Relative Abundances of CO2, CO, and CH4 in Atmospheres of Earth-like Lifeless Planets

Carbon is an essential element for life on Earth, and the relative abundances of major carbon species (CO2, CO, and CH4) in the atmosphere exert fundamental controls on planetary climate and biogeochemistry. Here we employed a theoretical model of atmospheric chemistry to investigate diversity in the atmospheric abundances of CO2, CO, and CH4 on Earth-like lifeless planets orbiting Sun-like (F-, G-, and K-type) stars. We focused on the conditions for the formation of a CO-rich atmosphere, which would be favorable for the origin of life. Results demonstrated that elevated atmospheric CO2 levels trigger photochemical instability of the CO budget in the atmosphere (i.e., CO runaway) owing to enhanced CO2 photolysis relative to H2O photolysis. Higher volcanic outgassing fluxes of reduced C (CO and CH4) also tend to initiate CO runaway. Our systematic examinations revealed that anoxic atmospheres of Earth-like lifeless planets could be classified in the phase space of CH4/CO2 versus CO/CO2, where a distinct gap in atmospheric carbon chemistry is expected to be observed. Our findings indicate that the gap structure is a general feature of Earth-like lifeless planets with reducing atmospheres orbiting Sun-like (F-, G-, and K-type) stars.


INTRODUCTION
The existence of over 5500 exoplanets has been confirmed since the discovery of the first in 1995 (Mayor and Queloz 1995).The focus of this field of research is gradually shifting from exoplanet detection to identification of signs of habitability and potential biosignatures.The traditional concept of planetary habitability has centered around the presence of liquid water on the planetary surface, given its vital role in supporting life on Earth (Hart 1979;Kasting et al. 1993Kasting et al. , 2014;;Selsis et al. 2007; Bartik et al. 2011;Seager et al. 2012;Kasting 2014).This concept is encapsulated in the habitable zone (HZ), which defines the circumstellar region in which a terrestrial planet with a CO2-H2O-N2 atmosphere could sustain liquid water on its surface (Huang 1959;Hart 1979;Kasting et al. 1993;Williams and Kasting 1997;Underwood et al. 2003;Selsis et al. 2007;Spiegel et al. 2008;Abe et al. 2011;Kaltenegger and Sasselov 2011;Kopparapu et al. 2013Kopparapu et al. , 2014)).Dozens of exoplanets have been discovered within the HZ (Anglada-Escudé et al. 2016;Gillon et al. 2017;Meadows et al. 2018;Hill et al. 2023).However, the presence of an exoplanet in the HZ does not guarantee its habitability because a range of additional factors, such as atmospheric composition, climatic conditions, and the availability of bioessential elements, also play key roles in planetary habitability.
