What enhances the capture and merge rates of pairs of small black holes orbiting around supermassive black holes?
I would think that the same reason that a gas disk enhances the growth of planetesimals. Drag from the disk enforces circular, co-planar orbits, which in turn means that objects that get close to each other have small relative velocities.
Edit: So what is thought to be going on is a little bit more complex than the simple answer above. The density of massive objects embedded in the accretion disk can be enhanced at certain orbital radii. These &quot;migration traps&quot; (Bellovary et al. 2016) are caused by torques exerted on the orbiting objects (in this case black holes) caused by gas accretion. For certain disk conditions it is possible to find locations where at smaller radii the torque acts to increase the orbit radius, but at greater orbital radii the opposite is true. This would cause objects to accumulate in these migration traps, giving them more chance to interact as per my original answer.