Relation between the Einasto shape parameter α_Einasto and the DM self-interaction cross section σ/m for several sets of numerical simulations with varying σ/m (Robertson et al. 2021). The left-hand panel shows the fitted mean values of α in the relaxed subsample for the CDM and SIDM cases, compared to the average value in the full X-COP sample (ALL) and in the regular X-ray subsample. In the right-hand panel, we show the dependence of α on σ/m. The solid blue line shows a fit to the relation with a power law, whereas the dashed vertical line indicates the average value in CDM. The black line and gray shaded area show the mean value of α_Einasto and the 1σ uncertainty in the regular X-COP subsample, with the corresponding constraints on σ/m.