–377 (2016). https://doi.org/10.1038/ nature18620, 1607.08265 K.O. Mason, X-ray emission from cataclysmic variables. Space Sci. Rev. 40(1–2), 99–115 (1985). https://doi.org/10.1007/BF00212872 G. Matt, D. de Martino, B.T. Gänsicke, I. Negueruela, R. Silvotti, J.M. Bonnet-Bidaud, M. Mouchet, K. Mukai, BeppoSAX observations of AM Herculis in intermediate and high states. A&A 358, 177–186 (2000). astro-ph/0004014 B.D. Metzger, T. Finzell, I. Vurm, R. Hascoët, A.M. Beloborodov, L. Chomiuk, Gamma-ray novae as probes of relativistic particle acceleration at non-relativistic shocks. MNRAS 450(3), 2739– 2748 (2015). https://doi.org/10.1093/mnras/stv742, 1501.05308 F. Meyer, E. Meyer-Hofmeister, Accretion disk evaporation by a coronal siphon flow. A&A 288, 175–182 (1994). M. Morii, H. Yamaoka, T. Mihara, M. Matsuoka, N. Kawai, Search for soft X-ray flashes at the fireball phase of classical/recurrent novae using MAXI/GSC data. PASJ 68, S11 (2016). https:// doi.org/10.1093/pasj/psw007, 1601.04394

4270

K. L. Page and A. W. Shaw

K. Mukai, The X-ray light curves of magnetic cataclysmic variables with non-zero shock heights, in Annapolis Workshop on Magnetic Cataclysmic Variables, ed. by C. Hellier, K. Mukai. Astronomical Society of the Pacific Conference Series, vol. 157 (1999), p. 33 K. Mukai, X-ray emissions from accreting white dwarfs: a review. PASP 129(976), 062001 (2017). https://doi.org/10.1088/1538-3873/aa6736, 1703.06171 K. Mukai, J.H. Wood, T. Naylor, E.M. Schlegel, J.H. Swank, The X-ray eclipse of the dwarf nova HT Cassiopeiae: results from ASCA and ROSAT HRI observations. ApJ 475(2), 812–822 (1997). https://doi.org/10.1086/303571 K. Mukai, A. Kinkhabwala, J.R. Peterson, S.M. Kahn, F. Paerels, Two types of X-ray spectra in cataclysmic variables. ApJ 586(1), L77–L80 (2003). https://doi.org/10.1086/374583, astroph/0301557 K. Mukai, V. Rana, F. Bernardini, D. de Martino, Unambiguous detection of reflection in magnetic cataclysmic variables: joint NuSTAR-XMM-Newton observations of three intermediate polars. ApJL 807, L30 (2015). https://doi.org/10.1088/2041-8205/807/2/L30, 1506.07213 U. Mürset, B. Wolff, S. Jordan, X-ray properties of symbiotic stars. II. Systems with colliding winds. A&A 319, 201–210 (1997) R.F. Mushotzky, A.E. Szymkowiak, Einstein Observatory solid state detector observations of cooling flows in clusters of galaxies, in NATO Advanced Science Institutes (ASI) Series C, vol. 229, ed. by A.C. Fabian (1988), pp. 53–62 M. Nauenberg, Analytic approximations to the mass-radius relation and energy of zero-temperature stars. ApJ 175, 417 (1972). https://doi.org/10.1086/151568 T. Nelson, K. Mukai, K.L. Li, I. Vurm, B.D. Metzger, L. Chomiuk, J.L. Sokoloski, J.D. Linford, T. Bohlsen, P. Luckas, NuSTAR detection of X-rays concurrent with gamma-rays in the nova V5855 Sgr. ApJ 872(1), 86 (2019). https://doi.org/10.3847/1538-4357/aafb6d, 1901.00030 J.U. Ness, The complications of learning from Super Soft Source X-ray spectra. Adv. Space Res. 66(5), 1202–1208 (2020). https://doi.org/10.1016/j.asr.2019.09.002, 1909.09711 J.U. Ness, J.J. Drake, S. Starrfield, M.F. Bode, T.J. O’Brien, A. Evans, S.P.S. Eyres, L.A. Helton, J.P. Osborne, K.L. Page, C. Schneider, C.E. Woodward, High-resolution X-ray spectroscopy of the evolving shock in the 2006 outburst of RS Ophiuchi. AJ 137(2), 3414–3436 (2009). https:// doi.org/10.1088/0004-6256/137/2/3414, 0810.2023 J.U. Ness, A.P. Beardmore, J.P. Osborne, E. Kuulkers, M. Henze, A.L. Piro, J.J. Drake, A. Dobrotka, G. Schwarz, S. Starrfield, P. Kretschmar, M. Hirsch, J. Wilms, Short-period Xray oscillations in super-soft novae and persistent super-soft sources. A&A 578, A39 (2015). https://doi.org/10.1051/0004-6361/201425178, 1503.00186 V.V. Neustroev, K.L. Page, E. Kuulkers, J.P. Osborne, A.P. Beardmore, C. Knigge, T. Marsh, V.F. Suleimanov, S.V. Zharikov, Superhumps linked to X-ray emission. The superoutbursts of SSS J122221.7-311525 and GW Lib. A&A 611, A13 (2018). https://doi.org/10.1051/00046361/201731719, 1712.03515 J.S. Nichols, J. DePasquale, E. Kellogg, C.S. Anderson, J. Sokoloski, J. Pedelty, Discovery of rapid hard X-ray variability and new jet activity in the symbiotic binary R Aquarii. ApJ 660(1), 651–661 (2007). https://doi.org/10.1086/512138, astro-ph/0701336 A.J. Norton, M.G. Watson, Spin modulated X-ray emission from intermediate polars. MNRAS 237, 853–874 (1989). https://doi.org/10.1093/mnras/237.4.853 A.J. Norton, G.A. Wynn, R.V. Somerscales, The spin periods and magnetic moments of white dwarfs in magnetic cataclysmic variables. ApJ 614(1), 349–357 (2004). https://doi.org/10.1086/ 423333, astro-ph/0406363 M. Orio, The ROSAT detection of RS Ophiuchi at quiescence. A&A 274, L41–L44 (1993) M. Orio, A. Zezas, U. Munari, A. Siviero, E. Tepedelenlioglu, Two SMC symbiotic stars undergoing steady hydrogen burning. ApJ 661(2), 1105–1111 (2007). https://doi.org/10.1086/ 514806, astro-ph/0702419 J.P. Osborne, K. Beuermann, P. Charles, L. Maraschi, K. Mukai, A. Treves, A new soft X-ray mode in the AM Herculis object E2003+225. ApJL 315, L123 (1987). https://doi.org/10.1086/184873 J.P. Osborne, K.L. Page, A.P. Beardmore, M.F. Bode, M.R. Goad, T.J. O’Brien, S. Starrfield, T. Rauch, J.U. Ness, J. Krautter, G. Schwarz, D.N. Burrows, N. Gehrels, J.J. Drake, A. Evans,

115 X-ray Emission Mechanisms in Accreting White Dwarfs

4271

S.P.S. Eyres, The supersoft X-ray phase of nova RS Ophiuchi 2006. ApJ 727(2), 124 (2011). https://doi.org/10.1088/0004-637X/727/2/124, 1011.5327 K.L. Page, J.P. Osborne, Super-soft X-ray Spectral Evolution in Novae. in Eds. by P.A. Woudt, V.A.R.M. Ribeiro, Stellar Novae: Past and Future Decades. Astronomical Society of the Pacific Conference Series, vol. 490 (2014), p. 345 K.L. Page, J.P. Osborne, N.P.M. Kuin, M. Henze, F.M. Walter, A.P. Beardmore, M.F. Bode, M.J. Darnley, L. Delgado, J.J. Drake, M. Hernanz, K. Mukai, T. Nelson, J.U. Ness, G.J. Schwarz, S.N. Shore, S. Starrfield, C.E. Woodward, Swift detection of the super-swift switch-on of the super-soft phase in nova V745 Sco (2014). MNRAS 454(3), 3108–3120 (2015). https://doi.org/10.1093/mnras/stv2144, 1509.04004 K.L. Page, A.P. Beardmore, J.P. Osborne, Neil Gehrels Swift Observatory studies of supersoft novae. Adv. Space Res. 66(5), 1169–1192 (2020). https://doi.org/10.1016/j.asr.2019.08.003, 1908.02004 D. Pandel, F.A. Córdova, XMM-Newton observes flaring in the polar UZ For during a low state. MNRAS 336(3), 1049–1055 (2002). https://doi.org/10.1046/j.1365-8711.2002.05846.x, astroph/0207263 J. Patterson, The DQ Herculis stars. PASP 106, 209–238 (1994). https://doi.org/10.1086/133375 J. Patterson, J.C. Raymond, X-ray emission from cataclysmic variables with accretion disks. I. Hard X-rays. ApJ 292, 535–549 (1985a). https://doi.org/10.1086/163187 J. Patterson, J.C. Raymond, X-ray emission from cataclysmic variables with accretion disks. II. EUV/soft X-ray radiation. ApJ 292, 550–558 (1985b). https://doi.org/10.1086/163188 J. Patterson, K. Beuermann, D.W. Lamb, G. Fabbiano, J.C. Raymond, J. Swank, N.E. White, VV Puppis: the soft X-ray machine. ApJ 279, 785–797 (1984). https://doi.org/10.1086/161947 I. Pelisoli, T.R. Marsh, V.S. Dhillon, E. Breedt, A.J. Brown, M.J. Dyer, M.J. Green, P. Kerry, S.P. Littlefair, S.G. Parsons, D.I. Sahman, J.F. Wild, Found: a rapidly spinning white dwarf in LAMOST J024048.51+195226.9. MNRAS, 509, L31–L36 (2022). https://doi.org/10.1093/ mnrasl/slab116, arXiv, 2108.11396 G.W. Pratt, K. Mukai, B.J.M. Hassall, T. Naylor, J.H. Wood, An XMM-Newton observation of the nova-like variable UX UMa: spatially and spectrally resolved two-component X-ray emission. MNRAS 348(3), L49–L53 (2004). https://doi.org/10.1111/j.1365-2966.2004.07574.x, astroph/0401176 M.L. Pretorius, D.M. Hewitt, P.A. Woudt, R.P. Fender, I. Heywood, C. Knigge, J.C.A. MillerJones, D.A.H. Buckley, H.L. Worters, S.B. Potter, D.R.A. Williams, Radio and optical observations of the possible AE Aqr twin, LAMOST J024048.51+195226.9. MNRAS 503(3), 3692–3697 (2021). https://doi.org/10.1093/mnras/stab498, 2102.08800 W. Priedhorsky, F.J. Marshall, D.R. Hearn, Disappearance of periodic X-ray minima in AM Her. A&A 173, 95–100 (1987) J.E. Pringle, G.J. Savonije, X-ray emission from dwarf novae. MNRAS 187, 777–783 (1979). https://doi.org/10.1093/mnras/187.4.777 N.V. Raguzova, Population synthesis of Be/white dwarf binaries in the Galaxy. A&A 367, 848–858 (2001). https://doi.org/10.1051/0004-6361:20000348 G. Ramsay, The X-ray spectrum of RX J1914.4+2456 revisited. MNRAS 384(2), 687–691 (2008). https://doi.org/10.1111/j.1365-2966.2007.12726.x, 0711.2449 G. Ramsay, M. Cropper, The energy balance of polars revisited. MNRAS 347(2), 497–507 (2004). https://doi.org/10.1111/j.1365-2966.2004.07220.x, astro-ph/0309527 G. Ramsay, K.O. Mason, M. Cropper, M.G. Watson, K.L. Clayton, ROSAT observations of an UMa and MR Ser: the status of the soft X-ray excess in AM HER stars. MNRAS 270, 692–702 (1994). https://doi.org/10.1093/mnras/270.3.692 G. Ramsay, K. Wu, M. Cropper, G. Schmidt, K. Sekiguchi, F. Iwamuro, T. Maihara, Optical/infrared spectroscopy and photometry of the short-period binary RX J1914+24. MNRAS 333(3), 575–582 (2002). https://doi.org/10.1046/j.1365-8711.2002.05421.x, astro-ph/0202281 G. Ramsay, M. Cropper, K. Wu, K.O. Mason, F.A. Córdova, W. Priedhorsky, XMM-Newton observations of polars in low accretion states. MNRAS 350(4), 1373–1384 (2004). https://doi. org/10.1111/j.1365-2966.2004.07732.x, astro-ph/0402526

4272

K. L. Page and A. W. Shaw

G. Ramsay, P. Hakala, T. Marsh, G. Nelemans, D. Steeghs, M. Cropper, XMM-Newton observations of AM CVn binaries. A&A 440(2), 675–681 (2005). https://doi.org/10.1051/0004-6361: 20052950, astro-ph/0505549 G. Ramsay, J.L. Sokoloski, G.J.M. Luna, N.E. Nuñez, Swift observations of the 2015 outburst of AG Peg – from slow nova to classical symbiotic outburst. MNRAS 461(4), 3599–3606 (2016). https://doi.org/10.1093/mnras/stw1546, 1606.07397 K. Reinsch, A. van Teeseling, A.R. King, K. Beuermann, A limit-cycle model for the binary supersoft X-ray source RX J0513.9-6951. A&A 354, L37–L40 (2000). astro-ph/0001081 M. Revnivtsev, E. Churazov, K. Postnov, S. Tsygankov, Quenching of the strong aperiodic accretion disk variability at the magnetospheric boundary. A&A 507, 1211–1215 (2009). https:// doi.org/10.1051/0004-6361/200912317, 0909.2996 M. Revnivtsev, S. Potter, A. Kniazev, R. Burenin, D.A.H. Buckley, E. Churazov, Observational evidence for matter propagation in accretion flows. MNRAS 411, 1317–1322 (2011). https:// doi.org/10.1111/j.1365-2966.2010.17765.x, 1009.6165 S.R. Rosen, K.O. Mason, F.A. Cordova, EXOSAT X-ray observations of the eclipsing magnetic cataclysmic variable EX Hya. MNRAS 231, 549–573 (1988). https://doi.org/10.1093/mnras/ 231.3.549 R.E. Rothschild, D.E. Gruber, F.K. Knight, J.L. Matteson, P.L. Nolan, J.H. Swank, S.S. Holt, P.J. Serlemitsos, K.O. Mason, I.R. Tuohy, The X-ray spectrum of AM Herculis from 0.1 to 150 keV. ApJ 250, 723–732 (1981). https://doi.org/10.1086/159420 T.D. Russell, J.C.A. Miller-Jones, G.R. Sivakoff, D. Altamirano, T.J. O’Brien, K.L. Page, M.R. Templeton, E.G. Körding, C. Knigge, M.P. Rupen, R.P. Fender, S. Heinz, D. Maitra, S. Markoff, S. Migliari, R.A. Remillard, D.M. Russell, C.L. Sarazin, E.O. Waagen, The reproducible radio outbursts of SS Cygni. MNRAS 460(4), 3720–3732 (2016). https://doi.org/ 10.1093/mnras/stw1238, 1605.07136 B.E. Schaefer, Comprehensive photometric histories of all known Galactic recurrent novae. ApJS 187(2), 275–373 (2010). https://doi.org/10.1088/0067-0049/187/2/275, 0912.4426 R. Schwarz, J. Greiner, G.H. Tovmassian, S.V. Zharikov, W. Wenzel A new two-pole accretion polar: RX J1846.9+5538. A&A 392, 505–514 (2002). https://doi.org/10.1051/0004-6361: 20021193, astro-ph/0208545 A.D. Schwope, H. Worpel, I. Traulsen, D. Sablowski, The various accretion modes of AM Herculis: Clues from multi-wavelength observations in high accretion states. A&A 642, A134 (2020). https://doi.org/10.1051/0004-6361/202037714, 2008.08402 A.W. Shaw, C.O. Heinke, K. Mukai, G.R. Sivakoff, J.A. Tomsick, V. Rana, Measuring the masses of intermediate polars with NuSTAR: V709 Cas, NY Lup, and V1223 Sgr. MNRAS 476(1), 554–561 (2018). https://doi.org/10.1093/mnras/sty246, 1801.08508 A.W. Shaw, C.O. Heinke, K. Mukai, J.A. Tomsick, V. Doroshenko, V.F. Suleimanov, D.J.K. Buisson, P. Gandhi, B.W. Grefenstette, J. Hare, J. Jiang, R.M. Ludlam, V. Rana, G.R. Sivakoff, Measuring the masses of magnetic white dwarfs: a NuSTAR legacy survey. MNRAS 498(3), 3457–3469 (2020). https://doi.org/10.1093/mnras/staa2592, 2008.09684 J.L. Sokoloski, S.J. Kenyon, B.R. Espey, C.D. Keyes, S.R. McCandliss, A.K.H. Kong, J.P. Aufdenberg, A.V. Filippenko, W. Li, C. Brocksopp, C.R. Kaiser, P.A. Charles, M.P. Rupen, R.P.S. Stone, A “Combination Nova” Outburst in Z Andromedae: Nuclear Shell Burning Triggered by a Disk Instability. ApJ 636(2), 1002–1019 (2006). https://doi.org/10.1086/498206, astro-ph/0509638 J.E. Solheim, AM CVn stars: status and challenges. PASP 122(896), 1133 (2010). https://doi.org/ 10.1086/656680 S. Starrfield, J.W. Truran, W.M. Sparks, J. Krautter, J. MacDonald, Soft X-Ray Emission from Classical Novae in Outburst, vol. 369 (Springer, 1990), p. 306. https://doi.org/10.1007/3-54053500-4_143 E. Steinberg, B.D. Metzger, The multidimensional structure of radiative shocks: suppressed thermal X-rays and relativistic ion acceleration. MNRAS 479(1), 687–702 (2018). https://doi. org/10.1093/mnras/sty1641, 1805.03223

115 X-ray Emission Mechanisms in Accreting White Dwarfs

4273

T.E. Strohmayer, Evidence for orbital decay of RX J1914.4+2456: gravitational radiation and the nature of the X-ray emission. ApJ 581(1), 577–584 (2002). https://doi.org/10.1086/344101, astro-ph/0204128 T.E. Strohmayer, Detection of nitrogen and neon in the X-ray spectrum of GP Comae Berenices with XMM/Newton. ApJL 608(1), L53–L56 (2004). https://doi.org/10.1086/422192, astroph/0404542 T.E. Strohmayer, Precision X-ray timing of RX J0806.3+1527 with Chandra: evidence for gravitational radiation from an ultracompact binary. ApJ 627(2), 920–925 (2005). https://doi. org/10.1086/430439, astro-ph/0504150 T.E. Strohmayer, High-resolution X-ray spectroscopy of RX J0806.3+1527 with Chandra. ApJL 679(2), L109 (2008). https://doi.org/10.1086/589439 V. Suleimanov, M. Revnivtsev, H. Ritter, RXTE broadband X-ray spectra of intermediate polars and white dwarf mass estimates. A&A 435(1), 191–199 (2005). https://doi.org/10.1051/00046361:20041283, astro-ph/0405236 V. Suleimanov, V. Doroshenko, L. Ducci, G.V. Zhukov, K. Werner, GK Persei and EX Hydrae: intermediate polars with small magnetospheres. A&A 591, A35 (2016). https://doi.org/10.1051/ 0004-6361/201628301, 1604.00232 V.F. Suleimanov, V. Doroshenko, K. Werner, Hard X-ray view on intermediate polars in the Gaia era. MNRAS 482(3), 3622–3635 (2019). https://doi.org/10.1093/mnras/sty2952, 1809.05740 S.S. Tsygankov, A.A. Lutovinov, V. Doroshenko, A.A. Mushtukov, V. Suleimanov, J. Poutanen, Propeller effect in two brightest transient X-ray pulsars: 4U 0115+63 and V 0332+53. A&A 593, A16 (2016). https://doi.org/10.1051/0004-6361/201628236, 1602.03177 S.S. Tsygankov, A.A. Mushtukov, V.F. Suleimanov, V. Doroshenko, P.K. Abolmasov, A.A. Lutovinov, J. Poutanen, Stable accretion from a cold disc in highly magnetized neutron stars. A&A 608, A17 (2017). https://doi.org/10.1051/0004-6361/201630248, 1703.04528 A. Ulla, The X-ray properties of AM Canum Venaticorum. A&A 301, 469 (1995). E.P.J. van den Heuvel, D. Bhattacharya, K. Nomoto, S.A. Rappaport, Accreting white dwarf models for CAL 83, CAL 87 and other ultrasoft X-ray sources in the LMC. A&A 262, 97– 105 (1992) A. van Teeseling, A.R. King, Wind-driven evolution of supersoft X-ray binaries with low-mass secondaries. A&A 338, 957–964 (1998) A. van Teeseling, F. Verbunt, ROSAT X-ray observations of ten cataclysmic variables. A&A 292, 519–533 (1994). N.M.H. Vaytet, T.J. O’Brien, K.L. Page, M.F. Bode, M. Lloyd, A.P. Beardmore, Swift observations of the 2006 outburst of the recurrent nova RS Ophiuchi. III. X-Ray Spectral Modeling. ApJ 740(1), 5 (2011). https://doi.org/10.1088/0004-637X/740/1/5, 1106.2824 B. Warner, Multiple optical orbital sidebands in intermediate polars. MNRAS 219, 347–356 (1986). https://doi.org/10.1093/mnras/219.2.347 B. Warner, Cataclysmic Variable Stars. Cambridge University Press, Cambridge, UK (1995), vol. 28 P.J. Wheatley, C.W. Mauche, J.A. Mattei, The X-ray and extreme-ultraviolet flux evolution of SS Cygni throughout outburst. MNRAS 345(1), 49–61 (2003). https://doi.org/10.1046/j.13658711.2003.06936.x, astro-ph/0306471 U. Woelk, K. Beuermann, Stationary radiation hydrodynamics of accreting magnetic white dwarfs. A&A 306, 232 (1996). W.M. Wolf, R.H.D. Townsend, L. Bildsten, Nonradial pulsations in post-outburst novae. ApJ 855(2), 127 (2018). https://doi.org/10.3847/1538-4357/aaad05, 1802.01525 M.A. Wood, Synthetic direct impact light curves of the ultracompact AM CVn binary systems V407 Vul and HM Cnc. MNRAS 395(1), 378–385 (2009). https://doi.org/10.1111/j.1365-2966. 2009.14520.x, 0901.2854 K. Wu, Structure of inhomogeneous accretion shocks. Proc. Astron. Soc. Aust. 11(1), 61–64 (1994) K. Wu, L.L. Kiss, High and low states of the system AM Herculis. A&A 481(2), 433–439 (2008). https://doi.org/y10.1051/0004-6361:20078556, 0802.0019

4274

K. L. Page and A. W. Shaw

K. Wu, G. Chanmugam, G. Shaviv, Structure of steady state accretion shocks with several cooling functions: closed integral-form solution. ApJ 426, 664 (1994). https://doi.org/10.1086/174103 G.A. Wynn, A.R. King, Theoretical X-ray power spectra of intermediate polars. MNRAS 255, 83–91 (1992). https://doi.org/10.1093/mnras/255.1.83 G.A. Wynn, A.R. King, K. Horne, A magnetic propeller in the cataclysmic variable AE Aquarii. MNRAS 286(2), 436–446(1997). https://doi.org/10.1093/mnras/286.2.436 T. Yuasa, K. Nakazawa, K. Makishima, K. Saitou, M. Ishida, K. Ebisawa, H. Mori, S. Yamada, White dwarf masses in intermediate polars observed with the Suzaku satellite. A&A 520, A25 (2010). https://doi.org/10.1051/0004-6361/201014542, 1006.5323

Part XII Galaxies Giuseppina Fabbiano and Marat Gilfanov

Introduction to the Section on Galaxies

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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The Part XII, “Galaxies” of the Handbook of X-ray and Gamma-Ray Astrophysics reviews the impact of high-resolution X-ray observations on the study of galaxies and their evolution. Five chapters of the section discuss the main aspects of these studies: populations of X-ray binaries and hot interstellar medium, X-ray diagnostics of hot halos around isolated massive galaxies and predictions from modern structure formation simulations, studies of circumgalactic medium by using X-ray absorption lines, and high-resolution Chandra studies of the interaction between AGN and the surrounding ISM. The goal of these introductory notes is to place the following discussion into the broader astrophysical context.

G. Fabbiano () Harvard-Smithsonian Center for Astrophysics (CfA), Cambridge, MA, USA e-mail: [email protected] M. Gilfanov Max-Planck-Institute for Astrophysics, Space Research Institute, Garching, Germany Space Research Institute, Moscow, Russia e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_107

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Introduction Galaxies are a fundamental component of the Universe that emit throughout the electromagnetic spectrum. Most of the observational studies of galaxies have been in the optical range and have resulted in the characterization of the properties and evolution of the stellar components that dominate the optical band emission, as well as that of the “warm” ∼104 Kelvin gaseous component. Observations at different wavelengths (radio, millimeter, infrared, and X-ray) give complementary information on both galaxy components and intervening physical processes that are needed to obtain a full picture of galaxies and their evolution: high-energy particles, magnetic fields, cold hydrogen gas, dust, molecular species in dense clouds, the end products of stellar evolution, and hot plasmas. The ⊲ Part XII, “Galaxies” of the Handbook of X-ray and Gamma-Ray Astrophysics reviews the impact of high-resolution X-ray observations on the study of galaxies and their evolution. These studies were first made possible by the Einstein Observatory, the first imaging X-ray telescope (Giacconi et al. 1979), which was instrumental in detecting the X-ray emission of galaxies, characterizing their X-ray spectra, and allowing both statistical and in a few cases detailed comparisons with optical and radio data. The Einstein observations led to the first X-ray Catalog and Atlas of normal galaxies (Fabbiano et al. 1992) and established connections of the X-ray emission with both the populations of low- and high-mass X-ray binaries, the hot interstellar medium produced by stellar winds and supernovae (Helfand 1984) in actively star-forming galaxies, and the extended hot halos present in some massive elliptical galaxies (see the review by Fabbiano (1989)). While the X-ray observatories following Einstein – ROSAT, ASCA, and XMM-Newton – have all contributed to some aspects of these investigations, significant qualitative advances are due to the Chandra X-ray Obsservatory, which provides sub-arcsecond imaging spectroscopy in the ∼0.3–7.0 keV band (see the contribution of Wilkes & Tananbaum in the ⊲ Part IV, “X-ray Missions”, for a discussion of the Chandra X-ray Observatory). Based on the results of Chandra observations, in this section we discuss the present view of the X-ray emission of galaxies, their emission components, and its relevance for a better understanding of galaxy evolution. While normal stars emit in the X-ray band (as revealed by the Einstein Observatory, Vaiana et al. (1981)), a significant fraction of the X-ray emission of galaxies (excluding the active galactic nuclei, discussed in the ⊲ Part XIII, “Active Galactic Nuclei in X- and Gamma-Rays” of this handbook) originates from accretion powered X-ray binaries (XRBs), where the atmosphere of a normal star is accreted by the stronger gravitational pull of a compact “dead” companion (white dwarf, neutron star, or black hole). The second significant component is due to hot (∼10 million degree) plasmas, connected either to supernova remnants or to the interstellar medium and gaseous halos, energized by stellar winds, supernovae explosions, and nuclear supermassive black holes. The Chandra X-ray Observatory, thanks to its sub-arcsecond angular resolution, unprecedented for X-ray astronomy, made it possible to resolve compact X-ray sources and to separate their contribution from

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the emission of the hot gaseous component. This permitted to study point source and diffuse components in an unbiased and uncontaminated manner, leading to major breakthroughs in our understanding of both. It became possible to obtain luminosity distributions of compact sources in many dozens of galaxies. A remarkable fact was revealed that their luminosity distributions in young and old galaxies obey respective universal luminosity functions (Grimm et al. 2003; Gilfanov 2004), further proving the association of compact X-ray sources in external galaxies with high- and low-mass X-ray binaries. On the other hand, X-ray observations permitted to set important constraints on the energy input (feedback) from stellar and active nuclear sources during galaxy evolution, and also on the dark matter halos associated with galaxies. Important insights into the XRB populations of galaxies, their gas content, role of the age, and metallicity are obtained from X-ray scaling relation for galaxies. These studies will soon receive significant new thrust, thanks to the ongoing X-ray all-sky survey by SRG X-ray observatory (Sunyaev et al. 2021) which will detect of the order of ∼104 nearby normal galaxies (in addition to over ∼3 million of AGN and over a ∼half a million of stars in the Milky Way). This number is about ∼100 times larger than detected in any of X-ray surveys to date and will permit to fully sample the parameter space of nearby normal galaxies and to increase the completeness and statistical accuracy of such studies. This section consists of the introduction and of five chapters that discuss the different aspects of the ongoing investigations on the properties and evolution of galaxies and their components, by means of X-ray observations. ⊲ Chapters 117, “X-ray Binaries in External Galaxies” and ⊲ 118, “The Hot Interstellar Medium” discuss the two main components of the X-ray emission of normal galaxies (e.g., galaxies lacking a luminous nuclear source): populations of accreting X-ray binaries (XRBs) and the hot interstellar medium (ISM). ⊲ Chapters 119, “X-ray Halos Around Massive Galaxies: Data and Theory” and ⊲ 121, “Probing the Circumgalactic Medium with X-ray Absorption Lines” discuss X-ray diagnostics of hot halos trapped in the gravitational potential of isolated massive galaxies, which can give us insights on the properties of their dark matter halos and constrain scenarios of galaxy evolution. ⊲ Chapter 120, “The Interaction of the Active Nucleus with the Host Galaxy Interstellar Medium” discusses high-resolution studies with Chandra of the interaction between the AGN and the surrounding ISM. These chapters are described individually below. ⊲ Chapter 117, “X-ray Binaries in External Galaxies” by Gilfanov et al. discusses the properties of the populations of X-ray binaries – compact accreting objects in binary systems that are responsible for a large amount of the X-ray emission of normal galaxies. These luminous X-ray sources were first discovered in the Milky Way but can now been studied in a number of galaxies of different morphology and stellar populations. The number of XRBs scales with both the star-formation rate and stellar mass of the host galaxy. Their luminosity distributions in young and old galaxies obey respective universal luminosity functions. In older stellar population galaxies, two separate XRB formation channels appear to coexist: the

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evolution of native field binary stars and the dynamical formation in globular cluster. The integrated output of luminous short-lived massive XRBs in young stellar populations at high redshift can be used to infer the star formation rates of these young galaxies. In the early Universe, X-ray binaries might have played an important role in preheating the intergalactic medium. ⊲ Chapter 118, “The Hot Interstellar Medium” (ISM) by Nardini, Kim, and Pellegrini introduces the hot gaseous component that reaches the temperature of several million degrees. The physical and chemical properties of this hot ISM can be investigated through imaging and spectroscopy in the X-rays. This hot ISM is found in both star-forming galaxies and early-type galaxies with old stellar populations, such as elliptical galaxies. This chapter reviews the current knowledge on the origin and retention of the hot ISM, from a combined theoretical and observational standpoint. As a complex interplay between gravitational processes, environmental effects, and feedback mechanisms contributes to its physical conditions, the hot ISM represents a key diagnostic of the evolution of galaxies. In elliptical galaxies, it provides a way to constrain the total mass of the galaxy, which is dominated by their dark halos. ⊲ Chapter 119, “X-ray Halos Around Massive Galaxies: Data and Theory” by Bogdan and Vogelsberger discusses measurements of hot halos surrounding very massive spiral galaxies from direct X-ray imaging and spectroscopy of the diffuse emission and compares these results with theory predictions. The presence of gaseous X-ray halos around massive galaxies is a basic prediction of all past and modern structure formation simulations. These models and simulations show that X-ray halos retain the signatures of the physical processes that shape the evolution of galaxies from the highest redshift to the present day. X-ray observations therefore provide a unique way to constrain these theoretical scenarios. This chapter reviews the current observational and theoretical understanding of hot gaseous X-ray halos around nearby massive galaxies and describes the prospects of observing X-ray halos with future instruments. ⊲ Chapter 121, “Probing the Circumgalactic Medium with X-ray Absorption Lines” by Mathur discusses a different method to study the circumgalactic medium (CGM) by using absorption lines in the high-resolution X-ray spectra of distant bright X-ray sources (e.g., quasars). The circumgalactic medium (CGM) fills the dark matter halo of a galaxy, serving as a gas reservoir between the intergalactic medium and the stellar disk. The properties of the CGM are governed by galaxy properties, and the CGM in turn may regulate the galaxy evolution. This chapter provides both the theoretical background and discusses the technical advances enabling the absorption line spectroscopy of the CGM, with particular emphasis on the study of the CGM of the Milky Way. The MW CGM is diffuse, extended, and massive and might account for the missing galactic baryons. Understanding the multiphase CGM is going to be a major area of research in the coming decade. Several outstanding questions are critical for understanding the CGM: the physical and hydrodynamic properties; the sources of heating/cooling and nonthermal motions; the chemical enrichment; the anisotropy and mixing in the CGM; and the relation between the CGM properties and the galaxy properties. The

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chapter ends with a discussion of future directions in observational studies of the CGM and comparisons with theoretical simulations. ⊲ Chapter 120, “The Interaction of the Active Nucleus with the Host Galaxy Interstellar Medium” by Fabbiano and Elvis discusses high-resolution studies with Chandra of the interaction between the AGN and the surrounding ISM. While motivated by the desire to explore observationally the region where AGN feedback may occur, these results have implications for both the AGN model and our understanding of AGN feedback. The X-ray emission is complex, requiring both photoionized and shock-ionized gas. It originates from high ionization regions (bicones) and is surrounded by cocoons of low ionization narrow line emission regions (LINERS). Bicone 3–6 keV continuum and 6.4 keV Fe Kα emission has been detected, contrary to the standard AGN model expectation that would confine this hard emission to the pc-size nuclear absorbing torus. Extended emission in the cross-cone direction also requires modifications to the AGN standard model. A porous torus, with a significant fraction of escaping AGN continuum, and jet interaction with ISM creating a “blow-back” toward the nuclear region seem to be required. The finding of hot and highly photoionized gas on 10s parsecs to several kiloparsec scales demonstrates that all three feedback mechanisms are at work: radiation affects the inner molecular clouds of the host on a 1 kpc scale; shocks of relativistic jets with the host ISM a few kpc from the central AGN; and photoionization of the ISM via winds on scales from pc to multiple kpc. These results demonstrate that X-rays are needed to develop a complete picture of AGN/host interaction along with radio continuum, mm and sub-mm molecular line emission, and optical/near-IR emission lines.

References G. Fabbiano, ARA&A 27, 87 (1989) G. Fabbiano, D.-W. Kim, G. Trinchieri, ApJS 80, 531 (1992) R. Giacconi et al., ApJ 230, 540 (1979) M. Gilfanov, MNRAS 349, 146 (2004) H.-J. Grimm, M. Gilfanov, R. Sunyaev, MNRAS 339, 793 (2003) D.J. Helfand, PASP 96, 913 (1984) R. Sunyaev et al., A&A 656, 29 (2021) G.S. Vaiana et al., ApJ 245, 163 (1981)

X-ray Binaries in External Galaxies

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Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . High- and Low-Mass X-Ray Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Scaling Relations and Luminosity Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Disentangling HMXB and LMXB Populations in External Galaxies . . . . . . . . . . . . . . . . X-Ray Scaling Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Luminosity Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . X-Ray Emission as a SFR Proxy for Normal Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . Expectations from SRG/eROSITA All-Sky Survey . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spatial Distribution of X-Ray Binaries in Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Primordial and Dynamically Formed LMXBs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . LMXB Formation Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clues from Luminosity Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Clues from the Spatial Distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ultraluminous X-Ray Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Association with Star Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Main Conclusions from Optical Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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M. Gilfanov () Max-Planck-Institute for Astrophysics, Space Research Institute, Garching, Germany Space Research Institute, Moscow, Russia e-mail: [email protected] G. Fabbiano Harvard-Smithsonian Center for Astrophysics (CfA), Cambridge, MA, USA e-mail: [email protected] B. Lehmer University of Arkansas, Fayetteville, AR, USA e-mail: [email protected] A. Zezas University of Crete, Crete, Greece e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_108

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Inferences from the Shape of the HMXB Luminosity Function . . . . . . . . . . . . . . . . . . . . . Possible Nature and Implications for Accretion Physics . . . . . . . . . . . . . . . . . . . . . . . . . . Population Synthesis Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relevant Results from Binary Evolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Summary of Population Synthesis Models and Their Results . . . . . . . . . . . . . . . . . . . . . . How Frequent Are X-Ray Binaries? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Connection to LIGO-Virgo Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cosmic Evolution of X-Ray Binaries and Their Contribution to CXB . . . . . . . . . . . . . . . . . Contribution of X-Ray Binaries to Cosmic X-Ray Background . . . . . . . . . . . . . . . . . . . . X-Ray Investigations of Cosmologically Distant Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . Drivers of the Redshift Evolution of X-Ray Binary Populations . . . . . . . . . . . . . . . . . . . . Recent Constraints on X-Ray Evolution of Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Contribution to (Pre)Heating of IGM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

X-ray appearance of normal galaxies is mainly determined by X-ray binaries powered by accretion onto a neutron star or a stellar mass black hole. Their populations scale with the star-formation rate and stellar mass of the host galaxy, and their X-ray luminosity distributions show a significant split between starforming and passive galaxies, both facts being consequences of the dichotomy between high- and low-mass X-ray binaries. Metallicity, IMF and stellar age dependencies, and dynamical formation channels add complexity to this picture. The numbers of high-mass X-ray binaries observed in star-forming galaxies indicate quite high probability for a massive star to become an accretionpowered X-ray source once upon its lifetime. This explains the unexpectedly high contribution of X-ray binaries to the cosmic X-ray background, of the order of ∼10%, mostly via X-ray emission of faint star-forming galaxies located at moderate redshifts which may account for the unresolved part of the CXB. Cosmological evolution of the LX − SFR relation can make high-mass X-ray binaries a potentially significant factor in (pre)heating of intergalactic medium in the early Universe. Keywords

X-ray binaries · Black holes · Neutron stars · Ultraluminous X-ray sources · X-ray populations · Metallicity dependence · X-ray scaling relations · Accretion · Preheating of IGM

Introduction X-ray binaries (XRBs) are binary stellar systems composed of a relativistic compact object – a neutron star (NS) or a black hole (BH) – and a stellar companion.

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They are powered by accretion of matter from the donor star onto the compact object (Shakura and Sunyaev 1973) and are the most common luminous compact X-ray sources in the Milky Way (see Lewin et al. (1995), Lewin and van der Klis (2006), and Gilfanov (2010) for a review). While some luminous XRBs were detected in the early days of X-ray astronomy in Local Group galaxies, it was only after the deployment of the first imaging X-ray telescope, the Einstein Observatory in 1978, that their presence as ubiquitous populations of X-ray sources in galaxies could be established (see Fabbiano (1989) for a review). A number of individual XRBs were resolved with Einstein in the more nearby galaxies (e.g., van Speybroeck et al. 1979; Long and van Speybroeck 1983a), leading to the first attempts at characterizing these populations with luminosity functions (see Fabbiano (1988) for a M81-M31 comparison). These individual detections included a new class of very luminous X-ray sources emitting in excess of the Eddington luminosity limit of a ∼10 solar mass accreting object (Long and van Speybroeck 1983b), now known as ultraluminous X-ray sources (ULXs). X-ray emission was detected from over 230 galaxies of all morphological types covered by the Einstein field of view, resulting in the publication of the Einstein Catalog and Atlas of Galaxies (Fabbiano et al. 1992). Studies of the Local Group galaxies led to the realization that different XRB populations reside in galaxies (e.g., Long and van Speybroeck 1983a; Helfand 1984), akin to those in the Milky Way (cf Grimm et al. 2002). For more distant galaxies, Einstein and, a decade later, ROSAT Observatory could not yet resolve compact X-ray populations to the sufficient depth and detail; however, meaningful correlations were found between integrated X-ray emission and various multiwavelength tracers such as optical, near- and far-infrared, and radio emission (David et al. 1992; Fabbiano and Shapley 2002; Kim et al. 1992). These discoveries led to formulation of many elements of the overall picture of X-ray binary populations in galaxies. It was realized, in particular, that young XRB population, identified with high-mass X-ray binaries (HMXBs), is prevalent in the arms of spiral galaxies and in late-type systems with young stellar population and more intense star-formation rate. An older population of low-mass X-ray binaries (LMXBs) is instead found in the older galaxy disks and in the bulges. Following the demise of the Einstein Observatory, the study of galaxies was continued with other X-ray telescopes (ROSAT, ASCA, XMM-Newton). However, the real new breakthroughs in the study of the XRB populations have only occurred thanks to the deployment of the Chandra X-ray Observatory (Weisskopf et al. 2000). With its Sub – arc second angular resolution, Chandra has revolutionized this field, leading to the widespread detection of rich populations of XRBs in galaxies well outside the Local Group (see reviews Fabbiano 2006, 2019; Gilfanov 2004b). In this chapter we give an overview of the contemporary understanding of populations of XRBs in external galaxies and of their properties. The following discussion is mostly based on the results of Chandra observations. For the comprehensive review of earlier findings, we refer the reader to Fabbiano (1989).

