Observational Imprints of Binary Evolution on B- and Be-star Populations (Springer Theses) 3031194888, 9783031194887

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Springer Theses Recognizing Outstanding Ph.D. Research

Julia Bodensteiner

Observational Imprints of Binary Evolution on Band Be-star Populations

Springer Theses Recognizing Outstanding Ph.D. Research

Aims and Scope The series “Springer Theses” brings together a selection of the very best Ph.D. theses from around the world and across the physical sciences. Nominated and endorsed by two recognized specialists, each published volume has been selected for its scientific excellence and the high impact of its contents for the pertinent field of research. For greater accessibility to non-specialists, the published versions include an extended introduction, as well as a foreword by the student’s supervisor explaining the special relevance of the work for the field. As a whole, the series will provide a valuable resource both for newcomers to the research fields described, and for other scientists seeking detailed background information on special questions. Finally, it provides an accredited documentation of the valuable contributions made by today’s younger generation of scientists.

Theses may be nominated for publication in this series by heads of department at internationally leading universities or institutes and should fulfill all of the following criteria • They must be written in good English. • The topic should fall within the confines of Chemistry, Physics, Earth Sciences, Engineering and related interdisciplinary fields such as Materials, Nanoscience, Chemical Engineering, Complex Systems and Biophysics. • The work reported in the thesis must represent a significant scientific advance. • If the thesis includes previously published material, permission to reproduce this must be gained from the respective copyright holder (a maximum 30% of the thesis should be a verbatim reproduction from the author’s previous publications). • They must have been examined and passed during the 12 months prior to nomination. • Each thesis should include a foreword by the supervisor outlining the significance of its content. • The theses should have a clearly defined structure including an introduction accessible to new PhD students and scientists not expert in the relevant field. Indexed by zbMATH.

Julia Bodensteiner

Observational Imprints of Binary Evolution on Band Be-star Populations Doctoral Thesis accepted by Institute of Astronomy, KU Leuven

Author Dr. Julia Bodensteiner European Southern Observatory Garching b. München, Bayern, Germany

Supervisor Prof. Hugues Sana Institute of Astronomy Leuven, Belgium

ISSN 2190-5053 ISSN 2190-5061 (electronic) Springer Theses ISBN 978-3-031-19488-7 ISBN 978-3-031-19489-4 (eBook) https://doi.org/10.1007/978-3-031-19489-4 © The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 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 Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland

Eind goed, al goed.

Supervisor’s Foreword

Stars with birth masses larger than about 8 times the mass of our Sun end their life in powerful explosions, as core-collapse supernovae and gamma-ray bursts. With large luminosities, strong stellar winds and spectacular explosions, these massive stars heat and enrich the surrounding gas clouds, where new generations of stars and planets form, and they drive the chemical evolution of galaxies. Entire populations of massive stars, and their final explosions, are so bright that they can be seen at very large distances and allow astronomers to study the properties of the Universe across cosmic times. The first generation of massive stars is thought to have played a pivotal role in the assembly of the first galaxies and to have contributed to the re-ionization of the early universe. Characterizing the first population of massive stars is actually one of the prime mission objectives of the James Webb Space Telescope, a NASAled flagship mission with significant participation from the European and Canadian Space Agencies whose first images have captured the minds of astronomers and the larger public alike. Massive stars are also the progenitors of neutrons stars and black holes, the coalescence of which produces bursts of gravitational waves that can now be detected by modern gravitational wave interferometers in Europe and in the United States. Given the decisive role of massive stars for a wide range of astrophysical problems, it is of paramount importance to understand their life cycle, that is how massive stars form, live and die in our Galaxy and in the Universe near and far. Unfortunately, too many uncertainties remain, including their formation mechanism, multiplicity, internal mixing, and stellar winds. The work presented in this book focuses on the role of multiplicity. In the last few decades, growing observational evidence have called for a paradigm shift in our thinking: massive stars rarely, if at all, form and live in isolation. The majority of massive stars have one or more nearby companions with which they form a binary or higher-order multiple stellar system. In addition, this companion is often so close that the two stars will exchange mass, or even merge, before any of the components explode as supernova. This interaction has severe consequences for the further evolution and final fate of both stars, their energy feedback, the properties of their end-of-life explosion and the nature of the compact companions that they

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leave behind. Precisely quantifying the binary evolution physics is of further importance as it plays a large role in the theoretical computations predicting the properties of the first galaxies seen by the James Webb Space Telescope and that of the gravitational wave events detectable by current and up-coming generations of gravitational wave interferometers. With her Ph.D. thesis, dr. Julia Bodensteiner brought new insights into the properties of binary interaction products. The main idea pursued in this work is that, given binary interactions are so frequent, there should be large populations of postinteraction objects, yet few such products had been identified before this research started. Characterizing these products is, however, key to confront models of binary evolution that are used to predict massive stars’ final stages and associated gravitational wave events. In this context, Julia Bodensteiner used new and archival observational data of B-type stars obtained at state-of-the-art facilities, both from the ground and in space, to search for the imprints of binary evolution. The first part of Julia Bodensteiner’s Ph.D. work focuses on Be stars, that is Btype stars displaying strong emission lines believed to be produced by a decretion disk sustained by the rapid-rotation of the B-type stars. By compiling the known properties of a large sample of Be stars, the author provides evidence for the Be phenomenon to largely result from binary interaction, opening a new way forward to identify hundreds of new binary interaction products. By an in-depth studies of the Be binary system HR 6819, Julia Bodensteiner further identified the a new class of post-interaction binaries where the initially most massive companion has recently been stripped of (most of) its envelope and is now in a short-live phase immediately following the mass transfer. In the second part of this book, the author used the MUSE integral field spectrograph at the ESO Very Large Telescope in Chile and presented the results of a groundbreaking spectroscopic campaign towards the 40 Myr-old star cluster NGC 330 in the Small Magellanic Clouds. With the support of photometry from the Hubble Space Telescope and the development of several novel algorithms for the spectral extraction, the correction of observational biases and the atmosphere modelling, the author characterized the upper-mass stellar population of NGC 330, revealing their multiplicity throughout the color-magnitude diagram and providing unique observational constraints on their (binary) evolution history. Leuven, Belgium September 2022

Hugues Sana

Preface

Context Massive stars are among the most important cosmic engines in the Universe. They have a profound impact not only on their immediate surroundings, but on their entire host galaxies. It is therefore crucial to understand their life cycle, from their birth in dense molecular clouds, through their lives where they forge new chemical elements, until their deaths which are often accompanied by energetic supernova explosions. While our understanding of the basic evolution of stars is well advanced, important open questions remain such as the impact of interior mixing, rotation, and magnetic fields. Our understanding is, however, further complicated by observations which show that a majority of stars are members of binary systems. The presence of a companion can strongly alter the evolution of both stars in the system, leading to a multitude of different evolutionary pathways, depending on the type and strength of the interaction. In order to better understand these possible binary pathways, a profound understanding of the complex interaction physics is crucial.

Scope of This Work One possible way of characterizing the physics and the outcome of binary interactions is to study post-interaction systems, so-called binary interaction products. Depending on the interaction channel the system went through, binary interaction products can have different observational characteristics which allow us to distinguish them from single stars. In this monograph, we aim to investigate the observational imprint of binary interactions on populations of B and Be stars. We first introduce massive stars and their evolution in Chap. 1, and discuss methods relevant for this monograph, in particular optical spectroscopy, in Chap. 2. In Chap. 3 we investigate whether classical Be stars are binary interaction products, while we study one particular potential Be binary in Chap. 4. We further study the

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Preface

occurrence and properties of binary interaction products in a population of stars, namely the open star cluster NGC 330 in the Small Magellanic Cloud in Chap. 5. The results are summarized in Chap. 6, where we also give an outlook into future work. In the original edition of this thesis, the peer-reviewed and published publications, which are the basis of Chaps. 3–5 were included in their published version. Here, however, we discuss them as part of the literature.

Overview In Chap. 3 we focus on classical Be stars, which are rapidly rotating, non-radially pulsating, early-type stars that are surrounded by a circumstellar decretion disk. Different mechanisms have been proposed to explain their rapid rotation, which is thought to be close to, or at, the critical break-up velocity. One possible mechanism explaining the rapid rotation is that they are mass gainers in previous binary interactions, implying that there should be a lack of Be stars with close main-sequence companion. To test this hypothesis, we search the literature of a large sample of massive classical Be stars for any reports of main-sequence companions on close orbits. While we find several reports of stripped-star or compact-object companions, there is no unambiguous report of a massive Be star in a close binary system with a main-sequence companion. This indicates that a majority of the massive classical Be stars are binary interaction products. In Chap. 4, we study the peculiar system HR 6819 which was proposed to not only contain the closest black hole to Earth, but also to contain an outer classical Be star which has evolved as such as a single star. This would make HR 6819 the smoking gun showing that the rapid rotation of Be stars can be explained with singlestar evolution and does not require previous binary interactions. By re-analyzing the available data, we find an alternative interpretation of the HR 6819 system: we argue that HR 6819 is a post-mass transfer system containing a stripped star and a classical Be star. While this is only one system, our alternative explanation makes HR 6819 a prime example for a Be star formed by the binary channel. In order to benefit from large sample statistics, and from the availability of a reference clock, we study the massive star population of the ~35 Myr-old cluster NGC 330 in Chap. 5. Given the total mass and age of NGC 330, the cluster is expected to contain a large number of binary interaction products. Using multiepoch integral field spectroscopy from VLT/MUSE we investigate the entire massive star content of NGC 330. We characterize the stellar content, classify the binary status, and estimate physical properties, in particular the rotation rates. By qualitative comparison with predictions from binary population synthesis computations, we find several indications that the population of stars is strongly impacted by previous binary interactions, such as the large number of classical Be stars, the presence of slowlyrotating stars above the cluster turnoff, and the binary fraction and rotation rates as a function of evolutionary status.

Preface

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Putting it all together, this monograph shows that the observational imprint of binary interactions on populations of early-type stars is strong. On the one hand, this is supported by the interpretation of classical Be stars as binary interaction products. On the other hand, it is in agreement with the large number of binary interaction products observed in NGC 330, which in fact dominate the massive star content above and around the cluster turnoff. The advent of integral field spectroscopy will allow us to extend our investigation of binary interaction products to additional clusters, covering different age ranges and metallicities. One possible line of investigation concerns the occurrence of classical Be stars as a function of cluster age. Comparing the obtained results with predictions from state-of-the-art single- and binary-star population synthesis predictions will provide new invaluable insights in our current understanding of massive star evolution and binary interaction physics. Munich, Germany September 2022

Julia Bodensteiner

Acknowledgements

First of all, I would like to thank my Ph.D. supervisor, Hugues Sana, who not only gave me the chance to come to Leuven in the first place, but who guided and advised me throughout the years. Apart from endless scientific expertise, he always had an open ear, no matter which time of the day, or day of the week. He encouraged me to follow my own interests and gave me the opportunity to work on new things that were originally not planned for my Ph.D. I would also like to thank Tomer Shenar, who has not only been a great supervisor and mentor, but also became a very good friend! To many more years of working together! I would like to gratefully acknowledge my supervisory committee, Laurent Mahy, Norbert Langer and Alex de Koter, who provided me with stimulating discussions and helpful feedback throughout the past years. I hope that our collaboration will continue in the future. Furthermore, I would like to thank the additional members of my examination committee for the interesting discussion during the defense and the ideas you have instigated. I would further like to thank everyone at the IvS, in particular the entire SPAMs group, who have provided me with continuous support and many possibilities to learn new things, also outside of science. Thanks also to all the other Ph.D. students at the IvS for creating such a great environment to work in, and for all the fun things we did outside of work. Particular thanks go to Ana and Michael, for being there from the beginning, and to Emily, for being there all the way. I would further like to acknowledge Dom and Cole for their ongoing feedback and input, not only concerning this monograph. A big thank also go to my friends from Munich, in particular to Sophi and Hannes, who are constant sources of support, great conversation partners, and who can make me smile even over large distance. Finally, I would like to thank my family. Thank you for always being there for me, for supporting me, and for believing in me. Thank you for everything.

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Contents

1 Scientific Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 The Evolution of Massive Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 Uncertain Physics in Stellar Evolution Theory . . . . . . . . . . . . 1.2.2 Stellar Populations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3 The Effect of Binarity on Stellar Evolution . . . . . . . . . . . . . . . . . . . . . 1.3.1 Different Binary Evolution Pathways . . . . . . . . . . . . . . . . . . . 1.3.2 Observational Constraints on Initial Multiplicity Properties of Massive Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 Predicted Occurrence and Properties of Binary Interaction Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.4 Observational Characteristics of Binary Interaction Products . . . . . . 1.5 Classical Be Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.6 Motivation and Open Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 1 2 5 8 9 10

12 14 17 22 24

2 Spectroscopy of Massive Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Stellar Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 Single-object Échelle Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 Integral-Field Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Extraction of Spectra in 3D Data Cubes . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Radial Velocity Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Determination of Stellar Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

31 31 34 35 37 40 42 48

3 On the Apparent Lack of Massive Be Stars with Main-Sequence Companions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Origin of the Rapid Rotation of Be Stars . . . . . . . . . . . . . . . . . . . 3.3 A Literature Search for Be Stars with MS Companions . . . . . . . . . .

51 51 51 53

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3.4 The Reported Multiplicity Statistics of Early-Type Be Stars . . . . . . . 3.5 Possible Detection Biases in the Search for Be+MS Binaries . . . . . . 3.6 Be Stars as Binary Interaction Products . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

53 56 59 61

4 The Post-interaction Be + Stripped Star Binary HR 6819 . . . . . . . . . . 4.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2 The Importance of Individual Systems Like HR 6819 . . . . . . . . . . . . 4.2.1 In the Context of Be Star Formation . . . . . . . . . . . . . . . . . . . . 4.2.2 In the Context of the Search for Quiescent Black Holes . . . . 4.3 HR 6819 as Triple System Hosting a Black Hole . . . . . . . . . . . . . . . . 4.4 HR 6819 as Post-interaction Binary System . . . . . . . . . . . . . . . . . . . . 4.4.1 Spectral Variability and the Orbit of the System . . . . . . . . . . 4.4.2 Spectral Disentangling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.3 A Detailed Spectroscopic Analysis of HR 6819 . . . . . . . . . . . 4.4.4 The Component Masses in HR 6819 . . . . . . . . . . . . . . . . . . . . 4.5 Revealing the Configuration of HR 6819 with Interferometry . . . . . 4.6 A Possible Evolutionary History of HR 6819 . . . . . . . . . . . . . . . . . . . 4.7 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

63 63 63 63 64 65 68 68 70 72 74 75 77 80 81

5 The Young Massive Small Magellanic Cloud Cluster NGC 330 Observed with MUSE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introductory Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 The Search for Binary Interaction Products . . . . . . . . . . . . . . . . . . . . . 5.3 The Young Massive SMC Cluster NGC 330 . . . . . . . . . . . . . . . . . . . . 5.4 Multi-epoch MUSE Spectroscopy of NGC 330 . . . . . . . . . . . . . . . . . 5.4.1 Observations, Data Reduction and Spectral Extraction . . . . . 5.4.2 The Stellar Content of NGC 330 . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 Radial Velocities, Multiplicity Criteria and the Bias Correction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.4 The Multiplicity Properties of NGC 330 . . . . . . . . . . . . . . . . . 5.5 Particular Systems of Interest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Comparison to Previous Observational Studies . . . . . . . . . . . . . . . . . . 5.6.1 Cluster Core Versus Outskirts . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6.2 Comparison to Other B-star Populations . . . . . . . . . . . . . . . . . 5.7 Comparison to Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.8 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

93 98 101 104 104 106 108 112 113

6 Summary and Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Future Prospects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2.1 The Search for Be Stars with MS Companions . . . . . . . . . . . 6.2.2 The Rotational Velocities of Cluster Stars . . . . . . . . . . . . . . . .

117 117 121 121 122

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Contents

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6.2.3 Binary Interaction Products at Different Cluster Ages and Different Metallicity Environments . . . . . . . . . . . . . . . . . 123 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Acronyms

ADU AGB AO BeXRB BiP BH BSG BSS CCD CCF CE CMD DIB EW ESO FEROS FLAMES FoV FWHM GAIA GALACSI GLAO GSSP HARPS HERMES HMXB HB HST IFS

Analog-to-Digital Unit Asymptotic Giant Branch Adaptive Optics Be X-Ray Binary Binary interaction Product Black Hole Blue Supergiant Blue Straggler Star Charge-Coupled Device Cross-Correlation Function Common Envelope Color-Magnitude Diagram Diffuse Interstellar Band Equivalent Width European Organisation for Astronomical Research in the Southern Hemisphere Fibre-fed Extended Range Optical Spectrograph Fibre Large Array Multi Element Spectrograph Field of View Full Width at Half Maximum Global Astrometric Interferometer for Astrophysics Ground Atmospheric Layer Adaptive OptiCs for Spectroscopic Imaging Ground-Layer Adaptive Optics Grid Search in Stellar Parameters High Accuracy Radial velocity Planet Searcher High Efficiency and Resolution Mercator Échelle Spectrograph High-Mass X-ray Binary Horizontal Branch Hubble Space Telescope Integral-Field Spectroscopy xix

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IFU IMF IR ISM LBV LGS LMC LTE MPG MS MSTO MUSE MW NFM NS PSF RGB RSG RV SB1 SB2 sdO/B SMC SN S/N TAMS UT UV UVES VLT VLTI WCS WD WFC3 WFM WR ZAMS

Acronyms

Integral-Field Unit Initial Mass Function Infra-Red Interstellar Medium Luminous Blue Variable Laser Guide Stars Large Magellanic Cloud Local Thermodynamic Equilibrium Max-Planck Gesellschaft Main Sequence MS Turnoff Multi-Unit Spectroscopic Explorer Milky Way Narrow-Field Mode Neutron Star Point Spread Function Red Giant Branch Red Supergiant Radial Velocity Single-lined Spectroscopic Binary Double-lined Spectroscopic Binary subdwarf O/B star Small Magellanic Cloud Supernova Signal-to-Noise ratio Terminal-Age Main Sequence Unit Telescope Ultra-Violet Ultraviolet and Visual Echelle Spectrograph Very Large Telescope Very Large Telescope Interferometer World Coordinate System White Dwarf Wide Field Camera 3 Wide-Field Mode Wolf-Rayet star Zero-Age Main Sequence

Chapter 1

Scientific Context

1.1 Introduction Massive stars, which are stars with birth masses larger than about eight times the mass of our Sun (M ) are rare (Salpeter 1955; Kroupa 2001) and short-lived (e.g., Meynet and Maeder 2000). Nevertheless, they have played a major role throughout the history of the Universe (Jamet et al. 2004; Bresolin et al. 2008; Aoki et al. 2014). With their strong stellar winds and ionizing radiation, they heat, shape and enrich their surroundings, and they can trigger or inhibit the formation of new generations of stars (Bromm et al. 2009; de Rossi et al. 2010). Their final explosions as core-collapse supernovae are some of the most energetic events in the Universe and provide unique probes of distant Galaxies (Hjorth et al. 2003; Tanvir et al. 2013). The final outcome of their evolution are exotic objects such as neutron stars (NSs) or black holes (BHs) (Heger et al. 2003). A majority of massive stars live their lives as members of binary or higher-order multiple systems (Sana et al. 2012; Kobulnicky et al. 2014). If the systems are close enough to interact, the presence of such close companions not only has a profound impact on the evolution of both components (Paczy´nski 1967; Podsiadlowski et al. 1992), but also makes them probable progenitors of the now frequently observed gravitational wave events (Belczynski et al. 2002; Abbott et al. 2019). Because massive stars are fundamental cosmic engines, their importance extends beyond the field of stellar astrophysics. Our understanding of these objects serves as input in many other astrophysical disciplines, such as supernova simulations (Laplace et al. 2020), gravitational wave progenitor studies (Belczynski et al. 2016), stellar population synthesis predictions (Eldridge and Stanway 2009), galaxy simulations (Lahén et al. 2020), and the reionization of the Universe (Robertson et al. 2010). As a consequence, understanding their life cycle, in particular taking into account the presence of a close companion, is crucial to further our understanding of the evolution of star clusters, galaxies and ultimately, the Universe in general.

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Bodensteiner, Observational Imprints of Binary Evolution on B- and Be-star Populations, Springer Theses, https://doi.org/10.1007/978-3-031-19489-4_1

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1 Scientific Context

1.2 The Evolution of Massive Stars The content of this section is mainly based on Prialnik (2009), Maeder and Meynet (2000b) and Langer (2012). Before giving a brief overview over the evolution of massive stars, it is important to define what a massive star is. A massive star is a star massive enough to end its live with a core-collapse, in most cases accompanied by the formation of a NS or a BH. This is in contrast to low- and intermediate-mass stars which end their lives as white dwarfs. At galactic metallicity, this roughly corresponds to an initial mass Mini > 8M (Poelarends et al. 2008). While there are still many open questions in massive star evolution (Langer 2012), the basic picture is well established and will be outlined in the following. We hereby (for now) do not consider the effects of rotation, metallicity and binarity on massive star evolution. Like all stars, massive stars form in large, dense, and cold molecular clouds (e.g., Rosen et al. 2020). Whether the formation of massive stars is just an upscaled version of low-mass star formation, or whether other processes are at play is still under debate. The rarity of massive stars implies that they are, in general, at larger distances, and observational constraints are sparse. Massive star formation therefore remains a largely open field, for which we refer to the recent reviews of Zinnecker and Yorke (2007) and Rosen et al. (2020). After a star reaches the zero-age main sequence (ZAMS), the primary factor determining its evolution is its initial mass (e.g., Brott et al. 2011). As shown by the empirical mass-luminosity relation (e.g., Kuiper 1938), the luminosity is proportional to the mass of the star: L ∝ Mα (with α = 4.0 for stars with masses between 2.4 and 7 M and α = 2.7 for stars between 7 and 32 M , Eker et al. 2015). The luminosity, together with the stellar radius, define the effective temperature of a star. This is illustrated in Fig. 1.1, which shows evolutionary tracks of three stars with different initial masses in the Hertzsprung-Russell diagram (HRD): the starting point of evolutionary pathways of massive stars are different depending on their initial mass, and all evolutionary tracks follow a distinct path in terms of effective temperature and luminosity (still ignoring the effects of rotation, metallicity and binarity). The evolutionary timescale of stars is determined by the fusion rate in the stellar core and by the amount of nuclear fuel that is available. The time a star spends on the main sequence (MS), the nuclear timescale τnuc , is therefore proportional to the mass of the star, and inversely proportional to its luminosity. Combining this with the mass-luminosity relation implies that the MS lifetimes of stars scale with their mass: the more massive a star, the shorter its MS lifetime. It further indicates that, after 20 Myrs, a star with an initial mass of 5 M is still in the beginning of its MS evolution, while a 10 M star just reached the end of its MS lifetime. A more massive star with 20 M has left the MS already after around 10 Myr. On the MS, stars fuse hydrogen to helium in their dense and hot cores. The energy generated in the core is transported outwards by convection and radiation. While low-mass stars (like our Sun) have radiative cores and convective envelopes, massive stars have convective cores (which are therefore fully chemically mixed)

1.2 The Evolution of Massive Stars

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Fig. 1.1 Evolution of three stars with initial masses of 5, 10, and 20 M on the Hertzsprung-Russell diagram. The evolutionary tracks are from Brott et al. (2011) for stars with initial rotation rate of ∼100 km s−1 . The color indicates the age of the star (i.e., the time after the star reached the ZAMS, where the evolutionary tracks start)

and radiative envelopes. Depending on their mass, H burning occurs via the p-p chain (mainly in low-mass stars) or the CNO bi-cycle (dominant in massive stars). In the CNO bi-cycle, carbon, nitrogen and oxygen nuclei serve as catalysts for the transformation of four protons into a 4 He nucleus, releasing ≈25 MeV of nuclear binding energy. The process is cyclic and while the overall number of C, N and O nuclei remains constant in time, their relative abundances depend on the reaction rate of the different individual reactions. The CNO cycle therefore leads to a depletion of C and O, and an enhancement of N in the stellar core. The energy generation rate qCNO scales with the density and strongly with the temperature: qCNO ∼ ρ T18 . Given the steep temperature dependence of the CNO cycle, the temperature in the core remains constant while the mean molecular weight μ increases as H is converted into He. To compensate, following the ideal gas law, the density in the core increases and as the core mass remains constant, the core radius shrinks. This in turn leads to an expansion of the stellar envelope following the virial theorem. The end of the MS lifetime of a star (the so-called terminal-age main sequence, TAMS) is reached when the star has converted most of the core-hydrogen into helium. Little nuclear fuel is left in the core, which is now mainly composed of helium, and in order to keep up the energy production, the core contracts and heats up. Once the H fuel in the core is fully exhausted, no more energy is produced in the core,

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the star gets out of thermal equilibrium and the core contracts. The further evolution is again strongly dependent on the mass of a star, and we focus here on stars with Mini > 8M . Due to the contraction, the temperature and density are high enough in a shell around the hot core so that hydrogen-shell burning sets in. During H-shell burning, the He core gradually grows, which speeds up the contraction, while the envelope above the burning shell expands and becomes convective. As soon as the central temperature exceeds 108 K, He-burning via the so-called triple-α process occurs and builds up carbon in the core. When the core exhausts all the available He, a similar sequence of events occurs: He burning is ignited in a shell around the core (between the core and the H-burning shell), and subsequently C burning sets in the core. These core-shell burning cycles continue with O- and Si-burning in the core and in concentric rings around it, and the star builds up what is often referred to as an onion structure. Heavier elements such as Ne, Na, Mg, S, P, Si, and ultimately Fe and Ni are produced. As the fusion of Fe or heavier elements is endothermal rather than exothermal, the nuclear fusion process ends when the star has build up an iron-nickel core. Due to the lack of an energy source in the center, the star collapses. Large uncertainties still surround the endpoint of massive stars, and the possible formation of NSs and BHs (see e.g., Sukhbold et al. 2016). Whether a core collapses into a NS or a BH is mainly determined by the mass of the Fe-Ni core, and the effectivity of the supernova (SN) explosion which might accompany the collapse (e.g., Fryer et al. 2009). Near the core-mass limit between NS and BH, it is likely that a NS is formed if the SN effectively carries away a significant fraction of the stellar envelope. If, however, large parts of the envelope fall back onto the previous core of the massive star, a BH might form. Additional mechanism such as pairinstabilities (see e.g., Farmer et al. 2019) further complicate the picture and might lead to a full dispersion of the star, leaving no remnant behind. Observationally, the different phases in the evolution of massive stars outlined above are thought to correspond to specific categories of objects which can be organized as an evolutionary sequence, the so-called Conti scenario (see e.g., Conti 1975; Chiosi and Maeder 1986; Maeder and Conti 1994; Lamers 2013). We here provide an adapted version for stars of different initial masses: ∼ 3 → 8 M :

B → RGB → HB → AGB → post-AGB → WD ?

?

→ BSG − → RSG) → SN → NS ∼ 8 → 15 M : B → RSG (− ∼ 15 → 25 M : O → BSG → RSG → SN → NS/BH?  25 M :

?

?

O− → BSG − → LBV − → WR − → SN/direct collapse? − → BH?

Here, RGB stands for red giant branch, HB for horizontal branch, AGB for asymptotic giant branch, WD for white dwarf, RSG for red supergiant, BSG for blue supergiant, LBV for luminous blue variable, and WR for Wolf-Rayet star. Even such simplified view of massive star evolution remains subject to intense debate (see e.g., Massey 2003; Smith and Tombleson 2015; Humphreys et al. 2016; Smith et al. 2018; Smith 2019).

