Catastrophic photometric redshift errors: weak-lensing survey requirements

We study the sensitivity of weak-lensing surveys to the effects of catastrophic redshift errorscases where the true redshift is mis-estimated by a significant amount. To compute the biases in cosmological parameters, we adopt an efficient linearized analysis where the redshift errors are directly related to shifts in the weak-lensing convergence power spectra. We estimate the number N spec of unbiased spectroscopic redshifts needed to determine the catastrophic error rate well enough that biases in cosmological parameters are below statistical errors of weaklensing tomography. While the straightforward estimate of N spec is 10 6 , we find that using only the photometric redshifts with z 2.5 leads to a drastic reduction in N spec to 30 000 while negligibly increasing statistical errors in dark-energy parameters. Therefore, the size of the spectroscopic survey needed to control catastrophic errors is similar to that previously deemed necessary to constrain the core of the z s -z p distribution. We also study the efficacy of the recent proposal to measure redshift errors by cross-correlation between the photo-z and spectroscopic samples. We find that this method requires 10 per cent a priori knowledge of the bias and stochasticity of the outlier population, and is also easily confounded by lensing magnification bias. The cross-correlation method is therefore unlikely to supplant the need for a complete spectroscopic-redshift survey of the source population.