Aligning Retrograde Nuclear Cluster Orbits with an Active Galactic Nucleus Accretion Disk

Stars and stellar remnants orbiting a supermassive black hole (SMBH) can interact with an active galactic nucleus (AGN) disk. Over time, prograde orbiters (inclination i < 90°) decrease inclination, as well as semi-major axis (a) and eccentricity (e) until orbital alignment with the gas disk. Captured stellar-origin black holes (BH) add to the embedded AGN population which drives BH-BH mergers detectable in gravitational waves using LIGO-Virgo-KAGRA (LVK) or BH-SMBH mergers detectable with LISA (Laser Interferometer Space Antenna). Captured stars can be tidally disrupted by BH or the SMBH or rapidly grow into massive ’immortal’ stars. Here, we investigate the behavior of polar and retrograde orbiters (i ≥ 90°) interacting with the disk. We show that retrograde stars are captured faster than prograde stars, flip to prograde during capture and decrease a dramatically towards the SMBH. For BH, we find a critical angle i_ret ∼ 110°, below which retrograde BH decay towards embedded prograde orbits (i → 0°), while for i > i_ret BH decay towards embedded retrograde orbits (i → 180°). BH near polar orbits (i ∼ 90°) and stars on nearly embedded retrograde orbits (i ∼ 180°) show the greatest decreases in a. Whether a star is captured by the disk within an AGN lifetime depends on disk density and stellar type. For BH, capture time is longest for polar orbits, low mass BH and lower density disks. Larger mass BH should typically spend more time in AGN disks, with implications for the embedded BH spin distribution.