Correlation between ICM and AGN properties for the galaxy clusters reported in Table 1. Upper left panel: Cavities power as function of the X-ray luminosity inside the cooling radius of each galaxy cluster. The diagonal lines indicate P_cav = L_cool assuming different values for the adiabatic index γ. All the uncertainties are set to 50% for consistency. Upper right panel: Cavity power as a function of the cooling time at 12 kpc from the clusters center. All the uncertainties on the cavity power are set to 50%, while the errors associated with the cooling time are reported in Table 1. Lower left panel: Number of outbursts required to counterbalance the radiative losses of the cooling gas as a function of the cavity energy. The green line represents the best-fit line derived using the BCES orthogonal regression method. All the uncertainties on the cavity energy and cooling luminosity are set to 50%, while the errors associated with the cooling time are reported in Table 1. Lower right panel: Number of outbursts required to counterbalance the radiative losses of the cooling gas as a function of the cavity power. The green line represents the best-fit line derived using the BCES orthogonal regression method. All the uncertainties on the cavity energy, cavity power and cooling luminosity are set to 50%, while the errors associated with the cooling time are reported in Table 1.