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1.2.1 Uncertain Physics in Stellar Evolution Theory The position of a star in the HRD, and in particular the core mass and the amount of hydrogen left in the envelope, strongly impacts the type of supernova that occurs (see e.g., Georgy et al. 2009; Smartt 2009), as well as the type of stellar remnant that is left behind (Heger et al. 2003). To better understand supernovae and the formation of compact objects, it is therefore crucial to improve our understanding of stellar evolution. The main physical uncertainties affecting predictions of current stellar evolution models of massive stars (which are mostly computed in 1D) are the treatment of internal mixing, mass loss by stellar winds, rotation, and binarity (which are inherently not 1D processes). Their implementation strongly affects the predictions of evolutionary tracks, in particular concerning the post-MS evolution and the endpoint of stellar evolution (e.g., Maeder and Meynet 2000b; Langer 2012; Ekström et al. 2020). To highlight one example of the large uncertainties in the post-MS evolution of massive stars is the question whether a star will undergo a so-called “blue loop” during core-He burning. Depending on the fraction of mass enclosed in the He core (which in turn depends on the implementation of stellar mass loss, rotational and internal mixing), evolutionary tracks predict that a RSG will undergo such a blue loop, where it moves back to the blue part of the HRD, becoming a BSG (though this time during core-He burning, Massey 2003; Meynet et al. 2011b). These predictions therefore have a strong impact on the ratio of RSGs to BSGs, a quantity which can be observed in far-away stellar population (Humphreys and Sandage 1980; DohmPalmer and Skillman 2002; Eggenberger et al. 2002), and which is often used as a diagnostic for stellar evolution models (Langer and Maeder 1995; Maeder and Meynet 2001). Internal Mixing Internal mixing describes the transport of matter and angular momentum inside of a star. If fresh material is transported into the core, more nuclear fuel is available and the effective core mass (and therefore the effective core radius) increases, also increasing the luminosity of the star. The MS lifetime of the star, which depends on both of these quantities, is also increased (Maeder and Meynet 2000b). On the other hand, if mixing is efficient, processed material enriched in nucleosynthesis products is brought to the surface of the star where it can be observed (e.g., Ekström et al. 2008; Brott et al. 2011). Several mechanisms were proposed to transport material, but also angular momentum, inside a star, including convective core overshooting (e.g., Maeder 1976; Bressan et al. 1981), rotational mixing (e.g., by meridional circulations or shear instabilities, Endal and Sofia 1976; Meynet and Maeder 2000; Maeder and Meynet 2000b), mixing through internal gravity waves (e.g., Rogers et al. 2013; Bowman et al. 2019), or magnetic torques (Spruit 2002; Maeder and Meynet 2004). Another important implication of internal mixing concerns the rotation of the stellar core and envelope. The stellar core contracts during the MS (and even more significantly during the post-MS) evolution (Langer 2012). If there is a coupling

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between core and envelope and angular momentum is transferred to the outer layers of the star by one of the above described mechanisms, the stellar envelope can spinup to critical velocities unless there is an additional mechanism slowing it down, such as tides in a close binary system (e.g., Zahn 1977) or stellar-wind mass loss (e.g., Puls et al. 2008). Stellar-Wind Mass Loss Stellar-wind mass loss is not only important in the evolution of massive stars because it carries angular momentum away, but also because it reduces the total mass of the star. Given the high mass-loss rates of massive stars, a star can lose a significant fraction of its mass due to stellar outflows during its evolution (see e.g. Castor et al. 1975) in the blue part of the HRD (i.e., on the MS, as BSG and WR star). These winds are driven by the radiation pressure of photons and caused by Doppler-shifted absorption of metallic lines (mainly ionized C, N, O and iron) in the UV part of the spectrum, where the spectral energy distribution of massive stars peaks (see e.g., Pauldrach et al. 1986; Puls et al. 2008). Since most of the lines that drive the wind are metal lines, the mass-loss rates strongly depend on the metallicity (they are weaker for lower metallicity, see e.g., Björklund et al. 2021). An accurate prediction of the wind-mass-loss rates at different metallicity environments is therefore important to predict the evolution of massive stars in the early Universe (see e.g., Kudritzki et al. 1987; Vink et al. 2001). A similar metallicity dependence of mass-loss in the RSG and LBV phases remains under debate, mostly given the lack of sufficient understanding of their respective mass-loss mechanisms (Humphreys and Davidson 1994; Maeder and Meynet 2000a; De Beck et al. 2010; Ekström et al. 2012; Cannon et al. 2021; Kee et al. 2021; Grassitelli et al. 2021). Rotation Observations show that a significant fraction of OB stars are moderately or rapidly rotating (see e.g., Simón-Díaz et al. 2006; Simón-Díaz and Herrero 2014; Hunter et al. 2008b; Dufton et al. 2013; Ramírez-Agudelo et al. 2013, 2015). Rapid rotation leads to rotational mixing in the star, effectively increasing the size of the core and therefore the MS lifetime. In extreme cases, if mixing is efficient enough to prevent a chemical gradient to form in a star, the star may become fully mixed. Such stars, which are called chemically homogeneous, are expected to contract during their evolution and therefore move to the left in the HRD, in contrary to stars with a well-defined core-envelope boundary (Maeder 1987; Langer 2012). Apart from inducing rotational mixing, rotation also has an effect on the geometry of a star: rapidly rotating stars are oblate and have different surface parameters (i.e., Teff and log g ) at the poles compared to the equator (von Zeipel 1924; Abdul-Masih 2021). Given that their equators are bulged out, those will be significantly cooler than the poles and rapid rotators appear cooler (redder) when observed, depending on the inclination angle (Townsend et al. 2004). It is therefore important to consider the critical rotation of a star, which is a measure of the rotational stability. It is defined as the rotational velocity at the surface at which the radiative and centrifugal forces

1.2 The Evolution of Massive Stars

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Fig. 1.2 Evolution of the rotational velocity of a star as a function of its evolution. The figure shows evolutionary tracks (Brott et al. 2011) for a star with Mini = 10 M , galactic metallicity, and three different initial surface rotation rates of 100, 300 and 500 km s−1 (corresponding to 15, 40, and 75% of the critical velocity at the ZAMS). Left panel: The color coding indicates the rotational velocity at the surface. Right panel: The color coding indicates the ratio of surface velocity to critical velocity

exactly balance gravity at the equator. If the star rotates at critical velocity, material at the equator can be lifted off the surface which can create an equatorial decretion ring around the star, further removing angular momentum from the star (Maeder et al. 1999). This could (at least partly) explain the Be phenomenon, which is described in Sect. 1.5. Figure 1.2 shows the evolution of the surface rotation of a star with an initial mass of 10 M (Brott et al. 2011). Due to the expansion of the envelope during the MS, the surface velocity decreases (but only slightly, because of efficient angular momentum transport from the core to the envelope, Maeder and Meynet 2000b; Hastings et al. 2020). At the same time, the critical velocity also decreases as the stellar radius increases. As the surface velocity decreases more slowly than the critical velocity, the ratio of v/vcrit increases during the evolution, and especially towards the end of the MS. Stars that are initially rapidly rotating can actually reach the critical velocity before the end of their MS lifetime. Ekström et al. (2008) showed that, in order to reach 90% critical velocity during the MS evolution at galactic metallicity, initial angular velocities of  0.6 critical are required, depending on the mass of the star. Observations, however, indicate that the coupling between core and envelope, and therefore the distribution of angular momentum throughout the star, is significantly stronger than predicted by theory (Aerts et al. 2019).

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1.2.2 Stellar Populations The HRD is one of the most important tools when investigating the evolution of a star or an entire stellar population. Placing a star on the HRD based on estimated stellar parameters Teff and L and comparing it to evolutionary models will give important information about its current evolutionary status (e.g., whether it is core-hydrogen burning), and an estimate of its age and mass (e.g., Schneider et al. 2014). The photometric version of the HRD is the color-magnitude diagram (CMD), providing colors instead of temperatures, and magnitudes instead of luminosities. For coeval populations of stars such as star clusters , the CMD (or HRD) provides a snapshot in time of the evolution of stars of different initial masses. By comparison of observed CMDs with isochrones from evolutionary models (see Fig. 1.3), important cluster properties can be estimated like the distance to the cluster and the interstellar extinction (see Sect. 2.1). Furthermore, the age of a given cluster can be inferred by fitting the tip of the MS, also called the MS turnoff (MSTO): stars more massive than the MSTO have already evolved off the MS given that their MS lifetimes are shorter. Typical assumptions concerning stellar clusters are that all stars were born simultaneously and share the same initial chemical composition, rotation rates, and are located at the same distance from the observer. If these assumptions are valid, and our current understanding and implementation of stellar evolution theory is accurate, then all stars of a given cluster should fall on the same isochrone. An example of a CMD is shown in Fig. 1.3, constructed from Hubble Space Telescope (HST) observations of the ∼40 Myr-old massive open cluster NGC 330 in the Small Magellanic Cloud (SMC, Milone et al. 2018, see also Chap. 5). Overplotted

Fig. 1.3 Color-magnitudediagram of the young open cluster NGC 330 in the Small Magellanic Cloud constructed from HST observations, originally presented by Milone et al. (2018). The pink line is an isochrone for stars on the MS (Chen Wang, priv. comm.) assuming an age of 35 Myr and an initial rotation of 50% of the critical velocity, computed with the MESA code for stellar evolution (Paxton et al. 2011, 2013, 2015, 2018, 2019)

1.3 The Effect of Binarity on Stellar Evolution

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is a single-star isochrone assuming an initial rotation rate of 50% critical for all stars. Apart from the foreground or field stars (stars with colors mF336W −mF814W  2), the broad MS of NGC 330 is not well represented by the single isochrone but seems to be made up by multiple components. Furthermore, the MSTO is not sharp but rather an extended region. These features are not only apparent in the CMD of NGC 330, but were found for many young open clusters in the Galaxy (Cordoni et al. 2018; Li et al. 2019) as well as in the Magellanic Clouds (Mackey et al. 2002; Li et al. 2017; D’Antona et al. 2017; Milone et al. 2018). Indications for the presence of multiple stellar populations were also found in much older Globular clusters (for a recent review see Bastian and Lardo 2018). These deviations from a perfect single-starburst isochrone could indicate that important physical mechanisms are not fully taken into account in the stellar models yet, such as internal mixing (Johnston et al. 2019). It could also imply that there are either multiple stellar populations of different ages (Milone et al. 2009; Goudfrooij et al. 2014) or different rotation rates (Bastian and de Mink 2009; Bastian et al. 2017; D’Antona et al. 2015; Kamann et al. 2020) in the cluster. This, however, gives rise to the question why different stars within the same cluster show different rotation rates. While most likely all the above-mentioned processes play an important role, we will discuss one in more detail in the following: the impact of binarity on the evolution of stars.

1.3 The Effect of Binarity on Stellar Evolution The content of this section is mainly based on Podsiadlowski et al. (1992), Hilditch (2001), and Langer (2012). In contrast to the evolutionary pathway of single stars (which, as outlined in Sect. 1.2, follows a well-defined though not fully understood path), interactions in binary systems can lead to a multitude of evolutionary pathways. The impact of binarity on stellar evolution depends most strongly on the initial mass ratio between the two components, and the initial orbital period of the system (Podsiadlowski et al. 1992; Langer 2012). While long-period systems evolve essentially as two single stars, the presence of a nearby companion can have a strong impact on the evolution of both stars (Paczy´nski 1967; Podsiadlowski et al. 1992). Observations have shown that a majority of massive stars are born as components of binary or higher-order multiple systems (see e.g., Sana et al. 2012, 2014; Kobulnicky et al. 2012; Dunstall et al. 2015; Moe and Di Stefano 2017). A high fraction of those binaries are on orbits tight enough so that they will interact during the course of their life (e.g., Sana et al. 2012, 2013). It is therefore crucial to take these effects into account to properly model the evolution of massive stars. In triple and higher-order multiple systems, the interplay between stellar dynamics and stellar evolution further complexifies the situation (see e.g., Toonen et al. 2020), an important aspect which we, however, do not cover further here.

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1.3.1 Different Binary Evolution Pathways Tidal interactions can change the orbital parameters of the binary systems and the rotation rates of the stars, without changing the mass of the stars themselves. They are particularly important for close binary systems and lead to a coupling of the rotation rate with the orbital revolution. Tides can lead to a circularization of the orbit as well as a synchronization of the rotation rates of the components of close binary systems. While the circularization is slower than the synchronization, both mechanisms occur faster than the nuclear timescale of the stars. Therefore, isolated close binary systems can be assumed to be synchronously rotating and on circular orbits at the end of their MS evolution (e.g., Zahn 1977; Hut 1981). A more profound change in stellar evolution occurs when the two components exchange mass, and therefore also angular momentum (see e.g., Paczy´nski 1967; Podsiadlowski et al. 1992; Vanbeveren and De Loore 1994; Vanbeveren and Mennekens 2017). This occurs when one of the stars (typically the more massive component which evolves faster) fills its Roche lobe, and transfers material to the companion through Roche-lobe overflow (RLOF). Mass transfer predominantly occurs at the end of the MS evolution, when the primary star expands due to H-shell burning (Case B transfer). Mass transfer can also occur when the donor is still on the MS (case A) or during or after the core-He burning phase (case C). Given that the radius of a star increases only slightly during the MS evolution, Case A mass transfer occurs in the tightest systems. Mass transfer via RLOF can further be distinguished based on its stability: if the total mass and angular momentum of the binary system is conserved, it is called stable or conservative mass transfer. The primary is stripped of its H-rich envelope (Kippenhahn and Weigert 1967), leaving the He core exposed. The companion accretes material and angular momentum, either by direct impact on the surface or via an accretion disk. The additional mass will also increase the core mass of the star, rejuvenating it. Packet (1981) showed that if a star accretes about 5–10% of its current total mass, it reaches the critical velocity. Mass gainers are therefore expected to be rapid rotators, depending on the amount of material transferred, and the ability of tides to spin it down (e.g., Pols et al. 1991; Petrovic et al. 2005; de Mink et al. 2013). Stable mass transfer usually leads to a widening of the binary orbit (e.g., Wellstein et al. 2001). If more material is transferred from the primary than the secondary can accrete, part of the mass (and angular momentum) will be lost to the system. The mass transfer is non-conservative and (often) unstable. The secondary will fill, or overfill, its Roche lobe and create a common envelope around the two components of the system. Common envelope (CE) evolution depicts one of the main uncertainties in binary interaction physics (see e.g., Ivanova et al. 2013). During the common envelope phase, friction between the envelope and the binary system will decrease the orbital separation of the two stars. It will either end in the ejection of the envelope, leaving behind a tight binary system in which the secondary will barely be changed given that the CE phase is very short. The other possible outcome of CE evolution

1.3 The Effect of Binarity on Stellar Evolution

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is a stellar merger (see e.g., Pols 1994; Taam and Sandquist 2000; Wellstein et al. 2001). In the case of a stellar merger, the two stars coalesce and form one single star (see e.g., Glebbeek et al. 2013; Justham et al. 2014). In particular, the merger product of two core-H burning (i.e., MS) stars is expected to be a core-H burning star again (e.g., Langer 2012). The further evolution of a MS+MS merger product was recently predicted by theoretical models but remains uncertain. Modeling the merger of two MS stars, Schneider et al. (2019, 2020) find that after a brief relaxation phase (which lasts ∼1000–10000 years) where the star is rapidly rotating and out of thermodynamic equilibrium, it settles back on the MS as a slow rotator and evolves similarly to a single star with the same mass that has no binary history. Furthermore, the merger product is predicted to be He-rich, and strongly rejuvenated in comparison to reference stars that were born at the same time, as fresh H is mixed into the core. Schneider et al. (2020) found that merger products have a large-scale magnetic field on the surface, which might explain (part of) the incidence of observed magnetic massive stars.

1.3.2 Observational Constraints on Initial Multiplicity Properties of Massive Stars In order to gain insight in to the multiplicity properties of massive stars, populations of massive stars in young clusters both in our Galaxy as well as in the Large Magellanic Cloud (LMC) have been well-studied. High-angular-resolution techniques which probe binary separations  10 AU, combined with literature information (mostly from spectroscopic and photometric work), showed that the average number of companions per O star within  15 − 20” (corresponding to 103 AU) is 2.2 Sana et al. 2014). While these systems are too wide to interact, the high number of companions indicate that the dominant outcome of star formation is a binary or multiple system (see also Mason et al. 2009; Aldoretta et al. 2015; Caballero-Nieves et al. 2020; Rainot et al. 2020, among others). Spectroscopic surveys, on the other hand, are typically sensitive to systems with periods up to about 10 years, with a decreasing sensitivity above a few years (e.g., Kobulnicky et al. 2012; Sana et al. 2012, 2013). Investigating O stars in young open Galactic clusters, Sana et al. (2012) found a bias-corrected close binary fraction of 69 ± 9%. This is comparable to the bias-corrected close binary fraction of OB stars in Cygnus OB2 of ∼ 55% (Kobulnicky et al. 2014). The bias-corrected close binary fraction of young O-type stars in the 30 Doradus region in the LMC was reported to be 54 ± 4% (Sana et al. 2013) and revised to about 60% by Almeida et al. (2017). Focusing on young B-type stars, Raboud (1996) estimated a lower limit of 52% on the observed close binary fraction in the young Galactic cluster NGC 6231 while Sana et al. (2006) obtained 67 ± 12 % for the O stars. In a recent study, Banyard et al. (2022) revisited the B-star population of NGC 6231 and found a bias-corrected close binary fraction of 44 ± 6%. In the LMC, Dunstall et al. (2015) investigated B

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stars in the young cluster 30 Dor and found a bias-corrected close binary fraction of 58 ± 11%. Investigations of the distributions of orbital parameters, most importantly the orbital period, eccentricity and mass ratio distributions, showed that they are quite similar for O- and early-B type stars (see e.g., Moe and Di Stefano 2017). Furthermore, they seem to be universal over different metallicities (see e.g., Sana et al. 2013; Moe and Di Stefano 2013; Sana 2017; Almeida et al. 2017). Young massive stars are therefore predominantly found in binary- or higher-order multiple systems, irrespective of their metallicity environment (see also Duchêne and Kraus 2013). Given that these studies mainly focus on young environments (i.e., 4 Myr, where most O stars are still on the MS and have not evolved yet), these surveys are supposed to probe the initial multiplicity properties where a majority of systems have not had time to interact yet (however, see Sana 2017; Ramírez-Tannus et al. 2021). As described above, apart from the closest systems which might interact during the MS through Case A mass-transfer, most interactions will occur at the end of the MS lifetime of massive stars. Sana et al. (2012) estimated that >70% of galactic O stars will interact during their lifetime while only ∼30% are either truly single or in binary systems wide enough that no significant interaction will occur. Among the interacting systems, ∼ 35% are expected to be stripped of their envelope, ∼15% experience spinup, accretion, or go through a CE phase, and ∼25% are expected to merge (Sana et al. 2012). The derived orbital parameter distributions and initial multiplicity fractions can therefore serve as input for detailed binary population synthesis calculations predicting the further evolution of such systems and the outcome of the interaction, which we will discuss in the following.

1.3.3 Predicted Occurrence and Properties of Binary Interaction Products Given that a high fraction of massive stars interact with a companion during their life time, the number of binary interaction products (BiPs) in a given population of massive stars is expected to be significant, in particular after a majority of the systems have had time to interact. de Mink et al. (2014) simulated a population of massive O-type stars at galactic metallicity, adopting the observed binary fraction and orbital parameter distributions from Sana et al. (2012) as initial conditions. Assuming continuous star formation, they found that the fraction of BiPs among all stars is as high as 30%. Those are either post-RLOF systems (17%), currently interacting systems (3%, mainly during slow case A mass transfer), and mergers (8%). While 22% of the stars live their lives as effectively single stars, the remaining 50% are binary systems before the interaction occurs. As described above, merger products and mass gainers after RLOF are rejuvenated (e.g., Glebbeek et al. 2013). When a comparison clock is available, such as other stars in a stellar cluster, mass gainers therefore appear younger and live longer on the

1.3 The Effect of Binarity on Stellar Evolution

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Fig. 1.4 Binary population synthesis predictions on the Hertzsprung-Russell diagram as a function of cluster age. Each dots corresponds to the primary of a simulated binary system where at least one component still undergoes H-burning. The color indicates the binary status or history of the system. The figure is adapted from Fig. 1 by Wang et al. (2020), ©AAS. Reproduced with permission

MS. In the CMD, they are expected to populate a region above the MSTO and are therefore referred to as blue straggler stars (BSSs). Schneider et al. (2015) simulated populations of coeval stars (corresponding to star clusters with a single star-formation event) and followed them over time. They found that the fraction of blue stragglers with respect to stars two magnitudes fainter than the MSTO is a function of the cluster age. Their population synthesis computations showed that the number of blue stragglers culminates at an age of 8 to 20 Myr, depending on the amount of mass transferred and of rejuvenation. Wang et al. (2020) recently showed that binary interactions have a profound impact on the MS morphology of star clusters in the HRD (or equally on the CMD). They compute grids of detailed binary-evolution models, representative of a massive star cluster with a total mass of 105 M at SMC metallicity, assuming a binary fraction of 100%. Following the evolution (and interaction) of the binary systems over time they predict the position of the more luminous binary component (as long as one component of the systems is still on the MS) in the HRD as a function of cluster age (see Fig. 1.4). In the beginning of the simulation, that is for young clusters with ages ∼2 Myr, most stars are on a single isochrone as predicted by single-star models. Only the most massive stars (i.e., stars at the bright end of the MS) are already evolving off the MS and begin to interact or merge. After 10 Myrs, most of these massive stars are not core-H burning anymore and are therefore not part of the simulation. While the singlestar isochrone of pre-interacting systems is still apparent, the MSTO predicted by the single-star model is populated by large numbers of different interaction products. This is comparable to the observed extended MSTO in young and intermediate-age clusters. Additionally, distinct MS components appear to the blue (mainly due to currently interacting systems, i.e., via case A mass transfer) and to the red (mainly post-interaction systems that went through case B mass transfer) of the single-star MS. After 30 Myrs, a clearer distinction of the different groups in terms of their position on the HRD occurs, while the MSTO still appears to be extended. Pre-

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interaction systems still lie on the single-star isochrone. Stellar mergers populate a region above the cluster turnoff, similarly to currently interacting binaries which are also found at hotter temperatures than the MS (i.e., bluewards). Post-mass transfer systems form a second MS which is shifted to cooler temperatures (to the red) compared to the single-star isochrone. Wang et al. (2020) furthermore find that the red sequence is made up by stars rotating close to their critical rotation. The three studies discussed here provide three implications that are important for this work: the number of binary interaction products in a given population of stars is significant; their relative number with respect to pre- or non-interaction stars increases as a function of cluster age (in the age range considered here); and the position of stars in the HRD (or CMD) provides important implications on their binary evolution history.

1.4 Observational Characteristics of Binary Interaction Products As described in the previous section, binary interactions can strongly alter the evolution of both components. They can furthermore lead to a multitude of different evolutionary pathways, and hence different outcomes, depending on the type of interaction that occurs. Some interaction products appear as single stars, in particular merger products, which are indeed single stars (if they were not initially part of a triple system), and post-RLOF systems where the mass gainer typically outshines the stripped companion. Furthermore, several properties characteristic for BiPs coincide with the expected observational properties of rapid rotators so that these characteristics can not be used as unique identifiers of BiPs. We have already discussed the predicted impact of binary interactions on the HRD positions of stars. Here, we want to summarize additional possible observational properties of BiPs: • relative age in comparison to a reference clock: when studying populations of stars, such as a star cluster, some mass gainers and mergers are expected to populate a region above the cluster turnoff because of rejuvenation (Schneider et al. 2015). These stars are the massive counterparts of the blue stragglers frequently observed in globular clusters (Sandage 1953; Shara et al. 1997; Ferraro et al. 1997; Sills et al. 2000, 2002). The same principle of an age discrepancy was recently proposed for stars in the red supergiant phase that appeared more luminous and are more massive than expected for single-star evolution with a common age. These stars are analogously called red stragglers (Britavskiy et al. 2019; Beasor et al. 2019). A similar argument holds for Algol-type binaries. Algol-type binaries are semidetached systems in which the less massive but more evolved component fills its Roche lobe and transfers mass to the more massive but less evolved (MS) companion (see e.g., Crawford 1955; Giuricin et al. 1983; Nelson and Eggleton 2001). Because stellar evolution theory predicts the more massive star to evolve faster,

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this is referred to as the Algol-paradox. It can be resolved by explaining Algolbinaries as systems that have undergone an earlier phase of mass transfer in which the mass ratio of the system was reversed. These currently interacting systems can be observationally detected for example by their Hα emission (Richards 1993; Richards and Albright 1999). • rotational velocity: mass gainers from RLOF are expected to be rapidly rotating because of the accreted angular momentum (see e.g., Pols et al. 1991; de Mink et al. 2013). Only a small fraction of the total mass of the star (∼ 5–10% of Mtot ) is enough to spin-up the BiP to critical rotation (Packet 1981). Depending of the assumed coupling between core and envelope, and if there is no other mechanism spinning down these stars (e.g., magnetic fields or winds), they are expected to remain rapidly rotating for a significant fraction of their lifetime and are thus observable as rapid rotators. Products of binary mergers, on the other hand, are expected to be slow rotators (Schneider et al. 2019). While a merger leads to an excess of angular momentum, the merger product is expected to be in an inflated stage right after the event which leads to efficient spin-down, before it settles as a MS star. Additionally, in the case that large-scale magnetic fields are produced by the merger event (Ferrario et al. 2009; Wickramasinghe et al. 2014, see below), the star is possibly further spun down due to magnetic breaking (Ud-Doula et al. 2009; Meynet et al. 2011a). Observations of large samples of O-type stars have shown that the distribution of rotational velocities has a high-velocity tail which has been attributed to BiPs (Ramírez-Agudelo et al. 2013; de Mink et al. 2013). • abnormal surface abundances: mass donors, mass gainers, and most merger products are expected to show abnormal surface abundances. In mass transfer through RLOF, the mass donor will be (partially) stripped of its H-rich envelope, exposing the inner layers that have been enriched with nucleosynthesis products. If the entire envelope is stripped, the mass donor on the one hand is expected to be a hot He-rich star (Wellstein et al. 2001; Götberg et al. 2017). The mass gainer, on the other hand, is expected to be enriched in nitrogen but depleted in carbon and oxygen if the accreted material contains material that was CNO-processed by the donor star. The amount of N enrichment on the surface depends on when, in the evolution of the primary star, the mass transfer occurs as well as on whether it is conservative or not (Langer 2012). The N enrichment of the mass gainer is expected to be less severe than for the donor star. Whether the products of a stellar merger show indications of CNO processed material on their surface is still under debate (Schneider et al. 2019). Observations of τ Sco, which was proposed to be a merger product, show a high N/C ratio (see e.g., Nieva and Przybilla 2014). Such surface abundance patterns are not an unambiguous diagnostic as O depletion and N enhancement is also expected through internal mixing in single stars (e.g., Brott et al. 2011; Pedersen et al. 2021) and as a result of wind stripping in early Otype stars (e.g., Kudritzki and Puls 2000). Hunter et al. (2008a) studied rotational velocities and surface abundances of a sample of apparently single B stars in the LMC. While they found a group of slow rotators with baseline N abundances which are expected from rotational mixing theory, they reported two other groups,

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unenriched rapid rotators and enriched slow rotators, that were both speculated to have a binary origin. • magnetic fields: About 10% of massive stars are observationally found to have strong and large-scale magnetic fields on their surface (Petit et al. 2013; Alecian et al. 2015; Morel et al. 2015). These fields are thought to be fossil, that is they are remnants of a magnetic field accumulated in an earlier phase of stellar evolution and are not currently sustained by a dynamo process (Donati et al. 2006; Donati and Landstreet 2009). Various explanations have been proposed: magnetic fields may be inherited from the parental clouds during star formation (Borra et al. 1982; Wade et al. 2016), or they may have been caused by stellar mergers (Ferrario et al. 2009; Schneider et al. 2019). These magnetic fields are thought to decay on timescales similar to the nuclear timescales of the stars, explaining the lack of magnetic stars close to the end of the MS (Fossati et al. 2016). Aside from the merger case (Schneider et al. 2019), whether or not mass transfer may impact the internal magnetic field remains a largely unanswered question (Song et al. 2018). • (lack of) binarity: compared to pre-interaction binaries, the number of BiPs in close binary systems with a MS companion is expected to be significantly lower. Merger products are indeed single stars (neglecting higher-order multiples). Postmass transfer systems with stripped companions are binaries but will most likely appear as single stars because the stripped companions are observationally hard to detect given their lower mass results in a small RV signal (de Mink et al. 2014). Furthermore, stripped stars are thought to emit most of their light in the UV so that they are probably outshone by the mass accretor in the optical (Wellstein et al. 2001; Götberg et al. 2017). If massive enough, the stripped star will undergo core-collapse in its further evolution. If the system remains bound in the possible supernova explosion, the system will appear as single-lined spectroscopic binary (SB1) system with a NS or BH companion. Those systems are only detected as such if the RV motion induced in the MS star by the compact companion is significant (see e.g., Langer et al. 2020). If the system is disrupted in a supernova, the mass gainer possibly gains a high space velocity (see below). • space velocity: binary systems in which the more massive star explodes as a supernova may become unbound in the explosion, creating a so-called runaway star (Blaauw 1961; Gies and Bolton 1986; Blaauw 1993; Hoogerwerf et al. 2001). While systems are predominantly unbound if half of the system mass is lost (Blaauw 1961), there might be an additional velocity kick if the explosion is asymmetric and/or because of neutrino emission (see e.g., Janka 2013, 2017). Observationally, the disruption of binary systems leads to an abnormal space motion of the former binary components, which can either be detected in the line-of-sight velocity, or in the proper motion of the stars. While historically runaway stars were typically defined as stars that exceed velocities > 30 km s−1 , recent theoretical works predicts a large number of such stars to exhibit moderate space velocities (Eldridge et al. 2011; Renzo et al. 2019). Runaway stars are often associated with a stellar bow shock detectable in the optical or near-IR, which occurs if the velocity difference to the ambient medium is larger than the sound speed (Peri et al. 2012; Kobulnicky et al. 2016).

