Gravitational clustering of galaxies in an expanding universe

Abstract

We inquire the phenomena of clustering of galaxies in an expanding universe from a theoretical point of view on the basis of ther- modynamics and correlation functions. The partial differential equation is developed both for the point mass and extended mass structures of a two-point correlation function by using thermodynamic equations in com- bination with the equation of state taking gravitational interaction between particles into consideration. The unique solution physically satisfies a set of boundary conditions for correlated systems and provides a new insight into the gravitational clustering problem. Galaxies interact gravitationally and the characterization of this clustering is a problem of current interest. The gravitational interaction between galaxies and galaxy clusters have played an important role in the evolution of the observed universe. Various the- ories of the cosmological many body problem have been developed mainly from a thermodynamic point of view. We have made use of the equations of state along with the correlation functions for the development of a theoretical model. This can be done by solving a system of Liouville's equation or BBGKY-hierarchy equations and have been discussed by workers like Saslaw (1972) and Peebles (1980). But BBGKY hier- archy equations are too complicated to handle for higher order correlation functions. However, the lowest order two-point correlation function is useful for discussing the phenomenon of gravitational clustering of galaxy clusters which contain information on all the higher n-particle correlations in the full BBGKY-hierarchy (Peebles 1980; Zhan & Dyer 1989; Hamilton 1993). The physical validity of the application of ther- modynamics in the clustering of galaxies and galaxy clusters has been discussed on the basis of N-body computer simulation results (Itohetal. 1993). In gravitational thermo- dynamics the value of b which is the ratio of gravitational correlation energy to twice kinetic energy measures two-point correlation function ξ2 and depends on the average number density ¯ n, temperature T and the interparticle distance r. Thus it is valuable to understand the functional form of ξ2 which depends upon the value of b(n, T ). The