Photometric Redshift Calibration Requirements for WFIRST Weak-lensing Cosmology: Predictions from CANDELS

In order for the Wide-Field Infrared Survey Telescope (WFIRST) and other stage IV dark energy experiments (e.g., Large Synoptic Survey Telescope, LSST; and Euclid) to infer cosmological parameters not limited by systematic errors, accurate redshift measurements are needed. This accuracy can be met by using spectroscopic subsamples to calibrate the photometric redshifts for the full sample. In this work, we find the minimal number of spectra required for the WFIRST weak-lensing redshift calibration by employing the Self-Organizing Map (SOM) spectroscopic sampling technique. We use galaxies from the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) to build the LSST+WFIRST lensing analog sample of ∼36,000 objects and to train the LSST+WFIRST SOM. We find that 26% of the WFIRST lensing sample consists of sources fainter than the Euclid depth in the optical, 91% of which live in color cells already occupied by brighter galaxies. We demonstrate the similarity between faint and bright galaxies as well as the feasibility of redshift measurements at different brightness levels. Our results suggest that the spectroscopic sample acquired for calibration to the Euclid depth is sufficient for calibrating the majority of the WFIRST color space. For the spectroscopic sample to fully represent the synthetic color space of WFIRST, we recommend obtaining additional spectroscopy of ∼0.2-1.2k new sources in cells occupied by mostly faint galaxies. We argue that either the small area of the CANDELS fields and the small overall sample size or the large photometric errors might be the reason for no/fewer bright galaxies mapped to these cells. Acquiring the spectra of these sources will confirm the above findings and will enable the comprehensive calibration of the WFIRST color-redshift relation.