Mapping the Galaxy Color-Redshift Relation: Optimal Photo-z Calibration Strategies for Cosmology Surveys

A primary objective of the upcoming dark energy surveys LSST, Euclid, and WFIRST is to map the 3D distribution of matter over a significant fraction of the universe via the weak lensing cosmic shear field. Doing so will require accurate distance estimates to billions of faint galaxies, meaning that photo-z's will be essential for the ultimate scientific success of these missions. Because galaxy colors drive photo-z estimates, spectroscopic calibration samples must at least be representative in color. Here we present a technique, based on the self-organizing map (Kohonen 1990), to map the empirical distribution of galaxies in the high-dimensional color space of a given survey. We apply the technique to Euclid-like data for ~131k galaxies from the COSMOS survey, allowing us to determine where - in galaxy color space - spectroscopic coverage exists and where it is systematically missing. We show that the mapping technique lets us develop efficient spectroscopic sampling strategies to measure the color-redshift relation by focusing effort on poorly constrained regions of multicolor space. We discuss the nature of the galaxies in un-sampled regions of galaxy color space, and show that a fiducial survey with Keck (making use of LRIS, DEIMOS, and MOSFIRE) could meet the Euclid calibration requirements in ~40 nights of observing.