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Circular Orbits of Particles around Compact Objects and Their Observability

中司 桂輔 立教大学 DOI:info:doi/10.14992/00020648

2021.05.11

概要

(1) 論文の構成
第1章の序論では、研究テーマの背景と研究に至った動機が示されている。第2章は本研究の基礎となる事項として、ブラックホール周辺の時空とブラックホールを中心とする粒子の円運動について解説されている。特に、静止したブラックホールと回転するブラックホール周辺の時空におけるテスト粒子の円運動について具体的に説明されている。第3章においては、2つの静止したブラックホール周辺における時空構造と、円軌道を描くテスト粒子の運動について解析的・数値的な結果が詳細に示されている。第4章では、回転するブラックホールの周辺で円軌道を描く光源から発せられた光について、詳細な解析が行われている。第5章では、結果のまとめと考察を行っている。

(2) 論文の内容の要旨
ブラックホールは直接観測することは出来ないが、その性質の理解はブラックホール周辺の強重力場中で起こる現象を理論的及び観測的に調べることにより可能となる。近年、強重力場中の現象に関する観測的研究が行われており、光学や重力波などにより強重力場中で起こる現象について活発に調べられている。特に、ブラックホールの影の撮影に成功するなどその進展は著しいものがある。

本論文では、テスト粒子のブラックホール周辺での円運動に着目し、その軌道を入念に調べている。円軌道は動径方向の座標にのみ依存し角度依存性が無いので、軌道を求めるときの基準となるものである。

本研究では、これまで詳しく調べられていなかった2つの場合について研究を行っている。

第1の場合は、2つのブラックホールが静止している時空でのテスト粒子の円軌道である。この連星ブラックホール周辺の時空構造は、1つの静止したブラックホール周辺の時空とは異なった構造をしており、テスト粒子の軌道を調べることにより、その時空構造の違いを知ることが出来ると期待される。そこで、始めに2つのブラックホールが同質量の場合のテスト粒子の円軌道を計算し、その安定軌道と不安定軌道を2つのブラックホール間の距離との関係として求めた。特に、2つのブラックホールの距離に依っては、テスト粒子が安定円軌道をとる領域が2つに分離する現象が起こることを見出した。更に、2つのブラックホールの質量が異なる場合についても解析し、同質量のブラックホールの場合からの変化を論じている。

第2の場合は、高速回転しているブラックホールの周辺で光源が円軌道を描くときに、光源からの光が無限遠方の観測者に到達する確率を調べた。これ は、ブラックホール周辺の降着円盤などで自然に実現される状態に対応する状況設定である。特に、光源の軌道半径が事象の地平面の半径に近づく場合の光の脱出確率を調べ、円運動をする光源から発せられた光は、観測者に対して静止した光源から発せられた光に比べて、無限遠方の観測者に到達する確率が大幅に増大するという結果を得た。更に、光源に対して前方に放たれた光は、光源の固有運動による青方偏移が重力により引き起こされる赤方偏移より大きくなり、遠方の観測者が観測するのに十分なエネルギーを得る可能性を示唆し た。

参考文献

[1] A. Einstein, The Field Equations of Gravitation, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. ) 1915 (1915) 844–847.

[2] A. Einstein, The Foundation of the General Theory of Relativity, Annalen Phys. 49 (1916), no. 7 769–822.

[3] C. M. Will, Theory and Experiment in Gravitational Physics. Cambridge University Press, 1993.

[4] K. Schwarzschild, On the gravitational field of a sphere of incompressible fluid according to Einstein’s theory, Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys. ) 1916 (1916) 424–434 [physics/9912033].

[5] R. P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett. 11 (1963) 237–238.

[6] LIGO Scientific, Virgo Collaboration, B. Abbott et. al., Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116 (2016), no. 6 061102 [1602.03837].

[7] Event Horizon Telescope Collaboration, K. Akiyama et. al., First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, Astrophys. J. 875 (2019), no. 1 L1 [1906.11238].

[8] Event Horizon Telescope Collaboration, K. Akiyama et. al., First M87 Event Horizon Telescope Results. II. Array and Instrumentation, Astrophys. J. Lett. 875 (2019), no. 1 L2 [1906.11239].

[9] Event Horizon Telescope Collaboration, K. Akiyama et. al., First M87 Event Horizon Telescope Results. III. Data Processing and Calibration, Astrophys. J. Lett. 875 (2019), no. 1 L3 [1906.11240].

[10] Event Horizon Telescope Collaboration, K. Akiyama et. al., First M87 Event Horizon Telescope Results. IV. Imaging the Central Supermassive Black Hole, Astrophys. J. Lett. 875 (2019), no. 1 L4 [1906.11241].

