Direct-collapse black hole formation induced by internal radiation of host haloes

We estimate the fraction of haloes 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 DC is limited only in chemically pristine haloes, we here suppose that DC can occur also in haloes with metallicity below a threshold value Z(th) = 0-10(-3) Z(circle dot), considering the supercompetitive 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 haloes, i.e. internal radiation. We find that with low threshold metallicities of Z(th) <= 10(-4) Z(circle dot), 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 neighbouring haloes is reduced. Only when Z(th) is as high as 10(-3) Z(circle dot), 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 x 10(9) to 9 x 10(8) M-circle dot. We also find that haloes with M-halo greater than or similar to 10(11)-10(12) M-circle dot 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.