Association between optically identified galaxy clusters and the underlying dark matter halos

Clusters of galaxies trace massive dark matter halos in the Universe, but they can include multiple halos projected along lines of sight. As a case study, we quantify the properties of halos contributing to clusters identified by the redMaPPer algorithm using the Cardinal simulation, which mimics the Dark Energy Survey data. For each cluster, we identify the halos hosting its member galaxies, and we define the main halo as the one contributing the most to the cluster's richness ($\lambda$, the estimated number of member galaxies). At $z=0.3$, for clusters with $\lambda > 60$, the main halo typically contributes to $92\%$ of the richness, and this fraction drops to $67\%$ for $\lambda \approx 20$. Defining "clean" clusters as those with $\geq50\%$ of the richness contributed by the main halo, we find that $100\%$ of the $\lambda > 60$ clusters are clean, while $73\%$ of the $\lambda \approx 20$ clusters are clean. Three halos can usually account for more than $80\%$ of the richness of a cluster. The main halos associated with redMaPPer clusters have a completeness ranging from $98\%$ at virial mass $10^{14.6}~h^{-1}M_{\odot}$ to $64\%$ at $10^{14}~h^{-1}M_{\odot}$. In addition, we compare the inferred cluster centers with true halo centers, finding that $30\%$ of the clusters are miscentered with a mean offset $40\%$ of the cluster radii, in agreement with recent X-ray studies. These systematics worsen as redshift increases, but we expect that upcoming surveys extending to longer wavelengths will improve the cluster finding at high redshifts. Our results affirm the robustness of the redMaPPer algorithm and provide a framework for benchmarking other cluster-finding strategies.