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

TL;DR

This work develops a coupled thermal-chemical evolution framework for sub-Neptunes that integrates planetary structure, thermal evolution, and global chemical equilibrium to model atmosphere–interior exchange. By comparing two 4 $M_\oplus$ planets formed inside and outside the water ice line, the study shows that chemical coupling can drastically alter the initial atmospheric mass, metallicity, and volatile partitioning, leading to divergent C/O and methane signatures over gigayear timescales. Importantly, radius evolution alone fails to distinguish formation location since atmospheric mass increases from volatile exsolution counteract cooling. The atmospheric CH$_4$ abundance and the atmospheric C/O ratio emerge as robust tracers of formation location, enabling observational discrimination with JWST and Ariel-era data, while highlighting the necessity of chemically coupled models to accurately infer a planet’s volatile inventory and origin.

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)

Figures (7)

• Figure 1: Comparison of the evolution of a $4\,M_\oplus$ with atmosphere-interior coupling (solid lines) and in the uncoupled case (dashed lines). The orange lines represent a sub-Neptune formed inside the water ice line, while the blue lines correspond to a planet formed outside the water ice line. Both planets have a total mass of $4\,M_\oplus$ and an equilibrium temperature of $T_\mathrm{eq}=800\,\K$. The top row shows the evolution of the atmosphere mass fraction and the temperature at the AMOI. The bottom row shows the evolution of the transit radius and the atmosphere metallicity. The symbols mark the snapshots at which the atmosphere mass and composition are recalculated in the chemically coupled case. For both planets, the outgassing of volatiles as the magma ocean cools leads to an increase in the atmosphere mass fraction. For the planet formed inside the water ice line, the outgassing is strong enough to lead to a slight increase in radius with time and a decrease in the metallicity. The high accreted water abundance of the planet formed outside the water ice line results in roughly constant radius and metallicity with time.
• Figure 2: Partitioning of H (left), C (middle), and O (right) into metallic (dotted line), silicate (dashed line), and gaseous phases (solid line) over time. The gas phase refers to the atmosphere of the planet, while the metallic and silicate phase refer to the deep planet interior. It is important to note that the fractions are normalized to the total abundance of each element and that only oxygen in non-silicate species is shown. The orange lines correspond to a planet formed inside the water ice line, while the blue lines shows a planet formed outside the water ice line. In both cases, the total planet mass is $4\,M_\oplus$. For the planet formed dry, carbon is predominantly in the metallic phase, while for the planet formed outside the water ice line carbon is primarily in the gas phase. The fraction of C in the silicate phase for the planet formed dry is negligible.
• Figure 3: Evolution of the atmospheric C/O ratio for the planet formed dry (orange line) and the planet formed outside the water ice line (blue line). The atmospheric C/O ratio differs by almost four orders of magnitudes between the two formation locations at the end of the evolution.
• Figure 4: Evolution of the mole fractions of major atmospheric species over time. The left planet shows the atmosphere composition for a planet formed inside the water ice line and the right plot for a planet formed outside the water ice line. The planet mass is $4\,M_\oplus$ in both cases. For both planets, H2 and H2O are the major atmospheric species. However, the mole fractions of CH4, CO2, and CO2 in the atmosphere of the planet formed outside the water ice line are several orders of magnitudes greater than the mole fractions in the planet formed inside the water ice line.
• Figure 5: Molar gas fraction of H2O versus CH4 (left plot) and molar gas fraction of CH4 versus atmospheric C/O ratio (right plot) for a synthetic population of planets (see Table \ref{['tab:parameterrange']}). The colors and symbols represent the accreted water mass content ($f_{\ce{H2O}}$) and thus indicates dry or water-rich formation. High CH4 abundances ($\geq10^{-2}$) and high atmospheric C/O ratios ($\geq$C/O$_{solar}$) are only found in atmospheres of planets formed water-rich ($f_{\ce{H2O}}\geq 0.1$).