Long-term Evolution of Tightly Packed Stellar Black Holes in AGN Disks: Formation of Merging Black Hole Binaries via Close Encounters

We study the long-term evolution of two or more stellar black holes (BHs) on initially separated but unstable circular orbits around a supermassive BH (SMBH). Such a close-packed orbital configuration can naturally arise from BH migrations in the AGN disk. Dynamical instability of the orbits leads to recurring close encounters between two BHs, during which the BH separation r p becomes less than the Hill radius R H . In rare very close encounters, a tight merging BH binary can form with the help of gravitational wave emission. We use N -body simulations to study the time evolution of close encounters of various degrees of closeness . For a typical “SMBH+2BH” system, the averaged cumulative number of close encounters (with r p ≲ R H ) scales approximately as ∝ t 0.5 . The minimum encounter separation r p follows a cumulative distribution P (< r p ) ∝ r p for r p ≪ R H . We obtain a semi-analytical expression for the averaged rate of binary captures that lead to BH mergers. Our results suggest that close-packed BHs in AGN disks may take a long time (≳10 7 orbits around the SMBH) to experience a sufficiently close encounter and form a bound binary. This time can be shorter if the initial BH orbits are highly aligned. The BH binary mergers produced in this scenario have high eccentricities when entering the LIGO band and broad distribution of orbital inclinations relative to the original AGN disk. We explore the effects of the gas disk and find that simple gas drags on the BHs do not necessarily lead to an enhanced BH binary capture rate.