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Cosmological constraints from current and upcoming galaxy cluster surveys arelimited by the accuracy of cluster mass calibration. In particular, opticallyidentified galaxy clusters are prone to selection effects that can bias theweak lensing mass calibration. We investigate the selection bias of the stackedcluster lensing signal associated with optically selected clusters, usingclusters identified by the redMaPPer algorithm in the Buzzard simulations as acase study. We find that at a given cluster halo mass, the residuals ofredMaPPer richness and weak lensing signal are positively correlated. As aresult, for a given richness selection, the stacked lensing signal is biasedhigh compared with what we would expect from the underlying halo massprobability distribution. The cluster lensing selection bias can thus lead tooverestimated mean cluster mass and biased cosmology results. We show that thelensing selection bias exhibits a strong scale-dependence and is approximately20 to 60 percent for $\Delta\Sigma$ at large scales. This selection biaslargely originates from spurious member galaxies within +/- 20 to 60 Mpc/halong the line of sight, highlighting the importance of quantifying projectioneffects associated with the broad redshift distribution of member galaxies inphotometric cluster surveys. While our results qualitatively agree with thosein the literature, accurate quantitative modelling of the selection bias isneeded to achieve the goals of cluster lensing cosmology and will requiresynthetic catalogues covering a wide range of galaxy-halo connection models.

Optical selection bias and projection effects in stacked galaxy cluster weak lensing