Spin Evolution of Stellar-mass Black Hole Binaries in Active Galactic
  Nuclei
  The astrophysical origin of gravitational wave (GW) events is one of the most
timely problems in the wake of the LIGO/Virgo discoveries. In active galactic
nuclei (AGN), binaries form and evolve efficiently by dynamical interactions
and gaseous dissipation. Previous studies have suggested that binary black hole
(BBH) mergers in AGN disks can contribute significantly to BBH mergers observed
by GW interferometers. Here we examine the distribution of the effective spin
parameter $\chi_\mathrm{eff}$ of this GW source population. We extend our
semi-analytical model of binary formation and evolution in AGN disks by
following the evolution of the binary orbital angular momenta and black hole
(BH) spins. BH spins change due to gas accretion and BH mergers, while the
binary orbital angular momenta evolve due to gas accretion and binary-single
interactions. We find that the distribution of $\chi_\mathrm{eff}$ predicted by
our AGN model is similar to the distribution observed during LIGO/Virgo O1 and
O2. On the other hand, if radial migration of BHs is inefficient,
$\chi_\mathrm{eff}$ is skewed toward higher values compared with the observed
distribution, because of the paucity of scattering events that would randomize
spin directions relative to the orbital plane. We suggest that high binary
masses and the positive correlation between binary mass and the standard
deviation of $\chi_\mathrm{eff}$ for chirp masses up to $\approx 20$
$\mathrm{M}_\odot$, can be possible signatures for mergers originating in AGN
disks. Finally, hierarchical mergers in AGN disks naturally produce properties
of the recent GW event GW190412, including a low mass ratio, a high primary BH
spin, and a significant spin component in the orbital plane.
