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 Alfven 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 Alfven waves can accelerate electrons up to gamma similar to 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 similar to 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 (less than or similar to muG) 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 nongravitational 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.