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

Efforts to spectrally characterize the atmospheric compositions of temperate terrestrial exoplanets orbiting M dwarf stars with JWST are now underway. Key molecular targets of such searches include O2 and CO, which are potential indicators of life. Recently, it was proposed that CO2 photolysis generates abundant (≳0.1 bar) abiotic O2 and CO in the atmospheres of habitable M dwarf planets with CO2-rich atmospheres, constituting a strong false positive for O2 as a biosignature and further complicating efforts to use CO as a diagnostic of surface biology. Importantly, this implied that TRAPPIST-1e and TRAPPIST-1f, now under observation with JWST, would abiotically accumulate abundant O2 and CO, if habitable. Here, we use a multi-model approach to reexamine photochemical O2 and CO accumulation on planets orbiting M dwarf stars. We show that photochemical O2 remains a trace gas on habitable CO2-rich M dwarf planets, with earlier predictions of abundant O2 and CO due to an atmospheric model top that was too low to accurately resolve the unusually high CO2 photolysis peak on such worlds. Our work strengthens the case for O2 as a biosignature gas, and affirms the importance of CO as a diagnostic of photochemical O2 production. However, observationally relevant false-positive potential remains, especially for O2's photochemical product O3, and further work is required to confidently understand O2 and O3 as biosignature gases on M dwarf planets.


INTRODUCTION
The launch of the James Webb Space Telescope (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 future, JWST will similarly seek to characterize the atmospheres of smaller exoplanets including potentially-habitable temperate terrestrial worlds, and such observations have already begun (Lustig-Yaeger et al. 2019;Lafreniere 2017;Lewis et al. 2017;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;Lehmer et al. 2020;Fauchez et al. 2020;Zhan et al. 2021;Ranjan et al. 2022).
Corresponding author: Sukrit Ranjan sukrit@arizona.edu Particularly relevant in the quest to characterize temperate terrestrial exoplanets are planets with anoxic, CO 2 -rich atmospheres orbiting M-dwarf stars.CO 2 -rich atmospheres are expected to be ubiquitous on terrestrial exoplanets, as they are in the Solar System, thanks to robust outgassing of CO 2 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 CO 2 -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 CO 2 -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 O 2 abundance in such atmospheres.While all models predicted accumulation of photochemical CO and O 2 on CO 2 -rich planets orbiting M-dwarf stars, the specific predicted concentrations of CO and O 2 varied by many orders of magnitudes between models run on identical planetary scenarios (Harman et al. 2015(Harman et al. , 2018)).This is problematic, because atmospheric O 2 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 understanding of photochemical CO and O 2 on CO 2 -rich planets orbiting M-dwarf stars.Initial efforts to simulate high-CO 2 atmospheres on planets orbiting M-dwarf stars resulted disagreement of up to 4 orders of magnitude in predicted pCO and pO 2 (Tian et al. 2014;Domagal-Goldman 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 CO 2 -N 2 atmosphere.These NO X species can drive catalytic chemistry which recombine CO and O 2 to CO 2 .Upon including a lightning rate corresponding to modern Earth and its production of catalytic NO X species, Harman et al. (2018) found photochemical O 2 to be low (pO 2 < 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 O 2 was examined by Hu et al. (2020), who highlighted that previous work did not include the key NO X reservoir species HNO 4 and N 2 O 5 .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 CO 2 when excluding HNO 4 and N 2 O 5 , but found that inclusion of HNO 4 and N 2 O 5 into the photochemical network led to generation of abundant photochemical CO and O 2 , even assuming Earth-like lightning and its concomitant production of catalytic NO X species.This mechanism is minimally affected by updated CO 2 and H 2 O 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 (Broussard et al. in prep).Applying this finding to the TRAPPIST-1 system, Hu et al. (2020) found that if TRAPPIST-1e and TRAPPIST-1f had enough CO 2 to be globally habitable, then they would necessarily accumulate abundant (≳ 0.1 bar, and possibly ≥ 1 bar) CO and O 2 , with high O 3 as well.This atmospheric state ("CO/O 2 runaway") would constitute an observable false positive for O 2 as a biosignature, would likely constitute a false positive for O 3 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 O 2 as a biosignature in the TRAPPIST-1 system, since abundant photochemical O 2 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 O 2 on the TRAPPIST-1 planets, to understand how to interpret potential detections of O 2 , O 3 , and CO.
Here, we explore further the possibility of substantial accumulation of CO and O 2 on CO 2 -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 (Abe et al. 2011;Gao et al. 2015;Kasting 1988;Madhusudhan et al. 2021;Glidden et al. 2022).Our basic goal is to confirm whether it is possible for the the photochemical decomposition of CO 2 to CO and O 2 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 O 2 , 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/O 2 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 Appendix A-E.

