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 nonlinear 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 as high as the linear estimate, without the degree of non-Gaussianity as quantified by skewness and kurtosis of the density field being unacceptably large. The results suggest that higher-order terms in the perturbative expansion may contribute significantly to galactic spin which contrasts with the straightforward Gaussian case.

Galactic angular momenta and angular momentum couplings in the large-scale structure

“…The resulting correlations in angular momentum have a range of about 1 Mpc h −1 for Milky Way sized haloes and can be fitted well with an empirical formula C L (r) ∝ exp (−[r/r 0 ] β ). Comparing our results to numerical and perturbative studies (Catelan & Theuns 1996b, 1997Porciani et al 2002a,b;Lee & Pen 2008) shows that linear tidal torquing would predict too large amplitudes for the angular momentum field and short-ranged correlations by neglecting non-linear dynamics and motion of haloes.…”

“…The gradient of the Zel’dovich potential displaces the protogalactic object, which is neglected in the further derivation, as we only trace differential advection velocities responsible for inducing rotation. Identifying the tensor of second moments of the mass distribution of the protogalactic object as the inertia I βσ : one obtains the final expression of the angular momentum L α : It is convenient to rewrite the time dependence of D + in terms of the scalefactor a by d D + /d t = aH ( a )d D + /d a , yielding The theory of angular momentum acquisition by tidal shearing has been extended to non‐linear stages by using second‐order perturbation theory (Catelan & Theuns 1996b) and to include effects of non‐Gaussian initial perturbations (Catelan & Theuns 1997), but for reasons of analytical computability, we restrict our model of angular momenta to the linear regime of structure formation of a Gaussian random field.…”

“…The theory of angular momentum acquisition by tidal shearing has been extended to non-linear stages by using second-order perturbation theory (Catelan & Theuns 1996b) and to include effects of non-Gaussian initial perturbations (Catelan & Theuns 1997), but for reasons of analytical computability, we restrict our model of angular momenta to the linear regime of structure formation of a Gaussian random field. Fig.…”

“…Our calculation would not include this population of haloes and it would be impossible to accommodate for them as we predict angular momentum statistics from a peak‐restricted Gaussian process. The description of tidal torquing used in this work is purely linear and uses the Zel’dovich approximation (Zel’dovich 1970; Catelan & Theuns 1996a). Higher order, non‐linear corrections to Lagrangian perturbation theory were shown to have some impact on tidal torquing (Catelan & Theuns 1996b, 1997), by increasing the angular momentum variance by about 30 per cent. Furthermore, dissipative processes in halo formation and tidal interactions between haloes are able to tilt the angular momentum away from the prediction from tidal torquing (Sugerman et al 2000; Song & Lee 2011).…”

Effects of merging histories on angular momentum distribution of dark matter haloes

“…They used the peak formalism of Gaussian random fields (Peacock & Heavens 1985;Bardeen et al 1986), in order to analyse statistically a density profile around the density peak maximum. Catelan & Theuns also considered the case of non-Gaussian initial conditions (Catelan & Theuns 1997). Susa, Sasaki & Tanaka investigated the angular momentum distribution by using the Press-Schechter formalism (Press & Schechter 1974) instead of the peak formalism.…”