Orbital Migration of Interacting Stellar Mass Black Holes in Disks
  around Supermassive Black Holes
  The merger rate of stellar-mass black hole binaries (sBHBs) inferred by the
Advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) suggests
the need for an efficient source of sBHB formation. Active galactic nucleus
(AGN) disks are a promising location for the formation of these sBHBs, as well
as binaries of other compact objects, because of powerful torques exerted by
the gas disk. These gas torques cause orbiting compact objects to migrate
towards regions in the disk where inward and outward torques cancel, known as
migration traps. We simulate the migration of stellar mass black holes in an
example of a model AGN disk, using an augmented N-body code that includes
analytic approximations to migration torques, stochastic gravitational forces
exerted by turbulent density fluctuations in the disk, and inclination and
eccentricity dampening produced by passages through the gas disk, in addition
to the standard gravitational forces between objects. We find that sBHBs form
rapidly in our model disk as stellar-mass black holes migrate towards the
migration trap. These sBHBs are likely to subsequently merge on short
time-scales. The process continues, leading to the build-up of a population of
over-massive stellar-mass black holes. The formation of sBHBs in AGN disks
could contribute significantly to the sBHB merger rate inferred by LIGO.
