Compressible turbulence in galaxy clusters: physics and stochastic particle re-acceleration

Abstract

We attempt to explain the non-thermal emission arising from galaxy clusters as a result of the re-acceleration of electrons by compressible turbulence induced by cluster mergers. On the basis of the available observational facts we put forward a simplified model of turbulence in clusters of galaxies focusing our attention on the compressible motions. In our model intracluster medium (ICM) is represented by a high-beta plasma in which turbulent motions are driven at large scales. The corresponding injection velocities are higher than the Alfvén velocity. As a result, the turbulence is approximately isotropic up to the scale at which the turbulent velocity gets comparable with the Alfvén velocity. These motions are most important for the energetic particle acceleration, but at the same time they are subjected to most of the plasma damping. Under the hypothesis that turbulence in the ICM is highly super-Alfvénic the magnetic field is passively advected and the field lines are bended on scales smaller than that of the classical, unmagnetized, ion–ion mean free path. This affects ion diffusion and the strength of the effective viscosity. Under these conditions the bulk of turbulence in hot (5–10 keV temperature) galaxy clusters is likely to be dissipated at collisionless scales via resonant coupling with thermal and fast particles. We use collisionless physics to derive the amplitude of the different components of the energy of the compressible modes, and review and extend the treatment of plasma damping in the ICM. We calculate the acceleration of both protons and electrons taking into account both transit time damping acceleration and non-resonant acceleration by large-scale compressions. We find that relativistic electrons can be re-accelerated in the ICM up to energies of several GeV provided that the rms velocity of the compressible turbulent-eddies is is the sound speed in the ICM. We find that under typical conditions ≈2–5 per cent of the energy flux of the cascading of compressible motions injected at large scales goes into the acceleration of fast particles and that this may explain the observed non-thermal emission from merging galaxy clusters.