The Importance of the Upper Atmosphere to CO/O₂ Runaway on Habitable Planets Orbiting Low-mass Stars

The launch of JWST has begun a new era in the characterization of exoplanet atmospheres. JWST has already revolutionized the study of gas giant exoplanet atmospheres, detecting novel chemical species and using them to infer operant chemical processes (Tsai et al. 2023). In the future, JWST will similarly seek to characterize the atmospheres of smaller exoplanets, including potentially habitable temperate terrestrial worlds, and such observations have already begun (Lafreniere 2017; Lewis et al. 2017; Lustig-Yaeger et al. 2019; Lim et al. 2021; Stevenson et al. 2021). Such observations may constrain surface processes such as volcanism, geochemical cycling, and the presence of life (Kaltenegger & Sasselov 2010; Kaltenegger et al. 2010; Misra et al. 2015; Krissansen-Totton et al. 2018; Fauchez et al. 2020; Lehmer et al. 2020; Zhan et al. 2021; Ranjan et al. 2022).

Particularly relevant in the quest to characterize temperate terrestrial exoplanets are planets with anoxic, CO₂-rich atmospheres orbiting M dwarf stars. CO₂-rich atmospheres are expected to be ubiquitous on terrestrial exoplanets, as they are in the solar system, thanks to robust outgassing of CO₂ by basaltic magmatism (Gaillard & Scaillet 2014; Catling & Kasting 2017). Such high mean molecular mass secondary atmospheres are only accessible to atmospheric characterization with JWST for planets orbiting M dwarf stars. Planets with CO₂-rich atmospheres orbiting M dwarf stars are therefore highly observationally relevant, and it is critical to understand their atmospheric photochemistry to accurately interpret anticipated observations of their atmospheres (Shields et al. 2016; Catling et al. 2018).

Atmospheric photochemical models of planets with CO₂-rich atmospheres orbiting M dwarf stars are historically discrepant, with observationally relevant implications for the abundance of spectroscopically active trace gases proposed as probes of surface processes. Disagreement has been particularly intense about photochemical CO and O₂ abundance in such atmospheres. While all models predicted the accumulation of photochemical CO and O₂ on CO₂-rich planets orbiting M dwarf stars, the specific predicted concentrations of CO and O₂ varied by many orders of magnitudes between models run on identical planetary scenarios (Harman et al. 2015, 2018). This is problematic because atmospheric O₂ and CO are proposed as remote probes of surface processes including the presence or absence of life (Meadows et al. 2018; Schwieterman et al. 2019; Wogan & Catling 2020). Uncertainty about the efficiency of photochemical generation of these gases neuters their value as probes of surface processes.

Recognizing the importance of this problem, extensive efforts have been invested to improve the understanding of photochemical CO and O₂ on CO₂-rich planets orbiting M dwarf stars. Initial efforts to simulate high-CO₂ atmospheres on planets orbiting M dwarf stars resulted in a disagreement of up to 4 orders of magnitude in predicted pCO and pO₂ (Domagal-Goldman et al. 2014; Tian et al. 2014; Harman et al. 2015). Harman et al. (2015) showed some of the inter-model disagreement was due to different lower boundary conditions. Harman et al. (2018) reconciled most of the remaining inter-model disagreement by showing that it was due to different assumptions regarding the photochemical effects of lightning, which generates NO_X species in a CO₂-N₂ atmosphere. These NO_X species can drive catalytic chemistry, which recombines CO and O₂ to CO₂. Upon including a lightning rate corresponding to modern Earth and its production of catalytic NO_X species, Harman et al. (2018) found photochemical O₂ to be low (pO₂ < 2 × 10⁻⁴ bar, below the false-positive threshold) across all models and planetary scenarios they considered.

Most recently, the possibility of abundant photochemical CO and O₂ was examined by Hu et al. (2020), who highlighted that previous work did not include the key NO_X reservoir species HNO₄ and N₂O₅. These species are relatively stable under M dwarf UV irradiation and serve to shuttle NO_X into the ocean due to their high solubility, reducing the efficacy of the NO_X-driven recombinative cycles. Hu et al. (2020) reproduced the results of Harman et al. (2018) for 0.05 bar CO₂ when excluding HNO₄ and N₂O₅, but found that the inclusion of HNO₄ and N₂O₅ into the photochemical network led to the generation of abundant photochemical CO and O₂, even assuming Earth-like lightning and its concomitant production of catalytic NO_X species. This mechanism is minimally affected by updated CO₂ and H₂O near-UV (NUV) cross sections (Ranjan et al. 2020) because M dwarf NUV emission is very low, rendering the photochemical effect of the updated cross sections modest for planets orbiting low-mass M dwarf stars (W. Broussard et al. 2023, in preparation). Applying this finding to the TRAPPIST-1 system, Hu et al. (2020) found that if TRAPPIST-1e and TRAPPIST-1f had enough CO₂ to be globally habitable, then they would necessarily accumulate abundant (≳0.1 bar, and possibly ≥1 bar) CO and O₂, with high O₃ as well. This atmospheric state (CO/O₂ runaway) would constitute an observable false positive for O₂ as a biosignature, would likely constitute a false positive for O₃ as a biosignature, and would further complicate efforts to use CO as a diagnostic of surface biology. Importantly, this false positive would persist in comparative planetological approaches to O₂ as a biosignature in the TRAPPIST-1 system, since abundant photochemical O₂ would specifically co-occur with habitable conditions on the outer planets. With observations of the TRAPPIST-1 system already underway, it is critical to confirm the prospects for the photochemical accumulation of CO and O₂ on the TRAPPIST-1 planets, to understand how to interpret potential detections of O₂, O₃, and CO.

Here, we explore further the possibility of substantial accumulation of CO and O₂ on CO₂-rich conventionally habitable planets orbiting M dwarf stars. By conventionally habitable, we refer to rocky planets with atmospheres and stable surface liquid water oceans, which are the prime targets for exoplanet biosignature search (Kopparapu et al. 2013; Kasting et al. 2014), as opposed to desiccated rocky planets, moist greenhouse rocky planets, Hycean worlds, or mini-Neptune aerial biospheres (Kasting 1988; Abe et al. 2011; Gao et al. 2015; Madhusudhan et al. 2021; Glidden et al. 2022). Our basic goal is to confirm whether it is possible for the photochemical decomposition of CO₂ to CO and O₂ to be favored in conventionally habitable planet atmospheres, even with a modern Earth-like lightning rate (Harman et al. 2018; Hu et al. 2020). We place specific emphasis on O₂, which is strongly motivated by the solar system as a biosignature gas (Sagan et al. 1993), and on the TRAPPIST-1 system, now under observation by JWST. However, our findings are relevant to multiple gases and to planets orbiting M dwarf stars in general. We reproduce the CO/O₂ runaway state in two independently developed photochemical models and determine its key controls. Our multi-model approach is critical because it enables us to be confident that our findings are not due to numerical or implementation errors of individual models. We describe our methods in Section 2, report and discuss our results in Sections 3 and 4, and summarize in Section 5. We provide additional background, supporting information, and methodological details in Appendices A–E.

