Coupled Thermal-Chemical Evolution Models of Sub-Neptunes Reveal Atmospheric Signatures of Their Formation Location

The observed masses and radii of sub-Neptunes are typically explained by the gas dwarf and the water world scenarios. While their evolutionary history on a population level has been proposed as a method to distinguish between these compositions, previous evolutionary models, neglected the crucial role of atmosphere-interior chemical interaction. We present a novel evolution framework for sub-Neptunes that combines the thermal evolution with the chemical coupling of the atmosphere and interior. Using this model, we examine how planets formed inside and outside the water-ice line can be observationally distinguished, with an emphasis on their atmospheric properties. Young sub-Neptunes store the majority of their volatile budget in the interior, regardless of formation location. Nevertheless, the atmospheric metallicity is a factor 4 higher for the planet formed outside the water-ice line. During cooling, hydrogen and oxygen exsolve from the interior, increasing the atmospheric mass fraction and counteracting the thermal contraction. Consequently, radius evolution alone cannot distinguish between the two formation scenarios. Instead, the primary discriminators are the abundance of carbon-bearing species and the resulting atmospheric C/O ratio. For sub-Neptunes formed beyond the water-ice line, nearly all carbon resides 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 water-ice line. In contrast, sub-Neptunes formed inside the water-ice line exhibit strongly suppressed CH$_4$ abundances, yielding C/O ratios ranging from $10^{-7}$ to $10^{-1}$.