Probing the Spins of Supermassive Black Holes with Gravitational Waves from Surrounding Compact Binaries

TL;DR

This paper proposes that gravitational wave signals from compact binaries near supermassive black holes can reveal the black holes' spins by analyzing orbital axis variations caused by frame-dragging effects.

Contribution

It introduces a method to infer supermassive black hole spins through gravitational wave observations of surrounding compact binaries, highlighting the resonance behavior of orbital axis dynamics.

Findings

Orbital axis variation encodes SMBH spin information.

Resonance phenomenon explains the orbital axis dynamics.

Waveform modulation can reveal SMBH spin properties.

Abstract

Merging compact black-hole (BH) binaries are likely to exist in the nuclear star clusters around supermassive BHs (SMBHs), such as Sgr A$^\ast$. They may also form in the accretion disks of active galactic nuclei. Such compact binaries can emit gravitational waves (GWs) in the low-frequency band (0.001-1 Hz) that are detectable by several planned space-borne GW observatories. We show that the orbital axis of the compact binary may experience significant variation due to the frame-dragging effect associated with the spin of the SMBH. The dynamical behavior of the orbital axis can be understood analytically as a resonance phenomenon. We show that rate of change of the binary orbital axis encodes the information on the spin of the SMBH. Therefore detecting GWs from compact binaries around SMBHs, particularly the modulation of the waveform associated with the variation of the binary orbital axis, can provide a new probe on the spins of SMBHs.