How realistic UV spectra and X-rays suppress the abundance of direct collapse black holes

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 (J_{21}^crit) for realistic spectra of Pop II stars through three-dimensional cosmological simulations. We derive the dependence of J_{21}^crit 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 J_{21}^crit is a few times 104 and only weakly depends on the adopted radiation spectra in the range between Trad = 2 × 104and105 K. For three simulated haloes of a few times 107 M⊙, J_{21}^crit varies from 2 × 104 to 5 × 104. The impact of X-ray ionization is almost negligible and within the expected scatter of J_{21}^crit for background fluxes of JX, 21 ≤ 0.1. The computed estimates of J_{21}^crit 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.