On the number density of `direct collapse' black hole seeds

Supermassive black holes (BHs) reside in the centre of most local galaxies, but they also power active galactic nuclei and quasars, detected up to z = 7. These quasars put constraints on early BH growth and the mass of BH seeds. The scenario of `direct collapse' is appealing as it leads to the formation of large mass BH seeds, 10⁴-10⁶ M_⊙, which eases explaining how quasars at z = 6-7 are powered by BHs with masses >10⁹ M_⊙. Direct collapse, however, appears to be rare, as the conditions required by the scenario are that gas is metal-free, the presence of a strong photodissociating Lyman-Werner flux, and large inflows of gas at the centre of the halo, sustained for 10-100 Myr. We performed several cosmological hydrodynamical simulations that cover a large range of box sizes and resolutions, thus allowing us to understand the impact of several physical processes on the distribution of direct collapse BHs. We identify haloes where direct collapse can happen, and derive the number density of BHs. We also investigate the discrepancies between hydrodynamical simulations, direct or post-processed, and semi-analytical studies. Under optimistic assumptions, we find that for direct collapse to account for BHs in normal galaxies, the critical Lyman-Werner flux required for direct collapse must be about two orders of magnitude lower than predicted by 3D simulations that include detailed chemical models. However, when supernova feedback is relatively weak, enough direct collapse BHs to explain z = 6-7 quasars can be obtained for Lyman-Werner fluxes about one order of magnitude lower than found in 3D simulations.