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Impacts of Atmospheric Carbon Species and Stellar Type on Climates of Terrestrial Planets

Jared Landry, Hiroyuki Kurokawa, Tetsuo Taki, Yuka Fujii, Kosuke Aoki and Hidenori Genda

Published 2025 September 4 • © 2025. The Author(s). Published by the American Astronomical Society.
The Planetary Science Journal, Volume 6, Number 9Citation Jared Landry et al 2025 Planet. Sci. J. 6 212DOI 10.3847/PSJ/adf7a1

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Received 2025 March 28
Revised 2025 July 4
Accepted 2025 August 1
Published 2025 September 4

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Planetary climates; Planetary atmospheres; Planetary science; Atmospheric evolution; Exoplanet atmospheres

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Abstract

The climates of terrestrial planets are largely determined by the composition of their atmospheres and the spectral types of their host stars. Previous studies suggest that a wide range of carbon species abundances (CO₂, CO, and CH₄) can result from variations in reducing fluxes and stellar spectral types that influence photochemistry. However, a systematic investigation of how varying carbon species, particularly CO, affect planetary climates across wide parameter spaces remains limited. Here, we employ a 1D radiative–convective equilibrium model to examine the dependence of planetary climate on the abundances of carbon species and host star type. We find that CO, due to weak absorption of stellar radiation, induces only moderate changes in stratospheric temperature, while its effect on surface temperature is negligible. Under Earth-like ${p}_{{{\rm{N}}}_{2}}$ (where p_i is the partial pressure on the surface of species i), for cases with fixed ${p}_{{{\rm{CO}}}_{2}}$ , an increase in CO leads to surface cooling on planets orbiting Sun-like stars unless the sum of ${p}_{{{\rm{CO}}}_{2}}$ and ${p}_{{{\rm{CH}}}_{4}}$ exceeds ∼1 bar, whereas it results in surface warming for planets around M-type stars. When the total pressure of carbon species is fixed, converting CO₂ or CH₄ into CO always induces cooling. These effects arise from a combination of CO Rayleigh scattering, pressure broadening of greenhouse gas absorption lines, and varying water vapor levels. We further discuss how CO- and CH₄-driven cooling (warming) can trigger positive (negative) climate-photochemistry feedback, influencing atmospheric evolution. Additionally, we suggest that CO-rich planets may be less susceptible to water loss and atmospheric oxidation due to lower stratospheric water vapor content.

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1. Introduction

The composition of an atmosphere controls a planet’s climate and thus its habitability because the various gases behave differently via scattering and absorbing stellar and planetary radiation (e.g., J. F. Kasting & T. P. Ackerman 1986; J. D. Haqq-Misra et al. 2008; D. C. Catling & J. F. Kasting 2017). The solar system terrestrial planets (Venus, Earth, and Mars) today and in the past exhibit a variety of atmospheres. Due to variations in host star and planetary properties, extrasolar terrestrial planets can have even greater diversity. Here we focus on carbon species (CO₂, CO, and CH₄), as they would typically be major atmospheric constituents.

The abundance of these carbon species is controlled by planetary processes. The CO₂ abundance in Earth’s atmosphere is thought to have been controlled by carbonate–silicate cycling: a balance between volcanic supply and loss through silicate weathering, carbonate precipitation, and subduction (J. C. G. Walker et al. 1981; B. J. Foley 2015; D. C. Catling & J. F. Kasting 2017). Thanks to the temperature dependence of the weathering rate, the carbonate–silicate cycling acts as a thermostat (J. C. G. Walker et al. 1981). This negative feedback likely contributed to keep early Earth habitable (J. C. G. Walker et al. 1981; J. Krissansen-Totton et al. 2018) and is considered to determine the extent of habitable zones (J. F. Kasting et al. 1993; R. K. Kopparapu et al. 2013).

Carbon speciation including CO and CH₄ is determined by the supply and loss of reducing power via volcanic outgassing and hydrogen escape, as well as atmospheric photochemistry. An oxidizing mantle such as modern Earth’s releases CO₂, while reducing systems release CO and CH₄ (D. C. Catling & J. F. Kasting 2017). It has been proposed that Earth’s mantle was more reducing in the Archean, releasing reduced gases (S. Aulbach & V. Stagno 2016; R. W. Nicklas et al. 2019; S. Kadoya et al. 2020), although the interpretation of geochemical data is controversial (F. Zhang et al. 2024). For rocky bodies in the solar system, oxygen fugacity spans a range of ∼10 orders of magnitude (C. Cartier & B. J. Wood 2019).

