We present numerical simulations of galaxy clusters with stochastic heating from active galactic nuclei (AGN) that are able to reproduce the observed entropy and temperature profiles of non-cool-core (NCC) clusters. Our study uses N-body hydrodynamical simulations to investigate how star formation, metal production, black hole accretion and the associated feedback from supernovae and AGN heat and enrich diffuse gas in galaxy clusters. We assess how different implementations of these processes affect the thermal and chemical properties of the intracluster medium (ICM), using high-quality X-ray observations of local clusters to constrain our models. For the purposes of this study we have resimulated a sample of 25 massive galaxy clusters extracted from the Millennium Simulation. Sub-grid physics is handled using a semi-analytic model of galaxy formation, thus guaranteeing that the source of feedback in our simulations is a population of galaxies with realistic properties. We find that supernova feedback has no effect on the entropy and metallicity structure of the ICM, regardless of the method used to inject energy and metals into the diffuse gas. By including AGN feedback, we are able to explain the observed entropy and metallicity profiles of clusters, as well as the X-ray luminosity-temperature scaling relation for NCC systems. A stochastic model of AGN energy injection motivated by anisotropic jet heating - presented for the first time here - is crucial for this success. With the addition of metal-dependent radiative cooling, our model is also able to produce CC clusters, without overcooling of gas in dense, central regions.

23 pages, accepted by MNRAS. Some changes in response to referee's comments. New figures 22 & 23