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High- and Low-Mass X-Ray Binaries Depending on the mass of the optical companion, X-ray binaries are broadly divided into two classes – high- and low- mass X-ray binaries (HMXBs and LMXBs), separated by a thinly populated region between ∼1 M⊙ and ∼5 M⊙ , where bright persistent X-ray sources are scarce, for the reasons discussed in section “Population Synthesis Results”. The difference in the mass of the donor star determines the difference in the formation timescales of these two classes of X-ray binaries, which are governed by a combination of the nuclear timescale of the donor stars and the time required for the onset of mass transfer from the donor star to the compact object. In the case of an HMXB, this timescale is determined by the nuclear evolution of the massive donor star. Correspondingly, they are X-ray bright within ∼100 Myrs after formation of the binary system (e.g., Verbunt and van den Heuvel 1995). This is comparable to the characteristic timescale of the star-formation episode; therefore one may expect that the number of such systems in a galaxy is proportional to its star-formation rate (SFR) (Sunyaev et al. 1978; Grimm et al. 2003; Mineo et al. 2012a): NHMXB , LX,HMXB ∝ SFR

(1)

Evolution of primordial LMXBs is determined by the rate of loss of the orbital angular momentum of the binary system or by the nuclear evolution of the lowmass star, both of which, on the contrary to prompt HMXBs, are typically in the ∼1 − 10 Gyrs range (Verbunt and van den Heuvel 1995). Correspondingly, one may expect that their population integrates the long-term star-formation history of the host galaxy and scales with the total mass of its stars (Gilfanov 2004a): NLMXB , LX,LMXB ∝ M∗

(2)

LMXBs can be also formed dynamically in globular clusters and galactic nuclei which complicates this simple picture; this is discussed in section “Primordial and Dynamically Formed LMXBs”.

X-Ray Scaling Relations and Luminosity Functions Disentangling HMXB and LMXB Populations in External Galaxies High- and low-mass X-ray binaries scale, respectively, with the SFR and stellar mass of their parent stellar populations (Section “High- and Low-Mass X-Ray Binaries”). They also share different evolutionary paths (e.g., Tauris and van den Heuvel 2023). For these reasons it is often useful to discriminate between the two classes in observations.

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With the exception of a few nearby galaxies (e.g., Magellanic Clouds; e.g., Antoniou et al. 2010; Haberl et al. 2012; Shtykovskiy and Gilfanov 2005a, b) or a few detailed HST-based studies (e.g., Garofali et al. 2018), it is extremely difficult to determine the nature of the donor star in galaxies located beyond ∼1 Mpc, which would allow us to directly discriminate between high- and low-mass X-ray binaries. However, given that HMXBs are fueled by short-lived early-type OB stars, they become extinct after a few hundred million years after their formation. Therefore, old stellar environments are populated by LMXBs. Similarly, young stellar environments are dominated by HMXBs, (a) because of the much higher formation efficiency of HMXBs (e.g., Antoniou et al. 2019; Mineo et al. 2012a) (Section “How Frequent Are X-Ray Binaries?”) and (b) because LMXBs did not have the time to form in environments much younger than ∼Gyr. Therefore, we can use estimates of relative fractions of old and young stellar populations in a galaxy to disentangle populations of HMXBs and LMXBs. A commonly used proxy for assessing the dominant XRB population is the specific SFR (sSFR) defined as the ratio of the SFR over the stellar mass at the same region of a galaxy. Generally, regions with sSFR higher than ∼10−10 yr−1 are dominated by HMXBs (Grimm et al. 2003; Mineo et al. 2012a; Lehmer et al. 2010), whereas sSFR≤ 10−11 yr−1 would suggest an LMXB-dominated environment, although these thresholds can vary depending on the recent star-formation history of the galaxy.

X-Ray Scaling Relations Chandra X-ray observatory presented an opportunity to observe compact sources in galaxies located at distances up to ∼30–50 Mpc (and more for the brightest sources) in a nearly confusion-free regime, to measure their luminosity functions and total luminosities of different (sub)populations. Observations of a large number (∼ hundred) of nearby galaxies have demonstrated that populations of LMXBs and HMXBs in a galaxy scale proportionally to its stellar mass and SFR, respectively (Fig. 1): LX,HMXB ≈ 2.6 · 1039 × SFR LX,LMXB ≈ 1039 ×

M∗ 1010 M⊙

NHMXB ≈ 10 × SFR NLMXB ≈ 14 ×

M∗ 1010 M⊙

(3) (4)

where LX is the total X-ray luminosity of X-ray binaries of the given type in the 0.5– 8 keV energy band, NX is the number of X-ray binaries with luminosity exceeding LX ≥ 1037 erg/s, SFR is the star-formation rate in M⊙ /yr, and M∗ is the stellar mass of the galaxy in solar units (Grimm et al. 2003; Mineo et al. 2012a; Gilfanov 2004a). Broadly consistent results were obtained in several other independent studies (e.g., Ranalli et al. 2003; Colbert et al. 2004; Kim and Fabbiano 2004; Lehmer et al. 2010; Sazonov and Khabibullin 2017). However, there is a caveat to keep in mind when comparing different scaling relations. The coefficients in Eq. (3), (4) depend first

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Fig. 1 Dependence of the total X-ray luminosity of X-ray binaries on the SFR (left panel) and stellar mass (right panel) of the host galaxy. Left panel shows star-forming galaxies, young stellar population of which is dominated by massive X-ray binaries; their population is roughly proportional to the SFR of the host galaxy. Right panel shows data for elliptical galaxies where star formation mostly stopped at least several Gyrs ago and only low-mass X-ray binaries are left. Their population is determined by the total stellar mass of the host galaxy. Solid lines show approximation of the data by the linear laws. In the left panel, we also show the data for ultraluminous infrared galaxies (ULIRGs, triangles) and star-forming galaxies from the Chandra Deep Fields. These galaxies are not resolved by Chandra; therefore the total luminosity is shown, including contribution of faint unresolved compact sources and diffuse emission. (Adapted from Gilfanov 2004a; Mineo et al. 2012a; Zhang et al. 2012)

of all on the methods used for estimating the stellar mass and SFR, their proxies, and assumed shape of the initial mass function (IMF). This is illustrated by Fig. 2 and explained later in this section. Secondly, they depend on the particular samples of galaxies, their age and star-formation history composition, metallicity, globular cluster content, etc. Various aspects of these dependencies are discussed in the following sections of this chapter. The LX − SFR relation is subject to a curious statistical effect, making it to appear steeper than linear and to have large dispersion at low SFR (Grimm et al. 2003; Gilfanov et al. 2004a, b). This behavior is caused by the poor sampling of the bright luminosity end of the X-ray luminosity function (XLF) at low SFR, and its magnitude depends on the XLF shape, in particular its slope and position of the high luminosity cutoff (Gilfanov et al. 2004a). It is much more pronounced for HMXBs because of their relatively flat XLF and is insignificant for LMXBs which XLF is steep at the high luminosity end (Section “X-Ray Luminosity Functions”). Note that this effect is not seen in Fig. 1 because of the observer bias (Mineo et al. 2012a). In order to account for the HMXB and the LMXB components simultaneously, Lehmer and collaborators (Lehmer et al. 2010) introduced a scaling relation of the form LX = βSFR + αM∗

(5)

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Fig. 2 Left: Dependence of the total X-ray luminosity per unit SFR on the sSFR of the host galaxy. The red dashed line indicates the contribution from LMXBs, while the blue dashed line indicates the contribution from HMXBs. Galaxies with sSFR greater than (∼10−10.5 M⊙ yr−1 M−1 ⊙ ) are dominated by HMXBs, while at lower values of sSFR, the contribution of LMBXs becomes increasingly more important. The gray shaded region and the dotted lines delineate the 1σ scatter resulting from uncertainties in the XLF of the resolved X-ray binaries for galaxies with median mass of 2 × 1010 and 3 × 109 . Right: Comparison of scaling parameters αLMXB and βHMXB from Eq. (6) derived in Lehmer et al. (2019) (MCMC contours) with those from Eqs. (3) and (4) (Gilfanov 2004a; Mineo et al. 2012a; Zhang et al. 2012) (blue cross with corresponding 1σ errors) after differences in assumed IMF and SFR and M∗ proxies are taken into account. The green cross shows the Chandra Deep Field-South independent estimates from Lehmer et al. (2016). See Lehmer et al. (2019) for more details. (Adapted from Lehmer et al. 2019)

An equivalent form in terms of specific SFR is also often used: LX /SFR = β + α × sSFR−1

(6)

−1 Lehmer et al. (2019) derived values of the scaling parameters: log α[erg s−1 M⊙ ]= +0.07 +0.14 29.25−0.06 and log β [erg s−1 (M⊙ yr−1 )−1 ] = 39.71−0.09 . Their best fit to the data is shown in Fig. 2. This parameterization allows one to combine the contribution of the LMXB and HMXB components in a single formulation, and it is particularly useful for galaxies with low sSFR such as early-type spiral galaxies that have a significant LMXB component. The parameters α and β in Eq. (6) characterizing X-ray scaling relations for LMXBs and HMXBs are in an apparent disagreement with those in Eqs. (3) and (4). The disagreement is not real, as discussed earlier in this section; it is caused by the differences in the assumed IMF and proxies used for the SFR and stellar mass estimations in the different analyses. When they are taken into account (Lehmer et al. 2019), the scaling relations from Gilfanov (2004a), Mineo et al. (2012a), Zhang et al. (2012), and Lehmer et al. (2019) are fully consistent with each other as it is illustrated in the right panel in Fig. 2.

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Time Dependence of HMXB Population Scaling relations in Figs. 1 and 2 are drawn for quantities integrated over entire galaxies. As such, they represent a result of averaging over a (typically large) number of star-forming regions. The details regarding ages, metallicities, and starformation histories of the individual star-forming regions are smeared out, and such scaling relations characterize populations of X-ray binaries globally, on the galactic scales. Spatially resolved analysis of individual galaxies, on the other hand, can reveal a more detailed picture of evolution of the population of HMXBs with time after their formation. A particularly promising way is to compare the spatial distribution of HXMBs in a galaxy with its spatially resolved star-formation history or the stellar population age. At present, this can be done only for the handful of the most nearby galaxies, and the results are limited by the statistical quality of the available data, in particular by the number of HMXBs and fairly poor sampling of their parameter (type, luminosity, etc.) space. In the case of the Magellanic Clouds, comparison of the X-ray binary populations with the star-formation history (SFH) of their parent stellar populations permitted the authors to reconstruct the HMXB formation efficiency ηHMXB (τ ) (see definition in Shtykovskiy and Gilfanov 2007) and the age distribution of HMXBs as shown in Fig. 3. It was shown that there is a peak at their formation efficiency at ∼30–60 Myr, consistent with increased formation of Be stars at the same timescales (Shtykovskiy and Gilfanov 2007; Antoniou et al. 2010, 2019; Antoniou and Zezas 2016). As it should have been expected, the peak in the population of HMXBs is delayed with respect to the peak in the formation rate of compact objects (left and middle panels in Fig. 3). The magnitude of the delay is determined by the time required to form the compact object (mostly neutron stars in the case of HMXBs in Magellanic Clouds) and for the nuclear evolution of the secondary star. These results give a formation rate of ∼1 X-ray binary per 200 observed stars of OB spectral types at ages of ∼30– 60 Myr, or equivalently ∼9 XRBs per 106 M⊙ of stars formed at a star-formation episode, which agrees very well with the theoretical models, as one can see in the left panel in Fig. 3 (see also Fig. 4). Magellanic Clouds have fairly low star-formation rates and their X-ray populations are dominated by low-luminosity sources (e.g., Gilfanov et al. 2004b). The ηHMXB (τ ) shown in Fig. 3 describes X/Be systems which these galaxies are populated with; hence it peaks at ∼several tens of Myrs. Similar analysis for high-SFR galaxies (e.g., Antennae or Cartwheel) would reveal a complex picture of the formation efficiencies and timescales depending on X-ray luminosity. In particular one might expect to see that ηULX (τ ) for ultraluminous X-ray sources peaks at much earlier times. However, such analysis would require to resolve stellar populations and to derive spatially resolved star-formation histories at distances of ∼10 − 100 Mpc. Metallicity and Age Effects X-ray binary population synthesis models (e.g., Fragos et al. 2013; Linden et al. 2010) showed that the number of X-ray binaries, the shape of their luminosity

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Fig. 3 Top-left panel: Dependence of the HMXB number on the time elapsed since the starformation event. The solid and dashed crosses were obtained using different reconstructions of spatially resolved star-formation histories (see Shtykovskiy and Gilfanov (2007) for details). The solid curve shows the type II supernova rate. The two vertical dashed lines mark formation times of the first black hole and the last neutron star calculated in the standard theory of evolution of a single star. The dashed curve represents the theoretical dependence of the number of Be/X systems with neutron stars from Popov et al. (1998). Top-right panel: The age distribution of HMXBs in the SMC. The solid histogram shows the distribution expected if HMXB numbers followed the core collapse supernova rate. The top panels adapted from Shtykovskiy and Gilfanov (2007). Bottom panel: The age distribution of HMXBs in the LMC. (Adapted from Antoniou and Zezas 2016)

function, and their integrated X-ray luminosity evolve strongly as a function of age and metallicity (Fig. 4). The general trend is that as a stellar population ages, the integrated X-ray luminosity of its X-ray binaries declines. In the case of metallicity, lower-metallicity stellar populations are associated with higher integrated X-ray luminosities.

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Fig. 4 The evolution of the X-ray luminosity of an initial stellar population of 106 M⊙ as a function of age. The bottom panel shows the ratio of the same model for subsolar (0.1Z⊙ ) and supersolar (1.5Z⊙ ) metallicity with respect to the solar metallicity model. (Adapted from Fragos et al. 2013)

These predictions have been confirmed from studies of the X-ray luminosity or the number of X-ray binaries as a function of the age of the stellar populations (e.g., Lehmer et al. 2019). Similarly, studies of the effect of metallicity showed strong anticorrelation of the integrated X-ray luminosity of galaxies and their metallicity (see discussion in section “Recent Constraints on X-Ray Evolution of Galaxies” and Fig. 13) (e.g., Brorby et al. 2016; Prestwich et al. 2013; Mapelli et al. 2009; Lehmer et al. 2016). Such behavior is attributed to the weaker stellar winds of lowmetallicity stars, resulting in tighter orbits at the start of the X-ray-emitting phase, and hence higher probability of systems undergoing Roche-lobe overflow (e.g., Linden et al. 2010). Metallicity dependence is further discussed in section “Cosmic Evolution of X-Ray Binaries and Their Contribution to CXB” in the context of cosmic evolution of X-ray binary populations in galaxies.

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Sub-galactic Scales Sub-galactic scales open a window into the complex picture of evolving X-ray populations (Section “Time Dependence of HMXB Population”) but require adequate angular resolution and sensitivity to properly resolve optical and X-ray populations. At present, beyond the Local Group, one can only study behavior on ∼few kpc scales of integrated (unresolved) X-ray luminosity and various SFR and mass proxies. Recent studies of the X-ray luminosity, stellar mass, and SFR scaling relations in sub-galactic scales as small as 1 kpc2 showed that unresolved X-ray luminosity follows the same qualitative trends as the galaxy-wide scaling relations Kouroumpatzakis et al. (2020). For larger sub-galactic regions of the ∼3 − 4 kpc size and SFR in excess of ∼10−2 M⊙ yr−1 , correlations of LX − SFR converge to the integrated galactic emission relations. In regions of smaller size and/or with extremely low SFR (Lx)/1010 MO.

10

scales and built a global XLF model accounting for both types of X-ray binaries and parameterized via SFR and stellar mass of the host galaxy. They found clear transition in XLF shape and normalization per SFR from the almost “pure” HMXB XLF at sSFR  5·10−10 yr−1 to the nearly pure LMXB XLF at sSFR  10−12 yr−1 . The large number of sources (over ∼4400) in their sample permitted them to accurately describe more subtle XLF features. Also, they found statistically significant evidence that the HMXB XLF in low-metallicity (≈0.5 Z⊙ ) galaxies contains an excess of high luminosity LX  1039 erg/s sources compared to the global average HMXB XLF, which has a median metallicity ≈Z⊙ (left panel in Fig. 6). This result is in line with findings that the integrated X-ray luminosity per SFR is anticorrelated with metallicity (e.g., Basu-Zych et al. 2013; Brorby et al. 2016) and with prediction of the population synthesis modeling (Section “Population Synthesis Results”). Thanks to their long evolution timescale, in the Gyrs range, time dependence of LMXB populations can be probed with the currently available data. Some dependence on the stellar age is natural to be expected; it is predicted in population synthesis modeling (Section “Population Synthesis Results”) and detected in observations (Zhang et al. 2012; Lehmer et al. 2019). There is clear evolution of the LMXB XLF with age – younger galaxies have more bright sources and fewer faint

10

100 36 Lx (10 erg/s)

1000

10 4

Fig. 6 Left: SFR-normalized incompleteness-corrected total XLF for five low-metallicity starforming galaxies (NGC 337, 925, 3198, 4536, and 4559), which have metallicities of ≈0.5 Z⊙ . The black curve shows the global model (Lehmer et al. 2019) prediction for this population, including HMXB, LMXB, and CXB contributions. Enhancements in the L  1039 source population are clearly observed. The bottom panel shows the ratio of data and population synthesis models with respect to the best-fit global model prediction. (Adapted from Lehmer et al. 2019). Right: XLFs of LMXBs in young and old galaxies in cumulative (upper panel) and differential (lower panel) forms. See Zhang et al. (2012) for description of the sample and further details. The data for old galaxies (red) is marked by circles in the lower panel and is surrounded by the shaded area showing the 1σ Poissonian uncertainty in the upper panel. Statistical uncertainty for young galaxies has comparable amplitude. (Adapted from Zhang et al. 2012)

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ones per unit stellar mass (right panel in Fig. 6). The XLF of LMXBs in younger galaxies appears to extend significantly beyond ∼1039 erg/s. Such bright sources seem to be less frequent in older galaxies. A natural question is to what degree the variability of the X-ray binary populations affects the shape of the X-ray luminosity function of a given galaxy. Systematic monitoring campaigns on a couple galaxies (the Antennae, M81) showed that while individual sources show significant variability, the shape of their X-ray luminosity functions is remarkably stable (Zezas et al. 2007). This indicates that a single snapshot of a galaxy can give us a representative picture of its X-ray binary populations.

X-Ray Emission as a SFR Proxy for Normal Galaxies The promptness of HMXBs (Section “Time Dependence of HMXB Population”) makes them a potentially good tracer of the recent star-formation activity in a galaxy (Sunyaev et al. 1978; Ghosh and White 2001). Indeed, existence of correlation of X-ray luminosity of star-forming galaxies with the classical SFR proxy, FIR emission, has been noticed over three decades ago in the Einstein Observatory data (Section “Introduction”, Griffiths and Padovani 1990; David et al. 1992). While there are other sources of X-ray emission in star-forming galaxies, such as ionized gas (e.g., Mineo et al. 2012b), in normal galaxies HMXBs dominate, and total X-ray emission correlates well with the SFR (Fig. 7). A multitude of various calibration methods are employed to estimate SFR in external galaxies, based on UV, Hα , FIR, or other wavelengths. Any SFR calibrator relies on certain assumptions concerning the environment in the galaxy which lead to various uncertainties, e.g., associated with the influence of dust, the escape fraction of photons, the shape of the IMF, etc. In fact, many of the commonly

Fig. 7 The relation between SFR and total X-ray luminosity of normal galaxies. The solid line shows the linear scaling relation LX = 4 · 1039 × SFR. (Adapted from Mineo et al. 2014a)

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used SFR indicators use the signatures of interaction of the ionizing emission from massive stars with the interstellar medium, i.e., may suffer from the same systematic effects. A new independent calibrator is therefore a useful addition to the suite of SFR diagnostics employed by modern astronomy. A significant advantage of X-ray emission as a diagnostic tool is its large penetrating power – X-rays are much less subject to attenuation by the neutral gas and dust than conventional SFR tracers. Galaxies are mostly transparent to X-rays above ∼2 keV, except for the densest parts of the most massive molecular clouds. The power law spectra of X-ray binaries are also less susceptible to the effect of the cosmological redshift (K-correction). The X-ray-based SFR proxy, quite naturally, suffers from its own uncertainties and systematic effects. The most important of these is contamination by the activity of supermassive black hole; others are related, for example, to the age and metallicity dependence of the X-ray binary populations. Stochastic effects and variability of the X-ray binaries make it less suitable for dwarf galaxies that are dominated by one or two HMXBs. Nonetheless, the X-ray emission of galaxies is a useful and promising proxy of the stellar populations and successfully complements other conventional indicators, particularly in heavily obscured environments. There are a number of its successful applications to reconstruction of the cosmic starformation history (e.g., Aird et al. 2017; Kurczynski et al. 2012; Norman et al. 2004).

Expectations from SRG/eROSITA All-Sky Survey eROSITA X-ray telescope (Predehl et al. 2021) aboard SRG orbital observatory (Sunyaev et al. 2021) in the course of its ongoing all-sky survey will detect of the order of ∼104 normal galaxies out to the distance of a few hundred Mpc (Prokopenko and Gilfanov 2009; Basu-Zych et al. 2020). Although the moderate angular resolution of eROSITA (∼30′′ HPD averaged over the field of view) will not allow for detailed investigations of X-ray populations beyond Local Group, the might of the all-sky coverage will make eROSITA data indispensable for detailed investigations of scaling relations and of the patterns of metallicity and age dependence. The main hurdle on this path will be identifying normal galaxies among over three million AGN and QSO dominating the eROSITA source catalog (Kolodzig et al. 2013) and isolating the contribution of active nuclei of low luminosity. Significant source of contamination is also X-ray active stars. To this end, multiwavelength data will play a critical role. Galiullin et al. (2023) constructed the first SRG/eROSITA – IRAS catalog of X-ray-bright star-forming galaxies on the eastern galactic sky which currently (after 2 years of sky survey) includes of the order of ∼103 star-forming galaxies. With this sample they studied dependence on the SFR and metallicity of the X-ray luminosity of star-forming galaxies, separating it into contributions of X-ray binaries and hot interstellar medium (ISM) and connecting their finding with the Chandra results described earlier in this section.

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Spatial Distribution of X-Ray Binaries in Galaxies It was realized since the first X-ray observations of nearby normal galaxies with the Einstein Observatory that the dominant emission above 2 keV – dominated by XRBs – follows that of the stellar surface brightness (see Fabbiano 1989, and references therein). With its sub – arc second angular resolution, Chandra has given us a unique opportunity to explore this connection, for both HMXB and LMXB populations. With Chandra observations XRBs can be individually detected and associate with different galaxy components in the optical band (see Fabbiano 2006, and references therein). For the HMXB population, two results are particularly notable: (1) the definitive association of ULXs with star-forming regions (e.g., in the Antennae (Fabbiano et al. 2001), the Cartwheel galaxy (Wolter and Trinchieri 2004), nearby colliding galaxy pair NGC 2207/IC 2163 (Mineo et al. 2013)), which supports the suggestion that most ULXs may be super-Eddington accreting HMXBs (King et al. 2001; Soria and Ghosh 2009; Gilfanov and Merloni 2015), and (2) the lack of HMXBs in region of very recent intense star formation, which is consistent with the evolutionary time for a massive binary to reach the HMXB stage. This effect was observed in M51 (Shtykovskiy and Gilfanov 2007) and the Magellanic Clouds (Shtykovskiy and Gilfanov 2005a; Antoniou and Zezas 2016). The study of the spatial distribution of LMXBs in elliptical galaxies has been motivated by the desire to understand the prevalent formation mechanism for these systems: from the evolution of field binaries, or from dynamical formation in globular clusters (GCs). In the first case, the radial distribution of LMXB may follow closely that of the stellar light, while in the second it may be more extended. While early studies were inconclusive (see review in Fabbiano 2006), more recently results show a possible excess of LMXB at larger radii than expected from the distribution of the optical surface brightness of the galaxies (Zhang et al. 2013; Mineo et al. 2014b). This line of investigation is further discussed in section “Clues from the Spatial Distributions”.

Primordial and Dynamically Formed LMXBs LMXB Formation Channels LMXB populations are expected to form through two basic pathways: (1) Rochelobe overflow of low-mass (2 − 3 M⊙ ) donor stars onto compact object companions in isolated binary systems that form in situ within galactic fields and (2) dynamical interactions (e.g., tidal capture and multibody exchange with constituent stars in primordial binaries) in high stellar density environments like globular clusters (GCs; Clark and Parkinson 1975; Fabian et al. 1975; Hills 1976) and near the centers of galaxies (e.g., Voss and Gilfanov 2007b; Zhang et al. 2011). The relative roles of these two channels have been debated. Given the very high

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formation efficiencies of GC LMXBs (a factor of ≈50–100 times higher per stellar mass than that of the field), it has been speculated that field LMXB populations may initially form dynamically within GCs and subsequently “seed” galactic fields through ejection or GC dissolution (e.g., Grindlay et al. 1984; Kremer et al. 2018). Chandra observations have shown strong evidence that both formation channels are important, with the normalization of the LMXB XLFs being primarily dependent on the integrated stellar mass, with an additional significant dependence on GC-specific frequency (number of GCs per galaxy stellar mass; see, e.g., Gilfanov 2004a; Irwin 2005; Juett 2005; Humphrey and Buote 2008; Kim et al. 2009; Boroson et al. 2011; Zhang et al. 2011; Lehmer et al. 2020). The combination of Chandra and Hubble Space Telescope surveys of relatively nearby (D  30 Mpc) early-type galaxies has allowed for disentanglement of field and GC LMXB populations through the direct multiwavelength classification of X-ray point sources (e.g., Kim et al. 2009; Voss et al. 2009; Paolillo et al. 2011; Luo et al. 2013; Lehmer et al. 2014, 2020; Mineo et al. 2014b; Peacock and Zepf 2016; Peacock et al. 2017; Dage et al. 2019). Studies of LMXBs directly associated with GCs have revealed that their formation efficacy depends on both local stellar interaction rates and metallicity (see, e.g., Pooley et al. 2003; Sivakoff et al. 2007; Cheng et al. 2018). The most apparent trends appear in observed GC colors, with metal-rich, red GCs hosting a factor of ≈3 times more LMXBs compared to metalpoor, blue GCs (e.g., Kim et al. 2013); however, no significant variation in the GC LMXB XLF slope is observed as a function of GC metallicity.

Clues from Luminosity Functions Variations in the shapes of the LMXB XLFs between field and GC environments have provided valuable insights into the nature and evolution of the LMXB population. Studies of the field and GC LMXB XLFs revealed that the shapes of the XLFs differ significantly, with the GC LMXB XLF appearing flatter than that of the field (Figs. 8 and 9) (Zhang et al. 2011; Peacock et al. 2014; Peacock and Zepf 2016). Furthermore, reports of an age dependence, in which the number of field LMXBs per galaxy stellar mass declines with increasing light-weighted stellar age (e.g., Kim and Fabbiano 2010; Lehmer et al. 2014), suggested that the field LMXB XLF appeared to evolve with stellar age, a result expected from XRB population synthesis models (e.g., Fragos et al. 2009, 2013) and indirectly observed in deep Chandra surveys as an increase of the LX (LMXB)/M⋆ scaling relation with increasing redshift (e.g., Lehmer et al. 2007, 2016; Aird et al. 2017). However, these studies suffered from small number statistics and large uncertainties on lightweighted stellar ages. A more recent study by Lehmer et al. (2020) culled 24 nearby early-type galaxies with Chandra, Hubble, and additional multiwavelength observations with the aim of investigating the nature of the field LMXB XLF. This work showed that early-type galaxies contain stellar-mass weighted ages that span only a narrow range where in-situ LMXB XLFs are not expected to vary. Global modeling of the field LMXB

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Fig. 8 Left: The stacked XLFs of LMXBs in different environments: field and GC sources in early-type galaxies and nucleus of M31. The contribution of CXB sources was subtracted and the incompleteness correction was applied. The field XLF (solid) is normalized to the stellar mass of 1010 M⊙ . The normalizations of GC (dashed) and M31 nucleus (dash-dotted) XLFs are arbitrary. The shaded areas around the curves show 1σ statistical uncertainty. (Adapted from Zhang et al. 2011)

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Fig. 9 (Left) Cumulative field (red solid) and GC (blue dashed) LMXB luminosity functions for NGC 4594 from Peacock et al. (2014), illustrating the flatter XLF of GC LMXBs relative to field LMXBs. (Right) X-ray luminosity per stellar mass versus GC specific frequency, SN , for a sample of 24 nearby elliptical galaxies (Lehmer et al. 2020). Contributions are shown for LMXBs that are formed “in situ” within the galactic fields (red long dashed), those that are observed in galactic fields, but suspected of being formed in and ejected from GCs (blue short dashed), and those that are directly coincident with GCs (purple dotted)

XLFs required scaling from both stellar mass and GC-specific frequency with high confidence. Furthermore, the shape of the GC-related field LMXB XLF component was shown to be consistent with the XLF of LMXBs directly coincident with GCs, suggesting that some seeding of the field LMXB population from GCs is likely and

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significant in massive early-type galaxies. The right panel of Fig. 9 shows the level of contributions expected to the integrated LX [LMXB]/M⋆ as a function of SN for in-situ LMXBs, GC-seeded LMXB observed in galactic fields, and LMXBs directly coincident with GCs.

Clues from the Spatial Distributions Evidence supporting at least some contribution of GC seeding has also been observed in the spatial distributions of LMXBs in early-type galaxies. Zhang et al. (2013) showed that the radial distributions of LMXBs in 20 early-type galaxies mainly followed the stellar light profiles but contained an excess of low-luminosity (5 × 1038 ergs s−1 ) X-ray sources out to ≈10 effective radii (Fig. 10). Such an excess is consistent with being associated with blue (metal-poor) GCs, which follow broader profiles relative to stellar light; however it is also observed in galaxies with low GC content – the extended LMXB halos must be a combined result of GC seeding and neutron-star LMXBs being kicked out of the main bodies of their host galaxies by asymmetric supernova explosions (Zhang et al. 2013). High stellar densities where stellar interactions become important are also reached in the galactic nuclei – similar to globular clusters, they may become the site of the dynamical formation of LMXBs. Voss and Gilfanov (2007a, b) found a significant increase of the specific frequency of X-ray sources in the nucleus of M31 (Fig. 10). The large volume of the bulge and correspondingly large number of dynamically formed LMXBs (about ∼20 with LX > 1036 erg/s) permitted them to directly probe the density profile of dynamically formed binaries which was shown to follow ρ∗2 law (Fig. 10, right bottom panel). As galactic bulges have ∼1–1.5 orders of magnitude larger velocity dispersion than globular clusters, the details of stellar interactions and composition of dynamically formed binary populations are different in bulges and clusters (Voss and Gilfanov 2007b). Detailed investigations of the spatial distributions of GC populations in the elliptical galaxies NGC 4261, NGC 4649, and NGC 4278 show anisotropies that are consistent with anisotropies observed in the distributions of both GC and field LMXBs (Zezas et al. 2003; D’Abrusco et al. 2014a, b). The GC anisotropies show arc and streamer-like morphologies, indicative of past dwarf-galaxy mergers. The observed anisotropies in the field LMXB distributions could be due to GC LMXB ejection or could be relics of past star formation in the merging systems. A particularly good study case is that of NGC 4649, a giant E in the Virgo cluster. This study was made possible by the coordinated complete deep coverage of both GC and LMXB populations with HST and Chandra surveys, which resulted in reliable identifications of X-ray sources with GC counterparts (Strader et al. 2012; Luo et al. 2013). Using these rich data sets, Mineo et al. (2014b) concluded that the evolution of field binaries and the dynamical formation in GCs are both likely to occur: LMXBs spatially coincident with GCs follow the same radial distribution as the overall distributions of red and blue GCs; instead those with no GC counterpart are radially distributed like the stellar surface brightness, except perhaps at larger

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Fig. 10 Left: Stacked radial source density profiles of LMXBs in nearby early-type galaxies, segregated by the source luminosity. Contribution of CXB sources subtracted. Solid histograms show predicted distribution based on the ks -band light. The x-axis shows radial distance in units of the effective radius. (Adapted from Zhang et al. 2013). Right: Dynamical formation of LMXB in the nucleus of M31. The top panel shows radial distribution of LMXBs in the nucleus of M31, excluding globular cluster sources. The CXB level is subtracted (shown by the dashed line). The solid histogram shows the projected distribution of the stellar mass. The normalization of the latter is from the best fit to the data outside 1 arcmin. The bottom panel shows distribution of the “surplus” X-ray sources, computed as a difference between the data and the stellar mass model shown in the top panel. The solid line shows the projected ρ∗2 distribution, computed from the same mass model of the M31 bulge. (Adapted from Voss and Gilfanov 2007b)

radii. Interestingly, in the two-dimensional distributions of LMXBs and GCs on the plane of the sky in NGC 4649 , there are arc-like distributions of GCs associated with similar over-densities of LMXBs (D’Abrusco et al. 2014a, b). However, a significant localized over-density of field LMXBs is found to the south of the GC arc, suggesting that these LMXBs may be somewhat connected with the arc of GCs. These sources occur at relatively large galactocentric radii and could contribute to the excess of field LMXB reported in Mineo et al. (2014b).

Ultraluminous X-Ray Sources An unusual class of compact sources – ultraluminous X-ray sources (ULXs) – was discovered in the first survey of nearby galaxies with the Einstein Observatory in the late 1970s (see reviews Fabbiano 1989; Kaaret et al. 2017). What characterizes these sources is their X-ray luminosity LX > 1039 erg/s, in excess of that expected

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from the Eddington limit for an object of 1–5 solar masses. This was at the time the range of known masses for the compact accretor in Milky Way XRBs (neutron stars and stellar mass black holes). This discovery led to the speculation that ULXs could represent an entirely new class of astrophysical objects, intermediate-mass black holes (IMBHs), with masses 100 − 104 solar masses, bridging the gap between the stellar black holes and the supermassive 108 solar mass black holes at the nuclei of galaxies (e.g., Colbert and Mushotzky 1999). However, a number of alternative models were advanced as well – from collimated radiation (Koerding et al. 2002) to ∼stellar mass black holes, representing the high mass tail of the standard stellar evolution sequence and accreting in the nearor slightly super-Eddington regime (King et al. 2001; Grimm et al. 2003; Gilfanov and Merloni 2015). Also, a critical review of the observational properties of ULXs demonstrated that their association to IMBH, while possible, was not proven beyond reasonable doubt (Fabbiano 2005). As discussed below, Chandra observations have shown a prevalent (but not unique) association of ULXs with regions of intense star formation in galaxies, supporting the hypothesis of a stellar nature for these objects. Recent gravitational wave observations have also demonstrated that stellar BHs can have much higher masses than previously thought (up to 100 solar masses (Barrera and Bartos 2022) (See also https://www.ligo.caltech.edu/image/ligo20171016a.)). More recently, the NuSTAR discovery of several pulsating ULXs (Bachetti et al. 2014; Walton et al. 2018) has changed dramatically the landscape of theoretical models, confirming the old theoretical prediction than the accretion column on the magnetic pole of a neutron star is less subject to the Eddington limit constraint (Basko and Sunyaev 1975, 1976; King et al. 2001). The present view on the nature of ULXs is more nuanced. It is quite possible that these luminous sources do not represent a unique astrophysical class of object. They may include super-Eddington XRBs (either NS of BH binaries), and also IMBH, especially in the case of very luminous ULXs at the outer radii of their associated galaxy (e.g., Kim et al. 2015).

Association with Star Formation The XLFs of compact X-ray sources in nearby early- and late-type galaxies (Fig. 5) make it quite obvious that luminous X-ray sources with LX  1039 erg/s are present in significant numbers only in star-forming galaxies where XLF extends into the range of luminosities attributed to ULXs, to LX ∼ 1040 erg/s. Detailed studies of X-ray binary populations in individual galaxies showed that ULXs are preferentially located in or near star-forming regions (e.g., Colbert et al. 2004; Mineo et al. 2013; Zezas and Fabbiano 2002; Zezas et al. 2007). Furthermore, comparison between the location of the ULXs and their nearest star clusters or star-forming regions set stringent constraints on the strength of surpernova kick velocities (Zezas and Fabbiano 2002; Kaaret et al. 2004).

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These results have been confirmed by more recent studies of ULXs in large samples of galaxies observed with Chandra (Kovlakas et al. 2020; Swartz et al. 2011), which showed that ULXs are predominantly located within late-type galaxies with high sSFR. A particularly strong trend is the prevalence of ULXs in galaxies with low metallicity (Mapelli et al. 2009; Brorby et al. 2016; Kovlakas et al. 2020; Prestwich et al. 2013). This trend is attributed to the weaker stellar winds of lower metallicity stars, resulting in tighter orbits and hence larger fraction of systems undergoing very efficient mass transfer (e.g., Linden et al. 2010; Fragos et al. 2013). In contrast, searches for ULXs in early-type galaxies showed that they are rather scarce and are found predominantly in young ellipticals (Fig. 6). Zhang et al. (2012) found 24 sources with LX > 1039 erg/s within D25 in a sample of 20 early-type galaxies with measured stellar age, the expected number of background AGN being equal to 11.8. The luminous sources are mostly associated with younger galaxies – 17 and 7 in galaxies younger and older than 6 Gyrs, with the CXB sources’ expectation of 5.8 and 6, respectively. The specific frequencies of luminous sources are 8.8 ± 3.2 sources per 1012 M⊙ in young galaxies with the 90% upper limit of 2.9 sources per 1012 M⊙ in galaxies older than 6 Gyrs (Zhang et al. 2012). Similarly, Kovlakas and collaborators (Kovlakas et al. 2020) found a small number of ULXs in early-type galaxies which appear to correlate nonlinearly with the stellar mass of their host galaxy. They interpreted this behavior in the context of variations in the star-formation history of the galaxies, in agreement with ULX population synthesis models (Kovlakas et al. 2020).

Main Conclusions from Optical Studies The association of ULXs with intensely star-forming galaxies provided the first indications that they are a subclass of HMXBs. However, systematic studies of their environment showed that ULXs are often located inside bubbles of ionized gas as witnessed for strong HeII or OIIIIII lines (e.g., Kaaret and Corbel 2009). While many of these bubbles are shock-excited by outflows from the ULX, the presence of strong excitation lines (e.g., HeII , NeV ) in some of them clearly indicates photoionization by a hard ionizing source. In this case they can provide a direct measure of the soft X-ray luminosity of the ULX and therefore stringent constraints on any beaming. The circular shape of many of these bubbles and the high inferred ionizing luminosity (e.g., >1040 erg s−1 in the case of HoII-X1 (Berghea et al. 2010)) suggest mild beaming. Searches for optical counterparts to ULXs have been successful for ∼20 sources (Tao et al. 2011; Gladstone et al. 2013). These tend to have V-band luminosities similar to early-type star supergiants and blue colors. However, their optical SEDs are not consistent with stellar spectra, indicating that they are dominated by the accretion disk component (Kaaret et al. 2017).

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Inferences from the Shape of the HMXB Luminosity Function As it has been well known, the maximum mass of a black holes produced in the course of standard stellar evolution at solar abundance of elements is limited to ≈10–20 M⊙ , whereas formation of more massive black holes with mass exceeding ∼100 is only possible at virtually zero abundance of metals (Zhang et al. 2008). It is not quite clear yet, whether this conventional picture contradicts the LIGO detections of ∼100 M⊙ black holes in coalescing binaries (Barrera and Bartos 2022). It is possible in principle that the most luminous sources are accreting IMBHs – descendants of Pop III stars, which acquired a massive companion in starforming regions. Obviously, the abundance of such systems should be significantly smaller than abundance of normal high-mass X-ray binaries formed in the course of standard stellar evolution. Therefore there must be a break in the luminosity function at the transition between “normal” X-ray binaries and these objects. However, observations show that the luminosity distribution of compact X-ray sources in starforming galaxies smoothly extends up to the luminosities of log LX ∼ 40–40.5, without any significant features or slope changes. In particular, unlike the LMXB LXF, it does not have any significant features at the luminosities corresponding to the Eddington limit of a neutron star (log LX ∼ 38.3) or of a black hole (log LX ∼ 39 − 39.5). On the other hand, it breaks at the luminosity log LX ≈ 40.0 − 40.5 (Fig. 11), corresponding to the Eddington luminosity of a ∼100 M⊙ object. Because of such a smooth shape of their XLF, it appears most likely that systems with luminosity log LX ≤ 40 − 40.5 are “normal” X-ray binaries formed in the course of standard stellar evolution and represent the tail of the distribution of black hole masses and mass accretion rates. We note here that luminosities exceeding the Eddington limit by several times are possible in the standard accretion model (Shakura and Sunyaev 1973; Grimm et al. 2003). The break in the HMXB XLF observed at log LX ∼ 40.5 (Figs. 5 and 11) may indicate the transition to a different Fig. 11 Detailed shape of the X-ray luminosity function of compact X-ray sources in star-forming galaxies. The figure shows the ratio of the X-ray luminosity function from Fig. 5 to a power law with slope of 1.6. Based on results of Mineo et al. (2012a)

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population of X-ray sources. The few known sources with luminosities exceeding this value may indeed be IMBHs – result of the evolution of Pop III stars.

