Radio polarization maps of shell-type SNRs I. Effects of a random magnetic field component, and thin-shell models

The maps of intensity and polarization of the radio synchrotron emission from shell-type supernova remnants (SNRs) contain a considerable amount of information, although of not easy interpretation. With the aim of deriving constraints on the 3-D spatial distribution of the emissivity, as well as on the structure of both ordered and random magnetic fields (MFs), we present here a scheme to model maps of the emission and polarization in SNRs. We first generalize the classical treatment of the synchrotron emission to the case in which the MF is composed by an ordered MF plus an isotropic random component, with arbitrary relative strengths. In the case of a power-law particle energy distribution, we derive analytic formulae that formally resemble those for the classical case. We also treat the case of a shock compression of a fully random upstream field and we predict that the polarization fraction in this case should be higher than typically measured in SNRs. We implement the above treatment into a code, which simulates the observed polarized emission of an emitting shell, taking into account also the effect of the internal Faraday rotation. Finally, we show simulated maps for different orientations with respect to the observer, levels of the turbulent MF component, Faraday rotation levels, distributions of the emissivity (either barrel-shaped or limited to polar caps), and geometries for the ordered MF component (either tangential to the shell, or radial). Their analysis allows us to outline properties useful for the interpretation of radio intensity and polarization maps.