Self-calibration of photometric redshift scatter in weak-lensing surveys

Photometric redshift (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 redshift 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 per cent for z < 2 galaxies. Among the several sources of calibration error that we identify and investigate, the 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.