Possible Nature and Implications for Accretion Physics The nature of ULXs has been a matter of debate since their discovery in the early 1980s, with potential models including super-luminous supernova remnants, accreting IMBHs, highly accreting X-ray binaries formed through dynamical capture or secular evolution (see, e.g., Zezas and Fabbiano 2002; Fabbiano 2006; Kaaret et al. 2017; Miller et al. 2003, for a critical summary of these models). Mounting evidence based on the their X-ray luminosity distribution, association with young stellar populations, scaling with SFR and metallicity, and their multiwavelength counterparts or surrounding nebulae suggests that the vast majority of ULXs are HMXBs undergoing a rapid mass-transfer episode. In this respect they are the upper end of the X-ray luminosity range of HMXBs. In fact, detailed modeling of the mass-transfer sequences of HMXBs (e.g., Rappaport et al. 2005) indicates that systems with massive donors (10 M⊙ ) can undergo brief phases (∼102 – 104 yr) of mildly super-Eddington accretion resulting in X-ray luminosities even in excess of 1040 . These episodes take place at the thermal timescale of the donor star. These results are supported by a growing volume of X-ray binary population synthesis models which show that indeed HMXBs can experience brief phases of super-Eddington mass transfer which in some cases can reach accretion rates well ˙ ; the fraction of these super-Eddington systems increases in excess of 103 MEdd dramatically in lower metallicities (e.g., Linden et al. 2010; Wiktorowicz et al. 2017; Marchant et al. 2017). Further evidence for supercritical accretion comes from the discovery of pulsarULXs which give a direct constraint on the compact object mass (e.g., Bachetti et al. 2014). A natural outcome of supercritical accretion is the formation of the so-called slim or thick accretion disks. The slim disks are expected to form at accretion rates exceeding ∼MEdd , and they have larger height (thickness) than the standard thin disks (Shakura and Sunyaev 1973; Szuszkiewicz et al. 1996), resulting in nonlinear scaling of the emerging X-ray luminosity with accretion rate and different spectral shape. In higher accretion rates, the radiation pressure further increases its thickness resulting in the formation of a funnel in its inner part (Szuszkiewicz et al. 1996). A natural outcome of this effect is mild beaming of the X-ray emission (e.g., King 2002). Recent general relativistic, radiation magneto-hydrodynamical simulations of supercritical mass accretion models for black holes confirmed this picture (e.g., Sadowski and Narayan 2016). The differences in the structure of the accretion disk in ULXs with respect to lower-luminosity X-ray binaries become evident in their X-ray spectra, which often show a curvature above ∼2 keV which can be described by a break at ∼7–10 keV (Poutanen et al. 2007; Kaaret et al. 2017, and references therein). Evidence of reflection of the pulsar emission from the walls of the accretion funnel has been also found (Bykov et al. 2022).

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Population Synthesis Results Relevant Results from Binary Evolution X-ray binary evolution models have provided important insights in the formation timescales of the different types of X-ray binaries. These are determined by a combination of the nuclear timescales of the donor stars and the time required for the onset of mass transfer from the donor star to the compact object. The mass transfer can take place in two main ways: (a) capture of material expelled from the donor star in the form of a stellar wind and (b) Roche-lobe overflow. The stellar winds are mostly relevant in the case of X-ray binaries with early-type donors (O, B stars, supergiants, or Wolf-Rayet stars), since lower-mass stars have very weak stellar winds that cannot produce observable X-ray emission. A special case of wind-fed X-ray binaries is the Be X-ray binaries (Be-XRBs) where the accreted material originates in an equatorial outflow (decretion disk) from the donor Oe or Be star (e.g., Reig 2011). On the other hand, the onset of Roche-lobe overflow (RLOF) requires that the radius of the donor star becomes larger than its Roche-lobe. This usually happens either as a result of the increase of the stellar radius as the star evolves off the main sequence or as a result of the shrinkage of the orbital radius of the system (e.g., due to tidal evolution, magnetic breaking, common-envelope evolution, etc.). Since the donor stars have lower mass than the primary star producing the compact objects, their nuclear evolution timescales are longer. High-mass X-ray binaries appear between a few Myr and ∼100 Myr from the formation of the binary stellar system. The low limit is driven by the time required for the most massive star of the system to produce a compact object. The upper range reflects the upper range of the timescale needed for the donor star (which in the case of HMXBs is of O or B spectral types) to evolve and initiate the mass transfer. In the case of low-mass X-ray binaries, their formation timescales are much longer, from a few hundred Myr up to several Gyr. This is because of the longer evolutionary timescales of lower-mass donor stars and the long timescale required for the shrinkage of the orbital radius. Binary stars are formed with a wide range of mass ratios, orbital separations, and eccentricity. Only a small fraction of these systems will eventually become X-ray binaries (Section “How Frequent Are X-Ray Binaries?”). Even before the formation of a compact object as a result of the nuclear evolution of the more massive star, the two stars may interact, exchanging mass. The supernova explosion may have a dramatic effect in the evolution of the system by imparting a kick onto the resulting compact object. The result of the kick is to increase the orbital separation and/or the eccentricity of the orbit. In the most extreme case, it may disrupt the binary system. However, as a result of the nuclear evolution of the secondary, mass transfer either through a stellar wind or RLOF may initiate, resulting in an X-ray binary. If the mass of the donor star is lower than ∼10 M⊙ , the initiation of mass transfer also requires shrinkage of the orbit. This can take place through a variety of mechanisms: magnetic breaking, tidal interaction, and emission of gravitational

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radiation. A particularly effective mechanism is common-envelope evolution (e.g., Taam and Sandquist 2000; Ivanova et al. 2020), which, however, in many cases may lead to the merging of the two systems.

Summary of Population Synthesis Models and Their Results X-ray binary population synthesis models are an invaluable tool for understanding the X-ray binary populations and their connection with fundamental parameters of the host galaxy and for constraining uncertain parameters of the theory through comparisons with observations. They calculate the populations of X-ray binaries at a given time of the evolution of a stellar population by combining distributions of the initial parameters of the binary systems together with prescriptions for the evolution of the stars in the binary systems and its orbital parameters (e.g., Belczynski et al. 2008; Riley et al. 2022; Fragos et al. 2013). As a result, one then can model the X-ray emission of different X-ray binary populations as a function of the star-formation history of their parent stellar populations. Figure 4 shows the dependence of the integrated X-ray luminosity of a stellar population as a function of its age and metallicity. It is clear that X-ray binary populations associated with younger and lower metallicity stellar populations tend to have higher X-ray luminosities. The metallicity dependence is particularly important for understanding the cosmological evolution of X-ray binary populations and their potential role in the early Universe (Section “Cosmic Evolution of X-Ray Binaries and Their Contribution to CXB”). The first attempts to model the X-ray binary populations observed with Chandra using population synthesis showed that despite the large number of parameters in these models, their results are relatively robust (e.g., Belczynski et al. 2008; Riley et al. 2022; Fragos et al. 2013). Nonetheless, comparison of the X-ray luminosity functions of X-ray binaries obtained in Chandra led to useful constraints on parameters such as the strength of the stellar winds, the common-envelope ejection efficiency, and the mass ratio of the stars in the binary system at the zero-age main sequence (Tzanavaris et al. 2013). Similar constraints can be set by looking at the integrated X-ray emission of X-ray binaries in unresolved galaxies (e.g., Fragos et al. 2013; Lehmer et al. 2016). Furthermore, comparison of the measured age evolution of the formation rate of X-ray binaries with predictions from X-ray binary population synthesis models showed (Fig. 3) that they reproduce well the increased populations at ages ∼10–50 Myr and the decline of their integrated X-ray luminosities at systems older than ∼5 Gyr, as well as their metallicity dependence (Shtykovskiy and Gilfanov 2007; Antoniou et al. 2010, 2019; Antoniou and Zezas 2016; Lehmer et al. 2021). In the case of ULXs, population synthesis models showed that their increased rates at low metallicities are driven by the reduced effect of stellar winds in removing mass and angular momentum from the system, hence resulting in tighter orbits and a larger fraction of systems undergoing RLOF mass transfer (e.g., Linden et al. 2010). Furthermore, detailed modeling of individual ULXs (and especially pulsar-ULXs)

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revealed additional formation channels for these rare but very luminous systems (e.g., Misra et al. 2020; Abdusalam et al. 2020).

How Frequent Are X-Ray Binaries? With the knowledge of the relation between the number of HMXBs and SFR, we can estimate the fraction of compact objects that become HMXBs (Mineo et al. 2012a). According to the HMXB XLF and scaling relation (Section “X-Ray Scaling Relations and Luminosity Functions”), the number of HMXBs with luminosity higher than 1035 erg/s is NHMXB (> 1035 erg s−1 ) ≈ 135 × SFR

(8)

On the other hand, the number of HMXBs can be expressed via the birth rate of compact objects N˙ co : NHMXB ∼ N˙ co



fX,k τX,k ∼ N˙ co fX τ¯X

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k

The N˙ co approximately equals to the birth rate of massive stars N˙ co ≈ N˙ ⋆ (M > 8 M⊙ ) ≈ 7.4 · 10−3 × SFR. (Use of the Salpeter IMF is explained in Mineo et al. 2012a.) The fX = k fX,k is the fraction of compact objects which become X-ray active in HMXBs, and τ¯X is the average X-ray lifetime of such objects. As discussed in Mineo et al. (2012a), the low and moderate luminosity sources are dominated by Be/X systems; therefore τ¯X ∼ 0.1 Myr (cf. Fig. 3) (Verbunt and van den Heuvel 1995). Combining Equations 8 and 9, we obtain fX ∼ 0.18 ×



τ¯X 0.1 Myr

−1

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Thus, we arrived to a remarkable conclusion that a large fraction of the order of  ten percent of all black holes and neutron stars once in their lifetime were X-ray sources with LX > 1035 erg/s, powered by accretion from a massive donor star in a high-mass X-ray binary (Mineo et al. 2012a). Similarly, given the scaling relation for ULXs NULX (> 1039 erg/s) ≈ 0.48 × SFR, one can show that −2

fULX ∼ 3.5 · 10

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−1

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i.e., a few percent of all black holes formed in a galaxy become ultraluminous X-ray sources with luminosity ≥1039 erg/s, explaining the observed population of ULXs.

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Interestingly, only fLMXB ∼ 10−6 of compact objects becomes X-ray bright in LMXBs (Mineo et al. 2012a). This is another manifestation of the fact that LMXBs are extremely rare objects and may be explained by the high probability of disruption of the binary system with a low mass companion in the course of the supernova explosion. These numbers provide valuable input for calibration of the population synthesis models.

Connection to LIGO-Virgo Sources X-ray binaries are one of the few easily observable phases in the evolution of binary stellar systems. Furthermore, since the onset of mass transfer requires small orbital separation, a fraction of X-ray binaries is expected to become binary compact object systems which will merge within a Hubble time producing gravitationalwave sources (e.g., Marchant et al. 2017). Therefore, the study of X-ray binaries is inextricably linked to the study of the gravitational-wave sources: X-ray binaries provide information on the demographics of the compact object populations (e.g., Farr et al. 2016) and constraints on X-ray binary formation and evolution models. Furthermore, joint study of the compact object populations inferred from gravitational-wave observations and X-ray binaries will provide a more complete picture of their overall mass spectrum and spin distribution (e.g., Fishbach and Kalogera 2022).

Cosmic Evolution of X-Ray Binaries and Their Contribution to CXB Contribution of X-Ray Binaries to Cosmic X-Ray Background Knowing how stellar mass was built in the Universe, a natural question to ask is how much X-ray binaries contribute to cosmic X-ray background (CXB). In order to answer this question, Dijkstra and collaborators (Dijkstra et al. 2012) combined the local LX −SFR and LX −M∗ relations with the cosmic star-formation history. They found that star-forming galaxies contribute ∼5–15 percent to soft (1 − 2 keV) CXB and ∼1–20 percent to the hard band (2 − 10 keV) CXB. The main source of uncertainty in this estimate was associated with the uncertainty in the spectra of ULXs for which (Dijkstra et al. 2012) allowed a conservatively broad range of photon index values Γ = 1 − 3. Assuming a more narrow interval of Γ = 1.7 − 2.0, contribution of star-forming galaxies to the soft CXB can be limited to ≈8–13 percent. The contribution to the CXB in the hard band is uncertain mostly because of a more uncertain K-correction at the corresponding high energies. For the parameters of the Chandra Deep Field North, they found that galaxies whose individual observed flux is below the detection threshold in the Chandra Deep Field North (CDF-N) can fully account for the unresolved part of the CXB

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in the soft band. This conclusion is insensitive to details in the model as long as the photon index, averaged over the entire population of X-ray-emitting star-forming galaxies, is Γ < 2, which corresponds to a very reasonable range given the existing observational constraints on Γ . The tightness of remaining unresolved CXB permits one to constrain the evolution of the LX − SFR relation with redshift. When it is parameterized as LX /SFR = A(1+z)b , the unresolved soft CXB requires that b < 1.6 (3σ ) (Dijkstra et al. 2012). Due to much lower formation efficiency (Section “How Frequent Are X-Ray Binaries?”), the contribution to CXB of LMXBs is at least an order of magnitude smaller (Dijkstra et al. 2012).

X-Ray Investigations of Cosmologically Distant Galaxies With the advent of deep extragalactic X-ray surveys (see, e.g., review by Brandt and Alexander 2015), it is now possible to place meaningful observational constraints on the cosmic evolution of X-ray binary populations. The first deep (≈1 Ms depth) Chandra surveys in the Chandra Deep Field-North (CDF-N; Hornschemeier et al. 2000; Brandt et al. 2001) and CDF-South (CDF-S; Giacconi et al. 2001) revealed substantial numbers of “normal” galaxies at z  1.5 with X-ray-to-optical flux ratios that were consistent with being powered primarily by XRBs and hot gas, without substantial contributions from active galactic nuclei (AGN). These discoveries gave way to the new and active field of X-ray studies of normal galaxies at cosmologically significant distances. Due to the dominance of XRB emission in normal galaxies at rest-frame wavelengths >1–2 keV, combined with the redshifting of rest-frame soft emission out of the Chandra observed frame, X-ray emission detected in these distant normal galaxies is expected to primarily trace XRB populations. As the Chandra Deep Fields (CDFs) and additional survey fields accumulated X-ray depth and multiwavelength data, the insights on the cosmic evolution of XRB populations in galaxies expanded. Studies of X-raydetected normal-galaxy samples in the CDFs have revealed that the galaxy XLF undergoes positive redshift evolution from the local Universe to z ≈ 1.5 (e.g., Ptak et al. 2007; Tzanavaris and Georgantopoulos 2008). The evolution is primarily driven by late-type galaxy populations, which show luminosity evolution of the XLF at the (1 + z)0.4−3.4 level. The XLFs of early-type galaxies may also evolve with redshift; however, the relatively small numbers of early-type galaxies detected in the CDFs yield weak constraints on XLF evolution. The overall normalgalaxy XLF evolution is primarily driven by the rising cosmic star-formation rate density from z = 0–1.5 (see, e.g., Madau and Dickinson 2014, for a review), and scaling relation investigations show that the X-raydetected galaxy population follows the local LX /SFR correlation within the relation scatter (e.g., Mineo et al. 2014a). However, thus far, X-ray-detected normal galaxies in deep surveys number in the hundreds of objects, which represent only a small fraction (as low as 1% for Hubble-detected sources) of the galaxy population that is known to be present in

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these fields. As such, X-raydetected normal-galaxy population studies suffer from significant selection biases. To investigate X-ray emission from more representative populations of galaxies, and scaling relations between X-ray binary population luminosity and galaxy properties, X-ray stacking of optically selected galaxies has often been employed. Early stacking efforts initially showed that X-ray properties of normal galaxies were nearly consistent with basic local scaling relations (e.g., LX /SFR and LX /M⋆ ) out to z ≈ 3 once corrections for optical extinction and Lopt to SFR were accounted for (Hornschemeier et al. 2002; Basu-Zych et al. 2013; Symeonidis et al. 2014). However, as multiwavelength data sets expanded and Chandra depths and coverage increased, significant positive redshift evolution was detected in the HMXB and LMXB luminosity scalings with SFR and M⋆ , respectively, out to z ≈ 2.5 (i.e., to a cosmic lookback time of ≈11 Gyr). The redshift evolution of these scaling relations has been found to roughly follow LX (HMXB)/SFR ∝ (1 + z) and LX (LMXB)/M⋆ ∝ (1 + z)2−3 (e.g., Lehmer et al. 2016; Aird et al. 2017; Fornasini et al. 2020), in good consistency with the CXB-based constraints (Dijkstra et al. 2012). Figure 12 illustrates constraints from Aird et al. (2017), which show that the X-ray luminosity of typical galaxies rises with increasing redshift for fixed stellar mass and SFR.

Drivers of the Redshift Evolution of X-Ray Binary Populations The combination of detailed XRB population synthesis models and cosmological models of evolving galaxy populations provided a framework to construct models

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of the evolution of X-ray emission from XRBs and their scaling relations with physical properties. Fragos et al. (2013) used Startrack XRB population synthesis models (Belczynski et al. 2008) and simulated galaxy models from the Millenium II simulation (Guo et al. 2011) to track the XRB emission throughout the Universe from z ≈ 20 to the present day. These models accounted for evolution in star-formation activity, stellar masses, stellar ages, and metallicities and identified best models that simultaneously reproduced local (i.e., z = 0) LX (HMXB)/SFR and LX (LMXB)/M⋆ scaling relations. As a byproduct, these models provided predictions for the redshift evolution of the scaling relations and the cosmic X-ray emissivity from XRB populations. The predicted scaling relation evolution from the best Fragos et al. models was found to be similar to that observed empirically in the CDFs, and the models provided physical insight for the drivers of this evolution. The rise of LX (HMXB)/SFR with redshift was expected to be driven by a corresponding decline in metallicity. Stellar wind mass loss is expected to increase with metal content, and in the context of XRBs, relatively low-metallicity systems are expected to lose less mass and angular momentum from stellar winds, allowing the binary orbits to remain relatively tight and yield larger mass-transfer rates and higher X-ray luminosities than relatively high-metallicity systems. For LMXBs, the increase of LX (LMXB)/M⋆ with increasing redshift was predicted theoretically as a result of the LMXB donor stars shifting to higher mass objects and higher mass-transfer rates as the ages of the stellar populations decline with increasing redshift.

Recent Constraints on X-Ray Evolution of Galaxies While theoretical models suggest that both metallicity and stellar age evolution are responsible for the observed evolution of XRB scaling relations, more direct empirical evidence has only recently supported these suggestions. For example, Fornasini et al. (2019, 2020) investigated HMXB-dominant galaxies (high SFR/M⋆ ) at z ≈ 0.1–2.6, located in the COSMOS and CDF-S fields, that had gas-phase metallicity measurements via strong emission-line indicators. They divided their galaxy samples into bins of redshift and gas-phase metallicity and used X-ray stacking to show that the mean LX (HMXB)/SFR ratio declined with increasing metallicity in a single relation that is consistent with local-galaxy LX (HMXB)-SFRZ relations (e.g., Brorby et al. 2016; Lehmer et al. 2021) – see left panel of Fig. 13. To investigate age evolution of XRB populations, Gilbertson et al. (2021) measured star-formation histories of galaxies in the CDFs and used a statistical method to construct a model of LX /M⋆ versus age consistent with the galaxy X-ray counts. A decline of 3 orders of magnitude was observed for LX /M⋆ from ≈10 Myr to ≈10 Gyr, mainly consistent with expectations from the Fragos et al. (2013) models (right panel of Fig. 13).

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Fig. 13 (Left) The X-ray luminosity per SFR (LX /SFR) versus gas-phase metallicity (12 + log(O/H)) for stacked samples of high specific star-formation rate galaxies at z ≈ 0.1–2.6 in the CDF and COSMOS survey fields. The X-ray emission for these galaxies is expected to be dominated by young populations of HMXBs, and a clear anticorrelation is observed (black curve indicates best-fit relation), consistent with theoretical models (the dot-dashed curve from Fragos et al. (2013)). (Adapted from Fornasini et al. 2020). (Right) Average age dependence of the 2– 10 keV luminosity per stellar mass (LX /M⋆ ) for 344 galaxies in the CDFs. A decline of ≈3 orders of magnitude is observed from 10 Myr to 10 Gyr as XRB populations become less luminous and powered by accretion from increasingly lower mass stars. (Figure modified from its original version in Gilbertson et al. 2021)

Contribution to (Pre)Heating of IGM The large mean free path of X-ray photons suggests that they can penetrate a larger volume of the interstellar medium around the X-ray source. This becomes particularly important in the early Universe (z > 10), where they may influence a larger volume around the primordial galaxies than the ultraviolet photons associated with the first Population III stars (e.g., Madau and Fragos 2017, and references therein). This results in heating of the primordial intergalactic medium even before the epoch of reionization, which has important implications for the subsequent galaxy formation (e.g., Artale et al. 2015). Extrapolation of the best XRB population synthesis models to z ≈ 3–20, where only weak empirical constraints are currently available, indicates that X-ray emissivity of the Universe from HMXBs is likely to exceed AGN at z  6–8 (e.g., Fragos et al. 2013; Madau and Fragos 2017). At these redshifts, LX (HMXB)/SFR is expected to be elevated over the local relation by a factor of ∼10 due to differences in metallicity. As an added result, the escaping radiation at low energies 2 keV may be further enhanced due to the lack of metal absorption edges that significantly impact the optical depth at these energies (e.g., Das et al. 2017). As a consequence of these effects, HMXB populations are of particular interest as having a potentially significant role in heating of the intergalactic medium at z  10. The impact of this heating is expected to be imprinted at these redshifts on the cosmic 21 cm brightness temperature relative to the cosmic microwave background, and numerous efforts are underway to directly observe these signatures. For example, the Hydrogen Epoch of Reionization Array (HERA; e.g., DeBoer et al. 2017) and Square Kilometre Array (SKA; e.g., Mellema et al. 2013) are predicted to directly constrain the 21 cm signal

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over a wider range of redshift and will enable constraints on LX (HMXB)/SFR associated with the galaxy populations there (see, e.g., The HERA Collaboration et al. 2021, for first results).

Conclusion Sub – arc second angular resolution of Chandra observatory led to a quantum leap in our understanding of populations of X-ray binaries in external galaxies, their content, evolution, and scaling with fundamental parameters of galaxies. In over 20 years of operation in space, Chandra observed hundreds of galaxies of various morphological types, ages, and metallicities. X-ray luminosity functions of compact sources in young and old galaxies to the meaningful depth have been obtained for many dozens of galaxies, providing the ultimate proof of their nature as high- and low-mass X-ray binaries. Their spatial distributions have been obtained and compared with the distributions of various tracers, confirming that different formation channels are in place, primordial and dynamical. These observations provided wealth of information for calibration and verification of population synthesis models which in turn gave valuable feedback to the theories of stellar and binary evolution. Deep Chandra fields permitted to study collective properties of high-mass X-ray binaries in distant galaxies, located at cosmological redshifts, to study their evolution and to make further comparisons with binary population modeling. These studies revealed an unanticipated role of star-forming galaxies and their X-ray binaries in preheating the intergalactic medium in early Universe and in shaping the cosmic X-ray background and also led to the proposition of a new independent method to measure star-formation rate in (distant) galaxies. Along with these remarkable advances, many unanswered questions still remain. The list of outstanding goals for future studies includes, to mention a few, the redshift evolution of X-ray binaries, the nature and formation channels of ultraluminous X-ray sources and their connection to LIGO-Virgo sources, the maximum mass of “stellar mass” black holes and role of the intermediate mass ones, detailed understanding of dynamical formation of LMXBs in globular clusters and galactic nuclei and their metallicity dependence and seeding of field populations, and the origin of the HMXB XLF, which maintains same slope over 5 orders of magnitude in luminosity, with only moderate deviations from the power law. On the other end of the luminosity range are fainter sources such as cataclysmic variables which extragalactic populations are yet to be explored. There are still many complexities in the data which we do not quite understand, but existence of many others is yet to be recognized. The progress of observational capabilities of modern astronomy, anticipated in the coming years and planned for the more distant future, will help to answer these questions and will inevitably raise the new ones. Eagerly awaited are the results from the SRG all-sky survey which is more than halfway through. Its eROSITA telescope, although lacking the angular resolution of Chandra, will survey the entire sky eight times. It will detect of the order of ∼104 normal galaxies of all morphological types, fully sampling the parameter space of normal galaxies. Critical role in many studies

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is played by observations at other wavelength, in particular optical and infrared. These will be advanced with the start of operations of the Vera C. Rubin Observatory and Euclid satellite. Smaller samples of carefully selected galaxies will be observed by the James Webb Space Telescope. At the X-ray wavelengths, the major new thrust will be given by Athena and Lynx X-ray observatories. Notably, the Lynx Observatory will deliver the angular resolution of Chandra but at ∼50 times higher throughput.

References K. Abdusalam, I. Ablimit, P. Hashim, G.-L. Lü, M.K. Mardini, Z.-J. Wang, ApJ 902, 125 (2020). https://doi.org/10.3847/1538-4357/abb5a8 M.C. Artale, P.B. Tissera, L.J. Pellizza, MNRAS 448, 3071 (2015). https://doi.org/10.1093/mnras/ stv218 J. Aird, A.L. Coil, A. Georgakakis, MNRAS 465, 3390 (2017). https://doi.org/10.1093/mnras/ stw2932 V. Antoniou, A. Zezas, D. Hatzidimitriou, V. Kalogera, ApJL 716, L140 (2010). https://doi.org/10. 1088/2041-8205/716/2/L140 V. Antoniou, A. Zezas, MNRAS 459, 528 (2016). https://doi.org/10.1093/mnras/stw167 V. Antoniou, A. Zezas, J.J. Drake, C. Badenes, F. Haberl, N.J. Wright, J. Hong et al., ApJ 887, 20 (2019). https://doi.org/10.3847/1538-4357/ab4a7a M. Bachetti et al., Nature 514, 202 (2014) O. Barrera, I. Bartos, ApJL 929, L1 (2022). https://doi.org/10.3847/2041-8213/ac5f47 M.M. Basko, R.A. Sunyaev, MNRAS 175, 395 (1976). https://doi.org/10.1093/mnras/175.2.395 M.M. Basko, R.A. Sunyaev, A&A 42, 311 (1975) A.R. Basu-Zych, B.D. Lehmer, A.E. Hornschemeier, R.J. Bouwens, T. Fragos, P.A. Oesch, K. Belczynski et al., ApJ 762, 45 (2013) A.R. Basu-Zych, A.E. Hornschemeier, F. Haberl, N. Vulic, J. Wilms, A. Zezas, K. Kovlakas et al., MNRAS 498, 1651 (2020). https://doi.org/10.1093/mnras/staa2343 K. Belczynski, V. Kalogera, F.A. Rasio, R.E. Taam, A. Zezas, T. Bulik, T.J. Maccarone et al. ApJS 174, 223 (2008) C.T. Berghea, R.P. Dudik, K.A. Weaver, T.R. Kallman, ApJ 708, 354 (2010). https://doi.org/10. 1088/0004-637X/708/1/354 B. Boroson, D.-W. Kim, G. Fabbiano, ApJ 729, 12 (2011) M. Brorby, P. Kaaret, A. Prestwich, I.F. Mirabel, MNRAS 457, 4081 (2016) W.N. Brandt, D.M. Alexander, A.E. Hornschemeier, G.P. Garmire, D.P. Schneider, A.J. Barger, F.E. Bauer et al., AJ 122, 2810 (2001) W.N. Brandt, D.M. Alexander, A&ARv 23, 1 (2015) S.D. Bykov, M.R. Gilfanov, S.S. Tsygankov, E.V. Filippova, MNRAS 516, 1601 (2022). https:// doi.org/10.1093/mnras/stac2239 Z. Cheng, Z. Li, X. Xu, X. Li, ApJ 858, 33 (2018) D.H. Clark, J.H. Parkinson, Nature 258, 408 (1975) E.J.M. Colbert, R.F. Mushotzky, ApJ 519, 89 (1999) E.J.M. Colbert et al., ApJ 602, 231 (2004) R. D’Abrusco, G. Fabbiano, S. Mineo, J. Strader, T. Fragos, D.-W. Kim, B. Luo et al., ApJ 783, 18 (2014a) R. D’Abrusco, G. Fabbiano, N.J. Brassington, ApJ 783, 19 (2014b) L.P. David, C. Jones, W. Forman, ApJ 388, 82 (1992). https://doi.org/10.1086/171131 K.C. Dage, S.E. Zepf, M.B. Peacock, A. Bahramian, O. Noroozi, A. Kundu, T.J. Maccarone, MNRAS 485, 1694 (2019)

117 X-ray Binaries in External Galaxies

4317

A. Das, A. Mesinger, A. Pallottini, A. Ferrara, J.H. Wise, MNRAS 469, 1166 (2017) D.R. DeBoer, A.R. Parsons, J.E. Aguirre, P. Alexander, Z.S. Ali, A.P. Beardsley, G. Bernardi et al., PASP 129, 045001 (2017) M. Dijkstra, M. Gilfanov, A. Loeb, R. Sunyaev, MNRAS 421, 213 (2012). https://doi.org/10.1111/ j.1365-2966.2011.20292.x G. Fabbiano, ApJ 325, 544 (1988) G. Fabbiano, ARA&A 27, 87 (1989) G. Fabbiano, Science 307, 533–534 (2005) G. Fabbiano, ARA&A 44, 323 (2006) G. Fabbiano, in The Chandra X-Ray Observatory, ed. by B. Wilkes, W. Tucker. IOP ebooks (IOP Publishing, Bristol, 2019), pp. 7-1-7-42. ISBN: 978-0-7503-2163-1 G. Fabbiano, A. Shapley, ApJ 565, 908 (2002) A.C. Fabian, J.E. Pringle, M.J. Rees, MNRAS 172, 15P (1975) G. Fabbiano, D.-W. Kim, G. Trinchieri, ApJS 80, 531 (1992) G. Fabbiano, A. Zezas, S.S. Murray, ApJ 554, 1035 (2001). https://doi.org/10.1086/321397 B. Farr, C.P.L. Berry, W.M. Farr, C.-J. Haster, H. Middleton, K. Cannon, P.B. Graff et al., ApJ 825, 116 (2016). https://doi.org/10.3847/0004-637X/825/2/116 M. Fishbach, V. Kalogera, ApJL 929, L26 (2022). https://doi.org/10.3847/2041-8213/ac64a5 F.M. Fornasini, M. Kriek, R.L. Sanders, I. Shivaei, F. Civano, N.A. Reddy, A.E. Shapley et al., ApJ 885, 65 (2019) F.M. Fornasini, F. Civano, H. Suh, MNRAS 495, 771 (2020) T.Fragos, V. Kalogera, B. Willems, K. Belczynski, G. Fabbiano, N.J. Brassington, D.-W. Kim et al., ApJL 702, L143 (2009) T. Fragos, B. Lehmer, M. Tremmel, P. Tzanavaris, A. Basu-Zych, K. Belczynski, A. Hornschemeier et al., ApJ 764, 41 (2013) I. Galiullin, M. Gilfanov, R. Sunyaev, MNRAS (2023), in preparation K. Garofali et al., MNRAS 479, 3526 (2018). https://doi.org/10.1093/mnras/sty1612 P. Ghosh, N.E. White, ApJL 559, L97 (2001). https://doi.org/10.1086/323641 R. Giacconi, P. Rosati, P. Tozzi, M. Nonino, G. Hasinger, C. Norman, J. Bergeron et al., ApJ 551, 624 (2001) W. Gilbertson, B. Lehmer, K. Doore, R. Eufrasio, A. Basu-Zych, W. Brandt, T. Fragos et al., (2021). arXiv, arXiv:2112.03194 M. Gilfanov, MNRAS 349, 146 (2004a) M. Gilfanov, Prog. Theor. Phys. Suppl. 155, 49 (2004b). https://doi.org/10.1143/PTPS.155.49 M. Gilfanov, A. Merloni, Space Sci. Rev. 183(1–4), 121–148 (2015). https://doi.org/10.1007/ s11214-014-0071-5 M. Gilfanov, H.-J. Grimm, R. Sunyaev, MNRAS 351, 1365 (2004a). https://doi.org/10.1111/j. 1365-2966.2004.07874.x M. Gilfanov, H.-J. Grimm, R. Sunyaev, MNRAS 347, L57 (2004b). https://doi.org/10.1111/j.13652966.2004.07450.x M. Gilfanov, The Jet Paradigm. Lecture Notes in Physics, vol. 794 (Springer, Berlin/Heidelberg, 2010), p. 17. https://doi.org/10.1007/978-3-540-76937-8_2, ISBN 978-3-540-76936-1 J.C. Gladstone, C. Copperwheat, C.O. Heinke, T.P. Roberts, T.F. Cartwright, A.J. Levan, M.R. Goad, ApJS 206, 14 (2013). https://doi.org/10.1088/0067-0049/206/2/14 H.-J. Grimm, M. Gilfanov, R. Sunyaev, A&A 391, 923 (2002). https://doi.org/10.1051/0004-6361: 20020826 H.-J. Grimm, M. Gilfanov, R. Sunyaev, MNRAS 339, 793 (2003). https://doi.org/10.1046/j.13658711.2003.06224.x J.E. Grindlay, P. Hertz, J.E. Steiner, S.S. Murray, A.P. Lightman, ApJL 282, L13 (1984) R.E. Griffiths, P. Padovani, ApJ 360, 483 (1990). https://doi.org/10.1086/169139 Q. Guo, S. White, M. Boylan-Kolchin, G. De Lucia, G. Kauffmann, G. Lemson, C. Li et al., MNRAS 413, 101 (2011) F. Haberl, R. Sturm, J. Ballet, D.J. Bomans, D.A.H. Buckley, M.J. Coe, R. Corbet et al., A&A 545, A128 (2012). https://doi.org/10.1051/0004-6361/201219758

4318

M. Gilfanov et al.

D.J. Helfand, PASP 96, 913 (1984). https://doi.org/10.1086/131455 The HERA Collaboration, Z. Abdurashidova, J.E. Aguirre, P. Alexander, Z.S. Ali, Y. Balfour, A.P. Beardsley et al., (2021). arXiv, arXiv:2108.02263 J.G. Hills, MNRAS 175, 1P (1976) A.E. Hornschemeier, W.N. Brandt, G.P. Garmire, D.P. Schneider, P.S. Broos, L.K. Townsley, M.W. Bautz et al., ApJ 541, 49 (2000) A.E. Hornschemeier, W.N. Brandt, D.M. Alexander, F.E. Bauer, G.P. Garmire, D.P. Schneider, M.W. Bautz et al., ApJ 568, 82 (2002) P.J. Humphrey, D.A. Buote, ApJ 689, 983 (2008) N. Ivanova, S. Justham, P. Ricker, cee..book. (2020). https://doi.org/10.1088/2514-3433/abb6f0 J.A. Irwin, ApJ 631, 511 (2005) A.M. Juett, ApJL 621, L25 (2005) P. Kaaret, A. Alonso-Herrero, J.S. Gallagher, G. Fabbiano, A. Zezas, M.J. Rieke, MNRAS 348, L28 (2004). https://doi.org/10.1111/j.1365-2966.2004.07516.x P. Kaaret, S. Corbel, ApJ 697, 950 (2009). https://doi.org/10.1088/0004-637X/697/1/950 P. Kaaret, H. Feng, T.P. Roberts, ARA&A 55, 303 (2017). https://doi.org/10.1146/annurev-astro091916-055259 D.-W. Kim, G. Fabbiano, ApJ 611, 846 (2004) D.-W. Kim, G. Fabbiano, ApJ 721, 1523 (2010) D.-W. Kim, G. Fabbiano, G. Trinchieri, ApJ 393, 134 (1992) D.-W. Kim, G. Fabbiano, N.J. Brassington, T. Fragos, V. Kalogera, A. Zezas, A. Jordán et al., ApJ 703, 829 (2009) D.-W. Kim, G. Fabbiano, N. Ivanov, T. Fragos, A. Jordán, G.R. Sivakoff, R. Voss, ApJ 764, 98 (2013) M. Kim et al., ApJ 814, 8 (2015) A.R. King, MNRAS 335, L13 (2002). https://doi.org/10.1046/j.1365-8711.2002.05745.x A.R. King et al., ApJ 552, 109 (2001) E. Koerding, H. Falcke, S. Markoff, A&A 382, L13 (2002) A. Kolodzig, M. Gilfanov, R. Sunyaev, S. Sazonov, M. Brusa, A&A 558, A89 (2013). https://doi. org/10.1051/0004-6361/201220880 K. Kouroumpatzakis, A. Zezas, P. Sell, K. Kovlakas, P. Bonfini, S.P. Willner, M.L.N. Ashby et al., MNRAS 494, 5967 (2020). https://doi.org/10.1093/mnras/staa1063 K. Kovlakas, A. Zezas, J.J. Andrews, A. Basu-Zych, T. Fragos, A. Hornschemeier, B. Lehmer et al., MNRAS 498, 4790 (2020). https://doi.org/10.1093/mnras/staa2481 K. Kremer, S. Chatterjee, C.L. Rodriguez, F.A. Rasio, ApJ 852, 29 (2018) P. Kurczynski, E. Gawiser, M. Huynh, R.J. Ivison, E. Treister, I. Smail, G.A. Blanc et al., ApJ 750, 117 (2012). https://doi.org/10.1088/0004-637X/750/2/117 B.D. Lehmer, W.N. Brandt, D.M. Alexander, E.F. Bell, D.H. McIntosh, F.E. Bauer, G. Hasinger et al., ApJ 657, 681 (2007) B. Lehmer et al., ApJ 724, 559 (2010) B.D. Lehmer, M. Berkeley, A. Zezas, D.M. Alexander, A. Basu-Zych, F.E. Bauer, W.N. Brandt et al., ApJ 789, 52 (2014) B.D. Lehmer, A.R. Basu-Zych, S. Mineo, W.N. Brandt, R.T. Eufrasio, T. Fragos, A.E. Hornschemeier et al., ApJ 825, 7 (2016) B.D. Lehmer, R.T. Eufrasio, P. Tzanavaris, A. Basu-Zych, T. Fragos, A. Prestwich, M. Yukita et al., ApJS 243, 3 (2019). https://doi.org/10.3847/1538-4365/ab22a8 B.D. Lehmer, A.P. Ferrell, K. Doore, R.T. Eufrasio, E.B. Monson, D.M. Alexander, A. Basu-Zych et al., ApJS 248, 31 (2020) B.D. Lehmer, R.T. Eufrasio, A. Basu-Zych, K. Doore, T. Fragos, K. Garofali, K. Kovlakas et al., ApJ 907, 17 (2021) W.H.G. Lewin, M. van der Klis, Compact Stellar X-ray Sources (Cambridge University Press, Cambridge, 2006) W.H.G. Lewin, I. van Paradijs, E.P.J. van den Heuvel (ed.), X-ray Binaries (Cambridge University Press, Cambridge, 1995)

