Orbital Migration of Interacting Stellar Mass Black Holes in Disks
  around Supermassive Black Holes II. Spins and Incoming Objects
  The masses, rates, and spins of merging stellar-mass binary black holes
(BBHs) detected by aLIGO and Virgo provide challenges to traditional BBH
formation and merger scenarios. An active galactic nucleus (AGN) disk provides
a promising additional merger channel, because of the powerful influence of the
gas that drives orbital evolution, makes encounters dissipative, and leads to
migration. Previous work showed that stellar mass black holes (sBHs) in an AGN
disk migrate to regions of the disk, known as migration traps, where positive
and negative gas torques cancel out, leading to frequent BBH formation. Here we
build on that work by simulating the evolution of additional sBHs that enter
the inner disk by either migration or inclination reduction. We also examine
whether the BBHs formed in our models have retrograde or prograde orbits around
their centers of mass with respect to the disk, determining the orientation,
relative to the disk, of the spin of the merged BBHs. Orbiters entering the
inner disk form BBHs with sBHs on resonant orbits near the migration trap. When
these sBHs reach ~80 Msun, they form BBHs with sBHs in the migration trap,
which over 10 Myr reach ~1000 Msun. We find 68% of the BBHs in our simulation
orbit in the retrograde direction, which implies BBHs in our merger channel
will have small dimensionless aligned spins, \chi_eff. Overall, our models
produce BBHs that resemble both the majority of BBH mergers detected thus far
(0.66 to 120 Gpc^-3 yr^-1 ) and two recent unusual detections, GW190412 (~0.3
Gpc^-3 yr^-1 ) and GW190521 (~0.1 Gpc^-3 yr^-1 ).
