The critical radiation intensity for direct collapse black hole
  formation: dependence on the radiation spectral shape
  It has been proposed that supermassive black holes (SMBHs) are originated
from direct-collapse black holes (DCBHs) that are formed at z gtrsim 10 in the
primordial gas in the case that H2 cooling is suppressed by strong external
radiation. In this work, we study the critical specific intensity J^crit
required for DCBH formation for various radiation spectral shapes by a series
of one-zone calculations of a collapsing primordial- gas cloud. We calculate
the critical specific intensity at the Lyman-Werner (LW) bands J^crit_LW,21 (in
units of 10^-21 erg s^-1 Hz^-1 sr^-1 cm^-2) for realistic spectra of metal-poor
galaxies. We find J^crit is not sensitive to the age or metallicity for the
constant star formation galaxies with J^crit_LW,21 = 1300-1400, while J^crit
decreases as galaxies become older or more metal-enriched for the instantaneous
starburst galaxies. However, such dependence for the instantaneous starburst
galaxies is weak for the young or extremely metal-poor galaxies: J^crit_LW,21 =
1000-1400 for the young galaxies and J^crit_LW,21 approx 1400 for the extremely
metal-poor galaxies. The typical value of J^crit for the realistic spectra is
higher than those expected in the literature, which affects the estimated DCBH
number density n_DCBH. By extrapolating the result of Dijkstra, Ferrara and
Mesinger, we obtain n_DCBH sim 10^-10 cMpc^-3 at z = 10, although there is
still large uncertainty in this estimation.