117 X-ray Binaries in External Galaxies

4319

T. Linden, V. Kalogera, J.F. Sepinsky, A. Prestwich, A. Zezas, J.S. Gallagher, ApJ 725, 1984 (2010). https://doi.org/10.1088/0004-637X/725/2/1984 K.S. Long, L.P. van Speybroeck, in Accretion-Driven Stellar X-ray Sources (A84-35577 16-90) (Cambridge University Press, Cambridge, 1983a), p. 117 K.S. Long, L.P. van Speybroeck, in Accretion-Driven Stellar X-ray Sources (A84-35577 16-90) (Cambridge University Press, Cambridge, 1983b), p. 141 B. Luo, G. Fabbiano, J. Strader, D.-W. Kim, J.P. Brodie, T. Fragos, J.S. Gallagher et al., ApJS 204, 14 (2013) P. Madau, M. Dickinson, ARA&A 52, 415 (2014) P. Madau, T. Fragos, ApJ 840, 39 (2017) M. Mapelli, M. Colpi, L. Zampieri, MNRAS 395, L71 (2009). https://doi.org/10.1111/j.17453933.2009.00645.x P. Marchant, N. Langer, P. Podsiadlowski, T.M. Tauris, S. de Mink, I. Mandel, T.J. Moriya, A&A 604, A55 (2017). https://doi.org/10.1051/0004-6361/201630188 G. Mellema, L.V.E. Koopmans, F.A. Abdalla, G. Bernardi, B. Ciardi, S. Daiboo, A.G. de Bruyn et al., ExA 36, 235 (2013) J.M. Miller et al., ApJ 585, 37 (2003) S. Mineo, M. Gilfanov, R. Sunyaev, MNRAS 419, 2095 (2012a) S. Mineo, M. Gilfanov, R. Sunyaev, MNRAS 426, 1870 (2012b). https://doi.org/10.1111/j.13652966.2012.21831.x S. Mineo, S. Rappaport, B. Steinhorn, A. Levine, M. Gilfanov, D. Pooley, ApJ 771, 133 (2013). https://doi.org/10.1088/0004-637X/771/2/133 S. Mineo, M. Gilfanov, B.D. Lehmer, G.E. Morrison, R. Sunyaev, MNRAS 437, 1698 (2014a) S. Mineo, G. Fabbiano, R. D’Abrusco, T. Fragos, D.-W. Kim, J. Strader, J.P. Brodie et al., ApJ 780, 132 (2014b) D. Misra, T. Fragos, T.M. Tauris, E. Zapartas, D.R. Aguilera-Dena, A&A 642, A174 (2020). https:// doi.org/10.1051/0004-6361/202038070 C. Norman, A. Ptak, A. Hornschemeier, G. Hasinger, J. Bergeron, A. Comastri, R. Giacconi et al., ApJ 607, 721 (2004). https://doi.org/10.1086/383487 M. Paolillo, T.H. Puzia, P. Goudfrooij, S.E. Zepf, T.J. Maccarone, A. Kundu, G. Fabbiano et al., ApJ 736, 90 (2011) M.B. Peacock, S.E. Zepf, ApJ 818, 33 (2016) M.B. Peacock, S.E. Zepf, T.J. Maccarone, A. Kundu, A.H. Gonzalez, B.D. Lehmer, C. Maraston, ApJ 784, 162 (2014) M.B. Peacock, S.E. Zepf, A. Kundu, T.J. Maccarone, B.D. Lehmer, A.H. Gonzalez, C. Maraston, MNRAS 466, 4021 (2017) D. Pooley, W.H.G. Lewin, S.F. Anderson, H. Baumgardt, A.V. Filippenko, B.M. Gaensler, L. Homer et al., ApJL 591, L131 (2003) S.B. Popov, V.M. Lipunov, M.E. Prokhorov, K.A. Postnov, ARep 42, 29 (1998) K. Postnov, Astron. Lett. 29, 372 (2003) J. Poutanen, G. Lipunova, S. Fabrika, A.G. Butkevich, P. Abolmasov, MNRAS 377, 1187 (2007). https://doi.org/10.1111/j.1365-2966.2007.11668.x P. Predehl et al., A&A 647, A1 (2021). https://doi.org/10.1051/0004-6361/202039313 A.H. Prestwich, M. Tsantaki, A. Zezas, F. Jackson, T.P. Roberts, R. Foltz, T. Linden et al., ApJ 769, 92 (2013). https://doi.org/10.1088/0004-637X/769/2/92 I.G. Prokopenko, M.R. Gilfanov, AstL 35, 294 (2009). https://doi.org/10.1134/ S1063773709050028 A. Ptak, B. Mobasher, A. Hornschemeier, F. Bauer, C. Norman, ApJ 667, 826 (2007) P. Ranalli, A. Comastri, G. Setti, A&A 399, 39 (2003) S.A. Rappaport, P. Podsiadlowski, E. Pfahl, MNRAS 356, 401 (2005). https://doi.org/10.1111/j. 1365-2966.2004.08489.x P. Reig, Ap&SS 332, 1 (2011). https://doi.org/10.1007/s10509-010-0575-8 J. Riley, P. Agrawal, J.W. Barrett, K.N.K. Boyett, F.S. Broekgaarden, D. Chattopadhyay, S.M. Gaebel et al., ApJS 258, 34 (2022). https://doi.org/10.3847/1538-4365/ac416c

4320

M. Gilfanov et al.

A. Sadowski, R. Narayan, MNRAS 456, 3929 (2016). https://doi.org/10.1093/mnras/stv2941 S. Sazonov, I. Khabibullin, MNRAS 466, 1019 (2017). https://doi.org/10.1093/mnras/stw3113 G.R. Sivakoff, A. Jordán, C.L. Sarazin, J.P. Blakeslee, P. Côté, L. Ferrarese, A.M. Juett et al., ApJ 660, 1246 (2007) N.I. Shakura, R.A. Sunyaev, A&A 24, 337 (1973) P. Shtykovskiy, M. Gilfanov, A&A 431, 597 (2005a). https://doi.org/10.1051/0004-6361:20041074 P. Shtykovskiy, M. Gilfanov, MNRAS 362, 879 (2005b). https://doi.org/10.1111/j.1365-2966. 2005.09320.x P.E. Shtykovskiy, M.R. Gilfanov, AstL 33, 299 (2007). https://doi.org/10.1134/S106377370 7050039 P.E. Shtykovskiy, M.R. Gilfanov, AstL 33, 437 (2007). https://doi.org/10.1134/S1063773707 07002X R. Soria, K.K. Ghosh, ApJ 696, 287 (2009). https://doi.org/10.1088/0004-637X/696/1/287 J. Strader, G. Fabbiano, B. Luo, D.-W. Kim, J.P. Brodie, T. Fragos, J.S. Gallagher et al., ApJ 760, 87 (2012). https://doi.org/10.1088/0004-637X/760/1/87 R.A. Sunyaev, B.M. Tinsley, D.L. Meier, ComAp 7, 183 (1978) R. Sunyaev et al., A&A 656, A132 (2021). https://doi.org/10.1051/0004-6361/202141179 D.A. Swartz, R. Soria, A.F. Tennant, M. Yukita, ApJ 741, 49 (2011). https://doi.org/10.1088/0004637X/741/1/49 M. Symeonidis, A. Georgakakis, M.J. Page, J. Bock, M. Bonzini, V. Buat, D. Farrah et al., MNRAS 443, 3728 (2014) E. Szuszkiewicz, M.A. Malkan, M.A. Abramowicz, ApJ 458, 474 (1996). https://doi.org/10.1086/ 176830 R.E. Taam, E.L. Sandquist, ARA&A 38, 113 (2000). https://doi.org/10.1146/annurev.astro.38.1. 113 L. Tao, H. Feng, F. Grisé, P. Kaaret, ApJ 737, 81 (2011). https://doi.org/10.1088/0004-637X/737/ 2/81 T.M. Tauris, E.P.J. van den Heuvel, pbse.book (2023) P. Tzanavaris, I. Georgantopoulos, A&A 480, 663 (2008) P. Tzanavaris, T. Fragos, M. Tremmel, L. Jenkins, A. Zezas, B.D. Lehmer, A. Hornschemeier et al., ApJ 774, 136 (2013). https://doi.org/10.1088/0004-637X/774/2/136 F. Verbunt, E. van den Heuvel, in X-ray Binaries (Cambrdige University Press, Cambridge, 1995), p. 457 L. van Speybroeck, A. Epstein, W. Forman, R. Giacconi, C. Jones, W. Liller, L. Smarr, ApJL 234, L45 (1979). https://doi.org/10.1086/183106 R. Voss, M. Gilfanov, A&A 468, 49 (2007a). https://doi.org/10.1051/0004-6361:20066614 R. Voss, M. Gilfanov, MNRAS 380, 1685 (2007b). https://doi.org/10.1111/j.1365-2966.2007. 12223.x R. Voss, M. Gilfanov, G.R. Sivakoff, R.P. Kraft, A. Jordán, S. Raychaudhury, M. Birkinshaw et al., ApJ 701, 471 (2009) D.J. Walton et al., ApJ 856, 128 (2018) M.C. Weisskopf, H.D. Tananbaum, L.P. Van Speybroeck, S.L. O’Dell, Proc. SPIE 4012, 2 (2000) G. Wiktorowicz, M. Sobolewska, J.-P. Lasota, K. Belczynski, ApJ 846, 17 (2017). https://doi.org/ 10.3847/1538-4357/aa821d A. Wolter, G. Trinchieri, A&A 426, 787 (2004). https://doi.org/10.1051/0004-6361:20047110 A. Zezas, G. Fabbiano, ApJ 577, 726 (2002). https://doi.org/10.1086/342135 A. Zezas, L. Hernquist, G. Fabbiano, J. Miller, ApJL 599, L73 (2003) A. Zezas, G. Fabbiano, A. Baldi, F. Schweizer, A.R. King, A.H. Rots, T.J. Ponman, ApJ 661, 135 (2007). https://doi.org/10.1086/513091 W. Zhang, S. Woosley, A. Heger, ApJ 679, 639 (2008) Z. Zhang, M. Gilfanov, R. Voss, G.R. Sivakoff, R.P. Kraft, N.J. Brassington, A. Kundu et al., A&A 533, A33 (2011) Z. Zhang, M. Gilfanov, A. Bogdan, A&A 546, 36 (2012) Z. Zhang, M. Gilfanov, Á. Bogdán, A&A 556, A9 (2013)

The Hot Interstellar Medium

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Emanuele Nardini, Dong-Woo Kim, and Silvia Pellegrini

Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Hot ISM of Star-Forming Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Shock Heating and Diffuse X-Ray Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theory and Observations of Superwinds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chemical and Physical Evolution of the Hot ISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Starbursts in Galaxy Mergers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . An Ideal Laboratory: NGC 6240 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Observational Properties of the Hot ISM in Early-Type Galaxies . . . . . . . . . . . . . . . . . . . . . From Discovery with the Einstein Observatory to Chandra and XMM-Newton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Global Properties of the Hot ISM: Scaling Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Mass of ETGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1D Radial Profiles of the X-Ray Surface Brightness and Temperature Distributions . . . . Radial Distributions of Fe Abundance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Entropy Profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2D Spatial Distributions of X-Ray Surface Brightness and Gas Temperature . . . . . . . . . . Origin and Evolution of the Hot ISM in Early-Type Galaxies . . . . . . . . . . . . . . . . . . . . . . . . Origin of the Hot ISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Relative Importance and Evolution of the Mass Sources . . . . . . . . . . . . . . . . . . . . . . . . . . Heating of the Mass Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Injection Temperatures and Observed Temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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E. Nardini () INAF – Arcetri Astrophysical Observatory, Firenze, Italy e-mail: [email protected] D.-W. Kim () Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA e-mail: [email protected] S. Pellegrini () Department of Physics and Astronomy, University of Bologna, Bologna, Italy e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_109

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Cooling and Evolution of the Hot ISM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Mass Deposition Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . AGN Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Various Forms and Effects of the SMBH Accretion Output . . . . . . . . . . . . . . . . . . . . Modeling of the Hot ISM: The Simplest Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Complex Lifetime of Hot Gas in ETGs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Global Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Two More Actors: Environment and AGN Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

The interstellar medium (ISM) of galaxies very often contains a gas component that reaches the temperature of several million degrees, whose physical and chemical properties can be investigated through imaging and spectroscopy in the X-rays. We review the current knowledge on the origin and retention of the hot ISM in star-forming and early-type galaxies, from a combined theoretical and observational standpoint. As a complex interplay between gravitational processes, environmental effects, and feedback mechanisms contributes to its physical conditions, the hot ISM represents a key diagnostic of the evolution of galaxies. Keywords

X-rays: ISM · X-rays: galaxies · ISM: evolution · Galaxies: ISM · Galaxies: halos · Galaxies: starburst · Galaxies: elliptical and lenticular · cD · Galaxies: evolution

Introduction One of the most surprising discoveries that came with the first images of galaxies in the X-ray band was the ubiquitous presence of diffuse emission, suggesting that a substantial fraction of the interstellar medium (ISM) is heated to temperatures of ∼106 –107 K, regardless of the galaxy type. A compelling question immediately emerged: what is the physical origin of this hot gas? At first, the solution did not appear to be straightforward, as no obvious source of energy input into the ISM (e.g., from fierce star formation or an active galactic nucleus, AGN) was systematically involved, especially in largely passive objects like early-type galaxies. We now know that the processes responsible for the creation and subsequent maintenance of the hot ISM are manifold and that their relative importance widely varies with the different galaxy classes. In star-forming galaxies, the luminosity of the hot ISM is proportional to the rate at which stars are assembled. The energy released by young, massive stars, while they age and when they finally explode as supernovae (SNe), can easily prevail over

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gravity and drive the expansion of a hot, high-pressure bubble into the cold ISM, which is shock heated and swept up. The resulting large-scale wind also functions as a carrier of the heavy elements synthesized in the stellar nurseries and as a feedback force whose activity can explain several properties of the global galaxy population. In early-type systems, instead, the hot ISM evolves under the effect of the gravitational field of the host galaxy and dark matter, of various forms of mass exchange with the galaxy and its environment (as provided by stellar evolution input, gas accretion from the circumgalactic medium, and mass deposition via cooling), and of major energy sources and radiative losses. Heating is provided by SN explosions, thermalization of the random and ordered kinetic energy of the stellar motions, and accretion onto the central supermassive black hole (SMBH) followed by a number of possible forms of energy injection. As star-forming and early-type galaxies can be thought of as the opposite ends of the same evolutionary sequence, linked through mergers in a hierarchical scenario, the overview we provide here practically covers the full life cycle of the hot ISM. This chapter is organized as follows. Section “The Hot ISM of Star-Forming Galaxies” is dedicated to star-forming galaxies and illustrates the connection between the hot ISM and the mass and energy deposited by core-collapse SNe. We describe the consequences of feedback from starburst-driven winds and their crucial role in the chemical enrichment of galaxy halos and intergalactic medium. Section “Observational Properties of the Hot ISM in Early-Type Galaxies” deals with the main properties of the hot ISM that can be derived from the X-ray observations of early-type galaxies. We discuss how the scaling relations between the various physical quantities and their spatial distributions compare with the predictions of theoretical models. Section “Origin and Evolution of the Hot ISM in Early-Type Galaxies” examines the origin of the hot gas in early-type galaxies, its heating sources, dynamical status, and relationship with the galactic properties. We outline a global picture of the hot gas origin and evolution in these galaxies, which takes into account the constraints from X-ray observations. Section “Future Prospects” briefly summarizes the future prospects of this research field.

The Hot ISM of Star-Forming Galaxies The birth, evolution, and death of stars constitute a key process in the lifetime of a galaxy, which eventually returns energy—in the form of radiation and winds—and metals to the ISM. The basic requirements for star formation are the availability of an ample reservoir of cold, dense gas and the existence of internal and/or external agents to prompt its gravitational collapse. Both conditions are usually met in latetype (spiral), dwarf/irregular, and interacting galaxies. The impact of star formation on the host environment is mostly dramatic during the so-called “starburst” phases. In a starburst galaxy (after Weedman et al. 1981), star formation is currently much

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more intense than in the past, as revealed by the fact that the ratio between stellar mass (M⋆ ) and star formation rate (SFR) is significantly smaller than the Hubble time (note that the most commonly used quantity is actually the reciprocal ratio SFR/M⋆ , which is named “specific star formation rate”, sSFR). In turn, this implies that the ongoing star formation episode must be short-lived (hence the notion of a burst), as it cannot be sustained over a long period without consuming the gas supply of the whole galaxy. Our own galaxy, the Milky Way, has a SFR of ≈2 M⊙ yr−1 (see Chomiuk and Povich 2011 and references therein), and the total atomic plus molecular gas mass in the disk plane within a galactocentric radius of 13.5 kpc is MGAS ≃ 6.6×109 M⊙ (Kennicutt and Evans 2012). Consequently, the gas depletion timescale (tdep = MGAS /SFR) is of the order of a few Gyr, qualifying the Milky Way as a “normal” star-forming galaxy. By contrast, the star formation efficiency (= 1/tdep ) of our largest companion in the Local Group, the Andromeda Galaxy (M 31), is remarkably lower (SFR ∼ 0.3 M⊙ yr−1 ; Tabatabaei and Berkhuijsen 2010), more similar to the quiescent, early-type galaxies (ETGs) that are discussed in the second part of this chapter. The presence of X-ray bubbles in the halo of the Milky Way (Predehl et al. 2020) proves beyond doubt that even in normal galaxies the hot ISM keeps a record of any past activity. Hence, without loss of generality, in this section, we will focus on galaxies that are now actively star forming, i.e., those in which star formation has been significantly enhanced by some recent form of instability or perturbation. These objects typically emit most of their luminosity in the infrared, as the light of newly formed stars is almost entirely reprocessed by dust.

Shock Heating and Diffuse X-Ray Emission The terminal stages of stellar evolution are characterized by violent, high-energy events that naturally lead to copious X-ray emission. Several different mechanisms can contribute to the X-ray spectrum of a starburst galaxy (see Persic and Rephaeli 2002 for a concise review), including accretion onto a compact object in highand low-mass X-ray binaries, shock heating and synchrotron radiation from young supernova remnants, and boosted Compton up-scattering of infrared photons by ambient relativistic electrons. Diffuse, thermal X-ray emission is also expected due to the combined shock-heating capacity of stellar winds (e.g., from Wolf-Rayet stars) and SN explosions. In the limit of strong, adiabatic shocks, the relation between shock velocity (vsh ) and post-shock temperature (Tsh ) is given by the following: 2 kTsh ≃ 3μmp vsh /16,

(1)

where k is Boltzmann’s constant, μ the mean molecular weight, and mp the proton mass. For μ ≃ 0.6, as per fully ionized gas with solar abundances, and vsh ≈

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1,000 km s−1 (section “Theory and Observations of Superwinds”), the ISM can be heated to temperatures of the order of ∼1 keV. In general, all of the above components have comparable weights, making it difficult to spectrally disentangle them when spatially mixed, in spite of their different shapes. The advent of sub-arcsecond resolution with the Chandra X-ray observatory (Weisskopf et al. 2002) eventually allowed astronomers to identify all the point sources in nearby galaxies down to luminosities of LX ≈ 1037 erg s−1 (see, for instance, the census of discrete X-ray sources in NGC 4278 by Brassington et al. 2009). The possibility of removing this contamination to the diffuse X-ray emission represented a huge leap forward in the study of the physical properties of the hot ISM. The existence of extended X-ray emission with complex morphological features in star-forming galaxies had been known since the Einstein mission (Giacconi et al. 1979), the first X-ray telescope with full imaging capabilities. In particular, the observation of M 82 (the Cigar Galaxy, at D ∼ 3.6 Mpc of distance) unveiled a patchy halo extending for several kpc along the minor axis of the highly inclined galactic plane, above and below the nuclear region (Watson et al. 1984). Intense, diffuse emission was also detected in the disk, closely matching the optical nucleus. The peculiar morphology of the X-ray halo, whose base coincides with the nuclear starburst, and the tight spatial correlation with the Hα filaments in the optical halo supported the notion that the hot gas was in an outflow state. Similar conclusions were drawn for NGC 253 (the Sculptor Galaxy, D ∼ 3.5 Mpc), whose Einstein image emphasized a plume-like structure protruding southward from the nucleus along the minor axis of the disk (Fabbiano and Trinchieri 1984). The remarkable overlap between extra-planar soft X-ray and optical (Hα) emission is now known to be a distinctive attribute of edge-on, star-forming galaxies in the local universe. This turned out to be instrumental in establishing the connection of the diffuse X-ray emission to the starburst wind phenomenon. In fact, while the X-ray study of the hot ISM was still in a pioneering phase, extensive imaging and spectroscopic observations in the optical had already provided a large body of evidence in favor of the wind model (Lehnert and Heckman 1996), taking advantage of the higher sensitivity and much finer spatial and spectral resolution, which allowed a superior grasp on the morphological, dynamical, and physical properties of the gas. The merits of a multiwavelength perspective for achieving a comprehensive picture of the physics involved are illustrated in Fig. 1, which displays the composite image of M 82 as obtained by the Hubble (optical), Spitzer (infrared), and Chandra (X-ray) space observatories. In this framework, the spatial coincidence between soft X-ray and Hα emission does not follow from the cooling of the hot, fast wind but from its interaction with the inhomogeneous ISM in the galaxy halo (e.g., Lehnert et al. 1999; Strickland et al. 2002). When the wind impinges on a cold, dense cloud, the slow, forward shock propagating into the cloud can heat the gas to temperatures T ∼ 104 K, leading to Hα emission via recombination, whereas the fast, reverse shock into the wind would simultaneously produce the X-rays (Equation 1). This is better understood by revisiting the basic physics of starburst winds.

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Fig. 1 Multiwavelength image of the starburst galaxy M 82, obtained by combining the data from Chandra (blue, hot gas), Hubble (green, starlight; orange, Hα), and Spitzer (red, cold gas and dust). While the optical semblance is that of a normal spiral galaxy, the broadband view immediately conveys the impression of a tremendous explosion taking place in the nuclear region. The ensuing wind is a complex, multiphase medium, as evinced by the coexistence between million-K gas and cold dust grains. (Credits: NASA/CXC/JHU/D. Strickland (X-ray), NASA/ESA/STScI/AURA/The Hubble Heritage Team (optical), NASA/JPL–Caltech/Univ. of AZ/C. Engelbracht (infrared))

Theory and Observations of Superwinds Massive stars and SNe can power galaxy-wide outflows, informally known as “superwinds,” when the kinetic energy of their ejecta is efficiently thermalized. The simplest analytical treatment of a superwind assumes spherical symmetry and neglects gravity, radiative cooling, and ambient gas (Chevalier and Clegg 1985). The starburst is described as a central region of radius RSB with constant mass (M˙ SB ) and energy (E˙ SB ) injection rates. Before discussing the solutions of the hydrodynamical equations for this “free-flowing” wind, it is useful to derive order-of-magnitude estimates for both M˙ SB and E˙ SB . Considering only core-collapse SNe, which are the most relevant to a starburst phase (section “Chemical and Physical Evolution of the Hot ISM”), the standard values of the mass and energy deposited by a single SN are 10 M⊙ and 1051 erg, respectively, while the scaling between SN rate and −1 SFR is ∼0.01 M⊙ . Hence, the characteristic mass and energy injection rates are as follows:

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M˙ SB ≈ 6.3 × 1024 (SFR/M⊙ yr−1 )

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g s−1 ,

(2)

erg s−1 .

(3)

and E˙ SB ≈ 3.2 × 1041 (SFR/M⊙ yr−1 )

These numerical expressions will be used in the remainder of this section. In the free-wind model, the kinetic energy of the colliding SN ejecta and stellar winds is thermalized via shocks. Radiative losses are indeed negligible, given the high temperatures and low densities involved. The complete solution to the flow equations (a detailed analytical derivation of the solution, applied to dense clusters of massive stars, can be found in Cantó et al. 2000) implies a central (r ≪ RSB ) temperature of the order of ∼108 K: kTSB = 0.4μmp (E˙ SB /M˙ SB ).

(4)

The central density of this hot gas is given by the following: 3/2 −1/2 −2 , ρSB ≃ 0.3 M˙ SB E˙ SB RSB

(5)

which, for RSB = 200 pc (as originally tailored to M 82), corresponds to a number density nSB ∼ 0.02 (SFR/M⊙ yr−1 ) cm−3 . The high-pressure (PSB ∼ 2nSB kTSB > 10−9 dyn cm−2 ), hot bubble expands adiabatically into the surrounding ISM, becoming supersonic at r = RSB . At larger distance (r ≫ RSB ), the wind temperature and density decline, respectively, as ∝ r −4/3 and ∝ r −2 . The velocity rapidly converges to the terminal value, which can be recovered by imposing the equality of energy injection rate and asymptotic kinetic energy flux: vwind = (2E˙ SB /M˙ SB )1/2 ,

(6)

that is, ≈3,000 km s−1 . As the typical escape velocity (vesc ) from spirals is around 500 km s−1 , neglecting gravity is then confirmed to be a fair working assumption. In a more realistic case (see Veilleux et al. 2005; Zhang 2018), one must include a thermalization efficiency (ξ ) and a mass-loading factor (β): the former accounts for radiative losses within the starburst region, while the latter allows for the amplification of the intrinsic mass injection rate due to the evaporation of cold ISM clouds (Suchkov et al. 1996). Intuitively, if ξ < 1 and/or β > 1, the wind is slowed down. The terminal velocity of the wind in Equation 6 should therefore be corrected by a (ξ/β)1/2 term. The thermalization efficiency is always expected to be rather high. Different hydrodynamical models of the superwind in M 82 comply with the observational constraints for ξ ≥ 0.3 (Strickland and Heckman 2009). This is empirically corroborated by the relation between intrinsic bolometric luminosity of the hot ISM and SFR obtained for a sample of 21 star-forming galaxies by Mineo et al. (2012), Lbol /SFR ∼ 1.5 × 1040 erg s−1 (M⊙ yr−1 )−1 , weighing the degree

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of radiative losses (cf. Equation 3). Mass loading can instead be considerable (up to β ∼ 10; Zhang et al. 2014), so that the velocity of real winds rarely exceeds ∼1,000 km s−1 . Although the surface brightness profile of the X-ray halo in M 82 was suggested to be consistent with a free wind (Fabbiano 1988), the presumed emissivity (which goes like ∝ n2 ) is thought to be too low for the observed X-rays to be directly emitted from the hot wind itself. Measuring the density of the hot, X-ray-emitting gas is not a trivial task. In the most popular spectral models of X-ray plasmas, the density is encapsulated in a quantity called “emission measure,” defined as  EM = ne nH dV ∼ n2e ηV , where ne and nH are the number densities of electrons and hydrogen ions, V is the geometrical volume occupied by the gas, and η is the (unknown) filling factor. Numerical models suggest that the hot (T ∼ 107 K) phase, which can be identified with the free wind, is volume filling, but it barely contributes to the observed X-ray emission because of its low density (ne ∼ 0.01 cm−3 ; Strickland and Stevens 2000). Only within the starburst region, where densities are higher (Equation 5), such a component becomes detectable (Strickland and Heckman 2007). Most of the soft X-ray emission from superwinds is predicted to originate from gas with higher density and much lower filling factor, in agreement with the “shocked-cloud” scenario. The uncertainty on η, however, heavily affects several key properties of the hot ISM that can be extracted from the X-ray spectra (e.g., gas mass, pressure, thermal energy).

Chemical and Physical Evolution of the Hot ISM The soft X-ray emission from starburst winds is typically consistent with one to three thermal components with temperatures in the range ∼0.2–0.7 keV, which mimic a likely more complex temperature distribution. The X-ray spectrum of an optically thin, hot plasma with kT ∼ 105 –107 K consists of a multitude of emission lines (Fig. 2), which arise from atomic transitions in collisionally excited ions and represent the most efficient channel of radiative cooling. The continuum, produced by free-free (bremsstrahlung) and free-bound (recombination) transitions, only dominates at low metallicities and high temperatures (Boehringer and Hensler 1989). The X-ray spectrum of the hot ISM thus provides information not only on the gas temperature and density, which, respectively, govern spectral shape and overall luminosity, but also on metallicity, through the strength of the main emission lines. Figure 2 shows the high-resolution X-ray spectra of NGC 253 obtained at different positions along the wind. All the most abundant elements usually accessible in the soft X-rays are present: oxygen, neon, magnesium, silicon (collectively referred to as α-elements, since they are produced in the nuclear reaction sequence known as “alpha process”), and iron. As the emission lines of interest are affected by intrinsic blending and/or instrumental broadening (which becomes severe at CCD resolution), an accurate determination of the underlying continuum is mandatory for a reliable evaluation of metal abundances. This, is turn, requires a correct physical interpretation of the whole spectrum. It has been argued that integrating the emission from regions with inhomogeneous properties, owing to, for instance, temperature gradients, delivers meaningless abundance values. Such limitation plagued most of

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Fig. 2 High-resolution, soft X-ray spectra of the hot ISM in NGC 253, obtained from different regions along the minor axis with the Reflection Grating Spectrometer (RGS) on board XMMNewton. The parameter “z” indicates the projected angular distance from the galaxy center (the physical scale is ∼1 kpc/arcmin). Note the progressive drop in emissivity moving away from the nuclear, denser region. The inherently photon-starving nature of grating spectroscopy makes these data absolutely unique: with the current facilities, such a quality can only be obtained for NGC 253 and M 82 (original figure from Bauer et al. 2007, reproduced with permission from Astronomy & Astrophysics, © ESO)

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the early enrichment studies, until Chandra enabled a spatially resolved investigation of the hot ISM properties (see, for instance, the analysis of local abundances in NGC 4038/4039, the Antennae Galaxies, by Baldi et al. 2006a, b). In general, however, high-quality data and adequate spectral and spatial resolution are needed to safely derive elemental abundances through X-ray spectroscopy. With these caveats in minds, the measurement of abundances and of their ratios can be directly related to the type of SNe that control the hot ISM enrichment. This is a consequence of the markedly different delay time distribution and chemical yields of thermonuclear (type Ia) and core-collapse (type II, Ib/c) SNe (e.g., Maoz and Graur 2017). The time delay distribution reflects the interval between the explosion of a given SN and the onset of the parent star formation event. As the lifetime of stars with initial mass 8 M⊙ is at most a few tens of Myr, virtually all core-collapse SNe will explode while the starburst episode is still in progress, so dominating the release and dispersal of metals on short timescales. Conversely, type Ia SNe occur on average at much later times, following the evolution of the companion of the white dwarf. The delay time distribution thus depends on the shape of the initial mass function (IMF, namely, the initial distribution of masses of a stellar population) and so do the various SN yields. Iron is almost equally produced by type Ia and corecollapse SNe, as the former have roughly a ten times larger yield (0.7 vs. 0.07 M⊙ of Fe per SN) but proportionally smaller rates (10−3 vs. 10−2 SNe per M⊙ of stellar mass formed). The bulk of α-elements is instead synthesized by core-collapse SNe. Accordingly, the α to Fe abundance ratios in the hot ISM of starburst galaxies are expected to be supersolar or, in the standard notation, [α/Fe] > 0 (where the brackets indicate that the scale is logarithmic and normalized to solar units). The value of [O/Fe] in the halo of edge-on, star-forming disk galaxies is indeed ∼0.4 (Strickland et al. 2004), although iron can be partly depleted onto the dust grains carried by the wind (see Fig. 1). Likewise, Grimes et al. (2005) found [α/Fe] ∼ 0.5, independent on SFR over four orders of magnitude in X-ray luminosity, in a sample that also included dwarf starbursts and ultraluminous infrared galaxies. Superwinds are not only relevant to the chemical evolution of galaxy halos. As the outflow and/or thermal velocity of the hot gas can exceed the escape velocity of the system, a non-negligible fraction of the metals produced by the starburst will contribute to the enrichment of the intergalactic medium (IGM). Such an efficient means of mass transport is required, for instance, by the metallicity of the intracluster medium (ICM), which already contained as much iron as the cluster galaxies several Gyr ago and even at redshift z ∼ 2 is far from being primordial in composition (e.g., Mantz et al. 2018). The maximum mass that can be lost to the IGM through a superwind can be derived from Equation 3 by assuming a constant SFR for 107 yr (see Heckman et al. 1990): Mesc < 4 × 107 (SFR/M⊙ yr−1 ) (vesc /500 km s−1 )−2

M⊙ .

(7)

In the most extreme cases, the entire hot ISM can be blown out of the galaxy. Unsurprisingly, Equation 7 also entails that the starburst-processed, superwind material is more likely to remain gravitationally bound in more massive galaxies

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(where the escape velocity is higher). This is a natural starting point toward the understanding of the so-called mass-metallicity relation (Tremonti et al. 2004), i.e., the tight correlation between stellar mass and gas-phase metallicity (as probed by the abundance of oxygen relative to hydrogen) observed in star-forming galaxies. An even more obvious consequence of superwinds is the self-limiting effect on the starburst activity. Once the original gas reservoir has been exhausted and any potential replenishment prevented (by either mechanical removal or radiative heating), star formation will rapidly subside. This negative feedback is a critical ingredient in the interpretation of the galaxy luminosity function (Benson et al. 2003) and bimodality (Strateva et al. 2001). The baryonic content of galaxies is well below the cosmological value (i.e., ∼1/6 of the dark matter content) at all masses. Feedback is a suitable solution to the “missing baryons” problem (Cen and Ostriker 2006), although in high-mass systems also an AGN contribution must be invoked (see Equation 7). Bimodality arises from the peculiar distribution of the main galaxy properties, such as color, morphology, and SFR. Most galaxies fall in two distinct classes: blue, late-type, star forming, against red, early-type, passive. Again, feedback can explain the relation between galaxy color and SFR, but an additional evolutionary step must be involved to also account for the different morphologies: galaxy mergers.

Starbursts in Galaxy Mergers As mentioned above, the highest levels of star formation or, equivalently, the shortest gas depletion times are typically found in interacting systems. Most of the prototypical starbursts in the local universe belong to galaxy groups and are subject to dynamical and gravitational perturbations. This is also the case for both M 82 (Yun et al. 1994) and NGC 253 (Davidge 2010). Close interactions and mergers coincide with the most dramatic and transformational phases in the evolution of galaxies. Numerical simulations show that the tidal forces at work in a major merger between two gas-rich spirals cause a global redistribution of the cold gas, which loses angular momentum and funnels down through the potential well, so powering star formation at starburst rates and possibly SMBH accretion (Mihos and Hernquist 1996). The end product of this process is believed to be a massive, quiescent elliptical on both theoretical and observational grounds (Hopkins et al. 2006; Dasyra et al. 2006). Simulations of galaxy mergers also suggest that the shocks associated with the collision can produce significant amounts of X-ray-emitting gas, whose temperature and luminosity strongly depend on the properties of the progenitors (mass, gas fraction, metallicity) and on the orbital parameters of the collision (relative orientation, angular momentum). A different time evolution is predicted based on whether galactic disks or halos are considered, whereby the peak X-ray luminosity is reached at the final coalescence or the first perigalactic passage, respectively (Cox et al. 2006; Sinha and Holley-Bockelmann 2009). However, none of these models properly include the role of starburst-driven shocks, which are actually responsible

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for the dominant heating effects. In fact, the observations of equal mass galaxy pairs caught at different epochs along the merger sequence indicate that the ratio between thermal X-ray luminosity of the hot ISM and SFR is nearly constant (with an rms scatter of ≈0.3 dex; Smith et al. 2018) irrespective of the merger stage, at the following value: LX,GAS /SFR ∼ 5.5 × 1039 erg s−1 (M⊙ yr−1 )−1 .

(8)

This implies that (i) the mechanical energy of starburst winds is converted into Xray radiation with a typical efficiency of a few percent (cf. Equation 3) and (ii) the diffuse X-ray emission must trace, almost instantaneously, the star formation history during the merger. It should be noted that merger-induced SMBH accretion is a competitive mechanism to heat and disperse the gas. For an AGN with bolometric luminosity Lbol ∼ 1045 erg s−1 and a coupling efficiency between radiation field and ISM of ≈1%, the energy input is commensurate with that from the starburst and capable of initiating a large-scale feedback process (e.g., Hopkins and Elvis 2010). Yet, the actual AGN contribution is expected to be minor until after the coalescence, as models and observations confirm that nuclear activity is heavily obscured at earlier times. Eventually, accretion becomes very efficient (i.e., Eddington-limited), the black hole quickly gains mass, and the resulting feedback regulates its further growth and quenches the global star formation by removing the gas supply from the inner regions (Springel et al. 2005; Hopkins et al. 2005). The presence of a powerful AGN and its complex interplay with the starburst therefore determine how rapidly the X-ray luminosity fades and how much of the hot gas remains bound to the system after the merger (see also section “Two More Actors: Environment and AGN Feedback”).

An Ideal Laboratory: NGC 6240 Deep X-ray observations of galaxy mergers are rather scarce, but they invariably reveal a wealth of details. One of the most spectacular examples is represented by NGC 6240 (D ∼ 107 Mpc), an IR-luminous, morphologically disturbed galaxy pair on its way to entering the final coalescence stage (see Nardini et al. 2013 and references therein). As NGC 6240 typifies in a single object the broad phenomenology of galaxy mergers and it can be regarded as an ideal test bed for the predictions of numerical models, it is worth discussing its properties at some length for illustrative purposes. The central kpc of NGC 6240 harbors two AGNs, still buried inside the remnants of the former galactic bulges, and ∼1010 M⊙ of molecular gas, ruffled by turbulence, shocks, and outflows. A ∼10-kpc wide, butterfly-shaped nebula, characterized by clumps, loops, and filaments seen in both soft X-rays (Fig. 3, blowup) and Hα, is the telltale signature of the action of superwinds, driven by a nuclear starburst that forms several tens of M⊙ yr−1 . The entire system is surrounded by a

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Fig. 3 Soft X-ray (0.5–1.5 keV) image of NGC 6240, obtained by coadding 182 ks of Chandra exposures. The 100-kpc wide field of view is almost entirely filled by the hot halo, which presents several substructures consistent with widespread superwind activity. The zoom-in on the right highlights the complex morphology of the central, butterfly-shaped nebula, powered by the most recent starburst episode. Both images were background-subtracted and adaptively smoothed with Gaussian kernels. The dynamic range of the color bar is 1,200 for the halo and 2,400 for the nebula, respectively, and the scale is logarithmic. (Adapted from Nardini et al. 2013)

huge halo of hot (∼0.65 keV, or 7.5 million K) gas, with an average radial extent of Rhalo ∼ 50 kpc, which accounts for about one third of the total diffuse X-ray emission (Fig. 3). Its luminosity exceeds 4 × 1041 erg s−1 and is more typical of galaxy groups (Mulchaey 2000) and massive ellipticals (Mathews and Brighenti 2003). Interestingly, the possible fossil group nature of NGC 6240 is supported by the recent discovery of a third nucleus in the previously unresolved southern component (Kollatschny et al. 2020), while the ultimate fate of the merger is anticipated by its stellar surface brightness, which is already conforming to the ∝ r 1/4 radial profile characteristic of spheroids (Bush et al. 2008). It can be easily demonstrated that the inelastic nature of the collision is not sufficient in itself to account for the thermal energy content of the halo. For simplicity, let two identical progenitors collide head-on with relative speed vcoll . The 2 /8, where kinetic energy dissipated in the merger is then approximately MX,GAS vcoll MX,GAS = ne ηV mp is the total mass of X-ray-emitting gas. As the thermal energy of the halo is Eth = 3ne ηV kT , it immediately follows that a collision velocity of vcoll ∼ 1,200 km s−1 is required to heat the gas up to kT ≃ 0.65 keV, far too high for any known galaxy merger. Also gravitational confinement, which is an important heating source for the halos of virialized systems (sections “The Mass of ETGs” and “Two More Actors: Environment and AGN Feedback”), does not seem

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a viable explanation for NGC 6240. Indeed, by using the gas velocity dispersion σ  as an equivalent probe of the depth of the potential well (note, however, that this strictly applies only for systems in hydrostatic equilibrium; see section “Injection Temperatures and Observed Temperatures”)., one gets a virial temperature kTVIR ∼ μmp σ 2 of only ∼0.25 keV for the average value of σ  ∼ 200 km s−1 found in the core (Treister et al. 2020). It is rather straightforward to ascribe the gas heating to starburst-driven winds instead. The kinetic luminosity of a starburst, i.e., the mechanical energy injected into the ISM per unit time (∼ ξ E˙ SB ; Equation 3), is roughly 1% of its bolometric luminosity (Leitherer et al. 1999). This is Lkin ∼ 3 × 1043 erg s−1 in NGC 6240, to be compared to the thermal energy of the halo, Eth ≃ 5 × 1058 η1/2 erg. Hence, it takes less than 50 Myr for the starburst to supply the required energy, as opposed to a dynamical age of the halo, 2Rhalo /cs (where cs is the adiabatic sound speed), of over 200 Myr. Given the halo size, however, a wind from a centrally localized starburst should have traveled at vwind  1,000 km s−1 , which is unlikely for dense environments like the nuclear regions of galaxy mergers (where β ≫ 1). Also, the mild decline with radius of the X-ray surface brightness is not compatible with a free-flowing wind. It seems then plausible that the hot halo stems from the superposition of successive winds, emanating from different locations and escaping in different directions over the last 50–200 Myr. As the physical properties of the halo do not seem to vary significantly with either radius or position angle, in keeping with the proposed “widespread wind” scenario, the single-temperature, kT ≃ 0.65 keV model provides a reasonable first approximation of the basic properties of the hot gas. This notwithstanding, the spectrum of the full halo is best described by two gas phases with different temperatures and metallicities: a “hot, metal-rich” component, with kT ∼ 0.8 keV, Zα consistent with (or slightly below) solar, and [α/Fe] ≈ 0.6, and a “warm, metalpoor” component, with kT ∼ 0.25 keV and Z ∼ 0.1 Z⊙ . It is therefore tempting to identify the hot phase with the chemically evolved, starburst-injected gas, which is dispersing into a pristine, preexisting ambient medium, heated itself to X-rayemitting temperatures by gravitational infall and/or merger-related dissipation (see above). As a matter of fact, this might still be an oversimplification, but the current data do not allow any more exhaustive analysis. To date, only a handful of X-ray observations exist with comparable quality to that of NGC 6240. Once some obvious differences (e.g., mass and gas fraction of the progenitors, merger stage) are considered, the general picture drawn from the case study of NGC 6240—widespread starburst winds and redistribution of metals across the halo—is broadly confirmed (Veilleux et al. 2014; Liu et al. 2019). This holds true even after moving to relatively larger samples, at the cost of shallower exposures. Most of the advanced mergers exhibit diffuse X-ray emission beyond a distance of 10 kpc (Huo et al. 2004). The metallicity of the gas in these extended halos is tentatively constrained to be significantly subsolar (Z ≈ 0.1 Z⊙ ), as if there had not yet been any pollution from the central starbursts. This is not unexpected, as mass loading is much more severe in mergers than in M 82-like objects, and this can substantially slow down the wind. More reliable measurements of both temperature

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and metallicity out the largest possible scales are needed to understand whether this pristine gas already belonged to the colliding galaxies or is accreted from the IGM and how much of the hot ISM will be retained to form the halo of a young elliptical galaxy once the merger is over.

