Galaxy Pairwise Velocity Distributions on Non-linear Scales

The redshift-space correlation function ξs for projected galaxy separations <∼ 1h 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 ξs 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(σ) of systems with velocity dispersion σ; (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 examine a third issue: the transfer of orbital kinetic energy to galaxy internal degrees of freedom. Although this effect is of secondary importance for the PVDF exponential shape, it is detectable in galaxy groups, indicating that galaxy merging is an ongoing process in the present Universe. We compare the ξs measured on non-linear scales from galaxy samples of the Center for Astrophysics 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. We expect that ξs will pose further constraints on the model of the Universe and will improve the knowledge of the dynamics of galaxy systems on very small scales if we improve (i) the galaxy coordinate determination and (ii) the measurement of relative velocities of galaxies with small projected separation. In fact, the redshift-space correlation function ξs depends sensitively on the internal pairwise velocity distribution of individual galaxy systems for projected pair separations <∼ 0.5h Mpc and relative velocities π <∼ 300 km s. Subject Headings: Cosmology: Dark Matter – Cosmology: Theory – Galaxies: Clustering – Galaxies: Interaction – Gravitation