Evolution of the two-point correlation function in the Zel’dovich approximation

We study the evolution of the mass autocorrelation function by describing the growth of density fluctuations through the Zel’dovich approximation. The results are directly compared with the predictions of the scaling hypothesis for clustering evolution extracted from numerical simulations (Hamilton et al. 1991), as implemented by Jain, Mo & White (1995). We find very good agreement between the correlations on mildly non–linear scales and on completely linear scales. In between these regimes, we note that the density fields evolved through the Zel’dovich approximation show more non–linear features than predicted by the scaling ansatz which is, however, forced to match the linear evolution on scales larger than the simulation box. In any case, the scaling ansatz by Baugh & Gaztañaga (1996), calibrated against large box simulations agrees better with ZA predictions on large scales, keeping good accuracy also on intermediate scales. We show that mode–coupling is able to move the first zero crossing of ξ(r) as time goes on. A detailed fit of the time dependence of this shifting is given for a CDM model. The evolution of the cross correlation of the density fluctuation field evaluated at two different times is also studied. The possible implications of the results for the analysis of the observed correlation function of high redshift galaxies are discussed.