A Simple Method for Computing the Nonlinear Mass Correlation Function with Implications for Stable Clustering

We propose a simple and accurate method for computing analytically the masscorrelation function for cold dark matter and scale-free models that fitsN-body simulations over a range that extends from the linear to the stronglynon-linear regime. The method, based on the dynamical evolution of the pairconservation equation, relies on a universal relation between the pair-wisevelocity and the smoothed correlation function valid for high and low densitymodels, as derived empirically from N-body simulations. An intriguingalternative relation, based on the stable-clustering hypothesis, predicts apower-law behavior of the mass correlation function that disagrees with N-bodysimulations but conforms well to the observed galaxy correlation function ifnegligible bias is assumed. The method is a useful tool for rapidly exploring awide span of models and, at the same time, raises new questions about largescale structure formation.Comment: 10 pages, 3 figure