METHODS
We employ two independent 1D photochemical models in our exploration of CO/O 2 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 physico-chemical 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(Harman et al. , 2018;;Ranjan et al. 2020).In this work, we employ MEAC and Atmos in a highly focused investigation of CO/O 2 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 initiative1 .

MEAC Model & Configuration.
We employ MEAC as updated by Ranjan et al. (2022), which is modified from the original Hu et al. (2012) version by elimination of errors and use of updated H 2 O cross-sections (Ranjan et al. 2020;Hu 2021).Importantly, this model is similar to the version of MEAC employed by Hu et al. (2020), which motivated the present work.MEAC is a 1D photochemical model that calculates the steady-state vertical trace gas composition of a planetary atmosphere given temperature-pressure and eddy diffusion (vertical transport) profiles, stellar irradiation, chemical network, and chemical boundary conditions.MEAC encodes processes including photolysis (computed via delta two-stream approximation), eddy diffusion and molecular diffusion of H and H 2 , surface emission and wet and dry deposition of chemical species, diffusion-limited escape of H and H 2 , and formation and deposition of S 8 and H 2 SO 4 aerosols.MEAC does not account for formation of organic haze, expected at elevated CH 4 /CO 2 ratios (DeWitt et al. 2009;Arney et al. 2016); we do not explore this regime in our work.We assign a high deposition velocity of 1 × 10 −5 cm s −1 for C 2 H 6 to account for this omission in an ad-hoc fashion following Hu et al. (2012).For our full CHOSN chemical network, we consider 86 species linked by 734 reactions, corresponding to the full chemistry of Hu et al. (2012) excluding the higher hydrocarbons.Appendix E summarizes further MEAC model set-up.

Atmos Model & Configuration
Atmos is a 1D photochemical-climate model first developed by Kasting et al. (1979) and recently modified by numerous workers including Arney et al. (2016); Lincowski et al. (2018); Teal et al. (2022); Leung et al. (2022).For this work, we use the publicly available version of the code2 with modifications as suggested by Ranjan et al. (2020).This code has 79 species with 397 reactions, including 65 photolysis reactions.Atmos also incorporates eddy diffusion, wet and dry deposition and sulfur aerosols to simulate terrestrial environments.While not explored in this work, the model has previously been used to simulated hazy Archean-like atmospheres and has an extensive history of use for other terrestrial exoplanet applications (e.g., Domagal-Goldman et al. 2011;Arney et al. 2016Arney et al. , 2018;;Schwieterman et al. 2019;Teal et al. 2022;Leung et al. 2022).

Planetary Scenario
We apply our photochemical models to a planetary scenario closely corresponding to the CO 2 -dominated abiotic Earth-like planet benchmark scenario detailed in Hu et al. (2012).We assume atmospheric structure from Hu et al.
(2012) (T (z), P (z), K z (z); Figure E.2).To emphasize enforcement of mass balance, we avoid fixed mixing ratio boundary conditions in favor of fixed surface flux and dry deposition velocity boundary conditions.We adopt surface emission of SO 2 , H 2 S, CH 4 , and H 2 broadly consistent with Earth-like volcanism, surface production of CO and NO broadly consistent with Earth-like lightning, and generally low dry deposition velocities to simulate an abiotic planet (Hu et al. 2012;Harman et al. 2018;Hu & Diaz 2019) (Table 6).We set wet deposition of H 2 , O 2 , CO, CH 4 , C 2 H 2 , C 2 H 4 , C 2 H 6 , and NH 3 to zero, to simulate saturation on a planet with abiotic oceans (Hu et al. 2012).For stellar irradiation, we adopt the TRAPPIST-1 model 1A spectrum of Peacock et al. (2019).Further details on the planet scenario are presented in Appendix E.
The high pCO 2 =0.9 bar in this scenario puts it well into the CO/O 2 runaway regime identified by Hu et al. (2020).We generally avoid intermediate pCO 2 corresponding to the runaway transition itself, where sensitivity to photochemical assumptions is enhanced (Ranjan et al. 2022).This choice ensures that our modeling reflects the fundamental cause of the CO/O 2 runaway, as opposed to "red herrings" which have enhanced importance solely in the runaway transition regime, but do not control the overall runaway phenomenon.

