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.
