On cross-correlating weak lensing surveys

The present generation of weak lensing surveys will be superseded by surveys run from space with much better sky coverage and high level of signal-to-noise ratio, such as the Supernova/Acceleration Probe ( SNAP ). However, removal of any systematics or noise will remain a major cause of concern for any weak lensing survey. One of the best ways of spotting any undetected source of systematic noise is to compare surveys that probe the same part of the sky. In this paper we study various measures that are useful in cross-correlating weak lensing surveys with diverse survey strategies. Using two different statistics – the shear components and the aperture mass – we construct a class of estimators which encode such cross-correlations. These techniques will also be useful in studies where the entire source population from a specific survey can be divided into various redshift bins to study cross-correlations among them. We perform a detailed study of the angular size dependence and redshift dependence of these observables and of their sensitivity to the background cosmology. We find that one-point and two-point statistics provide complementary tools which allow one to constrain cosmological parameters and to obtain a simple estimate of the noise of the survey.     

The pairwise velocity dispersion of galaxies: effects of non-radial motions

I discuss the effect of non-radial motions on the small-scale peculiar pairwise velocity dispersions (PVD) of galaxies in a cold dark matter (CDM) model and calculate the PVD for the SCDM model by means of the refined cosmic virial theorem (CVT), taking account of non-radial motions by means of the Del Popolo & Gambera model. I compare the results of the present model with the data from Davis & Peebles, the IRAS value at 1  h ⁻¹ Mpc of Fisher et al. and Marzke et al. I show that while the SCDM model disagrees with the observed values, as pointed out by several authors, taking account of non-radial motions produces smaller values for the PVD. At r ≤1  h ⁻¹ Mpc the result is in agreement with Bartlett & Blanchard. In the light of this last paper, the result may be also read as a strong dependence of the CVT prediction on the model chosen to describe the mass distribution around galaxies, suggesting that the CVT cannot be taken as a direct evidence for a low-density Universe. Similarly to what is shown by Del Popolo & Gambera and Del Popolo et al., the agreement of our model to the observational data is because of a scale-dependent bias induced by the presence of non-radial motions. As the assumptions on which CVT is based have been questioned by several authors, I also calculated the PVD using the redshift distortion in the redshift-space correlation function, ξ _z( r _p, π), and compared it with the PVD measured from the Las Campanas Redshift Survey by Jing et al. The result confirms that non-radial motions influence the PVD making them agree better with the observed data.     

Parameter information from non-linear cosmological fields

We develop a general formalism for analysing parameter information from non-Gaussian cosmic fields. The method can be adapted to include the non-linear effects in galaxy redshift surveys, weak lensing surveys and cosmic velocity field surveys as part of parameter estimation. It can also be used as a test of non-Gaussianity of the cosmic microwave background. Generalizing maximum-likelihood analysis to second order, we calculate the non-linear Fisher information matrix and likelihood surfaces in parameter space. To this order we find that the information content is always increased by including non-linearity. Our methods are applied to a realistic model of a galaxy redshift survey, including non-linear evolution, galaxy bias, shot-noise and redshift-space distortions to second order. We find that including non-linearities allows all of the degeneracies between parameters to be lifted. Marginalized parameter uncertainties of a few per cent will then be obtainable using forthcoming galaxy redshift surveys.     

Elastic solutions for stresses in a transversely isotropic half‐space subjected to three‐dimensional buried parabolic rectangular loads

In many areas of engineering practice, applied loads are not uniformly distributed but often concentrated towards the centre of a foundation. Thus, loads are more realistically depicted as distributed as linearly varying or as parabola of revolution. Solutions for stresses in a transversely isotropic half‐space caused by concave and convex parabolic loads that act on a rectangle have not been derived. This work proposes analytical solutions for stresses in a transversely isotropic half‐space, induced by three‐dimensional, buried, linearly varying/uniform/parabolic rectangular loads. Load types include an upwardly and a downwardly linearly varying load, a uniform load, a concave and a convex parabolic load, all distributed over a rectangular area. These solutions are obtained by integrating the point load solutions in a Cartesian co‐ordinate system for a transversely isotropic half‐space. The buried depth, the dimensions of the loaded area, the type and degree of material anisotropy and the loading type for transversely isotropic half‐spaces influence the proposed solutions. An illustrative example is presented to elucidate the effect of the dimensions of the loaded area, the type and degree of rock anisotropy, and the type of loading on the vertical stress in the isotropic/transversely isotropic rocks subjected to a linearly varying/uniform/parabolic rectangular load. Copyright © 2002 John Wiley & Sons, Ltd.     

Theoretical estimates of intrinsic galaxy alignment

It has recently been argued that the observed ellipticities of galaxies may be determined at least in part by the primordial tidal gravitational field in which the galaxy formed. Long-range correlations in the tidal field could thus lead to an ellipticity–ellipticity correlation for widely separated galaxies. We present a new model relating ellipticity to angular momentum, which can be calculated in linear theory. We use this model to calculate the angular power spectrum of intrinsic galaxy shape correlations. We show that, for low-redshift galaxy surveys, our model predicts that intrinsic correlations will dominate correlations induced by weak lensing, in good agreement with previous theoretical work and observations. We find that our model produces ' E -mode' correlations enhanced by a factor of 3.5 over B -modes on small scales, making it harder to disentangle intrinsic correlations from those induced by weak gravitational lensing.