2008MNRAS.391..521L

We use high-quality Very Large Array (VLA) images of the Fanaroff-Riley Class I radio galaxy 3C31 at six frequencies in the range 1365-8440MHz to explore the spatial scale and origin of the rotation measure (RM) fluctuations on the line of sight to the radio source. We analyse the distribution of the degree of polarization to show that the large depolarization asymmetry between the north and south sides of the source seen in earlier work largely disappears as the resolution is increased. We show that the depolarization seen at low resolution results primarily from unresolved gradients in a Faraday screen in front of the synchrotron-emitting plasma. We establish that the residual degree of polarization in the short-wavelength limit should follow a Burn law and we fit such a law to our data to estimate the residual depolarization at high resolution. We discuss how to interpret the structure function of RM fluctuations in the presence of a finite observing beam and how to address the effects of incomplete sampling of RM distribution using a Monte Carlo approach. We infer that the observed RM variations over selected areas of 3C31, and the small residual depolarization found at high resolution, are consistent with a power spectrum of magnetic fluctuations in front of 3C31 whose power-law slope changes significantly on the scales sampled by our data. The power spectrum P(f) can only have the form expected for Kolmogorov turbulence [P(f) ∝ f^–11/3] on scales ≲5kpc. On larger scales, we find. We briefly discuss the physical interpretation of these results. We also compare the global variations of RM across 3C31 with the results of three-dimensional simulations of the magnetic-field fluctuations in the surrounding magnetoionic medium. We infer that the RM variation across 3C31 is qualitatively as expected from relativistic-jet models of the brightness asymmetry wherein the apparently brighter jet is on the near side of the nucleus and is seen through less magnetoionic material than the fainter jet. We show that our data are inconsistent with observing 3C31 through a spherically symmetric magnetoionic medium, but that they are consistent with a field distribution that favours the plane perpendicular to the jet axis - probably because the radio source has evacuated a large cavity in the surrounding medium. We also apply our analysis techniques to the case of HydraA, where the shape and the size of the cavities produced by the source in the surrounding medium are known from X-ray data. We emphasize that it is essential to account for the potential exclusion of magnetoionic material from a large volume containing the radio source when using the RM variations to derive statistical properties of the fluctuations in the foreground magnetic field.