Turbulent Cosmic-Ray Reacceleration and the Curved Radio Spectrum of the
  Radio Relic in the Sausage Cluster
  It has often been thought that the northern radio relic in the galaxy cluster
CIZA J2242.8+5301 (the "Sausage" Cluster) is associated with cosmic ray (CR)
electrons that are accelerated at a shock through the diffusive shock
acceleration (DSA) mechanism. However, recent radio observations have shown
that the radio spectrum is curved, which is inconsistent with the prediction of
a simple DSA model. Moreover, the CR electron spectrum before being affected by
radiative cooling seems to be too hard for DSA. In this study, we show that
these facts are natural consequences if the electrons are reaccelerated in
turbulence downstream of the shock. In this model, DSA is not the main
mechanism for generating high-energy electrons. We find that the mean free path
of the electrons should be much shorter than the Coulomb mean free path for
efficient reacceleration. The scale of the turbulent eddies must be smaller
than the width of the relic. We also predict hard X-ray spectra of inverse
Compton scattering of photons.
