Radiation Transport Around Kerr Black Holes Jeremy David ...

More documents

Recommendations

Info

174 CHAPTER 6. ELECTRON SCATTERING These effects are clearly visible in the first panel of Figure 6-7, which shows the time-dependent spectrum of a monochromatic emitter, as viewed by an observer at 45 ◦ . The logarithmic color scale shows [#photons/s/cm 2 /keV/period], normalized to the peak intensity in each panel. At “0” phase, when the emitter is moving away from the observer, the spectrum shows two distinct lines, one blueshifted in the forward direction of hot spot motion, and one redshifted in the backward direction. As the hot spot comes around towards the observer, the directly beamed blueshifted line dominates, and then when the phase is ∼ 0.5 and the hot spot is on the near side of the black hole, a single line dominates. This is due to the gravitational demagnification of the secondary images formed by photons that have to complete a full circle around the black hole to reach the observer. While these features would most likely be unresolvable for black hole binaries, they may well be observable in X-ray flares from Sgr A ∗ as well as other supermassive black holes [e.g. see Baganoff et al. (2001)]. In the subsequent panels, the spectrum is modified by the scattering of the hot spot photons in the surrounding corona. As in Section 6.2, the temperature and density profile of the corona is given by an ADAF model with T e (r ISCO ) = 100 keV. The four panels of Figure 6-7 show increasing values of τ es = [0, 1, 2, 4]. The effects of scattering on the spectra are really quite profound. As we described qualitatively in Chapter 4, the electron corona is like a cloud of fog surrounding a lighthouse, spreading out the delta-function beam in time and frequency. Unlike the simple model there, where each photon was assigned some positive time delay, the Monte Carlo scattering code shows that some photons actually arrive earlier in time by taking a “shortcut” to the observer instead of waiting for the hot spot to come around and move towards the observer. And of course, the photons are also spread out in frequency due to the inverse-Compton effects. As the optical depth increases, the well-defined curve in Figure 6-7a is smeared out into a nearly constant blur at τ es = 4, with a broad spectral peak as in Figure 6-6. Only a slight trace of the original coherent light curve remains, composed of roughly 1% of the emitted photons that do not scatter before reaching the observer or get captured by the event horizon. When τ es > 1, multiple scattering become more common, so photon shortcuts become rarer, tending to spread the light curve preferentially to the right (delay in observer time), as seen in Figures 6-7c,d. We show a similar set of spectrograms in Figure 6-8, now with orbital inclination i = 75 ◦ . The qualitative effects are the same, but the higher inclination gives stronger relativistic effects and more powerful beaming. The strongly peaked light curve maintains a somewhat sharper contrast even for high optical depth. While the detailed spectral and timing features of Figures 6-7 and 6-8 promise to reveal much about the underlying physical processes at work, we are still a very long way from achieving such observational resolution in black hole binary sources, where the relevant time
6.3. EFFECT ON LIGHT CURVES 175 Figure 6-8: Spectrograms of a monochromatic, isotropic hot spot emitter, as in Figure 6-7, but now with inclination i = 75 ◦ .
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 and 10:
