Enhanced Black Hole Mergers in Active Galactic Nucleus Disks due to Precession-induced Resonances

Abstract

Recent studies have shown that active galactic nucleus (AGN) disks can host sources of gravitational waves. Compact binaries can form and merge in AGN disks through their interactions with the gas and other compact objects in the disk. It is also possible for the binaries to shorten the merging timescale due to eccentricity excitation caused by perturbations from the supermassive black hole (SMBH). In this paper, we focus on effects due to precession-induced (eviction-like) resonances, where the nodal and apsidal precession rates of the binary are commensurable with the mean motion of the binary around the SMBH. We focus on intermediate-mass black hole (IMBH)–stellar-mass black hole binaries and consider binary orbit inclined from the circum-IMBH disk, which leads to the orbital J 2 precession. We show that if a binary is captured in these resonances and is migrating toward the companion, it can undergo large eccentricity and inclination variations. We derive analytical expressions for the location of fixed points, libration timescale, and width for these resonances and identify two resonances in the near-coplanar regime (the evection and eviction resonances) as well as two resonances in the near-polar regime that can lead to mergers. We also derive analytical expressions for the maximum eccentricity that a migrating binary can achieve for given initial conditions. Specifically, the maximum eccentricity can reach 0.9 when captured in these resonances before orbital decay due to gravitational-wave emission dominates, and the capture is only possible for slow migration (∼10 Myr) two to three orders of magnitude longer than the resonance libration timescale. We also show that capture into multiple resonances is possible and can further excite eccentricities.