Nonlinear properties and time evolution of gravitational galaxy clustering

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Galactic Clusters, Galactic Evolution, Gravitation, Universe, Correlation, Distribution Functions, Nonlinearity

Scientific paper

Methods for comparing the quasi-equilibrium theory of gravitational galaxy clustering with other theories in the nonlinear regime are developed. The volume integrals of the gravitational N-point correlation functions are expressed as functions of the quasi-equilibrium parameter b in a closed form which is exact to all orders of b. A simple proof showing that all the volume integrals are invariant to random binomial selection of subsamples is provided. Properties of the skewness and kurtosis of the quasi-equilibrium distribution are also clarified. In addition, the nonlinear evolution of the volume integrals as the universe expands is derived. A physical measure of the transition from the linear to the nonlinear regime is provided by a new criterion, based on the maximum of the specific heat. These results are used to determine the nonlinear evolution of the galaxy velocity dispersions, the internal energy, and the entropy. As the universe expands, the average gravitational entropy is shown to always increase.

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