Size of the sphere of influence of the simulated AGNs in the centres of groups and clusters. Cool-core clusters are shown in blue, and hot-core clusters are shown in orange. Observational data from Rafferty et al. (2006) and Eckert et al. (2021) is shown with error bars at the 1σ level. Left panel: Size vs power. Shown is the maximum size or distance of cavities in observed groups and clusters versus cavity power, whereas for the simulation we show the ‘black hole sphere of influence’ versus the AGN energy injection. The dark blue solid line shows the power law fit described by Equation (9), and the dashed lines represent ±1σ confidence intervals. Right panel: Same as the left panel, but plotting versus M_500c in the X-axis.