Depolarization and Faraday effects in galaxies

Faraday rotation and depolarization of synchrotron radio emission are considered in a consistent general approach, under conditions typical of spiral galaxies, i.e. when the magneto-ionic medium and relativistic electrons are non-uniformly distributed in a layer containing both regular and fluctuating components of magnetic field, thermal electron density and synchrotron emissivity, We demonstrate that non-uniformity of the magneto-ionic medium along the line of sight strongly affects the observable polarization patterns. The degree of polarization p and the observed Faraday rotation measure RM are very sensitive to whether or not the source is symmetric along the line of sight. The RM may change sign in a certain wavelength range in an asymmetric slab even when the line-of-sight magnetic field has no reversals. Faraday depolarization in a purely regular magnetic field can be much stronger than suggested by the low observed rotation measures, A twisted regular magnetic field may result in p increasing with lambda - a behaviour detected in several galaxies. We derive expressions for statistical fluctuations in complex polarization and show that random fluctuations in the degree of polarization caused by Faraday dispersion are expected to become significantly larger than the mean value of p at lambda greater than or similar to 20-30cm, We also discuss depolarization arising from a gradient of Faraday rotation measure across the beam, both in the source and in an external Faraday screen. We briefly discuss applications of the above results to radio polarization observations. We discuss how the degree of polarization is affected by the scaling of synchrotron emissivity epsilon with the total magnetic field strength B, We derive formulae for the complex polarization at lambda --> 0 under the assumption that epsilon alpha (BBperpendicular to2)-B-2, which may arise under energy equipartition or pressure balance between cosmic rays and magnetic fields. The resulting degree of polarization is systematically larger than for the usually adopted scaling epsilon alpha B-perpendicular to(2); the difference may reach a factor of 1.5.