Photochemical Model Deployment
We perform 16 targeted simulations with a combination of MEAC and Atmos to test model and parameter sensitivities and explore CO/O 2 runaway (Table 1).This includes the stellar spectrum (including the Sun, TRAPPIST-1, and GJ 876), the partial pressure of CO 2 (pCO 2 ), the chemical network: the full CHOSN network as described for both models, then chemical networks without N 2 O 5 and HNO 4 (CHOSN -(N 2 O 5 +HNO 4 )), without nitrogen chemistry (CHOS), and without nitrogen and sulfur chemistry (CHO).We additionally test the impact of the shortwave UV cutoff in the stellar spectrum (λ crit ), the maximum altitude of the model (z max ) and model grid resolution (∆z), and the magnitude of vertical transport (scaled by a factor K scale ).The results of these tests are summarized in the last two columns of Table 1 in which we show the surface-level CO and O 2 partial pressures (pCO and pO 2 , respectively).

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. 2018Villanueva et al. , 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., Suissa et al. 2020;Fauchez et al. 2020;Pidhorodetska et al. 2020).We choose planetary and stellar parameters consistent with our photochemical simulations (i.e. 1 M ⊕ , 1 R ⊕ planet orbiting TRAPPIST-1 like star).We include absorption due to H 2 O, CH 4 , C 2 H 6 , CO 2 , O 2 , O 3 , CO, H 2 CO, NO, NO 2 , SO 2 , N 2 O, and N 2 , 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), where 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, which 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).

Photochemistry
We find that the occurrence of CO/O 2 runaway for conventionally habitable planets with high-CO 2 atmospheres is primarily controlled by the resolution of the CO 2 photolysis peak, via choice of z max and λ crit .
We find that the details of the photochemical network are not the primary control for CO/O 2 runaway.Previously, it was reported that inclusion of N 2 O 5 and HNO 4 into photochemical networks resulted in CO/O 2 runaway for CO 2dominated atmospheres orbiting M-dwarf stars, because the reactive nitrogen which could catalyze the recombination of CO and O 2 back to CO 2 was instead converted into HNO 4 and N 2 O 5 and sequestered into the ocean.Indeed, CO/O 2 runaway is sensitive to the details of the chemical network at intermediate pCO 2 , corresponding to the onset of runaway (Table 1, Run 8-9), 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 Table 1.Predicted pCO and pO2 for our baseline 0.9 bar CO2, 0.1 bar N2 planetary scenario for different model assumptions.We have bolded instances of CO/O2 runaway, which we define on an ad-hoc basis as pCO> 0.1 bar and pO2 > 0.1 bar.Assumptions regarding the details of the chemical scheme are not the main control on CO/O2 runaway.Rather, assumptions regarding the shortwave UV cutoff and especially regarding the model top are the main control on CO/O2 runaway, through their influence on resolution of the CO2 photolysis peak.This finding is multi-model.).However, our simulations show that for CO 2 -rich atmospheres which are firmly in the runaway regime, the runaway persists when N 2 O 5 and HNO 4 are removed from the photochemical network (Table 1, Run 1-2).Indeed, it persists even when nitrogen and sulfur chemistry are excised entirely from the network (Table 1, Run 3-4).This demonstrates that the details of the photochemical network are not the fundamental driver of CO/O 2 runaway.

