2009MNRAS.395.2317P

We have constructed an analytical model of active galactic nuclei (AGN) feedback and studied its implications for elliptical galaxies and galaxy clusters. The results show that momentum injection above a critical value will eject material from low-mass elliptical galaxies, and leads to an X-ray luminosity, L_X, that is ∝ σ^8–10, depending on the AGN fuelling mechanism, where σ is the velocity dispersion of the hot gas. This result agrees well with both observations and semi-analytic models. In more massive ellipticals and clusters, AGN outflows quickly become buoyancy dominated. This necessarily means that heating by a central cluster AGN redistributes the intracluster medium (ICM) such that the mass of hot gas, within the cooling radius, should be ∝ L_X(< r_cool)/[g(r_cool)σ], where g(r_cool) is the gravitational acceleration at the cooling radius. This prediction is confirmed using observations of seven clusters. The same mechanism also defines a critical ICM cooling time of ∼0.5Gyr, which is in reasonable agreement with recent observations showing that star formation and AGN activity are triggered below a universal cooling time threshold.