In this paper we investigate the level of hydrostatic equilibrium (HE) in the intra-cluster medium of simulated galaxy clusters, extracted from state-of-the-art cosmological hydrodynamical simulations performed with the Smoothed-Particle-Hydrodynamic code GADGET-3. These simulations include several physical processes, among which stellar and AGN feedback, and have been performed with an improved version of the code that allows for a better description of hydrodynamical instabilities and gas mixing processes. Evaluating the radial balance between the gravitational and hydrodynamical forces, via the gas accelerations generated, we effectively examine the level of HE in every object of the sample, its dependence on the radial distance from the center and on the classification of the cluster in terms of either cool-coreness or dynamical state. We find an average deviation of 10-20% out to the virial radius, with no evident distinction between cool-core and non-cool-core clusters. Instead, we observe a clear separation between regular and disturbed systems, with a more significant deviation from HE for the disturbed objects. The investigation of the bias between the hydrostatic estimate and the total gravitating mass indicates that, on average, this traces very well the deviation from HE, even though individual cases show a more complex picture. Typically, in the radial ranges where mass bias and deviation from HE are substantially different, the gas is characterized by a significant amount of random motions ( 30 per cent), relative to thermal ones. As a general result, the HE-deviation and mass bias, at given interesting distance from the cluster center, are not very sensitive to the temperature inhomogeneities in the gas.

We present an analysis of the properties of the intra-cluster medium (ICM) in an extended set of cosmological hydrodynamical simulations of galaxy clusters and groups performed with the TreePM+SPH GADGET-3 code. Besides a set of non-radiative simulations, we carried out two sets of simulations including radiative cooling, star formation, metal enrichment and feedback from supernovae (SNe), one of which also accounts for the effect of feedback from active galactic nuclei (AGN) resulting from gas accretion onto super-massive black holes. These simulations are analysed with the aim of studying the relative role played by SN and AGN feedback on the general properties of the diffuse hot baryons in galaxy clusters and groups: scaling relations, temperature, entropy and pressure radial profiles, and ICM chemical enrichment. We find that simulations including AGN feedback produce scaling relations between X-ray observable quantities that are in good agreement with observations at all mass scales. Observed pressure profiles are also shown to be quite well reproduced in our radiative simulations, especially when AGN feedback is included. However, our simulations are not able to account for the observed diversity between cool-core and non cool-core clusters, as revealed by X-ray observations: unlike for observations, we find that temperature and entropy profiles of relaxed and unrelaxed clusters are quite similar and resemble more the observed behaviour of non cool-core clusters. As for the pattern of metal enrichment, we find that an enhanced level of iron abundance is produced by AGN feedback with respect to the case of purely SN feedback. As a result, while simulations including AGN produce values of iron abundance in groups in agreement with observations, they over-enrich the ICM in massive clusters. The efficiency of AGN feedback in displacing enriched gas from halos into the intergalactic medium at high redshift also creates a widespread enrichment in the outskirts of clusters and produces profiles of iron abundance whose slope is in better agreement with observations. By analysing the pattern of the relative abundances of silicon and iron and the fraction of metals in the stellar phase, our results clearly show that different sources of energy feedback leave different imprints in the enrichment pattern of the hot ICM and stars. Our results confirm that including AGN feedback goes in the right direction of reconciling simulation predictions and observations for several observational ICM properties. Still a number of important discrepancies highlight that the model still needs to be improved to produce the correct interplay between cooling and feedback in central cluster regions.