• Tidak ada hasil yang ditemukan

Chapter IV: Black hole ringdown: the importance of overtones

4.7 Acknowledgments

The authors thank Vijay Varma for many valuable discussions. We also thank Katerina Chatziioannou and Leo Stein for useful comments. M.G. and M.S. are supported by the Sherman Fairchild Foundation and NSF grants PHY-1708212 and PHY-1708213 at Caltech. M.I. is a member of the LIGO Laboratory. LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation and operates under cooperative agreement PHY-0757058. M.I. is supported by NASA through the NASA Hubble Fellowship grant No. HST-HF2-51410.001-A awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA, under contract NAS5-26555. S.T. is supported in part by the Sherman Fairchild Foundation and by NSF Grants PHY- 1606654 and ACI-1713678 at Cornell. Computations were performed on the Wheeler cluster at Caltech, which is supported by the Sherman Fairchild Foundation and by Caltech. Computation were also performed on the Nemo computing cluster at the University of Wisconsin-Milwaukee, supported by NSF Grant PHY-1626190.

References

[1] Werner Israel. “Event Horizons in Static Vacuum Space-Times”. In:Phys.

Rev.164 (5 Dec. 1967), pp. 1776–1779. doi:10.1103/PhysRev.164.1776. url:https://link.aps.org/doi/10.1103/PhysRev.164.1776. [2] B. Carter. “Axisymmetric Black Hole Has Only Two Degrees of Freedom”. In:

Phys. Rev. Lett.26 (6 Feb. 1971), pp. 331–333. doi:10.1103/PhysRevLett.

26.331. url:https://link.aps.org/doi/10.1103/PhysRevLett.

26.331.

[3] S. W. Hawking. “Black holes in general relativity”. In:Commun. Math. Phys.

25 (1972), pp. 152–166. doi:10.1007/BF01877517.

[4] S. A. Teukolsky. “Rotating black holes - separable wave equations for gravitational and electromagnetic perturbations”. In: Phys. Rev. Lett. 29 (1972), pp. 1114–1118. doi:10.1103/PhysRevLett.29.1114.

[5] S. A. Teukolsky. “Perturbations of a Rotating Black Hole. I. Fundamental Equations for Gravitational, Electromagnetic, and Neutrino-Field Perturba- tions”. In:ApJ185 (Oct. 1973), pp. 635–648. doi:10.1086/152444. [6] W. H. Press and S. A. Teukolsky. “Perturbations of a Rotating Black Hole. II.

Dynamical Stability of the Kerr Metric”. In:ApJ185 (Oct. 1973), pp. 649–

674. doi:10.1086/152445.

[7] B. P. Abbott et al. “Observation of Gravitational Waves from a Binary Black Hole Merger”. In: Phys. Rev. Lett. 116.6 (Feb. 2016), p. 061102.

issn: 0031-9007. doi:10.1103/PhysRevLett.116.061102. url:http:

//link.aps.org/doi/10.1103/PhysRevLett.116.061102.

[8] B. P. Abbott et al. “GW151226: Observation of Gravitational Waves from a 22-Solar-Mass Binary Black Hole Coalescence”. In:Phys. Rev. Lett.116.24 (June 2016), p. 241103. issn: 0031-9007. doi:10.1103/PhysRevLett.116.

241103. url: http://link.aps.org/doi/10.1103/PhysRevLett.

116.241103.

[9] B. P. Abbott et al. “Binary Black Hole Mergers in the First Advanced LIGO Observing Run”. In: Phys. Rev. X6.4 (Oct. 2016), p. 041015. issn: 2160- 3308. doi: 10.1103/PhysRevX.6.041015. url:http://arxiv.org/

abs/1606.04856%20https://dcc.ligo.org/LIGO- %20P1600088/

public%20https://link.aps.org/doi/10.1103/%20PhysRevX.6.

041015.

[10] B. P. Abbott et al. “GW170104: Observation of a 50-Solar-Mass Binary Black Hole Coalescence at Redshift 0.2”. In:Phys. Rev. Lett.118.22 (June 2017), p. 221101. issn: 0031-9007. doi: 10.1103/PhysRevLett.118.

