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

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 delta(*), 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 delta(*) >> 1 for a small smoothing scale R (th) similar to 1 h (-1) Mpc and conversely delta(*) <<1 for a large smoothing scale R (th) > 10 h (-1) Mpc. In the range delta/delta(*) < 1, the shape of the PDF is almost solely determined by the outer slope of haloes and scales as a power law. The resultant non-Gaussian tails of the PDF then resemble log-normal PDFs in that range and show good agreement with N -body simulations, which can be ascribed to the universality of the outer slope of the halo profile. In contrast, the tails of the one-point PDF in the range delta/delta(*) > 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.