2021A&A...647A..51C

Context. Many galaxy clusters host megaparsec-scale diffuse radio sources called radio halos. Their origin is tightly connected to the processes that lead to the formation of clusters themselves. In order to reveal this connection, statistical studies of the radio properties of clusters combined with their thermal properties are necessary. For this purpose, we selected a sample of galaxy clusters with M₅₀₀≥6x10¹⁴M_☉ and z=0.08-0.33 from the Planck Sunyaev-Zel'dovich catalogue. In Paper I (Cuciti et al., 2021A&A...647A..50C), we presented the radio and X-ray data analysis that we carried out on the clusters of this sample.
Aims. In this paper we exploit the wealth of data presented in Paper I to study the radio properties of the sample, in connection to the mass and dynamical state of clusters.
Methods. 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, the scaling between the radio luminosity of radio halos and the mass of the host clusters, and the role of dynamics in 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 models developed in the framework of turbulent acceleration.
Results. We find 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 show 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. Moreover, we show 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 find that the fraction of radio halos drops from ∼70% in high-mass clusters to ∼35% in the lower mass systems in the sample and we show that this result is in good agreement with the expectations from turbulent re-acceleration models.