Spin Evolution of Stellar-mass Black Holes Embedded in AGN Disks: Orbital Eccentricity Produces Retrograde Circumstellar Flows

The spin evolution of stellar-mass black holes (sBHs) embedded in AGN accretion disks is an important process relevant to the production of gravitational waves from binary BH (BBH) merger events through the AGN channel. Because embedded sBHs are surrounded by circumstellar disks (CSDs), the rotation of CSD gas flows determines the direction of the angular momentum it accretes. In this Letter, we use global 2D hydrodynamic simulations to show that while a disk-embedded sBH on a circular orbit transforms the initial retrograde Keplerian shear of the background accretion disk into a prograde CSD flow, as in the classical picture of companion-disk interaction theory, moderate orbital eccentricity could disrupt the steady-state tidal perturbation and preserve a retrograde CSD flow around the sBH. This switch in CSD orientation occurs at a transition eccentricity that scales nearly proportional to the local sound speed. This bifurcation in the CSD flow and thereafter spin-up direction of SBHs leads to the formation of a population of nearly antialigned sBHs and should be incorporated in future population models of sBH and BBH evolutions.