Observational Properties of the Hot ISM in Early-Type Galaxies The hot ISM is the dominant phase of the ISM in early-type galaxies (ETGs). Its physical and chemical properties are shaped by the processes occurring during the formation and evolution of the host galaxy. By measuring the current status of the hot ISM, we can then infer how critical astrophysical processes worked throughout the galaxy’s history. These processes include AGN feedback, environmental effects (e.g., merger, accretion, and stripping), and star formation and its quenching (e.g., Kim and Pellegrini 2012 and references therein; see also section “The Hot ISM of Star-Forming Galaxies”). With state-of-art X-ray observations, we can measure the physical and chemical properties of the hot ISM. These measurements put constraints on the global ISM properties, such as X-ray luminosity (LX,GAS ), temperature (TX ), and also chemical abundances (primarily Fe; section “Chemical and Physical Evolution of the Hot ISM”). We can also study the spatial distributions of these properties and of the physical parameters that we can derive from them: density, entropy, pressure, mass of the hot ISM, and total galaxy mass. The observational constraints on these quantities can then be compared with theoretical predictions. In this section, we will describe what we have learned from the X-ray observations of hot ISM in ETGs.

From Discovery with the Einstein Observatory to Chandra and XMM-Newton Since the launch of the Einstein Observatory in 1978, X-ray bright, giant ETGs have been known to host large amounts of hot gas (e.g., Forman et al. 1985; Trinchieri and Fabbiano 1985). Early studies could only measure the integrated X-ray luminosity and temperature of ETGs (LX,TOT , and TTOT ), and these measurements were used to constrain the properties of the hot ISM (see the review by Fabbiano 1989). However, the X-ray emission is coming not only from the X-ray-emitting, hot gas but also from X-ray binaries—mostly low-mass X-ray binaries (LMXBs) in the old stellar populations of ETGs (Trinchieri and Fabbiano 1985). Moreover, active nuclei within the galaxy may also contribute to the X-ray emission, and the X-ray emission of background galaxies and AGNs may contaminate the data. While LX,TOT is close to LX,GAS in gas-rich, X-ray luminous ETGs, there are also gas-poor, X-ray faint ETGs where LX,TOT may be dominated by LMXBs (Trinchieri and Fabbiano 1985). Some ETGs may also host an AGN. Launched in 1999, the Chandra X-ray Observatory, with its sub-arcsecond spatial resolution, has revolutionized our understanding of the X-ray emission of ETGs.

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Typical Chandra observations of ETGs at distances of 10–20 Mpc, with an exposure of several hours, can detect some 100 point-like sources in an individual galaxy (e.g., NGC 1399, Angelini et al. 2001; NGC 4365 and NGC 4382, Sivakoff et al. 2003; see also Kim and Fabbiano 2004a and the review by Fabbiano 2006). These observations have led to a good characterization of the X-ray luminosity functions of LMXBs in different environments, e.g., in the field versus globular clusters (GCs), metal-rich versus metal-poor systems, and young versus old stellar populations (e.g., Fig. 4 in Kim and Fabbiano 2010 and references therein). The capability of detecting individual point sources is also valuable to exclude contaminating sources for accurate measurements of the hot gas properties. Thanks to Chandra, we can, for the first time, effectively separate the different X-ray emission components of ETGs and accurately measure the properties of the hot gas, LX,GAS and TX (e.g., Boroson et al. 2011; Kim et al. 2019b). With its large field of view and higher sensitivity, XMM-Newton, also launched in 1999, provides complementary observational data. XMM-Newton data are particularly useful in studying the faint diffuse emission in the outskirts of ETGs and in measuring chemical properties (e.g., Fe abundance) that often require high S/N ratio spectra (e.g., Islam et al. 2021).

Fig. 4 Comparison of the LX,GAS –TX relations in various samples (taken from Kim and Fabbiano 2015). From the bottom left, coreless ETGs and spirals have no correlation, while core (“pure”) E galaxies have a very tight correlation, LX,GAS ∝ TX4.5 . Groups have a similar trend as the core Es, but they are shifted toward higher LX,GAS . Clusters at the top right corner have a flatter relation (LX,GAS ∝ TX3 ), compared to the other subsamples. For a reference, the flatter self-similar expectation (LX,GAS ∝ TX2 ) is shown in dashed lines

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Global Properties of the Hot ISM: Scaling Laws X-ray scaling relations have been built starting from the Einstein X-ray mission based on the sample of observed ETGs and widely used to compare observations with model predictions. More recently, following the realization of the existence of two main families of ETGs, different X-ray scaling relations were derived for each of these ETG families: (i) core galaxies, with a flattened central surface brightness distribution, which typically have large stellar masses, high stellar velocity dispersion, round isophotes, old stellar populations, and slowly rotating stellar kinematics, and (ii) power-law (also called coreless) galaxies, which instead have a centrally rising surface brightness distribution and tend to be smaller, disky, fast rotating, and with some recent star formation (see Pellegrini 2005; Kormendy et al. 2009; Sarzi et al. 2013). Kormendy et al. (2009) suggested that core ETGs are primarily formed by dry mergers, while coreless ETGs may be the product of gas-rich, wet mergers, with an ensuing period of intense stellar formation (see also Binney 2004; Nipoti and Binney 2007). The X-ray scaling relations were separately built for core and coreless galaxies to understand their distinct characteristics (Kim and Fabbiano 2015) and subsequently compared with other systems (groups and clusters of galaxies) and simulations to constrain various model parameters (e.g., Negri et al. 2014a, b, 2015). The most used scaling relation in the early days, the LX –LB relation, compared the total X-ray and optical (B band) luminosities of ETGs. This relation, which showed a factor of 100 scatter in LX,TOT for a given LB , triggered a series of theoretical investigations (e.g., Fabbiano 1989 and references therein). Thanks to the resolution of Chandra, LX,GAS is now used in place of LX,TOT . In the LX,GAS – LB (or LX,GAS –LK , see section “The Global Picture”, Fig. 14) relation, the scatter is even more significant, a factor of 1,000 (Kim and Fabbiano 2015). This is because X-ray faint ETGs hold only a small amount of hot gas; therefore, LX,GAS may be considerably less than LX,LMXB (Boroson et al. 2011). The critical astrophysical factors that govern the amount of hot gas in ETGs are discussed in section “Origin of the Hot ISM”. The temperature of the hot ISM (TX ), instead, directly reflects the potential depth of a virialized system. Furthermore, LX,GAS and TX can be measured with a single X-ray observation but independent methods: LX,GAS with wideband photometry (or normalization of the best-fit model) and TX with model fits of observed spectral data. Once the gas contribution has been “cleaned” of contaminants (e.g., LMXBs) in the Chandra data, the LX,GAS –TX relation could be reliably built (Kim and Fabbiano 2015; Goulding et al. 2016) and extensively compared with model predictions (Choi et al. 2015, 2017; Ciotti et al. 2017). Figure 4 shows the LX,GAS –TX relation of systems ranging from massive clusters to individual galaxies. For coreless ETGs (at the bottom left)—these galaxies also tend to show stellar rotation, a flattened galaxy figure, and rejuvenation of the stellar population—LX,GAS and TX are not correlated. The LX,GAS –TX distribution of coreless ETGs is a scatter diagram clustered at LX,GAS < 1040 erg s−1 , similar to

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that reported for the hot ISM of spiral galaxies (e.g., Li and Wang 2013), suggesting that both the energy input from star formation and the effect of galactic rotation and flattening may disrupt the hot ISM. The relation is steep and tight for core ETGs (LX,GAS ∝ TX4.5 ). At the highluminosity end, the LX,GAS –TX correlation is similar to that found in samples of groups but shifted down toward relatively lower LX,GAS for a given TX . This relation is considerably steeper than both the relation for clusters (LX,GAS ∝ TX3 ; Arnaud and Evrard 1999) and the expectation from the self-similar model, where gravity dominates (LX,GAS ∝ TX2 , blue dashed line in Fig. 4). The slope of ∼3 in clusters, steeper than the self-similar case, indicates that baryonic physics is already important even on this large scale. The fact that the slope in core ETGs is even steeper (∼4.5) further demonstrates the increase of importance of nongravitational effects, including AGN and stellar feedback. Therefore, the overall trend may be understood by considering the relative importance of baryonic physics over pure gravity in the galaxy scale via AGN and stellar feedback (for more discussion see Kim 2017). Figure 5 shows a zoom-in view of core ETGs with the results of observations and simulations, from Kim and Fabbiano (2015). Only core elliptical (E) galaxies with no sign of recent star formation are plotted (open black circles with error bars). This relation is tight, with rms deviation of only 0.13 dex. For LX,GAS > 1040 erg s−1 , this correlation compares exceptionally well with the predictions of high-resolution hydrodynamical simulations for fully velocity-dispersion-supported galaxies (the model predictions are taken from Ciotti et al. 2017, their Fig. 2; see also Negri et al. 2014a, b; Choi et al. 2015, 2017. Simulations and model specifications are further discussed in sections “The Complex Lifetime of Hot Gas in ETGs” and “Two More Actors: Environment and AGN Feedback”).

Fig. 5 LX,GAS –TX relation for an E sample (black open circles, taken from Kim and Fabbiano 2015). The diagonal lines are the best fit (solid line) with rms deviations (dashed lines). The predictions (taken from Ciotti et al. 2017) from equivalent (i.e., low-rotation) models with three different AGN feedback recipes—full (FF, blue), mechanical (MF, green), no (NoF, red) feedback—are also plotted for comparison

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However, the observed correlation extends down to LX,GAS ∼ 1038.5 erg s−1 , contrary to the simulations, which predict a sudden drop in X-ray luminosity in cooler galaxies. The models predict considerably lower LX,GAS or higher TX (blue and green circles at the middle bottom). This can be understood because the hot ISM in small systems is in the outflow/wind state, and then it tends to be at higher TX than extrapolated from the LX,GAS –TX relation of the inflow state in large systems (e.g., Pellegrini 2011; Negri et al. 2014a, b). Such a discrepancy is yet to be understood, possibly suggesting a need to improve feedback recipes (see also section “Two More Actors: Environment and AGN Feedback”).

The Mass of ETGs The K-band luminosity is a good proxy for the integrated stellar mass of the galaxy (LK ∼ M⋆ in solar units; Bell et al. 2003), but it does not measure the amount of dark matter (DM), which may be prevalent especially at large radii. The total mass (MTOT = M⋆ + MDM ), out to radii comparable to the full extent of the hot halos of gas-rich ETGs, is the crucial quantity to effectively explore the importance of gravitational confinement for the hot gas retention (see Mathews et al. 2006). Note that the amount of gas mass itself is small in ETGs (unlike large-scale clusters) and not important for gravitational confinement (e.g., Canizares et al. 1987). Although MTOT could be measured with X-ray observations (e.g., Mathews et al. 2006) under the assumption that the hot gas is in hydrostatic equilibrium, the X-ray measurements suffer from a couple of issues: (i) this method is only applicable to hot, gas-rich systems; (ii) the hot ISM may deviate from hydrostatic equilibrium, as revealed by observed dynamical evidence (e.g., sloshing, cavities; see Kim et al. 2019a), and the X-ray measurements are sometimes appreciably different from other independent results (e.g., Paggi et al. 2017). These issues may be less significant in relaxed clusters of galaxies, but they are not negligible in typical ETGs. Dynamical masses have been measured for a large number of ETGs using integral field 2D spectroscopic data (e.g., Atlas3D , Cappellari et al. 2013; MaNGA, Li et al. 2018). However, these data are limited to radii within r < 0.5–1 Re (where Re is the effective, or half-light, radius), considerably smaller than the observed extent of the hot gas in gas-rich ETGs. Strong gravitational lenses also provide lensing masses (e.g., Auger et al. 2010), but the measurements are again limited to r < 0.5–1 Re . A (small) number of dynamical mass measurements at large radii have recently become available from the analysis of the kinematics of hundreds of GCs and planetary nebulae (PNe) in individual galaxies (Deason et al. 2012; Alabi et al. 2017). If a hot halo is gravitationally confined, the amount of this gas, which is related to the measured X-ray luminosity, ought to be related to the total mass of the ETG (stellar and dark matter). To test this hypothesis, Kim and Fabbiano (2013) compared LX,GAS with independently measured (i.e., non-X-ray based) MTOT of 14 ETGs taken from Deason et al. (2012). Forbes et al. (2017) extended to 29 ETGs with GC-based MTOT taken from Alabi et al. (2017) and found indeed a good correlation.

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Fig. 6 X-ray luminosity of the hot gas versus total mass within r < 5Re (taken from Forbes et al. 2017). ETGs are color-coded by their central optical light profile (blue, core; gold, intermediate; green, coreless; red, unknown). Model galaxies from Choi et al. (2015) are also shown as black stars

Figure 6 shows the LX,GAS –MTOT relation. The relation is tight, with a slope α , indicating that M α = 3.13 ± 0.32 in LX,GAS ∝ MTOT TOT is indeed the primary factor in regulating the amount of hot gas retained by the galaxy. This relation holds in the range of LX,GAS = 1038 –1043 erg s−1 (spanning five orders of magnitude) or MTOT = a few ×1010 – a few ×1012 M⊙ (spanning two orders of magnitude). Also shown in Fig. 6 are the results (black stars) from the cosmological simulations by Choi et al. (2015). Although they only cover a limited range, their predictions agree well with the observations of LX,GAS and MTOT within 5Re . Separating core (blue points) and coreless (green points) ETGs, both Kim and Fabbiano (2013) and Forbes et al. (2017) suggested that core ETGs reveal a tighter relation than coreless ETGs. This is consistent with the findings of Kim and Fabbiano (2015, see also Fig. 4) and suggests that other factors, such as stellar feedback, may play an increased role in coreless (low-mass) ETGs. Although LX,GAS of both core (high LX ) and coreless (low LX ) ETGs are primarily determined by total mass, hence the depth of the potential well, other factors may still play a non-negligible role for galaxies with lower mass. As a growing number of ETGs have reliable measurements of their central SMBH mass (MBH ), it is interesting to compare MBH and LX,GAS . This relationship provides another excellent example of how the hot gas properties can be used to address essential aspects of ETGs, i.e., how the central SMBHs, host galaxies, and DM halos coevolve. Through numerical simulations, Booth and Schaye (2010) suggested that the DM halo may determine MBH . However, Kormendy and Bender (2011) presented an opposing argument that MBH is not correlated directly with the DM halo (see also Kormendy and Ho 2013). Bogdán and Goulding (2015) investigated this issue by stacking the ROSAT all-sky survey data of the large sample of SDSS elliptical galaxies. They suggested that the central stellar velocity

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dispersion, hence the central gravitational potential, may be more tightly connected to the total (large-scale) mass, traced by LX,GAS with the relationship in Kim and Fabbiano (2013,similar to Fig. 6), than to the stellar mass (M⋆ ). Gaspari et al. (2019) further analyzed the Chandra and XMM-Newton data of 85 systems (including ETGs and clusters). They found that the tightest correlation is between MBH and the hot gas properties (LX,GAS and TX ), instead of those determined by the optical data (e.g., σ , M⋆ ). They again suggested that the hot halos play a more central role than stars in tracing and growing SMBHs. The direct (or indirect) connection between DM halos and SMBHs, if confirmed, can help us to fully understand the evolution of ETGs through feedback mechanisms.

1D Radial Profiles of the X-Ray Surface Brightness and Temperature Distributions Once the radial profile of the X-ray surface brightness of diffuse hot gas has been measured and compared with the optical light profiles, it was immediately noticed that the hot gas distribution is different from the stellar distribution (e.g., Trinchieri et al. 1986; Fabbiano et al. 1992). The hot gas is extended with a flatter slope than the stellar light in hot gas-rich galaxies, while it is steeper and confined to the central region in gas-poor galaxies. The hot gas-rich systems are typically giant, old (core) elliptical galaxies, often sitting at the center of DM-rich systems (e.g., NGC 1399 at the center of the Fornax Cluster). The hot gas-poor systems are relatively small and coreless and may have some ongoing star formation (e.g., NGC 3379, Trinchieri et al. 2008; NGC 4278, Pellegrini et al. 2012b). Another critical piece of evidence that was recognized from the early observational and theoretical investigations of the X-ray surface brightness profile is the absence of a strong central peak (e.g., Ciotti et al. 1991; Mathews and Brighenti 2003), which would result from the uncontrolled gas inflow (the cooling catastrophe) predicted by the early cooling flow models (e.g., Fabian 1994; see section “Origin and Evolution of the Hot ISM in Early-Type Galaxies” for the discussion of feedback mechanisms that control the gas flow). In addition to the X-ray surface brightness profile, the radial profiles of the spectral and chemical properties of the hot gas are of interest. They include the temperature, Fe abundance and α-elements to Fe ratios, density, pressure, and entropy. All the density-based quantities require 3D deprojection. Because of the uncertainties introduced in deprojection and limitations in data quality, the projected pressure and entropy (based on the projected surface brightness rather than the density) are sometimes used as a proxy. The radial profile of the hot gas temperature TX is shaped by various heating mechanisms, including AGN feedback (Fabian 2012), stellar feedback (Ciotti et al. 1991), and gravitational heating (Johansson et al. 2009). The theoretical aspects of the heating mechanisms are described in sections “Heating of the Mass Sources” and “AGN Heating”.

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Fig. 7 Examples of six different temperature profile types. The type and the example galaxy are specified in each plot. The data points in black are fitted with projected temperature profiles in blue, with the 3D model shown in a red dashed line. The inner red vertical line indicates r = 3 arcsec, where the AGN could affect the temperature measurement, and the outer red line indicates the maximum radius where the hot gas emission is reliably detected with an azimuthal coverage larger than 95 percent. The blue vertical line is at one effective radius. (Taken from Kim et al. 2020)

Diehl and Statler (2008) reported the first systematic study of 36 ETGs. More recently, Kim et al. (2020) derived temperature profiles for a sample of 60 ETGs using the data products of the Chandra Galaxy Atlas (CGA, Kim et al. 2019a). They grouped them into six representative profile types (see Fig. 7). They are, in order of the number of galaxies included, “hybrid-bump” (rising at small radii and falling at large radii), “hybrid-dip” (falling at small radii and rising at large radii), “negative” (falling all the way), “positive” (rising all the way), “double-break” (falling at small radii, rising at intermediate radii, and falling again at large radii), and “irregular.” The most common type is hybrid-bump. Together with the double-break type, they comprise 50 percent of the studied profiles. The main characteristic feature is that the temperature peaks at an intermediate radius, roughly a few percent of RVIR (the virial radius), and decreases both inward and outward from the peak. This behavior resembles that of the temperature profiles of galaxy groups and clusters, where however the peaks of T are observed at relatively larger radii, ∼10% of RVIR (Vikhlinin et al. 2005; Sun et al. 2009). Further considering the characteristic temperature and radius of the peak, dip, and break (when scaled by the gas temperature and virial radius of each galaxy) and the observational limitation at the outskirts of the galaxies, Kim et al. (2020) proposed a universal temperature profile that may explain 72 percent (possibly up to 82 percent) of the ETG sample (Fig. 8). In this scheme, TX peaks at RMAX = 35±20 kpc (or ∼0.04 RVIR ) and declines both inward and outward. The temperature

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Fig. 8 Left: Temperature (scaled by TMAX ) against radius (scaled by RVIR ) for all galaxies in the hybrid-bump and double-break types. Right: A schematic diagram of the proposed “universal” temperature profile. (Taken from Kim et al. 2020)

dips (or breaks) at RMIN (or RBREAK ) = 3–5 kpc (or ∼0.006 RVIR ). The mean slope between RMIN (RBREAK ) and RMAX is α = 0.3 ± 0.1 in TX ∝ r α . The temperature gradient inside RMIN (RBREAK ) varies widely, indicating different degrees of additional heating at small radii. The hot core of some ETGs with hybriddip, double-break, or negative profiles may be related to recent star formation.

Radial Distributions of Fe Abundance The Fe abundance profile is as important as the TX profile, because it gives a window on the effect of stellar evolution on the hot ISM. However, Fe abundance is harder to measure and requires higher S/N data. Regarding various issues including multitemperature gas, contamination by AGNs and LMXBs, background subtraction, resonance scattering, He sedimentation, and calibration uncertainty, we refer to the review in Kim and Pellegrini (2012). Fe profiles were measured and reported primarily for hot gas-rich systems. The typical profile shows that the Fe abundance is supersolar at the center of the galaxy and decreases with increasing radius, e.g., in NGC 1399 (Buote 2002), NGC 5044 (Buote et al. 2003), NGC 507 (Kim and Fabbiano 2004b). We can call this declining Fe profile a “negative” type using the same terminology of the T profile types in Fig. 7. For example, we show the Fe profile of NGC 1550 in Fig. 9 (left panel). This negative type is expected because the Fe enrichment from SNe Ia occurred mainly in the central region, and the Fe-enriched hot gas is slowly propagated to the outer region. High-resolution hydrodynamical simulations could qualitatively reproduce the negative gradient (e.g., see Pellegrini et al. 2020). The second type of the Fe profile is one with a central Fe deficit. This Fe profile (rising at small radii and falling at large radii) is a “hybrid-bump” type. NGC 4636

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Fig. 9 Radial profiles of Fe abundance of the hot gas in NGC 1550 (left) and NGC 4636 (right). The blue vertical line denotes the half-light radius, and the dotted red vertical lines are at r = 10 arcsec and 16 arcmin, which indicate the inner and outer boundaries set by the XMM-Newton point spread function and field of view. Note that the Fe abundance measurement at large radii (r > 100 kpc in NGC 1550 and r > 50 kpc in NGC 4636) is not reliable, even if the statistical error is small

(Fig. 9, right panel) is an example (more can be found in Rasmussen and Ponman 2009; Panagoulia et al. 2015). Panagoulia et al. (2015) showed that the central deficit is seen more often in galaxies with an X-ray cavity (as in NGC 4636) and a shorter cooling time and suggested that Fe may be incorporated in the central dusty filaments, which are dragged outward by the bubbling feedback process. However, this measurement in the complex central region (typically r < 10 kpc) is challenging, and it may suffer from unknown systematic errors, e.g., resonance scattering (Xu et al. 2002; see also Gilfanov et al. 1987; Kim and Pellegrini 2012). The Fe deficit in the center needs to be confirmed by future missions (e.g., XRISM, expected to be launched in 2023).

Entropy Profiles −2/3

Entropy (K ≃ T ne ) has been used to address the thermodynamic history of the ICM. The entropy radial profiles of the ICM have been measured and analyzed (e.g., Ponman et al. 2003). The observed K profiles were compared with theoretical predictions, e.g., K ∝ r 1.1 in the absence of nongravitational processes (Voit et al. 2005). The universal (or bimodal) K profile and the presence (or absence) of the entropy floor in the ICM were debated in connection with the presence of Hα emitting warm gas and cold molecular gas (Cavagnolo et al. 2009; Panagoulia et al. 2014). Babyk et al. (2018) investigated the entropy profiles of a sample of 40 ETGs. They show that ETGs have a higher rate of heating per gas particle compared to brightest cluster galaxies, which may explain the lack of star formation

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in ETGs. We note that the hot ISM in ETGs is somewhat different from the ICM in terms of thermodynamics. The hot gas primarily originated internally from stars, as opposed to the ICM with prevalent accretion or merging. Additionally, because the hot gas is rather complex in ETGs (as discussed in section “Heating of the Mass Sources”), measuring density profiles in the hot ISM via deprojecting the surface brightness (with variable temperature, variable metal abundance, and clumpiness) is not straightforward, unlike in the relaxed ICM.

2D Spatial Distributions of X-Ray Surface Brightness and Gas Temperature The high spatial resolution Chandra images show a range of spatial features in the hot ISM, which was previously considered smooth and relaxed. The features seen in the X-ray surface brightness maps include X-ray jets (e.g., NGC 315, Worrall et al. 2003), cavities coincident with radio jets/lobes (e.g., NGC 4374, Finoguenov et al. 2008), nested cavities (e.g., NGC 5813, Randall et al. 2015), cold fronts (e.g., NGC 1404, Su et al. 2017a), filaments (e.g., NGC 1399, Su et al. 2017b), and tails (e.g., NGC 7619, Kim et al. 2008). These hot gas features give us insight on critical astrophysical processes, including the interaction of the AGN with the ISM of the host galaxy through radio jets/lobes, sloshing (see illustrative examples in Figs. 16–17 of Markevitch and Vikhlinin 2007), ram pressure stripping of the hot halo interacting with the hotter ICM, and signatures of galaxy mergers. All of this is crucial for our understanding of galaxy formation and evolution via AGN feedback and environmental effects (e.g., Kim and Pellegrini 2012 and references therein; see also section “Two More Actors: Environment and AGN Feedback”). An excellent example of the importance of 2D maps is given by NGC 3402 (O’Sullivan et al. 2007), where the X-ray surface brightness of the diffuse gas appears to be smooth and relaxed, but the TX map clearly indicates a shell structure at 20–40 kpc, which is cooler than the surrounding gas (see Fig. 10). Another good example is NGC 4649 (see the 2D TX maps on the CGA website, https://cxc.cfa. harvard.edu/GalaxyAtlas/v1/cga_target_N4649_90601.html). The surface brightness map of this galaxy shows that the hot gas distribution is smooth near the center but asymmetric in the outer region with extended tails (or wings) toward the northeast and the southwest. Wood et al. (2017) suggested that these wings may be caused by Kelvin-Helmholtz instabilities. The 2D TX map further shows that while the cooler region is extended toward the same directions as seen in the surface brightness map, the asymmetrical features start from the center to the outskirts. This suggests a possible explanation by which the wings may be connected to the inner radio jets propagating toward the same directions, in addition to, or in place of, Kelvin-Helmholtz instabilities, which work at the outer surface. The spatial distribution of the Fe abundance poses observational constraints on the metal enrichment history of the hot ISM. The phenomena at play include the mass loss from evolved stars and SN explosions; the effect of internal mechanisms on the transport of the Fe, such as SN-driven winds and AGN-driven buoyant

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Fig. 10 (a) Surface brightness map (0.5–2 keV) and (b) TX map of the hot gas in NGC 3402. The cyan ellipse indicates the optical D25 ellipse, i.e., the 25 B-mag per square arcsecond isophote. (Taken from Kim et al. 2019a)

bubbles; and the effects of the interaction with the external environment, sloshing, and ram pressure stripping. The Chandra and XMM-Newton observations of NGC 7619 provide a good example of Fe-enriched gas in the X-ray tail asymmetrically propagating to a large radius (Kim et al. 2008; Randall et al. 2009). Islam et al. (2021) presented the Fe maps of 38 ETGs as a part of the XMMNewton Galaxy Atlas (NGA). In conjunction with the Chandra Galaxy Atlas, they compared a contrasting pair of ETGs, NGC 4636 and NGC 1550, to show how the Fe maps can be used to understand the metal transport processes. The Chandra and XMM-Newton observations of NGC 4636 revealed a complex hot gas morphology—cavities and a small-scale extension toward NW–SE at r < 10 kpc, an intermediate-scale (∼20 kpc) extension toward WSW, and a largescale (∼50 kpc) extension toward N. The fact that extended gas directions are different at different radii is the typical phenomenon of sloshing as the center of the galaxy has been perturbed, or sloshed, more than once (e.g., see the simulations by ZuHone et al. 2016). The TX and Fe abundance maps (see the spectral maps in the NGA website, https://cxc.cfa.harvard.edu/GalaxyAtlas/NGA/v1/nga_ target_N4636_90101.html) further show that the gas in the small-scale elongation, intermediate-scale extension, and large-scale enhancement is cooler and richer in Fe than the surrounding gas at similar distances. These spectral maps clearly show that the cooler, metal-enriched, low-entropy gas, originated from the stellar system by mass loss and SN ejecta, is stretched out primarily due to sloshing. Unlike NGC 4636, the hot gas in NGC 1550 is relatively smooth, but the spectral maps exhibit exciting features that are not seen in the surface brightness map—the cooler and Fe-enriched gas is extended toward the E–W direction at

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Fig. 11 Giant Metrewave Radio Telescope 610 MHz radio contours (from Kolokythas et al. 2020) showing the AGN jets and lobes, overlaid on the T map (left) and Fe map (right) of NGC 1550. The cyan ellipse indicates the D25 ellipse. (Taken from Islam et al. 2021)

r < 15 kpc (Fig. 11; see the Fe map in the NGA website, https://cxc.cfa.harvard. edu/GalaxyAtlas/NGA/v1/nga_target_N1550_90301.html). Interestingly the E–W extension is aligned with the radio jet-lobe direction (Kolokythas et al. 2020), possibly indicating that the elongated cooler, metal-enriched, low-entropy gas is caused by the uplift by radio lobes, although sloshing may also occur in the different direction (see Kolokythas et al. 2020; Islam et al. 2021). The asymmetric Fe distribution (by the uplift), aligned with the radio jets and lobes, has previously been seen in a small number of clusters, the best example being Hydra A (Kirkpatrick et al. 2009; McNamara et al. 2016). NGC 1550 may represent a nearby, smallerscale example. For more examples of interesting spatially resolved features, we refer to the Chandra Galaxy Atlas (Kim et al. 2019a) and XMM-Newton Galaxy Atlas (Islam et al. 2021).

Origin and Evolution of the Hot ISM in Early-Type Galaxies We examine here the origin of the hot gas in ETGs, its heating sources, its dynamical status, and its link with the galactic properties. In fact, the hot ISM has a tight relation with the host galaxy, being deeply influenced by its gravitational field, by various forms of mass exchange with it (as provided by stellar evolution, gas infall from the circumgalactic medium, and mass deposition via cooling), and by energy injections provided by SN explosions and accretion onto the central massive black hole. The following sections deal in turn with these topics and end with a global picture accounting for the observed LX,GAS and TX properties presented in section “Observational Properties of the Hot ISM in Early-Type Galaxies”. We remind that in the following LX,GAS is the galactic X-ray emission due to the hot gas only and TX is the average temperature of the X-ray-emitting gas.

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Origin of the Hot ISM How do ETGs get their hot ISM? There are a few possibilities, dominating at different epochs. We take the view that ETGs are old systems, whose formation started at redshift z > 2. At these early epochs, a major source for the galactic ISM was the infall of pristine gas within the DM halos; this gas was shock heated to the virial temperature of the halos, which for halo masses of MDM  1012 M⊙ is  a few million degrees (Mo et al. 2010). Part of this gas cooled and contributed to star formation, a process that presumably stopped when the combined effects of AGNs and SNe heated the gas and possibly also drove powerful outflows that displaced the ISM out to large radii or even cleared the galaxy of it (e.g., Naab and Ostriker 2017; section “The Hot ISM of Star-Forming Galaxies”). A hot circumgalactic corona (CGM) then formed, made of hot gas residing at large radii (out to the virial radius of the DM halo), further enriched by mass expelled from the galactic central regions; the CGM material could be falling back in at later times, making another source of galactic ISM (e.g., Mo et al. 2010; Hafen et al. 2019). At later epochs, the building of ETGs proceeded via minor merging, which affected mostly their external stellar envelopes and was mainly dissipationless (Oser et al. 2010); major galaxy merging may also have occurred (see Cox et al. 2006; Smith et al. 2018; sections “Starbursts in Galaxy Mergers” and “An Ideal Laboratory: NGC 6240” for its effects on the hot gas content). During this epoch, the normal aging of the stellar population also shed a significant amount of mass into the ISM. In summary, the main sources for the hot ISM of present epoch ETGs include gas residual of the star formation phase; accretion from the CGM; and the internal gas production from stellar evolution.

Relative Importance and Evolution of the Mass Sources Estimates of the amount of hot gas remaining after star formation and of the CGM material that falls in are provided by cosmological simulations; they thus depend on assumptions about the complex physics of the galaxy formation and evolution and on its implementation in the simulations. The residual gas mass should amount to a few percent of the present-day stellar mass M⋆ (e.g., Oser et al. 2010; Gan et al. 2019), and subsequent evolution may well have caused its mixing and/or removal from the ETG, by the present epoch (sections “The Complex Lifetime of Hot Gas in ETGs” and “Two More Actors: Environment and AGN Feedback”). The rate of accretion from the CGM (M˙ CGM ), though depending on poorly known factors, for example, the AGN feedback (section “AGN Heating”), was likely more important during the first few Gyr and then declined sharply; the total accreted mass could be of the order of ∼10% of M⋆ for massive ETGs. A suitable parameterization of this −(t/t )2 rate could be M˙ CGM = 2Macc e 0 2 t2 , where Macc is the total accreted mass 1−e−(Δt/t0 ) t0

over the time interval Δt and t0 determines the time at which the rate peaks (Gan et al. 2019); an example of this parameterization is shown in Fig. 12.

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Fig. 12 The rates of mass input to the ISM described in section “Relative Importance and Evolution of the Mass Sources”, normalized to M⋆ . The aging stellar population inputs are M˙ ⋆ (Equation 9, in black) and M˙ Ia (Equation 10, in red). The CGM infall M˙ CGM (in blue) is parameterized as suggested in section “Relative Importance and Evolution of the Mass Sources”, with t0 = 3 Gyr, Δt equal to the present age of the universe, and Macc providing an integrated mass input from 3 to 13 Gyr of 0.1M⋆

The internal mass input provided by the stellar population includes stellar mass losses (M˙ ⋆ ) and ejecta of type Ia SNe (SNe Ia), M˙ Ia ; type II SN events are confined to the first few Myr if the stellar population is overall old (section “Chemical and Physical Evolution of the Hot ISM”). The most important contributions to M˙ ⋆ are given during the red giant, asymptotic giant branch, and PN stellar evolutionary phases. In the hypothesis that the stellar population is “simple,” i.e., born in a single episode, the collective return rate M˙ ⋆ was estimated from stellar evolution theory; a robust approximation for M˙ ⋆ , after ∼2 Gyr of age, is as follows: −1.3 M˙ ⋆ (t) = 10−12 A M⋆ (M⊙ ) t12

M⊙ yr−1 ,

(9)

where A = 3.3 and 2.0 for the Kroupa and Salpeter IMFs, respectively, M⋆ refers to an age of 12 Gyr, and t12 is the age in units of 12 Gyr (e.g., Pellegrini 2012). The collective mass injection rate M˙ Ia is much smaller and can be calculated as the product of the mass contributed by one binary system exploding as SN Ia (1.4 M⊙ ) times the event rate RSN (t): −s M˙ Ia (t) = 1.4M⊙ RSN (t) = 0.22 × 10−12 h2 LB (LB⊙ ) t12

M⊙ yr−1 ,

(10)

−s where RSN (t) = 0.16 h2 × 10−12 LB (LB⊙ ) t12 (yr−1 ) describes the evolution of the SN Ia explosion rate after ∼2 Gyr of age, LB (LB⊙ ) is the present epoch Bband galactic luminosity, and h is the Hubble constant in units of 70 km s−1 Mpc−1 . RSN (t12 = 1) gives the rate observed in the local universe, and the slope s

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parameterizes its past evolution with time; current estimates indicate s ∼ 1.0 (e.g., Maoz et al. 2014). M˙ Ia is then ∼ M˙ ⋆ /90 at the present epoch, for a stellar massto-light ratio M⋆ /LB = 5.8 appropriate for a Kroupa IMF at an age of 12 Gyr (see Pellegrini 2012 for more details). ˙ The integration over ∼10 Gyr of M(t) = M˙ ⋆ (t) + M˙ Ia (t) gives a total mass input of ∼0.05–0.1 M⋆ , a figure close to that quoted above for the total accreted mass from the CGM; note, though, that the estimates for the stellar population are more certain and, also important, that the two rates follow different trends with time (Fig. 12). Finally, the internal mass input rate follows the spatial distribution of the stellar population; thus, if the latter has a density distribution ρ⋆ (x), where x is the position vector, stars and SNe Ia inject mass locally at rates ρ˙⋆ (x) ∝ ρ⋆ (x) and ρ˙Ia (x) ∝ ρ⋆ (x), respectively, and the hot ISM density distribution ρ(x) has a local gas injection rate ρ(x) ˙ = ρ˙⋆ (x) + ρ˙Ia (x). Note that ρ(x) derived from observations, via the deprojection of the X-ray surface brightness (section “1D Radial Profiles of the X-Ray Surface Brightness and Temperature Distributions”), in general does not follow the spatial distribution of ρ(x), ˙ because evolution of the hot gas and accretion from the CGM determine the total density profile (sections “Cooling and Evolution of the Hot ISM”, “The Complex Lifetime of Hot Gas in ETGs”, and “Two More Actors: Environment and AGN Feedback”).

Heating of the Mass Sources What heats the ISM to temperatures such that it radiates in the X-rays? Gas falling in from the outer regions of the galactic potential well is supposed to be shock heated to the virial temperature of the dark matter halo and reach temperatures of the order of kT ∼ 0.5 keV in ETGs (section “Origin of the Hot ISM”). Simple predictions for the properties of a hot ISM with this origin can be derived within the “self-similar” model, in which dark matter and baryons reach equilibrium under the action of gravity only (see section “Modeling of the Hot ISM: The Simplest Model”). Gas that is born within the galaxy, instead, as that originated by stellar mass losses, has very low temperatures when it is released by the stars. However, the interaction between the stellar ejecta and the surrounding ISM causes various shockand contact-driven hydrodynamical and thermal instabilities, which result in the mixing of (most of) the ejecta with the ISM and in its heating to approximately the temperature of the hot ambient medium, within few pc of the star, and on relatively short timescales (Mathews 1990; Parriott and Bregman 2008). In this process, the energy conveyed to the ISM is of the order of the thermalization of the random and ordered kinetic energies of the stars. Assuming a perfect mixing of the mass sources with the preexisting gas, the energy input rate Lσ for the random part of the stellar motions, over the whole galaxy volume V , is as follows: Lσ ≡

1 2



ρ˙ Tr(σ 2 )dV , V

(11)

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where σ is the velocity dispersion tensor of the stellar component. At the present epoch, Lσ is of the order of ∼(1–5) ×1040 erg s−1 in ETGs of central stellar velocity dispersion σc = 180–260 km s−1 (e.g., Pellegrini 2012). The ordered stellar motions provide an energy input rate Lv that depends on the difference in velocity between the streaming velocity of the stars (v) and the ISM velocity (u) and is calculated as follows:  1 Lv ≡ ρ˙ v − u 2 dV . (12) 2 V At variance with Lσ , this contribution cannot be estimated a priori, since it depends on the fluid velocity u. Of course, given the orbital nature of stars in ETGs, Lv < Lσ ; furthermore, this inequality is likely to be large, because simulations indicate that u tends to be similar to v (see Negri et al. 2014a for more details). SNe Ia contribute a major heating source for the ISM. The blast waves they originate dissipate their kinetic energy and form very hot bubbles that within a few million years disrupt by Rayleigh-Taylor instabilities and share their thermal energy with the ISM (Mathews 1990). Thus SNe Ia provide an energy injection rate, over the whole galaxy, of LSN (t) = ESN RSN (t) erg yr−1 , where ESN = 1051 erg is the kinetic energy of one SN Ia event. At the present epoch, rewriting LSN = 5h2 × 1030 LB (LB⊙ ) erg s−1 (see section “Relative Importance and Evolution of the Mass Sources”), one sees that LSN largely exceeds Lσ (for example, for σc = 260 km s−1 and then LB = 5 × 1010 LB⊙ from the Faber-Jackson relation, LSN = 2.5 × 1041 erg s−1 ). If a fraction of ESN is radiated before the mixing of the ejecta is completed, a scaling factor ξ  1 should multiply LSN (section “Chemical and Physical Evolution of the Hot ISM”). This factor is expected to be not much smaller than unity, because the SN Ia remnants evolve in a hot, low-density medium (Mathews 1990; Tang and Wang 2005). Note that SNe Ia explode at random in the galaxy volume, with a frequency not high enough to have their hot bubbles overlap each other before dissolving into the ISM; this has implications for the spatial uniformity of the SN Ia heating and the mixing of the iron content of each ejecta (Mathews 1990; Tang and Wang 2005, 2010; Li et al. 2020). Finally, the SN heating can also proceed via injection of cosmic rays or turbulence (Pfrommer et al. 2017; Li et al. 2020).

