On the connection between turbulent motions and particle acceleration in
  galaxy clusters
  Giant radio halos are Mpc-scale diffuse radio sources associated with the
central regions of galaxy clusters. The most promising scenario to explain the
origin of these sources is that of turbulent re-acceleration, in which MeV
electrons injected throughout the formation history of galaxy clusters are
accelerated to higher energies by turbulent motions mostly induced by cluster
mergers. In this Letter, we use the amplitude of density fluctuations in the
intracluster medium as a proxy for the turbulent velocity and apply this
technique to a sample of 51 clusters with available radio data. Our results
indicate a segregation in the turbulent velocity of radio halo and radio quiet
clusters, with the turbulent velocity of the former being on average higher by
about a factor of two. The velocity dispersion recovered with this technique
correlates with the measured radio power through the relation $P_{\rm
radio}\propto\sigma_v^{3.3\pm0.7}$, which implies that the radio power is
nearly proportional to the turbulent energy rate. Our results provide an
observational confirmation of a key prediction of the turbulent re-acceleration
model and possibly shed light on the origin of radio halos.
