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

Abstract: 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)