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.