Carbon is an element essential for life on Earth, and it exerts fundamental controls on planetary climate and biogeochemistry.Both CO2 and CH4 are potent greenhouse gasses that exert major control on the global climate.Conversely, CO is crucial for the early evolution of life, serving as an important source of carbon and energy for microorganisms owing to its high thermodynamic free energy or low electrode potential (Ragsdale 2004;Kharecha et al. 2005;Seager et al. 2012;Kasting 2014;Catling and Kasting 2017).Consequently, detailed understanding of those factors that govern the relative abundances of CO2, CO, and CH4 in planetary atmospheres has far-reaching implications in the search for habitable planets beyond our solar system.
Earth's early atmosphere before the emergence of life is thought to have been predominantly composed of CO2 (and N2) (Miller and Urey 1959;Walker et al. 1983;Sagan and Chyba 1997).However, early theoretical studies of atmospheric photochemistry have recognized the possible existence of a state called CO runaway (Kasting et al. 1983;Zahnle 1986;Kasting 2014;Hu et al. 2020;Ranjan et al. 2022Ranjan et al. , 2023)), in which the photochemical budget of CO is out of balance in the atmosphere.Under anoxic conditions, the primary production pathway for CO is photodissociation of CO2 by UV radiation (CO2 + hν (λ < 204 nm) → CO + O).The rate of the reverse reaction is slow because of the spin-forbidden condition (Kasting et al. 1983;Zahnle 1986;Kasting 2014;Wogan et al. 2020;Ranjan et al. 2022), and therefore the primary removal of CO is performed via reaction with OH radicals (CO + OH → CO2 + H), which are derived primarily from photodissociation of water (H2O + hν (λ < 240 nm) → H + OH).Consequently, under conditions where the rate of CO production increases to a level comparable to or larger than the rate of water vapor photolysis, the photochemical CO budget is imbalanced, which leads to CO accumulation over time until it becomes limited by surface deposition (Kasting et al. 1983;Kasting 2014;Ranjan et al. 2022).
The possibility of CO runaway is critical in resolving the fundamental problem regarding the origin of life on Earth because various organic compounds suitable for the prebiotic chemistry are more likely to form in a CO-rich atmosphere than in a CO2-rich atmosphere (Bar-Nun and Chang 1983;McGlynn et al. 2020;Zang et al. 2022).Previous UV irradiation experiments demonstrated that a range of organic matter (e.g., aldehydes and organic acids) can be formed in an anoxic atmosphere containing CO, N2O, and liquid water (Zang et al. 2022).Notably, CO might be important in the formation of peptides (Huber andWächtershäuser 1997, 1998).Furthermore, recent findings regarding extremely negative carbon isotopic values in the modern Martian atmospheric CO (Alday et al. 2023;Aoki et al. 2023) and organic matter buried in the Gale crater (House et al. 2022) suggest the importance of CO2 photodissociation-a major CO source-in the modern and past Martian atmosphere (Schmidt et al. 2013;Ueno et al. 2022;House et al. 2022;Yoshida et al. 2023).
Here, we employed a theoretical model of atmospheric chemistry to explore diversity in the abundances of CO2, CO, and CH4 in planetary atmospheres of Earth-like lifeless planets orbiting Sun-like (F-, G-, and K-type) stars to gain insights into the search for habitable planets that might facilitate the emergence of life.

