Explicit computation of shear three-point correlation functions: the one-halo model case

We present a method for calculating explicit expressions of the shear three-point function for various cosmological models. The method is applied here to the one-halo model in case of power law density profiles for which results are detailed. The three-point functions are found to reproduce to a large extent patterns in the shear correlations obtained in numerical simulations and may serve as a guideline to implement optimized methods for detecting the shear three-point function. In principle, the general method presented here can also be applied for other models of matter correlation.Comment: 8 pages, 6 figures, submitted to A

Properties of the Cosmological Density Distribution Function

The properties of the probability distribution function of the cosmological continuous density field are studied. We present further developments and compare dynamically motivated methods to derive the PDF. One of them is based on the Zel'dovich approximation (ZA). We extend this method for arbitrary initial conditions, regardless of whether they are Gaussian or not. The other approach is based on perturbation theory with Gaussian initial fluctuations. We include the smoothing effects in the PDFs. We examine the relationships between the shapes of the PDFs and the moments. It is found that formally there are no moments in the ZA, but a way to resolve this issue is proposed, based on the regularization of integrals. A closed form for the generating function of the moments in the ZA is also presented, including the smoothing effects. We suggest the methods to build PDFs out of the whole series of the moments, or out of a limited number of moments -- the Edgeworth expansion. The last approach gives us an alternative method to evaluate the skewness and kurtosis by measuring the PDF around its peak. We note a general connection between the generating function of moments for small r.m.s $\sigma$ and the non-linear evolution of the overdense spherical fluctuation in the dynamical models. All these approaches have been applied in 1D case where the ZA is exact, and simple analytical results are obtained. The 3D case is analyzed in the same manner and we found a mutual agreement in the PDFs derived by different methods in the the quasi-linear regime. Numerical CDM simulation was used to validate the accuracy of considered approximations. We explain the successful log-normal fit of the PDF from that simulation at moderate $\sigma$ as mere fortune, but not as a universal form of density PDF in general.Comment: 30 pages in Plain Tex, 1 table and 11 figures available as postscript files by anonymous ftp from ftp.cita.utoronto.ca in directory /cita/francis/lev, IFA-94-1

Construction of the one-point PDF of the local aperture mass in weak lensing maps

We present a general method for the reconstruction of the one-point Probability Distribution Function of the local aperture mass in weak lensing maps. Exact results, that neglect the lens-lens coupling and departure form the Born approximation, are derived for both the quasilinear regime at leading order and the strongly nonlinear regime assuming the tree hierarchical model is valid. We describe in details the projection effects on the properties of the PDF and the associated generating functions. In particular, we show how the generic features which are common to both the quasilinear and nonlinear regimes lead to two exponential tails for P(\Map). We briefly investigate the dependence of the PDF with cosmology and with the shape of the angular filter. Our predictions are seen to agree reasonably well with the results of numerical simulations and should be able to serve as foundations for alternative methods to measure the cosmological parameters that take advantage of the full shape of the PDF.Comment: 17 pages, final version published in A&

Vorticity generation in large-scale structure caustics

A fundamental hypothesis for the interpretation of the measured large-scale line-of-sight peculiar velocities of galaxies is that the large-scale cosmic flows are irrotational. In order to assess the validity of this assumption, we estimate, within the frame of the gravitational instability scenario, the amount of vorticity generated after the first shell crossings in large-scale caustics. In the Zel'dovich approximation the first emerging singularities form sheet like structures. Here we compute the expectation profile of an initial overdensity under the constraint that it goes through its first shell crossing at the present time. We find that this profile corresponds to rather oblate structures in Lagrangian space. Assuming the Zel'dovich approximation is still adequate not only at the first stages of the evolution but also slightly after the first shell crossing, we calculate the size and shape of those caustics and their vorticity content as a function of time and for different cosmologies. The average vorticity created in these caustics is small: of the order of one (in units of the Hubble constant). To illustrate this point we compute the contribution of such caustics to the probability distribution function of the filtered vorticity at large scales. We find that this contribution that this yields a negligible contribution at the 10 to 15 $h^{-1}$Mpc scales. It becomes significant only at the scales of 3 to 4 $h^{-1}$Mpc, that is, slightly above the galaxy cluster scales.Comment: 25 pages 16 figures; accepted for publication by A&A vol 342 (1999