Rapid growth of black holes accompanied with hot or warm outflows exposed to anisotropic super-Eddington radiation

We perform two-dimensional radiation hydrodynamical simulations of accretion flows onto a black hole (BH) with a mass of $10^3\leq M_{\rm BH}/M_{\odot} \lesssim 10^6$ 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 $\simeq 10^4~M_{\odot}(n_\infty/10^5~{\rm cm}^{-3})^{-1}(T_\infty/10^4~{\rm K})^{3/2}$, where $n_\infty$ and $T_\infty$ 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 ($L_{\rm Edd}$) due to collimation toward the bipolar directions. We find that, unlike the spherically symmetric case, even less massive BHs with $M_{\rm BH} < 10^4~M_{\odot}$ can be fed by surrounding gas at high accretion rates of $\gtrsim L_{\rm Edd}/c^2$ through the equatorial plane, while ionized regions expand to the polar directions producing hot outflows with $T\sim 10^5$K. For more massive BHs with $M_{\rm BH}\gtrsim 5\times 10^5~M_{\odot}$, 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 $T \simeq 8000~{\rm K}$ . The central BH is fed through the equator at the averaged rate of $\sim 5\times 10^4~L_{\rm Edd}/c^2$, which corresponds to $\sim 50~\%$ of the inflow rate from the Bondi radius. Moreover, radiation momentum absorbed by neutral hydrogen produces warm outflows toward the bipolar directions at $\sim 30~\%$ of the BH feeding rate and with a typical velocity of $\simeq 50~{\rm km~s}^{-1}$.