Reconstructing Redshift Distributions with Cross-Correlations: Tests and an Optimized Recipe

Many of the cosmological tests to be performed by planned dark energy experiments will require extremely well-characterized photometric redshift measurements. Current estimates are that the true mean redshift of the objects in each photo-z bin must be known to better than 0.002(1+z) if errors in cosmological measurements are not to be degraded. A conventional approach is to calibrate these photometric redshifts with large sets of spectroscopic redshifts. However, at the depths probed by Stage III surveys (such as DES), let alone Stage IV (LSST, JDEM, Euclid), existing large redshift samples have all been highly (25-60%) incomplete. A powerful alternative approach is to exploit the clustering of galaxies to perform photometric redshift calibrations. Measuring the two-point angular cross-correlation between objects in some photometric redshift bin and objects with known spectroscopic redshift allows the true redshift distribution of a photometric sample to be reconstructed in detail, even if it includes objects too faint for spectroscopy or if spectroscopic samples are highly incomplete. We test this technique using mock DEEP2 Galaxy Redshift survey light cones constructed from the Millennium Simulation semi-analytic galaxy catalogs. From this realistic test, we find that the true redshift distribution of a photometric sample can, in fact, be determined accurately with cross-correlation techniques. We also compare the empirical error in the reconstruction of redshift distributions to previous analytic predictions, finding that additional components must be included in error budgets to match the simulation results. We conclude by presenting a step-by-step, optimized recipe for reconstructing redshift distributions using standard correlation measurements.