Variability of the Sun and Sun-like Stars: from Asteroseismology to Space Weather 9782759821969, 9782759821952

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Variability of the Sun and Sun-like Stars: from Asteroseismology to Space Weather J.-P. Rozelot and E.S. Babayev, Eds

Printed in France ISBN(print): 978-2-7598-2195-2 – ISBN(ebook): 978-2-7598-2196-9 All rights relative to translation, adaptation and reproduction by any means whatsoever are reserved, worldwide. In accordance with the terms of paragraphs 2 and 3 of Article 41 of the French Act dated March 11, 1957, “copies or reproductions reserved strictly for private use and not intended for collective use” and, on the other hand, analyses and short quotations for example or illustrative purposes, are allowed. Otherwise, “any representation or reproduction – whether in full or in part – without the consent of the author or of his successors or assigns, is unlawful” (Article 40, paragraph 1). Any representation or reproduction, by any means whatsoever, will therefore be deemed an infringement of copyright punishable under Articles 425 and following of the French Penal Code. © EDP Sciences, 2018

Preface The topical issue of “Variability of the Sun and Sun-Like Stars: From Asteroseismology to Space Weather” is based on contributions presented at the first International Conference on Solar Physics which was organized in Baku, Azerbaijan in July 06–08, 2015. The primary goals were to highlight all aspects of modern solar physics research, including observation and theory that span from the interior of the Sun out into the wider heliosphere, as well as solar-terrestrial physics and particularly, sun-like stars. Around 120 people were gathered in Baku (both from domestic and abroad) to share the findings of their research in solar and solar-terrestrial physics. All international scientists appreciated to live a while in this beautiful capital and largest city of Azerbaijan, housing many scientific and cultural headquarters, including the Science Development Foundation under the President of the Republic of Azerbaijan. This foundation hosted and financed the Conference, for which one of the sessions has been held at the Shamakhy Astrophysical Observatory of the Azerbaijan National Academy of Sciences, a delightful place in the Caucasian mountains. This book does not cover all issues addressed in the Conference but tackled some of them to pinpoint the best of international research in the field of the Solar Variability and Space Weather. It is clear today that the Sun is a variable star. However, we are still far from fully understanding what and how causes this variability. Why does the Sun continue to go on, on a rhythmic scale, the so-called solar cycle, without damping? How to better understand the complicated relationships between the Sun, the heliosphere and the many proxies of long-term solar activity? How the data could be fully exploited for a better understanding of solar changes on the longest possible time scales? How our knowledge on the Sun can be transferred to other stars? These questions shape the architecture of the book. •• The first seven chapters in Section 1 “Solar Physics” focus on the Physics of the Sun. In the recent years helioseismology provided us with important information about the interior of the Sun. After recalling briefly the principles of helioseismology, Chapter 1 by S. Ehgamberdiev describes the scientific results obtained at the Ulugh Beg Astronomical Institute (UBAI) in the framework of an International Research on the Interior of the Sun. In a comprehensive review, A. Kosovichev et al. study in Chapter 2 the development of local helioseismology which provides a unique opportunity to investigate the subsurface structure and dynamics of active regions and their effect on the largescale flows and global circulation of the Sun. The two next Chapters (3 and 4) by Alan

II Preface

A. Wray et al. and I. Kitashvili focus on realistic numerical simulations, i.e., those that make minimal use of ad hoc modeling, which are essential for understanding the complex turbulent dynamics of the interiors and atmospheres of the Sun (and other stars) and the basic mechanisms of their magnetic activity and variability. Chapter 5 is a general up-to date history of the measurements of the solar diameter viewed from a critical quality assessment of the existing data. From an astrophysical point of view, this topic is closely link with the study of the solar Near Sub-Surface Layer (NSSL or “leptocline”) and therefore directly understood through mechanisms explained in Chapter 2. In the scope of the study of the solar cyclicity characteristics, V.N. Ishkov develops in Chapter 6 statistics leading to different scenarios of the regular changes of magnetic field in the solar convection zone generation regime, in accordance with the epoch of low or high activity. Lastly, Chapter 7 in this Section, by N.S. Dzhalilov, focuses on the wave instabilities in an anisotropic magnetized space plasma whose results are of importance for the description of wave processes in the solar corona and solar wind. Thus, this Chapter constitutes a good transition with Section (3) dedicated to space weather. •• The next Section 2 is devoted to “recent developments from helioseismology to asteroseismology” and are presented by J. ChristensenDalsgaard. Transposing the results obtained from helioseismology to asteroseismology has already been very profitable. In the last decade extensive observations of stellar oscillations, in particular from space photometry, have provided very detailed information about the global and internal properties of stars. As explained in this Chapter 8, remarkable insight has been obtained on the properties of evolved stars, and many new results are expected in the near future. •• Section 3 is dedicated to peculiar aspects of “Space Weather”. This concept was launched some 15 years ago to describe the short-term variations in the different forms of solar activity, and their effects in the near-Earth environment and technoculture. The ultimate goal is to get a better understanding of the full chain of effects from the Sun to the Earth. Here the focus is put on the influence of cosmic rays. In Chapter 9 by L. Dorman and E.S.Babayev, the authors deal with the issue of whether there is an appropriate role of Cosmic Rays on Satellites Operation, Technologies, Biosphere and People Health. By contrast, L. Dorman et al. focus in Chapter 10 on how to forecast exactly dangerous phenomena from space on the Earth’s civilization and propose steps for founding a cosmic ray warning system. Chapter 11 is dedicated to Space Weather effects on human health. S. Dimitrova and E.S.Babayev reviews here collaborative investigations performed at middle Earth latitudes and at different geographical



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places in order to study the potential effects of space weather on human physiological and psycho-physiological state and acute cardio-vascular incidences. •• Section 4 develops some “Impacts of the Sun on Earth climatology”, and is divided in three chapters. The first one (Chapter 12) by L. Dorman examines the Cosmic Rays and other Space Phenomena that influenced the Earth’s Climate and evidence inter alia that very big changes in climate could have been caused by some rarely phenomena as impacts of asteroids and nearby supernova explosions. Discussing issues on forecasting global climate change that could be important for saving present civilization from great climate catastrophes introduce Chapter 13. This Chapter by J.P. Rozelot and Z. Fazel explores the effects of drastic climate change on society vulnerabilities, such as the collapse of the Akkadian Empire, those of the Classical Mayan civilization or the Greenland colonies, to revisit the linked questions of the history of solar output, the history of the Earth’s climate and the history of past disasters. Lastly Chapter 14 by V. A. Dergachev focuses on the Influence of orbital forcing and solar activity on climate change in the past. In considering the question on the evolution of global surface temperature during the Holocene, it is addressed that the models have tendencies to suppress the variabilities of regional level fixed in the data from natural archives. The audience targeted by this book consists of researchers, PhD students, postdocs, and also all scientists seeking a complementary culture or evolving toward new research topics. The editors sincerely thanks the authors for the great quality of the lectures given in Baku and of the resulting papers published here. They hope that this Book will help to a better knowledge of our Star. J.-P. ROZELOT Université de la Cöte d’Azur (F) 77, Ch. Des Basses Moulières F-06130 Grasse, France E.S. BABAYEV Science Development Foundation under the President of the Republic of ­Azerbaijan AZ-1025, Yusif Safarov street-27, Baku, Azerbaijan

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Science Development Foundation under the President of the Republic of Azerbaijan SDF (Science Development Foundation under the President of the Republic of Azerbaijan), is a government non-profit organization, established in October 2009 within the National Strategy on Development of Science in Azerbaijan. SDF supports scientists and specialists from academic, education, ministerial, NGO structures, as well as employed and unemployed physical scientists/persons through research grants. Types of grant competitions are: so called “Classic Annual grant competition” covering all of branches and directions of science; Young scientists and specialists’ grant competition, up to 35 years old; “Shusha grant” competition, covering Karabakh studies; “Mobility grant” competition, full support of participation at scientific conferences and short-term trainings abroad; targeted grant competitions such as ICT, Industry grant, Science-Education Integration grant, University grant competitions, so on. Types of projects supported by SDF are: Fundamental; Applied; Innovative; Mega projects (more than 500 000 manats up to several millions and up to 500 000 manats) – so called “pilot projects” and “complex multidisciplinary program projects” aimed in equipping of scientific organizations with super-modern scientific devices, equipment etc. and creating new labs, as well as preparation and training staff abroad to work with these technologies; Material-technical support (scientific devices, equipment etc.) of labs, researchers; Support of publishing of monographs, books, atlases etc.; Support of organization of scientific conferences in Azerbaijan; support of participation at scientific conferences abroad; support of participation at short-term trainings abroad. International collaboration: HORIZON-2020 (BSH and EaP PLUS), BS ERA-NET; BSEC, UNECE; UNESCO; CNRS (France); Belarusian Republican Foundation of Basic Studies; Russian Republican Foundation of Basic Studies, TUBITAK (Turkey), Georgian Shota Rustaveli National Science Foundation, Kyiv National Technical University, Ukraine; “Science Foundation”, Kazakhstan; US “Karabakh Foundation”; Elsevier; Thosmson Reuters; Springer, etc. Advantages are: scientific priorities are changed for each year taking into account trends in world science and collaboration; All branches and directions of science are covered; Preparation of young professionals through trainings abroad; No limitation to scientific degree and title – only scientific content is major merit; Non dependence on sex, nationality and age; Grant budget directly goes to project leader’s bank account; they get additional salaries, they have ability to travel (business trips), to get ICT facilities, special scientific equipment, so on; SDF buys (dealing with custom, tax and other authorities itself saving time for scientists) and supplies all of scientific devices, equipment, materials directly to scientists; SDF prefers so called “temporary scientific collectives” at grant project application which brings scientists from different organizations (academic, university, NGO, so on) together and stimulate their collaboration; Special weekly tutorial seminars, including those of outside Baku (capital city), how to prepare applications. SDF each year organizes different international and domestic conferences, seminars, trainings, so on.

Table of contents Preface Jean-Pierre Rozelot and Elchin S. Babayev

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Section 1. Solar Physics Helioseismology in Uzbekistan: past and present Shuhrat Ehgamberdiev

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Local Helioseismology of Emerging Active Region: A Case Study Alexander G. Kosovichev, Junwei Zhao and Stathis Ilonidis

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Realistic Simulations of Stellar Radiative MHD Alan A. Wray, Khalil Bensassiy, Irina N. Kitiashvili, Nagi N. Mansour and Alexander G. Kosovichev

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Advances in Realistic MHD Simulations of the Sun and Stars Irina N. Kitiashvili

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A brief history of the solar diameter measurements: a critical quality ­assessment of the existing data Jean-Pierre Rozelot, Alexander G. Kosovichev and Ali Kilcik

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Solar sunspot-forming activity and its development on the reliable Wolf numbers series Vitaliy N. Ishkov

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Wave instabilities in an anisotropic magnetized space plasma Namig S. Dzhalilov

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Section 2. From Helioseismology to Asteroseismology Asteroseismology with solar-like oscillations J¿rgen Christensen-Dalsgaard

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Table of contents

Section 3. Cosmic rays and space weather Cosmic Rays and other Space Weather Phenomena Influenced on Satellites Operation, Technologies, Biosphere and People Health Lev Dorman and Elchin S. Babayev

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Cosmic Rays and other Space Phenomena Dangerous for the Earth's Civilization: Beginning Steps for Founding Cosmic Ray Warning System Lev Dorman, Elchin S. Babayev, Uri Dai, Fatima Keshtova, Lev Pustil’nik, Abraham Sternlieb and Igor Zukerman

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Space Weather Effects on Human Health Svetla Dimitrova and Elchin S. Babayev

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Section 4. Impact of the Sun on Earth climatology Cosmic Rays and other Space Phenomena Influenced on the Earth's Climate Lev Dorman

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Does climatic changes could have destroyed great civilizations? Jean-Pierre Rozelot and Zahra Fazel

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Influence of orbital forcing and solar activity on climate change in the past Valentin A. Dergachev

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Helioseismology in Uzbekistan: past and present Shuhrat Ehgamberdiev Ulugh Beg Astronomical Institute, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan E-mail: [email protected] Abstract. Ulugh Beg Astronomical Institute (UBAI) was involved in the (International Research on the Interior of the Sun) helioseismology project since the middle of 80s. The IRIS project is aimed at studying the deep interior of the Sun using a spectral line Doppler shift measurements integrated over the whole solar disk. For obtaining long, uninterrupted by day and night periodicity observational data a network of six stations almost regularly distributed around the globe and equipped with identical spectrophotometers was deployed. One of the IRIS network instruments was installed at Kumbel summit in Uzbekistan in 1988. Since 1996 UBAI has been involved in (Taiwan Oscillation Network) project aimed on helioseismic studies of subsurface structure of the Sun and its dynamics. The participation of UBAI in both projects was crucial not only for obtaining long term observational data, but in all processes of scientific analyses and publication of scientific papers. Many scientific results have come out from these two projects, but it is also important that many Ph.D. students have passed their dissertations and are still actively working in different astrophysical projects.

1

Introduction

After the discovery of the solar five-minute oscillations in the early sixties (Leighton et al. (1962)), it had taken about one decade before a clear understanding of this surface phenomenon as being the visible part of seismic waves penetrating in the interior of the Sun (Ulrich (1970) and Leibacher & Stein (1971)). Helioseismology as an efficient method of probing the interior structure and dynamics of the Sun started then to develop in the early 70s. Nearly 10 million of resonant modes of oscillation are observable at the solar surface. The response of the solar surface to the superposition of all seismic waves resembles motions at the surface of an ocean. The detection of these modes is a quite a challenging task, since the velocity amplitude of a typical acoustic mode (p-mode) is of the order of 1 cm/sec, with an associated intensity variation of about 10−7 . Such minute oscillations can be detected by measuring either the Doppler shifts of a spectral line or the intensity variation of the optical radiation. The main task of the observational helioseismology is the determination of the individual p-modes frequencies and their other parameters. The measurements must be made continuously over a long period of time in order to determine oscillation frequencies with the extremely high precision necessary for making useful inferences about the solar interior. Observational time series should be as much uninterrupted as possible, because gaps in the data produce spurious

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peaks (sidelobes) in the oscillation power spectrum, which hinder subsequent analyses. The first attempt to obtain uninterrupted observations was taken by Nice team at the Geographical South Pole during austral summer of 1979/1980 (Grec at al. (1980), Grec at al. (1980)). The 6-day nearly continuous observations allowed for the first time to resolve individual peaks in the solar oscillation power spectrum. For this pioneering work Eric Fossat, Gerard Grec and Martin Pomerantz were awarded a Gold medal by the Royal Academy of Belgium. Shortly later it was realized that the atmospheric conditions at South Pole would not allow obtaining observation longer than about one week in duration. However, in order to resolve multiple structure of an individual peak, uninterrupted observations as long as a few months were required. This fact explains why all observing programs developed in 80s aimed at obtaining continuous observations over periods of months, and even years for also tracking the variation of all helioseismic parameters along the solar cycle. Three main ideas have been used for obtaining continuous observation on time longer than the typical 8-12-hour daily run possible in any mid-latitude single site. The first one was to go to Antarctica, were, as mentioned above, atmospheric sky conditions allow to obtain uninterrupted time series as long as one week. Another possibility is to detect solar oscillations from space. An instrument suitably located in a full sunshine orbit could provide uninterrupted observations over period as long as the lifetime of a spacecraft mission. The third idea consisted in deploying a network of observing sites around the globe, suitably located on complementary longitudes and latitudes. In 1982 the IAU Commission 12 voted for a resolution ”recognizing the extreme importance of the observation of solar seismology” and ”strongly supporting international cooperation in establishing a worldwide network of observing stations”. The team of the Laboratoire d’Astrophysique of the University of Nice presented a IRIS project to the French astronomical agency - INSU in 1983 and it was funded since 1984. As the core instrument of the project, a sodium cell spectrophotometer providing full-disk Doppler shift measurements (Grec et al. (1983)) of the sodium D1 line was suggested. These instruments were planned to be installed at 6 complementary sites. The first instrument of the IRIS network was installed in 1988 on the remote mountaintop site of Kumbel, Uzbekistan. The IRIS network was further deployed at the rate of one site per year, until 1994 when its sixth instrument was commissioned at Culgoora, Australia. In fact, the first data was acquired in July 1989, with the only Kumbel site at the time, but it was immediately complemented by a summer campaign of a prototype MOF instrument designed by A. Cacciani and operated at JPL, California. Thus the first day of the data acquisition was already the beginning of a two-site network observation. The IRIS project headquarters were at University of Nice, France. Fig. 1 shows the worldwide IRIS network. Here it is necessary to mention that observations made with the IRIS instrument were spatially unresolved, combining light from the entire visible surface of the Sun (i.e. observing the Sun as a star), which limited the detectability to only those modes of oscillation whose wave-



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Fig. 1. The worldwide IRIS and TON networks. Those shown by red are stations of the other full-disk helioseismology projects whose data were merged with the IRIS data. See text for details. The network of asteroseismological TAT (Taiwan Automated Telescope) project is also shown.

lengths are comparable with the diameter of the Sun and hence can penetrate down to the solar core. P -modes registered with spatial resolution provide information on subsurface structure of the Sun (see paragraphs on TON project). Reviews of 11 years of the IRIS project activity have been presented in Fossat et al. (2002) and Fossat (2013). The present paper is mostly focused on the participation of the Uzbekistan team in the IRIS project.

2

The IRIS station at Kumbel mountain

Within the distribution of the northern hemisphere sites selected for the worldwide IRIS network, one instrument had had to be installed somewhere in the Central Asia. On the basis of analysis of meteorological data and after visual inspection of several preselected sites, it was finally decided to install an instrument on top of the Kumbel mountain, located at the distance of 75 km in North-East direction from Tashkent downtown and at the altitude 2300 m above sea level (Baijumanov et al. (1991)). Since Kumbel was an isolated remote mountain place, in contrast to other stations of the network it was necessary to build not only a shelter for the instrument, but also a pavilion of living facilities for observers. All this construction work was done during the summer of 1988 and the ”first light” at Kumbel was recorded in August, 1988. Fig. 2 shows the Kumbel station and the IRIS instrument installed there. During its 11 years of operation (one full solar cycle) the Kumbel station alone provided the IRIS data bank with more than 40% of the total observational data. Here we have to mention that before scientific analyses of the observational data, there was a long process of selection, characterization and calibration in

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Fig. 2. View of the Kumbel station and IRIS instrument installed there in 1988.

m/s of the velocity signal due to the solar oscillations. A first version of a software package which takes into account Doppler shifts caused by all known astronomical motions contributing to the line-of-sight velocity between the instrument and the solar surface was developed in Tashkent (Ehgamberdiev et al. (1991)). It also took into account the apparent residual velocity generated by the non-uniform integration of the solar rotation in stratified Earth atmosphere (Ehgamberdiev & Khamitov (1991)). During the Second IRIS workshop, Sh. Ehgamberdiev was elected as the Chairman of the Raw data calibration software team. The team members were: Bernard Gelly (Nice), Pere Palle (Tenerife), Shukur Kholikov (Tashkent), Eric Fossat (Nice), Luis Sanchez (Tenerife). The main duty of the team was to produce a complete software package, which would make the selection and the calibration of data in order to obtaining for each day and each site a velocity versus time signal. Data obtained in each station of the IRIS network had to be subject to this procedure before merging them into the resulting single data string. Fig. 3 illustrates two daily data records obtained at Kumbel and Oukaimeden stations on July 26th, 1989 after applying the calibration subroutine. The high coincidence of records (see, for example, the splash around 9.8hU T ) obtained at two sites separated by about 5 hours in longitude demonstrates the high sensitivity of the IRIS spectrophotometer to detect such a tiny signal of the solar oscillation, and the efficiency of the calibration software developed in Tashkent.

3

Data analyses and interpretation

In this section we present the data analyses process and most valuable results obtained in frame of IRIS project. 3.1

One single site data analyses

Usually an ”IRIS day” begun at Kumbel where observations were started around 1h U T . During first two years of operation of the Kumbel instrument since July 1989 there were collected many high quality daily data. However there was not



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Fig. 3. Two merged during 7.5 hours daily records of the solar oscillation obtained on 26th July of 1989 at Kumbel (black line) and Oukaimeden (red line) stations located 5 hours apart in longitude. It first demonstrates the high sensitivity of the IRIS spectrophotometer to detect minute signal of the solar oscillation, and second the efficiency of the calibration software developed in Tashkent.

possibility of compiling long duration network data, because at that time the network was not completely deployed yet. Other reason was an absence of appropriate data merging procedure. It was developed later (Fossat et al. (1992)). In such situation our curiosity to learn something about physics of the p-modes could be satisfied only with analyses of a single site data. One day of observations in one site lasts typically from 10 to 11 hours and thus provides a daily power spectrum with a frequency resolution of the order of 25 to 30µHz. This is not enough to resolve individual peaks, but it was enough to show the discrete nature of the power spectra. Peaks in daily power spectra imply 4 or 6 unresolved individual p-modes. Despite of not optimistic view of some theorists regarding this approach, two important scientific results were extracted from low resolution daily power spectra. For the study of the statistical properties of p-modes 99 days of data obtained at Kumbel station alone were used. Comparison of different daily power spectra showed that the strength of peaks looked differently from very low value to high. However, it was not by itself an indication of a temporal amplitude modulation of p-modes. Within certain assumption on the partial amplitude interdependence and individual p-mode phase independence the amplitude modulation rate was estimated to be about 25% ((Ehgamberdiev et al. 1992)). This result appears to be inconsistent with the more or less generally accepted theory of the interaction between oscillation and stochastic turbulent convection. Meanwhile, theories on the physical mechanism

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invoked for the p-mode excitation had to satisfy this new constraint, added to the facts that it must explain the p-mode energies, their frequency range and line-widths. Theorists from the Liege University (Belgium) dedicated a special research to the interpretation of this interesting observational result (Gabriel & Lazrek (1994)). Another result obtained with a single site data analyses was dedicated to the measurement of the acoustic cut-off frequency. Solar acoustic p-modes are trapped inside cavities in the interior of the Sun, were they are reflected back and forth between lower and upper boundaries of the cavity. Near the solar surface, the reflection occurs due to rapid changes of density and sound speed. Reflection take place only for waves with frequencies less than a critical one, commonly called the acoustic cut-off frequency. Acoustic waves with frequencies higher than cut-off frequency can propagate through the solar atmosphere. Average power spectrum of 309 days of observations made at the IRIS stations Kumbel, Oukaimeden, Izana and La Silla was used for analyses. Value of the acoustic cut-off frequency 5.55 ± 0.1mHz obtained using these observational data appears to be higher than any theoretical prediction ever made. A surprisingly precise measurement of the acoustic cut-off frequency of the solar atmosphere proved that heslioseismology is not necessarily limited to the deep interior. Using IRIS network data obtained in 1989-1996 we attempted to find any evidence of solar cycle change in the values of acoustic cut-off frequency of the solar low- p-modes. Applying three different methods of analysis we found of evidence that cut-off frequency is changing. Namely it is reduced from maximum to minimum of solar activity being equal to 5.77 ± 0.02mHz at maximum and 5.37 ± 0.04mHz at minimum of solar activity (Serebryanskiy et al. (1998)). The good quality of the IRIS data at high frequencies above this cut-off made possible to give to solar physicists an answer to an old question about the heating of the chromosphere. The acoustic power density that exists between the cut-off frequency and the frequency after which it becomes flat (photon noise) can be used to estimate the amount of acoustic energy flux that dissipate in the chromosphere. Estimated value of that energy (∼ 107 erg/cm2 /s) appeared to be just enough to compensate for the energy losses in the chromosphere (Athay (1970)). 3.2

The Sun as an instrument producing a repetitive music

In ideal case all helioseismology projects aim at obtaining the best temporal coverage of data as close as possible to 24 hours a day and 365 days per year. This is mainly for the sake of avoiding the presence of ”sidelobes” in the Fourier spectra. These sidelobes, or artificial secondary peaks interfere with other real peaks, thus making accurate p-mode parameters measurements difficult. However, the ultimate goal of 100 percent duty cycle (percentage of filling with data) has been never achieved by any kind of observing programs, so that the analyst is always facing the presence of gaps in the time series subject to Fourier analysis. The network duty cycle reached better than 60 percent only in boreal summers, but was down to much less than 50 percent during the winters due to the bias of the



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Fig. 4. The solar oscillation signal cut in three parts 4,1 hours apart and shown one under another. (The horizontal time span displayed here is one hour).

geographical locations of its stations (4 North against 2 South), and also due to the large longitudinal gap in the Pacific Ocean. Facing this situation, it was decided to develop cooperation between IRIS and scientific groups operating different helioseismic instruments. Merged with the IRIS signal (see Fig. 1) these time series were called IRIS + +. The duty cycle of the IRIS + + data was strikingly improved. But it still remained to be further improved. After testing different deconvolution algorithms, an interesting method of partial gap filling was developed. It should be noted here that the standard mathematical deconvolution technique completely ignore the specific properties of the signal. However taking into account what we know about a signal itself helped us to approach the problem from other perspective trying to predict with high level of confidence the signal which has not been observed (Fossat et al. (1999)). To take an advantage of what we have known about the solar oscillation at the time we turned our attention to the IRIS autocorrelation function. We filtered the signal in the p-mode frequency range from 1.5 to 5mHz and saw that the signal has a very high level of coherence (more than 70 per cent!) after roughly 4 hours. It was interpreted as the solar oscillations are very much like musical songs are almost periodic i.e. repetitive in time, with a quasi periodicity of a little more than 4 hours (Fossat et al. (1999)). This fact is demonstrated by Fig. 4, where a solar oscillation signal cut in three parts 4,1 hours apart and shown one under another. The very high similarity of these signals does not need any additional comments! With this specific feature of the solar oscillation it becomes obvious that simply replacing a gap by the signal collected 4 hours earlier or 4 hours later provides a gap filling method with a confidence level of more than 70 percent. The idea was extremely simple. Doing it in practice was also very simple, and it was demonstrated that p-mode helioseismology is not so demanding of the duty

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cycle. In the most extreme favorable situation, we can imagine a data set with 33 percent duty cycle, 4 hours of data followed by 8 hours of gap, and so on. After this ”repetitive music” gap filling it is hardly possible to distinguish a Fourier peak from the original one. Surprisingly what started as a pure mathematical problem finally acquired a physical meaning. We realized that what we see in the autocorrelation is the evidence for the returning acoustic waves after traveling all the way down to the other side of the Sun through the center and back to the visible surface! Roughly one hour along one radius, and thus 4 hours for the complete return trip. 3.3

Frequency determination from IRIS network and IRIS + + data

The seismic exploitation of helioseismological data requires extremely accurate measurements of the acoustic mode frequencies. With a line-width of the order of 1µHz, a large number of p-mode frequencies can be estimated within an uncertainty of half of their line-widths, i.e. about 10−4 in relative value. Although such accuracy looks impressively good, it appears insufficient when facing the demand of theoretical seismic inversions, which require relative accuracies of about 10−5 for improving the existing models of the Sun. At such a high level of demand, the task becomes tougher. A first attempt of p-mode frequency estimation from the IRIS data obtained during four summer seasons (1989 - 1992) was made by Gelly et al. (1997). Beside IRIS, the data bank included the magneto-optical filter measurements (Cacciani et al (1988)) and the data of the BiSON network potassium instrument in Tenerife (Elsworth et al. (1988)). Even with these additional data sets, the duty cycle did not exceed 50%. The next attempt for estimation of precise frequencies was made by Serebryanskiy et al. (2001) using 7.5 years of IRIS data, from 1989 to the end of 1996. This work included not only the p-mode frequencies, but also their variation along the solar cycle, their line-widths and profile asymmetries. However, the relatively low duty cycle (still less than 50%) was again limiting the results accuracy. After exploiting the ”repetitive music” gap filling method, an extended list of IRIS p-mode frequencies and rotational splitting was published by Fossat et al. (2002). The same year, a list of frequencies and splitting from nearly 2000 days of GOLF data was published by Gelly et al. (2002). Two lists of GOLF frequencies, from low activity and high activity, could be averaged and compared to the IRIS frequencies averaged on the complete solar cycle. The mean difference across all the frequency range was nearly zero (a few nHz). This precise low degree p-modes frequency determination and the subsequent modeling of the internal structure of the core was an important contribution to the resolution of one of the most important task of the solar physics - solar neutrino puzzle. The Sun is a natural nuclear fusion reactor. A proton-proton chain reaction converts four protons into helium nuclei, neutrinos, positrons and energy. The



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excess energy is released as gamma rays, as kinetic energy of the particles and as neutrinos - which travel from the Sun’s core to Earth without any appreciable absorption by the Sun’s outer layers. The measured neutrino flux (an extremely difficult measurement since neutrinos essentially do not interact with anything) was lower than that predicted by models of the solar interior, in the range between one third and one half of the predicted value. This discrepancy between the neutrino flux measurement and its prediction by theoretical models, lasting from the mid-1960s to about 2002, came to be known as the solar neutrino problem. Early attempts to explain this discrepancy proposed that the temperature and pressure in the interior of the Sun could be substantially different from what was computed in solar models. However, these solutions were more and more committed untenable by advances in helioseismology observations, which made it possible to measure the interior temperatures of the Sun, down to the Suns center, with an incredibly high precision, better than 10−3 . Helioseismology and ”cold” solar core were proved to be definitely inconsistent. The discrepancy has since been resolved by new understanding of neutrino physics. Essentially, as neutrinos have mass, they can oscillate changing from one type to another. However Davis’ detector was sensitive to only one type, so that it could not detect all solar neutrinos, but only one fraction of them, between one third and one half! For their pioneering work on the resolution of the solar neutrino problem Raymond Davis Jr. and Masatoshi Koshiba shared the 2002 Nobel Prize in Physics. 3.4

Solar core rotation

The Sun does not rotate as a solid body. The latitudinal differential rotation, easily visible at its surface, has been demonstrated by helioseismology to persist down to the base of the convection zone, at a depth of 0.71R . The rotation of the solar core could be much faster, if the loss of angular momentum by the solar wind during the 4,5 billion years life of the Sun on the Main Sequence has not been efficiently coupled to the very deep and dense layers. The rotation of the upper internal layers down to the base of the convection zone had been determined with amazing precision by imaging helioseismology (Libbrecht (1988)). The deeper layers of the Sun have remained inaccessible until the two main ground-based networks for full disk (i.e. unresolved) helioseismology, IRIS and BISON, were able to have accumulated long enough duration observations providing access to the measurements of the low degree p-modes splitting influenced by the rotation of the solar core. Since 1993, the IRIS group attempted to measure this value ((Loudagh et al. 1993; Fossat et al. 1995)). In 1996 the IRIS group published (Lazrek et al. (1996)) the result of its most reliable analyses based on three time series, each a little longer than 4 months, obtained on the boreal summers of 1990, 1991 and 1992. The unexpectedly low value of the rotational splitting implied a solar core rotation being not faster than the envelope, and even possibly slower. This result was confirmed by the BISON group (Elsworth et al. (1995)), and later by the 11-year data bank of IRIS, as well as by the

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Shuhrat Ehgamberdiev Shuhrat Ehgamberdiev

Fig. 5. The equatorial profile of the solar rotation obtained by M.P. Di Mauro using p-modes frequency splitting measurements from IRIS and MDI data on board of the SOHO spacecraft. Comparison of profiles obtained using low and intermediate modes (blue) and a one obtained using only low-degree (red) modes ( = 1 − 4) shows that the rotation profile along the whole solar radius can be obtained with only the low degree p-modes. That opens exciting perspectives for asteroseismology!

comparison between IRIS and GOLF measurements (Fossat et al. (2002)), that helped to reduce the error bar by one more step. The measurements of the solar core rotation is related to the classical question about interpretation of the Mercurys orbit precession. This problem was first addressed in 1800s. Due to various effects, such as tiny perturbations caused by other planets, the observed precession of the Mercurys orbit is about 532 arcsec/century. A significant part of this value was explained in frame of the Newtonian theory of gravity. The residual 43 arcsec/century, not explainable by Newtonian gravity, was the subject of long discussions. In 1915 Einsteins demonstration that his theory predicts exactly that residual amount was the first evidence in favor of the general relativity theory. If the solar core would rotate about ten times faster than its envelope (as all stellar evolution theories predict), then the Sun should be flattened near its equator spheroid. In this case it cannot be assumed that its gravity field would exactly suit the reverse square law. As soon as the Sun is not an ideal spherical body, then Einsteins theory can explain only a fraction of the residual effect. The IRIS measurements prove that the solar core does not rotate faster than its envelope i.e. with a period about one month. Due to this unprecedented result on the solar core rotation, obtained in frame of the IRIS project, deviations of the Suns gravity field from reverse square law can be neglected.



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Helioseismologyin in Uzbekistan Uzbekistan Helioseismology

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Concluding remarks

IRIS as a worldwide network project with 6 observing stations for full disc helioseismology was initiated by Eric Fossat and Gerard Grec from University of Nice, France, after almost 15 years work experience in the field of solar oscillations study. They have conceived a spectrophotometer detecting Doppler shifts of the sodium D1 line integrated over the whole visible solar disk, thus providing access for the observers to the deep interior of the Sun. The IRIS network provided to scientific community the longest available time series of full solar disk data. Freely available on the CDS data base, the 11 years of data from 1989 to 2000 cover a complete solar cycle, from the maximum of the cycle 22 to the maximum of the cycle 23.

Acknowledgment Author thanks the Science Development Foundation under the President of the Republic of Azerbaijan for providing financial support to attend Baku Solar conference in 2015.

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Bibliography Athay, R. G. 1970, ApJ, 161, 713 Baijumanov, A., Ehgamberdiev, Sh., Fossat, E., Grec, G., Ilyasov, S., Kamaldinov, A., Khalikov, Sh., Khamitov, I., Manigault, J. F., Menshikov, G., Raubaev, S. & Yuldashbaev, T. 1991, Solar Physics, 133, 51 Cacciani, A., Rosati, P., Ricci, D., Marquedant, R. & Smith, E. 1988, In: Seismology of the Sun and Sun-like stars, Ed. E.J.Rolf, Paris, ESA SP-286, 181 Di Mauro, M. P., Dziembowski, W. A., Paterno, L., 1998, Structure and Dynamics of the Interior of the Sun and Sun-like Stars SOHO 6/GONG 98 Workshop Abstract, June 1-4, Boston, Massachusetts, p. 759. Ehgamberdiev, Sh., Khalikov, Sh. & Fossat 1991, Solar Physics, 133, 69 Ehgamberdiev, Sh. A., Khamitov, I. M. 1991, Solar Physics, 133, 81 Ehgamberdiev, Sh., Khalikov, S., Lazrek, M., Fossat, E. 1992, A&A, 253, 252. Elsworth, Y. P., Isaak, G. R., Jefferies, S. M., McLeod, C. P., New, R., van der Raay, H. B., Palle, P., Regulo, C. & Roca Cortes, T. 1988, In: Advances in Helio- and Asteroseismology, IAU Symp. No 123, Eds. Christensen-Dalsgaard and S.Frandsen, Dordrecht: Reidel, 535 Elsworth, Y., Howe, R., Isaak, G. R., McLeod, C. P., Miller, B. A., Wheeler, S. J. & Dough, D. O. 1995, Nature, 376, Issue 6542, 669 Fossat, E., Regulo, C., Roca Cortes, T., Ehgamberdiev, S., Gelly, B., Grec, G., Khalikov, S., Khamitov, I., Lazrek, M., Palle, P. L., Sanchez Duarte, L. 1992, A&A, 266, 532 Fossat, E., Lazrek, M., Loudach, S., Pantel, A., Gelly, G., Grec, G., Schmider, F. X., Palle, P., Regulo, C., Ehgamberdiev, Sh., Khalikov, Sh. & Hoeksema, J. T., 1995, Proceedings ot the 4th SOHO Workshop: Helioseismology, Asilomar Conference Center, Pacific Grove, California, USA, 2-6 April, 64 Fossat, E., Kholikov, Sh., Gelly, B., Schmider, F. X., Fierry-Fraillon, D., Grec, G., Palle, P., Cacciani, A., Ehgamberdiev, Sh., Hoeksema, J. T. & Lazrek, M. 1999, A&A, 343, 608 Fossat, E. & the IRIS team 2002, SF2A-2002: Semaine de ’l Astrophysique Francaise, meeting held in Paris, France, Eds.: F. Combes and D. Barret, EdPSciences (Editions de Physique), Conference Series, 521 Fossat, E. 2013, Fifty Years of Seismology of the Sun and Stars. Proceedings of a Workshop held 6-10 May, 2013 in Tuscon, Arizona, USA. Edited by K. Jain, S. C. Tripathy, F. Hill, J. W. Leibacher, and A. A. Pevtsov. ASP Conference Proceedings, vol. 478. San Francisco: Astronomical Society of the Pacific, 73 Gabriel, M. & Lazrek, M. 1994, A&A, 286, 635 Gelly, B., Lazrek, M., Grec, G., Ayad, A., Schmider, F. X., Renaud, C., Salabert, D. & Fossat, E. 2002, A&A, 394, 285 Gelly, B., Fierry-Fraillon, D., Fossat, E., Palle, P., Cacciani, A., Ehgamberdiev, S., Grec, G., Hoeksema, J. T., Khalikov, S., Lazrek, M., Loudagh, S., Pantel, A., Regulo, C. & Schmider, F. X. 1997, A&A, 323, 235 Grec, G., Fossat, E., Pomerantz, M. A. 1980, Nature, 288, 541 Grec, G., Fossat, E., Pomerantz, M. A. 1983, Solar Physics, 82, 55

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Grec, G., Fossat, E., Gelly, B., Schmider, F.-X. 1991, Solar Physics, 133, 13. Harvey, J. 1985, Future Missions in Solar, Heliospheric and Space Plasma Physics, Eds. E.Rolfe & B.Pattrick (ESA SP-233, European Space Agency, Noordwijk), 199 Lazrek, M., Pantel, A., Fossat, E., Gelly, B., Schmider, F. X., Fierry-Fraillon, D., Grec, G., Loudach, S., Ehgamberdiev, Sh., Khamitov, I., Hoeksema, J. T., Palle, P. & Regulo, C. 1996, Solar Physics, 166, 1 Loudagh, S., Provost, J., Berthomieu, G., Ehgamberdiev, Sh., Fossat, E., Gelly, B., Grec, G., Khalikov, Sh., Lazrek, M., Palle, P., Sanchez, L. & Schmider, F. X. 1993, A&A, 275, L25-L28 Leibacher, J. W. & Stein, R. F. 1971, Astrophys. Lett., 7, 191 Leighton, R.B., Noyes, R.W. & Simon, G.W. 1962, ApJ, 135, 474 Libbrecht, K. G. 1988, Seismology of the Sun and Sun-Like Stars, 286, 131 Serebryanskiy, A., Ehgamberdiev, Sh., Khalikov, Sh., Fossat, E., Lazrek, M., Gelly, B., Schmider, F. X., Fierry-Fraillon, D., Grec, G., Palle, P., Cacciani, A. & Hoeksema, J. T. 1998, Proceedings of the Xth IRIS/TON Workshop, Parkent (Uzbekistan), 17 Serebryanskiy, A., Ehgamberdiev, Sh., Kholikov, Sh., Fossat, E., Gelly, B., Schmider, F. X., Grec, G., Cacciani, A., Palle, P., Lazrek, M. & Hoeksema, J. T. 2001, New astronomy, 6, 189 Ulrich, R. K. 1970, ApJ, 162, 993

Local Helioseismology of Emerging Active Region: A Case Study Alexander G. Kosovichev, Junwei Zhao, & Stathis Ilonidis New Jersey Institute of Technology, Newark, NJ 07103, USA; Stanford University, Stanford, CA 94305, USA E-mail: [email protected] Abstract. Local helioseismology provides a unique opportunity to investigate the subsurface structure and dynamics of active regions and their effect on the largescale flows and global circulation of the Sun. We use measurements of plasma flows in the upper convection zone, provided by the Time-Distance Helioseismology Pipeline developed for analysis of solar oscillation data obtained by the Helioseismic and Magnetic Imager (HMI) on board of Solar Dynamics Observatory (SDO), to investigate the subsurface dynamics of emerging active region NOAA 11726. The active region emergence was detected in deep layers of the convection zone about 12 hours before the first bipolar magnetic structure appeared on the surface, and 2 days before the emergence of most of the magnetic flux. The speed of emergence determined by tracking the flow divergence with depth is about 1.4 km/s, very close to the emergence speed in the deep layers. As the emerging magnetic flux becomes concentrated in sunspots local converging flows are observed beneath the forming sunspots. These flows are most prominent in the depth range 1-3 Mm, and remain converging after the formation process is completed. On the larger scale converging flows around active region appear as a diversion of the zonal shearing flows towards the active region, accompanied by formation of a large-scale vortex structure. This process occurs when a substantial amount of the magnetic flux emerged on the surface, and the converging flow pattern remains stable during the following evolution of the active region. The Carrington synoptic flow maps show that the large-scale subsurface inflows are typical for other active regions. In the deeper layers (10-13 Mm) the flows become diverging, and surprisingly strong beneath some active regions. In addition to the flows around active regions, the synoptic maps reveal a complex evolving pattern of large-scale flows on the scale much larger than supergranulation.

1

Introduction

Emergence and formation of magnetic active regions on the surface of the Sun is one of the central problems of solar physics. It is of the fundamental importance in astrophysics because active regions are one of the primary manifestations of the solar and stellar magnetism. In addition, solar active regions (AR) are the major drivers of the solar variability, geospace and planetary space environments and space weather. Understanding of the emergence and evolution of active regions is a key to developing the knowledge and capability to detect and predict extreme conditions in space. The uninterrupted

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Alexander G. Kosovichev, Junwei Zhao, & Stathis Ilonidis

helioseismology and magnetic data from Solar Dynamics Observatory provide unique opportunities for comprehensive studies that can uncover the basic mechanisms of active region formation, evolution, and their flaring and CME activity (Scherrer et al, 2012). Recent studies revealed that the emergence and magnetic structure of active regions are closely linked to the plasma flows on the surface and in the subsurface layers (Hindman et al, 2009; Komm et al, 2011, 2012; Kosovichev, 2012; Kosovichev and Duvall, 2006; Birch et al, 2013). For example, diverging subsurface flows have been detected prior the emergence of active regions, shearing and twisting flows are found to be associated with flaring activity, large-scale converging flows formed around active regions affect the meridional circulation and along with the tilt of active regions (Joys law) are believed to be among primary factors determining the strength and duration of the future solar cycles. The conventional wisdom is that the active regions are a result of emergence of toroidal magnetic flux ropes formed near the bottom of the convection zone by a dynamo process. This theory can explain the Joy’s law and the absence of active regions at high latitudes providing the initial magnetic field strength is about 60 kG (D’Silva and Choudhuri, 1993), which greatly exceeds the equipartition field strength and has not been reproduced by the dynamo theories. Current 3D MHD global-Sun models computed in the anelastic approximation have shown that the dynamo-generated field can be organized in the form of flux tubes but on much larger scale (Brun et al, 2004; Fan and Fang, 2014; Guerrero et al, 2016). These models indicates that the active regions and sunspots are probably formed in the near-surface layers, but the anelastic approximation becomes invalid close to the surface, where compressibility effects play significant role. With the currently available computational resources the realistic compressible radiative MHD simulations are capable to model only relatively shallow near-surface. These simulations have revealed a process of spontaneous formation of compact pore-like structures from initially distributed magnetic fields, maintained by converging downdrafts, however, other mechanisms of magnetic self-organization may be also involved (K¨ apyl¨ a et al, 2016; Kitiashvili et al, 2010; Masada and Sano, 2016). The magnetic self-organization process is probably a key to understand the formation of sunspots and active regions. It involves a complex interaction of turbulence with magnetic field, but in all cases the large-scale flow pattern includes compact regions of converging downdrafts around magnetic structures in shallow ∼ 5 Mm deep regions. In the deeper layers the flows are mostly diverging. This flow pattern corresponds to the Parker’s cluster model of sunspots. It has been observed by the time-distance helioseismology analysis of the SOHO/MDI and Hinode/SOT data (Zhao et al, 2001, 2009; Zhao and Kosovichev, 2003). The data analysis also showed that in the decaying sunspots the flows become diverging. Other helioseismology methods, such as the ring-diagram analysis and the helioseismic holography, pro-



Local Helioseismology of Emerging Active Region

vide the subsurface flow maps with a lower resolution than the time-distance helioseismology, and did not confirm the existence of the converging downdrafts beneath the sunspots. Instead, they inferred diverging flows of a larger scale around sunspots over the whole depth range probed by these techniques (Hindman et al, 2009). The current helioseismology measurements in regions of strong magnetic field are subject to significant systematic errors due to the uncertainties in the Doppler-shift measurements, large variations of the sound speed causing nonlinear wave effects, non-uniform distribution of acoustic sources and MHD wave transformation effects. These uncertainties mostly affect inferences of the sound-speed distribution beneath the sunspots (for a recent review see Kosovichev, 2012). The helioseismic inferences of subsurface flows are based on measuring and inverting the travel-time differences for the waves traveling along the same path in the opposite directions. Such reciprocal signals are less sensitive to the systematic uncertainties. However, a complete testing and calibration of the flow inferences based on numerical simulations of wave propagation in sunspots has not been completed. In this work we mostly focus on flows of active regions that are formed beneath sunspots, and, in particular, on the flow patterns during the formation and evolution of a large emerging active region. The primary goal is to investigate the process of formation of the large-scale converging flows that affect the meridional circulation and magnetic flux transport. As a case study we consider a large emerging active region NOAA 11726.

2

Time-Distance Helioseismology from SDO

The Helioseismic and Magnetic Imager (HMI) provides uninterrupted Dopplergrams with high spatial (0.5 arcsec per pixel, or 0.03 heliographic degrees at the disk center) and temporal (45 sec) resolutions. These data cover the whole spectrum of photospheric oscillations, and are ideal for local helioseismology studies. Developed as a part of the SDO helioseismology program, the Time-Distance Helioseismology Pipeline provides travel times of acoustic waves measured by two different methods, and also the maps of subsurface flows and sound-speed perturbations obtained by using the Multi-Channel Deconvolution technique and two different types of sensitivity kernels derived from the ray-path and Born approximations (Fig. 1a). Thus, the pipeline provides four different sets of inversions for the 3D flow velocities and wave-speed variations. Details of the pipeline procedures, and also the test results and estimation of errors are described by Couvidat et al (2012) and Zhao et al (2012). The pipeline data have been used to determine the distributions of the flow vorticity and helicity, and also variations of the meridional circulation and zonal flows with the solar cycle (Zhao et al, 2014; Kosovichev and Zhao, 2016).

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Alexander G. Kosovichev, Junwei Zhao, & Stathis Ilonidis Acoustic ray paths and inversion grid

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Fig. 1. a) Diagram of the HMI Time-Distance Helioseismology pipeline implemented at the SDO Joint Science Operations Center (Zhao et al, 2012). b) a set acoustic paths and the inversion grid illustrating the measurement scheme used in the Time-Distance Pipeline. The inversion grid includes 11 depth intervals: 0-1, 1-3, 3-5, 5-7, 7-10, 10-13, 13-17, 17-21, 21-26, 26-30, and 30-35 Mm. The horizontal grid spacing is 0.12 degrees (∼ 1.45 Mm).

