Direct Determination of Supermassive Black Hole Properties with Gravitational-Wave Radiation from Surrounding Stellar-Mass Black Hole Binaries
A significant number of stellar-mass black-hole (BH) binaries may merge in galactic nuclei or in the surrounding gas disks. With purposed space-borne gravitational-wave observatories, we may use such a binary as a signal carrier to probe modulations induced by a central supermassive BH (SMBH), which further allows us to place constraints on the SMBH's properties. We show in particular the de Sitter precession of the inner stellar-mass binary's orbital angular momentum (AM) around the AM of the outer orbit will be detectable if the precession period is comparable to the duration of observation, typically a few years. Once detected, the precession can be combined with the Doppler shift arising from the outer orbital motion to determine the mass of the SMBH and the outer orbital separation individually and each with percent-level accuracy. If we further assume a joint detection by space-borne and ground-based detectors, the detectability threshold could be extended to a precession period of ∼100 yr.
© 2021 American Physical Society. Received 8 September 2020; revised 27 October 2020; accepted 14 December 2020; published 11 January 2021. We are thankful for the helpful comments from Imre Bartos, Karan Jani, and the referees during the preparation of this work. We are grateful to Hiroyuki Nakano for kindly providing us the sensitivity curve of B-DECIGO. H. Y. acknowledges the support by the Sherman Fairchild Foundation. Y. C. is supported by the Simons Foundation (Grant No. 568762), and the National Science Foundation, through Grants No. PHY-2011961, No. PHY-2011968, and No. PHY-1836809. The authors also gratefully acknowledge the computational resources provided by the LIGO Laboratory and support by NSF Grants No. PHY-0757058 and No. PHY-0823459.
Published - PhysRevLett.126.021101.pdf
Accepted Version - 2009.02579.pdf
Supplemental Material - supp.pdf