The galaxy pairwise velocity dispersion as a function of local density

The standard method of measuring the galaxy pairwise velocity dispersion on small scales via the anisotropy in the two-point correlation function in redshift space suffers from the fact that it is a pair-weighted statistic, and thus is heavily weighted by the densest regions in a way that is difficult to calibrate. We propose a new statistic, the redshift difference of close projected pairs of galaxies as a function of local density, which is designed to measure the small-scale velocity dispersion as an explicit function of density. Computing this statistic for a volume-limited subsample of the Optical Redshift Survey, we find that the small-scale velocity dispersion rises from 220 km s^-1 in the lowest density bins to 760 km s^-1 at high density. We calculate this statistic for a series of mock catalogs drawn from a hydrodynamic simulation of an Ωh = 0.5 cold dark matter universe (standard CDM) and find that the observed velocity distribution lies ≳1 σ below the simulations in each of eight density bins; this measurement formally rules out this model at the 7.4 σ level and quantifies the well-known problem that this model produces too high a velocity dispersion. This comparison is insensitive to the normalization of the power spectrum, although it is quite sensitive to the density and velocity bias of galaxies relative to dark matter on small scales.