Papers
Topics
Authors
Recent
Search
2000 character limit reached

Detecting gravitational lensing in hierarchical triples in galactic nuclei with space-borne gravitational-wave observatories

Published 29 Jul 2021 in gr-qc and astro-ph.HE | (2107.14318v2)

Abstract: Stellar-mass binary black holes (BBHs) may merge in the vicinity of a supermassive black hole (SMBH). It is suggested that the gravitational-wave (GW) emitted by a BBH has a high probability to be lensed by the SMBH if the BBH's orbit around the SMBH (i.e., the outer orbit) has a period of less than a year and is less than the duration of observation of the BBH by a space-borne GW observatory. For such a BBH + SMBH triple system, the de Sitter precession of the BBH's orbital plane is also significant. In this work, we thus study GW waveforms emitted by the BBH and then modulated by the SMBH due to effects including Doppler shift, de Sitter precession, and gravitational lensing. We show specifically that for an outer orbital period of 0.1 yr and an SMBH mass of $107 M_\odot$, there is a 3\%-10\% chance for the standard, strong lensing signatures to be detectable by space-borne GW detectors such as LISA and/or TianGO. For more massive lenses ($\gtrsim 108 M_\odot$) and more compact outer orbits with periods <0.1 yr, retro-lensing of the SMBH might also have a 1%-level chance of detection. Furthermore, by combining the lensing effects and the dynamics of the outer orbit, we find the mass of the central SMBH can be accurately determined with a fraction error of $\sim 10{-4}$. This is much better than the case of static lensing because the degeneracy between the lens' mass and the source's angular position is lifted by the outer orbital motion. Including lensing effects also allows the de Sitter precession to be detectable at a precession period 3 times longer than the case without lensing. Lastly, we demonstrate that one can check the consistency between the SMBH's mass determined from the orbital dynamics and the one inferred from gravitational lensing, which serves as a test on theories behind both phenomena. The statistical error on the deviation can be constrained to a 1% level.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (53)
  1. LIGO Scientific Collaboration and Virgo Collaboration, Observation of Gravitational Waves from a Binary Black Hole Merger, Phys. Rev. Lett. 116, 061102 (2016), arXiv:1602.03837 [gr-qc] .
  2. LIGO Scientific Collaboration, Advanced LIGO, Classical and Quantum Gravity 32, 074001 (2015), arXiv:1411.4547 [gr-qc] .
  3. Kagra Collaboration and et al., KAGRA: 2.5 generation interferometric gravitational wave detector, Nature Astronomy 3, 35 (2019), arXiv:1811.08079 [gr-qc] .
  4. LIGO Scientific Collaboration and Virgo Collaboration, GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs, Physical Review X 9, 031040 (2019), arXiv:1811.12907 [astro-ph.HE] .
  5. LIGO Scientific Collaboration and Virgo Collaboration, GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo during the First Half of the Third Observing Run, Physical Review X 11, 021053 (2021), arXiv:2010.14527 [gr-qc] .
  6. W.-R. Hu and Y.-L. Wu, The Taiji Program in Space for gravitational wave physics and the nature of gravity, National Science Review 4, 685 (2017), https://academic.oup.com/nsr/article-pdf/4/5/685/31566708/nwx116.pdf .
  7. N. C. Stone, B. D. Metzger, and Z. Haiman, Assisted inspirals of stellar mass black holes embedded in AGN discs: solving the ‘final au problem’, MNRAS 464, 946 (2017), arXiv:1602.04226 [astro-ph.GA] .
  8. H. Tagawa, Z. Haiman, and B. Kocsis, Formation and Evolution of Compact Object Binaries in AGN Disks, arXiv e-prints , arXiv:1912.08218 (2019), arXiv:1912.08218 [astro-ph.GA] .
  9. R. M. O’Leary, B. Kocsis, and A. Loeb, Gravitational waves from scattering of stellar-mass black holes in galactic nuclei, MNRAS 395, 2127 (2009), arXiv:0807.2638 [astro-ph] .
