Direct determination of supermassive black hole properties with gravitational-wave radiation from surrounding stellar-mass black hole binaries

TL;DR

This paper proposes a method to measure supermassive black hole properties by observing gravitational waves from stellar-mass black hole binaries influenced by the SMBH's gravitational field, enabling precise constraints on SMBH mass and orbit.

Contribution

It introduces a novel approach to determine SMBH characteristics using gravitational-wave signals from surrounding stellar-mass black hole binaries, including detection of de Sitter precession.

Findings

De Sitter precession detectable within a few years of observation.

SMBH mass and orbital separation can be measured with percent-level accuracy.

Method extends to longer precession periods with combined space and ground-based detectors.

Abstract

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.