Gravitational binding, virialization, and the peculiar velocity distribution of the galaxies

We examine the peculiar velocity distribution function of galaxies in cosmological many-body gravitational clustering. Our statistical mechanical approach derives a previous basic assumption and generalizes earlier results to galaxies with halos. Comparison with the observed peculiar velocity distributions indicates that individual massive galaxies are usually surrounded by their own halos, rather than being embedded in common halos. We then derive the density of energy states, giving the probability that a randomly chosen configuration of N galaxies in space is bound and virialized. Gravitational clustering is very efficient. The results agree well with the observed probabilities for finding nearby groups containing N galaxies. A consequence is that our local relatively low-mass group is quite typical, and the observed small departures from the local Hubble flow beyond our group are highly probable.