Radiation Transport Around Kerr Black Holes Jeremy David ...

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10 CONTENTS
List of Figures 1-1 Sample of observations from black holes with QPOs . . . . . . . . . . 23 1-2 Power spectrum from hot spot model and data from RXTE . . . . . 28 2-1 Schematic picture of ray-tracing method . . . . . . . . . . . . . . . . 45 2-2 Projection of image plane onto disk plane . . . . . . . . . . . . . . . . 46 2-3 Relativistic transformation of an absorbing medium . . . . . . . . . . 52 2-4 Schematic of photon path for radiative transfer equation . . . . . . . 53 2-5 Redshift transfer function for flat disks . . . . . . . . . . . . . . . . . 61 2-6 Line broadening as a function of inclination . . . . . . . . . . . . . . 62 2-7 Line broadening as a function of spin; constant emission . . . . . . . 63 2-8 Observations of broad iron emission lines . . . . . . . . . . . . . . . . 64 2-9 Observational evidence for the Blandford-Znajek process . . . . . . . 66 2-10 Line broadening as a function of spin; power-law emission . . . . . . . 67 3-1 Spectrogram of hot spot on circular orbit . . . . . . . . . . . . . . . . 71 3-2 Required hot spot overbrightness for 1% rms modulation . . . . . . . 73 3-3 Light curves for a variety of inclinations . . . . . . . . . . . . . . . . 74 3-4 Light curve and power spectrum for circular hot spot orbit . . . . . . 75 3-5 Fourier amplitude a n (rms) as a function of inclination and hot spot size 76 3-6 Spectrograms for a variety of spins, i = 30 ◦ . . . . . . . . . . . . . . . 77 3-7 Spectrograms for a variety of spins, i = 75 ◦ . . . . . . . . . . . . . . . 78 3-8 Fourier amplitude a n (rms) as a function of inclination for a/M = 0.9 79 3-9 Radius of orbits with commensurate frequencies as a function of spin 80 3-10 Trajectory of hot spot with closed rosette orbit . . . . . . . . . . . . 81 3-11 Light curve and power spectrum for eccentric hot spot orbit . . . . . 82 3-12 Harmonic power in beat modes as a function of inclination . . . . . . 83 3-13 Harmonic power in beat modes as a function of eccentricity . . . . . . 84 3-14 Power spectra for sheared hot spot arcs . . . . . . . . . . . . . . . . . 86 3-15 Matching LFQPOs and HFQPOs as a function of spin . . . . . . . . 88 11
Page 1: Radiation Transport Around Kerr Bla
Page 5 and 6: 5 Acknowledgments Gravity can not b
Page 7 and 8: Contents 1 Introduction and Outline
Page 9: CONTENTS 9 A Formulae for Hamiltoni
Page 13 and 14: List of Tables 3.1 Black hole param
Page 15 and 16: Chapter 1 Introduction and Outline
Page 17 and 18: 1.2. HISTORICAL BACKGROUND 17 to th
Page 19 and 20: 1.2. HISTORICAL BACKGROUND 19 disk
Page 21 and 22: 1.2. HISTORICAL BACKGROUND 21 tral
Page 23 and 24: ¼ÐÀÓÐÒÖ× 1.3. OUTLINE OF ME
Page 25 and 26: 1.3. OUTLINE OF METHODS AND RESULTS
Page 31 and 32: 1.4. ALTERNATIVE QPO MODELS 31 isot
Page 33 and 34: 1.4. ALTERNATIVE QPO MODELS 33 jets
Page 35 and 36: Chapter 2 Ray-Tracing in the Kerr M
Page 37 and 38: 2.1. EQUATIONS OF MOTION 37 Killing
Page 39 and 40: 2.1. EQUATIONS OF MOTION 39 flat sp
Page 41 and 42: 2.1. EQUATIONS OF MOTION 41 conveni
Page 43 and 44: 2.1. EQUATIONS OF MOTION 43 in sepa
Page 45 and 46: 2.2. GEODESIC RAY-TRACING 45 basis
Page 47 and 48: 2.2. GEODESIC RAY-TRACING 47 throug
Page 49 and 50: 2.2. GEODESIC RAY-TRACING 49 with a
Page 51 and 52: 2.2. GEODESIC RAY-TRACING 51 since
Page 53 and 54: 2.2. GEODESIC RAY-TRACING 53 dx µ
Page 55 and 56: 2.2. GEODESIC RAY-TRACING 55 In the
Page 57 and 58: 2.3. NUMERICAL METHODS 57 a long pa
Page 59 and 60: 2.4. BROADENED EMISSION LINES FROM
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2.4. BROADENED EMISSION LINES FROM
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Chapter 3 The Geodesic Hot Spot Mod
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3.1. HOT SPOT EMISSION 71 Figure 3-
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3.2. NON-CIRCULAR ORBITS 77 Figure
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3.2. NON-CIRCULAR ORBITS 79 Figure
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3.2. NON-CIRCULAR ORBITS 81 paramet
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3.2. NON-CIRCULAR ORBITS 83 at (2/3
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3.2. NON-CIRCULAR ORBITS 85 form at
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3.3. NON-PLANAR ORBITS 87 3.3 Non-p
