Supermassive Black Hole Formation at High Redshifts via Direct Collapse:
  Physical Processes in the Early Stage
  We use numerical simulations to explore whether direct collapse can lead to
the formation of SMBH seeds at high-z. We follow the evolution of gas within DM
halos of 2 x 10^8 Mo and 1 kpc. We adopt cosmological density profiles and
j-distributions. Our goal is to understand how the collapsing flow overcomes
the centrifugal barrier and whether it is subject to fragmentation. We find
that the collapse leads either to a central runaway or to off-center
fragmentation. A disk-like configuration is formed inside the centrifugal
barrier. For more cuspy DM distribution, the gas collapses more and experiences
a bar-like perturbation and a central runaway. We have followed this inflow
down to ~10^{-4} pc. The flow remains isothermal and the specific angular
momentum is efficiently transferred by gravitational torques in a cascade of
nested bars. This cascade supports a self-similar, disk-like collapse. In the
collapsing phase, virial supersonic turbulence develops and fragmentation is
damped. For larger initial DM cores the timescales become longer. In models
with more organized initial rotation, a torus forms and appears to be supported
by turbulent motions. The evolution depends on the competition between two
timescales, corresponding to the onset of the central runaway and off-center
fragmentation. For less organized rotation, the torus is greatly weakened, the
central accretion timescale is shortened, and off-center fragmentation is
suppressed --- triggering the central runaway even in previously `stable'
models. The resulting SMBH masses lie in the range 2 x 10^4 Mo - 2 x 10^6 Mo,
much higher than for Population III remnants. We argue that the above upper
limit appears to be more realistic mass. Corollaries of this model include a
possible correlation between SMBH and DM halo masses, and similarity between
the SMBH and halo mass functions, at time of formation.
