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Black holes of a billion solar masses are observed in the infant universe afew hundred million years after the Big Bang. The direct collapse ofprotogalactic gas clouds in primordial halos with $\rm T_{vir} \geq 10^{4} K$provides the most promising way to assemble massive black holes. In this study,we aim to determine the characteristic mass scale of seed black holes and thetime evolution of the accretion rates resulting from the direct collapse model.We explore the formation of supermassive black holes via cosmological largeeddy simulations (LES) by employing sink particles and following theirevolution for twenty thousand years after the formation of the first sink. Asthe resulting protostars were shown to have cool atmospheres in the presence ofstrong accretion, we assume here that UV feedback is negligible during thiscalculation. We confirm this result in a comparison run without sinks. Ourfindings show that black hole seeds with characteristic mass of $\rm 10^{5}M_{\odot}$ are formed in the presence of strong Lyman Werner flux which leadsto an isothermal collapse. The characteristic mass is a about two times higherin LES compared to the implicit large eddy simulations (ILES). The accretionrates increase with time and reach a maximum value of 10 $\rm M_{\odot}/yr$after $\rm 10^{4}$ years. Our results show that the direct collapse model isclearly feasible as it provides the expected mass of the seed black holes.

The characteristic black hole mass resulting from direct collapse in the early universe