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Jakub Podgorný Polarisation of X-Ray Emission from Accretion Discs In MASTER THESIS Jakub Podgorn´y Polarisation of X-ray emission from accretion discs in active galactic nuclei Astronomical Institute of Charles University Supervisor of the master thesis: RNDr. Michal Dovˇciak, Ph.D. Study programme: Physics Study branch: Astronomy and astrophysics Prague 2020 I declare that I carried out this master thesis independently, and only with the cited sources, literature and other professional sources. It has not been used to obtain another or the same degree. I understand that my work relates to the rights and obligations under the Act No. 121/2000 Sb., the Copyright Act, as amended, in particular the fact that the Charles University has the right to conclude a license agreement on the use of this work as a school work pursuant to Section 60 subsection 1 of the Copyright Act. In Prague 27/05/2020 . Jakub Podgorn´y i I would like to thank my kind supervisor RNDr. Michal Dovˇciak,Ph.D., who was always there to bring valuable advices and who patiently dealt with my exhaus- tive questions. It was a devoted guidance over nearly two years that enhanced my abilities and perception of problems in many aspects, which I value a lot. Re- garding the discussions on various codes used in this work, I thank the authors, which I met in person or communicated with on distance, to be able to properly use the codes and to get more insight on the miscellaneous output. I would also like to thank my family and friends for incredible patience and support throughout my studies, which allowed me to study such a lovely field of physics until this point. ii Title: Polarisation of X-ray emission from accretion discs in active galactic nuclei Author: Jakub Podgorn´y Institute: Astronomical Institute of Charles University Supervisor: RNDr. Michal Dovˇciak,Ph.D., Astronomical Institute of Academy of Sciences of the Czech Republic Abstract: The presented thesis deals with theoretical modeling of the X-ray emis- sion from active galactic nuclei. It studies spectral and polarisation properties of local radiation reflected from the surrounding accretion disc, which is being illuminated by a hot corona above, as well as global observational perspectives at infinity for unobscured radio-quiet sources. Modeling of this kind could then serve for observational fitting of spin of the central supermassive black hole, con- straining the accretion disc’s or coronal properties, or determining observer’s inclination towards the systems. A radiative transfer Monte Carlo simulation code STOKES [Goosmann and Gaskell, 2007, Marin et al., 2012, 2015, Marin, 2018] is used for local computations. Its performance is compared to results of other attempts already existing in literature and analytical approximations. The local scheme is discussed mostly in terms of emergent polarisation that has been for the first time simulated for these types of objects with high accuracy. Integration over the accretion disc and superposition with the primary radia- tion in the so-called lamp-post or extended coronal model, including all general- relativistic effects in the vicinity of the central supermassive black hole, isthen performed on the basis of already existing routine KYNLPCR [Dovˇciaket al., 2004, 2011]. Such spectral and polarisation results utilizing the new reflection computa- tions are again compared to existing local tables and analytical approaches within the same integral scheme. The analysis is brought to a valuable end by testing the obtained total spectral and polarisation outcome within the observation sim- ulation software IXPEOBSSIM for the first forthcoming X-ray polarimetric mission IXPE (NASA, to be launched in April of 2021), in order to prepare the mod- els for fitting of polarimetric measurements of active galactic nuclei targets and to provide better estimates on observational times needed. Keywords: X-ray astrophysics, active galactic nuclei, relativistic astrophysics, black holes, polarisation iii Contents Introduction 2 1 Theoretical background and context 4 1.1 Definition of quantities and basic concepts . .4 1.1.1 Polarisation of light . .5 1.1.2 Polarigenesis . .8 1.1.3 Polarimetry . .9 1.2 Astronomical objects of interest . 11 1.2.1 X-ray polarimetry science cases . 11 1.2.2 The case of active galactic nuclei . 12 1.3 Modeling X-ray spectra and polarisation of radio-quiet AGNs . 15 1.3.1 Physical processes of particular interest . 15 1.3.2 Reasonable spectral and polarimetric model . 21 1.4 Relativistic description of the problem . 22 1.4.1 Emission from an accretion disc around a Kerr black hole . 23 1.4.2 Polarized light in general relativity . 25 1.5 Modern research in spectral and polarimetric properties of AGNs 26 1.5.1 Numerical codes . 26 1.5.2 Analytical approximations . 31 1.5.3 Space observatories . 32 2 Reflected local radiation from an accretion disc35 2.1 STOKES spectral results . 37 2.2 Comparison of STOKES with other codes . 38 2.3 STOKES polarisation results . 