221101. url:https://journals.aps.org/prl/abstract/10.1103/

%20PhysRevLett . 118 . 221101 % 20https : / / dcc . ligo . org / LIGO - P170104/%20public%20https://arxiv.org/abs/1706.01812. [11] B.. P.. Abbott et al. “GW170608: Observation of a 19-solar-mass Binary

Black Hole Coalescence”. In: Astrophys. J. 851.2 (2017), p. L35. doi:

10.3847/2041-8213/aa9f0c. arXiv:1711.05578 [astro-ph.HE]. [12] B. P. Abbott et al. “GW170814: A Three-Detector Observation of Gravita-

tional Waves from a Binary Black Hole Coalescence”. In:Phys. Rev. Lett.

119.14 (2017), p. 141101. doi: 10 . 1103 / PhysRevLett . 119 . 141101. arXiv:1709.09660 [gr-qc].

[13] B. P. 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”. In:Phys. Rev.X9.3 (2019), p. 031040. doi:

10.1103/PhysRevX.9.031040. arXiv:1811.12907 [astro-ph.HE]. [14] J. Aasi et al. “Advanced LIGO”. In:Class. Quant. Grav.32 (2015), p. 074001.

doi:10.1088/0264-9381/32/7/074001. arXiv:1411.4547 [gr-qc].

[15] F. Acernese et al. “Advanced Virgo: a second-generation interferometric gravitational wave detector”. In:Class. Quant. Grav.32.2 (2015), p. 024001.

doi:10.1088/0264-9381/32/2/024001.

[16] B. P. Abbott et al. “Tests of General Relativity with GW150914”. In:

Phys. Rev. Lett. 116.22 (May 2016), p. 221101. issn: 0031-9007. doi:

10.1103/PhysRevLett.116.221101. url: http://link.aps.org/

doi / 10 . 1103 / %20PhysRevLett . 116 . 221101 % 20https : / / arxiv . org/abs/1602.03841.

[17] Walter Del Pozzo and Alessandro Nagar. “Analytic family of post-merger template waveforms”. In: Phys. Rev. D95.12 (2017), p. 124034. doi: 10.

1103/PhysRevD.95.124034. arXiv:1606.03952 [gr-qc].

[18] Miriam Cabero et al. “Observational tests of the black hole area increase law”. In:Phys. Rev.D97.12 (2018), p. 124069. doi:10.1103/PhysRevD.

97.124069. arXiv:1711.09073 [gr-qc].

[19] Eric Thrane, Paul D. Lasky, and Yuri Levin. “Challenges testing the no-hair theorem with gravitational waves”. In:Phys. Rev.D96.10 (2017), p. 102004.

doi:10.1103/PhysRevD.96.102004. arXiv:1706.05152 [gr-qc]. [20] Richard Brito, Alessandra Buonanno, and Vivien Raymond. “Black-hole

Spectroscopy by Making Full Use of Gravitational-Wave Modeling”. In:

Phys. Rev.D98.8 (2018), p. 084038. doi:10.1103/PhysRevD.98.084038. arXiv:1805.00293 [gr-qc].

[21] Gregorio Carullo et al. “Empirical tests of the black hole no-hair conjec- ture using gravitational-wave observations”. In:Phys. Rev.D98.10 (2018), p. 104020. doi: 10.1103/PhysRevD.98.104020. arXiv: 1805.04760 [gr-qc].

[22] Gregorio Carullo, Walter Del Pozzo, and John Veitch. “Observational Black Hole Spectroscopy: A time-domain multimode analysis of GW150914”. In:

Phys. Rev.D99.12 (2019), p. 123029. doi:10.1103/PhysRevD.99.123029. arXiv:1902.07527 [gr-qc].

[23] Olaf Dreyer et al. “Black hole spectroscopy: Testing general relativity through gravitational wave observations”. In:Class. Quant. Grav.21 (2004), pp. 787–

804. doi: 10 . 1088 / 0264 - 9381 / 21 / 4 / 003. arXiv: gr - qc / 0309007 [gr-qc].

