The Velocity Dispersion Function for Quiescent Galaxies in the Local Universe

Abstract

We investigate the distribution of central velocity dispersions for quiescent galaxies in the SDSS at $0.03\le z\le 0.10$. 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.

Accepted for publication in ApJ. 10 pages, 8 figures. Comments welcome

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