We calculate the probability to form giant radio halos (~1 Mpc size) as a function of the mass of the host clusters by using a Statistical Magneto-Turbulent Model (Cassano & Brunetti, these proceedings). We show that the expectations of this model are in good agreement with the observations for viable values of the parameters. In particular, the abrupt increase of the probability to find radio halos in the more massive galaxy clusters (M ≳ 2 X 1015M⊙) can be well reproduced. We calculate the evolution with redshift of such a probability and find that giant radio halos can be powered by particle acceleration due to MHD turbulence up to z~0.5 in a ACDM cosmology. Finally, we calculate the expected Luminosity Functions of radio halos (RHLFs). At variance with previous studies, the shape of our RHLFs is characterized by the presence of a cut-off at low synchrotron powers which reflects the inefficiency of particle acceleration in the case of less massive galaxy clusters.

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