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We investigate the properties of accretion flows onto a black hole (BH) witha mass of $M_{\rm BH}$ embedded in an initially uniform gas cloud with adensity of $n_{\infty}$ in order to study rapid growth of BHs in the earlyUniverse. In previous work, the conditions for super-Eddington accretion fromoutside the Bondi radius were studied by assuming that radiation produced atthe 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 spectradepends on the BH mass and accretion rate. Here, we perform two-dimensionalmulti-frequency radiation hydrodynamical simulations taking into account morerealistic radiation spectra associated with the properties of nuclear accretiondisks. We find that the condition for a transition to super-Eddington accretionis alleviated for a wide range of masses ($10\lesssim M_{\rm BH}/M_{\odot}\lesssim 10^6$) because photoionization for accretion disk spectra are lessefficient than those for single-power-law spectra. For disk spectra, thetransition to super-Eddington is more likely to occur for lower BH massesbecause the radiation spectra become too hard to ionize the gas. Even whenaccretion flows are exposed to anisotropic radiation, the effect due toradiation spectra shrinks the ionized region and likely leads to the transitionto a wholly neutral accretion phase. Finally, by generalizing our simulationresults, we construct a new analytical criterion required for super-Eddingtonaccretion; $(M_{\rm BH}/10^5~M_{\odot}) (n_{\infty}/10^4~{\rm cm^{-3}}) \gtrsim2.4~ (\langle\epsilon\rangle /100~{\rm eV})^{-5/9}$, where$\langle\epsilon\rangle$ is the mean energy of ionizing radiation from thecentral BH.

Super-Eddington growth of black holes in the early Universe: effects of disk radiation spectra