The removal of shear-ellipticity correlations from the cosmic shear
  signal: Influence of photometric redshift errors on the nulling technique
  Cosmic shear is regarded one of the most powerful probes to reveal 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
intrinsic alignment, causing considerable parameter biases via correlations
between the intrinsic ellipticities of galaxies and the gravitational shear,
which mimic lensing. In an earlier work we have 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. 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 is close to optimal
in terms of bias removal, given high quality of photometric redshifts. For
excellent photometric redshift information, i.e. at least 10 bins with a small
dispersion, a negligible fraction of catastrophic outliers, and precise
knowledge about the redshift distributions, 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. 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.