  10. F. Antonini and H. B. Perets, Secular Evolution of Compact Binaries near Massive Black Holes: Gravitational Wave Sources and Other Exotica, ApJ 757, 27 (2012), arXiv:1203.2938 [astro-ph.GA] .
  11. F. Antonini and F. A. Rasio, Merging Black Hole Binaries in Galactic Nuclei: Implications for Advanced-LIGO Detections, ApJ 831, 187 (2016), arXiv:1606.04889 [astro-ph.HE] .
  12. C. Petrovich and F. Antonini, Greatly Enhanced Merger Rates of Compact-object Binaries in Non-spherical Nuclear Star Clusters, ApJ 846, 146 (2017), arXiv:1705.05848 [astro-ph.HE] .
  13. X. Chen and W.-B. Han, Extreme-mass-ratio inspirals produced by tidal capture of binary black holes, Communications Physics 1, 53 (2018), arXiv:1801.05780 [astro-ph.HE] .
  14. G. Fragione, N. W. C. Leigh, and R. Perna, Black hole and neutron star mergers in galactic nuclei: the role of triples, MNRAS 488, 2825 (2019), arXiv:1903.09160 [astro-ph.GA] .
  15. W.-B. Han and X. Chen, Testing general relativity using binary extreme-mass-ratio inspirals, MNRAS 485, L29 (2019), arXiv:1801.07060 [gr-qc] .
  16. X. Chen, Z.-Y. Xuan, and P. Peng, Fake Massive Black Holes in the Milli-Hertz Gravitational-wave Band, ApJ 896, 171 (2020), arXiv:2003.08639 [astro-ph.HE] .
  17. X. Chen, Distortion of Gravitational-wave Signals by Astrophysical Environments, arXiv e-prints , arXiv:2009.07626 (2020), arXiv:2009.07626 [astro-ph.HE] .
  18. L. Randall and Z.-Z. Xianyu, A Direct Probe of Mass Density near Inspiraling Binary Black Holes, ApJ 878, 75 (2019), arXiv:1805.05335 [gr-qc] .
  19. R. S. Chandramouli and N. Yunes, The Trouble with Triples: Ready-to-use Analytic Model for Gravitational Waves from a Hierarchical Triple with Kozai-Lidov Oscillations, arXiv e-prints , arXiv:2107.00741 (2021), arXiv:2107.00741 [gr-qc] .
  20. H. Yu and Y. Chen, Direct Determination of Supermassive Black Hole Properties with Gravitational-Wave Radiation from Surrounding Stellar-Mass Black Hole Binaries, Phys. Rev. Lett. 126, 021101 (2021), arXiv:2009.02579 [gr-qc] .
  21. C. M. Will, New General Relativistic Contribution to Mercury’s Perihelion Advance, Phys. Rev. Lett. 120, 191101 (2018), arXiv:1802.05304 [gr-qc] .
  22. B. Liu, D. Lai, and Y.-H. Wang, Binary Mergers near a Supermassive Black Hole: Relativistic Effects in Triples, ApJ 883, L7 (2019), arXiv:1906.07726 [astro-ph.HE] .
  23. A. Kuntz, F. Serra, and E. Trincherini, Effective two-body approach to the hierarchical three-body problem, Phys. Rev. D 104, 024016 (2021), arXiv:2104.13387 [hep-th] .
  24. B. M. Peterson, Measuring the Masses of Supermassive Black Holes, Space Sci. Rev. 183, 253 (2014).
  25. D. J. D’Orazio and A. Loeb, Repeated gravitational lensing of gravitational waves in hierarchical black hole triples, Phys. Rev. D 101, 083031 (2020), arXiv:1910.02966 [astro-ph.HE] .
  26. K. S. Virbhadra and G. F. R. Ellis, Schwarzschild black hole lensing, Phys. Rev. D 62, 084003 (2000), arXiv:astro-ph/9904193 [astro-ph] .
  27. V. Bozza, Gravitational lensing in the strong field limit, Phys. Rev. D 66, 103001 (2002), arXiv:gr-qc/0208075 [gr-qc] .
  28. V. Bozza and G. Scarpetta, Strong deflection limit of black hole gravitational lensing with arbitrary source distances, Phys. Rev. D 76, 083008 (2007), arXiv:0705.0246 [gr-qc] .
  29. E. F. Eiroa and C. M. Sendra, Gravitational lensing by a regular black hole, Classical and Quantum Gravity 28, 085008 (2011), arXiv:1011.2455 [gr-qc] .
  30. K. S. Virbhadra, Relativistic images of Schwarzschild black hole lensing, Phys. Rev. D 79, 083004 (2009), arXiv:0810.2109 [gr-qc] .
  31. J. P. Luminet, Image of a spherical black hole with thin accretion disk., A&A 75, 228 (1979).
  32. D. E. Holz and J. A. Wheeler, Retro-MACHOs: π𝜋\piitalic_π in the Sky?, ApJ 578, 330 (2002), arXiv:astro-ph/0209039 [astro-ph] .