We employ two independent 1D photochemical models in our exploration of CO/O₂ runaway: the MIT Exoplanet Atmospheric Chemistry Model (MEAC; Hu et al. 2012) and Atmos (Arney et al. 2016; Lincowski et al. 2018). These models implement conceptually similar chemistry, physics, and numerical schemes, but were developed independently and share no codebase. This means that results confirmed using both models are likely to be robust to implementation errors, though they may still suffer from common-mode errors in basic physicochemical understanding (Wen et al. 1989). This intercomparative approach has proved useful in past studies employing exoplanet photochemical models, which are extremely complex, often nonlinear, and feature numerous free parameters (Harman et al. 2015, 2018; Ranjan et al. 2020). In this work, we employ MEAC and Atmos in a highly focused investigation of CO/O₂ runaway. A more exhaustive intercomparison engaging a much broader diversity of models in a much broader range of planetary scenarios is underway in the form of the Photochemical model Intercomparison for Exoplanets (PIE) project (PI: C. E. Harman) as part of the CUISINES initiative. ¹⁰

2.1. MEAC Model and Configuration.

2.2. Atmos Model and Configuration

2.3. Planetary Scenario

2.4. Photochemical Model Deployment

2.5. Synthetic Spectra

To illustrate the observational implications of our photochemical simulations, we simulate planetary transmission spectra. We simulate these synthetic spectra using the Planetary Spectrum Generator (PSG; Villanueva et al. 2018, 2022) by adapting the example presented at https://github.com/nasapsg/globes/blob/main/atmos.py. PSG is a widely used community tool for simulating exoplanet transmission spectra (e.g., Fauchez et al. 2020; Pidhorodetska et al. 2020; Suissa et al. 2020). We choose planetary and stellar parameters consistent with our photochemical simulations (i.e., 1 M_⊕, 1 R_⊕ planet orbiting a TRAPPIST-1 like star). We include absorption due to H₂O, CH₄, C₂H₆, CO₂, O₂, O₃, CO, H₂CO, NO, NO₂, SO₂, N₂O, and N₂, as well as the effects of Rayleigh scattering, refraction, and all collision-induced absorption (CIA) included in PSG at a resolution of R = 500. PSG reports spectral fractional transit depths d(λ),

$$\begin{eqnarray}&&d(\lambda )={\left(\frac{{R}_{P}+{z}_{\mathrm{atm}}(\lambda )}{{R}_{\star }}\right)}^{2},\end{eqnarray} \tag{ 1 }$$

where R_P is the solid radius of the planet, R_⋆ is the radius of the star, and z_atm(λ) is the wavelength-dependent effective height of the atmosphere. d(λ) is specific to a given host star. To obtain a more general metric of the transmission spectrum that is not host star-specific and can be compared to other simulated transmission spectra, we also compute the effective height of the atmosphere z_atm(λ) by solving Equation (1) for z_atm(λ).

3.1. Photochemistry

We find that the occurrence of CO/O₂ runaway for conventionally habitable planets with high-CO₂ atmospheres is primarily controlled by the resolution of the CO₂ photolysis peak, via the choice of z_max and λ_crit.

We find that the details of the photochemical network are not the primary control for CO/O₂ runaway. Previously, it was reported that the inclusion of N₂O₅ and HNO₄ into photochemical networks resulted in CO/O₂ runaway for CO₂-dominated atmospheres orbiting M dwarf stars because the reactive nitrogen, which could catalyze the recombination of CO and O₂ back to CO_2, was instead converted into HNO₄ and N₂O₅ and sequestered into the ocean. Indeed, CO/O₂ runaway is sensitive to the details of the chemical network at intermediate pCO₂, corresponding to the onset of runaway (Table 1, Runs 8 and 9), as originally reported (Hu et al. 2020). In this intermediate atmospheric regime, sensitivity to photochemical details is enhanced because the dominant forcing on the atmosphere is changing (Ranjan et al. 2022). However, our simulations show that for CO₂-rich atmospheres that are firmly in the runaway regime, the runaway persists when N₂O₅ and HNO₄ are removed from the photochemical network (Table 1, Runs 1 and 2). Indeed, it persists even when nitrogen and sulfur chemistry are excised entirely from the network (Table 1, Runs 3 and 4). This demonstrates that the details of the photochemical network are not the fundamental driver of CO/O₂ runaway.

Instead, CO/O₂ runaway for high-CO₂ atmospheres is driven by the choice of z_max and λ_crit. Specifically, we found that either increasing z_max from 54 to 100 km or increasing λ_crit from 110 to 120 nm was adequate to inhibit the atmosphere from becoming CO/O₂ dominated, though concentrations of both gases remained high relative to the Sun-like star case (Table 1, Runs 0, 5, and 6). Both a low λ_crit and a low z_max were required to induce a runaway. Critically, this finding is multi-model: by adjusting z_max from 100 to 55 km, we were able to induce CO/O₂ runaway in the independently developed Atmos photochemical model ¹² as well, despite its omission of HNO₄ and N₂O₅ (Table 1, Runs 10 and 11). This confirms that λ_crit and z_max, and not the details of the photochemical network, are the main drivers of model predictions of CO/O₂ runaway.

To elucidate the mechanism by which λ_crit and z_max drive CO/O₂ runaway, we modeled atmospheres with pCO₂ = 0.01–0.1 bar (pN₂ = 0.99–0.9 bar). We explored both truncated atmospheres (model tops set at 0.34 μbar, as in the baseline 54 km case) and extended atmospheres (model tops set at 100 km; 4 nanobar for pCO₂ = 0.1 bar). We chose this pCO₂ range because it corresponded to the onset of runaway in the truncated atmospheres, enabling us to study the numerical drivers of this phenomenon, and because at higher pCO₂, photochemical O₂/O₃ layers emerge in the truncated atmospheres, which strongly suppresses tropospheric NUV radiation and makes it hard to study the subtle changes in CO₂ and H₂O photolysis rates that ultimately drive the runaway phenomenon.

