  We present the first implementation of Active Galactic Nuclei (AGN) feedback
in the form of momentum driven jets in an Adaptive Mesh Refinement (AMR)
cosmological resimulation of a galaxy cluster. The jets are powered by gas
accretion onto Super Massive Black Holes (SMBHs) which also grow by mergers.
Throughout its formation, the cluster experiences different dynamical states:
both a morphologically perturbed epoch at early times and a relaxed state at
late times allowing us to study the different modes of BH growth and associated
AGN jet feedback. BHs accrete gas efficiently at high redshift (z>2),
significantly pre-heating proto-cluster halos. Gas-rich mergers at high
redshift also fuel strong, episodic jet activity, which transports gas from the
proto-cluster core to its outer regions. At later times, while the cluster
relaxes, the supply of cold gas onto the BHs is reduced leading to lower jet
activity. Although the cluster is still heated by this activity as sound waves
propagate from the core to the virial radius, the jets inefficiently
redistribute gas outwards and a small cooling flow develops, along with
low-pressure cavities similar to those detected in X-ray observations. Overall,
our jet implementation of AGN feedback quenches star formation quite
efficiently, reducing the stellar content of the central cluster galaxy by a
factor 3 compared to the no AGN case. It also dramatically alters the shape of
the gas density profile, bringing it in close agreement with the beta model
favoured by observations, producing quite an isothermal galaxy cluster for
gigayears in the process. However, it still falls short in matching the lower
than Universal baryon fractions which seem to be commonplace in observed galaxy
clusters.