One-dimensional photochemical model
We employed a vertically resolved one-dimensional photochemical model, Atmos (Arney et al. 2016(Arney et al. , 2018)), which was originally developed by Jim Kasting and his colleagues (Kasting et al. 1983;Kasting 1990;Pavlov et al. 2001;Kharecha et al. 2005).The model divides a planetary atmosphere below the altitude of 100 km into 200 layers.In each atmospheric box, the chemical budgets of 58 long-lived species, 4 atmospheric particles, 11 short-lived species, and 1 inert species (N2) are evaluated.The long-lived species are transported vertically within the atmosphere via eddy and molecular diffusion.The model considers the rates of production and loss of these species via 383 chemical and photochemical reactions.The effects of lighting, irreversible escape to space, and surface removal via rainout and dry deposition are also considered.The chemical reactions and reaction coefficients are adopted from the latest version of the Atmos model (Wogan et al. 2020;Watanabe et al. 2023).A two-stream approximation is used for the radiation transfer in the atmosphere (Toon et al. 1989).The absorption cross sections of H2O and CO2 are updated following previous studies (Lincowski et al. 2018;Ranjan et al. 2020).The vertical profiles of the air temperature, number density of the air, and eddy diffusion coefficient used in our reference experiment are the same as those used in previous studies (Pavlov et al. 2001;Watanabe et al. 2023) (black line in Figure A1).The vertical mixing ratio of H2O is calculated based on local temperature.To determine how the prescribed temperature affects the model results, we conducted a sensitivity experiment with respect to the temperature profile (Section 3.4.).The mixing ratio of N2 is maintained at 0.8 at any altitude.Surface removal of long-lived species by dry deposition is calculated using the deposition velocities adopted in a previous study (Watanabe et al. 2023).The concentration of CO2 at the bottom of the atmosphere is treated as one of the model sensitivity parameters.For other atmospheric species, the lower and upper boundary conditions are given by the flux.The total volcanic outgassing rate of reducing gases (in terms of H2 equivalent) is expressed as follows: where Φ↑(X) represents the input flux of X to the atmosphere.The outgassing flux of both CO and CH4 is assumed proportional to that of H2 and determined as follows: The factors in this equation are determined based on estimates of the outgassing rates of H2, CO, and CH4 from volcanoes and hydrothermal systems for the present Earth (Catling and Kasting 2017).It has been shown that these factors strongly depend on oxygen fugacity in magma (Wogan et al. 2020).For this reason, we assess the effects of the relative outgassing fluxes of CO and CH4 on the results in Appendix B. The outgassing fluxes of SO2 and H2S are assumed constant (i.e., 0.945 and 0.0945 Tmol S yr −1 , respectively) (Wogan et al. 2020;Watanabe et al. 2023).
The surface pressure, PS, is calculated as follows: where P0 represents the reference value of the total pressure (1.0 bar), pN2 denotes the partial pressure of N2 at the surface (0.8 bar), and fCO2 denotes the mixing ratio of CO2 at the surface.The partial pressure of CO2 at the bottom of the atmosphere, pCO2, can be written as follows: 2.2.CO cycle in the ocean-atmosphere system The CO budget in the atmosphere can be written as follows: where Φ↑(CO) represents the volcanic outgassing flux of CO, Φhyd(CO) denotes the CO flux from the ocean to the atmosphere originating from the decomposition of H2CO and HCO at hydrothermal vents (see below), ΣΦreac(CO) is the net production rate of CO via chemical and photochemical reactions in the atmosphere, Φlight(CO) is the CO production rate by lightning in the troposphere, and Φ↓,dry(CO) is the dry deposition rate of CO (Figure 1).Note that the production rate of CO in the atmosphere higher than the upper boundary of the model atmosphere is included in ΣΦreac(CO).Such high-altitude CO production may have a strong influence on the conditions of CO runaway, especially in the case of M-type stars (Hu et al. 2020;Ranjan et al. 2023), but does not strongly affect the conditions for CO runaway in the case of the Sun-like stars investigated in this study.
In the Atmos model, CO is removed from the lower boundary of the atmosphere via dry and wet deposition, whereas earlier studies considered only dry deposition (Kharecha et al. 2005;Kasting 2014).To represent the slow removal of dissolved CO in seawater, a low depositional velocity of 10 −8 cm s −1 is adopted, as in previous studies (Kharecha et al. 2005;Kasting 2014).
The CO removed via wet deposition is assumed to immediately reach solubility equilibrium with the atmosphere.Therefore, the ultimate removal of CO at the bottom of the atmosphere is via slow abiotic chemical reactions (Kharecha et al. 2005;Kasting 2014).
In an anoxic atmosphere, formaldehyde (H2CO) is effectively produced and deposited into the ocean.Hydrothermal decomposition of H2CO in the ocean has been proposed as a possible source of atmospheric CO (Holland 1984;Cleaves 2008;Watanabe et al. 2023): The depositional flux of HCO could also be large, and we consider the following possible decomposition pathway: It is assumed that the deposited H2CO and HCO are readily decomposed by the above reactions and that H2 and CO return to the atmosphere: 123 () =  ↓ ( " ) +  ↓ (). (7)

