The Bright Side of Black Holes: Radiation From Black Hole Accretion Disks The Harvard community has made this article openly available. Please share how this access benefits you. Your story matters Citation Zhu, Yucong. 2015. The Bright Side of Black Holes: Radiation From Black Hole Accretion Disks. Doctoral dissertation, Harvard University, Graduate School of Arts & Sciences. Citable link http://nrs.harvard.edu/urn-3:HUL.InstRepos:17463143 Terms of Use This article was downloaded from Harvard University’s DASH repository, and is made available under the terms and conditions applicable to Other Posted Material, as set forth at http:// nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of- use#LAA The Bright Side of Black Holes: Radiation from Black Hole Accretion Disks A dissertation presented by Yucong Zhu to The Department of Astronomy in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the subject of Astronomy & Astrophysics Harvard University Cambridge, Massachusetts May 2015 c 2015 | Yucong Zhu All rights reserved. Dissertation Advisor: Prof. Ramesh Narayan Yucong Zhu The Bright Side of Black Holes: Radiation from Black Hole Accretion Disks Abstract An understanding of radiation is paramount for connecting observations of accretion disks with the theory of black holes. In this thesis, we explore via radiative transfer postprocessing calculations the observational signatures of black holes. We investigate disk spectra by analyzing general relativistic magnetohydrodynamic (GRMHD) simulations of accretion disks. For the most part there are no surprises { the resulting GRMHD spectrum is very close to the analytic Novikov & Thorne (1973) prediction from decades past, except for a small modification in the case of spinning black holes, which exhibit a high-energy power-law tail that is sourced by hot Comptonized gas from within the plunging region of the accretion flow. These conclusions are borne out by both 1D and 3D radiative transfer calculations of the disk. Significant effort was spent in developing from scratch the 3D radiative code that we used for the analysis. The code is named HERO (Hybrid Evaluator for Radiative Objects) and it is a new general purpose grid-based 3D general relativistic radiative solver. iii Contents Abstract iii Acknowledgments ix Dedication x 1 Introduction 1 1.1 Why Care About Black Holes? . .1 1.2 Mathematical Basis and Understanding . .3 1.2.1 Kerr Metric . .3 1.2.2 Conservation Laws . .5 1.2.3 Metric Singularities . .6 1.2.4 Ergosphere . .9 1.2.5 Circular Orbits . 11 1.3 Observational Evidence for Black Holes . 15 1.3.1 Spin Fitting Techniques . 19 1.3.2 Zoology of Disk States . 22 1.4 Disk physics . 27 1.4.1 Classic Thin Disk Model . 28 1.4.2 Relativistic Disk Model (Novikov & Thorne 1973) . 32 1.4.3 Open problems in Accretion Physics . 34 iv CONTENTS 1.5 Numerical Simulations . 36 1.5.1 Shearing Boxes . 38 1.5.2 Global Simulations . 39 1.5.3 Future Directions . 40 1.6 Including Radiation . 41 1.6.1 Radiation Hydrodynamics . 42 1.7 Chapter Summaries . 45 2 The Eye of the Storm: Light from the Inner Plunging Region of Black Hole Accretion Discs 49 2.1 Introduction . 50 2.2 GRMHD Simulations . 57 2.3 Annuli Spectra . 58 2.3.1 Assumptions in the TLUSTY model . 61 2.4 Slicing the GRMHD disc into Annuli . 62 2.4.1 Flux profile . 64 2.4.2 Vertical gravity profile . 68 2.4.3 Column density profile . 69 2.5 Ray Tracing . 73 2.6 Results . 76 2.6.1 Power law tail . 78 2.6.2 Quantitative effect on spin . 83 2.7 Discussion . 91 2.7.1 Other signatures of the plunging region . 95 2.7.2 How does our choice of cooling function influence the results? . 96 2.7.3 Equation of state . 98 2.8 Summary . 99 v CONTENTS 2.9 Luminosity Matching Model . 101 2.10 Generalized Novikov & Thorne Model . 102 2.11 Interpolation Methods . 105 2.12 An Alternative GRMHD Luminosity Profile . 108 2.12.1 Obtaining the GRMHD dissipation profile . 110 2.12.2 Net result of the luminosity calculation . 110 3 Thermal Stability in Turbulent Accretion Discs 113 3.1 Introduction . 114 3.2 Physical model . 117 3.2.1 Radial structure . 118 3.2.2 Vertical structure . 119 3.3 Disc solutions . 126 3.3.1 Classic unmixed disc . 128 3.3.2 Convective solutions . 131 3.3.3 Convective and turbulent disc solutions . 133 3.3.4 Radial structure of solutions . 139 3.4 Discussion . 144 3.4.1 Use of logarithmic temperature gradient . 145 3.4.2 Impact of Σscale ............................. 148 3.4.3 Scaling of Critical M_ with Black Hole Mass . 149 3.4.4 Choosing ζ { comparison with simulations . 151 3.4.5 ζ from observations . 158 3.4.6 Radiative Outer Zone . 158 3.4.7 Complete stabilization from turbulence . 162 3.5 Summary . 165 3.6 Acknowledgments . 166 vi CONTENTS 3.7 Solving for 8 unknowns . 167 4 HERO - A 3D General Relativistic Radiative Postprocessor for Accre- tion Discs around Black Holes 170 4.1 Introduction . 171 4.2 Radiative Solver . 176 4.2.1 Short Characteristics . 178 4.2.2 Implementation of Short Characteristics . 183 4.2.3 Long Characteristics . 185 4.2.4 Acceleration Schemes . 188 4.2.5 Raytracing . 190 4.2.6 Frequency Discretization . 191 4.2.7 Angular Discretization . 191 4.3 Numerical Tests . 194 4.3.1 1D Plane-parallel Grey Atmosphere . 195 4.3.2 Convergence Tests . 197 4.3.3 Multiray Temperature Solution . 198 4.3.4 Test of Spectral Hardening . 200 4.3.5 Effect of a Heating Source . 201 4.3.6 2D Solutions and Ray Defects . 204 4.3.7 3D Solutions . 209 4.3.8 GR Solutions . 216 4.4 Summary . 228 4.5 Acknowledgements . 229 4.6 Ray Defects . 230 4.6.1 Mathematical Origin of Ray Defects . 233 4.6.2 Ray Defect Correction Schemes . 235 vii CONTENTS 4.7 Analytic 1D Atmosphere Spectrum . 238 5 HEROIC - A Comptonization Module for the HERO radiative code 242 5.1 Introduction . 243 5.2 Radiative Transfer Solution . 246 5.2.1 Kompaneets-Ray . 248 5.2.2 Quadratic Variation of the Source Function . 250 5.3 Numerical Tests . 253 5.3.1 Kompaneets . 253 5.3.2 Escape Time Distributions . 256 5.4 Application { Accretion Disk . 264 5.4.1 Numerical Disk Setup . 265 5.4.2 Results . 267 5.5 Discussion . 274 5.6 Summary . 280 6 Summary and Future Directions 282 6.1 Summary . 282 6.2 Future Directions . 284 6.2.1 Astrophysical Applications . ..