Publication : t96/080

Abstract:
We present a series of results investigating the $\Omega$ dependence of the distribution function of the large scale local cosmic velocity divergence, $\nabla \cdot {\bf v}$. Analytical studies using perturbation theory techniques indicate that the shape of this distribution should be strongly dependent on $\Omega$. This dependence is all the more interesting as it does not involve biases of the galaxy distribution with respect to the underlying density distribution, making it a potentially promising and useful basis for new and alternative methods to obtain bias-independent estimates of $\Omega$. In addition, such methods would provide a promising test for gravitational instability scenarios with Gaussian initial conditions, by comparing the results for observational catalogues with the analytical predictions for such scenarios. After a description of the various statistical characteristics in which the $\Omega$ dependence of the velocity divergence PDF reveals itself, we study the properties of the distribution on the basis of a set of $N$-body simulations. To analyze the discretely sampled velocity field yielded by the latter, we apply a set of recently developed numerical tools, the ``Voronoi'' and ``Delaunay'' methods. These two methods were devised specifically for the purpose of investigating statistical properties of a velocity field in the case it has been sampled at a limited number of discrete locations. Through the resulting study we have been able to verify that the $\Omega$ dependence of the distribution function of the smoothed local velocity divergence, and related properties like its moments and shape, is indeed in perfect agreement with the predictions of perturbation theory. Given the good agreement between the analytical predictions and the outcome of $N$-body simulations, we subsequently analyse the situation in which the sample of velocity field tracers is diluted to number densities comparable to those available in galaxy catalogues. We find that the $\Omega$ dependent features remain intact. This provides further confidence in the use of the velocity divergence probability distribution function as a promising instrument for obtaining reliable bias-independent estimates of the value of $\Omega$ in practical circumstances.

publi.pdf