Active Galactic Nucleus Feedback and Entropy Injection in Galaxy Cluster Cores

We make the first estimate of non-gravitational energy profiles in galaxy cluster cores (and beyond) based on observational data. Comparing the observed entropy profiles within r ₅₀₀, from the Representative XMM-Newton Cluster Structure Survey to simulated base entropy profiles without feedback from both adaptive mesh refinement (AMR) and smoothed particle hydrodynamic (SPH) non-radiative simulations, we estimate the amount of additional non-gravitational energy, E _ICM, contained in the intracluster medium (ICM), as well as the total energy feedback, E _Feedback, from active galactic nuclei (AGNs; the central AGNs in most cases) into the clusters. The total feedback energy scales with the mean spectroscopic temperature as E_Feedback \propto T_sp^{2.52 +/- 0.08} and E_Feedback \propto T_sp^{2.17 +/- 0.11} for the SPH and AMR baseline profiles. The mean non-gravitational energy per particle within r ₅₀₀ remaining in the ICM after energy lost during cooling is epsilon_ICM = 2.8 ± 0.8 keV for the SPH theoretical relation and epsilon_ICM = 1.7 ± 0.9 keV for the AMR theoretical relation. We use the NRAO/VLA Sky Survey source catalog to determine the radio luminosity, L_R , at 1.4 GHz of the central source(s) of our sample. For T _sp > 3 keV, the E _Feedback correlates with L_R , although with different normalization for cool-core and non-cool-core clusters. We show that AGNs could provide a significant portion of the feedback.