Measurement examples of the transition radius ℜ_⋆: the Fornax-type cluster (top panel) from TNG50, and the Fornax cluster (bottom panel). From a total of 10⁶ sub-sample realisations and the 10⁶ moving average curves of the satellite mean stellar mass densities, we show here 200 (blue curves). Each curve is calculated with Eq. (17) with a sub-sample of $n_{\mathrm{sub},\mathrm{sat}}=n_{\mathrm{sat}}-\sqrt{n_{\mathrm{sat}}}$ satellites from a total of n_sat. The neighbour number is a random number between $q=2\sqrt{n_{\mathrm{sub}}}$ and $4\sqrt{n_{\mathrm{sub}}}$. The first method of measurement (ℜ_⋆[i]) uses Eq. (19) and is shown with vertical dot-dashed blue lines and their 1-sigma confidence region. The second method (ℜ_⋆[ii]) uses Eq. (20) and is shown with vertical dot dash orange lines and their 1-sigma confidence region. Bootstrapping reveals a small scatter in the moving average profiles, due to the satellite-to-satellite sub-sample variations and the different number of neighbours used. Lastly, we also show the moving average after first randomising (shuffling) the mean mass densities of the satellites, which erases the signature in the satellite population (see Null-hypothesis test in Sect. 5.2).