Modelling projection effects in optically selected cluster catalogues

The cosmological utility of galaxy cluster catalogues is primarily limited by our ability to calibrate the relation between halo mass and observable mass proxies such as cluster richness, X-ray luminosity, or the Sunyaev-Zeldovich signal. Projection effects are a particularly pernicious systematic effect that can impact observable mass proxies; structure along the line of sight can both bias and increase the scatter of the observable mass proxies used in cluster abundance studies. In this work, we develop an empirical method to characterize the impact of projection effects on redMaPPer cluster catalogues. We use numerical simulations to validate our method and illustrate its robustness. We demonstrate that modelling of projection effects is a necessary component for cluster abundance studies capable of reaching ≈ 5 per cent mass calibration uncertainties (e.g. the Dark Energy Survey Year 1 sample). Specifically, ignoring the impact of projection effects in the observable-mass relation - i.e. marginalizing over a lognormal model only - biases the posterior probability of the cluster normalization condition S₈ ≡ σ₈(Ω_m/0.3)^1/2 by ΔS₈ = 0.05, more than twice the uncertainty in the posterior for such an analysis.