EVOLUTION OF PEAKS IN WEAKLY NONLINEAR DENSITY FIELD AND DARK HALO PROFILES

Using the two-point Edgeworth series up to second order in the linear rms density fluctuation we construct the weakly non-linear conditional probability distribution function for the density field around an ove rdense region. This requires calculating the two-point analogues of th e skewness parameter S-3. We test the dependence of the two-point skew ness on distance from the peak for scale-free power spectra and Gaussi an smoothing. The statistical features of such a conditional distribut ion are given as the values obtained within linear theory corrected by the terms that arise as a result of weakly non-linear evolution. The expected density around the peak is found to be always below the linea r prediction while its dispersion is always larger than in the linear case. For large enough overdensities the weakly non-linear corrections can be more significant than the peak constraint introduced by Bardee n et al. We apply these results to the spherical model of collapse as developed by Hoffman & Shaham and find that in general the effect of w eakly non-linear interactions is to decrease the scale from which a pe ak gathers mass and therefore also the mass itself. In the case of an open universe this results in steepening of the final profile of the v irialized proto-object.