Polarization observations at 21cm and 18cm towards the local Taurus molecular cloud complex were made with the Effelsberg 100-m telescope. Highly structured, frequency-dependent polarized emission features were detected. We discuss polarization minima with excessive rotation measures located at the boundaries of molecular clouds. The multi-frequency polarization data have been successfully modeled by considering magneto-ionic Faraday screens at the surface of the molecular clouds. Faraday rotated background emission adds to foreground emission towards these screens in a different way than in its surroundings. The physical size of the Faraday screens is of the order of 2 pc for 140 pc distance to the Taurus clouds. Intrinsic rotation measures between about -18 rad/m2 to -30 rad/m2 are required to model the observations. Depolarization of the background emission is quite small (compatible with zero), indicating a regular magnetic field structure with little turbulence within the Faraday screens. With observational constraints for the thermal electron density from H-alpha observations of less than 0.8 cm^-3 we conclude that the regular magnetic field strength along the line of sight exceeds 20 muG. We discuss some possibilities for the origin of such strong and well ordered magnetic fields. The modeling also predicts a large-scale, regularly polarized emission in the foreground of the Taurus clouds which is of the order of 0.24 K at 21cm. This amount of synchrotron emission is clearly excessive when compared to previous estimates of the local synchrotron emissivity.
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