Run
Instead, CO/O 2 runaway for high-CO 2 atmospheres is driven by choice of z max and λ crit .Specifically, we found that either increasing z max from 54 km to 100 km or increasing λ crit from 110 nm to 120 nm was adequate to inhibit the atmosphere from becoming CO/O 2 dominated, though concentrations of both gases remained high relative to the Sun-like star case (Table 1, Run 0, 5-6).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 km to 55 km, we were able to induce CO/O 2 runaway in the independently-developed Atmos photochemical model3 as well, despite its omission of HNO 4 and N 2 O 5 (Table 1, Run 10-11).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/O 2 runaway.
To elucidate the mechanism by which λ crit and z max drive CO/O 2 runaway, we modeled atmospheres with pCO 2 =0.01-0.1 bar (pN 2 =0.99-0.9bar).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 pCO 2 = 0.1 bar).We chose this pCO 2 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 pCO 2 , photochemical O 2 /O 3 layers emerge in the truncated atmospheres, which strongly suppresses tropospheric near-UV (NUV) radiation and makes it hard to study the subtle changes in CO 2 and H 2 O photolysis rates that ultimately drive the runaway phenomenon.
Based on our pCO 2 =0.01-0.1 bar modeling, we attribute the influence of λ crit and z max on CO/O 2 runaway to their control on model resolution of the CO 2 photolysis peak4 .M-dwarf stars emit proportionately more of their UV radiation at far-UV (FUV) wavelengths compared to the Sun.CO 2 is a strong absorber of FUV light, and at high CO 2 abundances, this FUV radiation is absorbed high in the atmosphere (Appendix C).Terminating a high-CO 2 atmosphere at 54 km (0.34 µbar for our baseline 0.9 bar CO 2 , 0.1 bar N 2 atmosphere) results in a failure to resolve the distribution of CO 2 photolysis in the upper atmosphere with altitude (Figure 1).The failure to resolve the CO 2 FUV photolysis peak means that CO 2 photolysis, and therefore ultimately O production, is artificially confined to the topmost model grid layer.This confinement means that the O atoms which 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 → O 2 + 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 CO 2 recombination (Harman et al. 2018), it is unsurprising that as X OH falls, pCO and pO 2 rise (Figure B.1; Appendix B).That the CO/O 2 runaway is fundamentally driven by OH is signaled by the fact that CO increases before O 2 as pCO 2 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 O 2 's sinks are more diverse and its response to X OH more indirect.In this sense, CO is the "canary in the coal mine", signaling variations in X OH in advance of O 2 (Schwieterman et al. 2016).
We conducted additional numerical experiments to confirm our explanation that CO/O 2 runaway is driven by confinement of the O produced by CO 2 photolysis to a single model layer.If our explanation is correct, then more efficient vertical transport (higher K z (z)) should prevent or delay 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 = 10 3 K z,0 (z), where K z,0 (z) is the eddy diffusion profile in our baseline scenario (Figure E.2) suppresses pO 2 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 retard 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 km to 0.1 km suppresses pO 2 and pCO in our baseline scenario (Table 1, Run 12).
We also investigated if we could induce a CO/O 2 runaway in an extended model grid which resolved the CO 2 photolysis peak by varying K z (z) or the altitude resolution, and found that we could not.This suggests that models which resolve the CO 2 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/O 2 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 pO 2 and pCO to vertical resolution, with pO 2 increasing by 40% and pCO decreasing by 50% as vertical resolution increased from 1 km to 0.2 km.

