The impact of projection effects on cluster observables: stacked lensing and projected clustering.

An optical cluster finder inevitably suffers from projection effects, where it misidentifies a superposition of galaxies in multiple halos along the line-of-sight as a single cluster. Using mock cluster catalogs built from cosmological N-body simulations, we quantify the impact of these projection effects with a particular focus on the observables of interest for cluster cosmology, namely the cluster lensing and the cluster clustering signals. We find that "observed" clusters, i.e. clusters identified by our cluster finder algorithm, exhibit lensing and clustering signals that deviate from expectations based on a statistically isotropic halo model -- while both signals agree with halo model expectations on small scales, they show unexpected boosts on large scales, by up to a factor of 1.2 or 1.4 respectively. We identify the origin of these boosts as the inherent selection bias of optical cluster finders for clusters embedded within filaments aligned with the line-of-sight, and show that a minority ($\sim 30\%$) of such clusters within the entire sample is responsible for this observed boost. We discuss the implications of our results on previous studies of optical cluster, as well as prospects for identifying and mitigating projection effects in future cluster cosmology analyses.