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C 2013 by Hotaka Shiokawa. All Rights Reserved. GENERAL-RELATIVISTIC MAGNETOHYDRODYNAMICS SIMULATIONS of BLACK HOLE ACCRETION DISKS: DYNAMICS and RADIATIVE PROPERTIES

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C 2013 by Hotaka Shiokawa. All Rights Reserved. GENERAL-RELATIVISTIC MAGNETOHYDRODYNAMICS SIMULATIONS of BLACK HOLE ACCRETION DISKS: DYNAMICS and RADIATIVE PROPERTIES c 2013 by Hotaka Shiokawa. All rights reserved. GENERAL-RELATIVISTIC MAGNETOHYDRODYNAMICS SIMULATIONS OF BLACK HOLE ACCRETION DISKS: DYNAMICS AND RADIATIVE PROPERTIES BY HOTAKA SHIOKAWA DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Astronomy in the Graduate College of the University of Illinois at Urbana-Champaign, 2013 Urbana, Illinois Doctoral Committee: Professor Charles F. Gammie, Chair Professor Stuart L. Shapiro Associate Professor Paul M. Ricker Associate Professor Athol J. Kemball Abstract The goal of the series of studies in this thesis is to understand the black hole accretion process and predict its observational properties. The highly non-linear process involves a turbulent magnetized plasma in a general relativistic regime, thus making it hard to study analytically. We use numerical simulations, specifically general relativistic magnetohydrodynamics (GRMHD), to construct a realistic dynamical and radiation model of accretion disks. Our simulations are for black holes in low luminous regimes that probably possesses a hot and thick accretion disk. Flows in this regime are called radiatively inefficient accretion flows (RIAF). The most plau- sible mechanism for transporting angular momentum is turbulence induced by magnetorotational instability (MRI). The RIAF model has been used to model the supermassive black hole at the center of our Milky Way galaxy, Sagittarius A* (Sgr A*). Owing to its proximity, rich observational data of Sgr A* is available to compare with the simulation results. We focus mainly on four topics. First, we analyse numerical convergence of 3D GRMHD global disk simulations. Convergence is one of the essential factors in deciding quantitative outcomes of the simulations. We analyzed dimensionless shell-averaged quantities such as plasma β, the azimuthal correlation length (angle) of fluid variables, and spectra of the source for four different resolutions. We found that all the variables converged with the highest resolution (384x384x256 in radial, poloidal, and azimuthal directions) except the magnetic field correlation length. It probably requires another factor of 2 in resolution to achieve convergence. Second, we studied the effect of equation of state on dynamics of GRMHD simulation and radiative transfer. Temperature of RIAF gas is high, and all the electrons are relativistic, but not the ions. In addition, the dynamical time scale of the accretion disk is shorter than the collisional time scale of electrons and ions, which makes the gas have two temperatures. We assumed that the temperature ratio of the ions and electrons Tp=Te is constant and constructed a new Synge-type equation of state that takes the effect of two temperature fluid as well as variable adiabatic index caused by the non-relativistic to relativistic transition of the particles into account. We found that the effect of the Synge-type equation of state on ii the dynamical model is negligible since the temperature variation in the flow is small enough to keep the effective adiabatic index in time and space approximately constant. The spectra are not affected by the equation of state either. Thirdly, we studied effects of accretion rate on radiative properties of a black hole accretion disk. We used GRMHD simulation and general relativistic ray-tracing to formulate the relation between accretion rate and image size, as well as flux. The result will be compared to the expected change in emission of Sgr A* due to the interaction with the approaching gas cloud G2. Finally, we constructed a dynamical and radiative model of tilted black hole accretion disks. Rotational axis of accretion disks are not necessarily aligned with spin of black holes. When they are not aligned, deformation of the accretion disks (warps, twists, or emergence of new structure) are expected due to the gravito-magnetic effect. We initially tilted otherwise equilibrium RIAF disks, seeded with a weak magnetic 2 field, and evolved. We found that m = 2 standing waves show up for radius < 6GMBH =c with ratio of the mode amplitude of m = 2 and m = 0 2-5 times larger than that of untilted disks. Shocks produced along the waves heat up the gas and raise the temperature at inner radii. Resultant spectra of tilted disks have a substantial increase in flux of the order of 1-2 magnitude for 15◦ and 30◦ tilted disks in infrared and X-ray. The result assures the tilt is one of the fundamental parameters in modelling black hole accretion disks. iii To Father and Mother. iv Acknowledgments In finishing this thesis, I