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The interior as the dominant water reservoir in super-Earths and sub-Neptunes

Nature Astronomy volume 8, pages 1399–1407 (2024)Cite this article

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Abstract

Water is an important component of exoplanets, with its distribution, that is, whether at the surface or deep inside, fundamentally influencing the planetary properties. The distribution of water in most exoplanets is determined by yet-unknown partition coefficients at extreme conditions. Here we first conduct ab initio molecular dynamics simulations to investigate the metal–silicate partition coefficients of water up to 1,000 GPa and then model planet interiors by considering the effects of water content on density, melting temperature and water partitioning. Our calculations reveal that water strongly partitions into iron over silicate at high pressures and, thus, would preferentially stay in a planet’s core. The results of our planet interior model challenge the notion of water worlds as imagined before: the majority of the bulk water budget (even more than 95%) can be stored deep within the core and the mantle, and not at the surface. For planets more massive than ~6 M⨁ and Earth-size planets (of lower mass and small water budgets), the majority of water resides deep in the cores of planets. Whether water is assumed to be at the surface or at depth can affect the radius up to 15–25% for a given mass. The exoplanets previously believed to be water-poor on the basis of mass–radius data may actually be rich in water.

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Fig. 1: Partition coefficients of H2O.
Fig. 2: Four model scenarios employed in our study.
Fig. 3: The effect of water partitioning into the core and mantle on mass–radius relationships.
Fig. 4: Water mass fractions stored in the mantle and the core depending on planet mass (thick lines) and bulk water mass fraction (thin lines).
Fig. 5: Mass–radius curves compared with the sample of small transiting planets around M dwarfs from Luque and Pallé29.

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Data availability

Authors can confirm that all relevant data are included in the Article and Supplementary Information files. Data used in the figures and our raw simulation outputs are available from figshare at https://doi.org/10.6084/m9.figshare.25800577 (ref. 74).

Code availability

The VASP is a proprietary software available for purchase at https://www.vasp.at/. The code for performing planetary interior modelling is available from the corresponding authors on reasonable request.

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Acknowledgements

The work reported in this paper was conducted using the Princeton Research Computing, which is a consortium of groups led by the Princeton Institute for Computational Science and Engineering (PICSciE) and the Office of Information Technology’s Research Computing. J.D. acknowledges support from the National Science Foundation under grant no. EAR-2242946. C.D. acknowledges support from the Swiss National Science Foundation under grant TMSGI2_211313. In parts, this work has been carried out within the framework of the NCCR PlanetS supported by the Swiss National Science Foundation under grants 51NF40_182901 and 51NF40_205606 to C.D.

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  1. These authors contributed equally: Haiyang Luo, Caroline Dorn.

Authors and Affiliations

  1. Department of Geosciences, Princeton University, Princeton, NJ, USA

    Haiyang Luo & Jie Deng

  2. Institute for Particle Physics and Astrophysics, ETH Zurich, Zurich, Switzerland

    Caroline Dorn

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  1. Haiyang Luo
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Contributions

Conceptualization: J.D. and C.D. Methodology: H.L. and C.D. Investigation: H.L. and C.D. Formal analysis: H.L., C.D. and J.D. Writing—original draft: H.L. and C.D. Writing—review and editing: H.L., C.D. and J.D. Supversion: J.D. Funding acquistion: J.D. and C.D.

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Correspondence to Haiyang Luo, Caroline Dorn or Jie Deng.

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Extended data

Extended Data Fig. 1 Gibbs free energies.

Calculated Gibbs free energies of \({{\rm{Fe}}}_{1-x}{\left({{\rm{H}}}_{2}{\rm{O}}\right)}_{x}\) (a) and \({\left({{\rm{MgSiO}}}_{3}\right)}_{1-x}{\left({{\rm{H}}}_{2}{\rm{O}}\right)}_{x}\) (b) melts as a function of H2O mole fractions (\({X}_{{{\rm{H}}}_{2}{\rm{O}}}\)).

Extended Data Fig. 2 Chemical potentials of H2O.

Calculated chemical potentials of H2O in iron (Fe) and silicate (MgSiO3) melts and their differences (MgSiO3-Fe) at different temperatures under 500 GPa (a) and 1000 GPa (b). The 1 s.d. uncertainties of chemical potentials are shown. Lines connecting the data points are shown for clarity.

Extended Data Fig. 3 Partition coefficients of H2O.

Calculated partition coefficients of H2O between iron and silicate melts (\({D}_{{{\rm{H}}}_{2}{\rm{O}}}^{{\rm{Fe}}/{\rm{MgSi}}{{\rm{O}}}_{3}}\)) as a function of its concentrations in iron melt (\({X}_{{{\rm{H}}}_{2}{\rm{O}}}^{{\rm{Fe}}}\)) at different temperatures under 500 GPa (a) and 1000 GPa (b). The 1 s.d. uncertainties of \({D}_{{{\rm{H}}}_{2}{\rm{O}}}^{{\rm{Fe}}/{\rm{MgSi}}{{\rm{O}}}_{3}}\) at 8600 and 13000 K are represented by the shaded area.

Extended Data Fig. 4 Molecular dynamics simulations of water partitioning.

Two-phase coexistence simulations of water (\({X}_{{{\rm{H}}}_{2}{\rm{O}}}=1.54\) wt%) partitioning between iron (Fe) and silicate (MgSiO3) melts at 500 GPa/9000 K and 1000 GPa/14000 K. a, The initial configurations and the snapshots at 5000 femtoseconds (fs) are shown. b, The corresponding instantaneous coarse-grained density profile (filled circles) along the z-axis of the simulation box at 5000 fs and the best fitting curve (solid line). The dashed vertical lines represent the locations of Gibbs dividing surfaces.

Extended Data Fig. 5 Density profiles for planets of 2 M⨁ and 20 % bulk water mass fraction at Teq of 700 K.

The total radius for each of the scenarios is highlighted as a vertical line (red: B, lilac: C, blue: D). The different distributions of water in planets change density structure, thermal structure (not shown), melting temperatures (not shown), and hence the extent of molten layers. Wherever the density profiles seem to flatten, we checked that all densities increase at all pressures. The density difference at the core-mantle boundary here is larger than that shown in the Extended Data Fig. 4b due to pressure differences.

Extended Data Table 1 Calculated Gibbs free energies
Full size table
Extended Data Table 2 Calculated Gibbs free energies as a function of temperature at 500 and 1000 GPa
Full size table

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Supplementary Information

Supplementary discussion, Figs. 1–3 and Table 1.

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Luo, H., Dorn, C. & Deng, J. The interior as the dominant water reservoir in super-Earths and sub-Neptunes. Nat Astron 8, 1399–1407 (2024). https://doi.org/10.1038/s41550-024-02347-z

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