With the aim to investigate the statistical properties and the connection between thermal and non-thermal properties of the ICM in galaxy clusters, we have developed a statistical magneto-turbulent model which describes, at the same time, the evolution of the thermal and non-thermal emission from galaxy clusters. In particular, starting from the cosmological evolution of clusters, we follow cluster. mergers, calculate the spectrum of the magnetosonic waves generated in the ICM during these mergers, the evolution of relativistic electrons and the resulting synchrotron and Inverse Compton spectra. We show that the broad band (radio and hard x-ray) non-thermal spectral properties of galaxy clusters can be well accounted for by our model for viable values of the parameters (here we adopt a EdS cosmology).

• R. CASSANO(Dipartimento di Astronomia, Univ. di Bologna/Istituto di Radioastronomia del CNR)
• G. BRUNETTI(Istituto di Radioastronomia del CNR)