Self calibration of photometric redshift scatter in weak lensing surveys
  Photo-z errors, especially catastrophic errors, are a major uncertainty for
precision weak lensing cosmology. We find that the shear-(galaxy number)
density and density-density cross correlation measurements between photo-z
bins, available from the same lensing surveys, contain valuable information for
self-calibration of the scattering probabilities between the true-z and photo-z
bins. The self-calibration technique we propose does not rely on cosmological
priors nor parameterization of the photo-z probability distribution function,
and preserves all of the cosmological information available from shear-shear
measurement. We estimate the calibration accuracy through the Fisher matrix
formalism. We find that, for advanced lensing surveys such as the planned stage
IV surveys, the rate of photo-z outliers can be determined with statistical
uncertainties of 0.01-1% for $z<2$ galaxies. Among the several sources of
calibration error that we identify and investigate, the {\it galaxy
distribution bias} is likely the most dominant systematic error, whereby
photo-z outliers have different redshift distributions and/or bias than
non-outliers from the same bin. This bias affects all photo-z calibration
techniques based on correlation measurements. Galaxy bias variations of
$O(0.1)$ produce biases in photo-z outlier rates similar to the statistical
errors of our method, so this galaxy distribution bias may bias the
reconstructed scatters at several-$\sigma$ level, but is unlikely to completely
invalidate the self-calibration technique.
