THE OMEGA-DEPENDENCE OF THE VELOCITY DIVERGENCE DISTRIBUTION

Analytical studies based on perturbative theory have shown that the mo ments of the probability distribution function (PDF) of the local smoo thed velocity divergence are expected to have a very specific dependen ce on the density parameter D in the quasi-linear regime. This depende nce is particularly interesting as it does not involve the possible bi as between the galaxy spatial distribution and the underlying mass dis tribution. This implies a new and promising method for determining a b ias-independent value of Omega based on a reliable determination of th e velocity divergence PDF. In this paper we study the Omega dependence of the velocity divergence PDF and its first moments in a set of N-bo dy simulations, using the so-called Voronoi and Delaunay methods. We s how that this dependence is in agreement with the theoretical predicti on, even while the number density of velocity field tracers has been d iluted to a value comparable to that available in current galaxy catal ogues. In addition, we demonstrate that a sufficiently reliable determ ination of these statistical quantities is also possible when the meas urement of the galaxy peculiar velocities is restricted to the one com ponent along the line of sight. Under ideal, noise-free circumstances we can successfully discriminate between low and high Omega.