[11] Event Horizon Telescope Collaboration, K. Akiyama et. al., First M87 Event Horizon Telescope Results. V. Physical Origin of the Asymmetric Ring, Astrophys. J. Lett. 875 (2019), no. 1 L5 [1906.11242].

[12] Event Horizon Telescope Collaboration, K. Akiyama et. al., First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole, Astrophys. J. Lett. 875 (2019), no. 1 L6 [1906.11243].

[13] GRAVITY Collaboration, R. Abuter et. al., Detection of the gravitational redshift in the orbit of the star S2 near the Galactic centre massive black hole, Astron. Astrophys. 615 (2018) L15 [1807.09409].

[14] T. Do et. al., Relativistic redshift of the star S0-2 orbiting the Galactic center supermassive black hole, Science 365 (2019), no. 6454 664–668 [1907.10731].

[15] H. Saida et. al., A significant feature in the general relativistic time evolution of the redshift of photons coming from a star orbiting Sgr A*, Publ. Astron. Soc. Jap. 71 (2019), no. 6 126 [1910.02632].

[16] GRAVITY Collaboration, R. Abuter et. al., Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole, Astron. Astrophys. 636 (2020) L5 [2004.07187].

[17] I. Novikov and K. Thorne, Astrophysics and black holes, in Les Houches Summer School of Theoretical Physics: Black Holes, pp. 343–550, 1973.

[18] J. P. A. Clark and D. M. Eardley, Evolution of close neutron star binaries., Astrophys. J. 215 (July, 1977) 311–322.

[19] L. E. Kidder, C. M. Will and A. G. Wiseman, Coalescing binary systems of compact objects to (post)**(5/2)-Newtonian order. 3. Transition from inspiral to plunge, Phys. Rev. D 47 (1993) 3281–3291.

[20] LIGO Scientific, Virgo Collaboration, B. Abbott et. al., GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs, Phys. Rev. X 9 (2019), no. 3 031040 [1811.12907].

[21] LIGO Scientific, Virgo Collaboration, R. Abbott et. al., GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run, 2010.14527.

[22] K. Yamada and H. Asada, Collinear solution to the general relativistic three-body problem, Phys. Rev. D 82 (2010) 104019 [1010.2284].

[23] K. Yamada and T. Tsuchiya, The linear stability of the post-Newtonian triangular equilibrium in the three-body problem, 1612.08361.

[24] N. Seto, Relativistic Resonant Relations between Massive Black Hole Binary and Extreme Mass Ratio Inspiral, Phys. Rev. D 85 (2012) 064037 [1202.4761].

[25] P. Gupta, H. Suzuki, H. Okawa and K.-i. Maeda, Gravitational Waves from Hierarchical Triple Systems with Kozai-Lidov Oscillation, Phys. Rev. D 101 (2020), no. 10 104053 [1911.11318].

[26] H. Suzuki, P. Gupta, H. Okawa and K.-i. Maeda, Cumulative shift of periastron time of binary pulsar with Kozai–Lidov oscillation, Mon. Not. Roy. Astron. Soc. 486 (2019), no. 1 L52–L57 [1903.00287].

[27] L. Wen, On the eccentricity distribution of coalescing black hole binaries driven by the Kozai mechanism in globular clusters, Astrophys. J. 598 (2003) 419–430 [astro-ph/0211492].

[28] N. Seto, Highly Eccentric Kozai Mechanism and Gravitational-Wave Observation for Neutron Star Binaries, Phys. Rev. Lett. 111 (2013) 061106 [1304.5151].

[29] Y. Meiron, B. Kocsis and A. Loeb, Detecting triple systems with gravitational wave observations, Astrophys. J. 834 (2017), no. 2 200 [1604.02148].

[30] A. Bohn, W. Throwe, F. H´ebert, K. Henriksson, D. Bunandar, M. A. Scheel and N. W. Taylor, What does a binary black hole merger look like?, Class. Quant. Grav. 32 (2015), no. 6 065002 [1410.7775].

[31] H. Weyl, The theory of gravitation, Annalen Phys. 54 (1917) 117–145.

[32] S. Majumdar, A class of exact solutions of Einstein’s field equations, Phys. Rev. 72 (1947) 390–398.

[33] A. Papaetrou, A Static solution of the equations of the gravitational field for an arbitrary charge distribution, Proc. Roy. Irish Acad. A A51 (1947) 191–204.

[34] J. Hartle and S. Hawking, Solutions of the Einstein-Maxwell equations with many black holes, Commun. Math. Phys. 26 (1972) 87–101.

[35] D. Kramer and G. Neugebauer, The superposition of two Kerr solutions, Physics Letters A 75 (Jan., 1980) 259–261.

