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 (${\sim }50{{\ \rm per\ cent}}$) ΛCDM (cold dark matter, wCDM) parameter constraints. A residual constant photo-z bias of |δz| < 0.003(1 + z), the current LSST requirement, does not significantly degrade surveys smaller than ≈1300 (≈490) deg2 using peaks and ≈6500 (≈4900) deg2 using the power spectrum. Surveys smaller than ≈920 (≈450) deg2 and ≈4600 (≈4000) deg2 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 ≈60 (≈65) deg2 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 ≈200 (≈255) or ≈248 (≈315) deg2; 25 per cent degradations occur at survey sizes of ≈140 (≈180) deg2 or ≈165 (≈210) deg2. These results imply that the expected broad photo-z PDF significantly biases parameters, which must be further mitigated using more sophisticated photo-z treatments.