The properties of the central galaxies of clusters are tightly connected to their parent clusters, an aspect underlined by our findings: galaxy clusters efficiently provide gas for their central galaxy to fuel its central black hole.

Other cluster galaxies, not at the bottom of the potential well, are not affected. It is tempting to identify this additional gas supply for BCGs with the cooling flows observed in massive clusters and thus speculate that the heating due to the AGN activity balances the cooling rate, providing a solution to the cooling problem. However, we find no correlation of the radio-loud fraction with cluster velocity dispersion, whereas the cluster cooling rate (as indicated by their X-ray luminosity) scales steeply with it. While the AGN activity provides enough heating to balance cooling in isolated ellipticals (as demonstrated by [3]), the factor of 10 increase in radio-AGN activity in BCGs might be enough to balance cooling in galaxy groups and poor clusters, but not in the most massive clusters (which would require factors of 10-100). Thus, the increased radio-AGN activity of BCGs cannot account for (all) the heating needed to balance cooling flows in clusters.

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