We study the substructure statistics of a representative sample of galaxy clusters by means of two currently popular substructure characterisation methods, power ratios and centroid shifts. We use the 31 clusters from the REXCESS sample, compiled from the southern ROSAT All-Sky cluster survey REFLEX with a morphologically unbiased selection in X-ray luminosity and redshift, all of which have been reobserved with XMM-Newton. We investigate the uncertainties of the substructure parameters and examine the dependence of the results on projection effects, finding that the uncertainties of the parameters can be quite substantial. Thus while the quantification of the dynamical state of individual clusters with these parameters should be treated with extreme caution, these substructure measures provide powerful statistical tools to characterise trends of properties in large cluster samples. The centre shift parameter, w, is found to be more sensitive in general. For the REXCESS sample neither the occurence of substructure nor the presence of cool cores depends on cluster mass. There is a significant anti-correlation between the existence of substantial substructure and cool cores. The simulated clusters show on average larger substructure parameters than the observed clusters, a trend that is traced to the fact that cool regions are more pronounced in the simulated clusters, leading to stronger substructure measures in merging clusters and clusters with offset cores. Moreover, the frequency of cool regions is higher in the simulations than in the observations, implying that the description of the physical processes shaping cluster formation in the simulations requires further improvement.
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