Coupled thermal-chemical evolution models of sub-Neptunes reveal atmospheric signatures of their formation location

The observed masses and radii of sub-Neptunes can be explained by a variety of bulk compositions, with the two leading scenarios being the gas dwarf and the water world scenario. The evolutionary history of sub-Neptunes on a population level has been proposed as a method to distinguish between the possible bulk compositions. Previous evolutionary models, however, neglected the crucial role of chemical interactions between the atmosphere and interior. We present a novel evolution framework for sub-Neptunes that not only considers the thermal evolution but also takes the chemical coupling of atmosphere and interior into account. Using this model, we examine how planets formed inside and outside the ice line can be observationally distinguished. Young sub-Neptunes store the majority of their volatile budget in the interior, independent of formation location and thus initial composition. Nevertheless, the atmospheric metallicity is a factor 4 higher for the planet formed outside the ice line. As the planet cools, hydrogen and oxygen exsolve from the interior, leading to an increase in atmosphere mass fraction for both planets, counteracting the contraction due to cooling. Consequently, radius evolution alone cannot distinguish sub-Neptunes formed inside the water ice line from water-rich planets formed outside of it. Instead, a key discriminator is the abundance of carbon-bearing species and the resulting atmospheric C/O ratio. For water-rich sub-Neptunes formed outside the \ice line, almost all carbon is in the gaseous phase. We find that high molar fractions of CH$_4$ ($>10^{-2}$) and H$_2$O ($> 5\times10^{-2}$), and a high C/O ratio $(> 5\times10^{-1})$ are indicative of formation outside the ice line. In contrast, sub-Neptunes formed inside the ice line exhibit strongly suppressed CH$_4$ abundances, yielding C/O ratios ranging widely from $10^{-7}$ to $10^{-1}$. (Shortened version)

💡 Research Summary

The authors present a comprehensive evolution framework for sub‑Neptune‑size exoplanets that simultaneously treats thermal evolution and the chemical coupling between the atmosphere and the deep interior. Traditional models have treated the envelope and interior as chemically isolated, limiting their ability to distinguish between the “gas dwarf” (H₂/He‑dominated) and “water world” (high‑water‑mass‑fraction) scenarios that can both reproduce observed mass‑radius relationships. By incorporating a global chemical equilibrium (GCE) calculation at the atmosphere‑magma‑ocean interface (AMOI), the new model tracks the redistribution of 26 chemical species among three phases—metallic core, silicate mantle, and gaseous envelope—through a network of 19 independent reactions. The equilibrium condition includes temperature‑dependent Gibbs free energies, pressure corrections for gases, and a novel treatment of carbon partitioning into the metallic phase.

The planetary structure is built from a central iron core, a silicate mantle (solid and liquid phases) and an overlying atmosphere. The atmosphere is divided into an irradiated upper layer modeled with Guillot’s semi‑grey radiative‑convective scheme (including visible‑to‑thermal opacity ratio γ) and a deeper non‑irradiated region where radiative or convective gradients are applied. Opacities are taken from Jin et al. (2014) for γ and Freedman et al. (2014) for thermal Rosseland means. Interior thermal evolution follows the total‑energy conservation equation dE_tot/dt = −L, where E_tot includes gravitational and thermal contributions of both interior and envelope, plus a term for radiogenic heating from ⁴⁰K, ²³⁸U, and ²³²Th. The interior is approximated as an isothermal sphere of constant density to simplify the gravitational energy term, a choice justified by previous work showing negligible impact on long‑term cooling.

Two end‑member formation pathways are explored: (1) planets formed inside the water ice line that accrete only H₂/He (the gas‑dwarf case) and (2) planets formed beyond the ice line that accrete both H₂/He and a substantial amount of H₂O (the water‑rich case). In both cases, early evolution is characterized by most volatiles being stored in the deep magma ocean, but the water‑rich planets retain an atmospheric metallicity roughly four times higher than the gas‑dwarf counterparts. As the planets cool, hydrogen and oxygen exsolve from the interior, increasing the atmospheric mass fraction and partially offsetting the radius contraction that would otherwise occur. Consequently, radius evolution alone cannot reliably separate the two formation scenarios.

The decisive discriminants emerge from the atmospheric chemistry. In water‑rich planets, virtually all carbon remains in the gas phase, leading to molar fractions of CH₄ > 10⁻² and H₂O > 5 × 10⁻², and a carbon‑to‑oxygen ratio (C/O) exceeding 0.5. By contrast, gas‑dwarf planets exhibit strongly suppressed CH₄ abundances; their C/O ratios span a wide range from 10⁻⁷ to 0.1. These signatures are robust against variations in interior mixing because the chemical equilibrium at the AMOI directly controls the partitioning of carbon, oxygen, and hydrogen between phases. The authors argue that high‑precision transmission or emission spectroscopy with JWST or next‑generation facilities can detect the required CH₄, H₂O, and C/O levels, providing a clear observational test of formation location.

Additional insights include the role of metallic‑silicate mixing: the model assumes that metallic and silicate phases remain mixed throughout evolution, allowing carbon to dissolve partially into the metallic component. This contrasts with earlier studies that treated the core and mantle as fully separated, and it yields subtle differences in the timing and magnitude of volatile exsolution. The authors also deliberately omit atmospheric escape and silicate‑hydrogen miscibility to isolate the impact of atmosphere‑interior chemical coupling.

In summary, the paper demonstrates that coupled thermal‑chemical evolution models reveal distinct atmospheric fingerprints—particularly CH₄, H₂O abundances and C/O ratios—that can be used to infer whether a sub‑Neptune formed inside or outside the water ice line. This approach surpasses purely radius‑based population studies and offers a pathway to constrain planet formation histories using forthcoming spectroscopic observations.