Kurtosis and Large--Scale Structure

We discuss the non--linear growth of the excess kurtosis parameter of the smoothed density fluctuation field $\delta$, S_4\equiv[\lan\delta^{\,4}\ran-3\lan\delta^{\,2}\ran^2]/ \lan\delta^{\,2}\ran^3 in an Einstein--de Sitter universe. We assume Gaussian primordial density fluctuations with scale--free power spectrum $P(k)\propto k^{\,n}$ and analyze the dependence of $S_4$ on primordial spectral index $n$, after smoothing with a Gaussian filter. As already known for the skewness ratio $S_3$, the kurtosis parameter is a {\it decreasing function} of $n$, both in exact perturbative theory and in the Zel'dovich approximation. The parameter $S_4$ provides a powerful statistics to test different cosmological scenarios.Comment: 11 pages in Latex (plus 1 figure), SISSA 127/93/

Velocity Differences as a Probe of Non--Gaussian Density Fields

We examine the multi--point velocity field for non--Gaussian models as a probe of non--Gaussian behavior. The two--point velocity correlation is not a useful indicator of a non--Gaussian density field, since it depends only on the power spectrum, even for non--Gaussian models. However, we show that the distribution of velocity differences \bfv_1 - \bfv_2, where \bfv_1 and \bfv_2 are measured at the points \bfr_1 and \bfr_2, respectively, is a good probe of non--Gaussian behavior, in that p(\bfv_1 - \bfv_2) tends to be non--Gaussian whenever the density field is non--Gaussian. As an example, we examine the behavior of p(\bfv_1 - \bfv_2) for non--Gaussian seed models, in which the density field is the convolution of a distribution of points with a set of density profiles. We apply these results to the global texture model.Comment: 18 pages, LATEX style, SISSA-37-94-A, OSU-TA-4-9

Intrinsic and Extrinsic Galaxy Alignment

We show with analytic models that the assumption of uncorrelated intrinsic ellipticities of target sources that is usually made in searches for weak gravitational lensing due to large-scale mass inhomogeneities (``field lensing'') is unwarranted. If the orientation of the galaxy image is determined either by the angular momentum or the shape of the halo in which it forms, then the image should be aligned preferentially with the component of the tidal gravitational field perpendicular to the line of sight. Long-range correlations in the tidal field will thus lead to long-range ellipticity-ellipticity correlations that mimic the shear correlations due to weak gravitational lensing. We calculate the ellipticity-ellipticity correlation expected if halo shapes determine the observed galaxy shape, and we discuss uncertainties (which are still considerable) in the predicted amplitude of this correlation. The ellipticity-ellipticity correlation induced by angular momenta should be smaller. We consider several methods for discriminating between the weak-lensing (extrinsic) and intrinsic correlations, including the use of redshift information. An ellipticity--tidal-field correlation also implies the existence of an alignment of images of galaxies near clusters. Although the intrinsic alignment may complicate the interpretation of field-lensing results, it is inherently interesting as it may shed light on galaxy formation as well as on structure formation.Comment: 7 pages, submitted to MNRA

Correlations of Cosmic Tidal Fields

We study correlations amongst tidal fields originated by the large-scale distribution of matter in the Universe. The two-point tidal correlation is described as a rank-4 tensor, whose elements can be written in terms of four fundamental scalar functions ranging, with respect the spatial separation, from purely transversal to purely longitudinal correlations. Tidal fields, both on galaxy and cluster scales, reveal to be correlated over distances larger than the mass-density correlation lenght, though traceless tidal fields show anti-correlation between diagonal terms along orthogonal directions. The cross-correlation between mass and tidal field is also analyzed. These results are relevant for galaxy formation and the interpretation of large-scale weak lensing phenomena.Comment: 6 pgs, 4 figs, using amssym.sty and mn.sty - MNRAS (in press

On cold diluted plasmas hit by short laser pulses

Adapting a plane hydrodynamical model we briefly revisit the study of the impact of a very short and intense laser pulse onto a diluted plasma, the formation of a plasma wave, its wave-breaking, the occurrence of the slingshot effect.Comment: Latex file, 7 pages, 3 figures, now with higher resolution. To appear in NIMA. Proceedings of Proceedings of the "3rd European Advanced Accelerator Concepts (EAAC) Workshop", September 2017, Isola d'Elb

