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Spin evolution of stellar-mass Black Holes (sBHs) embedded in AGN accretiondisks is an important process relevant to production of gravitaional waves frombinary Black Hole (BBH) merger events through the AGN channel. Since embeddedsBHs are surrounded by circum-stellar disks (CSDs), the rotation of CSD gasflows determine the direction of the angular momentum it accretes. In thisLetter, we use global 2D hydrodynamic simulations to show that while adisk-embedded sBH on a circular orbit transforms the initial retrogradeKeplerian shear of the background accretion disk into a prograde CSD flow, asin the classical picture of companion-disk interaction theory, moderate orbitaleccentricity could disrupt the steady-state tidal perturbation and preserve aretrograde CSD flow around the sBH. This switch of CSD orientation occurs at atransition eccentricity that scales nearly proportional with local sound speed.This bifurcation in the CSD flow and thereafter spin-up direction of SBHs leadsto formation of a population of nearly anti-aligned sBHs and should beincorporated in future population models of sBH and BBH evolutions.

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