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Accretion Processes on a Black Hole Sandip K Contents Abstract ........................................... ............. 4 1: Introduction ..................................... .............. 5 1.1 Some General Issues Related to Black Hole Astrophysics . .................. 7 1.1.1 Formation of Black Holes ......................... ....................... 7 1.1.2 Fueling Active Galactic Nuclei . ........................ 9 1.1.3 Evolution of Galactic Centers .................... ....................... 12 1.1.4 Black Holes in Galactic Halos? .................... ..................... 13 1.1.5 Some Signatures of Black Holes .................... ..................... 14 1.2 Difference between Motions around a Newtonian Star and a BlackHole ... 16 1.3 Basics of Pseudo-Newtonian Geometries . .................... 21 1.4 Remarks About Units and Dimensions . .................. 23 2: Spherical Accretion ............................... ............ 24 2.1 Bondi Accretion on a Newtonian Star .................. ................... 25 2.1.1 Basic Equations ................................ ........................ 25 2.1.2 Phase Space Behaviour of the Bondi Flow . ................. 28 2.2 Bondi Flow on a Black Hole ........................... ................... 30 2.2.1 In Schwarzschild Geometry ....................... ....................... 30 2.2.2 In pseudo-Newtonian Geometry .................... ..................... 31 2.3 Bondi Flow with Simple Radiative Transfer . ................... 32 2.4 Bondi Flow with General Radiative Transfer . ................... 32 2.4.1 Single Temperature Solutions .................... ....................... 34 2.4.2 Two Temperature Solutions ....................... ...................... 35 2.4.3 General Relativistic Optically Thick Bondi Flow . .................... 40 2.4.4 Inclusion of Pair Production and Preheating . .................... 44 2.5 Shocks in Spherical Flows .......................... ...................... 47 2.6 Particle Acceleration at Shock Waves . ..................... 48 2.6.1 Basic Physical Processes . ........................ 48 arXiv:astro-ph/9605015v1 3 May 1996 2.6.2 Acceleration at Spherical Shocks and AGN Spectra . ................. 50 3: Thin Accretion Disk Models .......................... ........ 55 3.1 Standard Disk Model and Its Spectra .................. ................... 56 3.1.1 Model Equations ................................ ....................... 56 3.1.2 Structure of a Standard Disk ...................... ..................... 61 3.1.3 Emitted radiation from a Standard Disk ............. ................... 61 3.1.4 Stability of a Thin Disk .......................... ....................... 63 3.1.5 Viscosity in a Thin Disk .......................... ...................... 64 3.2 Two Temperature Disk Models ........................ ................... 65 3.3 Transonic Disk Models ............................. ...................... 65 3.4 Magnetized Disk Models ............................ ...................... 66 3.5 Thin Disks with Weber-Devis Magnetic Field Configuration ............... 69 3.5.1 Basic Equations and Magnetosonic Point Conditions . .................. 69 1 3.5.2 Solution Topologies of Magnetized Accretion . ..................... 72 qquad 3.6 Outflows by Extraction of Energy from Black Holes . .............. 73 4: Thick Accretion Disks .............................. .......... 75 4.1 Introduction .................................... .......................... 75 4.2 Pseudo-Newtonian Thick Disks . ..................... 77 4.3 General Relativistic Thick Disks . ....................... 78 4.4 Thermodynamic Conditions inside a Thick Accretion Disk ................ 79 4.5 Emitted Radiation from a Thick Accretion Disk . ................. 80 4.6 Ion Pressure Dominated Thick Disks . ................... 81 4.7 Magnetized Thick Disks ............................ ...................... 82 4.8 Thick Accretion Disk – To Be or Not to Be? . ............... 83 5: Advective Disks ................................... ............ 85 5.1 Model Equations and Multiplicity of Critical Points . .................... 87 5.2 Adiabatic Disks With Discontinuities . ...................... 90 5.2.1 Steady State Solutions .......................... ........................ 90 5.2.2 Sonic Point Conditions .......................... ....................... 91 5.2.3 When Does a Flow Contain Shocks? ................... ................. 92 5.2.4 Shock Conditions ............................... ........................ 93 5.2.5 Examples of Complete Solutions with Discontinuities .................... 94 5.3 Isothermal Advective Flow with Viscosity . ..................... 95 5.4 Most General Advective Flow and Unification of Accretion Disk Models . 96 5.5 ‘Advection Dominated’ Disk Models . .................... 