On the evolution of giant radio halos and their connection with cluster mergers

Giant radio halos are diffuse, Mpc-scale, synchrotron sources located in the central regions of galaxy clusters and provide the most relevant example of cluster non-thermal activity. Radio and X-ray surveys allow to investigate the statistics of halos and may contribute to constrain their origin and evolution. We investigate the distribution of clusters in the plane X-ray (thermal, L_X) vs synchrotron (P_{1.4})luminosity, where clusters hosting giant radio halos trace the P_{1.4}--L_X correlation and clusters without radio halos populate a region that is well separated from that spanned by the above correlation. The connection between radio halos and cluster mergers suggests that the cluster Mpc-scale synchrotron emission is amplified during these mergers and then suppressed when clusters become more dynamically relaxed. In this context, by analysing the distribution in the P_{1.4}--L_X plane of clusters from X-ray selected samples with adequate radio follow up, we constrain the typical time-scale of evolution of diffuse radio emission in clusters and discuss the implications for the origin of radio halos. We conclude that cluster synchrotron emission is suppressed (and amplified) in a time-scale significantly smaller than 1 Gyr. We show that this constraint appears difficult to reconcile with the hypothesis that the halo's radio power is suppressed due to dissipation of magnetic field in galaxy clusters. On the other hand, in agreement with models where turbulent acceleration plays a role, present constraints suggest that relativistic electrons are accelerated in Mpc-scale regions, in connection with cluster mergers and for a time-interval of about 1 Gyr, and then they cool in a relatively small time-scale, when the hosting cluster becomes more dynamically relaxed.