Revised statistics of radio halos and the re-acceleration model

Aims. The statistical properties of radio halos can be used to discriminate among the possible models for their origin. Therefore an unbiased and exhaustive investigation in this direction is crucial. Methods. With this goal in mind in this paper we revise the occurrence of radio halos in the redshift range 0-0.4, combining the low redshift (z<0.2) statistical study of XBACs clusters with the NVSS (by Giovannini et al. 1999) with our recent results from the radio follow up of REFLEX and eBCS clusters, the GMRT radio halo survey, at higher redshift (0.2<z<0.4). Results. We find a significant statistical evidence (at 3.7 sigma) of an increase of the fraction of clusters with Radio Halos with the X-ray luminosity (mass) of the parent clusters and show that this increase is in line with statistical calculations based on the re-acceleration scenario. We argue that a fundamental expectation of this scenario is that the probability to have radio halos emitting at hundred MHz is larger than that at GHz frequencies and thus that future radio interferometers operating at low frequencies, such as LOFAR and LWA, should detect a larger number of radio halos with respect to that caught by present GHz observations. We also show that the expected increase of the fraction of clusters with radio halos with the cluster mass as measured with future LOFAR and LWA surveys should be less strong than that in present surveys.