ALBERT

Description: We present the cluster selection function for three of the largest next-generation stage-IV surveys in the optical and infrared: Euclid -Optimistic, Euclid -Pessimistic and the Large Synoptic Survey Telescope (LSST). To simulate these surveys, we use the realistic mock catalogues introduced in the first paper of this series. We detected galaxy clusters using the Bayesian Cluster Finder in the mock catalogues. We then modelled and calibrated the total cluster stellar mass observable–theoretical mass ( $M^{\ast }_{\rm CL}\text{--}M_{\rm h}$ ) relation using a power-law model, including a possible redshift evolution term. We find a moderate scatter of $\sigma _{M^{\ast }_{\rm CL} | M_{\rm h}}$ of 0.124, 0.135 and 0.136 dex for Euclid -Optimistic, Euclid -Pessimistic and LSST, respectively, comparable to other work over more limited ranges of redshift. Moreover, the three data sets are consistent with negligible evolution with redshift, in agreement with observational and simulation results in the literature. We find that Euclid -Optimistic will be able to detect clusters with 〉80 per cent completeness and purity down to 8 x 10 13 h –1 M up to z 〈 1. At higher redshifts, the same completeness and purity are obtained with the larger mass threshold of 2 x 10 14 h –1 M up to z = 2. The Euclid -Pessimistic selection function has a similar shape with ~10 per cent higher mass limit. LSST shows ~5 per cent higher mass limit than Euclid -Optimistic up to z 〈 0.7 and increases afterwards, reaching a value of 2 x 10 14 h –1 M at z = 1.4. Similar selection functions with only 80 per cent completeness threshold have also been computed. The complementarity of these results with selection functions for surveys in other bands is discussed.