a, The fraction of quiescent satellites around central galaxies whose black holes have injected, relatively to their mass, more (red) and less (blue) total energy. b, Similarly, the same separation but in this case considering only the kinetic energy injected by the black holes. In both cases, the amplitude of the modulation is stronger when the total (a) and kinetic (b) energy released by the central black holes increase. Similar to Extended Data Fig. 4, panel c shows how the signal in IllustrisTNG depends on the relative mass of the central black hole, being stronger for more over-massive black hole galaxies. d, The observed signal in IllustrisTNG (red) and the de-projected signal (blue) using the underlying 3D satellite distribution. We note that in d we did not impose any cut in central stellar mass and therefore absolute values are different from the other panels. Error bars and shaded areas represent 1σ confidence intervals, and solid lines are the best-fitting solutions.