Measuring Sigma8 with Cluster Lensing : Biases from Unrelaxed Clusters
  We use gravitational lens models and X-ray spectral analysis of ten 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 sigma8 to be over-estimated by 20% if the cluster selection function is not accounted for correctly. This helps to explain the wide range in sigma8 derived from different techniques, sigma8~0.6-1, and offers a physically motivated explanation for some of the discrepancy. We also identify two further systematics in our analysis: (i) extrapolation of small field-of-view mass measurements to the cluster virial radius and (ii) projection of 3-dimensional masses contained in numerical simulations to the 2-dimensional information that is available from observations. We combine quantitative estimates of these two effects with our model fitting to estimate from the current data that sigma8=0.75+/-0.05(statistical)+/-0.15(systematic), where the systematic error reflects the extrapolation and projection uncertainties. All three systematics (substructure, extrapolation and projection) are fundamental to future cluster-based measurements of sigma8 regardless of the techniques employed. However, 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. 
Graham P. Smith, Alastair C. Edge, Vincent R. Eke, Robert C. Nichol,   Ian Smail, Jean-Paul Kneib