Based on our pCO₂ = 0.01–0.1 bar modeling, we attribute the influence of λ_crit and z_max on CO/O₂ runaway to their control on the model resolution of the CO₂ photolysis peak. ¹³ M dwarf stars emit proportionately more of their UV radiation at far-UV (FUV) wavelengths compared to the Sun. CO₂ is a strong absorber of FUV light, and at high CO₂ abundances, this FUV radiation is absorbed high in the atmosphere (Appendix C). Terminating a high-CO₂ atmosphere at 54 km (0.34 μbar for our baseline 0.9 bar CO₂, 0.1 bar N₂ atmosphere) results in a failure to resolve the distribution of CO₂ photolysis in the upper atmosphere with altitude (Figure 1). The failure to resolve the CO₂ FUV photolysis peak means that CO₂ photolysis, and therefore ultimately O production, is artificially confined to the topmost model grid layer. This confinement means that the O atoms that would normally be distributed across a wide altitude range are instead artificially sequestered into a single altitude bin, facilitating their mutual reaction via O+O+M → O₂ + M (Figure 2). This is a chain termination reaction, which removes reactive power in the form of radicals from the atmosphere (Grenfell et al. 2018). In particular, the mixing ratio of OH (X_OH) is strongly suppressed in truncated atmospheres, and since OH is the main catalyst driving CO₂ recombination (Harman et al. 2018), it is unsurprising that as X_OH falls, pCO and pO₂ rise (Figure B1; Appendix B). That the CO/O₂ runaway is fundamentally driven by OH is signaled by the fact that CO increases before O₂ as pCO₂ increases. This is because OH is the only effective photochemical sink on CO (Kasting 1990), meaning variations in X_OH translate immediately into variations in pCO, while O₂'s sinks are more diverse and its response to X_OH is more indirect. In this sense, CO is the canary in the coal mine, signaling variations in X_OH in advance of O₂ (Schwieterman et al. 2016).

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We conducted additional numerical experiments to confirm our explanation that CO/O₂ runaway is driven by the confinement of the O produced by CO₂ photolysis to a single model layer. If our explanation is correct, then more efficient vertical transport (higher K_z (z)) should inhibit the photochemical runaway because more of the O produced in the topmost layer of the atmosphere will be transported to lower altitudes instead of reacting with other O radicals in chain termination events. Indeed, increasing K_z (z) to K_z (z) = 10³ K_z,0(z), where K_z,0(z) is the eddy diffusion profile in our baseline scenario (Figure E2) suppresses pO₂ and pCO in our baseline scenario (Table 1, Run 13). Similarly, if our explanation is correct, then increasing the number of layers in the model grid by decreasing the size of the altitude layers should inhibit runaway because the O produced by photolysis is distributed over multiple atmospheric layers instead of being limited to a single layer where it can more readily react with other O. Indeed, increasing the vertical altitude resolution from 1 to 0.1 km suppresses pO₂ and pCO in our baseline scenario (Table 1, Run 12).

We also investigated if we could induce a CO/O₂ runaway in an extended model grid, which resolved the CO₂ photolysis peak by varying K_z (z) or the altitude resolution, and found that we could not. This suggests that models that resolve the CO₂ photodissociation peak are less sensitive to other details of the numerical scheme, as expected for physically accurate solutions. For ${z}_{\max }=100$ km, we were unable to induce a CO/O₂ runaway by decreasing K_z (z) by setting K_z z = 10⁻³ K_z,0(z) (Table 1, Run 14). We were similarly unable to induce a runaway by decreasing the vertical resolution by a factor of 5 to 5 km, or increasing the vertical resolution by a factor of 5 to 0.2 km. However, we noticed a weak sensitivity of pO₂ and pCO to vertical resolution, with pO₂ increasing by 40% and pCO decreasing by 50% as the vertical resolution increased from 1 to 0.2 km.

3.2. Synthetic Spectra

To explore the observational relevance of CO/O₂ runaway, we calculate synthetic transmission spectra of a planet in and out of CO/O₂ runaway. We specifically simulate and compare spectra of the model atmospheres corresponding to Runs 4 and 5 of Table 1, which are in and out of CO/O₂ runaway, respectively. These limited simulations do not constitute a rigorous spectral analysis of the potential observables from abiotic CO₂-rich planets orbiting M dwarf stars. Rather, they are narrowly intended to demonstrate the large amplitude of the spectral features that CO/O₂ runaway can generate, and therefore the observational relevance of better understanding this theoretical phenomenon and its triggers.

Our synthetic spectra show large variations between the runaway (Run 4) and non-runaway (Run 5) atmospheres (Figure 3). The scale of the spectral features from the runaway atmosphere is comparable to the scale of the spectral features expected from modern Earth-like planets orbiting late M dwarf stars (Fauchez et al. 2020). The overall amplitude of the transmission spectrum is higher for the runaway case due to the lower mean molecular mass of its atmosphere. The runaway atmosphere displays stronger CO spectral features compared to the non-runaway atmosphere and O₂ and O₃ spectral features, which are absent from the non-runaway atmosphere. The runaway atmosphere displays O₃ features as strong as 50 ppm, which are absent from the non-runaway atmosphere. By comparison, JWST has already achieved a precision of <50 ppm in transmission spectroscopy, with even higher precision potentially achievable with additional observation time given the lack of evidence of a photometric noise floor down to a precision of 5 ppm (Lustig-Yaeger et al. 2023). This means that CO/O₂ runaway is observationally relevant because it can lead to spectral features that are potentially accessible to JWST. The spectral features due to CO/O₂ runaway are also relevant to other facilities such as the Large Interferometer for Exoplanets (LIFE) mission concept (Quanz et al. 2022), and potentially to ground-based facilities as well if observational challenges can be overcome (Currie et al. 2023; Hardegree-Ullman et al. 2023).

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Our work strengthens the case for O₂ as a biosignature gas on conventionally habitable planets orbiting M dwarf stars. Abundant atmospheric oxygen is the single strongest remotely detectable evidence of life on Earth (Sagan et al. 1993), and O₂ detection often motivates design requirements for facilities and surveys to detect life on exoplanets (Brandt & Spiegel 2014; Rodler & López-Morales 2014; Bixel & Apai 2021; Checlair et al. 2021; Hardegree-Ullman et al. 2023). However, care is required when using O₂ as a biosignature because of theoretically proposed mechanisms for the abiotic accumulation of O₂ in the atmospheres of conventionally habitable worlds (Meadows et al. 2018). In particular, it was recently argued that conventionally habitable planets with CO₂-rich atmospheres orbiting M dwarf stars would abiotically generate abundant (≥0.1 bar) atmospheric oxygen due to photochemical processes (Hu et al. 2020). This regime is highly observationally relevant because (1) CO₂-rich atmospheres are expected in the absence of biology, especially for planets orbiting toward the outer edge of the habitable zone (Gaillard & Scaillet 2014; Lehmer et al. 2020), and (2) due to observational biases, only planets orbiting M dwarf stars are accessible to atmospheric characterization with near-term (∼10–20 yr) facilities (Shields et al. 2016). Notably, TRAPPIST-1e and f, the most observationally favorable potentially habitable exoplanets and which are already targeted by JWST observations, fall into this regime, if conventionally habitable (Wolf 2017). Our results demonstrate that the generation of abundant (≥0.1 bar) O₂ on conventionally habitable worlds purely through CO₂ photodissociation is unlikely, strengthening the case for O₂ as a biosignature. However, photochemical false positives remain possible for cold, desiccated worlds that are not conventionally habitable (Gao et al. 2015), and escape-driven false-positive mechanisms remain possible for a broad range of worlds (Ramirez & Kaltenegger 2014; Wordsworth & Pierrehumbert 2014; Luger & Barnes 2015; Tian 2015; Wordsworth et al. 2018).

