The case for super-critical accretion onto massive black holes at high redshift

Short-lived intermittent phases of super-critical (super-Eddington) growth, coupled with star formation via positive feedback, may account for early growth of massive black holes (MBH) and coevolution with their host spheroids. We estimate the possible growth rates and duty cycles of these episodes, both assuming slim accretion disk solutions, and adopting the results of recent numerical simulations. The angular momentum of gas joining the accretion disk determines the length of the accretion episodes, and the final mass a MBH can reach. The latter can be related to the gas velocity dispersion, and in galaxies with low-angular momentum gas the MBH can get to a higher mass. When the host galaxy is able to sustain inflow rates at 1-100 msunyr, replenishing and circulation lead to a sequence of short (~1e4-1e7 years), heavily obscured accretion episodes that increase the growth rates, with respect to an Eddington-limited case, by several orders of magnitude. Our model predicts that the ratio of MBH accretion rate to star formation rate is 1e2 or higher, leading, at early epochs, to a ratio of MBH to stellar mass higher than the "canonical" value of ~1e-3, in agreement with current observations. Our model makes specific predictions that long-lived super-critical accretion occurs only in galaxies with copious low-angular momentum gas, and in this case the MBH is more massive at fixed velocity dispersion.