Radiation Transport Around Kerr Black Holes Jeremy David ...

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º¾ßÖÝÐØÙÖÚ×¸×ÔØÖÒÐÙÑÒÓ×ØÝØ ¾ 64 CHAPTER 2. RAY-TRACING IN THE KERR METRIC promising observations is that of the relativistically broadened Fe Kα emission line seen in both stellar-mass black holes and active galactic nuclei (AGN), easily seen with the remarkable spectral resolution and large collecting areas of Chandra and XMM-Newton. An example of such a line is shown in Figure 2-8a from the black hole binary XTE J1650–500, reproduced from Miller et al. (2002a). Similar lines have been seen in the Seyfert 1 galaxy MCG–6-30-15 [Tanaka et al. (1995); Wilms et al. (2001); Lee et al. (2002); see Fig. 2-8b], and both have been interpreted as consistent with a near-maximal black hole spin (a/M = 0.998). ×ÑÖÒÐÒÙ×ØÖ×ÔÓÒ×ÑØÖ×ÓØØØÓÖ×ÖÙÒÖØÒºÌ× ÚÒÒÖÝÖ×ÓÐÙØÓÒÓÓÒÐÝÏÀÅ½¾ÎØÃ«µºÌÖÓÒ «×ØÙ×ÓÒÙ×ÒÊÌÒÒ×Ù«ÖÓØÙ×ØÒÖÝÖ×ÓÐÙØÓÒ ×ÐÓÝÒÔÓÛÖßÐÛÓÑÔÓÒÒØ×´ÅÐÐÖØÐº¾¼¼¾µºÆÓØØÒÓÒ¹ Ù××Ò×ÔÒÐÓÛ¹ÒÖÝÜØÒØÓØÐÒÔÖÓ¬Ðº ºººØ»ÑÓÐÖØÓÓÖÌÂ½¼¼ß¼¼ºÌÑÓÐÓÒ××Ø×ÓÑÙÐØÓÐÓÖ ¢ ¦ Ò×ØÖÙÑÒØ×ÒÙ×ØÓ×ØÑØØÛØ×ÓØÐÒ×¸ÙØÐÑ×ØØÐÒ× Ò³ØÒØÐº¾¼¼¾µÒÌÂ½¼·¼´Ò³ØÒØÐº¾¼¼¾µÓÛÚÖØ× ØÐº¾¼¼½ÆÓÛØÐº¾¼¼¾µº Ã«ºÖÓÐÒÔÖÓ¬Ð×´ßÎµÚÒÓ×ÖÚÓÖËÂ½½½ºß¿¼ ÒÖ×ÓÐÚÒØÓÑÙÐØÔÐÓÑÔÓÒÒØ××ÓÙÐØÖØÛØÖ×ÖÚºËÓÑÖÓÒ ÖÓ¬Ð×ÖÖØÖ×ÝÑÑØÖÒÑÝÑÓÖÔÖÓÙØÓÓÑÔØÓÒ×ØØÖÒ ÙÖ²ÙÖ¾¼¼¼µÌÂ½ß¾´ÅÐÐÖØÐº¾¼¼½µÒ¿¿ß´Ò ÈßËÈØØÓÖ×ÓÖÔÔÓË¸ÛÚÖ×ÓÐÙØÓÒÓ¼ÎØ «×ÓÙÖ×ØØÚÒ×ØÙÛØÊÌÒÐÙÊÇÂ½ß¼´ÐÙÒ×ß ÒÖÐØÚ×ØÖÓÒÒºÔÔÓË×ØÙ×ÚÐ×ÓÖÚÐÓØÖ×Ý×ØÑ× ØÖÓ¸×ÝÑÑØÖÃ«ÐÒÔÖÓ¬Ð×ØØ¬ØØÐÐÓÖÖÐØÚ×Ø×ÑÖÒ ÊË½½·½¼´ÅÖØÓØÐº¾¼¼¾µÒÎ½ËÖ´ÅÐÐÖØÐº¾¼¼¾µº ÅÓÖØÐÐÒ×ØÙ×ÓØÃ«ÐÒÚÒÚÙ×ÒØÅËÒ ¢« Figure 2-8: (left) A broadened Fe Kα line from the black hole binary XTE J1650– 500, observed with XMM-Newton. (right) A similar line from the Seyfert 1 galaxy MCG–6-30-15, observed with ASCA (blue) and Chandra (black). Both plots show the excess emission with respect to a background model with blackbody and powerlaw components for a multicolor disk. The lines extend well below the rest energy of 6.4 keV, suggesting emission for highly relativistic regions of the inner accretion ÒØÖ×ØÒÐÝ¸ÓÖÓØ×Ý×ØÑ×ØÒÒÖ×ÖÙ×ÙÖÓÑØÐÒÔÖÓ¬Ð× disk. [Reproduced from Miller et al. (2002a) and Lee et al. (2002) with permission] ÓÒ××ØÒØÛØØÑÖÒÐÐÝ×ØÐÖÙÐÖÓÖØÓËÛÖÞ×ÐÀºÃÖÖ ÅÅßÆÛØÓÒÒÒÖºÍ×ÒØÓÖÑÖÓ×ÖÚØÓÖÝ³×ÈÁßÅÇË½ØØÓÖ¸ ØÖ×ÒÓØÖÕÙÖº This interpretation is heavily dependent on the assumption that the accretion disk ÊÒØÐÝ¸Ö×ÙÐØ×Ó×ØÙ×ØÖÖ×ÓÐÙØÓÒÚÔÔÖØØÑÙ×Ó has a relatively sharp edge at the inner-most stable circular orbit (ISCO). But many relativistic magnetohydrodynamic (MHD) simulations find no such cut-off (Gammie, McKinney, & Toth, 2003; De Villiers, Hawley, & Krolik, 2003), with significant pressure and density (and thus emission) all the way in to the horizon. This point has been made by Reynolds & Begelman (1997), but has unfortunately not been fully appreciated by much of the high-energy astrophysics community. Using simplified yet is attributed to the relativistically broadened Fe K«emission. . 3.— The iron K«emission profile from the long (4.5 day) ASCA ob-
2.4. BROADENED EMISSION LINES FROM THIN DISKS 65 reasonable physical estimates (and without putting undue emphasis on the ISCO), Reynolds, Brenneman, & Garofalo (2004) are able to confirm some sort of spinning black hole in MCG–6-30-15 as well as the galactic black hole binary GX 339–4, but they still cannot provide a clear measurement of that spin. In addition to the uncertainty around the treatment of the disk boundary conditions at the ISCO, there is also not an unambiguous illumination mechanism that would cause the disk to produce a