The impact of photometric redshift errors on lensing statistics in ray-tracing simulations

Abstract

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 (∼50 per cent)ΛCDM(cold darkmatter,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.