A new statistic for redshift surveys: The redshift dispersion of galaxies

We present a new statistic - the redshift dispersion - which may prove useful for comparing next generation redshift surveys (e.g., the Sloan Digital Sky Survey) and cosmological simulations. Our statistic is specifically designed for the projection of phase space which is directly measured by redshift surveys. We find that the redshift dispersion of galaxies as a function of the projected overdensity has a strong dependence on the cosmological density parameter Ω. The redshift dispersion statistic is easy to compute and can be motivated by applying the cosmic virial theorem (CVT) to subsets of galaxies with the same local density. We show that the velocity dispersion of particles in these subsets is proportional to the product of Ω and the local density. Low resolution N-body simulations of several cosmological models (open/closed CDM, CDM + Λ, HDM) indicate that the proportionality between velocity dispersion, local density and Ω holds over redshift scales in the range 50 km s^-1 to 500 km s^-1. The redshift dispersion may provide an interesting means for comparing volume-limited subsamples of the Sloan Digital Sky Survey to equivalent N-body/hydrodynamics simulations.