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• circumstellar medium: apart from bow shocks that can be observable tracers of BiPs moving through the circumstellar medium, binary interactions may lead to the formation of circumstellar nebulae. If the mass transfer is non-conservative, that is if mass is lost to the surroundings either in a merger event, CE evolution, or non-conservative RLOF, this material is surrounding the BiP. Depending on the dispersion velocity of the material, the amount of mass, and the local density, these nebulae can be observed at different wavelengths. If the temperature is low enough for dust to form, they are observable in the near- and mid-IR (e.g., Bodensteiner et al. 2018). If a stripped star is present in the system, it can provide additional ionizing radiation for the surrounding gas and emission can also be seen in the optical, for example in Hα. Indeed, several circumstellar nebulae have been attributed to binary mergers (Leitherer and Chavarria-K. 1987; Pasquali et al. 2000; Mahy et al. 2017; Frost et al. 2021). • UV or X-ray excess: Depending on the companion, additional signatures are expected in other regimes of the electromagnetic spectrum. Due to their high temperatures, stripped stars are predicted to emit most of their flux in the UV. Depending on the effective temperature of the primary and the mass ratio, they can contribute significantly to the UV flux (Götberg et al. 2017). And indeed a handful of them, in particular subdwarf O (sdO) stars, have been detected based on observations in the far-UV (see e.g., Gies et al. 1998; Wang et al. 2017, 2018, 2021). Binary systems with NSs and BHs are X-ray bright when the compact object accretes material from the stellar wind of the massive star companion (Verbunt 1993; Reig 2011; Haberl and Sturm 2016). Such systems are called high-mass X-ray binaries (HMXBs). • core sizes: binary interaction products, in particular mass gainers and merger products, are expected to have larger stellar cores than single stars at the same mass because their cores are more He-rich due to previous nuclear reactions that occurred (e.g., Langer 2012). Information about the inner structure of stars, and in particular the size of the core, can be obtained through the analysis of the pulsational properties of a star (Aerts et al. 2010).

1.5 Classical Be Stars Be stars are B-type stars whose spectra show emission components in the hydrogen lines. The first Be star was discovered by Secchi (1866), who reported that γ Cas, the central star of the Cassiopeiae constellation, shows “a particularly interesting spectrum”. Comparing it to the spectra of other close-by stars such as β Cas, Secchi found that γ Cas shows an “inverse spectrum”, showing bright, luminous lines where other stars show dark lines. Following this observation, and as the name implies, Be stars are B-type stars with emission lines in their spectra. Struve (1931) offered the first physical interpretation of the origin of the emission lines in Be stars. Based on the observation that the spectra of Be stars show broad absorption lines indicative of rapid stellar rotation, Struve proposed that Be stars are

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“lens-shaped bodies which eject matter at the equator” leading to the formation of a “nebulous ring” around the star, in which the emission is formed. Despite this physical interpretation, the standard classification of the class of Be stars remains very broad. The most commonly used definition was given by Jaschek et al. (1981), who classified a Be star as “a non-supergiant B star whose spectrum has, or had at some time one or more hydrogen lines in emission” (see also Collins 1987, who replaced “hydrogen lines” with “Balmer lines”). This purely observational classification, however, includes a large variety of stars that are not rapidly-rotating oblate stars surrounded by a circumstellar disk as proposed by Struve (1931), but have a different physical nature. This includes young stellar objects such as Herbig Ae/Be stars (Waters and Waelkens 1998), so-called B[e] stars (which have forbidden emission lines in their spectra, see e.g., Lamers et al. 1998), supergiants with strong stellar winds (see e.g., Puls et al. 2008), magnetic stars (for which in particular the Hα line can be in emission; Sundqvist et al. 2012; Petit et al. 2013), and currently interacting binaries where mass transfer via an accretion disk can lead to the formation of emission lines (e.g., Horne and Marsh 1986). In order to differentiate these objects based on their physical nature, the term “classical Be star” was introduced. The working definition was provided by Rivinius et al. (2013): Classical Be stars are rapidly rotating, non-radially pulsating B-type stars that are surrounded by a circumstellar decretion disk. The definition is strictly speaking limited to stars of spectral type B, but the Be phenomenon is also detected in other spectral types, namely in late-O and early-A stars (Negueruela et al. 2004; Waters et al. 1988). While there are only few Oe stars known, the spectral-type distribution of Be stars peaks at early-B spectral type and declines strongly towards late-B and early-A stars (Zorec and Briot 1997). Overall, in the Galaxy, around 20% of the B-type stars show the Be phenomenon (e.g., Zorec and Briot 1997; McSwain and Gies 2005). Several authors have studied the occurrence of Be stars as a function of metallicity. Martayan et al. (2006) found that the frequency of Be stars in the LMC is similar to the one reported for the Milky Way (MW). In SMC clusters, such as NGC 330, the number is significantly higher, that is up to 40% (Grebel et al. 1992; Keller et al. 1999; Martayan et al. 2007). This could be due to the fact that stars at lower metallicity are closer to their critical rotational velocity (Maeder and Meynet 2000a). The spectral signature of Be stars depends highly on the inclination angle (e.g., Porter and Rivinius 2003, and Fig. 1.5). This effect has two components. A rapidlyrotating star only shows broad absorption lines when viewed equator-on. When observed pole-on, that is when the line of sight is aligned with the rotation axis, the star will appear to be slowly rotating. Additionally, the signature of the disk depends strongly on the inclination angle: While a pole-on viewed disk leads to a so-called “winebottle” profile in Hα (Hanuschik et al. 1988), more equator-on inclinations lead to the observation of double-peaked emission lines (see the right panel of Fig. 1.5 for observed line profiles of stars with different inclination angles). The Keplerian decretion disk around Be stars is thought to be gaseous, outwardflowing, and governed by viscosity (Lee et al. 1991; Meilland et al. 2007; Carciofi et al. 2009). Quirrenbach et al. (1997) directly measured disks around seven Be

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Fig. 1.5 Schematic view of two emission lines in three example Be stars (middle and right panel), viewed from different inclination angles (left panel). All Be stars were observed with the HERMES spectrograph at the Mercator telescope (Raskin et al. 2011)

stars for the first time and reported that they are geometrically thin, with typical radii of approximately 10 R∗ . Observations show that the characteristic emission lines in classical Be stars are not only highly variable (so-called V/R variations, see e.g., Štefl et al. 2003), but can appear and disappear on timescales of months, years, or decades (Wisniewski et al. 2010). The variability is commonly assigned to onearmed spiral density enhancements (Carciofi et al. 2009), which might be introduced by the presence of a companion star (Panoglou et al. 2016). The disappearance of the emission lines implies that the circumstellar decretion disk forms and dissipates on similarly short timescales (Rivinius et al. 2013). The exact formation mechanism of the disk is not well understood yet, but there is a consensus that rapid rotation is one of the prerequisites. Rapid rotation leads to a deformation of the star (Domiciano de Souza et al. 2003), which induces differences in the surface temperature and gravity, and reduces the escape velocity at the equator (Townsend et al. 2004). If the star is rotating close to critical velocity (veq /vcrit ≈ 0.95), then probably an additional mechanism (Owocki 2004), for example nonradial pulsations (Osaki 1986; Baade 1988; Semaan et al. 2018) or turbulence, can efficiently lift material off the surface of the star and lead to the formation of a disk. The fraction of critical velocity that is required for a star to become a Be star, or if all Be stars are actually critical rotators, is still debated. The exact determination of the rotational velocity is observationally difficult: the measurable quantity is v sin i and the inclination is difficult to determine (but see Sigut et al. 2020). Furthermore the spectrum of rapidly rotating Be stars is dominated by emission from the polar regions due to the gravity darkening effect (von Zeipel 1924). Observations seem to indicate, however, that Be stars show a broad range of rotational velocities, suggesting that not all Be stars are rotating close to critical (Yudin 2001; Cranmer 2005; Zorec et al. 2016). While the question remains whether all Be stars are rapid rotators, the origin of the rapid rotation of classical Be stars is also highly debated (McSwain and Gies 2005). Three main formation channels have been proposed: (1) Be stars could be born as rapid rotators (Bodenheimer 1995), (2) they could spin-up towards the end of their

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Fig. 1.6 The formation of Be stars with exotic companions through mass transfer according to the binary channel. Image credit Pablo Marchant

MS evolution (due to angular momentum transfer from the core to the envelope, see e.g., Crampin and Hoyle 1960; Ekström et al. 2008; Granada et al. 2013), or (3) they could be mass gainers in previous binary interactions (Kriz and Harmanec 1975; Pols et al. 1991; Shao and Li 2014; Schürmann and Langer 2021). While the first two channels are rooted in single-star evolution, the third channel presumes Be stars to be binary interaction products. According to the first channel, Be stars are born as rapid rotators, having inherited angular momentum from the molecular cloud they formed in (Bodenheimer, 1995). This would, on the one hand, imply that star formation works differently for a subset of stars, that is for rapid versus slow rotators. On the other hand, the fraction of Be stars would be expected to be highest in young stellar populations. Depending on whether stars spin down efficiently during their evolution, the Be star fraction would either remain constant, or decrease when studying older populations. This channel is, however, contradicted by observations: Firstly, reports of Be stars exist for clusters of any age (Abt 1979; Mermilliod 1982; Slettebak 1985). Secondly, the Be star fraction was reported to reach a maximum in clusters with ages between 13 and 25 Myr (Fabregat and Torrejón 2000; Tarasov 2017). Additionally, the rotational velocities of young B-type stars were found to be lower than the limit required for the formation of a Be star (Huang et al. 2010). If angular momentum is efficiently transferred from the core to the envelope (Langer and Heger 1998; Meynet and Maeder 2000; Ekström et al. 2008; Granada et al. 2013), B stars may effectively spin up during the course of their MS evolution (see Sect. 1.2). Ekström et al. (2008) found that single stars reach critical rotation rates at the end of their MS evolution (mainly due to meridional currents, and if the mass loss rates are not too high). According to their single star evolutionary models they can reproduce the observed fractions of Be star if v/vcrit = 0.7 is enough for the Be phenomenon to occur. Similar results were recently found by Hastings et al. (2020). However, as the authors discuss, the single-star channel encounters two main problems when confronted with observations: the high number of Be stars below the turnoff in star clusters such as NGC 330 (see Chap. 5), and the lack of observed nitrogen enhancement reported (Ahmed and Sigut 2017). A further problem is that the authors adopted the rotational velocity distribution observed for single B-type stars in the VFTS sample (Dufton et al. 2013) as initial rotation rates in their models. Given the star formation history of the VFTS sample (Schneider et al. 2018), a large fraction of the rapidly-rotating stars could be interaction products (see e.g., de Mink et al. 2014), and therefore the input rotational velocities might be overestimated.

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Alternatively, Be stars could be binary interaction products that were spun up by previous mass and angular momentum transfer in a close binary system (Kriz and Harmanec 1975; Pols et al. 1991). According to the binary channel, depicted in Fig. 1.6, Be stars received mass from a companion star that was initially more massive and evolved faster (see e.g., Shao and Li 2014). Together with the mass transfer via RLOF, also angular momentum is transferred, which spins up the star close to the critical velocity, leading to the formation of a Be star. If the mass-transfer phase did not lead to a merger of the mass donor, the original primary, and the progenitor of the Be star, the mass donor is (partially) stripped off its hydrogen-rich envelope. The remainder of such interaction is a stripped Helium star that, after a brief contraction phase, will observationally appear as a subdwarf O and B star (sdO/sdB) or WolfRayet star (if it is of higher mass). While lower-mass stars (i.e. stars with masses below the Chandrasekhar-limit) will subsequently evolve into a white dwarf, the more massive ones will end their live with a core-collapse. If the mass donor explodes as a supernova, the system may be disrupted, forming a single Be star with a history of binary interaction (Blaauw 1961; Gies and Bolton 1986). Whether mergers can also lead to the formation of Be stars is still a topic of debate. Based on detailed binary evolution calculations, Shao and Li (2014) reported that most Be stars may be the products of binary interactions. Further evidence is provided by the detection of Be stars in binary systems with evolved companions. The systems with the most massive companions are Be/X-ray binaries (BeXRBs, see e.g., Reig 2011). While the nature of the companion is still unknown for a significant fraction of BeXRBs, most known companions are NSs. There is currently only one Be star proposed to have BH companion (Casares et al., 2014), which was, however, recently challenged by Rivinius et al. (2022). Using observations in the ultraviolet from the International Ultraviolet Explorer (IUE) satellite and the HST, a handful of Be binaries with sdB or sdO companions were confirmed, including the well-known case of ϕ Per (Peters et al. 2008, 2013, 2016; Wang et al. 2017, 2018; Schootemeijer et al. 2018; Wang et al. 2021). Indications for the presence of a stripped star in optical spectroscopy were found in very few cases such as LB-1 (Shenar et al. 2020), HR 6819 (see Chap. 4) and HD 55606 (Chojnowski et al. 2018). The possible binary origin of classical Be stars has previously been investigated by several authors. Already in the 1980s, Abt and Levy (1978) performed a multiepoch spectroscopic survey of approximately 60 galactic Be stars of spectral type B2 to B5 to investigate their binary properties. They report similar binary fractions for B-type stars and Be stars, which is based on low number statistics. Investigating the period distribution, they find a significant difference between the two sub-samples: While a significant fraction of the B-type stars detected in binaries have periods less than 100 d, no Be binary was found with similarly short period. Among their list of Be binaries, there is further no double-lined spectroscopic binary (SB2). Using high-angular-resolution imaging, Oudmaijer and Parr (2010) further investigated the Be star binary fraction, comparing it to the B star binary fraction. Based on similar observed binary fractions for both B and Be stars, they concluded that it is unlikely that most Be stars form according to the binary channel. A caveat of this study, however, is that the observational data are only sensitive to periods larger than ≈5000 d. Post-interaction Be binaries are, on the other hand, expected to have

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periods that are of the order of one year (e.g., Langer et al. 2020). A similar argument holds for the recent survey performed by Horch et al. (2020) using speckle imaging: the data are not sensitive to periods, which are relevant in the binary interaction context. By a photometric survey of stars in Southern open clusters, McSwain and Gies (2005) studied if the number of Be stars changes as a function of evolutionary stage and stellar age. Similar to findings by Zorec and Briot (1997) and Martayan et al. (2010), they reported that the Be star fraction is higher for earlier-type and slightly evolved stars. Based on this, McSwain and Gies (2005) argued that the fraction of late-type Be stars would be expected to be higher, if classical Be stars were indeed born as rapidly-rotating stars of if they spun-up as single stars towards the end of their MS evolution. They concluded that the observed distribution of spectral types agrees with the interpretation of Be stars as binary interaction products. In contrast, Shokry et al. (2018) argued that there is no real change in the Be star fraction as a function of the spectral type, as the observed fraction of Be stars among late-type stars is underestimated. Using previously published radial velocities (RVs) and Hipparcos proper motions, Berger and Gies (2001) investigated the kinematics of ∼350 classical Be stars and found that 3–7% of the Be stars are runaway stars. They interpreted this as further evidence that at least a fraction of all classical Be stars gained their rapid rotation in previous binary interactions. A similar study was performed more recently by Boubert and Evans (2018) who investigated data from the first Gaia data release of ∼650 Be stars. They reported on a runaway fraction of 13.1+2.6 −2.4 % among their Be star sample. Assuming all Be stars are binary interaction products, they predicted the number of runaway Be stars and found that it agrees with their observed number. Using multi-band photometry also covering the IR part of the spectrum, Klement et al. (2019) searched for any indications of disk truncation and disk disruption in the spectral energy distribution of several Be stars. Those would be an indirect indication of the presence of a close companion to the Be stars. While they could not constrain the nature of the companions, they concluded that many, if not all, of the Be stars they investigated have close companions, which have an impact on their outer disks. It remains unclear whether the origin of rapid rotation in Be stars is rooted primarily in one of the above-mentioned mechanisms, or in a combination thereof.

1.6 Motivation and Open Questions Our understanding of the evolution of massive stars remains plagued by many open questions, for example concerning the role of mixing, rotation, or the effect of metallicity. In this thesis, we particularly focus on the uncertainties related to the impact of binarity (which will, as outlined above, also have a profound effect on the stellar rotation rates). In particular, we focus on investigating objects which are expected to have been impacted by binary evolution, that is Be stars, and massive star populations in slightly evolved clusters. We thereby study the following questions:

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Question 1: Are massive classical Be stars binary interaction products? There are many open questions around classical Be stars. How close to critical rotation are they? Why is the Be phenomenon transient? Which physical mechanism can explain the observed V/R-variations? Are all classical Be stars non-radial pulsators? It is likely that all of these open questions are (more or less strongly) linked to the fundamental question of why 20% of the B-type stars are rapid rotators, and whether a majority, if not all, of the massive Be star have gained the rapid rotation in previous binary interactions. While the binary channel explains classical Be stars as binary interaction products, and several observational constraints support this explanation, the relative importance of the binary channel with respect to the two proposed single-star channels remains unclear. Constraining the relative contribution of these channels is thus crucial to understand the origin of the rapid rotation in Be stars. A better understanding of the origin of Be stars and their evolutionary history will, on the one hand, provide a better understanding of rapid rotation in (massive) stars in general. As mentioned above, it is still debated how close to the critical limit Be stars are actually rotating. Furthermore neither the angular momentum transport inside of stars nor the angular momentum transfer in binary systems is well understood. On the other hand, if Be stars are indeed binary interaction products, they are the ideal places to search for rare late stages of stellar evolution (such as stripped stars, NSs or black holes). Given that only a handful of binary systems with such evolved companions are known, each new detection will provide important new insights which can be used as stringent test for our current stellar evolution theory. In this context, individual systems such as HR 6819 and LB-1 are of great importance as they can be used as exemplary systems. Question 2: Is HR 6819 indeed a triple system containing a B+BH binary and a wide, Be-star tertiary? HR 6819 was proposed to contain a triple system with an inner, close binary system of a B star and a BH, and a tertiary Be star on a wider orbit (Rivinius et al. 2020). Given the distance of only 340 pc to the system, HR 6819 is not only visible with the bare eye, but it would also make the putative BH the closest one to Earth observed so far. If this interpretation as hierarchical triple indeed describes the configuration of the system, then the system would be interesting for two reasons: (1) it would be one of the very few known X-ray quiet BHs, and (2) it would provide a clear indication that the outer Be star gained its rapid rotation following one of the two single-star channels for the formation of Be stars. We are therefore re-visiting the available data set to investigate if the observational data are possibly compatible with an alternative explanation.

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Question 3: Is there an observable imprint of binary interactions in a slightly evolved population of massive stars? As discussed in Sect. 1.3, the HRD of a population of stars such as a stellar cluster is predicted to be strongly shaped by binary interactions after a few Myrs where the binary systems had time to interact. The three main predictions in the context of this work are: (1) the overall number of binary interaction products is significant, while (2) their relative fraction peaks at cluster ages of ∼20-40 Myr. (3) The position of stars in the CMD can be used as a tracer of their interaction history, including predictions for stellar parameters, such as the surface rotation rates. While these have been proposed to explain the long-standing open questions about the morphology of cluster HRDs it remains unclear if observations match these predictions from binary population synthesis calculations. Measuring the observed stellar parameters such as Teff , log g , and v sin i , but also the current binary fraction, of a population of massive stars in the given age range will provide stringent tests for these binary population synthesis predictions. They will allow to investigate the imprint of binary interactions on massive star populations. Furthermore, if the predictions are correct, they will allow us the identify a large number of binary interaction products, providing important constraints of their properties and therefore allowing us to gain new insights in the outcome of the interaction.

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Chapter 2

Spectroscopy of Massive Stars

In Chap. 1 we have briefly described our current understanding of the evolution of massive single stars, the impact of binary interactions on their evolution, and the observational characteristics of such binary interaction products. In this context, we have also discussed classical Be stars. In this chapter, we want to give a brief overview of observationally accessible properties of hot and massive stars. We describe their observed optical spectra, the main diagnostics used in this work, how to measure them with optical spectrographs, and how to derive fundamental stellar parameters from them.

2.1 Stellar Spectroscopy The content of this section is mainly based on Gray (2005), Gray and Corbally (2009) and Crivellari et al. (2019). The shape of the flux profile emitted by the stellar component is mainly defined by the temperature of the star, where the effective temperature is defined as the temperature of a black body which emits the same amount of electromagnetic radiation from its surface. Superimposed on the continuum flux emitted by a star, there are absorption lines. Absorption lines are formed when light coming from the hot, dense interior of a star travels through the cooler, outer layers, called photosphere, and photons of a certain wavelength are either scattered out of the line of sight, or absorbed. The wavelength of the absorption lines corresponds to specific line transitions in atoms (or ions) and thus gives information about the atoms (or ions) present in the photosphere. Emission lines are formed when circumstellar material (e.g., disks, stellar winds, surrounding nebulae) is excited by the light of the star, which may emit light due to thermal radiation or scattering processes. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Bodensteiner, Observational Imprints of Binary Evolution on B- and Be-star Populations, Springer Theses, https://doi.org/10.1007/978-3-031-19489-4_2

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When observing a star with optical ground-based telescopes, several different components are visible in the spectrum: • a broad continuum extending from the near UV to the near IR (corresponding to the wavelength range in which the Earth’s atmosphere is transmissive), • absorption (and possibly emission lines) superimposed on the continuum, • emission from material in the immediate proximity of the star, for example the disks around Be stars, or nebular lines formed in gas clouds surrounding the star, • diffuse interstellar bands (DIBs) and interstellar lines, which are absorption features caused by the interstellar medium (ISM) between the star and the observer ˚ (Herbig 1995). While DIBs are typically several Angstroms broad, interstellar lines are narrow features, such as the Na D lines, • telluric lines formed by molecules (such as H2 O, O2 or CH4 ) in the Earth’s atmosphere (see e.g., Smette et al. 2015; Rudolf et al. 2016). Those are typically wide bands composed of many narrow lines. An example of the normalized spectrum of ω Sco, a spectral standard star for B1V (see Gray and Corbally 2009, and Chap. 5) is shown in Fig. 2.1 where stellar lines as well as tellurics and DIBs are indicated. Despite the fact that some information about the star can be gained from DIBs and nebular lines1 , the affected regions are typically either avoided or the effects are corrected for (see e.g., Smette et al. 2015; Abdul-Masih et al. 2019, for telluric and nebular correction,respectively). Apart from causing distinct features such as DIBs, gas and dust in the ISM also cause interstellar extinction. This is due to absorption and scattering of the stellar light by ISM particles. Given the typical size of dust grains in the ISM, blue light is scattered and absorbed more than the red part of the spectrum. As this causes stars to appear redder, this effect is also referred to as interstellar reddening. The amount of reddening of a stellar spectrum is directly proportional to the amount of

Fig. 2.1 Normalized spectrum of the spectral standard ω Sco observed with the HERMES spectrograph (see Sect. 2.2). The most important spectral lines, the Na D interstellar lines as well as a region affected by tellurics are indicated

1

Just to mention two examples: The strength of DIBs correlates with the amount of material on the line of sight between the observer and the star, and is hence a diagnostic for the distance. Nebular lines, on the other hand, can be used to constrain the UV flux of a star.

2.1 Stellar Spectroscopy

33

dust along the line-of-sight, and therefore typically increasing with the distance to the star (strongly dependent of the amount of material along the line of sight: the Galactic center, for example, is so obscured by dust that basically all optical light is blocked). Interstellar reddening can be approximated by empirical reddening laws (see e.g., Cardelli et al. 1989; Fitzpatrick et al. 2019), which describes the total extinction A(λ) as a function of wavelength. These can be used to apply reddening to stellar models when comparing to observations. The total extinction in the V-band A(V) is defined as A(V) = E(B–V) · RV where E(B–V) is the color excess and RV is usually fixed to 3.1. Each spectral line corresponds to a certain transition in an atom, which implies that spectral lines are sharp features (in principle δ-functions) centered at a discrete wavelength. This wavelength corresponds to the well-defined energy of the line transition. Observations, however, show that spectral lines are broadened. There are two types of mechanisms which lead to the broadening of lines: those of intrinsic (atomic) origin, and those of extrinsic origin which are caused by the Doppler effect. The intrinsic broadening is natural broadening which is related to the Heisenberg uncertainty principle. It is due to the fact that the energy levels of an atom have an intrinsic energy uncertainty and therefore a natural energy width. Several different mechanisms lead to additional broadening by the Doppler effect, that is they are caused by the line-of-sight motion of atoms or ions in the gas. Thermal broadening is due to the Doppler shift of spectral lines caused by random small-scale thermal motion in the photosphere, which is directly related to the temperature of the gas. Pressure broadening (also called collision broadening) is due to collisions with other atoms or ions which perturb the energy levels of the atom or ion. Two additional broadening mechanism are microturbulence and macroturbulence, which are also due to the motion in the stellar photosphere. While microturbulence is used to describe motion on scales similar to the mean free path of a photon, macroturbulence acts on scales significantly larger than the photon mean free path. Both micro- and macroturbulence are ad-hoc parameters that are introduced to fit the observed spectral lines. They are attributed to large-scale gas cell motions in the stellar atmosphere, whose origin in massive stars is still debated. While it was proposed that microturbulence is caused by subsurface convective motion (Cantiello et al. 2009), macroturbulence was attributed to turbulent pressure (Grassitelli et al. 2016) or gravity modes (Aerts et al. 2009; Simón-Díaz et al. 2010, 2017). Another broadening mechanism in stellar spectra is rotational broadening. This is caused by the fact that part of the atmosphere of a star is approaching the observer, while part of the atmosphere is stationary or receding when a star is revolving around its own axis. The maximum red- or blue-shift of the spectrum is determined by the velocity extremes at the outermost parts of the star along the equator. As spectroscopic observations yield the integrated light of the entire stellar surface, the observed line profile will be rotationally broadened, depending on the rotational velocity and inclination angle.

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2.2 Single-object Échelle Spectroscopy Spectrographs record a signal coming from a distant star that is proportional to the incoming flux as a function of wavelength. They are one of the most important type of instruments in modern astronomy as they allow to gain insights on reliable diagnostics of the stellar atmosphere. The working principle behind a spectrograph is that the light from a telescope enters the spectrograph, is collimated, dispersed (by a prism or a grating) and focused onto a detector (typically a CCD camera in optical spectroscopy). There are different ways of collecting the light of a star that enters the spectrograph, for example the light can be collected in one (or more) fibre(s), or with the use of one (or multiple) slits. For an observer, important properties of spectrographs are the spectral range that is covered as well the spectral resolving power λ/ λ which defines the finest details that can be distinguished. The flux observed of a star with a spectrograph is proportional to the luminosity of the star, but reduced due to for example interstellar and atmospheric extinction, as well as the efficiency of the optics and the detector. A conversion of the measured flux which is typically given in ADUs2 into an absolute flux unit can be obtained when the response curve of the optical system consisting of the telescope, the instrument and the detector is known. The response function of a given spectrograph can be characterized by comparing the observed flux of a standard star with the nominal flux of the star. As in this work, we mainly work with normalized spectra (i.e., spectra that are divided by their continuum), an absolute flux calibration is not required. Many modern-day spectrographs are Échelle spectrographs (such as HERMES, FEROS, HARPS, UVES; see e.g., Kaufer et al. 1999; Mayor et al. 2003; Raskin et al. 2011). They use two dispersive elements, typically an échelle grating and a crossdisperser, to disperse the light in two orthogonal directions. The échelle grating, which is a specific type of diffraction grating, disperses the incoming light covering the whole wavelength range in several spatially overlapping orders, which are then cross-dispersed by a second dispersive element (a prism for example) onto a twodimensional detector. The main advantage of Échelle spectrographs is that they allow to efficiently cover a a wide wavelength range with a high spectral resolution. In this work, we use data from two such spectrographs: FEROS and HERMES. The Fibre-fed Extended Range Optical Spectrograph (FEROS, Kaufer et al. 1999) is an échelle spectrograph mounted at the 2.2-m MPG/ESO telescope situated in the La Silla Observatory, Chile. To provide instrument stability and therefore a good radial velocity accuracy, the spectrograph is situated in a temperature- and humiditycontrolled room below the telescope. It is fed by two fibres, one object-fibre capturing 2.0" on the sky, and one sky- or calibration-fibre. By dispersing the light into 39 orders, FEROS covers a wavelength range between 3500 and 9200 Å with a spectral resolving power of 48 000. The RV precision of FEROS is about 100 to 300 m s−1 . ADU stands for analog-to-digital units. ADUs represent the number of e− that are read-out in a given pixel of a CCD. This charge is caused by photons entering the CCD and creating electron-hole pairs.

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2.3 Integral-Field Spectroscopy

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A similar spectrograph in the Northern Hemisphere is the High Efficiency and Resolution Mercator Échelle Spectrograph (HERMES), mounted at the 1.2-m Mercator telescope in La Palma, Spain (Raskin et al. 2011). The instrument design of HERMES is comparable to the one of FEROS providing a slightly smaller wavelength coverage of 3770–9000 Å with a higher spectral resolving power of 85 000.