Eulerian Perturbation Theory in Non-Flat Universes: Second-Order Approximation

The problem of solving perturbatively the equations describing the evolution of self-gravitating collisionless matter in an expanding universe considerably simplifies when directly formulated in terms of the gravitational and velocity potentials: the problem can be solved {\it exactly}, rather than approximately, even for cosmological models with arbitrary density parameter $\Omega$. The Eulerian approach we present here allows to calculate the higher-order moments of the initially Gaussian density and velocity fields: in particular, we compute the gravitationally induced skewness of the density and velocity-divergence fields for any value of $\Omega$, confirming the extremely weak $\Omega$-dependence of the skewness previously obtained via Lagrangian perturbation theory. Our results show that the separability assumption of higher-order Eulerian perturbative solutions is restricted to the Einstein-de Sitter case only.Comment: 17 pages, Latex (mn.sty), 1 figure, revised version (1 figure is dropped; eq.46 is corrected and some consequent results are re-discussed), to be published in Monthly Notices of the Royal Astronomical Societ

Excursion set approach to the clustering of dark matter haloes in Lagrangian space

We present a stochastic approach to the spatial clustering of dark matter haloes in Lagrangian space. Our formalism is based on a local formulation of the `excursion set' approach by Bond et al., which automatically accounts for the `cloud-in-cloud' problem in the identification of bound systems. Our method allows to calculate correlation functions of haloes in Lagrangian space using either a multi-dimensional Fokker-Planck equation with suitable boundary conditions or an array of Langevin equations with spatially correlated random forces. We compare the results of our method with theoretical predictions for the halo auto-correlation function considered in the literature and find good agreement with the results recently obtained within a treatment of halo clustering in terms of `counting fields' by Catelan et al.. The possible effect of spatial correlations on numerical simulations of halo merger trees is finally discussed.Comment: LaTeX, 19 pages, 3 figures. Submitted to MNRA

On the spatial distribution of dark matter halos

We study the spatial distribution of dark matter halos in the Universe in terms of their number density contrast, related to the underlying dark matter fluctuation via a non-local and non-linear bias random field. The description of the matter dynamics is simplified by adopting the `truncated' Zel'dovich approximation to obtain both analytical results and simulated maps. The halo number density field in our maps and its probability distribution reproduce with excellent accuracy those of halos in a high-resolution N-body simulation with the same initial conditions. Our non-linear and non-local bias prescription matches the N-body halo distribution better than any Eulerian linear and local bias.Comment: 4 pages, LaTeX (uses emulateapj; included psfig.tex), 3 figures, 1 table. Shortened version, matching the size requirements of ApJ Letters. Accepted for publicatio

Towards a working model for the abundance variations within Globular Clusters stars

A popular self--enrichment scenario for the formation of globular clusters assumes that the abundance anomalies shown by the stars in many clusters are due to a second stage of star formation occurring from the matter lost by the winds of massive asymptotic giant branch (AGB) stars. Until today, the modellizations of the AGB evolution by several different groups failed, for different reasons, to account for the patterns of chemical anomalies. Here we show that our own modelling can provide a consistent picture if we constrain the three main parameters which regulate AGB evolution: 1) adopting a high efficiency convection model; 2) adopting rates of mass loss with a high dependence on the stellar luminosity; 3) assuming a very small overshooting below the formal convective regions during the thermal pulse (TP) phase. The first assumption is needed to obtain an efficient oxygen depletion in the AGB envelopes, and the second one is needed to lose the whole stellar envelope within few thermal pulses, so that the sum of CNO elements does not increase too much, consistently with the observations. The third assumption is needed to fully understand the sodium production. We also show that the Mg - Al anticorrelation is explained adopting the higher limit of the NACRE rates for proton captures by Mg25 and Mg26, and the models are consistent with the recently discovered F-Al correlation. Problems remain to fully explain the observed Mg isotopes ratios