Redshift requirements for cosmic shear with intrinsic alignment

Intrinsic alignment (IA) modelling and photometric redshift estimation are two of the main sources of systematic uncertainty in weak lensing surveys. We investigate the impact of redshift errors and their interplay with different IA models. Generally, errors on the mean Sz and on the width a -z of the redshift bins can both lead to biases in cosmological constraints. We find that such biases can, however, only be partially resolved by marginalizing over Sz and az. For Stage-III surveys, Sz and a -z cannot be well constrained due to limited statistics. The resulting biases are thus sensitive to prior volume effects. For Stage-IV surveys, we observe that marginalizing over the redshift parameters has an impact and reduces the bias. We derive requirements on the uncertainty of a -z and Sz for both Stage-III and Stage-IV surveys. We as-sume that the redshift systematic errors on S8 should be less than half of the statistical errors, and the median bias should be smaller than 0.25a. We find that the uncertainty on Sz has to be <= 0.025 for the NLA IA model with a Stage-III survey. We find no requirement threshold for a -z since the requirements are met even for our maximum prior width of 0.3. For the TATT IA model, the uncertainty on Sz has to be <= 0.02 and the uncertainty on az has to be <= 0.2. Cur-rent redshift precision of Stage-III surveys is therefore high enough to meet these requirements. For Stage-IV surveys, systematic effects will be more important due to the higher statistical precision. In this case, the uncertainty on Sz has to be <= 0.005 and the uncertainty on az should be <= 0.1, with no significant dependence on the IA model. This required high precision will be a challenge for the redshift calibration of these future surveys. Finally, we investigate whether the interplay between redshift systematics and IA modelling can explain the S8-tension between cosmic shear results and CMB measurements. We find that this is unlikely to explain the current S8-tension. The code that was used to conduct this analysis is publicly available.1