In addition, we have developed a complementary pipeline for tracking the subsurface dynamics of active regions. This pipeline takes the Carrington coordinates of active regions from the Solar Region Summary (SRS) database, compiled by the NOAA Space Weather Prediction Center (SWPC), and uses these coordinates as the central points of 30 × 30-degree areas tracked for 10 days during their passage on the solar disk. This setup allows us to follow the evolution of active region areas even before the magnetic flux emergence and after the decay. The 3D subsurface flow maps are calculated from the tracked Dopplergrams that are remapped onto the heliographic coordinates using the Postel’s projections. Each tracked, 8-hour long, datacube consists of 640 Dopplergrams of 512 × 512 pixels with the spatial resolution of 0.06 degree/pixel, and 45-sec time cadence. The tracked datacubes are processed through the Time-Distance Helioseismology Pipeline (Fig. 1a), and the output represents acoustic travel-time maps calculated with 0.12-deg sampling for the whole tracked areas (256×256 pixels). The travel-times are calculated for eleven annuli located at different distances from the central points representing 2 × 2-binned original Dopplergram pixels. The signals of acoustic waves traveling between the central points and the surrounding annuli are calculated from the HMI Doppler velocity measurements as the corresponding cross-covariance functions. The



Local Helioseismology of Emerging Active Region

cross-covariances are computed in the Fourier space, and phase-space filters are applied to isolate the signals corresponding to each of the travel distances. The travel times are calculated by two different methods: 1) the Gabor wavelet fitting (Kosovichev and Duvall, 1997) and 2) a cross-correlation with reference cross-covariance functions obtained by averaging over a large area (Gizon and Birch, 2002). Then, the travel times are used to infer the 3D maps of subsurface flows and sound-speed perturbations, by solving an inverse acoustic tomography problem. It is formulated in the form of linear integral equations the kernels of which are calculated by using the ray-path theory (Kosovichev and Duvall, 1997) and the first Born approximation (Birch and Kosovichev, 2000, 2001; Birch et al, 2001, 2004; Birch and Gizon, 2007). Regularized solutions to the inverse problem are determined by the MultiChannel Deconvolution (MCD) method (Jacobsen et al, 1999; Couvidat et al, 2006), and the regularization parameters were chosen to suppress noise and represents a smooth solution. The depth coverage is illustrated in Fig. 1b, which shows a vertical cut of the inversion grid together with the acoustic ray paths corresponding to the selected set of 11 annuli. Thus, the inversion results provide the 3D flow and sound-speed maps up to the depth of 30 Mm. However, for analysis we use only the top layers less than 20 Mm because the pipeline results become less robust as the ‘realization noise’ of solar oscillations increases with depth. The deeper interior of the Sun can be probed by increasing the spatial and temporal averaging of the oscillation cross-covariance function and extending the range of the acoustic ray paths. The deeper penetrating waves travel to longer distances on the solar surface. The primary factors that restrict the resolving power of the time-distance helioseismology with depth are the increasing wavelength of acoustic waves and the increasing ‘realization noise’. The realization noise is a consequence of random excitation of solar acoustic waves (Woodard, 1984). Because the number of deeply-penetrating waves with long horizontal wavelength (that can be represented in terms of normal modes with relatively low angular degree) is smaller than the number of short acoustic waves (high-degree modes) the realization noise increases for deep measurements. Nevertheless, by averaging the cross-covariance signals for two years (Zhao et al, 2013) were able to measure the meridional flows up to the base of the convection zone. One of the great advantages of time-distance helioseismology is that observations of solar oscillations over the whole disk allow us to construct special measurement scheme to select and accumulate signals of acoustic waves traveling through particular regions below the surface. For instance, (Ilonidis et al, 2013) developed a special deep-focusing procedure that is capable of detecting large emerging active regions 2 days before they emerge on the surface (Fig. 2). This procedure will be illustrated in our case study of helioseismic diagnostics of emerging active region NOAA 11726.

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Alexander G. Kosovichev, Junwei Zhao, & Stathis Ilonidis Deep-focus measurement scheme

Magnetogram (G), April 19, 2013, 3:00 UT

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Fig. 2. Detection of emerging active region AR 11726: a) the HMI magnetogram of April 19, 2013, 3:00 UT, prior the emergence; the rings show the area where the acoustic oscillation signal was measured to detect the subsurface signal at the central point; the square is the area of the subsurface detection shown in panel c; b) schematic illustration of the deep-focus measurement scheme; c) variations of a travel-time index showing the AR perturbation located the depth of 62 − 75 Mm at April 19, 2013, 3:00 UT; d) variations of the helioseismic perturbation associated with the emerging AR at two different depths: 42 − 55 Mm and 62 − 75 Mm, as a function of time.

3

Detection of active region before it becomes visible on the surface

The deep-focuse measurement scheme used for the subsurface detection of AR 11726 is shown in Fig. 2a-b. In this scheme the cross-covariance function is calculated for the ray paths with the lower turning points located at the depth 42 − 75 Mm. This range of depth corresponds to the travel distance on the surface of 111 − 198 Mm. Thus, the cross-covariance function is calculated using the HMI Doppler velocity measurements located on the opposite side of the annuli shown in Fig. 2b. In this case, the calculated



Local Helioseismology of Emerging Active Region

cross-covariance function is mostly sensitive to perturbations located beneath the central point at the depth 42 − 75 Mm, and is not affected by potential perturbations in the flux emergence area. The central point of the annuli is moved to different positions on the surface, and the cross-covariance calculations are repeated. Phase shifts of the local cross-covariance function from the mean profile provide a map of subsurface perturbations at this depth. This approach was optimized for subsurface detection of emerging active regions by Ilonidis et al (2013). Figure 2c shows the distribution of an effective phase shift (‘helioseismic index’) in the range of depth 62 − 75 Mm, measured on April 19, 2013, 03:00 UT when there was no significant magnetic flux on the surface (Fig. 2b). Figure 2d shows variations of the helioseismic perturbation associated with the emerging AR at two different depths: 62 − 75 Mm and 42 − 55 Mm, as a function of time. This approach allows us to track the development of subsurface perturbations with time, and estimate the speed of emergence, which in this case is about 1.4 km/s. The emergence of magnetic flux on the surface starts on the following day, and most of the magnetic flux emerged 2 days after it was first detected below the surface. Currently, this method provides an early detection only large active regions. Thus, a strong helioseismic perturbation below the surface observed prior the emergence may serve as a precursor of large active regions on the solar surface.

4

Subsurface dynamics of emerging active region

Figure 3 showing the horizontal flow maps at four different depth at the initial emergence of a bipolar magnetic structure on April 19, 2012, 12:00 UT, overlaid over the photospheric magnetogram. In the near-surface 1 − 5 Mm deep layers (Fig 3a-b) the magnetic flux appeared near the boundaries of a supergranulation cell. However, in the deeper layers, at the depth of 10 − 21 Mm, no characteristic flow pattern associated with the emerging flux can be visually identified. Thus, the near surface flow maps prior the emergence do not reveal a distinct large-scale flow pattern which would indicate that a large magnetic structure is coming up. Nevertheless these maps allow us to track the process of emergence. Figure 4a shows a time-space slice of divergence of the horizontal velocity through the subsurface layers in the East-West direction in the depth interval of 7 − 10 Mm. The initial perturbation associated with the flux emergence appeared in our domain, centered at Carrington longitude of 322.0 degrees and −15.3 degrees latitude, at x0 ≈ 250 Mm. The perturbation represents diverging flows localized around the emerging Ω-loop like structure. In Figure 4b we plot the divergence at x0 as a function of time and depth. It shows that the emergence speed (indicated by the inclined dotted white line) is about 1.4 km/s which is very similar to the speed observed in the deep convection zone.

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Alexander G. Kosovichev, Junwei Zhao, & Stathis Ilonidis AR11726, 2013.04.19, 12:00 TAI, d=1-3 Mm φ=+13.0, λ=-15.3, λc=322.0, Gabor-Born

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Fig. 3. Subsurface flow maps and the photospheric magnetogram at the initial moment of appearance of emerging bipolar magnetic flux on the solar surface at 12:00 UT, April 19, 2013, about 12 hours after the initial detection of the subsurface perturbation at four depth: a) 1 − 3 Mm, b) 3 − 5 Mm, c) 10 − 13 Mm, and d) 17 − 21 Mm. The point x = 0, y = 0 is located at the heliographic coordinates: latitude φ = 13◦ , longitude λ = −15.3◦ , and the Carrington longitude λc = 322◦ . The travel times were calculated by using the Gabor-wavelet fitting technique, and the inversion for flows was performed by using the Born-approximation kernels.



Local Helioseismology of Emerging Active Region

AR11726, div(V), depth=7-10 Mm 24-Apr 23-Apr 22-Apr 21-Apr 20-Apr 19-Apr 0

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Fig. 4. a) Evolution of the horizontal flow divergence in the depth range of 7 − 10 Mm is shown as a slice along the longitudinal coordinate x at y = 0. b) the evolution of the horizontal divergence as a function of depth at the horizontal coordinates: x = 250 Mm, y = 0, corresponding the earliest perturbation in panel a.

During the further process the subsurface flows are substantially affected by the emerging magnetic field. The flow evolution in four different depth ranges is illustrated in Figures 5-8. In the subsurface layer, 1 − 3 Mm deep, the initial flow pattern corresponds to the two flux concentrations moving away from each other (Fig. 5a). However, 12 hours later we observe formation of converging flows around the positive polarity, associated with the formation of a sunspot (Fig. 5b). In later times, a similar converging flow pattern is established beneath the leading negative polarity, and is also associated with the formation of sunspots (Fig. 5c-d). Such converging flows have been observed in the time-distance analysis of the SOHO/MDI Doppler velocity and Hinode/SOT intensity data by using the ray-approximation kernels and a different inversion technique (Zhao et al, 2001, 2010; Zhao and Kosovichev, 2003). The converging flow pattern beneath the sunspots is very stable and supports the cluster model of sunspots suggested by Parker (1979). Around the sunspots, the flows become diverging, and are probably associated with the horizontal expansion of the active region. From the evolution of the photospheric magnetic field it is clear that the leading polarity is pushed forward,

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Alexander G. Kosovichev, Junwei Zhao, & Stathis Ilonidis AR11726, 2013.04.19, 20:00 TAI, d=1-3 Mm φ=+13.0, λ=-10.9, λc=322.0, Gabor-Born

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Fig. 5. Evolution of subsurface flows during the emergence of active region NOAA 11726 in the depth range 1-3 Mm for four different moments of time: a) 2013.04.19, 20:00 UT; b) 2013.04.20, 08:00 UT, c) 2013.04.21, 20:00 UT, d) 2013.04.22, 08:00 UT. The corresponding surface magnetograms from HMI are shown in the color background.



Local Helioseismology of Emerging Active Region AR11726, 2013.04.19, 20:00 TAI, d=3-5 Mm φ=+13.0, λ=-10.9, λc=322.0, Gabor-Born

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Fig. 6. The same as in Fig. 5 for the depth of 3-5 Mm.

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Alexander G. Kosovichev, Junwei Zhao, & Stathis Ilonidis AR11726, 2013.04.19, 20:00 TAI, d=5-7 Mm φ=+13.0, λ=-10.9, λc=322.0, Gabor-Born

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Fig. 7. The same as in Fig. 5 for the depth of 5-7 Mm.



Local Helioseismology of Emerging Active Region AR11726, 2013.04.19, 20:00 TAI, d=13-17 Mm φ=+13.0, λ=-10.9, λc=322.0, Gabor-Born

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Alexander G. Kosovichev, Junwei Zhao, & Stathis Ilonidis

and the following polarity is moved backward. One can also notice that the between the polarities, in the middle of the active region, the horizontal flows are suppressed. In the deeper layer (3 − 5 Mm), the flows are mostly diverging and are concentrated at the boundaries of the active region. Beneath the following sunspot the flows are weaker but still converging (Fig. 6). However, beneath the leading polarity the diverging flows dominate. At the depth of 5 − 7 Mm the diverging flow pattern is dominant around both, the leading and following sunspot (Fig. 7). While in this range of depth the diverging flows are localized around the individual magnetic structures, at greater depths the diverging flow surrounds the whole active region and extends to larger distances, as illustrated in Fig. 8 that shows the flows in the 13 − 17 Mm deep layer. Perhaps, this corresponds to the increasing horizontal extend of the subsurface magnetic region with depth.

5

Formation of large-scale inflows

Previous investigations by the ring-diagram technique (Haber et al, 2003) and time-distance helioseismology (Kosovichev, 1996) revealed large-scale converging flows around active regions, which alter the mean meridional circulation (Haber et al, 2002; Zhao and Kosovichev, 2004; Kosovichev and Zhao, 2016) and, thus, the magnetic flux transport affecting the strength and duration of the solar activity cycles. The detailed flow maps from the HMI Time-Distance Helioseismology Pipeline allow us to investigate the process of formation of these flows during the emergence of active regions. To isolate large-scale flow patterns from the full-resolution flow maps, samples of which are shown in Figures 5-8, we applied a Gaussian smoothing filter with the standard deviation of 30 Mm. This filter smooths the supergranulation-size flows and reveals larger-scale patterns. The result of this filtering applied to the area of emergence of AR 11726 are shown in Figure 9. Prior the emergence the subsurface flow pattern represents a shearing zonal flow (Fig. 9a). At the start of the emergence the zonal flows on the both sides of the emerging magnetic flux are diverted towards the active region, forming a vortex-like structure in the northern part of the area (Fig. 9b). Then, the converging inflows are amplified and remain stable when most of the flux had emerged on the surface (Fig. 9c-d). To investigate the relationship between the flux emergence and formation of the converging inflow in Figure 10a we compare the mean flow divergence with the mean unsigned magnetic field strength, calculated for the area shown in Fig. 9. It shows that the mean divergence became sharply negative after most of the magnetic flux emerged on the surface. The process of formation of the converging flow took about 24 hours. Figure 10b shows a similar comparison for the kinetic helicity proxy: (∇ · V ) · (∇ × V )z . However, while the divergence value quickly saturates the helicity value keeps increasing. The



Local Helioseismology of Emerging Active Region AR11726, 2013.04.16, 21:00 TAI, d=0.50 Mm φ=+13, λ=-50, λc=322, Gabor-Born

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Fig. 9. Formation of the large-scale converging flow pattern during the active emergence illustrated for four moments of time: a) 2013.04.16 21:00 UT; b) 2013.04.19 16:00 UT; c) 2013.04.21 04:00 UT; d) 2013.04.22 05:00 UT. The flow maps are obtained by applying a Gaussian smoothing filter with the standard deviation of 30 Mm.

helicity increase means that a large-scale vortex structure is formed beneath the active region. The previous study of Kosovichev and Zhao (2016) showed that the largescale inflows affect the mean meridional flow in a 10 Mm-deep layer at the top of the convection zone, by effectively reducing the flow speed at 2040 degrees latitude. As the solar cycle progresses the zone of the reduced speed migrates towards the equator. However, the mean helicity proxy has a strong hemispheric asymmetry (being positive in the Northern hemisphere), and remains largely unchanged during the solar cycle. This, probably means that most of the helicity value comes from the supergranulation. The helicity associated with the active region flows has the opposite sign to the mean helicity but contributes only a few percent. These initial results show that the subsurface flows that develop in and around of emerging active regions have a complex multi-scale structure which is important for the understanding of how the active regions are formed and how they affect the global Sun’s dynamics and magnetic activity.

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AR11726 large-scale divergence, depth=1-3Mm, Gabor_Born 2·10-7

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Fig. 10. Evolution of a) the mean flow divergence, and b) the mean kinetic helicity beneath the emerging active region NOAA 11726 at the depth of 1-3 Mm.

6

Synoptic flow maps

To get some insight in the global structure of large-scale flows on the Sun, sometimes called ‘Solar Subsurface Weather’ (Haber et al, 2003) we used the smoothed large-scale flow maps to construct synoptic flow maps similar to the Carrington magnetic field maps. For this, we applied a cos4 (1.5φ) filter centered at the central meridian with latitude φ = 0 to the individual full-disk flow maps smoothed with the Gaussian filter as described in Section 5. Then, the filtered flow maps calculated with the 8-hour cadence were combined into the Carrington rotation maps by assigning the appropriate Carrington longitude to the central meridian of the individual flow maps. Figure 11a shows the synoptic flow map for Carrington Rotation 2136 and the depth range of 1 − 3 Mm. The color background in the corresponding HMI synoptic map for the radial magnetic field. This Carrington Rotation includes the AR 11726 presented in the previous sections (indicated by arrow in Fig. 11). During its passage through the central meridian (approximately



Local Helioseismology of Emerging Active Region AR11726

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Fig. 11. Subsurface synoptic flow maps for two consecutive Carrington rotations at two different depth intervals: a) CR 2166 at 1 − 3 Mm, b) CR 2166 at 10 − 13 Mm; c) CR 2167 at 1 − 3 Mm; and d) CR 2167 at 10 − 13 Mm. The corresponding synoptic maps for the radial magnetic field component are shown in the background. Location of the emerging active region NOAA 11726 is indicated by arrow.

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at 16:00 UT, 2013.04.20) the active region was in the middle of the flux emergence process when the large-scale converging flows were still forming. The converging flows are clearly seen around other active regions on this map. In the deeper layers (10 − 13 Mm) shown in Fig. 11b we observe very prominent outflows two active regions. However, the outflow associated with AR 11726 is not centered on this region and displaced to the south of it. Perhaps, this is a signature of the continuing flux emergence. Indeed, the synoptic maps of the following Carrington Rotation 2137 shows AR 11726 grew into a very large active region which has a new NOAA number 11745 (Fig. 11c-d). Of course, a substantial statistical study is required to determine whether the deep subsurface flow patterns can be used for prediction of further evolution of active regions. The synoptic flow maps reveal also persistent flow patterns on the scale substantially larger than the scale of the active region flows. An apparent correlation of the flows with the distribution of large-scale fields outside active regions is particularly intriguing, and requires further investigation.

7

Conclusion

As a case study we presented a local helioseismology analysis of the subsurface dynamics of emerging active region NOAA 11726 which is the largest emerging region observed by the SDO/HMI instrument during the first five years of operation. The active region emergence was detected at the depth of 62 − 75 Mm about 12 hours before the first bipolar magnetic structure appeared on the surface, and 2 days before the emergence of most of the magnetic flux. The characteristic speed of emergence estimated from the signal delay in two layers, 62 − 75 Mm and 42 − 55 Mm deep, is about 1.4 km/s. During emergence of the initial bipolar structure no specific large-scale flow pattern in the depth range 0 − 20 Mm were identified. Nevertheless, the region of the flux emergence is characterized by an enhanced horizontal flow divergence that corresponds to the spatial separation of the magnetic polarities. The speed of emergence determined by tracking the initial divergence signal with depth is about 1.4 km/s, very close to the emergence speed in the deep layers. As the emerging magnetic flux becomes concentrated in sunspots local converging flows are observed beneath the forming sunspots. The converging flows are most prominent in the depth range 1−3 Mm, and remain converging after the formation process is completed. The structure of the converging flows is complicated and apparently reflects the sunspot structural evolution and interaction with the surrounding convection flows. The characteristic speed of these flows is about 0.3 km/s. In the deeper layers the flows beneath the sunspots are predominantly diverging and occupy larger areas. At the depth about 15 Mm the diverging flows occupy a large area around the whole active region.



Local Helioseismology of Emerging Active Region

By applying a Gaussian filter to smooth the supergranulation-scale flows we investigated the formation of large-scale converging flows around the active region. The scale of these flows is much larger than the size of the active region, and the typical flow speed is about 30 m/s. The formation of the converging flows appears as a diversion of the zonal shearing flows towards the active region, accompanied by formation of a large-scale vortex structure. This process occurs when a substantial amount of the magnetic flux emerged on the surface, and the converging flow pattern remains stable during the following evolution of the active region. The flow helicity is opposity in sign to the subsurface hemispheric helicity mostly determined by the supergranulation flows, but does not significantly contributes to the helicity balance. The primary effect of the converging large-scale flows is in changing the speed of the mean meridional flow in the top 10 Mm-deep layer. The synoptic flow maps presented for the Carrington rotation that includes our case study of AR 11726 show that the large-scale subsurface inflows are typical for other active regions. In the deeper layers (10 − 13 Mm) the flows become diverging, and quite strong beneath some active regions. The active region 11726 in the synoptic map is presented at the beginning of the emergence, but in the deep layers is accompanied by an area of strong divergence, which is off-side of the emerged flux. It remains to be seen if the deep diverging flows indicate on the future development of active regions, but the synoptic map of the following rotation shows that the active region continued to grow on the far side of the Sun and became very large (it received the new NOAA number 11745). In addition to the flows around active regions the synoptic maps reveal a complex evolving pattern of large-scale flows on the scale much larger than supergranulation. It appears that these flows correlate with the large-scale magnetic field outside active region. The exact relationship has not been established, but the presented case study encourages further in-depth investigations of the solar subsurface dynamics, both observationally and by numerical MHD simulations.

Acknowledgment This work was supported by the NASA grant NNX14AB70G .

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Kosovichev AG, Duvall TL (2006) Active region dynamics. Space Sci. Rev. 124:1–12, DOI 10.1007/s11214-006-9112-z, URL http://adsabs. harvard.edu/abs/2006SSRv..124....1K Kosovichev AG, Duvall TL Jr (1997) Acoustic tomography of solar convective flows and structures. In: Pijpers FP, Christensen-Dalsgaard J, Rosenthal CS (eds) SCORe’96 : Solar Convection and Oscillations and their Relationship, Astrophysics and Space Science Library, vol 225, pp 241–260, URL http://adsabs.harvard.edu/abs/1997ASSL..225..241K Kosovichev AG, Zhao J (2016) Reconstruction of solar subsurfaces by local helioseismology. In: Rozelot JP, Neiner C (eds) Lecture Notes in Physics,Springer International Publishing Switzerland, Lecture Notes in Physics, Springer International Publishing, Switzerland, vol 914, pp 25–41 Masada Y, Sano T (2016) Spontaneous formation of surface magnetic structure from large-scale dynamo in strongly stratified convection. Astrophys. J. Lett. 822:L22, DOI 10.3847/2041-8205/822/2/L22, 1604.05374 Parker EN (1979) Sunspots and the physics of magnetic flux tubes. i - the general nature of the sunspot. ii - aerodynamic drag. Astrophys. J. 230:905– 923, DOI 10.1086/157150 Scherrer PH, Schou J, Bush RI, Kosovichev AG, Bogart RS, Hoeksema JT, Liu Y, Duvall TL, Zhao J, Title AM, Schrijver CJ, Tarbell TD, Tomczyk S (2012) The helioseismic and magnetic imager (hmi) investigation for the solar dynamics observatory (sdo). Solar Phys. 275:207–227, DOI 10.1007/ s11207-011-9834-2, URL http://adsabs.harvard.edu/abs/2012SoPh. .275..207S Woodard MF (1984) Short-period oscillations in the total solar irradiance. PhD thesis, UNIVERSITY OF CALIFORNIA, SAN DIEGO. Zhao J, Kosovichev AG (2003) Helioseismic observation of the structure and dynamics of a rotating sunspot beneath the solar surface. Astrophys. J. 591:446–453, DOI 10.1086/375343, URL http://adsabs.harvard.edu/ abs/2003ApJ...591..446Z Zhao J, Kosovichev AG (2004) Torsional oscillation, meridional flows, and vorticity inferred in the upper convection zone of the sun by time-distance helioseismology. Astrophys. J. 603:776–784, DOI 10.1086/381489, URL http://adsabs.harvard.edu/abs/2004ApJ...603..776Z Zhao J, Kosovichev AG, Duvall TL Jr (2001) Investigation of mass flows beneath a sunspot by time-distance helioseismology. Astrophys. J. 557:384–388, DOI 10.1086/321491, URL http://adsabs.harvard.edu/ abs/2001ApJ...557..384Z Zhao J, Kosovichev AG, Sekii T (2009) Subsurface structures and flow fields of an active region observed by hinode. In: Lites B, Cheung M, Magara T, Mariska J, Reeves K (eds) The Second Hinode Science Meeting: Beyond Discovery-Toward Understanding, Astronomical Society of the Pacific Conference Series, vol 415, p 411, URL http://adsabs.harvard.edu/abs/ 2009ASPC..415..411Z



Local Helioseismology of Emerging Active Region

Zhao J, Kosovichev AG, Sekii T (2010) High-resolution helioseismic imaging of subsurface structures and flows of a solar active region observed by hinode. Astrophys. J. 708:304–313, DOI 10.1088/0004-637X/708/1/304, URL http://adsabs.harvard.edu/abs/2010ApJ...708..304Z, 0911.1161 Zhao J, Couvidat S, Bogart RS, Parchevsky KV, Birch AC, Duvall TL, Beck JG, Kosovichev AG, Scherrer PH (2012) Time-distance helioseismology data-analysis pipeline for helioseismic and magnetic imager onboard solar dynamics observatory (sdo/hmi) and its initial results. Solar Phys. 275:375–390, DOI 10.1007/s11207-011-9757-y, URL http:// adsabs.harvard.edu/abs/2012SoPh..275..375Z, 1103.4646 Zhao J, Bogart RS, Kosovichev AG, Duvall TL Jr, Hartlep T (2013) Detection of equatorward meridional flow and evidence of double-cell meridional circulation inside the sun. Astrophys. J. Lett. 774:L29, DOI 10.1088/2041-8205/774/2/L29, URL http://adsabs.harvard.edu/abs/ 2013ApJ...774L..29Z, 1307.8422 Zhao J, Kosovichev AG, Bogart RS (2014) Solar meridional flow in the shallow interior during the rising phase of cycle 24. Astrophys. J. Lett. 789:L7, DOI 10.1088/2041-8205/789/1/L7, URL http://adsabs.harvard.edu/ abs/2014ApJ...789L...7Z, 1406.2735

37

Realistic Simulations of Stellar Radiative MHD Alan A. Wray1 , Khalil Bensassi1,2 , Irina N. Kitiashvili1 , Nagi N. Mansour1 , Alexander G. Kosovichev3 1

NASA Ames Research Center, Moffett Field, CA 94035-1000, USA University of California, Los Angeles (UCLA), Los Angeles, CA 90095-1567, USA 3 New Jersey Institute of Technology, Newark, NJ 07102, USA 2

Abstract. Realistic numerical simulations, i.e., those that make minimal use of ad hoc modeling, are essential for understanding the complex turbulent dynamics of the interiors and atmospheres of the Sun and other stars and the basic mechanisms of their magnetic activity and variability. The goal of this paper is to present a detailed description and test results of a compressible radiative MHD code, ‘StellarBox’, specifically developed for simulating the convection zones, surface, and atmospheres of the Sun and moderate-mass stars. The code solves the three-dimensional, fully coupled compressible MHD equations using a fourth-order Pad´e spatial differentiation scheme and a fourth-order Runge-Kutta scheme for time integration. The radiative transfer equation is solved using the Feautrier method for bi-directional ray tracing and an opacitybinning technique. A specific feature of the code is the implementation of subgrid-scale MHD turbulence models. The data structures are automatically configured, depending on the computational grid and the number of available processors, to achieve good load balancing. We present test results and illustrate the code’s capabilities for simulating the granular convection on the Sun and a set of main-sequence stars. The results reveal substantial changes in the near-surface turbulent convection in these stars, which in turn affect properties of the surface magnetic fields. For example, in the solar case initially uniform vertical magnetic fields tend to self-organize into compact (pore-like) magnetic structures, while in more massive stars such structures are not formed and the magnetic field is distributed more-or-less uniformly in the intergranular lanes.

1

Motivations

During the last few decades, there has been a major increase in the use of highperformance computing in computational physics in general and in space science in particular. Massively parallel algorithms have been developed to implement accurate physical models in order to provide efficient and realistic simulations of astrophysical phenomena, for instance, stellar and solar interior dynamics, which is the focus here. Such computational tools are used to support and analyze ground and spacecraft observations. The coupling between observations and numerical simulations is necessary for improving our understanding of complex phenomena on the Sun and other stars because the two approaches are complementary. Recent high-resolution observations of the Sun have uncovered a rich small-scale dynamics which plays a key role in the observed large-scale phenomena. For example, observations and simulations led to the discovery of small-scale vortex tubes generated in intergranular lanes (Brandt et al. 1988; Bonet et al. 2008, 2010; Steiner et al. 2010), which are a source of the Sun’s acoustic emission

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Alan A. A. Wray Alan Wrayetetal.al.

and magnetic flux concentrations (Kitiashvili et al. 2010, 2011, 2012). Stellar observations from the Kepler mission and ground-based telescopes have revealed that solar-type acoustic oscillations are common in other stars, giving rise to the rapid development of asteroseismology. Also, these observations have found a broad range of magnetic activity, including magnetic activity cycles, starspots, and surprisingly strong energy release events (‘superflares’). Because the structure and dynamics of the surface of stars other than the Sun are not resolved in observations, it is important to develop numerical simulations capable of reproducing realistic stellar conditions. For solar conditions such simulations can be verified by comparing with high-resolution observations, providing confidence for using these simulations in the interpretation of stellar observations. One particular class of these numerical investigations is the realistic simulation of the upper part of the convection zone and the lower part of the atmosphere of the Sun (Nordlund 1982; Keller et al. 2004; Carlsson et al. 2004; V¨ogler et al. 2005; Stein & Nordlund 2006; Georgobiani et al. 2012) and other stars (Giorgobiani 2003; Steffen et al. 2005; Kupka 2009; Steffen et al. 2009; Muthsam et al. 2011; Georgobiani et al. 2012; Ludwig & Kuˇcinskas 2012; Grimm-Strele et al. 2015; Mundprecht et al. 2015). Such investigations typically consist of compressible radiative MHD simulations in which the governing conservation equations of mass, momentum, energy, and magnetic flux are integrated in time. The stellar composition is modeled using a specific tabular equation of state (EOS) and optical opacity, both based on given stellar chemical abundances. The computational cost of this approach is high, and currently only a relatively small part of a stellar body can be simulated with a resolution sufficient to study the turbulent dynamics of the surface and atmosphere in detail, e.g., to resolve in detail granulation and acoustic events. Nevertheless, these small-scale simulations provide knowledge about the structure and dynamics of the near-surface turbulent layer—one of the most complex regions inside stars. This layer plays a key role in energy and mass transport from a star’s interior to its corona and wind, as result of strong coupling among plasma dynamics, radiation, and magnetic fields. This leads to turbulent convection forming high-speed downdrafts driven by radiative cooling and to the magnetic field becoming organized into strong-field structures that dominate the outer envelope. Knowledge of this dynamics, gleaned from high-resolution local simulations, can then be used in global-star models with relatively low resolution. The current paper describes the implementation and testing of the radiative MHD code ‘StellarBox’. The code provides realistic simulation of solar and stellar convection zones and atmospheres and has been used for a wide range of problems, such as multi-scale dynamics and self-organization processes in turbulent magneto-convection, acoustic wave excitation, formation of stable magnetic structures (such as pores and sunspots), eruptions, generation of magnetic fields by local dynamos, simulation of specific local conditions (e.g., sunspot umbrae and penumbrae), and interactions of the turbulent surface and subsurface with atmospheric layers (Jacoutot et al. 2008; Kitiashvili et al. 2009, 2010, 2013a) . In addition, the code makes it possible to use as initial conditions various models



StellarRadiative Radiative MHD Stellar MHD

41 3

of interior structure pre-calculated for stars with specific chemical compositions, masses, and rotation rates. For F- and A-type stars it is feasible to extend the computational domain into the radiative zone to study the dynamics of convective overshoot layers between the radiative and convection zones. In this paper we first focus on a description of the code and tests of its numerical methods. Then, as an example application, we show the code’s capabilities in simulating turbulent magnetoconvection on the Sun and several main-sequence, moderatemass stars. A detailed analysis of the stellar simulations will be presented in a separate paper. The paper is structured as follows. After a brief description of the code modules and components, the governing equations and the physical models are given. Details of the numerical methods and boundary conditions are described. After this, validation and scalability tests are provided. Finally, example results from simulations of solar and stellar magnetoconvection are presented.

2

Code Description

StellarBox was developed at the NASA Ames Research Center to solve the three-dimensional, fully coupled compressible radiative MHD equations using a fourth-order compact implicit Pad´e scheme for spatial differentiation and a fourth-order Runge-Kutta scheme for time integration. The choice of the numerical scheme is motivated by previous experience in numerical turbulence modeling (e.g., Miyauchi et al. 1993; Chow & Moin 2003). The computational domain is a rectangular volume typically encompassing a horizontal span of tens to hundreds of megameters and a vertical span of a few to several tens of megameters. The domain is discretized using a Cartesian grid. Spatial resolution is typically in the range of 100 km down to 6 km in the horizontal directions. Arbitrary (user-specifiable) mesh stretching is used in the vertical direction. The vertical grid spacing typically increases with depth and ranges from from 10 km to 100 km. Periodic boundary conditions are used in the horizontal directions and characteristic boundary conditions are applied in the vertical. Stellar rotation is accommodated by an f-plane approximation at a user-specified latitude and rotation rate. The code incorporates the following user-selectable subgrid-scale turbulence models for the transport of heat and momentum: compressible Smagorinsky (1963) model, dynamic Smagorinsky (Moin et al. 1991; Germano et al. 1991), and implicit hyperviscosity (Caughey & Jothiprasad 2002). The radiative transport equation (RTE) is solved at every full time-step by using a ray-tracing, long characteristic algorithm along 18 rays. A second-order Feautrier (1964) method is used to solve the RTE along each ray. Frequencies are opacity-binned into logarithmic bins, typically four in number. At depths at which the medium is optically thick, diffusive radiative transport may be optionally used instead of ray-tracing for improved efficiency and accuracy. The opacity wavelength-dependent code provided by the Opacity Project

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(Seaton 1995; Badnell et al. 2005) (http://cdsweb.u-strasbg.fr/topbase/TheOP.html)

A tabular Equation of State (EOS) (Rogers et al. 1996) and opacity are used. StellarBox is a massively parallel code that uses algorithms optimized for parallelization. The parallel data structures are automatically configured, for given mesh dimensions and number of processors, to optimize load balancing. Differentiation and the radiative transfer solution are accomplished by transposing these data structures so that x, y, or z is memory-resident as needed. The overall code structure consists of four main components: Radiation, Time Advance, Utility, and Thermodynamics. Figure 1 shows the code components and subcomponents. Their functions are described in the following bullets: • Radiation: implements the opacity-binning model, interpolation algorithms for the opacity and radiation source functions, and the RTE solver. • Time Advance: implements the convective and diffusive flux calculations, the shock-capturing and turbulence models, and the boundary conditions to perform the time advance. • Utility: implements various utility functions needed by the other modules. • Thermodynamics: implements the equation of state (EOS) and calculates thermodynamic properties. 2.1

Governing Equations

The equations governing compressible radiative MHD flows are conservation of mass, momentum, energy, and magnetic flux. The code solves grid-cell averaged conservation equations for these quantities.

RTE solver

Opacity binning

Fluxes

Radiation

Turbulence Boundary Time Advance conditions model

Opacity and source lookup

Shock capturing

Stellar model

FFT

Utility

EOS

Thermodynamics Transpose

Timing I/O

Thermodynamic properties

Fig. 1. Illustration of the block scheme of the StellarBox code.



StellarRadiative Radiative MHD Stellar MHD

43 5

The mass conservation equation: ∂t ρ + (ρuj ),j = 0

(1)

where ∂t denotes the time derivative operator. The subscript , j denotes the space derivative operator in the j th direction with j = {1, 2, 3}. Quantity ρ is the averaged mass density and uj is the Favre-averaged, i.e., density-weighted average, velocity component in the j th direction. The momentum conservation equation with gravitational and magnetic fields can be written, in the stellar rotation frame, as: ∂t (ρui ) + (ρui uj + pδij ),j = Πij,j + Bij,j − ρφ,i − 2ijk Ωj ρuk

(2)

where p is the pressure, δij the Kronecker symbol, φ the gravitational potential, Πij the viscous stress tensor, ijk the permutation tensor, Ωj the stellar meanrotation vector, and Bij the magnetic stress tensor Bij =

1 1 Bi Bj − Bk Bk δij 4π 8π

(3)

The total energy conservation equation reads ∂t E + [(E + p) uj ],j = − (φj ui ),j + (Πij ui ),j + (Bij ui ),j − Qj,j − Qrad j,j

(4)

where Π is the viscous tensor, Q is the non-radiative heat flux (diffusive and is the radiative heat flux, and E is the total energy per unit Joule heating), Qrad j volume given by: 1 1 Bj Bj E = ρe + ρuj uj + ρφ + 2 8π

(5)

where e is the internal energy per unit mass. The radiative heat flux is obtained by solving the radiative transfer equation, and the viscous tensor and the nonradiative heat flux are written in terms of transport coefficients and gradients of resolved variables. The magnetic flux conservation equation can be expressed in Gaussian units as  2  c ∂t Bi + (uj Bi − ui Bj ),j = [Bi,j − Bj,i ] (6) 4πσ ,j where Bj is the magnetic flux density in the j th direction, c the speed of light, and σ the electrical conductivity. 2.2

Subgrid Stress Tensor

Since it is currently impossible to achieve realistic Reynolds numbers in solar and stellar simulations, StellarBox utilizes a Large-Eddy Simulation (LES) approach

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Alan A. A. Wray Alan Wrayetetal.al.

in which models are used to approximate the effect of subgrid motions on the resolved scales. Modeled subgrid quantities will be denoted by a subscript T . The subgrid stress tensor is represented in the form:   1 Πij = 2µT Sij − uk,k δij − kT δij (7) 3 in which µT is the subgrid viscosity given by the Smagorinsky (1963) model, augmented for compressible flows with a shock capturing term: µT = ρ∆2 (CS |S| + CD |uk,k |)

(8)

where CS is a Smagorinsky  coefficient, CD is a shock-capturing coefficient, ∆ is the grid spacing, |S| = (2Sij Sij ), and Sij is the strain-rate tensor

1 (ui,j + uj,i ) ; (9) 2 kT is the subgrid kinetic energy density given by 2 (10) kT = CC ρ∆2 |S|2 3 where CC is a second Smagorinsky coefficient. The code provides a dynamic option for determining CS and CC based on the associated Germano et al. (1991) identities. Alternatively, they can be specified by the user, as is CD . Sij =

2.3

Heat Fluxes and Turbulent Resistivity

The total non-radiative heat flux is the sum of two contributions: a term due to temperature gradients, that is, Fourier’s law, and a second due to Joule heating:  c 2 1 Qj = κT T,j + (Bi,j Bi − Bi Bj,i ) , (11) 4π σT where κT is the subgrid heat conductivity cp µ T κT = (12) P rT in which P rT is the turbulent Prandtl number and cp is the specific heat at constant pressure per unit mass taken from the Equation Of State (EOS) tables. The turbulent Prandtl number P rT can be specified by the user; it is typically taken to be near unity. The turbulent electrical conductivity, σT , in Gaussian units is given by σT =

c2 , 4πηT

(13)

where c is the speed of light and ηT is the turbulent magnetic diffusivity, modeled following Balarac et al. (2010) and Theobald et al. (1994): η T = CB ∆ 2

| ijk Bk,j | , √ ρ

(14)

where CB a user-specified constant chosen through comparison to fully resolved MHD turbulent simulations. A typical value is 0.25.



2.4

StellarRadiative Radiative MHD Stellar MHD

45 7

Radiative Heat Flux

The radiative heat flux is given by  ∞ Qrad = j 0

Ωj Iν (Ω, x) d2 Ωdν,

(15)

4π

where the quantity Ω is a direction unit vector, ν is the frequency, and Iν is the radiative intensity at frequency ν given by the radiative transfer equation: Ω · ∇Iν (Ω, x, t) = χν (x, t) [Sν (x, t) − Iν (Ω, x, t)] ,

(16)

where non-isotropic scattering, polarization, and the finiteness of the speed of light are neglected. Sν is the radiation source function and χν the opacity. Eq. (16) is solved using the Feautrier (1964) method, which is based on bi-directional ray tracing. The algorithm implemented in the code uses 18 rays (9 bi-directional rays), shown in Fig. 2. In the Feautrier method, the intensity function along a ray is divided into forward- and backward-travelling intensities (Iν+ , Iν− respectively) as a function of distance s along the ray:   dIν+ = χν Sν − Iν+ ds   dIν− = −χν Sν − Iν− ds

(17) (18)

By subtracting Eq. (18) from Eq. (17), we obtain

  d (Iν+ − Iν− ) = 2χν Sν − χν Iν+ + Iν+ ds

(19)

and by adding Eq. (17) and Eq. (18), we have

  d (Iν+ + Iν− ) = −χν Iν+ − Iν+ ds

Fig. 2. The 18 rays used to cover direction space Ω.

(20)

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Alan A. A. Wray Alan Wrayetetal.al.

Defining IνD ≡ Iν+ − Iν− and IνS ≡ Iν+ + Iν− and combining Eqs. (19) and (20), we obtain a single second-order differential equation 1 dχν dIνS d2 IνS − χ2ν IνS = −2χ2ν Sν . − ds2 χν ds ds

(21)

Equation (21), as written, is for a monochromatic intensity IνS . As mentioned earlier, the code treats frequency space by using an opacity-binning technique, in which the opacity of a given bin b, χb , is taken to be the Rosseland mean opacity of the frequencies assigned to that bin. Similarly, the source function Sb for bin b is the source Sν integrated over those frequencies. The RTE for the integrated intensity Ib in bin b is then 1 dχb dIbS d2 IbS − χ2b IbS = −2χ2b Sb − ds2 χb ds ds Eq. (15) becomes, expressed in terms of bins nb   Qrad = Ωj Ib (Ω, x) d2 Ω j b=1

(22)

(23)

4π

where nb is the number of opacity bins, typically four in running StellarBox. Upon discretizing Ω, the integral over Ω in Eq. (23) becomes an appropriately weighted sum over the 18 rays shown in Fig. 2. The weights are chosen to maximize the Taylor-series order of accuracy of the solid-angle integration. 2.5

Numerical Methods

The computational domain is a rectangular volume of dimensions Lx × Ly × Lz defined by the user. The volume is discretized into a cartesian grid, where the number of grid points along each axis, nx , ny , and nz , is set by the user as well. By convention, negative values of z correspond to locations below the nominal photosphere and positive values above it. The basic finite difference differentiation scheme is 4th-order Pad´e and is used to compute derivatives appearing in the diffusive fluxes and also the derivatives of the convective and diffusive fluxes themselves in equations (1), (2), (4), and (6). The scheme must of course be supplemented with boundary conditions, as described in the next section.  The basic stencil to compute the first derivative F of a quantity F in the j th direction (j = {1, 2, 3}) is  1  3 1  Fk−1 + Fk + Fk+1 = j (Fk+1 − Fk−1 ) , 4 4 4hk

(24)

where the subscripts are grid point indices in the j th direction and hjk is a measure of the grid spacing at point k in that direction. Eq. (24) is all that is required in the periodic x and y directions, where h1k ≡ ∆x =

Ly Lx and h2k ≡ ∆y = . nx ny

(25)



StellarRadiative Radiative MHD Stellar MHD

47 9

In the vertical direction z (j = 3), the grid spacing is arbitrary, meaning that h3k may depend on k. Typically, the z-grid is stretched below the photosphere where structures are larger. For one-sided derivatives at the boundaries, Eq. (24) is supplemented, e.g., at the bottom in z, by the second-order boundary form   1 1  F1 + F2 = 3 (F2 − F1 ) 2 h1

(26)

and analogously at nz . Some z-derivatives are computed by specifying derivative values at the boundaries, such as where characteristic boundary conditions are used. h3k is defined as 1 (zk+1 − zk−1 ) ∀ k = {2...nz − 1} 2 = z2 − z1 = znz − znz −1

h3k =

(27)

h31 h3nz

(28) (29)

The source term in Eq. (4) involves the computation of ∇ · Qrad which, as mentioned in Sec. (2.4), requires solving Eq. (22). The latter is discretized using second order finite differences and solved for the quantity IbS − 2Sb so that the limiting case of an optically thick medium is handled accurately. The system of equations Eqs. (24) and the discretized form of Eq. (22) are tridiagonal and are solved using the Thomas algorithm. The code has various tridiagonal solvers implemented for each type of boundary condition. 2.6

Boundary Conditions

In order to close the system of equations (1), (2), (4), and (6), boundary conditions are required. Periodic boundary conditions are applied in the horizontal directions (j = 1, 2). For the z direction, the user has a choice of both boundaries closed (impenetrable, i.e., u3 = 0), or both open, or the top open and the bottom closed. The open boundaries are implemented by a characteristic method (e.g. Sun et al. 1995). This top-open, bottom-closed set of boundary conditions is the one typically used in StellarBox. To simulate the energy flowing from the stellar core, the bottom boundary condition for the total energy is modified by adding an incoming energy flux per unit area equal to the stellar value. In addition, to preserve exact conservation of mass, momentum, energy, and magnetic flux in the domain, inward fluxes equal to the sum of those convected and diffused outward through the top and bottom boundaries are introduced at the bottom boundary as an areal average. This does not apply to the outgoing radiative flux at the top boundary — the system is allowed to find its own radiative equilibrium wherein the radiative flux emitted through the top boundary statistically balances the incoming energy flux at the bottom boundary. The state that attains this last condition serves as a sanity check on the general correctness of the simulation.

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Alan A. A. Wray Alan Wrayetetal.al.

Time Integration

The discretized system of equations (1), (2), (4), and (6) can be written compactly as dU = R(U) (30) dt T

where R(U) includes all the spatially discretized terms, and U = (ρ, ρu, E, B) is the vector of conserved variables. Eq. (30) is solved using the following 4th order Runge-Kutta scheme: Un+1 = Un +

∆t (k1 + 2k2 + 2k3 + k4 ) 6

(31)

∆t is the time step, the superscript n stands for the time step, and the quantities k1 , k2 , k3 , and k4 are defined as follows k1 = R(Un )   ∆t n k2 = R U + k 1 2   ∆t n k3 = R U + k2 2 k4 = R (Un + k3 ∆t)

3

(32) (33) (34) (35)

Parallel Scaling

It is essential, for efficient parallel computation, to understand the scaling properties of a massively parallel code such as StellarBox. Various means of describing these properties have been devised. Here we present the results of our scaling tests in a particularly simple format based on comparison to an ideally performing code and computer system. By “ideal” we mean that the time associated with communication among the processors increases no faster than the amount of data communicated. Since all the significant computation in StellarBox involves an equal amount of work for each processor and for each grid point, an expression for the time, tideal , for such an ideal system to compute one time step would have the following form: tideal = α

nx n y n z Nproc

(36)

in which nx , ny , nz are the mesh dimensions and Nproc is the number of processors. The factor α, which is the time per step per processor per grid point, is constant in the ideal case for any mesh dimensions or number of processors. Of course, any real code and computer system will show performance degradation, reflected by an increasing α, as the number of processors increases for a fixed problem size, principally due to contention for limited resources such as interprocessor communication hardware. In Figure 3 we show the α values obtained



StellarRadiative Radiative MHD Stellar MHD

49 11

_ (sec. / step / processor / grid point)

0.0003 3

1024 mesh 3 1500 mesh

0.00025 0.0002 0.00015 0.0001

5e-05 0

0

10000

20000

30000

40000

50000

Number of Processors

60000

70000

Fig. 3. Scaling results for StellarBox: α, time per step per processor per grid point, as a function of the number of processors.

for various numbers of processors on two different mesh sizes: 10243 and 15003 ; all runs were conducted on the Pleiades computer system at NASA Ames Research Center. It is clear from this figure, for meshes of these approximate sizes, that the code behaves well — only slowly growing α — up to 45,000 processors or so, and that performance is seriously degraded for 65,000 processors with a mesh of 10243 , on this computer system. Larger mesh dimensions would presumably result in better performance for 65,000 processors and beyond, though we have not tested this at this time.

4

Test Cases

SolarBox has been exercised for a large number of test cases to ensure physical and numerical accuracy. A subset of the more interesting tests is given in the subsections to follow.

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4.1

Sod Shock Tube

The Sod shock tube problem (Sod 1978) is often used as a one-dimensional test case to check the ability of a compressible code to capture shocks, contact surfaces, and rarefaction waves present in the flow. The initial conditions are:  (0.125, 0, 0.1) if x ≤ 0.5 (ρ, u, p)t=0 = (1., 0, 1.) if x > 0.5 The gas is taken to be perfect with a specific heat ratio γ = 5/3. Different runs were performed using different grid resolutions and different numerical diffusion coefficients in order to find a balance between damping numerical instabilities and resolving the sharp discontinuities. In the case of the Sod shock tube, and as a general rule, less numerical diffusion is required for 1D, non-radiative, non-stratified problems than for stellar simulations. Figure 4 shows the numerical solution for pressure and density profiles along the x axis at time t = 0.1, using 480 grid points. The solid line is the numerical solution obtained using the differentiation, shock capturing, and time-advance algorithms in the code, and the symbols show the solution provided by an exact Riemann solver (Toro 1997). Good agreement is obtained for both the positions and the amplitudes of all the flow structures (shock, contact surface, and expansion fan). 4.2

Orszag-Tang Problem

The Orszag & Tang (1979) problem is a popular MHD test for two dimensional codes and is also known as the ∇·B = 0 test condition. It is used to check the robustness of a code in handling MHD shocks, including shock-shock interactions. 1

1 Exact_RS Pade

Exact_RS Pade

0.8

density

pressure

0.8

0.6

0.6

0.4

0.4

0.2

0.2

a)

0

0.2

0.4

0.6 X

0.8

1

b)

0

0.2

0.4

0.6

0.8

1

X

Fig. 4. Sod shock-tube test: a) Pressure and b) density profiles at t = 0.1 . Solid line is the numerical solution and symbols represent the exact Riemann solver solution (ExactRS).



StellarRadiative Radiative MHD Stellar MHD

a)

b)

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c)

Fig. 5. Solution of the Orszag-Tang problem at t = 0.25, obtained with the StellarBox using the Pad´e scheme: a) density (the linear color map ranges from 0.06 to 0.52), b) magnetic energy (from 2.×10−8 to 0.3), c) kinetic energy (from 2.×10−8 to 0.65).

