Open AccessEvolution of peaks in weakly non‐linear density field and dark halo profiles
Author(s) -
Łokas Ewa L.
Publication year - 1998
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.1998.01377.x
Subject(s) - physics , halo , statistical physics , gaussian , halo mass function , skewness , smoothing , astrophysics , linear scale , distribution (mathematics) , conditional probability distribution , field (mathematics) , probability density function , galaxy , statistics , quantum mechanics , mathematical analysis , geodesy , mathematics , geography , pure mathematics
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 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 a conditional distribution 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 linear 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 Bardeen 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 weakly non‐linear interactions is to decrease the scale from which a peak 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 virialized proto‐object.