The Small Scatter in BH-Host Correlations & The Case for Self-Regulated
  BH Growth
  Supermassive black holes (BHs) obey tight scaling relations between their
mass and their host galaxy properties such as total stellar mass, velocity
dispersion, and potential well depth. This has led to the development of
self-regulated models for BH growth, in which feedback from the central BH
halts its own growth upon reaching a critical threshold. However, models have
also been proposed in which feedback plays no role: so long as a fixed fraction
of the host gas supply is accreted, relations like those observed can be
reproduced. Here, we argue that the scatter in the observed BH-host
correlations, and its run with scale, presents a demanding constraint on any
model for these correlations, and that it favors self-regulated models of BH
growth. We show that the scatter in the stellar mass fraction within a radius R
in observed ellipticals and spheroids increases strongly at small R. At fixed
total stellar mass (or host velocity dispersion), on very small scales near the
BH radius of influence, there is an order-of-magnitude scatter in the amount of
gas that must have entered and formed stars. In short, the BH appears to 'know
more' about the global host galaxy potential on large scales than the stars and
gas supply on small scales. This is predicted in self-regulated models;
however, models where there is no feedback would generically predict
order-of-magnitude scatter in the BH-host correlations. Likewise, models in
which the BH feedback in the 'bright' mode does not regulate the growth of the
BH itself, but sets the stellar mass of the galaxy by inducing star formation
or blowing out a mass in gas much larger than the galaxy stellar mass, are
difficult to reconcile with the scatter on small scales.