2.3 Integral-Field Spectroscopy Integral-field spectroscopy (IFS) combines principles of photometry and spectroscopy. Rather than obtaining an image of a certain region of the sky, or a spectrum of a small slit or an optical fibre, IFS provides an image of the sky in which each pixel contains a spectrum (referred to as ‘spaxel’). Alternatively, IFS data can be seen as a large set of spectrally resolved monochromatic images. The output data of an integral-field spectrograph is therefore a 3D data cube containing two spatial and one spectral dimension (see Fig. 2.2). In this thesis we will make use of the Multi Unit Spectroscopic Explorer (MUSE, Bacon et al. 2010), mounted at Yepun, one of the four unit telescopes at the Very Large Telescope (VLT) in Paranal, Chile. In wide-field mode (WFM), the MUSE field of view (FoV) continuously covers 1 × 1 on the sky with a spatial pixel scale of 0.2"/px. In narrow-field mode (NFM), the FoV covers 7.5" × 7.5" with a spatial pixel scale of 0.025 /px.

Fig. 2.2 Schematic view of a 3D data cube observed with MUSE. Adapted from: ESO/MUSE consortium/R. Bacon/L. Calçada

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Fig. 2.3 Schematic view of the image slicing in MUSE. The 1 × 1 FoV is stretched in y-direction and sliced into 24 channels. Each of these 24 channels, entering a different IFU, is further cut into 48 mini-slits. During data reduction, the FoV is reconstructed. Image credit: https://www.eso.org/ sci/facilities/paranal/instruments/muse/inst.html

Equipped with ground-layer adaptive optics (GLAO), using a deformable secondary mirror, four laser guide stars (LGSs), and the Ground Atmospheric Layer Adaptive OptiCs for Spectroscopic Imaging (GALACSI) module, MUSE observations are corrected for turbulence in the atmospheric ground layers. This correction significantly increases the image quality. After light enters the instrument, the MUSE FoV is split into 24 slices (called channels), which are sent to 24 individual spectrographs. In each of these individual integral field units (IFUs), a given slice is further cut into 48 mini-slits. Finally, each of these mini-slits is injected into a spectrograph and arranged on a detector. Recombining all 48 mini-slits of each of the 24 channels allows the construction of a 3D data cube with 320 × 321 spaxels, and 3801 wavelength bins (see Fig. 2.3). MUSE-WFM observations are offered in two wavelength setups. In the extended wavelength mode, which is used in this work, the observations cover a wavelength range between 4650 and 9300 Å, with a spectral resolving power of between ∼1800 and 3700 and a wavelength step of 1.25 Å. The region between 5780 and 5990 Å is blocked by a notch filter when the observations are supported with AO, as scattered light from the four sodium LGSs would cause saturation in this wavelength region. The MUSE calibrations are set up in two parts: the calibrations that are performed individually for each of the 24 IFUs, and the global calibrations for the entire observing setup. On each of the individual IFUs, bias, dark, flat-field and wavelength calibrations are performed to correct for electronic effects and to map the pixels onto a wavelength scale. Furthermore, a second and third order flatfield and illumination correction is performed on the entire FoV and an absolute flux calibration is done with the help of a spectrophotometric standard star. The last step of the calibration is the sky subtraction, which removes possible contamination of the background (or foreground) sky in the stellar spectra on a pixel-

2.4 Extraction of Spectra in 3D Data Cubes

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by-pixel basis. In general, the average sky spectrum is computed from the spectra of the faintest pixels in a data cube. Stars and other bright sources are excluded to avoid an over-subtraction of stellar signal. This average sky spectrum is then subtracted from each spaxel in the cube. The MUSE pipeline offers two main procedures to estimate the average sky spectrum: it can either be determined in the science data itself, or in a dedicated sky observation. Dedicated sky observations, which are usually taken in the beginning or at the end of an observing block, usually point to an empty region in the sky, which is close to the science region of interest. This insures both similar observing conditions, which also impact the background flux, as well as little contamination by stars. This method is mainly used when observing single objects such as nebulae or galaxies which are effectively isolated. It is less effective when studying objects in densely populated regions, such as the SMC cluster NGC 330 (see Chap. 5), where no empty sky regions are available nearby. In such cases, where the sky field is equally crowded as the science field, the first sky subtraction procedure is preferred as they ensure that the average sky spectrum is computed under the exact same observing conditions. To perform the data reduction, a software package is provided by ESO and the MUSE consortium.3 The outcome of the reduction is a 3D data cube containing observed flux as a function of spatial location and wavelength. While this process is standardized, we note that the reduction of data taken with AO support with previous ESO MUSE pipeline versions (earlier than v2.6) large-scale wiggles were introduced mainly in the continuum region of the blue part of the spectrum, that is bluewards of 6000 Å. We identified that the problem occurred when correcting for the transmission curve of the notch filter, which has been solved by the ESO pipeline team in newer versions of the pipeline.

2.4 Extraction of Spectra in 3D Data Cubes In order to extract the spectra of individual stars from the 3D data cube, different techniques with different levels of sophistication are possible. The simplest way of extracting a spectrum of a given source is by determining the central spaxel of the source and measuring the flux in this spaxel in every monochromatic image. Concatenating these individual flux measurements with their respective wavelength results in a spectrum. While this method would indeed allow the extraction of the spectrum of a source, the point-spread function (PSF) of a typical spectrograph spreads the light of an incoming point-like source into several adjacent pixels on the detector. This is not only defined by the instrument characteristics, but also, for example, by the seeing conditions and the quality of the AO correction during the observations. In order to increase the signal-to-noise (S/N) ratio of the spectrum and to include all available information of the source, a more accurate way of measuring the flux of a given source in each wavelength image is by performing aperture photometry. Here, the 3

https://www.eso.org/sci/software/pipelines/muse/.

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flux of a source is measured in a typically circular aperture of a given radius around the central spaxel of the source (see e.g., Da Costa 1992). The local background is estimated in an annulus around the source and then subtracted. While this technique works well for isolated sources, it has its limitations in crowded fields where the PSFs of different sources are blended with each other. The crowding of stars can be taken into account by PSF fitting (see e.g., Kamann 2018; Bodensteiner et al. 2020). In this technique, the flux of a given star in a monochromatic image is measured by fitting a PSF model to the source. Such a PSF model can, for example, be a 2D Gaussian function, or it can be an effective PSF (ePSF) model (Anderson and King 2000) that is derived from the data itself. The chosen model is then fitted to each source, for all images available. Several tools for the extraction of spectra in 3D data cubes exist, which mostly follow similar procedures. One of the most commonly used software is pampelmuse (Kamann 2018). Here, we describe the python package extract- ifu- spectra4 in further detail, which is spectral extraction routine based on a slice-by-slice PSF fitting (see also Bodensteiner et al. 2020, 2021). It is based on the python package photutils (Bradley et al. 2019), which is a translation of the commonly-used IRAF package daophot (Stetson 1987). By performing PSF fitting not only on the source in question, but also on close-by sources simultaneously, blending in crowded fields is effectively taken into account when extracting the spectra. As an input, the routine requires a catalog containing the position and approximate brightness of stars. This can either be constructed from the observations themselves, or, ideally, is provided from a different set of observations with a higher spatial resolution. Those can be, for example, photometric observations with the HST, providing a spatial resolution that is approximately ten times higher than the one provided by MUSE under average weather conditions. This input list is used for two purposes: (1) in the PSF fitting, the stellar positions are fixed to those of the input catalogue, reducing the number of degrees of freedom in the fit, and (2) the magnitudes given in the input catalog are used to select targets for which spectra are extracted, and stars which are taken into account for the extraction of other sources. Before extracting the spectra, the coordinate systems of the input catalogue and the actual science data cube have to be aligned. A shift between the two is possible if the world coordinate systems (WCSs), which are derived from the pointing of the respective telescopes, are slightly inaccurate or offset. The coordinate transformation between MUSE coordinate system (x, y) and the HST coordinate system (x  , y  ), which includes both a translation and a rotation, is computed with x = +x  · cos(θ ) + y  · sin(θ ) + x 



y = −x · sin(θ ) + y · cos(θ ) + y.

(2.1) (2.2)

x and y correspond to the translation while the terms including θ are responsible for the rotation (see also Kamann 2018; Bodensteiner et al. 2020). The values of x, 4

https://github.com/jbodenst/extract-ifu-spectra.

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Fig. 2.4 Coordinate transformation between the MUSE and HST WCS. Orange circles show the input list of stars, turquoise circles show the adjusted starlist after the coordinate transformation, overlain over an example MUSE observation of NGC 330 (Bodensteiner et al. 2021, see also Table 5.1, epoch 3). Here, x = 1.29 ± 0.17 px, y = 1.80 ± 0.16 px, and θ = 0.49 ± 0.03◦

y, and θ are determined by selecting several bright and isolated targets in the HST catalogue, determining their corresponding positions in the MUSE observations via PSF fitting, and computing the difference in position between the two. The thereby derived coordinate transformation is then applied to all sources of the input catalogue. An example of such a coordinate transformation is shown in Fig. 2.4. In a second step, the ePSF is determined by fitting the PSF of a handful of selected stars that are bright and isolated. The ePSF is an empirical function that describes which fraction of the stellar light falls within which particular pixel on the CCD. It is therefore a 2D look-up table which is oversampled, that is finer spaced than the pixel size (in this work we chose an oversampling factor of 4). The ePSF is normalized such that the sum over the PSF pixels over a given radius is 1, which corresponds to setting the flux in a circular aperture with the given radius to 1. Figure 2.5 shows the example of an ePSF model obtained from the MUSE data used in this thesis. It can be seen that the ePSF can be approximated by a 2D Gaussian. This would, however, underestimate the core and overestimate the wings of the PSF of the MUSE data. We therefore use the ePSF rather than a 2D Gaussian in this work. When extracting the spectrum of a certain star, in every wavelength image, the amplitude of the ePSF is fitted while the shape is fixed. Surrounding stars that are

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Fig. 2.5 Example ePSF obtained from the MUSE data used in Bodensteiner et al. (2020), further discussed in Chap. 5. The left panel shows the shape of the ePSF where color indicated the normalized flux, and the right panel shows 2D cuts through the ePSF along the y-axis

closer than a certain distance (i.e. 12 pixels in this work, corresponding to 2.4"), and brighter than a chosen brightness (in this work: all stars that are up to one magnitude fainter than the extraction brightness limit) are taken into account simultaneously fitting the ePSF of the target star and the surrounding sources. This ensures that the contribution of the adjacent sources is not attributed to the star in question. An example of effective deblending with extract- ifu- spectra was shown in Bodensteiner et al. (2020) and Bodensteiner et al. (2021) who applied the method to MUSE data of the dense cluster core of NGC 330 (see also Chap. 5). One example of deblended spectra is shown in Fig. 2.6. It shows that the extraction leads to clean spectra of all the sources, also the fainter ones. In particular, it shows that it is possible to effectively take into account the strong Hα emission line in the extraction of the surrounding sources, which demonstrates the reliability of the here described PSF-fitting routine. The method described here, extract- ifu- spectra is flexible and can be easily adapted to other instruments, as for the SPHERE instrument in the context of the Carina High-contrast Imaging Project for massive Stars (CHIPS Rainot et al. 2020, 2021).

2.5 Radial Velocity Measurements If a star is moving towards or away from an observer, the spectral lines emitted by the star are blue- or red-shifted according to the Doppler effect. The radial velocity of a star, that is the component of its three-dimensional velocity vector along the observer’s line-of-sight, can be measured by measuring the shift in wavelength space of spectral lines. As described in Sect. 1.3, stars in a binary system orbit around each other. Depending on the viewing angle, that is the inclination of the orbital plane with respect to the observer, this motion leads to periodic shifts of spectral lines in wavelength

2.5 Radial Velocity Measurements

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Fig. 2.6 Example spectral extraction for a star (# 459) in the MUSE data of NGC 330. Left panel: The colored circles indicate all stars with a given distance (here, this critical distance is chosen to be 12 px), which are fitted simultaneously in the spectral extraction of star #459. Right panel: Extracted spectra for all stars taken into account during the extraction. The spectrum of the star star (# 459) is not contaminated by any of the surrounding stars, in particular not by the bright Hα-emitter (#482). This figure was originally published by Bodensteiner et al. (2020), their Fig. A.1. Reproduced with permission ©ESO

space which can be detected in stellar spectra. In the case of double-lined spectroscopic binaries (SB2s), the spectral signature of both components are discernible in a composite spectrum and, often, RVs can be measured for both. In single-lined spectroscopic binaries (SB1s), only one component can be seen. There are, however, other mechanisms that can lead to line profile variability and can cause an apparent shift of specific parts of spectral lines. While wind variability is the dominant mechanisms causing line profile variability in O-type supergiants (Fullerton et al. 1996), in the B-star domain, the main other cause of RV shifts are stellar pulsations (see e.g., Aerts et al. 2009; Simón-Díaz et al. 2017). In the case of radial pulsations, the entire star expands and shrinks, while in the case of non-radial pulsations, parts of the surface move up while others move down. The observed line profiles of pulsating stars can therefore be highly variable. Typical RV variability induced by non-radial stellar pulsations are on the order of 20 km s−1 or lower (e.g., Aerts et al. 2009). An example of a star, HR 6819, showing both variability attributed to pulsation as well as RV shifts caused by the binary nature of the system, is discussed in Sect. 4.4. Different techniques can be used to estimate the RV of a star or a binary system from the observed spectra, which comes down to accurately measuring the central wavelength of the core of the spectral line. Two commonly used techniques are analytic profile fitting and cross-correlation to measure the RVs of a star. For slow and medium rotators, most spectral lines (and in particular stellar absorption lines) are well represented by Gaussian or Lorentzian profiles. RVs can thus be estimated by fitting the central wavelength of such analytic profiles to one or more spectral lines in question (see e.g., Sana et al. 2013; Evans et al. 2015; Banyard et al. 2022). In the case of SB2s, double-Gaussians are fitted, one for each binary component. The RV can then be computed by comparing the determined central wavelength of the fit to

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the rest wavelength of the line5 in question using the Doppler formula. Errors on the RVs are estimated from the error on the fitted central wavelength of the Gaussian. Another method to measure radial velocities is using the cross-correlation technique (see e.g., Zucker 2003; Dunstall et al. 2015), which in principle measures the similarity of two curves or, in this case two line profiles, as a function of the relative shift between the two. The cross-correlation technique is thus based on a grid of possible RVs, corresponding to wavelength shifts. For each RV, the observed spectrum is shifted accordingly in wavelength space with respect to a comparison spectrum, called the template, and the similarity of the two spectra is measured. By repeating this for each RV, the so-called cross-correlation function (CCF) is defined. While the peak of the CCF corresponds to the best-fitting shift in wavelength and thus the RV is determined, the RV error is estimated by fitting a parabola to the upper part of the CCF. As a template, a model spectrum or another observed spectrum, ideally the one with the highest S/N, can be used. The cross-correlation technique works well if the spectral lines are intrinsically not variable but only exhibit a shift in RV. Another caveat of this method is that the RV is computed with respect to the template. In order to convert this relative RV to an absolute one, as measured by Gaussian fitting, the rest wavelength of the template is required. While this is known for model spectra, this is typically not the case when using an observed spectrum as template. Figure 2.7 shows an example of a Gaussian fit (top panel) and the CCF method (bottom panel) to derive RVs of an example star. We here use HR 6819 (see Chap. 4) and focus on one particular Si ii lines at λ 6347.10 Å. The absorption line is wellrepresented by a Gaussian profile and the fit shown in the top panel indicates that RV = 62.6±0.5 km s−1 . In the CCF shown in the bottom panel, a different observational epoch of the same star is used as a template. Therefore, in this case only the relative RV between the two spectra can be determined, which amounts to RV = 70.8±0.4 km s−1 . Knowledge about the rest wavelength of the template is required to compare the two measurements. Both methods described here assume that the line profiles are stable (i.e., that their shape does not change). The determination of RVs and their uncertainty can, for example, be hampered by the quality of the spectra or variability in spectral lines (see for example Sect. 4.4).

2.6 Determination of Stellar Parameters Because spectral lines in stellar spectra depend on the local physical conditions at the location they are formed in the atmosphere, they can be used as powerful diagnostics to constrain key stellar parameters such as the effective temperature, the surface gravity or the rotation rate of the star. The oldest and simplest way of classifying a star is by the appearance of the stellar spectrum, in particular by comparing the relative strengths and widths of absorption 5

In this work, rest wavelengths are taken from the NIST Atomic Spectra database accessible under https://physics.nist.gov/PhysRefData/ASD/lines_form.html.

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Fig. 2.7 Example of the two RV determination methods for HR 6819. Top panel: Gaussian fitting of the Si ii line at λ 6347.10 Å, where the black line is the observed spectrum and the red is the bestfitting Gaussian profile. Bottom panel: Left: Cross-correlation of the same spectrum as in the top panel (black) with a template spectrum (green). In this case, the template is an observed spectrum as well, which was taken at a different orbital phase. The orange curve shows the shifted template corresponding to the maximum of the CCF. Right panel: CCF (dark blue) as a function of input RV. The upper part of the CCF is fitted with a parabola to estimate the errors in RV (light blue)

lines, a process called spectral classification. Spectral classification was pioneered by Secchi (1866) and expanded, among others, by Pickering (1890). The classification system still in use today, the so-called MK system, is described by Morgan and Keenan (1973), which for OB stars has been refined over the years by Walborn (1971, 1972, 1973, 1977, 1980, 1982) and Walborn and Fitzpatrick (1990, 2000). Following the MK system, stars are classified with respect to standard stars along two axis: the spectral class, which is a proxy for temperature, and the luminosity class, indicative of the approximate surface gravity (which is the gravitational acceleration at the surface of a star). While such a comparison to standard-star spectra is often performed by eye, it can also by done by comparing the equivalent width (EW) of diagnostic spectral lines (see e.g., Kerton et al. 1999; Kobulnicky et al. 2012; Zeidler et al. 2018; McLeod et al. 2019). Due to the construction of most (also historic) spectrographs, commonly used spectral classification schemes in the O- and B-type regime mainly utilize the blue part of the optical spectrum (usually between 4200 and 4600 Å Conti and Alschuler 1971; Walborn and Fitzpatrick 1990). However, with the advent of new instruments such as MUSE at the VLT, which do not cover the blue part but focus on longer wavelengths, new diagnostic lines are used and new classifications schemes have to be derived. Furthermore, given the large amount of data produced by current large-scale surveys, automatic classification procedures are required. An example of such an automatic classification scheme for OB stars was presented by Bodensteiner et al. (2020), focusing on three diagnostic lines in the red part of the optical spectrum, namely He ii λ 5412, He i λ 6678, and the O i triplet at λ 7774. To calibrate the EW-to-spectral-type classification, Bodensteiner et al. (2020)

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Fig. 2.8 Atlas of spectral standard stars from Bodensteiner et al. (2020). The spectra are shown in narrow wavelength regions around three diagnostic lines (see text) and their spectral types are indicated on the right. For clarity reasons, the normalized spectra are shifted vertically and moved to rest wavelength. For each star, the continuous black lines show the original HERMES or FEROS spectra, while dotted lines show the spectra after degrading them to the resolution and wavelength binning of MUSE. This figure was originally published by Bodensteiner et al. (2020), their Fig. 7. Reproduced with permission ©ESO

used a set of commonly used standard stars (Gray and Corbally 2009). The highresolution high-S/N observations of all standard stars, obtained with the HERMES spectrograph at the Mercator telescope in La Palma (Raskin et al. 2011), and the FEROS spectrograph at the ESO/MPG 2.2m-telescope in La Silla, are shown in Fig. 2.8. It shows the change of the diagnostic spectral lines as a function of spectral type and illustrates the different sensitivity of certain lines to different spectral types. On the one hand, the He ii line is strongest for the earliest-type stars and disappears at a spectral type B0. On the other hand, the O i triplet only appears in spectral types later than B3. The three lines combined thus allow to classify stars into spectral types from O7 to A7. Based on the observed spectra of standard stars, Bodensteiner et al. (2020) measured the EW (and the corresponding EW error). Using those, they derived a relation between EW and spectral type described by a second-degree polynomial. Figure 2.9

2.6 Determination of Stellar Parameters

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Fig. 2.9 Relations between spectral type and equivalent width of diagnostic spectral lines. The three panels show the relation derived by Bodensteiner et al. (2020) for the He ii line at λ 5412, the He i line λ 6678, and the O i triplet at λ 7774, from top to bottom. In each panel, black dots indicate all measured EW values while the black crosses show which EW measurements were used for the polynomial fit which is marked by black lines. The shaded gray region below 0.1 Å is excluded as well, because spectral lines with such small EWs can usually not be distinguished from noise in the spectra. The two blue triangle in the top panel indicate a contamination by metal lines (in particular by Fe i and Ne i) at a similar wavelength than the considered He ii line. These relations allow to automatically assess the spectral type of a star by measuring the EW of the three diagnostic lines. This figure was originally published by Bodensteiner et al. (2020), their Fig. 8. Reproduced with permission ©ESO

shows these relations graphically for the three considered diagnostic spectral lines. Classifying a new star based on this relations thus requires a measurement of the EW of the diagnostic lines, which provides a direct translation into spectral type. This can be automatized and therefore allows the automatic classification of a large sample of stars. The quality of spectral classification strongly depends on the availability of suitable spectral standard stars. This is complicated by the fact that most historic standards were found to be variable stars or members of binary systems with modern instrumentation (see table 1 of Bodensteiner et al. 2020). One example is the star

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ν Ori, which is listed as B0 V standard in Gray and Corbally (2009). HERMES spectra of the star, however, clearly show that it has the composite spectrum of an SB2 system, making it unsuitable for spectral type calibrations (Bodensteiner et al. 2020). Nevertheless, spectral type classifications can give a first idea of the physical properties of a star. To obtain an absolute estimate of the stellar parameters such as the effective temperature Teff , the surface gravity log g , as well as the metallicity or abundances of individual elements requires a comparison to synthetic spectra. Such synthetic spectra are computed solving the radiative transfer equations in stellar atmosphere models. Examples of such are the Kurucz-models (Kurucz 1993), LLmodels (Tsymbal 1996), tlusty (Hubeny and Lanz 1995; Lanz and Hubeny 2007), fastwind (Puls et al. 2008), cmfgen (Hillier and Miller 1998) or powr (Hamann and Gräfener 2003). While all of these codes are calculated in 1D, they differ in the adopted frame (i.e., observers frame vs. co-moving frame), the assumed geometry (plane-parallel or spherical geometry), the inclusion and treatment of winds, as well as their assumptions on local thermodynamic equilibrium (LTE) in the stellar atmosphere (i.e., LTE vs. non-LTE). As different assumptions are valid for different types of stars, in particular for different temperature regimes, different codes are preferably used (i.e., Kurucz- and LLmodels for stars with lower temperatures, tlusty for stars with higher temperatures but weak stellar winds, and fastwind or powr for stars with strong stellar winds). The comparison between model and observed spectrum is often performed by eye. For larger samples, or when a more quantitative approach is desired, a χ 2 minimization is typically used to find the best-matching model. Several tools are available to efficiently compare observed spectra to a set of model spectra. One example is the Grid Search in Stellar Parameters (GSSP, Tkachenko 2015) which compares the observed spectrum with a grid of synthetic LLmodel spectra and computes the χ 2 for each model in the grid. The model with the minimum χ 2 is taken as best-fit model which most accurately represents the stellar parameters. GSSP allows to simultaneously fit five stellar parameters, that is Teff , log g , metallicity, vmicro , and vmacro . GSSP works with LLmodel spectra which are computed assuming LTE. While this assumption is valid for stars with low temperatures and high densities, it is not valid for stars with high temperatures and low densities. Focusing on the MS, nonLTE effects become important for Teff > 20 000 K (Kudritzki 1979; Kilian 1994; Nieva and Przybilla 2007), that is for O- and early-B stars. In these temperature- and density-regimes, LTE computations do not accurately describe the population numbers of spectral lines which strongly impacts the determination of stellar parameters and abundances. Figure 2.10 shows a comparison between tlusty and LLmodel spectra. The different panels show synthetic spectra with four different temperatures (i.e., Teff = 15000, 20000, 25000 and 30000 K) while the other stellar parameters are fixed to log g = 4.0 dex, solar metallicity, vrot = 100 km s−1 , and vmicro = 2.0 km s−1 . The comparison shows that the synthetic spectra differ at all temperatures while the

2.6 Determination of Stellar Parameters

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Fig. 2.10 Comparison of synthetic non-LTE tlusty spectra (black) with synthetic LTE spectra computed with GSSP from four LLmodels (red) assuming solar metallicities. The different rows are for different effective temperatures (i.e., Teff = 15000, 20000, 25000, and 30000 K) while the other stellar parameters (log g , Z, vrot , and vmicro , indicated in the left panel of each row) are kept constant. The lower panels of each plot show the residuals and important spectral lines are indicated

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differences become significant above around 20000 K. At lower temperatures, small differences in the depth of metallic lines can be seen. Those are most likely due to different assumed abundances for the individual elements.6 At higher temperatures, the differences between the two spectra become more obvious: while the metal lines are systematically weaker in LTE, the most affected lines are the Balmer as well as He lines, which are significantly deeper but also wider in NLTE. Deriving stellar parameters for hot stars with LTE models will therefore strongly impact the determination of Teff and log g (for example, the derived log g would systematically be overestimated).

References M. Abdul-Masih, H. Sana, J. Sundqvist et al., ApJ 880, 115 (2019) C. Aerts, J. Puls, M. Godart, M.A. Dupret, A&A 508, 409 (2009) J. Anderson, I.R. King, PASP 112, 1360 (2000) R. Bacon, M. Accardo, L. Adjali et al., in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, Volume 7735, Ground-based and Airborne Instrumentation for Astronomy III, vol. 773508 (2010) G. Banyard, H. Sana, L. Mahy et al., A&A 658, A69 (2022) J. Bodensteiner, H. Sana, L. Mahy et al., A&A 634, A51 (2020) J. Bodensteiner, H. Sana, C. Wang et al., A&A 652, A70 (2021) L. Bradley, B. Sipocz, T. Robitaille et al., astropy/photutils: v0.6 (2019) M. Cantiello, N. Langer, I. Brott et al., Commun. Asteroseismol. 158, 61 (2009) J.A. Cardelli, G.C. Clayton, J.S. Mathis, ApJ 345, 245 (1989) P.S. Conti, W.R. Alschuler, ApJ 170, 325 (1971) L. Crivellari, S. Simón-Díaz, M.J. Arévalo, Radiative Transfer in Stellar and Planetary Atmospheres (2019) G.S. Da Costa, in Astronomical Society of the Pacific Conference Series, Volume 23, Astronomical CCD Observing and Reduction Techniques, ed. by S.B. Howell, vol. 90 (1992) P.R. Dunstall, P.L. Dufton, H. Sana et al., A&A 580, A93 (2015) C.J. Evans, M.B. Kennedy, P.L. Dufton et al., A&A 574, A13 (2015) E.L. Fitzpatrick, D. Massa, K.D. Gordon, R. Bohlin, G.C. Clayton, ApJ 886, 108 (2019) A.W. Fullerton, D.R. Gies, C.T. Bolton, ApJS 103, 475 (1996) L. Grassitelli, L. Fossati, N. Langer et al., A&A 593, A14 (2016) D.F. Gray, The Observation and Analysis of Stellar Photospheres (2005) Gray, R. O. & Corbally, Christopher, J. 2009, Stellar Spectral Classification W.R. Hamann, G. Gräfener, A&A 410, 993 (2003) G.H. Herbig, ARA&A 33, 19 (1995) D.J. Hillier, D.L. Miller, ApJ 496, 407 (1998) I. Hubeny, T. Lanz, ApJ 439, 875 (1995) S. Kamann, PampelMuse: Crowded-Field 3D Spectroscopy (2018) A. Kaufer, O. Stahl, S. Tubbesing et al., Messenger 95, 8 (1999) 6 The difference between tlusty and LLmodels is quite strong in the Mg ii line at λ 4481 Å). Given that the ratio of the Mg ii line and the He i line at λ 4471 Å is an often-used spectral type diagnostic, this has to be taken with caution.

