Conditions for Super-Eddington Accretion onto the First Black Holes

Observations of supermassive black holes at high redshift challenge our understanding of the evolution of the first generation of black holes (BHs) in proto-galactic environments. One possibility is that they grow much more rapidly than current estimates of feedback and accretion efficiency permit. Following our previous analysis of super-Eddington accretion onto stellar-mass black holes in mini-haloes under no-feedback conditions, we now investigate whether this can be sustained when thermal feedback is included. We use four sets of cosmological simulations at sub-pc resolution with initial black hole masses varying from $1 \times 10^3 - 6 \times 10^4 M_\odot$, exploring a range of feedback efficiencies. We also vary the feedback injection radius to probe the threshold of numerical overcooling. We find that super-Eddington growth sustained on the order of $\sim$$100 \, \rm kyr$ is possible with very weak thermal feedback efficiency in all environments and moderate efficiency for two of the BHs. Trans-Eddington growth is possible for a $3 \times 10^3 - 6 \times 10^3 M_\odot$ BH at moderate feedback efficiencies. We discuss the effectiveness of thermal feedback in heating the gas, suppressing accretion, and driving outflows at these parameter configurations. Our results suggest that super-Eddington growth may be possible in the presence of thermal feedback for black holes formed from the first stars.