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Magnetic fields are predicted to have a crucial impact on the structure,evolution and chemistry of protoplanetary disks. However, a direct detection ofthe magnetic field towards these objects has yet to be achieved. In order tocharacterize protoplanetary disk magnetic fields, we investigate the impact ofthe Zeeman effect on the (polarized) radiative transfer of emission fromparamagnetic molecules excited in protoplanetary disks. While the effects ofthe Zeeman effect are commonly studied in the circular polarization of spectrallines, we perform a comprehensive modeling also of the Zeeman-inducedbroadening of spectral lines and their linear polarization. We developsimplified radiative transfer models adapted to protoplanetary disks, which wecompare to full three-dimensional polarized radiative transfer simulations. Wefind that the radiative transfer of circular polarization is heavily affectedby the expected polarity-change of the magnetic field between opposite sides ofthe disk. In contrast, Zeeman broadening and linear polarization are relativelyunaffected by this sign change due to their quadratic dependence on themagnetic field. We can match our simplified radiative transfer models to fullpolarization modeling with high fidelity, which in turn allows us to prescribestraight-forward methods to extract magnetic field information from Zeemanbroadening and linear polarization observations. We find that Zeeman broadeningand linear polarization observations are highly advantageous methods tocharacterize protoplanetary disk magnetic fields as they are both sensitiveprobes of the magnetic field and are marginally affected by any sign change ofthe disk magnetic field. Applying our results to existing circular polarizationobservations of protoplanetary disk spectral lines suggests that the currentupper limits on the toroidal magnetic field strengths have to be raised.

Three-dimensional magnetic field imaging of protoplanetary disks using Zeeman broadening and linear polarization observations