The initial conditions are: 5 25 ; p= 36π 12π u = − sin(2πy); v = sin(2πx) Bx = − sin(2πy); By = sin(4πx)

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The computation was performed using a 512 × 512 grid. At time t = 0.25, Figure 5 shows snapshots of the density, magnetic energy, and kinetic energy fields. The images are directly comparable with ones in Stone et al. (2008) and good quantitative agreement is obtained even though the numerical methods used in the two codes are quite different. Figure 6 shows the pressure and density profiles for t = 0.25 at y = 0.4277. These results compare very well with those in Londrillo & Del Zanna (2000), Jiang & Wu (1999), and Ryu et al. (1998). 0.45

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Fig. 7. Brio and Wu shock-tube test at t = 0.1: the solid line is the numerical result obtained with the Pad´e scheme, and the dashed line is the solution provided by the exact MHD Riemann solver of Torrilhon (2003): a) density profile, b) pressure profile, c) magnetic filed profile.

4.3

Brio and Wu Shock Tube

This test is a simulation of an MHD shocktube (Brio & Wu 1988); the hydrodynamic portion of the initial conditions are the same as for the Sod shock tube problem. However, the B field makes the algebraic equations of the Riemann problem highly non-linear and complex in a five-dimensional parameter space. Moreover, the presence of so-called non-regular waves in the MHD system causes the Riemann problem to be non-unique in some cases (Torrilhon 2003). The right and left states are initialized as follows:  (0.125, 0, 0, 1, 0, 0.1) if x ≤ 0.5 (ρ, u, v, By , Bz , p)t=0 = (1, 0, 0, −1, 0, 1) if x > 0.5 where Bx =0.75 is constant and γ = 2. The numerical results are compared to the solution provided by the exact MHD Riemann solver (Exact− RS) of Torrilhon (2003). Figure 7 shows the density, pressure, and By profiles at t = 0.1. Good agreement is obtained for both the regular and non-regular waves. 4.4

Radiative Transfer Test

In order to test the ray tracing algorithm that is used in StellarBox to solve the radiative transfer equation (Eq. 16), two three-dimensional radiative transfer computations were performed using a box of 6×6×6 Mm that includes 1 Mm of the lower solar atmosphere; the grid dimensions were 64×64×128. In the first computation, the ray tracing algorithm was used everywhere; in the second, it was only used in the part of the domain defined by z  −2 Mm (as previously mentioned, by convention negative values of z correspond to locations below the nominal photosphere and positive values above it), and a purely diffusive treatment was used everywhere else (z  −2 Mm). The latter is a good approximation in optically thick regions, which is the case below z ≈ −2 Mm. The ray-tracing portion was computed using four opacity bins as usual, as described above,



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and the diffusive portion was computed using a single, all-frequency Rosselandaverage opacity value at each point to obtain the diffusion coefficient. Figures 8 and 9 compare the local radiative cooling obtained for these two simulations. The profiles are at a single time and are averaged over x-y planes. They clearly agree very well over the full domain in z (Fig. 8), and, in the optically thick region below z = −2 Mm (Fig. 9), agreement is also good, though it is worth noting that the profile is smoother for the diffusive method, most likely because it does not involve a discrete angular quadrature; in any case, the values are very close between the two approaches.

5

Simulations of Stellar Magnetoconvection

In this Section we present some results of our simulations of solar and stellar magnetoconvection. While the main goal is to demonstrate the code’s capabilities for understanding the dynamics of near-surface turbulent convection, the results give important insights into stellar surface dynamics and magnetic effects.

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Fig. 8. Comparison of radiative transfer calculations over the full domain; red line with squares: full ray-tracing; black line: diffusive radiation treatment in the optically thick region (below z = −2.277 Mm).

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5.1

Effects of Numerical Grid Resolution

Despite substantial growth in computing power, our computational capabilities for 3D simulations are still quite limited, and it is important to investigate the effects of numerical grid spacing on the resolution of the important turbulent convective structures, such as granulation. Figure 10 presents snapshots of the vertical velocity at the solar surface for simulations with grid spacings of 100, 50, 25, and 12.5 km. The results show the granulation structure, which has a characteristic size of about 1 Mm and consists of relatively slow upflows occupying most of the area and fast downdrafts concentrated in the intergranular lanes. The primary effect of the decreasing grid spacing is in resolving the smallscale structures and dynamics in the intergranular lanes; the primary granulation structure is well-resolved at all resolutions. This is also evident from the turbulent energy spectra shown in Figure 11. The energy spectra show that resolving small-scale turbulence may significantly reduce the large-scale energy of the granulation. This effect has to be taken into account in stellar simulations which are generally performed with relatively low resolution. The small-scale dynamics of the intergranular lanes of solar convection, illustrated in Figure 12, is associated with shearing flows and plays a critical role in the formation of tornado-like vortex tubes (Kitiashvili et al. 2012), excitation of acoustic waves (Kitiashvili et al. 2011), creation of local dynamos (Kitiashvili



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Fig. 10. Snapshots of the simulated solar granulation (vertical velocity shown) at the photosphere for different resolutions: a) 100 km, b) 50 km, c) 25 km and d) 12.5 km.

et al. 2013b), etc. For example, powerful vortex tubes are evident in Fig. 12 as rounded structures, ∼ 100 km across, with dark cores corresponding to nearly supersonic downdrafts. Undoubtedly such shearing and twisting flows in the intergranular lanes are also extremely important on other stars. These effects will be a topic in future investigations using the StellarBox code. 5.2

Structure of Granulation on the Sun and Moderate Mass Stars

As stellar mass increases, the outer convection zone shrinks, and turbulent motions become more vigorous because of the increased energy flux. The granulation structure also changes quite significantly. Figure 13 shows the distribution of the vertical velocity on the surface of the Sun and five main-sequence stars with masses of 1.17 M , 1.29 M , 1.35 M , 1.47 M , and 1.60 M . The simulations were performed for a computational domain of 100 × 100 Mm horizontally, 40 − 50 Mm in depth, and 1 Mm above the photosphere. The initial conditions in each case are for standard zero-age main-sequence models calculated for the solar composition using the CESAM code (Morel 1997). The initial conditions for the solar simulations are constructed by combining the standard

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Fig. 12. High-resolution simulations (∆x = 6.25 km) of solar convection revealing a very inhomogeneous distribution of the vertical velocity at the photosphere.



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model S ((Christensen-Dalsgaard et al. 1996)) and the VAL model of the solar atmosphere ((Vernazza et al. 1973)). These hydrostatic initial conditions are perturbed by random velocity fluctuations to initiate convective motion, and simulation runs are continued for several hours of stellar time until statistically stationary conditions are achieved. No magnetic fields were included in these simulations. The simulation results show that the characteristic size of granulation increases from ∼ 1 Mm in the case of the Sun to more than 10 Mm for the 1.60 M A-type star. For this latter type of star, standard stellar evolution theory using a mixing-length model predicts that the outer convection develops only in the hydrogen and helium ionization zones, separated by a stable layer. However, the simulations show that these layers are mixed, creating a shallow convection zone with a well-defined granulation pattern. For reference, the pressure scale heights for the Sun and the 1.17 M , 1.29 M , 1.35 M , 1.47 M , and 1.60 M stars are approximately 140, 173, 236, 267, 270, and 359 km, respectively. An interesting question concerns the large-scale organization of granulation, observed on the Sun as meso- and super-granulation. Our results show that the solar granulation tends to form rather irregular clusters of several granules. However, the simulations do not explicitly show any large-scale (20-30 Mm) patterns which could correspond to supergranulation, at least for zero rotation and the simulation domain dimensions tried so far (the domain extended to 20 Mm deep for stars with masses ≤ 1.35 M and to approximately 50 Mm deep for heavier stars). This means that some essential physics may be missing in these simulations, e.g., large-scale magnetic fields or rotation. This question requires further investigation. Mesoscale clustering can be seen in the more massive stars. It is particularly pronounced in the 1.47 M case, in which large-scale convection cells become crossed, “shredded”, by a series of aligned intergranular lanes. This type of granular instability also exists in solar granulation (Kitiashvili et al. 2012) but is substantially less pronounced. The shredding process is accompanied by generation of intense acoustic waves which are seen as diffuse darker patches in the snapshots. These results demonstrate the capabilities of the StellarBox code in simulating turbulent stellar convection and reveal very complex multi-scale convective structures. A more detailed understanding of their dynamics will be a goal of our future studies. 5.3

Magnetic Field Structuring

To illustrate the effects of magnetic fields on near-surface stellar convection, we present simulation results following the injection of a uniform 100 G vertical magnetic field into a fully developed convection layer. The boundary conditions conserve the mean vector magnetic field but do not prescribe any field structure. The domain is 12.8 × 12.8 Mm horizontally, 5.5 Mm in depth below the photosphere, and 0.5 Mm above the photosphere. Results for the Sun and a 1.35 M star are shown in Figure 14. In the case of the Sun, the initially uniform magnetic field becomes concentrated into compact, self-organized, 3-4 Mm

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Fig. 13. Variation of the scales of granulation for main-sequence stars with increasing stellar mass; from top, left to right: 1 M , 1.17 M , 1.29 M , 1.35 M , 1.47 M , 1.60 M . Distribution of the vertical velocity is plotted for a range of ±6 km/s in all plots.



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wide pore-like magnetic structures maintained by strong dowdrafts. This process of spontaneous formation has been previously described in detail by Kitiashvili et al. (2010) for simulations in a smaller, 6 × 6 Mm domain. The new simulations confirm these results and show that the larger domain did not lead to formation of a larger structure. Instead, two compact structures of a similar size were formed, indicating that the structures are independent of the simulation domain size. What determines the scale of these self-organized magnetic domains has not been established. Curiously, the simulations for the 1.35 M star did not result in formation of such large-scale structures, but instead the magnetic field became concentrated in small-scale patches in the intergranular lanes. In addition, the magnetic field formed diffuse patches of 100-200 G in the bodies of the stellar granules, whereas the magnetic fields inside the solar granules were much weaker. The reason for this difference is also unclear. Nevertheless, this indicates that the background (‘basal’) magnetic field may have quite different structures on different types of stars. From the numerical point of view, our simulations have shown that, for simulating the process of spontaneous structure formation, the grid spacing should be 25 km or smaller. For coarser grids the structures do not form. This indicates the importance of accurate simulation of the flow dynamics in intergranular lanes.

Fig. 14. Distribution of magnetic field in the photosphere from simulations with an initially uniform vertical 100 G magnetic field: a) in the Sun, and b) in a 1.35M star. Panels c) and d) show corresponding vertical cuts along the x-axis at the locations indicated by the arrows in a) and b). The fields shown are typical of the statistically stationary state.

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Summary

We have presented the basic features and some test results of the 3D radiative MHD code ‘StellarBox’. The code is designed to accurately simulate turbulent magnetoconvection processes in solar and stellar envelopes. It is based on a high-order Pad´e finite-difference scheme and implements subgrid-scale LargeEddy Simulation (LES) turbulence modeling. This is expected to provide a more accurate description, as compared to using more ad hoc turbulence models or lower-accuracy numerics, of complex physical phenomena in the highly turbulent radiating plasma in the Sun and other stars. Such phenomena include the formation and dynamics of surface granulation, large-scale convective structures, excitation of acoustic, gravity, and MHD waves, magnetic self-organization, etc. The code has been carefully tested using standard CFD and MHD solutions and shows good accuracy and robustness. The code’s capabilities were demonstrated by performing simulations of the upper convection zones of the Sun and several moderate mass stars, first without magnetic field and then with an imposed, initially uniform, vertical magnetic field. The solar convection simulations were performed for different numerical grid spacings, from 6.25 km to 100 km. The results show that, while the coarse, 100 km grid is sufficient for resolving the granulation structure, the rich dynamics of intergranular lanes can only be resolved with smaller grid spacings, e.g. 12 km. The importance of such resolution is revealed by the observation that the intergranular lanes are a source of strong, almost supersonic shearing flows and compact (∼ 100 km across) vortex tubes, which play important roles in the formation of magnetic structures. For an initial comparative analysis of stellar convection, we performed largescale (100 × 100 × 40 Mm) simulations for six main-sequence stars with masses from 1.0 M to 1.60 M . The results showed a substantial increase in the granulation size with stellar mass, from 1 to 20 Mm. Further, the granulation for stars more massive than the sun was often clustered on mesogranulation scales (on the scale of several granules). It was found that magnetic field effects can be quite different in stars of different classes. The simulations showed that, in the solar mass case, an initially uniform magnetic field forms self-organized, stable ‘pore-like’ structures of the size of several granules. But, in the case of more massive stars, such structures are not formed, and the magnetic field is distributed in the intergranular lanes in the form of small kilogauss magnetic flux tubes. In conclusion, 3D radiative MHD simulations, which are becoming more and more feasible on modern supercomputer systems, allow us to simulate stellar magnetoconvection with a great degree of realism and provide an important tool for understanding the complex physics of turbulent stellar envelopes.

Acknowledgments The work was partially supported by NASA grants NNX09AJ85G and NNX14AB70G.



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Advances in Realistic MHD Simulations of the Sun and Stars Irina N. Kitiashvili NASA Ames Research Center/Bay Area Environmental Institute, Moffett Field, CA 94035-1000, USA Abstract. Modern high-resolution observations from ground and space telescopes reveal a complicated dynamics of turbulent magnetoconvection and its effects in the solar and stellar atmosphere and corona, showing intense interactions across different temporal and spatial scales. Interpretation of the observed complex phenomena and understanding of their origins is impossible without advanced numerical models. The rapid growth of computational capabilities has made possible 3D radiative MHD numerical simulations that reproduce conditions in solar and stellar interiors and atmospheres with a high degree of realism. Such simulations allow us to determine physical processes hidden from direct observations. They also provide synthetic data for calibration of observational data and for developing and testing ideas for improved diagnostics. This review describes current advances and challenges of modeling multi-scale turbulent magnetoconvection, MHD waves, magnetic self-organization phenomena in the photosphere, their dynamical interaction with the chromospheric layers, and modeling of spectro-polarimetric observations for different instruments.

1

Introduction

Recent observations of the Sun and solar-type stars have revealed a tremendous complexity of physical processes in solar and stellar convection zones and atmospheres. These processes, driven by the energy flux from the stellar interiors, involves intense turbulent dynamics, generation of magnetic fields, spontaneous magnetic self-organization, excitation of oscillations and waves, and supersonic plasma eruptions. The observations show that the traditional 1D models of stellar structure, based on mixing-length theory and semi-empirical atmospheric models, are no longer satisfactory. An emerging paradigm is that the convection zone and atmosphere are strongly coupled to each other through intense turbulent motions and magnetic selforganization processes and cannot be separated into well-defined spherical layers. The previous understanding of convective energy transport from the deep interior to the atmosphere as a sequence of slowly rising bubbles of hotter material is no longer valid. The convective motions themselves appear driven by convective downdrafts that originate at the surface and in some cases can penetrate through the entire convection zone. The outer layers of stars appear as highly non-uniform and dynamic, accompanied by numerous multi-scale phenomena that not only significantly affect the basic mean properties but also result in the generation of magnetic fields, oscillations, shocks, and plasma eruptions. Understanding and characterizing these phenomena is important, not only from the

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point of view of fundamental stellar and solar astrophysics and interpretation of observational data, but also for developing new methods of spectro-polarimetric diagnostics of solar and stellar properties and in the search for and characterization of exoplanets. Because of the complexity of non-linear turbulent MHD processes, realistic numerical simulations play a key role in advancing our knowledge of the Sun and stars. Based on first principles, such simulations became achievable only recently through the rapid development and availability of massive parallel supercomputer systems. The principal approach, initiated by the pioneering studies of Nordlund and Stein (2001), is to model as accurately as possible all essential physical processes by solving the mass, momentum, and energy conservation equations, coupled with the equations for magnetic field, radiative energy transfer, and equation of state. This approach is capable of reproducing the observed phenomena with a high-degree of realism and uncovering their principal physical mechanisms. It has been successfully used for understanding granulation structure (Stein and Nordlund 2001), mechanisms of wave excitation and propagation (Georgobiani et al. 2000; Jacoutot et al. 2008; Kitiashvili et al. 2011a,b), small-scale dynamo processes (Sch¨ ussler & V¨ ogler 2008; Rempel 2014; Kitiashvili et al. 2015), dynamics of sunspots (Rempel et al. 2009; Kitiashvili et al. 2009; Kitiashvili et al. 2011b), and formation of magnetic structures (Kitiashvili et al. 2010; Stein and Nordlund 2012). The primary characteristic feature of realistic simulations is that they do not include ad hoc structuring or artificial driving terms in the model. The physical phenomena are reproduced as naturally as possible. However, despite the attractiveness of this approach, there is a principal limitation: both the hydrodynamic and magnetic Reynolds numbers are so large that there is no hope of performing direct numerical simulations, i.e., fully resolving all turbulent scales. A systematic approach to overcome this difficulty is to apply a Large Eddy Simulation (LES) methodology, the basic principle of which is to resolve the essential turbulent scales and model the unresolved, subgrid-scale turbulent motions and dissipation. In terms of the turbulence spectrum, this means that the turbulent scales must be resolved down to the Kolmogorov inertial range. This approach has been implemented in the StellarBox code described in Wray et al. (2016). That paper presents an overview of a wide range of results obtained with the StellarBox code showing its capability to model the turbulent dynamics of stellar and solar convection, generation of magnetic fields, spontaneously excited eruptive dynamics of stellar atmospheres, and many other phenomena.

2

Dynamics and Structure of Stellar Convection Zones

Solar-type stars are characterized by acoustic oscillation modes excited by turbulent convection in the upper convective boundary layer. As the stellar mass increases, the convection zone shrinks and the scale and intensity of the turbulent motions increase, providing more energy for excitation of acoustic modes. When the stellar mass reaches about 1.6 solar masses the upper convection zone



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Fig. 1. Kepler-target stars and models of interior structure for various masses from 0.9M to 2.0M and compositions Y = 0.248, Z = 0.02 in the log g – log Tef f diagram (panel a). Panels b and c show three standard models of the density and temperature distributions with depth for stars of 1.35, 1.47 and 1.7 M . Horizontal axis at the bottom corresponds to stars with 1.35 and 1.47M , and the top axis corresponds to a 1.7M star.

consists only of two very thin layers corresponding to H and He ionization, and, in addition to the acoustic modes, the stars show strong internal gravity modes. This thin convection zone is often considered insignificant for stellar dynamics and variability. Modeling of stellar convection in realistic way requires an initial interior structure model that is consistent with the observed properties of the star. The initial background models of the stellar interior structure used here were obtained using the standard 1D stellar evolution code ‘CESAM’ (Morel 1997; Morel & Lebreton 2008). In this study, 14 bright stars with masses (estimated from evolutionary models) between 0.9M and 1.8M have been chosen. These targets are shown in Fig. 1a, on the logg – log Tef f diagram. Figure 1b-c shows examples of interior structure models for stars with mass 1.35, 1.47 and 1.70M . These standard models were used as initial conditions in the present numerical model. The simulations of stellar convection were performed using the 3D radiative MHD code ‘StellarBox’ (Wray et al. 2016).

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Fig. 2. Snapshots of the temperature distribution for the Kepler target star KIC11342880 (1.35 M ) at the photosphere (panel a), 2 (b) and 10 Mm (c) below the stellar surface. Panel d shows a vertical cut of the simulation domain for the vertical component of the velocity.

2.1

Multi-scale Structure of Stellar Convection

Numerical simulations of stars more massive than the Sun show that the dynamics of convective flows in these stars strongly deviate from the solar convection dynamics. Figure 2 shows horizontal cuts of the temperature distribution in the photosphere (panel a), 2 and 10 Mm below the photosphere (panels b and c), and a vertical cut of the vertical velocity. In the case of a Kepler-target star, KIC11342880 (1.35 M ), two basic scales of stellar granulation can be identified. In addition to solar-like granulation with a characteristic diameter of 1 – 2 Mm, larger granules can be identified (Fig. 2a). Such double-scale structuring disappears below the photosphere, and in the deeper layers the scale of convective patterns increases (Fig. 2b, c) similarly to previous simulations of solar convection (Nordlund et al. 2009). However, the convective downflows in the intergranular lanes are essentially stronger than in solar convection and can reach up to 16 km/s and extend down to 30 Mm below the photosphere (Fig. 2d). In the case of stars with mass 1.47 M , the 3D radiative hydrodynamic simulations span the entire convection zone. The stellar photosphere is cov-



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Fig. 3. Vertical velocity distribution for the simulated F-type star (1.47 M ) at eight depths throughout the convective zone and into the radiative zone, 0, 5, 10, 20, 30, and 40 Mm below the surface (r = R). To display small-scale details, the color scales are chosen shorter than the full velocity range.

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Fig. 4. Vertical slices of: a) vertical velocity, Vz ; and fluctuations of b) temperature, T  , c) density, ρ ; and d) sound speed, cs , for the modeled star (1.47 M ). Depth z is defined as z = r − R.

ered by cells, that, like granules on the Sun, are characterized by upflows in the middle and narrow downflows in the surrounding lanes (Fig. 3a). The size of stellar granules varies from ∼ 2 Mm to ∼ 12 Mm, and clusters of several granules (resembling mesogranulation) are evident. Most granules of an intermediate size are stretched by larger-scale upflows. The multi-scale property of the convection vanishes in subsurface layers, where the scale of the convective eddies increases with depth (Fig. 3a − d) and reaches a size of 40–45 Mm at about 25 Mm depth (near the bottom of the convection zone). Deeper down the influence of the overshoot region becomes more and more noticeable as prominent finely structured upflows are formed around edges of strong downflows. Figure 3e illustrates a horizontal slice of the overshoot region at 30 Mm depth, where high-speed downflows (Fig. 4a) penetrate through the whole convection zone and hit the radiative zone, causing splashes in the horizontal directions and generating numerous small-scale turbulent helical structures and upflows around the plumes (Kitiashvili et al. 2016). The overshoot region can be defined as a zone of penetration of convective flows below the adiabatic boundary at zcz . Below the overshoot region, at a depth of 40 Mm, in the radiative zone, which is a convectively stable layer, the velocity perturbations quickly decrease, and the dynamics is dominated by internal gravity waves (Fig. 3f ). Simulation results show that narrow high-speed downdrafts (Fig. 4a) driven by surface radiative cooling can often penetrate through the whole convection zone, but they quickly stop in the overshoot layer. The downflows are accelerated up to 21 km s−1 and initiate strong perturbations in the radiative zone. Such perturbations are clearly visible in the density, temperature, and sound-speed fluctuations (Fig. 4b − c). The downdrafts are associated with positive density perturbations and negative temperature perturbations (Kitiashvili et al. 2016). However, the penetrating downflows also locally heat the overshoot region. The



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downdraft impacts also lead to the excitation of internal gravity waves (g-modes) in the radiative interior. a) 10

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To summarize the dynamical structuring from the stellar photosphere down to the radiative zone, it is convenient to consider the mean vertical profiles of the fluctuations for various turbulence quantities. The rms velocity profiles show the relative strength of the vertical and horizontal flows (Fig. 5a). The horizontal flows gradually decrease in strength from the photosphere to the bottom of the convection zone. In the overshoot region, the amplitude of the horizontal velocities increases slightly due to splashing of downdrafts. The rms vertical velocity profile shows a strong deviation from the horizontal flows near the stellar surface layer. In particular, an additional broad bump at about 5 Mm below the surface corresponds to one of the characteristic scales of the granulation layer. In deeper layers, the vertical velocity gradually decreases. It is interesting to note that, in the range of depths of 6 – 10 Mm, the horizontal and vertical flows behave very similarly. Below 10 Mm the fluctuations of the vertical velocities are stronger than the horizontal ones, probably reflecting the influence of the penetrating high-speed downdrafts. In the overshoot layer, the vertical velocity sharply decreases. The distribution of temperature fluctuations with depth (Fig. 5b, black curve) shows the strongest variations near the surface layers and in the overshoot region. Despite the similarity of the fluctuation amplitudes, their nature is different. The near-surface fluctuations (peaked at ∼ 5 Mm) are mostly related to strong radiative cooling in the intergranular lanes and are associated with downflows that determine the granulation scales (Kitiashvili et al. 2016). A sharp increase in temperature fluctuations between −10 and −5 Mm corresponds to the HeII ionization zone. In this region the rms of vertical velocity (Fig. 5a) and the convective energy flux also increase, indicating an enhancement of turbulent

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Fig. 6. Panel a): deviations between the 3D simulation and 1D model of a star with mass M = 1.47 M as a function of depth, z = r − R, for the squared sound speed, δc2 /c2 . Panel b): the squared relative sound speed deviations obtained by helioseismology inversion (Kosovichev 1999; Kosovichev 2011) from the 1D standard solar model (Christensen-Dalsgaard et al. 1996). Vertical dotted lines show the location of the bottom boundary of the convection zone.

convection in the ionization zone, perhaps confirming the theoretical predictions of Rast & Toomre (1993). 2.2

Convective Overshoot and Comparison with Standard Stellar Structure Theory and Helioseismology Results

The region of convective overshoot is defined in terms of the temperature gradient as a transition zone between the adiabatic and radiative gradients (e.g. Christensen-Dalsgaard et al. 2011). This closely corresponds to the region of negative enthalpy flux, which is a distinct feature of convective overshooting. The simulation results clearly show that the overshooting region consists of two parts: the upper part represents an almost adiabatic extension of the convection zone, while the lower part shows a significant peak of increased subadiabaticity. However, most previous ‘semi-empirical’ models (see Christensen-Dalsgaard et al. 2011, for a review) described the overshoot region as an extension of the depth of the convection zone with a smooth monotonic transition between the adiabatic and radiative temperature (or entropy) gradients. The numerical simulations presented in the previous section show that the braking of penetrating convective plumes results in heating of the overshoot region (Kitiashvili et al. 2016). This leads to a sharp decrease of the temperature gradient in the lower part of the overshoot region. This effect has to be taken into account in the construction of 1D models of convective overshoot based on modification of the temperature gradient in the standard solar and stellar models. The sound-speed variations are of particular interest because asteroseismic estimations based on p-mode frequencies are mostly sensitive to the sound-speed profile. Usually the sound-speed profile calculated from a 1D stellar model is used as a reference; therefore, it is important to investigate the deviations in sound speed between the 3D simulation and 1D model. Figure 6a shows the relative



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sound-speed difference. This profile reveals strong deviations from the 1D model. These deviations are qualitatively similar to the findings of global helioseismology analysis reproduced in Fig. 6b (e.g. Kosovichev 1999). In particular, the 3D simulations reproduce the characteristic ‘bump’ at the bottom of the convection zone (z ≈ −33 Mm in Figure 6a). This bump corresponds to the overshoot layer, which is about 8 Mm thick. Simulation results show a qualitative agreement for the bump’s shape with helioseismology results, but the amplitude of the variations in the stellar simulations is much larger than in the solar measurements, probably because the convection is much more vigorous in the F-type star than in the Sun. Nevertheless, the surprising similarity supports an idea about the influence of the convective overshoot in the solar sound-speed inversions (Fig. 6). The good correspondence leads us to the suggestion that the structure of the overshooting region in the Sun is similar to the overshoot structure obtained in the simulations (Kitiashvili et al. 2016).

3

Generation of Small-Scale Magnetic Fields and Magnetic Self-organization

Magnetic field generation is a key problem for understanding solar variability across a wide range of scales. Theories of small-scale (or turbulent) dynamo processes have been intensively studied in the past. In particular, the similarity between the MHD induction and vorticity equations (Batchelor 1950) initiated discussions about magnetic field amplification due to turbulent flows. By analogy with vortices when stretching makes them stronger, twisting and stretching of magnetic field lines can amplify the field strength. Thus, repeating stretching, twisting, and folding of magnetic field lines can provide a local increase in the magnetic flux and its recirculation in a dynamo process (Vainshtein & Ruzmaikin 1972). Previous studies were mostly done with direct numerical simulations (DNS) performed for artificially forced turbulent flows (e.g., Meneguzzi & Pouquet 1989; Schekochihin et al. 2005) and also for convectively driven flows for a wide range of parameters (e.g., Nordlund et al. 1992; Cattaneo 1999; Brandenburg et al. 2012). In addition, recent ‘realistic’-type radiative MHD simulations have reproduced the solar surface conditions with a high degree of realism and have demonstrated that magnetic fields can be quickly amplified by local dynamos in the upper convection zone from a very weak (∼ 10−2 G) seed field, leading to more than 1 kG magnetic elements (V¨ ogler & Sch¨ ussler 2007; Rempel 2014; Kitiashvili et al. 2015). Numerical simulations of local dynamos on the Sun have two specific features that must be taken into account: 1) solar turbulence is driven by near-surface convective flows in a highly stratified medium; 2) the hydrodynamic and magnetic Reynolds numbers are so high that direct numerical simulations (DNS) with fully resolved turbulent scales are not possible. The first feature requires accurate modeling of solar conditions including radiative transfer with realistic opacities and a realistic equation of state. This means that direct numerical

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simulations of flows with artificially forced turbulence have limited applicability to the solar dynamo problem. The second feature of solar simulations requires implementation of sub-grid scale (SGS) turbulence models. Previous solar magnetoconvection simulations (e.g. V¨ ogler & Sch¨ ussler 2007; Rempel 2014) used either artificial or numerical viscosity to model, explicitly or implicitly, dissipation due to turbulence at unresolved scales. Our work was performed with a Large-Eddy Simulation (LES) approach implemented in the StellarBox code. For detailed description of the StellarBox code see chapter by (Wray et al. 2016) in this book. 3.1

Subsurface Turbulent Dynamo

Magnetic field amplification in turbulent solar convection can roughly be divided into three basic mechanisms: 1) magnetic field concentration due to converging flows (e.g. Nordlund 1983), 2) convective collapse (Parker 1978; Spruit & Zweibel 1979), and 3) dynamo processes driven by helical or shearing motions (e.g. Batchelor 1950; Vainshtein & Ruzmaikin 1972; Brandenburg 1995). The turbulent nature of the photospheric layers, where intense radiative cooling drives downward convective motions, makes it impossible to separate different sources of the locally growing magnetic energy (Spruit 1984), and therefore magnetic field amplification can be discussed only in terms of a dominant mechanism. To avoid confusion in separating dynamo and non-dynamo field amplification, no additional magnetic flux was introduced into the computational domain after the ‘seed’-field initialization. This provides an important test for the dynamo action: if there were no dynamo process then local magnetic patches would only be formed due to converging flows in the intergranular lanes, and then convective downdrafts would transport these patches into deeper layers, from which a part of the flux would be recycled by turbulent motions. In contrast, with small-scale dynamo action, magnetic field patches are continuously formed, resulting in a rapid growth of magnetic energy. Note that during very early times of the ‘dynamo’ simulations (shorter than one overturning time) the evolution of the ‘seed’-field magnetic elements behaves similarly to corks in distributed turbulent flows: they tend to collect in the intergranular lanes where the convective flows converge. Because the weak field mostly follows the turbulent flow, the regular field distribution becomes deformed. During this stage local magnetic field amplification is primarily caused through compression by converging flows in the intergranular lanes. Shortly after this initial phase the dynamo process begins: small-scale helical motions in the intergranular lanes drag magnetic field lines and stretch them, and can even reverse the initial local polarity of the field. The dynamo process becomes stronger with time as turbulent flows on larger scales become involved, and the mean magnetic energy density becomes saturated after 7 – 8 solar hours (Kitiashvili et al. 2015). The maximum magnetic field magnitude reaches 2 kG (Fig. 7a), and the photospheric mean magnitude reaches ∼ 20 G. In these numerical simulations, the molecular scales are unresolved, and LES turbulence models are used to estimate the plasma dynamics and diffusivities due



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to motion on sub-grid scales. Therefore, in the simulations the magnetic Prandtl number reflects the properties of plasma and magnetic fields only on turbulent scales, and is defined as the ratio of the local turbulent viscous and magnetic t t t diffusion coefficients (P rm = ν t /ηm ). According to the simulation results, P rm can vary by several orders of magnitude, with most values in the range of 0.1 − 1 (Fig. 7b). Because the local dynamo is driven by turbulent motions that cause magnetic field amplification due to the stretching and twisting of field lines, it is natural to consider the relationship between turbulent plasma motions and the local evolution of the magnetic field. To quantify the apparent close relation between the appearance of magnetic patches and local twisting motions observed in the simulations, the correlation between the kinetic helicity, H = v ·(∇×v), and the time derivative of the magnetic energy density is investigated. Vertical profiles of the kinetic helicity, displayed in Figure 7c, show that the strongest turbulent flows occupy a relatively thin 1-Mm deep layer just below the solar surface. Despite the similarity of the vertical profiles for velocity and helicity, the kinetic helicity is more concentrated in the upper 1-Mm subsurface layer. An example of development of magnetic structures due to helical flows and shearing flows along an intergranular lane is illustrated in Figure 8, which shows a time sequence of the vertical velocity, vertical magnetic field, magnitude of the electric current density, the time derivative of vertical magnetic field with overlaid contour lines of enstrophy, and the electric current density (dashed curves correspond to negative values). An interesting feature of this example is a different scenario for the development of magnetic elements of opposite polarity (determined by the sign of the vertical field component): the positive-polarity magnetic patch evolves following the ‘classical’ scenario of field amplification due to helical flows described in the first example, whereas the negative-polarity patch starts forming in the intergranular lane mostly due to converging flows (magnetic collapse). The evolution of the magnetic elements of this bipolar structure is accompanied by locally growing electric current (Fig. 8 c). 0

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Fig. 8. Evolution of a bipolar magnetic structure in the photospheric layer (z = 0) illustrated in a sequence of four images with cadence 90 sec for different parameters: a) vertical velocity; b) vertical magnetic field; and c) magnitude of electric current density.

The distribution of vertical electric current density (Fig. 9a − c) shows a strong correlation with the horizontal velocity of swirling flows in the subsurface layers. In deeper layers, the magnitude of the electric current increases, but its distribution becomes diffuse and does not show a clear association with the nearsurface dynamics. The kinetic helicity patterns show that the scale of the swirling motions increases with depth, from ∼ 50 − 60 km at the photospheric layer (Fig. 9d) up to ∼ 200 km at a depth of 200 km below the photosphere (panel e). In the deeper layers, the scale of helical motions continues to increase, but the distribution of kinetic helicity becomes complicated and consists of opposite-sign helical flows, which however continue swirling together (Fig. 9f ) and disappear at a depth of about 500 km below the solar surface.



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Fig. 9. The electric current density (color background in panels a – c) and the kinetic helicity, H (panels d–f ), at different depths, from the photosphere (panel a) to 400 km below the photosphere. The horizontal velocity field is shown by arrows.

3.2

Link to Atmospheric Layers

From previous numerical studies it is known that important dynamical and energetic links between subsurface turbulent convective flows and the low atmosphere are established through small-scale vortex tubes. In the presence of magnetic field, the vortex tubes represent channels of energy exchange between the convective layers and the chromosphere and can result in the heating of chromospheric layers. This may be a source of small-scale spicule-like eruptions and Alfv´en waves (Kitiashvili et al. 2012, 2013). In addition to these effects, simulations of the local dynamo show that anisotropy between the vertical and horizontal magnetic field components takes place only in the photosphere and above. The nature of this anisotropy has been the subject of recent debate (e.g Orozco Su´ arez et al. 2007; Lites et al. 2008; Danilovic et al. 2010; Ishikawa & Tsuneta 2010; Steiner & Rezaei 2012; Stenflo 2013). The anisotropy changes with height, but there is no dependence on the ‘seed’ field. According to simulation results, the distributions of the vertical and horizontal magnetic fields are statistically similar in the convection zone. The difference between the vertical and horizontal field strengths is small with a weak dominance of the horizontal fields below the solar surface (Kitiashvili  et al. 2015).

Indeed, the ratio between the transverse field, defined as Bh = Bx2 + By2 , and √ the unsigned vertical field is only slightly above 2 (Fig. 10), meaning that the strength of all the field components is similar. Near the surface layers the vertical magnetic flux becomes dominant. Above the photosphere the mean vertical unsigned flux slowly decreases, whereas the horizontal field increases and becomes dominant (Fig. 10). Note that these results are different from the pre-

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vious simulations by Sch¨ ussler & V¨ ogler (2008) and Rempel (2014) who found that the mean horizontal component of magnetic field is larger than the vertical component in the whole range, from the deep photosphere to the chromosphere. Present simulation results indicate that the horizontal component is dominant only in the upper photosphere and low chromosphere, from about 300 km to 700 km. This dominance of the vertical or horizontal fields in the different layers reflects the topological properties of the dynamo-generated magnetic fields, which are characterized by field lines organized in small-scale magnetic loops above the photosphere (Fig. 11). Such a topological structure resembles the magnetic canopy suggested from observations (Giovanelli 1980; Jones & Giovanelli 1982; Schrijver & Title 2002). According to the simulation results, in the intergranular lanes magnetic field is mostly vertical and becomes horizontal above the photosphere. The height of these loops is greater when the magnetic field is stronger at the loop footpoints. Such a topology of the magnetic field lines was suggested both by observations (e.g. Lites et al. 2008) and simulations (e.g. Sch¨ ussler & V¨ogler 2008; Steiner et al. 2008; Kitiashvili et al. 2015). The horizontal magnetic fields are stronger at the granule edges and in the regions where strong turbulent motions are present.

4

Magnetohydrodynamics of Atmospheric Layers

The solar surface is covered by high-speed jets transporting mass and energy into the solar corona and feeding the solar wind. The most prominent of these jets are known as spicules. The mechanism initiating these eruption events is still unknown. According to the realistic numerical simulations, the small-scale eruptions are produced by ubiquitous magnetized vortex tubes generated by the Sun’s turbulent convection in subsurface layers. The swirling vortex tubes (resembling tornadoes) penetrate into the solar atmosphere, capture and stretch background magnetic field, and push the surrounding material up, generating 2.25

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Fig. 11. Illustration of the topology of magnetic field lines above the photosphere in the local dynamo simulations. The horizontal plane shows the distribution of the vertical magnetic field in the photosphere. Red color corresponds to positive polarity and blue color to negative polarity of the vertical magnetic field. The range of field strength is from −800 G to 300 G.

shocks. The simulations reveal complicated high-speed flow patterns and thermodynamic and magnetic structure in the erupting vortex tubes. Specifically, the simulations show (Kitiashvili et al. 2012, 2013; Kitiashvili 2014): 1) the eruptions are initiated in the subsurface layers and are driven by high-pressure gradients in the subphotosphere and photosphere and by the Lorentz force in the higher atmosphere layers; 2) the fluctuations in the vortex tubes penetrating into the chromosphere are quasi-periodic with a characteristic period of 2-5 min; 3) the eruptions are highly non-uniform: the flows are predominantly downward in the vortex tube cores and upward in their surroundings; the plasma density and temperature vary significantly across the eruptions. 4.1

Ubiquitous Small-Scale Eruptions

It has been revealed that the vortex tubes can penetrate into the chromosphere, strongly affecting its thermodynamic properties (Kitiashvili et al. 2012, 2013). An example of an erupting vortex tube in Figure 12 shows that in the vortex core the photospheric temperature is lower than the mean temperature, whereas in the chromospheric layers, ∼ 600 km above the photosphere, the temperature is higher. Such chromospheric helical structures have been observed by WedemeyerB¨ ohm & Rouppe van der Voort (2009). Vortex-tube penetration upward into the solar atmosphere is often quasiperiodic, with a period in the range of 2 – 5 min and accompanied by spontaneous

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Fig. 12. Snapshots of a fraction of the simulation domain in the photosphere (row a) and 625 km above (row b), and vertical cuts through the vortex tube (row c) for different quantities (from left to right): vertical velocity, density, temperature, and vertical magnetic field.

flow ejections and generation of chromospheric shocks (Kitiashvili et al. 2013) . Figure 12 illustrates the complicated structure and dynamics of the eruptions, with downflows in the vortex core and upward eruption flows in the surrounding region. As seen in the temperature distribution, these eruptions are hotter than the surrounding plasma and can provide extra chromospheric heating in addition to the heating through the vortex core (Fig. 12). Due to the turbulent nature of the helical motions along the vortex and its interaction with the surface and atmospheric layers, the structure of the eruption is highly inhomogeneous. Figure 13a shows an example of 3D rendering of the kinetic helicity in a small fraction of the computational domain during the eruption, where darker colors correspond to stronger helicity of the flows and demonstrate clustering of those flows. On the scale of the whole vortex tube, upand downflows take place at the same time. Figure 13b shows the topological structure of plasma during the eruption, where the isosurface corresponds to constant temperature, 5800 K, the streamlines represent a sample of the velocity field, illustrating a coexistence of plasma ejection with highly twisted flows on



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Fig. 13. a) 3D rendering of the kinetic helicity during a vortex tube eruption; b) streamlines illustrating the structure of the velocity field in the vicinity of the vortex core. The vortex core is shown as an isosurface of temperature. In panel a the horizontal and vertical size of the snapshot is about 1.7 Mm

the vortex periphery and helical downflows in the vortex core. Thus, the flow structure during the eruption phase remains twisted (Kitiashvili 2014): the material around the vortex core moves up from the subsurface and near surface layers, and also towards the vortex core from the surrounding region. The plasma is moved up by the twisting flows into the higher atmospheric layers, and, at the same time, in the lower layers the plasma flows down though the vortex core (Fig. 13b). Figure 14 illustrates various stages of a flow ejection, where the streamlines show the general behavior of the velocity field; yellow-blue isosurfaces represent the pressure gradient, normalized by density, of 5 × 104 cm/s2 (grey) and −5 × 104 cm/s2 (black), and the mesh isosurfaces correspond to T = 6400 K. In the atmospheric layers the flow ejection starts with the formation of a vertically oriented vortex tube, as described in Kitiashvili et al. (2012) and Porter & Woodward (2000). This creates strong vertical pressure gradients, negative in the vortex core and positive at the vortex periphery (Fig. 14a). The swirling motions get concentrated at a height of about 500 km (which corresponds to the temperature minimum region, panels b and c), and then erupt (panel d). Figure 15 shows the mean vertical velocity variations with time at different heights, from −300 km to 780 km. These diagrams show that the velocity perturbations are initiated at depths of ∼ 60−120 km below the surface (superadiabatic zone), and then propagate in both directions, upward and downward. Such perturbations are quasiperiodic with a period of 2 − 5 min, which can be related to the characteristic oscillation properties of the near-surface plasma, where the vortex tube is rooted. The period is also similar to the oscillations of large-scale acoustic (p) modes excited in the domain. However, these oscillations do not show correlation in phase with the vortex-tube oscillations, and their amplitude is essentially smaller. The mean vertical velocity of the perturbations

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Fig. 14. Different stages of the flow ejection: a) vortex tube penetration into the atmosphere layers, b) intensification of the swirling motions, c) concentration of the swirling motion in a ring-like structure, and d) flow ejection along the vortex tube. Black streamlines illustrate the velocity field in the vicinity of the vortex tube. Semitransparent light grey surfaces correspond to a constant temperature of 6400 K. Yellow and blue isosurfaces correspond to the normalized-by-density vertical pressure gradient (−∇p/ρ) for the values 5 × 104 cm/s2 (yellow color) and −5 × 104 cm/s2 (blue color).

increases up to 5 – 8 km/s at ∼ 800 km above the solar surface. These upflows can be identified as small-scale flow ejections. The amplitude and quasi-period of the eruptions vary with the vortex tube properties and their evolution (e.g., changes in their size, shape, and height of penetration) or/and interactions with other vortices, as a result of which the ejections can be magnified or suppressed. In the vortex core, the upward speed of the velocity perturbations increases with height from 6 km/s in the near-surface layers to more than 12 km/s above 700 km. The downward perturbations propagate much more slowly, with a speed of 3 − 3.5 km/s, and their amplitudes apparently increase as they descend.



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4.2

Source and Drivers of Spontaneous Flow Eruptions

The complicated dynamics of strong swirling flows in the presence of magnetic field across many pressure scale-heights represents an interesting interplay of hydro- and magnetic effects. In general, there are two type of forces that are responsible for driving the flow eruptions: hydrodynamic, due to pressure excess, and magnetic, caused by the Lorentz force. A comparison of the contributions from the hydrodynamic and magnetic effects can be done by estimating the various terms in the flow-velocity equation: J × B ∇p ∂v + (v · ∇)v = − − g, ∂t cρ ρ where v is the velocity vector, J is the electric current density, B is the magnetic field vector, p is the gas pressure, ρ is the density, and g and c are the gravitational acceleration and the speed of light. In this form, Eq. (1) describes the flow acceleration on the left-hand side, and, on the right-hand side, the contributions of the Lorentz force (first term) and the pressure gradient and gravity. In the initial equilibrium state the pressure gradient and gravity are balanced. Figure 16 shows a comparison of the pressure gradient excess and the Lorentz force in the vortex core. The profiles of both non-magnetic and magnetic forces reveal a clear connection with the upward and downward velocity perturbations associated with the flow ejection, showing a similar decrease in the perturbation amplitude in the vortex surrounding regions, and also a time lag with height. Propagation of the perturbations is better visible in the Lorentz force (Fig. 16b), with a clear indication of acceleration in higher layers of the atmosphere, indicating a strong increase of magnetic field effects at a height h ≥ 700 km. The

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Fig. 16. Temporal profiles of mean of the pressure gradient variations (panel a) and the Lorentz force normalized by density (FL )z /ρ (panel b) at different levels below the surface and in the atmosphere. Thick black curve shows the variations in the photosphere layer. The height difference between the curves is 60 km.

propagation of the Lorentz force perturbations upward and downward along the vortex tube gives us an additional estimate for the depth of the initialization source, which varies for different events from the photosphere down to ∼ 120 km below the surface. This process corresponds to the non-magnetic case, where the source of the vortex eruptions is hydrodynamic. Magnetic field effects become important above the temperature minimum region, where the plasma upflows are accelerated by the Lorentz force. Figure 17a and b shows the contributions of the magnetic (black curves) and nonmagnetic acceleration (grey curves) in two layers: 780 km and in the photosphere layer. Dashed curves represent the vertical velocity for these same layers, given for comparison. The results show that the Lorentz force is most important for the flow acceleration in the higher layers, where strong Lorentzforce fluctuations are correlated with strong flow acceleration (e.g. at t = 9 min). The flow eruption is much weaker for those events in which the most contribution comes from hydrodynamic forces (e.g. t = 3 min). Nevertheless, close to the surface and in the subsurface layers hydrodynamic effects are significantly more important (Fig. 17b) than the Lorentz force. Generally, the flow structure during the eruption phase remains twisted: the material around the vortex core moves up from the subsurface layers, and also towards the vortex from the surrounding region, and collects near the vortex edge. The plasma is moved up by the twisting flows into the higher atmospheric layers, and, at the same time, in the lower layers the plasma flows down though the vortex core (Fig. 17c). The eruptions have a complicated dynamical structure with mostly continuous swirling downflows, decreasing density and heating in the vortex core, and spontaneous upflows mostly propagating along the vortex core periphery, forming shock waves in the higher atmosphere. Schematically, the flow pattern of the eruptions, which resembles the mass circulation in tornados, is illustrated in Fig. 17. The plasma flow in the eruptions accelerate in the higher (mid-



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Fig. 17. Comparison of the contributions to the flow ejection of the hydrodynamic ((−∇p/ρ − g)/g, gray curves) and magnetic (Lorentz force, FL /(ρg), black curves) vertical accelerations (normalized by the gravitational acceleration) at different altitudes: a) h = 780 km, b) h = 0 km (photosphere). Dashed curves correspond to the vertical velocity, Vz , given for reference at the same layers. Panel c shows a schematic illustration of the flow pattern in eruptions driven by magnetized vortex tubes. The red arrows illustrate downdraft in the low-density, relatively cool vortex tube core (gray area); blue lines and arrows show swirling upflows around the vortex core. The vortex tube is rooted below the surface, and the flow eruptions are initiated by a pressure excess 60 – 120 km below the surface, then further accelerated by the Lorentz force in the mid-chromosphere.

chromospheric) layers from 6 to 12−15 km/s. Also, the perturbations associated with the flow ejection propagate into the solar interior along the vortex tube core with a speed of about 3 − 3.5 km/s and increasing amplitude. The process of flow ejection originates in a subsurface layer about 100 km deep, where vortex compression by converging flows increases the pressure gradient and accelerates swirling flows. This compressed vortex tube starts penetrating into the low-atmosphere layers, and induces the surrounding atmospheric plasma into swirling motion. Accumulation of the swirling flows at a height of ∼ 500 km (the temperature minimum region) forms a ring-like structure which propels the swirling flows into higher layers along the vortex tube. The flows are mostly accelerated by the pressure gradient in the subsurface and near-surface layers, and by the Lorentz force in the higher layers (≥ 700 km).

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The described mechanism of flow ejection in vortex tubes works also in the purely hydrodynamic case, but in this case the velocity perturbations are much smaller and the eruptions almost immediately fall back to the photosphere. Nevertheless, in this case the vortex tube eruptions also generate shocks in the lowdensity atmospheric layers.