[36] D. Nitta, T. Chiba and N. Sugiyama, Shadows of Colliding Black Holes, Phys. Rev. D 84 (2011) 063008 [1106.2425].

[37] M. Patil, P. Mishra and D. Narasimha, Curious case of gravitational lensing by binary black holes: a tale of two photon spheres, new relativistic images and caustics, Phys. Rev. D 95 (2017), no. 2 024026 [1610.04863].

[38] T. Assumpcao, V. Cardoso, A. Ishibashi, M. Richartz and M. Zilhao, Black hole binaries: ergoregions, photon surfaces, wave scattering, and quasinormal modes, Phys. Rev. D 98 (2018), no. 6 064036 [1806.07909].

[39] P. V. Cunha, C. A. Herdeiro and M. J. Rodriguez, Shadows of Exact Binary Black Holes, Phys. Rev. D 98 (2018), no. 4 044053 [1805.03798].

[40] J. Shipley and S. R. Dolan, Binary black hole shadows, chaotic scattering and the Cantor set, Class. Quant. Grav. 33 (2016), no. 17 175001 [1603.04469].

[41] A. Wunsch, T. Mu¨ller, D. Weiskopf and G. Wunner, Circular orbits in the extreme Reissner-Nordstrøm dihole metric, Phys. Rev. D 87 (2013), no. 2 024007 [1301.7560].

[42] S. R. Dolan and J. O. Shipley, Stable photon orbits in stationary axisymmetric electrovacuum spacetimes, Phys. Rev. D 94 (2016), no. 4 044038 [1605.07193].

[43] K. Nakashi and T. Igata, Innermost stable circular orbits in the Majumdar-Papapetrou dihole spacetime, Phys. Rev. D 99 (2019), no. 12 124033 [1903.10121].

[44] K. Nakashi and T. Igata, Effect of a second compact object on stable circular orbits, Phys. Rev. D 100 (2019), no. 10 104006 [1908.10075].

[45] K. Gebhardt, J. Adams, D. Richstone, T. R. Lauer, S. M. Faber, K. Gu¨ltekin, J. Murphy and S. Tremaine, THE BLACK HOLE MASS IN M87 FROM GEMINI/NIFS ADAPTIVE OPTICS OBSERVATIONS, The Astrophysical Journal 729 (Feb, 2011) 119.

[46] J. L. Walsh, A. J. Barth, L. C. Ho and M. Sarzi, THE M87 BLACK HOLE MASS FROM GAS-DYNAMICAL MODELS OF SPACE TELESCOPE IMAGING SPECTROGRAPH OBSERVATIONS, The Astrophysical Journal 770 (May, 2013) 86.

[47] Y. Mizuno, Z. Younsi, C. M. Fromm, O. Porth, M. De Laurentis, H. Olivares, H. Falcke, M. Kramer and L. Rezzolla, The Current Ability to Test Theories of Gravity with Black Hole Shadows, Nature Astron. 2 (2018), no. 7 585–590 [1804.05812].

[48] V. Cardoso and P. Pani, Testing the nature of dark compact objects: a status report, Living Rev. Rel. 22 (2019), no. 1 4 [1904.05363].

[49] S. S. Doeleman et. al., Jet Launching Structure Resolved Near the Supermassive Black Hole in M87, Science 338 (2012) 355 [1210.6132].

[50] Y.-R. Li, Y.-F. Yuan, J.-M. Wang, J.-C. Wang and S. Zhang, Constraining spins of supermassive black holes from TeV variability. II. fully general relativistic calculations, Astrophys. J. 699 (2009) 513 [0904.2335].

[51] J. Feng and Q. Wu, Constraint on the black-hole spin of M87 from the accretion-jet model, Mon. Not. Roy. Astron. Soc. 470 (2017) 612 [1705.07804].

[52] A. Lupsasca, A. P. Porfyriadis and Y. Shi, Critical Emission from a High-Spin Black Hole, Phys. Rev. D 97 (2018), no. 6 064017 [1712.10182].

[53] T. Igata, H. Ishihara and Y. Yasunishi, Observability of spherical photon orbits in near-extremal Kerr black holes, Phys. Rev. D 100 (2019), no. 4 044058 [1904.00271].

[54] K. Ogasawara, T. Harada, U. Miyamoto, T. Igata and M. Patil, Escape probability of the super-Penrose process, Phys. Rev. D 95 (2017), no. 12 124019 [1609.03022].

[55] K. Ogasawara, T. Igata, T. Harada and U. Miyamoto, Escape probability of a photon emitted near the black hole horizon, Phys. Rev. D 101 (2020), no. 4 044023 [1910.01528].