Reducing power is lost from a planet via hydrogen escape to space. While various escape mechanisms dictate the hydrogen escape rate, on Earth and elsewhere in the solar system, the escape of hydrogen is thought to be limited by the rate at which it can diffuse to the upper atmosphere, where it then escapes (D. C. Catling & J. F. Kasting 2017). This is called diffusion-limited escape. On modern Earth, the supply of hydrogen to the upper atmosphere depends largely on the amount of water vapor in the stratosphere (D. M. Hunten 1973; D. C. Catling & J. F. Kasting 2017). When the mixing ratio of water vapor in the stratosphere increases to a certain threshold, the escape of hydrogen is no longer limited by its supply to the upper atmosphere and is instead limited by the energy supply flux from X-ray and extreme ultraviolet (XUV) radiation, called energy-limited escape (A. J. Watson et al. 1981; D. C. Catling & J. F. Kasting 2017). Thus, the climate affects the rate of hydrogen escape by determining the water vapor content in the stratosphere.

Finally, photochemistry induced by ultraviolet (UV) irradiation from the host star also controls carbon speciation. While CO₂ dissociates to CO and O with ≲200 nm radiation, their direct recombination is spin-forbidden (D. C. Catling & J. F. Kasting 2017). A catalytic cycle with OH radicals, formed with dissociation of H₂O, stabilizes CO₂ in habitable worlds with CO₂-rich atmospheres (M. B. McElroy & T. M. Donahue 1972; D. C. Catling & J. F. Kasting 2017). However, the runaway dissociation of CO₂ (also called the CO runaway) may be triggered on planets orbiting M-type stars with fewer H₂O-dissociating photons (F. Tian et al. 2014; C. E. Harman et al. 2015) and with colder climates such as early Mars where the water vapor content is lower (K. Zahnle et al. 2008). Y. Watanabe & K. Ozaki (2024) recently performed an extensive parameter survey for the volcanic reducing flux and stellar type and summarized the conditions for CO runaway.

In climate modeling, CO₂, as it is the most abundant greenhouse gas in the current Earth’s atmosphere aside from water vapor, has been the focus of most climate studies that contain carbon compounds (S. Manabe & R. T. Wetherald 1967; J. F. Kasting & T. P. Ackerman 1986; R. D. Wordsworth & R. T. Pierrehumbert 2013; R. M. Ramirez et al. 2014). Since CO₂ has strong absorption bands in the wavelength range for planetary blackbody radiation, increasing CO₂ levels typically increase surface temperatures (J. F. Kasting & T. P. Ackerman 1986; R. D. Wordsworth & R. T. Pierrehumbert 2013; R. M. Ramirez et al. 2014). However, there are also situations where increasing CO₂ content may decrease temperatures. Here, water content decreases with increasing ${p}_{{{\rm{CO}}}_{2}}$ (hereafter p_i represents the partial pressure of the species i at the surface) because the sensible heat (energy required for a change in temperature) of the atmosphere exceeds the latent heat (energy required for a change of phase). When the sensible heat of an expanding, upwelling air parcel is greater than the latent heat, the work being done is supplied by internal energy rather than by the release of latent heat from a change of phase. This leads to a decrease in temperature and thus limits the amount of water vapor in the upper atmosphere (R. D. Wordsworth & R. T. Pierrehumbert 2013). In addition to this water vapor effect, the CO₂ greenhouse effect eventually saturates at high levels, while Rayleigh scattering does not, leading to a decrease in temperatures (J. F. Kasting 1993). This phenomenon is responsible for setting an outer edge to the habitable zone of stellar systems; otherwise, CO₂ could be added continuously to counteract the diminishing top-of-atmosphere (TOA) flux with increasing orbital radii.