Injection Temperatures and Observed Temperatures The two heating sources Lσ and LSN are distributed over the galactic volume as ρ⋆ (x) and locally provide the unit mass of injected gas an internal energy of 3kTinj (x)/2μmp , where Tinj (x) is the local mass-weighted injection temperature. Tinj is contributed by the thermalization of the motions of the gas-losing stars (Tstar ) and of the velocity of the SN Ia ejecta (TSN ), so that Tinj = Tstar + TSN = ˙ then (M˙ ⋆ T⋆ + M˙ Ia Tej )/M˙ (e.g., Pellegrini 2012). By approximating M˙ ⋆ ≈ M, ˙ ˙ Tstar ≃ T⋆ and TSN ≃ MIa Tej /M⋆ . Assuming that ESN is entirely turned into heat,

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Tej = 2μmp ESN /(3kMSN ) = 1.4 × 109 K. Therefore TSN is independent of the position in the galaxy and evolves with time as M˙ Ia /M˙ ⋆ ; at the present epoch, for a Kroupa IMF (section “Relative Importance and Evolution of the Mass Sources”), TSN ≃ 1.6 × 107 K. Tstar is instead independent of time with good approximation but depends on the position in the galaxy, because T⋆ (x) is determined by the local stellar motions; for example, considering only the random part of the stellar motions, T⋆ (x) = μmp Tr(σ 2 (x))/3k. The average mass-weighted T⋆ for the whole galaxy is as follows:  1 μmp

T⋆  = ρ⋆ Tr(σ 2 )dV . (13) 3k M⋆ V The integral in Equation 13 gives  the kinetic energy Ekin associated with the stellar random motions, Ekin = 0.5 dV ρ⋆ Tr(σ 2 ), thus T⋆  can be seen as the “stellar virial temperature.” An approximation for T⋆  often used is T⋆  ≈ μmp σc2 /k; this gives, for σc = 150 and 250 km s−1 , respectively, T⋆  ≈ 1.7×106 K and 4.7×106 K (i.e., 150 and 400 eV). In conclusion, at the present epoch, Tinj (x) = T⋆ (x) + 1.6 × 107 K, with the average Tinj  = T⋆  + 1.6 × 107 K, where the term due to SNe Ia dominates. Observed emission-weighted temperatures for the hot ISM are smaller than Tinj  and closer to T⋆  (section “Global Properties of the Hot ISM: Scaling Laws”). Indeed, a significant part of the energy available to the gas that originates within ETGs, when it is injected, is conveyed in kinetic energy of the gas bulk flow, or in work done to uplift the gas in the galactic potential well (section “The Complex Lifetime of Hot Gas in ETGs”), or in emitted radiation (section “Cooling and Evolution of the Hot ISM”); it could also be that the energy transmitted by SNe Ia is lower than LSN (Pellegrini 2011). The considerations above concern the sources of mass for the ISM and illustrate how the various (cold) mass inputs experience heating processes expected to bring them to temperatures of a few million degrees. Note that, similarly to what is pointed out for the gas density ρ(x), also the gas temperature does not follow necessarily the Tinj (x) distribution (as indeed observed; section “1D Radial Profiles of the X-Ray Surface Brightness and Temperature Distributions”). In fact, during its life, the ISM as a whole experiences additional sources of heating, as could be the compression resulting from the action of the gravitational field, thermal conduction from an external hot medium, and various forms of energy input from accretion on a central massive black hole (section “AGN Heating”). These processes are briefly illustrated below (section “Cooling and Evolution of the Hot ISM”), after presenting the loss of energy via radiation, and the consequences it determines for the ISM evolution.

Cooling and Evolution of the Hot ISM Emission of radiation represents an energy loss for the hot gas that can be so important to influence its evolution and determine its properties. Since its temperature is of a few million degrees and its density is typically low (ne 

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0.1 cm−3 ), the hot ISM is highly ionized (with only the heavier species not fully ionized), optically thin, in a collisional ionization equilibrium state: the atoms are ionized or excited by collisions with electrons and shortly after recombine or decay radiatively, emitting a photon that is lost by the gas (Peterson and Fabian 2006). These radiative processes, plus thermal bremsstrahlung, produce an emissivity ǫν (the radiative power per unit frequency and per unit volume) that is written as ǫν = n2H Λν , and Λν (T , Z) is the cooling function that depends on the temperature and metal abundance Z. The definition of ǫν sometimes uses the electron number density ne or the total number density n = ρ/(μmp ); the relations between the various number densities allow the conversion between definitions (e.g., for the solar composition, n = 2.33nH , and ne = 1.21nH ). At the temperatures of interest for ETGs, Λν has an important contribution from emission lines due to highly ionized neon, oxygen, magnesium, and silicon and from the L-shell Fe transitions (see Fig. 2). The integration of Λν over a frequency interval gives the emission in the corresponding energy band (e.g., the Chandra 0.3–8 keV sensitivity band); an example of the bolometric cooling function Λ for various Z is given in Sutherland and Dopita (1993). The hot  gas luminosity in an X-ray band from a volume V is then given by LX,GAS = V d 3 x n2H (x) ΛX (T (x), Z(x)). The hot gas radiates and cools, especially in the central, more dense galactic region; the loss via radiation of thermal energy (which per unit volume is 3nkT /2) takes place on a timescale known as the radiative cooling time tcool = 3nkT /(2n2H Λ). Measured tcool values can be as low as a few ×107 yr or less, within a radius of ∼1 kpc (Lakhchaura et al. 2018). Across the region where tcool is lower than the galaxy age (the central “cooling region”), if not heated to compensate for the radiative losses, the gas cools and is pushed in by the weight of the gas layers surrounding it; a cooling-induced inflow is thus established. A simultaneous density increase within the cooling region is also produced, which makes tcool shorter and shorter, until cooling becomes catastrophic in the innermost part of the galaxy; in fact, compressional heating, and even the SN Ia heating, cannot prevent rapid cooling (e.g., Ciotti et al. 1991; Mathews and Brighenti 2003). This process is very similar to that described by the cooling flow model introduced for galaxy clusters (Peterson and Fabian 2006), where, however, there are no distributed mass sources and an infinite gas mass reservoir is present at the outer boundary of the cooling region. Cooling inflows are expected to be important in more massive ETGs (see sections “The Complex Lifetime of Hot Gas in ETGs” and “The Global Picture”).

The Mass Deposition Problem During unarrested cooling, the gas should cross the warm phase and end in the cold one; actually, the flow could be multiphase across all radii of the cooling region (e.g., Vedder et al. 1988). The phenomenon by which mass is dropped out of the hot flow, and definitively becomes cold, is called mass deposition. The possibility for thermal instabilities to undergo nonlinear growth and condense the gas out of the hot

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flow (Field 1965) has been long debated, as they seem to be damped by conduction, ram pressure, or buoyancy but instead may survive in the presence of a magnetic field and even be triggered by turbulent motions (Loewenstein and Fabian 1990; Pizzolato and Soker 2005; Sharma et al. 2012; Gaspari et al. 2013). In any case, if the gas radiatively cools down to low temperatures, the expected mass cooling rate predicted by the cooling flow model (M˙ cool ∝ LX,GAS /TX , Peterson and Fabian 2006) or a modeling more specific for the hot ISM in ETGs (Sarazin and White 1988; Ciotti et al. 1991; Bregman et al. 2005; section “The Complex Lifetime of Hot Gas in ETGs”) is of the order of ∼1 M⊙ yr−1 . Corresponding signs of mass deposition should be present, in the form of optical and UV filaments, molecular gas and dust, and signs of recent star formation; however, cooled or cooling material is observed at a lower (or far lower) level than expected. Exceptions are the central ETGs in groups and galaxy clusters, when surrounded by massive cooling flows (Werner et al. 2014; McNamara et al. 2016); some of them also suggest a link between the molecular gas content and the (shorter) cooling time (Lakhchaura et al. 2018; Babyk et al. 2019). In normal ETGs, optical emission lines with spatial coincidence with the X-ray cooling gas are seen in some cases (e.g., Werner et al. 2014; Lakhchaura et al. 2018), but X-ray, optical, and UV spectroscopy in general indicate gas cooling rates lower than expected (Bregman et al. 2005). Also signs of past mass deposition are not consistent with accumulation that lasted for a few Gyrs: only some ETGs show H I and CO emission and in a relatively small amount of 106 – 108 M⊙ (Werner et al. 2019); recent or ongoing star formation is also insufficient (Ford and Bregman 2013; Kuntschner et al. 2010). Therefore, empirical evidence requires the presence of a mechanism to compensate or prevent all the gas cooling expected in the simple modeling above; this could act via direct heating and/or the displacement of the gas from the central regions. To compensate for the cooling losses, the possibility of thermal conduction from the hotter, outer gas layers has been considered; however, it is unclear whether conduction can be effective, since thermal conductivity could be much reduced, for example, by a tangled magnetic field that shortens the electrons mean free path. The existence of hot gas coronae embedded in a hotter ICM is taken as an indication that conductivity must be largely suppressed compared to the theoretical maximum (the Spitzer value) to avoid evaporation (Sun et al. 2007; Sarazin 2012).

AGN Heating A promising way to avoid the growth of large cooled gas masses is the release of energy caused by accretion onto the central SMBH, a phenomenon known as “AGN feedback”; the accretion energy should be transferred to the ISM in an amount of the order of that lost in radiation (Fabian 2012). This release of energy could be continuous, compensating isotropically for cooling, or intermittent and possibly also anisotropic. Intermittency matches well with AGN variability observed in various bands and is linked to the idea of an activity cycle: gas cooling feeds accretion, and the consequent energy injection heats and possibly also displaces the gas from the

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galactic center, so that cooling and accretion stop; since the gas inflow from the outer galactic regions and the internal input of mass continue, the density starts increasing again in the central part of the galaxy, cooling is resumed, and then accretion follows another time (e.g., Pizzolato and Soker 2005; Ciotti and Ostriker 2007; Gaspari et al. 2012; Ciotti et al. 2017). The accretion output can take different forms, mainly including radiation, AGN winds (King and Pounds 2015), jets (Blandford et al. 2019), and cosmic rays (Guo and Oh 2008). Their importance is first of all measured by the respective rates of ˙ into the ISM, which are not injection of energy (L) and momentum (p˙ = Mv) completely known. Then, their effectiveness in stopping cooling, or in reheating, depends on how they interact with the ISM, which is also currently a subject of intense theoretical and observational study (e.g., section “2D Spatial Distributions of X-Ray Surface Brightness and Gas Temperature”). A short summary is given below.

The Various Forms and Effects of the SMBH Accretion Output The radiative output consists of photons with total luminosity: Lrad = ǫrad M˙ BH c2 ,

(14)

where M˙ BH is the mass accretion rate onto the SMBH; the radiative efficiency ǫrad ranges from a maximum of ∼0.1 for high accretion rates [m ˙ = M˙ BH /M˙ Edd ≫ 0.01, 2 ˙ where MEdd = LEdd /(0.1c ) is the Eddington rate], when a standard (cold, optically thick, geometrically thin) accretion disk forms, down to orders of magnitude lower values, when accretion is radiatively inefficient and hot and a geometrically thick disk forms (m ˙ ≪ 0.01; Yuan and Narayan 2014). The radiative output dominates the accretion output when m ˙ ≫ 0.01, in a regime known as quasar mode or radiative mode. Radiation transfers energy and momentum (the latter produced at rate p˙ rad = Lrad /c) to the ISM, via Compton heating and photoionization heating and through the gradient of the radiation pressure, which is contributed by dust absorption, photoionization opacity, and electron scattering (e.g., Ciotti and Ostriker 2007). The accretion output in the form of AGN winds and outflows (Lw ) and jets (Lj ) is known as the kinetic or mechanical mode, since it takes the form of mechanical energy (McNamara and Nulsen 2012; King and Pounds 2015). The rate of kinetic energy injection due to winds and jets can be written as follows: Lw = ǫw M˙ BH c2 ,

Lj = ǫj M˙ BH c2 ,

(15)

where ǫw and ǫj are the efficiencies of mechanical energy generation with a wind and a jet, respectively (e.g., Ciotti et al. 2009, 2017; Hardcastle and Croston 2020). Like ǫrad , also ǫw increases with m, ˙ reaching a maximum presumably 5 × 10−4 in the quasar mode, as indicated by observations and theoretical investigations

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(see Harrison et al. 2018 for a review). Therefore Lrad is larger than Lw at high m ˙ and presumably also at low m, ˙ where ǫrad and ǫw are less well-known. It is acknowledged that, when present, jets (Lj ) are an important energy output, at all m ˙ (Yuan and Narayan 2014); at m ˙ ≪ 0.01, they largely dominate over radiation (Lj ≫ Lrad ), and therefore this accretion regime is named “radio mode” (see also Werner et al. 2019). Winds are an important source of momentum (produced at rate 2 , with v the AGN wind velocity), which likely p˙ w = M˙ w vw , where M˙ w = 2Lw /vw w dominates over p˙ rad at low m ˙ and is still significant at high m. ˙ Moreover, thanks to their large opening angle, winds effectively impact the ISM, producing shocks that heat the gas and push it outward; during the high m ˙ accretion mode, these effects can reach distances of the order of ∼1 kpc (Ciotti et al. 2017; Arav et al. 2020). Jets interact with the ISM in a different way: they drill through the ISM and discharge energy at larger distance from the SMBH, even outside the galaxies where radio lobes can be observed (Vernaleo and Reynolds 2006). In ETGs residing in groups or clusters, jets often inflate bubbles of hot plasma within the ISM (section “2D Spatial Distributions of X-Ray Surface Brightness and Gas Temperature”) and could couple to the ISM via a number of mechanisms, which include the work done by the expanding bubbles, which displace and uplift the ISM; the dissipation of shocks or sound waves that the jet/bubbles can drive into the ISM; the mixing of the lobe plasma, with the release in the ISM of streaming cosmic rays and magnetic energy; and the dissipation of turbulent motions originating from the flow around the rising buoyant bubbles (see the reviews in McNamara and Nulsen 2012; Werner et al. 2019). Turbulence has also been suggested to induce overdensities that develop into cold gas clumps, which in turn feed accretion onto the SMBH (Pizzolato and Soker 2005; Gaspari et al. 2013; McNamara et al. 2016). Turbulent motions cause the broadening of the X-ray spectral lines, which could be observed by future highresolution X-ray spectrometers.

Modeling of the Hot ISM: The Simplest Model In a simple hierarchical model of structure formation, where increasingly larger systems are formed under the action of gravity only, all structures from galaxies to galaxy groups to galaxy clusters are expected to be scaled versions of each other. A natural question is then whether also the hot gas permeating ETGs, groups, and clusters shows a continuity of properties, which is embodied in scaling laws followed by all these structures. Actually, predictions exist for such laws, within a simple model where only gravity acts, and then the mass M is the only parameter determining all the properties of a structure on a given scale (the self-similar model; Kaiser 1986). If the gas evolves neglecting cooling and other forms of heating other than those linked to gravitationally induced motions, it ends in hydrostatic equilibrium at an average temperature (TX ) close to the virial temperature of the potential well where it has fallen. Its LX,GAS and TX scale then with M as power laws: TX ∝ M 2/3 , LX,GAS ∝ TX2 (for bremsstrahlung emission), and then LX,GAS ∝ M 4/3 (Kaiser 1986; Mo et al. 2010). These expectations are not fully met by the

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observed gas in clusters and are markedly broken by the hot ISM of ETGs, which shows instead much steeper LX,GAS ∝ TX4.5 and LX,GAS ∝ M 3 relations (Kim and Fabbiano 2013; section “Global Properties of the Hot ISM: Scaling Laws”). Moreover, these relations are tight when restricting to ETGs that are massive and slow rotators but become poorly defined, or disappear, for ETGs of medium-low luminosity LK (Kim and Fabbiano 2015). The steeper LX,GAS –TX relation indicates that gas is less X-ray luminous than predicted, at any given TX ; an effect of this kind is produced if the gas density is lower than expected, which comes from a loss of gas and/or a form of gas heating that prevented compression (e.g., Voit 2005). Indeed, deviations from the simple self-similar model are easy to foresee in ETGs: the hot gas originated also within the galaxy, not only from cosmological infall, and underwent significant cooling and heating, as detailed in sections “Cooling and Evolution of the Hot ISM”, “The Mass Deposition Problem”, “AGN Heating”, and “The Various Forms and Effects of the SMBH Accretion Output”. The effects of these “nongravitational” processes were naturally more dramatic in ETGs with a shallower potential well than groups and clusters. A more complex picture of the hot ISM evolution in ETGs that aims at reproducing its observed X-ray properties in the local universe is illustrated below.

The Complex Lifetime of Hot Gas in ETGs Before its discovery with X-ray observations, the absence of an observed ISM in ETGs was explained with the action of galactic winds. Assuming as mass source for the ISM only the aging stellar population, the first models showed that the energy input from SNe Ia was large enough to drive the ISM in a steady outflow that escapes the galaxy (note that these models did not include dark matter halos; Mathews and Baker 1971). The amount of hot gas in the galaxy is then very small, its LX,GAS is very low (LX,GAS < 1039 erg s−1 ), and the total X-ray emission is dominated by stellar sources (section “From Discovery with the Einstein Observatory to Chandra and XMM-Newton ”). Later, X-ray observations of ETGs revealed that their LX,GAS spans a large range of values (section “Global Properties of the Hot ISM: Scaling Laws”), from those expected for the collective emission of X-ray binaries (and then presumably corresponding to galaxies with the hot ISM in wind) up to ∼2– 3 orders of magnitude larger values, thus incompatible with winds. The modeling then focused on the possibility of retaining the hot ISM within the galaxies, in a steady global inflow similar to the “cooling flow” described in section “Cooling and Evolution of the Hot ISM” (Sarazin and White 1988). This solution reproduced the largest observed LX,GAS of noncentral ETGs; however, in most ETGs, LX,GAS is lower than in global inflows. Intermediate LX,GAS values could be explained with a gas flow that couples inflowing and outflowing regions (Fig. 13). The SN Ia heating keeps then the ISM mostly outflowing in galaxies with the lowest LX,GAS /LK ratio, and for increasing LX,GAS /LK , the inflowing region becomes more and more important. This idea was confirmed by high resolution Chandra observations, which showed how the collective emission of X-ray binaries accounts

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Fig. 13 Two examples of decoupled gas flows resulting from 2D hydrodynamical simulations, at the present epoch (∼9 Gyr of age; Negri et al. 2014a, b); colors indicate the temperature in K, on a meridional section, and superimposed arrows show the meridional velocity field, with the longest arrows corresponding to 170 km s−1 . The galaxy of LB = 3 × 1010 LB⊙ has a flat shape and is nonrotating (left), with a strong equatorial degassing, and rotating as an isotropic rotator (right), with the formation of a cold inner disk. (Adapted from Negri et al. 2014a, b)

for the total X-ray emission, in ETGs with the lowest LX /LK ratio (Boroson et al. 2011; section “From Discovery with the Einstein Observatory to Chandra and XMM-Newton”). At the lowest LK , all ETGs are mostly outflowing; at the largest, all ETGs host global inflows. These differences of the flow at the same LK are naturally produced by observed variations in the galaxy properties, even at the same LK ; these include, e.g., the shape of the stellar mass distribution (its flattening, Sersic index, effective radius), the central stellar velocity dispersion (indicative of the depth of the potential well), the importance of ordered rotation in the stellar kinematics, and the SN Ia rate (Pellegrini 2012; Negri et al. 2014a, b). For example, flatter ETGs are observed to have a lower LX,GAS /LK than rounder ones (Negri et al. 2014b; Juráˇnová et al. 2020), which can be produced by a shallower potential well that favors the outflow. This is confirmed by hydrodynamical simulations, in low-mass ETGs; in medium- to high-mass ETGs, instead, it is a larger galactic rotation, which accompanies a flat shape, to produce a reduction of LX,GAS (Fig. 14). In fact, the rotation of the stars is transferred to the stellar mass losses, and conservation of the angular momentum of the ISM injected at large radii causes the formation of a cold gas disk at lower radii; the hot gas density in the central galactic region is thus reduced. Indeed, slow rotators seem to have, on average, higher temperatures and higher LX,GAS than fast rotators (Sarzi et al. 2013). Other causes of variation for LX,GAS /LK are environmental effects, as gas stripping and galaxy interactions that decrease the gas content (Cox et al. 2006; Roediger et al. 2015; Smith et al. 2018), and gas confinement due to an external medium that increases LX,GAS , especially in central ETGs in groups and clusters (Mathews and Brighenti 2003; Sun et al. 2007; Sarazin 2012; see also section “Two More Actors: Environment and AGN Feedback”).

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Fig. 14 Observed and model LX,GAS in the 0.3–8 keV band, from within 5Re versus the K-band luminosity LK of ETGs. Observed ETGs (open circles), with luminosity distance D < 100 Mpc, are from the Chandra Galaxy Atlas (CGA, in black; Kim et al. 2019a) and from Kim and Fabbiano (2015) (KF15, in blue). Model LX,GAS values from hydrodynamical simulations refer to the present epoch. The left panel illustrates the possibility of varying LX,GAS in galaxies that, at fixed LK , are in all equal except for their shape and/or internal kinematics (Negri et al. 2014b): full black circles indicate spherical (E0) galaxies; filled and empty ellipses indicate, respectively, fully velocity dispersion supported (VD) galaxies and isotropic rotators (rot); two magenta open ellipses show two cases of a lower rotational level (Negri et al. 2015). See section “The Complex Lifetime of Hot Gas in ETGs” for more details. In the right panel, the model galaxies, at fixed LK , are in all equal but have been evolved without (full black circles) and with (red symbols) AGN feedback (mechanical or mechanical and radiative); the models are described in Pellegrini et al. (2018). See section “Two More Actors: Environment and AGN Feedback” for more details

The Global Picture The picture outlined above, supported by hydrodynamical simulations of the hot gas behavior, can account for the observed values of LX,GAS and TX and their trends with the galaxy properties, at least for relatively isolated ETGs (e.g., Negri et al. 2014b; section “Global Properties of the Hot ISM: Scaling Laws”). In this view, the average LX,GAS –LK correlation (or the LX,GAS –MTOT one, given that plausibly MTOT increases with LK ) is fundamentally due to the increase of the binding energy per unit mass of the gas with LK , as implied by the observed Faber-Jackson relation, the steep scaling between luminosity and central stellar velocity dispersion σc of ETGs (Ciotti et al. 1991; Pellegrini 2012). However, LX,GAS does not increase with LK in a tight and “self-similar” fashion, as if the flows were of the same kind at all LK : at the lowest LK , the flow is an outflow sustained by the SN Ia heating, while it becomes a global inflow at the largest LK , which produces the steep observed

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3 , Kim and relations (LX,GAS ∼ L3K , Kim and Fabbiano 2015; and LX,GAS ∼ MTOT Fabbiano 2013; Forbes et al. 2017). Superimposed onto the main effect of LK or MTOT , there are secondary effects determined by other factors (the shape, stellar kinematics, environment, etc.), which cause a range of LX,GAS values at the same LK . Importantly, these secondary factors have a stronger impact at medium-low LK , where the gas is less bound, and they become less and less effective at the largest LK , where global inflows are not easily disturbed; this explains the large scatter in the observed LX,GAS –LK (and LX,GAS –TX ) relations at low and medium LK and their tightness at large LK (section “Global Properties of the Hot ISM: Scaling Laws”; Kim and Fabbiano 2015). Being primarily dependent on the depth of the potential well, also TX shows correlations with LK and σc ; however, temperatures are measured with larger uncertainties than luminosities, and therefore these correlations are poorer than those involving LX,GAS , and it is more difficult to derive the possible dependence of TX on secondary factors. Note that measured TX values are close to, or slightly larger than, the value of T⋆ , the stellar temperature (sections “Global Properties of the Hot ISM: Scaling Laws” and “Injection Temperatures and Observed Temperatures”; Pellegrini 2011); therefore, other forms of heating, for example, the AGN feedback, do not seem to affect the average TX . AGN feedback, indeed, is shown by numerical modeling to produce temperature fluctuations limited to the central region (Pellegrini et al. 2012a; Gaspari et al. 2013; Li and Bryan 2014). More on the effects of AGN feedback as shown by numerical simulations is briefly summarized below, together with those of the environment.

Two More Actors: Environment and AGN Feedback For relatively isolated ETGs, the mass input from internal sources alone can account for LX,GAS  (5–6) × 1041 erg s−1 , while the largest observed values can reach LX,GAS ∼ 1042 erg s−1 and more (section “Global Properties of the Hot ISM: Scaling Laws”; Fig. 14). These, though, pertain to central or brightest galaxies in clusters and groups, for which it is difficult to separate the cluster/group emission from that of the ETG itself. Moreover, for galaxies at the center of a group, a cluster, or a substructure in it, the intragroup/intracluster medium has an important confinement effect, which significantly increases LX,GAS ; gas accretion from outside can also be more important than in noncentral ETGs (Mathews and Brighenti 2003). Noncentral ETGs, instead, may suffer from depletion of their hot gas content when moving in a dense external medium, due to the ram pressure stripping or the Kelvin-Helmholtz instability caused by the velocity shears between the two media. Evidence of ongoing gas stripping is provided by upstream truncation of the hot coronae and downstream gas tails, as observed in the Virgo and Fornax clusters (section “2D Spatial Distributions of X-Ray Surface Brightness and Gas Temperature”; Sarazin 2012; Roediger et al. 2011, 2015). Infall of ETGs in the ICM is often accompanied by the phenomenon of “sloshing,” which creates

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prominent cold fronts in this medium (section “2D Spatial Distributions of X-Ray Surface Brightness and Gas Temperature”; Roediger et al. 2011). The environment has an effect also on the temperature profile in the outer galactic region, where the temperature tends to the large intragroup/intracluster medium values, when this medium is present, due to an external pressure effect (Vedder et al. 1988); this characteristic of the outer temperature profile is indeed observed (section “1D Radial Profiles of the X-Ray Surface Brightness and Temperature Distributions”). Another important aspect concerning the hot gas evolution is that large cooling rates (and cooled masses) expected from inflowing gas must be prevented (section “The Mass Deposition Problem”); and indeed, various forms of heating can originate from gas accretion onto the central SMBH (section “The Various Forms and Effects of the SMBH Accretion Output”) and are presumably at work (section “2D Spatial Distributions of X-Ray Surface Brightness and Gas Temperature”). How much effective is this heating? Has it a role in the explanation of the observed X-ray properties (LX,GAS , TX ), and does it have an impact on the scenario outlined in section “The Global Picture”? Simulations of AGN feedback face the challenge of the large range of physical lengths involved, from the pc scale at the center, to resolve the region close to the accretion radius of the SMBH (Ciotti et al. 2017), to the ∼100 kpc scale of the outer galactic regions. In terms of the high spatial resolution required and the need to resort to 3D simulations, particularly challenging is the investigation of the effects of jets and bubbles. Therefore, in these cases, hydrodynamical simulations often zoom a limited spatial region close to the SMBH and/or focus on a short time span, for example, covering one activity cycle. The coupling efficiency with the ISM is in general assumed to be high, and jets are shown to provide an energy injection able to balance the cooling of the gas and maintain it in quasi-equilibrium (e.g., Vernaleo and Reynolds 2006; Gaspari et al. 2012; Li and Bryan 2014; Yang and Reynolds 2016). Investigations with pc-scale resolution close to the SMBH and covering the last few Gyr of the lifetime, for a large set of representative model ETGs, were performed with 2D hydrodynamical simulations of the radiative and mechanical (due to AGN winds) feedback effects (Ciotti et al. 2017). It was found that the SMBH spends a very small fraction of time in a radiatively bright high-m ˙ mode (with a duty cycle of ∼10−2 ), while most of the time the accretion rate is small and the AGN is faint. The main, important effect of this AGN feedback is to reduce the amount of cooled gas and prevent an excessive growth of the SMBH mass due to accretion. During outbursts, LX,GAS is first increased and then drops down by a large factor within the central Re , because the gas is temporarily displaced from this region (Fig. 15); this behavior adds then another source of variation in LX,GAS to those mentioned in section “The Complex Lifetime of Hot Gas in ETGs”. The gas mass lost from the galaxy during its evolution is increased, but AGNs cannot clear (massive) ETGs from their hot ISM. As shown also by other simulations (Pellegrini et al. 2012a; Gaspari et al. 2013; Li and Bryan 2014), the central temperature fluctuates as a consequence of nuclear outbursts (see also Fig. 15), which could explain the central cusps and dips frequently observed in the TX profiles within few

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Fig. 15 Evolution of the gas density (upper panels), temperature (middle panels), and radial component of the velocity (lower panels) right before, during, and after the end of a nuclear outburst caused by accretion, from the 2D hydrodynamical simulations of Ciotti et al. (2017). From left to right, the four panels span a time interval of 0.1 Gyr. See section “Two More Actors: Environment and AGN Feedback” for more details. (Adapted from Ciotti et al. 2017)

kpc from the center (section “1D Radial Profiles of the X-Ray Surface Brightness and Temperature Distributions”). Overall, when considering a large set of models, the effect of this type of AGN feedback on LX,GAS and TX seems marginal, and thus the range of the observed LX,GAS is similarly reproduced, with and without this feedback (Fig. 14; Pellegrini et al. 2018). It is important to note, though, that these models do not include accretion from a CGM and confinement from an external medium; if these are important, a larger feedback effect may be required to avoid excessive cooling.

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Future Prospects With respect to the landscape of hot ISM astrophysics, the forthcoming (or planned) space missions are undoubtedly expected to be very exciting. While XMM-Newton and Chandra have significantly improved our knowledge of the properties of the hot ISM in both star-forming and early-type galaxies, in the medium to long term, they are going be replaced by two other flagship observatories, which will extend their capabilities by one to two orders of magnitude, thus opening a new discovery space for X-ray astronomy: Athena (e.g., Barret et al. 2020) and Lynx (e.g., Gaskin et al. 2019). The former was selected by the European Space Agency within its Cosmic Vision program, while the latter has been recently endorsed by the 2020 Astronomy and Astrophysics Decadal Survey of the National Academy of Sciences in the United States. These revolutionary facilities, however, will hardly become operative before the second half of the next decade. By contrast, the eROSITA telescope (Predehl et al. 2021) aboard the SRG orbital observatory (Sunyaev et al. 2021), launched in 2019, is performing an all-sky survey that will be 20 times more sensitive than the existing ROSAT maps once completed after 4 years. The new, allsky data will be particularly useful to explore the outskirts of extended hot halos (in starbursts, mergers, and ETGs) and large-scale interactions with other galaxies and the underlying IGM (or ICM). XRISM (Tashiro et al. 2020), currently scheduled for launch in 2023, will provide extremely high-resolution (ΔE ≤ 7 eV) spectra thanks to the long-awaited, innovative technology of its X-ray microcalorimeter array (called Resolve). High spectral resolution is essential to tackle various open issues related to the abundance measurements of heavy elements and to investigate for the first time the dynamics of the hot, X-ray-emitting gas (e.g., Hitomi Collaboration et al. 2017, 2018). Although microcalorimeters are outperformed by gratings in terms of resolving power at low energies (i.e., long wavelengths), they ensure a huge improvement over CCD detectors. Separating the components of the Kα triplet from He-like ions, for instance, can be a powerful method to probe the interaction between the hot starburst winds and the cold ISM, via charge exchange emission at the interface between the highly ionized and nearly neutral phases (Liu et al. 2012). As we have pointed out earlier in this chapter, spatial resolution is definitely the most critical characteristic of any X-ray instrumentation for the study of the hot ISM, not only for excising the point sources but also to identify and inspect any substructures like clumps, filaments, and cavities. The sub-arcsecond resolution of Chandra will only be matched by Lynx (whereas Athena has a goal of ∼5 arcsec), which is expected to be also equipped with a spectrometer with resolving power λ/Δλ ≥ 5,000 and effective area Aeff ∼ 4,000 cm2 (as opposed to λ/Δλ ≤ 800 and Aeff ∼ 150 cm2 of the XMM-Newton RGS). Smaller-class missions, based on either spatial or spectral resolution as those anticipated for Lynx, have also been proposed to NASA; if selected, they might fly within this decade and considerably advance this research field. In any case, Athena and Lynx hold the greatest potential of transformational science. With their unprecedented sensitivity (afforded by the

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combination of larger collecting area and good angular resolution), these two observatories will finally reveal the emission from the most tenuous gas components of the hot ISM, such as the starburst superwind bubbles and the ETG halos well beyond 5 Re . Simultaneously, future progress in numerical coding and an increased power of the computing resources will allow us to perform simulations with higher resolution, in terms of mass and length, with a larger dynamic range, covering a region extending from the nucleus to the circumgalactic environment and elapsing for a simulated time that represents a significant part of the galaxy lifetime. A few important lines of investigation, not entirely new but addressed more adequately, could then be the following: (1) properly evaluate the mass accretion rate close to the SMBH (with ∼ pc-scale resolution), and measure the effectiveness and the consequences of the various forms of AGN feedback, in the nuclear region and on the galactic scale; (2) include a more complete list of physical processes acting on the gas (as angular momentum, magneto-hydrodynamical phenomena, cosmic ray injection, turbulence); (3) follow the evolution of the various metal species, produced by star formation and SNe, and investigate possible inhomogeneities in their spatial distribution; (4) evolve the ISM in the galactic environment, by considering also the interaction with the circumgalactic medium; (5) map the hot ISM evolution for a set of model galaxies with different structural properties, representative of the whole galactic population.

References A.B. Alabi, D.A. Forbes, A.J. Romanowsky et al., MNRAS 468, 3949 (2017) L. Angelini, M. Loewenstein, R.F. Mushotzky, ApJL 557, L35 (2001) N. Arav, X. Xu, T. Miller, G.A. Kriss, R. Plesha, ApJS 247, 37 (2020) M. Arnaud, A.E. Evrard, MNRAS 305, 631 (1999) M.W. Auger, T. Treu, A.S. Bolton et al., ApJ 724, 511 (2010) I.V. Babyk, B.R. McNamara, P.E.J. Nulsen et al., ApJ 862, 39 (2018) I.V. Babyk, B.R. McNamara, P.D. Tamhane et al., ApJ 887, 149 (2019) A. Baldi, J.C. Raymond, G. Fabbiano et al., ApJS 162, 113 (2006a) A. Baldi, J.C. Raymond, G. Fabbiano et al., ApJ 636, 158 (2006b) D. Barret, A. Decourchelle, A. Fabian et al., Astronomische Nachrichten 341, 224 (2020) M. Bauer, W. Pietsch, G. Trinchieri et al., A&A 467, 979 (2007) E.F. Bell, D.H. McIntosh, N. Katz, M.D. Weinberg, ApJS 149, 289 (2003) A.J. Benson, R.G. Bower, C.S. Frenk et al., ApJ 599, 38 (2003) J. Binney, MNRAS 347, 1093 (2004) R. Blandford, D. Meier, A. Readhead, ARAA 57, 467 (2019) H. Boehringer, G. Hensler, A&A 215, 147 (1989) Á. Bogdán, A.D. Goulding, ApJ 800, 124 (2015) C.M. Booth, J. Schaye, MNRAS 405, L1 (2010) B. Boroson, D.-W. Kim, G. Fabbiano, ApJ 729, 12 (2011) N.J. Brassington, G. Fabbiano, D.W. Kim et al., ApJS 181, 605 (2009) J.N. Bregman, E.D. Miller, A.E. Athey, J.A. Irwin, ApJ 635, 1031 (2005) D.A. Buote, ApJL 574, L135 (2002) D.A. Buote, A.D. Lewis, F. Brighenti, W.G. Mathews, ApJ 595, 151 (2003) S.J. Bush, Z. Wang, M. Karovska, G.G. Fazio, ApJ 688, 875 (2008)

118 The Hot Interstellar Medium

4365

C.R. Canizares, G. Fabbiano, G. Trinchieri, ApJ 312, 503 (1987) J. Cantó, A.C. Raga, L.F. Rodríguez, ApJ 536, 896 (2000) M. Cappellari, N. Scott, K. Alatalo et al., MNRAS 432, 1709 (2013) K.W. Cavagnolo, M. Donahue, G.M. Voit, M. Sun, ApJS 182, 12 (2009) R. Cen, J.P. Ostriker, ApJ 650, 560 (2006) R.A. Chevalier, A.W. Clegg, Nature 317, 44 (1985) E. Choi, J.P. Ostriker, T. Naab, L. Oser, B.P. Moster, MNRAS 449, 4105 (2015) E. Choi, J.P. Ostriker, T. Naab et al., ApJ 844, 31 (2017) L. Chomiuk, M.S. Povich, AJ 142, 197 (2011) L. Ciotti, J.P. Ostriker, ApJ 665, 1038 (2007) L. Ciotti, A. D’Ercole, S. Pellegrini, A. Renzini, ApJ 376, 380 (1991) L. Ciotti, J.P. Ostriker, D. Proga, ApJ 699, 89 (2009) L. Ciotti, S. Pellegrini, A. Negri, J.P. Ostriker, ApJ 835, 15 (2017) T.J. Cox, T. Di Matteo, L. Hernquist et al., ApJ 643, 692 (2006) K.M. Dasyra, L.J. Tacconi, R.I. Davies et al., ApJ 651, 835 (2006) T.J. Davidge, ApJ 725, 1342 (2010) A.J. Deason, V. Belokurov, N.W. Evans, I.G. McCarthy, ApJ 748, 2 (2012) S. Diehl, T.S. Statler, ApJ 687, 986 (2008) G. Fabbiano, ApJ 330, 672 (1988) G. Fabbiano, ARAA 27, 87 (1989) G. Fabbiano, ARAA 44, 323 (2006) G. Fabbiano, G. Trinchieri, ApJ 286, 491 (1984) G. Fabbiano, D.W. Kim, G. Trinchieri, ApJS 80, 531 (1992) A.C. Fabian, ARAA 32, 277 (1994) A.C. Fabian, ARAA 50, 455 (2012) G.B. Field, ApJ 142, 531 (1965) A. Finoguenov, M. Ruszkowski, C. Jones et al., ApJ 686, 911 (2008) D.A. Forbes, A. Alabi, A.J. Romanowsky et al., MNRAS 464, L26 (2017) H.A. Ford, J.N. Bregman, ApJ 770, 137 (2013) W. Forman, C. Jones, W. Tucker, ApJ 293, 102 (1985) Z. Gan, L. Ciotti, J.P. Ostriker, F. Yuan, ApJ 872, 167 (2019) J.A. Gaskin, D.A. Swartz, A. Vikhlinin et al., J. Astron. Telescopes Instrum. Syst. 5, 021001 (2019) M. Gaspari, F. Brighenti, P. Temi, MNRAS 424, 190 (2012) M. Gaspari, M. Ruszkowski, S. Oh, MNRAS 432, 3401 (2013) M. Gaspari, D. Eckert, S. Ettori et al., ApJ 884, 169 (2019) R. Giacconi, G. Branduardi, U. Briel et al., ApJ 230, 540 (1979) M.R. Gilfanov, R.A. Sunyaev, E.M. Churazov, SvAL 13, 3 (1987) A.D. Goulding, J.E. Greene, C.-P. Ma et al., ApJ 826, 167 (2016) J.P. Grimes, T. Heckman, D. Strickland, A. Ptak, ApJ 628, 187 (2005) F. Guo, S.P. Oh, MNRAS 384, 251 (2008) Z. Hafen, C.-A. Faucher-Giguère, D. Anglés-Alcázar et al., MNRAS 488, 1248 (2019) M.J. Hardcastle, J.H. Croston, New Astron. Rev. 88, 101539 (2020) C.M. Harrison, T. Costa, C.N. Tadhunter et al., Nat. Astron. 2, 198 (2018) T.M. Heckman, L. Armus, G.K. Miley, ApJS 74, 833 (1990) Hitomi Collaboration, F. Aharonian, H. Akamatsu et al., Nature 551, 478 (2017) Hitomi Collaboration, F. Aharonian, H. Akamatsu et al., PASJ 70, 9 (2018) P.F. Hopkins, M. Elvis, MNRAS 401, 7 (2010) P.F. Hopkins, L. Hernquist, T.J. Cox et al., ApJ 630, 705 (2005) P.F. Hopkins, L. Hernquist, T.J. Cox et al., ApJS 163, 1 (2006) Z.Y. Huo, X.Y. Xia, S.J. Xue, S. Mao, Z.G. Deng, ApJ 611, 208 (2004) N. Islam, D.-W. Kim, K. Lin et al., ApJS 256, 22 (2021) P.H. Johansson, T. Naab, J.P. Ostriker, ApJL 697, L38 (2009) A. Juráˇnová, N. Werner, P.E.J. Nulsen et al., MNRAS 499, 5163 (2020) N. Kaiser, MNRAS 222, 323 (1986)