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C.R. Kerton, D.R. Ballantyne, P.G. Martin, AJ 117, 2485 (1999) J. Kilian, A&A 282, 867 (1994) H.A. Kobulnicky, M.J. Lundquist, A. Bhattacharjee, C.R. Kerton, AJ 143, 71 (2012) R.P. Kudritzki, in Liege International Astrophysical Colloquia, Volume 22, Liege International Astrophysical Colloquia, ed. by A. Boury, N. Grevesse, L. Remy-Battiau (1979), pp. 295–318 R. Kurucz, ATLAS9 stellar atmosphere programs and 2 km/s grid, in Kurucz CD-ROM No. 13. (Cambridge, 1993) T. Lanz, I. Hubeny, ApJS 169, 83 (2007) M. Mayor, F. Pepe, D. Queloz et al., Messenger 114, 20 (2003) A.F. McLeod, J.E. Dale, C.J. Evans et al., MNRAS 486, 5263 (2019) W.W. Morgan, P.C. Keenan, ARA&A 11, 29 (1973) M.F. Nieva, N. Przybilla, A&A 467, 295 (2007) E.C. Pickering, Ann. Harv. College Obs. 27, 1 (1890) J. Puls, J.S. Vink, F. Najarro, A&A Rev. 16, 209 (2008) A. Rainot, M. Reggiani, H. Sana, J. Bodensteiner, in prep (2021) A. Rainot, M. Reggiani, H. Sana et al., A&A 640, A15 (2020) G. Raskin, H. Van Winckel, H. Hensberge et al., A&A 526, A69 (2011) N. Rudolf, H.M. Günther, P.C. Schneider, J.H.M.M. Schmitt, A&A 585, A113 (2016) H. Sana, A. de Koter, S.E. de Mink et al., A&A 550, A107 (2013) A. Secchi, Comptes Rendus des Séances de l’Académie des Sciences 63, 364 (1866) S. Simón-Díaz, M. Godart, N. Castro et al., A&A 597, A22 (2017) S. Simón-Díaz, A. Herrero, K. Uytterhoeven et al., ApJ 720, L174 (2010) A. Smette, H. Sana, S. Noll et al., A&A 576, A77 (2015) P.B. Stetson, PASP 99, 191 (1987) A. Tkachenko, A&A 581, A129 (2015) V. Tsymbal, in Astronomical Society of the Pacific Conference Series, Volume 108, M.A.S.S., Model Atmospheres and Spectrum Synthesis, ed. by S.J. Adelman, F. Kupka, W.W. Weiss (1996), p. 198 N.R. Walborn, ApJS 23, 257 (1971) N.R. Walborn, AJ 77, 312 (1972) N.R. Walborn, ApJ 180, L35 (1973) N.R. Walborn, ApJ 215, 53 (1977) N.R. Walborn, ApJS 44, 535 (1980) N.R. Walborn, AJ 87, 1300 (1982) N.R. Walborn, E.L. Fitzpatrick, PASP 102, 379 (1990) N.R. Walborn, E.L. Fitzpatrick, PASP 112, 50 (2000) P. Zeidler, E. Sabbi, A. Nota et al., AJ 156, 211 (2018) S. Zucker, MNRAS 342, 1291 (2003)

Chapter 3

On the Apparent Lack of Massive Be Stars with Main-Sequence Companions

3.1 Introductory Remarks As described in Sect. 1.5, the Be phenomenon is observed in roughly 20% of lateO and B-type stars in our Galaxy. It is now established that the formation of the circumstellar decretion disk, which leads to the characteristic emission lines giving Be stars their name (the ‘e’ in ‘Be’ stands for emission), is linked to the rapid rotation of the star. However, the origin of this rapid rotation still remains an open question. Three different mechanisms have been proposed to explain their rotational spin-up, which may all be at work in nature. Understanding the relative importance of the three channels and quantifying their occurrence rates is therefore crucial to establish a better understanding of angular momentum transport of massive stars, their rotational properties, and the Be phenomenon as a whole. In this chapter, we discuss the literature search presented in Bodensteiner et al. (2020b), which investigates if there is a lack of MS companions to early-type Be stars. In Sect. 3.2 we discuss why a lack of Be+MS companions would be expected according to the binary channel proposed for the formation of Be stars. Section 3.3 describes the sample selection and the procedure that was followed during the literature study. In Sect. 3.4 we describe the binary properties that were reported. In Sect. 3.5 we discuss possible detection biases which may have impacted the number of reported binary systems, and discuss the main findings and their implications in Sect. 3.6.

3.2 The Origin of the Rapid Rotation of Be Stars While it remains unclear how close to the critical velocity Be stars are rotating (cf. Yudin 2001; Zorec et al. 2016), rapid rotating seems to be a prerequisite for the Be phenomenon to occur. The cause of this rapid rotation, however, remains poorly

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Bodensteiner, Observational Imprints of Binary Evolution on B- and Be-star Populations, Springer Theses, https://doi.org/10.1007/978-3-031-19489-4_3

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understood. In Sect. 1.5 we have discussed the three main theoretical channels that were proposed to explain the rotation rates of classical Be stars: 1. they could be born as rapid rotators (cf., Bodenheimer 1995), 2. they could spin-up towards the end of their MS evolution as single stars (cf., Ekström et al. 2008), or 3. they could have gained angular momentum in previous binary interactions (see e.g., Pols et al. 1991). We have also presented several observational studies testing the different proposed channels and trying to quantify their relative contributions. We have shown several indications implying that at least a part of the massive Be star population are mass gainers in previous binary interactions (cf., Casares et al. 2014; Schootemeijer et al. 2018; Klement et al. 2019; Wang et al. 2021; Hastings et al. 2021), and that the single-star channel alone cannot explain the large number of observed classical Be stars (e.g., Hastings et al. 2020). The relative importance of all the channels, and whether they are all at play in nature, remains unclear. A different, new approach testing whether classical Be stars gained their rapid rotation in previous binary interactions was proposed by Bodensteiner et al. (2020b): if Be stars are indeed BiPs that were spun up by mass and angular momentum transferred from a companion in a close binary system, then there should not be any Be stars with close MS companions. Instead, depending on the evolutionary status of the system, Be stars should have stripped star or compact object companions, or should be runaway stars if the companion exploded as a supernova that disrupted the system. It is important to note that Bodensteiner et al. (2020b) defined close binary systems as systems with a current orbital period P  5 000 d, which should exclude wide binary systems that do not interact in the course of their evolution. Possible Be + MS binaries on longer periods are therefore not relevant in this context. In contrast, if Be stars would be normal B-type stars that gained their rapid rotation as single stars, due to internal angular momentum transfer towards the end of their MS evolution, their multiplicity statistics would be similar the ones of normal B-type stars. Large-scale spectroscopic studies of B-type stars have shown that they are predominantly found in B + MS binary systems (see e.g., Kobulnicky et al. 2014; Dunstall et al. 2015; Banyard et al. 2022), with a period distribution that is approximately flat in log P. The detection of many B+MS systems is at least partly due to the fact that those systems are, in general, the easiest to spot observationally. Additionally, these studies targeted very young stellar populations which should sample the initial multiplicities as most binaries did not have time to interact yet (see also Chapter 5). Unfortunately, homogeneous multi-epoch spectroscopy of a large, unbiased sample of classical Be stars, which would be necessary to directly investigate their multiplicity properties, is currently not available. Hence, Bodensteiner et al. (2020b) resorted to a literature study to test the prediction emerging from the Be binary hypothesis that there should be a clear lack of close Be + MS binaries. They further argued that the report of one counter example of a close Be + MS binary would

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immediately prove that the other formation mechanisms of classical Be stars can in principle work.

3.3 A Literature Search for Be Stars with MS Companions The input sample of 505 stars was selected from the BeSS database (Neiner et al. 2011), a comprehensive catalogue of classical Be stars that is continuously updated. All stars in the sample are Galactic Be stars. In addition to a magnitude cut at V < 12 mag, a spectral-type cut including only stars of spectral type B1.5 and earlier was introduced. This ensures a focus on massive stars with Mini  8 M , as the spectral type B1.5 corresponds roughly to a current stellar mass of 13M . In the binary context, this cut also ensures that the putative primary, which evolved already and transferred mass to the present-day Be star, was a massive star at the beginning of its evolution. The sample was first cleaned from stars that are emission-line objects but no classical Be stars, and stars that are reported with an uncertain or later spectral type in the literature, leaving 287 early-type classical Be stars in the sample. For each star in the final sample, a detailed literature study of the publication history was performed to search for any indications of binarity. Possible indications include whether the star shows RV variations, photometric variability (such as ellipsoidal variations or eclipses), is a known X-ray source, a runaway star, or was detected to have a companion. This could be a MS star, a stripped companion, or a compact object (such as a NS or a BH).

3.4 The Reported Multiplicity Statistics of Early-Type Be Stars Bodensteiner et al. (2020b) used all available literature to divide the final sample (containing 287 early-type Be stars) in four classes: (i) binaries with a confirmed post-MS companion: this class consists of Be binaries in which the companion is confirmed to be a post-MS object, for example a stripped sdO/B star, a NS or a BH. Examples of objects in this group are the BeXRB V831 (a Be+NS star system, Liu et al. 2000), or the Be+sdO binary FY CMa (Peters et al. 2008). (ii) suspected binaries with unknown, uncertain, or debated companions: this class combines all objects that were reported to show any indication of a companion, but where the nature of the companion could not be clarified with the existing data. One example in this group is δ Sco, a classical Be star of spectral type B0.2 IV (Chini et al. 2012), which was reported to have a companion on a highly eccentric orbit (see e.g., Miroshnichenko et al. 2001; Tango et al. 2009;

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Fig. 3.1 Distribution of the sample of Bodensteiner et al. (2020b) over the sky. The gray dots mark stars in the input sample while the 287 stars in the final sample are shown in color according to the class they were attributed to. Green circles mark class i, which are binary systems with known post-MS companions (13 stars), pink stars indicate class ii systems with unknown, uncertain, or debated companions (11 stars), and blue triangles show the presumably single stars of class iii (263 stars). No star was assigned to class iv. This figure was originally published by Bodensteiner et al. (2020b), their Fig. 1. Reproduced with permission from ©ESO

Meilland et al. 2011). The nature of this companion is highly debated and therefore remains uncertain. (iii) Be stars with confirmed MS companions: this class consists of Be stars with confirmed MS companions. Bodensteiner et al. (2020b) did not find any report of such a system in the literature, and therefore this class currently remains empty. Given the large fraction of normal B-type stars in binary systems with MS companions, however, this class would be expected to contain most of the sample, if Be stars were not BiPs. (iv) presumably single stars: this class includes all stars for which no indication of the presence of a possible close companion was reported in the literature. Stars in this class are either truly single stars, or binary systems in which the companion has not been detected so far. Given that a large part of the sample was not studied in detail yet, for example by multi-epoch spectroscopy, it is likely that this class contains many undetected binary systems. The spatial distribution of the input and final sample of stars on the sky is shown in Fig. 3.1, where these four classes are also indicated. As Fig. 3.2 shows, most earlytype Be stars were found to be presumably single (class iv), namely 263 objects, based on the available literature. While 13 Be stars are reported to have a post-MS companion (class i), additional 11 Be stars are binaries with uncertain, unknown or debated companions (class ii). Importantly, there is no clear and unambiguous report of a Be+MS binary (class iii).

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Fig. 3.2 Distribution of V-band magnitudes of the 287 stars in the final sample of Bodensteiner et al. (2020b, using the same color coding as Fig. 3.1). The reported binary statistics of the final sample are given in the top-left inset: a majority of the sample stars (263 stars) are presumably single (class iv), while roughly 4.5% are in binary systems with a confirmed non-MS companion (class i, 13 stars). 3.8% of the sample are suspected binaries where the nature of the companion is unknown, uncertain or debated (class ii, 11 stars). The latter class is subdivided by detection method: spectroscopic detections are shown without a hatch while the ones detected by other methods are hatched. Class iii, that is Be stars with MS companions, remains empty. This figure is adapted from Figs. 2 and 3 originally published by Bodensteiner et al. (2020b). Reproduced with permission from ©ESO

A difficulty in assessing the multiplicity properties of a large sample of stars from a literature study is the inhomogeneity of the underlying literature that is available for each of the stars. Some stars have been studied for several years, with different techniques and by multiple authors, and possibly even with a focus on the detection of a putative binary companion. One such example is the prototypical Be star γ Cas, which has been classified as Be star already in the 19th century and has been systematically studied with different observing techniques since then (e.g., Secchi 1866; Haberl 1995; Postnov et al. 2017; Harmanec et al. 2000; Borre et al. 2020). Other stars are barely mentioned in the literature and only their spectral types, sometimes based on photometric plates, are available. While it is thus difficult to quantitatively assess multiplicity statistics, a general picture of the multiplicity properties of the entire sample of stars can be established.

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The clear lack of reports of any Be star with a MS companion, compared to the high fraction of B-type stars in binary systems with MS companions, indicates that the underlying multiplicity properties are fundamentally different. If Be stars were merely rapidly rotating B-type stars without a particular binary history, they should have similar multiplicity properties than normal B-type stars. However, interpreting them as binary interaction products not only explains the reported lack of MS companions, but also accounts for all Be stars with stripped-star of compact-object companions that were categorized in class i.

3.5 Possible Detection Biases in the Search for Be+MS Binaries Before concluding that Be stars are predominantly the products of binary interactions, it is important to investigate if the observed lack of Be stars with MS companions could not be explained by detection biases. Those include observational biases as well as other, intrinsic aspects that effectively reduce the number of observed Be+MS binaries, which will be discussed in the following. In principle, to convert an observed binary fraction to the intrinsic binary fraction of a sample of stars, a correction for observational biases has to be performed. For example, in the context of a spectroscopic survey, the bias correction takes into account the cadence and time span of the observations, the S/N ratio of the spectra, and the achieved RV accuracy. Assuming parent distributions of the orbital parameters allows then to estimate the fraction of binary systems, which would have been missed with the given observational setup (see e.g., Sana et al. 2012; Banyard et al. 2022; Bodensteiner et al. 2021, and Chap. 5). This, however, requires a homogeneous and well-known observational setup, which is not given in the case of a literature study. Bodensteiner et al. (2020b) therefore tried to conservatively estimate the detection biases of the literature study as an order-of-magnitude estimate, which is complicated by the inhomogeneity of the different techniques used, and the varying depth of the studies. In principle, this estimate assumes that Be stars follow similar multiplicity properties as normal B-type stars, and assesses how many such systems should have been detected, despite the detection biases discussed in the following. Firstly, the observed number of Be+MS binaries might be reduced due to two effects intrinsic to the nature of such systems. On the one hand, close companions can have a profound impact on the disk of a Be star, either by truncating or fully destroying it. This would lead to a reduction or complete disappearance of the emission line forming in the disk, which is the main characteristic in the classification of Be stars (Klement et al. 2019). On the other hand, tidal braking might be at play, which is caused by a synchronization of the orbital and rotational velocities in the tightest binary systems (Zahn 1977). A sufficient spin down of the Be component might prevent a decretion disk from forming. Both effects described here would effectively

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reduce the timescale a Be+MS binary would appear as such, and therefore reduce their observed numbers. Secondly, in order to evaluate how many Be+MS binaries might have been missed in the literature, it is important to estimate the number of stars that were studied in detail with spectroscopic observations. Given that most binary systems are detected due to RV variations (only very few are detected because their spectra show an SB2 signature), Bodensteiner et al. (2020b) used the number of stars that have multiepoch spectroscopy in the BeSS archive as a proxy for how well they were studied (stars with more than 10 spectra available were considered as well-studied). They found that only few stars were observed multiple times but noted that usually only detections are published while more RV-stable apparently single Be star might have been established but not mentioned in the literature. Furthermore, while this estimate focuses on spectroscopic detections, binary Be stars can also be detected by other methods such as interferometric observations (Tango et al. 2009; Meilland et al. 2011). Lastly, whether a binary system is actually detected as such in multi-epoch spectroscopic observations depends on many different aspects. On the one hand, it depends on the observational setup such as the time coverage and cadence, the S/N ratio of the data, and the achievable RV accuracy. Bodensteiner et al. (2020b) estimated that, depending on the data quality, standard surveys could detect binaries as such if their RV amplitudes exceed 24 km s−1 or 12 km s−1 , assuming low-quality and moderate-quality data, respectively. On the other hand, whether a system is detected as binary system or not, also depends on intrinsic parameters of the system such as the light ratio (which defines the contribution of each of the components to the observed spectrum), the mass ratio (which directly translates to the observable RV amplitudes), the system’s eccentricity and the inclination. Figure 3.3 summarizes all of the above discussed bias consideration and provides a tool to asses how many Be+MS binaries would have been detected in the literature if Be stars had similar intrinsic binary properties as B-type stars. It shows the simulated RV amplitude of a 15 M Be star as a function of the orbital period of the system and the mass of the companion (considering mass ratios between 0.3 and 1), assuming a fixed eccentricity of 0.5 and an inclination angle of i = 60◦ . Below a period of 10 days, no Be binaries are expected to exist because of disk truncation and tidal breaking. Systems with periods longer than 5000 days are wide enough that binary interactions do not play a significant role. The RV amplitude sensitivity limits of standard surveys with low or moderate data quality are also indicated. Figure 3.3 shows that even with low-quality data, a majority of the Be binaries that were wellstudied would have been detected as such. In order to further ensure that the reported lack of detected Be+MS systems is not based on the fact that the brightest stars were the ones that are best studied, Fig. 3.4 shows a division of the entire input sample in magnitude bins. It shows that the lack of reported Be+MS systems is significant, independent of the magnitude cut applied. It further investigates the statistical likelihood of observing a certain number of binary candidates (which correspond to stars in class ii among the intrinsic number of detectable Be binaries), computed assuming that Be and B stars follow similar

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Fig. 3.3 RV semi-amplitude K Be of a simulated 15 M Be star in a binary system (with an inclination i = 60◦ and an eccentricity e = 0.5) as a function of the orbital period and secondary mass. Be binaries are only expected to exist with P > 10 days corresponding to the limit for tidal disk disruption (left red line). Furthermore, systems with periods larger than 5000 days are not relevant as they are too wide to interact (right red line). The grey contours correspond to the estimated RV amplitudes standard spectroscopic surveys would be sensitive to. This figure was originally published by Bodensteiner et al. (2020b), their Fig. 5. Reproduced with permission from ©ESO

multiplicity statistics. This likelihood is always close to zero (with the exception of the first magnitude bin, which suffers from low number statistics). Combining all of these estimates, Bodensteiner et al. (2020b) concluded that roughly 6% (that is more than 15 stars) of the 287 Be stars included in the literature search should have been detected as binary systems, if Be stars followed similar multiplicity statistics as B-type stars. The literature study, however, only revealed a handful of systems with unknown or debated companions (most of which have mass ratios outside of the range considered in the bias estimation). As the probability of detecting so few binaries among the larger predicted population by chance is negligible, the authors concluded that the reported lack of Be+MS binaries cannot be explained by detection biases. This indicates that B and Be stars do not follow the same intrinsic multiplicity properties.

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Fig. 3.4 Top panel: fractions (and their associated binomial errors) of stars classified in class i (green), class ii (pink), and class iv (blue) as a function of stellar magnitude. The black line shows the fraction of stars which are considered well-studied (i.e., more than 10 spectra are available in the BeSS database). Middle panel: Comparison of the observed fraction of Be+MS candidates (a subset of the objects in class ii, blue) with the expected fraction of Be+MS systems assuming similar binary statistics as for B-type stars (red). The yellow curve shows the corresponding binomial likelihood that the difference between the observed and expected fractions is a chance coincidence. Bottom panel: number of Be+MS systems that would be expected but have not been observed as a function of the magnitude cut. This figure was originally published by Bodensteiner et al. (2020b), their Fig. 6. Reproduced with permission from ©ESO

3.6 Be Stars as Binary Interaction Products The study performed by Bodensteiner et al. (2020b) investigated the reported binary properties of early-type classical Be stars based on a literature search. It showed that no Be+MS binaries were reported in the literature, while there is a handful of Be binaries with stripped, evolved or compact companions, or companions whose

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nature remains unclear or debated. This is in strong contrast to the observed binary properties of normal B-type stars, which are predominantly found in Be+MS systems. This discrepancy shows that the intrinsic multiplicity properties of early-type Be stars are fundamentally different from normal B-type stars, which implies that the two groups of stars have a different evolutionary history. The lack of reported Be+MS binaries, combined with the known Be binaries with stripped or compact companions (which are typically much harder to detect observationally), strongly argues that Be stars gained their rapid rotation due to previous interactions with a binary companion. This finding is in line with previous works investigating the possible binary origin of classical Be stars from different angles (discussed in more detail in Sect. 1.5, and see e.g., Boubert & Evans 2018; Klement et al. 2019; Wang et al. 2021; Bodensteiner et al. 2021). It has two major implications: firstly, classical Be stars are ideal laboratories to investigate the physics of binary interactions, such as the stability and conservativeness of mass transfer. Secondly, if classical Be stars are indeed the mass gainers in previous binary interactions, they are the ideal place to look for exotic companions such as stripped stars and compact objects (if the system was not disrupted in a supernova event). Future large-scale homogeneous multi-epoch spectroscopic surveys are required to directly measure the binary fraction of classical Be stars and to establish the nature of their binary companions. The lack of reported Be+MS companions has another interesting implication: while the single-star channel explaining the rapid rotation of classical Be stars has been theoretically predicted, an observational confirmation in the massive star regime is still missing. On the other hand, the detection of Be stars in post-interaction binary systems gives a direct observational confirmation that the binary channel is viable in nature. Prime example for such post-interaction systems are, on the one hand, BeXRBs (see e.g., Reig 2011) as well as post-mass-transfer systems with stripped companions like HR 6819 and LB-1 (see Chap. 4 for more details). The above described study focused on early-type Be stars. This restriction was introduced to ensure that any putative previous companion was initially also a massive star. It remains unclear whether the derived findings also hold for lower-mass Be stars. While the initial fraction of binary systems decreases with stellar mass, there is no reason to assume that there is a different origin of the rapid rotation in lower-mass Be stars. However, in the lower-mass regime, one system was proposed in which the Be star was interpreted to have formed according to the single-star channel. This is the triple system ν Gem (Klement et al. 2021), which was proposed to consist of an inner B+B binary and an outer, unrelated classical Be star. The three stars (the two inner B-type stars as well as the Be star) were estimated to have a similar mass of ∼3 M . Unless the system was initially a hierarchical quadruple system, and without invoking any more complicated evolutionary pathways, the classical Be star most likely gained its rapid rotation as a single star. Another system that was proposed to be a hierarchical triple with an outer, unrelated Be star is HR 6819 (Rivinius et al. 2020). Rather than consisting of an inner B+B binary like ν Gem, the inner binary in HR 6819 was proposed to be comprised of a B-type star and a stellar-mass BH. Given the proximity of the system to the Earth,

References

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it was in fact proposed to host the closest BH to Earth. In Chap. 4 we will discuss an alternative interpretation for HR 6819 and show how new observations could settle the debate around the nature of this system (Rivinius et al. 2020; Bodensteiner et al. 2020a; El-Badry and Quataert 2021; Frost et al. 2022).

References G. Banyard, H. Sana, L. Mahy et al., A&A 658, A69 (2022) P. Bodenheimer, ARA&A 33, 199 (1995) J. Bodensteiner, H. Sana, C. Wang et al., A&A 652, A70 (2021) J. Bodensteiner, T. Shenar, L. Mahy et al., A&A 641, A43 (2020a) J. Bodensteiner, T. Shenar, H. Sana, A&A 641, A42 (2020b) C.C. Borre, D. Baade, A. Pigulski et al., A&A 635, A140 (2020) D. Boubert, N.W. Evans, MNRAS 477, 5261 (2018) J. Casares, I. Negueruela, M. Ribó et al., Nature 505, 378 (2014) R. Chini, V.H. Hoffmeister, A. Nasseri, O. Stahl, H. Zinnecker, MNRAS 424, 1925 (2012) P.R. Dunstall, P.L. Dufton, H. Sana et al., A&A 580, A93 (2015) S. Ekström, G. Meynet, A. Maeder, F. Barblan, A&A 478, 467 (2008) K. El-Badry, E. Quataert, MNRAS 502, 3436 (2021) A.J. Frost, J. Bodensteiner, T. Rivinius et al., A&A 659, L3 (2022) F. Haberl, A&A 296, 685 (1995) P. Harmanec, P. Habuda, S. Štefl et al., A&A 364, L85 (2000) B. Hastings, N. Langer, C. Wang, A. Schootemeijer, A.P. Milone, A&A 653, A144 (2021) B. Hastings, C. Wang, N. Langer, A&A 633, A165 (2020) R. Klement, A.C. Carciofi, T. Rivinius et al., ApJ 885, 147 (2019) R. Klement, P. Hadrava, T. Rivinius et al., ApJ 916, 24 (2021) H.A. Kobulnicky, D.C. Kiminki, M.J. Lundquist et al., ApJS 213, 34 (2014) Q.Z. Liu, J. van Paradijs, E.P.J. van den Heuvel, A&AS 147, 25 (2000) A. Meilland, O. Delaa, P. Stee et al., A&A 532, A80 (2011) A.S. Miroshnichenko, J. Fabregat, K.S. Bjorkman et al., A&A 377, 485 (2001) C. Neiner, B. de Batz, F. Cochard et al., AJ 142, 149 (2011) G.J. Peters, D.R. Gies, E.D. Grundstrom, M.V. McSwain, ApJ 686, 1280 (2008) O.R. Pols, J. Cote, L.B.F.M. Waters, J. Heise, A&A 241, 419 (1991) K. Postnov, L. Oskinova, J.M. Torrejón, MNRAS 465, L119 (2017) P. Reig, Ap&SS 332, 1 (2011) T. Rivinius, D. Baade, P. Hadrava, M. Heida, R. Klement, A&A 637, L3 (2020) H. Sana, S.E. de Mink, A. de Koter et al., Science 337, 444 (2012) A. Schootemeijer, Y. Götberg, S.E. de Mink, D. Gies, E. Zapartas, A&A 615, A30 (2018) A. Secchi, Astron. Nachrichten 68, 63 (1866) W.J. Tango, J. Davis, A.P. Jacob et al., MNRAS 396, 842 (2009) L. Wang, D.R. Gies, G.J. Peters et al., AJ 161, 248 (2021) R.V. Yudin, A&A 368, 912 (2001) J.P. Zahn, A&A 500, 121 (1977) J. Zorec, Y. Frémat, A. Domiciano de Souza et al., A&A 595, A132 (2016)

Chapter 4

The Post-interaction Be + Stripped Star Binary HR 6819

4.1 Introductory Remarks In this chapter, we will discuss the enigmatic galactic binary or multiple system HR 6819. Recently, different interpretations were brought forward to explain the observational characteristics of the system: It was first proposed to be a triple system, hosting the closest BH ever observed with respect to the Earth in the inner binary, and an outer Be star as triple companion (Rivinius et al. 2020). Subsequently, it was interpreted as a binary system consisting of a stripped mass-donor star and a mass gainer that observationally appears as a classical Be star (Bodensteiner et al. 2020; El-Badry and Quataert 2021). In the following chapter, we will first discuss the importance of systems like HR 6819 in the wider context of Be star formation and BH detection in Sect. 4.2. In Sect. 4.3, we describe the interpretation of the system by Rivinius et al. (2020), and explain in Sect. 4.4 how the re-analysis of the same dataset lead to a fully different interpretation of the system. We further demonstrate how new high-spatial resolution observations settled the debate about the nature of HR 6819 in Sect. 4.5. Finally, we describe a possible evolutionary history of the system in Sect. 4.6 and discuss HR 6819 and its implication for the formation of classical Be stars in Sect. 4.7.

4.2 The Importance of Individual Systems Like HR 6819 4.2.1 In the Context of Be Star Formation As discussed in Chaps. 1 and 3, the origin of the rapid rotation of classical Be stars remains unclear. Two main competing channels were proposed in the literature that are predicted to effectively produce large numbers of classical Be stars: firstly, that Be stars are either spun up as single stars, due to efficient internal angular momentum © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Bodensteiner, Observational Imprints of Binary Evolution on B- and Be-star Populations, Springer Theses, https://doi.org/10.1007/978-3-031-19489-4_4

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transport at the end of their MS evolution, and secondly, that Be stars are mass gainers in previous binary interactions. The importance and the relative occurrence rates of these channels, however, remain unclear, and observations of systems like HR 6819 can aid in further constraining them. In the context of the binary channel, several different pieces of observational evidence indicate that it is indeed at play in nature. First and foremost, the observation that a majority of massive stars live their lives in (interacting) binary systems (e.g., Sana et al. 2012; Kobulnicky et al. 2014; Banyard et al. 2022) indicates that there should be many stars, which were spun up by these binary interactions (de Mink et al. 2013, 2014). Another observational evidence is the detection of evolved Be binaries such as Be+sdO binaries (such as φ Per, see e.g., Schootemeijer et al. 2018) and BeXRBs (cf. Reig 2011). Additionally, faint Be stars were observed far from the MS turnoff of star clusters, which are not at the end of their MS evolution (Hastings et al. 2021; Bodensteiner et al. 2021). Concerning the single-star channel, a clear and unambiguous observational evidence that the single-star channel can work in nature is still lacking, in particular for massive Be stars. One possible low-mass counter-example was mentioned in Chap. 3, namely ν Gem, which was reported to host a low-mass Be star that formed according to the single star channel. Furthermore, based on theoretical considerations, Hastings et al. (2021) investigated the maximum fraction of Be stars that can form through the binary channel. They found that very distinct assumptions on the input binary physics are required in order to reproduce the fraction of Be stars in star clusters, which might be unlikely. In general, on a system-to-system basis, it is difficult (if not impossible) to observationally prove that a Be star formed according to the single-star channel. While one indication might be the presence of a MS companion (see Chap. 3), more exotic evolutionary scenarios involving triples or higher-order multiple systems could always be invoked and are difficult to disprove. This is further enhanced by the ambiguous observational appearances of BiPs, which might be hiding in single-star populations (see Sect. 1.4). One of the most promising types of systems to prove the viability of the single-star channel are nevertheless triple systems like ν Gem, which host an outer Be star that is far enough from the inner binary to not have been impacted by it.

