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A cool runaway greenhouse without surface magma ocean


Water vapour atmospheres with content equivalent to the Earth’s oceans, resulting from impacts1 or a high insolation2,3, were found to yield a surface magma ocean4,5. This was, however, a consequence of assuming a fully convective structure2,3,4,5,6,7,8,9,10,11. Here, we report using a consistent climate model that pure steam atmospheres are commonly shaped by radiative layers, making their thermal structure strongly dependent on the stellar spectrum and internal heat flow. The surface is cooler when an adiabatic profile is not imposed; melting Earth’s crust requires an insolation several times higher than today, which will not happen during the main sequence of the Sun. Venus’s surface can solidify before the steam atmosphere escapes, which is the opposite of previous works4,5. Around the reddest stars (Teff  <  3,000 K), surface magma oceans cannot form by stellar forcing alone, whatever the water content. These findings affect observable signatures of steam atmospheres and exoplanet mass–radius relationships, drastically changing current constraints on the water content of TRAPPIST-1 planets. Unlike adiabatic structures, radiative–convective profiles are sensitive to opacities. New measurements of poorly constrained high-pressure opacities, in particular far from the H2O absorption bands, are thus necessary to refine models of steam atmospheres, which are important stages in terrestrial planet evolution.

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Fig. 1: Steam atmosphere thermal profiles.
Fig. 2: Outgoing thermal emission as a function of surface temperature.
Fig. 3: Spectra of T-1b with a steam atmosphere.

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Data availability

Data generated by the atmospheric codes Exo_k and Generic PCM and used in this study are available at

Code availability

Exo_k is an open-source software. A complete documentation on how to install and use it can be found at The Generic PCM (Generic Global Climate Model; formerly known as LMDZ.generic) used in this work is v.2528, and it can be downloaded with documentation from the SVN repository at More information and documentation are available at


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We thank the Generic Planetary Climate Model team for teamwork development and improvement of the model. This research made use of NASA’s Astrophysics Data System. F.S. and J.L. acknowledge funding from the European Research Council under the European Union’s Horizon 2020 Research and Innovation Programme (679030/WHIPLASH) and from the French state through CNES, Programme National de Planétologie and the ANR (ANR-20-CE49-0009: SOUND) and in the framework of the Investments for the Future Programme IdEx, Université de Bordeaux/RRI ORIGINS. F.S. and M.T. acknowledge support from BELSPO BRAIN (B2/212/PI/PORTAL). M.T. acknowledges support from the Tremplin 2022 programme of the Faculty of Science and Engineering of Sorbonne University and the use of the high-performance computing resources of Centre Informatique National de l’Enseignement Superieur (A0080110391) made by Grand Equipement National de Calcul Intensif, which was essential to compute the three-dimensional GCM simulations presented in this work. G.C. and É.B. acknowledge support from the Swiss National Science Foundation (200021_197176). Their work was carried out within the framework of the NCCR PlanetS supported by the Swiss National Science Foundation (51NF40_182901 and 51NF40_205606).

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Authors and Affiliations



F.S. and J.L. laid the foundations for the study. F.S. wrote most of the paper, performed the one-dimensional runs and made the figures with guidance from J.L., M.T., G.C. and É.B., and J.L. developed the code Exo_k that made the study possible and wrote a significant part of the text, including the Exo_k description and manual. M.T. performed the 3D simulations, which were important to validate Exo_k 1D profiles and pointed to radiative deep atmospheres. J.L., M.T. and G.C. worked on the spectroscopic data and formatted them for the study. All authors contributed to the response to the reviewers and revisions of the article.

Corresponding author

Correspondence to Franck Selsis.

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Nature thanks Kevin Zahnle, Raymond Pierrehumbert, Robin Wordsworth and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Extended data figures and tables

Extended Data Fig. 1 Converged versus fully convective profiles.

The steam atmosphere is modelled here a solar flux of 445.7 Wm−2 (Seff = 1.3), no internal heat flux, a 1g gravity and a 270 bar surface pressure (1 vaporized Earth ocean). Panel a: Net fluxes computed for a “convective” P-T profile used as the initial structure in panels c and d. Panel b: Net fluxes at equilibrium. Blue (resp. red) area indicate a downward (resp. upward) net radiative flux. Convection transporting energy upward can only balance a downward radiative flux. Red area therefore indicate a departure from thermal equilibrium. Panel c) Evolution from the initial dashed “convective” profile towards the converged state, computed with the Exo_k suite22 evolution package. It takes more than 40,000 yrs to reach the converged state and more than 280 millions steps and 40 hrs of CPU time. Panel d) Evolution computed with an acceleration mode (see Methods) of Exo_k, in 165,000 steps and less than 1 min of CPU time. In the acceleration mode, iterations and intermediate profiles do not correspond to physical times and structures.

Extended Data Fig. 2 Steam atmosphere converged P-T profiles as a function of instellation and stellar type.

Dashed lines indicate dry convection. Adiabatic profiles satisfying top-of-the-atmosphere radiative balance for the minimum and maximum fluxes are in grey.

Extended Data Fig. 3 1D/3D comparison.

Panel a, b and c) Thermal profiles obtained with Exo_k (solid blue lines) and the 3D Generic PCM (dashed red lines) for TRAPPIST-1, Proxima and a M3 star. For the Generic PCM, the spatial and temporal average is shown as well as the range of variations (red area). Panel d) Stellar heating rates with Exo_k (solid lines) and with the Generic PCM (dashed lines). The 10 bar atmosphere consists of 95% of H2O and 5% of N2 and the instellation is 500 Wm−2 (Seff = 1.42) in all cases. The opacities used in both models are the same, differences come from circulation and cloud radiative effects.

Extended Data Fig. 4 Influence of the cp value on the converged T profiles.

The black curves are the nominal P-T profiles, obtained with a cp set by iterations to its value at the mean temperature in the dry convection layers. To show the sensitivity to the cp value we used the lowest and highest temperatures (Tmin and Tmax) found in these dry convective layers and computed the blue profile with cp(Tmin) and the red profile with cp(Tmax).

Extended Data Fig. 5 Sensitivity to a significant change in the H2O-H2O continuum.

Profiles are computed for a solar spectrum and three different insolations with versions 3.5 and 4.0.1 of the MT_CKD continuum.

Extended Data Fig. 6 Influence of the surface pressure and internal heat flux.

a) Profiles for Venus gravity and insolation 4.5 Gyrs ago. b) Profiles for an Earth gravity with an ISR of 378 Wm−2 and T-1 spectrum. At ϕint = 0 both cases have an OTR of 378 Wm−2. Dashed lines indicate convective layers. Dots indicate the surface of each individual profile.

Extended Data Table 1 Influence of the surface pressure and internal heat flux

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Selsis, F., Leconte, J., Turbet, M. et al. A cool runaway greenhouse without surface magma ocean. Nature 620, 287–291 (2023).

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