Experimental setup
We conducted a series of numerical experiments with four different types of stellar spectra, assuming the young Sun (4.0 Ga) and F-/G-/K-type stars.For the case of the G-type star, the present solar spectrum (G2V) was adopted.For the F-and K-type stars, the spectra of σ Bootis (F2V) and ε Eridani (K2V) were employed, respectively (Figure 2).These stellar spectra were scaled such that the received energy is equal to the present Earth condition, which allows exploration of the typical conditions of the orbital semi-major axis within the HZ of each central star (Arney et al. 2017;Schwieterman et al. 2019).For each stellar spectrum, sensitivity experiments with respect to the partial pressure of CO2 at the bottom of the atmosphere, pCO2, and the volcanic outgassing rate of reducing gasses, Φ↑(red), were performed.For improved convergence, each experiment was repeated three times using the results of the previous run as the initial conditions.

Sensitivity to atmospheric CO2 level and volcanic outgassing rate of reducing gasses
The underlying factors controlling CO runaway are (i) the atmospheric CO2 level (pCO2), (ii) the external input flux of reducing gases (Φ↑(red)) that consume OH radicals, (iii) the availability of H2O (as a function of temperature), and (iv) the stellar spectrum of the central star (especially the irradiance in UV wavelengths).Here, we examine the response of atmospheric chemistry to changes in atmospheric pCO2 and Φ↑(red) assuming the spectrum of the young Sun (4 Ga).
In the pCO2 experiment, we varied atmospheric pCO2 level from 5 × 10 −4 to ~2 bar while maintaining a constant Φ↑(red) (~46.2Tmol H2 equiv.yr −1 ).The results demonstrate that the atmospheric partial pressure of CO, pCO, increases with increasing pCO2 (Figure 3a).This can be attributed to enhanced CO2 photodissociation (the primary source of CO) and suppressed availability of OH radicals (the primary sink of CO) linked to the shielding of tropospheric water vapor from UV radiation by CO2 (see Appendix C for further explanation).Under low pCO2 conditions (<0.2 bar), the external input of CO to the atmosphere via volcanoes and hydrothermal decomposition of H2CO and HCO is balanced mainly by photochemical removal (Figure 3b).We find that further increase in pCO2 leads to marked increase in pCO.This corresponds to CO runaway, whereby photochemical CO removal is overwhelmed by source fluxes, leading to buildup of CO in the atmosphere until it is limited by surface deposition (Figure 3b).Indeed, under CO runaway conditions, dry deposition is one of the primary pathways of CO removal because the sink of the photochemical reactions becomes less effective and the production of CO by lightning is also enhanced.Production of CO from hydrothermal decomposition of H2CO and HCO is less effective under CO runaway conditions.
As might be expected, the abundance of reducing gases (H2, CO, and CH4) in the atmosphere increases with increasing Φ↑(red) (Figure 3d).Because these gases consume OH radicals, increase in Φ↑(red) leads to CO runaway (>~50-90 Tmol H2 equiv.yr −1 ).As in the pCO2 experiment, the external input of CO is balanced by photochemical reactions in the atmosphere before CO runaway.
However, once CO runaway occurs, photochemical reactions become a net source of CO and excess CO is removed via dry deposition (Figure 3e).

Conditions required for CO runaway
We analyzed the above results to better understand the processes that lead to CO runaway.We found that the inception of CO runaway is controlled primarily by the relative flux between OH production from H2O photodissociation (Fhv(H2O)) and the input of reducing carbon species (Φ↑(CO) + Φhyd(CO) + Φ↑(CH4)) (Figure 3c and 3f).The conditions under which these fluxes balance correspond well to the occurrence of CO runaway.We found that CO runaway occurs when these fluxes become comparable even when the model is run without either CO or CH4 in volcanic gases (Figure B1).In such cases, the values of atmospheric pCO2 and Φ↑(red) required for triggering CO runaway tend to be higher than those shown in Figure 3. Specifically, assuming no external input of reducing carbon species, CO runaway is not observed at the parameter ranges that we investigated.
The findings of further systematic sensitivity experiments also support the above mechanistic understanding of CO runaway (Figure 4a).The conditions for Fhv(H2O) = Φ↑(CO) + Φhyd(CO) + Φ↑(CH4) correspond well to the marked increase in atmospheric pCO.The present result also demonstrates that the threshold value of pCO2 for CO runaway decreases with increasing Φ↑(red), and that elevated pCO levels are accompanied by elevated pCH4 (Figure 4b).
Under CO runaway conditions, atmospheric pCH4 levels tend to be high (~>10 −4 bar) because of the high outgassing rate and reduction in the mixing ratios of OH radicals (Figure C1).
Nevertheless, unlike the runaway behavior in atmospheric pCO, atmospheric pCH4 does not exhibit such dramatic change.

