Abstract
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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Data availability
Data generated by the atmospheric codes Exo_k and Generic PCM and used in this study are available at https://doi.org/10.5281/zenodo.6877001.
Code availability
Exo_k is an open-source software. A complete documentation on how to install and use it can be found at http://perso.astrophy.u-bordeaux.fr/~jleconte/exo_k-doc/index.html. 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 https://svn.lmd.jussieu.fr/Planeto/trunk/LMDZ.GENERIC/. More information and documentation are available at http://www-planets.lmd.jussieu.fr.
References
Sleep, N. H., Zahnle, K. J. & Lupu, R. E. Terrestrial aftermath of the Moon-forming impact. Philos. Trans. A Math. Phys. Eng. Sci. 372, 20130172 (2014).
Ingersoll, A. P. The runaway greenhouse: a history of water on Venus. J. Atmos. Sci. 26, 1191–1198 (1969).
Kasting, J. F. Runaway and moist greenhouse atmospheres and the evolution of Earth and Venus. Icarus 74, 472–494 (1988).
Hamano, K., Abe, Y. & Genda, H. Emergence of two types of terrestrial planet on solidification of magma ocean. Nature 497, 607–610 (2013).
Lebrun, T. et al. Thermal evolution of an early magma ocean in interaction with the atmosphere. J. Geophys. Res. Planets 118, 1155–1176 (2013).
Kasting, J. F., Whitmire, D. P. & Reynolds, R. T. Habitable zones around main sequence stars. Icarus 101, 108–128 (1993).
Selsis, F. et al. Habitable planets around the star Gliese 581? Astron. Astrophys. 476, 1373–1387 (2007).
Goldblatt, C., Robinson, T. D., Zahnle, K. J. & Crisp, D. Low simulated radiation limit for runaway greenhouse climates. Nat. Geosci. 6, 661–667 (2013).
Kopparapu, R. K. et al. Habitable zones around main-sequence stars: new estimates. Astrophys. J. 765, 131 (2013).
Ding, F. & Pierrehumbert, R. T. Convection in condensible-rich atmospheres. Astrophys. J. 822, 24 (2016).
Graham, R. J., Lichtenberg, T., Boukrouche, R. & Pierrehumbert, R. T. A multispecies pseudoadiabat for simulating condensable-rich exoplanet atmospheres. Planet. Sci. J. 2, 207 (2021).
Koll, D. D. B. et al. Identifying candidate atmospheres on rocky M dwarf planets via eclipse photometry. Astrophys. J. 886, 140 (2019).
Turbet, M. et al. Day-night cloud asymmetry prevents early oceans on Venus but not on Earth. Nature 598, 276–280 (2021).
Nakajima, S., Hayashi, Y.-Y. & Abe, Y. A study on the ’runaway greenhouse effect’ with a one-dimensional radiative-convective equilibrium model. J. Atmos. Sci. 49, 2256–2266 (1992).
Chaverot, G., Turbet, M., Bolmont, E. & Leconte, J. How does the background atmosphere affect the onset of the runaway greenhouse? Astron. Astrophys. 658, A40 (2022).
Kopparapu, R. K. et al. Habitable zones around main-sequence stars: dependence on planetary mass. Astrophys. J. Lett. 787, L29 (2014).
Watson, A. J., Donahue, T. M. & Kuhn, W. R. Temperatures in a runaway greenhouse on the evolving Venus: implications for water loss. Earth Planet. Sci. Lett. 68, 1–6 (1984).
Abe, Y. & Matsui, T. Evolution of an impact-generated H2O-CO2 atmosphere and formation of a hot proto-ocean on Earth. J. Atmos. Sci. 45, 3081–3101 (1988).
Hamano, K., Kawahara, H., Abe, Y., Onishi, M. & Hashimoto, G. L. Lifetime and spectral evolution of a magma ocean with a steam atmosphere: its detectability by future direct imaging. Astrophys. J. 806, 216 (2015).
Salvador, A. et al. The relative influence of H2O and CO2 on the primitive surface conditions and evolution of rocky planets. J. Geophys. Res. Planets 122, 1458–1486 (2017).
Lichtenberg, T. et al. Vertically resolved magma ocean-protoatmosphere evolution: H2, H2O, CO2, CH4, CO, O2, and N2 as primary absorbers. J. Geophys. Res. Planets 126, e06711 (2021).
Leconte, J. Spectral binning of precomputed correlated-k coefficients. Astron. Astrophys. 645, A20 (2021).
Boukrouche, R., Lichtenberg, T. & Pierrehumbert, R. T. Beyond runaway: initiation of the post-runaway greenhouse state on rocky exoplanets. Astrophys. J. 919, 130 (2021).
Thorngren, D., Gao, P. & Fortney, J. J. The intrinsic temperature and radiative-convective boundary depth in the atmospheres of hot Jupiters. Astrophys. J. Lett. 884, L6 (2019).
Goldblatt, C. Habitability of waterworlds: runaway greenhouses, atmospheric expansion, and multiple climate states of pure water atmospheres. Astrobiology 15, 362–370 (2015).
Nikolaou, A. et al. What factors affect the duration and outgassing of the terrestrial magma ocean? Astrophys. J. 875, 11 (2019).
Turbet, M., Ehrenreich, D., Lovis, C., Bolmont, E. & Fauchez, T. The runaway greenhouse radius inflation effect. An observational diagnostic to probe water on Earth-sized planets and test the habitable zone concept. Astron. Astrophys. 628, A12 (2019).