Synthetic Spectra
To explore the observational relevance of CO/O 2 runaway, we calculate synthetic transmission spectra of a planet in and out of CO/O 2 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/O 2 runaway, respectively.These limited simulations do not constitute a rigorous spectral analysis of the potential observables from abiotic CO 2 -rich planets orbiting M-dwarf stars.Rather, they are narrowly intended to demonstrate the large amplitude of the spectral features that CO/O 2 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   ).However, care is required when using O 2 as a biosignature because of theoretically-proposed mechanisms for the abiotic accumulation of O 2 in the atmospheres of conventionally habitable worlds (Meadows et al. 2018).In particular, it was recently argued that conventionally habitable planets with CO 2 -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) CO 2 -rich atmospheres are expected in the absence of biology, especially for planets orbiting towards 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 years) facilities (Shields et al. 2016 This paper is the latest in a long series to demonstrate extreme sensitivity of predicted photochemical concentrations of O 2 and CO in CO 2 -rich conventionally habitable planet atmospheres to diverse background model assumptions, including the lightning flash rate, the absorption cross-sections of CO 2 and H 2 O, 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. 2015Harman et al. , 2018;;Ranjan et al. 2020).Such sensitivity is distressing given the desire to use O 2 and CO to constrain the presence or absence of biology on exoplanets (Schwieterman et al. 2018;Meadows et al. 2018;Schwieterman et al. 2019;Wogan & Catling 2020), for which one desires a robust, assumption-insensitive prediction of photochemical CO or O 2 .
Unfortunately, the regime of conventionally habitable planets with thick CO 2 -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 H 2 O with O( 1 D), sourced primarily from O 3 photolysis (Riedel & Lassey 2008).On anoxic planets with low CO 2 abundances (e.g.Neoarchaean Earth) or CO 2 -dominated but thin atmospheres (modern Mars), OH is robustly produced by the direct photolysis of H 2 O.This robust production of OH efficiently destroys atmospheric trace gases and triggers catalytic cycles which drive the atmosphere back towards equilibrium (Harman et al. 2018).On anoxic planets with abundant CO 2 (e.g., Eoarchaean Earth), this atmospheric forcing is severely inhibited because CO 2 largely competes for the same photons as H 2 O, 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 CO 2 -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 CO 2 and H 2 O are still uncertain (Wen et al. 1989;Ranjan et al. 2020;Broussard et al in prep).Importantly, this means that while our results contravene the previously proposed inevitability of CO/O 2 runaway on CO 2 -rich M-dwarf exoplanets, they do not completely eliminate the possibility of CO/O 2 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 O 2 due to thermospheric dissociation of CO 2 driven by intense M-dwarf stellar energetic particle fluxes (J.Kasting, private communication, 5/1/2023).It also neglects novel photoreaction channels for H 2 O, CO 2 , 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 a unexplored potential source of CO/O 2 runaway.
While our results show abundant (≥ 0.1 bar) photochemical O 2 is unlikely, they nonetheless admit the possibility of trace photochemical O 2 .Our models predict abiotic pO 2 = 2×10 −5 −4×10 −3 bar depending on model branch, assumed stellar SED, and assumed lightning flash rate.Such O 2 abundances, while comparable to biotic O 2 concentrations on Proterozoic Earth (Harman et al. 2015), do not constitute an observationally relevant biosignature false positive in the near-to-medium-term, because O 2 itself is undetectable at such low concentrations -even much higher, modern Earthlike O 2 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 O 2 will likely require 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 O 2 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 O 3 , 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 pO 2 produced in our modeling, meaning that photochemistry may produce observationally relevant O 3 false positives on M-dwarf planets.Additionally, there remain parameters we have not explored which may expand pO 2 beyond the pO 2 = 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 pO 2 .For example, the the rate of direct recombination of CO and O 2 in marine waters unconstrained, and if efficient may also suppress pO 2 and pCO (Harman et al. 2015).We highlight aqueous reactions like O 2 -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(Fortney et al. , 2019)).In summary, further theoretical and experimental work is required to establish rigorous limits on predicted trace photochemical O 2 and O 3 for CO 2 -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 CO 2 -rich planets orbiting Sun-like stars, for which the pressure CO 2 photodissociation peak pressure is at ≥ 1.9 µbar (Appendix C).However, a model top of 0.34 µbar is not adequate when modeling CO 2 -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 CO 2 -rich atmospheres orbiting M-dwarf stars.Most exoplanet photochemical models, including all models currently focused on understanding O 2 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 CO 2 -rich planets orbiting M-dwarf stars, the CO 2 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 O 2 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 H 2 only).Accurately modeling CO 2 -rich atmospheres orbiting M-dwarf stars will require resolving the thermosphere, and ideally the entire atmosphere from surface to exobase.Efforts towards resolving exoplanet photochemistry in the upper atmosphere alone have been implemented for oxic, steam, and CO 2 -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 CO 2 -dominated atmospheres, which will strongly enhance our understanding of abiotic false positive scenarios for CO and O 2 .
Our finds affirm the importance of CO as a discriminant of photochemical O 2 production (Schwieterman et al. 2016;Wang et al. 2016).CO/O 2 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 O 2 .Consequently, when CO/O 2 runaways do occur in our model, CO rises before O 2 .We can concoct scenarios where CO is scrubbed from the atmosphere while O 2 rises (e.g, through efficient surface deposition of CO but not O 2 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 O 2 /O 3 abundances when seeking to employ O 2 as a biosignature, as has also been argued when seeking to employ CH 4 as a biosignature (Thompson et al. 2022).Similarly, our work affirms the value of "capstone" biosignatures to corroborate potentially-ambiguous primary biosignatures like O 2 (Leung et al. 2022).