Production of organic compounds
In the prebiotic atmosphere, a series of organic compounds are produced in the atmosphere.The largest removal pathway of organic compounds from the atmosphere is deposition of H2CO, which is shown as a function of atmospheric pCO2 and Φ↑(red) (Figure 5).Under CO runaway conditions, the H2CO deposition rate is smaller than under conditions without CO runaway.When CO runaway occurs, the production rate of H radicals in the troposphere decreases dramatically owing to depletion of OH radicals (see Appendix C), suppressing the production of tropospheric HCO: Consequently, the concentration of tropospheric HCO is decreased under CO runaway conditions, which further leads to decline in the reactions between pairs of HCO molecules that form H2CO: Thus, the rate of formation of tropospheric H2CO decreases when CO runaway occurs (Figure 5b and 5c).It also leads to decline in the rate of supply of prebiotic organic compounds to the ocean.
Under CO runaway conditions, the depositional flux of H2CO is <1 Tmol C yr −1 , while that of HCO is typically ~0.01 Tmol C yr −1 (Figure 5b and 5c); therefore, it does not strongly affect the atmospheric CO budget (Figure 3b).Instead of these organic compounds, the removal of CO is the primary sink of reduced C in the atmosphere under CO runaway conditions (Figures 3b, 3e, and 5a).This implies that CO chemistry in the aqueous phase is critical for the formation of organic compounds in prebiotic oceans.

Dependency on temperature
In this study, we employ a photochemistry model prescribing the temperature and H2O profiles in the atmosphere.However, the climatic state would affect the conditions for CO runaway because it exerts fundamental control on the availability of OH in the atmosphere.For example, climate warming would lead to increase in H2O in the troposphere, suppressing CO runaway by promoting production of OH.To examine the impact of uncertainty in temperature (climate) on our results, we conducted additional sensitivity experiments with respect to an elevated surface temperature (300 K at the surface) (Figure 6).As expected, the atmospheric CO2 levels and the outgassing rate of reducing gases (Φ↑(red)) required for CO runaway tend to be larger than in the standard case (cf. Figure 3).Quantifying the interrelationship between photochemistry and climate using a fully coupled model of photochemistry and climate (Arney et al. 2016(Arney et al. , 2017(Arney et al. , 2018;;Garduno Ruiz et al. 2023) will be a fruitful topic for future research.

Dependency on spectrum of the central stars
The effect of the stellar spectrum type on the response of the atmospheric carbon composition and photodissociation rates of CO2 and H2O was examined by performing additional experiments with the spectrum of F2V and K2V stars.For the case of the F2V star (Figure 7), CO runaway does not occur even at the maximum value of atmospheric pCO2 that we explored.This can be attributed to the stronger UV flux of the F2V star than that of the Sun.Consequently, the photodissociation rates of CO2 and H2O are more than one order of magnitude larger than those shown in Figure 3c.
This allows elevation of the rate of production of OH in the atmosphere, which suppresses the onset of CO runaway.In contrast, for the case of the K2V star (Figure 8), CO runaway occurs at a lower level of atmospheric pCO2 (~1-2 × 10 −3 bar) than that for the case of the early Sun.This can be attributed to the relatively small UV flux from the K2V star.Specifically, the UV flux at ~160-200 nm is smaller than that of the Sun.This suppresses the photodissociation rate of H2O, which promotes the occurrence of CO runaway.These results indicate that the characteristics of the stellar spectra are an important factor controlling the conditions for CO runaway.

