Non-linear evolution of the tidal angular momentum of protostructures — II. Non-Gaussian initial conditions

Abstract

The formalism that describes the non-linear growth of the angular momentum L of protostructures from tidal torques in a Friedmann universe, as developed in a previous paper, is extended to include non-Gaussian initial conditions. We restrict our analysis here to a particular class of non-Gaussian primordial distributions, namely multiplicative models. In such models, strongly correlated phases are produced by obtaining the gravitational potential via a non-linear local transformation of an underlying Gaussian random field. The dynamical evolution of the system is followed by describing the trajectories of fluid particles using second-order Lagrangian perturbation theory. In the Einstein-de Sitter universe, the lowest order perturbative correction to the variance of the linear angular momentum of collapsing structures grows as t^8/3 for generic non-Gaussian statistics, which contrasts with the t^10/3 growth rate characteristic of Gaussian statistics. This is a consequence of the fact that the lowest order perturbative spin contribution in the non-Gaussian case arises from the third moment of the gravitational potential, which is identically zero for a Gaussian field. Evaluating these corrections at the maximum expansion time of the collapsing structure, we find that these non-Gaussian and non-linear terms can be comparable to or even bigger than the linear estimate. These results suggest that for some statistics, higher order terms in the perturbative expansion may contribute significantly to the galactic spin in contrast to the Gaussian case.