4.2.2 In the Context of the Search for Quiescent Black Holes HR 6819 was initially reported to host a quiescent BH, that is a BH that does not interact with its companion star and is therefore not detectable due to copious X-ray emission as in HMXBs (see e.g., Liu et al. 2006). Such systems have recently gotten more and more in the spotlight as they represent an intermediate evolutionary phase in the formation of double-BH binaries (e.g., Belczynski et al. 2002; Marchant et al. 2016), which might eventually merge and emit gravitational waves, now detectable by LIGO/VIRGO/KAGRA (cf., Abbott et al. 2019, 2021). Population synthesis com-

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putations further predict that a large fraction of massive stars are in binary systems with a quiescent BH (Shao and Li 2019; Yi et al. 2019; Langer et al. 2020). Yet, not many such system have been found so far. Recently, two O+BH systems were proposed, namely VFTS 243 in the LMC (Shenar et al. 2022), and HD 130298 in the Milky Way (Mahy et al. 2022). Further quiescent-BH-candidates include, for example, the candidate B[e]+BH binary system AS 386 (Khokhlov et al. 2018), and the putative triple system HD 96670 proposed to contain a 7 M BH (Gomez and Grindlay 2021). One of the most prominent examples, that is the proposed quiescent Be+BH system MWC 656 (Casares et al. 2014), was recently challenged by Rivinius et al. (2022). Additional systems, which were initially proposed to host a quiescent BH, but were subsequently challenged, include NGC 1850 BH1 (Saracino et al. 2022, but see also El-Badry and Burdge 2022), NGC 2004 #115 (Lennon et al. 2022, but see El-Badry et al. 2022a), and the so-called ‘Unicorn’ and ‘Giraffe’ systems (Jayasinghe et al. 2021, 2022, but see El-Badry et al. 2022b). For a current, more complete overview over proposed quiescent BH candidate systems, we refer the reader to Bodensteiner et al. (2022). The probably most famous system in this context, however, is LB-1, which was initially proposed to host a ∼70 M quiescent BH in orbit with a B-type companion (Liu et al. 2019). This, on the one hand, triggered theoretical studies to explore new ways to explain the formation of such a massive BH from binary evolution theory (Belczynski et al. 2020). On the other hand, it stimulated several follow-up studies that scrutinized the initial observational analysis and proposed the adjustments of several observational findings, for example reducing the mass of the unseen companion (Abdul-Masih et al. 2020; El-Badry and Quataert 2020; Irrgang et al. 2020; SimónDíaz et al. 2020; Liu et al. 2020). Based on spectral disentangling, Shenar et al. (2020) proposed that the system actually consists of two luminous stars, a stripped Be star and rapidly rotating B-type star, a classical Be star, interpreting the system as a post-interaction binary. In the following, we focus on HR 6819, which was initially proposed to be a triple system hosting a black hole, but later interpreted as post-interaction binary with a similar configuration as LB-1. The two possible interpretations, which will be discussed in more detail in the two subsequent sections, are schematically depicted in Fig. 4.1.

4.3 HR 6819 as Triple System Hosting a Black Hole HR 6819 has been subject of observational studies already for more than 50 years. It was reported to be a variable star (Buscombe and Morris 1960), and Hiltner et al. (1969) detected two components in the optical spectrum of the star, a narrow-lined and a broad-lined one. Dachs et al. (1981) further classified HR 6819 as emissionline star with a spectral type B3 IIIep (which was confirmed by Slettebak 1982), but withdrew their finding of a composite nature of the spectrum later (Dachs et al. 1986). Maintz (2003) proposed that HR 6819 might be a binary system consist of a B and a

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Fig. 4.1 Schematical depiction of the two scenarios proposed for HR 6819. The left panel shows the configuration according to the binary scenario while the right panel shows the triple configuration. The schematics are not to scale, but approximate expected distances between the components, given the GAIA distance to HR 6819 (Bailer-Jones et al. 2018), are indicated

Be component that orbit around each other every ∼30 − 60 days. No observational signature was detected in the UV that might indicate the presence of a hot compact companion such as a subdwarf star (Wang et al. 2018). Two sets of optical spectra of HR 6819 were obtained with FEROS, one in 1999 while it was mounted at the ESO 1.52-m telescope in La Silla, Chile, and one in 2004 after it was moved to the 2.2-m MPG/ESO telescope (also in La Silla). The first data set is comprised of 12 spectra while 51 additional spectra were taken during the second observing period. FEROS spectra cover the entire optical wavelength range, from 3500 to 9200 Å with a resolving power of 48 000. The calibration and data reduction was described in detail in Rivinius et al. (2020). Figure 4.2 shows the 51 spectra obtained in 2004, in a narrow window centered around the Hα-line. It illustrates that two components contribute to the composite spectra of HR 6819 (as previously mentioned by Hiltner et al. 1969), a seemingly stationary Hα-emitting component (which also shows broad absorption lines in different parts of the spectrum), and a narrow-lined RV-variable component manifesting itself in the C ii doublet around λ 6580Å. Rivinius et al. (2020) interpreted the two visible components as a normal, giant Btype star (of spectral type B3 III, similarly to Slettebak 1982), and a rapidly rotating B-type star with emission lines, that is a classical Be star. Based on spectral disentangling of prominent He lines, they found that the B-type giant moves on a 40-day orbit, while the Be star is stationary. They therefore deduced that the Be star is an unrelated, distant tertiary star with an orbital period larger than the time spanned by the observing campaign, that is of the order of ten years. Interpreting the Be star not to be a member of the inner binary system implies that the B-type star must orbit around another, yet unseen object. Combining the binary mass function, which was found to be ( f M = 0.96 M ) with the mass of the B3 III star, estimated to be M ≥ 5 M based on the derived spectral type, Rivinius et al. (2020) inferred that the mass of the unseen binary companion must be > 4 M .

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Fig. 4.2 FEROS spectroscopy of HR 6819, originally presented by Rivinius et al. (2020). Each line corresponds to one of the 51 spectra obtained during the second observing period, which are all normalized and shifted arbitrarily in flux for clarity. They are centered around the Hα-line, which is dominated by the broad-lined component, but also include two carbon lines originating from the narrow-lined component (see text)

Given that there is no signature of a third, luminous star in the spectra, and that this mass estimate exceeds the maximum mass of a NS, Rivinius et al. (2020) concluded that the unseen object must be a BH. Based on the analysis of multi-epoch spectroscopic data presented by Rivinius et al. (2020), HR 6819 could thus be a hierarchical triple, consisting of an inner B+BH binary on a 40-d orbit, and an outer classical Be star with an orbital period of the order of ten years or longer. This configuration is depicted in the right panel of Fig. 4.1. Furthermore, Rivinius et al. (2020) proposed that the before mentioned LB-1 system has a similar configuration. According to this interpretation, HR 6819 and LB-1 are interesting because of two aspects: firstly, because they are proposed to host a quiescent stellar-mass BH. In particular, the proximity and brightness of HR 6819 would thus imply that there should be many more such BH systems out there. Sec-

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ondly, the presence of the unrelated outer Be star was interpreted as a direct evidence that Be stars can form according to the single star channel. The findings of Rivinius et al. (2020) were, however, subsequently challenged from different angles. Safarzadeh et al. (2020) argued that the proposed triple configuration is highly unlikely for three reasons: first, the brightness of HR 6819 would imply that there should be many other similar systems with BHs, which is in contrast with the expected BH budget of the MW. Second, the current configuration of the system is only stable for a very narrow parameter space, and therefore unlikely. Third, the initial orbital parameters require fine-tuning in order to not have disrupted the system in the previous SN explosion of the BH. Yet another interpretation of the system was brought forward by Mazeh and Faigler (2020) who argued that even if the triple interpretation was correct, the unseen companion does not necessarily have to be a BH, but could also be a so-far undetected binary system formed by two A0 stars. This would make HR 6819 a quadruple system. Three different, independent teams further re-analyzed the optical spectra. Gies and Wang (2020) re-visited the Hα line and found that there is indeed a small reflex motion, expected if the B and the Be star form a binary system. Furthermore, they found spectral lines of the Be star varying on timescales of the period of the inner orbit, which they interpreted as yet another evidence of the Be star being part of the inner binary. Bodensteiner et al. (2020) and El-Badry and Quataert (2021) performed a very similar analysis, repeating the spectral disentangling by Rivinius et al. (2020), but using different spectral lines. They came to an alternative interpretation of the HR 6819-system, which will be explained in the subsequent section in detail. We here focus on the analysis by Bodensteiner et al. (2020) but note that the one carried out by El-Badry and Quataert (2021) is very similar in terms of the methods that were used and the results that were derived.

4.4 HR 6819 as Post-interaction Binary System In the following, we will refer to the narrow-lines star as primary, while we denote the rapidly-rotating component as secondary. It is important to note that the independent analysis of HR 6819 performed by Bodensteiner et al. (2020) was based on the same observational data set as used by Rivinius et al. (2020). We therefore refrain from explaining the observations again.

4.4.1 Spectral Variability and the Orbit of the System Bodensteiner et al. (2020) investigated if the multi-epoch spectra show any signs of spectral variability and reported on variability on different timescales, namely on timescales of days, weeks, and years which manifest themselves in different spectral lines of both the primary and the secondary star. On the one hand, the wings of

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Fig. 4.3 Best-fit orbit of the narrow-lined component in HR 6819. The top panel shows the phasefolded RVs of both data sets (from 1999 and 2004, blue crosses) and the best-fit orbit (blue line). The bottom panel shows the residuals of the fit. The derived orbital period is 40 days while the orbit is circular within the errors

several He i lines show variability on short timescales probably caused by non-radial gravity-mode pulsations, which are predicted in simulations (Aerts et al. 2009) and which are often observed in classical Be stars (e.g. Baade 1984; Rivinius et al. 2003). On the other hand, several metal lines, such as the Si ii doublet λλ 4128, 4131, which come from the primary component, also show variability. This might imply that the narrow-lined star is also pulsating. This is in agreement with the photometric analysis of SMEI and TESS lightcurves performed by Rivinius et al. (2020), which also indicates the presence of non-radial pulsations. Additionally, the Hα line of HR 6819 shows long-term variability on timescales of years which is most likely due to changes in the circumstellar disk, a common phenomenon in classical Be stars (Lacy 1977; Rivinius et al. 2013). The re-derived orbit of the narrow-lined primary, based on RVs measured by Gaussian fits to several spectral lines in both spectroscopic data sets, is shown in Fig. 4.3. The derived orbital parameters agree well with the ones reported in Rivinius et al. (2020), in particular the orbit is found to be circular within the errors. An overview of the orbital and stellar parameters derived by Bodensteiner et al. (2020) is given in Table 4.1.

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4.4.2 Spectral Disentangling The main difference in the analysis of Bodensteiner et al. (2020, and also El-Badry and Quataert 2021) with respect to the initial analysis by Rivinius et al. (2020) is the choice of lines used in the spectral disentangling. While Rivinius et al. (2020) used photoshperic absorption lines (mainly He i) for the disentangling, Bodensteiner et al. (2020) also utilized emission lines formed in the circumstellar disk (for example Fe ii and O i), and lines that are a combination of the both (i.e., the Balmer lines, though excluding Hα because of the aforementioned variability). The disentangling presented by Bodensteiner et al. (2020) is performed as griddisentangling, varying the RV semi-amplitude of the Be star, K 2 . It thus implicitly assumes that the Be star and the B star are bound on the 40-day orbit. If this is the case, a non-zero K 2 should be estimated by the grid disentangling. On the other hand, if the Be star and the B star are not bound on the 40 day orbit, the best-fitting K 2 provided by the grid disentangling should be zero. The disentangling performed by Bodensteiner et al. (2020) is based on the shiftand-add technique (see e.g., Marchenko et al. 1998; Shenar et al. 2018). It is illustrated in Fig. 4.4 for two epochs observed at quadrature, which demonstrates that, in general, the disentangling of the two components works well. Figure 4.5 further shows the results of the grid disentangling along the K 2 -axis, and provides a best-fitting K 2 value for the Be star. Overall, the grid disentangling shows that the RV semi-amplitude of the Be star is not zero: the weighted mean of the three approaches based on three sets of spectral lines is K 2 = 4.0 ± 0.8 km s−1 . This implies that the Be star and the B star are indeed bound on the same orbit. Apart from yielding a best-fit K 2 value, the grid disentangling also provides the disentangled spectra of the two components. Figure 4.5 further shows that the significance of the derived K 2 value strongly varies with the spectral lines that are used for the grid disentangling. While the sharp emission lines, both the metal lines and the Balmer lines, constrain K 2 fairly well, the broad photospheric He i lines are inconclusive and yield large error bars. In fact, the He i lines are consistent with K 2 = 0 km s−1 , that is a stationary Be star as was found by Rivinius et al. (2020). The difference in the two analyses therefore boils down to the spectral lines that were used for the disentangling. The spectral disentangling based on the emission lines indicated that the B and the Be star orbit around each other on a 40-d orbit (see the left panel of Fig. 4.1 for a schematic depiction of the binary). The derived RV semi-amplitudes of K 1 = 60.4 ± 1.0 km s−1 and K 2 = 4.0 ± 0.8 km s−1 can directly be translated into a mass ratio of 2 = 15 ± 3. This implies that the secondary star, the Be star, is approximately q= M M1 15 times heavier than the primary, the narrow-lined star.

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Fig. 4.4 Illustration of the shift-and-add disentangling. The three rows focus on different spectral lines, that is the He i λ4388 line (top), the Fe ii λ4584 line (middle), and the Hβ line (bottom). The two columns show spectra at quadrature, where the left column shoes φ = 0.25 and the right column shows φ = 0.75. Each panel illustrates the observed composite spectrum in black. It also indicates the disentangled spectra of the narrow-lined component in red and the spectra of the broad-line component in blue, shifted for appropriate RVs. The green line, which is a sum of the two disentangled spectra, demonstrates the fit quality between the individual observations. This figure was originally published by Bodensteiner et al. (2020), their Fig. 6. Reproduced with permission from ©ESO

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Fig. 4.5 Results of the shift-and-add disentangling. The three panels focus on the three different line groups that were used to constrain K 2 (as indicated in the top left corner of each panel). Each panel shows the reduced χ 2 (K 2 ) of the disentangling as a function of the input RV. The RV of the minimum in the χ 2 -distribution corresponds to the best-fitting K 2 measurement, while the 1σ confidence interval is indicated by the red line. This figure was originally published by Bodensteiner et al. (2020), their Fig. 5. Reproduced with permission from ©ESO

4.4.3 A Detailed Spectroscopic Analysis of HR 6819 Masses of stars are notoriously difficult to determine from observations. The aforementioned mass ratio of q = 15 ± 3 can thus be interpreted in two different ways. Either the B-type star is indeed a normal B3 III giant star with a mass that is typical for such a spectral type (M1 ∼ 5 M , see Rivinius et al. 2020). Then the Be star would have a mass of M2 ∼ 75 M , which is not compatible with the spectral appearance of the star in the optical. The other option is that the Be star is a normal Be star, that has a mass of roughly M2 = 7 M based on its spectral type of B2-B3 (Hohle et al. 2010). This would imply that the narrow-lined B-type primary star has a mass of only M1 ∼ 0.5 M . Figure 4.6 indeed shows differences between the disentangled spectrum of the narrow-lined primary and the spectrum of a typical B3 III giant, namely 18 Peg (Nieva and Przybilla 2014). In particular, the wings of the Balmer lines of 18 Peg are significantly wider than the ones of primary, indicating that the log g is higher in 18 Peg. Another difference can be seen in elements affected by the CNO cycle, mainly O ii and N ii. Especially the N lines are significantly deeper in the primary of HR 6819, implying that the surface abundances of the star are altered by the CNO cycle (assuming that 18 Peg is indeed a normal giant star with standard surface abundances). In contrast, the spectrum of the secondary closely resembles the spectra of other classical Be stars of similar spectral type (see Fig. 4.7), namely HD 45995 (with a spectral type B2Vne, Jaschek and Egret 1982) and HD 37657 (spectral type B3 Ve, Guetter 1968). Apart from a different strength of the emission lines, the spectra of the three stars qualitatively agree very well, implying that the secondary in HR 6819 is indeed a classical Be star of spectral type B2-B3Ve. A further, more detailed spectroscopic analysis by comparison to tlusty (Hubeny and Lanz 1995; Lanz and Hubeny 2007) and PoWR (Gräfener et al. 2002; Hamann

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Fig. 4.6 Comparison of the primary to the prototypical B3 III giant 18 Peg. The red line shows the disentangled spectrum of the narrow-lined star while the orange line shows a spectrum of 18 Peg, obtained with the HERMES spectrograph (Raskin et al. 2011) at the Mercator telescope. To facilitate comparison, both spectra are shifted to rest wavelength and important spectral lines are indicated. This figure was originally published by Bodensteiner et al. (2020), their Fig. 8. Reproduced with permission from ©ESO

and Gräfener 2003; Sander et al. 2015) atmosphere models was performed by Bodensteiner et al. (2020). The derived stellar parameters of Teff,1 = 16000 ± 1000 K and log g = 2.8 ± 0.2 of the primary, and Teff,2 = 20000 ± 2000 K and log g = 4.0 ± 0.3 for the secondary, agree well with the spectral classification illustrated in Figs. 4.6 and 4.7. From the broadening of the spectral lines, they estimated the rotational velocities v sin i  25 km s−1 for the primary, and v sin i = 180 ± 10 km s−1 for the secondary, respectively. A large macroturbulent velocity was found for both stars, which can be interpreted as a signature of stellar pulsations (Simón-Díaz et al. 2017), agreeing with the line variability discussed above.

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Fig. 4.7 Comparison of the secondary star to two prototypical classical Be stars. The disentangled secondary spectrum of HR 6819 in dark blue is compared to the spectrum of HD 45995 (turquoise) and HD 37657 (pink), also observed with HERMES. The spectra are again shifted to rest wavelength, binned with λ = 0.2 Å, and main spectral lines are indicated. This figure was originally published by Bodensteiner et al. (2020), their Fig. 11. Reproduced with permission from ©ESO

4.4.4 The Component Masses in HR 6819 Based on additional photometry, assuming a the GAIA distance of d = 340 ± 20 pc to HR 6819 (Bailer-Jones et al. 2018) and taking the light ratio f between the two components (see Table 4.1), Bodensteiner et al. (2020) estimated the luminosities of both components. They found a luminosity of log L 1 = 3.05 ± 0.10 L  for the primary, and a luminosity of log L 2 = 3.35 ± 0.10 L  for the secondary. Having similar temperatures and similar luminosities, the stars also have similar radii according to the Stefan-Boltzmann law: The radius of the primary is R1 = 4.4 ± 0.4 R while

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the one of the secondary is R2 = 3.9 ± 0.7 R . The similar radii are surprising given the extreme mass ratio of the system derived from the disentangling. Having estimated log g and the stellar radii R1 and R2 , Bodensteiner et al. (2020) derived spectroscopic masses using Mspec ∝ g R 2 . They found that the spectro+0.3 M , while the one of the secondary scopic mass of the primary is Mspec,1 = 0.4−0.1 +5 is Mspec,2 = 6−3 M . The spectroscopic mass of the secondary thus agrees well with the mass estimated from its spectral type. The mass of the primary, however, is much lower than the one of a normal B3 III giant, which was assumed by Rivinius et al. (2020). A summary of the systemic and stellar parameters derived by Bodensteiner et al. (2020) is provided in Table 4.1. Based on these derived low mass, Bodensteiner et al. (2020) and similarly ElBadry and Quataert (2021) proposed that the narrow-lined component in HR 6819 is a bloated stripped star. Previous stripping in a binary system not only provides a natural explanation for the abnormal CNO abundances measured in the star, but also explains the Be companion as a mass gainer in the previous binary interactions. The interpretation is therefore very similar to the one proposed by Shenar et al. (2020) for LB-1. This interpretation of both systems is also important for the possible binary origin of classical Be stars (see Sect. 4.2), as it explains the Be stars in both systems as binary interaction products. The stripped stars, in both cases, are the mass donors that were stripped off their envelope in the past interaction.

4.5 Revealing the Configuration of HR 6819 with Interferometry As outlined in the last sections, two possible interpretations of the HR 6819-system were brought forward. One observational characteristic, which allows to distinguish between the two proposed scenarios, is the separation between the B-type star and the Be star: while they orbit each other every 40 d according to the binary scenario, the orbital period of the Be star is of the order of ten years according to the triple scenario. At the distance of HR 6819, a 40-d orbit translates to a spatial separation of ∼1 mas following the binary scenario, which also predicts that the two stars change their position on the sky approximately every three weeks. According to the triple scenario, the separation of the B- and the Be star corresponds to ∼100 mas, in which the position of the Be star should also be stable over short timescales. The two proposed configurations are depicted schematically in Fig. 4.1. A first attempt to determine the spatial separation between the B- and the Be star was undertaken with the Zorro imager at the Gemini South telescope in Las Campanas, Chile (Klement et al. 2021). The speckle observations indicated a second source located at 120 mas from the central (unresolved) star. Unfortunately, it was not possible to measure the magnitude of the second source, or the magnitude difference between the two. It thus remained unclear whether this second source is the Be star

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Table 4.1 Systemic and stellar parameters of HR 6819. Upper part: Orbital parameters and 1σ errors of HR 6819 derived by Bodensteiner et al. (2020). Lower part: Physical parameters of the two stellar components in HR 6819 based on the disentangling and spectral analysis presented in Bodensteiner et al. (2020). This table was originally published by Bodensteiner et al. (2020), their Table 1. Reproduced with permission from ©ESO Parameter Primary Secondary Spectral type Porb [d] T0 [MJD] ( = 0) e γ [km s−1 ] K [km s−1 ] M sin3 i [M ] a sin i [R ] 2 q( M M1 ) Mdyn [M ] i [deg] Teff [kK] log g [cgs] flux f / f tot (V ) log L [L  ] R [R ] Mspec [M ] v sin i [km s−1 ] veq [km s−1 ] vmacro [km s−1 ] vmicro [km s−1 ]

Stripped star

60.4 ± 1.0 0.07 ± 0.03 48.2 ± 0.8 0.46 ± 0.26 16 ± 1 2.8 ± 0.2 0.45 (fixed) 3.05 ± 0.10 4.4 ± 0.4 +0.3 0.4−0.1 25 40 35 ± 5 10 (fixed)

B2-3 Ve 40.335 ± 0.007 53116.9 ± 1.1 0 (fixed) 9.13 ± 0.78 4.0 ± 0.8 1.05 ± 0.02 3.2 ± 0.6 15 ± 3 7 ± 2 (fixed) 32±4 20 ± 2 4.0 ± 0.3 0.55 (fixed) 3.35 ± 0.10 3.9 ± 0.7 6+5 −3 180 ± 10 340 ± 40 70 ± 25 2 (fixed)

(i.e., as predicted by the triple star model), or if it is an unrelated fore- or background star. Frost et al. (2022) revisited HR 6819 with new observations obtained with the VLT and VLTI in Paranal, Chile. Firstly, they analyzed MUSE data, taken in NarrowField mode, covering a larger FoV of 7.5 × 7.5 with a spatial sampling of 25 mas in both spatial directions. A second source at 100 mas should easily be resolvable with the MUSE data. They showed, however, only one central source with a spectrum comparable to the FEROS spectra obtained with a fiber of 1 diameter. This indicates that the B and the Be star are both situated in the central source, and that the second source reported in the speckle observations of the Zorro imager is not the Be star in HR 6819 (in fact, the second source might have been an observational artifact as it does not appear in the higher-quality MUSE data). Secondly, they used two epochs of interferometric data obtained with GRAVITY at the VLTI, separated by approximately two weeks. The GRAVITY data reveal that

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two luminous sources are present in HR 6819 with a spatial separation of 1.2 mas. The spectral capabilities of GRAVITY in the K-band (covering the Brγ line, which is usually in absorption for B-type stars, and in emission for Be stars) allow to identify the two stars. In the second epoch, the position of the two stars is approximately switched on the plane of the sky, which indicates that the two stars indeed orbit each other on a 40-d orbit. The orbital parameters derived by Frost et al. (2022) generally agree well with the ones derived from spectroscopy alone (Rivinius et al. 2020; Bodensteiner et al. 2020). These new observations unambiguously demonstrate that HR 6819 is indeed a binary system consisting of a B-type star and a classical Be star, and not a triple system hosting a stellar-mass BH and an outer Be star. Further interferometric observations tracing the astrometric orbit of the two components of HR 6819 will provide precise mass estimates of the two components, which are important inputs for binary evolution models.

4.6 A Possible Evolutionary History of HR 6819 The recent GRAVITY and MUSE observations have settled the debate around the nature of HR 6819, and combined with the FEROS spectroscopy, allowed the determination of accurate properties of the current binary system and the two stellar components (e.g., El-Badry and Quataert 2021; Bodensteiner et al. 2020; Frost et al. 2022). However, different initial parameters and evolutionary pathways could have led to the current situation. Bodensteiner et al. (2020) further investigated the past evolution of HR 6819. They used the analytic expression from Soberman et al. (1997) linking the orbital period with the mass ratio of a binary system, which assumes that the orbits are circular, that the mass transfer efficiency was constant, and that no additional angular momentum was lost from the system by other mechanisms. The relation is depicted in Fig. 4.8, which shows the period of a binary system as a function of the mass ratio of the two components, for different current mass ratios. Using the current orbital parameters, it allows to trace back to possible initial conditions of the system. Overplotted is a selection of short-period spectroscopic binary systems containing at least one Bstar component, taken from the S B 9 catalogue (Pourbaix et al. 2004). Those systems illustrate possible progenitor systems of HR 6819. In particular, Fig. 4.8 demonstrates that HR 6819 most likely underwent conservative mass transfer (in the fully non-conservative case, orbital periods below one day are required) and gives a guess for the initial orbital period and mass ratio of the system. The short initial orbital periods required (of the order of several hours up to roughly one day) indicate that the system most like underwent case-A mass transfer, that is the primary filled its Roche-lobe during its MS evolution. The comparison to known spectroscopic binary systems shows that there are several possible progenitor systems that will evolve to a system with a similar mass ratio than HR 6819, if they undergo conservative mass transfer.

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qr qr = 1 qr = 2 1 = 5 18

78

Conservative Fully non-conservative SB 9 , B type, P < 2 d

P [days]

101 100 10−1

Time

100 101 q = MBe /Mstripped Fig. 4.8 Past orbital evolution of HR 6819 for three different current mass ratios q = 12, 15 and 18, within the errors of the observationally derived value. Time increases towards the right of the figure, and the currently observed values correspond to the rightmost points of each curve. Overplotted are known binary systems from the S B 9 catalogue (Pourbaix et al. 2004) that contain at least one Btype component: detached and semidetached binaries are marked by green circles while systems for which it is unclear if the mass ratio was inversed in the past are shown by two connected gray crosses. This figure was originally published by Bodensteiner et al. (2020), their Fig. 15. Reproduced with permission from ©ESO

Guided by these results, Bodensteiner et al. (2020) computed a MESA model (Paxton et al. 2011, 2013, 2015, 2018, 2019) to represent one possible evolutionary pathway that can explain the current properties of of HR 6819. They found that a system with an initial period of 2 days, initial masses of M1,ini = 6 M and M2,ini = 2 M , and assuming fully conservative mass transfer, will produce a system like HR 6819 after undergoing case-A and case-AB mass transfer. Figure 4.9 shows the evolution of the stripped component, that is the donor star, both in an HRD and a Kiel diagram (i.e., in terms of effective temperature and surface gravity). The evolutionary track shows that the donor fills its Roche lobe during its MS evolution and undergoes case-A mass transfer, which continues until all hydrogen in the core is burned to helium. A second phase of mass transfer follows while the donor is H-shell burning, so-called case-AB mass transfer, after which the mass of the donor star is only ∼0.5 M . After the system detaches, the stripped star contracts and heats up, until He-burning is ignited in the core. The currently observed parameters of the stripped star in HR 6819 correspond to the evolutionary stage just after the mass transfer stopped where the star is not yet in thermal equilibrium, but bloated and luminous. El-Badry and Quataert (2021) found that the luminosity in this evolutionary stage is dominated by H-shell burning. Once the stripped star has fully contracted, reached thermal equilibrium, and ignited He burning in its core, it will observationally appear as sdO or sdB star (most likely an sdB given its mass of ∼0.5 M ). The system will further evolve into a Be+sdO binary and resemble systems such as φ Per (Schootemeijer et al.

