Water worlds or Gas Dwarfs? Coupled Interior-Atmosphere Models Blur the Lines in Sub-Neptune Radius Evolution

The low bulk density of sub-Nepuntes suggest that these planets contain a significant amount of volatile elements, yet their precise composition remains uncertain. The two leading composition models are the gas dwarf scenario and the water world scenario. In the first scenario, sub-Neptunes are Earth-like planets surrounded by an H₂/He-dominated atmosphere. In the second scenario, sub-Neptunes form beyond the ice line and accrete several tens of percents of water as well as a few weight percent of H₂/He (Burn et al. 2024). Current evolution models predict that the evolution of the planet radius with time differs significantly between the gas dwarfs and water worlds, making it possible to distinguish between the two composition types (Aguichine et al. 2024, Rogers 2025).  However, these models assume that all water is confined to the atmosphere of the planet, overlooking the chemical exchange between the atmosphere and the molten interior.

We present a novel evolution framework that incorporates global chemical equilibrium calculations and fractionated mass loss to quantify the effects of the atmosphere-interior coupling on the radius evolution. Recent works by Werlen et al. (in prep) demonstrate that the chemical coupling between the atmosphere and interior modifies the atmospheric water mass fraction. Figure 1 below shows the water mass fraction in the envelope as a function of the total accreted water mass for planets with masses between 2 and 15 Earth masses, based on the results from Werlen et al. (in prep). The red line denotes the solar water mass fraction of 0.02. The colors represent the molar bulk C/O ratio, which can be seen as an indicator for the formation location of the planet. For water worlds that form outside the ice line as indicated by a high C/O ration and M_H2O/M_tot (accreted) > 10%, the bulk of the accreted water is sequestered into the interior of the planet. The water mass fraction in the atmosphere is thus limited to ~10%. Planets formed inside the ice line on the other hand can have high water mass fractions in the atmosphere due to the endogenic production of water.

Motivated by the results of Werlen et al. (in prep), we integrate global chemical equilibrium calculations into our planetary structure models to track the distribution of volatiles between atmosphere and interior. The updated structure models are then embedded in a thermal evolution framework that accounts for the cooling by radiation and the radiogenic heating. Figure 2 below compares the evolution of the atmosphere thickness, defined as R_transit - R_solid, between a gas dwarf with a pure H₂/He atmosphere and a water world with a realistic water distribution. In both cases, the total planet mass is 5 Earth masses, the envelope mass is 0.05 Earth masses and the equilibrium temperature is 880 K. As expected, the atmosphere thickness of the water world is smaller than the one of the gas dwarf. Nevertheless, both scenarios display similar temporal evolution trends. An important implication of our findings is that it will be challenging to distinguish between sub-Neptunes that formed inside or outside the ice line using the population of planets with different ages observed by TESS. 

Our evolution framework also incorporates fractionated mass loss driven by photoevaporation, following the approach of Valatsou et al. (in prep). The mass loss model self-consistently calculates the EUV and X-ray absorption depth (R_XUV), the sound speed at the R_XUV, and the resulting mass loss rate for atmospheres containing a mix of H₂, He, and H₂O. More importantly, the model includes the dissociation of the H₂ and H₂O into atomic hydrogen and oxygen. Due to the mass difference, hydrogen escapes more efficiently, while the oxygen escape rate is regulated by the balance between the gravitational settling and the diffusive drag from the escaping hydrogen. Valatsou et al. (in prep) find that this progress leads to significant atmospheric fractionation: oxygen is largely retained in the atmosphere, while hydrogen escapes efficiently. As a result, the atmospheres of sub-Neptunes become enriched in oxygen over time. 

Our evolution framework offers a more complete picture of the evolution of sub-Neptune by including both the chemical coupling of the atmosphere and interior, as well as the fractionated atmospheric escape. The predicted similarity in the radius evolution of gas dwarfs and water worlds, suggests that the radius-age relation alone may not be enough to distinguish between the two composition types. Instead, our framework lays the groundwork for understanding the bulk composition and formation location of sub-Neptunes based on their radius, age, and atmospheric composition.

References:

• Aguichine, A., Batalha, N., Fortney, J. J., et al. 2024, arXiv e-prints, arXiv:2412.17945
• Burn, R., Mordasini, C., Mishra, L., et al. 2024b, Nature Astronomy, 8, 463
• Rogers, J. G. 2025, MNRAS, 539, 2230
• Valatsou, M., Owen, J., Dorn, C., in prep
• Werlen, A., Dorn, C., Burn, R., Schlichting, H., Grimm, S., Young, E., in prep