Top: Clusters (coloured by gas density) detected at t = 0.75 Myr in simulation L1.0, plotted over the gas density map (grey scale). Middle panel: Momentum loading factor (f_p) distributions (Eq. (9); box and whisker plots) in simulations with different AGN luminosities. Circles highlight outliers beyond 1.5 times the interquartile range covered by the whiskers. The horizontal dashed line highlights f_p = 1, which corresponds to pure momentum driving, for ease of comparison. Bottom panels: Momentum loading factor (f_p) as a function of d_cl (left) and mean gas density (right) in simulations L0.5 (red), L1.0 (green), and L2.0 (blue).