CO runaway gap
When the simulated atmospheric pCO2, pCH4, and pCO are plotted in the phase space of pCO/pCO2 versus pCH4/pCO2, the atmospheric chemistry is clearly divided into the groups before and after the occurrence of CO runaway (Figure 9).These relationships, in principle, can be explained by the chemical reactions that determine the atmospheric levels of pCO and pCH4.
Before CO runaway, atmospheric pCO and pCH4 are balanced by reactions with OH radicals.
Under such conditions, the mixing ratios of CO and CH4 (fCO and fCH4, respectively) can be approximated as follows: where KCO+OH and KCH4+OH are the reaction rate coefficients for reaction R11 and R12 in Appendix C, respectively, and nOH and natm represent the number density of OH radicals and the air, respectively.By neglecting the temperature-and pressure-dependencies of KCO+OH and KCH4+OH, the CH4/CO2 and CO/CO2 relationship can be approximated as follows: This equation indicates that CH4/CO2 and CO/CO2 would have almost linear dependence because the outgassing rates of CO and abiotic CH4 would also be linearly dependent.
Under CO runaway conditions, the reactions that consume atmospheric CO are different from those before CO runaway.In such cases, the CO mixing ratio in the atmosphere could be represented approximately as follows: where KCO+O is the reaction rate coefficient for reaction R13 (Appendix C).The high fCO is caused by the high CO outgassing rate and/or low value in the denominator.When CO runaway occurs in the atmosphere, the atmospheric CH4 cycle tends to be balanced by photodissociation at high altitudes (~>80 km) because of insufficient OH radicals at lower altitudes.Because photodissociation of CH4 effectively consumes CH4, the sudden increase in atmospheric pCH4 is not caused by the scarcity of OH radicals when CO runaway occurs in the atmosphere.This would suppress the change in atmospheric pCH4 compared with the atmospheric pCO, leading to the gap structure shown in Figure 9.When the outgassing rate of CH4 is small, the CO runaway branch does not exhibit a clear structure.Nevertheless, the sudden increase in atmospheric pCO contributes to the gap structure (Figure B2).
This gap structure originates from the different behavior of atmospheric CO and CH4, and therefore it might be a ubiquitous feature for various Earth-like exoplanets (Figure 9).Indeed, compared with the case of the G2V star, the gap structure is clearly seen in the case of the K2V star because of the ease with which CO runaway is caused.For the parameter ranges that we explored, most calculations for the case of the F2V star lay on the left branch because it is difficult to cause CO runaway with a high H2O photodissociation rate (Figure 7c and 7f).Nonetheless, some results did demonstrate CO runaway, especially for high atmospheric pCO2 and/or elevated Φ↑(red) cases, representing the existence of the CO runaway gap structure.4. DISCUSSION

Possibility of CO runaway on the early Earth and Mars
The atmospheric pCO2 level and the volcanic input flux of reducing carbon species (CO and CH4) exert fundamental controls on the conditions for CO runaway by changing the photodissociation rate of water in the atmosphere (Figure 4).For our standard case, the critical pCO2 level for CO runaway is a few tenths of one bar for the outgassing rate of reducing gases of a few tens Tmol H2 equivalent yr −1 .In terms of atmospheric CO2 levels, this would be feasible for the early Earth because the steady-state atmospheric pCO2 would have been elevated via the carbonate-silicate geochemical cycle owing to the low solar luminosity (Gough 1981;Walker et al. 1981;Tajika and Matsui 1992;Sleep and Zahnle 2001;Krissansen-Totton et al. 2018a;Kadoya and Tajika 2019;Kadoya et al. 2020;Lehmer et al. 2020;Watanabe and Tajika 2021).Specifically, previous theoretical models of the global carbon cycle have estimated steady-state atmospheric pCO2 levels of ~0.1-1 bar or higher during the Hadean-early Archean (Tajika and Matsui 1992;Sleep and Zahnle 2001;Krissansen-Totton et al. 2018a).
An additional condition for CO runaway is a high volcanic outgassing rate of reducing gases, Φ↑(red).Previous studies estimated that Φ↑(red) would typically be ~1 Tmol H2 eq.yr −1 or less on the early Earth (Holland 1984;Catling and Kasting 2017;Thompson et al. 2022), while the maximum outgassing flux from serpentinization is estimated to be ~50 Tmol H2 eq.yr −1 (Krissansen-Totton et al. 2018b).Our results demonstrate that a value of Φ↑(red) of ~>10 Tmol H2 eq.yr −1 is required for CO runaway for a level of atmospheric pCO2 of ~<1 bar (Figure 4).This is within the possible maximum value estimated by Krissansen-Totton et al. (2018).From a more mechanistic perspective, the relative outgassing fluxes of reduced C (CO and CH4) would be critical for the occurrence of CO runaway (Appendix B).The outgassing rates of CO and CH4 relative to H2 reflect the conditions of the thermodynamic equilibrium between magma and gas bubbles.Specifically, the high-pressure conditions for submarine volcanism would be preferable for the outgassing of CH4 relative to H2 (Gaillard et al. 2011;Wogan et al. 2020), promoting CO runaway.The high-temperature conditions and high oxygen fugacity in magma would have promoted the outgassing of CO relative to CH4 (Wogan et al. 2020).Therefore, for better constraint on the conditions required for CO runaway, coupled modeling of atmospheric and solid-Earth processes is critical.In addition to the outgassing flux from the interior of the Earth, impact events would have played a crucial role in providing CO on early Earth, at least transiently (Kasting 1990(Kasting , 2014;;Kress and McKay 2004;Zahnle 2006;Schaefer and Fegley 2007;Genda et al. 2017;Zahnle et al. 2020).This would also have helped initiate CO runaway in the early atmosphere.
Nevertheless, our results clearly demonstrate the conditions for CO runaway in terms of the levels of atmospheric CO2 and Φ↑(red) (Figure 4).