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3.3. NON-PLANAR ORBITS 89 Table 3.1
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3.4. SUMMARY 91 binaries in many wa
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Chapter 4 Features of the QPO Spect
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4.2. PARAMETERS FOR THE BASIC HOT S
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4.3. PEAK BROADENING FROM HOT SPOTS
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4.3. PEAK BROADENING FROM HOT SPOTS
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4.4. DISTRIBUTION OF COORDINATE FRE
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4.5. ELECTRON SCATTERING IN THE COR
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4.6. FITTING QPO DATA FROM XTE J155
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4.6. FITTING QPO DATA FROM XTE J155
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4.7. HIGHER ORDER STATISTICS 117 ob
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4.7. HIGHER ORDER STATISTICS 119 bi
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4.7. HIGHER ORDER STATISTICS 121 Fi
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4.7. HIGHER ORDER STATISTICS 123 12
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4.8. SUMMARY 125 els. Clearly the h
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Chapter 5 Steady-state α-disks The
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5.1. STEADY-STATE DISKS OUTSIDE THE
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5.2. GEODESIC PLUNGE INSIDE THE ISC
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5.2. GEODESIC PLUNGE INSIDE THE ISC
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5.3. NUMERICAL IMPLEMENTATION 143 F
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5.3. NUMERICAL IMPLEMENTATION 145 a
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5.3. NUMERICAL IMPLEMENTATION 147 (
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5.4. OBSERVED SPECTRUM OF THE DISK
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Chapter 6 Electron Scattering If we
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6.1. PHYSICS OF SCATTERING 159 Θ
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6.1. PHYSICS OF SCATTERING 161 the
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6.1. PHYSICS OF SCATTERING 163 and
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6.1. PHYSICS OF SCATTERING 165 colo
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6.2. EFFECT ON SPECTRA 167 Let g(z)
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6.2. EFFECT ON SPECTRA 169 (1979);
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6.2. EFFECT ON SPECTRA 171 Figure 6
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6.3. EFFECT ON LIGHT CURVES 173 Fig
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6.4. IMPLICATIONS FOR QPO MODELS 17
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Chapter 7 Conclusions and Future Wo
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7.1. SUMMARY OF RESULTS 183 the low
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7.2. CAVEATS 185 back to the coordi
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7.3. NEW APPLICATIONS OF CURRENT CO
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7.4. NEW FEATURES FOR CODE 189 grou
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7.5. DEVELOPMENT OF NEW MODELS 191
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Appendix A Formulae for Hamiltonian
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195 The relevant spatial derivative
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Appendix B Summing Periodic Functio
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199 Over a sample time T f ≫ T l
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Bibliography Abramowicz, M. A., Lan
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BIBLIOGRAPHY 203 Damour, T., & Espo
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BIBLIOGRAPHY 205 Hawler, J. F., & G
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BIBLIOGRAPHY 207 McClintock, J. E.,
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BIBLIOGRAPHY 209 Psaltis, D. 2001b,
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BIBLIOGRAPHY 211 Stern, B., et al.
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