Early growth of typical high redshift black holes seeded by direct
  collapse
  Understanding the growth of high redshift massive black holes (MBHs) is a
problem of great astrophysical interest. The most luminous quasars at $z>6$ are
frequently observed but they represent only the tip of the iceberg as the
majority of the low luminosity AGN population remains undetected. In the
present study, we perform a radiation hydrodynamics cosmological simulation to
study the growth of "normal" black holes in the high redshift universe. In our
simulation we model the formation of Pop III and Pop II stars along with their
chemical, mechanical and radiative feedback. We consider both UV and X-ray
emission from an accreting BH to simulate its radiative feedback. The selected
halo has a mass of $\rm 3 \times 10^{10}~M_{\odot}$ at $z=7.5$ and we turn on
radiative feedback from a MBH seed of $\rm 10^5~M_{\odot}$ along with in-situ
star formation at $z=12$ when the halo mass reaches well above the atomic
cooling limit. We find that the MBH accretes only about 2200 $\rm M_{\odot}$
during 320 Myr and the average mass accretion onto the MBH is a few times $\rm
10^{-6}~M_{\odot}/yr$. Our results suggest that the stunted growth of MBH is a
consequence of supernovae in tandem with MBH feedback which drive large
outflows and evacuate the gas from MBH vicinity. This may explain why a
population of low luminosity AGN has not been detected so-far at $z>6$; the
large contrast between the star formation rate and the MBH accretion rate may
make then hard to detect even in upcoming deep surveys.
