Depleted Galaxy Cores and Dynamical Black Hole Masses
  Shallow cores in bright, massive galaxies are commonly thought to be the
result of scouring of stars by mergers of binary supermassive black holes. Past
investigations have suggested correlations between the central black hole mass
and the stellar light or mass deficit in the core, using proxy measurements of
$M_{\rm BH}$ or stellar mass-to-light ratios ($\Upsilon$). Drawing on a wealth
of dynamical models which provide both $M_{\rm BH}$ and $\Upsilon$, we identify
cores in 23 galaxies, of which 20 have direct, reliable measurements of $M_{\rm
BH}$ and dynamical stellar mass-to-light ratios ($\Upsilon_{\star,{\rm dyn}}$).
These cores are identified and measured using Core-S\'ersic model fits to
surface brightness profiles which extend out to large radii (typically more
than the effective radius of the galaxy); for approximately one fourth of the
galaxies, the best fit includes an outer (\sersic) envelope component. We find
that the core radius is most strongly correlated with the black hole mass and
that it correlates better with total galaxy luminosity than it does with
velocity dispersion. The strong core-size-- $M_{\rm BH}$ correlation enables
estimation of black hole masses (in core galaxies) with an accuracy comparable
to the $M_{\rm BH}$--$\sigma$ relation (rms scatter of 0.30 dex in $\log M_{\rm
BH}$), without the need for spectroscopy. The light and mass deficits correlate
more strongly with galaxy velocity dispersion than they do with black hole
mass. Stellar mass deficits span a range of 0.2--39 \mbh, with almost all (87%)
being $< 10 \, M_{\rm BH}$; the median value is 2.2 $M_{\rm BH}$.
