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

Stars and stellar remnants orbiting a supermassive black hole (SMBH) can interact with an active galactic nucleus (AGN) disc. Over time, prograde orbiters (inclination $i<90^{\circ}$) decrease inclination, as well as semi-major axis $(a)$ and eccentricity $(e)$ until orbital alignment with the gas disc ('disc capture'). Captured stellar-origin black holes (sBH) add to the embedded AGN population which drives sBH-sBH mergers detectable in gravitational waves using LIGO-Virgo-KAGRA (LVK) or sBH-SMBH mergers detectable with LISA (Laser Interferometer Space Antenna). Captured stars can be tidally disrupted by sBH or the SMBH or rapidly grow into massive 'immortal' stars. Here, we investigate the behaviour of polar and retrograde orbiters $(i \geq 90^{\circ})$ interacting with the disc. We show that retrograde stars are captured faster than prograde stars, flip to prograde orientation $(i<90^{\circ})$ during capture, and decrease $a$ dramatically towards the SMBH. For sBH, we find a critical angle $i_{\rm ret} \sim 113^{\circ}$, below which retrograde sBH decay towards embedded prograde orbits $(i \to 0^{\circ})$, while for $i_{\rm o}>i_{\rm ret}$ sBH decay towards embedded retrograde orbits $(i \to 180^{\circ})$. sBH near polar orbits $(i \sim 90^{\circ})$ and stars on nearly embedded retrograde orbits $(i \sim 180^{\circ})$ show the greatest decreases in $a$. Whether a star is captured by the disc within an AGN lifetime depends primarily on disc density, and secondarily on stellar type and initial $a$. For sBH, disc capture-time is longest for polar orbits, low mass sBH and lower density discs. Larger mass sBH should typically spend more time in AGN discs, with implications for the embedded sBH spin distribution.