Radiation Transport Around Kerr Black Holes Jeremy David ...

More documents

Recommendations

Info

22 CHAPTER 1. INTRODUCTION AND OUTLINE the X-ray light curve of this source has QPO variability in the power spectrum (Aschenbach et al., 2004). • Shortly after the launch of RXTE at the end of 1995, Strohmayer et al. (1996) discovered a pair of high frequency QPOs (HFQPOs) in neutron star binary system. Remillard et al. (1996) found a broader, weaker HFQPO in the black hole binary GRO J1655–40, soon followed by similar features in the power spectra of 4U 1543–47, XTE J1858+226, and XTE J1550–564 (Remillard & Morgan, 1998; Markwardt, Swank, & Taam, 1999; Remillard et al., 1999; Homan et al., 2001). • McClintock & Remillard (2004) compiled a representative sample of photon energy spectra and light curve power spectra for many of these black hole systems, reproduced here in Figure 1-1. The QPOs typically are seen in the “Very High” or “Steep Power Law” spectral state, described in more detail later in this Thesis. • Miller et al. (2001) first identified the 3:2 ratio of HFQPO pairs in XTE J1550– 564, followed by identical ratios in GRO J1655–40, GRS 1915+105, and H1743– 322 (Remillard et al., 2002; Homan et al., 2004; Remillard et al., 2004). Recently, similar ratios have been reported in intermediate-mass and even super-massive black holes (Abramowicz et al., 2004; Fiorito & Titarchuk, 2004; Aschenbach et al., 2004; Aschenbach, 2004; Torok, 2004), but these results are still quite preliminary and widely open to other interpretations. • Miller & Homan (2005) have recently found evidence linking the phase of a low frequency QPO with the shape of the iron emission line in GRS 1915+105, giving a promising connection between the two leading methods of probing strong field gravity. 1.3 Outline of Methods and Results 1.3.1 Ray-tracing in the <strong>Kerr</strong> Metric The central framework on which the results in this Thesis are based is a relativistic ray-tracing code that calculates the trajectories of photons in the <strong>Kerr</strong> spacetime of a spinning black hole. By tracing the photons from either the emitter to the observer or backwards in time from the observer to the emitter, we can reconstruct timedependent images and spectra of the accretion region. When starting at the observer, the image plane is divided into pixels of equal solid angle, each corresponding to a
¼ÐÀÓÐÒÖ× 1.3. OUTLINE OF METHODS AND RESULTS 23 ½ÀÞÒ¿¼¼ÀÞ¸Ö×ÔØÚÐÝ´ÊÑÐÐÖØÐº¾¼¼¾µºÌÖÐØÓÒ×ÔØÛÒ ×ÓÙÖ×ÙÖÒÔÓÒØÓ×ÖÚØÓÒ×ÛØÊÌ´ËÓÞØÐº¾¼¼¼ËÓÞØÐº ½µÑÓÖÓÚÖ¸ÓØÓ×ÖÚØÓÒ×ÖÚÐØÔÖ×ÒÓßÖÕÙÒÝÉÈÇ×¸ ÖÐÖ¬ÙÖ×º ÔÖ×ÒÓßÖÝÉÈÇ×ºÌ×ÒÓØØÐÒ×ÓÐÐÓÛØÓÒÚÒØÓÒÓ ºº½ºßÖÝ×ÔØÖÓÀ×ÒØËÈÄ×ØØ¸Û×ÖØÖÞÝ ×ØÖÓÒÒ×ØÔÔÓÛÖßÐÛÓÑÔÓÒÒØÒØÒÖÝ×ÔØÖÙÑ¸ÐÓÒÛØØ ØËÈÄ×ØØÒßÖÕÙÒÝÉÈÇ×ÛÐÐ×Ù××ÒÙÖØÖÒÜºº¿º À×ºÓÖØÖÓØ×ÓÙÖ×ÛÚÒÖßÑÜÑÙÑµÙÜ×ØØÚÒ ÁÒºº½Û×ÓÛ×ÔØÖÓØËÈÄ×ØØÓÖØÖÀ×ÒØÛÓØÓÒÐ Figure 1-1: On the left is shown a collection of RXTE photon energy spectra from black hole binaries in the “Very High” state, characterized by a dominant steep power-law (dashed curve), a weaker thermal component (solid), and a faint broad iron emission line (dotted). On the right, RXTE power spectra from X-ray timing observations of the same sources show the presence of QPOs from ∼ 5 −500 Hz. [Reproduced from McClintock & Remillard (2004) with permission]
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: 1.2. HISTORICAL BACKGROUND 21 tral
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
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:
3.1. HOT SPOT EMISSION 73 Figure 3-
Page 75 and 76:
3.1. HOT SPOT EMISSION 75 Figure 3-
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 131 and 132:
Page 133 and 134:
Page 135 and 136:
Page 137 and 138:
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 151 and 152:
Page 153 and 154:
Page 155 and 156:
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 and 174:
6.3. EFFECT ON LIGHT CURVES 173 Fig
Page 175 and 176:
Page 177 and 178:
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?