Effects of Photometric Redshift Uncertainties on Weak‐Lensing Tomography

Abstract

We perform a systematic analysis of the effects of photometric redshift uncertainties on weak-lensing tomography. We describe the photo- z distribution with a bias and Gaussian scatter that are allowed to vary arbitrarily between intervals of δ z = 0.1 in redshift. While the mere presence of bias and scatter does not substantially degrade dark energy information, uncertainties in both parameters do. For a fiducial next-generation survey each would need to be known to better than about 0.003-0.01 in redshift for each interval in order to lead to less than a factor of 1.5 increase in the dark energy parameter errors. The more stringent requirement corresponds to a larger dark energy parameter space, when redshift variation in the equation of state of dark energy is allowed. Of order 10 4 -10 5 galaxies with spectroscopic redshifts fairly sampled from the source galaxy distribution will be needed to achieve this level of calibration. If the sample is composed of multiple galaxy types, a fair sample would be required for each. These requirements increase in stringency for more ambitious surveys; we quantify such scalings with a convenient fitting formula. No single aspect of a photometrically binned selection of galaxies such as their mean or median suffices, indicating that dark energy parameter determinations are sensitive to the shape and nature of outliers in the photo- z redshift distribution.