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We explore the shock acceleration model for giant radio relics, in whichrelativistic electrons are accelerated via diffusive shock acceleration (DSA)by merger-driven shocks in the outskirts of galaxy clusters. In addition toDSA, turbulent acceleration by compressive MHD mode downstream of the shock isincluded as well as energy losses of postshock electrons by Coulomb scattering,synchrotron emission, and inverse Compton scattering off the cosmic backgroundradiation. Considering that only a small fraction of merging clusters hostradio relics, we favor the reacceleration scenario in which radio relics aregenerated preferentially when shocks encounter the regions containinglow-energy ($\gamma_{\rm e} \lesssim 300$) cosmic ray electrons (CRe). Weperform time-dependent DSA simulations of spherically expanding shocks withphysical parameters relevant for the Sausage radio relic, and calculate theradio synchrotron emission from the accelerated CRe. We find that significantlevel of postshock turbulent acceleration is required in order to reproducebroad profiles of the observed radio flux densities of the Sausage relic.Moreover, the spectral curvature in the observed integrated radio spectrum canbe explained, if the putative shock should have swept up and exited out of thepreshock region of fossil CRe about 10~Myr ago.

Shock Acceleration Model with Postshock Turbulence for Giant Radio Relics