43 2.4 STOKES and total reflectivity . 49 3 Total X-ray spectral and polarisation modeling of AGNs 52 3.1 Conversion of STOKES output into FITS format . 52 3.2 Implementing the STOKES FITS tables into the KYNLPCR integration scheme . 54 3.3 Total emission using the STOKES tables and in comparison with other local computations within the same integration scheme . 55 3.3.1 Spectral results . 56 3.3.2 Polarisation results . 58 4 Preparation of the models for IXPE mission 63 4.1 Preparation of auxiliary codes to IXPEOBSSIM ........... 63 4.2 Selected testing objects . 64 4.3 Test results and discussion . 65 Conclusion 74 Bibliography 77 A Appendix 88 1 Introduction Despite the recent success of gravitational-wave astronomy, electromagnetic ra- diation is still by far the most prevalent way of exploring the most extreme parts of our universe. Light contains multiple types of information that each provide a valuable insight into such environments and which all together give a unique portion of understanding. Namely, it is the direction of photons tracing its sources, time of arrival of each photon, energetic spectrum of the incoming super- posed radiation, and the way in which the light can be macroscopically polarized. The last property, which brings three important parameters into the global picture – the degree, angle and ellipticity of macroscopic polarisation, may sometimes be overshadowed by the others due to the difficulty of measurement, especially in the X-ray part of the incoming spectrum, if it appears. However, technological development in the past decades made a significant progress in the study of X-ray sources, which can be now polarimetrically ob- served with sufficient precision for the first time in history in this frequency band. Thus, it is high time to (re)investigate the theoretical background of astrophys- ical sources, which are known to embrace the phenomenon of X-ray emission in the view of spectroscopy and polarimetry, because only by a sound and consis- tent physical theory can be the upcoming observations understood. And here, in between theoretical studies and observations, two up-to-date scientific fields, is, where majority of this thesis lies. Linking a theory to observations is in fact a whole branch of astrophysics by itself, these days mostly probed by the means of numerical simulations. It is a goal of this thesis to correctly interpret results of various numerical computations, which have roots in common astrophysical the- ories, such as the general theory of relativity, the theory of radiative transfer, and the theory of interaction of matter with light. In particular, the thesis will focus on accretion discs of active galactic nuclei (AGN), as such sources are unique laboratories of extreme physics. Here X-ray polarimetry may bring an important insight into the broad and consistent picture of both, these common objects on the sky and the physical theories themselves. It is for this reason, why AGNs are also of top interest by the upcoming X-ray polarimetric space missions, such as the NASA IXPE mission [Weisskopf et al., 2016] or the Chinese eXTP mission [Zhang et al., 2016]. The aim of this thesis is to dig more into the understanding of light emerging from accretion discs of AGNs by interpreting and connecting results of various codes that have been developed recently in this field. Correctly simulated spectral and polarisation properties of these sources can then serve as state-of-the-art foundations for the missions mentioned. Chapter 1 brings a brief overview of the theoretical and observational back- ground of X-ray spectrography and polarimetry with focus on accretion discs in AGNs. This includes the basics of the related physical theories, specifying the adopted formalism, and providing definitions of the physical quantities later used in the text. Important observational facts are mentioned, as well as some modern numerical simulations that support them. Chapter 2 describes a pos- sible use of one such code STOKES [Goosmann and Gaskell, 2007, Marin et al., 2012, 2015, Marin, 2018] and its performance in reproducing spectral and po- larimetric properties of locally emitted radiation from accretion discs in AGNs 2 illuminated by a hot corona above. This is compared to results of other codes and approaches in the literature, namely the XILLVER [Garc´ıaand Kallman, 2010, Garc´ıaet al., 2011] numerical computations and analytical approximation of po- larisation given by the Chandrasekhar’s formulae [Chandrasekhar, 1960]. Chapter 3 brings the results from Chapter 2 into a broader picture, where we incorporate the outcome into a wide scheme of parametric spectral and polarimetric fitting of AGNs, adapting the already published KYNLPCR routine [Dovˇciaket al., 2004, 2011], which is suitable for computing the total spectrum of AGNs or X-ray binary systems, including general-relativistic effects. This also allows for a comparison of the total unfolded AGN models using the STOKES local tables with other codes and approaches in the literature.
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