The removal of shear-ellipticity correlations from the cosmic shear signal via nulling techniques

Aims. To render cosmic shear an astronomical tool of high precision, it is essential to eliminate systematic effects upon its signal, one of the most significant ones being the intrinsic alignment of galaxies. The alignment in tidal fields that are created by the surrounding matter structure induces correlations between the intrinsic ellipticities of source galaxies, as well as correlations between the gravitational shear and the intrinsic ellipticity. While the former effect is restricted to physically close galaxy pairs and thus relatively easy to control, shear-ellipticity correlations occur for pairs at large separations. Because of the crudeness of current models of intrinsic alignment, we have developed a model-independent, purely geometrical method for removing the contamination of the cosmic shear signal by shear-ellipticity correlations. Methods. We remove the contributions to a tomographic cosmic shear signal that may be subject to contamination by shear-ellipticity correlations, making use of the characteristic dependence of these correlations on redshift. By introducing an appropriately chosen weight function to the lensing efficiency that nulls signals stemming from certain distances, new second-order measures of cosmic shear can be constructed that are free from intrinsic alignment. We present three approaches to determining such weight functions, optimized with respect to the amount of information the weighting preserves. After generalizing the construction of weight functions, the loss of information induced by this nulling technique and the subsequent degradation of constraints on cosmological parameters is quantified in a likelihood analysis. Results. For constructing optimal weight functions, good agreement is achieved between all approaches considered. In particular, a simplified analytical ansatz is shown to approximate the numerical results closely, significantly lowering computational efforts. For a survey divided into 20 redshift bins, we find that the area of credible regions increases by 20% up to about 50% after the application of nulling, depending on the cosmological parameters considered. We demonstrate that, due to the optimization of the weight functions, nearly all information is contained in a small subset of the new second-order measures. The use of a significantly smaller number of redshift bins than 20 for the nulling considerably degrades parameter constraints under conservative assumptions, emphasizing the need for detailed redshift information.