This paper is the latest in a long series to demonstrate the extreme sensitivity of predicted photochemical concentrations of O₂ and CO in CO₂-rich conventionally habitable planet atmospheres to diverse background model assumptions, including the lightning flash rate, the absorption cross-sections of CO₂ and H₂O, the rainout rate and atmosphere/ocean redox balance, and now the altitude of the model top (Wen et al. 1989; Selsis et al. 2002; Segura et al. 2007; Harman et al. 2015, 2018; Ranjan et al. 2020). Such sensitivity is distressing given the desire to use O₂ and CO to constrain the presence or absence of biology on exoplanets (Meadows et al. 2018; Schwieterman et al. 2018, 2019; Wogan & Catling 2020), for which one desires a robust, assumption-insensitive prediction of photochemical CO or O₂.

Unfortunately, the regime of conventionally habitable planets with thick CO₂-rich atmospheres is highly sensitive to background assumptions because it corresponds to a regime with reduced atmospheric forcing from OH, permitting second-order processes to become important. The trace gas composition of modern Earth's atmosphere is to first order controlled by OH, the "detergent of the atmosphere" whose reactivity is the main photochemical control on the abundances of a wide range of trace gases on modern Earth and Mars, and is thought to have done the same for much of their histories (McElroy & Donahue 1972; Parkinson & Hunten 1972; Riedel & Lassey 2008; Catling & Kasting 2017). On planets with oxic atmospheres (e.g., modern Earth), OH is robustly produced by the reaction of H₂O with O(¹D), sourced primarily from O₃ photolysis (Riedel & Lassey 2008). On anoxic planets with low CO₂ abundances (e.g., Neoarchaean Earth) or CO₂-dominated but thin atmospheres (modern Mars), OH is robustly produced by the direct photolysis of H₂O. This robust production of OH efficiently destroys atmospheric trace gases and triggers catalytic cycles that drive the atmosphere back toward equilibrium (Harman et al. 2018). On anoxic planets with abundant CO₂ (e.g., Eoarchaean Earth), this atmospheric forcing is severely inhibited because CO₂ largely competes for the same photons as H₂O, suppressing OH production (Ranjan et al. 2020). The suppression of the first-order atmospheric control from OH opens the door for second-order effects to become important, explaining the outsized relevance of details of the photochemical scheme in this regime. This effect is amplified on planets orbiting M dwarf stars because these stars emit proportionately less light at OH-producing NUV wavelengths (Segura et al. 2005). One might be forgiven for wanting to avoid this regime entirely. However, thick CO₂-dominated atmospheres are predicted for Earth early in its history, and are predicted for conventionally habitable planets orbiting near the outer edges of their habitable zones, including the most near-term observationally accessible habitable zone planet, TRAPPIST-1e (Wolf 2017; Rugheimer & Kaltenegger 2018; Lehmer et al. 2020). Therefore, this is not a regime that can be neglected in the search for life on exoplanets.

To address this regime properly, we will need to treat the details, which are not yet fully understood in most cases. For example, the NUV cross sections of CO₂ and H₂O are still uncertain (Wen et al. 1989; Ranjan et al. 2020; W. Broussard et al. 2023, in preparation). Importantly, this means that while our results contravene the previously proposed inevitability of CO/O₂ runaway on CO₂-rich M dwarf exoplanets, they do not completely eliminate the possibility of CO/O₂ runaway because it is possible that we have omitted or incorrectly implemented one of these second-order processes. These processes are much less important (and therefore poorly constrained) in a solar system context, but may be highly relevant for M dwarf planets. In particular, our modeling neglects ion chemistry in the upper atmosphere, which may be an important source of CO and O₂ due to the thermospheric dissociation of CO₂ driven by intense M dwarf stellar energetic particle fluxes (J. Kasting, private communication, 2023 May 1). It also neglects novel photoreaction channels for H₂O, CO₂, and CO, which may be relevant in the uppermost atmosphere (An et al. 2021; Lo et al. 2021; Yang et al. 2023). We conclude that the upper atmosphere is an unexplored potential source of CO/O₂ runaway.

While our results show abundant (≥0.1 bar) photochemical O₂ is unlikely, they nonetheless admit the possibility of trace photochemical O₂. Our models predict abiotic pO₂ = 2 × 10⁻⁵–4 × 10⁻³ bar depending on the model branch, assumed stellar spectral energy distribution (SED), and assumed lightning flash rate. Such O₂ abundances, while comparable to biotic O₂ concentrations on Proterozoic Earth (Harman et al. 2015), do not constitute an observationally relevant biosignature false positive in the near-to-medium term because O₂ itself is undetectable at such low concentrations—even much higher, modern Earth-like O₂ concentrations (0.2 bar) will be extremely challenging to characterize with either JWST or ELTs (Fauchez et al. 2020; Currie et al. 2023; Hardegree-Ullman et al. 2023). Detection of trace O₂ will likely require the advent of purpose-built instruments such as the Habitable Worlds Observatory (Checlair et al. 2021; Clery 2023), but HWO will primarily target Sun-like (FGK) stars and will therefore be relatively unaffected by M dwarf O₂ false positives (our work may be relevant to the handful of M dwarf stars on the HWO target list). More observationally relevant is the false-positive potential for O₃, which begins to produce IR spectral features in emission at 2 × 10⁻³ bar for M dwarf planets (Kozakis et al. 2022). This falls within the range of photochemical pO₂ produced in our modeling, meaning that photochemistry may produce observationally relevant O₃ false positives on M dwarf planets. Additionally, there remain parameters we have not explored which may expand pO₂ beyond the pO₂ = 2 × 10⁻⁵–4 × 10⁻³ range spanned by our sensitivity tests to date to model choice, lightning flash rate, and assumed stellar SED, such as volcanic outgassing level, combustion chemistry, and temperature–pressure profile (Selsis et al. 2002; Segura et al. 2007; Hu et al. 2012; Grenfell et al. 2018; Harman et al. 2022). Lastly, oceanic chemistry may also impact pO₂. For example, the rate of direct recombination of CO and O₂ in marine waters is unconstrained, and if efficient may also suppress pO₂ and pCO (Harman et al. 2015). We highlight aqueous reactions like O₂–CO recombination as priority targets for experimental characterization relevant to understanding exoplanet atmospheres, complementing the acknowledged community priority to characterize gas-phase kinetics (Fortney et al. 2016, 2019). In summary, further theoretical and experimental work is required to establish rigorous limits on predicted trace photochemical O₂ and O₃ for CO₂-rich planets orbiting M dwarf stars, and understand their context-dependent false-positive potential.

