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C Copyright by Jonathan C. Mckinney, 2004 BLACK HOLE ACCRETION SYSTEMS

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C Copyright by Jonathan C. Mckinney, 2004 BLACK HOLE ACCRETION SYSTEMS °c Copyright by Jonathan C. McKinney, 2004 BLACK HOLE ACCRETION SYSTEMS BY JONATHAN C. MCKINNEY B.S., Texas A&M University of College Station, 1996 M.S., University of Illinois at Urbana-Champaign, 1999 DISSERTATION Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Physics in the Graduate College of the University of Illinois at Urbana-Champaign, 2004 Urbana, Illinois Abstract Accretion onto a black hole is the most efficient known process to convert gravitational energy into radiation. Some gamma-ray bursts (GRBs), some X-ray binaries, and all active galactic nuclei (AGN) are likely powered by accretion onto a rotating black hole. I model the global, time- dependent accretion flow around a black hole using the nonradiative viscous hydrodynamic (VHD), Newtonian magnetohydrodynamic (MHD), and general relativistic MHD (GRMHD) equations of motion, which are integrated numerically. I wrote the VHD and nonrelativistic MHD numerical codes, and coauthored the GRMHD code (Gammie et al., 2003). I first studied VHD accretion disk models, such as those studied by Igumenshchev et al. (1999, 2000) and Stone et al. (1999), hereafter IA and SPB. IA and SPB use the VHD model of accretion, but they gave qualitatively different measurements of the energy per baryon accreted, angular momentum per baryon accreted, and the radial scaling law for various quantities. While there was concern in the community that the different results were due to numerical error, I found that the different results could be reproduced using my single VHD code to model the accretion flow (McKinney and Gammie, 2002). The differences in their results were due to differences in their experimental designs. Seemingly small changes to the VHD model introduced nonnegligible changes to the results. This suggests that a self-consistent MHD, rather than phenomenological VHD, model for turbulence is required to study accretion flow. First discovered during the VHD study described above, I found that VHD, nonrelativistic MHD, and GRMHD numerical accretion disk models can produce significant numerical artifacts unless the flow near the inner radial boundary condition, at rin, is out of causal contact with the flow at r > rin. For the VHD model, this corresponds to setting rin so the flow there is always ingoing at supersonic speeds. For the MHD models, this corresponds to setting rin so the flow there is always ingoing at superfast speeds. For the GRMHD model, this is easily constructed by using Kerr-Schild (horizon-penetrating) coordinates. In this case, rin is chosen to be inside the horizon, where all waves are ingoing. I next studied MHD and GRMHD numerical accretion disk models to test the results of previ- ously studied phenomenological disk models. These models are based on the Shakura & Sunyaev ®-disk model and suggest the disk should terminate at the innermost stable circular orbit (ISCO) of a black hole. Simplified GRMHD models predict super-efficient accretion due to energy extraction from a rotating black hole. I found that MHD and GRMHD numerical models show that the disk does not terminate at the ISCO, and magnetic fields continue to exert a torque on the disk inside the ISCO. The disk will likely continue to emit radiation inside the ISCO, altering the predicted spectra of accretion disks. GRMHD numerical models of thick and thin disks show that the energy iii per baryon accreted closely follows the thin disk efficiency, so super-efficient accretion does not seem to be a generic property of thick magnetized relativistic disks (McKinney and Gammie, 2004). The Blandford-Znajek (BZ) effect, describing the extraction of spin energy of a rotating black hole by the magnetosphere, plausibly powers the jet in some GRBs, some microquasars, and all AGN. I found that GRMHD numerical models of thick disks around a rotating black hole show that an evacuated, nearly force-free magnetosphere develops as predicted by BZ (McKinney and Gammie, 2004). The BZ solution for the energy extracted is remarkably accurate in this region for a black hole with a=M . 