Towards a self-consistent evaluation of gas dwarf scenarios for temperate sub-Neptunes

The recent JWST detections of carbon-bearing molecules in a habitable-zone sub-Neptune have opened a new era in the study of low-mass exoplanets. The sub-Neptune regime spans a wide diversity of planetary interiors and atmospheres not witnessed in the solar system, including mini-Neptunes, super-Earths, and water worlds. Recent works have investigated the possibility of gas dwarfs, with rocky interiors and thick H$_2$-rich atmospheres, to explain aspects of the sub-Neptune population, including the radius valley. Interactions between the H$_2$-rich envelope and a potential magma ocean may lead to observable atmospheric signatures. We report a coupled interior-atmosphere modelling framework for gas dwarfs to investigate the plausibility of magma oceans on such planets and their observable diagnostics. We find that the surface-atmosphere interactions and atmospheric composition are sensitive to a wide range of parameters, including the atmospheric and internal structure, mineral composition, volatile solubility and atmospheric chemistry. While magma oceans are typically associated with high-temperature rocky planets, we assess if such conditions may be admissible and observable for temperate sub-Neptunes. We find that a holistic modelling approach is required for this purpose and to avoid unphysical model solutions. We find using our model framework and considering the habitable-zone sub-Neptune K2-18 b as a case study that its observed atmospheric composition is incompatible with a magma ocean scenario. We identify key atmospheric molecular and elemental diagnostics, including the abundances of CO$_2$, CO, NH$_3$ and, potentially, S-bearing species. Our study also underscores the need for fundamental material properties for accurate modelling of such planets.