Magnetic fields play an important role during star formation1. Direct magnetic field strength observations have proven particularly challenging in the extremely dynamic protostellar phase2,3,4. Because of their occurrence in the densest parts of star-forming regions, masers, through polarization observations, are the main source of magnetic field strength and morphology measurements around protostars2. Of all maser species, methanol is one of the strongest and most abundant tracers of gas around high-mass protostellar disks and in outflows. However, as experimental determination of the magnetic characteristics of methanol has remained largely unsuccessful5, a robust magnetic field strength analysis of these regions could hitherto not be performed. Here, we report a quantitative theoretical model of the magnetic properties of methanol, including the complicated hyperfine structure that results from its internal rotation6. We show that the large range in values of the Landé g factors of the hyperfine components of each maser line lead to conclusions that differ substantially from the current interpretation based on a single effective g factor. These conclusions are more consistent with other observations7,8 and confirm the presence of dynamically important magnetic fields around protostars. Additionally, our calculations show that (nonlinear) Zeeman effects must be taken into account to further enhance the accuracy of cosmological electron-to-proton mass ratio determinations using methanol9,10,11,12.

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Support for this work was provided by the Swedish Research Council (VR), and by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013), through the European Research Council consolidator grant agreement no. 614264.

Author information


  1. Department of Space, Earth and Environment, Onsala Space Observatory, Chalmers University of Technology, Onsala, Sweden

    • Boy Lankhaar
    •  & Wouter Vlemmings
  2. Joint Institute for VLBI ERIC, Dwingeloo, Netherlands

    • Gabriele Surcis
    •  & Huib Jan van Langevelde
  3. INAF, Osservatorio Astronomico di Cagliari, Selargius, Italy

    • Gabriele Surcis
  4. Sterrewacht Leiden, Leiden University, Leiden, Netherlands

    • Huib Jan van Langevelde
  5. Theoretical Chemistry, Institute for Molecules and Materials, Radboud University, Nijmegen, Netherlands

    • Gerrit C. Groenenboom
    •  & Ad van der Avoird


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B.L., A.v.d.A. and W.V. wrote the paper. B.L., A.v.d.A. and G.C.G. modelled the Zeeman effect in methanol. B.L. and W.V. performed the analysis of the astrophysical maser spectra, based on methanol’s Zeeman model. W.V., H.J.v.L. and G.S. provided expertise on maser polarization in astrophysics and initiated the project. All authors discussed the results and commented on the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to Boy Lankhaar.

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    Supplementary text, Supplementary Figures 1–2, Supplementary Tables 1–18, Supplementary references.

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