The observed $M - \sigma$ relations imply that SMBHs grow by cold
  chaotic accretion
  We argue that current observations of $M - \sigma$ relations for galaxies can
be used to constrain theories of super-massive black holes (SMBH) feeding. In
particular, assuming that SMBH mass is limited only by the feedback on the gas
that feeds it, we show that SMBHs fed via a planar galaxy scale gas flow, such
as a disc or a bar, should be much more massive than their counterparts fed by
quasi-spherical inflows. This follows from the relative inefficiency of AGN
feedback on a flattened inflow. We find that even under the most optimistic
conditions for SMBH feedback on flattened inflows, the mass at which the SMBH
expels the gas disc and terminates its own growth is a factor of several higher
than the one established for quasi-spherical inflows. Any beaming of feedback
away from the disc and any disc self-shadowing strengthens this result further.
Contrary to this theoretical expectation, recent observations have shown that
SMBH in pseudobulge galaxies (which are associated with barred galaxies) are
typically under- rather than over-massive when compared with their classical
bulge counterparts at a fixed value of $\sigma$. We conclude from this that
SMBHs are not fed by large (100 pc to many kpc) scale gas discs or bars, most
likely because such planar flows are turned into stars too efficiently to allow
any SMBH growth. Based on this and other related observational evidence, we
argue that most SMBHs grow by chaotic accretion of gas clouds with a small and
nearly randomly distributed direction of angular momentum.
