The impact of numerical viscosity in SPH simulations of galaxy clusters
  A SPH code employing a time-dependent artificial viscosity scheme is used to
construct a large set of N-body/SPH cluster simulations for studying the impact
of artificial viscosity on the thermodynamics of the ICM and its velocity field
statistical properties. Spectral properties of the gas velocity field are
investigated by measuring for the simulated clusters the velocity power
spectrum E(k). The longitudinal component E_c(k) exhibits over a limited range
a Kolgomorov-like scaling k^{-5/3}, whilst the solenoidal power spectrum
component E_s(k) is strongly influenced by numerical resolution effects. The
dependence of the spectra E(k) on dissipative effects is found to be
significant at length scales 100-300Kpc, with viscous damping of the velocities
being less pronounced in those runs with the lowest artificial viscosity. The
turbulent energy density radial profile E_{turb}(r) is strongly affected by the
numerical viscosity scheme adopted in the simulations, with the
turbulent-to-total energy density ratios being higher in the runs with the
lowest artificial viscosity settings and lying in the range between a few
percent and ~10%. These values are in accord with the corresponding ratios
extracted from previous cluster simulations realized using mesh-based codes. At
large cluster radii, the mass correction terms to the hydrostatic equilibrium
equation are little affected by the numerical viscosity of the simulations,
showing that the X-ray mass bias is already estimated well in standard SPH
simulations. Finally, simulations in which the gas can cool radiatively are
characterized by the presence in the cluster inner regions of high levels of
turbulence, generated by the interaction of the compact cool gas core with the
ambient medium.
