Galaxies and Supermassive Black Holes at z <= 0.1: The Velocity Dispersion Function

Abstract

We study the distribution of central velocity dispersion, sigma, for >100000 galaxies in the SDSS at 0.01 <= z <= 0.1. We construct the velocity dispersion function (VDF) from samples complete for all sigma, where galaxies with sigma greater than the sigma-completeness limit of the SDSS spectroscopic survey are included. We compare two different sigma estimates; one based on SDSS spectroscopy (sigma_spec) and another on photometric estimates (sigma_mod). The sigma_spec for our sample is systematically higher than sigma_mod for all ranges of sigma, implying that rotational velocity may affect sigma_spec measurements. The VDFs measured from these quantities are remarkably similar for lower sigma values, but the sigma_mod VDF falls faster than the sigma_spec VDF at log sigma > 2.35. Very few galaxies are observed to have sigma > 350 km/s. Despite differences in sample selection and methods, our VDFs are in close agreement with previous determinations for the local universe, and our results confirm that complete sampling is necessary to accurately discern the shape of the VDF at all ranges. We also find that both late and early type galaxies have sigma_spec > sigma_mod, suggesting that the rotation component of most galaxies figure significantly into sigma_spec measurements. Early-type galaxies dominate the population of high sigma galaxies, while late-type galaxies dominate the low sigma statistic. Our results warrant a more thorough and cautious approach in using long-slit spectroscopy to derive the statistics of local galaxies. Higher quality photometric measurements will enable more accurate and less uncertain measurements of the sigma_mod VDF, as described here. A follow-up paper uses the final samples from this work in conjunction with the MBH-sigma relation to derive the z<=0.1 black hole mass function (BHMF).