Super-Eddington growth of black holes in the early Universe: effects of
  disk radiation spectra
  We investigate the properties of accretion flows onto a black hole (BH) with
a mass of $M_{\rm BH}$ embedded in an initially uniform gas cloud with a
density of $n_{\infty}$ in order to study rapid growth of BHs in the early
Universe. In previous work, the conditions for super-Eddington accretion from
outside the Bondi radius were studied by assuming that radiation produced at
the vicinity of the central BH has a single-power-law spectrum $\nu^{-\alpha}$
at $h\nu \geq 13.6~{\rm eV}$ ($\alpha \sim 1.5$). However, radiation spectra
depends on the BH mass and accretion rate. Here, we perform two-dimensional
multi-frequency radiation hydrodynamical simulations taking into account more
realistic radiation spectra associated with the properties of nuclear accretion
disks. We find that the condition for a transition to super-Eddington accretion
is alleviated for a wide range of masses ($10\lesssim M_{\rm BH}/M_{\odot}
\lesssim 10^6$) because photoionization for accretion disk spectra are less
efficient than those for single-power-law spectra. For disk spectra, the
transition to super-Eddington is more likely to occur for lower BH masses
because the radiation spectra become too hard to ionize the gas. Even when
accretion flows are exposed to anisotropic radiation, the effect due to
radiation spectra shrinks the ionized region and likely leads to the transition
to a wholly neutral accretion phase. Finally, by generalizing our simulation
results, we construct a new analytical criterion required for super-Eddington
accretion; $(M_{\rm BH}/10^5~M_{\odot}) (n_{\infty}/10^4~{\rm cm^{-3}}) \gtrsim
2.4~ (\langle\epsilon\rangle /100~{\rm eV})^{-5/9}$, where
$\langle\epsilon\rangle$ is the mean energy of ionizing radiation from the
central BH.
