Triggering the formation of direct collapse black holes by their congeners

TL;DR

This study explores how existing direct collapse black holes (DCBHs) can facilitate the formation of new DCBHs by providing the necessary radiation, suggesting they could be more common than previously thought.

Contribution

It demonstrates that DCBHs can generate sufficient radiation to trigger further DCBH formation, reducing the required external radiation intensity compared to star-forming galaxies.

Findings

Critical radiation threshold for DCBH formation is much lower than for galaxies.

X-ray background from DCBHs modestly increases the critical radiation needed.

DCBHs could be more prevalent in the early universe than models with only galaxies predict.

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 $\rm H_2$ 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 $N_{\rm H}$, we derive the critical field intensity, $J_{\rm LW}^{\rm crit}$, to suppress $\rm H_2$ formation and cooling. For the SED model with $N_{\rm H}=1.3\times10^{25}$ cm$^{-2}$, $8.0\times10^{24}$ cm$^{-2}$ and $5.0\times10^{24}$ cm$^{-2}$, we obtain $J_{\rm LW}^{\rm crit}\approx22$, 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 $J_{\rm LW}^{\rm crit}$. However, we find that in the three SED models $J_{\rm LW}^{\rm crit}$ only increases to $\approx80$, 170 and 390 respectively even when $\dt{\rho}_\bullet$ reaches the maximum value allowed by the present-day XRB level ($0.22, 0.034, 0.006~M_\odot$yr$^{-1}$Mpc$^{-3}$), still much smaller than the galactic value. Although considering the XRB from first galaxies may further increase $J_{\rm LW}^{\rm crit}$, 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.