Relation to rotation measure and polarization data

Kim et al. (1990) and Kim et al. (1991) derived magnetic field properties from RM observations. The excess RM due to a magnetic field in the intracluster gas gives a measurement of the quantity B^2r_0. To derive the magnetic field strength B or the scale length of the field r_0 requires another measurement of a different combination of these two quantities. Radio source depolarization is one possibility (Tribble 1991). The observation of granularity in a radio halo is another that I consider here. The observations require that r_0< 15 kpc. This scale length differs from that used in the RM analysis which is r_0' = integral f dz; the two are related by a factor of order unity. If f is Gaussian then r_0' = sqrt(2pi) r_0 so the limit translates to r_0' < 40 kpc. Even for this relatively weak limit on the scale length of the field the magnetic field in the Coma cluster is still required to have an rms strength exceeding 1microGauss.

No polarized emission has been detected from the halo. Kim et al. (1990) report that the polarization at 20 cm and 1 arcmin resolution varies from less than 1% at the centre to less than 30% in the outer halo. As discussed in Section 2.1, the simplest models predict that the halo polarization should be about the same as the intensity contrast, so that polarization at about the 5% level might be expected. This is not observed and one might be tempted to conclude that the intensity contrast is really only about 1%. Unfortunately this conclusion is not very robust, as both galactic wakes and dynamo fields give low levels of polarization. In the case of the dynamo field, the field is wound into ropes from which the polarization cancels by symmetry---the same would be true of a single turbulent vortex.

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Peter Tribble,