received tremendous amount of help and support from many people. First, I would like to give the greatest appreciation to Professor Charles Gammie for being my advisor. I am very honored to be a student of the most intelligent person I have ever met and supervised under his deepest knowledge and insight. My appreciation to his kindness and patience in often slow progress of my research and countless grammatical mistakes and wording problems in my papers can not be expressed in any words. I am truly fortunate that I met Professor You-Hua Chu, whom I appreciate for introducing me to Professor Charles Gammie six years ago. It was absolutely impossible to complete this thesis without his great advise and guidance. I would like to thank all the committee members, Professor Charles Gammie, Professor Stuart Shapiro, Professor Paul Ricker, and Professor Athol Kemball for reading this thesis and giving me helpful suggestions. I would like to thank Professor Charles Gammie, Professor Stuart Shapiro, and Professor Paul Ricker for writing the recommendation letters for my job applications and patiently sending them out to dozens of universities and research institutions. Also, Sue Berndt is appreciated for kindly helping the application process. My thanks to all the AFD group members, especially Joshua Dolence, Monika Mo´scibrodzka, Po Kin Leung, and Xiaoyue Guan with whom I had useful discussions and occasional fun conversations. I would like to thank Professor Stuart Shapiro for great suggestions in all of my talks, and his group members for inspiring and motivating me to work harder in the weekly journal club discussions. I thank Scott Noble for coding HARM3D, the code I used in my entire graduate life and publications. Many thanks to all my friends in the same year for sharing the fun and difficulties of the graduate life: David Rebolledo, Katherine Lee, Kuo-Chuan Pan, Nachiketa Chakraborty, and Yiran Wang. Above all I thank Kuo-Chuan Pan for always being very nice and offering help without any hesitation including being my best man in my wedding. I thank Nick Hakobian, Mani Chandra, and Ian Stephens for proof reading my writing and giving professional suggestions and comments. I thank Jeri Cochran for welcoming me on the first day of my visit to the department, and after all for providing help in every single things in living. v This thesis is dedicated to my parents. I appreciate their respecting my dream and letting me go study abroad without any objection, and providing the financial help in academic and medical expenses. Thanks to father, for showing the importance of being diligent and retaining one's will. Thanks to mother, for introducing the mysteries and excitements of the space in my childhood. And thanks to both of them for all the care and support I received in my life. Finally, I thank my beloved wife, Katherine Lee, for always being beside me and sharing difficulties and happiness in both daily and academic life. I really appreciate her consideration of my health, cooking great dishes, and staying with me during the time I was in hospital. I thank her for giving up all the great job offers to come with me, and for loving me. vi Table of Contents List of Tables . ix List of Figures . x List of Abbreviations . xii List of Symbols . xiii Chapter 1 Introduction . 1 1.1 Theoretical Models . 1 1.1.1 Disk Theory . 1 1.1.2 Effect of General Relativity on Accretion Disk . 2 1.1.3 Effect of Magnetic Field . 3 1.1.4 Disk Types . 4 1.2 Observation: Sgr A* and G2 Cloud . 5 1.2.1 Sgr A* . 5 1.2.2 G2 Cloud . 6 1.3 Numerical Modelling . 6 1.3.1 Dynamical Models . 7 1.3.2 Equation of State . 8 1.3.3 Convergence . 9 1.3.4 Radiative Model of Sgr A* . 10 1.4 Tilted disks . 12 Chapter 2 Global GRMHD Simulations of Black Hole Accretion Flows: a Convergence Study . 18 2.1 Introduction . 18 2.2 Simulations . 20 2.3 Radial profiles of non-dimensional variables . 23 2.4 Correlation lengths . 24 2.5 Spectra . 27 2.6 Summary . 29 Chapter 3 Effect of Equation of State on Spectra of Radiatively Inefficient Accretion Flows ................................................. 41 3.1 Introduction . 41 3.2 Model, Numerical Methods, and Equation of State . 42 3.2.1 Conserved and Primitive Variables . 43 3.2.2 Equation of State . 44 3.2.3 Implementation in HARM . 47 3.2.4 Radiative Transfer . 49 3.3 Models . 50 vii 3.4 Spectra . 51 3.5 Discussion . 52 3.6 Conclusion . 53 Chapter 4 Galactic Center Weather Forecast . 63 4.1 Introduction . 63 4.2 Change of Sgr A* sub-mm luminosity and size for enhanced M_ . 65 4.3 Spectra . 69 4.4 Discussion . 70 Chapter 5 Dynamical and Radiative Models of Tilted Accretion Flow onto Spinning Black Hole . 74 5.1 Introduction . 74 5.2 Simulations . 77 5.2.1 Model . 77 5.2.2 Initial Conditions . 78 5.3 Results . 79 5.3.1 Tilted Disk Coordinate . 79 5.3.2 Plunging Streams . 80 5.3.3 Temperature Distribution . 81 5.3.4 Disk Shape . 82 5.4 Spectral Energy distribution .
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