Feedback in active galactic nucleus heating of galaxy clusters

One of the challenges that models of active galactic nucleus (AGN) heating of the intracluster medium (ICM) face is to explain how the mechanical luminosity of the AGN is tuned to the radiative losses of the ICM. Here we implement a simple one-dimensional model of a feedback mechanism that links the luminosity of the AGN to the accretion rate. We demonstrate how this simple feedback mechanism leads to a quasi - steady state for a broad range of parameters. Moreover, within this feedback model, we investigate the effect of thermal conduction and find that its relative importance depends strongly on the cluster mass.