Measuring σ₈ with Cluster Lensing: Biases from Unrelaxed Clusters

Abstract

We use gravitational lens models and X-ray spectral analysis of 10 X-ray-luminous galaxy clusters at z~=0.2 to study the impact of cluster substructure on attempts to normalize the matter power spectrum. We estimate that unrelaxed clusters are 30% hotter than relaxed clusters, causing σ₈ to be overestimated by 20% if the cluster selection function is not accounted for. This helps to explain the wide range in σ₈ derived from different techniques, σ₈~0.6-1, and offers a physically motivated explanation for some of the discrepancy. We identify two further systematics: (1) the extrapolation of small field-of-view mass measurements to cluster virial radii and (2) the projection of three-dimensional mass estimates from n-body simulations to match two-dimensional observables. We quantify these effects and estimate from the current data that σ₈=0.75+/-0.05(statistical)+/-0.15(systematic), where the systematic error reflects the extrapolation and projection uncertainties, and we assume Ω_M=0.3 and Ω_Λ=0.7. All three systematics (substructure, extrapolation, and projection) are fundamental to future cluster-based measurements of σ₈ regardless of the techniques employed. We identify gravitational lensing as the tool of choice for such studies because a combination of strong and weak lensing offers the most direct route to control the systematics and thus achieve an unbiased comparison between observation and theory.