CONCLUSIONS
We have used a multi-model approach to show that accumulation of abundant (> 0.1 bar) photochemical CO and O 2 on conventionally habitable rocky planets with CO 2 -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/O 2 on M-dwarf planets was a model artefact, due to a model top that was too low to resolve the CO 2 photolysis peak.This model artefact occured because on M-dwarf planets with CO 2 -rich atmospheres, the CO 2 photolysis peak is shifted to very high altitudes, meaning that model tops which are appropriate for solar system planets are too low for the M-dwarf regime.Resolving the CO 2 photolysis peak robustly eliminates predictions of abundant (> 0.1 bar) CO and O 2 .However, accumulation of trace photochemical O 2 (2 × 10 −4 bar < pO 2 <0.1 bar) together with > 1% CO remain a possibility.Such O 2 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 O 3 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 O 2 false positives on M-dwarf planets, because on such worlds the CO 2 photolysis peak can extend into the heterosphere.Overall, our work strengthens the case for O 2 as a biosignature gas by reducing its false positive potential, but further work is required to fully understand the context-dependent use of O 2 and O 3 as biosignature gases.
We thank an anonymous referee for constructive criticism which substantially improved this paper.We thank Roger Yelle and James Kasting for helpful discussions.We thank Thomas Fauchez and Ana Glidden for answers to questions.S.R., E.W.S. and M.L. gratefully acknowledge support by NASA Exoplanets Research Program grant # 80NSSC22K0235.R.H. was supported by NASA Exoplanets Research Program grant # 80NM0018F0612.This research has made use of NASA's Astrophysics Data System.The MEAC input and output files underlying Figures 1, B.1, 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-toshareand via Zenodo (Ranjan 2023).
Software: MEAC (Hu et al. 2012), Atmos (Arney et al. 2016) APPENDIX Table 2. Column-Integrated Rates of CO2 Photolysis and Recombination, following Harman et al. (2018).We compare truncated and nontruncated 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 CO2photolysis, meaning we have identified the main CO2 recombination mechanisms.

Reaction
Column the truncated and untruncated atmospheres with pCO 2 =0.1 bar (Table 2).The rate of the net catalytic cycle is set by the slowest reaction within the cycle.
The chemical cycles in the C-H-O system are complex and nonlinear, but the catalysis tables lend some insight (Harman et al. 2018) The higher FUV/NUV ratio associated with M-dwarf irradiation leads to lower CO 2 photolysis peak pressures (higher CO 2 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 CO 2 in the atmospheres of CO 2 -dominated planets orbiting different stars.This calculation is crude; for example, CO 2 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 wellmixed case.However, the general trends of this calculation give some intuition for why M-dwarf SEDs lead to higher P peak,CO2 .
The pressure of peak photodissociation of a gas g occurs when the UV optical depth of that gas τ g,U V (measured traveling from space downwards normal to the planet surface) satisfies (Catling & Kasting 2017): where θ 0 is the stellar angle of incidence.For an atmosphere in hydrostatic equilibrium (Catling & Kasting 2017), 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 τ U V,g = N g σ U V,g , where σ U V,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 C21 into Equation C20 to write We apply Equation C22 to estimate the peak CO 2 photolysis pressure for planets orbiting different kinds of stars for our CO 2 -dominated baseline scenario.For our CO 2 -dominated baseline scenario, r CO2 = 0.9, g = g ⊕ , µ = 42.4 amu, and we have chosen θ 0 = 57.3• (Zahnle et al. 2008).To calculate σ U V,CO2 , we calculate the mean CO 2 cross-section weighted by the stellar number flux F * : We calculate σ U V,CO2 and P peak,CO2 for Solar irradiation, TRAPPIST-1 irradiation (Peacock et al. 2019 model 1a) with λ 0 = 110 nm, and TRAPPIST-1 irradiation with λ 0 = 120 nm (Table 3).σ CO2 (λ) and F * (λ) for both scenarios are illustrated in Figure C.1.In all cases, λ 1 = 202 nm, corresponding to the end of detected CO 2 absorption at room temperature (Ityaksov et al. 2008).The higher FUV/NUV ratio of TRAPPIST-1 irradiation increases σ U V,g by 50× relative to Solar irradiation, decreasing P peak,g proportionately.This means that to resolve the CO 2 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 Sunlike stars.In this calculation, we have approximated CO 2 as well-mixed.This is a good assumption for the lower atmosphere, but our extended atmospheric simulations extend into the heterosphere where CO 2 is not well-mixed, and its abundance decreases with altitude.Therefore, our calculation, which assumes constant CO 2 abundance with altitude, formally constitutes a lower bound on P peak,CO2 .Nevertheless, it illustrates the general mechanism by which P peak,CO2 is decreased on planets orbiting M-dwarf stars, i.e. the higher FUV/NUV ratio increasing σ U V,g .