Our work illustrates the challenges of projecting atmospheric photochemical models calibrated on solar system planets to the novel photochemical regimes accessible on exoplanets. A model top of 0.34 μbar is capable of reproducing the trace gas composition of modern Earth (Hu et al. 2012). A model top of 0.34 μbar is marginally adequate when modeling CO₂-rich planets orbiting Sun-like stars, for which the pressure CO₂ photodissociation peak pressure is at ≥1.9 μbar (Appendix C). However, a model top of 0.34 μbar is not adequate when modeling CO₂-rich planets orbiting M dwarf stars, for which the photodissociation peak may be as high as 0.04 μbar (Appendix C). Care must be taken when projecting to the novel photochemical regimes accessible on exoplanets to ensure that the large diversity of background parameters in photochemical models are correctly calibrated.

Our work demonstrates the need to consider the upper atmosphere when modeling planets with CO₂-rich atmospheres orbiting M dwarf stars. Most exoplanet photochemical models, including all models currently focused on understanding O₂ false positives on temperate terrestrial worlds, focus on the lower atmosphere of the planet (troposphere, stratosphere, mesosphere) because this is the part of the atmosphere most relevant to trace gas detectability and planetary habitability. However, for CO₂-rich planets orbiting M dwarf stars, the CO₂ photodissociation peak can be well above the homopause, which corresponds to the thermosphere in the terrestrial atmosphere (Appendix D; Rumble 2017). This part of the atmosphere is partially ionized, and ion chemistry is important (Tian et al. 2008; Johnstone et al. 2018), which is rarely implemented in the exoplanet photochemistry models being used to study O₂ false positives. Similarly, above the homopause, transport is dominated by molecular diffusion, not eddy diffusion, which is not well captured for all molecules in all models (e.g., MEAC implements molecular diffusion of H and H₂ only). Accurately modeling CO₂-rich atmospheres orbiting M dwarf stars will require resolving the thermosphere, and ideally the entire atmosphere from surface to exobase. Efforts toward resolving exoplanet photochemistry in the upper atmosphere alone have been implemented for oxic, steam, and CO₂-dominated exoplanet atmospheres (Tian 2009; Garcia-Sage et al. 2017; Johnstone et al. 2019; Johnstone 2020; Nakayama et al. 2022), and from the surface to the upper atmosphere for oxic exoplanet atmospheres (Chen et al. 2019; Herbst et al. 2019; Cooke et al. 2023). We advocate for the extension of such work to abiotic CO₂-dominated atmospheres, which will strongly enhance our understanding of abiotic false-positive scenarios for CO and O₂.

Our findings affirm the importance of CO as a discriminant of photochemical O₂ production (Schwieterman et al. 2016; Wang et al. 2016). CO/O₂ runaway is ultimately driven by the suppression of OH, but OH is effectively the only photochemical sink on CO in conventionally habitable planet photochemical networks, while numerous pathways can suppress O₂. Consequently, when CO/O₂ runaways do occur in our model, CO rises before O₂. We can concoct scenarios where CO is scrubbed from the atmosphere while O₂ rises (e.g., through efficient surface deposition of CO but not O₂ into the ocean), but this scenario is unlikely on an abiotic planet based on our current understanding of aqueous chemistry (Kharecha et al. 2005; Harman et al. 2015; Hu et al. 2020). We therefore continue to advocate for constraining CO abundances in tandem with O₂/O₃ abundances when seeking to employ O₂ as a biosignature, as has also been argued when seeking to employ CH₄ as a biosignature (Thompson et al. 2022). Similarly, our work affirms the value of capstone biosignatures to corroborate potentially ambiguous primary biosignatures like O₂ (Leung et al. 2022).

We have used a multi-model approach to show that accumulation of abundant (>0.1 bar) photochemical CO and O₂ on conventionally habitable rocky planets with CO₂-rich atmospheres orbiting M dwarf stars (e.g., TRAPPIST-1e, -1f, if habitable) is unlikely, within the limits of current knowledge. An earlier prediction of abundant photochemical CO/O₂ on M dwarf planets was a model artifact, due to a model top that was too low to resolve the CO₂ photolysis peak. This model artifact occurred because on M dwarf planets with CO₂-rich atmospheres, the CO₂ photolysis peak is shifted to very high altitudes, meaning that model tops that are appropriate for solar system planets are too low for the M dwarf regime. Resolving the CO₂ photolysis peak robustly eliminates predictions of abundant (>0.1 bar) CO and O₂. However, accumulation of trace photochemical O₂ (2 × 10⁻⁴ bar < pO₂ <0.1 bar) together with >1% CO remains a possibility. Such O₂ concentrations do not constitute an observationally relevant biosignature false positive in the near-to-medium term because they are likely too low to be detected directly with JWST, but are high enough that they may drive an observationally relevant false positive for O₃ as a biosignature, and further work is required to address this possibility. Our work demonstrates the need to accurately resolve the upper atmosphere in order to model O₂ false positives on M dwarf planets because on such worlds the CO₂ photolysis peak can extend into the heterosphere. Overall, our work strengthens the case for O₂ as a biosignature gas by reducing its false-positive potential, but further work is required to fully understand the context-dependent use of O₂ and O₃ as biosignature gases.

We thank an anonymous referee for constructive criticism that substantially improved this paper. We thank Roger Yelle and James Kasting for their helpful discussions. We thank Thomas Fauchez and Ana Glidden for their answers to questions. S.R., E.W.S., and M.L. gratefully acknowledge support by NASA Exoplanets Research Program grant No. 80NSSC22K0235. R.H. was supported by NASA Exoplanets Research Program grant No. 80NM0018F0612. This research has made use of NASA's Astrophysics Data System. The MEAC input and output files underlying Figures 1, B1, 2, and Table 1, along with the scripts used to analyze them and to conduct the calculations presented in Appendices C and D, are publicly available at https://github.com/sukritranjan/co-o2-runaway-revisited-toshare and via Zenodo: doi:10.5281/zenodo.8148741 (Ranjan et al. 2023).

Software: MEAC (Hu et al. 2012), Atmos (Arney et al. 2016), PSG (Villanueva et al. 2018, 2022).

In this appendix, we briefly review the problem of CO₂ photochemical instability, with application to M dwarf planets.

