  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/$\epsilon$,
where $\epsilon$ 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.
