Bubbles as tracers of heat input to cooling flows

We examine the distribution of injected energy in three-dimensional, adaptive-grid simulations of the heating of cooling flows. We show that less than 10 per cent of the injected energy goes into bubbles. Consequently, the energy input from the nucleus is underestimated by a factor of order 6 when it is taken to be given by PV gamma/(gamma - 1), where P and V are the pressure and volume of the bubble, and gamma is the ratio of principal specific heats.