Simulating galaxy clusters -- I. Thermal and chemical properties of the   intra-cluster medium
  We have performed a series of N-body/hydrodynamical (TreeSPH) simulations of clusters and groups of galaxies, selected from cosmological N-body simulations within a $\Lambda$CDM framework: these objects have been re-simulated at higher resolution to $z$=0, in order to follow also the dynamical, thermal and chemical input on to the ICM from stellar populations within galaxies. The simulations include metal dependent radiative cooling, star formation according to different IMFs, energy feedback as strong starburst-driven galactic super-winds, chemical evolution with non-instantaneous recycling of gas and heavy elements, effects of a meta-galactic UV field and thermal conduction in the ICM. In this Paper I of a series of three, we derive results, mainly at $z=0$, on the temperature and entropy profiles of the ICM, its X-ray luminosity, the cluster cold components (cold fraction as well as mass--to--light ratio) and the metal distribution between ICM and stars.   In general, models with efficient super-winds, along with a top-heavy stellar IMF, are able to reproduce fairly well the observed $L_X-T$ relation, the entropy profiles and the cold fraction. Observed radial ICM temperature profiles can be matched, except for the gradual decline in temperature inside of $r\sim$~0.1$R_{\rm{vir}}$. Metal enrichment of the ICM gives rise to somewhat steep inner iron gradients; yet, the global level of enrichment compares well to observational estimates after correcting for the stars formed at late times at the base of the cooling flows; also the metal partition between stars and ICM gets into good agreement with observations. 
A.D. Romeo (1,3), J. Sommer-Larsen (1), L. Portinari (1,4), V.   Antonuccio-Delogu (2) ((1) Copenhagen; (2) INAF-Catania; (3...