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Energy flux determines magnetic field strength of planets and stars

Nature volume 457, pages 167–169 (2009)Cite this article

Abstract

The magnetic fields of Earth and Jupiter, along with those of rapidly rotating, low-mass stars, are generated by convection-driven dynamos that may operate similarly1,2,3,4 (the slowly rotating Sun generates its field through a different dynamo mechanism5). The field strengths of planets and stars vary over three orders of magnitude, but the critical factor causing that variation has hitherto been unclear5,6. Here we report an extension of a scaling law derived from geodynamo models7 to rapidly rotating stars that have strong density stratification. The unifying principle in the scaling law is that the energy flux available for generating the magnetic field sets the field strength. Our scaling law fits the observed field strengths of Earth, Jupiter, young contracting stars and rapidly rotating low-mass stars, despite vast differences in the physical conditions of the objects. We predict that the field strengths of rapidly rotating brown dwarfs and massive extrasolar planets are high enough to make them observable.

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Figure 1: Scaling law versus results from dynamo models.
Figure 2: Scaling law versus magnetic fields of planets and stars.

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Acknowledgements

Reviews by C. Johns-Krull helped to sharpen the paper. U.R.C. thanks M. Rempel for prompting this study by asking if planetary scaling laws also apply to stars.

Author Contributions U.R.C. suggested the basic concept, performed dynamo simulations and wrote the paper. V.H. calculated stellar models. A.R. provided magnetic field data and other stellar data. All authors discussed results and commented on the manuscript.

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Authors and Affiliations

  1. Max-Planck-Institut für Sonnensystemforschung, Max Planck Strasse 2, 37191 Katlenburg-Lindau, Germany ,

    Ulrich R. Christensen & Volkmar Holzwarth

  2. Institut für Astrophysik, Universität Göttingen, Friedrich Hund Platz 1, 37077 Göttingen, Germany ,

    Ansgar Reiners

Authors
  1. Ulrich R. Christensen
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  2. Volkmar Holzwarth
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  3. Ansgar Reiners
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Corresponding author

Correspondence to Ulrich R. Christensen.

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Christensen, U., Holzwarth, V. & Reiners, A. Energy flux determines magnetic field strength of planets and stars. Nature 457, 167–169 (2009). https://doi.org/10.1038/nature07626

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