Revised statistics of radio halos and the reacceleration 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 of these properties 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 the X-ray-brightest Abell-type clusters (XBACs) with the NRAO VLA Sky Survey (NVSS, by Giovannini et al. 1999) with our recent results from the radio followup of the ROSAT-ESO Flux-Limited X-Ray (REFLEX) clusters and extended ROSAT Brightest Cluster Sample (eBCS), i.e., the Giant Metrewave Radio Telescope (GMRT) radio halo survey, at higher redshift (0.2 < z < 0.4). Results. We find 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 reacceleration scenario. We argue that a fundamental expectation of this scenario is that the probability of having radio halos emitting at hundred MHz is larger than the probability at GHz frequencies, and thus future radio interferometers operating at low frequencies, such as the Low Frequency Array (LOFAR) and the Long Wavelength Array (LWA), should detect a larger number of radio halos with respect to those 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 the increase in present surveys.