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The super-Eddington accretion onto intermediate seed BHs is a potentialformation mode of supermassive black holes exceeding $10^9~M_\odot$ in theearly universe. We here investigate how such rapid accretion may occur withfinite amounts of heavy elements contained in the gas and dust. In our 1Dradiation-hydrodynamics simulations, the radiative transfer is solved for boththe direct UV lights emitted by an accretion disk and the diffuse IR lightsthermally emitted by dust grains. Our results show that the radiative force bythe IR lights causes a strong feedback to regulate the mass accretion. Theresulting mean accretion rate is lower with the higher metallicity, and thereis the critical metallicity $Z \sim 10^{-2}~Z_\odot$, above which thesuper-Eddington accretion is prevented by the radiation pressure of the IRlights. With this taken into account, we examine if the dusty super-Eddingtonaccretion occurs in young galaxies using a simple model. We show that asufficient number of galaxies at $z \gtrsim 10$ can be such potential sites ifBHs accrete the cold dense gas with $T \sim 10^2$ K, approximately the thermalequilibrium value at $Z = 10^{-2}~Z_\odot$. We argue that the efficiency of theBH growth via the rapid accretion depends on the metallicity, and that themetallicity slightly lower than $10^{-2}~Z_\odot$ provides a chance for themost efficient growth.

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