CO₂ alone is unstable to photolytic conversion to CO and O₂ in conventionally habitable planet atmospheres. CO₂ photolyzes efficiently under UV irradiation (Ityaksov et al. 2008):

$$\begin{eqnarray}&&{{\rm{CO}}}_{2}+{\rm{h}}\nu {| }_{\lt 202\,\mathrm{nm}}\to {\rm{CO}}\,{\rm{+}}\,{\rm{O}}\end{eqnarray} \tag{ A1 }$$

The recombination reaction CO + O + M → CO₂ + M is spin forbidden and slow, leaving O₂ to accumulate via (Krasnopolsky 2019)

$$\begin{eqnarray}&&{\rm{O}}\,{\rm{+}}\,{\rm{O}}\,{\rm{+}}\,{\rm{M}}\to {{\rm{O}}}_{2}{\rm{+M}}.\end{eqnarray} \tag{ A2 }$$

However, photodissociation of non-CO₂ trace gases can trigger catalytic cycles that recombine CO and O₂ back to CO₂. For example, on Mars, OH ultimately sourced from H₂O photolysis ¹² (Kasting & Walker 1981; Nair et al. 1994; Harman et al. 2015; Ranjan et al. 2020):

$$\begin{eqnarray}&&{{\rm{H}}}_{2}{\rm{O}}+{\rm{h}}\nu {| }_{\lt 240\,\mathrm{nm}}\to {\rm{H}}\,{\rm{+}}\,{\rm{OH}}\end{eqnarray} \tag{ A3 }$$

stabilizes ¹³ CO₂, via cycles like (Harman et al. 2018):

$$\begin{eqnarray}&&{\rm{CO}}\,{\rm{+}}\,{\rm{OH}}\to {{\rm{CO}}}_{2}+{\rm{H}},\end{eqnarray} \tag{ A4 }$$

$$\begin{eqnarray}&&{{\rm{O}}}_{2}{\rm{+H+M}}\to {{\rm{HO}}}_{2}+{\rm{M}},\end{eqnarray} \tag{ A5 }$$

$$\begin{eqnarray}&&{{\rm{HO}}}_{2}+{\rm{O}}\to {{\rm{O}}}_{2}+{\rm{OH}}.\end{eqnarray} \tag{ A6 }$$

The challenge for M dwarf exoplanets is that M dwarfs emit proportionately less NUV (>200 nm) radiation due to their cooler photospheres, while their emission of FUV (<200 nm) remains robust due to their enhanced magnetic activity (Loyd et al. 2016). At habitable temperatures, CO₂ known to photoabsorb significantly only at FUV wavelengths (Ityaksov et al. 2008), while H₂O is known to photoabsorb at both FUV and NUV wavelengths (Ranjan et al. 2020). The high FUV-to-NUV emission ratio of M dwarf stars therefore results in reduced efficacy of the H₂O photolysis-driven chemical cycles, which recombine CO₂ relative to CO₂ photolysis, resulting in predictions of enhanced CO and O₂ relative to planets orbiting M dwarf stars. The problem is exacerbated for high-CO₂ planets because abundant CO₂ shields H₂O from photodissociation, as H₂O is restricted to the lower atmosphere by condensation (Harman et al. 2015). If the relative efficacy of H₂O photolysis-driven CO₂ recombination cycles decreases below a critical point, the atmosphere can enter a state of photochemical runaway, where CO and O₂ accumulate to appreciable atmospheric concentrations; this state is termed CO/O₂ runaway (Zahnle et al. 2008; Harman et al. 2015; Hu et al. 2020). The debate in the field has been about which conventionally habitable M dwarf planets, if any, access this CO/O₂ runaway atmospheric state (Domagal-Goldman et al. 2014; Tian et al. 2014; Gao et al. 2015; Harman et al. 2015, 2018; Hu et al. 2020). In the most recent iteration of this debate, Hu et al. (2020) find the CO/O₂ runaway regime is robustly accessed for high-CO₂ terrestrial planets orbiting M dwarf stars; in this paper, we test this finding.

In this appendix, we more closely examine the mechanism by which suppressed O abundances in truncated atmospheres lead to decreased production of OH and therefore reduced stability of CO₂-rich atmospheres to photolysis. Specifically, we follow Harman et al. (2018) in constructing tables of the main catalytic cycles stabilizing CO₂ and their rates in the truncated and non-truncated atmospheres with pCO₂ = 0.1 bar (Table 2). The rate of the net catalytic cycle is set by the slowest reaction within the cycle.

Table 2. Column-Integrated Rates of CO₂ Photolysis and Recombination, Following Harman et al. (2018)

Reaction	Column-integrated Rate (${z}_{\max }{| }_{P=0.34\,\mu bar}$)	Column-integrated Rate (${z}_{\max }=100$ km)
	(cm−2 s−1)	(cm−2 s−1)
CO2 Photolysis
CO2 + hν → CO+O	2.1E12	3.8E12
CO2 + hν → CO + O(1D)	2.6E11	1.2E11
Total CO2 Photolysis	2.4E12	3.9E12
CO2 Recombination Cycle 1
H + O2 + M → HO2 + M	3.0E11	2.3E12
O + HO2 → OH + O2	1.0E12	2.6E12
CO+OH → CO2 + H	1.4E12	3.5E12
Net (CO+O → CO2)	3.0E11	2.3E12
CO2 Recombination Cycle 2
H+CO+M → CHO+M	9.7E11	7.4E11
CHO+O2 → CO+HO2	9.6E11	7.1E11
O+HO2 → OH+O2	1.0E12	2.6E12
CO+OH → CO2 + H	1.4E12	3.5E12
Net (CO+O → CO2)	9.6E11	7.1E11
CO2 Recombination Cycle 3
H2O2 + hν → 2OH	9.5E10	1.3E11
2CO + 2OH → 2CO2 + 2H	7.1E11	1.8E12
2H + 2O2 + 2M → 2HO2 +2M	1.5E11	1.1E12
2HO2 → H2O2 + O2	8.6E10	1.0E11
Net (2CO+O2 → 2CO2)	8.6E10	1.0E11
Direct CO2 Recombination
CO+O+M → CO2 + M	9.5E11	3.7E11
Total CO2 Recombination	2.4E12	3.6E12
(Cycle 1 + Cycle 2 + 2×Cycle 3 + Direct Recomb.)

Note. We compare truncated and non-truncated atmospheres for pCO₂ = 0.1 bar, CHO chemistry only. Cycles 1 and 3 are ultimately drawn from the work of Stock et al. (2012) on the Martian atmosphere. Cycle 2 is identified in this work, where it is relevant to the high-CO₂, high-CO atmospheres we consider. The CO₂ recombination mechanisms we identify here balance >90% of CO₂ photolysis, meaning we have identified the main CO₂ recombination mechanisms.

