Super-Eddington accretion of dusty gas onto seed black holes: metallicity-dependent efficiency of mass growth

The super-Eddington accretion onto intermediate seed BHs is a potential formation mode of supermassive black holes exceeding $10^9~M_\odot$ in the early universe. We here investigate how such rapid accretion may occur with finite amounts of heavy elements contained in the gas and dust. In our 1D radiation-hydrodynamics simulations, the radiative transfer is solved for both the direct UV lights emitted by an accretion disk and the diffuse IR lights thermally emitted by dust grains. Our results show that the radiative force by the IR lights causes a strong feedback to regulate the mass accretion. The resulting mean accretion rate is lower with the higher metallicity, and there is the critical metallicity $Z \sim 10^{-2}~Z_\odot$, above which the super-Eddington accretion is prevented by the radiation pressure of the IR lights. With this taken into account, we examine if the dusty super-Eddington accretion occurs in young galaxies using a simple model. We show that a sufficient number of galaxies at $z \gtrsim 10$ can be such potential sites if BHs accrete the cold dense gas with $T \sim 10^2$ K, approximately the thermal equilibrium value at $Z = 10^{-2}~Z_\odot$. We argue that the efficiency of the BH growth via the rapid accretion depends on the metallicity, and that the metallicity slightly lower than $10^{-2}~Z_\odot$ provides a chance for the most efficient growth.
Comment: 15 pages, 9 figures. Accepted for publication in MNRAS. Eq. (14) and (21) were corrected