Speaker
Description
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 when using different IA models. We show that both errors on the mean of the redshift bin $\delta_z$ and errors of the width of the redshift bin $\sigma_z$ can lead to biases in cosmological constraints. We find that such biases can only be partially resolved by marginalizing over $\delta_z$ and $\sigma_z$. For a Stage-III survey, data does not have enough information to constrain $\delta_z$ and $\sigma_z$. We find that these biases are dominated by prior volume effects. For a Stage-IV survey, we observe that marginalizing over redshift parameters has an impact and reduces the bias. We compute requirements on $\sigma_z$ and $\delta_z$ for both Stage-III and Stage-IV surveys. Assuming that the contribution of the redshift systematics should account for less than half of the statistical noise contribution, and the median bias should be smaller than $0.25\sigma$, we find that the uncertainty on $\delta_z$ has to be $<0.025$ for NLA as IA model in a Stage-III survey. We find no requirement threshold for $\sigma_z$ since we meet the requirements even for our maximum prior width of 0.3. For TATT, the uncertainty on $\delta_z$ has to be $<0.02$ and the uncertainty on $\sigma_z$ has to be $<0.2$. Current redshift precision of Stage-III surveys is therefore high enough to meet these requirements. Due to the increasing precision, systematic effects will become much more important in Stage-IV surveys. To meet the requirement from above, the uncertainty of $\delta_z$ has to be $<0.005$ and the uncertainty of $\sigma_z$ should be $<0.1$ with no significant dependence on the IA model. The required high precision will be a major challenge for the future. Finally, we investigate if redshift systematics combined with IA modelling errors can explain the $S_8$-tension between cosmic shear results and CMB measurements. We find that redshift systematics alone are unlikely to explain the $S_8$-tension. However, we find that the noise contribution of a Stage-III survey can lead to biases of up to $-0.5\sigma$.
