Limits on the growth rate of supermassive black holes at early cosmic
  epochs
  The effect of AGN wind feedback on the accretion rate and mass evolution of
supermassive black holes (SMBH) is considered. It is shown, under reasonable
assumptions, that the rate at which gas can be supplied to a SMBH at the center
of a young galaxy, is limited to $\sim 20 (\sigma/350~ {\rm km
~s^{-1}})^4~M_\odot/yr$ (where $\sigma$ is the velocity dispersion of the host
bulge) by interaction of winds expelled from the innermost regions of the
accretion flow with the gas in the bulge. This rate is independent of the black
hole mass but is sensitive to the properties of the host bulge. It is further
argued that the interaction of the wind and the inflowing gas in the bulge can
strongly affect the structure of the accretion flow in the super-Eddington
regime, potentially leading to highly super-Eddington accretion into the SMBH.
About 300 Myr after the onset of the accretion phase, the AGN wind expels all
the gas from the bulge and the accretion rate is strongly suppressed. This
scenario is in remarkable agreement with recent observations, as it (i) reveals
the origin of the maximal observed accretion rates, (ii) accounts for the
inferred growth rate of SMBHs at high redshift (independent of their initial
seeds masses), (iii) elucidates the decline in the accretion rate at lower
redshifts, and (iv) explains the relation between $\sigma$ and the mass
$M_{BH}$ of the central SMBH, measured in the local Universe.
