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The Toothbrush radio relic associated the merging cluster 1RXS J060303.3 ispresumed to be produced by relativistic electrons accelerated at merger-drivenshocks. Since the shock Mach number inferred from the observed radio spectralindex, $M_{radio}\approx 2.8$, is larger than that estimated from X-rayobservations, $M_{X-ray}\lesssim 1.5$, we consider the re-acceleration model inwhich a weak shock of $M_s\approx 1.2-1.5$ sweeps through the intraclusterplasma with a preshock population of relativistic electrons. We find the modelswith a power-law momentum spectrum with the slope, $s\approx 4.6$, and thecutoff Lorentz factor, $\gamma_{e,c}\approx 7-8\times 10^4$ can reproducereasonably well the observed profiles of radio fluxes and integrated radiospectrum of the head portion of the Toothbrush relic. This study confirms thestrong connection between the ubiquitous presence of fossil relativistic plasmaoriginated from AGNs and the shock-acceleration model of radio relics in theintracluster medium.

Re-acceleration model for the "Toothbrush" Radio Relic