The removal of shear-ellipticity correlations from the cosmic shear signal Influence of photometric redshift errors on the nulling technique

Aims. Cosmic shear, the gravitational lensing on cosmological scales, is regarded as one of the most powerful probes for revealing the properties of dark matter and dark energy. To fully utilize its potential, one has to be able to control systematic effects down to below the level of the statistical parameter errors. Particularly worrisome in this respect is the intrinsic alignment of galaxies, causing considerable parameter biases via correlations between the intrinsic ellipticities of galaxies and the gravitational shear, which mimic lensing. Since our understanding of the underlying processes of intrinsic alignment is still poor, purely geometrical methods are required to control this systematic. In an earlier work we proposed a nulling technique that downweights this systematic, only making use of its well-known redshift dependence. We assess the practicability of nulling, given realistic conditions on photometric redshift information. Methods. For several simplified intrinsic alignment models and a wide range of photometric redshift characteristics, we calculate an average bias before and after nulling. Modifications of the technique are introduced to optimize the bias removal and minimize the information loss by nulling. We demonstrate that one of the presented versions of nulling is close to optimal in terms of bias removal, given the high quality of photometric redshifts. Although the nulling weights depend on cosmology, being composed of comoving distances, we show that the technique is robust against an incorrect choice of cosmological parameters when calculating the weights. Moreover, general aspects such as the behavior of the Fisher matrix under parameter-dependent transformations and the range of validity of the bias formalism are discussed in an appendix. Results. Given excellent photometric redshift information, i.e. at least 10 bins with a dispersion sigma(ph) less than or similar to 0.03, a negligible fraction of catastrophic outliers, and precise knowledge about the bin-wise redshift distributions as characterized by a scatter of 0.001 or less on the median redshifts, one version of nulling is capable of reducing the shear-intrinsic ellipticity contamination by at least a factor of 100. Alternatively, we describe a robust nulling variant which suppresses the systematic signal by about 10 for a very broad range of photometric redshift configurations, provided basic information about sigma(ph) in each of greater than or similar to 10 photometric redshift bins is available. Irrespective of the photometric redshift quality, a loss of statistical power is inherent to nulling, which amounts to a decrease of the order 50% in terms of our figure of merit under conservative assumptions.