Studies investigating methane’s influence on climate have also been performed (A. A. Pavlov et al. 2000; J. D. Haqq-Misra et al. 2008; G. Arney et al. 2016; G. N. Arney et al. 2017). Methane has direct and indirect effects on the atmosphere; absorption as a greenhouse gas (A. A. Pavlov et al. 2000; R. M. Ramirez & L. Kaltenegger 2018) and scattering from haze produced by CH₄ via photochemical reactions (J. D. Haqq-Misra et al. 2008; G. Arney et al. 2016). It was found that increasing the CH₄ content causes warming up to ${f}_{{{\rm{CH}}}_{4}}/{f}_{{{\rm{CO}}}_{2}}\lesssim 0.1$ (hereafter f_i represents the volume mixing ratio of the species i; A. A. Pavlov et al. 2000; J. D. Haqq-Misra et al. 2008). However, when ${f}_{{{\rm{CH}}}_{4}}/{f}_{{{\rm{CO}}}_{2}}\gtrsim 0.1$ , photochemical hazes form in the atmosphere as a result of CH₄ photochemical reactions, and these hazes can lead to significant cooling due to scattering of incoming radiation for planets orbiting G-type stars or possible warming from absorption of outgoing radiation for planets orbiting M-type stars (G. N. Arney et al. 2017). The inclusion of hazes, however, is beyond the scope of this study.

Compared to CO₂ and CH₄, the climate effects of CO have received less attention. However, photochemical modeling shows that CO can be a major carbon species on planets orbiting M-type stars (F. Tian et al. 2014; C. E. Harman et al. 2015; R. Hu et al. 2020) and on early Mars (K. Zahnle et al. 2008), the latter of which is also supported by carbon-isotopic evidence (Y. Ueno et al. 2024). Because CO is infrared-inactive, the primary influence of CO is thought to be scattering of stellar irradiation, which causes a decrease in temperatures. On the other hand, CO causes pressure broadening of absorption lines of coexisting greenhouse gases, which increases temperatures. R. Hu et al. (2020) modeled climates of CO-rich atmospheres by using another nongreenhouse gas, N₂, instead of CO. However, CO has weak but nonnegligible absorption lines in near-to-mid-infrared wavelengths (I. E. Gordon et al. 2017), whose effects on the atmospheric temperature profile remain unexplored. Moreover, a systematic investigation of how varying carbon species, particularly CO, affect planetary climates across a wide parameter space remains limited. In the extensive survey for the CO runaway by Y. Watanabe & K. Ozaki (2024), a fixed atmospheric temperature profile is used. Therefore, the climate effects of the CO production and their feedback on photochemistry remain to be investigated.

We aim to perform a comprehensive study of the climate effects of carbon species including CO as well as CO₂ and CH₄ and discuss the feedback on atmospheric chemistry. Here, we utilize a one-dimensional (1D) radiative–convective equilibrium model to understand the relationships between the planetary climate and atmospheric carbon species (CO₂, CO, CH₄), as well as the spectral type of the host star. Furthermore, we discuss how these different dependencies of the climate influence photochemical feedback on the atmospheric oxidation state to understand how atmospheres evolve over time. We also discuss the fate of surface water based on the calculated stratospheric water content and associated hydrogen escape to space.

2. Methods

2.1. Temperature and Water Vapor Profiles

To calculate the 1D temperature and water vapor profiles of the atmosphere for given sets of partial pressures of carbon species and spectral types of host stars, we used CLIMA, a module of the ATMOS code⁷ (J. F. Kasting et al. 1984; G. Arney et al. 2016). Because the original CLIMA only considers CO₂ and CH₄ for carbon species, we newly included the effect of CO on absorption and scattering of radiation and on the heat capacity.

In the radiative–convective equilibrium model adapted by CLIMA, the atmosphere consists of two layers: the stratosphere and the troposphere. The troposphere is characterized by convection, and its temperature and water vapor profiles are modeled with the moist adiabat. Convection is assumed for layers where the temperature lapse rate (−dT/dz, where T is the temperature and z is the height from the surface) is larger than that of the adiabat. This procedure finds the tropopause, the boundary between the troposphere and stratosphere. The moist adiabatic lapse rate takes the release of the latent heat from condensation of saturated water vapor into account (A. P. Ingersoll 1969; J. F. Kasting et al. 1984; J. F. Kasting 1988; D. C. Catling & J. F. Kasting 2017). Given the saturation vapor pressure of each layer calculated from the adiabat, the mixing ratio of water vapor is then obtained by adapting a relative humidity (RH) model. The original CLIMA code assumes the RH model of S. Manabe & R. T. Wetherald (1967), which is developed to mimic that of current Earth. Since we consider planets with a higher temperature where a higher RH is expected (C. Goldblatt et al. 2013; R. M. Ramirez et al. 2014), we adopt the model of J. F. Kasting & T. P. Ackerman (1986). To add CO in the convection model, its heat capacity is taken from the NIST database.⁸