[24] Emanuele Berti, Vitor Cardoso, and Clifford M. Will. “On gravitational-wave spectroscopy of massive black holes with the space interferometer LISA”. In:

Phys. Rev.D73 (2006), p. 064030. doi:10.1103/PhysRevD.73.064030. arXiv:gr-qc/0512160 [gr-qc].

[25] S. Gossan, J. Veitch, and B. S. Sathyaprakash. “Bayesian model selection for testing the no-hair theorem with black hole ringdowns”. In:Phys. Rev.

D85 (2012), p. 124056. doi: 10 . 1103 / PhysRevD . 85 . 124056. arXiv:

1111.5819 [gr-qc].

[26] J. Meidam et al. “Testing the no-hair theorem with black hole ringdowns using TIGER”. In: Phys. Rev. D90.6 (2014), p. 064009. doi: 10.1103/

PhysRevD.90.064009. arXiv:1406.3201 [gr-qc].

[27] Emanuele Berti et al. “Testing General Relativity with Present and Future Astrophysical Observations”. In:Class. Quant. Grav.32 (2015), p. 243001.

doi:10.1088/0264-9381/32/24/243001. arXiv:1501.07274 [gr-qc]. [28] Emanuele Berti et al. “Spectroscopy of Kerr black holes with Earth- and

space-based interferometers”. In:Phys. Rev. Lett.117.10 (2016), p. 101102.

doi:10.1103/PhysRevLett.117.101102. arXiv:1605.09286 [gr-qc]. [29] Vishal Baibhav and Emanuele Berti. “Multimode black hole spectroscopy”.

In: Phys. Rev. D99.2 (2019), p. 024005. doi: 10 . 1103 / PhysRevD . 99 . 024005. arXiv:1809.03500 [gr-qc].

[30] Alessandra Buonanno, Gregory B. Cook, and Frans Pretorius. “Inspiral, merger and ring-down of equal-mass black-hole binaries”. In: Phys. Rev.

D75 (2007), p. 124018. doi: 10 . 1103 / PhysRevD . 75 . 124018. arXiv:

gr-qc/0610122 [gr-qc].

[31] Vishal Baibhav et al. “Black Hole Spectroscopy: Systematic Errors and Ringdown Energy Estimates”. In:Phys. Rev.D97.4 (2018), p. 044048. doi:

10.1103/PhysRevD.97.044048. arXiv:1710.02156 [gr-qc].

[32] Ioannis Kamaretsos et al. “Black-hole hair loss: learning about binary progenitors from ringdown signals”. In:Phys. Rev.D85 (2012), p. 024018.

doi:10.1103/PhysRevD.85.024018. arXiv:1107.0854 [gr-qc]. [33] Lionel London, Deirdre Shoemaker, and James Healy. “Modeling ringdown:

Beyond the fundamental quasinormal modes”. In:Phys. Rev.D90.12 (2014).

[Erratum: Phys. Rev.D94,no.6,069902(2016)], p. 124032. doi:10.1103/

PhysRevD.90.124032. arXiv:1404.3197 [gr-qc].

[34] Swetha Bhagwat, Maria Okounkova, Stefan W. Ballmer, Duncan A. Brown, Matthew Giesler, Mark A. Scheel, and Saul A. Teukolsky. “On choosing the start time of binary black hole ringdowns”. In:Phys. Rev.D97.10 (2018), p. 104065. doi: 10.1103/PhysRevD.97.104065. arXiv: 1711.00926 [gr-qc].

[35] Yi Pan et al. “Inspiral-merger-ringdown waveforms of spinning, precessing black-hole binaries in the effective-one-body formalism”. In: Phys. Rev.

D89.8 (2014), p. 084006. doi: 10.1103/PhysRevD.89.084006. arXiv:

1307.6232 [gr-qc].

[36] Andrea Taracchini et al. “Effective-one-body model for black-hole binaries with generic mass ratios and spins”. In:Phys. Rev. D89.6 (2014), 061502(R).

doi:10.1103/PhysRevD.89.061502. arXiv:1311.2544 [gr-qc].

