Intermediate mass black holes in AGN disks: I. Production & Growth
  Here we propose a mechanism for efficiently growing intermediate mass black
holes (IMBH) in disks around supermassive black holes. Stellar mass objects can
efficiently agglomerate when facilitated by the gas disk. Stars, compact
objects and binaries can migrate, accrete and merge within disks around
supermassive black holes. While dynamical heating by cusp stars excites the
velocity dispersion of nuclear cluster objects (NCOs) in the disk, gas in the
disk damps NCO orbits. If gas damping dominates, NCOs remain in the disk with
circularized orbits and large collision cross-sections. IMBH seeds can grow
extremely rapidly by collisions with disk NCOs at low relative velocities,
allowing for super-Eddington growth rates. Once an IMBH seed has cleared out
its feeding zone of disk NCOs, growth of IMBH seeds can become dominated by gas
accretion from the AGN disk. However, the IMBH can migrate in the disk and
expand its feeding zone, permitting a super-Eddington accretion rate to
continue. Growth of IMBH seeds via NCO collisions is enhanced by a pile-up of
migrators.
  We highlight the remarkable parallel between the growth of IMBH in AGN disks
with models of giant planet growth in protoplanetary disks. If an IMBH becomes
massive enough it can open a gap in the AGN disk. IMBH migration in AGN disks
may stall, allowing them to survive the end of the AGN phase and remain in
galactic nuclei. Our proposed mechanisms should be more efficient at growing
IMBH in AGN disks than the standard model of IMBH growth in stellar clusters.
Dynamical heating of disk NCOs by cusp stars is transferred to the gas in a AGN
disk helping to maintain the outer disk against gravitational instability.
Model predictions, observational constraints and implications are discussed in
a companion paper (Paper II).
