Distribution function for the system of galaxies for any ratio of gravitational potential to kinetic energies

Abstract

We evaluate a distribution function for the system of galaxies clustering gravitationally in an expanding universe on the basis of statistical mechanics. We extend our previous work to incorporate the effect of any ratio of gravitational potential to kinetic energies. We determine the cosmological many-body partition function inclusive of higher order terms and calculate all thermodynamic quantities and the distribution function from it. We find that our new results are consistent with the previous ones, particularly in the large N (average number of galaxies) limit. We also investigate the effect on clustering parameter b and find our new results in very good agreement with the previous ones in the small b limit. We find that for large b, the departure from the original distribution function is greater. We also observe that the effect of softening on the distribution function is consistent with our previous work.