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Three-point correlations in weak lensing surveys: Model predictions and applications

We use the halo model of clustering to compute two- and three-point correlation functions for weak lensing, and apply them in a new statistical technique to measure properties of massive haloes. We present analytical results on the eight shear three-point correlation functions constructed using a combination of the two shear components at each vertex of a triangle. We compare the amplitude and configuration dependence of the functions with ray-tracing simulations and find excellent agreement for different scales and models. These results are promising, since shear statistics are easier to measure than the convergence. In addition, the symmetry properties of the shear three-point functions provide a new and precise way of disentangling the lensing E mode from the B mode due to possible systematic errors. We develop an approach based on correlation functions to measure the properties of galaxy-group and cluster haloes from lensing surveys. Shear correlations on small scales arise from the lensing matter within haloes of mass M ? 10 1 3 M O .. Thus, the measurement of two- and three-point correlations can be used to extract information on halo density profiles, primarily the inner slope and halo concentration. We demonstrate the feasibility of such an analysis for forthcoming surveys. We include covariances in the correlation functions due to sample variance and intrinsic ellipticity noise to show that 10 per cent accuracy on profile parameters is achievable with surveys such as the CFHT Legacy survey, and significantly better with future surveys. Our statistical approach is complementary to the standard approach of identifying individual objects in survey data and measuring their properties. It can be extended to perform a combined analysis of the large-scale, perturbative regime down to small, subarcminute scales, to obtain consistent measurements of cosmological parameters and halo properties.