5

Conclusions

Fast growing computational capabilities make it possible to model the dynamics of turbulent solar and stellar magnetoconvection and its atmospheric effects based on first physical principles with a high degree of realism, taking into account radiative energy transport, ionization, chemical composition, magnetic field effects, and others. In the paper several examples of realistic type simulations obtained with the StellarBox code (Wray et al. 2016) are presented. It is shown the realistic modeling approach is applicable to a broad range of problems of solar and stellar structure and dynamics. For instance, Section 2 briefly describes results of detailed 3D, fully compressible radiative hydrodynamic simulations of some Kepler-target stars, noting the structural and dynamical differences between turbulent convection in the Sun and more massive stars. In some cases, when the convection zone is shallow enough that the computational domain can include layers from the upper radiative zone to the atmosphere, the transition ilayer between the convection and radiative zones (‘overshoot zone’), which is poorly described by mixing-length theory, can be included. According to the simulation results the photosphere granules show a co-existence of several granulation scales, and the convection pattern in F-type stars shows well-defined clusters of several granules. In deeper layers of the convection zone, the scale of the convection patterns gradually increases (Fig. 3). The downflows in the intergranular lanes of the bigger granules penetrate through the whole convection zone, reaching velocities of more than 20 km s−1 , close to the local speed of sound (Fig. 4). These downdrafts penetrate into the radiative zone, form an overshoot layer, and cause local heating, thus increasing the sound speed and initiating strong density variations that can be a source of internal gravity oscillations (g-modes). Comparison of the 1D model (calculated from the stellar evolution code CESAM) with the corresponding mean profiles from the 3D numerical simulation (”StellarBox” code) shows that, in the 3D simulations, the stellar radius is increased by about 800 km, and the convection zone is expanded in depth due to the development of an overshoot region of about 8 Mm (1/2 of the pressure scale height) thickness. The overshoot region is characterized by a negative enthalpy flux and, most importantly, has a two-layer structure: the upper part represents an almost adiabatic extension of the convection zone, while the lower part shows a significant peak of increased subadiabaticity, caused by heating of the overshooting region due to the braking of penetrating convective plumes. In addition, close to the surface the simulations reveal a layer of enhanced tur-



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bulence, associated with the ionization zones, which affects variations of the adiabatic exponent. The deviations of the mean properties between the 3D and 1D models are remarkably similar to the corresponding deviations between the helioseismology inversions (Kosovichev 1999) and the standard 1D solar model (Fig. 6), indicating that, perhaps, the helioseismology results including the characteristic sound-speed bump may be explained by dynamical effects of solar convection and overshooting. The differences in the radius between the 3D and 1D models may be partially explained by adjusting the mixing-length parameter, but may also be related to the observed difference between the photospheric and seismic radii of the Sun (Schou et al. 1997). Realistic solar simulations have a specific special use because of the availability of high-resolution observational data at different wavelengths that make possible validation of numerical models that are difficult to perform for other stars. In this paper two effects are discussed: small-scale (local) dynamos (section 3) that are probably responsible for a significant fraction of the background magnetic fields on the solar surface, and spontaneous flow eruptions (section 4) that are initiated near the photosphere due to the interaction of turbulent vortex tubes and magnetic field. To investigate the small-scale dynamo problem, a random, very weak seed field was injected in a fully developed hydrodynamic flow. Afterwards no magnetic flux was added to or removed from the computational domain. Due to turbulent dynamo action, the magnetic field can be locally magnified above the equipartition strength (∼ 600 G), reaching more than 2000 G in the photosphere. This magnetic field amplification is driven by converging flows into the intergranular lanes, shearing flows, and helical motions. All these mechanisms of magnetic field amplification are present in the numerical model and linked to each other. Thus, the local dynamo process represents a complicated interplay of multiple mechanisms that are difficult to separate from each other and that can contribute differently in individual magnetic field amplification events. The local dynamo works most efficiently in the 1-Mm deep subsurface layer, where the turbulent flows are strongest and cause the vortical plasma motions that result in magnetic field amplification due to twisting and stretching (Nordlund et al. 1992; Brandenburg 1995; Brandenburg et al. 1996). The magnetic patches generated due to shearing and vortical motions are transported into deeper layers by downdrafts. In the deeper layers the magnetic field can be further amplified by compression. The primary topology of the dynamo-generated magnetic field is represented by compact magnetic loops appearing as bipolar structures in the intergranular lanes (Fig. 11); these loops contain stronger magnetic field concentrations at their footpoints. Formation of magnetic loops in the solar atmosphere reflects the observed height-dependent anisotropy of vertical and transverse small-scale magnetic fields (Fig. 10). According to the simulation results, equipartition of the field components occurs in layers deeper than 2-Mm below the solar surface, but above the solar surface the transverse magnetic fields are dominant because of the compact loop topology. This variation of the ver-

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tical and horizontal field anisotropy can explain discrepancies among different observations (e.g Orozco Su´ arez et al. 2007; Lites et al. 2008; Danilovic et al. 2010; Ishikawa & Tsuneta 2010; Stenflo 2013) and supports previous numerical analysis (Sch¨ ussler & V¨ ogler 2008; Steiner et al. 2008). Extending the computational domain into the atmospheric layers shows strong coupling between subsurface layers and the chromosphere. In particular, the numerical simulations with an initial mean 10 G vertical magnetic field show a complicated mixture of hydrodynamic and magnetic effects associated with spontaneous quasi-periodic (with period 2 – 5 min) flow ejections from the subsurface layers into the higher atmosphere along magnetized vortex tubes, in which the magnetic field strength at the surface is typically ∼ 1 kG. The quasi-periodic character of the eruptions reflects vortex tube interaction with the environment at different dynamical scales. It is quite possible that the flow eruptions described in Section 4 represent a mechanism for spicules observed on the solar limb and other small-scale jetlike eruptions, which have puzzled solar astronomers for more than a century since their discovery by (Secchi 1877) (for a recent review and references see Tsiropoula et al. 2012). The possible mechanism that follows from the numerical simulations and is schematically illustrated in Fig. 17 requires further detailed investigation. However, it seems to be capable of solving a number of puzzling features of solar spicules, such as the regions of low temperature and temperature gradients perpendicular to the spicule axis (Athay 1961), disparity between spicule velocities measured in different lines (Krat & Krat 1961; Socas-Navarro & Elmore 2005), the double-thread structure (Suematsu et al. 2008), the apparent rotation of spicules around their axis (Beckers 1968), the quasi-periodic behavior (Pasachoff et al. 1968), and the apparent fading away of some spicules without the material falling back (Mouradian 1967) (because it can be drained down in the vortex core). In conclusion, realistic numerical simulations of turbulent magnetoconvection pioneered by Nordlund and Stein (2001) have opened new perspectives for our understanding of very complex phenomena observed on the Sun and other stars, and will certainly play a pivotal role in future studies.

Acknowledgments The simulation results were obtained on NASA’s Pleiades supercomputer at NASA Ames Research Center. This work was partially supported by NASA grants NNX10AC55G, NNH11ZDA001N-LWSCSW and the LWS NASA/NSF Strategic Capabilities. I thank Drs. Nagi Mansour, Alan Wray, Alexander Kosovichev, Christopher Henze, Timothy Sandstrom and other members of the NASA Ames Heliophysics Modeling and Simulation and Visualization teams for very fruitful collaboration and support.



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A brief history of the solar diameter measurements: a critical quality assessment of the existing data Jean Pierre Rozelot1 , Alexander G. Kosovichev2 , & Ali Kilcik3 1

Universit´e de la Cˆ ote d’Azur (CNRS-OCA, Nice) & 77 ch. des Basses Mouli`eres, 06130 Grasse (F) E-mail: [email protected] 2 New Jersey Institute of Technology, Newark, NJ 07103, USA E-mail: [email protected] 3 Akdeniz University, Faculty of Science, Dpt of Space Science & Technologies, 07058, Antalya (T) E-mail: [email protected] Abstract. The size of the diameter of the Sun has been debated for a very long time. First tackled by the Greek astronomers from a geometric point of view, an estimate, although incorrect, has been determined, not truly called into question for several centuries. The French school of astronomy, under the impetus of Mouton and Picard in the XVIIth century can be considered as a pioneer in this issue. It was followed by the German school at the end of the XIXth century whose works led to a canonical value established at 959 .63 (second of arc). A number of ground-based observations has been made in the second half of the XIXth century leading to controversial results mainly due to the difficulty to disentangle between the solar and atmospheric effects. Dedicated space measurements yield to a very faint dependence of the solar diameter with time. New studies over the entire radiation spectrum lead to a clear relationship between the solar diameter and the wavelength, reflecting the height at which the lines are formed. Thus the absolute value of the solar diameter, which is a reference for many astrophysical applications, must be stated according to the wavelength. Furthermore, notable features of the Near Sub-Surface Layer (NSSL), called the leptocline, can be established in relation to the solar limb variations, mainly through the shape asphericities coefficients. The exact relationship has not been established yet, but recent studies encourage further in-depth investigations of the solar subsurface dynamics, both observationally and by numerical MHD simulations.

1

Following Greek and Islamic scholars

From time immemorial men have striven to measure the sizes of celestial bodies and among them the solar diameter holds an important place. Aristarchus of Samos (circa 310-230 BC), by a brilliant geometric procedure was able to set up the solar diameter D as the 720th part of the zodiacal circle, or 1800 seconds of arc ( ) (i.e. 360◦ /720). A few years later, Archimedes (circa 287-212 BC) wrote in the Sand-reckoner that the apparent diameter of the Sun appeared to lie between the 164th and the 200th part of the right angle, and so, the solar diameter D could be estimated between 1620 and 1976 (or 27 00 and 32 56 (Lejeune,

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1947; Shapiro, 1975). These values, albeit a bit erroneous are not too far from the most recent determinations, indicating the great skillfulness of the Greek astronomers. Curiously, such values were not truly questioned during several centuries, except during the fourteen century under the impetus of the Mar˜agha School (Iran) when Ibn-al-Shatir (1304-1375) wrote in his book untitled “The Final Quest Concerning the Rectification of Principles” that the solar diameter varies from 29 .5 (at apogee) to 32 .32 (at perigee), a fact that obviously Greek astronomers could not evoke in their geometric demonstration. The ratio found by Ibn-al-Shatir, of 0.913, is still erroneous, as the best present estimate is 0.967, but not too much (6 %). A bit later on, in 1656, Giovanni Battista Riccioli (1598-1671) in reviewing the measures of the solar diameter, reported a lower limit of 30 .30 (given by Kepler) and an upper limit of 32 .44 (given by Copernicus). Lastly, the French school led by Gabriel Mouton (1618-1694) and Jean Picard (1620-1682) can be considered as a pioneer in this field, as the two astronomers were able to report the first solar radius measurements with a modern astrometric accuracy (0.8 %)1 . Major results of the solar semi-diameter as obtained from telescope observations from 1667 to 1955 have been compiled by Wittmann (1977). A more complete history of the solar diameter determinations, at least up to the year 2011, can be found, for example, in Rozelot & Damiani (2012), or Rozelot et al. (2018).

2

The solar diameter: a not so obvious parameter

The solar sphere is not a stainless steel ball, for which the diameter would be easy to define. As the Sun is a fluid body in rotation, the passage of the flow from the interior to the gaseous external layers is progressive and the solar radius needs a definition. The most commonly used definition stipulates that the radius is defined as the half distance between the inflection points of the darkening edge limb function, at two opposite ends of a line passing through the disk center. Other definitions could be used, for instance the location of the limb at the minimum of temperature, or an equipotential level of gravity which defines the outer shape, etc. From the ground, measurements of the solar radius suffer from different flaws. One of the main effect is due to the terrestrial atmospheric disturbances. When the solar ray travels from the upper to lower layers of our atmosphere, it can be affected by various factors such as moving pockets of air masses, changes in the refractive index, winds or jet streams (Badache-Damiani et al., 2007), etc. The other effects are scintillation and blurring (R¨osch & Yerle, 1983). The convolution of the edge of a uniformly bright half-plane by a spread function having a center of symmetry gives a smooth symmetrical profile. In such a case, the inflection point is exactly on the edge of the object, whereas if the object is limb-darkened, this inflection point is shifted inside increasingly with the width of the spread function. Except rare cases, such effects have been, up to now, 1

As an example, Picard found R = 964 .8 on March 9, 1670, a remarkably accurate value.



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poorly taken into account, leading to spurious ground-based measurements. The past (ground-based) radius data can be used for historical studies, but must be carefully examined for astrophysical purposes. Even in the case of space measurements, major problems may occur, such as thermal or misalignment effects of the instruments in space. Thus, there is still a need for more accurate measurements.

3

On the necessity to measure the solar radius R with a high accuracy

3.1 In astrophysics (and geophysics), the diameter of the Sun is a fundamental parameter that is used in physical models of stars. First of all, the diameter of stars are defined relative to that of the Sun. Therefore, a change in the absolute value of the solar diameter, as well as its temporal variations, if any, could have an impact on the inferred stellar structures. Secondly, concerning our star, a diameter estimate permits to compute the amount of energy transmitted to the Earth. The total radiative output of the Sun establishes the Earth’s radiation environment and influences its temperature and atmospheric composition. Recent studies indicate that small but persistent variations in the solar energy flux may play a significant role in climate changes through direct influence on the upper terrestrial atmosphere (see for instance Suhhodolov et al., 2016). 3.2 In solar physics, a change in the solar size is indicative of a change in the potential energy which could be driven by such means. To the first order, a change in the radius of the Sun causes changes of its luminosity, according to 2 the Stephan’s law: L = (4πR )σT 4 , which gives ∆L/L = 4∆T /T + 2∆R /R , where L is the solar irradiance, and T the solar effective temperature. Taking L = 1361 W/m2 , T = 5772 K (as recommended by the IAU) and ∆L/L = 0.01%, it turns out that ∆R = 9.4 mas (6.8 km) if ∆T = 1.35 K over the solar cycle as found by Caccin & Penza (2003). Note that if the quiet Sun were immutable as suggested by Livingston (2005), ∆T ≈ 0. K, there would be neither sunspots nor faculae, hence ∆L/L ≈ 0. % as the irradiance variability reflects their presence (see for example Krivova et al., 2003). In such a case, ∆R would be ≈ 0. mas. This result (∆R in any case is less than 15 mas) is not surprising. Dziembowski et al. (2001) calculated a photospheric radius shrinkage of about 2-3 km/year with the rising solar activity. Goode et al. (2003) using a helioseismology analysis of high-degree oscillation modes from SOHO/MDI (Scherrer et al., 1995) found a shrinking of the solar surface/convection layer (which seems to be cooler) with the increasing activity, at a level consistent of the direct radius measurements based on the SOHO/MDI intensity data. Lastly, using a selfconsistent approach taking into account the solar oblateness, Fazel et al. (2008) obtained an upper limit on the amplitude of the cyclic solar radius variations (a non-homologous shrinking) between 3.87 and 5.83 km, deduced from the gravitational energy variations (see also section 7). Such results rule out all observed variations which can be found in several papers claiming that the solar diameter

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may change in time by some 300 mas or more. 3.3 Precise limb shape (curvature) changes both in latitude and time, due to an aspherical thermal structure. Such alterations play a role in the physics of the solar sub-surface layers. According to the observed temporal variation of f-mode frequencies, the near sub-surface solar layer (NSSL) is stratified in a thin double layer, interfacing the convective zone and the surface (Lefebvre & Kosovichev, 2005). This shear layer called “leptocline” -from the Greek “leptos”: thin and “klino”: hill- (Godier and Rozelot, 2001, Lefebvre et al., 2009) is the seat of many phenomena: an oscillation phase of the seismic radius, together with a non-monotonic expansion of this radius with depth, likely an inversion in the radial gradient of the rotation velocity rate at about 50◦ in latitude, opacities changes, superadiabicity, the cradle of hydrogen and helium ionisation processes and probably the seat of in-situ magnetic fields (Lefebvre et al., 2006; Barekat et al., 2016). A possible mechanism has already been stated as followed (Pap et al., 2001): although the ultimate source of the solar energy is the nuclear reactions taking place in the center of the Sun, the immediate source of the radiating energy is the solar surface. The nuclear reactions are almost certainly constant on the time scales shorter than millions of years, but the mechanisms which carry the energy to the solar surface may not be. Indeed, observations of the solar radiation integrated over the entire solar spectrum (total irradiance), obtained by spacebased experiments now over several decades, have demonstrated that the total irradiance varies on the time scales from minutes to the 11-yr solar cycle. If the central energy source remains constant while the rate of energy emission from the surface varies, there must be an intermediate reservoir where the energy can be stored or released depending on the variable rate of energy transport. The gravitational field of the Sun is one such energy reservoir. If the energy is stored in this energy reservoir, it will result in a change in the solar radius. Thus, a careful determination of the time dependence of the solar radius can provide a constraint on models of total irradiance variations. Recent analysis of the high-degree oscillation modes revealed a sharp gradient of the sound speed in a narrow 30-Mm deep layer just beneath the solar surface (Reiter et al., 2015). The complex physics of this near surface shear layer (the leptocline) presumably plays an important role in the solar dynamo (Pipin & Kosovichev, 2011). To this respect, new features of the Solar Dynamics Observatory/Helioseismic and Magnetic Imager (SDO/HMI) analysis is that the HMI data allow us to reconstruct the flows in this shallow subsurface layer, and match these to the directly observed surface flows (Fig. 1). Such flows maps permit to investigate other important properties of the subsurface dynamics of the Sun, which previously were not accessible (e.g. Kosovichev & Zhao, 2016). 3.4 Temporal solar size variations, even faint, imply changes of the gravitational moments, J2 and J4 . Let us recall that the gravitational moments are linked to both the distribution of mass and the (differential) rotation of the body, from the core to the surface. Precise knowledge of such gravitational moments



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Fig. 1. Left (a): Evolution of the subsurface meridional flows obtained from the 5-years of the SDO/HMI observations during Solar Cycle 24. The red and yellow colors show the flow components towards the North pole, the green and blue colors show the Southward flow. The color scale range is from -20 to 20 m/s. Right (b): The mean meridional flow averaged for the whole period of observations at four different depths, showing the importance of the Near Sub-Surface Layers (NSSL, or leptocline). After Kosovichev & Zhao (2016).

is required to develop high precision astrometry and in addition, may constraint gravitational theories, both from a theoretical and experimental points of view. In such prospect, the Eddington-Robertson parameters, γ, and β contributes to the relativistic precession of planets. Note that γ encodes the amount of curvature of space-time per unit rest-mass, and the post-Newtonian parameter β encodes the amount of non-linearity in the superposition law of gravitation. In the case of the solar system, it is still difficult to disentangle J2 , γ and β. However, by accurately measuring the limb curvature over the latitudes -that is to say the solar shape (and to first order the oblateness)-, it is possible to get a good estimate of the solar quadrupole moment, to an accuracy of one part in 200 of its size of around 10−7 . Recent analysis includes the Lense-Thirring precession effect, which is not negligible. In the case of Mercury for instance, it may have been canceled to a certain extent by the competing precession caused by a small mismodeling in the quadrupole mass moment J2 of the Sun (Iorio, 2011).

4

A quick tour of solar diameter measurements

4.1 The so-called Danjon Astrolabe, was redesigned in the early 1970’s in a solar astrolabe in order to get measurements of the diameter of the Sun2 . After a protecting glass density at the front window of the instrument, the image is 2

The principle of the astrolabes have been described in Kovalevsky J., Lecture Notes in Physics: Astrom´etrie Moderne, 1990, Vol. 358, Springer (Heidelberg-D), chapter 7, pp 173-194.

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split by a reflector prism and a mercury mirror and then focused by a refracting telescope. In the case of a perfect setting, the direct and reflected images are symmetric in relation to the axes of a reticule. The time of their coincidence in the center of the eyepiece field corresponds to the exact moment when the observed Sun edge crosses the parallel of altitude corresponding to the angle of the prism. In principle, this kind of apparatus is suited for solar observations and series of measurements were obtained, first in France showing a periodicity in the radius data of about 900 days, in antiphase with the solar activity. This question of the time dependence of the solar radius had already been debated by Secchi and Rosa (1872)3 and numerous other observers. However, it seems that Cimino (1944) following previous works made by Gialanella (1941)4 was the first to put in evidence two oscillations in the solar observations made in Roma (I) from 1876 to 1906: a first one of 22.5-yrs, of amplitude 0 .2 - 0 .5, for a mean radius of 961 .30, attributed to the solar variability, and a second one of (6.5-8.5) -yrs, that the author did not identified with a solar mechanism, ascribing it rather to an atmospheric effect. Giannuzi (1953, 1955), in her analysis of the solar radius observed at Greenwich (UK) from 1851 to 1937, confirmed the basic cycle of 22 to 23-yrs, modulated by a shorter one of about 7.5 -yrs, in anti-phase to solar activity, “leading -according to the author- to a great suspicion of its atmospheric origin”. This last periodicity is three times longer than the one found in the Calern data i.e. ≈ 900 days (Laclare 1983; D´ebarbat & Laclare (1999), as 7.5 yrs * 365.25 is 2739 days; dividing by 900 this gives ≈ 3.0(4), so that such estimates are harmonics. In any event, disregarding the Gianuzzi publications, the CERGA’s results inflamed the scientific community. The solar astrolabe was duplicated and used in Algeria, Brazil (Rio de Janeiro and S˜ ao Paulo), Chile, Spain and Turkey. However, the results were disparate and it was not possible, in spite of considerable efforts, to conciliate the data obtained in different places. Moreover, the amplitude of the modulation found for the cyclic variation of the solar radius with time was so high5 that no theory was able to explain them. On a pure statistical basis, without knowing the part due to the atmospheric fluctuations and the part due to the solar component, it was found from the photoelectric astrolabe (DORAYSOL, installed at Calern -F) a mean solar radius of (959.48 ± 0.32) as deduced from 19169 measurements between the years 1999 and 2006, two times more measurements than with the visual astrolabe during 26 years, from 1978 to 2004. By comparison, over the same period (1999-2006), a mean solar radius 3

4

5

The so-called Secchi-Rosa law stipulates that the solar radius variability is out of phase of the sunspot activity. He reported a mean radius of 961 .38 from observations made (by means of a meridian telescope) at Campidoglio and Monte Mario (near Roma, I), from 1876 to 1937 pointing out a possible effect of the atmosphere. See Commentationes, Accademico Ponteficio Giuseppe Armellini nella Tornata, November, 30, Vol. VI, 25, pp. 11421200. Some 0 .7 at the beginning of the observations, a value which was progressively reduced down to 0 .5 twenty years later.



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of (959.55 ± 0.01) was deduced from 371 solar visual astrolabe observations (Morand et al. 2010). The Picard-sol program implemented also at Calern (F), led to a solar radius of (959.78 ± 0.19) (or 696 113 ± 138 km) at 535.7 nm (Meftah et al., 2014) between 2011 and 2013. Such inconsistent results which are supposed to measure the same astronomical object, obtained at the same site, during similar periods of time, show evidently a mix of atmospheric and solar signals, and may reinforce what was earlier detected in Roma. Lastly, temporal variations over the solar cycle, larger than 0 .5, found in the astrolabe data are incompatible with modern relativistic theories. The network of the solar astrolabes was progressively abandoned. 4.2. Several other radius measurements were made from the grounds which cannot be all reported here. To be mentioned: • The drift-time measurements of the solar diameter made with two optically identical 45-cm aperture solar telescopes at Iza˜ na (SP) and Locarno (CH) by Wittmann & Bianda (2000, and references herein). Their last results show that the radius is (960.63 ± 0.02) , from 7583 visual transit observations made in Iza˜ na during 1990-2000 and (960.66 ± 0.03) , from 2470 visual transits made in Locarno during 1990-1998, both at the wavelength about 550 nm. The data show no long term variations in excess of about 0.0003 /yr and no cycle-dependent variations in excess of about ± 0 .05. • The Mt Wilson (USA) system (by spectrography) measures the Sun’s apparent radius in the neutral iron spectral line at 525 nm (Ulrich & Bertello, 1995). The radius measured by the authors is derived from the drop-off of brightness of the solar disk at its edge and is a function of the temperature and density profile. This definition is different from the usual one based on the inflection points and, moreover, the measurements are made using a spectral line and not in white light. From 1982 to 1994, the authors found a time dependence of the solar radius in phase with the solar activity, in contradiction with the CERGA’s observations in France. Analysis of the Mt Wilson (USA) data over 30-yrs were completed by Lefebvre et al. (2006) leading to the conclusion that there is no clear correlation between the temporal variations of the apparent solar radius and the variations in the sunspot number. However, the data show a distortion of the observed apparent solar figure: a bulge appears near the equator extending through 20◦ -30◦ of heliographic latitudes, followed by a depression at higher latitudes. The global behavior of the shape remains oblate. This result is qualitatively consistent with other measurements taken at the Pic du Midi (F) observatory. From a physical point of view, this distorted shape of the Sun reflects the influence of the gravitational moments (J2 and J4 ). • The Solar Diameter Monitor (SDM), a dedicated instrument} at the High Altitude Observatory (USA), to measure the duration of solar meridian transits during the 6 years 1981-1987, spanning the declining half of solar cycle 21. The Brown’s (1987) report stated that for this period, the annual

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averages of the diameters differed from each other by less than 0 .05. Such results seem to be contradictory to the Bertello and Ulrich measurements, albeit one set is obtained using a single spectral line and the other one in white light. Combining the SDM photoelectric measurements with models of the solar limb-darkening function, Brown & Christensen-Dalsgaard (1988) were able to derive a mean value for the solar near-equatorial radius of (695.508 ± 0.026) Mm. Annual averages of the radius were found identical within the measurement error of ± 0.037 Mm. • The Reflecting Heliometer, an improved version of the solar astrolabe operating by drift scans, is operating at the “Observatorio Nacional” in Rio de Janeiro (BR) since 2011. It measures the solar diameter at all heliographic latitudes by rotating around its axis. A linear fit of the data recorded up to 2015 (about 11500 measurements per calendar year) leads to a value of the solar radius of 958 .7, with a dispersion of around ± 0 .5, more or less in phase with the solar activity (Boscardin et al. 2016). However, after a pure statistical study at a site where the seeing is rather high, no deconvolution of the atmospheric parameters has been made. • An interesting study has been made by Hiremath (2015) in compiling the Solar White-light Images of the Sun obtained at the Kodaikanal Observatory (IN). Photographic data extend back to 1904 and cover 106 years. All the plates are digitized and available (31800 plates covering about 31000 days). The solar radius has been extracted after removing the limb darkening using an original method. Results, still in progress, seems to show that during the years 1923-1945, the Sun’s radius is constant and does not change with the solar cycle. • Historical archives of the Royal Observatory of the Spanish Navy (today the “Real Instituto y Observatorio de la Armada -ROA-“ located at Cadiz -SP) has been recently reanalyzed by Vaquero et al. (2016) in the scope to recover the solar radius measurements since 1753, i.e. during the past 250 years. From this long-term perspective, the data do not present any significant trend from the statistical point of view, and if any, it would be within the measurement uncertainty. Thus, the Spanish solar observations show that the solar diameter did not change in the past 250 years. The mean value has been estimated after applying corrections for refraction and diffraction to (958.87 ± 1.77) . 4.3 The first measurements in the near outer atmosphere were made by means of a dedicated instrument embarked in a balloon nacelle (Sofia et al. 1991). The primary goal was to determine the solar oblateness, with a precision of ≈ 10−5 , for which it was envisaged at that time to test the Brans-Dicke theory (see a review in Damiani et al., 2011). Seven flights were made in the Arizona desert (USA) spanning the years 1992 to 2011 (first flight in May 4, 1990 at an altitude of 120 000 feet). Data have been several times revisited. The last values are listed in Table 1 (Sofia et al., 2013). Inspection of this table shows how it is difficult to measure the solar radius, as the amplitude variation with time is 244 mas, about 10 times larger than the



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Table 1. Summary of the Solar Radius Observations made by means of the balloon SDS experiment given here as an example, the amplitude being 244 mas, about 10 times larger than the one deduced from satellite observations. The last column displays the solar oblateness, i.e. the difference between the equatorial and polar radius in millisecond of arc (mas). Flight number 6 7 8 9 10 11 12

Year R at 1 AU in  Oblateness ∆ r in mas 1992.82 959.638 ± 0.020 4.13 ± 1.92 1994.81 959.675 ± 0.020 8.16 ± 2.02 1995.82 959.681 ± 0.020 8.25 ± 1.34 1996.85 959.818 ± 0.020 9.88 ± 1.82 2001.83 959.882 ± 0.040 2009.87 959.750 ± 0.020 2011.86 959.856 ± 0.020

one deduced from satellite observations (see section 6). Moreover, the records permitted to deduce the solar oblateness (last column in Table 1), but the SDS1992 estimate is not in agreement with inferences based on the rotation at the solar surface, and far below (of expected 7.8 ∗ 10−6 for a uniform rotation; and the differential rotation at the surface increases the oblateness (see a discussion in Rozelot et al., 2009).

5

Solar Diameter from Eclipse data

The diameter of the Sun can be measured during eclipse times, a technique that covers now about three centuries. Such observations present, in theory some advantages since atmospheric effects are less important than in any other groundbased solar observation techniques. The main difficulty lies in the complexity of the lunar profile (due to the presence of valleys and craters) superimposed on the solar limb, and the technique depends upon the libration of the Moon. Another difficulty arises from the limited number of data obtained because of the few events per year. However, because of the short eclipse duration and the fast-moving trajectory in space, total and annular solar eclipse observations can provide more accurate calibration points by comparison to other data (Pasachoff & Nelson, 1987; Fiala et al., 1994; Dunham et al., 2005; Lamy et al., 2014). The oldest reliable observation goes back to 1715 (Danylevsky, 1999), and the interest in solar eclipses for estimating the solar diameter increased in the early 1980s (Dunham et al., 1980). Several tables listing the solar radius measurements from solar eclipses since 1715 are available, such as in Dunham et al. (2016) or in Kilcik et al. (2009). As an example, the last authors determined the solar radius of (959.22 ± 0.04) , calibrated to 1 AU. Lamy et al. (2014), averaging a set of 17 estimations at the 2010, 2012, 2013 and 2015 eclipses found a solar radius of (959.99 ± 0.06) (or 696 246 ± 45 km according to the authors). New

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measurements are scheduled for the next total solar eclipse in 2017 (August 21), for which the path of totality is very favorable for observations.

6

Solar diameter from satellite missions

Historical data suggest that the Sun’s radius may have changed over short or long periods of times. But, as seen in the previous sections, the question remained open at the eve of satellite missions. The ground-based contradictory results, as well as the difficulty to measure the solar radius from balloons, highlighted the necessity of more sensitive space experiments. The first mission of that kind was provided by the Michelson Doppler Imager (MDI) instrument (Scherrer et al. 1995), on board the Solar and Heliospheric Observatory (SOHO) satellite6 . It offered for the first time very accurate solar radius measurements from space. The MDI results had been analyzed by Emilio et al. (2000, 2004), who found a variation within the solar cycle of drcycle = (+21 ± 3) mas, 5 times smaller than the best ground-based measurements, and furthermore, in phase with the solar activity. A re-analyis of the data, taking into account instrumental corrections (Bush et al., 2010) led to the conclusion that any intrinsic changes in the solar radius, that are synchronous with the sunspot cycle, must be smaller than 23 mas, peak-to-peak. In addition, the authors find that the average solar radius must not be changing (on average) by more than 1.2 mas yr−1 . According to Kuhn (2004), if ground -and space- based measurements are both correct, the pervasive difference between the constancy of the solar radius seen from space and the apparent ground-based solar astrometric variability can only be accounted for by long-term changes in the terrestrial atmosphere. Adopting the value 1 AU = 1.495979 ∗ 108 km, the MDI observations gives the Sun’s radius R = (6.9574 ± 0.0011) ∗ 105 km. This is slightly smaller than the Brown & Christensen-Dalsgaard (1998) measurements (see above), but is consistent with the highly precise helioseismic determination made by Schou et al. (1997) of (6.9568 ± 0.0003) ∗ 105 km. The difference between what is called the “seismic” and the “photospheric” radius of (0.347 ± 0.006) Mm with respect to τ5000 = 1, has been explained by the difference between the height at disk center (where τ5000 = 1) and the inflection point of the intensity profile on the limb (Habeirreter et al. 2008). Early as in 1996, a group of solar physicists led by Dam´e, Rozelot and Thuillier (Dam´e et al. 2000) proposed a dedicated mission focused on the accurate measurement of the solar diameter from space, which was accepted by the French Agency CNES as the PICARD mission, and launched in 2010. Unfortunately, the influence of the space environment (ultra-violet radiation, thermal cycling, etc), led to considerable degradation of the instruments in orbit (contamination, temperature variations, abnormal detector responses, etc) and the mission was shortened. However, the data were analyzed by Meftah et al. (2015) who found 6

Section 2.3.10 of this paper stipulated that MDI will make the first photometric observations of the complete solar limb from above the atmosphere, determining the shape of the solar disk to an accuracy of about 0. 0007 each minute.



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that changes in the solar radius amplitudes obtained by the PICARD space telescope were less than ± 20 mas (i.e. ± 14.5 km) during the years 2010-2011. Considering this short period of time, the observations could not provide any direct link between solar activity and significant fluctuations in the solar radius. The authors concluded that the variations, if they exist, are within the range of values, which could be modulated by a typical periodicity of 129.5 days with a ± 6.5 mas variation7 . Other space missions were used in attempts to measure the solar diameter, although they were not specifically designed for such a purpose. Indeed they were more focused in determining the shape of the Sun, its oblateness at first. The distortion of the limb under the influence of the gravitational moments provides a “true figure” of the Sun. Such a topic, “how round is the Sun” could be another story. 1. The primary goal of the RHESSI (Reuven Ramaty High Energy Solar Spectroscopic Imager) mission was to explore the basic physics of particle acceleration and explosive energy release in solar flares, but it was used also to measure the solar limb using the optical solar aspect sensor. The results had been described by Fivian et al. (2008) and Hudson & Rozelot (2010), for the oblateness part, and in Battaglia & Hudson (2014) concerning the limb heights. Their first attempts to determine a solar radius in X-ray observations sound good, but a more detailed analysis remains to be done. Nevertheless, an extrapolation of the measured points shown on the left part of the curve given in Fig. 48 leads to R ≈ 969 .0, at 1 nm. It would be useful to explore this issue in future solar limb measurements by RHESSI. 2. The Solar Dynamics Observatory (SDO) satellite was launched on February 11, 2010, with a specific program designed to understand the causes of solar variability and its impacts on Earth. Among a broad spectrum of scientific themes, two were specifically mentioned at the beginning of the mission: the study of the impact of active regions on the solar diameter and the monitoring of a deep Sun survey (using an imaging spectropolarimeter, Helioseismic and Magnetic Imager -HMI-, Scherrer al., 2012) at 617.3 nm dedicated to helioseismology and magnetic field study). With regard to the measurements of the solar diameter, results have been analyzed by Emilio et al. (2015) during the Venus transit of 20129 . They found in the continuum wing of the 617.3 nm line by means of the HMI instrument, a solar 7

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Shall we consider this period as a sub-harmonic of the 7.5-8.5 years periodicity found by Cimino as previously quoted (i.e.: 8.5 ∗ 365.25/129.5 ≈ 24) ? See Rozelot et al., 2015, Fig. 3: R = 4.426 ∗ 10−5 x2 − 4.226 ∗ 10−2 x + 969.056, where x is the wavelength in nm. Let us recall the observations made by the French astronomer Le Gentil in his several attempts to measure the solar diameter through the Venus transits. He reported 979 .55 during the passage of Venus on December 21rst, 1768 and 946 .75 on June 21rst, 1769, that is a mean of 963 .15, an estimate not too far from the real value. In Le Gentil, G.J. 1779, “Voyage dans les mers de l’Inde fait par ordre du Roi”, Vol. I, Paris, Imprimerie Royale, p. 505 and 509.

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radius at 1 AU of (959.57 ± 0.02) (or 695 946 ± 15 km). The AIA instrument observed simultaneously the Venus transit at ultraviolet wavelengths which gave (963.04 ± 0.03) at 160.0 nm and (961.76 ±0.03) at 170.0 nm. Oblateness measurements have been substantially analyzed by Meftah et al. (2016) who employed several descriptions and analysis already made in their previous publications.

7

Helioseismic measurements

The significance of the actual number of the solar radius (and we need to know it precisely- see section 3) lies to a large extend on our increasing knowledge in helioseismology (see for example Ehgamberdiev, S. this book, the Standford site: http://soi.stanford.edu/results/heliowhat.html, or Kosovichev, 2011 for a comprehensive review). It was only in 1997 that Schou et al. (1997) succeeded for the first time, in obtaining a helioseismic determination of the solar radius by using high-precision measurements of oscillation frequencies of the f-modes of the Sun, obtained from the MDI experiment on board the SOHO spacecraft. They determined a “seismic radius” of about 300 km smaller than the photospheric adopted radius. A similar conclusion was reached by Antia (1998) on the basis of analysis of data from the GONG network. The question remained open until an attempt to reconciliate the two values by Haberreiter et al. (2008) as previously seen. As pointed out by Di Mauro (2003), the helioseismic investigation of the solar radius is based on the principle that the frequencies of the f modes of intermediate angular degree depend primarily on the gravity and on the variation of density in the region below the surface, where the modes propagate. It can −3/2 be shown from the asymptotic dispersion relation10 that ω ∝ R and by applying a variational principle, one can deduced a simple relation between f mode frequencies, ωl,o = 2πνl,o , so that the correction ∆R that has to be imposed to the photospheric radius R assumed for the standard solar model is:   ∆R 2 ∆νl,0 =− R 3 νl,0 where < > denotes the average weighted by the inverse square of the measurement errors. Dziembowski et al. (1998), inferring a relation between the f-mode frequency and radius variations in the subsurface layers, with the aim of determining a possible solar cycle dependence, analyzed first the period from May 1996 to April 1997. They show that the maximal relative variation of the solar radius during the observed period was about ∆R/R = 6 ∗ 10−6 , which corresponds to approximately ∆R = 4 km. In a second step, Dziembowski et al. (2000) analyzed a larger set of data spanning a period from mid-1996 to mid-1999, and 10

The dispersion relation of the f-modes is: ω 2  g kh where kh = [l(l + 1)]1/2 /R is 2 the horizontal component of the wave number and g = GM/R .



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Fig. 2. Top, temporal variation of DR near the solar surface at r = 1 R ; bottom, variation of the sunspot number for the same period. The variation of the seismic radius at the surface is found to be in antiphase with the solar cycle, with an amplitude of about 2 km. Computations have been made for l ranging from angular degree 125 to 285 with the reference year 1996; without information at higher l the surface radius cannot be constrained better. After Lefebvre & Kosovichev (2005) and Lefebvre et al. (2007).

they found that the systematic trend of ∆R/R was not correlated with the magnetic activity. However, such results have been obtained assuming that dr/r is constant with depth. Lefebvre & Kosovichev (2005) and Lefebvre et al. (2007) re-analyzed the time series 1996-2005 and showed that helioseismic radius varies in anti-phase with solar activity (Fig. 2) in the outer region of the Sun, but involving a change in behavior in deeper layers, the radius being non-homologous in the subsurface layers11 . Such radius variations can give a real insight into changes of the Sun’s subsurface stratification (Lefebvre et al. 2009). From another point of view, using a self-consistent approach, assuming either homologous (n = 1) or nonhomologous variations (n = 2, ...), Fazel et al. (2004, 2009) calculated ∆R/R and ∆L/L associated with the energies responsible for the expansion of the upper layer of the convection zone. They obtained an upper limit on the amplitude of cyclic solar radius variations (anticorrelated with the solar activity) between 5.8 (n = 1) and 3.9 (n = 2) km. Lastly, a recent analysis of f-modes by Kosovichev & Rozelot (2016) covering the degree range l up to 1200 shows an anticorrelated variation of the seismic radius with the magnetic activity (Fig. 2). In this range (l between 600 and 11

An attempt to derive a better approximation for the kernel linking the relative frequency changes and the solar radius variation in the subsurface layers has been made also by Chatterjee & Antia with no substantial conclusions: see arXiv:0810.4213v1 [astro-ph] 23 Oct 2008.

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Fig. 3. Seismic radius variation relative to the solar minimum value of 1996 as deduced from the analysis of f-modes during the years 1996-2015. The radius is clearly in opposite phase with the cycle sunspot activity. The peak-to-peak ∆R amplitude is ≈ 50 mas.

1200), the f-mode kinetic energy is concentrated within a layer of approximately 2 Mm of the solar photosphere.

8

Solar radius dependence with wavelength

The importance of limb shape dependence on the wavelength, from 303 nm up to 2400 nm, was recognized since a long time (Pierce & Slaughter (1977a); Pierce et al. (1977b); Neckel & Labs (1987, 1994)). It was found that the limb-darkening function could be fitted by a fifth order polynomial with no significant variations during the solar cycle. Since then, few measurements of the solar radius variations with the wavelength have been made. An investigation of the existing literature shows that the solar radius has been observed: - in the UV part of the spectrum, using the Extreme Ultraviolet Imager (EIT) aboard the SOHO spacecraft and analyzed by Selhorst, Silva & Costa (2004) on the one hand, and using the AIA (Atmospheric Imaging Assembly) (Lemen et al. (2012)) instrument aboard the SDO (Solar Dynamics Observatory) satellite, during the 2012 Venus transit on the other hand; - in the visible light spectral lines, as deduced from Mercury transits in 2003 and 2006 and from the Venus transit in June 2012, through the Michelson Doppler Imager (MDI) aboard the Solar and Heliospheric Observatory (SOHO) and from the HMI/SDO images (Helioseismic and Magnetic Imager instrument -HMI- aboard the Solar Dynamics Observatory). Sigimondi et al. (2015) observed also the Venus transit in 2004 in Athens to measure the solar radius in Hα;



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Fig. 4. Solar radius variations from EUV to Ha (on the left side) and to millimeter radio waves (on the right side) as a function of wavelength in the decimal logarithm scale. A second order polynomial correctly fits the data showing a strong wavelength dependence of the solar radius. The mid-domain (curve in dots) ranging from 677 nm to 742,060 nm (404 GHz) is presently still unexplored. A minimum is obtained for about 6.6 µm with an estimated error of ± 1.9 µm. No unique model can currently explain such an important wavelength variation. See also Rozelot et al. (2015, 2016) for further descriptions.

- in the visible broad band continuum by the Picard-sol instrument installed at the Calern observatory, South of France (Meftah et al. (2014)12 ), and by the “Heliometer” instrument installed at the Pic du Midi Observatory (South of France) (Rozelot et al. (2013)); - in the radio band, several determinations of the solar radius have been made by radio telescopes at millimeter waves, including eclipse observations at centimeter and decimeter waves, and interferometric observations at meter waves (Selhorst et al. (2004); Gim´enez de Castro et al. (2007), (2009)). Fig. 4 taken in Rozelot & Kosovichev (2015) shows all the data plotted together. A strong wavelength dependence of the solar radius is highlighted. How12

A new summary of the PICARD solar radius observations at different wavelengths, based on the determination of the inflection point position, can be found in Meftah et al., 2016, SPIE Conference Paper, Vol. 9904, DOI: 10.1117/12.2232027.

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ever, a large wavelength domain from 667 to 742,060 nm is currently unexplored. In this range the polynomial fit suggests a minimum in the mid-IR region at about (6.6 ± 1.9) µm that must be confirmed by other means (observations are scheduled with the Atacama Large Millimeter Array - ALMA- in Chile within the cycle 4 program). No model can reproduce today the entire variation from X-UV to radio. Lastly, albeit the measurements were obtained at different periods of time, no significant radius temporal variations have been found, at least at the level of the uncertainty at which the observations were made.

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Conclusion: a quest for more accurate data

This chapter shows evidently that the determination of the solar radius with a high accuracy is maybe one of the most difficult problem to solve today. The IAU General Assemblies in Pekin (2012) and in Honolulu (2015) adopted for the Astronomical Unit 1 AU = 149 597 870 700 m exactly and for the solar radius R = 6.957 ∗ 108 m, so that in arc second, the radius is now fixed to 959. 22. It results a difference of 0. 41 with the previous canonical value as defined by Auwers (1891), or 297 km taking into account the new value of the Astronomical Unit. According to our graph (Fig. 4), this would lead to a nominal wavelength of 400.00 nm. In any event, further accurate observations are needed. As far as the temporal variations of the solar radius are concerned, here also, the quest is not finished. New space dedicated satellites must be designed and launched. Such data would also help to understand the underlying mechanisms of the solar-cycle variations and physical processes in the Near Sub-Surface Layers of the Sun. Such determinations are still a challenge.

Acknowledgments This work was partly supported by the International Space Science Institute (ISSI) in Bern (CH) where one of the author (JPR) is repeatedly invited as a visitor scientist, and also by a NASA grant NNX14AB70. JPR and AGK thanks also the Science Development Foundation under the President of the Republic of Azerbaijan for providing financial support to attend Baku Solar conference in June 2015.



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data assessment quality ASolar briefdiameter history measurements: of the solar diameter measurements

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Jean Pierre Kosovichev & Ali Kilcik Jean PierreRozelot, Rozelot,Alexander Alexander G. Kosovichev, & Ali Kilcik

Shapiro, A.E. 1975. Journal of Historical Astronomy 75-80. Sigismondi, C., Ayiomamitis, A., Wang, X., Xie W., Carinci, M. & Mimmo, A. 2015. http://de.arxiv.org/ftp/arxiv/papers/1507/1507.03622.pdf Sofia, S., Maier, E. & Twigg, L. 1991. Adv. Spa. Res. Vol. 11, 4, 123-132. Sofia, S., Girard, T. M., Sofia, U. J. et al. 2013. MNRAS 436, 2151. Sukhodolov, T., Rozanov, E., Ball, W.T. and 15 co-authors 2016. J. Geophys. Atmos. 121, 6066-6084. Ulrich, R.K. & Bertello, L. 1995. Nature 377(6546), 214-215. Vaquero, J.M., Gallego, M.C., Ruiz-Lorenzo, J.J., L´opez-Moratalla T., Carrasco, V.M.S., Aparicio, A.J.P., Gonz´ alez-Gonz´ alez, F.J. & Hern´andez-Garc´ıa, E. 2016. Sol. Phys. 291, 1599-1612. Wittmann, A. 1997. A&A 61, 225-227. Wittmann, A.D. & Bianda, M. 2000. In “The solar cycle and terrestrial climate, Solar and Space Weather Euroconference”, Santa Cruz de Tenerife, Tenerife, Spain, ESA SP, A. Wilson, A. (ed). Vol. 463, 113-116, Noordwijk (NL).

Solar sunspot-forming activity and its development on the reliable Wolf numbers series V.N. Ishkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation (IZMIRAN), Troitsk, Moscow, Russia Geophysical Center, Russian Academy of Sciences, Moscow, Russia E-mail: [email protected] Abstract. The modern period of decreasing solar activity put on the agenda the study of the solar cyclicity characteristics, using only reliable series of relative sunspot numbers (timeline in ∼177-yrs – 16 solar cycles). These statistics leads to the scenario of the regular changes of magnetic field in the solar convection zone generation regime in the transition period from the epoch of “increased” () solar activity and vice versa – from the epoch of the “lowered” to “increased” solar activity. The epochs significantly differ from each other in parameters, evolution characteristics and manifestations of sunspot-forming activity.

