  We use three-dimensional high-resolution adaptive-mesh-refinement simulations
to investigate if mechanical feedback from active galactic nucleus jets can
halt a massive cooling flow in a galaxy cluster and give rise to a
self-regulated accretion cycle. We start with a 3 x 10^9MSun black hole at the
centre of a spherical halo with the mass of the Virgo cluster. Initially, all
the baryons are in a hot intracluster medium in hydrostatic equilibrium within
the dark matter's gravitational potential. The black hole accretes the
surrounding gas at the Bondi rate and a fraction of the accretion power is
returned into the intracluster medium mechanically through the production of
jets. The accretion, initially slow (~0.0002MSun/yr), becomes catastrophic, as
the gas cools and condenses in the dark matter's potential. Therefore, it
cannot prevent the cooling catastrophe at the centre of the cluster. However,
after this rapid phase, where the accretion rate reaches a peak of ~0.2MSun/yr,
the cavities inflated by the jets become highly turbulent. The turbulent mixing
of the shock-heated gas with the rest of the intracluster medium puts a quick
end to this short-lived rapid-growth phase. After dropping by almost two orders
of magnitudes, the black hole accretion rate stabilises at ~0.006MSun/yr,
without significant variations for several billions of years, indicating that a
self-regulated steady-state has been reached. This accretion rate corresponds
to a negligible increase of the black hole mass over the age of the Universe,
but is sufficient to create a quasi-equilibrium state in the cluster core.
