Evolution of peaks in weakly nonlinear density field and dark halo profiles

Using the two-point Edgeworth series up to second order we construct the weakly nonlinear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of the skewness parameter $S_{3}$. We test the dependence of the two-point skewness on distance from the peak for scale-free power spectra and Gaussian smoothing. The statistical features of such conditional distribution are given as the values obtained within linear theory corrected by the terms that arise due to weakly nonlinear evolution. The expected density around the peak is found to be always below the linear prediction while its rms fluctuation is always larger than in the linear case. We apply these results to the spherical model of collapse as developed by Hoffman & Shaham (1985) and find that in general the effect of weakly nonlinear interactions is to decrease the scale from which a peak gathers mass and therefore also the mass itself. In the case of open universe this results in steepening of the final profile of the virialized protoobject.