1

Introduction

At the present time the statistics of Wolf number series observations gives an opportunity to investigate the scenario of solar activity (SA) cycles, its property, characteristic and rules of the development on a reliable (1849 – 2015) series of Wolf numbers (Fig. 1) in the time scale of 166 year – 14 total solar cycles (SCs). It is necessary to note that for such studies of SC characteristics we in principle cannot use the restored series (1755 – 1848), since the reliable and restored series of the Wolf numbers have completely different spectral characteristics and significantly differ in the statistical parameters [Ishkov, Shibaev, 2005, 2012]. From the comparison of reliable and restored series it can be noted that: – the nature of the behavior “instantaneous” frequencies and envelopes in interval of 1749 – 1849 strongly differs from a reliable series; – an increase in the length of a series leads to declining in resolution quality of some significant spectral characteristics (usually the situation is opposite); – an absence or the essential distortion of “high-frequency” part of the spectrum. As have been shown in the work [Shibaev, Ishkov, 2012], for the reliable cycles exists the inverse correlation (−0.658) between the duration of the SC rise branch and the value of the maximum of SC (hence Waldmeyer’s rule) and absence of correlation (0.055) between the branch of the decrease and the value of maximum. These connections have other scenario for the restored cycles, where even the stronger inverse correlation (−0.898) between the first parameters passes

110 2

V.N. Ishkov V.N. Ishkov

Fig. 1. Reliable series of the relative sunspots numbers (dark cycles) with the boundaries of the structural “lowered” (1) and “increased” (2) epochs of SA with the transition periods between them. Probable period of “increased” SA (2*), which includes cycles of SA ( 100) by Kohl et al. (1998) and Cranmer et al. (1999); of protons by Cranmer et al. (1999); and of the coronal hole temperature by Dodero et al. (1998) and Antonucci et al. (2000). An opposite ion temperature relation T⊥ /T < 1 is also found in solar wind observations (Marsch 2006). It is now generally accepted that the observed large ion temperature anisotropies are related to the physical mechanism by which the solar corona and solar wind are heated (Hollweg & Isenberg 2002; Marsch 2006). We consider the largescale wave peculiarities and instabilities that can appear in the coronal and wind plasmas. It is shown that in areas with a weak magnetic fields (B < 1 G) aperiodical mirror instability can develop in the slow MHD waves, and in the areas with strong magnetic fields (B > 10 G) may develop a periodical ionacoustic instability. Growth rates of the instabilities are found and temporal and spatial scales of development and decay of the periodic instability are estimated. It was shown that this instability may play a key role in the energy balance of the coronal heating. The main source of instability development is the energy of Alfv´enic and fast MHD waves which propagate from the lower atmosphere, where the plasma are dominantly collisional. Macroscopic turbulence observed in the solar wind and in the stable coronal turbulent background (appearing in the nonthermal broadening of coronal emission line profiles) may be a consequence of these instabilities. Near the Sun heavy ions are stronger heated than protons and electrons. These findings have strengthened the arguments in favor of the kinetic ion-cyclotron model of heating and acceleration of particles in the solar wind. However, this mechanism has a number of shortages. For example, the observed properties of low-frequency wave turbulence are close to those of Alfv´enic modes and their power spectrum



instabilities in an anisotropicmagnetized magnetizedspace space plasma plasma WaveWave instabilities in an anisotropic

123 5

has a maximum around one–two hours. In order to realize the ion-cyclotron resonance, Hollweg assumed that low-frequency waves by the nonlinear cascade should finally turn to high-frequency modes. However we think that within the frames of anisotropic fluid model such observed low-frequency modes can easily be explained. The new observed facts which can essentially modify our understanding about the physical nature of the solar wind are presented in a recent paper Brovsky (2010). It appears that the solar wind consists of sets of magnetic filaments. We think that the nonlinear evolution of the large-scale compressible fluid mirror mode instability is capable of creating such structures. The solutions obtained in the anisotropic MHD model agree well with those in the low frequency limit of the kinetic model, so we can conclude that the approximate MHD model under consideration here provides a correct description of the large scale dynamics of collisionless anisotropic plasmas (such as solar corona, solar wind, and ionospheric–magnetospheric plasma). It should be kept in mind, however, that the applicability of the hydrodynamic description of a collisionless plasma in the singlefluid hydrodynamic model is restricted because the electron temperature is to be constant in time and uniform in space and because the cold ion approximation implies that the plasma should be nonisothermal (Te  Ti ). The use of the 16-moment MHD approximation for describing a collisionless plasma with temperature anisotropy makes it possible to study MHD waves and instabilities when there are heat fluxes directed along the magnetic field and related to dilatational and transverse thermal motions of particles (γ = γ⊥ ). The analysis of the effect of heat fluxes on the properties of instability waves indicates that all three kinds of compressible instabilities—second kink, mirror, and thermal oscillatory instabilities—appreciably change with changes in the γ⊥ parameter. The presence of a heat flux related to transverse thermal motions of particles strengthens instabilities and shifts their thresholds. Since the presence of temperature anisotropy in the solar wind and corona has been established in numerous observations (based on radiation characteristics of heavy ions), the discovered instabilities can take place and play a significant role in generating large scale turbulence, which may be a source of heating the solar corona and accelerating solar wind. For all instabilities occurring in the MHD approach (the normal incompressible firehose instability, the second compressible almost longitudinal firehose instability, and the almost transverse mirror instability of slow magnetosonic modes, as well as thermal instability caused by the heat flux directed along the magnetic field), their kinetic analogs are considered. The kinetic dispersion relation in the low-frequency range in the vicinity of the ion thermal velocity is analyzed. The flow of plasma ions along the magnetic field is taken into account. The thresholds and instability growth rates obtained in the MHD and kinetic approaches are found to be in good agreement. This indicates that the 16-moment MHD equations adequately describe the dynamics of collisionless plasma. About the obtained results in more detail can be found in our recent publications Dzhalilov et al. (2008, 2009, 2010, 2011, 2012, and 2013).

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Bibliography Chew G. F., M. L. Goldberger, and F. E. Low, Proc. Roy. Soc. London A236, 112 (1956). Chandrasekhar S., A. N. Kaufman, and K. M. Watson, Proc. R. Soc. London A245, 435 (1958). Vedenov, A.A. and Sagdeev, R.Z., Dokl. Akad. Nayk SSSR, 3, 278 (1958). Parker E. N., Phys. Rev. 109, 1874 (1958). Hellinger P. and H. Matsumoto, J. Geophys. Res. 105, 10519 (2000). Hollweg J.V. and H. J. V¨ olk, J. Geophys. Res. 75, 5297 (1970). Hau L. N., J. Geophys. Res. 101, 2655 (1996). Oraevskii V. N. , Konikov Yu. V., Khazanov G. V., Transport Processes in the Near Earth Plasma (Nauka, Moscow, 1985) [in Russian]. Ramos J. J., Phys. Plasmas 10, 3601 (2003). Landi S. and F. G. E. Pantellini, Astron. Astrophys. 372, 686 (2001). Feldman W. C., Asbridge J. A., Bame S. J., Montgomery, M. D., Rev. Geophys. Space Phys., 12, 715 (1974). Marsch E., M¨ uhlh¨ uauser K.-H., Schwen R., Rosenbauer H., Pilipp,W. G., Neubauer, F. M., J.G.R, 87, 52 (1982). Kohl J. L., Noci G., Antonucci E., & 28 coauthors., ApJ, 501, L127 (1998). Cranmer S. R., Kohl J. L., Noci G., & 28 coauthors., ApJ, 511, 481(1999). Dodero M. A., Antonucci E., Giordano S., Martin, R., Sol.Phys., 183, 77 (1998). Antonucci E., Dodero M. A., Giordano S., Sol. Phys., 197,115 (2000). Marsch E., Living Rev. Solar Phys., 3, 1 (2006). Hollweg J. V., Isenberg P. A., J. Geophys. Res., 107, 1147 (2002). Brovsky J. E., Phys. Rev. Letters 105, 111102 (2010). Dzhalilov N.S., Kuznetsov V.D., Staude J., Astron. Astrophys. 489, 769 (2008). Kuznetsov V.D., Dzhalilov N.S. Plasma Phys. Rep. 35, 962 (2009). Kuznetsov V.D., Dzhalilov N.S. Plasma Physics Reports, 36, 788 (2010). Dzhalilov N.S., Kuznetsov V.D., Staude J. Contrib. Plasma Phys. 51 (7), 621 (2011). Dzhalilov N.S., Kuznetsov V.D. Astronomy Letters, 37, 649 (2012). Dzhalilov N.S., Kuznetsov V.D. Plasma Phys. Rep., 39, 1026 (2013).

Asteroseismology with solar-like oscillations Jørgen Christensen-Dalsgaard Stellar Astrophysics Centre Department of Physics and Astronomy, Aarhus University Ny Munkegade 120, 8000 Aarhus C, Denmark E-mail: [email protected] Abstract. Almost 100 years ago Sir Arthur Eddington noted that the interiors of stars were inaccessible to observations. The advent of helio- and asteroseismology has completely changed this assessment. Helioseismology has provided very detailed information about the interior structure and dynamics of the Sun, highlighting remaining issues in our understanding of the solar interior. In the last decade extensive observations of stellar oscillations, in particular from space photometry, have provided very detailed information about the global and internal properties of stars. Here I provide an overview of these developments, including the remarkable insight that has been obtained on the properties of evolved stars.

1

Introduction

In his seminal book The internal constitution of the stars Eddington (1926) pondered ‘What appliance can pierce through the outer layers of a star and test the conditions within?’. He answered the question through his theoretical investigations of stellar interiors which, despite the limited physical knowledge at the time, were remarkably successful in uncovering the basic principles underlying stellar internal structure. Modelling stellar structure and evolution has undoubtedly become much more sophisticated and, presumably, realistic since Eddington’s time, but the basic question remains: which observations can pierce through the outer layers of a star and test the conditions within? The answer is now well-established: the study of stellar interiors through the observation of oscillations on their surface, in other words, asteroseismology. The detailed observational study of stellar interiors started with the development of helioseismology, from extensive observations of oscillations on the solar surface (for a review, see, e.g., Christensen-Dalsgaard 2002, see also Kosovichev, these proceedings). However, as indicated in Fig. 1 oscillations are found in a broad range of stars, providing opportunities for studies of stars in essentially all phases of their evolution. In this brief review I focus on stars showing oscillations similar to those of the Sun which, as discussed below, are intrinsically stable and excited stochastically by the near-surface convection. Modes of solar-like oscillations are generally characterized by extremely small amplitudes, in the solar case up to about 20 cm s−1 in radial velocity and a few parts per million in intensity. The difficult observations of such oscillations in distant stars had a modest beginning in the nineties (e.g., Brown et al. 1991; Kjeldsen et al. 1995; Bouchy & Carrier 2001), but they have evolved dramatically

126 J¿rgen 2 Jørgen Christensen-Dalsgaard Christensen-Dalsgaard

in the last few years through space-based photometric observations from the CoRoT (Baglin et al. 2013) and, in particular, the NASA Kepler mission (Borucki et al. 2010; Gilliland et al. 2010) launched in March 2009. Thus we stand at the beginning of a new phase of strongly observationally constrained studies of stellar interiors.

Fig. 1. Hertzsprung-Russell diagram showing the location of various groups of pulsating stars. The dashed line shows the zero-age main sequence and the solid lines show selected evolutionary tracks. The dotted line schematically indicates the white-dwarf cooling track. Here I focus on solar-like pulsators, indicated by horizontal hatching and situated to the right of the Cepheid instability strip (marked ‘Ceph’). For further details, see Aerts et al. (2010).



2

Asteroseismology with solar-like oscillations Asteroseismology

127 3

Basic properties of stellar oscillations

Here I only give a brief overview of the main features of stellar oscillations. For a detailed description, see Aerts et al. (2010). Stellar oscillations are characterized by the dominant restoring forces and the mechanisms exciting the modes. Another important characteristic is the geometrical structure of the mode. In (nearly) spherically symmetric stars this is characterized by a spherical harmonic Ylm (θ, φ) as a function of co-latitude θ and longitude φ. Here the degree l measures the total number of nodal lines on the stellar surface and the azimuthal order m, with |m| ≤ l, gives the number of nodal lines crossing the equator. Spherically symmetric modes, with l = 0, are known as radial oscillations. In addition, a mode is characterized by the radial order n related, sometimes in a rather complex manner (Takata 2012), to the number of nodes in the radial direction. In distant stars, where only oscillations in light integrated over the stellar surface have so far been analysed, cancellation suppresses the modes of higher degree, and only modes up to typically l = 2 − 3 are observed. The two dominant restoring forces are pressure, and buoyancy acting on density differences. The pressure-driven modes, known as p modes, are essentially standing sound waves. These are the modes observed in the Sun and solarlike oscillations in moderately evolved stars. They tend to have relatively high frequency, in the solar case between 1000 and 5000 µHz, corresponding to periods between 17 and 3 minutes, and high radial order. Consequently, their properties are well characterized by their asymptotic behaviour, according to which, to leading order, the cyclic frequency satisfies   l (1) νnl  ∆ν n + +  , 2 where  is a frequency-dependent phase largely determined by the near-surface properties. Here the large frequency separation is given by   ∆ν = 2

0

r

dr c

−1

,

(2)

where c is the adiabatic sound speed and the integral is over distance r to the centre, between the centre and the surface radius R. It may be shown that ∆ν, and hence the frequencies, scales as the square root of the stellar mean density, ∆ν ∝ (M/R3 )1/2 (Ulrich 1986), where M is the mass of the star. The departure from the simple relation (1) contains important diagnostic information. This is characterized by the small frequency separation δνnl = νnl − νn−1 l+2

∆ν  −(4l + 6) 2 4π νnl



R 0

dc dr , dr r

(3)

where the last expression is valid only for main-sequence stars. Here the integral is weighted towards the centre and hence is sensitive to the sound-speed structure

128 J¿rgen 4 Jørgen Christensen-Dalsgaard Christensen-Dalsgaard

Fig. 2. Power spectrum of the solar-like pulsator 16 Cygni A, from 35 months of Kepler data, smoothed with a 0.6 µHz boxcar filter. The lower panel shows a short segment; the degrees of the modes and the large and small frequency separations are indicated. The inferred frequency νmax in the top panel, marked by a vertical dashed line, and the fitted frequencies, marked by vertical dotted lines in the lower panel, were obtained by Lund et al. (in preparation).



Asteroseismology with solar-like oscillations Asteroseismology

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in the core. For an approximately ideal gas, c2 ∝ T /µ, where T is temperature and µ is the mean molecular weight; therefore δνnl is sensitive to the composition of the core, and hence to the amount of hydrogen that has been converted to helium by nuclear fusion, determined by the age of the star. As noted by e.g. Christensen-Dalsgaard (1988) this provides a simply way to determine stellar ages, if other properties of the star are known. The properties of the acoustic-mode spectrum in main-sequence stars are illustrated in Fig. 2 showing the power spectrum of the star 16 Cygni A as observed by Kepler. The lower panel identifies the large and small frequency separations, based on frequency fits to the power which in this case allows detection of modes of degree up to 3. The second restoring force is gravity, acting through buoyancy on density differences across horizontal surfaces; consequently, this only operates for l > 0. The resulting modes are standing internal gravity waves, or g modes. They are characterized by the so-called buoyancy, or Brunt-V¨ais¨al¨a, frequency N , given by   1 d ln p d ln ρ N2 = g − , (4) Γ1 dr dr

where g is the local gravitational acceleration, p is pressure, ρ is density and Γ1 is the adiabatic compressibility. In convection zones N 2 is negative, and hence the gravity waves are evanescent. In main-sequence stars the g modes have relatively low frequency, and their detection in the Sun has been hotly debated for decades (Garc´ıa et al. 2007; Appourchaux et al. 2010). However, in evolved stars the gravitational acceleration, and hence N 2 , gets very high in the compact core of the stars, and hence g modes may have high frequency, in the range of the solar-like p modes. This gives rise to the very interesting phenomena of mixed modes to which we return below. As for p modes, the relevant g modes are often of high radial order, making their asymptotic behaviour of great diagnostic value. This is most simply expressed in terms of the oscillation period Π = 1/ν which approximately satisfies Πnl = ∆Πl (n + g ) ,

(5)

where g is a phase that may depend on the degree. Here the period spacing is 2π 2 ∆Πl = [l(l + 1)]1/2



dr N r

−1

.

(6)

For spherically symmetric stars the frequencies are independent of the azimuthal order m. This degeneracy is broken by departures from spherical symmetry, of which by far the most important is rotation. Rotation gives rise to a splitting which, for slow rotation, can be written as νnlm = νnl0 + mδrot νnlm

(7)

where δrot νnlm reflects an average of the internal rotation rate, weighted by the properties of the oscillations. In the solar case, this has allowed a detailed

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determination of solar internal rotation (for a review, see Howe 2009). In the stellar case less information is obviously available, but, as discussed below, some very interesting results have been obtained. Solar-like oscillations are intrinsically damped but gain their energy from the acoustic noise generated by the near-surface convection. The result are peaks in the power spectrum with an amplitude that is determined by the balance between the energy input and the damping and a width that, for sufficiently long observations, is determined by the intrinsic damping rate (e.g., ChristensenDalsgaard et al. 1989). Early estimates of the energy input and the resulting amplitudes in the solar case were made by Goldreich & Keeley (1977), while Christensen-Dalsgaard & Frandsen (1983) made a first estimate of the amplitudes of solar-like oscillations across the relevant part of the Hertzsprung-Russell diagram. The damping is dominated by the effects of convection, involving the perturbations to both the convective heat flux and the turbulent pressure (e.g., Balmforth 1992). The treatment of these effects is highly uncertain, although various formulations of time-dependent convection have been established (see Houdek & Dupret 2015, for a review). With appropriate choice of parameters a reasonable fit can be obtained to the observed solar line widths (Chaplin et al. 2005; Houdek 2006). The combined result of the excitation and damping is a characteristic distribution of power with frequency (Goldreich et al. 1994), as shown in Fig. 2 for the observations of 16 Cyg A. This is characterized by the frequency νmax at maximum power. There is substantial empirical evidence that νmax scales as the acoustic cut-off frequency in the stellar atmosphere (e.g., Brown et al. −1/2 1991; Stello et al. 2008), leading to νmax ∝ M R−2 Teff , where Teff is the effective temperature. The physical reason for this scaling has not been definitely established, although Belkacem et al. (2011) pointed out some likely relevant factors.

3

Asteroseismic determination of stellar properties

The space-based asteroseismic observations from CoroT and Kepler have set the scene for extensive investigations of stellar properties, ranging from ensemble studies of large numbers of stars to detailed studies of individual targets. These missions were, in part, motivated by the study of extra-solar planetary systems (exoplanets) through the transit technique, with the common requirement with asteroseismology of very high photometric precision over long periods of time. We are still only at the beginning of exploring the potential of these asteroseismic data, and here I can just give a brief indication of the results obtained. A recent review of asteroseismology based on solar-like oscillations was provided by Chaplin & Miglio (2013). The most basic observed properties of solar-like oscillations are the frequency νmax at maximum power and the large frequency separation ∆ν. These can be determined even from data with a low signal-to-noise ratio. Assuming that Teff is determined independently, the scaling relations with acoustic cut-off frequency



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and stellar mean density then provide two equations which can be solved for the mass and radius (Kallinger et al. 2010). Even this simple analysis provides stellar quantities that are otherwise very difficult to determine. It can be refined by including constraints based on stellar model grids, including also information about the stellar composition (Gai et al. 2011). A detailed test of these techniques was carried out by Silva Aguirre et al. (2012). Alternatively, given the somewhat shaky foundations of the scaling for νmax , fits to grids of models can be carried out just based on ∆ν and Teff (Lundkvist et al. 2014). These techniques provide simple methods to determine the basic properties of large numbers of stars. They have been applied extensively to the CoRoT and Kepler observations, and only a few examples can be given here. Chaplin et al. (2011, 2014) analysed Kepler observations of substantial samples of main-sequence stars, in the early paper also comparing with the predicted distributions, from Galactic modelling, in mass and radii of stars in the solar neighbourhood. Data for huge numbers of red giants have been obtained by CoRoT and Kepler, allowing detailed characterization of the population of these stars (e.g., Hekker et al. 2011). Analysis of stars in open clusters is particularly interesting. Thus, based on Kepler data, Miglio et al. (2012) estimated the red-giant mass loss in two open clusters from determination of stellar masses in different evolutionary stages. A very important application of basic asteroseismology of red giants is in Galactic archaeology, relating stellar properties to the location of the stars in the Galaxy (Miglio et al. 2009). For red giants there is a close relation between stellar mass and age, and hence just the simple asteroseismic analysis provides a measure of stellar age (Miglio et al. 2013). When combined with large-scale spectroscopic investigations this provides the basis for a detailed investigation of the chemical and dynamical evolution of the Galaxy (e.g., Casagrande et al. 2016). When individual frequencies have been determined much more detailed and accurate investigations of stellar overall and internal properties are possible. A difficulty in such analyses is the uncertain treatment of the near-surface layers in the star and their effects on the oscillation frequencies, giving rise to what is known as the near-surface error in the computed frequencies. In the solar case this can be isolated in the analysis owing to the availability of observations over a large range of degrees. Various techniques have been developed to correct for the effect in distant stars, based on an assumed similarity with the solar correction (e.g., Kjeldsen et al. 2008; Christensen-Dalsgaard 2012) or with a somewhat stronger physical basis (Ball & Gizon 2014). Alternatively, model fits can be based on suitable ratios between small and large frequency separation which are largely insensitive to the near-surface effects (Roxburgh & Vorontsov 2003; Ot´ı Floranes et al. 2005). An early analysis of Kepler data was carried out by Metcalfe et al. (2010), for a star in the subgiant phase where hydrogen has been exhausted in the core. The resulting compact helium core increased the frequencies of gravity waves in the deep interior, giving rise to modes of mixed p- and g-mode nature. The

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frequencies of such modes are very sensitive to the internal properties of the star, including its age, and hence the fit to the observed frequencies in principle may result in very precise determinations of stellar properties. However, several solutions were in fact found, each tightly constrained by the data. This is an example of the importance of including additional information about the star, supplementing the asteroseismic data, as constraints on the stellar properties. A detailed analysis of a sample of stars observed by Kepler was carried out by Mathur et al. (2012) who also obtained some information about the dependence of the surface correction on stellar properties. Extensive modelling of two stars observed by Kepler was carried out by Silva Aguirre et al. (2013), using several different modelling and fitting techniques to test the range of systematic uncertainties involved in such fits. Interestingly, one of the stars, with a mass of around 1.25 M , had clear evidence for a convective core, with some additional mixing outside the unstable region. This is a first indication of the potential for using asteroseismology of solar-like stars to study the physics of stellar interiors. Metcalfe et al. (2015) fitted the full set of Kepler data for the two components of the binary star 16 Cygni (see also Fig. 2). As an encouraging test of consistency the independent analysis of the two components yielded the same age, around 7 Gyr, within the errors of 0.25 Gyr, in accordance with the assumption of contemporaneous formation of the pair. Asteroseismology is playing an important role in the determination of properties of exoplanet host stars, benefitting from the fact that the same photometric observations can be used both for the characterization of the exoplanets and for asteroseismology. To determine the properties of an exoplanet we need the radius and mass of the host star which can be determined much more accurately with asteroseismology than with ‘classical’ astrophysical techniques. Furthermore, asteroseismology allows determination of the age of the host star and hence the planetary system. In this way Batalha et al. (2011) found that Kepler’s first rocky exoplanet, with a radius of 1.4RE , orbited a star with an age of around 10 Gyr, twice the age of the Sun. Analysis of further data for this system by FogtmannSchulz et al. (2014) yielded a value of the age of 10.4 ± 1.4 Gyr and, remarkably, allowed a determination of the radius of the planet with a precision of 125 km. A similar age was obtained by Campante et al. (2015) for a system containing 5 planets with sizes at or smaller than that of the Earth. These striking results demonstrate that planet formation took place already in the early phases of the history of the Galaxy. I also note that a detailed analysis of a CoRoT exoplanet host was carried out by Lebreton & Goupil (2014), who investigated the extent to which different combinations of seismic and non-seismic data could constrain the properties of the star. Silva Aguirre et al. (2015) carried out a detailed analysis of the 33 Kepler confirmed or potential exoplanet host stars for which extensive asteroseismic data are available. Taking into account also systematic effects of the use of different modelling or fitting techniques, they were able to determine the radii and masses with median uncertainties of 1.2 and 3.3 per cent, respectively, whereas the ages were determined with a median uncertainty of 14 per cent. The distributions of



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Fig. 3. Distributions of fractional uncertainties in asteroseismic determinations of radius, mass and age for 33 Kepler (potential) exoplanet hosts. Adapted from Silva Aguirre et al. (2015).

uncertainties are shown in Fig. 3. I note that the age is determined predominantly from the decrease in the central hydrogen abundance; thus the fractional uncertainty in age, as illustrated, is unavoidably higher for unevolved stars. As mentioned in Section 2 (see Eq. 7) rotation causes a splitting of the frequencies according to the azimuthal order m which in fact has been observed in a number of cases in the Kepler data. The resulting information about the stellar rotation rate is obviously of substantial interest. However, in the exoplanet context an even more interesting aspect is information about the orientation of the rotation axis. For stochastically excited modes it is not unreasonable to assume that the average amplitude, for given n and l, is independent of m. However, the observed amplitude depends on the inclination of the rotation axis with respect to the line of sight (Gizon & Solanki 2004). In the limiting case of a rotation axis in the plane of the sky only modes with even l − m are observed, while if the rotation axis points towards the observer only modes with m = 0 are seen. For exoplanets detected with the transit technique one would naively expect the rotation axis of the host star to be in the plane of the sky: the planets are assumed to form from a disk left over from the formation of an initially rapidly rotating star and hence lying in the star’s equatorial plane; thus the rotation axis would be approximately orthogonal to the plane of the planetary orbits, as is indeed the case for the solar system. Such systems have indeed been found (e.g., Chaplin et al. 2013). However, in other cases there is a large misalignment between the rotation axis and the axis of the planetary orbits (e.g., Huber et al. 2013; Lund et al. 2014). Understanding the origin of

134 J¿rgen 10 Jørgen Christensen-Dalsgaard Christensen-Dalsgaard

this behaviour is an important part of the study of the formation and evolution of planetary systems.

4

Asteroseismology of red giants

As a background to the discussion of the asteroseismology of red giants it is useful to give a brief overview of red-giant evolution; for a detailed review, see Salaris et al. (2002). This phase of stellar evolution follows after the end of central hydrogen burning. The star continues to obtain its energy from hydrogen fusion, but now in a shell around the gradually growing helium core. The core contracts while the outer layers expand and cool, establishing a deep outer convection zone. When the star reaches the Hayashi track the continuing expansion takes place at nearly constant effective temperature, leading to a drastic increase in the luminosity (see also Fig. 1), which in the solar case will reach as high as one thousand times the present luminosity, along the red-giant branch. At this point the temperature in the helium core has reached a level, around 100 million degrees, where helium fusion to carbon and oxygen sets in. The core expands and the outer layers contract, until the star settles down to a phase of quiescent helium burning, a substantial fraction of the energy still coming from the hydrogen shell burning. After the end of central helium burning the outer layers again expand greatly in the asymptotic giant phase, after which the star sheds its envelope and is left with the central very compact carbon-oxygen core, a white dwarf. Given the deep outer convection zone it was expected (Christensen-Dalsgaard & Frandsen 1983) that red giants would show solar-like oscillations. The first detection was made by Frandsen et al. (2002), followed by a few other ground-based studies which, however, were hampered by the very long observation periods required to resolve the low frequencies resulting from the low mean density of the stars. However, as already mentioned, a major break-through in the study of solar-like oscillations in red giants came with the space-based observations from CoRoT and Kepler which have shown oscillations in tens of thousands of stars. The oscillations can be followed to the most luminous stars observed by Kepler, with a power envelope similar to what is observed on the main sequence (cf. Fig. 2) but with a dominant frequency less than 1 µHz, corresponding to a period of more than 10 days (Stello et al. 2014). Indeed, the oscillations observed by Kepler merge with the even slower oscillations seen in highly evolved giants with ground-based surveys (Mosser et al. 2013), and there is evidence that semi-regular variables, with periods of many months and typically observed by amateur astronomers, show solar-like oscillations (Christensen-Dalsgaard et al. 2001). From the first observations there were indications that the red-giant modes had a very short damping time, leading to broad peaks in the power spectrum and hence limited frequency precision, even though an early theoretical estimate indicated life times several times the typical solar values (Houdek & Gough 2002). Also, apparently only radial modes were observed. This would further limit the diagnostic value of the observations. A first indication of nonradial oscillations in



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a red giant was obtained by Hekker et al. (2006) from observations of line-profile variations. A definite proof that red giants showed the full range of solar-like oscillations was obtained by De Ridder et al. (2009) in an early analysis of CoRoT data which also demonstrated the similarity of the power envelope over a broad range of stellar luminosities and hence frequencies of maximum power.

Fig. 4. Power spectrum from 49 months of Kepler observations of the red giant KIC 6779699, smoothed with a 0.09 µHz boxcar filter. In the small segment of the spectrum in the lower panel the degrees of the modes are indicated, the horizontal line marking the l = 1 mixed modes. See Bedding et al. (2011).

Although the detection of non-radial modes in solar-like oscillations of red giants was an important step, the full, huge diagnostic potential of these obser-

136 J¿rgen 12 Jørgen Christensen-Dalsgaard Christensen-Dalsgaard

vations became apparent with the identification of mixed modes in a red giant by Beck et al. (2011), in Kepler observations. This was followed by studies of ensembles of red giants by Bedding et al. (2011) from Kepler, and Mosser et al. (2011) from CoRoT, observations. An example of an observed power spectrum is shown in Fig. 4. This is superficially similar (albeit at lower frequencies) to the main-sequence power spectrum in Fig. 2, with pairs of peaks of degree l = 0 and 2; but instead of a single intermediate l = 1 peak there is now a group of peaks; these are modes of mixed p- and g-mode behaviour.

Fig. 5. Properties of oscillations in a red-giant model, of mass 1 M and radius 7 R . The upper panel shows the normalized mode inertia (cf. Eq. 8) for modes of degree l = 0 (circles and solid line) and 1 (triangles and dashed line). The lower panel shows the computed period spacings for l = 1, the dotted horizontal line marking the asymptotic value (cf. Eq. 6).



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To understand this behaviour it is instructive to consider the properties of modes in a stellar model, characterized in terms of the normalized mode inertia  ρ|δδ r|2 dV E= V , (8) M |δδ r|2phot where the integral is over the volume of the star, δ r is the displacement vector and |δδ r|phot is its magnitude at the photosphere. With this normalization E is relatively small for modes trapped in the outer parts of the star, whereas E can be very large for modes trapped in the deep interior. E is plotted in Fig. 5 as a function of frequency for modes of degree l = 0 and 1 in a red-giant model. The radial modes are purely acoustic and have a small inertia that generally decreases with increasing frequency. The l = 1 modes are generally predominantly g modes, trapped in the deep interior below the convective envelope, and hence have large inertia. However, there are acoustic resonances where the inertia decreases to values not much higher than the radial-mode inertia at the corresponding frequency. Here the modes have their largest amplitude in the envelope where they have an acoustic character. The location of these resonances, and the radialmode frequencies, approximately satisfy the asymptotic relation in Eq. (1). Given that the processes exciting and damping the modes predominantly take place in the near-surface layers where the convective velocities are large, it is intuitively clear that modes with low inertia are easier to excite and hence are expected to be more visible in the power spectra of the observations (see Dupret et al. 2009; Grosjean et al. 2014). This is the origin of group of l = 1 peaks in Fig. 4; these are modes with inertia somewhat higher than the radial-mode inertia, but still excited to observable amplitudes. Given the asymptotic behaviour of g modes (Eq. 5) the properties of the mixed modes are most naturally analysed in terms of period spacings which, as shown in the lower panel of Fig. 5, are also affected by the acoustic resonances. For the modes that are predominantly of g-mode character the spacing ∆Π = Πnl − Πn−1 l is close to the asymptotic value (cf. Eq. 6) shown by the horizontal line. However, at the acoustic resonances the period spacing takes on a characteristic ‘V’-shape as a function of frequency. It was indeed this behaviour that led Beck et al. (2011) to the first identification of mixed modes in red-giant observations. From the observed frequencies of the mixed modes one can determine the period spacings around the acoustic resonances and, most reliably from a fit to the detailed asymptotic behaviour of the frequencies (Mosser et al. 2012a), determine the asymptotic period spacing ∆Πl (Eq. 6). It was shown by Bedding et al. (2011) and Mosser et al. (2011) that the period spacing provides a clear separation between otherwise very similar stars ascending the red-giant branch with just shell hydrogen fusion and stars in the core helium-fusion phase: the period spacing was substantially smaller in the former case than in the latter. This can be understood from Eq. (6), according to which the asymptotic period spacing is determined by an integral over the buoyancy frequency (Eq. 4). When the star moves to the core helium-burning phase the core expands, and this de-

138 J¿rgen 14 Jørgen Christensen-Dalsgaard Christensen-Dalsgaard

creases the local gravitational acceleration and hence the buoyancy frequency. A further reduction of the integral results from the convective core caused by helium fusion, since the integration in Eq. (6) excludes the convective core. Both effects decrease the magnitude of the integral and hence increase the asymptotic period spacing. Combining the period spacing with the large frequency separation ∆ν, which varies strongly with stellar radius, allows detailed diagnostics of stellar evolution, as discussed by Mosser et al. (2014). Further information about stellar interior structure, such as the properties of the convective core in helium-burning stars, may in principle be obtained from detailed fitting of the individual oscillation frequencies. Although such fits have been attempted in a few cases (e.g., Di Mauro et al. 2011; Jiang et al. 2011) much work is still required to explore these possibilities.

Fig. 6. Asteroseismically inferred core rotation periods in red giants (crosses) and core helium-burning stars (triangles and squares), plotted against stellar radius in solar units. The colour code indicates stellar mass. The right-hand boxes show typical errors, depending on the period. From Mosser et al. (2012b).

From a determination of the rotational splitting (cf. Eq. 7) in Kepler observations of a red giant Beck et al. (2012) concluded that the core of the star rotated faster than the surface by around a factor 10. This was based on determining the splitting for mixed modes, including modes with a substantial g-mode component where the splitting was dominated by the core. Fast core rotation was also found through asteroseismic inversion in less evolved stars, in the sub-giant phase and near the base of the red-giant branch, by Deheuvels et al. (2012, 2014) and Di Mauro et al. (2016). As shown in Fig. 6 Mosser et al. (2012b) determined the core rotation of a large number of stars on the red-giant branch and in the core helium-burning phase. Combined with the nearly uniform rotation inferred in the solar interior (cf. Howe 2009) and a recent asteroseismic determination of



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overall rotation in old field stars (van Saders et al. 2016) these results provide indications of the evolution of stellar interior rotation with age, a process that may also have important consequences for stellar structure evolution as a result of related instabilities and mixing processes. In fact, the rapid core rotation in red giants should come as no surprise. As discussed above the evolution on the red-giant branch involves a strong contraction of the core. If there were local conservation of angular momentum this would result a spin-up of the core to far higher rotation rates on the red-giant branch than in fact inferred from the asteroseismic determinations. Thus some angular-momentum transport mechanism must be operating in the stellar interior, leading to a reduction of the angular momentum and hence the rotation rate in the core. The normally considered mechanisms for angular-momentum transport in stellar interiors are somewhat uncertain. However, it has been found that they are insufficient, by one to two orders of magnitude, to account for the observed rotation in red-giant stars (e.g., Eggenberger et al. 2012; Marques et al. 2013; Cantiello et al. 2014). Thus additional transport mechanisms are required. It has recently been suggested that internal gravity waves (Fuller et al. 2014) or mixed modes (Belkacem et al. 2015) may play an important role. Even so, it is clear that we are still not close to understanding these important aspects of stellar evolution. An early mystery in the study of solar-like oscillations in red giants was the suppression of the l = 1 modes in some stars with otherwise apparently normal oscillation spectra (Mosser et al. 2012; Garc´ıa et al. 2014). Stello et al. (2016) demonstrated that these stars had a mass, slightly higher than the Sun, such that they would have had convective cores on the main sequence. On this basis Fuller et al. (2015) proposed that the l = 1 modes were suppressed by scattering by a fossil magnetic field in the core of the star, generated through dynamo action when the star was on the main sequence. Although this model needs to be tested through more detailed calculations, it represents yet another instance of the power of asteroseismology to probe the evolution of these evolved stars.

5

Future prospects

The CoRoT mission ended operations in December 2013 after 7 years and the Kepler nominal mission ended in the spring of 2013 with the breakdown of two of its four moment wheels. This, however, is far from the end of space asteroseismology. Operations of Kepler are continuing in the K2 mission, where successive fields along the Ecliptic are observed for three-months periods (Howell et al. 2014). With this orientation stable pointing of the satellite can be achieved with just the remaining two moment wheels. Early results from this mode of operation are promising, both for asteroseismology of stars near the main sequence (Chaplin et al. 2015) and for red-giant observations as applied to Galactic archaeology (Stello et al. 2015). This will be followed by the TESS mission (Transiting Exoplanet Survey Satellite, Ricker et al. 2014) scheduled for launch by NASA in 2017. Over a two-year period TESS will make a survey of nearly the entire

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sky, to search for exoplanets and carry out asteroseismology. Most fields will be observed for around 28 days, but for two fields at the ecliptic poles the observations will be continuous for a year each. A major advantage of TESS compared with Kepler is the focus on relatively nearby stars which greatly enhances the possibilities for supplementary ground- and space-based observations. This advantage is shared by ESA’s PLATO mission (Rauer et al. 2014), selected for launch in 2024. PLATO will observe several fields much larger than Kepler’s, in two cases for two or three years, and with emphasis on the characterization of Earth-like planets in the habitable zone. Asteroseismology will be possible for a large fraction of the exoplanet candidates detected and, obviously, for a large number of other stars. Despite the success of space-based asteroseismology, ground-based observations should not be ignored. In fact, solar observations have demonstrated that the intrinsic stellar background ‘noise’ from near-surface convection and activity is a much more serious concern in photometric asteroseismic observations than in radial-velocity observations. This is the motivation for the creation of the Danish-led SONG (Stellar Observations Network Group) network of 1 m telescopes dedicated to asteroseismology and exoplanet studies (Grundahl et al. 2014). The first telescope in the network, the Hertzsprung SONG Telescope, is in operation on Tenerife, and the second telescope is in commissioning in Delingha in western China. Funding for further telescopes will be sought from Danish sources and through international collaboration. Thus, referring again to Eddington, there are excellent prospects to obtain certain, or at least much improved, knowledge of that which is hidden behind the substantial barriers of the stellar surface.

Acknowledgment I am grateful to the organizers for the invitation to participate in this very interesting conference and the opportunity to visit Azerbajan. I thank Rasmus Handberg for help with producing Fig 2 and 4, Victor Silva Aguirre for providing Fig. 3 and Benoˆıt Mosser for providing Fig. 6. Funding for the Stellar Astrophysics Centre is provided by The Danish National Research Foundation (Grant DNRF106). The research is supported by the ASTERISK project (ASTERoseismic Investigations with SONG and Kepler) funded by the European Research Council (Grant agreement no.: 267864).



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Cosmic Rays and other Space Weather ­Phenomena Influenced on Satellites Operation, Technologies, ­Biosphere and People Health Lev Dorman (Israel Cosmic Ray & Space Weather Centre and Israeli-Italian Emilio Segre’ Observatory, affiliated to Tel Aviv University, Golan Research Institute, and Israel Space Agency, ISRAEL). Elchin Babayev (Shamakhy Astrophysical Observatory, ANAS, AZERBAIJAN)

1 The matter of the problem This report is an example how fundamental research in Cosmic Ray (CR) Astrophysics and Geophysics can be applied to very important modern practical problem: monitoring by cosmic rays space weather and prediction by using ­on-line cosmic ray data space phenomena dangerous for satellites electronics and astronauts health in the space, for crew and passengers health on commercial jets in atmosphere, and in some rare cases for technology and people on the ground, role of CR and other space weather factors in climate change and influence on agriculture production. Satellite anomalies (or malfunctions), including total distortion of electronics and loose of some satellites cost for Insurance Companies billions dollars per year. During especially active periods the probability of satellite anomalies and their loosing increased very much. Now, when a great number of civil and military satellites are continuously worked for our practice life, the problem of satellite anomalies became very important. Many years ago about half of satellite anomalies were caused by technical reasons (for example, for Russian satellites Kosmos), but with time with increasing of production quality, this part became smaller and smaller. The other part, which now is dominated, caused by different space weather effects (energetic particles of CR and generated/trapped in the magnetosphere, and so on). Here we consider only satellite anomalies not caused by technical reasons: the total number of such anomalies about 6000 events. No relation was found between low and high altitude satellite anomalies. Daily numbers of satellite anomalies, averaged by a superposed epoch method around sudden storm commencements and solar proton event onsets for high (1500 km) altitude orbits revealed a big difference in a behavior. Satellites were divided on several groups according to the orbital characteristics (altitude and inclination). The relation of satellite anomalies to the environmental parameters was found to be different for various orbits that should be taken into account under developing of the anomaly frequency models and forecasting. We consider also influence

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of CR on frequency of gene mutations and evolution of biosphere (we outlined that if it will be no CR, the Earth’s civilization will be start only after milliards years later, what will be too late), CR role in thunderstorm phenomena and discharges, space weather effects on space technologies and radiation effects from solar and galactic CR in dependence of cutoff rigidities and altitude, influence magnetic storms accompanied by CR Forbush-effects on people health (increasing frequency of infarct myocardial and brain strokes), increasing frequency of car accidents (possible through people factor-increased time of reaction), increasing frequency of malfunctions in railway operation (possible, through induction currents), catastrophes in long-distance electric power lines and transformators, and in other ground technologies. Are very important also rarely space effects of asteroids impacts and nearby Supernova explosions.

2 Satellite anomalies For investigation of the coupling of Space Weather with satellites anomalies was ­organized a special “Anomaly” team (L.I. Dorman, A.V. Belov, N. Iucci, G. Villoresi, E. Eroshenko, V. Yanke, N. Ptizina, and others , see in Belov et al., 2004; Dorman et al., 2005; Iucci et al., 2006). Theaim of this research is to review methods of safeguarding satellites in the Earth’s magnetosphere from the negative effects of the space environment. Anomaly data from the USSR and Russia satellites “Kosmos” series in the period 1971–1995 to combine in one database, together with similar information on other spacecrafts. This database contains, beyond the anomaly information, various characteristics of the space weather: geomagnetic activity indices (Ap, AE and Dst), fluxes and fluencies of electrons and protons at different energies, high energy cosmic ray variations and other solar, interplanetary and solar wind data. A comparative analysis of the distribution of each of these parameters relative to satellite anomalies was carried out for the total number of anomalies (about 6000 events), and separately for high (5000 events) and low (about 800 events) altitude orbit satellites. No relation was found between low and high altitude satellite anomalies. Daily numbers of satellite anomalies, averaged by a superposed epoch method around sudden storm commencements and proton event onsets for high (>1500 km) and low ( 10 MeV and >60 MeV) fluxes. Lower panel – geomagnetic activity: Kp- and Dstindices.Vertical arrows on the upper panel correspond to the malfunction moments.

magnetic storm. In upper part the variations of groundlevel cosmic rays. These proton events were groundlevel enhancements. Arrows are moments of satellite malfunctions. We have 3 clusters of malfunctions and they coincide with maximal proton fluxes. In Fig. 4 we see other example of a lot of satellite malfunctions in April – May 1991. Here the majority of the satellite malfunctions coincides with period of magnetic storm and enhancement of high-energy electron flux.The malfunctions are absent entirely in the high altitude - high inclination group, which played the main role in preceding example (Fig. 3). Only a few malfunctions were in GEO group and huge majority – in “blue” group (low altitude - high inclination). In Fig. 5 are shown seasonal variations of malfunctions frequency (per day and per one satellite) in comparison with Ap index of geomagnetic activity. The dependence of malfunction frequency from the flux of solar protons is shown in Fig. 6 for different groups of satellites. On the Fig. 7 is shown average values of fluencies for energetic protons (> 10 MeV) and electrons (> 2 MeV) in days of satellite malfunctions for different groups of satellites. Let us consider important results for the green group (high altitude – low inclinations, mostly GEO type), which can be used for forecasting of satellite malfunctions (Figs. 8 – 10). Let us suppose that the Probabilities of correct forecasting of GEO type satellite malfunction on the basis of geomagnetic activity, fluence of energetic electrons, and ­velocity of solar wind are correspondingly PAp, PFe, and PSW. In this case the total



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Fig. 4.  Space weather in April-May 1991 and satellite malfunctions. Upper panel – ­cosmic ray activity near the Earth: variations of 10 GV cosmic ray density; electron (> 2 MeV) fluxes – hourly data.Vertical arrows correspond to the malfunction moments. Lower row – all malfunctions.Lower panel – geomagnetic activity: Kp- and Dst-indices.

Fig. 5.  Satellite anomalies frequency and Ap-index averaged over the period 1975-1994. The curve with points is the 27-day running mean values; the grey band corresponds to­ the 95 % confidence interval. The sinusoidal curve is a semiannual wave with maxima in equinoxes best fitting the frequency data.

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Fig. 6.  The dependence of malfunction frequency (per day and per one satellite) from the flux of solar protons with energy > 10 MeV in the 0 and 1-st days of enhancement for different groups of satellites.Other kind of special period. Here 0-day is proton event onset day. The biggest effect is in 0- and 1-days and in red group (high altitude – high inclinations). Much smaller effect is in green group (high altitude – low inclination), and practically nothing effect on low altitudes.

Fig. 7.  Average values of fluencies for energetic protons (> 10 MeV) and electrons (> 2 MeV) in days of satellite malfunctions for different groups of satellites. It can be seen that red group of satellites (high altitude – high inclinations) is influenced mostly by energetic protons, the blue group (low altitude – high inclinations) – mostly by energetic electrons, and green group (high altitude – low inclinations) – little by energetic protons, but mostly by energetic electrons. These results are in good agreement with shown in Fig. 6 for energetic protons.



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Fig. 8.  Ap-index of magnetic activity as function of time relative to day of malfunction event (0-day). It can be seen that Ap-index starts to sufficiently increase not at the 0-day, but several days before. This phenomenon can be used for forecasting.

Fig. 9.  The same as in Fig. 8 but for the fluence of electrons Fewith energy > 2 MeV. It can be also seen that the fluence of energetic electrons (they often called as “killing” electrons) starts to sufficiently increase not at the 0-day, but several days before. It means that this phenomenon also can be used for forecasting.

probability P of correct forecasting satellite malfunction will be P = 1-(1-PAp)* (1-PFe)*(1-PSW). If, for example, PAp= 0.6,PFe= 0.6, and PSW= 0.6, we obtain P = 0.936.

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Fig. 10.  The same as in Fig. 8, but for the velocity of solar wind (SW). It can be seen that velocity of solar wind starts several days before day of satellite malfunctions to sufficiently increase from 460 km/s up to 510 km/s. It means that this phenomenon also can be used for forecasting.

3 Forecastig of Great Radiation Hazards from Solar Energetic Particles For forecasting satellite malfunctions from solar energetic protons was developed special method,which consists from 5 steps: 1. Automatically determination of the SEP (Solar Energetic Particles) event starting by one minute neutron monitor data; 2. Determination of energy spectrum out of magnetosphere by the method of coupling functions; 3. Determination of time of ejection, source function and parameters of propagation by solving the inverse problem; 4. Forecasting of expected SEP fluxes, comparison with observations, and correction of the inverse problem solution; 5. Combined forecasting on the basis of neutron monitor and satellite data. This method is described in other report of the Baku Conference (Dorman et al., 2016).

4 Effects of great magnetic storms (accompanied by CR Forbush effects) on the frequency of infarct myocardial, brain strokes, care accidents, and technology There are numerous indications that natural, solar variability-driven time variations of the Earth’s magnetic field can be hazardous in relation to health and



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safety. There are two lines of their possible influence: effects on physical systems and on human beings as biological systems. High frequency radio communications are disrupted, electric power distribution grids are blacked out when geomagnetically induced currents cause safety devices to trip, and atmospheric warming causes increased drag on satellites. An example of a major disruption on high technology operations by magnetic variations of large extent occurred in March 1989, when an intense geomagnetic storm upset communication systems, orbiting satellites, and electric power systems around the world. Several large power transformers also failed in Canada and United States, and there were hundreds of misoperations of relays and protective systems (Kappenman and Albertson, 1990; Hruska and Shea, 1993). Some evidence has been also reported on the association between geomagnetic disturbances and increases in work and traffic accidents (Ptitsyna, Villoresi, Dorman, and Tyasto, 1998 and refs. therein). These studies were based on the hypothesis that a significant part of traffic accidents could be caused by the incorrect or retarded reaction of drivers to the traffic circumstances, the capability to react correctly being influenced by the environmental magnetic and electric fields. The analysis of accidents caused by human factors in the biggest atomic station of former USSR, “Kurskaya”, during 1985-1989, showed that ~70% of these accidents happened in the days of geomagnetic storms. In Reiter (1954, 1955) it was found that work and traffic accidents in Germany were associated with disturbances in atmospheric electricity and in geomagnetic field (defined by sudden perturbations in radio wave propagation). On the basis of 25 reaction tests, it was found also that the human reaction time, during these disturbed periods, was considerably retarded. Retarded reaction in connection with naturally occurred magnetic field disturbances was observed also by Koenig and Ankermueller (1982). Moreover, a number of investigations showed significant correlation between the incidence of clinically important pathologies and strong geomagnetic field variations. The most significant results have been those on cardiovascular and nervous system diseases, showing some association with geomagnetic activity; a number of laboratory results on correlation between human blood system and solar and geomagnetic activity supported these findings (Ptitsyna et al. 1998 and refs. therein). Recently, the monitoring of cardiovascular function among cosmonauts of “MIR” space station revealed a reduction of heart rate variability during geomagnetic storms (Baevsky et al. 1996); the reduction in heart rate variability has been associated with 550% increase in the risk of coronary artery diseases (Baevsky et al. 1997 and refs. therein). On the basis of great statistical data on several millions medical events in Moscow and in St. Petersburg were found an sufficient influence of geomagnetic storms accompanied with CR Forbush-decreases on the frequency of myocardial infarcts, brain strokes and car accident road traumas (Villoresi et al., 1994, 1995; Dorman et al., 1999). Earlier we found that among all characteristics of geomagnetic activity, Forbush decreases are better related to hazardous effects of solar variability-driven disturbances of the geomagnetic field (Ptitsyna et al., 1998). Figure 11 shows the correlation between cardiovascular diseases, car ­accidents and different characteristics of geomagnetic activity (planetary index AA, major

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Fig. 11.  Left: average daily numbers of infarctions myocardia (a), brain strokes (b), and heavy road accidents (c). Right: infarctions myocardia (left scale) and heavy road accidents (right scale) during CR Forbush decreases with one day decreasing (top) and two days decreasing (bottom).

geomagnetic storms MGS, sudden commencement of geomagnetic storm SSC, occurrence of downward vertical component of the interplanetary magnetic field Bz and also decreasing phase of Forbush decreases (FD)). The most remarkable and statistically significant effects have been observed during days of geomagnetic perturbations defined by the days of the declining phase of Forbush decreases in CR intensity. During these days the average numbers of road accidents, infarctions, and brain strokes increase by (17.43.1)%, (10.51.2)% and (7.01.7)%, respectively.

