Study of the Universe populated by Clusters of Galaxies with halo using Newtonian Gravity modified by Tohline.

Abstract

We consider a model for galaxies with halo advanced by Tohline. With it we discuss galaxy clusters within the strictures of Gibbs' ensembles in statistical mechanics. We consider (1) the case in which the Universe is finite and also (2) the one for which is infinite. In case (1) we find that the system is self-gravitating, while in (2) it is not. We have found that in both cases the distribution function is the same and it is uniform. Since the integrals that define the partition function diverge in both cases, we have appealed to overcome this problem to the generalization of the dimensional regularization of Bollini and Giambiagi and also to the regularization of integrals proposed by Guelfand.