The Velocity Dispersion Function for Quiescent Galaxies in the Local
  Universe
  We investigate the distribution of central velocity dispersions for quiescent
galaxies in the SDSS at $0.03 \leq z \leq 0.10$. To construct the field
velocity dispersion function (VDF), we construct a velocity dispersion complete
sample of quiescent galaxies with Dn4000$ > 1.5$. The sample consists of
galaxies with central velocity dispersion larger than the velocity dispersion
completeness limit of the SDSS survey. Our VDF measurement is consistent with
previous field VDFs for $\sigma > 200$ km s$^{-1}$. In contrast with previous
results, the VDF does not decline significantly for $\sigma < 200$ km s$^{-1}$.
The field and the similarly constructed cluster VDFs are remarkably flat at low
velocity dispersion ($\sigma < 250$ km s$^{-1}$). The cluster VDF exceeds the
field for $\sigma > 250$ km s$^{-1}$ providing a measure of the relatively
larger number of massive subhalos in clusters. The VDF is a probe of the dark
matter halo distribution because the measured central velocity dispersion may
be directly proportional to the dark matter velocity dispersion. Thus the VDF
provides a potentially powerful test of simulations for models of structure
formation.
