Dwarf Galaxies and the Black-Hole Scaling Relations
  The sample of dwarf galaxies with measured central black hole masses $M$ and
velocity dispersions $\sigma$ has recently doubled, and gives a close fit to
the extrapolation of the $M \propto \sigma$ relation for more massive galaxies.
We argue that this is difficult to reconcile with suggestions that the scaling
relations between galaxies and their central black holes are simply a
statistical consequence of assembly through repeated mergers. This predicts
black hole masses significantly larger than those observed in dwarf galaxies
unless the initial distribution of uncorrelated seed black hole and stellar
masses is confined to much smaller masses than earlier assumed. It also
predicts a noticeable flattening of the $M \propto \sigma$ relation for dwarfs,
to $M \propto \sigma^2$ compared with the observed $M \propto \sigma^4$. In
contrast black hole feedback predicts that black hole masses tend towards a
universal $M \propto \sigma^4$ relation in all galaxies, and correctly gives
the properties of powerful outflows recently observed in dwarf galaxies. These
considerations emphasize once again that the fundamental physical black-hole --
galaxy scaling relation is between $M$ and $\sigma$. The relation of $M$ to the
bulge mass $M_b$ is acausal, and depends on the quite independent connection
between $M_b$ and $\sigma$ set by stellar feedback.
