Using Galaxy Two‐Point Correlation Functions to Determine the Redshift Distributions of Galaxies Binned by Photometric Redshift

We investigate how well the redshift distributions of galaxies sorted intophotometric redshift bins can be determined from the galaxy angular two-pointcorrelation functions. We find that the uncertainty in the reconstructedredshift distributions depends critically on the number of parameters used ineach redshift bin and the range of angular scales used, but not on the numberof photometric redshift bins. Using six parameters for each photometricredshift bin, and restricting ourselves to angular scales over which the galaxynumber counts are normally distributed, we find that errors in thereconstructed redshift distributions are large; i.e., they would be thedominant source of uncertainty in cosmological parameters estimated fromotherwise ideal weak lensing or baryon acoustic oscillation data. However,either by reducing the number of free parameters in each redshift bin, or by(unjustifiably) applying our Gaussian analysis into the non-Gaussian regime, wefind that the correlation functions can be used to reconstruct the redshiftdistributions with moderate precision; e.g., with mean redshifts determined toaround 0.01. We also find that dividing the galaxies into two spectral types,and thereby doubling the number of redshift distribution parameters, can resultin a reduction in the errors in the combined redshift distributions.Comment: 11 pages, to be submitted to Ap