D. HOMOPAUSE ESTIMATES
In this Appendix, we estimate the homopause pressure for CO 2 -dominated temperate terrestrial planets to demonstrate that the CO 2 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 where D 12 (T, n) is the diffusion coefficient of gas g 1 diffusing through a background gas g 2 at temperature T and atmospheric number density n.D 12 (T, n) takes general form (Banks & Kockart 1973): where A 12 and s 12 are specific to each (g 1 , g 2 ) pair.Combining equations D24 and D25 with the ideal gas law (P = nkT ), we can write In Earth's upper atmosphere near the homopause, K z (z) = 4 × 10 5 − 2 × 10 6 cm 2 s −1 , depending on which tracer is used (Hunten 1975;Swenson et al. 2019).We adopt an Earth upper atmosphere K z,homo,⊕ = 1 × 10 6 cm 2 s −1 , which may be scaled to K z,homo,CO2−dominated = 29.042.4 (1 × 10 6 cm −2 s −1 ) = 7 × 10 5 cm −2 s −1 for our CO 2 -dominated benchmark scenario (Hu et al. 2012).Further, in the upper atmosphere, T = 175K in our baseline scenario, meaning we can set T homo = 175 K.With these values, we evaluate Equation D26 for Ar, H 2 , and H diffusing through CO 2 and find homopause pressures of 0.07 µbar, 0.4 µbar, and 0.6 µbar, respectively (Table 4).For comparison, the photolysis peak pressure is 0.1 µbar for pCO 2 =0.1 bar (Figure 1), and 0.01 µbar for pCO 2 =0.9 bar as in our baseline scenario.This means that to accurately model the photochemistry of CO 2 -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 CO 2 -rich atmospheres orbiting M-dwarf stars, and especially their propensity to accumulate photochemical CO and O 2 .Top: Top-of-atmosphere number flux from the Sun and TRAPPIST-1 (left y-axis).Also co-plotted are the photolysis cross-sections of CO2 (right abscissa).Bottom: CO2 cross-sections weighted by the stellar emission of TRAPPIST-1 and the Sun.The bluer spectrum of TRAPPIST-1 increases the weight of shortwave σCO 2 , which is larger, driving an increase in σUV,g.

E. DETAILED PLANET SCENARIO
In this Appendix, we give more details of our planetary scenario to facilitate reproduction of our work.Table 5 summarizes the further details on our general planetary scenario and model set-ups.Table 6 presents the detailed species-by-species boundary conditions employed in our simulations.Figure E.1 shows the stellar SEDs assumed in this work.Figures E.2 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 pCO 2 runs shown in Figures 1, B.1, and 2, we followed Hu et al. (2012), i.e. assuming dry adiabatic evolution to a 175K stratosphere (with thermodynamic parameters drawn from Pierrehumbert 2010) and scaling modern Earth's eddy diffusion profile by bulk atmospheric mean molecular mass.
We draw our TRAPPIST-1 spectrum from Peacock et al. (2019), model #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).MEAC ATMOS (cm −2 s −1 ) (relative to CO2+N2) (cm s −1 ) (cm −2 s −1 ) Note-(1) For species type, for each model, "X" means the full continuity-diffusion equation is solved for the species; "F" means it is treated as being in photochemical equilibrium; "A" means it is an aerosol and falls out of the atmosphere; "C" means it is treated as chemically inert; and "-" means that it is not included in that model.Note that boundary conditions like dry deposition velocity are not relevant for Type "F" species, since transport is not included for such species.The exclusion of a species from a model does not necessarily mean that the model is incapable of simulating the species, but just that it was not included in the atmospheric scenario selected here.For example, following Hu et al. (2012), the MEAC model was deployed here without N species because the planet scenario selected here precludes reactive N, though it is capable of simulating nitrogenous chemistry.(2) For the bottom boundary condition, either a surface flux is specified, or a surface mixing ratio.N2 is a special case in the Kasting model and in ATMOS; in these models, [N2] is adjusted to set the total dry pressure of the atmosphere to be 1 bar (to account for outgassed species and photochemical intermediates).Consequently, pN2 ≲ 0.1 bar in these models.
(3) TOA flux refers to the magnitude of outflow at the top-of-the-atmosphere (TOA); hence, a negative number would correspond to an inflow.(4) For model runs where we exclude S and N chemistry entirely, the emission fluxes of S-and N-containing species to 0, but otherwise retain the full 734-reaction photochemical network.

