What's Inside Matters: The Effect of Oxygen Fugacity and Initial Volatile Abundance on the Atmospheres of the TRAPPIST-1 Planets

TL;DR

This study addresses how interior state variables, notably mantle oxygen fugacity ($fO_2$) and initial volatile budgets, shape the atmospheres of rocky exoplanets around M-dwarfs. It advances an atmosphere–interior exchange model by incorporating the carbon cycle, deep-water cycling, surface-temperature coupling, and diffusion-limited hydrogen escape, and it validates the Earth case before applying the model to TRAPPIST-1 d, e, and f. The results show that $fO_2$ strongly modulates $H_2$ and $CO_2$, while the water abundance (WMF) principally controls $H_2$; the inclusion of atmospheric sinks (CO oxidation and hydrogen escape) significantly shifts $H_2$ and $CO$ abundances. These findings underscore the need to embed interior geochemistry in interpretations of future atmospheric observations and provide a flexible framework for linking JWST data to planetary interiors.

Abstract

The TRAPPIST-1 planets have become prime targets for studying the atmospheric and geophysical properties of planets around M-dwarf stars. To effectively identify their atmospheric composition, we first must understand their geological evolution. For this study, we focus on enhancing an existing atmosphere-interior exchange model by incorporating additional geological processes relevant to rocky planets. We have extended the model to include the carbon cycle, which enables the model to track four key gas species - CO$_2$, CO, H$_2$O, and H$_2$ - across four planetary reservoirs: the mantle, plate, ocean, and atmosphere. Major features added include surface temperature calculations which are crucial for the carbon cycle, oxygen fugacity as a planetary interior parameter in the model, and oxidation reactions and diffusion-limited escape calculations to the atmosphere portion of the model. We successfully validated the model for Earth and applied this model to study the effect of oxygen fugacity and initial water abundance on TRAPPIST-1 d, e and f. Our results for present-day abundances show that oxygen fugacity significantly affects the partial pressures of H$_2$ and CO$_2$ for all three planets with minor effects for CO on two of the planets. We also found that H$_2$ is strongly dependent on water mass fraction (WMF). The addition of atmospheric processes produced a significant difference in the H$_2$ and CO abundances at present-day. These results highlight the importance of considering interior parameters to be able to further constrain the geological evolution of these planets and effectively put atmosphere observations into context.

Figures (8)

• Figure 1: Overview of the atmosphere-interior exchange model we use for this study including the various geological processes that we simulate and the various parameters we consider in this model. The carbon cycle is the major overarching process added to this model, which is a negative feedback cycle that regulates the temperature of the planet over geologic timescales, which is crucial for studying habitability.
• Figure 2: Partial pressure evolution of the atmospheric gases for the nominal cases for TRAPPIST-1 d (left), e (middle), and f (right). The oxygen fugacity is set to IW+4 and water mass fraction is set to a nominal value following agol_2021. CO$_{2}$ is given by the red line, CO by the orange line, H$_{2}$ by the pink line and H$_{2}$O by the blue line. We see that for the nominal cases, planet d is mostly dominated by H$_2$O and CO$_2$ over its evolution. Planet e and f have higher gas abundances for all gas species over their evolution with the difference that TRAPPIST-1e is dominated by CO$_2$ and H$_2$O and TRAPPIST-1f is dominated by CO$_2$, H$_2$ followed by H$_2$O. Planet f is the only one that has a CO dominated atmosphere at present-day.
• Figure 3: Evolution of the ocean mass for the nominal cases for TRAPPIST-1 e and f. Planet d is not shown because it does not have sufficient surface water to produce an ocean over its evolution. We normalize the ocean mass to its initial water abundance, which differs by planet. We observe that with increasing orbital distance from the star for the nominal cases, the outer planets are able to retain their water in liquid form on their surface for most of its evolution with planet e beginning to lose water to the interior around 1 billion years and planet f retaining the highest amount of liquid water at present day. Planet d has most of its water in the plate, with the remaining water surface mass in the atmosphere.
• Figure 4: Surface temperature evolution of TRAPPIST-1d, e and f for the nominal cases over time. Planet d is given by the purple line, planet e by the olive-green line and planet f by the blue line. The dashed lines are their respective equilibrium temperatures. Planet e is the hottest planet of the three in the first 100 million years due to its high CO$_2$ abundance in its atmosphere and its equilibrium temperature, followed by planet f which also has a similarly high CO$_2$ abundance but a lower equilibrium temperature. Planet d starts at the lowest temperature of all the planets, despite a higher equilibrium temperature, due to the low atmospheric pressures. However, at present day, planet d is the hottest with its surface temperature exceeding the equilibrium temperature, followed by planet e reaching its equilibrium temperature and planet f being the coldest of all the planets with a surface temperature below its equilibrium temperature and significantly below the freezing point of water (273 K).
• Figure 5: Comparison of the partial pressure evolution of the atmospheric gases for TRAPPIST-1e either with (solid lines) or without (dashed-lines) diffusion-limited escape and the CO-oxidation reaction. We assume the water mass fraction is the nominal value following agol_2021. Left panel is for an oxygen fugacity of IW-2, middle panel is IW, and right panel is IW+4. CO$_{2}$ is given by the blue line, CO by the green line, H$_{2}$ by the pink line and H$_{2}$O by the orange line. We show both the effect of including CO oxidation reaction and diffusion limited escape to our model, which affects CO and hydrogen abundances significantly, as well as shows the the effect of oxygen fugacity on the partial pressures for TRAPPIST-1e.