Radio relics are synchrotron emission found on the periphery of galaxy clusters. From the position and the morphology, it is often believed that the relics are generated by cosmic-ray (CR) electrons accelerated at shocks through a diffusive shock acceleration (DSA) mechanism. However, some radio relics have harder spectra than the prediction of the standard DSA model. One example is observed in the cluster 1RXS J0603.3+4214, which is often called the "Toothbrush Cluster." Interestingly, the position of the relic is shifted from that of a possible shock. In this study, we show that these discrepancies in the spectrum and the position can be solved if turbulent (re)acceleration is very effective behind the shock. This means that for some relics turbulent reacceleration may be the main mechanism to produce high-energy electrons, contrary to the common belief that it is the DSA. Moreover, we show that for efficient reacceleration, the effective mean free path of the electrons has to be much smaller than their Coulomb mean free path. We also study the merging cluster 1E?0657?56, or the "Bullet Cluster," in which a radio relic has not been found at the position of the prominent shock ahead of the bullet. We indicate that a possible relic at the shock is obscured by the observed large radio halo that is generated by strong turbulence behind the shock. We propose a simple explanation of?the morphological differences of radio emission among the Toothbrush, the Bullet, and the Sausage (CIZA J2242.8+5301) Clusters.
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