We use numerical simulations to explore whether direct collapse can lead to the formation of supermassive black hole ( SMBH ) seeds at high redshifts .
Using the adaptive mesh refinement code ENZO , we follow the evolution of gas within slowly tumbling dark matter ( DM ) halos of M _ { vir } \sim 2 \times 10 ^ { 8 } M _ { \odot } and R _ { vir } \sim 1 kpc .
For our idealized simulations , we adopt cosmologically motivated DM and baryon density profiles and angular momentum distributions .
Our principal goal is to understand how the collapsing flow overcomes the centrifugal barrier and whether it is subject to fragmentation which can potentially lead to star formation , decreasing the seed SMBH mass .
We find that the collapse proceeds from inside out and leads either to a central runaway or to off-center fragmentation .
A disk-like configuration is formed inside the centrifugal barrier , growing via accretion .
For models with a more cuspy DM distribution , the gas collapses more and experiences a bar-like perturbation and a central runaway on scales of \mathrel { \raise 1.29 pt \hbox { $ < $ } \mkern - 14.0 mu \lower 2.58 pt \hbox { $ \sim$ } } 1 - 10 pc .
We have followed this inflow down to \sim 10 ^ { -4 } pc ( \sim 10 AU ) , where it is estimated to become optically thick .
The flow remains isothermal and the specific angular momentum , j , is efficiently transferred by gravitational torques in a cascade of nested bars .
This cascade is triggered by finite perturbations from the large-scale mass distribution and by gas self-gravity , and supports a self-similar , disk-like collapse where the axial ratios remain constant .
The mass accretion rate shows a global minimum on scales of \sim 1 - 10 pc at the time of the central runaway .
In the collapsing phase , virial supersonic turbulence develops and fragmentation is damped .
Models with progressively larger initial DM cores evolve similarly , but the timescales become longer .
In models with more organized initial rotation — when the rotation of spherical shells is constrained to be coplanar — a torus forms on scales \sim 20 - 50 pc outside the disk , and appears to be supported by turbulent motions driven by accretion from the outside .
The overall evolution of the models depends on the competition between two timescales , corresponding to the onset of the central runaway and of off-center fragmentation .
In models with less organized rotation — when the rotation of spherical shells is randomized ( but the total angular momentum remains unchanged ) — 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 seed SMBH masses is found in the range M _ { \bullet } \sim 2 \times 10 ^ { 4 } M _ { \odot } -2 \times 10 ^ { 6 } M _ { \odot } , substantially higher than the mass range of Population III remnants .
We argue that the above upper limit on M _ { \bullet } appears to be more realistic , and lies close to the cutoff mass of detected SMBHs .
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 .