We utilize two different models: the “forward” and “inverse” models. In the forward model, the temperature profile in the stratosphere is modeled with a profile that satisfies the net radiation flux (the sum of incoming and outgoing flux) equal to zero. Here, the tropopause is determined via a minimum in the temperature profile we calculate.

In the inverse model, the stratospheric temperature profile is assumed to be isothermal. Here the water vapor mixing ratio in the stratosphere is assumed to be constant because of the temperature dependence of the saturation vapor pressure. Here, the tropopause is found where the adiabatic temperature profile reaches an assumed temperature of the stratosphere. Following previous studies (e.g., R. M. Ramirez et al. 2014), we assumed 200 K, which roughly corresponds to Earth’s skin temperature (D. C. Catling & J. F. Kasting 2017).

As we show in Section 3.1, the results of forward and inverse calculations show only a moderate difference in the stratosphere, while the surface temperature is not affected significantly. Moreover, forward calculations are computationally more expensive and sometimes cause difficulty in finding equilibrium solutions. Thus, we performed forward modeling for limited parameter sets to investigate the effect of CO absorption on stratospheric temperature and water vapor content and to validate the inverse modeling (see Section 3.1). Then we performed an extensive parameter survey with inverse modeling (Sections 3.2–3.5).

2.2. Radiative Transfer

Radiative transfer in CLIMA is broken into two different bandpasses: stellar and planetary (thermal) radiation (J. F. Kasting et al. 1984; G. Arney et al. 2016). The transmissivity for each individual gas is determined by the correlated-k method (S. Kato et al. 1999), where absorption of photons in different wavelengths within a single bin is only treated statistically to maximize computational efficiency while maintaining accuracy in the flux for the wavelength bin. The two-stream approximation is assumed for the calculation of radiative fluxes into and out of each layer of the atmosphere (O. B. Toon et al. 1989).

Because the version of CLIMA we are based on originally only contained CO₂, CH₄, and H₂O as absorbing gases, we added CO to the code for this study. CO is a weak absorber, but the strongest absorption feature of CO occurs outside of the stellar wavelength range considered in the original CLIMA (J. F. Kasting et al. 1984; L. S. Rothman et al. 2009; D. C. Catling & J. F. Kasting 2017). For the stellar wavelength range, CLIMA originally ranges from 0.25 to 4.5 μm, broken up into 38 wavelength bins (J. F. Kasting et al. 1984; G. Arney et al. 2016), but because of CO’s absorption spectrum, we extended the range to 5.4 μm and added an additional wavelength bin, making 39 total. We calculated the coefficients of the correlated-k method for spectral bins including the new bin. The absorption data for the original gases in CLIMA come from HITRAN 2008, except for H₂O, which come from HITEMP 2010, and the data for CO are taken from the HITRAN 2016 database (L. S. Rothman et al. 2009; I. E. Gordon et al. 2017). The thermal-infrared spectrum is broken up into 55 bins from 0.7 to 500 μm (J. F. Kasting et al. 1984; G. Arney et al. 2016). Finally, the scattering parameters for CO are taken from I. M. Vardavas & J. H. Carver (1984).

2.3. Input Parameters and Calculation Procedures

The inputs into the CLIMA code include the partial pressures of the noncondensable gases at the surface, the radiation spectrum of the host star, the incoming stellar flux, the Bond albedo of the surface A, the gravitational acceleration g, and the pressure at the top of the atmosphere p^TOA. The partial pressures of carbon species, host stellar type, and incoming flux were varied as detailed below. For the other input parameters, we assumed fixed values. We assumed ${p}_{{{\rm{N}}}_{2}}=0.8\,\mathrm{bar}$ , A = 0.32, which is consistent with the assumption of modern Earth modeled without clouds, g = 9.8 m s⁻², and p^TOA = 10⁻⁶ bar.

