# The Velocity Dispersion Function for Quiescent Galaxies in the Local Universe

## TL;DR

This study measures the distribution of central velocity dispersions in quiescent galaxies within the local universe, revealing a flat low-dispersion tail and differences between field and cluster environments, offering insights into dark matter halo distributions.

## Contribution

It presents the first velocity dispersion function for quiescent galaxies in the local universe, highlighting a flat low-dispersion tail and environmental differences, challenging previous assumptions.

## Key findings

- VDF is flat below 200 km/s, contrary to previous decline.
- Cluster VDF exceeds field VDF above 250 km/s.
- VDF can serve as a test for dark matter halo models.

## Abstract

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.