Linear velocity fields in non-Gaussian models for large-scale structure

Abstract

Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.