Central gas entropy excess as a direct evidence for AGN feedback in galaxy groups and clusters

By analyzing Chandra X-ray data of a sample of 21 galaxy groups and 19 galaxy clusters, we find that in 31 sample systems there exists a significant central ($R^{<}_{\sim} 10h_{71}^{-1}$ kpc) gas entropy excess ($\Delta K_{0}$), which corresponds to $\simeq 0.1-0.5$ keV per gas particle, beyond the power-law model that best fits the radial entropy profile of outer regions. We also find a distinct correlation between the central entropy excess $\Delta K_{0}$ and $K$-band luminosity $L_{K}$ of the central dominating galaxies (CDGs), which is scaled as $\Delta K_{0} \propto L_{K}^{1.6\pm0.4}$, where $L_{K}$ is tightly associated with the mass of the supermassive black hole hosted in the CDG. In fact, if an effective mass-to-energy conversion-efficiency of 0.02 is assumed for the accretion process, the cumulative AGN feedback $E^{\rm AGN}_{\rm feedback} \simeq \eta M_{\rm BH}c^{2}$ yields an extra heating of $\simeq 0.5-17.0$ keV per particle, which is sufficient to explain the central entropy excess. In most cases the AGN contribution can compensate the radiative loss of the X-ray gas within the cooling radius ($\simeq 0.002-2.2$ keV per particle), and apparently exceeds the energy required to deviate the scaling relations from the self-similar predictions ($\simeq 0.2-1.0$ keV per particle). In contrast to the AGN feedback, the extra heating provided by supernova explosions accounts for $\simeq 0.01-0.08$ keV per particle in groups and is almost negligible in clusters. Therefore, the observed correlation between $\Delta K_{0}$ and $L_{K}$ can be considered as a direct evidence for AGN feedback in galaxy groups and clusters.