0:5 and qualitatively accurate for all a=M, where a is the Kerr spin parameter and M is the mass of the black hole. GRMHD numerical models with a=M & 0:5 show a mildly relativistic (Lorentz factor Γ » 1:5 ¡ 3) collimated Poynting jet around the polar axis. Currently, no self-consistent MHD model of the accretion flow around a black hole shows a jet with Γ & 3. Additional physics is likely required to obtain Γ » 100 as models predict in GRBs, and to obtain Γ » 3 ¡ 10 as seen in some microquasars and AGN. I studied the VHD, MHD, and GRMHD accretion models by performing numerical simulations on our group’s Beowulf computer clusters, which I designed and constructed. For about $50,000, one can buy a private cluster of computers that will provide as much computing power as today’s typical time-shared “supercomputer.” I give an account of the procedures necessary to design, build, and test a Beowulf cluster. The main conclusion is obvious: test one’s code on test nodes before purchasing the entire cluster in order to confirm the performance and reliability of the chosen components (CPUs, motherboard, network, etc.). iv To my mom. v Acknowledgments I strongly express my gratitude to my supervisor, Prof. Charles Forbes Gammie, whose expertise, understanding, and patience added considerably to my graduate experience. Charles demonstrates a broad-minded, razor-sharp knowledge of astrophysics, and his example has driven me to become a better scientist. Charles has tirelessly reviewed many of my written works, and with his help, I have gradually improved my skills as a writer. I express a special thanks to Scott Noble and Ruben Krasnopolsky, who both proofread the unpublished parts of my thesis. They gave excellent comments that greatly improved the focus, clarity, and readability of the thesis. Throughout their careers as postdocs for Charles, they have provided me with many stimulating conversations and uncountable helpful pointers. I thank Paul Ricker for excellent comments about the Beowulf cluster appendix. I thank the members of my thesis committee: Charles Gammie, Stu Shapiro, Susan Lamb, and Jen-Chieh Peng. Their time is precious and I am grateful for all the comments on my written thesis and oral defense. I particularly thank Stu Shapiro for being a great source of inspiration and guidance in the study of relativity and compact objects. I thank Charles Gammie, Stu Shapiro, Bill Watson, David Campbell, and Peter Anninos for writing recommendation letters for my future career as a postdoc at Harvard with Ramesh Narayan, who I thank for hiring me and being patient while I finish my thesis. I thank and love my family for the support they provided me through my entire life and in par- ticular, I must acknowledge my fianc´eand best friend, Elena, without whose love, encouragement, and editing assistance I would not have finished this thesis. My financial support was largely provided by a NASA GSRP Fellowship Grant NGT5-50343 (S01-GSRP-044) and partially supported by a GE fellowship. During my thesis work, Charles was supported by an NCSA Faculty Fellowship, the UIUC Research Board, NSF ITR grant PHY 02-05155, and NSF PECASE grant AST 00-93091. Computations were done in part under NCSA grants AST010012N and AST010009N using the Origin 2000 and Posic Linux cluster at NCSA. Some computations were performed on Platinum. vi Table of Contents List of Figures . x List of Tables . xiv List of Abbreviations and Acronyms . xv Summary . xix 1 Observations, Theory, and Models . 1 1.1 Summary of Introduction . 1 1.2 Introduction to Black Hole Systems . 4 1.2.1 Formation of Black Holes . 5 1.2.2 Gamma-Ray Bursts . 7 1.2.3 Black Hole X-ray Binaries . 9 1.2.4 Normal and Active Galactic Nuclei and Quasars . 12 1.3 Basic Accretion Disk Theory . 15 1.3.1 Accretion Luminosity and Mass of the Compact Object . 15 1.3.2 Some Accretion-Based Arguments . 19 1.4 Models of Accretion Disks and GRBs . 24 1.4.1 Angular Momentum Transport Models . 25 1.4.2 Radiative Disk Models . 29 1.4.3 Gamma-Ray Bursts Models . 33 1.5 Characteristic Quantities and Model Validity Estimates . 38 1.5.1 Estimated State and Structure of Accretion Flow . 38 1.5.2 Validity of the Fluid, MHD, and ideal MHD Approximations . 46 1.6 Summary of Motivation for a GRMHD Model and Open Questions . 49 1.7 Summary of Dissertation Results . 50 1.7.1 Viscous Hydrodynamics Summary . 52 1.7.2 Global 2D/3D MHD Summary . 54 1.7.3 HARM / GRMHD Summary . 56 1.7.4 BZ Effect Summary . 57 1.7.5 BZ/Inflow Solution Comparison Summary . 58 2 Numerical Models of Viscous Accretion Flows Near Black Holes . 60 2.1 Summary of Chapter . 60 2.2 Introduction . 60 2.3 Model . 62 2.4 Numerical Methods . 65 2.4.1 Numerical Treatment of Low Density Regions . 66 2.4.2 Diagnostics . 66 vii 2.4.3 Code Tests . 67 2.5 Results . 68 2.5.1 Fiducial Model Evolution . 69 2.5.2 Dependence on Inner Boundary Location and Gravitational Potential . 74 2.5.3 Comparison of Torus and Injection Models . 76 2.5.4 Other Parameters . 77 2.6 VHD Summary . 78 2.7 Global 2D MHD Simulations . 79 2.8 Global 3D MHD Simulation . 81 3 HARM: A Numerical Scheme for General Relativistic Magnetohydrodynamics 82 3.1 Summary of Chapter . 82 3.2 Introduction . 82 3.3 A GRMHD Primer . 84 3.4 Numerical Scheme . 86 3.4.1 Constrained Transport . 88 3.4.2 Wave Speeds . 89 3.4.3 Implementation Notes .
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