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log L [L ]

3 ZAMS Case A start Case A end Case AB start Case AB end Max Teff

2

log g [cm s−2 ]

1

Companion depletes H

2

4

6

40

30

20 Teff [kK]

10

Fig. 4.9 Evolution of the donor star. Top panel: HRD showing the evolution of the donor star of a binary system with an initial period of 2 d and initial masses of 6 M and 2 M (blue track). The currently observed parameters of the stripped star in HR 6819 are indicated by the orange cross, including the derived errors. As described in the legend, different colored symbols mark different evolutionary phases. Bottom panel: same as the above, but visualized on a so-called Kiel diagram that shows the evolution of the surface gravity as a function of the effective stellar temperature. This figure was originally published by Bodensteiner et al. (2020), their Fig. 16. Reproduced with permission from ©ESO

2018), FY CMa (Peters et al. 2008), or 59 Cyg (Peters et al. 2013). During its future evolution, HR 6819 will most likely undergo yet another phase of mass transfer when the Be stars expands after the end of its MS evolution. Given the extreme current mass ratio, the system will most likely merge (Bodensteiner et al. 2020). Figure 4.9 also provides an explanation why the stripped star in HR 6819 was initially classified as normal B-type giant star. Especially the top panel indicates that, despite the large difference in mass (by almost a factor of 10), such stripped star have similar temperatures and luminosities to normal B-type stars on the MS. One possibility to detect them, and to discriminate between stripped stars and normal B-type stars, however, is the surface gravity. As shown in Fig. 4.9, it is predicted to be almost one dex lower for a stripped star at a similar temperature. This also agrees with the observed spectrum of HR 6819 compared to a giant star of a similar temperature (see Fig. 4.6).

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4.7 Discussion In this chapter, we presented the highly debated system HR 6819 in the context of Be star formation and BH detection (see Sect. 4.2). We showed that it can be interpreted as a triple system hosting a BH (Sect. 4.3), or a post-interaction binary systems with a stripped star and a Be star (Sect. 4.4). We further demonstrated that high-angular resolution observations with MUSE and GRAVITY unambiguously constrained the nature of the system without invoking the presence of a stellar-mass BH (Sect. 4.5). In Sect. 4.6, we described that HR 6819 is a post-mass transfer binary consisting of the stripped donor star, which observationally looks similar to a normal B-type star despite its low mass of around 0.5 M , and the rapidly rotating mass gainer, observationally characterized by the strong emission lines indicative of a classical Be star. The brightness and proximity of HR 6819 indicates that more similar systems should exist. Possible candidates for systems in a similar evolutionary stage are LB1 (Shenar et al. 2020; El-Badry and Quataert 2021), and possibly also NGC 1850 BH1 (El-Badry and Burdge 2022). However, Bodensteiner et al. (2020) estimated that the current evolutionary phase of HR 6819 only lasts about 1 Myrs, which corresponds to roughly 1% of the entire lifetime of the system, implying that systems in this brief observationally phase should be rare. Taken at face value, this indicates that for every detection of a stripped-star binary, 100 binaries in the other evolutionary phases should be detected. However, the larger radius and higher luminosity of the star during the stripped-star phase, in particular in comparison to the Be+sdO phase, make it easier to detect systems in this phase. It is thus highly likely that many more such systems are hiding in large-scale surveys of massive stars, such as the VFTS survey (Evans et al. 2011). So far, the unique observational characteristics of these stripped star systems are a composite spectrum showing strong Balmer emission lines, coupled with narrow, RV-variable absorption lines. Future spectroscopic surveys will surely detect many more such systems. These post-interaction systems are very interesting in the context of Be-star formation as they provide direct examples of classical Be stars that gained their rapid rotation in previous binary interactions. A further investigation of their parameters, including stellar and orbital parameters, and a detailed modeling with current binary evolution codes, will provide a better understanding of the complex interaction physics that are at play. Those include, for example, further understanding about how conservative and stable the mass transfer process is, and how efficiently angular momentum is transferred from one binary component to the other. A first step in this direction was recently undertaken by Schürmann et al. (2022). Increasing the sample of post-interaction binaries briefly after the mass transfer stopped is thus important. This includes also better constraining the nature and configuration of the other possible candidate systems, like LB-1 and NGC 1850 BH1. GRAVITY observations for LB-1 were obtained recently, however, given the larger distance to the system, the two scenarios are not easily distinguished as the sources

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would not be resolved according to the binary scenario. Being situated in the LMC, interferometric follow-up observations of NGC 1850 BH1 are not possible with current instrumentation. Another, different approach is to study large samples of stars, namely stellar populations. While such a detailed study as performed for HR 6819 is, in general, not possible for large samples of stars, the study of stellar populations provides other advantages. In the next chapter, we will describe those and present one particular stellar population study, namely a spectroscopic study of the SMC cluster NGC 330 with VLT/MUSE.

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Chapter 5

The Young Massive Small Magellanic Cloud Cluster NGC 330 Observed with MUSE

5.1 Introductory Remarks In the previous chapter, one particular binary system, namely HR 6819, was discussed in detail. While important insights can be gained by such individual studies, the investigation of entire populations of stars provides statistically significant samples that can be used as probes to trace different aspects of binary evolution. Star clusters are ideal targets in this respect because, at least to a first approximation, they provide large samples of stars that are born at the same time, from the same material, and that are situated at the same distance from us. Those aspects are some of the most difficult stellar properties for observers to constrain when studying individual stars in the field. Given the large number of stars that reside in interacting binary systems, a large number of binary interaction products are expected to exist. A better characterization of their properties and occurrence rates would not only better constrain the previous interactions, but also provide insights on their future evolution. In particular, open questions involve how they affect their surroundings, how they evolve in the future, and how they end their lives. This is particularly important when investigating endpoints of stellar evolution, the occurrence of different supernova types, possible supernova kicks, and the multiplicity properties of compact objects in late stages of stellar evolution. All of these aspects are important in understanding the nature and quantity of gravitational wave events. In the following chapter, we will describe why star clusters are an ideal place to look for binary interaction products (see Sect. 5.2). We will further introduce NGC 330, a young massive star cluster in the SMC (Sect. 5.3), and present a detailed spectroscopic survey of NGC 330 with MUSE (Sect. 5.4), including a characterization of the stellar content and the estimation of the present-day binary fraction (Bodensteiner et al. 2020, 2021). In Sect. 5.5, we will discuss particular systems of interest. We will compare the findings of Bodensteiner et al. (2020, 2021) to previous observational studies in Sect. 5.6 and to model predictions in Sect. 5.7. We finally put the overall findings into context in Sect. 5.8. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Bodensteiner, Observational Imprints of Binary Evolution on B- and Be-star Populations, Springer Theses, https://doi.org/10.1007/978-3-031-19489-4_5

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5.2 The Search for Binary Interaction Products One possible way to better constrain binary interaction physics and their outcome is by investigating the products of the interaction. As a large number of stars are expected to interact with a companion during their evolution, a large number of interaction products is expect to exist (de Mink et al. 2014; Britavskiy et al. 2019; Wang et al. 2020). Depending on the type of binary interaction that occurred, however, the nature of BiPs can strongly vary, which makes their identification difficult. Unfortunately, none of the various stellar properties and observational characteristics allow the unambiguous identification of BiPs (see Sect. 1.4). Nevertheless, several searches for BiPs based on different observational aspects were carried out in the past. One example is the search for Algol systems, which are currently interacting binary systems that have undergone a previous phase of mass transfer (see e.g., Crawford 1955; Richards and Albright 1999). Blue straggler stars are ubiquitously detected in photometric studies of stellar cluster of different ages, metallicities and masses (see, e.g., Ferraro et al. 1997; Ahumada and Lapasset 2007; Gosnell et al. 2014). In the context of the VFTS survey, Ramírez-Agudelo et al. (2013, 2015) interpreted a large population of rapidly rotating single O-type stars as possible BiPs, which is consistent with the predictions of binary population synthesis calculations (de Mink et al. 2013, 2014). Investigating the mass function of very young stellar populations, Schneider et al. (2014) found possible signatures of previous binary interactions. The Binary and Magnetism survey (BinaMIcS, Alecian et al. 2015; Schneider et al. 2016) studied the magnetic properties of stars in close binary systems in order to shed light on the interplay between magnetism and binarity. Another proposed tracer for BiPs are their direct surroundings as ejected material may form large-scale circumstellar nebulae visible in the infrared (Bodensteiner et al. 2018). Simulating massive star clusters assuming a single phase of star formation, Schneider et al. (2015) gave a theoretical prediction about where to find BiPs. Their simulations of star clusters showed that the relative fraction of BiP with respect to the rest of the cluster members changes with cluster age. In particular, Schneider et al. (2015) showed that the fraction of interaction products peaks at cluster ages of ∼ 8 − 40 Myr, where a significant number of the initial binary systems have interacted already. In clusters of such ages, most O stars have evolved off the MS already and the TO region of the cluster is dominated by early-type B stars (Ekström et al. 2008; Brott et al. 2011). Further theoretical work implied that also the currently observed binary fraction varies as a function of cluster age (see e.g., Wang et al. 2022). This is due to two aspects: on the one hand, the intrinsic binary fraction decreases, for example due to the mergers of the tightest systems or the possible break-up of systems due to a SN kick. On the other hand, it is generally easier to spectroscopically detect pre-interaction binaries consisting of two luminous stars, rather than post-interaction systems, which may consist of one stripped or compact companion (e.g., Bodensteiner et al. 2021). The two aforementioned aspects make star clusters in that slightly older age range

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ideal laboratories to search for possible imprints of previous binary interactions on the current multiplicity fraction, and to investigate the occurrence and properties of BiPs.

5.3 The Young Massive SMC Cluster NGC 330 Previous spectroscopic studies of star clusters mainly focused on the investigation of the stellar characteristics and multiplicity properties of very young clusters with ages 10 Myr. In the Galaxy, several studies of young clusters were performed, for example of Westerlund 1 (Clark et al. 2014), M 17 (Ramírez-Tannus et al. 2018), IC 2944 and the Cen OB2 association (Sana et al. 2011a). In the LMC, the seminal VFTS survey targeted young massive stars in the 30 Doradus region (Evans et al. 2011, and references therein). In such clusters, most binary systems did not have time to interact yet. The derived binary statistics thus are thought to represent the initial binary properties after star formation, and the number of BiPs is still expected to be low. Not many massive star clusters (massive enough to provide a statistically significant sample of massive stars) in the intermediate age range between ∼10 and 40 Myr exist. Additionally, most of the Galactic ones are highly reddened (like RSGC 1, 2 and 3, Portegies Zwart et al. 2010), making observations especially of the massive star population difficult. While there are several massive intermediate-aged clusters in the LMC (see Sect. 6.2.3), NGC 330 in the SMC is a suitable target in a lower-metallicity environment. NGC 330 is a young open cluster with age estimates ranging between 26 and 45 Myr, depending on the different analysis techniques and data used (Sirianni et al. 2002; Martayan et al. 2007b; Milone et al. 2018; Patrick et al. 2020). Being located in the SMC, the distance to NGC 330 is well-defined to 60 ± 1 kpc (Harries et al. 2003; Hilditch et al. 2005; Deb and Singh 2010). The dynamical mass of the cluster 4 is estimated to be Mdyn = 15.8+7.6 −5.1 × 10 M (Patrick et al. 2020). This agrees with photometric mass estimates which vary between Mphot ≈ 3.8 × 104 M (Mackey et al. 2002) and Mphot ≈ 3.6 × 104 M (McLaughlin and van der Marel 2005). The high cluster mass ensures a large population of stars, in particular also massive stars, to be present. The metallicity of NGC 330 was suggested to be [Fe/H] −1.0 (Grebel and Richtler 1992; Gonzalez and Wallerstein 1999; Piatti et al. 2019), which is slightly lower than the average metallicity of [Fe/H]= −0.7 reported for the SMC field population (e.g., Luck et al. 1998; Korn et al. 2000; Keller and Wood 2006). NGC 330 was the target of several studies in the past, which mainly focused either on a handful of bright stars in the core, or targeted the outskirts of NGC 330. Due to the high stellar density in the cluster core, a detailed study of the stars in the cluster core was not possible with past instrumentation. A common finding of previous studies is the high fraction of classical Be stars, estimated to be ∼50% or higher (Feast 1972; Grebel et al. 1992; Lennon et al. 1993; Grebel et al. 1996; Mazzali et al. 1996; Keller and Bessell 1998; Keller et al. 1999). This fraction, which

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was also reported for other SMC clusters (Martayan et al. 2007b), is significantly higher than the Be star fraction of ∼ 20% reported for field stars in the Milky Way (e.g., McSwain and Gies 2005). Maeder et al. (1999) interpreted this difference as an indication for a relation between the Be star fraction and the metallicity of the host galaxy, implying that the fraction of Be stars is higher at lower metallicity. This was partly challenged by Evans et al. (2006), who studied a large number of O- and B-type stars with VLT FLAMES as part of a larger spectroscopic study of massive stars in Magellanic Cloud clusters and found similar Be star fractions in the outskirts of NGC 330 and in the LMC cluster NGC 2004. Milone et al. (2018) recently studied the dense core of NGC 330 with multiband HST photometry. Using observations obtained in 2015 and 2017 with the Wide Field Camera 3 (WFC3), the authors constructed a CMD from magnitudes in the F336W and F814W filters. Based on excess flux in the narrow-band filter F656N, they additionally identified Hα-emitting stars, confirming the large number of Hαemitters previously observed. In the CMD, they detected a split MS and an extended MSTO feature, which have both been interpreted as binary interaction signatures in the literature (see e.g., Wang et al. 2020, 2022). Excluding runaway stars, most massive interaction products are expected to be found in the core of the cluster. This is due to mass segregation, which might either be primordial (Sirianni et al. 2002) or occur due to dynamical interactions among cluster members (Portegies Zwart et al. 2010). MUSE spectroscopy of a handful of stars in the cluster core was recently presented by Carini et al. (2020). Based on one epoch of MUSE observations in WFM, they extracted spectra and measured stellar parameters (in particular rotational velocities and He abundances) for ten of the brightest MS stars. As the observations were taken before the MUSE AO upgrade in 2017, crowding and the thereby induced contamination of stellar spectra prevented the authors from studying more, and also fainter stars.

5.4 Multi-epoch MUSE Spectroscopy of NGC 330 In the subsequent section, we will describe the spectroscopic study of NGC 330 presented in Bodensteiner et al. (2020, 2021). Using multi-epoch MUSE spectroscopy, they characterized the stellar content and assessed the multiplicity properties of the massive star population. In contrast to Carini et al. (2020), these newer MUSE observations were supported by AO, which greatly increases the image quality and therefore reduces the blending of sources. MUSE-AO observations make it thus possible to spectroscopically resolve stars in the dense core of NGC 330 for the first time.

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5.4.1 Observations, Data Reduction and Spectral Extraction Six epochs of observations of NGC 330 were obtained with MUSE (Bacon et al. 2010) mounted at UT4 of the VLT in Paranal, Chile, spanning an overall time frame of approximately 1.5 years. All epochs were obtained in the extended wavelength mode (covering a wavelength range from 4650 Å to 9300 Å with a gap between 5780 and 5990 Å) with a spectral resolving power λ/λ between 1700 in the blue and 3700 in the red. The MUSE observations were reduced according to the standard MUSE data reduction recipes, which are described in Sect. 2.3 (together with a detailed description of integral field spectroscopy). Table 5.1 gives an overview of the observations. It includes observing dates, weather conditions, and the image quality of the final cubes after data reduction. The image quality takes into account both the seeing during the observations as well as the improvement by the AO. It is given by the average FWHM of the PSF, which can estimated in the reduced, collapsed white-light image by fitting the brightness distribution of a handful of bright and isolated stars with a 2D Gaussian profile. It shows that the image quality was consequently below 1 in all the epochs. The spatial coverage of the MUSE observations is indicated in Fig. 5.1, which shows a three-color image constructed from one epoch of observation, compared to the finding chart used in the study of Evans et al. (2006). With a 1’×1’ FoV and a distance of 60 ± 1 kpc, (see e.g., Harries et al. 2003), the MUSE observations cover the central 20 by 20 pc of the cluster core, a region that was previously not accessible with spectroscopy. In particular, there are only two stars in common between this work and the study by Evans et al. (2006), who focused on the outskirts of NGC 330. Spectra of the brightest star in NGC 330 were extracted with the python package extract- ifu- spectra described in Sect. 2.4. An extraction of the spectra via PSFfitting is necessary because of the high stellar density in the core of NGC 330. The HST data of Milone et al. (2018), described in Sect. 5.3, were used as photometric

Table 5.1 Journal of the observations of NGC 330 with MUSE, giving the observing date and the modified Julian date (MJD) at the start of each observation. It further provides the average seeing during the observations, and image quality (FWHM) of the reduced data cubes. This table was originally published by Bodensteiner et al. (2021), their Table 1. Reproduced with permission from ©ESO Epoch nr. date MJD Seeing FWHM [d] [ ] [ ] 1 2 3 4 5 6

2017-08-15 2017-09-18 2018-11-06 2018-11-19 2018-11-22 2018-12-18

57980.22523264 58014.12963530 58428.09317181 58441.07863659 58444.04752694 58470.03819326

0.4–0.9 1.2–1.9 0.8–1.1 0.4–0.7 0.6–0.8 0.6–0.8

0.7–0.8 0.8–0.9 0.8–1.0 0.6–0.7 0.7–0.8 0.7–0.8

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Fig. 5.1 Left panel: Cutout of the finding chart of Evans et al. (2006), where target stars are indicated with black circles. The size and position of the MUSE FoV is marked by the blue rectangle. Right panel: Three-color image of one MUSE epoch (red corresponds to an image in the I -filter, green to the V -filter, and blue to the I -filter). This figure was originally published by Bodensteiner et al. (2020), their Fig. 1. Reproduced with permission from ©ESO

input catalogue for the extraction. The HST catalogue has a significantly higher spatial resolution and covers a larger region on the sky than the MUSE FoV, which is why it is in general fairly complete down to m F814W = 22 mag. To efficiently deblend the spectra of stars in crowded regions, all stars up to two magnitudes fainter than the target star, which are closer than 2.4 on the sky (corresponding to 12 pixel on the MUSE detector), are taken into account in the extraction. Spectra for approximately 350 stars brighter than m F336W = 17.5 mag were extracted from the MUSE observations. The brightness cut in the extraction ensures that all extracted spectra have a sufficient S/N (i.e., S/N>80). For several stars, especially faint stars in crowded regions, the extraction was not possible or lead the insufficient S/N ratios in the resulting spectra. All extracted spectra for every star at each epoch were automatically normalized. In total the sample consists of 324 B-type stars, ten RSGs and six BSGs. The average S/N in the normalized spectra varies between 80 and 300 for the faintest and brightest B-type stars, respectively. It reaches up to 400 for the RSGs and BSGs (Bodensteiner et al. 2020).

5.4.2 The Stellar Content of NGC 330 As described in Sect. 2.6, a first step to estimate stellar parameters, mainly effective temperature and surface gravity, is by assigning a spectral type. This is usually done by comparison to standard-star spectra, either by eye, or by comparing the EWs of diagnostic spectral lines to the ones measured for the standard stars.

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Fig. 5.2 Example spectra for stars of each spectral group, namely of a classical Be star (green), a B-type star (yellow), a BSG (blue), and a RSG (red), from top to bottom. A conversion of the F336W-magnitude to the more commonly used V -band magnitude is indicated for each star. No spectral information is obtained in the gray-shaded wavelength region, which is blocked to avoid saturation because of the laser guide system. Important spectral lines are indicated. This figure was originally published by Bodensteiner et al. (2020), their Fig. 6. Reproduced with permission from ©ESO

Given the age of NGC 330, the population of massive stars is expected to mainly contain B-type stars, that is both normal B-type stars as well as Be stars, which can be easily characterized by Balmer emission. Additionally, several red and blue supergiants are clearly identified because of their brightness in the HST data (i.e., they are approximately two magnitudes brighter than the brightest MS stars). Based on one epoch of MUSE observations, Bodensteiner et al. (2020) reported on the presence of 208 B stars, 116 Be stars, six BSGs and ten RSGs. An example spectrum of a member of each of the four groups is shown in Fig. 5.2. After categorizing the B-type stars into normal B-type stars and Be stars, spectral types were estimated by comparison to standard stars (following the procedure outlined in Sect. 2.6). For the B-type stars, and the Be stars that showed only little contamination, spectral types were assigned by comparing the measured EW of diagnostic spectral lines to the EW measured for standard stars. In this case, a focus was put on the He II λ 5412 line, the He I λ 6678, line, and the O I triplet at λ 7774. The spectra of the more strongly contaminated Be stars and the spectra of the BGSs were compared to standard stars by eye. Detailed spectral types for the RSGs were provided by Patrick et al. (2020), who investigated 15 RSGs in NGC 330 (several of which were outside the MUSE FoV). As mentioned above, the spectral typing indicated that there are basically only B-type MS stars in NGC 330 (i.e. few O-type and no A-type MS stars), most of which are of spectral type B3-B6. A similar result is found for the Be stars, which are mostly of mid- to late spectral type. Bodensteiner et al. (2020) further reported on the presence of only two O-type stars in the core of NGC 330. Interestingly, both of those show Balmer emission lines in their spectra, with spectral types O9.5eV and O9.5/B0eV. The lack of late-B to A-type MS stars is most likely due to the magnitude cut, which was applied in the extraction of the spectra. The BSGs are mostly early A-type supergiants, mainly with luminosity class Ib, but there is also

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one late-A supergiant (Bodensteiner et al. 2020). The RSGs, studied by Patrick et al. (2020), are mostly late-G or early-K stars with luminosity classes around Ib. Combining the spectral information from the MUSE data with the HST data from Milone et al. (2018), in particular the F336W and F814W bands, Bodensteiner et al. (2020) constructed a spectroscopically informed CMD for NGC 330 (see Fig. 5.3). As eight (two BSGs and six RSGs) of the brightest stars are saturated in one or both of the HST filters, they cannot be placed on the CMD. The CMD includes the entire HST catalogue, that is also stars in the outskirts of NGC 330 that are not covered by the MUSE observations. Spectroscopy of several stars in the core is further missing because the stars were too faint or located in severely crowded regions. Overplotted on the CMD are single-star non-rotating Padova isochrones (Bressan et al. 2012; Chen et al. 2014, 2015; Tang et al. 2014; Marigo et al. 2017; Pastorelli et al. 2019) for SMC metallicity, scaled for the appropriate distance and foreground extinction (Deb and Singh 2010; Keller et al. 1999). A comparison of the observed position of stars with the theoretical isochrones confirms previous age estimates of NGC 330 between 35 and 40 Myr. The turnoff magnitude of NGC 330, which is difficult to define precisely, is estimated to be at m F814W ≈ 16.5 mag, which corresponds to a mass of M ≈ 7.5 M on the MS. This agrees with the lack of O stars in the cluster. Figure 5.3 demonstrates that the spectral classification agrees well with what is expected from position of the stars in the CMD. It further agrees with the reports of Milone et al. (2018) of a large fraction of Hα-emitting stars, which they interpreted as Be stars. The MUSE data confirm that the spectra of those stars are indeed dominated by Balmer emission lines. Most of the Be stars (though notably not all of them) form a second sequence which is rewards of the main MS of the cluster. This is most likely due to a combination of the rapid rotation of Be stars, which makes them appear cooler on average, and the flux contribution of the disk in the near-IR, which leads to a flux excess in F814W. There are, however, also several Be stars among the main MS, and several faint Be stars far from the cluster turnoff. Figure 5.3 further shows several stars that are situated above the cluster turnoff, that is they are brighter and hotter than the stars at the turnoff. Both B and Be stars are found in that location. Such stars, so-called blue stragglers, are usually interpreted as BiPs, which can be located in that CMD position due to different binary evolution channels. Firstly, they could be currently interacting binaries. Such systems are undergoing mass-transfer where material is transferred from one component to the other through an accretion disk. Observationally, currently interacting systems might appear like classical Be stars, and interestingly the two Oe stars are situated in this CMD region. Secondly, the Blue Straggler stars could be merger products, which were rejuvenated by the merger process. Those stars, which are thought to be more massive than the stars at the cluster turnoff, are expected to be slow rotators (see e.g., Schneider et al. 2019). Lastly, these systems could be systems like HR 6819 (described in Chap. 4), that is post-interaction systems briefly after the mass transfer phase in which both stars contribute similarly to the optical flux. As mentioned above, among the 324 MS stars with spectral type classifications there were 116 Oe or Be stars. This leads to a spectroscopic Be star fraction of

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Fig. 5.3 Spectroscopically informed CMD of NGC 330. Their entire photometric HST catalogue (Milone et al. 2018) is plotted in gray, while stars that were observed with MUSE are colored by the spectral type found by Bodensteiner et al. (2020) in the MUSE data. Similarly to Fig. 5.2, Be stars are marked with green symbols, B-type stars with yellow ones, RSGs with red ones, and BSGs with blue symbols. Eight sources in common between the MUSE data and the spectroscopic study by Evans et al. (2006) are marked with black circles. Single-star non-rotating Padova isochrones for ages between 30 and 45 Myr are overplotted (in shades of purple). This figure was originally published by Bodensteiner et al. (2020), their Fig. 16. Reproduced with permission from ©ESO

f Be = 36±3%. This is a bit lower than the high Be star fractions previously reported for NGC 330 (see e.g., Feast 1972; Keller et al. 1999; Martayan et al. 2007b), but still high compared to the typical Be star fractions reported for the Milky Way (cf. Zorec and Briot 1997). The fraction reported by Bodensteiner et al. (2020) is further a lower limit to the true Be star fraction. This is due to the duty cycle of Be stars, which remains ill-constrained but probably works on timescales of years or decades. While Galactic Be star fractions are usually derived from years of subsequent observations of both field and cluster stars, which are therefore more likely to catch a Be star

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during the emission-line-phase, the six epochs used in the study of NGC 330 only span ∼1.5 years, indicating that some Be stars might not have been detected as such. Given that the CMD presented in Fig. 5.3 indicates that most Be stars are situated near or at the cluster turnoff, Bodensteiner et al. (2020) considered the distribution of B and Be stars as a function of F814W magnitude. Figure 5.4 shows that stars above the cluster turnoff (covering a magnitude range between m F814W = 16.5 mag to m F814W = 15.0 mag) are predominantly Be stars, with a Be fraction between 50 and 65%. It drops rapidly at m F814W = 16.5 mag down to ∼20% for stars fainter than m F814W = 17.0 mag. This might imply that there is a cutoff luminosity below which B-type stars do not appear as Be stars anymore (which could indicate that such stars cannot build up a disk, or that they do not produce enough flux to ionize a disk, see e.g., Bastian et al. 2017). Figure 5.3 further gives a translation of F814W magnitude into mass, illustrating that the stars considered by Bodensteiner et al. (2020) are in a narrow mass range between 5.5 M and 7.5 M . The cluster turnoff, and therefore also the most massive stars in NGC 330, are at 7.5 M (not considering any possible mass gainers from binary interactions). The distribution of B and Be stars as a function if magnitude demonstrates three important points: firstly, it explains why the Be star fraction measured by Bodensteiner et al. (2020) is lower than the one previously measured for NGC 330. Previous studies focused on the brightest stars and therefore were only sensitive to the turnoff region. As the Be star fraction is defined as the number of Be stars with respect to all B-type stars, going to fainter stars means including more B-type stars in the sample, effectively reducing the Be star fraction. Secondly, it shows that the cluster turnoff in NGC 330 is dominated by Be stars. As mentioned above, those could be classical Be stars, that is mass gainers in previous binary interactions. Observationally, however, it is also possible that some of the systems classified as Be stars are currently interacting binary systems in which the emission lines originate from an accretion disk. Lastly, while the Be star fraction drops towards fainter magnitudes, it does not go to zero. This demonstrates that ‘unevolved’ Be stars exist, which are far from the cluster turnoff and therefore far from the end of their MS evolution. According to the single-star channel for Be formation, the rotational spin-up occurs only towards the end of the MS evolution. The detection of ‘unevolved’ Be stars is thus a direct evidence for the binary channel in Be star formation. The stellar content of the core of NGC 330, assessed by MUSE spectroscopy, already gives first indications about the presence of possible interaction products. These include the stars above the cluster turnoff, which are most likely Blue Straggler stars, as well as the large number of Be stars, both around the cluster turnoff, which might be classical Be stars or currently interacting binaries, as well as the ‘unevolved’ Be stars at fainter magnitudes. Another possibility to investigate the imprint of binary interactions on NGC 330 is by investigating the present-day binary fraction, which is described in Sect. 5.4.3.

