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The present generation of weak lensing surveys will be superseded by surveys run from space with much better sky coverage and high level of signal-to-noise ratio, such as the Supernova/Acceleration Probe ( SNAP ).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.