[37] Stanislav Babak, Andrea Taracchini, and Alessandra Buonanno. “Validating the effective-one-body model of spinning, precessing binary black holes against numerical relativity”. In:Phys. Rev.D95.2 (2017), p. 024010. doi:

10.1103/PhysRevD.95.024010. arXiv:1607.05661 [gr-qc]. [38] http://www.black-holes.org/waveforms.

[39] Abdul H. Mroue et al. “A Catalog of 174 Binary Black Hole Simulations for Gravitational Wave Astronomy”. In:Phys. Rev. Lett.111 (2013), p. 241104.

doi:10.1103/PhysRevLett.111.241104. arXiv:1304.6077 [gr-qc]. [40] C. V. Vishveshwara. “Stability of the Schwarzschild Metric”. In:Phys. Rev.

D 1 (10 May 1970), pp. 2870–2879. doi: 10.1103/PhysRevD.1.2870. url:https://link.aps.org/doi/10.1103/PhysRevD.1.2870. [41] William H. Press. “Long Wave Trains of Gravitational Waves from a Vibrating

Black Hole”. In:Astrophys. J.170 (1971), pp. L105–L108. doi:10.1086/

180849.

[42] S. A. Teukolsky. “Perturbations of a rotating black hole. 1. Fundamental equations for gravitational electromagnetic and neutrino field perturbations”.

In:Astrophys. J.185 (1973), pp. 635–647. doi:10.1086/152444.

[43] S. Chandrasekhar and S. Detweiler. “The Quasi-Normal Modes of the Schwarzschild Black Hole”. In:Proc. R. Soc. A344.1639 (1975), pp. 441–

452. issn: 00804630. url:http://www.jstor.org/stable/78902. [44] E. Berti, V. Cardoso, and A. O. Starinets. “TOPICAL REVIEW: Quasinormal

modes of black holes and black branes”. In: Class. Quantum Grav.26.16 (Aug. 2009), p. 163001. doi:10.1088/0264-9381/26/16/163001. arXiv:

0905.2975 [gr-qc].

[45] http://pages.jh.edu/~eberti2/ringdown.

[46] E. T. Newman and R. Penrose. “Note on the Bondi–Metzner–Sachs Group”.

In:J. Math. Phys.7 (1966), pp. 863–870. doi:10.1063/1.1931221. url:

http://link.aip.org/link/?JMP/7/863/1.

[47] J. N. Goldberg et al. “Spin-s Spherical Harmonics and ð”. In: Journal of Mathematical Physics 8.11 (1967), pp. 2155–2161. doi: 10.1063/1.

1705135. url:http://link.aip.org/link/?JMP/8/2155/1.

[48] Kip S. Thorne. “Multipole expansions of gravitational radiation”. In:Rev.

Mod. Phys.52.2 (Apr. 1980), pp. 299–339. doi:10.1103/RevModPhys.52.

299.

[49] Emanuele Berti and Antoine Klein. “Mixing of spherical and spheroidal modes in perturbed Kerr black holes”. In:Phys. Rev.D90.6 (2014), p. 064012.

doi:10.1103/PhysRevD.90.064012. arXiv:1408.1860 [gr-qc].

[50] Vijay Varma et al. “Surrogate model of hybridized numerical relativity binary black hole waveforms”. In:Phys. Rev.D99.6 (2019), p. 064045. doi:

10.1103/PhysRevD.99.064045. arXiv:1812.07865 [gr-qc].

[51] Ernst Nils Dorband et al. “A Numerical study of the quasinormal mode excitation of Kerr black holes”. In:Phys. Rev.D74 (2006), p. 084028. doi:

10.1103/PhysRevD.74.084028. arXiv:gr-qc/0608091 [gr-qc]. [52] E. W. Leaver. “An Analytic representation for the quasi normal modes of

Kerr black holes”. In:Proc. Roy. Soc. Lond.A402 (1985), pp. 285–298. doi:

10.1098/rspa.1985.0119.

[53] Edward W. Leaver. “Spectral decomposition of the perturbation response of the Schwarzschild geometry”. In:Phys. Rev.D34 (1986), pp. 384–408. doi:

10.1103/PhysRevD.34.384.