Other
processes not yet fully included in the model warrant future consideration, e.g., the effect of climate on the conditions for CO runaway.Variation in the planetary climate and the associated change in the water mass in the troposphere would play a role in the conditions for CO runaway by changing the availability of OH in the troposphere (Figure 6).The uncertainty in the climatic state does not alter our overarching conclusions regarding the fundamental role of atmospheric CO2 and Φ↑(red), and the gap structure in the pCH4/pCO2-pCO/pCO2 phase space.
However, complete treatment of the coupled relationship between atmospheric chemistry and the climate will be essential for quantitative understanding of how the relative abundances of CO2, CO, and CH4 affect planetary habitability and (bio)geochemistry, thereby representing a fruitful topic for future research.
The effect of climate on the relative abundances of CO2, CO, and CH4 in the atmosphere would be even more critical for the case of Mars.The climate of early Mars has been a subject of active discussion (Pollack et al. 1987;Kasting 1991;Forget et al. 2013;Wordsworth 2016;Wordsworth et al. 2017;Ramirez and Craddock 2018;Kamada et al. 2020).If a cold and dry environment were pervasive on early Mars, it might have promoted CO runaway if the level of atmospheric pCO2 was sufficiently high.In contrast, if a warm and wet environment were pervasive, a higher atmospheric pCO2 level would have been required.The recent findings of anomalously low negative carbon isotopic values of the Martian atmospheric CO and organic matter buried in Gale crater suggest the importance of CO production via CO2 photolysis in the modern and past Martian atmosphere (Zahnle et al. 2008;Krasnopolsky 2015;House et al. 2022;Yoshida et al. 2023;Alday et al. 2023;Aoki et al. 2023), opening new vistas for future work intended to better understand the possibility of CO runaway on early Mars.

Implications for the origin of life
Studies have discussed that CO runaway conditions promote the formation of organic compounds, aldehydes, peptides, and/or amino acids suitable for prebiotic chemistry (Bar-Nun and Chang 1983;Huber andWächtershäuser 1997, 1998;McGlynn et al. 2020;Zang et al. 2022).Our model demonstrates that elevated atmospheric CO2 levels and/or the high volcanic outgassing flux of reducing gases promote the formation of CO-rich atmospheres suitable for the origin of life.Our results also indicate that the rate of CO deposition is exceptionally high when CO runaway occurs (Figures 4b,4d,and 5a).This would have also played a key role in supplying reduced C species to the ocean, which might indicate that the oceanic chemistry of CO and other organic compounds is crucial in understanding prebiotic chemistry.The CO concentrations in the ocean, [CO], can be estimated using the simple oceanic chemistry model constructed by Kharecha et al. (2005) (Appendix D).The results demonstrate that under CO runaway conditions, [CO] reaches an order of 100 μM (blue and light blue lines in Figure D1a and D1b).We can also estimate the maximum concentration of H2CO in the ocean (Figure D1c).Although the deposition flux of H2CO decreases under CO runaway conditions (Figure 5b), the maximum concentration of H2CO in the ocean would exceed 1 mM, which would have helped the formation of the building blocks of life together with CO in the ocean.

