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The Sausage radio relic is the arc-like radio structure in the cluster CIZAJ2242.8+5301, whose observed properties can be best understood by synchrotronemission from relativistic electrons accelerated at a merger-driven shock.However, there remain a few puzzles that cannot be explained by the shockacceleration model with only in-situ injection. In particular, the Mach numberinferred from the observed radio spectral index, $M_{\rm radio}\approx 4.6$,while the Mach number estimated from X-ray observations, $M_{\rm X-ray}\approx2.7$. In an attempt to resolve such a discrepancy, here we consider there-acceleration model in which a shock of $M_s\approx 3$ sweeps through theintracluster gas with a pre-existing population of relativistic electrons. Wefind that observed brightness profiles at multi frequencies provide strongconstraints on the spectral shape of pre-existing electrons. The models with apower-law momentum spectrum with the slope, $s\approx 4.1$, and the cutoffLorentz factor, $\gamma_{e,c}\approx 3-5\times 10^4$ can reproduce reasonablywell the observed spatial profiles of radio fluxes and integrated radiospectrum of the Sausage relic. The possible origins of such relativisticelectrons in the intracluster medium remain to be investigated further.

Re-acceleration model for the `Sausage' Radio Relic