Evolution of Quiescent and Star-Forming Galaxies Since z~1.5 as a
  Function of Their Velocity Dispersions
  We measure stellar masses and structural parameters for 5,500 quiescent and
20,000 star-forming galaxies at 0.3<z\leq1.5 in the Newfirm Medium Band Survey
COSMOS and UKIDSS UDS fields. We combine these measurements to infer velocity
dispersions and determine how the number density of galaxies at fixed inferred
dispersion, or the Velocity Dispersion Function (VDF), evolves with time for
each population. We show that the number of galaxies with high velocity
dispersions appears to be surprisingly stable with time, regardless of their
star formation history. Furthermore, the overall VDF for star-forming galaxies
is constant with redshift, extending down to the lowest velocity dispersions
probed by this study. The only galaxy population showing strong evolution are
quiescent galaxies with low inferred dispersions, whose number density
increases by a factor of ~4 since z=1.5. This build-up leads to an evolution in
the quiescent fraction of galaxies such that the threshold dispersion above
which quiescent galaxies dominate the counts moves to lower velocity dispersion
with time. We show that our results are qualitatively consistent with a simple
model in which star-forming galaxies quench and are added to the quiescent
population. In order to compensate for the migration into the quiescent
population, the velocity dispersions of star-forming galaxies must increase,
with a rate that increases with dispersion.
