We perform two-dimensional radiation hydrodynamical simulations of accretion flows onto a black hole (BH) with a mass of 10 3 M BH /M 10 6 in order to study rapid growth of BHs in the early Universe. For spherically symmetric flows, hyper-Eddington accretion onto the BH from outside the Bondi radius can occur unimpeded by radiation feedback only when the BH mass is higher than 10, where n ∞ and T ∞ are the density and temperature of ambient gas. Here, we study the properties of accretion flows exposed to anisotropic radiation from a nuclear accretion disk with a luminosity higher than the Eddington value (L Edd ) due to collimation toward the bipolar directions. We find that, unlike the spherically symmetric case, even less massive BHs with M BH < 10 4 M can be fed by surrounding gas at high accretion rates of L Edd /c 2 through the equatorial plane, while ionized regions expand to the polar directions producing hot outflows with T ∼ 10 5 K. For more massive BHs with M BH 5 × 10 5 M , neutral gas through the equatorial plane totally covers the central radiating region due to the non-radial gas motions, and thus the emergent radiation in all directions is blocked. Because of efficient recombination by hydrogen, the entire flow results in neutral and warm gas with T 8000 K. The central BH is fed through the equator at the averaged rate of ∼ 5 × 10 4 L Edd /c 2 , which corresponds to ∼ 50 % of the inflow rate from the Bondi radius. Moreover, radiation momentum absorbed by neutral hydrogen produces warm outflows toward the bipolar directions at ∼ 30 % of the BH feeding rate and with a typical velocity of 50 km s −1 .

Abstract We perform two-dimensional radiation hydrodynamical simulations of accretion flows onto black holes (BHs) at the nuclei of protogalaxies, and study the impact of mechanical and radiative feedback on rapid growth of BHs. The outflows deposit mass, momentum and energy into the surrounding medium and prevent mass accretion onto the BH, resulting in the reduction of radiative output. We find that when the BH is embedded in a dense gas core, ionizing radiation attenuated by inefficient BH feeding owing to mechanical feedback hardly affects the gas dynamics at the BH gravitational sphere of influence, from which intense inflows of neutral gas occur at rates substantially exceeding the Eddington limit without impeded by photoionization and heating. Since mechanical power of outflows driven by the rapidly accreting BH is sufficiently strong, bipolar outflows completely evacuate the surrounding gas in the polar region but mass inflows through the equatorial region maintain the BH accretion rate as high as $\sim 300-10^3~\dot{M}_{\rm Edd}$, which is reduced by one order of magnitude from those with radiative feedback alone. Furthermore, we find that the critical gas density required for rapid accretion is lower by a factor of ∼3, when mechanical feedback is considered. By studying the dependence on outflow parameters (e.g., opening angle, mass-loading degree into outflows, velocity), we conclude that contrary to naive expectation, the stronger outflow leads to the transition to rapid accretion more efficiently. Rapidly growing BHs inject mechanical power with $\sim 0.1-1\%$ of the radiative luminosity into their host galaxy scales, which is used for cosmological simulations.

We investigate the properties of accretion flows onto a black hole (BH) with a mass of M BH embedded in an initially uniform gas cloud with a density of n ∞ in order to study rapid growth of BHs in the early Universe. In previous work, the conditions required 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 singlepower-law spectrum ν −α at hν ≥ 13.6 eV (α ∼ 1.5). However, radiation spectra surely depends on the BH mass and accretion rate, and determine the efficiency of radiative feedback. 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 critical density of gas surrounding the BH, above which a transitions to super-Eddington accretion occurs, is alleviated for a wide range of masses of seed BHs (10 M BH /M 10 6 ) because photoionization for accretion disk spectra are less efficient than those for single-power-law spectra with 1 α 3. 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 BH /10 5 M )(n ∞ /10 4 cm −3 ) 2.4 ( /100 eV) −5/9 , where is the mean energy of ionizing radiation from the central BH.