99 5.6 Axisymmetric Shock Waves in a Few Other Systems . ............. 100 5.6.1 In Kerr Geometry ................................ ..................... 100 5.6.2 In Magnetized Flows ............................. ..................... 100 5.7 Non-Axisymmetric Spiral Shock Waves . .................. 101 5.7.1 Introduction .................................. ......................... 101 5.7.2 Basic Flow Equations ............................ ...................... 102 5.7.3 Examples of Spiral Shocks in Accretion Disks . .................. 105 6: Numerical Simulations of Accretion Disks . ....... 106 6.1 Introduction .................................... ......................... 106 6.2 Simulation of Bondi-Hoyle-Littleton Accretion . ..................... 106 6.3 Simulations of Inviscid Flows . ...................... 108 6.4 Simulations of Viscous Disks ....................... ..................... 110 6.5 Simulations of Flows using Radiative Transfer . ................... 115 7: Observational Signatures of Black Hole Accretion . 117 7.1 Introduction .................................... ......................... 117 7.2 Continuum Emission ............................... ..................... 118 7.3 Variability of AGN Spectrum ........................ .................... 123 7.4 Correlated Variabilities ......................... ......................... 124 7.5 Variability of Disk Line Emission . ..................... 125 7.5.1 Temporal Variation ............................. ....................... 126 7.5.2 Spatial Variation .............................. ........................ 127 7.6 Quasi-Periodic Oscilaltions ...................... ........................ 129 2 7.7 Our Galactic Center ............................... ...................... 129 8 Concluding Remarks ................................. ........ 134 9 Note Added in Proof .................................. ......... 138 10 References ....................................... ........................ 140 11 Figure Captions ................................... .................. 157-167 3 Accretion Processes On a Black Hole Sandip K. Chakrabarti Tata Institute Of Fundamental Research, Bombay, 400005 INDIA Abstract We describe astrophysical processes around a black hole keeping primarily the physics of accretion in mind. In 1, we briefly discuss the formation, evolution and detection of black holes. We also§ discuss the difference of flow properties around a black hole and a Newtonian star. In 2, we present past and present developments in the study of spherically accreting flows.§ We study the properties of Bondi flow with and without radiative transfer. In the presence of significant angular momentum, which is especially true in a binary system, matter will be accreted as a thin Keplerian disk. In 3, we discuss a large number of models of these disks including the more popular § standard disk model. We present magnetized disk models as well. Since the angular momentum is high in these systems, rotational motion is the most dominant component compared to the radial or the vertical velocity components. In 4, we study thick disk § models which are of low angular momentum but still have no significant radial motion. The accretion rates could be very high causing the flow to become radiation dominated and the disk to be geometrically thick. For low accretion rates, ion pressure supported disks are formed. In 5, we extensively discuss the properties of transonic flows which has with sub-Keplerian§ angular momentum. In the absence of shock discontinuities, these sub-Keplerian flows are basically advecting, similar to Bondi flows, close to the black holes, though far away they match Keplerian or sub-Keplerian disks. In presence of shocks, the post-shock flow becomes rotation dominated similar to thick disks. In 6, we present results of important numerical simulations of accretion flows. Significant results§ from the studies of evolution of viscous transonic flows are reported. In 7, we § discuss some observational evidences of the black hole accretion. We also present a detailed model of a generalized accretion disk and present its spectra and compare with observations. In 8, we summarize the review and make concluding remarks. § 4 1. Introduction Among all the celestial objects, black holes are the simplest to describe math- ematically. The simplest among the black holes, known as a Schwarzschild black hole, is characterized by its mass M alone, and has occupied a very popular place in models of active galaxies, quasars and some compact X-ray binaries. Along with the constant of gravitation, G and the velocity of light c, one can obtain a length-scale 2 14 3 lbh = GM/c =1.5 10 M9 cm, and a time scale tbh = GM/c = 5000M9s (M9 is the mass of the central× black hole in units
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