Magnetic field tomography, helical magnetic fields and Faraday depolarization

Wide-band radio polarization observations offer the possibility to recover information about the magnetic fields in synchrotron sources, such as details of their three-dimensional configuration, that has previously been inaccessible. The key physical process involved is the Faraday rotation of the polarized emission in the source (and elsewhere along the wave's propagation path to the observer). In order to proceed, reliable methods are required for inverting the signals observed in wavelength space into useful data in Faraday space, with robust estimates of their uncertainty. In this paper, we examine how variations of the intrinsic angle of polarized emission $\psi_{0}$ with the Faraday depth $\phi$ within a source affect the observable quantities. Using simple models for the Faraday dispersion $F(\phi)$ and $\psi_{0}(\phi)$, along with the current and planned properties of the main radio interferometers, we demonstrate how degeneracies among the parameters describing the magneto-ionic medium can be minimised by combining observations in different wavebands. We also discuss how depolarization by Faraday dispersion due to a random component of the magnetic field attenuates the variations in the spectral energy distribution of the polarization and shifts its peak towards shorter wavelengths. This additional effect reduces the prospect of recovering the characteristics of the magnetic field helicity in magneto-ionic media dominated by the turbulent component of the magnetic field.