A GENERAL STUDY OF THE INFLUENCE OF CATASTROPHIC PHOTOMETRIC REDSHIFT ERRORS ON COSMOLOGY WITH COSMIC SHEAR TOMOGRAPHY

A goal of forthcoming imaging surveys is to use weak gravitational lensing shear measurements to constrain dark energy. A challenge to this program is that redshifts to the lensed, source galaxies must be determined using photometric, rather than spectroscopic, information. We quantify the importance of uncalibrated photometric redshift outliers to the dark energy goals of forthcoming imaging surveys in a manner that does not assume any particular photometric redshift technique or template. In so doing, we provide an approximate blueprint for computing the influence of specific outlier populations on dark energy constraints. We find that outlier populations whose photo-z distributions are tightly localized about a significantly biased redshift must be controlled to a per-galaxy rate of (1-3) x 10(-3) to insure that systematic errors on dark energy parameters are rendered negligible. In the complementary limit, a subset of imaged galaxies with uncalibrated photometric redshifts distributed over a broad range must be limited to fewer than a per-galaxy error rate of F-cat less than or similar to (2-4) x 10(-4). Additionally, we explore the relative importance of calibrating the photo-z's of a core set of relatively well-understood galaxies as compared to the need to identify potential catastrophic photo-z outliers. We discuss the degradation of the statistical constraints on dark energy parameters induced by excising source galaxies at high-and low-photometric redshifts, concluding that removing galaxies with photometric redshifts z(ph) greater than or similar to 2.4 and z(ph) less than or similar to 0.3 may mitigate damaging catastrophic redshift outliers at a relatively small (less than or similar to 20%) cost in statistical error. In an Appendix, we show that forecasts for the degradation in dark energy parameter constraints due to uncertain photometric redshifts depend sensitively on the treatment of the nonlinear matter power spectrum. In particular, previous work using Peacock & Dodds may have overestimated the photo-z calibration requirements of future surveys.