We investigate the distribution of central velocity dispersions for quiescent galaxies in the SDSS at 0.03 ≤ z ≤ 0.10. To construct the field velocity dispersion function (VDF), we construct a velocity dispersion complete sample of quiescent galaxies with D n 4000 > 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 σ > 200 km s-1. In contrast with previous results, the VDF does not decline significantly for σ . In contrast with previous results, the VDF does not decline significantly for σ -1. The field and the similarly constructed cluster VDFs are remarkably flat at low velocity dispersion (σ . The field and the similarly constructed cluster VDFs are remarkably flat at low velocity dispersion (σ -1). The cluster VDF exceeds the field for σ > 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.