high-energy emission line such as the Fe Kα at 6.4 keV. One likely possibility is that the iron emission is produced by hard X-rays from a hot electron corona reflecting off the relatively cool disk [see, e.g. McClintock & Remillard (2004)]. Another option is that it simply follows the intensity of the thermal emission from the disk itself (Agol & Krolik, 1999). If the line emission indeed tracks the total flux at each point in the disk, it may be possible to measure more exotic processes in the disk, including magnetic torques at the ISCO. In observations of MCG–6-30-15, Reynolds et al. (2004) claim to find evidence of a torque on the inner edge of the disk, presumably caused by some version of the Blandford-Znajek process, which provides a mechanism for extracting energy from the spin of a black hole through magnetic fields that thread the accretion disk as well as the black hole horizon (Blandford & Znajek, 1977). This effect can be seen in Figure 2-9, reproduced from Reynolds et al. (2004). The added stress on the inner disk puts a greater weight on the portions of the iron line spectrum produced there, generally highlighting the broader features caused by the strong relativistic effects near the ISCO. For lack of a clear picture of the disk+corona geometry, many accretion disk models include an emissivity that simply scales as a power of the radius. Following Bromley, Chen, & Miller (1997), we apply an emissivity factor proportional to r −2 , giving an added weight to the inner, presumably hotter, regions. However, unlike the model of Reynolds et al. (2004), where the iron line emission traces that of the thermal disk, here we should note that the emission is coming essentially from the corona, but fluorescing off the much cooler disk. Thus, even though we will see in Chapter 5 that almost no thermal emission comes from inside of the ISCO, there is still enough matter in that region to reflect the high energy photons from the hot corona and contribute significantly to the iron emission line profile. As can be seen in Figure 2-10, this extra emission from close to the black hole can serve to break the otherwise weak dependence on spin, but only if we assume all emission is truncated at the ISCO. For an inclination of i = 30 ◦ , five different spin values are shown: (a/M = −0.99, −0.5, 0, 0.5, 0.99), corresponding to inner disk boundaries at (R ISCO /M = 8.97, 7.55, 6.0, 4.23, 1.45). Since the sign of a is defined with respect to the angular momentum of the accretion disk, negative values of a imply retrograde orbits that do not survive as close to the black hole, plunging at larger values of R ISCO . The disks that extend in closer produce more low-energy red-shifted
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Radiation Transport Around Kerr Bla
Page 5 and 6:
5 Acknowledgments Gravity can not b
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Contents 1 Introduction and Outline
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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 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 63: 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 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 107 and 108: 4.5. ELECTRON SCATTERING IN THE COR
Page 113 and 114: 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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Radiation Transport Around Kerr Black Holes Jeremy David ...

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