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Fig. 5.4 Be star fraction as a function of F814W magnitude. The yellow and green histograms show the distribution of B and Be stars, respectively, as a function of their F814W magnitude taken from Milone et al. (2018). The left axis indicates the number of stars, while the right axis illustrates the Be star fraction. The gray stars (with binomial errors) indicate the Be star fraction computed for each magnitude bin. A conversion of the F814W magnitude into mass (computed with the Padova isochrones) is indicated in the top axis. The cluster turnoff is located at m F814W = 16.5 mag. This figure was originally published by Bodensteiner et al. (2020), their Fig. 17. Reproduced with permission from ©ESO

5.4.3 Radial Velocities, Multiplicity Criteria and the Bias Correction As described in Sect. 5.2, the current binary fraction of a population of stars also gives an indication about the presence of interaction products. Binary population synthesis computations predict that the observed binary fraction in slightly evolved populations is lower than in very young populations. This is due to the fact that binary systems had time to interact and have either merged or produced post-interaction systems that are difficult to detect observationally. SB1 binaries are usually classified based on RV variations. Using the six available MUSE epochs (see Table 5.1), Bodensteiner et al. (2021) measured RVs of the MS stars as well as the BSGs in NGC 330 via Gaussian fitting. The binary status of the

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RSGs was investigated by Patrick et al. (2020). For the B and Be stars, Bodensteiner et al. (2021) considered all He i lines covered by the MUSE observing range, namely at λλ 4713.15, 4921.93, 5015.68, 5047.74, 6678.15, and 7065.19 Å. Depending on the S/N of the spectra and considering possible emission-line contamination in the Be stars, a subset of those lines was chosen for each star. For the BSGs, more metal lines are available and as many lines as possible were considered when determining the RVs. Based on the MUSE observations, RV measurements were possible for approximately 290 stars. For the remaining stars with a spectral type classification, the S/N in the spectra was not sufficient to measure RVs. Before classifying a RV-variable star as candidate binary system, the statistical significance of the RV variations has to be demonstrated (cf., Sana et al. 2012; Dunstall et al. 2015; Banyard et al. 2022). Furthermore, there are other possible causes for RV variations apart from the star being in a binary system, for example pulsations (Aerts et al. 2009) or wind variability (Fullerton et al. 1996). Bodensteiner et al. (2021) therefore applied two multiplicity criteria to the measured RVs, to ensure that the RV variations are statistically significant and have amplitudes larger than the ones usually caused by other mechanisms. Applying those, Bodensteiner et al. (2021) detected 24 binary candidates among the 189 B-type stars, five binary candidates among the 93 Be stars, and one binary candidate among the six BSGs. They further visually inspected all spectra for the signature of SB2 systems, which manifest themselves in composite, possibly variable spectra. Despite the low resolution of MUSE, they detected six B-type SB2 candidates and two SB2 candidates among the Be stars. Those could either be true SB2s, that is binary systems where both components contribute similarly to the spectra, or they could also be stars that by chance lie on the same line of sight. Given the high density of stars in the core of NGC 330, this cannot be excluded. Taking both the few identified SB2 systems as well as the binaries detected based on RV variations, Bodensteiner et al. (2021) reported an overall observed spectroobs = 13.2 ± 2.0%, based on a sample of almost 300 scopic binary fraction of f SB massive OB stars for which RVs could be measured. To convert this observed binary fraction into an intrinsic binary fraction, knowledge about the observational biases and the sensitivity of the observing campaign is required. It further requires input assumptions on the distribution of binary orbital parameters such as the distribution of the orbital period, the mass ratio and the eccentricity. To assess this in terms of a bias correction, Bodensteiner et al. (2021) considered two types of biases, one related to SB1s and the other to SB2s, which are described in the following. Firstly, Bodensteiner et al. (2021) investigated a bias due to unidentified SB2 systems. Those are binary systems with composite spectra in which the two sets of spectral lines never fully deblend. Instead, their periodic shift with respect to each other mimics lines broadening and reduces the measured RVs. Such systems might either appear as stars with lower RV amplitude or no significant RV amplitude (Sana et al. 2011b). This effect is strongest in binary systems where both stars have similar spectral types and contribute similarly to the overall line strength. Additionally, it is stronger for stars with broader lines, which can either be due to the intrinsic rotation of the stars, or due to the spectral resolution of the instrument. The SB2 bias can be

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lifted when the system is identified as SB2 and the composite spectra are fitted with a double-Gaussian profile taking into account the contributions from both stars. The SB2 bias thus reduces the chance of classifying a system as binary according to the above mentioned detection criteria. To assess the impact of this bias on MUSE observations, Bodensteiner et al. (2021) performed detailed simulations using synthetic spectra from the tlusty Bstar grid (Lanz and Hubeny 2007). They constructed mock binary systems with a B2 V star as primary and companions with mass ratios q ranging from 1 (an equalmass binary) to 0.5, which in turn defines the flux contribution of the two stars to the composite spectrum. After broadening both individual spectra for a rotational velocity of 200 km s−1 , the two component spectra were shifted in RV and added together according to their light ratio. Adopting the same Gaussian fitting procedure as for the actual observations, RVs of these composite spectra were measured after degrading them to MUSE S/N, resolution and wavelength binning. Similar to the observations, a visual inspection was performed to check for obvious SB2 signatures. The results of the simulation are depicted in Fig. 5.5, which shows the measured RV of the primary as a function of the input RV separation (which is twice the primary RV). Figure 5.5 demonstrates that the impact of the SB2 bias is strongest for equalmass and nearly equal-mass systems, in which both stars contribute strongly to the composite spectrum. If the blue- and red-shifted contributions cannot be deblended, they effectively broaden the spectral line but do not lead to measurable RV shifts. Figure 5.5 also indicates that the effect is less severe for binaries with mass ratios q < 0.6. In such systems, the composite spectra are dominated by the spectral lines of the primary. The visual inspection of the spectra further implied that systems would only be identified as SB2s if the RV separations is above 200–300 km s−1 . Due to a combination of factors, the SB2 bias particularly affects the MUSE observations of NGC 330, which is also reflected by the comparable low number of SB2s detected in the cluster (Bodensteiner et al. 2021). On the one hand, this is related to the comparably low resolution of the MUSE observations (between 1700 and 3700 in the blue and red, respectively). On the other hand, it is further enhanced by the large number of rapid rotators detected in NGC 330, and by the fact that the typical RV amplitudes of B-type binaries rarely exceed of 200 km s−1 . The SB1 bias quantifies the likelihood of detecting significant RV variations (that meet the above-mentioned binary criteria) of simulated binary systems with the adopted observing strategy. To assess this, Bodensteiner et al. (2021) simulated almost 300 binary systems, randomly assigning a primary mass from a Salpeter initial mass function (Salpeter 1955) between 5 and 8 M (corresponding to the mass range found for NGC 330, see Sect. 5.4.2). Those primaries were then paired with a binary companion by randomly selecting orbital parameters, in particular the binary period, the mass ratio, and the eccentricity from observationally derived orbital parameter distributions (Sana et al. 2012, 2013; Dunstall et al. 2015). It was further assumed that the binaries have a random orientation and are observed at a random time of the orbit, with a similar time sampling as the actual observations. Translating the mass to a brightness, realistic RV errors were assigned to each binary guided by the MUSE

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Fig. 5.5 Simulation of the SB2 bias. The colored points show the measured RVs of simulated binary systems with different mass ratios between 0.5 and 1 (see legend), assuming the primary to be a B2 V star, as a function of the input RV separation. Additionally, the RVs of a single B2 V star are shown in gray to demonstrate the accuracy of the RV measurements. All spectra are broadened for a rotational velocity of v sin i = 200 km s−1 . The dashed gray line indicates the assumed RV of the primary star, showing that in most simulated binaries, especially the ones with mass ratios close to 1, the measured RVs are highly underestimated. This figure was originally published by Bodensteiner et al. (2021), their Fig. 3. Reproduced with permission from ©ESO

observations. It was then verified if the systems would be classified as binaries by applying the same multiplicity criteria as for the real RV data. An overall detection probability of the observing campaign as a function of period, mass ratio, and eccentricity was then computed by repeating the simulation of the approximately 300 binaries 10 000 times and computing the average fraction of detected binaries. Applying this sensitivity correction factor to the observed binary fraction allows to asses the intrinsic binary fraction, including both the SB1 and the SB2 bias. The bias correction for NGC 330 was performed twice, once considering the SB1 bias only as in previous studies (cf. Sana et al. 2013; Dunstall et al. 2015), and once taking into account both SB1 and SB2 biases (Bodensteiner et al. 2021). Furthermore, a magnitude-dependent bias correction was computed, which takes into account the varying RV accuracy achieved for stars of different brightness (see also Fig. 5.8 and Table 5.2). Figure 5.6 shows the two versions of the bias correction as a function of orbital period and mass ratio. Firstly, it indicates that the SB2 bias reduces the overall

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Fig. 5.6 Simulation of the binary detection probability, taking into account only the SB1 bias (black continuous line), and both SB1 and SB2 biases (orange dotted line, see text). The top panel shows the detection probability as a function of the orbital period P, while the bottom panel shows it as a function of mass ratio q, defined as q = M2 /M1 . The mass ratios of the simulated binary systems (see Fig. 5.5) are indicated by colored arrows in the bottom panel. This figure was originally published by Bodensteiner et al. (2021), their Fig. 2. Reproduced with permission from ©ESO

detection probably. This reduction varies strongly with the mass ratios of the systems and is rather insensitive to the periods of the systems. Secondly, it shows that the overall binary detection probability is close to 80% for the short-period systems and steadily drops towards roughly 3000 days (the longest periods considered in the bias correction). The dips in the detection probability correspond to the time coverage of the observations. The bias correction comes with an additional caveat: it strongly depends on the assumed binary parameter distributions. Those were measured in young populations of stars and reflect the initial properties of massive binary populations (Sana et al. 2013). They do, however, not take into account any impact of binarity on these initial distributions, which is expected to be significant (Wang et al. 2020, 2022). Given

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that these effects are difficult to model, and have not been observed in detail yet, the bias correction presented by Bodensteiner et al. (2021) is a reasonable first step to assess the intrinsic multiplicity properties of NGC 330. The bias correction for the MUSE data on NGC 330 shows that the overall sensitivity of the observational data set is low (i.e., the overall detection probability is only ∼40% overall, but strongly depends on the period and mass ratio), and that a large number of binary systems would not be detected in the spectroscopic observations. This has two main reasons: firstly, the study by Bodensteiner et al. (2021) is based on only six epochs, spread over 1.5 years. This impedes the detection of long-period binaries. However, theoretical computations predict a large number of post-mass transfer binaries on longer periods (see e.g., Langer et al. 2020). Secondly, the low spectral resolution of the MUSE data makes it difficult to spot SB2 systems, especially if the lines are also rotationally broadened, and only provides a moderate RV accuracy. Nevertheless the multiplicity study of Bodensteiner et al. (2021) provides a first idea on the binary properties of NGC 330, which could not be assessed yet. Additional MUSE observations would help to detect more binary systems and further characterize the ones reported so far.

5.4.4 The Multiplicity Properties of NGC 330 As mentioned above, the overall observed spectroscopic binary fraction of massive obs = 13.2 ± 2.0%. Correcting this for observational biases as stars in NGC 330 is f SB described above and illustrated in Fig. 5.6 leads to an intrinsic, bias-corrected binary +8 intrinsic = 34−7 % (Bodensteiner et al. 2021). fraction of f bin Using the spectral and photometric classification of stars into B stars, Be stars, and BSGs, Bodensteiner et al. (2021) investigated if the binary fraction differs among these groups. In this context, Be stars are defined according to the spectroscopic definition (that is, all stars that show Balmer emission lines), not according to their position in the CMD (as described in Sect. 5.7). The comparison shows that the observed binary fraction indeed differs for the different groups: While the observed obs = 15.9 ± 2.6%, it is only spectroscopic binary fraction of the B-type stars is f SB,B obs obs f SB,Be = 7.5 ± 2.7% for the Be stars. The fraction for the BSGs is f SB,BSG = 17 ± 15%, which, however, suffers from low number statistics. No bias correction is applied here as a large number of Be stars might be interaction products, invalidating the assumed orbital parameter distributions. The CMD in Fig. 5.7 gives an overview of the position and therefore the evolutionary status of the detected binary systems (constructed similarly to Fig. 5.3). The CMD shows that most detected SB1 and SB2 binaries are located on the main MS, also at fainter magnitudes. It further indicates that there is only one SB1 detected in the second, redder Be sequence. Additionally, several of the detected binaries are located in the region around and above the cluster turnoff. Two B-type binaries (one SB1 and one SB2) are bluewards of the MS, one of which is well below the turnoff.

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Fig. 5.7 CMD of NGC 330, based on HST photometry (Milone et al. 2018), indicating the binary status of the massive stars. As in Fig. 5.3, RGSs are marked in red, BSGs in blue, B stars in yellow, and Be stars in green. The binary information is coded in the symbol of each star: triangles indicate SB2 systems, diamonds marks stars that were classified as binaries because of significant RV variations, filled circles indicate stars with no significant RV variability (which could either be truly single stars or stars that have avoided binary detection), and open small circles identify stars for which no RVs could be measured. Two Padova isochrones are overlain, and additional HST sources from Milone et al. (2018), which are outside of the MUSE FoV, are indicated by gray dots. The inset on the right focuses on the upper MS. This figure was originally published by Bodensteiner et al. (2021), their Fig. 4. Reproduced with permission from ©ESO

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Fig. 5.8 Binary statistics of the B and Be stars as a function of F814W magnitude. Top panel: distribution of F814W magnitudes, similar to Fig. 5.4 but indicating stars with measured RVs (in dark gray). Bottom panel: Observed and bias-corrected close binary fraction as a function of F814W magnitude. The binary fraction computed from the RV variable systems alone is shown in red while the one including also SB2s is shown in yellow. The bias-corrected binary fraction, applying a magnitude-dependent bias correction (see text) is indicated in dark red. This figure was originally published by Bodensteiner et al. (2021), their Fig. 6. Reproduced with permission from ©ESO

The detected binary BSG could not be placed on the CMD as no magnitudes were available for it in the photometric HST catalogue (Milone et al. 2018). The binary classification of the RSGs performed by Patrick et al. (2020) is not included in this Figure (but further discussed in Sect. 5.7). Figure 5.8 shows the distribution of F814W magnitudes, as well as the observed and bias-corrected binary fraction as a function of F814W magnitude, including both B and Be stars. Firstly, the magnitude distribution implies that the sample is incomplete from m F814W > 18.5 mag, which possibly also affects the distribution below m F814W > 18.0 mag. In the brightest bins, the numbers statistics are very low (i.e., excluding the BSGs there is only a handful of stars brighter than m F814W = 15.0 mag), Secondly, and excluding those brightest bins, Fig. 5.8 shows that the observed binary fraction decreases steadily with F814W magnitude, from ∼30% around the cluster turnoff down to less than 10% for the faintest stars considered. This could be an observational effect, caused by the lower RV accuracy in fainter stars related to the lower S/N, which decreases the chance of detecting a system as a binary. Applying the magnitude-dependent bias correction (see Sect. 5.4.3), which takes the lower RV accuracy into account, indicates that this is not the case. Despite large error bars, which are mainly dominated by the uncertainty of the bias

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correction and the small sample size in each magnitude bin, Fig. 5.8 implies that the bias-corrected binary fraction decreases with magnitude: it is almost 60% for the brightest stars, and drops to roughly 25% for the faintest ones. Bodensteiner et al. (2021) showed that this decreasing trend is indeed statistically significant at the 5% level. This finding indicates that the multiplicity properties of the stars studied by Bodensteiner et al. (2021) are intrinsically different, despite the narrow mass range considered (i.e., masses range from 7.5 M to 5.5 M , see Fig. 5.4). The decrease in the bias-corrected binary fraction could either imply that the binary fraction decreases with F814W magnitude, and therefore with stellar mass, or that the period distribution is shifted towards longer orbital periods for the fainter stars (again corresponding to the less-massive ones). Longer-period systems would be harder to detect in the MUSE data (see Fig. 5.6).

5.5 Particular Systems of Interest Several individual systems in NGC 330 are worth mentioning. They include a possible BeXRB, a BSG binary, an O+B binary, and a binary hotter than the MS. Each of the systems will be further detailed in the following. A Possible BeXRB Based on XMM observations, a high-mass X-ray binary candidate, namely [SG2005] SMC38, was previously reported in NGC 330 (Shtykovskiy and Gilfanov 2005; Sturm et al. 2013; Haberl and Sturm 2016). The XMM position of the source with a 1σ positional uncertainty of 0.7" is illustrated in Fig. 5.9. The high stellar density in the field (Fig. 5.9 indicates that six stars are within the 3σ error circle of XMM) makes it difficult to unambiguously match the X-ray source to a star observed with MUSE. The two stars closest to the XMM position are # 94, a Be star of spectral type B5 Ve, and # 97, a Be star with spectral B1 Ve. While # 97 was classified as presumably single star, given it does not show significant RV variations, no RVs were measured by Bodensteiner et al. (2021) for # 94 because of the strong emission-line contamination in the spectrum. Further, ongoing work re-estimating the RVs of # 94 based on the CCF-technique (see Sect. 2.5), however, showed that the star exhibits significant RV variations. This estimate was based on the Balmer emission lines (as only contaminated absorption lines were available in the MUSE wavelength range). Given that only six observational epochs are available, it is, however, not possible to assess the orbital parameters like the period of the system. Nevertheless, the position of the system so close to the core of NGC 330 may indicate that the unseen companion is a BH. If the companion was a NS, a kick associated with the SN explosion would be expected, which most likely would have ejected the system outside of the MUSE FoV, even at low kick velocities. In any case, [SG2005] SMC38 is a post-interaction system residing in the core of NGC 330.

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Fig. 5.9 X-ray source in NGC 330. The position of [SG2005] SMC38 is overlain over a white-light image of one MUSE epoch in pink, together with the formal positional error circle of XMM. The 3σ uncertainty on the position is indicated by the black dotted circle. MUSE sources from Bodensteiner et al. (2020, 2021) within the 3σ error circle are indicated in turquoise

A BSG in a binary system Based on the six epochs of observations, one BSG was identified to have significant RV variations (Bodensteiner et al. 2021). This is # 729, initially referred to as Cl* NGC 330 ARP 35 by Arp (1959). While it was classified as B9 I star by Feast (1964), Bodensteiner et al. (2020) derived a spectral type of early-A and a luminosity class Ia-Ib. Feast and Black (1980) already estimated RVs for # 729. Their values, which varied between 134 to 154 km s−1 , are similar to the RVs measured in the MUSE observations, but given large uncertainties the star was classified as presumably single by Feast and Black (1980). The RVs measured in the MUSE data, however, clearly demonstrate that the star is a member of a binary system (see Fig. 5.10), with a RV amplitude of 20 km s−1 . Again, no orbital parameters can be derived because only six epochs of observations are available. Bodensteiner et al. (2021) noted that no secondary star can be discerned in the spectrum, implying the companion is significantly fainter than the primary star. An SB2 system consisting of an O star and a B star The MUSE data of NGC 330 revealed that there are only two O-type stars in the cluster core, which both show emission lines in their spectra (Bodensteiner et al. 2020). One of the two, namely # 119, was identified as SB2 system by Bodensteiner et al. (2021). In addition to He ii absorption lines, which were the basis of the classification as an O star, the spectra of # 119 show line-profile variations that are indicative of the presence of a companion star. In order to contribute enough flux to the composite spectrum to be discernible, the companion must be an early-type B star.

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Fig. 5.10 RV curve of the binary candidate # 729 or Cl* NGC 330 ARP 35, derived from the MUSE data. The RVs measured at each epoch are marked with turquoise crosses while the average SMC velocity (Patrick et al. 2020) is indicated by the orange line

Furthermore, the Hα-line of # 119 is filled in with emission, which might indicate the presence of an accretion disk around one of the two stars, or of a circumbinary disk. As indicated in Fig. 5.12, # 119 is located above the cluster turnoff of NGC 330, in a region that is populated by BiPs, mainly mergers and currently interacting systems (Wang et al. 2020). Given the observational characterization as O+B binary system, possibly with an accretion disk, # 119 is most likely not the product of a merger but could be a currently interacting binary system. Additional observations are required to further constrain the nature of # 119. A binary system in a peculiar place in the CMD One of the faintest stars considered in Bodensteiner et al. (2020) was detected to be a binary system based on its RV variations. The star # 604, indicated by a yellow diamond in Fig. 5.12 is in a peculiar position in the CMD. The color of ∼−1.6 derived from HST photometry implies that it is significantly bluer, and most likely hotter, than the stars on the MS. The spectral type derived by Bodensteiner et al. (2020) of B5 V, however, implies that the star is not particularly hot. Apart from indicating that the system is a binary, the RV analysis implied that the average RV of # 604 is 58 ± 8 km s−1 . This is roughly 100 km s−1 off the average RV of the SMC (which is 153.7 ± 1km s−1 , see e.g., Patrick et al. 2020). This might imply that # 604 is a foreground star that is not spatially related to NGC 330. The peculiar position in the CMD could, however, also be explained by a binary system consisting of a normal B-type star and a hot, envelope-stripped companion (e.g., Götberg et al. 2018). Such a companion would contribute significantly to the UV flux of the system, therefore impacting the F336W magnitude, but not be discernible in the optical spectrum. Again, further observations are required to constrain the nature of this system. In particular, knowledge about the proper motion of the system would allow to further assess whether # 604 is a cluster member or not.

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5.6 Comparison to Previous Observational Studies In the following, the findings for NGC 330 will be compared to previous works. This includes a comparison to stars in the outskirts of NGC 330, as well as to other multi-epoch spectroscopic studies of B-type stars at different ages and metallicities.

5.6.1 Cluster Core Versus Outskirts As discussed in Sect. 5.3, NGC 330 was previously studied both photometrically and spectroscopically. While photometry of the inner regions is available (Milone et al. 2018), previous instrumentation did not allow to spectroscopically resolve the dense cluster core (Grebel et al. 1996; Evans et al. 2006; Martayan et al. 2007a). This implies that only a handful of stars included in the sample of Bodensteiner et al. (2020) were previously studied with spectroscopy. A comparison of the spectral types derived for those few stars indicates that they are overall similar, validating the methods used in the different works. Evans et al. (2006) used the VLT/FLAMES multi-object spectrograph to study almost 500 stars in two SMC and two LMC clusters, including approximately 120 stars in NGC 330. Based on multi-epoch spectroscopy, they characterized the stars in terms of their spectral types and measured RVs to assess binarity. Figure 5.1 indicates that most of the stars investigated by Evans et al. (2006) are located in the outskirts of NGC 330 (only eight starsa are within the MUSE FoV). Comparing the findings of Evans et al. (2006) to the ones of Bodensteiner et al. (2020, 2021) thus provides a comparison of the cluster core with the outskirts of the cluster. The spectral type distributions derived in the two studies is shown in Fig. 5.11. To enable the comparison, the MUSE sample is restricted in brightness to follow the magnitude cut of V < 17 mag of Evans et al. (2006), reducing it to 22 MS stars. The comparison of the spectral type distribution shows that significantly more early-type stars are located in the outskirts of NGC 330. In particular, while there are only two O-type stars in the core (i.e., one O9 Ve star, and one O9-B0 Ve) star, several O stars and a large number of B0 and B1 stars are found in the outskirts. Given that the stars in common between the two studies have similar spectral types, it is unlikely that a systematic difference in spectral typing is causing this shift. As the MUSE data continuously cover the central region, it is further unlikely that an O-type star in the core could have been missed. This is reinforced by the clear spectroscopic delimitation of O-type stars based on He ii absorption. Taken at face value, this indicates that the stars in the outskirts are more massive than in the ones in the core, which might imply that the outskirt population is younger than the central one. Figure 5.11 further indicates that there are more Be stars in the core than in the outskirts. While, with the restricted sample, the Be star fraction in the core is f Be,core = 46 ± 10 %, the Be star fraction detected by Evans et al. (2006) in the

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Fig. 5.11 Comparison of the spectral type distribution of the core and the outskirts. As in previous Figures, the B stars are shown in yellow while the Be stars are shown in green. The outskirt population studied by Evans et al. (2006) is shown in light colors while the one presented in Bodensteiner et al. (2020), restricted to stars brighter than is m V = 17 mag, is shown in bright colors. This figure was originally published by Bodensteiner et al. (2020), their Fig. 18. Reproduced with permission from ©ESO

outskirts is f Be,outskirts = 23 ± 4 %, implying that fraction of Be star is significantly higher in the core than in the outskirts. Interpreting Be stars as binary interaction products, this might indicate that there are more BiPs in the core of the cluster, which would indicate that binary interactions occur predominantly in the central regions of the cluster. A further difference between the core and the outskirts is the observed binary fraction. While Bodensteiner et al. (2021) find a binary fraction of f bin,V 10 000M ) are known (cf. Portegies Zwart et al. 2010). As discussed above, galactic clusters are typically less massive and contain only few massive stars. In the SMC, there are only two such massive clusters known, NGC 346 and NGC 330. The LMC, on the other hand, provides a

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Fig. 6.2 Overview of massive young clusters in the Milky Way, the LMC and the SMC, where the approximate ages are taken from Portegies Zwart et al. (2010). The color of the frame around each cluster indicates whether observational data is readily available (green, either with HERMES for Northern Galactic clusters, or with FLAMES for Southern Galactic and LMC clusters), or whether observations are planned or requested (orange, mainly with the MUSE instrument at the VLT)

rich cluster population that allows to probe large samples of massive stars at different cluster ages. Such clusters include 30 Dor, NGC 2100, NGC 2004, NGC 1847, NGC 1818, and NGC 2214 (see Fig. 6.2). Given the distance of the LMC and the high density of stars in the cluster cores, previous spectrosocpic studies have mainly focused on the RSG population as well as on the outskirts of the clusters. Since VLT-MUSE was equipped with adaptive optics, however, the cluster cores can be resolved spectroscopically for the first time with a ground-based telescope. These clusters are therefore ideal targets to investigate not only the Be star fraction as a function of cluster age, at a given metallicity, but also the occurrence and properties of binary interaction products as a whole. Ultimately it would be interesting to extend the search for massive binary interaction products not only to clusters of different ages, but also covering the different metallicity environments that we can currently resolve spectroscopically. A direct comparison of the occurrence and properties of binary interaction products in clusters (of the same age) in the Milky Way, the SMC and the LMC will allow to investigate if the metallicity of the host cluster (or galaxy) has a strong effect on binary interactions. To mention one possible example: weaker winds in lower metallicity environments lead to a less severe spin-down of rapid rotators which would lead to more rapidly rotating binary interaction products at lower metallicity. Once we have established this knowledge for the currently observable metallicity environments, it can be extrapolated to environments with an even lower metallicity, and eventually maybe even for the metallicity environment of the first stars.

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6 Summary and Future Work

Figure 6.2 provides a comprehensive overview of young and intermediate-age massive star clusters (i.e., below 45 Myr in age) in the Milky Way, the SMC and the LMC covering different ages. Their homogeneous analysis would allow to directly confront population synthesis predictions and therefore help to shed important new light on binary interaction physics and their outcome.

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Index

A Angular momentum transport, 5, 7, 10, 15, 20, 51, 64, 119

Hertzsprung-Russell diagram, 2, 6, 8, 78 HR 6819, 21, 60, 63, 118, 119 Hubble Space Telescope, 8, 86, 87, 90, 112

B Be X-Ray binary, 21, 60, 101, 102 Bias correction, 56, 97, 98, 107, 110 Binary interaction, 10, 52, 75, 84, 86, 113 binary action product, 56, 59, 84, 90, 113, 117, 122 binary interaction product, 64, 75, 83 mass transfer, 12, 60, 78, 80, 84 stripped star, 10, 17, 52, 60, 63, 75, 78, 84, 117, 118, 122 Binary system SB1, 16, 41, 93, 98, 118 SB2, 21, 41, 57, 94, 98, 103, 118 Black hole, 1, 4, 16, 21, 53, 63, 64, 122 Blue supergiant, 4, 89, 102, 118

L Large Magellanic Cloud, 11, 81, 106, 125 LB-1, 21, 60, 65, 67, 80, 119

C Classical Be star, 17, 51, 63, 85, 89, 92, 105, 112, 117 Color-magnitude diagram, 8, 14, 90, 100, 108, 109 F FEROS, 34, 44, 66, 118 FLAMES, 86, 104, 118 H HERMES, 34, 44, 73, 124

M Main sequence, 2, 51, 52, 64, 78, 118, 121 Milky Way, 18, 53, 65, 86, 106, 125 MUSE, 35, 38, 76, 86, 112, 119

N Neutron star, 4, 53, 122 NGC 330, 8, 37, 39, 40, 81, 118 Nuclear fusion, 2, 78 CNO cycle, 3, 15, 72 triple-α process, 4

R Radial velocity, 22, 34, 40, 42, 56, 57, 69, 72, 93 Red supergiant, 4, 89, 118 Roche-lobe overflow, 10, 12, 15, 21, 77

S Small Magellanic Cloud, 8, 18, 37, 81, 85, 106, 125 Star cluster, 1, 8, 11, 14, 20, 22, 81, 122, 125

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2022 J. Bodensteiner, Observational Imprints of Binary Evolution on B- and Be-star Populations, Springer Theses, https://doi.org/10.1007/978-3-031-19489-4

127

128 blue straggler, 13, 14, 84, 90, 108, 113, 120 cluster turnoff, 8, 20, 64, 90, 92, 100, 108, 118, 123 Stellar rotation, 6, 33, 42, 51, 63, 73, 86, 122 Stellar wind, 6, 41, 46, 125

Index Subdwarf O/B star, 17, 21, 53, 64, 78, 117 Supernova, 4, 60, 68, 120

V VLT, 35, 76, 86, 87, 120