Magnetic field amplification by shocks in galaxy clusters: application to radio relics

Merger shocks induce turbulence in the intra-cluster medium (ICM), and, under some circumstances, accelerate electrons to relativistic velocities to form so-called radio relics. Relics are mostly found at the periphery of galaxy clusters and appear to have magnetic fields at the microGauss level. Here we investigate the possible origins of these magnetic fields. Turbulence produced by the shock itself cannot explain the magnitude of these fields. However, we argue that if the turbulent pressure support in the ICM upstream of the merger shock is of the order of 10 to 30 percent of the total pressure on scales of a few times 100 kpc, then vorticity generated by compressive and baroclinic effects across the shock discontinuity can lead to a sufficient amplification of the magnetic field. Compressional amplification can explain the large polarisation of the radio emission more easily than dynamo turbulent amplification. Finally, clumping of the ICM is shown to have a negligible effect on magnetic field amplification.