Abstract

The ability of metal-free gas to cool by molecular hydrogen in primordial haloes is strongly associated with the strength of ultraviolet (UV) flux produced by the stellar populations in the first galaxies. Depending on the stellar spectrum, these UV photons can either dissociate H$_{2}$ molecules directly or indirectly by photodetachment of H$^{-}$ as the latter provides the main pathway for H$_{2}$ formation in the early universe. In this study, we aim to determine the critical strength of the UV flux above which the formation of molecular hydrogen remains suppressed for a sample of five distinct haloes at z $\gt$ 10 by employing a higher order chemical solver and a Jeans resolution of 32 cells. We presume that such flux is emitted by Pop II stars implying atmospheric temperatures of 10$^{4}$ K. We performed three-dimensional cosmological simulations and varied the strength of the UV flux below the Lyman limit in units of J$_{21}$. Our findings show that the value of J\_$\{$21$\}$\^{}crit varies from halo to halo and is sensitive to the local thermal conditions of the gas. For the simulated haloes, it varies from 400 to 700 with the exception of one halo where J\_$\{$21$\}$\^{}crit {\ge} 1500. This has important implications for the formation of direct collapse black holes and their estimated population at z $\gt$ 6. It reduces the number density of direct collapse black holes by almost three orders of magnitude compared to the previous estimates.