We use gravitational lens models and X-ray spectral analysis of ten X-ray luminous galaxy clusters at z \simeq 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 \mathrel { \sigma _ { 8 } } to be over-estimated by 20 % if the cluster selection function is not accounted for correctly .
This helps to explain the wide range in \mathrel { \sigma _ { 8 } } derived from different techniques , \mathrel { \sigma _ { 8 } } \sim 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 \mathrel { \sigma _ { 8 } } = 0.75 \pm 0.05 ( { statistical } ) \pm 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 \mathrel { \sigma _ { 8 } } 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 .