This plot is provided as an illustration of the energetics derived from our simplified version of the model taken from Bîrzan et al. (2004) and Lin & Mohr (2007). The black points are the ratio of integrated AGN energy to the thermal energy of the ICM plotted against cluster mass, assuming the same radio luminosity (
) across all masses. η is the efficiency coefficient and the dashed line is a fit to the points. We speculate that when the energy injection from the AGN reaches 10 per cent of the thermal energy in the core, it can begin to have a significant influence on the ICM and assume this value is reached at TX∼ 2 keV which corresponds to the crossover between the steepened and self-similar-like relations in Sections 3.2 and 3.3. We therefore estimate that η∼ 5.5 on average so that, when in combination with a ∼2.5 × heating enhancement in the central region (Lin & Mohr 2007), EAGN/EICM > 0.1 at 
. Therefore the lower horizontal dotted line represents an estimate of where EAGN/EICM > 0.1 in cluster cores. The upper horizontal dotted line represents an estimate of where EAGN/EICM > 1.0 in cluster cores, which may lead to a significant disruption of the ICM at TX < 1 keV. The shaded regions represent where ICM cooling dominates and where AGN feedback becomes influential, for this simple treatment.
