A Simple Condition for Sustained Super-Eddington Black Hole Growth

One of the most pressing questions in cosmology is how the black holes (BHs) powering quasars at high redshift grow to supermassive scales within a billion years of the Big Bang. Here we show that sustained super-Eddington accretion can be achieved for BHs with Eddington fractions $f_{\rm Edd}$ > 2/$ε$, where $ε$ is the efficiency with which radiation is generated in the accretion process. In this regime, the radiation carries too little momentum to halt the accretion flow and the infalling gas traps the radiation. The BH growth then proceeds unimpeded until the gas supply is exhausted, in contrast to accretion at lower rates which is limited by the radiation generated in the accretion process. The large gas supply available in massive high-redshift quasar host galaxies may be readily accreted onto seed BHs via this supply-limited mode of accretion, providing an explanation for how such supermassive BHs are assembled in the early universe. This sustained super-Eddington growth may also explain the short lifetimes inferred for the H II regions surrounding high-redshift quasars, if the bulk of the BH growth occurs without the associated radiation escaping to ionize the intergalactic medium. It furthermore implies that a population of obscured rapidly growing BHs may be difficult to detect, perhaps explaining why so few quasars with Eddington fractions higher than a few have been observed. Finally, this simple condition for sustained super-Eddington growth can easily be implemented in cosmological simulations which can be used to assess in which environments it occurs.