Many galaxy clusters host Mpc scale diffuse radio sources called radio halos. Their origin is connected to the processes that lead to the formation of clusters themselves. In order to unveil this connection, statistical studies of radio halos are necessary. We selected a sample of galaxy clusters with M500>6e14Msun and z=0.08-0.33 from the Planck SZ catalogue. In paper I, we presented the radio and X-ray data analysis that we carried out on these clusters. Here, we study the radio properties of the sample, in connection to the mass and dynamical state of clusters. We used the dynamical information derived from the X-ray data to assess the role of mergers in the origin of radio halos. We studied the distribution of clusters in the radio power-mass diagram and the role of dynamics on the radio luminosity and emissivity of radio halos. We measured the occurrence of radio halos as a function of the cluster mass and we compared it with the expectations of turbulent acceleration models. We found that more than the 90% of radio halos are in merging clusters and that their radio power correlates with the mass of the host clusters. The correlation shows a large dispersion. Interestingly, we showed that cluster dynamics contributes significantly to this dispersion with more disturbed clusters being more radio luminous. Clusters without radio halos are generally relaxed and the upper limits to their diffuse emission lie below the correlation. We showed that the radio emissivity of clusters exhibits an apparent bimodality, with the emissivity of radio halos being at least 5 times larger than the non-emission associated with more relaxed clusters. We found that the fraction of radio halos drops from ~70% in high mass clusters to ~35% in the lower mass systems of the sample and we showed that this result is in good agreement with the expectations from turbulent re-acceleration models.
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