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Observations of high-redshift quasars at z > 6 indicate that they harbour supermassive black holes (SMBHs) of a billion solar masses. The direct collapse scenario has emerged as the most plausible way to assemble SMBHs. The nurseries for the direct collapse black holes are massive primordial haloes illuminated with an intense UV flux emitted by Population II (Pop II) stars. In this study, we compute the critical value of such a flux (J21crit) for realistic spectra of Pop II stars through three-dimensional cosmological simulations. We derive the dependence of J21crit on the radiation spectra, on variations from halo to halo, and on the impact of X-ray ionization. Our findings show that the value of J21crit is a few times 104 and only weakly depends on the adopted radiation spectra in the range between Trad = 2 × 104 and 105 K. For three simulated haloes of a few times 107 M⊙, J21crit varies from 2 × 104 to 5 × 104. The impact of X-ray ionization is almost negligible and within the expected scatter of J21crit for background fluxes of JX,21 ≤ 0.1. The computed estimates of J21crit have profound implications for the quasar abundance at z = 10 as it lowers the number density of black holes forming through an isothermal direct collapse by a few orders of magnitude below the observed black hole density. However, the sites with moderate amounts of H2 cooling may still form massive objects sufficient to be compatible with observations. [ABSTRACT FROM AUTHOR]

Numerous cosmological simulations have been performed to study the formation of the first objects. We present the results of high-resolution 3D cosmological simulations of the formation of primordial objects using the adaptive mesh refinement code by including in an approximate manner the radiative transfer effects of Lyman α photons. We compare the results of a Lyman α trapping case inside gas clouds with atomic and molecular hydrogen cooling cases. The principal objective of this research is to follow the collapse of a zero metallicity halo with an effective equation of state (that accounts for the trapping) and to explore the fate of a halo in each of the three cases, specifically the impact of thermodynamics on the fragmentation of haloes. Our results show that in the case of Lyman α trapping, fragmentation is halted and a massive object is formed at the centre of a halo. The temperature of the gas remains well above 10 K and the halo is not able to fragment to stellar masses. In the atomic cooling case, gas collapses into one or two massive clumps in contrast to the Lyman α trapping case. For the molecular hydrogen cooling case, gas cools efficiently and fragments. The formation of massive primordial objects is thus strongly dependent on the thermodynamics of the gas. A salient feature of our results is that for the formation of massive objects, e.g. intermediate-mass black holes, feedback effects are not required to suppress cooling, as molecular hydrogen is collisionally dissociated at temperatures higher than 10 K as a consequence of Lyman α trapping. [ABSTRACT FROM AUTHOR]