  Observed clusters of galaxies essentially come in two flavors: non cool core
clusters characterized by an isothermal temperature profile and a central
entropy floor, and cool-core clusters where temperature and entropy in the
central region are increasing with radius. Using cosmological resimulations of
a galaxy cluster, we study the evolution of its intracluster medium (ICM) gas
properties, and through them we assess the effect of different (sub-grid)
modelling of the physical processes at play, namely gas cooling, star
formation, feedback from supernovae and active galactic nuclei (AGN). More
specifically we show that AGN feedback plays a major role in the pre-heating of
the proto-cluster as it prevents a high concentration of mass from collecting
in the center of the future galaxy cluster at early times. However, AGN
activity during the cluster's later evolution is also required to regulate the
mass flow into its core and prevent runaway star formation in the central
galaxy. Whereas the energy deposited by supernovae alone is insufficient to
prevent an overcooling catastrophe, supernovae are responsible for spreading a
large amount of metals at high redshift, enhancing the cooling efficiency of
the ICM gas. As the AGN energy release depends on the accretion rate of gas
onto its central black hole engine, the AGN responds to this supernova enhanced
gas accretion by injecting more energy into the surrounding gas, and as a
result increases the amount of early pre-heating. We demonstrate that the
interaction between an AGN jet and the ICM gas that regulates the growth of the
AGN's BH, can naturally produce cool core clusters if we neglect metals.
However, as soon as metals are allowed to contribute to the radiative cooling,
only the non cool core solution is produced.
