Evolution of Retrograde Orbiters in an Active Galactic Nucleus Disk

Active galactic nucleus (AGN) disks have been proposed as promising locations for the mergers of stellar-mass black hole binaries (BBHs). Much recent work has been done on this merger channel, but the majority focuses on stellar-mass black holes (BHs) orbiting in the prograde direction. Little work has been done to examine the impact of retrograde orbiters (ROs) on the formation and mergers of BBHs in AGN disks. Quantifying the retrograde contribution is important, as roughly half of all orbiters should initially be on retrograde orbits when the disk forms. We perform an analytic calculation of the evolution of ROs in an AGN disk. Because this evolution could cause the orbits of ROs to cross those of prograde BBHs, we derive the collision rate between a given RO and a given BBH orbiting in the prograde direction. In the examples given here, ROs in the inner region of the disk experience a rapid decrease in the semimajor axis of their orbits while also becoming highly eccentric in less than a million years. This rapid orbital evolution could lead to extreme mass ratio inspirals detectable by the Laser Interferometer Space Antenna. The collision rates of our example ROs with prograde BBHs in the migration trap depend strongly on the volume of the inner radiation-pressure-dominated region, which depends on the mass of the supermassive black hole (SMBH). Rates are lowest for larger-mass SMBHs, which dominate the AGN merger channel, suggesting that merger rates for this channel may not be significantly altered by ROs.