A New Object-Weighted Measure of the Small-Scale Velocity Dispersion

We describe a new statistic for measuring the small-scale velocity dispersion of galaxies directly from redshift surveys. This statistic is based on the object-weighted statistic proposed by Davis, Miller, & White (1997). Compared with the traditional pair-weighted velocity dispersion, our statistic is less sensitive to the presence or absence of rare, rich clusters of galaxies. This measure of the thermal energy of the galaxy distribution is ideally suited for use with a filtered version of the cosmic energy equation. We discuss the application of the statistic to the Las Campanas Redshift Survey. The low observed dispersion strongly favors cosmological models with low matter density, Omega_m ~ 0.2.