Evolution of steam worlds: energetic aspects

TL;DR

This work develops a time-evolving, compositionally consistent model for steam worlds by coupling a five-layer interior structure with a pure-H2O atmosphere grid. The approach reveals that pure-water envelopes yield radii smaller by up to ~10% and contract more slowly than previous static models, with deep water potentially transitioning from plasma to superionic ice influencing thermal evolution. A grid of evolutionary tracks is provided to infer bulk water content from mass, radius, and age, and comparisons with prior models highlight significant EOS- and gradient-driven differences in inferred WMF. The study emphasizes the importance of fully modeling volatile-rich planets and offers pathways to connect interior physics to JWST- and Gaia-era observations, while noting limitations and avenues for future extensions (e.g., H2-He mixtures, hazes).

Abstract

Sub-Neptunes occupy an intriguing region of planetary mass-radius space, where theoretical models of interior structure predict that they could be water-rich, where water is in steam and supercritical state. Such planets are expected to evolve according to the same principles as canonical H$_2$-He rich planets, but models that assume a water-dominated atmosphere consistent with the interior have not been developed yet. Here, we present a state of the art structure and evolution model for water-rich sub-Neptunes. Our set-up combines an existing atmosphere model that controls the heat loss from the planet, and an interior model that acts as the reservoir of energy. We compute evolutionary tracks of planetary radius over time. We find that planets with pure water envelopes have smaller radii than predicted by previous models, and the change in radius is much slower (within $\sim$10\%). We also find that water in the deep interior is colder than previously suggested, and can transition from plasma state to superionic ice, which can have additional implications for their evolution. We provide a grid of evolutionary tracks that can be used to infer the bulk water content of sub-Neptunes. We compare the bulk water content inferred by this model and other models available in the literature, and find statistically significant differences between models when the uncertainty on measured mass and radius are both smaller than 10\%. This study shows the importance of pursuing efforts in the modeling of volatile-rich planets, and how to connect them to observations.

Figures (4)

• Figure 1: Evolution of the radius of a GJ1214b-like planet of mass 6.55 $\mathrm{M}_\oplus$ with 97% H2O and equilibrium temperature of 555 K orbiting an M-type star. Red, black, and blue lines are this work, case IIb from Nettelmann2011, and the static model from Aguichine2021. The A21 and A25 models assume $P_{\mathrm{tr}}=1$$\mu$bar, and N11 assumes $P_{\mathrm{tr}}=20$ mbar. The A25 model is shown for $t_0=10$ Myr (solid), 1 Myr (dashed) and 0 Myr (dotted). Points along the curve and labels represent values of $T_{\mathrm{int}}$ in K. The red dashed line after 20 Gyr shows evolution towards full exhaustion (see Section \ref{['sec:coupling-method']}). The horizontal dashed black line corresponds to the central value of the radius of GJ 1214b, and the shaded area is the associated uncertainty Charbonneau2009.
• Figure 2: Phase diagram of water with Pressure-Temperature profiles in the planet interior and atmosphere at several given times of the planet evolution, for the planet evolution shown in Figure \ref{['fig:compare-radius']}. Red lines are the profiles of the A25 model, shown for $T_{\mathrm{int}}=$ 400, 132, 70, 53, and 30 K. The red dashed line represents the theoretical fully exhausted state of this planet. Black dash-dotted lines are the profiles of the N11 model, shown for $T_{\mathrm{int}}=$ 132, 70, 53, and 30 K. The corresponding ages for for the A25 and N11 models, for each value of $T_{\mathrm{int}}$, are given on the figure. The blue line corresponds to the structure computed in Aguichine2021 for a 5 $\mathrm{M}_\oplus$ planet with $T_{\mathrm{eq}}=700$ K and $x_{\mathrm{H_2O}}=1$. This structure does not correspond to the planet radius depicted in Figure \ref{['fig:compare-radius']}, but is the structure available closest to parameters of GJ 1214b. Phase boundaries are from Wagner2011 and Nettelmann2011.
• Figure 3: Interior structure models in the mass-radius plane (left panel) and slice at $5~\mathrm{M}_\oplus$ in the radius-time plane (right panel): evolving steam worlds (red solid lines, A25), static steam worlds (blue dashed lines, A21), 50% isothermal steam worlds (teal solid line, Z19), Earth-like planets (brown solid line, Z16), and 5% H2-He planets (yellow solid lines, LF14). Red and blue lines are shown for bulk water content of 10%, 50% and 100%, and for the red lines an M-type host star is assumed. Red and yellow shaded regions represent the span of evolution models of A25 and LF14, respectively. LF14 evolution is shown between 0.1 and 10 Gyr. A25 evolution is shown between 0.02 Gyr and 20 Gyr. All models assume an equilibrium temperature of 700 K, except the red dashed line in the right panel, which shows the A25 model at 500 K. Red dotted lines correspond to cases where the steam atmosphere thickness is underestimated by $1\%$ because of constant surface gravity (see Appendix \ref{['sec:appendix-constant-g']}). Exoplanets properties are obtained from the NASA Exoplanet Archive, including 6 planets of interest shown with orange stars (see Appendix \ref{['sec:appendix-catalog']} for details). Solar system planets are shown with orange circles.
• Figure 4: Inferred water mass fraction of 5 exoplanets, 4 of which have been observed with JWST and found to have high mean molecular weight atmospheres. The WMF were inferred using the Z16 Zeng2016, A21 Aguichine2021 and A25 (this work) models. Green values correspond to the range of WMF inferred by the model of Nixon2024. Planets were ordered by decreasing central value of planetary radius.