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The masses, rates, and spins of merging stellar-mass binary black holes(BBHs) detected by aLIGO and Virgo provide challenges to traditional BBHformation and merger scenarios. An active galactic nucleus (AGN) disk providesa promising additional merger channel, because of the powerful influence of thegas that drives orbital evolution, makes encounters dissipative, and leads tomigration. Previous work showed that stellar mass black holes (sBHs) in an AGNdisk migrate to regions of the disk, known as migration traps, where positiveand negative gas torques cancel out, leading to frequent BBH formation. Here webuild on that work by simulating the evolution of additional sBHs that enterthe inner disk by either migration or inclination reduction. We also examinewhether the BBHs formed in our models have retrograde or prograde orbits aroundtheir centers of mass with respect to the disk, determining the orientation,relative to the disk, of the spin of the merged BBHs. Orbiters entering theinner disk form BBHs with sBHs on resonant orbits near the migration trap. Whenthese 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 simulationorbit in the retrograde direction, which implies BBHs in our merger channelwill have small dimensionless aligned spins, \chi_eff. Overall, our modelsproduce 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 (~0.3Gpc^-3 yr^-1 ) and GW190521 (~0.1 Gpc^-3 yr^-1 ).

Orbital Migration of Interacting Stellar Mass Black Holes in Disks around Supermassive Black Holes II. Spins and Incoming Objects