Correlations Between Supermassive Black Holes, Velocity Dispersions, and
  Mass Deficits in Elliptical Galaxies with Cores
  High-dynamic-range surface photometry in a companion paper makes possible
accurate measurement of the stellar light deficits L_def and mass deficits
M_def associated with the cores of elliptical galaxies. We show that L_def
correlates with the velocity dispersion sigma of the host galaxy bulge averaged
outside the central region that may be affected by a supermassive black hole
(BH). We confirm that L_def correlates with BH mass MBH. Also, the fractional
light deficit L_def/L correlates with MBH/M, the ratio of BH mass to the galaxy
stellar mass. All three correlations have scatter similar to or smaller than
the scatter in the well known correlation between MBH and sigma. The new
correlations are remarkable in view of the dichotomy between ellipticals with
cores and those with central extra light. Core light deficit correlates closely
with MBH and sigma, but extra light does not. This supports the suggestion that
extra light Es are made in wet mergers with starbursts whereas core Es are made
in dry mergers. After dry mergers, cores are believed to be scoured by BH
binaries that fling stars away as their orbits decay or by BHs that sink back
to the center after recoiling from anisotropic gravitational radiation emitted
when they merge. Direct evidence has been elusive. We interpret the new
correlations as the "smoking gun" that connects cores with BHs. Together, the
MBH - sigma and MBH - L_def correlations give us two independent ways to
estimate BH masses in core ellipticals.
