Direct collapse within dark matter haloes is a promising path to form supermassive black hole seeds at high redshifts. The outer part of this collapse remains optically thin. However, the innermost region of the collapse is expected to become optically thick and requires to follow the radiation field in order to understand its evolution. So far, the adiabatic approximation has been used exclusively for this purpose. We apply radiative transfer in the flux-limited diffusion (FLD) approximation to solve the evolution of coupled gas and radiation for isolated haloes. We find that (1) the photosphere forms at 10−6 pc and rapidly expands outwards. (2) A central core forms, with a mass of 1 M, supported by gas pressure gradients and rotation. (3) Growing gas and radiation pressure gradients dissolve it. (4) This process is associated with a strong anisotropic outflow; another core forms nearby and grows rapidly. (5) Typical radiation luminosity emerging from the photosphere is 5 × 1037–5 × 1038 erg s−1, of the order the Eddington luminosity. (6) Two variability time-scales are associated with this process: a long one, which is related to the accretion flow within the central 10−4–10−3 pc, and 0.1 yr, related to radiation diffusion. (7) Adiabatic models evolution differs profoundly from that of the FLD models, by forming a geometrically thick disc. Overall, an adiabatic equation of state is not a good approximation to the advanced stage of direct collapse, because the radiation is capable of escaping due to anisotropy in the optical depth and associated gradients.

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Published in Monthly Notices of the Royal Astronomical Society, v. 476, issue 3, p. 3523-3539.

This article has been accepted for publication in Monthly Notices of the Royal Astronomical Society ©: 2018 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved.

The copyright holders have granted the permission for posting the article here.

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This work has been partially supported by the Hubble Theory grant HST-AR-14584 and JSPS KAKENHI grant 16H02163 (to I.S.). J.H.W. acknowledges support from NSF grant AST-1614333, Hubble Theory grants HST-AR-13895 and HST-AR-14326, and NASA grant NNX-17AG23G. M.B. acknowledges NASA ATP grants NNX14AB37G and NNX17AK55G and NSF grant AST-1411879. The STScI is operated by the AURA, Inc., under NASA contract NAS5-26555.