Can Supermassive Black Holes Sufficiently Heat Cool Cores of Galaxy Clusters?

Activities of a supermassive black hole or active galactic nucleus in the central galaxy of a cluster of galaxies have been promising candidates for heating sources of cool cluster cores. We estimate the masses of black holes using known correlations between the mass of a black hole and the velocity dispersion or the luminosity of the host galaxy. We find that the masses are \~10^8-9 M_sun and the central X-ray luminosities of the host clusters (``the strength of the cooling flow'') are well below the Eddington luminosities. However, we do not find a correlation between the mass and the central X-ray luminosity of the host cluster. If the heating is stable, this seems to contradict a simple expectation if supermassive black holes are the main heating source of a cluster core. Moreover, if we assume a canonical energy conversion rate (10%), black holes alone are unable to sufficiently heat the clusters with strong centrally peaked X-ray emission (``massive cooling flows'') over the lifetime of cluster cores. These results may indicate that massive cooling flows are a transient phenomenon, which may be because the black holes are activated periodically. Alternatively, in the massive cooling flow clusters, the energy conversion rate may be larger than 10%, that is, the black holes may be Kerr black holes.