Magnetic field structures of galaxies derived from analysis of Faraday rotation measures, and perspectives for the SKA

The forthcoming new-generation radio telescope SKA (Square Kilometre Array) and its precursors will provide a rapidly growing number of polarized radio sources. Our analysis aims on what can be learned from these sources concerning the structure and evolution of magnetic fields of external galaxies. Recognition of magnetic structures is possible from Faraday rotation measures (${\rm RM}$) towards background sources behind galaxies. We construct models for the ionized gas and magnetic field patterns of different azimuthal symmetry (axisymmetric, bisymmetric and quadrisymmetric spiral, and superpositions) plus a halo magnetic field. $\RM$ fluctuations with a Kolmogorov spectrum due to turbulent fields and/or fluctuations in ionized gas density are superimposed. Assuming extrapolated number density counts of polarized sources, we generate a sample of $\RM$ values within the solid angle of the galaxy. Applying various templates, we derive the minimum number of background sources and the minimum quality of the observations. For a large number of sources, reconstruction of the field structure without precognition becomes possible. Any large-scale regular component of the magnetic field can be clearly recognized from $\RM$ data with help of the $\chi^2$ criterium. Under favourite conditions, about a few dozens of polarized sources are sufficient for a reliable result.