Because the mixing of different gases changes their partial pressures from those obtained when they exist alone, we define two partial pressures: the partial pressure in the mixed gas ${\tilde{p}}_{i}$ and the pressure when it exists by itself p_i, where the subscript i represents a gas species of interest, consistent with previous studies (M. J. Way et al. 2017). (The latter is our input parameter and is hereafter what we are concerned with when discussing the partial pressure of carbon species. The prior is only used within our code for calculations.) This is necessary because the atmosphere is a mixture of gases with varying molar weights, and ${\tilde{p}}_{i}$ and p_i are only equal when each individual gas has the same molar weight. Those two partial pressures can be converted as follows. The partial pressure in the mixed gas ${\tilde{p}}_{i}$ is defined as

where p is the total pressure, which is given by

The mixing ratio f_i in Equation (1) is described by

where σ_i is the column density, given by

Here m_i is the molecular mass of species i.

For the partial pressures of the three carbon species, we made our calculations for two cases to summarize our results in 2D parameter spaces (Table 1). The first is where we fixed ${p}_{{{\rm{CO}}}_{2}}$ and treated p_CO and ${p}_{{{\rm{CH}}}_{4}}$ as independent parameters. This case mimics a situation where ${p}_{{{\rm{CO}}}_{2}}$ is controlled by carbonate–silicate cycling (J. C. G. Walker et al. 1981; B. J. Foley 2015), while p_CO and ${p}_{{{\rm{CH}}}_{4}}$ vary due to changing the reducing flux. We note that this is simplification; changing p_CO and ${p}_{{{\rm{CH}}}_{4}}$ can change the surface temperature, which then influences the weathering rate and thus ${p}_{{{\rm{CO}}}_{2}}$ in reality.

Table 1. Input Parameters for Our Study

	Fixed ${p}_{{{\rm{CO}}}_{2}}$ Case	Fixed p_Ctotal Case
Variable	Range	Variable	Range
p_CO (bar)	10⁻⁶–10²	${p}_{{\rm{CO}}}/{p}_{{{\rm{CO}}}_{2}}$	10⁻⁶–10²

${p}_{{{\rm{CH}}}_{4}}$ (bar)	10⁻⁶–10²	${p}_{{{\rm{CH}}}_{4}}/{p}_{{{\rm{CO}}}_{2}}$	10⁻⁶–10²

${p}_{{{\rm{CO}}}_{2}}$ (bar)	10⁻², 1	p_Ctotal (bar)	0.1

Host star	Sun, GJ 876	Host star	Sun

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The second case is a closed system where the total pressure of carbon species ( ${p}_{{\rm{Ctotal}}}\equiv {p}_{{{\rm{CO}}}_{2}}+{p}_{{\rm{CO}}}+{p}_{{{\rm{CH}}}_{4}}$ ) is fixed, mimicking a system without an active carbonate–silicate cycle. We expect such cases to be possible because the carbonate–silicate cycle is largely dependent on tectonic activity. If a terrestrial planet is tectonically inactive, there can be limited burial or degassing of carbon species. In addition to Earth and perhaps other solar system terrestrial planets earlier in their history, such worlds likely exist beyond our solar system, giving us cause to include such situations in our model. However, it is worth noting that studies have investigated the ability of terrestrial planets with stagnant lids to maintain a carbon cycle (e.g., B. J. Foley & A. J. Smye 2018).

We consider two different host stars: the Sun and an M-type star, GJ 876, whose spectra can be found in Figure 1. For the former case, we assumed that a planet receives an incoming flux equivalent to that of current Earth. For the latter case, we assumed an incoming flux with which a planet with ${p}_{{{\rm{N}}}_{2}}=0.8\,\mathrm{bar}$ and ${p}_{{\mathrm{CO}}_{2}}=0.003\,\mathrm{bar}$ has an equilibrium surface temperature of 285 K (consistent with modern Earth). At the top of the atmosphere in this case, the incoming flux is 1192.5 W m^–2, equal to 0.8726 times the solar constant.

