Interior structures and tidal heating in the TRAPPIST-1 planets

¹ Planetary Science Institute, 1700 E. Ft. Lowell, Suite 106, Tucson, AZ 85719, USA
e-mail: amy@psi.edu
² Konkoly Thege Miklós Astronomical Institute, Research Centre for Astronomy and Earth Sciences, Hungarian Academy of Sciences, 1121 Konkoly Thege Miklós út 15–17, Budapest, Hungary
³ Geodetic and Geophysical Institute, Research Centre for Astronomy and Earth Sciences, Hungarian Academy of Sciences, 9400 Csatkai Endre u. 6–8, Sopron, Hungary
⁴ ELTE Eötvös Loránd University, Gothard Astrophysical Observatory, Szombathely, Szent Imre h. u. 112, Hungary
⁵ Sydney Institute for Astronomy, School of Physics A28, University of Sydney, NSW 2006, Australia

Received: 25 September 2017
Accepted: 14 December 2017

Abstract

Context. With seven planets, the TRAPPIST-1 system has among the largest number of exoplanets discovered in a single system so far. The system is of astrobiological interest, because three of its planets orbit in the habitable zone of the ultracool M dwarf.

Aims. We aim to determine interior structures for each planet and estimate the temperatures of their rock mantles due to a balance between tidal heating and convective heat transport to assess their habitability. We also aim to determine the precision in mass and radius necessary to determine the planets’ compositions.

Methods. Assuming the planets are composed of uniform-density noncompressible materials (iron, rock, H₂O), we determine possible compositional models and interior structures for each planet. We also construct a tidal heat generation model using a single uniform viscosity and rigidity based on each planet’s composition.

Results. The compositions for planets b, c, d, and e remain uncertain given the error bars on mass and radius. With the exception of TRAPPIST-1c, all have densities low enough to indicate the presence of significant H₂O. Planets b and c experience enough heating from planetary tides to maintain magma oceans in their rock mantles; planet c may have surface eruptions of silicate magma, potentially detectable with next-generation instrumentation. Tidal heat fluxes on planets d, e, and f are twenty times higher than Earth’s mean heat flow.

Conclusions. Planets d and e are the most likely to be habitable. Planet d avoids the runaway greenhouse state if its albedo is ≳0.3. Determining the planet’s masses within ~0.1–0.5 Earth masses would confirm or rule out the presence of H₂O and/or iron. Understanding the geodynamics of ice-rich planets f, g, and h requires more sophisticated modeling that can self-consistently balance heat production and transport in both rock and ice layers.