CONTENTS 9 A Formulae for Hamiltoni
Page 11 and 12:
List of Figures 1-1 Sample of obser
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 27 and 28:
Page 29 and 30:
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
Page 61 and 62:
Page 63 and 64:
Page 65 and 66:
Page 67 and 68:
Page 69 and 70:
Chapter 3 The Geodesic Hot Spot Mod
Page 71 and 72:
3.1. HOT SPOT EMISSION 71 Figure 3-
Page 73 and 74:
Page 75 and 76:
Page 77 and 78:
3.2. NON-CIRCULAR ORBITS 77 Figure
Page 79 and 80:
3.2. NON-CIRCULAR ORBITS 79 Figure
Page 81 and 82:
3.2. NON-CIRCULAR ORBITS 81 paramet
Page 83 and 84:
3.2. NON-CIRCULAR ORBITS 83 at (2/3
Page 85 and 86:
3.2. NON-CIRCULAR ORBITS 85 form at
Page 87 and 88:
3.3. NON-PLANAR ORBITS 87 3.3 Non-p
Page 89 and 90:
3.3. NON-PLANAR ORBITS 89 Table 3.1
Page 91 and 92:
3.4. SUMMARY 91 binaries in many wa
Page 93 and 94:
Chapter 4 Features of the QPO Spect
Page 95 and 96:
4.2. PARAMETERS FOR THE BASIC HOT S
Page 97 and 98:
4.3. PEAK BROADENING FROM HOT SPOTS
Page 99 and 100:
4.3. PEAK BROADENING FROM HOT SPOTS
Page 101 and 102:
4.4. DISTRIBUTION OF COORDINATE FRE
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
4.5. ELECTRON SCATTERING IN THE COR
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
4.6. FITTING QPO DATA FROM XTE J155
Page 115 and 116:
4.6. FITTING QPO DATA FROM XTE J155
Page 117 and 118:
4.7. HIGHER ORDER STATISTICS 117 ob
Page 119 and 120:
4.7. HIGHER ORDER STATISTICS 119 bi
Page 121 and 122:
4.7. HIGHER ORDER STATISTICS 121 Fi
Page 123 and 124: 4.7. HIGHER ORDER STATISTICS 123 12
Page 125 and 126: 4.8. SUMMARY 125 els. Clearly the h
Page 127 and 128: Chapter 5 Steady-state α-disks The
Page 129 and 130: 5.1. STEADY-STATE DISKS OUTSIDE THE
Page 139 and 140: 5.2. GEODESIC PLUNGE INSIDE THE ISC
Page 141 and 142: 5.2. GEODESIC PLUNGE INSIDE THE ISC
Page 143 and 144: 5.3. NUMERICAL IMPLEMENTATION 143 F
Page 145 and 146: 5.3. NUMERICAL IMPLEMENTATION 145 a
Page 147 and 148: 5.3. NUMERICAL IMPLEMENTATION 147 (
Page 149 and 150: 5.4. OBSERVED SPECTRUM OF THE DISK
Page 157 and 158: Chapter 6 Electron Scattering If we
Page 159 and 160: 6.1. PHYSICS OF SCATTERING 159 Θ
Page 161 and 162: 6.1. PHYSICS OF SCATTERING 161 the
Page 163 and 164: 6.1. PHYSICS OF SCATTERING 163 and
Page 165 and 166: 6.1. PHYSICS OF SCATTERING 165 colo
Page 167 and 168: 6.2. EFFECT ON SPECTRA 167 Let g(z)
Page 169 and 170: 6.2. EFFECT ON SPECTRA 169 (1979);
Page 171 and 172: 6.2. EFFECT ON SPECTRA 171 Figure 6
Page 173: 6.3. EFFECT ON LIGHT CURVES 173 Fig
Page 177 and 178: 6.3. EFFECT ON LIGHT CURVES 177 Fig
Page 179 and 180: 6.4. IMPLICATIONS FOR QPO MODELS 17
Page 181 and 182: Chapter 7 Conclusions and Future Wo
Page 183 and 184: 7.1. SUMMARY OF RESULTS 183 the low
Page 185 and 186: 7.2. CAVEATS 185 back to the coordi
Page 187 and 188: 7.3. NEW APPLICATIONS OF CURRENT CO
Page 189 and 190: 7.4. NEW FEATURES FOR CODE 189 grou
Page 191 and 192: 7.5. DEVELOPMENT OF NEW MODELS 191
Page 193 and 194: Appendix A Formulae for Hamiltonian
Page 195 and 196: 195 The relevant spatial derivative
Page 197 and 198: Appendix B Summing Periodic Functio
Page 199 and 200: 199 Over a sample time T f ≫ T l
Page 201 and 202: Bibliography Abramowicz, M. A., Lan
Page 203 and 204: BIBLIOGRAPHY 203 Damour, T., & Espo
Page 205 and 206: BIBLIOGRAPHY 205 Hawler, J. F., & G
Page 207 and 208: BIBLIOGRAPHY 207 McClintock, J. E.,
Page 209 and 210: BIBLIOGRAPHY 209 Psaltis, D. 2001b,
Page 211 and 212: BIBLIOGRAPHY 211 Stern, B., et al.
show all

Radiation Transport Around Kerr Black Holes Jeremy David ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?