Cooling Flows as a Calorimeter of AGN Mechanical Power

The assumption that radiative cooling of gas in the centers of galaxy clusters is approximately balanced by energy input from a central supermassive black hole implies that the observed X-ray luminosity of the cooling flow region sets a lower limit on AGN mechanical power. The conversion efficiency of AGN mechanical power into gas heating is uncertain, but we argue that it can be high even in the absence of strong shocks. These arguments inevitably lead to the conclusion that the time averaged mechanical power of AGNs in cooling flows is much higher than the presently observed bolometric luminosity of these objects. The energy balance between cooling losses and AGN mechanical power requires some feedback mechanism. We consider a toy model in which the accretion rate onto a black hole is set by the classic Bondi formula. Application of this model to the best studied case of M87 suggests that accretion proceeds at approximately the Bondi rate down to a few gravitational radii with most of the power (at the level of a few percent of the rest mass) carried away by an outflow.