Modelling the evolution of correlation functions in gravitational clustering

Abstract

Padmanabhan has suggested a model to relate the non-linear two-point correlation function to the linear two-point correlation function. In this paper, we extend this model in two directions: (1) by averaging over the initial Gaussian distribution of density contrasts, we estimate the spectral dependence of the scaling between non-linear and linear correlation functions; (2) by using a physically motivated Ansatz, we generalize the model to N-point correlation functions and relate the non-linear, volume averaged N-point correlation function ξ^__N(x, α) with the linearly extrapolated volume averaged two-point correlation function ξ^_₂(l, α) evaluated at a different scale. We compare the point of transition between the different regimes obtained from our model with that from numerical simulations, and show that the spectral dependence of the scaling relations seen in the simulations can be easily understood. A comparison of the calculated form of ξ^__N with the simulations shows reasonable agreement. We discuss several implications of the results.