Null-hypothesis test: Example with the Fornax galaxy cluster. For each of the 10⁶ measurements of ℜ_⋆ ([ii]), the corresponding distribution of the minimum values of the moving average curves of the mean stellar mass densities is shown (purple histogram). The distribution of the measurements of ℜ_⋆ for the randomised (shuffled) satellite densities (turquoise histogram) is produced by randomly shuffling the density values between the satellites while keeping their spatial positions within Fornax. A more visual comparison is shown in Fig. 6. Using these distributions we calculate that the probability of the randomised distributions resulting in densities as low as or lower than the most probable value measured in Fornax (i.e. ∼ 5.1 × 10⁵ M_⊙ kpc⁻³) is of p_NH​ = ​4.0%. We use the same procedure to calculate these probabilities, p_NH, for Virgo, MW, M31 and certain simulation examples.