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We estimate the fraction of halos that host supermassive black holes (SMBHs) forming through the direct collapse (DC) scenario by using cosmological N -body simulations combined with a semi-analytic model for galaxy evolution. While in most of earlier studies the occurrence of the DC is limited only in chemically pristine halos, we here suppose that the DC can occur also in halos with metallicity below a threshold value Z ₓ₇ = 0--10^-3~ Z_, considering the super-competitive accretion pathway for DC black hole (DCBH) formation. In addition, we consider for the first time the effect of Lyman-Werner (LW) radiation from stars within host halos, i. e. , internal radiation. We find that, with low threshold metallicities of Z ₓ₇ 10^-4~ Z_, the inclusion of internal radiation rather reduces the number density of DCBHs from 0. 2--0. 3 to 0. 03--0. 06~ Mpc^-3. This is because star formation is suppressed due to self-regulation, and the LW flux emitted by neighboring halos is reduced. Only when Z ₓ₇ is as high as 10^-3~ Z_, internal radiation enhances the number density of DCBHs from 0. 4 to 1~ Mpc^-3, thereby decreasing the threshold halo mass above which at least one DCBH forms from 2 10^9 to 9 10^8~ M_. We also find that halos with M ₇₀₋₎ 10^11--10^12~ M_ can host more than one DCBH at z = 0. This indicates that the DC scenario alone can explain the observed number of SMBH-hosting galaxies.
Chiaki et al. (Fri,) studied this question.