STATE OF ART

The Intra Cluster Medium is an environment characterized by a very complex velocity structure.
Accretion processes of the gaseous and DM components are always present, and continuously induce the ICM to mix and possibily gain vorticity. At any time of observation, the gravitational forces have the leading role in the overall dynamical behaviour; nevertheless, secondary forces (as gradient of pressure, gradient of temperature or shears due to viscosity) act in a subtle way which model the fine structure of the velocity field. To detect and study this tiny signal in the velocity structure some accurate method has to be conceived, with the aim of disentangling the mean velocity field (due to the bulk, so laminar-like, motions) from the local structure (mainly due to non-gravitaional forces). In this very peculiar environment, this issue obliges to conceive some much more accurate method with respect to the ones usually taken into account by terrestrial studies.
So as a very first step in my work, I developed Bepi Tormen's suggestion of building up a 'local mean velocity field', with respect to which evaluate dispersion of velocity. This gave the wonderful finding that also SPH simulations (contrarirly to previous suggestions) do contain turbulence, and can be (or become) object of study concerning turbulence. All that followed is a consequence of this un-expected fact!

Galaxy Clusters simulated with Smoothed Particles Hydrodynamics, even if they are not specifically buit for the purpose of following hydro-dynamical turbulence, are found to host a relevant part of chaotic kinetic energy (from the 1% to the 15% of the total kinetic content). As the SPH scheme at the present day represents the most powerful way to investigate the dynamics of the gaseous component of the Universe during the cosmological evolution, it is also able to furnish a great insight in the knowledges of plasma turbulence over cosmological scales.

The most simple and robust theory predicting the statistical properties of the incompressible turbulence is the one of Kolmogorov & Obhukov (1941): its fundaments are some very simple (surprisingly simple, in truth!) dimensional considerations, but its main conclusion (the prediction of the slope for the power spectrum of the velocity fluctuations) is a very well testable point. Even if the ICM is clearly an environment characterized by a non-stationary density, the time scales involved in the compression processes are larger than the turnover time for the turbulent eddies, so the Kolmogorov-Obhukov theory can be applyed as a reasonable first step. And indeed...it works! The overall shape of the spectrum is consistent with the ~k^-5/3 trend predicted by the model, for more than a decade in the range of spatial scales. Moreover, clear spectral imprints (consistent with energy injections via Kelvin-Helmoltz and Rayleigh-Tayolor modes) are left in the power spectrum of the ICM whenever sufficiently strong accretion proccesses are present.

As the effective viscosity in fluids is the main parameter that rules the onsetting of fluid-dynamical instabilities, and since its tunes the value of the overall Reynolds number, its role in the production of turbulence is extremely relevant. In Dolag et al. 2005 ( 2005astro.ph..7480D ) it is clearly proved out that a proper treatment of the artificial viscosity in SPH increases the final turbulent energy of up to an order of magnitude.

If coupled with an adequate model for the production of MHD waves from chaotic motions, turbulence induced by accretion processes within the ICM is pretty well able to mimic the phenomenology of radio-halos. In paricular, the coupling with the Magneto-Sonic model of electrons reacceleration (Cassano & Brunetti 2004) seems to produce a perfect agreement with the observed frequency, power of emission and rate of occurrence of observed radio-halos.

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