Nonlinear theory of the two-point correlation function

Abstract

We consider the influence of the nonlinear stage of gravitational instability on the two-point correlation functions of gravitationally bound objects. Based on the theory of nonlinear gravitational contraction of a single density peak of dissipationless matter (Gurevich and Zybin, 1988a,b; 1990) we develop a method for calculating the two-point correlation functions of different objects of any mass. The method works good in the region of strong correlations and can be easily extended to calculate higher correlation functions. We show that the main contribution to the correlation function ξi in the region of strong correlations ξi ≫ 1 is made by pair systems located outside large clusters of objects. In this region the shape of ξi is determined only by the nonlinear dynamics of gravitational contraction of dissipationless matter and has the form ξi ≈Cτ−α, where α≈1.8 is a universal parameter.