Galaxies' clustering generalized theory

Abstract

In the present work we present, for the first time ever, the exact configuration integral entering the partition function Z that allows for a statistical mechanics treatment of galactic clustering. Thus, the general distribution function and the general clustering parameter for point mass systems is obtained from a grand canonical ensemble discussion. Such distribution is also approximated starting from the general Poisson distribution. The two ensuing distributions are similar. The advantage of the Poissonian distribution (PD) is that it facilitates finding a suitable probability factor f to introduce within it without going into the deep mathematical intricacies involved in dealing with Z. The specific heat is paid special attention.