Implications for the search for habitable planets
Our results demonstrate that anoxic atmospheres of Earth-like lifeless planets can be clearly classified in the pCH4/pCO2-pCO/pCO2 phase space.The sensitivity experiments with respect to different types of central stars also indicate that the CO runaway gap structure would be a general feature of Earth-like planets orbiting Sun-like stars.Our results indicate that the most preferable condition for CO runaway is near the outer edge of the HZ because atmospheric pCO2 is expected to be high in this region owing to the operation of carbonate-silicate geochemical cycles (Walker et al. 1981;Kadoya and Tajika 2019;Kadoya et al. 2020;Lehmer et al. 2020;Watanabe and Tajika 2021).In this study, we did not consider planets orbiting M-type stars.Nevertheless, because such planets receive less near-UV radiation than planets orbiting Sun-like stars, we expect that CO runaway would tend to be promoted in the atmospheres of such planets.More systematic examinations that comprehensively consider astronomical factors and planetary endogenous factors will be the subject of future work.

CONCLUSION
Understanding the factors that control the relative abundances of CO2, CO, and CH4 in planetary atmospheres has important implications in the search for habitable planets beyond our solar system because atmospheric composition exerts fundamental controls on planetary climate and biogeochemistry.In this study, we employed an atmospheric photochemistry model to understand the diversity of atmospheric CO2, CO, and CH4 abundances in the atmosphere of Earth-like planets orbiting Sun-like stars.Our results for the prebiotic Earth conditions demonstrate that photochemical instability of CO (i.e., CO runaway) tends to be triggered by higher atmospheric For this reason, the supply rate of CH4 affects the onset of CO runaway in the same way as the CO is supplied into the atmosphere.
If there is no reduced C outgassing from volcanoes (that is, it is limited to only CO supply from hydrothermal systems), the runaway behavior is not observed because the H2O photodissociation rate and the reduced C outgassing rate does not get closer (dotted lines in Figure B2a-B2d).because the H2O photolysis (i.e., primary OH production) is suppressed owing to the shielding by atmospheric CO2 (Figure C1g).This is the primary mechanism responsible for CO runaway.In CO runaway regimes, the three-body reaction with O( 3 P) converts much-but not all-of the excess CO into CO2, (This reaction is slow before CO runaway because it is spin-forbidden): CO + O( 3 P) + M → CO2 + M .(R13) As a result, the O( 3 P) mixing ratio in the lower atmosphere becomes very small.Thus, CO runaway is accompanied by the transition of the buffering mechanism of CO in the atmosphere (from Reaction R11 to R13).The surface dry and wet deposition of CO also helps to remove the excess CO from the atmosphere.

Figure 1 .
Figure 1.Schematic of the CO cycling in the ocean-atmosphere system considered in this study.

Figure 3 .
Figure 3. Steady-state response of atmospheric chemistry to changes in (left) atmospheric pCO2

Figure 4 .
Figure 4. Steady-state response of atmospheric CO and CH4 abundances in a phase space of

Figure 5 .
Figure 5. Same as Figure 4 but showing the depositional flux of (a) CO, (b) H2CO, and (c) HCO

Figure 6 .
Figure 6.Same as Figure 3 but when a higher tropospheric temperature (red line in Figure A1) is

Figure 7 .
Figure 7. Same as Figure 3 but when the stellar spectrum of the F2V star is adopted.

Figure 8 .
Figure 8. Same as Figure 3 but when the stellar spectrum of the K2V star is adopted.

Figure 9 .
Figure 9. Steady-state response of atmospheric CH4/CO2 and CO/CO2 for different types of central Figure A1.The temperature profile adopted in this study: the standard profile (black line; Pavlov

Figure B1 .
Figure B1.Steady-state response of atmospheric pCO (blue) level (a, c) and a relationship between

Figure B2 .
Figure B2.Steady-state response of atmospheric CH4/CO2 and CO/CO2 for different types of

Figure
Figure 3d also demonstrates that higher input rates of the reducing gases (Φ↑(red)) result

Figure C1 .
Figure C1.Steady-state response of atmospheric chemistry to changes in pCO2, assuming the

Figure D1 .
Figure D1.The responses of concentrations of (a) CO in the surface and deep oceans (light and