Figure 1. Refer to the following caption and surrounding text. — **Figure 1.** Spectra of the Sun and GJ 876 for the wavelength range 0.25–5.4 μm used in our calculations, divided by the wavelength range in each bin, and found at the top of the atmosphere. The Sun case is found for an Earth-like terrestrial planet orbiting at 1 au, and the GJ 876 case is found for an Earth-like terrestrial planet at an orbital distance where 0.003 bar CO₂ and 0.8 bar N₂ in the atmosphere yield an equilibrium surface temperature of 285 K, consistent with modern Earth.
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For each parameter set, we determined the atmospheric structure in equilibrium by changing the surface temperature iteratively. We determined that an equilibrium solution was obtained when the relative difference between incoming and outgoing flux at the top of the atmosphere fell below 10⁻³. We note that, in cases with very high ${p}_{{{\rm{CH}}}_{4}}$ (≳10 bars) and the M-type host star, the equilibrium surface temperature exceeds 646.96 K, the triple point of H₂O. Because we are only interested in potentially habitable worlds (i.e., worlds with liquid water on the surface), we excluded those cases.

3. Results

3.1. The Effect of CO Absorption on Temperature and Water Vapor Profiles

The predominant effect of CO absorption occurs as moderate heating of the stratosphere. Figure 2 shows the temperature and water vapor profiles for a CO-rich case (p_CO = 1 bar and ${p}_{{\mathrm{CO}}_{2}}=1{0}^{-3}\,\mathrm{bars}$ with the Sun as the host star) obtained with the forward and inverse modeling, where a result without CO absorption is shown for comparison. We found that, without CO absorption, the stratospheric temperature is lower by 20–30 K in the forward model than Earth’s skin temperature assumed in the inverse model (Figure 2(a)). This is caused by the nongray effect of the atmosphere (R. T. Pierrehumbert 2010; R. D. Wordsworth & R. T. Pierrehumbert 2013; H. F. Goessling & S. Bathiany 2016). In a gray atmosphere, the temperature at the top of the atmosphere follows the skin temperature. In contrast, in a nongray atmosphere with an atmospheric window, radiation in the window wavelengths travels directly from the surface or troposphere to space through the stratosphere. To maintain radiative balance, the upward radiative flux in the opaque bands must weaken, which results in persistent stratospheric cooling. In the forward model with CO absorption, however, the stratospheric temperature recovers. This is because of absorption of incoming stellar radiation by CO and associated heating, while the similarity in the stratospheric temperature with that in the inverse model is a coincidence. As a result, the stratospheric water vapor content is comparable between the forward model with CO absorption and the inverse model, while it is lower in the forward model without CO absorption (Figure 2(b)). Because of the exponential dependence of saturation vapor pressure on the temperature, the modest change in the cold trap temperature impacts the H₂O mixing ratio by an order of magnitude. We note that the cold trap is defined as where the saturation mixing ratio of water vapor reaches a minimum due to the temperature decrease with altitude, limiting the transport of water vapor to the upper atmosphere and forcing remixing with the lower atmosphere (D. C. Catling & J. F. Kasting 2017). In our model, we set the boundary between the convective troposphere and the isothermal radiative stratosphere (i.e., the tropopause) as the cold trap.

Figure 2. Refer to the following caption and surrounding text. — **Figure 2.** Temperature (a) and water vapor (b) profiles for p_CO = 1 bar and ${p}_{{\mathrm{CO}}_{2}}=1{0}^{-3}\,\mathrm{bars}$ with the Sun being the host star. Solid red, solid black, dashed red, and dashed black lines show the results obtained with the forward model with CO absorption, forward model without CO absorption, inverse model with CO absorption, and inverse model without CO absorption, respectively.
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**Figure 2.** Temperature (a) and water vapor (b) profiles for p_CO = 1 bar and ${p}_{{\mathrm{CO}}_{2}}=1{0}^{-3}\,\mathrm{bars}$ with the Sun being the host star. Solid red, solid black, dashed red, and dashed black lines show the results obtained with the forward model with CO absorption, forward model without CO absorption, inverse model with CO absorption, and inverse model without CO absorption, respectively.
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In contrast, the surface temperature is unchanged between the three cases (Figure 2(a)). This allows us to utilize the inverse calculations for our parameter survey. Our interests lie largely in surface conditions, as they are most relevant for a planet’s habitability. However, we note that this simplification may have some impacts on the stratospheric water content and the discussion of water loss. We discuss the influences of applying the inverse model on our results in Section 4.4. In the following sections, we show the dependence of surface temperature and water vapor content on partial pressures of carbon species and on the stellar type, obtained with the inverse model.