5 Possible influence of cosmic rays on the Earth’s ­biosphere evolution CR particles (especially muons and neutrons) can go much deeper inside biosphere objects than products of ground radioactivity. Moreover, CR can go deep into water of rivers, sees, and oceans. It means that CR can play important role in the increasing of genes mutation rate and give sufficient ­



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­ cceleration of the biosphere evolution. It is i­mportant because on the Earth we a have good ­conditions for evolution only for the several billion years. Moreover, it was shown that CR play an important role in thunderstorm phenomena and discharges (see review in Dorman, M2004), what is very important for the early studies of biosphere evolution.

6 Possible influence on the Earth’s climate and biosphere ­collisions of the Solar system with galactic molecular-dust clouds As it will be shown in report tomorrow on space factors influenced on c­ limate, collisions of the Solar system with galactic molecular-dust clouds lead to decrease annual averaged planetary temperature on several degrees what leads to deep ice periods of many thousand years. We cannot avoid this catastrophic phenomenon but by CR will be possible to predict it and the Earth’s Civilization will have enough time to preparing life in new conditions.

7 The Influence of Asteroids on the Earth’s Biosphere It is well known that asteroids had in the past, struck the Earth with sufficient force to make major changes in biosphere (the famous dinosaur-killing mass extinction at the end of the Cretaceous, which began the Tertiary era, has been convincingly identified with such an asteroid impact (Alvarez et al., 1980; Sharpton et al.,1993). Recently in Mexico was found corresponding crater, possibly, from this asteroid. Asteroid had dimension about 10-15 km. Fortunately today, and in near future, with modern methods of Astronomy, the trajectory of dangerous asteroids can be determined exactly and together with modern rocket power, could possibly be deflected.

8 The Influence of Nearby Supernova on the Earth’s ­Climate and Biosphere Evolution It is well known that the Sun is a star of the second generation, it was born together with solar system from Supernova explosion about 5x109 years ago. From the energetic balance of CR in the Galaxy it follows that the full power for CR production is about 331033 W. Now it is commonly accepted that the Supernova explosions are the main source of galactic CR. At each explosion the average energy transferred to CR is about 1043 – 1044 J. From this quantity we can determine the expected frequency of Supernova explosions in our Galaxy and in vicinity of the Sun, and estimate the probability of Supernova explosions at different distances from the Sun.In each case it can be calculated expected UV radiation flux (destroyer of our ozone layer and hence a significant player in our Earth’s climate), and the expected CR flux. It has been estimated in ­Dorman et al. (1993a,b,c) and Dorman (2008) that if such an event does take

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place, the level of CR radiation reaching our Earth could be extremely dangerous for our civilization and biosphere. According to Ellis and Schramm (1995), in case of nearby Supernova, UV radiation would destroy the Earth’s ozone layer over a period of about 300 years. The recent observations of Geminga, PSR J0437-4715, and SN 1987A strengthen the case for one or more supernova extinctions having taken place during the Phanerozoic era. In this case a nearby supernova explosion would have depleted the ozone layer, exposing both marine and terrestrial organisms to potentially lethal solar ultraviolet radiation. In particular, photosynthesizing organisms including phytoplankton and reef communities would most likely have been badly affected. A big, up to lethal radiation dose for people from additional CR during several hundred years is expected.

9 What we need to do for automatically Forecasting of bed Space Weather for decreasing level of hazardous for people and technology 1. Necessary to organize exist network of CR neutron monitors and satellite on-line one minute observations in real time for automatically prediction of hazardous radiation impacts from solar CR on people and technology. 2. Necessary to organize exist network of CR stations (neutron monitors and muon telescopes one hour data in real time) for automatically prediction of hazardous magnetic storms accompanied by CR Forbush effects. 3. It is necessary to organize continue observations of CR on several station with energies about 1013-1014 eV to observe and predict collisions the Solar system with dust-molecular clouds. (this can be made for about hundred years before collisions). These observations will give important information also on CR generation and propagation from nearby Supernova, what is important for prediction of expected hazardous of nearby Supernova and prepare according protection infrastructure, people, and biosphere. 4. It is very important to organize and develop special service for observations and forecasting dangerous asteroids and develop methods to prevent catastrophic hazardous. 5. We hope that in near future will be organized also deep research of nearby stars for determining potential dangerous nearby Supernova explosions.

Acknowledgements L.D. acknowledged Ministry of Science of State Israel, Tel Aviv University, Israel Space Agency, and Golan Research Institute for continue support, and Azerbaijan Science Foundation for kind invitation to take part in Baku Conference and productive collaboration.



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Bibliography Baevsky, R.M. et al. 1996, Proc. MEFA Int. Fair of Medical Technology & Pharmacy (Brno, Chec Republic). Baevsky R.M., V.M. Petrov, G. Cornelissen, F. Halberg, K. Orth-Gomur, T. Ekerstedt, K. Otsuka, T. Breus, J. Siegelova, J. Dusek, and B. Fiser, 1997. “Meta-analyzed heart rate variability, exposure to geomagnetic storms, and the risk of ischemic heart disease”, Scriptamedica, 70, No. 4-5, 201-206. BelovA.V., J. Villoresi, L.I. Dorman, E.A. Eroshenko, A.E. Levitin, M. Parisi, N.G. Ptitsyna, M.I. Tyasto, V.A. Chizhenkov, N.Iucci, and V.G. Yanke, 2004. “Effect of the Space on Operation of Satellites”, Geomagn.andAeronomy, 44, No. 4, 461–468. Dorman L.I., M2006. Cosmic Ray Interactions, Propagation, and Acceleration in Space, Springer, Netherlands. Dorman L.I., 2008. “Forecasting of radiation hazard and the inverse problem for SEP propagation and generation in the frame of anisotropic diffusion and in kinetic approach”, Proc. 30-th Intern. Cosmic Ray Conf., Merida, Mexico, 1, 175-178. Dorman L.I, Iucci N., Villoresi G., 1993a. “The use of cosmic rays for continuos monitoring and prediction of some dangerous phenomena for the Earth’s civilization”.Astrophysics and Space Science, 208, 55-68. Dorman L.I., Iucci N. and Villoresi G., 1993b. “Possible monitoring of space processes by cosmic rays”. Proc. 23-th Intern. Cosmic Ray Conf., Calgary, 4, 695-698. Dorman L.I., Iucci N. and Villoresi G., 1993c. “Space dangerous phenomena and their possible prediction by cosmic rays”.Proc. 23-th Intern. Cosmic Ray Conf., Calgary, 4, 699-702. Dorman L.I., N. Iucci, N.G. Ptitsyna, G. Villoresi, 1999. “Cosmic ray Forbushdecrease as indicators of space dangerous phenomenon and possible use of cosmic ray data for their prediction”, Proc. 26-th Intern. Cosmic Ray Conference, Salt Lake City, 6, 476-479.. DormanL.I., A.V. Belov, E.A. Eroshenko, L.I. Gromova, N. Iucci, A.E. ­Levitin, M. Parisi, N.G. Ptitsyna, L.A. Pustil’nik, M.I. Tyasto,E.S. Vernova, G. Villoresi, V.G. Yanke, and I.G. Zukerman, 2005. “Different space weather effects in anomalies of the high andlow orbital satellites”, Advances in Space Research,36, 2530–2536. Hruska J. and Shea M.A., 1993, Adv. Space Res. 13, 451. Iucci N., L.I. Dorman, A.E. Levitin, A.V. Belov, E.A. Eroshenko, N.G. P ­ titsyna, G. Villoresi, G.V. Chizhenkov, L.I. Gromova, M. Parisi, M.I. Tyasto, and V.G. Yanke, 2006. “Spacecraft operational anomalies and space weather impact hazards”, Adv. Space Res.,37, No. 1, 184-190. Kappenman J.G. and V.D. Albertson, 1990.“Bracing for the geomagnetic storms”, IEEE Spectrum, 27, No. 3, 27-33. Koenig, H., &Ankermueller, F. 1982, Naturwissenscahften,17, 47.

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Ptitsyna N.G., G. Villoresi, L.I. Dorman, N. Iucci, and M.I. Tyasto. 1998. ­“Natural and man-made low-frequency magnetic fields as a potential health hazard”, UFN (Uspekhi Physicheskikh Nauk), 168, No 7, 767-791. Reiter R., 1954. “The importance of the atmospheric long radiation disturbances for the statistical biometeorology”, Archiv fur Physikalische Therapie, 6, No. 3, 210-216. Reiter R., 1955.“Bio-meteorologie auf physikalisher Basis”, Phys. Blaetter, 11, 453-464. Villoresi G., Breus T.K., Dorman L.I., Iucci N., Rapoport S.I., 1994. “The influence of geophysical and social effects on the incidences of clinically important pathologies (Moscow 1979-1981)”.Physica Medica, 10, No 3, 79-91. Villoresi G., Dorman L.I., Ptitsyna N.G., Iucci N., Tyasto M.I., 1995. “Forbushdecreases as indicators of health-hazardous geomagnetic storms”.Proc. 24-th Intern. Cosmic Ray Conf., Rome, 4, 1106-1109.

Cosmic Rays and other Space Phenomena Dangerous for the Earth’s Civilization: Beginning Steps for Founding Cosmic Ray Warning System Lev Dorman1,2, Elchin Babayev3, Uri Dai1, Fatima Keshtova4, Lev Pustil’nik1, Abraham Sternlieb1, and Igor Zukerman1 1

Israel Cosmic Ray & Space Weather Centre and Emilio Ségre Observatory (Mt. Hermon) affiliated to Tel Aviv University, Golan Research Institute, and Israel Space Agency, ISRAEL 2 Cosmic Ray Department of IZMIRAN, Moscow, RUSSIA 3 Shamakhy Astrophysical Observatory, ANAS, AZERBAIJAN 4 Universitäten Oldenburg, GERMANY

1 The matter of the problem It is well known that in periods of great SEP (Solar Energetic Particle) events, the fluxes can be so big that memory of computers and other electronics in space may be destroyed, satellites and spaceships became dead (each year Insurance Companies paid billions dollars for these failures). Let us outlined that if it will be event as February 23, 1956 (see detail description in Dorman, M1957), will be destroyed about all satellites in few hours, the price of this will be more than 10-20 billion dollars, will be total destroying satellite communications and a rose a lot of other problems. In periods of great SEP events is necessary to switch off some part of electronics for short time to protect computer memories. These periods are also dangerous for astronauts on space-ships, and International Space Station (ISS), passengers and crew in commercial jets (especially during S5-S7 radiation storms). The problem is how to forecast exactly these dangerous phenomena. We show that exact forecast can be made by using high-energy particles (about 2-10 GeV/nucleon and higher) which transportation from the Sun is characterized by much bigger diffusion coefficient than for small and middle energy particles. Therefore high energy particles came from the Sun much more early (8-20 minutes after acceleration and escaping into solar wind) and later - main part of smaller energy particles caused dangerous situation for electronics and people health (about 60 and more minutes later). As the first step, we use automatically working program “SEP-Start”, supposed, developed and checked in the Emilio Segre’ Observatory of Israel Cosmic Ray and Space Weather Center (Mt. Hermon, 2050 m above sea level, cut-off

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rigidity 10.8 GV). Using of this program on many CR stations and on satellites allowed determining automatically the beginning of SEP event. The second step is “SEP-Coupling” – using developed in Dorman (M1957, M1958, M2004) method of coupling functions for transformation obtained at different altitudes and cutoff rigidities data on CR intensity to the space and calculation CR energy spectrum and angle distribution out of the Earth’s atmosphere and magnetosphere, directly in the interplanetary space near the Earth. Before we made these complicated operations step by step on the basis of historical SEP events data during long time and determined flare energetic particle spectrum in the interplanetary space and its change with time by method of coupling functions (in scientific literature called as Dorman functions). Now we prepared algorithms and try to create program which will be made these calculations automatically after each new minute of CR data very quickly for time not more than few seconds (Dorman et al., 206a). The Third Step “SEP-Inverse Problem” is based on theoretically solved by Dorman et al. (2006b) about 10 years ago inverse problem and determine time of ejection energetic particles, source function and transport parameters in dependence from particle energy and distance from the Sun. Several years ago we made corresponding calculations very long time, so obtained results cannot be practically used for forecasting. Now we prepared all algorithms and try to create program which will be made these calculations automatically after each new minute of CR data very quickly for time not more than few seconds. The Fourth Step “SEP-Forecasting” based on the theoretically solved direct problem and parameters founded in the Third Step and known coupling functions, we calculate time evolution of solar CR spectrum with time and expected total fluence (radiation hazards) in the interplanetary space for spaceships at different distances from the Sun in dependence of shielding, in the Earth’s magnetosphere for satellites with different orbits, in the Earth’s atmosphere for airplanes on different airlines in dependence of altitude and cutoff rigidities, and for ground at different air pressure and cutoff rigidities. Again, we checked all these mathematical procedures basing on real data of historical SEP events and it need so long time that it was not possible to use these results for forecasting of expected radiation hazards. Now we for this step also prepared all algorithms and try to create program which will be made these calculations automatically after each new minute of CR data very quickly for time not more than few seconds. To determine the quality of obtained results, after 5-10 minutes from beginning starts to work the final, Fives Step. The Fives Step “Checking of Forecasting Quality and Alerts” starts to work at 5-10 minutes after the event beginning. In this Step we compare expected (calculated in the Fourth Step by using coupling functions CR intensity for neutron monitors on different stations and on satellites) with observed. If the difference will be small enough (smaller than 10-20%) and the radiation hazards expected to be dangerous for spaceships in the interplanetary space, for some satellites in the Earth’s magnetosphere, for airplanes on some airlines or for some objects on the ground, will be send corresponding Alerts with detail



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information on the expected radiation hazards calculated in the Fourth Step. After few minutes a new, more exact Alerts will be sent. More and more exact new Alerts will be repeated each few minutes during the dangerous event. Let us outline that Step 1 finished to work after determining the beginning of SEP event, but Steps 2 – 5 continued to work for each new minute. They will be finished to work only when the difference between consequences Alerts became much smaller than statistical errors. In our report “Cosmic Rays and other Space Weather Effects Influenced on Satellites Operation, Technologies, Biosphere and People Health” by Lev Dorman and Elchin Babaev it was shown that very important element of Space Weather, influenced on satellites operation, technologies, and people health are not only great SEP events, but also strong magnetic storms, accompanied usually by CR Forbush effects. The founded in near future “Cosmic Ray Warning System” will be possible to forecast automatically also this phenomenon, which is dangerous for the Earth’s Civilization. In other report “Cosmic Rays and other Space Phenomena Influenced on the Earth’s Climate” by Lev Dorman on this Conference it was shown that very big changes in climate, dangerous for the Earth’s Civilization, are caused by interactions of Solar system with molecular-dust clouds (caused the Great Ice Periods during many thousand years; the last finished about twenty thousand years ago and now we are near maximum of planetary temperature and the Earth start to move during several thousand years in direction to the next Great Ice Period). For this forecasting we need to add to the “Cosmic Ray Warning System” in near future few special CR Laboratories for continue measuring CR with much higher energies (at least 1013 – 1015 eV). In this case will be possible continue monitoring of high energy CR distribution out of the Heliosphere for estimation distance to the dust-molecular cloud, its dimension, and direction of moving for prediction possible collisions with Solar system and expected influence on the Earth’s climate. We plane the first of this type CR Laboratory to organize in Azerbaijan in the frame of Azerbaijan – Israel collaboration. Very dangerous for the Earth’s Civilization is also nearby Supernova explosions with great influence on biosphere, climate, technology, and people health. We show that by CR data in the frame of “Cosmic Ray Warning System” is possible to forecast for many years before starting this very dangerous phenomenon, so the Earth’s Civilization will have enough time for preparing to the new type of life. For this forecasting we need in near future the same special CR Laboratories for continue measuring CR with energies 1013 – 1014 eV for monitoring and forecasting space weather out of Heliosphere (as we mentioned above, the first is planned to be in Azerbaijan).

2 Block Scheme of Great Radiation Hazards Forecasting In Figs. 2.1-2.3 are shown three steps of the block scheme of great radiation hazards from great Solar Energetic Particles (SEP) forecasting on the basis

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of online one-minute data of neutron monitor network data and satellite oneminute CR data.

Fig. 2.1.  The first step of block scheme of radiation hazards from great SEP event forecasting.

Fig. 2.2.  The second step of block scheme of radiation hazards from great SEP event forecasting.



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Fig. 2.3.  The thirds step of block scheme of radiation hazards from great SEP event forecasting.

3 What we need to prepare before start the automatically on-line forecasting procedure? 3.1. Data what we need to use for automatically on-line forecasting procedure. As we outlined in the Section 2, we will use one-minute CR data, available from Internet (first of all – NMDB data): high-latitude stations with RC < 1 GV (Oulu, Apatite, South Pole, and some other), middle-latitude stations with RC = 2–4 GV (Moscow, Kiel, Novosibirsk, Yakutsk, Lomnitsky Stit, Yungfraujokh, and others), stations with RC = 6–7 GV (Rome, Athens, Tjan Shan, and others), and low-latitude stations with RC = 1016 GV (Mt. Hermon, Mt. Norikura, ­Mexico, Haleacala, and others). For very small energy solar CR we will use satellite one-minute data, also available from Internet (e.g., GOES data). For automatically worked forecasting system we need to prepare also following: 3.2. For each used CR stations we need to know exactly values of cutoff rigidities Rc and how they change with secular variations of the main geomagnetic field and with magnetic activity. 3.3. For each used CR stations we need to know exact values of atmospheric pressure h (in units 1000 g/cm2 ) at the point of CR detector. 3.4. For each used CR stations we need to calculate coupling functions according to following formulas. For the polar normalized coupling function for any secondary component of type i (i = n – for total neutron component, i = m – for

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neutron multiplicities m = 1,2,3,..., i = h¹ – for hard muons, i = s¹ – for soft muons, i = ep – for electron-photon component, and so on) can be approximated by the special function

(

− k ( h ) +1 Woi ( R, h ) = ai ( h ) ki ( h ) R ( i ) exp −ai ( h ) R − ki ( h )



)

(3.1)

and for the normalized coupling functions at any point on Earth with cut off rigidity Rc will be 0  Wi ( Rc , R, h ) =  −( ki ( h ) +1) 1 − ai ( h ) Rc− ki ( h ) ai ( h ) ki ( h ) R

(



)

−1

if R < Rc

(

exp −ai ( h ) R

− ki ( h )

) if

R ≥ Rc .

(3.2) 

The dependence of an and kn for total neutron component and am and km for neutron multiplicities m = 1, 2, 3, ..... on the CR station with pressure h (in atm = 1000 g/cm2) and solar activity level characterized by the logarithm of CR intensity per one hour (we used here monthly averaged of Climax NM ln(NCl), available starting from 1952) can be approximated by the functions (Dorman, M2004):

(

)

(

an = −2.915h 2 − 2.237 h − 8.654 ln ( N Cl ) + 24.584h 2 + 19.460h + 81.230

(

)

(

kn = 0.180h 2 − 0.849h + 0.750 ln ( N Cl ) + −1.440h 2 + 6.403h − 3.698

(

)

(

)

(3.3)

)

(3.4)

)

am =  −2.915h 2 − 2.237 h − 8.638 ln ( N Cl ) + 24.584h 2 + 19.46h + 81.23 

(

)

× 0.987 m 2 + 0.225m + 6.913 9.781,

(

)

(3.5) 

(

)

km =  0.180h 2 − 0.849h + 0.750 ln ( N Cl ) + −1.440h 2 + 6.403h − 3.698  × ( 0.081m + 1.819 ) 1.940

(3.6) 

where multiplicities m = 1, 2, 3, ..... Instead of Climax NM, one can also use monthly averages of any other CR station with appropriate recalculation of the coefficients determined by correlation between monthly data NCl of Climax NM and this station for several years. For example, the recalculated coefficients for ESOI 6NM-64 are ln ( N Cl ) = (1.947 ± 0.022 ) × ln ( N ESOI ) − (1.75 ± 0.11) ;



CC = 0.892 ± 0.003..

(3.7) 

For Rome 17NM-64 these recalculation coefficients are ln ( N Cl ) = ( 2.048 ± 0.005 ) × ln ( N Roma ) − (1.965 ± 0.024 ) ;



CC = 0.9819 ± 0.0004.

(3.8) 



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For 18 NM-64 Apatite the found recalculation coefficients are ln ( N Cl ) = (1.178 ± 0.003) × ln ( N Apat ) − ( 2.256 ± 0.016 ) ;



CC = 0.9922 ± 0.0002.

(3.9) 

For Athens station with 6 NM-64 the recalculation coefficients are ln ( N Cl ) = ( 2.278 ± 0.017 ) × ln ( N Ath ) − ( 0.828 ± 0.069 ) ;



CC = 0.947 ± 0.002 2.

(3.10) 

For Moscow station with 24 NM-64 the recalculation coefficients are ln ( N Cl ) = (1.194 ± 0.003) × ln ( N Mosc ) + (1.853 ± 0.017 ) ;



CC = 0.9845 ± 0.0003.

(3.11) 

For McMurdo station with 18 NM-64 the recalculation coefficients are ln ( N Cl ) = (1.121 ± 0.002 ) × ln ( N McMur ) + ( 2.074 ± 0.010 ) ;



CC = 0.9805 ± 0..0002.

(3.12) 

For Kiel station with 18 NM-64 the recalculation coefficients are ln ( N Cl ) = (1.152 ± 0.002 ) × ln ( N Kiel ) + ( 2.395 ± 0.010 ) ;



CC = 0.9764 ± 0.0002.

(3.13)



For Oulu station with 18 NM-64 the recalculation coefficients are ln ( N Cl ) = (1.1794 ± 0.0013) × ln ( N Oulu ) + ( 2.8424 ± 0.0013) ;

CC = 0.9915 5 ± 0.0001.

(3.14)

For Almata (high-mountain) station with 24 NM-64 the recalculation coefficients are ln ( N Cl ) = (1.875 ± 0.004 ) × ln ( N Almata ) − ( 5.277 ± 0.029 ) ;



CC = 0.9746 ± 0.0003.

(3.15) 

Substituting Eqs. 3.73.15 in Eqs. 3.33.6, we obtain the coupling functions as a function of the level of solar activity on the basis of monthly NM data of ESOI, Rome, Athens, Moscow, McMurdo, Kiel, Oulu, Almata. By this way it is easy to find corresponding recalculation coefficients for any CR station with NM in the World. Because in our method of determining spectrum of solar CR out of magnetosphere can be used also other CR secondary components, let us outlined that according to Dorman (M2004), the coefficients ai, ∙i in the analytical form described by Eq. 3.1 for different CR secondary components will be as following: 1) for neutron component at ho = 312 mb (about 10 kmaltitude of many airlines) an = 8.30, ∙n = 1.45; 2) for neutron component at ho = 680 mb (mountains at about 3 km), an = 13.62, ∙n = 1.26; 3) for hard muon component at sea level ho = 1030 mb ah¹ = 35.3, ∙h¹ = 0.95; and 4) for hard muon component underground at the depth 7 m w.e., ah¹ = 58.5, ∙h¹ = 0.94.

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3.5. For estimation of small changes of coefficients ai,∙i in Eqs. 3.1 and 3.2 with changing h and solar activity, characterized by ln(NCl ), let us use Eq. 3.3 – 3.6: δ an = ( ∂an ∂h ) δ h + ( ∂an ∂ ln ( N Cl ) ) δ ln ( N Cl ) = ( −5.830h − 2.237 ) × ln ( N Cl ) + ( 49.168h + 19.460 )  δ h

(

)

+ −2.915h 2 − 2.237 h − 8.654 δ ln ( N Cl ) ,



(3.16) 

δ kn = ( ∂kn ∂h ) δ h + ( ∂kn ∂ ln ( N Cl ) ) δ ln ( N Cl ) = ( 0.360h − 0.849 ) × ln ( N Cl ) + ( −2.880h + 6.403)  δ h

(

)

+ 0.180h 2 − 0.849h + 0.750 δ ln ( N Cl ) ,



(3.17) 

δ am = ( ∂am ∂h ) δ h + ( ∂am ∂ ln ( N Cl ) ) δ ln ( N Cl ) = ( −5.830h − 2.237 ) × ln ( N Cl ) + ( 49.168h + 19.460 ) 

( (

) )

(

×  0.987 m 2 + 0.225m + 6.913 9.781 δ h + −2.915h 2 − 2.237 h − 8.638 ×  0.987 m 2 + 0.225m + 6.913 9.781 δ ln ( N Cl ) ,

(3.18)

) 

δ km = ( ∂km ∂h ) δ h + ( ∂km ∂ ln ( N Cl ) ) δ ln ( N Cl ) = ( 0.360h − 0.849 ) × ln ( N Cl ) + ( −2.880h + 6.403) 

(

× ( 0.081m + 1.819 ) 1.940  δ h + 0.180h 2 − 0.849h + 0.750



× ( 0.081m + 1.819 ) 1.940  δ ln ( N Cl ) , (3.19)

(3.19)

) 

3.6. Tabulating special functions Fi(Rc,°) for each used CR station and each component For calculating on-line expected spectrum of solar CR out of the Earth atmosphere and magnetosphere we need to know for each used CR station and each component functions

(

(

Fi ( Rc , γ ) = ai ki 1 − exp −ai Rc− ki

∞

)) ∫ R ( −1

Rc

− ki +1+γ )

(

)

exp −ai R − ki dR

where Rc, ai, ki were described above (for NM by Eqs. 3.3 – 3.6).

(3.20) 



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3.7. For using on-line data of pairs CR stations with different cutoff rigidities we need to tabulate special functions Ψ kl ( Rc1 , Rc 2 , γ ) Rfor each pair of used CR stations with the same or different type of measured component, and with the same or different h In this case the ratio of CR enhancements on both stations will be where

δ N k ( Rc1 , t ) δ N l ( Rc 2 , t ) = Ψ kl ( Rc1 , Rc 2 , γ )

(3.21)



Ψ kl ( Rc1 , Rc 2 , γ ) = Fk ( Rc1 , γ ) Fl ( Rc 2 , γ ) (3.22) After tabulating Ψ kl ( Rc1 , Rc 2 , γ ) according to Eq. 3.22, we obtain on the basis of Eq. 3.21:

γ ( t ) = Ω kl (δ N k ( Rc1 , t ) δ N l ( Rc 2 , t ) ) (3.23) and then b(t) can be determined from:



b ( t ) = δ N m ( Rc1 , t ) Fm ( Rc1 , γ ( t ) ) = δ N n ( Rc 2 , t ) Fn ( Rc 2 , γ ( t ) )



(3.24)

Here the spectrum of primary solar CR variation ∆D ( R, t ) we describe as

∆D ( R, t ) Do ( R ) = b ( t ) R −γ (t ) (3.25)

where Do(R) is the differential spectrum of galactic CR at t = 0 (for which coupling functions are defined). In Eq. 3.25 the parameters b(t) and °(t) depend on t. 3.8. We need to determine the differential spectrum of galactic CR Do(R) from balloon or satellite measurements in quite periods, and for long term changing Do(R) with time by NM world network. The information on solar CR intensity out of the atmosphere and magnetosphere according to Eq. 3.25:

∆D ( R, t ) = b ( t ) Do ( R ) R −γ (t )



(3.26)

4 Algorithms for the first stage: automatically determining the start of SEP event 4.1. How automatically determine the start of SEP event. The determination of increasing flux we suppose to made by comparison with intensity averaged for one day (1440 minutes) from 1560 to 120 minutes before the present Z-th one-minute data. For each Z minute data, start the program “SEP-Search”. The program for each Z-th minute determines the values

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(4.1)



k = Z −120   DAZ = ln ( I AZ ) − ∑ ln ( I Ak ) 1440  σ k = Z −1560   

(4.2)



k = Z −120   DBZ = ln ( I BZ ) − ∑ ln ( I Bk ) 1440  σ k = Z −1560   

where IAk and IBk are one-minute counting rate in the sections of neutron supermonitor A and B, and ¾ is the statistical error for one minute: σ = 〈 I Ak 〉 -1/ 2 ≅ 〈 I Bk 〉 -1/ 2 



(4.3)

For NM at Mt. Hermon the average counting rate in each sections 〈 I Ak 〉 ≅ 〈 I Bk 〉 is about 5000 per one minute, and σ ≅ 0.014 = 1.4% . If simultaneously

DAZ ≥ 2.5, DBZ ≥ 2.5 

(4.4)

the program “SEP-Search” repeat the calculation for the next Z+1-th minute and if Eq. 4.4 is satisfied again, the onset of great SEP is determined and starts the program “SEP-Research/Spectrum”. In this case we use the last value of average intensities in both sections, determined on the basis of one day (1440 minute data). If Eq. 4.4 is not satisfied, the program ”SEP-Search” continue to check next minutes up to the moment when Eq. 4.4 will be satisfied at least for two nearest minutes. 4.2. The probability of false alarms. Because the probability function, (2.5) = 0.9876, that the probability of an accidental increase with amplitude more than 2.5s in one channel will be (1 – (2.5))/2 = 0.0062 min, that means one in 161.3 minutes (in one day we expect 8.93 accidental increases in one channel). The probability of accidental increases simultaneously in both channels will be ((1 – (2.5))/2)2 = 3.845 10-2 min-1 that means one in 26007 minutes  18 days. The probability that the increases of 2.5s will be accidental in both channels in two successive minutes is equal to ((1 – (2.5))/2)4 = 1.478 10-9 min-1 that means one in 6.76108 minutes ≈1286 years. If this false alarm (one in about 1300 years) is sent, it is not dangerous, because the first alarm is preliminary and can be cancelled if in the third successive minute is no increase in both channels bigger than 2.5¾ (it is not excluded that in the third minute there will be also an accidental increase, but the probability of this false alarm is negligible: ((1-(2.5))/2)6 = 5.685 10-14 min-1 that means one in 3.34  10-7years). Let us note that the false alarm can be sent also in the case of solar neutron event (which really is not dangerous for electronics in spacecrafts or for astronauts health), but this event usually is very short (only few minutes, see in Dorman, M2010) and this alarm will be automatically canceled in the successive minute after the end of a solar neutron event.



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4.3. The probability of missed triggers. The probability of missed triggers depends very strong on the amplitude of the increase. Let us suppose for example that we have a real increase of 7¾ (that for ESOI corresponds to an increase of about 10 %). The trigger will be missed if in any of both channels and in any of both successive minutes if as a result of statistical fluctuations the increase of intensity is less than 2.5¾. For this the statistical fluctuation must be negative with amplitude more than 4.5¾. The probability of this negative fluctuation in one channel in one minute is equal (1 – (4.5))/2 = 3.39 10-6 min-1, and the probability of missed trigger for two successive minutes of observation simultaneously in two channels is 4 times larger: 1.36  10-5. It means that missed trigger is expected only one per about 70000 events. In Table 1 are listed probabilities Pmt of missed triggers for ESOI (where standard deviation for one channel for one minute ¾ = 1.4%) as a function of the amplitude of increase A. Table 4.1.  Probabilities Pm of missed triggers as a function of amplitude of increase A (in % and in s) A, % 4.9 4.6 6.3 7.0 7.7 8.4 9.1 9.8 10.5 A, ¾ 3.5 4.0 4.5 4.0 4.5 6.0 6.5 7.0 7.5 Pmt 6.310-1 2.710-1 2.710-1 2.510-2 4.410-3 9.310-4 1.310-4 1.410-5 1.110-6

4.4. Discussion on the method of automatically search of the start of great SEP events. Obtained results show that the considered method of automatically searching for the onset of great, dangerous SEP on the basis of one-minute NM data practically does not give false alarms (the probability of false preliminary alarm is one in about 1300 years, and for false final alarm one in 3.34 107 years). None dangerous solar neutron events also can be separated automatically. We estimated also the probability of missed triggers; it was shown that for events with amplitude of increase more than 10% the probability of a missed trigger for successive two minutes NM data is smaller than 1.36 10-5 (this probability decreases sufficiently with increased amplitude A of the SEP increase, as shown in Table 2). Historical ground SEP events show very fast increase of amplitude in the start of event. For example, in great SEP event of February 23, 1956 amplitudes of increase in the Chicago NM were at 3.51 UT - 1%, at 3.52 UT – 35%, at 3.53 UT – 180%, at 3.54 UT – 280 %. In this case the missed trigger can be only for the first minute at 3.51 UT. The described method can be used in many CR Observatories where one-minute data are detected. Since the frequency of ground SEP events increases with decreasing cutoff rigidity, it will be important to introduce described method in high latitude Observatories. For low latitude CR Observatories the SEP increase starts earlier and the increase is much faster; this is very important for forecasting of dangerous situation caused by great SEP events.

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5 Algorithms for the second stage: automatically determining the spectrum of the primary SEP and its change with time. 5.1. Analytical approximation for rigidity spectrum of primary solar CR ­variation. In the first approximation the spectrum of primary solar CR D(R,t) can be described as D(R,t)/Do(R)=b(t)R-°(t)

(5.1)

where Do R is the differential spectrum of galactic CR at t = 0 (for which coupling functions are defined). In Eq. 5.1 the parameters b(t) and g(t) depend on t. The approximation described by Eq. 5.1 can be used for describing a limited interval of rigidities in the sensitivity range corresponding to different CR secondary components (determined by coupling function). On the other hand, many historical GLE (Ground Level Event from solar CR) data show that, in the broad energy interval, the rigidity spectrum for this type of CR primary variation has a maximum, and the parameter °(t) in Eq. 5.1 depends also on particle rigidity R (usually °(t) increases with increasing R). 5.2. Determination of the rigidity spectrum of primary CR variation in the magnetically quiet period by data from one station with at least two different components. In this case, for rigidity spectrum described by Eq. 5.1, the observed variation ±Ni(Rc,t)´Ni(Rc,t)/Nio(Rc)(5.2) in some component i can be described in the first approximation by the function Fi(Rc, °(t)): ±Ni(Rc,t)=b(t)Fi(Rc, °(t)),(5.3) where

(

(

Fi ( Rc , γ ) = ai ki 1 − exp −ai Rc− ki

∞

)) ∫ R ( −1

Rc

− ki +1+γ )

(

)

exp −ai R − ki dR

(5.4) 

is a known function (it must be tabulated for any CR station in the world in dependence of Rc and pressure h for any component i, as it was described in Section 1). Let us compare the data for two components m and n. According to Eq. 5.4 we obtain where

±Nm(Rc,t)/±Nn(Rc,t)= ªmn(Rc, °(t)),(5.5)

ªmn(Rc, °)=Fm(Rc, °)/Fn(Rc, °)(5.6)



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can be also tabulated using Eq. 5.4. Comparison of experimental results with function mn(Rc,°) according to Eq. 5.6 gives the value °(t), and then from Eq. 5.3 the value of the parameter b(t). Eq. 5.6 shows that on the basis of CR observation data in atmosphere and underground one can determine the parameters b(t) and °(t) of the rigidity spectrum of primary solar CR variation in the quiet period at the top of atmosphere. 5.3. Determination of the rigidity spectrum of primary CR variation in the magnetically quiet period by data from two stations with different cutoff rigidities. The rigidity spectrum of primary solar CR variation can be determined by the spectrographic method. In this case for determining b(t) and °(t) in Eq. 5.1 we need to have data at least of one component on each station. If it is the same component m at both stations, parameter g(t) will be evaluated from the equation ±Nm(Rc1,t)/±Nm(Rc1,t)= ªmn(Rc1, Rc2, °),(5.7) where ªmn(Rc1, Rc2, °)=Fm(Rc1,°)/Fm(Rc2,°),(5.8) and then we can determine b(t)=±Nm(Rc1,t)/Fm(Rc1,°(t))=±Nm(Rc2,t)/Fm(Rc2,°(t))(5.9) If two different components m and n are used on both stations, the solution for °(t) will be determined by equation: ±Nm(Rc1,t)/±Nn(Rc2,t)= ªmn(Rc1, Rc2, °),(5.10) where ªmn(Rc1, Rc2, °)=Fm(Rc1,°)/Fn(Rc2,°),(5.11) and then b(t) can be determined from: b(t)=±Nm(Rc1,t)/Fm(Rc1,°(t))=±Nn(Rc2,t)/Fn(Rc2,°(t))(5.12)

6 Algorithms for the Stage 3: The solving on-line the inverse problem for solar CR generation and propagation. On this stage we develop algorithms for automatically worked programs “SEP-Research/Time of Ejection”, “SEP-Research/Source Function”, and ­ “SEP-Research/Propagation Parameters”). Let us consider two cases.

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6.1. The inverse problem for the case when diffusion coefficient depends only from particle rigidity. In this case the solution of isotropic diffusion for the pointing instantaneous source described by function Q(R,r,t) = No(R)±(r)±(t)(6.1) will be

− 2   32 1 N ( R, r , t ) = N o ( R ) × 2π 1 2 (κ ( R ) t )  × exp  − r      4κ ( R ) t  ,

(6.2)

where r is the distance from the Sun, t is the time after ejection SEP into interplanetary space, NO(R) is the rigidity spectrum of total number of SEP at the source, and k(R) is the diffusion coefficient in the interplanetary space during SEP event. Let us suppose that at distance from the Sun r = r1 = 1 AU and at several moments of time ti (i = 1, 2, 3, ...) after SEP ejection into solar wind the observed rigidity spectrum out of the Earth’s atmosphere N(R,r1,ti)´Ni(R) are determined in high energy range on the basis of ground CR measurements by neutron monitors and muon telescopes (by using method of coupling functions, spectrographic and global spectrographic methods, see review in Dorman, M2004)) as well as determined directly in low energy range on the basis of satellite CR measurements. Let us suppose also that the UT time of ejection Te as well as the diffusion coefficient k(R) and the SEP rigidity spectrum in source NO(R) are unknown. To solve the inverse problem, i.e. to determine these three unknown parameters, we need information on SEP rigidity spectrum Ni(R) at least at three different moments of time T1, T2, and T3 (in UT). In this case for these three moments of time after SEP ejection into solar wind we obtain: t1 = T1¡Te = x, t2 = T2¡Te = T2¡T2 + x, t2 = T3¡Te = T3¡T1 + x,(6.3) where T2¡T1 and T3¡T1 are known values and x = T1¡Te is unknown value to be determined (because Te is unknown). From three equations for t1, t2 and t3 of the type of Eq. 6.2 by taking into account Eq. 6.3 and dividing one equation on other for excluding unknown parameter No(R), we obtain two equations for determining unknown two parameters x and k(R):





 N ( R ) 4κ ( R ) 3 2 T2 − T1  =− × ln  1 x (T2 − T1 + x ) )  ,(6.4) ( 2 x (T2 − T1 + x ) r1 N R ( )   2  N ( R ) 4κ ( R ) 3 2 T3 − T1  =− × ln  1 x (T3 − T1 + x ) )  .(6.5) ( 2 x (T3 − T1 + x ) r1 N R ( )   3

To exclude unknown parameter k(R) let us divide Eq. 6.4 by Eq. 6.5; in this case we obtain equation for determining unknown x = T1¡Te: x = [(T2¡T1)ª(x)¡(T3¡T1)/(1¡ª(x)),(6.6)



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where

32 ln  N1 ( R ) ( x (T2 − T1 + x ) ) N 2 ( R )    Ψ ( x ) = (T3 − T1 ) (T2 − T1 )  × (6.7) 32 ln  N1 ( R ) ( x (T3 − T1 + x ) ) N 3 ( R )    Equation 6.6 can be solved by the iteration method: as a first approximation, we can use x1 = T1¡Te ¼ 500 sec, which is the minimum time propagation of relativistic particles from the Sun to the Earth’s orbit. Then, by Eq. 6.7 we determine ª(x1) and by Eq. 6.6 we determine the second approximation x2. To put x2 in Eq. 6.7 we compute ª(x2) , and then by Eq. 6.6 we determine the third approximation x3, and so on. After solving Eq. 6.6 and determining the time of ejection, we can compute very easily diffusion coefficient from Eq. 6.4 or Eq. 6.5:

κ ( R) = −

r12 (T2 − T1 ) 4 x (T2 − T1 + x )

 3 2  N ( R ) ln  1 x (T2 − T1 + x ) )  ( N R  2 ( ) 

=−

r12 (T3 − T1 ) 4 x (T3 − T1 + x )

(6.8)

 3 2  N ( R ) ln  1 x (T3 − T1 + x ) )  ( N R  3 ( )  

After determining the time of ejection and diffusion coefficient, it is easy to determine the SEP source spectrum: No(R) = 2¼1/2N1(R) £ (∙(R)x)3/2 exp(r12/(4∙(R)x))

= 2¼1/2N2(R) £ (∙(R)(T2¡T1 + x))3/2 exp(r12/(4∙(R)(T2¡T1 + x))) = 2¼1/2N3(R) £ (∙(R)(T3¡T1 +  x))3/2 exp(r12/(4∙(R)(T3¡T1 + x)))

(6.9) 

2. The inverse problem for the case when diffusion coefficient depends from particle rigidity and from the distance to the Sun. Let us suppose, according to Parker (M1963), that the diffusion coefficient ∙(R,r) = ∙1(R)£(r/r1)¯

(6.10)

In this case the solution of diffusion equation will be

N ( R, r , t ) =

N o ( R ) × r13 β

( 2− β )

( 4+ β ) ( 2− β

(2 − β )

( )   (κ ( R ) t ) r r  ,(6.11)  × exp − )  (2 − β ) κ ( R)t  Γ (3 ( 2 − β ))   −3 2 − β

1

β 1

2− β

2

1

where t is the time after SEP ejection into solar wind. So now we have four unknown parameters: time of SEP ejection into solar wind Te, ¯, ∙1(R), and No(R). Let us assume that according to ground and satellite measurements at the distance r = r1 = 1 AU from the Sun we know N1(R), N2(R), N3(R), N4(R) at UT times T1, T2, T3, T4. In this case t1 = T1¡Te = x, t2 = T2¡T1 + x, t3 = T3¡T1 + x, t4 = T4¡T1 + x,(6.12)

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For each Ni(R,r = r1,Ti) we obtain from Eq. 6.11 and Eq. 6.12:

N i ( R, r = r1 , Ti ) =

(κ ( R ) (T − T + x ) ) ( ( 2 − β ) ) ( ) Γ (3 ( 2 − β ))

N o ( R ) × r13 β

( 2− β )

1

4+ β

i

2− β

−2   r12 ( 2 − β ) , × exp  −  κ1 ( R ) (Ti − T1 + x )   



−3 ( 2 − β )

1

(6.13) 

where i = 1, 2, 3, and 4. To determine x let us step by step exclude unknown parameters No(R), ∙1(R), and then ¯. In the first we exclude No(R) by forming from four Eq. 6.13 for different i three equations for ratios

N1 ( R, r = r1 , T1 )

  x =  N i ( R, r = r1 , Ti )  Ti − T1 + x 

−3 ( 2 − β )

 r12 × exp  −  ( 2 − β )2 κ ( R ) 1 

 1 1    −  x Ti − T1 + x  

(6.14)

where i = 2, 3, and 4. To exclude ∙1(R) let us take logarithm from both parts of Eq. 6.14 and then divide one equation on another; as result we obtain following two equations:

ln ( N1 N 2 ) + ( 3 ( 2 − β ) ) ln ( x (T2 − T1 + x ) ) ln ( N1

(1 x ) − (1 (T2 − T1 + x ) ) , N 3 ) + ( 3 ( 2 − β ) ) ln ( x (T3 − T1 + x ) ) (1 x ) − (1 (T3 − T1 + x ) ) 

(6.15)

(1 x ) − (1 (T2 − T1 + x ) ) ,(6.16) N 4 ) + ( 3 ( 2 − β ) ) ln ( x (T4 − T1 + x ) ) (1 x ) − (1 (T4 − T1 + x ) )

ln ( N1 N 2 ) + ( 3 ( 2 − β ) ) ln ( x (T2 − T1 + x ) ) ln ( N1

=

=

After excluding from Eq. 6.15 and Eq. 6.16 unknown parameter ¯, we obtain equation for determining x: x2(a1a2 ¡ a3a4) + xd(a1b2 + b1a2 ¡ a3b4 ¡ b3a4) + d2(b1b2 ¡ b3b4) = 0,

(6.17)

where d = (T2 ¡ T1)(T3 ¡ T1)(T4 ¡ T1),

(6.18)

a1 = (T2¡T1)(T4¡T1)ln(N1/N3)¡(T3¡T1)(T4¡T1)ln(N1/N2),(6.19) a2 = (T3¡T1)(T4¡T1)ln(x/T2¡T1+x))¡(T2¡T1)(T3¡T1)ln(x/T4¡T1+x)),(6.20) a3 = (T2¡T1)(T3¡T1)ln(N1/N4)¡(T3¡T1)(T4¡T1)ln(N1/N2),(6.21) a4 = (T3¡T1)(T4¡T1)ln(x/T2¡T1+x))¡(T2¡T1)(T4¡T1)ln(x/T3¡T1+x)),(6.22)



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b1 = ln(N1/N3)¡ln(N1/N3), b2 = ln(x/T2 ¡T1+ x))¡ln(x/T4 ¡T1+ x),(6.23) b3 = ln(N1/N4)¡ln(N1/N2), b4 = ln(x/T2 ¡T1+ x))¡ln(x/T3 ¡T1+ x),(6.24) As it can be seen from Eq. 6.20 and Eqs. 6.22-6.24, coefficients a2,a4,b2,b4 very weekly (as logarithm) depend from x. Therefore Eq. 6.17 we solve by iteration method, as above we solved Eq. 6.6: as a first approximation, we use x1=T1¡Te ¼  500 sec (which is the minimum time propagation of relativistic particles from the Sun to the Earth’s orbit). Then by Eq. 6.20 and Eqs. 6.22-6.24 we determine a2(x1), a4(x1), b2(x1), b4(x1) and by Eq. 6.17 we determine the second approximation x2, and so on. After determining x, i.e. according Eq. 6.12 determining t1, t2, t3, t4, the final solutions for ¯, ∙1(R), and No(R) can be found. Unknown parameter ¯ in Eq. 6.10 we determine from Eq. 6.15 and Eq. 6.16: −1

    t (t − t ) t (t − t ) β = 2 − 3 ( ln ( t2 t1 ) ) − 3 2 1 ln ( t3 t1 )  × ( ln ( N1 N 2 ) ) − 3 2 1 ln ( N1 N 3 )  . t2 ( t3 − t1 ) t2 ( t3 − t1 )     (6.25) Then we determine unknown parameter ∙1(R) in Eq. 6.10 from Eq. 6.14:

κ1 ( R ) = =

(

r12 t1−1 − t2−1

)

3 ( 2 − β ) ln ( t2 t1 ) − ( 2 − β ) ln ( N1 N 2 ) 2

(

r12 t1−1 − t3−1

)

(6.26)

3 ( 2 − β ) ln ( t3 t1 ) − ( 2 − β ) ln ( N1 N 3 ) 2



After determining parameters ¯ and ∙1(R) we can determine the last unknown parameter, source function No(R) from Eq. 6.13: ( 4+ β ) ( 2− β )

No ( R ) = Ni ( 2 − β )



Γ ( 3 ( 2 − β ) ) r1−3 β

 r12 × exp   ( 2 − β )2 κ ( R ) t 1 i 

   

( 2− β )

3 ( 2− β )

(κ ( R ) t ) 1

i

(6.27) 

where index i = 1, 2 or 3. Let us outline that for all i results must be the same (it can be used as control of correct calculations.

