Evolution of Retrograde Orbiters in an AGN Disk

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, since 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. ROs experience a rapid decrease in the semi-major axis of their orbits while also becoming highly eccentric in less than a million years. This rapid orbital evolution leads to very small collision rates between retrograde BHs and prograde BBHs, meaning that they are unlikely to break apart or ionize existing BBHs in AGN disks. The rapid orbital evolution of ROs could instead lead to extreme mass ratio inspirals and gravitationally lensed BBH inspirals. These could be detected by the Laser Interferometer Space Antenna (LISA), and even cause disruption of the inner disk, which may produce electromagnetic signatures.