Study of gravitational clustering of non-point mass system of galaxies

Abstract

Cosmic energy equation is actually the representation of law of conservation of energy in the region expanding with time as Universe expands. It gives the evolution of kinetic and gravitational correlation potential energies with time in a cluster expanding as Universe expands. In order to understand the gravitational galaxy clustering in the expanding Universe, cosmic energy equation is very important tool. We use Cosmic energy equation for extended structures (galaxies with halos) to obtain an expression for correlation parameter $b_{V}$ . Correlation parameter $b_{V}$ is an essential parameter as it provides an information regarding the extent up to which galaxies are clustered under the influence of gravitational force. The expression obtained for correlation parameter $b_{V}$ may help us to understand the different states of clustering because it depends on evolution time for a cluster. Further, Cosmic energy equation for extended structures is used to derive an expression for the asymptotic behavior of correlation parameter. A condition for virialization of a cluster of galaxies is also obtained from the same Cosmic energy equation.