A cosmic virial theorem

Abstract

A new type of cosmic virial theorem is derived, representing a relation among the two-point and three-point galaxy correlation functions and the mean square relative peculiar velocity 〈v 2(r)〉 averaged over pairs of galaxies separated by distancer. The two correlation functions seem to be fairly well known, but 〈v 2(r)〉 at best is only very roughly estimated from available data. It might be possible to improve the estimate through a systematic program of redshift measurements in sample areas. If so, the cosmic virial theorem might yield an interesting measure of the mean mass density due to galaxies.