Massive and refined. II. The statistical properties of turbulent motions in massive galaxy clusters with high spatial resolution

We study the properties of chaotic motions in the intra cluster medium using a set of 20 galaxy clusters simulated with large dynamical range, using the adaptive mesh refinement code ENZO. The adopted setup allows us to study the spectral and spatial properties of turbulent motions in galaxy clusters with unprecedented detail, achieving an maximum available Reynolds number of the order of R_e ~ 500-1000 for the largest eddies. We investigated the correlations between the energy of these motions in the intra cluster medium and the dynamical state of the host systems. We find that the statistical properties of turbulent motions and their evolution with time imply that major merger events are responsible for the injection of the bulk of turbulent kinetic energy into the cluster. Turbulence is found to account for ~20-30 per cent of the thermal energy in merging clusters, and ~5 per cent in relaxed clusters. We compare the energies of turbulence and motions in our simulated clusters with upper-limits for real nearby clusters derived from XMM-Newton data. When turbulent motions are compared on the same spatial scales, the data from simulations are well within the range presently allowed by observations. Finally, we comment on the possibility that turbulence may accelerate relativistic particles leading to the formation of giant radio halos in turbulent (merging) clusters. On the basis of our simulations, we confirm the conclusions of previous semi-analytical studies that the fraction of turbulent clusters appears to be consistent with that of clusters hosting radio halos.