In inhomogeneous optically thick synchrotron sources a substantial part of the electron population at low energies can be hidden by self-absorption and overpowered by high energy electrons in optically thin emission. These invisible electrons produce Faraday rotation and conversion, leaving their footprints in the linear and circular polarized radiation of the source. An important factor is also the magnetic field structure, which can be characterized in most cases by a global magnetic field and a turbulent component. We present the basic radiative transfer coefficients for polarized synchrotron radiation and apply them to the standard jet model for relativistic radio jets. The model can successfully explain the unusual circular and linear polarization of the Galactic Centre radio source Sgr A* and its sibling M81*. It also can account for the circular polarization found in jets of more luminous quasars and X-ray binaries. The high ratio of circular to linear polarization requires the presence of a significant fraction of hidden matter and low-energy electrons in these jets. The stable handedness of circular polarization requires stable global magnetic field components with non-vanishing magnetic flux along the jet, while the low degree of total polarization implies also a significant turbulent field. The most favoured magnetic field configuration is that of a helix, while a purely toroidal field is unable to produce significant circular polarization. If connected to the magnetosphere of the black hole, the circular polarization and the jet direction determine the magnetic poles of the system which is stable over long periods of time. This may also have implications for possible magnetic field configurations in accretion flows.
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