  33. E. F. Eiroa and D. F. Torres, Strong field limit analysis of gravitational retrolensing, Phys. Rev. D 69, 063004 (2004), arXiv:gr-qc/0311013 [gr-qc] .
  34. V. Bozza, Gravitational lensing by black holes, General Relativity and Gravitation 42, 2269 (2010), arXiv:0911.2187 [gr-qc] .
  35. E. F. Eiroa, Strong deflection gravitational lensing, arXiv e-prints , arXiv:1212.4535 (2012), arXiv:1212.4535 [gr-qc] .
  36. R. Takahashi and T. Nakamura, Wave Effects in the Gravitational Lensing of Gravitational Waves from Chirping Binaries, ApJ 595, 1039 (2003), arXiv:astro-ph/0305055 [astro-ph] .
  37. C. Cutler, Angular resolution of the LISA gravitational wave detector, Phys. Rev. D 57, 7089 (1998), arXiv:gr-qc/9703068 [gr-qc] .
  38. D. J. D’Orazio and R. Di Stefano, Periodic self-lensing from accreting massive black hole binaries, MNRAS 474, 2975 (2018), arXiv:1707.02335 [astro-ph.HE] .
  39. T. T. Nakamura and S. Deguchi, Wave Optics in Gravitational Lensing, Progress of Theoretical Physics Supplement 133, 137 (1999).
  40. V. Bozza and L. Mancini, Time Delay in Black Hole Gravitational Lensing as a Distance Estimator, General Relativity and Gravitation 36, 435 (2004), arXiv:gr-qc/0305007 [gr-qc] .
  41. T. Robson, N. J. Cornish, and C. Liu, The construction and use of LISA sensitivity curves, Classical and Quantum Gravity 36, 105011 (2019), arXiv:1803.01944 [astro-ph.HE] .
  42. C.-M. Claudel, K. S. Virbhadra, and G. F. R. Ellis, The geometry of photon surfaces, Journal of Mathematical Physics 42, 818 (2001), arXiv:gr-qc/0005050 [gr-qc] .
  43. L. Lindblom, B. J. Owen, and D. A. Brown, Model waveform accuracy standards for gravitational wave data analysis, Phys. Rev. D 78, 124020 (2008), arXiv:0809.3844 [gr-qc] .
  44. Y. Fang, X. Chen, and Q.-G. Huang, Impact of a Spinning Supermassive Black Hole on the Orbit and Gravitational Waves of a Nearby Compact Binary, ApJ 887, 210 (2019), arXiv:1908.01443 [astro-ph.HE] .
  45. C. M. Will, Propagation Speed of Gravity and the Relativistic Time Delay, ApJ 590, 683 (2003), arXiv:astro-ph/0301145 [astro-ph] .
  46. C. M. Will, The Confrontation between General Relativity and Experiment, Living Reviews in Relativity 17, 4 (2014), arXiv:1403.7377 [gr-qc] .
  47. Z. Hongsheng and F. Xilong, Poisson-Arago spot for gravitational waves, arXiv e-prints , arXiv:1809.06511 (2018), arXiv:1809.06511 [gr-qc] .
  48. C. S. Reynolds, The spin of supermassive black holes, Classical and Quantum Gravity 30, 244004 (2013), arXiv:1307.3246 [astro-ph.HE] .
  49. B. Liu and D. Lai, Probing the Spins of Supermassive Black Holes with Gravitational Waves from Surrounding Compact Binaries, arXiv e-prints , arXiv:2105.02230 (2021), arXiv:2105.02230 [astro-ph.HE] .
  50. V. Bozza, Quasiequatorial gravitational lensing by spinning black holes in the strong field limit, Phys. Rev. D 67, 103006 (2003), arXiv:gr-qc/0210109 [gr-qc] .
  51. V. Bozza, F. de Luca, and G. Scarpetta, Kerr black hole lensing for generic observers in the strong deflection limit, Phys. Rev. D 74, 063001 (2006), arXiv:gr-qc/0604093 [gr-qc] .
  52. A. Torres-Orjuela, X. Chen, and P. Amaro-Seoane, Excitation of gravitational wave modes by a center-of-mass velocity of the source, arXiv e-prints , arXiv:2010.15856 (2020), arXiv:2010.15856 [astro-ph.CO] .
  53. V. Cardoso, F. Duque, and G. Khanna, Gravitational tuning forks and hierarchical triple systems, arXiv e-prints , arXiv:2101.01186 (2021), arXiv:2101.01186 [gr-qc] .
Citations (8)
View on Semantic Scholar

Summary

No one has generated a summary of this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Summarize

Whiteboard

No one has generated a whiteboard explanation for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Sign Up to Generate

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up