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The chemical cycles in the C-H-O system are complex and nonlinear, but the catalysis tables lend some insight (Harman et al. 2018). H plays a key role in recombining CO₂ because it facilitates the generation of intermediate species en route to OH:

$$\begin{eqnarray}&&{{\rm{H+O}}}_{2}+{\rm{M}}\to {{\rm{HO}}}_{2}+{\rm{M}},\end{eqnarray} \tag{ B1 }$$

$$\begin{eqnarray}&&{\rm{O}}+{{\rm{HO}}}_{2}\to {{\rm{OH+O}}}_{2},\end{eqnarray} \tag{ B2 }$$

$$\begin{eqnarray}&&\mathrm{Net}:\ {\rm{O}}\,{\rm{+}}\,{\rm{H}}\to {\rm{OH}},\end{eqnarray} \tag{ B3 }$$

and

$$\begin{eqnarray}&&{\rm{H+CO+M}}\to {\rm{CHO}}\,{\rm{+}}\,{\rm{M}},\end{eqnarray} \tag{ B4 }$$

$$\begin{eqnarray}&&{{\rm{CHO+O}}}_{2}\to {{\rm{CO}}\,{\rm{+}}\,{\rm{HO}}}_{2},\end{eqnarray} \tag{ B5 }$$

$$\begin{eqnarray}&&{{\rm{O+HO}}}_{2}\to {{\rm{OH+O}}}_{2},\end{eqnarray} \tag{ B6 }$$

$$\begin{eqnarray}&&\mathrm{Net}:\ {\rm{O}}\,{\rm{+}}\,{\rm{H}}\to {\rm{OH}}.\end{eqnarray} \tag{ B7 }$$

However, OH and O are also main sources of H, via

$$\begin{eqnarray}&&{\rm{OH}}\,{\rm{+}}\,{\rm{CO}}\to {{\rm{CO}}}_{2}+{\rm{H}},\end{eqnarray} \tag{ B8 }$$

$$\begin{eqnarray}&&{\rm{O+OH}}\to {{\rm{O}}}_{2}+{\rm{H}}.\end{eqnarray} \tag{ B9 }$$

A decrease in O therefore decreases H production, which decreases OH production, which further decreases H production, which relies on OH. This is a positive feedback loop, whereby small changes in [O] can be amplified into larger changes in [OH]. We suggest this positive feedback loop as the mechanism whereby the relatively modest changes in [O] driven by the truncated model top (Figure B1) can be amplified into relatively large changes in [OH], and therefore pCO and pO₂.

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The higher FUV/NUV ratio associated with M dwarf irradiation leads to lower CO₂ photolysis peak pressures (higher CO₂ photolysis peak altitudes) relative to Sun-like stars. To illustrate this phenomenon, we derive an estimate of the pressure of peak dissociation for a well-mixed gas g in hydrostatic equilibrium, P_peak,g, and apply it to CO₂ in the atmospheres of CO₂-dominated planets orbiting different stars. This calculation is crude; for example, CO₂ mixing ratios may decrease with altitude in the uppermost planetary atmosphere due to robust photolysis and diffusive separation, therefore necessitating going deeper into the atmosphere to get the same absorption compared to the well-mixed case. However, the general trends of this calculation give some intuition for why M dwarf SEDs lead to higher ${P}_{\mathrm{peak},{\mathrm{CO}}_{2}}$.

The pressure of peak photodissociation of a gas g occurs when the UV optical depth of that gas τ_g,UV (measured traveling from space downward normal to the planet surface) satisfies (Catling & Kasting 2017)

$$\begin{eqnarray}&&\displaystyle \frac{{\tau }_{{\rm{g}},\mathrm{UV}}}{\cos ({\theta }_{0})}=1,\end{eqnarray} \tag{ C1 }$$

where θ₀ is the stellar angle of incidence. For an atmosphere in hydrostatic equilibrium (Catling & Kasting 2017),

$$\begin{eqnarray}&&P=\bar{\mu }{gN},\end{eqnarray} \tag{ C2 }$$

where P is the pressure, μ is the mean molecular weight of the atmosphere, g is the acceleration due to gravity, and N is the number column density of the atmosphere above pressure P. Since ${\tau }_{\mathrm{UV},{\rm{g}}}={N}_{g}\overline{{\sigma }_{\mathrm{UV},{\rm{g}}}}$, where $\overline{{\sigma }_{\mathrm{UV},{\rm{g}}}}$ is the mean UV photolysis cross section of g, for a well-mixed gas with molar concentration r_g (i.e., N_g = r_g N), we can substitute Equation (C2) into Equation (C1) to write

$$\begin{eqnarray}&&{P}_{\mathrm{peak},{\rm{g}}}=\displaystyle \frac{\cos ({\theta }_{0})\bar{\mu }g}{{r}_{g}\overline{{\sigma }_{\mathrm{UV},{\rm{g}}}}}.\end{eqnarray} \tag{ C3 }$$

We apply Equation (C3) to estimate the peak CO₂ photolysis pressure for planets orbiting different kinds of stars for our CO₂-dominated baseline scenario. For our CO₂-dominated baseline scenario, ${r}_{{\mathrm{CO}}_{2}}=0.9$, g = g_⊕, μ = 42.4 amu, we have chosen θ₀ = 573° (Zahnle et al. 2008). To calculate $\overline{{\sigma }_{\mathrm{UV},{\mathrm{CO}}_{2}}}$, we calculate the mean CO₂ cross-section weighted by the stellar number flux F_*:

$$\begin{eqnarray}&&\overline{{\sigma }_{\mathrm{UV},{\rm{g}}}}=\displaystyle \frac{{\int }_{{\lambda }_{0}}^{{\lambda }_{1}}d\lambda {F}_{* }(\lambda ){\sigma }_{{{CO}}_{2}}(\lambda )}{{\int }_{{\lambda }_{0}}^{{\lambda }_{1}}d\lambda {F}_{* }(\lambda )}.\end{eqnarray} \tag{ C4 }$$

We calculate $\overline{{\sigma }_{\mathrm{UV},{\mathrm{CO}}_{2}}}$ and ${P}_{\mathrm{peak},{\mathrm{CO}}_{2}}$ for solar irradiation, TRAPPIST-1 irradiation (Peacock et al. 2019 model 1a) with λ₀ = 110 nm, and TRAPPIST-1 irradiation with λ₀ = 120 nm (Table 3). σ_CO2(λ) and F_*(λ) for both scenarios are illustrated in Figure C1. In all cases, λ₁ = 202 nm, corresponding to the end of detected CO₂ absorption at room temperature (Ityaksov et al. 2008). The higher FUV/NUV ratio of TRAPPIST-1 irradiation increases $\overline{{\sigma }_{\mathrm{UV},{\rm{g}}}}$ by 50× relative to Solar irradiation, decreasing P_peak,g proportionately. This means that to resolve the CO₂ photolysis peak correctly for planets orbiting M dwarf stars, it is necessary to extend the model grid to much lower pressures compared to planets orbiting Sun-like stars.

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Table 3. Estimates of $\overline{{\sigma }_{\mathrm{UV},{\rm{g}}}}$ and ${P}_{\mathrm{peak},{\mathrm{CO}}_{2}}$ for Different Stellar Irradiation

Star	λ0	$\overline{{\sigma }_{\mathrm{UV},{\rm{g}}}}$	${P}_{\mathrm{peak},{\mathrm{CO}}_{2}}$
	(nm)	cm2	(μbar)
Sun	110	2 × 10−20	2
TRAPPIST-1	120	7 × 10−20	0.6
TRAPPIST-1	110	9 × 10−19	0.04

Note. The higher FUV/NUV ratio of M dwarf stars (here represented by the late M endmember TRAPPIST-1) leads to higher $\overline{{\sigma }_{\mathrm{UV},{\rm{g}}}}$ and lower ${P}_{\mathrm{peak},{\mathrm{CO}}_{2}}$ relative to Sun-like stars.

