Mass-matched null bootstrap test. Each panel here corresponds to the second vertical panel of each column in Figs. 2 and 3. The control samples matched in M_200m (hatched regions for the (16 − 84)% percentiles, dashed lines for the medians) show the expected distributions under the null hypothesis of no Γ_200m dependence. The solid lines, along with the shaded regions, reproduce the original results (red: low-Γ_200m; green: high-Γ_200m). The separation of the solid lines beyond the hatched regions proves that the observed effects cannot be explained solely by the mass distribution of the low- and high-Γ_200m subsamples.