  Non-thermal motions in the intra-cluster medium (ICM) are believed to play a
non-negligible role in the pressure support to the total gravitating mass of
galaxy clusters. Future X-ray missions, such as ASTRO-H and ATHENA, will
eventually allow us to directly detect the signature of these motions from
high-resolution spectra of the ICM. In this paper, we present a study on a set
of clusters extracted from a cosmological hydrodynamical simulation, devoted to
explore the role of non-thermal velocity amplitude in characterising the
cluster state and the relation between observed X-ray properties. In order to
reach this goal, we apply the X-ray virtual telescope PHOX to generate
synthetic observations of the simulated clusters with both Chandra and ATHENA,
the latter used as an example for the performance of very high-resolution X-ray
telescopes. From Chandra spectra we extract global properties, e.g. luminosity
and temperature, and from ATHENA spectra we estimate the gas velocity
dispersion along the line of sight from the broadening of heavy-ion emission
lines (e.g. Fe). We further extend the analysis to the relation between
non-thermal velocity dispersion of the gas and the L_X-T scaling law for the
simulated clusters. Interestingly, we find a clear dependence of slope and
scatter on the selection criterion for the clusters, based on the level of
significance of non-thermal motions. Namely, the scatter in the relation is
significantly reduced by the exclusion of the clusters, for which we estimate
the highest turbulent velocities. Such velocity diagnostics appears therefore
as a promising independent way to identify disturbed clusters, in addition to
the commonly used morphological inspection.
