Disentangling correlated scatter in cluster mass measurements

The challenge of obtaining galaxy cluster masses is increasingly being addressed by multiwavelength measurements. As scatters in measured cluster masses are often sourced by properties of or around the clusters themselves, correlations between mass scatters are frequent and can be significant, with consequences for errors on mass estimates obtained both directly and via stacking. Using a high-resolution 250 h^-1 Mpc side N-body simulation, combined with proxies for observational cluster mass measurements, we obtain mass scatter correlations and covariances for 243 individual clusters along ∼96 lines of sight each, both separately and together. Many of these scatters are quite large and highly correlated. We use principal component analysis (PCA) to characterize scatter trends and variations between clusters. PCA identifies combinations of scatters, or variations more generally, which are uncorrelated or non-covariant. The PCA combination of mass measurement techniques which dominate the mass scatter is similar for many clusters, and this combination is often present in a large amount when viewing the cluster along its long axis. We also correlate cluster mass scatter, environmental and intrinsic properties, and use PCA to find shared trends between these. For example, if the average measured richness, velocity dispersion and Compton decrement mass for a cluster along many lines of sight are high relative to its true mass, then in our simulation the cluster's mass measurement scatters around this average are also high, its sphericity is high and its triaxiality is low.

Our analysis is based upon estimated mass distributions for fixed true mass. Extensions to observational data would require further calibration from numerical simulations, tuned to specific observational survey selection functions and systematics.