Acknowledgements LD uses this opportunity to acknowledge Ministry of Science of State Israel, Tel Aviv University, Israel Space Agency, and Golan Research Institute for continue support of Israeli Cosmic Ray & Space Weather Centre, and Azerbaijan Science Foundation for kind invitation to take part in very interesting Baku Solar Conference and productive collaboration.

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Bibliography Dorman L.I., M1957. Cosmic Ray Variations. Gostekhteorizdat, Moscow , pp 495. In Russian. In English: M1958, US Department of Defense, Washington, DC. Dorman L.I., M2004. Cosmic Rays in the Earth's AtmosphereandUnderground. Kluwer Ac. Publ., Dordrecht/Boston/London. Dorman L.I., M2010. Solar Neutrons and Related Phenomena, Springer, Heidelberg, Germany. L.I. Dorman, L.A. Pustil’nik, A. Sternlieb, and I.G. Zukerman, 2006a. “Forecasting of radiation hazard: 1. Alerts on great FEP events beginning; probabilities of false and missed alerts; on-line determination of solar energetic particle spectrum by using spectrographic method”, Advances in Space Research, 37, 1124-1133. L.I. Dorman, N. Iucci, M. Murat, M. Parisi, L.A. Pustil’nik, A. Sternlieb, G. Villoresi, and I.G. Zukerman, 2006b “Forecasting of radiation hazard: 2. Online determination of diffusion coefficient in the interplanetary space, time of ejection and energy spectrum at the source; on-line using of neutron monitor and satellite data”, Advances in Space Research, 37, 1134-1140).

Space Weather Effects on Human Health

Svetla Dimitrova1 , Elchin Babayev2 1

Space Research and Technologies Institute, Bulgarian Academy of Sciences Shamakhy Astrophysical Observatory, ANAS, AZERBAIJAN E-mail: svetla [email protected] 2

Abstract. This study reviews collaborative investigations performed at middle latitudes at different geographical places concerning the potential effects of space weather on human physiological and psycho-physiological state and acute cardio-vascular incidences.

1

Introduction

The main driver of Space Weather is Solar Activity (SA). Solar wind as a mediator of SA is the main driving agent of geomagnetic storms, which are indirect indicators of geo-effective solar phenomena. Two main types of structures in the solar wind can cause geomagnetic storms: eruptive solar structures or coronal mass ejections (CME) and not-eruptive solar structures or high-speed solar wind streams (HSSWS) from Coronal Holes. The sources of the most intense geomagnetic storms are considered CMEs. Studies indicate the most geo-effective from CMEs are Magnetic Clouds (MC), Georgieva et al. (2006). MCs storms prevail in the years of maximal SA. During the declining phase of the solar cycle the main drivers of terrestrial disturbances are HSSWS originating from solar coronal holes, which tend to be most numerous in the years following sunspot maximum. It is well known that space weather can affect GPS systems, satellite communications, HF radio communications, electric power transmission. It can cause satellite drags, damage to satellites, radiation hazards to humans (astronauts and onboard aircrafts). A lot of scientific investigations performed in the last years indicate that SA is the main factor for the Earths climate. Beautiful manifestations of space weather are auroras. The fact that space weather variations are related to changes of different natural environmental factors, which are ingredients of our living surroundings, should not be underestimated. Human beings have accommodated to the habitual environmental variations in the course of evolution. However any sharp deviations (similar to meteorological weather) can be a stress factor, requiring strong compensatory abilities for the adaptation process under sudden and temporal alterations of the environmental factors. There is a growing body of evidence during the last years that geomagnetic activity (GMA), used as an indirect indicator of SA, affects different functional systems and in particular cardiovascular and nervous system. Research studies

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Svetla Dimitrova, Dimitrova, Elchin Svetla ElchinBabayev Babayev

revealed that electromagnetic fields (EMF), including geomagnetic field (GMF), could affect blood pressure, worsen the baro-reflective sensitivity and microcirculation, may alter the capillary blood flow in patients with ischemic heart disease and heart rate variability (Gmitrov & Gmitrova 1994; Gurfinkel et al. 1995; Stoupel et al. 1995; Baevsky et al. 1997, 1998; Ghione et al. 1998; Braune et al. 1998; Oraevskii et al. 1998; Otsuka et al. 2001; Gmitrov & Ohkubo 2002; Oinuma et al. 2002; Cornelissen et al. 2002; Gmitrov 2005; Okano 2008; Otsuka et al. 2009). The enumerated established effects on the circulation and cardiovascular parameters indicate that GMA variations may be related to the dynamics of cardiac arrhythmias, myocardial infarction, sudden cardiac death and other cardiovascular diseases. This hypothesis has been supported by different studies (Gurfinkel et al. 1998; Villoresi et al. 1998; Halberg et al. 2000; Cornelissen et al. 2002). Two quantifiable measures are used in the field of heliobiology to study the potential effects: 1) indirect indicators - essentially epidemiological data like emergency calls and hospital admissions, dynamics of various accidents, etc. and 2) direct indicators - physiological parameters, which can be objectively verified and which are acquired either in vivo, directly on the subject or in vitro by laboratory measurements.

2

Material and Methods

We have performed a joint collaboration to study the effects of space weather on both epidemiological data and physiological parameters of healthy persons at middle latitudes but at different longitudes – Sofia and Baku. The effect of the following space weather factors was studied: GMA indices, GMA according to the type of solar driver and cosmic rays intensity (CRI). GMA was divided into several levels regarding the values of geomagnetic indices (Ap, Kp, Dst). In the subsequent analyses GMA was divided into 3 types depending on the solar driver of the storms – MC and HSSWS. CRI was divided into levels by step of 1% decrease for each level. ANalysis Of VAriance (ANOVA) was applied to establish statistical significance of the effect of the studied space weather factors on medical data. ANOVA and superimposed epoch method were used to study the effect of space weather factors up to 3 days before and 3 days after their occurrence. In the subsequent analyses Post-hoc analysis (Newman-Keuls test) was used to establish statistical significance of the differences between the average values of the medical data in the separate factors levels. Physiological parameters, registered in most of the examinations were: arterial blood pressure (ABP), heart rate (HR) and subjective psycho-physiological complaints (SPPC) comprising 3 groups of questions regarding: cardiovascular system, nervous system and common functional state. In part of the experiments, electrocardiogram (ECG) recordings were performed to derive HR and heart rate variability (HRV). HR is the number of the heartbeats per unit of time. HRV is variation in the beat-to-beat (RR) interval in ECG. HRV can be



Space WeatherEffects Effectson onHuman Human Health Health Space Weather

179 3

assessed by several indices in time domain (RRavg, RRmin, RRmax, SDNN, RMSSD, pNN50) and frequency domain (low frequency (LF), high frequency (HF), LF/HF). HRV is an important indicator of the activity of the autonomous (vegetative) nervous system. Both reduced and increased HRV is a negative prognostic factor, often preceding and/or accompanying various cardiovascular diseases including fatal diseases as well as cases of sudden cardiac death (Task Force 1996). The first physiological examinations were performed in Sofia during maximal SA and GMA. A group of 86 volunteers was examined and ABP, HR and SPPC were registered every working day at one and the same daytime for each person in years of maximal SA (autumn 2001 and spring 2002). Later, in the years of declining SA two additional experiments in Sofia were conducted. One concerned 2 persons who recorded for a period of one year (April 2008 – April 2009) every day two 5 minutes ECGs (in the morning after awakening and in the evening before falling asleep). The second experiment was in the spring of 2009 and concerned a group of 14 healthy persons and the registration of ECGs, ABP and SPPC. In Baku a 2-year experiment during declining SA was performed. ECGs of a group of 7 healthy volunteers were registered every working day from 2006 to 2008. Studied epidemiological data concerned acute cardiac events and can be divided into 2 groups: morbidity and mortality from acute myocardial infarctions (AMI) in Sofia and Baku and sudden cardiac deaths (SCD) in Baku. Bulgarian data spanned a period of 9 years (01.12.1995 - 31.12.2004), covering most of the 23rd SA cycle. They referred to daily distribution of patients admitted in Sofia Regional Hospital. Azerbaijani data were for the period 2003-2005, covering the declining phase of the same SA cycle. They referred to pre-hospital incidences gathered from Emergency and First Medical Aid Stations in the Grand Baku Area (several millions of inhabitants).

3 3.1

Results Results from Sofia volunteers during solar maximum

Results from the group of 86 volunteers in Sofia during maximal SA (Dimitrova et al. 2004a,b; Dimitrova 2005, 2006, 2008) revealed that average values of ABP and SPPC increased during geomagnetic storms and there was a quantitative exposure-response relation between increment of physiological parameters and GMF: the more GMF intensity was the more average values of physiological parameters increased. Variations in physiological parameters under GMA changes were not only statistically significant but biologically significant: ABP increased above 10% and percentage of the persons with SPPC reached 30% under changes of all of geomagnetic indices under consideration. It was established through interaction effects that females in the group were more sensitive to GMF intensity increase than males (Dimitrova 2006, 2008).

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The results indicated that with the increase of the blood pressure degree the sensitivity of the persons to GMF intensity also increased (Dimitrova 2005, 2006), i.e. hypertensive persons were most vulnerable to environmental changes. Analyses supported the hypothesis that persons on medication (both males and females) were more sensitive than persons with no medication to GMA changes (Dimitrova 2005, 2006, 2008). The changes obtained in the examined physiological parameters were registered from the day before until the second day after geomagnetic storms (Dimitrova et al. 2004a,b). Similar variations in the studied physiological parameters were established at CRI decreases (Dimitrova 2009). Effects of storms driven by MC on ABP and HR (Dimitrova & Georgieva 2015) were more pronounced and clearly expressed in comparison to the storms caused by HSSWS, Fig.1. However HSSWS storms were related to larger number of persons reporting SPPC. 3.2

Results from Sofia volunteers during declining SA cycle

GMA effects on ABP, HR (from ECGs) and SPPC of the group before, during and after geomagnetic storms revealed statistically significant increase of ABP and SPPC of the group from 0 day till +2nd day of the weak storms. During the period of investigation several weak storms were registered, but there were no storms with higher intensities. A trend for HR decrease of the group was established on the days before the weak storms and an increase on the days immediately after that. HRV indices of the group varied around the days of weak geomagnetic storms (Dimitrova et al. 2013). Results from ECG records data for a period of year during declining SA of 2 volunteers in Sofia showed that morning registrations of the both volunteers were more sensitive to space weather variations while the evening registrations showed higher sensitivity to anthropogenic EMFs. Both persons reacted to geomagnetic storms however these reactions were not proportional to GMF intensity. Both of them increased HR on the days before, during and after major storms. However both persons decreased HR on the days before moderate storms and after that increased it. HRV indices of both persons varied widely on the days around geomagnetic storms, especially moderate and major storms, Fig. 2 (Dimitrova et al. 2013). 3.3

Results from Baku volunteers during declining SA cycle

The results from ECGs of Baku volunteers during declining SA (Mavromichalaki et al. 2008; Dimitrova et al. 2009a; Papailiou et al. 2009; Mavromichalaki et al. 2012) showed a trend for decrease of the average HR value of the group during geomagnetic storms. However, it is interesting that in addition to the peak decrease on the days of major storms, there was a peak increase on the days immediately before and after these events.



Space WeatherEffects Effectson onHuman Human Health Health Space Weather

Fig. 1. GMA effect, estimated by the types of storm, on Systolic and Diastolic Blood Pressure

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Fig. 2. GMA effect on HRV index (low frequency) before, during and after geomagnetic storms

More detailed analyses revealed strong variations of the HR of the group on the days around geomagnetic storms with higher intensities as well as around the days with more expressed CRI decreases, registered during the examination period, Fig. 3. 3.4

Results from Sofia AMI data

ANOVA revealed statistically significant increase of AMI incidences and lethal outcomes on the days with high levels of GMA in comparison to days with quiet GMA and weak geomagnetic storms. Furthermore results revealed that AMI morbidity and mortality had peak increases on the days before, during and after geomagnetic storms with higher intensities, Fig. 4 (Dimitrova et al. 2008a,b, 2009b). 3.5

Results from Baku AMI data

Results about AMI morbidity and mortality dynamic showed a negative correlation for monthly averaged AMI data in Baku and GMA indices for the considered period of descending phase of SA. It was established that AMI morbidity and mortality in Baku increased on the days with highest GMF intensity as well as on the days before, during and after major and severe storms. It turned out also that AMIs were quite high on the days of lowest GMA, Fig. 5 (Dimitrova et al. 2008a, 2009c,d). Having these results for Baku data during declining SA cycle, additional analyses were performed for Sofia data for the coinciding period of the data rows 2003-2004. It was obtained that AMI morbidity and mortality in Sofia was also quite high on the days of lowest GMA in addition to the peak increases around the days of major and severe storms (Dimitrova et al. 2008a).

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Fig. 3. CRI effect on HR of Baku group before, during and after CRI variations

3.6

Fig. 4. GMA effect (estimated by Apindex) on AMI morbidity before, during and after geomagnetic storms; Sofia data, 1995-2004

GMA effect, estimated by the type of geomagnetic storms on AMI morbidity and mortality in Baku and Sofia

Analyses regarding the driver of the storm (Dimitrova et al. 2008a, 2009c,d) revealed for Sofia data that AMI morbidity and mortality increased statistically significantly on the days with storms caused by MC in comparison to days with quiet GMA and storms driven by HSSWS. Furthermore that difference was confirmed by Post-hoc analysis. It was established that AMI morbidity and mortality in Baku increased during the storms caused by MC and decreased on the days of storms caused by HSSWS in comparison with the days of quiet GMA. Regarding the days of the different storms types, AMI morbidity and mortality in Sofia showed a trend for a significant increment on the days immediately prior, during and after geomagnetic storms, caused by MC, Fig. 6. Similar trend was established for Baku data. 3.7

Results from Baku SCD data

Strong negative correlation was established between monthly averaged number of SCDs in Baku and GMA indices (Am, Km-sum, Ap and Kp-sum) for the considered period of declining SA. The effect of GMA on SCD number was not proportional to GMF intensity (Dimitrova et al. 2009d,e). SCD number was largest on the days of lowest GMA, on days when major and severe geomagnetic storms occurred and on the second day after the end of severe storms. Regarding the type of storm it turned out that SCD incidences increased on days when storms were caused by HSSWs and remained at high level up to two days after they finished alongside with the days of lowest GMA.



Space WeatherEffects Effectson onHuman Human Health Health Space Weather

Fig. 5. GMA effect (estimated by Dstindex) on AMI mortality before, during and after geomagnetic storms development; Baku data, 2003-2005

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Fig. 6. GMA effect, estimated by the types of storm, on AMI incidences before, during and after geomagnetic storms, Sofia data, 1995-2004

Conclusions and discussion Results from the performed studies of physiological parameters at middle latitudes during distinct stages of SA cycle indicate: • Different dependences but all related to adaptation variations of physiological parameters towards physical environmental factors on the days before, during and after geo-effective solar events. • Healthy people manifest an adaptation reaction to accommodate to space weather variations, which is not threatening to their physiological and cardiohealth state but within the normal range. • Further investigations should be performed in this direction. It is necessary to determine those helio-geophysical factors features which most strongly affect human physiological state. • The determination of the impact degree of the space weather factors and their synergetic effect on the cardio-vascular parameters would help for medical prevention especially for the vulnerable persons. Studies performed on data from two middle-latitude locations on cardiovascular incidences enabled us to obtain more suggestive evidence about the effects of space weather variations on cardio-vascular diseases in general: • Results revealed similar trends for two regions data and differences in distinct SA cycle stages. • It was obtained that both lowest and highest GMA levels are related to an increase in the number of the considered cardiac incidences and fatal outcomes. • The obtained results possibly indicate that different types of geomagnetic storms, through their specific parameters, can affect in distinct ways living organisms, including the human health state and cardio-vascular system.

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• The clinical course of AMI and SCD seems to be related to space weather variations alongside other affecting factors. • Different pathophysiological mechanisms of the varied cardio-vascular diseases should be considered as well, i.e. SCD and AMI are defined by diverse conditions. This review of the performed collaborative studies on the space weather effects on human health at middle latitudes show the necessity of long-period and detailed studies at different latitudes and longitudes. The possible adverse effect of very low GMA on cardio-vascular state and the role of environmental physical factors becoming more active on the days of very low GMA should be object of further studies. Additional investigations of the effects of some not studied by now space weather parameters and synergetic effects of environmental factors should be performed. It is necessary to clarify the possible mechanisms through which different GMA indices and levels as an indirect indicator of space weather affect cardio-vascular system.



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Gurfinkel, Iu.I., Kuleshova, V.P., Oraevskii, V.N., 1998, Biofizika, 43(4), 654-658. Halberg, F., Cornelissen, G., Otsuka, K., Watanabe, Y., Katinas, G.S., Burioka, N., Delyukov, A., Gorgo, Y., Zhao, Z.Y., Weydahl, A., Sothern, R.B., Siegelova, J., Fiser, B., Dusek, J., Syutkina, E.V., Perfetto, F., Tarquini, R., Singh, R.B., Rhees, B., Lofstrom, D., Lofstrom, P., Johnson, P.W.C., & Schwartzkop, O. 2000, Neuroendocrinology Letters 21, 233258. Mavromichalaki, H., Papailiou, M., Dimitrova, S., Babayev, E.S., & Mustafa F. R. 2008, ECRS 21, 351-356. Mavromichalaki, H., Papailiou, M., Dimitrova, S., Babayev, E.S., & Loucas, P. 2012, Natural Hazards 64(2), 1447-1459. Oinuma, S., Kubo, Y., Otsuka, K., Yamanakata, T., Murakami, S., Matsuoka, O., Ohkawa, S., Cornelissen, G., Weydahl, A., Holmeslet, B., Hall, C., & Halberg, F. 2002, Biomed & Pharmac, 56(2), 284-288. Okano, H. 2008, Current hypertension reviews, 4(1), 63-72. Oraevskii, V.N., Kuleshova, V.P., Gurfinkel, Iu.F., Guseva, A.V. & Rapoport, S.I. 1998, Biofizika, 43(5), 844-848. Otsuka, K., Cornlissen, G., Weydahl, A., Holmeslet, B., Hansen, T.L., Shinagawa, M., Kubo, Y., Nishimura, Y., Omori, K., Yano, S., & Halberg, F. 2001, Biomed & Pharmac, 55, 51-56. Otsuka, K., Izumi, R., Ishioka, N., Ohshima, H., & Mukai, C. 2009, Resp Phys & Neurob, 169(1), 69-72. Papailiou, M., Dimitrova, S., Babayev, E.S., & Mavromichalaki H. 2009, CP1203, IC BPU 7, American Inst.Phys, 748-753. Stoupel, E., Wittenberg, C., Zabludowski, & Boner, J.G. 1995, J Human Hypertension, 9, 293-294. Task Force, 1996. Task force of the European society of cardiology and the North American society of pacing and electrophysiology. Eur Heart J 17:354381. Villoresi, G., Ptitsyna, N.G., Tiasto, M.I., & Iucci, N. 1998, Biofizika, 43(4), 623-631.

Cosmic Rays and other Space Phenomena Influenced on the Earth’s Climate Lev Dorman1,2 1 Israel Cosmic Ray & Space Weather Centre and Emilio S´egre Observatory (Mt. Hermon) affiliated to Tel Aviv University, Golan Research Institute, and Israel Space Agency, Israel 2 Cosmic Ray Department of IZMIRAN, Moscow, Russia

Abstract. We consider effects of cosmic rays (CR) and some other space phenomena on the Earth’s climate change. It is well known that the system of internal and external factors formatting the Earth’s climate is very unstable: decreasing of planetary average annual temperature leads to an increase of planetary snow surface, and decreasing of the total annual solar energy input into the system decreases the planetary temperature even more. And inverse: increasing planetary temperature leads to an decrease of snow surface, and increasing of the total solar energy input into the system increases the planetary temperature even more. From this follows that even energetically small factors acted long time in one direction may have a big influence on climate change. In our opinion, the most important of these factors are CR (mostly through its influence on planetary cloudiness) and space dust (SD) through their influence on the flux of solar irradiation and on formation of clouds. It is important that CR and SD influenced on global climate change in the same direction. Increasing of CR planetary intensity leads to increasing of formation clouds (especially low clouds on altitudes smaller than 3 km), increasing annual average of raining and decreasing of annual average planetary temperature. Increasing of SD decreases of solar irradiation and increases cloudiness what leads also to decreasing of annual average planetary temperature. Moreover, interactions of CR particles with dust granules increases their density what increased effectiveness of their actions on clouds. We consider data on great variations of planetary temperature much before the beginning of the Earth’s technological civilization (mostly caused by moving of the solar system around Galaxy centre and collisions with molecular-dust clouds). We consider in details not only situation during the last hundred years, but also situation in the last one thousand years (especially, in Maunder minimum of solar activity), during many thousand and many millions years. It is shown that very big changes in climate were caused also by some rarely phenomena as impacts of asteroids and nearby supernova explosions with great influence on biosphere. We discuss also the problem on forecasting of global climate change what is especially important for saving present civilization from great climate catastrophes.

1

The Matter of Problem

In recent years, among the population, as well as among many scientists have caused great concern to the observations showing a rapid increase in average annual temperature of the planetary-sea level (about 0.8 ◦ C over the last hundred years). The fact is that if we extrapolate the growth in the near future, it would

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appear that for some countries the situation may be catastrophic because of heavy melting of glaciers in the mountains and ice in the Arctic and Antarctic. This is a serious concern for many governments and the UN. Many scientists believe that the main reason of global warming - the so-called greenhouse effect due to the rapid increase in the Earth’s atmospheric carbon dioxide due to the rapid development of technological civilization and the increasing consumption of coal, oil and gas. In this report I will discuss some concerns with a number of scientists of the correctness of this hypothesis, and most importantly, the observed in the past on the scales of many millions, and many thousands of years (long before the technological revolution) massive changes mid-year planetary temperature at sea level increasing and decreasing with respect to the current level at 3-4 ◦ C. Of course, such large changes in climate significantly affect the biosphere. And what causes these changes? Of course, some of them - are processes in the crust and the Earth’s atmosphere. But the data for the last 100 years show that even very large volcanic eruptions cause a lowering of the average annual planetary temperature on 0.1 - 0.2 ◦ C only for a few years (see below Fig. 12). The main reason for changing the Earth’s climate and the corresponding impact on the biosphere are outside of the Earth - are processes in space, or as they say now, space weather and space climate. The main channels through which space affects the terrestrial climate and biosphere, is electromagnetic radiation, cosmic rays and cosmic dust. As it happens - will also be discussed in this report. Of course, I’ll also touch on issues such as the motion of the Sun in the Galaxy and collisions with molecular-dust clouds.

2

Long-Term CR Intensity Variations and Climate Change

About two hundred years ago famous astronomer William Herschel (1801) suggested that the price of wheat in England was directly related to the number of sunspots with periodicity about 11 years. He noticed that less rain fell when the number of sunspots was big (Joseph in the Bible, recognised a similar periodicity in food production in Egypt, about 4,000 years ago). The solar activity level is known from direct observations over the past 450 years and from data of cosmogenic nuclides (through CR intensity variations) for more than 10,000 years. Over this period there is a striking qualitative correlation between cold and warm climate periods and high and low levels of galactic CR intensity (low and high solar activity). As an example, Fig. 1 shows the change in the concentration of radiocarbon during the last millennium (a higher concentration of radiocarbon corresponds to a higher intensity of galactic CR and to lower solar activity). It can be seen from Fig. 1 that during 1000-1300 AD the CR intensity was low and solar activity high, which coincided with the warm medieval period (during this period Vikings settled in Greenland). After 1300 AD solar activity decreased and CR intensity increased, and a long cold period followed (the so

CosmicCosmic Raysother and other Space Phenomena Influenced theEarth’s Earth’s Climate Climate Rays and Space Phenomena Influenced onon the

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Fig. 1. The change of CR intensity reflected in radiocarbon concentration during the last millennium. The Maunder minimum refers to the period 1645-1715, when number of sunspots was very small. From Swensmark (2000). Table 1. Global annual mean forcing due to various types of clouds, from the Earth Radiation Budget Experiment (ERBE), according to Hartmann (1993). The positive forcing increases the net radiation budget of the Earth and leads to a warming; negative forcing decreases the net radiation and causes a cooling. (Note that the global fraction implies that 36.7% of the Earth is cloud free.) Parameter

High clouds Middle clouds Low clouds Total Thin Thick Thin Thick All 10.1 8.6 10.7 7.3 26.6 63.3

Global fraction/(%) Forcing (relative to clear sky): Albedo (SW radiation)/(W·m−2 ) -4.1 Outgoing LW radiation/(W·m−2 ) 6.5 Net forcing/(W·m−2 ) 2.4

-15.6 -3.7 8.6 4.8 -7.0 1.1

-9.9 2.4 -7.5

-20.2 -53.5 3.5 25.8 -16.7 -27.7

called Little Ice Age, which included the Maunder minimum 1645-1715 AD and lasted until the middle of 19th century).

3

Role of Solar Activity and Solar Irradiance in Climate Change

Friis-Christiansen and Lassen (1991), Lassen and Friis-Christiansen (1995) found, from four hundred years of data, that the filtered solar activity cycle length is closely connected to variations of the average surface temperature in the northern hemisphere. Labitzke and Van Loon (1993) showed, from solar cycle data, that the air temperature increases with increasing levels of solar activity. Swensmark (2000) also discussed the problem of the possible influence of solar activity on the Earth’s climate through changes in solar irradiance. But the direct satellite measurements of the solar irradiance during the last two solar cycles showed that the variations during a solar cycle was only about 0.1%, corresponding to

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Fig. 2. Changes in the Earth’s cloud coverage: triangles - from satellite Nimbus 7, CMATRIX project); squares - from the International Satellite Cloud Climatology Project, ISCCP); diamonds – from the Defense Meteorological Satellite Program, DMSP). Solid curve – CR intensity variation according to Climax NM, normalized to May 1965. Broken curve – solar radio flux at 10.7 cm. All data are smoothed using twelve months running mean. From Swensmark (2000).

about 0.3 W/m2 . This value is too small to explain the present observed climate changes (Lean et al., 1995). Much bigger changes during a solar cycle occur in UV radiation (about 10%, which is important in the formation of the ozone layer). High (1996), and Shindell et al. (1999) suggested that the heating of the stratosphere by UV radiation can be dynamically transported into the troposphere. This effect might be responsible for small contributions towards 11 and 22 years cycle modulation of climate but not to the 100 years or more of climate change that broadly considered now in scientific literature.

4

Cosmic Rays as Link between Solar Activity and Climate Change

Many authors have considered the influence of galactic and solar CR on the Earth’s climate. Cosmic Radiation is the main source of air ionization below 4035 km (only near the ground level, lower than 1 km, are radioactive gases from the soil also important in air ionization) – see review in Dorman, M2004. The first who suggest a possible influence of air ionization by CR on the climate was Ney (1959). Swensmark (2000) noted that the variation in air ionization caused by CR could potentially influence the optical transparency of the atmosphere, by either a change in aerosol formation or influence the transition between the different phases of water. Many authors considered these possibilities (Dickinson, 1975; Pudovkin and Raspopov, 1992, and others). The possible statistical connections between the solar activity cycle and the corresponding long term CR intensity variations with characteristics of climate change were considered in Dorman et al. (1987, 1988). Dorman et al. (1997) reconstructed CR intensity variations over the last four hundred years on the basis of solar activity data and compared the results with radiocarbon data.

CosmicCosmic Raysother and other Space Phenomena Influenced theEarth’s Earth’s Climate Climate Rays and Space Phenomena Influenced onon the

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Fig. 3. CR intensity obtained at the Huancayo/ Haleakala Neutron Monitor (normalized to October 1965, curve 2) in comparison with global average monthly cloud coverage anomalies (curves 1) at heights, H, for: a – high clouds, H > 6.5 km, b – middle clouds, 6.5 km >H > 3.2 km, and c – low clouds, H < 3.2 km. From Marsh and Swensmark (2000).

Cosmic rays play a key role in the formation of thunderstorms and lightnings (see extended review in Dorman, M2004, Chapter 12). Many authors (Markson, 1978; Price, 2000; Tinsley, 2000; Schlegel et al., 2001; Dorman and Dorman, 1995, 2005; Dorman et al, 2003) have considered atmospheric electric field phenomena as a possible link between solar activity and the Earth’s climate. Also important in the relationship between CR and climate, is the influence of long term changes in the geomagnetic field on CR intensity through the changes of cutoff rigidity (see review in Dorman, M2009). It can be consider the general hierarchical relationship: (solar activity cycles + long-term changes in the geomagnetic field) → (CR long term modulation in the Heliosphere + long term variation of cutoff rigidity) → (long term variation of clouds covering + atmospheric electric field effects) → climate change.

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Fig. 4. Eleven year average Northern hemisphere marine and land air temperature anomalies ∆t (broken curve), compared with eleven year average CR intensity (thick solid curve – from ion chambers 1937-1994, normalized to 1965, and thin solid curve – from Climax NM, normalized to ion chambers). According to Swensmark (2000).

5

The Connection between Galactic Cosmic Ray Solar Cycles and the Earth’s Cloud Coverage

Recent research has shown that the Earth’s cloud coverage (observed by satellites) is strongly influenced by CR intensity (Tinsley, 1996; Swensmark, 2000; Marsh and Swensmark, 2000) – see Figs. 2 and 3. Clouds influence the irradiative properties of the atmosphere by both cooling through reflection of incoming short wave solar radiation, and heating through trapping of outgoing long wave radiation (the greenhouse effect). The overall result depends largely on the height of the clouds. According to Hartmann (1993), high optically thin clouds tend to heat while low optically thick clouds tend to cool (see Table 1).

6

On Connection of Cosmic Ray Intensity Variations with Surface Planetary Temperature

The comparison is shown in Fig. 4.

7

CR Influence on the Earth’s Climate during Maunder Minimum

Results are shown in Fig. 5.

8

The Connection between Ion Generation in the Atmosphere by Cosmic Rays and Surface Covering by Clouds

Results, based on direct satellite measurements of surface covered by clouds and measurements on small balloons of ion generation in atmosphere by CR are shown in Fig. 6.

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Fig. 5. Situation in the Maunder minimum: a – reconstructed solar irradiance (Labitzke and Van Loon, 1993); b - cosmogenic concentration (Beer et al., 1991); c – reconstructed relative change of air surface temperature, ∆t, for the northern hemisphere (Jones et al., 1998). From Swensmark (2000).

Fig. 6. The relationship between the relative changes of total clouds covering surface over Atlantic Ocean ∆S/S (in %) in the period January 1984–August 1990 (Swensmark and Friis-Christiansen, 1997) and the relative changes of integral rate of ion generation ∆q/q (in %) in the middle latitude atmosphere in the altitude interval 2–5 km. From Stozhkov et al. (2001).

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The Influence of Galactic Cosmic Ray Forbush Decreases and Solar Cosmic Ray Events on Rainfall

A decrease of atmospheric ionization leads to a decrease in the concentration of charge condensation centres. In these periods, a decrease of total cloudiness and atmosphere turbulence together with an increase in isobaric levels is observed (Veretenenko and Pudovkin, 1994). As a result, a decrease of rainfall is also expected. Stozhkov et al. (1995a,b, 1996), and Stozhkov (2002) analyzed 70 events of CR Forbush decreases (defined as a rapid decrease in observed galactic CR intensity, and caused by big geomagnetic storms) observed in 1956-1993 and compared these events with rainfall data over the former USSR. It was found that during the main phase of the CR Forbush decrease, the daily rainfall levels decreases by about 17%. Similarly, Todd and Kniveton (2001, 2004) investigating 32 Forbush decreases over the period 1983-2000, found reduced cloud cover of 12-18%. During big solar CR events, when CR intensity and ionization in the atmosphere significantly increases, an inverse situation is expected and the increase in cloudiness leads to an increase in rainfall. A study of Stozhkov et al. (1995a,b, 1996), and Stozhkov (2002) involving 53 events of solar CR enhancements, between 1942-1993, showed a positive increase of about 13 % in the total rainfall over the former USSR.

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The Influence of Geomagnetic Disturbances and Solar Activity on the Climate through Energetic Particle Precipitation from Inner Radiation Belt

Near the equator, in the Brazilian Magnetic Anomaly (BMA) region, the main part of galactic and solar CR is shielded by a geomagnetic field. Significant magnetic disturbances can produce precipitation of energetic particles from the inner radiation belt and subsequent ionization of the atmosphere. The influence of solar-terrestrial connections on climate in the BMA region was studied by Pugacheva et al. (1995). Two types of correlations were observed: 1) a significant short and long time scale correlation between the index of geomagnetic activity Kp and rainfall in Sao Paulo State; 2) the correlation-anti-correlation of rainfalls with the 11 and 22 year cycles of solar activity for 1860-1990 in Fortaleza. It was found that with a delay of 5–11 days, almost every significant increase of the Kp-index (more than 3.0) is accompanied by an increase in rainfall. The effect is most noticeable at the time of the great geomagnetic storm of February 8 1986, when the electron fluxes of inner radiation belt reached the atmosphere between 18–21 February and the greatest rainfall of the 1986 was recorded on 19 February. Again, after a series of solar flares, great magnetic disturbances were registered between 19–22 March, 1991. On the 22 March 1991 a Sao Paolo station showed the greatest rainfall of the year.

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Fig. 7. Prediction of long-term CR variation on the basis of convection diffusion + drift modulation mechanisms (Dorman, 2005a,b, 2006) and comparison with observations (Climax Neutron Monitor, 11 month moving average). Table 2. Vertical cut-off rigidities (in GV) for various epochs 1600, 1700, 1800, 1900, and 2000, as well as change from 1900 to 2000 owed to changes of geomagnetic field. According to Shea and Smart (2003). Lat. 55 50 50 40

Long. (E) 30 0 15 15

Epoch 2000 2.30 3.36 3.52 7.22

Epoch 1900 2.84 2.94 3.83 7.62

Epoch 1800 2.31 2.01 2.85 5.86

Epoch 1700 1.49 1.33 1.69 3.98

Epoch 1600 1.31 1.81 1.76 3.97

Change 1900–2000 −0.54 +0.42 −0.31 −0.40

45 40 20 20

285 255 255 300

1.45 2.55 8.67 10.01

1.20 3.18 12.02 7.36

1.52 4.08 14.11 9.24

2.36 4.88 15.05 12.31

4.1 5.89 16.85 15.41

+0.25 −0.63 −3.35 +2.65

N. N. N. N.

50 40 35

105 120 135

4.25 9.25 11.79

4.65 9.48 11.68

5.08 10.24 12.40

5.79 11.28 13.13

8.60 13.88 14.39

−0.40 −0.23 +0.11

Asia Asia Japan

−25 −35 −35

150 15 300

8.56 4.40 8.94

9.75 5.93 12.07

10.41 8.41 13.09

11.54 11.29 10.84

11.35 12.19 8.10

−1.19 −1.53 −3.13

Australia S. Africa S. Amer.

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Region Europe Europe Europe Europe Amer. Amer. Amer. Amer.

Description of Long-Term Galactic Cosmic Ray Variation by Both Convection-Diffusion and Drift Mechanisms with Possibility of Forecasting of Some Part of Climate Change in Near Future Caused by Cosmic Rays

The propagation and modulation of galactic CR (generated mostly during Supernova explosions and in Supernova remnants in our Galaxy) in the Heliosphere

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are determined by their interactions with magnetic fields frozen in solar wind and in coronal mass ejections (CME) with accompanied shock waves (produced big magnetic storms during their interactions with the Earth’s Magnetosphere). The most difficult problem of monitoring and forecasting the modulation of galactic CR in the Heliosphere is that the CR intensity in some space-time 4D-point is determined not by the level of solar activity at this time-point of observations and electro-magnetic conditions in this space-point but by electromagnetic conditions in total Heliosphere for period of many months. By other words, the conditions in total Heliosphere are determined by development of solar activity during many months before the time-point of observations. It is main cause of so called hysteresis phenomenon in connection galactic CR – solar activity. From other hand, detail investigations of this phenomenon give important possibility to estimate conditions in and dimension of Heliosphere. To solve described above problem of CR modulation in the Heliosphere, we considered as the first step behavior of high energy particles (more than several GeV, for which the diffusion time of propagation in Heliosphere is very small in comparison with characteristic time of modulation) on the basis of neutron monitor data in the frame of convection diffusion theory, and then take into account drift effects. For small energy galactic CR detected on satellites and space probes we need to take into account also additional time lag caused by diffusion in the Heliosphere. Then we consider the problem of CR modulation forecasting for several months and years ahead. Results are shown in Fig. 7.

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Influence of Long-Term Variation of Main Geomagnetic Field on Global Climate Change through Cosmic Ray Cut-Off Rigidity Variation

As it was shown in Dorman (M1957, M2009), CR intensity of any CR component IK changed with variation of cut-off rigidity RC as ∆IK /IK0 = −∆RC ∗ WK (RC , RC ), where WK (RC , R) is the coupling function. Results of CR cut-off rigidity variations for the last 400 years are shown in Table 2. Let us outlined that geomagnetic long-term CR variations have local character, in some places of our planet RC decreases and CR intensity increases (what leads to increasing cloudiness, raining, and decreasing surface temperature), but in other places (as we can see from Table 2) the sign of changes is inverse. It is important to investigate, may be some great historical processes in the past, connected with sudden climate change, were caused by big local changes of CR cut-off rigidities.

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Project ‘Cloud’ in CERN as an Important Step in Understanding the Link Between Cosmic Rays and Cloud Formation

In Fig. 8 is shown the ‘CLOUD’ detector, and in Fig. 9 – the scheme of clouds formation.

CosmicCosmic Raysother and other Space Phenomena Influenced theEarth’s Earth’s Climate Climate Rays and Space Phenomena Influenced onon the

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Fig. 8. Vertical section through the CLOUD detector in CERN. According to Fastrup et al (2000).

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Fig. 9. The scheme on possible role of cosmic rays in the clouds formation. From Fastrup et al (2000).

Fig. 10. Changes of air temperature near the Earth’s surface for the last 520 million years according to the paleo-environmental records. From Veizer et al. (2000).

CosmicCosmic Raysother and other Space Phenomena Influenced theEarth’s Earth’s Climate Climate Rays and Space Phenomena Influenced onon the

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Fig. 11. Changes of planetary surface temperature ∆t relative to modern epoch (bottom thick curve) and dust concentration (upper thin curve) over the last 420 000 years. From Petit et al. (1999).

Fig. 12. Yearly average values of the global air temperature t (in ◦ C) near the Earth’s surface for the period from 1880 up to 2005. Arrows show the dates of the volcano eruption with the dust emission to the stratosphere and short times cooling after eruptions. From Ermakov et al. (2006).

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The Influence on the Earth’s Climate of the Solar System Moving around the Galactic Centre: Mostly Effects of Cosmic Rays and Cosmic Dust

In Fig. 10 are shown changes of planetary average surface air temperature for the last 520 million years according to the paleo-environmental records.

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The Influence of Molecular-Dust Galactic Clouds and Interplanetary Zodiac Cloud on Earth’s Climate

Results are shown in Fig. 11.

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Global Climate Change and Volcano Eruptions

In Fig. 12 are shown average values of the global air temperature near the Earth’s surface for the period from 1880 up to 2005. It can be seen influences of big volcano eruptions: after eruption temperature decreased on 0.1-0.2 ◦ C and then in few days temperature increased to the level before eruptions. From Fig. 12 follows that in the present period volcano eruptions cannot be cause of the observed global warming.

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Discussion and Conclusions

Many factors from space and from anthropogenic activities can influence the Earth’s climate. It is important that all possible space and internal factors will be considered, and from an analysis of past climate changes, we can identify our present phase and can predict future climate change. For example, when considering CR variations as one of the possible causes of long-term climate change we need to take into account not only CR modulation by solar activity but also the local change of geomagnetic cut-off rigidities (internal factor). Paleo-magnetic investigations show that during the last 3.6 × 106 years the magnetic field of the Earth changed sign several times, and the Earth’s magnetic moment sometimes having a value of only one-fifth of its present value (Cox et al., 1967); during these periods CR intensity will increase with corresponding increase cloudiness and decrease of the surface temperature. During the last several hundred million years the Sun has moved around the Galactic Centre through the galactic arms several times with resultant climate changes. For example, considering the effects due to galactic molecular-dust and Supernova concentrated in the galactic arms, we can see that during the past 5.2 × 108 years (Fig. 10), there were four periods with surface temperatures lower than at present time, and four periods with higher temperatures. On the other hand, during the past 420 thousand years there were four decreases of temperature (the last one was 20 – 40 thousand years ago: the so called big ice period), and five increases of temperature, the last of which starts 15-20 thousand years ago. From Fig. 11 can be seen, that now we are near the maximum of planetary temperature and at present time on scale of thousand years more probably is expected slowly cooling with time during about 10-20 thousand years forward to the next big ice period.

Acknowledgements Let me use this opportunity to acknowledge Ministry of Science of State Israel, Tel Aviv University, Israel Space Agency, and Golan Research Institute for continue support of our Observatory, and Azerbaijan Science Foundation for kind invitation to take part in Baku Conference and productive collaboration.



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Bibliography Cox A., G.B. Dalrymple, and R.R. Doedl, 1967. Scietific American, 216, No. 2, 44−54. Dickinson R.E., 1975. Bull. Am. Met. Soc., 56, 1240−1248. Dorman L.I., M1957. Cosmic Ray Variations, Gostechteorizdat, Moscow. Dorman L.I., M2004. Cosmic Rays in the Earth’s Atmosphere and Underground, Kluwer Academic Publishers, Dordrecht/Boston/London. Dorman L.I., 2005a. Adv. Space Res., 35, 496–503. Dorman L.I., 2005b. Annales Geophysicae, 23, No. 9, 3003–3007. Dorman L.I., 2006. Adv. Space Res., 37, 1621–1628. Dorman L.I., M2009. Cosmic Rays in Magnetospheres of the Earth and other Planets, Springer, Germany. Dorman L.I. and I.V. Dorman, 2005. Adv. Space Res., 35, 476–483. Dorman L.I., I.Ya. Libin, M.M. Mikalayunas, and K.F. Yudakhin, 1987. Geomagnetism and Aeronomy, 27, 303–305. Dorman L.I., I.Ya. Libin, and M.M. Mikalajunas, 1988a. Regional Hydrometeorology, Vilnius, 12, 119–134. Dorman L.I., I.Ya. Libin, and M.M. Mikalajunas, 1988. Regional Hydrometeorology, Vilnius, 12, 135–143. Dorman L.I., G. Villoresi, I.V. Dorman, N. Iucci, and M. Parisi, 1997. Proc. 25-th Intern. Cosmic Ray Conference, Durban (South Africa), 7, 345–348. Dorman L.I., I.V. Dorman, N. Iucci, M. Parisi, Y. Ne’eman, L.A. Pustil’nik, F. Signoretti, A. Sternlieb, G. Villoresi, and I.G. Zukerman, 2003. J. Geophys. Res., 108, No. A5, 1181, SSH 2 1–8. Ermakov V., V. Okhlopkov, and Yu. Stozhkov, 2006. Proc. European Cosmic Ray Symp., Lesboa, Paper 1–72. Fastrup B., E. Pedersen, E. Lillestol et al. (Collaboration CLOUD), 2000. Proposal CLOUD, CERN/SPSC, (2000-021. Friis-Christiansen E. and K. Lassen, 1991. Science, 254, 698–700. Haigh J.D., 1996. Science, 272, 981–984. Hartmann D.L., 1993. In Aerosol-Cloud-Climate Interactions (ed. P.V. Hobbs), Academic Press, 151. Herschel H., 1801. Philosophical Transactions of the Royal Society, London, 91, 265–318. Labitzke K. and H. van Loon, 1993. Ann. Geophys., 11, 1084–1094. Lassen K. and E. Friis-Christiansen, 1995. J. Atmos. Solar-Terr. Phys., 57, 835– 845. Lean J., J. Beer, and R. Breadley, 1995. Geophys. Res. Lett., 22, 3195–3198. Markson R., 1978. Nature, 273, 103–109. Marsh N. and H. Swensmark, 2000. Space Sci. Rev., 94, 215–230. Ney E.R., 1959. Nature, 183, 451–452. Petit J.R., J. Jouzel, D. Raunaud, at.al., 1999. Nature, 399, 429–436. Price C., 2000. Nature, 406, 290–293. Pudovkin M.I. and O.M. Raspopov, 1992. Geomagn. and Aeronomy, 32, 593– 608.

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Pugacheva G.I., A.A. Gusev, I.M. Martin et al., 1995. Proc. 24th Intern. Cosmic Ray Conf., Rome, 4, 1110–1113. Schlegel K., G. Diendorfer, S. Them, and M. Schmidt, 2001. J. Atmos. SolarTerr. Phys., 63, 1705–1713. Shea M.A. and D.F. Smart, 2003. Proc. 28th Intern. Cosmic Ray Conf., Tsukuba, 7, 4205–4208. Shindell D., D. Rind, N. Balabhandran, J. Lean, and P. Lonengran, Science, 284, 305–308. Stozhkov Yu.I., 2002. J. Phys. G: Nucl. Part. Phys., 28, 1–11. Stozhkov Yu.I., P.E. Pokrevsky, I.M. Martin et al., 1995a. Proc. 24th Intern. Cosmic Ray Conf., Rome, 4, 1122–1125. Stozhkov Yu.I., J. Zullo, I.M. Martin et al., 1995b. Nuovo Cimento, C18, 335– 341. Stozhkov Yu.I., P.E. Pokrevsky, J.Jr. Zullo et al., 1996. Geomagn. and Aeronomy, 36, 211–216. Stozhkov Yu.I., V.I. Ermakov, and P.E. Pokrevsky, 2001. Izv. Russian Ac. of Sci., Ser. Phys., 65, No. 3, 406–410. Swensmark H., 2000. Space Sci. Rev., 93, 175–185. Swensmark H. and E. Friis-Christiansen, 1997. J. Atmos. Solar-Terr. Phys., 59, 1225–1232. Tinsley B.A., 1996. J. Geomagn. Geoelectr., 48, 165–175. Tinsley B.A., 2000. Space Sci. Rev., 94, 231–258. Todd M.C. and D.R. Kniveton, 2001. J. Geophys. Res., 106, No. D23, 32031– 32042. Todd M.C. and D.R. Kniveton, 2004. J. Atmosph. and Solar-Terrestrial Physics, 66, 1205–1211. Veizer J., Y. Godderis, and I.M. Francois, 2000. Nature, 408, 698–701. Veretenenko S.V. and M.I. Pudovkin, 1994. Geomagnetism and Aeronomy, 34, 38–44.

Does climatic changes could have destroyed great civilizations? Jean Pierre Rozelot1 , Zahra Fazel2 1 Universit´e de la Cˆ ote d’Azur (CNRS-OCA, Nice) & 77 ch. des Basses Mouli`eres, 06130 Grasse (F) E-mail: [email protected] 2 University of Tabriz, Fac. of Phys., Dep. of Theoretical and Astrophys., Tabriz, Iran. E-mail: [email protected]

Abstract. Most of the past civilizations have undergone a collapse, i.e. a loss of political and socio-economic power, usually accompanied by a dramatic decline in demography. We will briefly explore here the effects of drastic climate change on society vulnerabilities, such as the collapse of the Akkadian Empire, those of the Classical Mayan civilization or the Greenland colonies. We recall the disastrous effect on commodity prices at the beginning of the Little Ice Age. We show that if social signatures of the collapse varied geographically, such dislocations were sufficient to destabilize the region and to fundamentally alter the social, political, and economic fabric of unified culture. Some cultures were able to dominate such abrupt climatic changes (the Tang dynasty in China for instance, due to a more structured society). However, taking as an example the Nile floods, which seem to regularly follow the solar activity cycle and due to the irradiance reconstruction more than 8000 years in the past, we wonder if a large modulation of the solar output cannot be retrieved from these analysis. Thus, the history of solar output, the history of the Earth’s climate and the history of past disasters shape a new global knowledge that encourage us to revisit the question posed in the title of this paper.

1

Introduction

It is undeniable that the Earth’s temperature has increased over the past century, as all studies in progress on the question do show; several reports agree on this. The focus is on scenarios for the future, the main idea being to draw attention to the reduction of human production of greenhouse gazes, considered as the main driver of global warming. Underlying this idea is the protection of mankind and the protection of our world, which otherwise could be profoundly altered and could be subject to big modifications leading to deterioration in our lives and our way of life. However, little attention has been paid up to now to big climatic changes that may have occurred in the past, and which could have lead to the flourishing of civilizations, or on the contrary to their destruction. Obviously, major exceptions to this opinion are the Little Ice Age and the Climatic Medieval Optimum periods of time, which have already been extensively studied.