Andrault, D. et al. Deep and persistent melt layer in the Archaean mantle. Nat. Geosci. 11, 139–143 (2018).
Salvador, A. & Samuel, H. Convective outgassing efficiency in planetary magma oceans: insights from computational fluid dynamics. Icarus 390, 115265 (2023).
Leconte, J., Forget, F., Charnay, B., Wordsworth, R. & Pottier, A. Increased insolation threshold for runaway greenhouse processes on Earth-like planets. Nature 504, 268–271 (2013).
Turbet, M. et al. Revised mass-radius relationships for water-rich rocky planets more irradiated than the runaway greenhouse limit. Astron. Astrophys. 638, A41 (2020).
Agol, E. et al. Refining the transit-timing and photometric analysis of TRAPPIST-1: masses, radii, densities, dynamics, and ephemerides. Planet. Sci. J. 2, 1 (2021).
Acuña, L. et al. Characterisation of the hydrospheres of TRAPPIST-1 planets. Astron. Astrophys. 647, A53 (2021).
Dorn, C. & Lichtenberg, T. Hidden water in magma ocean exoplanets. Astrophys. J. Lett. 922, L4 (2021).
Turbet, M. et al. Modeling climate diversity, tidal dynamics and the fate of volatiles on TRAPPIST-1 planets. Astron. Astrophys. 612, A86 (2018).
Makarov, V. V., Berghea, C. T. & Efroimsky, M. Spin-orbital tidal dynamics and tidal heating in the TRAPPIST-1 multiplanet system. Astrophys. J. 857, 142 (2018).
Barr, A. C., Dobos, V. & Kiss, L. L. Interior structures and tidal heating in the TRAPPIST-1 planets. Astron. Astrophys. 613, A37 (2018).
Papaloizou, J. C. B., Szuszkiewicz, E. & Terquem, C. The TRAPPIST-1 system: orbital evolution, tidal dissipation, formation and habitability. Mon. Not. R. Astron. Soc. 476, 5032–5056 (2018).
Bolmont, E. et al. Solid tidal friction in multi-layer planets: application to Earth, Venus, a super Earth and the TRAPPIST-1 planets. Potential approximation of a multi-layer planet as a homogeneous body. Astron. Astrophys. 644, A165 (2020).
Fulton, B. J. et al. The California-Kepler Survey. III. A gap in the radius distribution of small planets. Astron. J. 154, 109 (2017).
Bean, J. L., Raymond, S. N. & Owen, J. E. The nature and origins of sub-Neptune size planets. J. Geophys. Res. Planets 126, e06639 (2021).
Luque, R. & Pallé, E. Density, not radius, separates rocky and water-rich small planets orbiting M dwarf stars. Science 377, 1211–1214 (2022).
Mousis, O. et al. Irradiated ocean planets bridge super-earth and sub-Neptune populations. Astrophys. J. Lett. 896, L22 (2020).
Aguichine, A., Mousis, O., Deleuil, M. & Marcq, E. Mass-radius relationships for irradiated ocean planets. Astrophys. J. 914, 84 (2021).
Toon, O. B., McKay, C. P., Ackerman, T. P. & Santhanam, K. Rapid calculation of radiative heating rates and photodissociation rates in inhomogeneous multiple scattering atmospheres. J. Geophys. Res. 94, 16287–16301 (1989).
Seeley, J. T. & Wordsworth, R. D. Episodic deluges in simulated hothouse climates. Nature 599, 74–79 (2021).
Gordon, I. E. et al. The HITRAN2016 molecular spectroscopic database. J. Quant. Spec. Radiat. Transf. 203, 3–69 (2017).
Rothman, L. S. et al. HITEMP, the high-temperature molecular spectroscopic database. J. Quant. Spec. Radiat. Transf. 111, 2139–2150 (2010).
Mlawer, E. J. et al. Development and recent evaluation of the MT_CKD model of continuum absorption. Philos. Trans. A Math. Phys. Eng. Sci. 370, 2520–2556 (2012).
Rajpurohit, A. S. et al. Spectral energy distribution of M-subdwarfs: a study of their atmospheric properties. Astron. Astrophys. 596, A33 (2016).
Wordsworth, R. D. et al. Gliese 581d is the first discovered terrestrial-mass exoplanet in the habitable zone. Astrophys. J. Lett. 733, L48 (2011).
Lechevallier, L. et al. The water vapour self-continuum absorption in the infrared atmospheric windows: new laser measurements near 3.3 and 2.0 μm. Atmos. Meas. Tech. 11, 2159–2171 (2018).
Matsui, T. & Abe, Y. Impact-induced atmospheres and oceans on Earth and Venus. Nature 322, 526–528 (1986).
Matsui, T. & Abe, Y. Evolution of an impact-induced atmosphere and magma ocean on the accreting Earth. Nature 319, 303–305 (1986).
Sossi, P. A., Tollan, P. M. E., Badro, J. & Bower, D. J. Solubility of water in peridotite liquids and the prevalence of steam atmospheres on rocky planets. Earth Planet. Sci. Lett. 601, 117894 (2023).
Acknowledgements
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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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.
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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.
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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). https://doi.org/10.1038/s41586-023-06258-3
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DOI: https://doi.org/10.1038/s41586-023-06258-3
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