Slowing down of cosmic growth of supermassive black holes: Theoretical
  prediction of the Eddington ratio distribution
  We show the Eddington ratio distributions of supermassive black holes at a
wide redshift range (0 < z < 8) obtained with a semi-analytic model of galaxy
formation. The distribution is broadly consistent with observational estimates
at low redshift. We find that the growth rate of black holes at higher redshift
is more likely to exceed the Eddington limit because the typical gas fraction
of the host galaxies is higher at higher redshift. We also find that the super-
Eddington growth is more common for less massive supermassive black holes,
supporting an idea that supermassive black holes have been formed via
super-Eddington accretion. These results indicate the "slowing down" of cosmic
growth of supermassive black holes: the growth of supermassive black holes with
a higher Eddington ratio peaks at higher redshift. We also show the effect of
the sample selection on the shape of the Eddington ratio distribution functions
and find that shallower observations will miss active galactic nuclei with not
only the smaller but also higher Eddington ratios.