Figure 2 .
Figure2.Vertically resolved reaction rates of key OH-producing (left column) and radical-radical (right column) reactions, for both truncated (solid lines) and extended (dashed lines) model atmospheres.The top row shows pCO2 = 0.01 bar, for which both model tops return the same results, while the bottom shows pCO2 = 0.1 bar, for which CO/O2 runaway has begun in the truncated model top (but for which an NUV-attenuating ozone layer has not yet formed).CHO chemistry only (S, N excluded).The key reaction O+O+M→ O2+M in the right column is highlighted with a thicker line.Concentration of O production in a single model bin in the truncated atmosphere leads to more intense O-O reactions, which are chain termination reactions which remove radicals from the atmosphere and impede the radical-driven recombination of CO and O2.
Figure C.1.Top: Top-of-atmosphere number flux from the Sun and TRAPPIST-1 (left y-axis).Also co-plotted are the photolysis cross-sections of CO2 (right abscissa).Bottom: CO2 cross-sections weighted by the stellar emission of TRAPPIST-1 and the Sun.The bluer spectrum of TRAPPIST-1 increases the weight of shortwave σCO 2 , which is larger, driving an increase in σUV,g.
Figure E.1.TRAPPIST-1 spectra employed by MEAC and Atmos in this study.

Figure E. 2 .
Figure E.2.T-P and Eddy diffusion profiles employed by MEAC and Atmos in this study.
(Quanz et al. 2022)l.2023)heCO2 photolysis peak drives CO/O2 runaway.Concentrations of key atmospheric species (left column) and CO2 and H2O photolysis rates (right column) as a function of altitude, for pCO2=0.01,0.03,and0.1 bar, CHO chemistry only (S, N excluded).The key photochemical products CO and O2 are highlighted with thicker lines in the left column."Drypressure"referstotheatmosphericpressure due to CO2 and N2, excluding the contribution from water vapor.Solid lines correspond to calculations with model top at 0.34 µbar, while dashed lines correspond to calculations with a higher 100 km model top.At 0.01 bar, the photolysis peak is resolved by both models, and they report identical results.As pCO2 increases, the CO2 photodissociation peak moves upward and is not resolved by the calculations with 0.34 µbar model top, resulting in large increases in pCO and especially pO2.and O 2 and O 3 spectral features which are absent from the non-runaway atmosphere.The runaway atmosphere displays O 3 features as strong as 50 ppm, which are absent from the non-runaway atmosphere.By comparison, JWST has already achieved precision of < 50 ppm in transmission spectroscopy, with even higher precision potentially achievable with additional observation time given lack of evidence of a photometric noise floor down to a precision of 5 ppm(Lustig-Yaeger et al. 2023).This means that CO/O 2 runaway is observationally relevant because it can lead to spectral features that are potentially accessible to JWST.The spectral features due to CO/O 2 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 (Hardegree-Ullman et al.Abundant atmospheric oxygen is the single strongest remotely detectable evidence of life on Earth(Sagan et al. Currie et al. 2023)2023).4.DISCUSSIONOur work strengthens the case for O 2 as a biosignature gas on conventionally habitable planets orbiting M-dwarf stars.
Figure3.Simulated transmission spectra of an Earth-sized planet orbiting a late-M dwarf star with a CO2-dominated atmosphere in and out of CO/O2 runaway, corresponding to Runs 4 and 5 of Table1.Key molecular absorption features that differ between the runaway/non-runaway cases are highlighted.Runaway spectral features are as strong as 50 ppm and the runaway/non-runaway spectra differ by 10s of ppm, which is potentially detectable with JWST.
. H plays a key role in recombining CO 2 , because it facilitates generation of intermediate species en route to 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 B.1) can be amplified into relatively large changes in [OH], and therefore pCO and pO 2 .

Table 3 .
Estimates of σUV,g and P peak,CO 2 for different stellar irradiation.The higher FUV/NUV ratio of M-dwarf stars (here represented by the late-M endmember TRAPPIST-1) lead to higher σUV,g and lower P peak,CO 2 relative to Sun-like stars.

Table 4 .
Homopause estimates for different gases in our CO2-dominated baseline planetary scenario.The CO2 photodissociation peak for CO2-dominated atmospheres lie in the heterosphere.

Table 6
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