Title: Cross-Correlation Redshift Calibration Without Spectroscopic Calibration Samples in DES Science Verification Data,
Abstract: Galaxy cross-correlations with high-fidelity redshift samples hold the
potential to precisely calibrate systematic photometric redshift uncertainties
arising from the unavailability of complete and representative training and
validation samples of galaxies. However, application of this technique in the
Dark Energy Survey (DES) is hampered by the relatively low number density,
small area, and modest redshift overlap between photometric and spectroscopic
samples. We propose instead using photometric catalogs with reliable
photometric redshifts for photo-z calibration via cross-correlations. We verify
the viability of our proposal using redMaPPer clusters from the Sloan Digital
Sky Survey (SDSS) to successfully recover the redshift distribution of SDSS
spectroscopic galaxies. We demonstrate how to combine photo-z with
cross-correlation data to calibrate photometric redshift biases while
marginalizing over possible clustering bias evolution in either the calibration
or unknown photometric samples. We apply our method to DES Science Verification
(DES SV) data in order to constrain the photometric redshift distribution of a
galaxy sample selected for weak lensing studies, constraining the mean of the
tomographic redshift distributions to a statistical uncertainty of $\Delta z
\sim \pm 0.01$. We forecast that our proposal can in principle control
photometric redshift uncertainties in DES weak lensing experiments at a level
near the intrinsic statistical noise of the experiment over the range of
redshifts where redMaPPer clusters are available. Our results provide strong
motivation to launch a program to fully characterize the systematic errors from
bias evolution and photo-z shapes in our calibration procedure.