Oxygen feedback on water loss during the runaway greenhouse phase on terrestrial planets around M dwarfs

Terrestrial planets currently in the habitable zone around M dwarfs are primary targets for exoplanet characterization. Because the pre-main-sequence phase of M dwarfs can last up to about 1 Gyr, such planets are expected to have undergone a prolonged runaway greenhouse (RG) phase, during which surface water is entirely evaporated to form an H₂O-dominated atmosphere (e.g., Kasting 1988; Ramirez & Kaltenegger 2014; Luger & Barnes 2015). H₂O photolysis followed by hydrodynamic hydrogen escape, driven by stellar X-ray and extreme-ultraviolet (XUV) heating, then results in significant planetary water loss over this prolonged phase (e.g., Kasting & Pollack 1983; Johnstone 2020; Yoshida et al. 2022).

The behavior of the oxygen produced by H₂O photolysis affects water loss. If the hydrogen outflow is sufficiently intense, oxygen can be dragged to space along with hydrogen, but the oxygen mass loading lowers the hydrodynamic escape efficiency and thereby slows water loss (e.g., Hunten et al. 1987; Guo 2019; Johnstone 2020). Otherwise, the oxygen left behind forms an O₂-accumulated atmosphere, which can limit the upward diffusive supply of hydrogen to the escape region and thereby slow water loss (e.g., Hunten 1973; Luger & Barnes 2015). Such abiotic O₂ accumulation also bears on the discussion of exoplanet habitability because the resulting oxidizing environment can hinder prebiotic chemistry (e.g., Schlesinger & Miller 1983) and may produce false positives for life (e.g., Wordsworth & Pierrehumbert 2014; Meadows et al. 2018). The behavior of oxygen during the RG phase is therefore central to understanding the habitability of terrestrial planets currently in the habitable zone around M dwarfs.

However, the feedback of the retained oxygen on water loss and habitability remains poorly understood. Kawamura et al. (2024) showed that UV shielding by O₂ retained in the atmosphere reduces the water loss rate. Such chemically mediated feedback can in turn modify both the water loss process and the formation of O₂-accumulated atmospheres. Yet such feedback remains unresolved in existing hydrodynamic escape models, which are confined to the upper atmosphere and treat neither lower-atmosphere chemistry and diffusion nor the long-term evolution of the RG phase.

Building on the 1D photochemical model of Kawamura et al. (2024), we develop a new 1D hydrodynamic escape model for an H₂O-dominated atmosphere on an Earth-like planet orbiting an M dwarf. The model extends from the thermosphere down to the surface and couples atmospheric dynamics, photochemistry, molecular and eddy diffusion, and radiative transfer, allowing us to track the transport of H- and O-bearing species under both diffusive separation and hydrodynamic outflow.

The bulk atmospheric motion is calculated by solving the 1D hydrodynamic equations for mass, momentum, and energy, following the framework of Johnstone et al. (2018). The energy equation includes stellar XUV heating, chemical heating and cooling, thermal conduction, and radiative cooling by H₂O and chemical products such as OH, treated following Yoshida et al. (2022). We adopt the H- and O-bearing chemical network of Chaffin et al. (2017), as in Kawamura et al. (2024), and calculate photolysis rates using the stellar UV spectrum of TRAPPIST-1 (Wilson et al. 2021).

To integrate the coupled advection–diffusion–chemistry continuity equation over the runaway greenhouse phase, we use a semi-IMEX Runge–Kutta scheme (Ding 2025), treating advective transport explicitly and stiff diffusion and chemical terms implicitly. The equation is solved with the “modified pass flow” algorithm, following Chaufray et al. (2024), to improve numerical stability and efficiency. We assume the runaway greenhouse phase to last 1 Gyr (Ramirez & Kaltenegger 2014). Using this model, we quantify how the retained oxygen feeds back on water loss and shapes the post-RG atmospheric composition of terrestrial planets around M dwarfs, with implications for their habitability.