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 (λ, the estimated number of member galaxies). At z = 0.3, for clusters with λ > 60, the main halo typically contributes to 92% of the richness, and this fraction drops to 67% for λ ≈ 20. Defining “clean” clusters as those with ≥ 50% of the richness contributed by the main halo, we find that 100% of the λ > 60 clusters are clean, while 73% of the λ ≈ 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 1014.6h−1M⊙ to 64% at 1014h−1M⊙. 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.
