Radio emission in a random magnetic field: Radio haloes and the structure of the magnetic field in the Coma cluster

Abstract

Models of cluster radio haloes have been constructed allowing for a random magnetic field. The resulting halo is far from smooth, both in intensity and polarization. The magnetic field must therefore be tangled on sufficiently small scales to reduce intensity fluctuations to observed levels. The smoothness of the inner regions of the radio halo in the Coma cluster, with fluctuations at about the 5 percent level at 1-arcmin resolution, indicates that the outer scale of magnetic field fluctuations is less than 15 kpc. Similar considerations indicate that less than 10 percent of the total halo emission can be due to galactic wakes and demonstrate that the halo emission and the magnetic field are spread throughout the whole volume of the cluster and are not localized with a small filling factor. In the simplest models the fractional polarization should be similar to the fluctuation level, although the polarization can be substantially decreased if the field has a high degree of symmetry.