  We study the effects of radiative cooling, star formation and stellar
feedback on the properties and evolution of galaxy clusters using
high-resolution Adaptive Mesh Refinement N-body+gasdynamics simulations of
clusters forming in the LCDM universe. Cooling leads to the condensation of gas
in the inner regions of clusters, which in turn leads to steepening of the dark
matter profile. The cooling gas is replaced by the higher-entropy gas from the
outer regions, which raises the entropy and temperature of gas in the cluster
core. The magnitude of these effects is likely overestimated in the current
simulations because they suffer from the overcooling problem: a much larger
fraction of baryons is in the form of cold gas and stars than is observed. We
find that the thermal stellar feedback alone does not remedy this problem.
Additional ad-hoc preheating can lower the amount of cold gas but a simple
uniform preheating results in incorrect star formation history, as it delays
the bulk of star formation until z<1. Our analysis shows that the overcooling
in a cluster as a whole is really the overcooling in the central galaxy and its
progenitors at high redshifts. This indicates that an additional heating
mechanism that can continuously heat the gas in the cluster core is required to
reproduce the observed cluster properties. Energy injection by the Active
Galactic Nuclei, which may provide such heating, may thus be an important
missing ingredient in the current theoretical models of cluster formation.
