Cool cores of galaxy clusters are thought to be heated by low-power active galactic nuclei ( AGN ) , whose accretion is regulated by feedback .
However , the interaction between the hot gas ejected by the AGN and the ambient intracluster medium is extremely difficult to simulate , as it involves a wide range of spatial scales and gas that is Rayleigh-Taylor ( RT ) unstable .
Here we use a subgrid model for RT-driven turbulence to overcome these problems and present the first observationally-consistent hydrodynamical simulations of AGN self-regulation in galaxy clusters .
For a wide range of parameter choices the cluster in our three-dimensional simulations regulates itself for at least several 10 ^ { 9 } years .
Heating balances cooling through a string of outbreaks with a typical recurrence time of \approx 80 Myrs , a timescale that depends only on the global cluster properties .