4366

E. Nardini et al.

R.C. Kennicutt, N.J. Evans, ARAA 50, 531 (2012) D.-W. Kim, Galaxies 5, 60 (2017) D.-W. Kim, G. Fabbiano, ApJ 611, 846 (2004a) D.-W. Kim, G. Fabbiano, ApJ 613, 933 (2004b) D.-W. Kim, G. Fabbiano, ApJ 721, 1523 (2010) D.-W. Kim, G. Fabbiano, ApJ 776, 116 (2013) D.-W. Kim, G. Fabbiano, ApJ 812, 127 (2015) D.-W. Kim, S. Pellegrini (eds.), Hot Interstellar Matter in Elliptical Galaxies. Astrophysics and Space Science Library, vol. 378 (Springer, Heidelberg, 2012) D.-W. Kim, E. Kim, G. Fabbiano, G. Trinchieri, ApJ 688, 931 (2008) D.-W. Kim, C. Anderson, D. Burke et al., ApJS 241, 36 (2019a) D.-W. Kim, N. James, G. Fabbiano, D. Forbes, A. Alabi, MNRAS 488, 1072 (2019b) D.-W. Kim, L. Traynor, A. Paggi et al., MNRAS 492, 2095 (2020) A. King, K. Pounds, ARAA 53, 115 (2015) C.C. Kirkpatrick, M. Gitti, K.W. Cavagnolo et al., ApJL 707, L69 (2009) W. Kollatschny, P.M. Weilbacher, M.W. Ochmann et al., A&A 633, A79 (2020) K. Kolokythas, E. O’Sullivan, S. Giacintucci et al., MNRAS 496, 1471 (2020) J. Kormendy, R. Bender, Nature 469, 377 (2011) J. Kormendy, L.C. Ho, ARAA 51, 511 (2013) J. Kormendy, D.B. Fisher, M.E. Cornell, R. Bender, ApJS 182, 216 (2009) H. Kuntschner, E. Emsellem, R. Bacon et al., MNRAS 408, 97 (2010) K. Lakhchaura, N. Werner, M. Sun et al., MNRAS 481, 4472 (2018) M.D. Lehnert, T.M. Heckman, ApJ 462, 651 (1996) M.D. Lehnert, T.M. Heckman, K.A. Weaver, ApJ 523, 575 (1999) C. Leitherer, D. Schaerer, J.D. Goldader et al., ApJS 123, 3 (1999) Y. Li, G.L. Bryan, ApJ 789, 54 (2014) J.-T. Li, Q.D. Wang, MNRAS 428, 2085 (2013) H. Li, S. Mao, M. Cappellari et al., MNRAS 476, 1765 (2018) M. Li, Y. Li, G.L. Bryan, E.C. Ostriker, E. Quataert, ApJ 898, 23 (2020) J. Liu, Q.D. Wang, S. Mao, MNRAS 420, 3389 (2012) W. Liu, S. Veilleux, K. Iwasawa et al., ApJ 872, 39 (2019) M. Loewenstein, A.C. Fabian, MNRAS 242, 120 (1990) A.B. Mantz, Z. Abdulla, S.W. Allen et al., A&A 620, A2 (2018) D. Maoz, O. Graur, ApJ 848, 25 (2017) D. Maoz, F. Mannucci, G. Nelemans, ARAA 52, 107 (2014) M. Markevitch, A. Vikhlinin, Phys. Rep. 443, 1 (2007) W. Mathews, ApJ 354, 468 (1990) W.G. Mathews, J.C. Baker, ApJ 170, 241 (1971) W.G. Mathews, F. Brighenti, ARAA 41, 191 (2003) W.G. Mathews, F. Brighenti, A. Faltenbacher et al., ApJL 652, L17 (2006) B.R. McNamara, P.E.J. Nulsen, New J. Phys. 14, 055023 (2012) B.R. McNamara, H.R. Russell, P.E.J. Nulsen et al., ApJ 830, 79 (2016) J.C. Mihos, L. Hernquist, ApJ 464, 641 (1996) S. Mineo, M. Gilfanov, R. Sunyaev, MNRAS 426, 1870 (2012) H. Mo, F. Van den Bosch, S. White, Galaxy Formation and Evolution (Cambridge University Press, Cambridge, 2010) J.S. Mulchaey, ARAA 38, 289 (2000) T. Naab, J.P. Ostriker, ARAA 55, 59 (2017) E. Nardini, J. Wang, G. Fabbiano et al., ApJ 765, 141 (2013) A. Negri, L. Ciotti, S. Pellegrini, MNRAS 439, 823 (2014a) A. Negri, S. Posacki, S. Pellegrini, L. Ciotti, MNRAS 445, 1351 (2014b) A. Negri, S. Pellegrini, L. Ciotti, MNRAS 451, 1212 (2015) C. Nipoti, J. Binney, MNRAS 382, 1481 (2007) L. Oser, J.P. Ostriker, T. Naab, P.H. Johansson, A. Burkert, ApJ 725, 2312 (2010)

118 The Hot Interstellar Medium

4367

E. O’Sullivan, J.M. Vrtilek, D.E. Harris, T.J. Ponman, ApJ 658, 299 (2007) A. Paggi, D.-W. Kim, C. Anderson et al., ApJ 844, 5 (2017) E.K. Panagoulia, A.C. Fabian, J.S. Sanders, MNRAS 438, 2341 (2014) E.K. Panagoulia, J.S. Sanders, A.C. Fabian, MNRAS 447, 417 (2015) J.R. Parriott, J.N. Bregman, ApJ 681, 1215 (2008) S. Pellegrini, MNRAS 364, 169 (2005) S. Pellegrini, ApJ 738, 57 (2011) S. Pellegrini, Hot gas flows on global and nuclear galactic scales, in Hot Interstellar Matter in Elliptical Galaxies, ed. by D.-W. Kim, S. Pellegrini. Astrophysics and Space Science Library, vol. 378 (Springer, Heidelberg, 2012), p. 21 S. Pellegrini, L. Ciotti, J.P. Ostriker, ApJ 744, 21 (2012a) S. Pellegrini, J. Wang, G. Fabbiano et al., ApJ 758, 94 (2012b) S. Pellegrini, L. Ciotti, A. Negri, J.P. Ostriker, ApJ 856, 115 (2018) S. Pellegrini, Z. Gan, J.P. Ostriker, L. Ciotti, Astron. Nachr. 341, 184 (2020) M. Persic, Y. Rephaeli, A&A 382, 843 (2002) J.R. Peterson, A.C. Fabian, Phys. Rep. 427, 1 (2006) C. Pfrommer, R. Pakmor, K. Schaal, C.M. Simpson, V. Springel, MNRAS 465, 4500 (2017) F. Pizzolato, N. Soker, ApJ 632, 821 (2005) T.J. Ponman, A.J.R. Sanderson, A. Finoguenov, MNRAS 343, 331 (2003) P. Predehl, R.A. Sunyaev, W. Becker et al., Nature 588, 227 (2020) P. Predehl, R. Andritschke, V. Arefiev et al., A&A 647, A1 (2021) S.W. Randall, C. Jones, R. Kraft, W.R. Forman, E. O’Sullivan, ApJ 696, 1431 (2009) S.W. Randall, P.E.J. Nulsen, C. Jones et al., ApJ 805, 112 (2015) J. Rasmussen, T.J. Ponman, MNRAS 399, 239 (2009) E. Roediger, M. Brüggen, A. Simionescu et al., MNRAS 413, 2057 (2011) E. Roediger, R.P. Kraft, P.E.J. Nulsen et al., ApJ 806, 103 (2015) C.L. Sarazin, Feedback and environmental effects in elliptical galaxies, in Hot Interstellar Matter in Elliptical Galaxies, ed. by D.-W. Kim, S. Pellegrini. Astrophysics and Space Science Library, vol. 378 (Springer, Heidelberg, 2012), p. 55 C.L. Sarazin, R.E. White I, ApJ 331, 102 (1988) M. Sarzi, K. Alatalo, L. Blitz et al., MNRAS 432, 1845 (2013) P. Sharma, M. McCourt, E. Quataert, I. Parrish, MNRAS 420, 3174 (2012) M. Sinha, K. Holley-Bockelmann, MNRAS 397, 190 (2009) G.R. Sivakoff, C.L. Sarazin, J.A. Irwin, ApJ 599, 218 (2003) B.J. Smith, K. Campbell, C. Struck et al., AJ 155, 81 (2018) V. Springel, T. Di Matteo, L. Hernquist, MNRAS 361, 776 (2005) I. Strateva, Ž. Ivezi´c, G.R. Knapp et al., AJ 122, 1861 (2001) D.K. Strickland, T.M. Heckman, ApJ 658, 258 (2007) D.K. Strickland, T.M. Heckman, ApJ 697, 2030 (2009) D.K. Strickland, I.R. Stevens, MNRAS 314, 511 (2000) D.K. Strickland, T.M. Heckman, K.A. Weaver, C.G. Hoopes, M. Dahlem, ApJ 568, 689 (2002) D.K. Strickland, T.M. Heckman, E.J.M. Colbert, C.G. Hoopes, K.A. Weaver, ApJS 151, 193 (2004) Y. Su, R.P. Kraft, E. Roediger et al., ApJ 834, 74 (2017a) Y. Su, P.E.J. Nulsen, R.P. Kraft et al., ApJ 847, 94 (2017b) A.A. Suchkov, V.G. Berman, T.M. Heckman, D.S. Balsara, ApJ 463, 528 (1996) M. Sun, C. Jones, W. Forman et al., ApJ 657, 197 (2007) M. Sun, G.M. Voit, M. Donahue et al., ApJ 693, 1142 (2009) R. Sunyaev, V. Arefiev, V. Babyshkin et al., A&A 656, A132 (2021) R.S. Sutherland, M.A. Dopita, ApJS 88, 253 (1993) F.S. Tabatabaei, E.M. Berkhuijsen, A&A 517, A77 (2010) S. Tang, Q.D. Wang, ApJ 628, 205 (2005) S. Tang, Q.D. Wang, MNRAS 408, 1011 (2010) M. Tashiro, H. Maejima, K. Toda et al., in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 11444, p. 1144422 (2020)

4368

E. Nardini et al.

E. Treister, H. Messias, G.C. Privon et al., ApJ 890, 149 (2020) C.A. Tremonti, T.M. Heckman, G. Kauffmann et al., ApJ 613, 898 (2004) G. Trinchieri, G. Fabbiano, ApJ 296, 447 (1985) G. Trinchieri, G. Fabbiano, C.R. Canizares, ApJ 310, 637 (1986) G. Trinchieri, S. Pellegrini, G. Fabbiano et al., ApJ 688, 1000 (2008) P.W. Vedder, J.J. Trester, C.R. Canizares, ApJ 332, 725 (1988) S. Veilleux, G. Cecil, J. Bland-Hawthorn, ARAA 43, 769 (2005) S. Veilleux, S.H. Teng, D.S.N. Rupke, R. Maiolino, E. Sturm, ApJ 790, 116 (2014) J.C. Vernaleo, C.S. Reynolds, ApJ 645, 83 (2006) A. Vikhlinin, M. Markevitch, S.S. Murray et al., ApJ 628, 655 (2005) G.M. Voit, Rev. Mod. Phys. 77, 207 (2005) G.M. Voit, S.T. Kay, G.L. Bryan, MNRAS 364, 909 (2005) M.G. Watson, V. Stanger, R.E. Griffiths, ApJ 286, 144 (1984) D.W. Weedman, F.R. Feldman, V.A. Balzano et al., ApJ 248, 105 (1981) M.C. Weisskopf, B. Brinkman, C. Canizares et al., PASP 114, 1 (2002) N. Werner, J.B.R. Oonk, M. Sun et al., MNRAS 439, 2291 (2014) N. Werner, B.R. McNamara, E. Churazov, E. Scannapieco, Space Sci. Rev. 215, 5 (2019) R.A. Wood, C. Jones, M.E. Machacek et al., ApJ 847, 79 (2017) D.M. Worrall, M. Birkinshaw, M.J. Hardcastle, MNRAS 343, L73 (2003) H. Xu, S.M. Kahn, J.R. Peterson et al., ApJ 579, 600 (2002) H.-Y.K. Yang, C.S. Reynolds, ApJ 829, 90 (2016) F. Yuan, R. Narayan, ARAA 52, 529 (2014) M.S. Yun, P.T.P. Ho, K.Y. Lo, Nature 372, 530 (1994) D. Zhang, Galaxies 6, 114 (2018) D. Zhang, T.A. Thompson, N. Murray, E. Quataert, ApJ 784, 93 (2014) J.A. ZuHone, K. Kowalik, E. Ohman, E. Lau, D. Nagai, arXiv e-prints, arXiv:1609.04121 (2016)

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Ákos Bogdán and Mark Vogelsberger

Contents Introducing X-Ray Halos Around Massive Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Overview of Past X-Ray Observations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Simulating X-Ray Halos Around Massive Spiral Galaxies . . . . . . . . . . . . . . . . . . . . . . . . . . Confronting the Observed and Simulated Properties of the CGM . . . . . . . . . . . . . . . . . . . . . X-Ray Scaling Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Metallicity of the CGM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Missing Baryon Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Importance of AGN Feedback on the Observed Properties of the CGM . . . . . . . . . . Missing Feedback Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Future Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Abstract

The presence of gaseous X-ray halos around massive galaxies is a basic prediction of all past and modern structure formation simulations. The importance of these X-ray halos is further emphasized by the fact that they retain signatures of the physical processes that shape the evolution of galaxies from the highest redshift to the present day. In this review, we overview our current observational and theoretical understanding of hot gaseous X-ray halos around nearby massive galaxies, and we also describe the prospects of observing X-ray halos with future instruments. Á. Bogdán () Center for Astrophysics | Harvard & Smithsonian, Cambridge, MA, USA e-mail: [email protected] M. Vogelsberger Massachusetts Institute of Technology, Cambridge, MA, USA e-mail: [email protected] © Springer Nature Singapore Pte Ltd. 2024 C. Bambi, A. Santangelo (eds.), Handbook of X-ray and Gamma-ray Astrophysics, https://doi.org/10.1007/978-981-19-6960-7_110

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Keywords

Spiral galaxies · Elliptical galaxies · X-ray halos · Galaxy formation · X-ray emission

Introducing X-Ray Halos Around Massive Galaxies Motivation The first gaseous X-ray emitting halos around massive galaxies in the Virgo cluster were observed nearly 50 years ago using the Einstein Observatory (Mathews 1978; Forman et al. 1979), but theoretical considerations suggesting the existence of such halos date back even earlier. The existence of an extended gaseous halo around the Milky Way was first hypothesized by Spitzer (1956), who suggested that this circumgalactic medium (henceforward CGM) would have a temperature of 106 K and an electron density of 5 × 10−4 cm−3 . Based on these properties, the radiation from the CGM is expected to fall in the X-ray waveband. Interestingly, studies performed with modern-day X-ray telescopes, such as the Chandra X-ray Observatory, confirmed the presence of the CGM around the Milky Way (e.g. Gupta et al. 2017) and established that the X-ray properties of the hot gas are, in fact, comparable to those suggested by Spitzer (1956). Although the initial prediction by Spitzer (1956) only forecasted the presence of an X-ray emitting CGM around the Milky Way, about two decades later, White and Rees (1978) generalized this picture and suggested that luminous X-ray halos are an essential part of galaxy formation. They proposed a two-stage theoretical picture of galaxy formation. In the first stage, the baryonic material originating from the intergalactic medium is accreted onto the dark matter halos of galaxies. During the infall, accretion shocks heat the gas to the virial temperature of the galaxies, which – for massive dark matter halos – is a few million Kelvin. Therefore, the X-ray halos of massive galaxies are expected to emit in the X-ray waveband. In the second stage of galaxy formation, the radiative cooling of the hot X-ray emitting gas results in cooling flows, which provide material for star formation, thereby building up the stellar content of galaxies. This initial model of galaxy formation was further improved by White and Frenk (1991), who suggested that the X-ray emitting CGM can extend beyond the stellar body of galaxies and they are ubiquitous around all Milky Way-type (i.e., diskdominated) galaxies. They also established that the X-ray gas cools via line emission and thermal bremsstrahlung and provides material to the formation of stars. These processes were shown to be essential to reproduce the observed diversity of galaxy morphology, the disruption of disks due to mergers, and bar instabilities. Overall, White and Frenk (1991) demonstrated that the CGM is an integral part of galaxies, and the physical processes associated with its heating and cooling play a profound effect on the overall evolution of galaxies. Therefore, to understand the evolution of galaxies from high redshifts to the present epochs, it is indispensable to model the evolution of the CGM. In fact, comparing the theoretical predictions of the CGM

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with its observable properties allows to probe and constrain a multitude of complex physical processes, which are not easily accessible by other observational studies. Because observations of the CGM around present-day galaxies can provide a wealth of information about the origin and evolution of galaxies, it is important to investigate the basic characteristics of the CGM. The infalling gas is expected to be shock-heated to the virial temperature of the host galaxy’s dark matter halo, which temperature can be described as T200 =

2  μ  v200 1 μmp 2 , v200 = 3.6 × 105 K 3 kB 0.59 100 km s−1

(1)

where μ is the mean molecular weight, mp is the proton mass, kB is the Boltzmann constant, and v200 is the circular velocity of the galaxy. For massive galaxies that exhibit v200  200 km s−1 , this characteristic temperature will be a few million Kelvin (or  0.1 keV), and the gas will emit in the soft X-ray regime. Because the cooling time of the X-ray gas around massive galaxies exceeds the dynamical time, the X-ray halos will be quasi-static on timescales comparable to the Hubble time. This directly implies that the infalling gas that was heated to X-ray temperatures at the formation of the galaxies should remain observable even in the presentday Universe as the CGM. During the evolution of galaxies, the characteristics of the CGM are expected to change due to various physical processes. Thus, the large-scale CGM reflects both the basic principles of galaxy formation and retains a memory of the physical processes that shaped the galaxies throughout their evolution. Therefore, the CGM of galaxies provides a superb observational probe to simultaneously constrain both the basic principles of galaxy formation and the high-level physics of galaxy evolution.

Overview of Past X-Ray Observations Recognizing the importance of the CGM around massive galaxies, a large number of observational campaigns were carried out in the past decades to detect the hot gaseous halos and characterize their properties. In the following subsections, we overview the main observational efforts to explore the CGM around massive elliptical and disk-dominated galaxies.

Massive Elliptical Galaxies In elliptical galaxies, the hot X-ray emitting gas can have two different origins. First, similar to disk-dominated galaxies, part of it may arise from the infall of the primordial gas onto the dark matter halos, which gas was shock-heated to the virial temperature of the dark matter halo. Second, the gas ejected from evolved stars and planetary nebulae may collide with ambient gas and gets shock-heated to the kinetic temperature of the galaxy, which is equivalent with the galaxy’s stellar velocity dispersion. However, the relative contribution of these different sources to the overall emission has remained unclear.

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The existence of luminous X-ray halos around elliptical galaxies was established based on Einstein and ROSAT X-ray observations (Forman et al. 1985; Trinchieri and Fabbiano 1985; Mathews 1990; Mathews and Brighenti 2003). These studies demonstrated the ubiquitous nature of extended X-ray halos around elliptical galaxies and showed that these halos often extend beyond the galaxy’s stellar distribution. While the luminous nature of the X-ray emission has been established around ellipticals, the relative contribution of different types of sources and the physical state of the hot gas has been debated. This was drastically changed with the launch of Chandra and XMM-Newton, which instruments provided a definite edge on previous instruments. Specifically, the high angular resolution of these instruments allowed to resolve bright point sources in the galaxies, such as lowmass X-ray binaries or AGN (Gilfanov 2004; Fabbiano 2006). In addition, detailed studies of the Milky Way and some nearby galaxies, e.g., M32 or NGC3379, allowed detailed studies of even fainter X-ray stellar sources, such as active binaries and cataclysmic variables, and to estimate the contribution of these unresolved point sources to the integrated emission of the galaxies (Sazonov et al. 2006; Revnivtsev et al. 2006, 2008). Since X-ray halos were routinely detected around massive elliptical galaxies, many studies explored the most fundamental properties of the gas, namely, its X-ray luminosity and gas temperature. Since a substantial number of galaxies were observed, a statistically significant sample could be studied, and basic correlations could be established. Specifically, the luminosity of the gas correlates with the gas temperature for all virialized systems, including galaxy clusters, galaxy groups, and galaxies. However, the slope of the LX,gas − Tgas relation exhibits differences: 2−3 , galaxy groups have a steeper relation While galaxy clusters exhibit LX,gas ∝ Tgas 3−4 with LX,gas ∝ Tgas ; on galaxy scales, the relation may become even steeper, 4.5 . The breakdown in the scaling relation in galaxies is likely due to LX,gas ∝ Tgas the baryon physics, such as the feedback from AGN and supernovae, which play a more significant role than gravity. Additionally, it was established that the X-ray luminosity of elliptical galaxies exhibits a correlation with the optical properties of galaxies. Specifically, O’Sullivan et al. (2001) concluded that the X-ray luminosity of the hot gas approximately correlates with the B-band luminosity of galaxies. Since the B-band mass-to-light ratios exhibit large scatter, follow-up studies used the K-band luminosity and/or the stellar mass of galaxies to establish trends between the X-ray luminosity of gaseous halos and the physical properties of galaxies. These studies established that there is a correlation between these properties, but the scatter in the LX,gas –M⋆ relation is larger than expected based on a simple expectation. The large scatter can be attributed to physical processes that influence the physical properties of the gas, notably the energetic feedback of the AGN and the rotation properties of the galaxies. To further explore these scaling relations, Kim and Fabbiano (2013) probed the relation between the X-ray luminosity and the total mass of galaxies within five effective radii (Mtot ). They found a tight correlation for galaxies in the LX,gas = 1038 − 1043 erg s−1 luminosity range with an rms deviation of a factor of three. Surprisingly, this correlation is much tighter

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than that obtained between the X-ray luminosity and the stellar mass. This hinted that the most important factor in regulating the luminosity and amount of gas may be the total gravitating mass of the galaxy. As a caveat, it needs to be considered that this work is based on a relatively small sample of galaxies, and the total mass measurements only extend out to five effective radii, which corresponds to 3–30 kpc, and hence are a small fraction of the virial radius of galaxies, implying that only a few percent of the total gravitating mass is included in these regions. To establish the relations for large samples, volume-limited surveys were used. The ATLAS3D sample explored all nearby early-type galaxies with MK < −21.5 mag. Due to the nearby nature of the galaxies in this survey, this survey contains very few massive M⋆ > 1011 M⊙ galaxies. They found evidence that slow rotators exhibit lower X-ray luminosity at a given stellar mass than fast rotators. To explore more massive galaxies, the volume-limited MASSIVE survey focused on the most massive nearby galaxies in the local (D < 100 Mpc) universe. They 4.5 and demonstrated established a universal scaling law such that LX,gas ∝ Tgas that the scatter in the X-ray luminosity around the stellar mass is driven by the temperature of the gas. See also the chapter on the hot ISM in section (Nardini, Kim & Pellegrini). To study a large statistical sample of galaxies, which is not feasible using pointing X-ray telescopes, archival ROSAT data was used. Because most of these galaxies are not detected individually, the stacking technique has been applied to enhance the signal-to-noise ratios. In the stacking analysis, the X-ray photons associated with many different galaxies are co-added (i.e., stacked). While individual galaxies are too faint to be detected above the noise, by co-adding them a statistically significant could be detected since the random noise cancels out, while the signal from the galaxies becomes enhanced. By stacking the ROSAT X-ray data of more than 2000 isolated galaxies, the X-ray emission was detected, and they could establish an average luminosity of ∼1040 erg s−1 . Interestingly, they did not find a statistically significant difference between the luminosity of elliptical and spiral galaxies (Anderson et al. 2013). While the nominal X-ray luminosity of ellipticals is slightly higher, this may be due to the fact that elliptical galaxies are – on average – more massive than their spiral counterparts. In a similar study, the X-ray halos of more than 3000 elliptical galaxies were stacked, and galaxies with ∼4 × 1010 M⊙ were detected (Bogdán and Goulding 2015). Since ROSAT does not have the angular resolution or the energy resolution to distinguish the emission from hot X-ray halos and the population of unresolved X-ray sources (X-ray binaries), scaling relations were used to estimate the contribution of hot gas, which found that substantial fraction of the emission originates from truly diffuse hot gas.

Massive Disk Galaxies Although the ubiquity and luminous nature of the CGM around massive elliptical galaxies have been established based on observations with the Einstein and ROSAT X-ray satellites decades ago (see section “Massive Elliptical Galaxies”), observations of disk-dominated galaxies were much less successful. However, these

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detections are especially important because the characterization of the CGM around massive disk-dominated galaxies can provide a unique insight into the formation and evolution of galaxies. The main advantage of disk-dominated galaxies is their environment. Because elliptical galaxies form through a series of mergers, they tend to reside in galaxy groups or galaxy clusters. Indeed, due the high galaxy density of rich environments, the likelihood of galaxy-galaxy interactions is much higher, thereby facilitating the formation of ellipticals. As opposed to this, disk-dominated galaxies may not undergo many merger events; hence a substantial population of these galaxies will reside in relatively isolated environments. In fact, the existence of a disk signifies that a galaxy did not experience strong mergers, because galaxy disks are destroyed during such violent events. Moreover, the relatively quiescent merger history of disk-dominated galaxies also assures that the characteristics of the CGM were not drastically altered by the energetic events that are typically initiated by mergers. A potential disadvantage of disk galaxies is the presence of other luminous X-ray emitting components, such as ultra-luminous X-ray sources or starburstdriven winds, that may either play an important role or even dominate the large-scale X-ray emission. However, using various observational techniques, it is fairly easy to identify disk galaxies, whose overall emission is dominated by these X-ray emitting components. Excluding these – typically very actively star forming – galaxies can result in a clean galaxy sample containing relatively quiescent isolated disk galaxies that should host quasi-static X-ray halos. While the bulk of the CGM is expected to originate from the accreted pristine gas at the earliest epochs of galaxy formation, the physical properties and spatial structure of the gas will reflect an imprint of the physical processes that shaped these galaxies. Thus, isolated disk-dominated galaxies are a unique population of galaxies that offer a view into the complex physical processes that influence the evolution of galaxies. Similar to ellipticals, disk-dominated galaxies were the subject of multiple observing campaigns carried out with all major X-ray telescopes. However, these searches were not conclusive, and due to the lack of significant detections, serious doubts were cast on galaxy formation models, and the basic principles of galaxy formation were questioned. Initial studies of disk-dominated galaxies used the ROSAT X-ray observatory but failed to detect luminous X-ray halos (Benson et al. 2000). Because the CGM around these galaxies was fainter than predicted by early galaxy formation models, the search continued using more sensitive X-ray telescopes, such as Chandra and XMM-Newton. However, X-ray observations of “normal” (i.e., non-starburst) disk galaxies led to controversial results and nondetections (Rasmussen et al. 2009). While these attempts remained unsuccessful, a fair number of disk galaxies were shown to host X-ray gas. However, these disk galaxies have high star-formation rates, and the morphology of the gas exhibits a bipolar morphology, suggesting that it is driven by starburst (Strickland et al. 2004; Tüllmann et al. 2006). This suggests that the bulk of the X-ray emission associated with the CGM of these galaxies is of internal origin (i.e., gas lifted by supernovae) and does not originate from the infall of primordial gas.

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The first success in the detection of the CGM around “normal” disk-dominated galaxies was achieved for NGC 1961 and NGC 6753 (Anderson and Bregman 2011; Bogdán et al. 2013b). These galaxies are extremely massive (M⋆ = (3 − 4) × 1011 M⊙ ) and fairly isolated and have relatively low star-formation rates (∼12 − 15 M⊙ yr−1 ) given their stellar mass. Based on Chandra and XMM-Newton observations, the presence of luminous X-ray gas was demonstrated that exhibits a luminosity of ∼6 × 1040 erg s−1 beyond the optical extent of the galaxies. The gaseous emission could be traced out to ∼60 kpc radius for both galaxies, implying that the gas is indeed extended and not confined to the optical body (Figs. 1 and 2). However, it must be realized that this radius is still a relatively small fraction of the galaxy’s virial radius (∼15%r200 ). The azimuthal distribution of the CGM exhibits an approximately uniform distribution, suggesting that it resides in hydrostatic equilibrium rather than in a starburst-driven bipolar outflow. Thus, the detection of the large-scale CGM of these two massive galaxies confirmed that our basic picture of galaxy formation is correct and massive disk galaxies indeed host luminous X-ray emitting CGM. Besides the detection of these X-ray halos, the physical characteristics of the X-ray gas could also be established, which were further improved using deep follow-up XMM-Newton observations (Anderson et al. 2016; Bogdán et al. 2017). These studies established that the temperature of the gas is approximately consistent with the virial temperature of the dark matter halos and that the gas temperature slowly declines with increasing radius from ∼0.7 keV in the innermost regions to ∼0.4 keV at ∼60 kpc. Surprisingly, the metallicity of the gas was found to be strictly sub-Solar, ∼(0.1 − 0.2)Z⊙ , at every radius, which is at odds with that obtained for massive elliptical galaxies, whose X-ray halos typically exhibit Solar metallicity. The physical properties of the gas and the implications of the results are further discussed in section “Metallicity of the CGM”. In addition, based on the gas density and temperature profiles of the galaxies, their baryon mass fractions were estimated. Bogdán et al. (2017) found fb ∼ 0.08–0.1, implying that NGC 1961 and NGC 6753 are missing about half of their baryons (see section “Missing Baryon Problem” for further discussion). These initial detections of the CGM were followed by other encouraging studies: extended hot gas was identified around UGC 12591 or NGC 266 (Dai et al. 2012; Bogdán et al. 2013a). A systematic study of six massive edge-on galaxies (including UGC 12591), the so-called Circum-Galactic Medium of MASsive Spirals (CGMMASS) sample, also demonstrated the presence of hot gas extending to 30– 100 kpc from the galactic center (Li et al. 2017). Although it was not possible to carry out in-depth studies of the CGM in these disk-dominated galaxies, the basic properties of the gas, such as the luminosity, temperature, gas density profile, could be established. Surprisingly, the X-ray luminosity of the hot gas around the CGMMASS galaxies was found to be much lower than that around NGC 1961 or NGC 6753. Overall, these detections hint that extended CGM is universal around massive disk-dominated galaxies. As a caveat, it must be noted that despite these successful detections, X-ray observations of several other (edge-on) disk galaxies did not result in statistically significant detections of the CGM (Bogdán et al. 2015).

Fig. 1 Denoised surface brightness image of NGC 1961 (left panel) and NGC 6753 (right) based on XMM-Newton observations. The size of the images is 10′ × 10′ , which corresponds to 162 × 162 kpc for NGC 1961 and 127 × 127 kpc for NGC6753. These were the first normal (i.e., non-starburst) galaxies that were shown to have a luminous CGM. The diffuse X-ray emission extends beyond the stellar light, which is shown with the green contours. The X-ray emission appears to be symmetric, suggesting that the gas may be in hydrostatic equilibrium in the gravitational potential. (The figure was adapted from Bogdán et al. 2013b)

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Fig. 2 X-ray surface brightness profile of the diffuse emission around NGC 1961 in the 0.4– 1.25 keV band based on XMM-Newton data. The two sets of black data points show the background subtracted profiles. From the lower set of points, all background components were subtracted. However, from the upper set of points, the sky background was not removed. The diffuse emission can be robustly traced out to ∼60 kpc, beyond which radius the systematic uncertainties associated with the background subtraction start to dominate. (The figure is adapted from Anderson et al. 2016)

This suggests that the highly luminous nature of the CGM around NGC 1961 and NGC 6753 may be the exception and not the rule and that the X-ray characteristics of the CGM exhibit notable galaxy-to-galaxy variations. Overall, despite the decades of endeavors, our understanding of the CGM around massive disk galaxies is far from being answered. Our in-depth knowledge about the large-scale CGM around massive disk galaxies is mostly based on the Chandra and XMM-Newton observations of NGC 1961 and NGC 6753 (Anderson et al. 2013; Bogdán et al. 2017). Interestingly, the properties of the CGM are markedly similar for both galaxies. The X-ray surface brightness profiles reveal the presence of diffuse emission beyond the stellar body (∼15 kpc) of the galaxies, which can be traced out to ∼60 kpc. While diffuse emission is likely to be present beyond this radius, it cannot be reliably mapped due to systematic uncertainties associated with the X-ray background subtraction. From the X-ray surface brightness profile, the assumed temperature, and metallicity profiles (see the next paragraphs), the gas density profile can be inferred. These measurements allowed to determine that the gas density drops from ne ∼ 3 × 10−3 cm−3 to ne ∼ 3 × 10−4 cm−3 between 10–60 kpc. This measurement is of great importance for galaxy formation simulations: it carries crucial information about the energetic

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feedback from supernovae and AGN that shape the distribution of the hot gas. For example, more powerful feedback processes will push the gas to larger radii, resulting in more evacuated dark matter halos, hence lower densities and a more rapidly declining density profile. Due to the available deep X-ray observations, the temperature and metallicity profile of the CGM around NGC 1961 and NGC 6753 could also be measured. For both galaxies, the gas temperature profile exhibits a negative gradient, with the temperature decreasing from kT ∼ 0.75 keV in the innermost regions to kT ∼ 0.4 keV at about 50 kpc radius. This result is similar to that observed for elliptical galaxies that typically have flat or declining temperature profiles (Fukazawa et al. 2006; Humphrey et al. 2006). The deep X-ray observations of these galaxies also allow tracing the spatial distribution of the CGM. By studying the gas in circular surface brightness profiles, it was established that the X-ray gas has an approximately uniform distribution around the galaxies, which suggests that the gas is in hydrostatic equilibrium and is not dominated by a bipolar outflow driven by starburst or AGN. Similarly, the temperature structure of NGC 1961 and NGC 6753 was explored. Using simple one-component temperature models, it was established that the gas temperature exhibits some variations, which hint at the presence of a potentially more complex temperature structure. However, interpretation of these results is not trivial since the X-ray temperature measurements are luminosity-weighted, implying that the observed values are dominated by the gas at about 20–30 kpc radius. To explore the temperature structure of CGM in more detail, a temperature map was computed for NGC 6753, which also highlighted the rather complex temperature structure of the CGM.

Simulating X-Ray Halos Around Massive Spiral Galaxies Modern cosmological simulations include a wide range of physical processes ranging from supernova feedback to the feedback related to active galactic nuclei. Such hydrodynamic simulations have led to impressive progress over the last decade producing galaxy populations that agree with many observable properties. These simulations can roughly be divided in two types: large volume and zoom-in simulations. The former aims to simulate large samples of galaxies simultaneously (e.g., IllustrisTNG, Eagle), whereas the latter focuses typically on individual galaxies (e.g., FIRE, Auriga) or galaxy clusters (C-Eagle). The simulations are based on three key ingredients: a cosmological framework, numerical discretization schemes for the matter components, and the implementation of various astrophysical processes. The cosmological framework includes the nature of gravity (e.g., general relativity), the type of dark matter (e.g., cold dark matter), and the type of dark energy (e.g., a cosmological constant). Furthermore, the type of initial conditions also belongs to the overall cosmological framework. The numerical discretization of the matter components (baryons, mostly in the form of gas, and dark matter) is typically implemented using a wide range of

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methods. The dark matter component is typically modeled with N-body methods representing a Monte Carlo scheme. The gas dynamics is modeled using different hydrodynamical methods. Most commonly employed methods are smoothed particle hydrodynamics (Lagrangian) and adaptive mesh refinement (Eulerian) methods. More recently, also arbitrary Lagrangian-Eulerian methods have been employed, which use moving meshes for the underlying discretization. In addition to the hydrodynamics, these models are also frequently extended to take into account the effects of magnetic fields, cosmic rays, radiation fields, and cooling/heating processes. Most astrophysical processes are typically not resolved in cosmological simulations. They are therefore incorporated in the form of sub-resolution models. These processes include star formation, stellar feedback, supermassive black holes, and active galactic nuclei. Different simulations typically differ in how these subresolution models are constructed in detail. However, in all cases, the models provide numerical closer at the resolution limit of the simulation, i.e., they represent the physics occurring on scales that cannot be resolved by the cosmological simulation. Stellar feedback also plays an important role in regulating star formation, especially in lower mass systems. Also the implementation of stellar feedback requires sub-resolution models due to the numerical limitations of cosmological simulations. Any kind of interaction of stars with their surrounding gas contributes to the stellar feedback process. This occurs through the injection of energy and momentum that causes a regulation of the local star formation. Different numerical implementations have been developed to model the stellar feedback process in cosmological simulations.

Confronting the Observed and Simulated Properties of the CGM X-Ray Scaling Relations Measuring the properties of the CGM around a statistically significant galaxy sample allowed to establish various X-ray scaling relations in elliptical galaxies (section “Massive Elliptical Galaxies”). These relations connect the basic and easily observable properties of the hot gas, such as its luminosity or temperature, with the fundamental properties of galaxies, such as the stellar or virial mass. These scaling relations play an essential role in understanding various physical processes that influence the evolution of the hot X-ray emitting gas. By confronting the observed and simulated properties of the CGM, we can thoroughly probe simulations. Specifically, these tests allow to verify the accuracy of a broad range of physics modules that play an essential role in shaping the hot gas content of galaxies. These processes include the heating from supernova and AGN feedback, enrichment by stellar and supernova yields, or mixing of the uplifted metals with the large-scale CGM.

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The CGM around massive elliptical galaxies was routinely detected, which led to well-studied scaling relations of the hot X-ray gas (section “Massive Elliptical Galaxies”). However, establishing scaling relations for large samples of diskdominated galaxies is much more difficult, which is mostly due to the X-ray faint nature of these galaxies. However, it is important to realize that disk galaxies are not necessarily X-ray faint at the same stellar (or virial) mass, but they are – on average – less massive than elliptical galaxies, making them appear fainter. Due to the faint nature of the CGM around spiral galaxies, the X-ray properties of the inner and outer halos were separately explored in many studies. A comprehensive study of the X-ray scaling relations of disk-dominated galaxies were carried out in Li et al. (2017), who focused on the inner regions of a substantial sample of galaxies (Fig. 3). They included the X-ray emission from a wide range of galaxies,

Fig. 3 The 0.5–2 keV band X-ray luminosity of the hot gas in the inner regions of galaxies (60 kpc, due to the low surface brightness of the CGM beyond 60 kpc, presentday X-ray observatories cannot probe the presence and the metallicity at large radii. However, exploring this avenue will be the subject of future observations of the next generation of X-ray telescopes (see section “Future Outlook”). Because the observed metallicity profile is inconsistent with a pure metal-rich outflow, the low metallicities observed in the CGM of massive disk-dominated galaxies may be (partly) explained by metal-poor inflows of the pristine gas, which, in turn, should result in a negative metallicity gradient. While none of the above described scenarios can explain the observed low metallicities in itself, it is likely that the ecosystem of

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metals is much more complex, including inflows and outflows, mixing, and stirring of the (primordial) hot gas with that expelled from the disk of the galaxies due to stellar and starburst driven winds and due to the energetic feedback from AGN. Theoretically, modeling metallicities in the CGM with hydrodyanmical simulations is a rather challenging problem. Incorporating the metal production in these models is in principle straightforward. However, significant uncertainties remain in terms of the exact metal yields and, therefore, the overall metal production of stars during their lifetime in the simulation. Furthermore, resolving the detailed phase structure of the gas in the CGM is also a numerical challenging for hydrodynamical simulations. Therefore, refinement mechanisms are typically employed to increase the numerical resolution within the CGM (e.g. van de Voort et al. 2019).

Missing Baryon Problem In cosmology, we differentiate the missing baryon problems on different scales. The long-standing global missing baryon problem is probably one of the most wellknown challenges of modern astrophysics. Based on constraints from the Big Bang Nucleosynthesis (Fields et al. 2014) and measurements from the cosmic microwave background (Planck Collaboration et al. 2016), the baryon content of the highredshift universe can be accurately determined. To maintain consistency with these constraints, we must be able to account for all the baryons even in the low-redshift (z  2) universe. However, when attempting to calculate the total baryon content at low redshifts, about one-third of the baryons appear to be missing, which defines the global missing baryon problem. Additionally, the local missing baryon problem refers to a similar discrepancy, but on the scales of individual dark matter halos. According to the local missing baryon problem, the easily observable baryonic mass (stars, cool gas, hot gas in the centers of galaxies) of individual galaxies is much lower than expected based on the cosmic baryon fraction. This implies that either a substantial fraction of the baryons are hidden from observations or galaxies may have lost a fraction of the baryons throughout their evolution. In the following section, we focus on the local missing baryon problem and its potential resolution.

