Nonthermal Emissions from Particles Accelerated by Turbulence in   Clusters of Galaxies
  We consider nonthermal emission from clusters of galaxies produced by particle acceleration by resonant scattering of Alfv\'{e}n waves driven by fluid turbulence through the Lighthill mechanism in the intracluster medium. We assume that the turbulence is driven by cluster mergers. We find that the resonant Alfv\'{e}n waves can accelerate electrons up to   \gamma ~10^5 through resonant scattering. We also find that the turbulent resonant acceleration can give enough energy to electrons to produce the observed diffuse radio relic emission from clusters if the clusters have a pool of electrons with \gamma ~10^3.   This mechanism can also explain the observed hard X-ray emission from clusters if the magnetic field in a cluster is small enough (~<   \mu G) or the fluid turbulence spectrum is flatter than the Kolmogorov law. The fluid turbulence could be observed with Astro-E2 in the regions where diffuse radio emission is observed. Although non-gravitational heating before cluster formation (preheating) steepens a relation between radio luminosity and X-ray temperature, our predicted relation is still flatter than the observed one. 
Yutaka Fujita, Motokazu Takizawa, and Craig L. Sarazin