Photon Trapping Enables Super-Eddington Growth of Black-Hole Seeds in
  Galaxies at High Redshift
  We identify a physical mechanism that would have resulted in rapid, obscured
growth of seed super-massive black-holes in galaxies at z>6. Specifically, we
find that the density at the centre of typical high redshift galaxies was at a
level where the Bondi accretion rate implies a diffusion speed of photons that
was slower than the gravitational infall velocity, resulting in photons being
trapped within the accretion flow and advected into the black-hole. We show
that there is a range of black-hole masses (M_bh ~ 10^3-10^5 solar masses)
where the accretion flow traps radiation, corresponding to black-holes that
were massive enough to generate a photon trapping accretion flow, but small
enough that their Bondi radii did not exceed the isothermal scale height of
self-gravitating gas. Under these conditions we find that the accretion reaches
levels far in excess of the Eddington rate. A prediction of this scenario is
that X-ray number counts of active galactic nuclei at z>6 would exhibit a
cutoff at the low luminosities corresponding to black-hole masses below ~10^5
solar masses. At low redshifts we find photon trapping to be unimportant
because it could only occur in rare low spin halos, and would require
black-hole masses in excess of expectations from the observed black-hole - halo
mass relation. The super-Eddington growth of ~10^5 solar mass seed black-holes
at high redshift may have provided a natural acceleration towards the growth of
super-massive black-holes at z~6-7, less than a billion years after the Big
Bang.
