Galaxy Pairwise Velocity Distributions on Non-Linear Scales

The redshift-space correlation function $\xi_s$ for projected galaxy separations $\simless 1h^{-1}$ Mpc can be expressed as the convolution of the real-space correlation function with the galaxy pairwise velocity distribution function (PVDF). An exponential PVDF yields the best fit to the $\xi_s$ measured from galaxy samples of different redshift surveys. We show that this exponential PVDF is not merely a fitting function but arises from well defined gravitational processes. Two ingredients conspire to yield a PVDF with a nearly exponential shape: (i) the number density $n(\sigma)$ of systems with velocity dispersion $\sigma$; (ii) the unrelaxed dynamical state of most galaxy systems. The former ingredient determines the exponential tail and the latter the central peak of the PVDF. We compare the $\xi_s$ measured on non-linear scales from galaxy samples of the CfA redshift surveys with different models of the PVDF convolved with the measured real-space correlation function. This preliminary comparison indicates that the agreement between model and observations depends strongly on both the underlying cosmological model and the internal dynamics of galaxy systems. Neither parameter dominates. Moreover, the agreement depends sensitively on the accuracy of the galaxy position and velocity measurements.