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 H2β 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 NHβ, we derive the critical field
intensity, JLWcritβ, to suppress H2β formation and
cooling. For the SED model with NHβ=1.3Γ1025 cmβ2,
8.0Γ1024 cmβ2 and 5.0Γ1024 cmβ2, we obtain
JLWcritββ22, 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 JLWcritβ. However, we find
that in the three SED models JLWcritβ only increases to
β80, 170 and 390 respectively even when \dt{\rho}_\bullet reaches the
maximum value allowed by the present-day XRB level (0.22,0.034,0.006Β Mββyrβ1Mpcβ3), still much smaller than the galactic value.
Although considering the XRB from first galaxies may further increase JLWcritβ, 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.Comment: 18 pages, 14 figures, 5 tables, ApJ in pres