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) less than or similar to R-H) scales approximately as proportional to t(0.5). The minimum encounter separation r(p) follows a cumulative distribution P(

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This study investigates the long-term evolution of the orbital configuration of two or more stellar black holes around a supermassive black hole, finding that the degree of closeness between the black holes affects the number of interactions and minimum separation distance.