The Impact of Photometric Redshift Errors on Lensing Statistics in Ray-Tracing Simulations

Weak lensing surveys are reaching sensitivities at which uncertainties in the galaxy redshift distributions n(z) from photo-z errors degrade cosmological constraints. We use ray-tracing simulations and a simple treatment of photo-z errors to assess cosmological parameter biases from uncertainties in n(z) in an LSST-like survey. We use the power spectrum and the abundance of lensing peaks to infer cosmological parameters, and find that the former is somewhat more resilient to photo-z errors. We place conservative lower limits on the survey size at which different types of photo-z errors degrade LCDM (wCDM) parameter constraints by 50%. A residual constant photo-z bias of |dz| < 0.003(1+z), satisfying the current LSST requirement, does not significantly degrade constraints for surveys smaller than ~1300 (~490) square degrees using lensing peaks and ~6500 (~4900) square degrees using the power spectrum. Adopting a recent prediction for LSST's full photo-z probability distribution function (PDF), we find that simply approximating n(z) with the photo-z galaxy distribution directly computed from this PDF would degrade surveys as small as ~60 (~65) square degrees using lensing peaks or the power spectrum. Assuming that the centroid bias in each tomographic redshift bin can be removed from the photo-z galaxy distribution, using lensing peaks or the power spectrum still degrades surveys larger than ~200 (~255) or ~248 (~315) square degrees. These results imply that the expected broad photo-z PDF significantly biases parameters, which needs to be further mitigated using more sophisticated photo-z treatments.