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.
