Direct collapse black holes (DCBHs) are excellent candidates for seeds of supermassive black holes observed at z ≳; 6. The formation of a DCBH requires a strong external radiation field to suppress H2 formation and cooling in a collapsing gas cloud. Such a strong field is not easily achieved by first stars or normal star-forming galaxies. Here we investigate a scenario in which a previously formed DCBH can provide the necessary radiation field for the formation of additional ones. Using a one-zone model and simulated DCBH Spectral Energy Distributions (SEDs) filtered through absorbing gas initially having column density N H, we derive the critical field intensity, Jcrit LW, to suppress H2 formation and cooling. For the SED model with cm-2, 8.0 ×1024 cm-2, and 5.0 ×1024 cm-2, we obtain , 35, and 54, all much smaller than the critical field intensity for normal star-forming galaxies X-ray photons from previously formed DCBHs build up a high-z X-ray background (XRB) that may boost the Jcrit LW. However, we find that in the three SED models, only increases to ≈80, 170, and 390, even when reaches the maximum value allowed by the present-day XRB level (0.22, 0.034, 0.006 M o yr-1 Mpc-3), which is still much smaller than the galactic value. Although considering the XRB from first galaxies may further increase Jcrit LW, we conclude that our investigation supports a scenario in which DCBHs may be more abundant than predicted by models only including galaxies as external radiation sources.
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