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In this calculation, we have approximated CO₂ as well mixed. This is a good assumption for the lower atmosphere, but our extended atmospheric simulations extend into the heterosphere where CO₂ is not well mixed, and its abundance decreases with altitude. Therefore, our calculation, which assumes constant CO₂ abundance with altitude, formally constitutes a lower bound on ${P}_{\mathrm{peak},{\mathrm{CO}}_{2}}$. Nevertheless, it illustrates the general mechanism by which ${P}_{\mathrm{peak},{\mathrm{CO}}_{2}}$ is decreased on planets orbiting M dwarf stars, i.e., the higher FUV/NUV ratio increasing $\overline{{\sigma }_{\mathrm{UV},{\rm{g}}}}$.

In this appendix, we estimate the homopause pressure for CO₂-dominated temperate terrestrial planets to demonstrate that the CO₂ photodissociation peak can extend into the heterosphere for M dwarf planets, demonstrating the need to resolve the upper atmosphere when modeling such worlds.

The homopause pressure is the pressure level in the atmosphere when

$$\begin{eqnarray}&&{K}_{z}(z)={D}_{12}(T,n),\end{eqnarray} \tag{ D1 }$$

where D₁₂(T, n) is the diffusion coefficient of gas g₁ diffusing through a background gas g₂ at temperature T and atmospheric number density n. D₁₂(T, n) takes the general form (Banks & Kockart 1973)

$$\begin{eqnarray}&&{D}_{12}(T,n)=\displaystyle \frac{{A}_{12}{T}^{{s}_{12}}}{n},\end{eqnarray} \tag{ D2 }$$

where A₁₂ and s₁₂ are specific to each (g₁, g₂) pair. Combining Equations (D1) and (D2) with the ideal gas law (P = nkT), we can write

$$\begin{eqnarray}&&{P}_{\mathrm{homo}}=\displaystyle \frac{{{kA}}_{12}{T}_{\mathrm{homo}}^{1+{s}_{12}}}{{K}_{{\rm{z}},\mathrm{homo}}},\end{eqnarray} \tag{ D3 }$$

In Earth's upper atmosphere near the homopause, K_z (z) = 4 × 10⁵ − 2 × 10⁶ cm² s⁻¹, depending on which tracer is used (Hunten 1975; Swenson et al. 2019). We adopt an Earth upper atmosphere K_z,homo,⊕ = 1 × 10⁶ cm² s⁻¹, which may be scaled to ${K}_{{\rm{z}},\mathrm{homo},{\mathrm{CO}}_{2}-\mathrm{dominated}}=\tfrac{29.0}{42.4}(1\times {10}^{6}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1})\,=7\,\times \,{10}^{5}\,{\mathrm{cm}}^{-2}\,{{\rm{s}}}^{-1}$ for our CO₂-dominated benchmark scenario (Hu et al. 2012). Further, in the upper atmosphere, T = 175 K in our baseline scenario, meaning we can set T_homo = 175 K. With these values, we evaluate Equation (D3) for Ar, H₂, and H diffusing through CO₂ and find homopause pressures of 0.07, 0.4, and 0.6 μbar, respectively (Table 4). For comparison, the photolysis peak pressure is 0.1 μbar for pCO₂ = 0.1 bar (Figure 1), and 0.01 μbar for pCO₂ = 0.9 bar as in our baseline scenario. This means that to accurately model the photochemistry of CO₂-rich planets orbiting M dwarf stars, it is necessary to extend model grids well into the heterosphere. We have done so here, but our calculation is not accurate because it does not accurately represent vertical transport in this part of the atmosphere, especially molecular diffusion, and because it does not include the ion chemistry important in the thermosphere and above. We advocate for the construction of exoplanet photochemistry models that resolve the atmosphere from surface to exobase to accurately treat the important, observationally relevant problem of CO₂-rich atmospheres orbiting M dwarf stars, and especially their propensity to accumulate photochemical CO and O₂.

In this appendix, we give more details of our planetary scenario to facilitate the reproduction of our work. Table 5 summarizes further details on our general planetary scenario and model setups. Table 6 presents the detailed species-by-species boundary conditions employed in our simulations. Figure E1 shows the stellar SEDs assumed in this work. Figure E2 shows the baseline atmospheric structure profiles (T(z), P(z), and K_z (z)) assumed in this work. In constructing the atmospheric structure profiles for the variable pCO₂ runs shown in Figures 1, B1, and 2, we followed Hu et al. (2012), i.e., assuming dry adiabatic evolution to a 175 K stratosphere (with thermodynamic parameters drawn from Pierrehumbert 2010) and scaling modern Earth's eddy diffusion profile by bulk atmospheric mean molecular mass.

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Table 5. Simulation Parameters For Planetary Scenario

Scenario Parameter	MEAC	ATMOS
Model reference	Hu et al. (2012)	Arney et al. (2016)
Reaction network	As in Ranjan et al. (2022) a	Archean Scenario
	(excludes, C>2-chem)	(includes Ranjan et al. 2020 updates)
Stellar type	TRAPPIST-1 (Peacock et al. 2019)	TRAPPIST-1 (Peacock et al. 2019)
Stellar constant relative to modern Earth	0.592	0.592
Planet size	1 M⊕, 1 R⊕	1 M⊕, 1 R⊕
Surface albedo	0.	0.25
Major atmospheric components	0.9 bar CO2, 0.1 bar N2 b	0.9 bar CO2, 0.1 bar N2 b
Surface temperature (z = 0 km)	288 K	288 K
Surface ${r}_{{{\rm{H}}}_{2}{\rm{O}}}$ (lowest atmospheric bin)	0.01	0.01
Eddy diffusion profile	See Figure E2	See Figure E2
Temperature–pressure profile	See Figure E2	See Figure E2
Vertical resolution	1 km	0.5 km
Rainout	Earth-like; rainout turned off for	Earth-like (all species)
	H2, CO, CH4, NH3, N2, C2H2,
	C2H4, C2H6, and O2 to simulate
	saturated ocean on an abiotic planet
Lightning	Simulated via ϕCO (z = 0) = ϕNO(z = 0) = 1 × 108	On
Global redox conservation	No	No

Notes.

^a In MEAC, pN₂ is fixed. In Atmos, pN₂ is adjusted to maintain dry P = 1 bar. ^b Default full chemistry CHOSN model runs contain 86 species linked by 734 reactions. For model runs where we exclude HNO₄ and N₂O₅, our network contains 84 species linked by 723 reactions. For model runs where we exclude S and N chemistry entirely, we set the initial concentrations and emission fluxes of S- and N-containing species to 0, but otherwise retain the full 734-reaction photochemical network.

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We draw our TRAPPIST-1 spectrum from Peacock et al. (2019), model number 1A. This spectrum is binned to 1 nm resolution for use in MEAC, and to the standard Atmos model 750 point grid for use in Atmos (Lincowski et al. 2018).