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Magma oceans and enhanced volcanism on TRAPPIST-1 planets due to induction heating

Nature Astronomy volume 1, pages 878–885 (2017)Cite this article

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Abstract

Low-mass M stars are plentiful in the Universe and often host small, rocky planets detectable with current instrumentation. These stars host magnetic fields, some of which have been observed to exceed a few hundred gauss. Recently, seven small planets have been discovered orbiting the ultra-cool M dwarf TRAPPIST-1, which has an observed magnetic field of 600 G. We suggest electromagnetic induction heating as an energy source inside these planets. If the stellar rotation and magnetic dipole axes are inclined with respect to each other, induction heating can melt the upper mantle and enormously increase volcanic activity, sometimes producing a magma ocean below the planetary surface. We show that induction heating leads the four innermost TRAPPIST-1 planets, one of which is in the habitable zone, either to evolve towards a molten mantle planet, or to experience increased outgassing and volcanic activity, while the three outermost planets remain mostly unaffected.

We calculate the energy dissipation in spherical geometry and consider a planet to be a sphere made up of concentric layers with uniform conductivity6. We solve the induction equation in every layer and find the magnetic field and current. Knowing the current and conductivity, we find the energy release within each layer (see the Methods section for details).

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Fig. 1: Sketch of the induction heating mechanism.
Fig. 2: Interior profiles and skin depth for all seven TRAPPIST-1 planets.
Fig. 3: Induction heating inside the seven TRAPPIST-1 planets showing the energy release rate inside the planets, normalized to the radius of each planet.
Fig. 4: Model results for ten different example parameter cases.
Fig. 5: Mantle depletion due to melting for TRAPPIST-1c (parameter case 1).

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Acknowledgements

We acknowledge support by the Austrian Fonds zur Förderung der Wissenschaftlichen Forschung Nationales Forschungs Netzwerk (FWF NFN) project S116-N16 and the subprojects S11607-N16, S11604-N16 and S11606-N16. L.N. was funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office through the Planet Topers alliance. L.N. and M.G. acknowledge support of the COST Action TD 1308. P.O. acknowledges FWF project P27256-N27. V.V.Z. acknowledges RSF project 16-12-10528. The authors acknowledge ISSI for the support of the ISSI team “The early evolution of the atmospheres of Earth, Venus, and Mars”. M.L.K. also acknowledges the FWF projects I2939-N27, P25587-N27, P25640-N27, Leverhulme Trust grant IN-2014-016 and grant no. 16-52-14006 of the Russian Foundation for Basic Research.

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Authors and Affiliations

  1. Space Research Institute, Austrian Academy of Sciences, Schmiedlstrasse 6, A-8042, Graz, Austria

    K. G. Kislyakova, L. Fossati, H. Lammer, M. L. Khodachenko & P. Odert

  2. University of Vienna, Department of Astrophysics, Türkenschanzstrasse 17, A-1180, Vienna, Austria

    K. G. Kislyakova, C. P. Johnstone & M. Güdel

  3. Royal Observatory of Belgium, Department Reference Systems and Planetology, Avenue Circulaire 3, 1180, Uccle, Belgium

    L. Noack

  4. Free University of Berlin, Department of Earth Sciences, Malteserstrasse 74-100, 12249, Berlin, Germany

    L. Noack

  5. Institute of Applied Physics, Russian Academy of Sciences, 46 Ul’yanov Street, 603950, Nizhny Novgorod, Russia

    V. V. Zaitsev

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  1. K. G. Kislyakova
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Contributions

K.G.K. calculated the induction heating. L.N. modelled the mantle effects. C.P.J. calculated stellar magnetic fields at a given orbital distance. V.V.Z. helped to derive the equations. L.F. suggested that induction heating could be substantial. H.L. provided knowledge on the habitability of exoplanets. M.L.K. checked the influence of the ionosphere. P.O. helped to write the paper. M.G. contributed expertise in exoplanetary research. All authors contributed to the text.

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Correspondence to K. G. Kislyakova.

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Kislyakova, K.G., Noack, L., Johnstone, C.P. et al. Magma oceans and enhanced volcanism on TRAPPIST-1 planets due to induction heating. Nat Astron 1, 878–885 (2017). https://doi.org/10.1038/s41550-017-0284-0

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