A Simple Condition for Sustained Super-Eddington Black Hole Growth
  One of the most pressing questions in cosmology is how the black holes (BHs)
inferred to power quasars at high redshift are able to grow to supermassive
scales well 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, carrying it into the BH. The BH growth then proceeds
unimpeded until the gas supply in its vicinity 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 be 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 radiation generated in the process escaping to ionize the
intergalactic medium. It also 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 how often and in which
environments it occurs.
