Revised Mass-radius Relationships For Water-rich Terrestrial Planets Beyond The Runaway Greenhouse Limit


This figure shows an example of scenario for TRAPPIST-1 planets where masses and radii follow an interior isocomposition line (gray line; 10% Fe, 90% MgSiO3 composition) chosen to be consistent with 2-σ uncertainty ellipses of Grimm et al. 2018. While the seven large ellipses indicate the known current estimates (95% confidence) for the masses and radii of the seven TRAPPIST-1 planets, the seven small circles indicate the positions (in the mass, radius diagram) of the seven planets as speculated in our scenario. Each planet (associated to a current uncertainty ellipse, and a speculated position) is identified by a distinct color. This figure also shows mass-radius relationships for terrestrial core planets, in some cases endowed with either a condensed layer of water (solid blue line) or a steam H2O atmosphere of various masses (dashed purple lines). The mass-radius relationships for steam planets can be built following the procedure described in Appendix D. The 6% condensed water (with a terrestrial core) mass-radius relationship has been added to show that the isocomposition line followed by the TRAPPIST-1 planets speculated positions is highly degenerate (the solid blue and gray lines are almost superimposed). This indicates that, in this particular scenario, the position of the planets along this isocomposition line can be explained in principle either by (i) dry planets with a 10% Fe, 90% MgSiO3 core, or (ii) wet planets with a denser core (e.g. 6% water with a terrestrial core). However, for the later case (6% water with a terrestrial core), the three innermost TRAPPIST-1 planets should follow instead the uppermost dashed purple mass-radius relationship (e.g. 6% steam water with a terrestrial core), as indicated by the black arrows and the indicated new planet positions. This ’jump’ from one mass-radius relationship (condensed water; solid blue line) to another (steam water; dashed purple line) can be used to break the composition degeneracy of the system (see main text).

Mass-radius relationships for water-rich terrestrial planets are usually calculated assuming most water is present in condensed (either liquid or solid) form.

Planet density estimates are then compared to these mass-radius relationships even when these planets are more irradiated than the runaway greenhouse irradiation limit (around 1.06x the Earth irradiation for planets orbiting a Sun-like star), for which water has been shown to be unstable in condensed form and should rather form a thick H2O-dominated atmosphere. Here we use the LMD Generic numerical climate model to derive new mass-radius relationships appropriate for water-rich terrestrial planets located beyond the runaway greenhouse limit, i.e. planets endowed with a steam, water-dominated atmosphere. These new mass-radius relationships significantly differ from those traditionnally used in the literature. For a given water-to-rock mass ratio, these new mass-radius relationships lead to planet bulk densities much lower than calculated when water is assumed to be in condensed form.

In other words, using traditional mass-radius relationships for planets that are more irradiated than the runaway greenhouse limit tends to dramatically overestimate their bulk water content. In particular, this result applies to TRAPPIST-1b, c and d, that should not have more (assuming planetary core with a terrestrial composition) than 2, 0.3 and 0.08% of water, respectively. In addition, we show with the example of the TRAPPIST-1 multiplanetary system that the jumps in mass-radius relationships (related to the runaway greenhouse transition) can be used to remove usual composition degeneracies in mass-radius relationships. Finally, we provide an empirical formula for the H2O steam atmosphere thickness that can easily be used to construct mass-radius relationships for water-rich, terrestrial planets located beyond the runaway greenhouse limit.

Martin Turbet, Emeline Bolmont, David Ehrenreich, Pierre Gratier, Jérémy Leconte, Franck Selsis, Nathan Hara, Christophe Lovis
(Submitted on 20 Nov 2019)
Comments: Submitted for publication to A&A. The abstract is abridged to meet ArXiv size limit
Subjects: Earth and Planetary Astrophysics (astro-ph.EP); Atmospheric and Oceanic Physics (physics.ao-ph); Geophysics (physics.geo-ph)
Cite as: arXiv:1911.08878 [astro-ph.EP] (or arXiv:1911.08878v1 [astro-ph.EP] for this version)
Submission history
From: Martin Turbet
[v1] Wed, 20 Nov 2019 13:15:07 UTC (2,613 KB)
https://arxiv.org/abs/1911.08878
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