The Ω dependence of the velocity divergence distribution

Analytical studies based on perturbative theory have shown that the moments of the probability distribution function (PDF) of the local smoothed velocity divergence are expected to have a very specific dependence on the density parameter Ω in the quasi-linear regime. This dependence is particularly interesting as it does not involve the possible bias between the galaxy spatial distribution and the underlying mass distribution. This implies a new and promising method for determining a bias-independent value of Ω based on a reliable determination of the velocity divergence PDF. In this paper we study the Ω dependence of the velocity divergence PDF and its first moments in a set of N-body simulations, using the so-called Voronoi and Delaunay methods. We show that this dependence is in agreement with the theoretical prediction, even while the number density of velocity field tracers has been diluted to a value comparable to that available in current galaxy catalogues. In addition, we demonstrate that a sufficiently reliable determination of these statistical quantities is also possible when the measurement of the galaxy peculiar velocities is restricted to the one component along the line of sight. Under ideal, noise-free circumstances we can successfully discriminate between low and high Ω.