[56] R. Takahashi and M. Takahashi, Anisotropic radiation field and trapped photons around the Kerr black hole, Astron. Astrophys. 513 (2010) A77 [1002.4245].

[57] C. T. Cunningham and J. M. Bardeen, The Optical Appearance of a Star Orbiting an Extreme Kerr Black Hole, Astrophys. J. 183 (July, 1973) 237–264.

[58] C. Cunningham, The effects of redshifts and focusing on the spectrum of an accretion disk around a Kerr black hole, Astrophys. J. 202 (1975) 788–802.

[59] J.-P. Luminet, Image of a spherical black hole with thin accretion disk, Astron. Astrophys. 75 (1979) 228–235.

[60] J. Fukue and T. Yokoyama, Color photographs of an accretion disk around a black hole, Publ. Astron. Soc. Jpn. 40 (Jan., 1988) 15–24.

[61] H. Falcke, F. Melia and E. Agol, Viewing the shadow of the black hole at the galactic center, Astrophys. J. Lett. 528 (2000) L13 [astro-ph/9912263].

[62] R. Takahashi, Shapes and positions of black hole shadows in accretion disks and spin parameters of black holes, J. Korean Phys. Soc. 45 (2004) S1808–S1812 [astro-ph/0405099].

[63] T. Kawashima, M. Kino and K. Akiyama, Black Hole Spin Signature in the Black Hole Shadow of M87 in the Flaring State, Astrophys. J. 878 (2019), no. 1 27 [1905.10717].

[64] S. E. Gralla and A. Lupsasca, Lensing by Kerr Black Holes, Phys. Rev. D 101 (2020), no. 4 044031 [1910.12873].

[65] J. M. Bardeen, W. H. Press and S. A. Teukolsky, Rotating black holes: Locally nonrotating frames, energy extraction, and scalar synchrotron radiation, Astrophys. J. 178 (1972) 347.

[66] D. Kapec and A. Lupsasca, Particle motion near high-spin black holes, Class. Quant. Grav. 37 (2020), no. 1 015006 [1905.11406].

[67] T. Igata, K. Nakashi and K. Ogasawara, Observability of the innermost stable circular orbit in a near-extremal Kerr black hole, Phys. Rev. D 101 (2020), no. 4 044044 [1910.12682].

[68] M. Heusler, Black Hole Uniqueness Theorems. Cambridge Lecture Notes in Physics. Cambridge University Press, 1996.

[69] R. Wald, General Relativity. University of Chicago Press, 1984.

[70] C. A. Herdeiro and J. M. Oliveira, On the inexistence of solitons in Einstein–Maxwell-scalar models, Class. Quant. Grav. 36 (2019), no. 10 105015 [1902.07721].

[71] B. Carter, Killing horizons and orthogonally transitive groups in space-time, J. Math. Phys. 10 (1969) 70–81.

[72] K. Nakashi and M. Kimura, Towards rotating non-circular black holes in string-inspired gravity, 2008.04003.

[73] B. Carter, Global structure of the Kerr family of gravitational fields, Phys. Rev. 174 (1968) 1559–1571.

[74] M. Walker and R. Penrose, On quadratic first integrals of the geodesic equations for type [22] spacetimes, Commun. Math. Phys. 18 (1970) 265–274.

[75] E. Teo, Spherical Photon Orbits Around a Kerr Black Hole, General Relativity and Gravitation 35 (Nov., 2003) 1909–1926.

[76] V. Cardoso, A. S. Miranda, E. Berti, H. Witek and V. T. Zanchin, Geodesic stability, Lyapunov exponents and quasinormal modes, Phys. Rev. D 79 (2009) 064016 [0812.1806].

[77] T. Igata, H. Ishihara and Y. Takamori, Stable Bound Orbits around Black Rings, Phys. Rev. D 82 (2010) 101501 [1006.3129].

[78] T. Igata, H. Ishihara and H. Yoshino, Integrability of Particle System around a Ring Source as the Newtonian Limit of a Black Ring, Phys. Rev. D 91 (2015), no. 8 084042 [1412.7033].

[79] S. Chandrasekhar, The mathematical theory of black holes. Oxford classic texts in the physical sciences. Oxford Univ. Press, Oxford, 2002.

[80] K. S. Thorne, Disk accretion onto a black hole. 2. Evolution of the hole., Astrophys. J. 191 (1974) 507–520.

[81] D. E. Gates, S. Hadar and A. Lupsasca, Photon Emission from Circular Equatorial Kerr Orbiters, 2010.07330.

[82] L. Bernard, V. Cardoso, T. Ikeda and M. Zilh˜ao, Physics of black hole binaries: Geodesics, relaxation modes, and energy extraction, Phys. Rev. D 100 (2019), no. 4 044002 [1905.05204].

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