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 of gravitaional waves from
binary Black Hole (BBH) merger events through the AGN channel. Since embedded
sBHs are surrounded by circum-stellar disks (CSDs), the rotation of CSD gas
flows determine 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 of CSD orientation occurs at a
transition eccentricity that scales nearly proportional with local sound speed.
This bifurcation in the CSD flow and thereafter spin-up direction of SBHs leads
to formation of a population of nearly anti-aligned sBHs and should be
incorporated in future population models of sBH and BBH evolutions.
