  We explore the dependence of the ratio of a galaxy's circular velocity,
Vcirc, to its central velocity dispersion, sigma_0, on morphology, or
equivalently total light concentration. Such a dependence is expected if light
traces the mass. Over the full range of galaxy types, masses and brightnesses,
and assuming that the gas velocity traces the circular velocity, we find that
galaxies obey the relation log(Vcirc/sigma_0)= 0.63-0.11*C28 where
C28=5log(r80/r20) and the radii are measured at 80 percent and 20 percent of
the total light. Massive galaxies scatter about the Vcirc = sqrt(2)*sigma_0
line for isothermal stellar systems. Disk galaxies follow the simple relation
Vcirc/sigma_0=2(1-B/T), where B/T is the bulge-to-total light ratio. For pure
disks, C28~2.8, B/T -> 0, and Vcirc~=2*sigma_0. Self-consistent equilibrium
galaxy models from Widrow & Dubinski (2005) constrained to match the
size-luminosity and velocity-luminosity relations of disk galaxies fail to
match the observed Vcirc/sigma_0 distribution. Furthermore, the matching of
dynamical models for Vcirc(r)/sigma(r) with observations of dwarf and
elliptical galaxies suffers from limited radial coverage and relatively large
error bars; for dwarf systems, however, kinematical measurements at the galaxy
center and optical edge suggest Vcirc(Rmax) > 2*sigma_0 (in contrast with past
assumptions that Vcirc = sqrt(2)*sigma_0 for dwarfs.) The Vcirc-sigma_0-C28
relation has direct implications for galaxy formation and dynamical models,
galaxy scaling relations, the mass function of galaxies, and the links between
respective formation and evolution processes for a galaxy's central massive
object, bulge, and dark matter halo.
