Rotation measure (RM) Synthesis was recently developed as a new tool for the interpretation of polarized emission data in order to separate the contributions of different sources lying on the same line of sight. Until now, the method was mainly applied to discrete sources in Faraday space (Faraday screens). Here we consider how to apply RM Synthesis to reconstruct the Faraday dispersion function, aiming at the further extraction of information concerning the magnetic fields of extended sources, for example galaxies. We pay attention mainly to two related novelties in the method, i.e. the symmetry argument in Faraday space and the wavelet technique.
We give a relation between our method and the previous applications of RM Synthesis to point-like sources. We demonstrate that the traditional RM Synthesis for a point-like source indirectly implies a symmetry argument and, in this sense, can be considered as a particular case of the method presented here. Investigating the applications of RM Synthesis to polarization details associated with small-scale magnetic fields, we isolate an option which was not covered by the ideas of the Burn theory, i.e. using quantities averaged over small-scale fluctuations of the magnetic field and electron density. We describe the contribution of small-scale fields in terms of Faraday dispersion and beam depolarization. We consider the complex polarization for RM Synthesis without any averaging over small-scale fluctuations of the magnetic field and electron density and demonstrate that it allows us to isolate the contribution from a small-scale field.
A general conclusion concerning the applicability of RM Synthesis to the interpretation of the radio polarization data for extended sources, such as galaxies, is that quite severe requirements (in particular to the wavelength range covered by observations) are needed to recognize at least the principal structure of the Faraday dispersion function. If the wavelength range of observations is not adequate, we describe which features of this function can be reconstructed.