Triggering the formation of direct collapse black holes by their congeners

Abstract

Direct collapse black holes (DCBHs) are excellent candidates as seeds of supermassive black holes (SMBHs) observed at $z \gsim 6$. The formation of a DCBH requires a strong external radiation field to suppress ${\mathrm{H}}_2$ formation and cooling in a collapsing gas cloud. Such strong field is not easily achieved by first stars or normal star-forming galaxies. Here we investigate a scenario in which the previously-formed DCBH can provide the necessary radiation field for the formation of additional ones. Using one-zone model and the simulated DCBH Spectral Energy Distributions (SEDs) filtered through absorbing gas initially having column density $N_{\mathrm{H}}$, we derive the critical field intensity, $J_{\mathrm{LW}}^{\mathrm{crit}}$, to suppress ${\mathrm{H}}_2$ formation and cooling. For the SED model with $N_{\mathrm{H}}=1.3\times 10^{25}$ cm${}^{-2}$, $8.0\times 10^{24}$ cm${}^{-2}$ and $5.0\times 10^{24}$ cm${}^{-2}$, we obtain $J_{\mathrm{LW}}^{\mathrm{crit}}\approx 22$, 35 and 54, all much smaller than the critical field intensity for normal star-forming galaxies ($J_{\rm LW}^{\rm crit}\simgt 1000$). X-ray photons from previously-formed DCBHs build up a high-$z$ X-ray background (XRB) that may boost the $J_{\mathrm{LW}}^{\mathrm{crit}}$. However, we find that in the three SED models $J_{\mathrm{LW}}^{\mathrm{crit}}$ only increases to $\approx 80$, 170 and 390 respectively even when $\dtρ_\bullet$ reaches the maximum value allowed by the present-day XRB level ($0.22,0.034,0.006M_{\odot }$yr${}^{-1}$Mpc${}^{-3}$), still much smaller than the galactic value. Although considering the XRB from first galaxies may further increase $J_{\mathrm{LW}}^{\mathrm{crit}}$, we conclude that our investigation supports a scenario in which DCBH may be more abundant than predicted by models only including galaxies as external radiation sources.

18 pages, 14 figures, 5 tables, ApJ in press

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