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

Abstract

Merging compact black hole (BH) binaries are likely to exist in the nuclear star clusters around supermassive BHs (SMBHs), such as Sgr A*. 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 angular momentum vector of the compact binary ( L in ) may experience significant variation due to the frame-dragging effect associated with the spin of the SMBH. The dynamical behavior of L in can be understood analytically as a resonance phenomenon. We show that the rate of change of L in 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 L in , can provide a new probe of the spins of SMBHs.