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Our intention here is to assess some known dramatic climate episodes from an historical perspective, linked as far as possible with atmospheric physics and/or solar physics. We are aware that our modest review is not a complete tour of this question, but we will just give an overview of what could be done, and suggest some ideas that could be further developed. One of the major issues shown here is that some significant climatic events observed today may have already occurred in the past and the positive trend observed today could be part (but only a part) of a large modulation in amplitude of the solar irradiance variability, at least in its EUV component, the only one which could have an impact on our atmosphere. In a first part of the paper we will review some climatic episodes which have caused collapses of civilizations. By collapse, we imply significant and major environmental problems leading to a destruction of the society, which was flourishing. Some of the societies were able to progressively restore their cultural highlights, some of the others completely disappeared (for instance the vanishing of the Easter Islanders, certainly due to a large deforestation by the inhabitants themselves, but still controversial). Our conclusion emphasizes the need to better link the past social disasters with major episodes of climate change and probably with significant variations of the solar UV irradiance.

2

The Flood

One of the oldest natural disasters is certainly the Flood, reported in Genesis, chapter 6. It is known today that this narrative was definitely written first by the Sumerians, with a nearly identical text, the arrival of ATU–Napishtim (or Outanapishim) on the Nashir Mount; Babylonian writings on the same topic were also discovered. This flood left such a memory of distress that it was regarded as a means of getting rid of humanity. Three versions have reached us: the Poem of Atrahasis, the Ziusudra Epic (circa -1600) and most notably the Gilgamesh Epic, which is known by copies made in particular in Niniveh, during the 1st millennium BC. Many points of the Babylonian text coincide with that of the Bible, and the similarity is too striking to be due to chance. Thus clay tablet 11, lines 127 to 131 recounts that ”during seven days and seven nights, the wind persisted, the torrential hurricane crushed the Earth (...). When arrived the seventh day, the torrential hurricane (which) prevailed, was calmed, then the sea was kept silent and the bad wind ceased”. The Mesopotamian discoveries confirmed what was said in the Bible, ensuring certain veracity to these accounts, although the Babylonian flood lasts seven days and the biblical one forty. This first known devastating cataclysm left such a mark on the spirits that it was referred to again in several languages. It is highly likely that the climate of the Near East was particularly affected, maybe due to a deglacial time and a rise in the water level.The Sumerian texts indicate that agriculture developed again after the flood, or at least



Climatic chage and great civilizations

survived. Interpretation is not a matter here; what counts is the fact that a major climatic event took place (some 3000 years ago, see Figure 1), which then made it possible to restore a flourishing civilization.

3

The collapse of the Akkadian Empire

The Fertile Crescent, a region, alongside Mesopotamia (which lies between the rivers Tigris and Euphrates) saw the emergence of early complex and high state level societies during the succeeding Bronze Ages (mainly during the early dynastic periods from around 2900 to 2334 BC). The Akkadian Empire, under the rule of Sargon, who reigned from ca. 2334 to 2218 BC, extended to modern-day Syria, Asia Minor, Iran and North of the Persian Gulf. During that time,the flourishing civilization linked the agricultural hinterlands of northern Mesopotamia with the complex city-states in the South. The Akkadians were thus able to control long-distance trade, developing agricultural processes, recording their policy in increasingly sophisticated writings. The Sumerian civilization lasted more than three thousand years, but they lost their influence after more than a century of prosperity, and collapsed abruptly near 2200 BC (Weiss et al., 1993). A new prosperous era re-initialized by smaller sedentary populations occurred approx 300 years later. It was suggested (Weiss et al., 1993) that this decline occurred due to a marked increase in aridity and wind circulation, subsequent to a volcanic eruption, which induced a considerable degradation of land-use conditions. After four centuries of urban life, this abrupt climatic change seems to have caused abandonment of the city of Tell Leilan1 , accompanied by a regional desertion, and driving the collapse of the Akkadian empire based in southern Mesopotamia, mainly by famines. Paleoclimate records from the Middle East have documented shifts to much more arid conditions commencing around 2200 BC, as indicated by Cullen (2000). They report that the geochemical correlation of volcanic ash shards between the archeological site and marine sediment record establish a direct temporal link between Mesopotamian aridification and social collapse, implicating a sudden shift to more arid conditions as a key factor contributing to the collapse of the Akkadian empire. Synchronous collapses in adjacent regions suggest that the impact of the abrupt climatic change was extensive (see for example the abrupt climatic shift recorded on the eastern margin of the Tibetan Plateau, in the western part of the Chinese Loess Plateau and in the vast Inner Mongolian Plateau, and its cultural response in Chinese cultural domains, Liu and Feng (2012)). 1

Tell Leilan was one of the three major city-states integrated into the Akkadian empire. In the nearby site of Abu Hgeira, archeologists noted a thin (0.5 cm) volcanic ash layer.

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The collapse of the Classical Maya civilization (800 AD-1000 AD)

The ancient Maya civilization occupied the eastern third of Mesoamerica, primarily the Yucatan Peninsula. It was not one unified empire, but rather a multitude of separate entities with a common cultural background. The early pre-classical period lasting from 2000 BC to 250 AD was followed by the major flowering of the Mayan society, the Classical period, from perhaps the 2nd century AD to the late 8th century. For generations, the Maya thrived in an advanced, complex civilization in modern-day Central America. In particular, they built large stone monuments, water-storage systems, developed a system of writing, using elaborate symbols. Astronomy was well developed and they conceived a novel and very accurate (and complicated) calendar. Then, the Mayans entered a new period of partial ”Collapse” called the ”Terminal Classic” (800 AD to 1000 AD). In 800 AD, before this collapse, the population has been estimated at about 3 million. By 1000 AD it was less than a million or so. Then, around A.D. 1100 Mayan civilization disintegrated. Various causes have been suggested including foreign invasion, intercity warfare, soil exhaustion, and revolt of the lower classes. All of these events appear to have taken place at diverse places throughout the region during the collapse, but what was the initiating cause? Climate change might have been one of the major reasons. Hodell et al. (2001) analyzed lake-sediment cores from the Yucatan Peninsula (Mexico), to reconstruct the climate history of the region over the past 2600 years. They found a recurrent pattern of drought with a dominant periodicity of 208 years (similar to the documented 206-year period in records of cosmogenic nuclide production), that they thought to reflect variations in solar activity, concluding that a significant component of century-scale variability in Yucatan droughts could be explained by solar forcing. Furthermore, they noted that some of the maxima in the 208-year drought cycle correspond with discontinuities in Mayan cultural evolution, suggesting ”that the Maya were affected by these bicentennial oscillations in precipitation”. Haug et al. (2003), analyzing the sediments in the Cariaco Basin of the southern Caribbean, reported that the rapid expansion of the Maya from 550 to 750 AD took place during a relatively wet period. However, from 750 to 950 the southern Maya experienced devastating climate change, a generally dry period began about 760 AD. The dry period continued for about 140 years. It was punctuated by a series of more severe multi-year droughts, about 760 AD, 810 AD, 860 AD, and 910 AD, which are shown in the detailed record of the rainfall (see also Feynman (2007)). They are not the first authors to suggest dry spells brought about the end of the Maya. Ridley et al. (2012) reconstructed a monthly-scale palaeo-rainfall through the analysis of a Belizean stalagmite to trace a 2,000-year history of rainfall in more detail than ever before. They show that pre-Columbian deforestation would have biased the climate in Mesoamerica towards a drier



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mean state, amplifying drought in the region. They noted that ”Classic Maya civilization collapsed over centuries as rain dried up, disrupting agriculture and causing instability that led to wars and the crumbling of large cities. A final major drought after the political collapse of the Maya may be what kept the civilization from bouncing back”. Cook et al. (2012), using reconstructions of vegetation stretching back 2,000 years, revealed how much the switch from forest to crops, such as corn, would alter climate. Their results suggested that when deforestation was at its maximum, it could account for up to 60 percent of the drought; the switch from trees to corn reduces the amount of water transferred from the soil to the atmosphere, which reduces rainfall. Thus deforestation does not explain the entire drought, but it does explain a substantial portion of the overall drought that is thought to have occurred. Turner et al. (2012) indicated that large-scale Maya landscape alterations and demands placed on resources and ecosystem services generated highstress environmental conditions that were amplified by increasing climatic aridity. Such changing environmental conditions generated increasing societal conflicts, contributing to diminished control by the Maya elite, that ”led to decisions to move elsewhere in the peninsular region rather than incur the high costs of maintaining the human–environment systems in place”. In other words, by clearing the forest, the Mayans may have aggravated a natural drought, which peaked about the time the empire came to an end and population declined dramatically. This last version highlights the fact that ”the Maya case lends insights for the use of paleo–and historical analogs to inform contemporary global environmental change and sustainability”. Other authors (Dunning et al., 2012), (Luzzader et al., 2012) studied also in details the Maya collapse to conclude that three factors influence the vulnerability and resilience of coupled human–environment systems: ”options for change, system rigidity, and resilient capacity”. Authors state Maya may have collapsed, if excluding internal political strife and foreign invasions, because of the cascading effects of an overextended irrigation system due to climate change (severe droughts). They abandoned canal maintenance and territories became places of ill fortune and returned to the forest.

5

The collapse of the Greenland colonies

At the time of the Maya collapse, i.e. around the year 1000, the Norse were leaving their home territories and were marauding in Europe and beyond. Erik the Red, a Viking explorer sailed from Iceland in 982 AD and discovered a new land with an inviting fjord landscape and fertile green valleys. He was extremely impressed with this new country’s resources and he called the territory ”Greenland”. He was certainly very persuasive, as a new expedition was sent in 985. His son returned to Greenland and by the year 1000, the Viking societies numbered some 3,000 inhabitants dispersed on 300-400

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Fig. 1. The Total Solar Irradiance (TSI) reconstruction as done through the magnetic components of the solar surface (sunspots and faculae), after (Vieira et al., 2011) and through the Holocene period (different curves are shown dut to the use of different proxies). It can be seen that in the past, TSI peaked as high as it is to-day (such as around the years -2000). We tried to identify periods of time where the TSI was of very low activity with the collapse of civilizations. Even if this identification is still crude, its appear that the correlation could be convincing. Note that the influence of the TSI on the upper atmosphere can be done only in the EUV and UV part of the irradiance, for which the ratio max/min can reach a factor of 2. However uncertainties show how complicated evidence for Collapses can be and how difficult it is to assign drivers based on archeo–climatic effects.

farms up to the North. The Viking society survived for about 500 years but the colonies collapse definitively in 1420–1430. The reason for its disappearance remains a great mystery. Until the twentieth century, the collapse was attributed to the aggressive nature of the Vikings and their contacts with the the ancestors of the modern Inuit (Seaver , 1996). However, more recently, emanating from both the limited documentary evidence for the period and the expanding archaeological record, colder climate was advanced as a better argument. Most notably, recent analysis of the central Greenland ice-core, largely corroborated by data obtained from tree-ring studies and sea-sediments have produced an apparently incontrovertible paleo-climatic argument for the failure of the Norse colony in Greenland (see a nice discussion by Slak (2002)). Fluctuation in climate is significant because it affects the length of growing seasons and the movement of prey animals such as seals, caribou and walrus. During the 15th century, ship communication dwindled between Greenland and supporting population centers. Icebergs also choked



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fjords where the Greenlanders hunted the dying migratory seal population. Lastly the growing season became too short to support the preferred livestock kept by the Norse (Diamond , 2006; Norman, 2011). D’Andrea et al. (2011) reconstructed 5,600 years of climate history from two lakes in Kangerlussuaq, near the Norse ”Western Settlement”. Unlike ice cores taken from the Greenland ice sheet hundreds of miles inland, their core measurements in this new lake reflect air temperatures where the Vikings lived (as well as those experienced by the Saqqaq and the Dorset Stone Age cultures that preceded them). The records show that temperatures dropped several degrees in a span of decades, and mainly in timing with the archaeological records of abandonment of the Norse cultures. They concluded by suggesting that abrupt temperature changes profoundly impacted on human civilization in this region. Ribeiro focusing on analysis of a marine sediment record to reconstruct climate change over the last 1500 years (at a 30-40 years resolution) in Disko Bay (Western Greenland) reported that the AD 1350 collapse of Viking settlers may have been caused by declining temperatures and a rise in sea-ice. The authors suggest the collapse of the Greenland Norse presents a historical example of a society which failed to adapt to climate change. The authors noted that circa 500 to 1050 AD, the sea-surface temperatures in Disko Bay were out-of-phase with Greenland ice-core reconstructed temperatures and marine proxy data from South and East Greenland. This was probably governed by an NAO-type pattern, which results in warmer sea-surface conditions with less extensive sea ice in the area for the later part of the Dark Ages cold period (circa AD 500 to 750) and cooler conditions with extensive sea ice inferred for the first part of the Medieval Climate Anomaly (MCA) (c. AD 750 to 1050). After c. AD 1050, the marine climate in Disko Bay becomes in-phase with trends described for the NE Atlantic, reflected in the warmer interval for the remainder of the MCA (circa AD 1050-1250), followed by cooling towards the onset of the Little Ice Age after AD 1460. They concluded that inferred scenario of climate deterioration and extensive sea ice is concomitant with the collapse of the Norse Western Settlement in Greenland at circa AD 1350. Two criticisms have been made, one of the date of the ”collapse” and the other one of the locus of the sediment analysis, which does not cover the whole of Greenland, but only a small geographic era. On the first point, it is testified that the last official contact with the Greenland settlements was a wedding at Hvalsøfjord Church in the Eastern Settlement on September 16, 1408. The last recorded ship left Greenland in 1410. The last contact the Greenlander Vikings had with other Europeans was in 1448 as seen by a letter sent to the Vatican city. On the second point, it can be answered that the Vikings primarily settled in two areas on the western coast of Greenland, known confusingly as Eastern Settlement and Western Settlement (approximately 300 miles north). At the peak of prosperity, the Western Settlement supported

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perhaps 4,000 inhabitants spread out in small farms, and the smaller Eastern settlement comprised about 1,000 inhabitants. Archaeological and written records show the Western Settlement persisted until sometime around the mid-1300s, with a dramatic drop in population. The Eastern Settlement is believed to have completely vanished in the first decade of the 1400s, as said by the last above-mentioned letter (see Francis (2011))2 .

Fig. 2. Reconstruction of the Total Solar Irradiance (TSI) since the beginning of our era, after (Vieira et al., 2011). Identification of the Maya and Norse collapses can be easily done with low TSI activity (same remark as in the previous figure). The England prices transition (see figure 3) appears clearly, as well as the deep LIA.

6

Nile floods

Egypt is a gift of the Nile, and gives life, said Herodotus. Each spring, water ran off the mountains and the Nile flooded. As the flood waters receded, 2

”In the early 1340s, something was amiss in the Western Norse Settlement in Greenland. They usually paid their taxes and church tithes with natural goods as they lacked money. While sometimes late to be sure, they usually managed to send walrus tusks and tough walrus skin rope, polar bear skins and other furs, and the valuable white or grey gyrfalcons favored by kings, to pay their bills in Norway. The Western Settlement had not paid its taxes since 1327 (...). This date of 1342 made historical sense based on sailing dates.



Climatic chage and great civilizations

black rich fertile soil was left behind. Thus floods provided a crucial role in the development of Egyptian civilization. Silt deposits from the river made the surrounding land fertile because the river overflowed its banks nearly annually. Because of the annual flooding of the Nile, the ancient Egyptians enjoyed a high standard of living compared to other ancient civilizations. The rhythm of the level of the Nile river is well known due to Prince Omar Toussoun (1925) who transcribed data recorded between 622 and 1470 by a nilometer located at the Rawdah island in Cairo. Other data extending the period of time up to 1915 (at the end of the British occupation) can be found in many Arabic history books, such as those of Ibn Taghribirdi (1970) (during the years 1382–1469) and Al-Ayni (1988). A collection and a compilation has been made by Basha (1916) in 1890 and 1916. There have been many nilometers since Old Kingdom, all of them using the same scale. Periodograms made by Basurah (2005) and Ruzmaikin et al. (2006) show that periods of 667, 435, 323, 244-260 for long term periods of time can be retrieved, as well as 143, 125 years, 88, 64, and 24 years for shorter term periods. Their conclusion is that the Nile flooding is an indirect indicator of long solar cycles.

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Does Solar activity pay a role?

The evolution of the averaged magnetic flux can be computed from decadal values of cosmogenic isotope concentrations recorded in natural archives employing a series of physics-based models connecting the processes from the modulation of the cosmic ray flux in the heliosphere to their record in natural archives (Vieira et al., 2011). Mixing these two sets of parameters, it has thus been possible to reconstruct the solar irradiance back to the years -1000 and -8000 (i.e. BC). Results are presented in Figures 1 and 2. It can be seen that the solar irradiance reached in the past significant high values, of a level quasi similar as it is today (such as in ≈ -2000). The analysis is in agreement with earlier reconstructions of the solar activity. Obviously, as can be seen through a rough computation, the total solar irradiance variations are too small to account for significant variations in our atmosphere, and consequently in our climate. By contrast, the amplitude of the spectral solar irradiance in UV and EUV is far higher, reaching a factor of two at around 120 nm (Marchand , 2010). Its effect on the upper atmosphere is thus more substantial, as described for instance by Lefebvre et al. (2010); the signal may react on the chemistry of the atmosphere, and particularly at 130 nm. Most of the existing mechanisms –attempting to explain the transition of the solar signal from stratosphere to the Earth surface– put the accent on the dynamical interaction between stratosphere and troposphere (Kodera et al., 2005; Haigh et al., 2005; Haigh and Blackburn, 2006).

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We tried to identify the collapses of civilizations with significant drops in the TSI, as shown in Figure 1 and 2, bearing in mind the above considerations. We added the dramatic climatic transition at ≈ 4000 yr BP as seen before. We are aware that such links are subject to some controversy. Indeed, many previous discussions have already been made (see for example, for recent papers Montgomery (2012), Butzer and Endfield (2012)), but we think that more careful attention must be paid in addressing solar UV and EUV variability. The list of possible examples can be extended with what happened during the Little Ice Age (LIA), a well known period of cold winters that occurred not only all over Europe, but also in the western part of the US, in Canada and very likely on other parts of the world. LIA spans a period of time ranging from around 1550 to 1850, the years 1590–1675 being of severe icy winters. If no civilizations disappeared at that time, it is mainly due to the structure of the societies, which were more organized than the oldest civilizations studied before. However, prices of essential goods rose significantly. An example is shown in Figure 3. The link with the lack of solar activity has attracted special attention because these two indicators have been proposed to correlate (by several authors, among them M¨ orner (2010) or Soon (2009), Soon (2013) for example). If ”collapse” of the European civilizations is not really an appropriate term, societies were considerably weakened and populations were particularly vulnerable. The lesson of this history is that modern societies may carry capacities to deal with long-term threats.

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Conclusion: Are they feedbacks between climate change and human evolution?

Several other (unexplained) dramatic collapses of civilization occurred in the past. One well known is the Mycenaean cultural period of the Bronze Age (c. 1600 BC – c. 1100 BC). The Mycenaean civilization flourished during the period roughly between 1600 BC and 1100 BC, when it perished with the collapse of Bronze-Age civilization in the eastern Mediterranean. The collapse is commonly attributed to invasions, which is not historically verified. Other theories describing natural disasters and climate change have been advanced as well. The Hittites, in Anatolia, were the first people to work iron, from about 1500 BC. They were also one of the first people to use writings, inventing cuneiform and reaching its height during the mid 14th century (BC). They establish an empire which reaches northern Syria, east of the Euphrates, and extends down the Mediterranean coast to confront the Egyptians. In the 12th century BC, the Hittite empire suddenly collapses, may be due to terrifying intruders, here also not testified by historical chronicles. They collapse around the same time as the Mycenaeans. Coincidence or long dry period for which finally famines were particularly disastrous?



Climatic chage and great civilizations

Fig. 3. Price history is always linked to social history and the study of living conditions. This figure shows the influence of Solar Activity (Maunder Minimum) on the state of the Wheat Market in Medieval Ages. When climate became more and more colder, prices were increasing. After Lev A. Pustil’nik & Gregory Yom Din, Sol. Phys., 2004, 223, p. 225-356. See also: S¨ oderberg, J., Prices in the Medieval Near East and Europe, in ”Towards a Global History of Prices and Wages”, 19-21 Aug. 2004, http://www.iisg.nl/hpw/conference.html

The Tang dynasty in China (one of the most creative imperial dynasties, ranging from 618 to 907) collapses around the same time as the Mayas. Is this also pure coincidence? Are all these civilizations destroyed by the same factors? In his book ”Collapse”, Jared Diamond postulates five factors which may lead to the decline and fall of civilizations: (i) Hostile relations with neighbors, (ii) loss of support from ”home” or trade partners, (iii) environmental degradation, (iv) climate change and (v) faulty social values. We think here that culture and values significantly affect a society’s ability to adapt and respond to change, particularly with rapid and severe climatic conditions. However, a lot of other elements could potentially also contribute to a collapse, such as a loss in the ecosystems and/or deforestation, leading to a rarefaction of animals and plants, essential for human survival; epidemiological factors decimating population, etc... What we have tried to underline here is the possible physical origin of important climatic changes, for which the severity in temperature could be linked to the deep variations in the UV part of the solar irradiance.

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The reasons for the decline and dissolution of all the civilizations described in the previous sections cannot with certainty be attributed to a unique factor, but there are obvious criteria for thinking that the climate played a major role: prolonged periods of droughts or floods, successive severe winters, lead to lack of agriculture crops and famines. Historical studies of such disasters continue to occupy a marginal position, but this is slowly changing today. It would be of interest to link historical climatology and disaster studies, as Christian Pfister wrote in his paper ”Weeping in the Snow, the second period of Little Ice Age-type impacts” (Pfister , 2005). Without forgetting, and without sinking in the catastrophism, that our own and current civilization may also collapse, as underlined by Ehrlich and Ehrlich (2012). There are undoubtedly significant lessons to be learn from all these collapses and it is a lesson of adaptation, of being able to adjust our values and our life style when climate is changing (such as at the present time). Historical collapse of ancient states poses intriguing social-ecological questions as stated by (Butzer , 2012). That is a crucial challenge we are facing today.

Acknowledgments Authors cordially thank the organizers of the Solar Conference held in Baku in June 2015 by the Science Development Foundation under the President of the Republic of Azerbaijan, and the fruitful time spent there. One of us (JPR) is grateful to the International Space Science Institute (ISSI) in Bern (CH) where he is repeatedly invited as a visitor scientist.



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Haigh, J.D., Blackburn, M., Day, R. (2005), The Response of Tropospheric Circulation to Perturbations in Lower-Stratospheric Temperature, J. Clim., 18, 3672–3685. doi: 10.1175/JCLI3472.1 Haigh J.D. and Blackburn, M. (2006), Solar Influences on Dynamical Coupling Between the Stratosphere and Troposphere, Space Sci. Rev., 125, 331–344. doi: 0.1007/s11214-006-9067-0 Hodell, D.A., Brenner, M., Curtis, J.H., Guilderson, T. (2001), Solar forcing of drought frequency in the MayaLowlands. Science, 292, 1367–1370. doi:10.1126/science.1057759 Haug, G., G¨ unther, D., Peterson, L.C., Sigman, D.M., Hughen, K.A., Aeschlimann, B. (2003), Climate and the collapse of Maya civilization. Science, 299, 1731–1735. doi: 10.1126/science.1080444 Ibn Taghribirdi (1970) in ”Al-Nujum al-zahira fi akhbar al-Misr wa-l-Qahira”, new edition by the General Egyptian Agency of Culture ed., Cairo (E). Kodera, K., and Kuroda, Y. (2002), Dynamical response to the solar cycle, Space Sci. Rev., 107 (D24), 47–49. doi: 10.1029/2002JD002224 Lefebvre, S., Marchand, M., Bekki, S., Kechhut, Ph., et al. (2010), Influence of the solar radiation on Earth’s climate using the LMDz-REPROBUS model, Solar and Stellar Variability: Impact on Earth and Planets, Proceedings of the International Astronomical Union, IAU Symp. 264, Cambridge University Press, UK, 264, 350–355. doi: 10.1017/S1743921309992900 Luzzadder-Beach, S., Beach T. P. and Dunning, N.P. (2012) Wetland fields as mirrors of drought and the Maya abandonment, Proc. Natl Acad. Sci. USA 109 (10) 3646–3651. doi:10.1073/pnas.1114919109 Marchand, M. (2010), Journ´ees Soleil-Terre, CNES-IPSL, Impact de l’UV sur la photochimie atmosph´erique. Montgomery D.R. (2012), Dirt: The erosion of civilizations. Berkeley, CA (USA), University of California Press. M¨orner, N.A. (2010), Solar Minima, Earth’s rotation and Little Ice Ages in the past and in the future, The North Atlantic European case. Global and Planetary Change, 72, 282–293. doi:10.1016/j.gloplacha.2010.01.004 Norman, B. (2011), Did climate change cause Greenland’s ancient Viking community to collapse? ScienceDaily, Wiley-Blackwell ed. See http://www.sciencedaily.com/releases/2011/06/110620095238.htm Pfister, C. and Brazdil, R. (2006), Clim. Past Discuss, 2, 123–155 Toussoum, O. (or T¯ us¯ un, U.) (1925), in ”M´emoire sur l’Histoire du Nil”. Inst. Fran. d’Arch´eol. Orient, 264 p. Ribeiro, S., Matthias Moros, Marianne Ellegaard, Antoon Kuijpers, (2011) Climate variability in West Greenland during the past 1500 years: evidence from a high-resolution marine palynological record from Disko Bay, Boreas, p. 68-83. doi: 10.1111/j.1502-3885.2011.00216.x Ridley, H., Baldini, J.U.L., Macpherson, C.G., Prufer, K.M., Kennett, D.J. Amserom, Y. (2012), Monthly-scale palaeo-rainfall reconstructed using a Belizean stalagmite, EGU General Assembly 2012, held 22–27 April, 2012 in Vienna, Austria., p. 10725.



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Ruzmaikin, A., Feynman, J., Yung, Y. (2006), Does the Nile reflect solar variability? Solar Activity and its Magnetic Origin, Proceedings of the 23rd Symposium of the International Astronomical Union held in Cairo, Egypt, March 31–April 4, 2006, Edited by Volker Bothmer and Ahmed Abdel Hady. Cambridge University Press,, 233, 511–518. doi: 10.1017/S1743921306002560 Soon, W., Yaskell, S. H., 2004, in ”The Maunder Minimum and the Variable Sun-Earth Connection”, World Scientific ed., and Jour. of Astron., (Dec 2004), History and Heritage, vol. 7, no. 2, p. 125 Soon, W., Legates, D. R., 2013, Solar irradiance modulation of Equator-toPole (Arctic) temperature gradients: Empirical evidence for climate variation on multi-decadal timescales, Jour. of Atmosph. and Solar-Terrestrial Physics, Vol. 93, 45-56. doi:10.1016/j.jastp.2012.11.015 Seaver, K.A. (1996), in ”The Frozen Echo: Greenland and the Exploration of North America, ca. A.D. 1000-1500”, Stanford University Press (USA). Slak, A. (2002), Why did Norse Greenland fail as a colony? in ”York Medieval Yearbook”, The University of York, 1, Published by the Centre for Medieval Studies, University of York, G.B. Turner, B. L., Sabloff, J.A. (2012), Classic Period collapse of the Central Maya Lowlands: Insights about human-environment relationships for sustainability, Proc. Natl Acad. Sci. USA, 109 (35), 13908–13914. doi:10.1073/pnas.1210106109 Vieira, L. E. A., Solanki, S. K., Krivova, N. A., Usoskin, I. (2011), Evolution of the solar irradiance during the Holocene, Astronomy & Astrophysics, Vol. 531, A6, 20 p. doi: 10.1051/0004-6361/201015843 Weiss, H., Courty, M.A., Wetterstrom, W., Guichard, F., Senior, L., Meadow, R., Curnow, A. (1993), The Genesis and Collapse of Third Millennium North Mesopotamian Civilization, Science, 261 (5124), 995-1004. doi: 10.1126/science.261.5124.995

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Influence of orbital forcing and solar activity on climate change in the past Valentin A. Dergachev Cosmic Ray Laboratory Ioffe Institute, Politekhnicheskaya street, 26, Sankt-Peterburg, 194021, Russia E-mail: [email protected] Abstract. Understanding natural climate variability and its forcing factors is crucial to assess future climate change. The effect of the external factors (changes in solar radiation and activity) on long-term climate changes has become a very important problem. This is related to the fact that the global temperature almost monotonically increased during the last centuries. The physical reasons of this warming are now intensively discussed. Over the entire time span of the Earth’s climate evolution the main external and internal natural mechanisms of climate variability are related to changes in plate tectonics, orbital changes with different periodicities, the Sun’s output on different time scales, cosmic rays, and volcanism. The available data on climatic changes and the cyclic influence of solar radiation on the climate change during the last glacial and interglacial periods are analyzed and the problem of current interglacial duration is discussed.

1

Introduction

Our planet Earth was formed about 4.6 billion years ago, and during its evolution the Earth has seen a large variety of climate states. The evolution of life on the Earth was closely linked to climate and its change. The usual definition of climate is that it includes the slowly varying aspects of the atmosphere-hydrosphereland surface system. The atmosphere, continents and oceans form a complicated system and understanding climate and climate changes requires understanding how all the parts fit together. Many aspects of climate changes in the past was considered by Quante (2010). The investigation of climatic changes in the past and their possible reasons is a complicated problem. The main external and internal natural mechanisms of global climate variability are related to changes in plate tectonics, orbital changes with different periodicities, the sun’s output on different time scales. For the last about five millennia (the Holocene Epoch) three natural forcing factors influenced global climate: orbital forcing, solar forcing and volcanic considered in (Wanner et al. 2008). Astronomical theories (e.g., Milankovitch 1941; Imbrie et al. 1993) of paleoclimate attributes large-scale climate cycles to changes in the Earth’s orbital parameters: eccentricity (∼400, ∼100 kyr), obliquity (∼41 kyr), precession (∼22 kyr: 23 and 19 kyr). Small variations in solar radiation can have large climate effects. It is necessary to take into account that feedbacks can amplify or reduce the insolation changes. It has been established from the paleoclimate and

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paleo-oceanographic data that during the last more than 50 millions of years (Myr) planetary temperatures were several degrees warmer than today (Zachos et al. 2001), but there has been a progressive decrease in the average surface temperature on this time interval. Substantial glacial and interglacial temperature fluctuations are imposed on progressive decrease in the average surface temperature since about 2.8 Myr ago (Berger & Loutre 1991). The last interglacial (peak at 125 kyr ago) was a period with significantly higher temperatures in many parts of the Northern Hemisphere compared to the current interglacial (start data is ∼11.5 kyr ago). Detailed analysis of recent oscillations in temperature shows a clear 100 kyr correlation with interglacials coinciding with maxima of the ellipticity of the Earth’s orbit. To understand better our current interglacial (the Holocene, MIS-1 [Marine Isotope Stage]) and its future, it is necessary to investigate the response of the climate system to the peaks of interglacials in the past. Start of the last interglacial period occurred at 130 kyr ago (MIS-5). A similar to the Holocene latitudinal and seasonal distribution of the incoming solar radiation show two interglacials: MIS 11 (start - 427 kyr ago) and MIS 19 (start - 790 kyr ago). At present natural climate change is acting interactively with human-induced changes in the climate system. To extract the natural variability and humaninduced changes in the climate system on the global climate, a critical analysis of climate change in the past may propose a better understanding of the processes that drive the global climate system. One of the most difficult aspects of climate change is the wide variety of standpoints we must hold to fully understand it. The media often talks about how climate change, especially human-induced changes in the climate system may result in a sudden disaster or apocalypse. Every few ten thousand years and hundred thousand years the Earth as a whole undergoes drastic climatic changes, known as glaciations. Only ∼20 kyr ago the Earth was in a deep glaciation, where ice and snow covered most of today’s landmass. It is established that these changes are driven by the Earth’s relationship to the Sun. Since the climate has become a major issue the most part of current climate problems have focused on its the human impact. While anthropogenic climate change is important it should not be the driving factor of this talk, as it is far too controversial. The future of our civilization requires the progression of our understanding of how the climate functions on long-term scale. The solar irradiance remains the main source of the energy affecting the Earth’s atmosphere. The question arises, what is the driving mechanism of this climatic changes on century and millennial scales? It will be noted that the effect of solar variability on the Holocene climate is still controversial among physicists and climatologists. The aim of the present work is to perform such an analysis in order to estimate the contribution of the natural factors to the global climate change.



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Orbitalforcing forcingand andsolar solar activity activity Orbital

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The Sun as the external factor of climate variability and climate changes

Energy from the Sun is very important to the Earth climate system. The Sun warms our planet, heating the surface, the oceans and the atmosphere. Solar energy drives the external heat motor of the Earth and thus regulates the oceanic and atmospheric processes on the Earth’s surface. Interactions between the amount and distribution of solar energy reaching the Earth’s atmosphere, the composition of the atmosphere, and the nature of the surface of the Earth all may produce changes in the climate system. Both long- and short-term variations in solar intensity are known to affect global climate. The Sun is a variable star, which emits both electromagnetic radiation and energetic particles (the solar wind). Fig. 1a illustrates the Heliosphere, the large volume of space that is directly affected by the Sun through the solar wind - a plasma of electrons, atomic nuclei and associated magnetic fields from the solar atmosphere. The magnetic structure of the solar wind helps to shield the solar system from incoming cosmicray particles of relatively low energy. Variability in solar activity affects both the radiative output of the Sun and the strength of the interplanetary magnetic field (IMF) carried by the solar wind. The IMF shields the heliosphere from galactic cosmic radiation which, consists of energetic particles. Consequently, solar variability modulates both the flux of incoming galactic cosmic rays (GCR) and the amount of solar radiation received by our planet. It is known that fluxes of galactic cosmic rays produce radioactive isotopes, the so-called cosmogenic isotopes, e.g., 14 C and 10 Be, during the interaction with the constituents of the Earth’s atmosphere. These isotopes participate in different exchange processes in the atmossphere, hydrossphere and biosphere and then fall in the Earth’s archives: tree rings, peat layers, lacustrine sediments, glaciers, seafloor sediments, and loess. Both isotopes are produced in a similar manner, when the cosmic ray flux enters the Earth’s atmosphere. The physics of the production processes of these isotopes is well understood. Solar modulation affects both isotopes in a very similar manner, but climate modulation is expected to be different due to the different geochemical systems for these isotopes. From comparison of their records one can distinguish between the solar and climatic modulation of the production origin of both isotopes. Fig. 1b illustrates the scheme (Dergachev et al. 2006), which makes it possible to trace the relation of variations in solar activity, the geomagnetic field, and cosmic ray fluxes to climate changes. This scheme allows one to take into account the relation of total solar irradiance, solar ultraviolet, and cosmic ray fluxes to climatic and meteorological processes in the Earth’s atmosphere on short time scales. Cosmogenic 14 C and 10 Be are proxy of cosmic rays on long time scales, which makes it possible to trace the regularities of large-scale climate changes and the possible role of cosmic rays in these changes. The physical mechanism related to the GCR flux, which reaches the Earth’s lower atmosphere and is modulated by the solar and geomagnetic fields, can more extensively than the variation in the total solar irradiance or solar ultraviolet affect climate changes. Changes in

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cloud processes under the action of cosmic rays, which are of importance for abundance of condensation nuclei and for ice formation in cyclones, can act as a connecting link between solar variability and changes in weather and climate on the whole.

Fig. 1. a - The Earth in the Heliosphere under the influence of the Sun and galactic cosmic rays, b - Schematic interrelation between the variations in the cosmic ray intensity, solar activity, geomagnetic field, and climate changes.

An important influence of the Earth’s climate system comes from Earth’s position in space. As was proposed by Milutin Milankovitch (1941) periodic variations in the Earth’s orbital cycle varies both the amount and distribution of heat that the Earth receives from the Sun, and this variation causes periodic glacial and interglacial cycles. Although the precise cause of glacial/interglacial cycles is still under debate, the idea of periodic fluctuations in insolation (the amount of solar radiation reaching the Earth’s atmosphere) due to orbital changes has been accepted as a major forcing function of climatic change. Milankovitch cycles consist of three components: eccentricity, obliquity, and precession. Concentration of stable oxygen isotope 18 O (hereafter, δ 18 O) in ice cores and marine sediments is as a rule used as a paleoclimatic parameter. Observed 18 O concentration in precipitated sediments is the function of air temperature. Concentration of this isotope factually informs about temperature of the environment where sediments were accumulated. The oxygen isotopic composition of the ocean reflects a combination of processes, including seawater temperature and the volume of seawater stored on land as glacial ice. During evaporation, water containing the lighter isotope of oxygen (16 O), is preferentially evaporated, so precipitation is enriched in 16 O. During glacial intervals, more 16 O is locked up as ice on land, and the oceans become enriched in 18 O. Thus the oxygen isotopic composition of calcareous organisms recovered from marine sediment cores serves as a proxy record of seawater chemistry, ocean temperature, and glacial ice volume. There are many feedback mechanisms in the climate system that moderate the magnitude of climate change. Positive feedbacks stimulate continued change, while negative feedbacks stopping change.



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Climate of the past and orbital forcing

Deep past climate (the first billion years of the Earth existence), for which the geological record is almost non-existent or sparse, is very poorly understood. It has been established from the paleoclimate and paleo-oceanographic data that during the past 100 Myr in the Cretaceous epoch, which ended 65 Myr BP, surface air temperatures were higher than they are at present. Approximately 5 Myr temperature started to go down rather substantially, by ∼ 5◦ C. The latest of the glacial epochs (the Pleistocene epoch) began almost 2 Myr ago, when the occurrence of continental ice sheets and periodicity of glaciations were noted in the Northern Hemisphere. During this epoch there were colder periods, when ice sheets and alpine glaciers increased, thick ice sheets covered large parts of North America, Northern Europe and Siberia, and interglacial times characterized by an ice covering only in Antarctica and sometimes Greenland, as is the case today. Oscillations in the Earth’s orbit (Fig. 2a) produce quasi-periodic variations in solar input to high latitudes (but not overall to Earth). Most widely used, discussed and accepted of theories of Ice Age. Quasi-periodic variations in the Earth’s orbital parameters (Fig. 2a) change the solar energy input to higher latitudes with periods of multiple tens of thousand of years. As solar energy inputs and data on past climate variations are both subject to quasi-periodic variations over similar time periods, it indicate that they may be coupled. To some extent this viewpoint is supported by spectral analysis. This variability of solar input to higher latitudes has a significant effect on the ability of surface and sea ice at higher northern latitudes to withstand the attack of summer. When the solar energy input to higher northern latitudes is lower than average it may lead to spreading of ice cover and the start of Ice Ages. Conversely, time periods with higher solar energy input may cause melting , leading to deglaciation. Peak summer solar intensity at latitude when the Earth is closest to the Sun (depends on eccentricity and obliquity). Analysis of the oxygen isotopes in 57 core-samples from deep-sea, globally distributed oceanic sediments (Lisiecki & Raymo 2005) show that alpine glaciers appeared in the Northern Hemisphere and ice sheets covered the lands of the northern Atlantic. In this time interval, the climate change trend points to a gradual lowing of the temperature. In the Northern Hemisphere, the deep fall in temperature reached its maximum around 2.8-2.5 Myr (Karabanov et al. 2001). The repeated advance and retreat of glaciers and substantial oscillations of the climate at the polar and midlatitudes are typical of the last 2-2.5 Myr (Fig. 2b). The most recent 0.9-0.7 Myr period is characterized by both continental glaciations with thick ice sheets, covering considerable potions of North America, northern Europe, and Siberia, and interglacial intervals, during which the ice cover remains only in Antarctica and partly in Greenland (which is currently observed). A new climate type characterized by alternation of glacial and interglacial conditions has appeared. Terrestrial climate has varied significantly and continuously on time scales ranging from years to glacial periods and to hundreds of million years. Fig. 2c

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a

b c

Fig. 2. a - Earth’s orbital parameters: eccentric orbit, precession of of the ellipse and the equinoxes, axial tilt or obliquity. Precession modulated by eccentricity, eccentricity and precession affect low latitudes, obliquity affects high latitudes; b - Oxygen isotope measurements of benthic foraminifers (Lisiecki & Raymo 2005); c - Power spectrum of climate variability over the last 10 Myr (Ghil 2002), which is a composite of several climatic time series.

shows the temporal variability of the climate system over the last 10 million years. The temperature data obtain from the instrumental record and proxy indicators such as coral reef records, tree rings, marine sediment cores, and ice core records. This power spectrum (Ghil 2002)) for temperature near the surface reflects the influence of both an interannual and external variability. The periods between 1,000 years to about 1 million years in Fig. 2c represents the paleoclimatic variability. The main orbital periodicities in the Earth’s orbit are the eccentricity (∼100 kyr and ∼400 kyr), precession (∼20 kyr) and obliquity (∼40 kyr) cycles (Laskar et al. 2004). The combined effect of these orbital cycles causes long term changes in the amount of sunlight hitting the Earth in different seasons, particularly at high latitudes. Since the relation between the orbital cycles, the quantities of which are known with a high accuracy, and past climate change can be used to predict future climate change. Dergachev & Dmitriev (2015) analyzed the climate variability in time series of Lisiecki & Raymo (2005) covering the last three million years to find what quasi-periodic oscillations are characteristic of the temporal structure and to examine whether they contain the quasi-periods corresponding to the orbital cycles, and, if they exist, to analyze the character of their change during this 3 Myr. Authors considered in more detail the temporal structure of this time series and the characteristic features that served for dividing this series into four parts. These features are temporal changes in the following parameters of the series: the trend, i.e., its ”current” mean quantity; the dispersion, i.e., the amplitude of its neighbor values; and the quasi-periodic alternations of its local



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extremum values, i.e., local maxima and minima. Quasi-harmonic components in the temporal structure of the initial data are sought in the classic problem of revealing hidden periodicity (Serebrennikov & Pervozvanskii 1965). The authors have found in this time interval five periodicities of about 19, 22.4, 23.7, 41 and 98 kyrs which are similar to the Earth’ orbital cycles. In whole, the 41-kyr oscillation very clearly manifests itself and remains for the whole 3 Myr period; consequently, it may be the result of complex orbital effects on the Earth’s climate. The 100-kyr oscillation reveals itself in the past from 3 to 1.7 Myr less distinctly, as compared to the first; then it disappears and appears again in the interval from 600 kyr, which is probably caused by geologic effects on the Earth’s climate. It is clear that the climatic system does not respond linearly to the insolation variations though astronomical frequencies corresponding to orbital cycles are found in almost all paleoclimatic records. Orbital insolation changes at the 100 kyr period are insignificant, and cannot explain the strongly nonlinear ∼100 kyr glacial cycles. Ice growth occurs during times when summer insolation is low in high northern latitude. The shorter periods of precession and obliquity act as drivers of the smaller 20 kyr and 41 kyr cycles in ice volume. Internal nonlinear processes (or thresholds) are required to set the duration of the ∼100 kyr cycles. Potential candidates are: bedrock response, ice calving, basal sliding, see ice. The modulation of precession by eccentricity at 100 kyr periods has the potential to set the timing of the glacial terminations. Classical Problem is how do these very small variations in orbital insolation impact climate and global ice volume?

4

Interglacials and orbital parameters as an analogue for the future current interglacial duration

In the context of future global warming induced by human activities, it is important to assess the role of natural climatic variations. Precise knowledge of the duration of past interglacial periods is fundamental for the understanding of the potential future evolution of the Holocene. Past ice age cycles provide a natural laboratory for investigation of advance and duration of interglacial climate. 37 paleoclimate records of ice, marine and terrestrial covering the last 800 kyr was compilated by Lang & Wolff (2011) in order to assess the pattern of glacial and interglacial strength, and termination amplitude.These paleorecords revealing eight glacial-interglacial cycles, with a range of insolation and greenhouse gas influences. The interglacials display a correspondingly large variety of intensity and duration, thus providing an opportunity for major insights into the mechanisms involved in the behavior of interglacial climates. A comparison of the duration of these interglacials, however, is often difficult, as the definition of an interglacial depends on the archive that is considered. Therefore, to compare interglacial length and climate conditions from different archives, a consistent definition of interglacial conditions is required. An analysis of the available data on an investigation of glacial-interglacial cycles doesn’t allow making an unequivocal conclusion about the end of the

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current interglacial. According to some investigations, the Holocene should end in the near future; according to others, it will last for tens of thousands of years from the present time. To predict our future climate, it is extremely important to understand the dynamics of glacial-interglacial cycles. In many cases past interglacials were warmer than the current one, yet they did not have higher CO2 concentrations. How can that be? To understand better our current interglacial and its future, it is necessary to investigate the response of the climate system to insolation at the peaks of the interglacials similar latitudinal and seasonal distribution of the incoming solar radiation over the past 800 kyr, which can lead to similar climate response to insolation. Fig. 3 shows the comparison of the orbital parameters (a) and various interglacial intervals (b) during the last 800 kyr. The temperature changes reconstructed from (1) Antarctic ice cores for various glacial-interglacial intervals (∆T ) (L¨ uthi et al. 2008) and (2) δ 18 O in ocean sediment cores (Lisiecki & Raymo 2005). Comparison of the last Eemian interglacial (peak at 125 kyr ago) and the current Holocene interglacial shows some peculiarities of orbital element changes for these two interglacials: the value of the Eemian excentricity is higher than the Holocene excentricity; the effects of precession and obliquity were more pronounced in the Eemian; the effect of insolation was also more pronounced in the Eemian. It does not allow one to make a correct comparison. It would be desirable to notice that three astronomical analogs of our Holocene interglacial one can see in the vicinity of next Marine Isotope Stages (Fig. 3): MIS-1 (0 BP), MIS-11 (∼400 kyr BP) and MIS-19 (800 kyr BP) are labeled by arrows.

Fig. 3. Comparison of a - the orbital parameters and b - temperature changes for various glacial-interglacial intervals reconstructed from (1) Antarctic ice cores (∆T ) (L¨ uthi et al. 2008) and (2) δ 18 O in ocean sediment cores (Lisiecki & Raymo 2005) during the last 800 kyr. The numerals in Fig. 3b indicate interglacial isotope stages (MIS - Marine Isotope Stages) from 1 to 19. Orbital parameters during the last Eemian interglacial (peak at 125 kyr ago) - MIS-5 is shown by dash-and-dot lines. Three astronomical analogs of our Holocene interglacial are labelled by arrows.

The numerals indicate interglacial isotope stages (MIS - Marine Isotope Stages). Detailed records from ice cores show that three previous interglacials (MIS-5, -7, -9) in Fig. 3 differ from the fourth (MIS-11) which, as well as Holocene (MIS-11), fall to the period of time when orbital eccentricity gets on a minimum



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of a 400-kyr orbital cycle. Duration interglacial which took place ∼400 kyr ago, is estimated much longer, than by the subsequent. MIS 11 is a frequent candidate as a potential Holocene and near future analogue because of similar orbital configurations. But the estimated length of MIS11 seems to vary from 20 to 33 kyr. Besides, MIS-11 has long been shown to consist of at least two insolation peaks. The warm period around 400 kyr ago remains a contradiction. MIS-19 shares a very similar insolation minimum and similar orbital configurations to the Holocene (MIS-1) and MIS-11, but lasted for only 10.5-12.5 kyr. We also know that CO2 concentrations at the time were approximately 240 ppm. Thus with respect to the Holocene, MIS-19 may act as a good analogue for climatic change under ”natural” conditions, i.e. CO2 levels not influenced by man. Assuming the Holocene followed the pattern seen during MIS-19, we would have expected glacial inception to start shortly, if not already underway. This brings up interesting questions about whether preindustrial CO2 concentrations were actually natural or whether the effects of human activity actually started changing atmospheric composition much earlier.

5

Evolution of global surface temperature during the Holocene

Reconstructions of local and global temperature from paleoarchives for the last 11300 years show the tendency of cooling from ∼5 kyr ago (e.g., Marcott et al. 2013; Kotlyakov 2012). This global cooling is particularly puzzling because it is opposite to the expected and modelled tendencies of global warming due to vanishing of the ice sheets and increasing of the greenhouse gases concentration (Liu et al. 2014). To resolve this puzzle of the Holocene temperature is important for understanding the mechanisms of climate response to external and internal factors and accurate identifying the termination time of the modern interglacial. It is important to emphasize that the models have tendencies to suppress the variabilities of regional level fixed in the data from natural archives. To distinguish between natural variabilities and human-induced impact in the behavior of climatic system and to estimate the moment of termination of the modern interglacial period one should critically analyze the climate change in the past, understanding that the climate operates on a long-term time scale.

Acknowledgment I am grateful to organizers of the International Conference ”Variability of the Sun and Sun-like Stars: from Asteroseismology to Space Weather” (Baku, Azerbaijan, 06-8 July 2015) (”Baku Solar Conference-2015”) , especially Dr. Namig Dzhalilov and Dr. Elchin Babayev for their invitation and the Science Development Foundation (SFD) under the President of the Republic of Azerbaijan for financial support.

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