Modeling 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 modeling of projection effects is a necessary component for
cluster abundance studies capable of reaching $\approx 5\%$ 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 log-normal model only --- biases the posterior of the
cluster normalization condition $S_8 \equiv \sigma_8 (\Omega_{\rm
m}/0.3)^{1/2}$ by $\Delta S_8 =0.05$, more than twice the uncertainty in the
posterior for such an analysis.
