Calibrating Redshift Distributions beyond Spectroscopic Limits with Cross‐Correlations

We describe a new method for measuring the true redshift distribution of any set of objects studied only photometrically. The angular cross-correlation between objects in a photometric sample with objects in some spectroscopic sample as a function of the spectroscopic z, in combination with standard correlation measurements, provides sufficient information to reconstruct the true redshift distribution of the photometric sample. This technique enables the robust calibration of photometric redshifts even beyond spectroscopic limits. The spectroscopic sample need not resemble the photometric one in galaxy properties, but must overlap in sky coverage and redshift range. We test this new technique with Monte Carlo simulations using realistic error estimates. RMS errors in recovering both the mean and sigma of the true, Gaussian redshift distribution of a single photometric redshift bin are 1. 4x10^ (-3) (sigmaᵦ/0. 1) (Sigmaₚ/10) ^ (-0. 3) (dNₛ/dz / 25, 000) ^ (-0. 5), where sigmaᵦ is the true sigma of the redshift distribution, Sigmaₚ is the surface density of the photometric sample in galaxies/arcmin², and dNₛ/dz is the number of galaxies with a spectroscopic redshift per unit z. We test the impact of redshift outliers and of a variety of sources of systematic error; none dominate measurement uncertainties in reasonable scenarios. With this method, the true redshift distributions of even arbitrarily faint photometric redshift samples may be determined to the precision required by proposed dark energy experiments (errors in mean and sigma below 3x10^ (-3) at z~1) using expected extensions of current spectroscopic samples.