Non-Gaussian tails of cosmological density distribution function from dark halo approach

Abstract

We present a simple model based on the dark halo approach which provides a useful way to understand key points that determine the shape of the non-Gaussian tails of the dark matter one-point probability distribution function (PDF). In particular, using scale-free models with a power-law profile of dark haloes, we derive a simple analytic expression for the one-point PDF. It is found that the shape of the PDF changes at a characteristic value of δ*, which is defined by the smoothed density of a halo with characteristic mass M* at the epoch. In cold dark matter models with top-hat smoothing filters, the characteristic smoothed density at the present time typically takes the value δ*≫ 1 for a small smoothing scale Rth∼ 1 h−1 Mpc and conversely δ*≪ 1 for a large smoothing scale Rth > 10 h−1 Mpc. In the range δ/δ* 1 basically follow the steep exponential tails of the halo mass function, which exhibit a strong sensitivity on both the outer slope of the halo profile and the initial power spectrum. Based on these results, a discussion on the PDF of galaxy distribution and application to weak lensing statistics are also presented.