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

Yu, Hang and Wang, Yijun and Seymour, Brian and Chen, Yanbei (2021) Detecting gravitational lensing in hierarchical triples in galactic nuclei with space-borne gravitational-wave observatories. Physical Review D, 104 (10). Art. No. 103011. ISSN 2470-0010. doi:10.1103/physrevd.104.103011.

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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_⊙, 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 (≳10⁸ M_⊙) and more compact outer orbits with periods ≲0.1  yr, retrolensing of the SMBH (which is closely related to the glory scattering) might also have a 1%-level chance of detection. Furthermore, by combining the lensing effects and the dynamics of the outer orbit, we find that the mass of the central SMBH can be accurately determined with a fraction error of ∼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. Finally, 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 between two masses can be constrained to a 1% level.

Item Type:Article
Related URLs:
URLURL TypeDescription Paper
Yu, Hang0000-0002-6011-6190
Wang, Yijun0000-0002-5581-2001
Seymour, Brian0000-0002-7865-1052
Chen, Yanbei0000-0002-9730-9463
Additional Information:© 2021 American Physical Society. Received 2 August 2021; accepted 4 October 2021; published 8 November 2021. We thank Kumar Shwetketu Virbhadra, Xilong Fan, and the anonymous referee for useful comments about this work. H. Y. acknowledges the support of the Sherman Fairchild Foundation. B. S. acknowledges support by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-1745301. The research of Y. W. and Y. C. is supported by the Simons Foundation (Grant No. 568762), the Brinson Foundation, and the National Science Foundation (Grants No. PHY-2011968, No. PHY-2011961 and No. PHY-1836809).
Group:Astronomy Department, LIGO, TAPIR
Funding AgencyGrant Number
Sherman Fairchild FoundationUNSPECIFIED
NSF Graduate Research FellowshipDGE-1745301
Simons Foundation568762
Brinson FoundationUNSPECIFIED
Issue or Number:10
Record Number:CaltechAUTHORS:20211116-154641854
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:111888
Deposited By: Tony Diaz
Deposited On:16 Nov 2021 17:15
Last Modified:16 Nov 2021 17:15

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