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Giant radio halos are Mpc-scale diffuse radio sources associated with thecentral regions of galaxy clusters. The most promising scenario to explain theorigin of these sources is that of turbulent re-acceleration, in which MeVelectrons injected throughout the formation history of galaxy clusters areaccelerated to higher energies by turbulent motions mostly induced by clustermergers. In this Letter, we use the amplitude of density fluctuations in theintracluster medium as a proxy for the turbulent velocity and apply thistechnique to a sample of 51 clusters with available radio data. Our resultsindicate a segregation in the turbulent velocity of radio halo and radio quietclusters, with the turbulent velocity of the former being on average higher byabout a factor of two. The velocity dispersion recovered with this techniquecorrelates with the measured radio power through the relation $P_{\rmradio}\propto\sigma_v^{3.3\pm0.7}$, which implies that the radio power isnearly proportional to the turbulent energy rate. Our results provide anobservational confirmation of a key prediction of the turbulent re-accelerationmodel and possibly shed light on the origin of radio halos.

On the connection between turbulent motions and particle acceleration in galaxy clusters