  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.
