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

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