[54] Emanuele Berti and Vitor Cardoso. “Quasinormal ringing of Kerr black holes. I. The Excitation factors”. In:Phys. Rev.D74 (2006), p. 104020. doi:

10.1103/PhysRevD.74.104020. arXiv:gr-qc/0605118 [gr-qc]. [55] Zhongyang Zhang, Emanuele Berti, and Vitor Cardoso. “Quasinormal ringing

of Kerr black holes. II. Excitation by particles falling radially with arbitrary energy”. In:Phys. Rev.D88 (2013), p. 044018. doi:10.1103/PhysRevD.

88.044018. arXiv:1305.4306 [gr-qc].

[56] David H. Shoemaker et al. Advanced LIGO anticipated sensitivity curves. Tech. rep. LIGO-T0900288. LIGO Laboratory, 2009. url:https://dcc.

ligo.org/LIGO-T0900288/public.

[57] Reinhard Prix. Bayesian QNM search on GW150914. Tech. rep. LIGO- T1500618. LIGO Scientific Collaboration, 2016. url:https://dcc.ligo.

org/LIGO-T1500618/public.

[58] B. Farr and W. M. Farr. “kombine: a kernel-density-based, embarrassingly parallel ensemble sampler”. in prep. 2015. url:https://github.com/

bfarr/kombine.

[59] D. Foreman-Mackey et al. “emcee: The MCMC Hammer”. In:PASP125 (Mar.

2013), p. 306. doi:10.1086/670067. arXiv:1202.3665 [astro-ph.IM]. [60] Eanna E. Flanagan and Scott A. Hughes. “Measuring gravitational waves from

binary black hole coalescences: 2. The Waves’ information and its extraction, with and without templates”. In:Phys. Rev.D57 (1998), pp. 4566–4587. doi:

10.1103/PhysRevD.57.4566. arXiv:gr-qc/9710129 [gr-qc].

[61] Lee Lindblom, Benjamin J. Owen, and Duncan A. Brown. “Model Waveform Accuracy Standards for Gravitational Wave Data Analysis”. In:Phys. Rev.

D 78 (2008), p. 124020. doi: 10.1103/PhysRevD.78.124020. arXiv:

0809.3844 [gr-qc].

[62] Sean T. McWilliams, Bernard J. Kelly, and John G. Baker. “Observing mergers of non-spinning black-hole binaries”. In: Phys. Rev.D82 (2010), p. 024014. doi: 10 . 1103 / PhysRevD . 82 . 024014. arXiv: 1004 . 0961 [gr-qc].

[63] Vijay Varma and Parameswaran Ajith. “Effects of nonquadrupole modes in the detection and parameter estimation of black hole binaries with nonprecessing spins”. In:Phys. Rev.D96.12 (2017), p. 124024. doi:10.1103/PhysRevD.

96.124024. arXiv:1612.05608 [gr-qc].

[64] Collin Capano, Yi Pan, and Alessandra Buonanno. “Impact of higher har- monics in searching for gravitational waves from nonspinning binary black holes”. In:Phys. Rev.D89.10 (2014), p. 102003. doi:10.1103/PhysRevD.

89.102003. arXiv:1311.1286 [gr-qc].

[65] Tyson B. Littenberg et al. “Systematic biases in parameter estimation of binary black-hole mergers”. In: Phys. Rev. D 87 (2013), p. 104003. doi:

10.1103/PhysRevD.87.104003. arXiv:1210.0893 [gr-qc].

[66] J. Calderón Bustillo, P. Laguna, and D. Shoemaker. “Detectability of grav- itational waves from binary black holes: Impact of precession and higher modes”. In: PRD95.10, 104038 (May 2017), p. 104038. doi: 10.1103/

PhysRevD.95.104038. arXiv:1612.02340 [gr-qc].

[67] Vijay Varma et al. “Gravitational-wave observations of binary black holes:

Effect of nonquadrupole modes”. In:Phys. Rev. D90.12 (2014), p. 124004.

doi:10.1103/PhysRevD.90.124004. arXiv:1409.2349 [gr-qc].