Searching for the Missing Baryons with X-Ray Emission Measurements Theoretical studies suggest that (at least fraction of) the baryons “missing” from the individual galaxies may reside in the form of tenuous hot gas. This gas is predicted to be very extended, and it is believed to fill the entire dark matter halo of galaxies and may extend even beyond the virial radius of galaxies (White and Frenk 1991; Fukugita and Peebles 2006). To derive the baryon mass fraction of galaxies, we must derive (1) the total gravitating mass of galaxies and (2) the total mass of all baryonic components. For disk-dominated galaxies, the total gravitating mass (or virial mass – M200 ) can be computed via multiple methods. The virial mass of disk galaxies could be derived from the baryonic Tully–Fisher relation for the cold dark matter cosmogony

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3.23 relation, (Navarro et al. 1997; McGaugh et al. 2000), using the M200 ∝ Vmax where Vmax is the maximum rotational velocity of the galaxies. The advantage of this method is that for disk galaxies it is relatively easy to determine the maximum rotational velocity using the rotation curves of galaxies. However, this method cannot be applied for elliptical galaxies, which systems are not supported by rotation. An alternative method to compute the virial mass of galaxies utilizes the hot X-ray gas around galaxies and makes the (reasonable) assumption that this gas is in hydrostatic equilibrium. If the gas is spherically symmetric, only the gas pressure is significant with other forces being insignificant; the mass profile of galaxies can be derived from the equation of hydrostatic equilibrium:

M(r) =

kB T (r)r  d log ne d log T  , + μmp G d log r d log r

(2)

where μ is the molecular weight, T is the gas temperature, kB is the Boltzmann constant, μp is the proton mass, and ne is the electron density. Thus, the total mass of galaxies can be derived if the density and temperature of the X-ray gas are measured as a function of galactocentric radius. Based on X-ray observations, the derivative of the gas density is usually evaluated using a parameterized model (e.g., a β-model) for the gas density, where the parameters are determined by fitting the surface brightness profile of the X-ray gas. Similarly, the derivative of the temperature can be found using models that describe the temperature variation of the gaseous X-ray halo. The main advantage of this method is that it only employs X-ray measurements of the hot gas and is applicable to galaxies with all kinds of morphology. However, for low-mass galaxies, which lack a luminous X-ray halo, this method cannot be applied. To derive the baryon content of galaxies, all major baryonic components need to be accounted: the stellar mass of the galaxies, the cold gas, the hot X-ray emitting gas that may permeate the entire dark matter halo, and the mass of other less massive systems that reside within the galaxy’s virial radius. We define the baryon mass fraction of galaxies as fb = Mb /(Mb + MDM ) ,

(3)

where Mb is the mass of baryons and MDM is the mass of the dark matter and the sum of these two components is equivalent with the total gravitating mass. While it is relatively easy to account for the mass associated with stars and cold gas, precisely measuring the mass of the X-ray emitting hot gas presents a challenge. The main difficulty is due to the fact that X-ray emission studies only detect the gas out to a small fraction of the virial radius. However, the hot gas is expected to fill the entire dark matter halo, and the bulk of the mass from this component will reside at large radii. To overcome this issue and derive the total hot gas mass, the density profiles can be extrapolated out to the virial radius, which can provide an estimate on the total mass. Using this approach, the baryon mass fraction of the massive disk-dominated galaxies, NGC 1961 and NGC 6753, were computed. For

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Fig. 5 Baryon fraction of disk-dominated galaxies as a function of the rotation velocity: for NGC 1961 and NGC 6753, for the CGM-MASS galaxies, and for low-mass non-starburst galaxies. The cosmic baryon mass fraction is shown with the dotted line with errors (shaded area). The left panel shows the baryon fraction of galaxies taking into account all components. Note that for galaxy groups and galaxy clusters, only the hot gas mass is included, which however dominates the baryon budget. The right panel shows the baryon fraction computed by considering only the hot gas mass for the disk galaxies. Note that massive disk-dominated galaxies and even galaxy groups are missing fraction of their baryons. (The plot was adapted from Li et al. 2018)

these galaxies, a baryon mass fraction of fb = 0.05 − 0.08 was obtained (Anderson et al. 2016; Bogdán et al. 2017). The sample of CGM-MASS galaxies also has similar, fb ≈ 0.05, baryon mass fractions (Li et al. 2018). Given that the cosmic value of the baryon mass fraction is fb,WMAP = 0.156±0.002 (Planck Collaboration et al. 2016), we can conclude that massive disk galaxies are missing about half of their baryons and that the hot gas component cannot account for the missing baryons. In Fig. 5, we present the baryon mass fraction obtained for a sample of disk-dominated galaxies, galaxy groups, and galaxy clusters. Using a similar approach, Humphrey et al. (2006) computed baryon mass fractions for a sample of nearby massive elliptical galaxies. The virial mass of the galaxies was determined using the X-ray emitting gas and assuming that it is in hydrostatic equilibrium. After accounting for the baryonic components (most importantly the stars and the hot gas), they computed the baryon mass fraction and found that these galaxies have fb = 0.04–0.09. Thus, the results are good agreement with that obtained for disk-dominated galaxies. This suggests that galaxies of all morphological type are missing about half of their baryons. When considering the relative contribution of various baryonic components, it was found that the hot gas plays a major role. Specifically, in massive galaxies, the hot X-ray emitting gas can account for about half of the total baryons. However, as discussed above, the bulk of this gas cannot be directly observed by X-ray emission studies, and its contribution is estimated by extrapolating the gas density and metallicity profiles out to the virial radius. Therefore, it is essential to briefly overview the main sources of uncertainties in the estimate of the total hot gas mass. The main source of uncertainty is associated with the unexplored nature of the hot

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gas beyond ∼60 kpc radius. Clearly, a significant temperature or metallicity gradient could result in different density profiles and hence total gas masses. Deviations from the hydrostatic equilibrium in the outskirts of the dark matter halos could also alter the total gas mass measurements. Finally, the true virial radius of galaxies may be different than the virial radius inferred from the virial mass of the galaxies. A smaller/larger virial radius will result in a lower/higher total gas mass due to the different volume. Additionally, the measurement of the total gravitating mass from the hydrostatic equilibrium may also have substantial uncertainties. The main assumption of this calculation is that the X-ray emitting gas resides in hydrostatic equilibrium, which is the only (or dominant) source of pressure. Because the pressure may originate from other sources, such as magnetic fields, cosmic rays, or the bulk motion of the gas, the masses obtained through the simple assumption of hydrostatic equilibrium could be underestimated. To verify the accuracy of the masses obtained through this method, masses computed via velocity dispersion and weak lensing were compared with the X-ray estimates, and it was found that they agree within a few tens of percent. The only significant differences were obtained for systems that undergo mergers, in which objects the assumption of hydrostatic equilibrium is clearly not valid. In general, simulations suggest that due to the bulk motions of the gas, the hydrostatic mass approximation will underestimate the mass by 5–20% (Nagai et al. 2007). However, this difference cannot account for the fact that massive galaxies appear to be missing a substantial fraction of their baryons. Despite the above discussed uncertainties, the conclusion that individual galaxies are missing about half of their baryons is not entirely surprising. Indeed, a similar conclusion was obtained for galaxy groups, which also exhibit a baryon deficiency (e.g., Giodini et al. 2009). The fact that massive galaxies not baryonically closed systems indicate that strong feedback from supernovae and AGN played a crucial role in the evolution of galaxies and pushed about half of the baryons beyond the virial radius of galaxies. Hydrodynamical cosmological simulations have proven to be a useful tool to investigate the location and distribution of baryons in the cosmic web (e.g., Cen and Ostriker 1999, 2006; Davé et al. 2001; Shull et al. 2012; Suresh et al. 2017). In fact, several analyses based on hydrodynamical simulations predict that the missing baryons are in the form of warm-hot diffuse gas located between galaxies in the CGM and beyond the virial radius in the IGM. Such simulations have, for example, shown that star formation regulates the production rate of metals, while processes such as supernova feedback, galactic winds, and AGN feedback are capable of expelling the enriched hot gas into the CGM and IGM (e.g., Cen and Ostriker 2006; Theuns et al. 2002; Oppenheimer and Davé 2006; Wijers et al. 2020).

Searching for the Missing Baryons with X-Ray Absorption Studies Because X-ray emission measurement of massive galaxies suggests that these systems are not barionically closed, the missing baryons were likely expelled from the galaxies and reside either around the dark matter halos of the galaxies or in the form of the warm-hot intergalactic medium (WHIM). Since the emission

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measure of the X-ray gas is proportional with the density square (EM ∝ n2 ), X-ray emission studies are less effective to probe the low-density gas around X-ray halos. A powerful method to probe the low-density gas in the outskirts of dark matter halos and beyond the virial radius of galaxies is to use X-ray absorption studies (see the chapter by Mathur in this Section). The X-ray halos of galaxies can imprint absorption lines on the X-ray spectrum of background quasars. Absorption studies in the UV wavelength, in particular, with Hubble’s Cosmic Origin Spectrograph, demonstrated the robustness of this approach. However, due to the much lower collecting area and spectral energy resolution of X-ray grating instruments, detecting X-ray absorption lines from the CGM of galaxies has been a major challenge. A major success in this field was the detection of O VII absorption lines from the hot gas around the Milky Way toward various AGN sightlines (Gupta et al. 2012, 2017), which allowed to estimate the CGM mass around our own Galaxy. However, exploration of the CGM around external galaxies in absorption was much less successful. For example, Yao et al. (2010) probed the CGM along multiple luminous AGN sightlines, but could not obtain a statistically significant detection. In the absence of detections, they placed upper limits on the mean column densities of various ion species for the galaxies, such as the O VII column density is NOVII ≤ 6 × 1014 cm−2 . Converting this to an upper limit on the total mass, they concluded that the total mass enclosed in the CGM is Mgas  6 × 1010 M⊙

 0.5  0.3Z  R 2 ⊙ , fO VII Z 500 kpc

(4)

where fO VII is the ionization fraction of O VII, Z is the metallicity, and R is the radius within which the mass of the CGM is measured. Using these characteristic values, we can conclude that it is unlikely that the bulk of the missing baryons reside in the outskirts of dark matter halos in low-density gas with temperatures of 105.5 –106.5 K, which is the sensitivity range of X-ray absorption studies. Thus, it is likely that a substantial fraction of baryons left the dark matter halos of galaxies. Using the Chandra LETG observations of the luminous quasar, H1821+643, and a stacking approach, Kovács et al. (2019) detected a 3.3σ detection of an O VII absorption line originating from the outskirts of galaxies and the WHIM. The obtained column density is NOVII = (1.4 ± 0.4) × 1015 cm−2 , which exceeds the upper limit of Yao et al. (2010). However, this signal is likely dominated by large-scale WHIM filaments rather than from the CGM of individual galaxies, which contributions cannot be easily differentiated. To further improve the constraints on the CGM in the outskirts of external galaxies, further absorption studies with the next-generation X-ray telescopes will be essential (section “Future Outlook”; also Chapter by Mathur, this Section).

Sunyaev–Zel’dovich Effect An alternative and powerful method to probe the low-density gas in the outskirts of dark matter halos and even beyond the galaxy’s virial radius is to utilize the

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Sunyaev–Zel’dovich effect. When photons from the cosmic microwave background pass through galaxies, galaxy groups, or galaxy clusters, they will be scattered by the free electrons in these objects. The thermal motion of the electrons will cause the so-called thermal SZE (tSZE), and the bulk motion of electrons will cause the kinetic SZE (kSZE) on the CMB photons. Therefore, probing the SZE of galaxies, galaxy groups, and galaxy clusters in the CMB allows us to probe the low-density gas associated with the extended dark matter halos of these galaxies. The observed SZE signal (Y ) for a single object is proportional to the product of the total gas mass (Mgas ) and the virial temperature (Tvir ) and if Mgas ∝ Mhalo , 5/3 we find that the SZE signal can be described as Y ∝ Mhalo . For this reason, the most massive halos will have the highest signal, which, in turn, makes them easily detectable. Indeed, SZE signal from individual galaxy clusters is routinely detected (Planck Collaboration et al. 2016). Although the SZE signal associated with individual galaxies is much weaker and may remain below the detection threshold, the signal-to-noise ratios can be boosted by co-adding (i.e., stacking) the signal from a large number of individual galaxies. By performing a stacking analysis of a 260,000 locally brightest galaxies, including galaxy groups and individual galaxies, the SZE signal was detected for systems with masses as low as M500 = 4 × 1012 M⊙ (Planck Collaboration et al. 2013). This mass is approximately comparable with the massive disk and elliptical galaxies observed in X-ray emission studies. Similar studies were performed by Greco et al. (2015), who stacked the SZE signal of locally brightest galaxies to probe the hot gas around galaxies with similar halo masses. They also detected signals for galaxies with similar dark matter halo mass, but could not detect lower mass systems. When computing the total mass of the hot gas based on the SZE signal, it was established that the baryons missing from individual halos are, in fact, at larger scales. While these studies stacked large samples of galaxies, the tSZE of nearby individual galaxies was also studied using Planck data. By analyzing a sample of 12 nearby spiral galaxies, Bregman et al. (2021) detected SZE signal in the stack of these galaxies and could estimate the total gas mass within 250 kpc. They found that the total gas mass is about one-third of the predicted baryon content of the average galaxy in their sample. Based on their results, Bregman et al. (2021) suggests that the remaining baryons reside at an even larger radius and extend to the 400–500 kpc volume. This conclusion is in agreement with that established based on large galaxy samples and suggests that a substantial fraction of the gas was indeed expelled beyond the virial radius of galaxies. Hydrodynamical cosmological simulations have been used to study both the tSZE and kSZE. For the tSZE signal from halos, the observational results and the predictions from simulations indicate a certain degree of deviation from the selfsimilar case due to feedback mechanisms that strongly impact the gas content of halos with M500 ∼ 1012 (Lim et al. 2021). Furthermore, different simulations lead to different tSZE signal predictions because of the different implementation of the underlying physical model. The Illustris simulation, for example, predicts a significantly lower thermal energy of gas in halos with M500 ∼ 1013–13.5 . This is

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due to the stronger AGN feedback adopted in that simulation compared to more recent simulations like IllustrisTNG. The predictions for Y˜5 00 from IllustrisTNG and EAGLE on the other hand are remarkably similar. SZ observations can therefore also be used to constrain the underlying galaxy formation model.

The Importance of AGN Feedback on the Observed Properties of the CGM The energetic feedback from AGN plays a crucial role in many aspects of galaxy evolution from the earliest epochs to the present day. Naturally, these energetic events also have a profound effect on the observed properties of the CGM. Most importantly, the feedback energy from AGN can change the thermodynamic properties of the hot gas, and it can drastically alter the distribution of the hot gas. The importance of energetic feedback from AGN was recognized based on different observational results. Here, we briefly discuss two of these observational evidences: the lack of intense star formation associated with brightest cluster galaxies and the surprisingly low X-ray luminosity of the hot CGM around individual galaxies. According to the well-known cooling flow problem, the central density of the intracluster medium (ICM) is low enough that it should cool on a timescale much shorter than the Hubble time, resulting in very rapid cooling onto the central galaxy, the so-called brightest cluster galaxy, of the galaxy cluster. Considering the total mass of the ICM in the central regions of galaxy clusters and the average gas density, and taking into account the cooling time, the typical cooling rate of the gas should be 100–1000 M⊙ yr−1 . This, in turn, would suggest that the central regions of galaxy clusters exhibit strong cooling flows and BCGs should have extremely high starformation rates (Fabian and Nulsen 1977; Cowie and Binney 1977; Fabian 1994). However, a wide range of Chandra and XMM-Newton observations demonstrated that only a small fraction of gas cools to low temperatures and provides material to star formation (David et al. 2001; Peterson et al. 2003). To resolve the cooling flow problem, it was suggested that the hot gas in the central regions of galaxies are reheated by the feedback energy from AGN (Churazov et al. 2001; Peterson and Fabian 2006). The observational signatures of AGN feedback are most apparent in the large-scale distribution of the hot gas on galaxy, galaxy groups, and galaxy cluster scales. Specifically, AGN inflates large bubbles in the X-ray gas, which rise buoyantly to a large radius (Jones et al. 2002; David et al. 2011; Randall et al. 2011; Blanton et al. 2011; Fabian 2012). In addition, the energy from AGN is also transported to the X-ray gas via shocks and turbulent mixing. According to theoretical calculations, it was established that the mechanical energy from AGN can offset the radiative losses due to cooling, implying that this energetic feedback can prevent the runaway cooling of the central gas (McNamara and Nulsen 2007, 2012). Since this energetic feedback is present in both galaxies, galaxy groups, and galaxy clusters, this underlines the importance of accurate modeling of the AGN feedback.

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Although the first analytic description of galaxy formation models suggested that the CGM should be ubiquitous around individual galaxies, the predicted X-ray luminosity of these gaseous halos was overestimated. For example, White and Frenk (1991) predicted that a dark matter halo with a circular velocity of 300 km s−1 should have an X-ray luminosity of 3 × 1042 erg s−1 . Such high X-ray luminosity around disk-dominated galaxies should have been detected by the ROSAT X-ray observatory, but these galaxies remained undetected. The reason for the overly high predicted X-ray luminosity is that they neglected gas ejection and assumed that the hot gas follows the dark matter distribution. Hydrodynamical simulations performed by Toft et al. (2002) predicted about two orders of magnitude lower X-ray luminosity for the CGM component. However, the main reason of the low X-ray luminosity was the absence of energetic feedback, which, in turn, resulted in an overly massive stellar component and therefore a less massive and less luminous CGM component. The X-ray properties of disk-dominated galaxies were simulated by Crain et al. (2010), who incorporated efficient feedback from supernovae. This feedback prevents the conversion of halo gas into stars, hence preventing the overcooling and the formation of an overly massive stellar component. In addition, the entropy profile of the CGM is also changing due to the feedback energy, as a fraction of the baryons are expelled to larger radii resulting in shallower gas density profiles in the central regions of galaxies. However, these simulations did not include the energetic AGN feedback, which further alters the predicted properties of the CGM. Specifically, powerful AGN feedback is likely responsible for the fact that even the most massive galaxies appear to be missing a substantial fraction of their baryons. Indeed, due to the energy input from AGN, about half of the baryons were expelled beyond the virial radius of galaxies. Hydrodynamical simulations also incorporate AGN feedback due to supermassive black holes. However, numerically resolving the relevant scales is particularly problematic for AGN feedback. For example, the highly collimated jets of relativistic particles can in general cosmological simulations not be resolved because jets themselves cover an enormous dynamic range, being launched at several Schwarzschild radii, and propagating outwards to tens of kpc. The feedback of active galactic nuclei is commonly divided in two models: quasar and radio. Quasar mode feedback represents the efficient mode of black hole growth and is typically implemented through energy or momentum injection. It is assumed that the bolometric luminosity is proportional to the accretion rate, which is in the simplest case derived from a Bondi-Hoyle accretion model. Some fraction of this energy is then deposited in the form of feedback energy. Highly collimated jets of relativistic particles lead radio mode feedback, which is often associated with X-ray bubbles that can offset cooling losses. This mode of feedback is particularly important to regulate star formation in massive galaxies. The prescription to incorporate AGN feedback (or the complete lack thereof) in galaxy formation simulations drastically alters the predicted physical properties of the CGM. The most simple observational tests to probe the accuracy of AGN feedback models are to (1) measure the X-ray luminosity of the CGM and (2) probe the X-ray gas density (or entropy) profile. Both of these observables strongly depend

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on the implementation of the AGN feedback. For example, if the AGN feedback is weak (or completely lacking), galaxies will host a large amount of X-ray gas in their dark matter halo, resulting in high CGM luminosity. If, however, the AGN feedback is strong, the hot gas will be expelled to the outskirts of the dark matter halo or could be completely removed from the halo, which will result in a low X-ray luminosity. Similarly, the X-ray gas density profile will also depend on the feedback implementation: powerful feedback will result in shallower profiles in the central regions of the galaxies. Based on these considerations, the characteristics of the CGM around diskdominated galaxies were compared with modern galaxy formation simulations. For example, the X-ray properties of a substantial sample of disk galaxies were compared with the Galaxies–Intergalactic Medium Interaction Calculation (GIMIC) simulation (Li et al. 2014). While there was a reasonable agreement between the observed and predicted X-ray properties, the scatter in the LX −M200 LX −SF R was extremely small and was inconsistent with observations. This pointed out a major shortcoming of the GIMIC simulation, namely, the lack of AGN feedback and the adoption of constant stellar feedback parameters. In a similar study, Bogdán et al. (2015) utilized a sample of massive disk-dominated galaxies to probe the Illustris simulation. They found that the simulation broadly agrees with the observed X-ray luminosity and upper limits of the disk galaxies. However, for the most massive galaxies, the predicted X-ray luminosity of the CGM fell short of the observed values. This suggested that the AGN in these massive galaxies provided overly powerful radio-mode feedback, which pushed the gas out from the dark matter halo and, hence, resulted in low X-ray luminosity. These comparisons illustrate the powerful constraining nature of observations of the CGM. Indeed, the comparison between observational studies and theoretical predictions played an important role in revising these simulations and essentially in the production of the EAGLE and IllustrisTNG simulation suites (Fig. 6).

Missing Feedback Problem While the large-scale CGM of disk galaxies is in a quasi-static state, the inner regions of disks are affected by very complex physical processes. Notably, there is an active interplay between the CGM, the stellar ejecta from evolved stars and supernovae, and the energy input from supernova feedback, which are capable to drive galactic-scale winds. When considering the energy input from supernovae and comparing it with the X-ray luminosity of the hot gas in the innermost regions of disk galaxies, a stark discrepancy is observed. Specifically, the coupling efficiency, which is defined as the ratio of the X-ray luminosity of the hot gas to the energy input from supernovae, is only ∼0.004 (Li and Wang 2013). This surprisingly low value implies that the bulk of the supernova energy is missing, which is often referred to as the “missing feedback” problem. To understand how the missing feedback problem could be resolved, we must consider how the supernova-heated gas may evolve. First, the hot gas could be

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Fig. 6 Comparison between the observed and predicted 0.5–2 keV band X-ray luminosity of disk galaxies for different radial ranges. The specific regions were chosen to match the observational results from Bogdán et al. (2015) (top panels), Li et al. (2017) (bottom left), and Anderson et al. (2016) (bottom right). The observed data points are shown with black symbols. The shaded regions show the 15th and 85th percentiles for simulated galaxies using three different feedback implementations: blue curves show the reference simulation, red curves show a simulation without AGN feedback, and the green curves show a modified AGN feedback in which each feedback event leads to a temperature change of ΔTAGN = 109 K. The different prediction underscore the importance of feedback implementation. (The figure was adapted from the work of Kelly et al. 2021)

expelled from the dark matter halo of the galaxy and become part of the largescale galaxy group or cluster atmosphere or it could join the warm-hot intergalactic medium. In this case, the hot gas will reside beyond the galaxy’s virial radius, and hence it will be “hidden” from the X-ray observations of galaxies. Second, the gas could be ejected from the galactic disk, but stay associated with the dark matter halo of the galaxy. In this scenario, the metal-enriched uplifted gas will mix with the CGM that was previously dominated by the infalling pristine gas. Third, the outflowing hot gas could rapidly cool down in the proximity of the disk and then fall back to the galaxy disk, thereby rejoining the interstellar medium. To differentiate between these scenarios, the characteristics of the hot X-ray gas (both in the disk and on larger scales) must be investigated. For example, if the gas is ejected to large radii or even expelled from the dark matter halo, the amount

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and the luminosity of the X-ray emitting gas in the innermost regions will decrease. Additionally, if the gas leaves the central regions of the galaxy, the density profile of the gas should be flatter in the innermost regions and should further decrease outwards. If, however, the gas falls back to the disk in a galactic fountain, highdensity gas and luminous X-ray emission are expected in the central regions of the galaxy. Considerations of the energy budget can also hint at the fate of the supernova-heated gas. Because of the gravitational potential of galaxies and the available feedback energy from supernovae, the gas from the innermost regions can only leave the dark matter halos of low-mass galaxies but cannot leave the dark matter halos of massive galaxies (Li et al. 2017). In addition, because of the inefficient nature of gas cooling, the rate of infall to the disk is also low, which makes the galactic fountain scenario unlikely. Taken these together and considering the observed X-ray properties of disk galaxies, the most plausible scenario is that the gas heated by the energetic feedback of supernovae remains in the dark matter halo of massive galaxies and mixes with the CGM. The coupling efficiency was measured for a large sample of disk galaxies by Li and Wang (2013) and Li et al. (2017) (Fig. 7). They found that this parameter exhibits an increasing trend with the total mass of galaxies (Li and Wang 2013). This can be attributed to the deeper potential well of more massive galaxies: they can retain more gas heated by the supernova feedback. Hydrodynamical simulations can directly probe the X-ray coupling efficiency as a function of the total mass of the galaxies. Based on the EAGLE simulation, Kelly et al. (2021) found that the coupling efficiency – in agreement with the observations – increases with the total mass of galaxies. Upon investigating the evolution of the gas due to the energetic feedback processes, they concluded that the bulk of the feedback energy is lost as hot gas is ejected from the galaxy disks. In the case of low-mass dark matter halos

Fig. 7 Energy budget of disk galaxies. The left panel shows the X-ray luminosity of disk galaxies measured within r < 0.1r200 as a function of the total energy injection from supernovae (core collapse and Type Ia). The right panel shows the X-ray coupling efficiency as a function of baryonic to stellar mass ratio of the galaxies. The dashed line and shaded regions represent the nonlinear fit to the data points and the 1σ confidence interval for the sub-samples in the Li and Wang (2013) sample. (The figure was adapted from Li et al. 2017)

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(M  1011 M⊙ ), the gas can be completely ejected from the halo on a timescale of ∼108 years. However, for more massive galaxies, the supernova feedback energy is not sufficient to drive the gas from the dark matter halo. This conclusion is in agreement with the energetic considerations discussed above (Li et al. 2017). In these massive galaxies, the gas will be retained in higher density regions, where it can radiate the energy injected by supernovae, which in turn results in higher X-ray luminosity. This theoretical picture is consistent with the fact that the most massive disk-dominated galaxies, NGC 1961 and NGC 6753, have much higher X-ray luminosity than their lower-mass counterparts.

Future Outlook The X-ray halos of galaxies were studied in the past with every major X-ray observatory, including ROSAT, Chandra, and XMM-Newton. All these telescopes had various advantages that contributed to the understanding of the X-ray halos. Notably, ROSAT allowed the detection of large samples of galaxies and could provide a volume-limited galaxy sample that was free from selection effects. However, due to the low sensitivity and poor spatial resolution, observations taken by ROSAT could not collect a large number of photons from the CGM of galaxies, and it was not possible to identify contaminating sources in the emission associated with galaxies. Overall, these complications made it challenging to interpret the results obtained through the ROSAT All-Sky Survey. Due to the superior, 0.5′′ , angular resolution of Chandra, it became possible to detect bright point sources, notably AGN, LMXBs, and HMXBs, associated with galaxies and exclude them from the study of the diffuse emission. Because of the understanding of the X-ray scaling relations of X-ray binaries with the stellar mass and star-formation rate, it even became possible to estimate the contribution of unresolved X-ray binaries to the overall emission level. This, in turn, allowed to precisely account for the population of resolved and unresolved X-ray sources and resulted in the accurate study of the truly diffuse emission. However, the identification of discrete sources required deep observations, implying that it was difficult to study large galaxy samples. In addition, many studies focused only on the most nearby and brightest galaxies; hence the galaxy sample observed by Chandra is hampered by a wide range of selection effects. While there were attempts to carry out more systematic surveys, such as the ATLAS3D or MASSIVE surveys, these still did not provide a large galaxy sample covering galaxies with various stellar masses and star-formation rates. XMM-Newton with its large collecting area allowed the detection of relatively faint emission from X-ray halos in the outskirts of galaxies, as discussed for the massive spiral galaxies NGC 1961 or NGC 6753. However, the relatively high instrumental background of this telescope limits the sensitivity of the observations since the emission at the outskirts of galaxies becomes dominated by systematic uncertainties. With its modest angular resolution, it was possible to identify some of the point sources, but many of them remained unresolved and contributed to the truly

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diffuse emission. Similarly to Chandra, this pointing X-ray telescope also studied individual galaxies rather than carrying out large systematic surveys, implying that the XMM-Newton archive cannot be used to study the X-ray halos of galaxies in an unbiased manner. The understanding of the X-ray halos will be dramatically improved by observations carried out by the Spektr-RG (SRG) telescope, which was launched in July 2019. The main instrument aboard SRG is the eROSITA telescope that consists of seven identical mirror modules, providing excellent sensitivity. During its first 4 years of operation, eROSITA will carry out eight full-sky surveys – once every 6 months. Given the high sensitivity of eROSITA, this survey will be 30–50 times more sensitive than its predecessor, the ROSAT All-Sky Survey. In addition to the greater sensitivity, eROSITA also has ∼3 times higher angular resolution than ROSAT; hence it will be possible to identify bright point sources. Thanks to the greater sensitivity and our much-improved understanding of the X-ray binary population, it will be possible to carry out an unbiased volume-limited study of the CGM around large galaxy samples in the nearby Universe. For example, it will be possible to probe how the X-ray emission of gaseous halos scales with the stellar mass, star-formation rate, or morphology based on large galaxy samples in a statistical manner – similar to studies that were carried out in optical waveband using the wealth of SDSS data. For example, Oppenheimer et al. (2020) suggested based on state-of-the-art X-ray simulations that the X-ray halos of massive nearby galaxies will be observed out to ∼150 kpc radii when stacking the X-ray photons of eROSITA galaxies. On a longer timescale, the next-generation X-ray telescopes can completely revolutionize our understanding of the X-ray halos of galaxies. The proposed ARCUS X-ray observatory will study the CGM of galaxies in absorption: it will use bright background quasars that illuminate the hot gas in the outskirts of galaxies (and galaxy clusters). Thanks to the much larger collecting area of ARCUS and by studying multiple quasar sightlines, it will be able to map the structure, the temperature, and even the gas motions of the X-ray gas. This will not only allow to address the missing baryon problem on galaxy scales but can also lead to a much better understanding of the metal cycling in and out of galaxies. These studies will be further elevated by the proposed Lynx observatory that will have large throughput and sub-arcsecond angular resolution. Therefore, Lynx will be able to probe the X-ray halos of galaxies even around low-mass (Milky Way-type) galaxies close to their virial radius, which remains impossible with the present generation telescope. Such studies will be carried out both in emission and absorption using background quasars. This will allow the detailed mapping of energetic feedback on galaxy scales: in low-mass galaxies, in winds driven by supernovae, and in massive galaxies, the effects of supermassive black holes will be mapped. This will lead to a comprehensive picture of the most fundamental processes that influence the evolution of galaxies from their birth to the present day. On the theoretical frontier, hydrodynamical simulations have to incorporate more fine-grained and predictive models that are less calibration dependent. Currently, large-volume simulations can provide large samples of galaxies. However, these

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simulations rely on rather crude models that have to be calibrated against a few key observables. On the other hand, the galaxy formation models of high-resolution simulations are less calibration dependent and allow more detailed modeling of the actual physical processes. Ideally, these two approaches should be combined in the near future to allow simulations of large samples of galaxies with detailed galaxy formation models.

References M.E. Anderson, J.N. Bregman, ApJ 737, 22 (2011) M.E. Anderson, J.N. Bregman, X. Dai, ApJ 762, 106 (2013) M.E. Anderson, E. Churazov, J.N. Bregman, MNRAS 455, 227 (2016) A. Baldi, J.C. Raymond, G. Fabbiano et al., Chemical Enrichment of the Complex Hot ISM of the Antennae Galaxies. I. Spatial and Spectral Analysis of the Diffuse X-Ray Emission 162, 113–133 (2006) A.J. Benson, R.G. Bower, C.S. Frenk, S.D.M. White, MNRAS 314, 557 (2000) E.L. Blanton, S.W. Randall, T.E. Clarke et al., ApJ 737, 99 (2011) Á. Bogdán, A.D. Goulding, ApJ 800, 124 (2015) Á. Bogdán, W.R. Forman, R.P. Kraft, C. Jones, ApJ 772, 98 (2013a) Á. Bogdán, W.R. Forman, M. Vogelsberger et al., ApJ 772, 97 (2013b) Á. Bogdán, M. Vogelsberger, R.P. Kraft et al., ApJ 804, 72 (2015) Á. Bogdán, H. Bourdin, W.R. Forman et al., ApJ 850, 98 (2017) B. Boroson, D.-W. Kim, G. Fabbiano, ApJ 729, 12 (2011) J.N. Bregman, E. Hodges-Kluck, Z. Qu et al., 2021, arXiv e-prints, arXiv:2107.14281 F. Brighenti, W.G. Mathews, ApJ 630, 864 (2005) R. Cen, J.P. Ostriker, ApJ 514, 1 (1999) R. Cen, J.P. Ostriker, ApJ 650, 560 (2006) E. Churazov, M. Brüggen, C.R. Kaiser, H. Böhringer, W. Forman, ApJ 554, 261 (2001) L.L. Cowie, J. Binney, ApJ 215, 723 (1977) R.A. Crain, I.G. McCarthy, C.S. Frenk, T. Theuns, J. Schaye, MNRAS 407, 1403 (2010) X. Dai, M.E. Anderson, J.N. Bregman, J.M. Miller, ApJ 755, 107 (2012) R. Davé, R. Cen, J.P. Ostriker et al., ApJ 552, 473 (2001) L.P. David, P.E.J. Nulsen, B.R. McNamara et al., ApJ 557, 546 (2001) L.P. David, E. O’Sullivan, C. Jones et al., ApJ 728, 162 (2011) G. Fabbiano, ARA&A 44, 323 (2006) A.C. Fabian, ARA&A 32, 277 (1994) A.C. Fabian, ARA&A 50, 455 (2012) A.C. Fabian, P.E.J. Nulsen, MNRAS 180, 479 (1977) B.D. Fields, P. Molaro, S. Sarkar, 2014, arXiv e-prints, arXiv:1412.1408 W. Forman, J. Schwarz, C. Jones, W. Liller, A.C. Fabian, ApJL 234, L27 (1979) W. Forman, C. Jones, W. Tucker, ApJ 293, 102 (1985) Y. Fukazawa, J.G. Botoya-Nonesa, J. Pu, A. Ohto, N. Kawano, ApJ 636, 698 (2006) M. Fukugita, P.J.E. Peebles, ApJ 639, 590 (2006) M. Gilfanov, MNRAS 349, 146 (2004) S. Giodini, D. Pierini, A. Finoguenov et al., ApJ 703, 982 (2009) A.D. Goulding, J.E. Greene, C.-P. Ma et al., ApJ 826, 167 (2016) J.P. Greco, J.C. Hill, D.N. Spergel, N. Battaglia, ApJ 808, 151 (2015) N. Grevesse, A.J. Sauval, SSR 85, 161 (1998) A. Gupta, S. Mathur, Y. Krongold, F. Nicastro, M. Galeazzi, ApJL 756, L8 (2012) A. Gupta, S. Mathur, Y. Krongold, ApJ 836, 243 (2017) P.J. Humphrey, D.A. Buote, F. Gastaldello et al., ApJ 646, 899 (2006)

4398

Á. Bogdán and M. Vogelsberger

C. Jones, W. Forman, A. Vikhlinin et al., ApJL 567, L115 (2002) A.J. Kelly, A. Jenkins, C.S. Frenk, MNRAS 502, 2934 (2021) D.-W. Kim, G. Fabbiano, ApJ 776, 116 (2013) O.E. Kovács, Á. Bogdán, R.K. Smith, R.P. Kraft, W.R. Forman, ApJ 872, 83 (2019) J.-T. Li, Q.D. Wang, MNRAS 435, 3071 (2013) J.-T. Li, R.A. Crain, Q.D. Wang, MNRAS 440, 859 (2014) J.-T. Li, J.N. Bregman, Q.D. Wang et al., ApJS 233, 20 (2017) J.-T. Li, J.N. Bregman, Q.D. Wang, R.A. Crain, M.E. Anderson, ApJL 855, L24 (2018) S.H. Lim, D. Barnes, M. Vogelsberger et al., MNRAS 504, 5131 (2021) F. Mannucci, M. Della Valle, N. Panagia et al., A&A 433, 807 (2005) W.G. Mathews, ApJ 219, 413 (1978) W.G. Mathews, ApJ 354, 468 (1990) W.G. Mathews, F. Brighenti, ARA&A 41, 191 (2003) S.S. McGaugh, J.M. Schombert, G.D. Bothun, W.J.G. de Blok, ApJL 533, L99 (2000) B.R. McNamara, P.E.J. Nulsen, ARA&A 45, 117 (2007) B.R. McNamara, P.E.J. Nulsen, NJPh 14, 055023 (2012) F. Mernier, N. Werner, K. Lakhchaura et al., Astronomische Nachrichten 341, 203 (2020) D. Nagai, A. Vikhlinin, A.V. Kravtsov, ApJ 655, 98 (2007) J.F. Navarro, C.S. Frenk, S.D.M. White, ApJ 490, 493 (1997) B.D. Oppenheimer, R. Davé, MNRAS 373, 1265 (2006) B.D. Oppenheimer, Á. Bogdán, R.A. Crain et al., ApJL 893, L24 (2020) E. O’Sullivan, D.A. Forbes, T.J. Ponman, MNRAS 328, 461 (2001) E. O’Sullivan, T.J. Ponman, R.S. Collins, MNRAS 340, 1375 (2003) J.R. Peterson, A.C. Fabian, PhR 427, 1 (2006) J.R. Peterson, S.M. Kahn, F.B.S. Paerels et al., ApJ 590, 207 (2003) Planck Collaboration, P.A.R. Ade, N. Aghanim et al., A&A 557, A52 (2013) Planck Collaboration, P.A.R. Ade, N. Aghanim et al., A&A 594, A13 (2016) S.W. Randall, W.R. Forman, S. Giacintucci et al., ApJ 726, 86 (2011) J. Rasmussen, J. Sommer-Larsen, K. Pedersen et al., ApJ 697, 79 (2009) M. Revnivtsev, S. Sazonov, M. Gilfanov, E. Churazov, R. Sunyaev, A&A 452, 169 (2006) M. Revnivtsev, E. Churazov, S. Sazonov, W. Forman, C. Jones, A&A 490, 37 (2008) S. Sazonov, M. Revnivtsev, M. Gilfanov, E. Churazov, R. Sunyaev, A&A 450, 117 (2006) J.M. Shull, B.D. Smith, C.W. Danforth, ApJ 759, 23 (2012) L.J. Spitzer, ApJ 124, 20 (1956) D.K. Strickland, T.M. Heckman, E.J.M. Colbert, C.G. Hoopes, K.A. Weaver, ApJS 151, 193 (2004) J. Suresh, K.H.R. Rubin, R. Kannan et al., MNRAS 465, 2966 (2017) T. Theuns, M. Viel, S. Kay et al., ApJL 578, L5 (2002) S. Toft, J. Rasmussen, J. Sommer-Larsen, K. Pedersen, MNRAS 335, 799 (2002) G. Trinchieri, G. Fabbiano, ApJ 296, 447 (1985) R. Tüllmann, W. Pietsch, J. Rossa, D. Breitschwerdt, R.J. Dettmar, A&A 448, 43 (2006) F. van de Voort, V. Springel, N. Mandelker, F.C. van den Bosch, R. Pakmor, MNRAS 482, L85 (2019) S.D.M. White, C.S. Frenk, ApJ 379, 52 (1991) S.D.M. White, M.J. Rees, MNRAS 183, 341 (1978) N.A. Wijers, J. Schaye, B.D. Oppenheimer, MNRAS 498, 574 (2020) Y. Yao, Q.D. Wang, S.V. Penton et al., ApJ 716, 1514 (2010)

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Contents Introduction and Chapter Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Theoretical and Multiwavelength Observational Background . . . . . . . . . . . . . . . . . . . . . . . . Galaxy Evolution and Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Multiwavelength Imaging of Radio-Quiet AGN Interactions with Host Galaxies . . . . . . The “Unified Scheme” of AGNs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Early X-Ray Observations of Extended AGN Emission Through Chandra . . . . . . . . . . . . . . The Spectral Components of CT AGN Emission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chandra Imaging: The Soft Component . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Prevalence of Extended X-Rays . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chandra High-Resolution Imaging Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Broad-Band (∼0.3–2.5 keV) Soft X-Ray Morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . Narrow-Band X-Ray Emission Line Imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectra: Photoionization and Shock Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Seyfert and