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