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 Mvir ~ 2 × 108 M and Rvir ~ 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 ≲ 1-10 pc. We have followed this inflow down to ~10–4 pc (~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 ~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 ~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 ~ 2 × 104 M-2 × 106 M, substantially higher than the mass range of Population III remnants. We argue that the above upper limit on M 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.

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Published in The Astrophysical Journal, v. 774, no. 2, 149, p. 1-18.

© 2013. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

The copyright holder has granted the permission for posting the article here.

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I.S. acknowledges support from the NSF AST-0807760 and from the HST/STScI AR-12639.01-A. M.C.B. acknowledges support from the NSF under AST-0907872. Support for HST/STScI AR-12639.01-A was provided by NASA through a grant from the STScI, which is operated by the AURA, Inc., under NASA contract NAS5-26555.

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