Time variability of active galactic nuclei and heating of cooling flows

There is increasing evidence that active galactic nucleus (AGN) feedback is important in the energetics of cooling flows in galaxies and galaxy clusters. It is possible that, in most cooling-flow clusters, radiative losses from the thermal plasma are balanced, over the cluster lifetime, by mechanical heating from the central radio source. We investigate the implications of the variability of AGN mechanical luminosity L_m on observations of cooling flows and radio galaxies in general. It is natural to assume that l= ln (L_m/L_X) is a Gaussian process. Then L_m will be lognormally distributed at fixed cooling luminosity L_X, and the variance in a measure of L_m will increase with the time resolution of the measure. We test the consistency of these predictions with existing data for cooling flows and radio galaxies. These tests hinge on the power spectrum P(ω) of the Gaussian process l(t). General considerations suggest that P is a power law P~1/ω^β. Long-term monitoring of Seyfert galaxies combined with estimates of the duty cycle of quasars imply that β~= 1, which corresponds to flicker noise. The power spectra of microquasars have similar values of β. We combine a sample of sources in cooling flows that have cavities with the assumption that the average mechanical luminosity of the AGN equals the cooling flow's X-ray luminosity. Given that the mechanical luminosities are characterized by flicker noise, we find that their spectral amplitudes ωP(ω) lie between the estimated amplitudes of quasars and the measured values for the radio luminosities of microquasars. The model, together with the observation that powerful radio galaxies lie within a narrow range in optical luminosity, predicts the luminosity function of radio galaxies. Both the shape and the normalization of the predicted function are in agreement with observations. Forthcoming radio surveys will test the prediction that the luminosity function turns over at about the smallest luminosities so far probed.