Testing KiDS cross-correlation redshifts with simulations
  Measuring cosmic shear in wide-field imaging surveys requires accurate
knowledge of the redshift distribution of all sources. The clustering-redshift
technique exploits the angular cross-correlation of a target galaxy sample with
unknown redshifts and a reference sample with known redshifts, and is an
attractive alternative to colour-based methods of redshift calibration. We test
the performance of such clustering redshift measurements using mock catalogues
that resemble the Kilo-Degree Survey (KiDS). These mocks are created from the
MICE simulation and closely mimic the properties of the KiDS source sample and
the overlapping spectroscopic reference samples. We quantify the performance of
the clustering redshifts by comparing the cross-correlation results with the
true redshift distributions in each of the five KiDS photometric redshift bins.
Such a comparison to an informative model is necessary due to the
incompleteness of the reference samples at high redshifts. Clustering mean
redshifts are unbiased at $|\Delta z|<0.006$ under these conditions. The
redshift evolution of the galaxy bias can be reliably mitigated at this level
of precision using auto-correlation measurements and self-consistency
relations, and will not become a dominant source of systematic error until the
arrival of Stage-IV cosmic shear surveys. Using redshift distributions from a
direct colour-based estimate instead of the true redshift distributions as a
model for comparison with the clustering redshifts increases the biases in the
mean to up to $|\Delta z|\sim0.04$. This indicates that the interpretation of
clustering redshifts in real-world applications will require more sophisticated
(parameterised) models of the redshift distribution in the future. If such
better models are available, the clustering-redshift technique promises to be a
highly complementary alternative to other methods of redshift calibration.
