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 lensing peak counts and the power spectrum to infer cosmological parameters, and find that the latter 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 significantly degrade (similar to 50 per cent) Lambda CDM(cold darkmatter, wCDM) parameter constraints. A residual constant photo-z bias of vertical bar delta z vertical bar < 0.003(1 + z), the current LSST requirement, does not significantly degrade surveys smaller than approximate to 1300 (approximate to 490) deg(2) using peaks and approximate to 6500 (approximate to 4900) deg(2) using the power spectrum. Surveys smaller than approximate to 920 (approximate to 450) deg(2) and approximate to 4600 (approximate to 4000) deg(2) avoid 25 per cent degradation. 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 computed from this PDF significantly degrades surveys as small as approximate to 60 (approximate to 65) deg(2) using peaks or the power spectrum. If the centroid bias in each tomographic bin is removed from the photo-z galaxy distribution, using peaks or the power spectrum still significantly degrades surveys larger than approximate to 200 (approximate to 255) or approximate to 248 (approximate to 315) deg(2); 25 per cent degradations occur at survey sizes of approximate to 140 (approximate to 180) deg(2) or approximate to 165 (approximate to 210) deg(2). These results imply that the expected broad photo-z PDF significantly biases parameters, which must be further mitigated using more sophisticated photo-z treatments.