THE FINITE-SIZE EFFECT OF GALAXIES ON THE COSMIC VIRIAL-THEOREM AND THE PAIRWISE PECULIAR VELOCITY DISPERSIONS

We discuss the effect of the finite size of galaxies on estimating sma ll-scale relative pairwise peculiar velocity dispersions from the cosm ic virial theorem (CVT). Specifically, we evaluate the effect by incor porating the finite core radius r(c) in the two-point correlation func tion of mass, i.e., xi(rho)(r) proportional to (r + r(c))-(gamma), and the effective gravitational force softening r(s) on small scales. We analytically obtain the lowest order correction term for gamma < 2, wh ich is in quantitative agreement with the full numerical evaluation. W ith a nonzero r(s) and/or r(c), the cosmic virial theorem is no longer limited to the case of gamma < 2. We present accurate fitting formula e for the CVT-predicted pairwise velocity dispersion for the case of g amma > 2. Compared with the idealistic point-mass approximation (r(s) = r(c) = 0), the finite-size effect can significantly reduce the small -scale velocity dispersions of galaxies at scales much larger than r, and r,. Even without considering the finite size of galaxies, nonzero values for r(c) are generally expected, for instance, for cold dark ma tter (CDM) models with a scale-invariant primordial spectrum. For thes e CDM models, a reasonable force softening r(s) less than or equal to 100 h(-1) kpc would have a rather tiny effect. We present the CVT pred ictions for the small-scale pairwise velocity dispersion in the CDM mo dels normalized by the COBE observations. The implications of our resu lts for confrontation of observations of galaxy pairwise velocity disp ersions and theoretical predictions of the CVT are also discussed.