3.2. Dependence on CO and CH₄ Partial Pressure

The amounts of individual carbon species control the climate of terrestrial planets when all other factors remain constant. Here, we show results with fixed ${p}_{{{\rm{CO}}}_{2}}$ to mimic a planet with active carbonate–silicate cycling and vary p_CO and ${p}_{{{\rm{CH}}}_{4}}$ (Section 2.3). We assumed the host star to be the Sun.

Increasing CO causes cooling for planets orbiting G-type stars, except for high ${p}_{{{\rm{CH}}}_{4}}$ and ${p}_{{{\rm{CO}}}_{2}}$ cases (≳1 bar). Figure 3 shows the dependencies of surface temperature, planetary albedo (the Bond albedo, defined as the ratio of scattered/reflected outgoing and incoming fluxes of stellar light measured at the top of the atmosphere), stratospheric water vapor mixing ratio, and water vapor column density on p_CO and ${p}_{{{\rm{CH}}}_{4}}$ , with a fixed ${p}_{{\mathrm{CO}}_{2}}=0.01\,\mathrm{bar}$ . When ${p}_{{\mathrm{CH}}_{4}}\lesssim 1\,\mathrm{bar}$ , we found that increasing p_CO causes significant cooling at p_CO ≳ 1 bar, which exceeds the background ${p}_{{{\rm{N}}}_{2}}$ (Figure 3(a)). This is because CO itself is not a greenhouse gas and is instead a scatterer (D. C. Catling & J. F. Kasting 2017). The Rayleigh scattering is responsible for the decrease in temperature by increasing planetary albedo (Figure 3(b)).

Figure 3. Refer to the following caption and surrounding text. — **Figure 3.** Dependence of (a) surface temperature, (b) planetary albedo (the Bond albedo measured at the top of the atmosphere), (c) H₂O mixing ratio in the stratosphere, and (d) H₂O column density on the partial pressures of CO and CH₄ for a planet orbiting the Sun with ${p}_{{{\rm{CO}}}_{2}}=0.01\,{\rm{bar}}$ .
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**Figure 3.** Dependence of (a) surface temperature, (b) planetary albedo (the Bond albedo measured at the top of the atmosphere), (c) H₂O mixing ratio in the stratosphere, and (d) H₂O column density on the partial pressures of CO and CH₄ for a planet orbiting the Sun with ${p}_{{{\rm{CO}}}_{2}}=0.01\,{\rm{bar}}$ .
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However, when ${p}_{{\mathrm{CH}}_{4}}\gtrsim 1\,\mathrm{bar}$ , the effect of CO gradually shifts to warming of the surface (Figure 3(a)). As previously reported for N₂, the warming can be explained by pressure broadening of absorption lines of greenhouse gases (C. Goldblatt et al. 2009; R. D. Wordsworth & R. T. Pierrehumbert 2013), combined with additional contributions from the greenhouse effect of water vapor (C. Goldblatt et al. 2009). Higher pressure induces frequent collisions and, consequently, broadening of the absorption lines of the other greenhouse gases (CO₂, CH₄, and H₂O), leading to efficient absorption of thermal radiation (D. C. Catling & J. F. Kasting 2017). The warming due to CO is also attributed in part to the associated change in the water vapor content (Figure 3(d)).

At high CH₄ levels ( ${p}_{{{\rm{CH}}}_{4}}$ ≳ 10 bars), the surface temperature begins to decrease with increasing ${p}_{{{\rm{CH}}}_{4}}$ (Figure 3(a)). This is attributed to the decline of another greenhouse gas, H₂O (Figures 3(c) and (d)). The surface temperature decrease following that of H₂O content with increasing a greenhouse gas has been reported for CO₂ (J. F. Kasting 1993; R. D. Wordsworth & R. T. Pierrehumbert 2013; R. M. Ramirez et al. 2014). In this regime, increasing ${p}_{{{\rm{CO}}}_{2}}$ lowers the mixing ratio of water vapor at the surface. Consequently, the sensible heat of noncondensable gases exceeds the latent heat of water vapor, and the entire atmosphere up to the stratosphere becomes dry (R. D. Wordsworth & R. T. Pierrehumbert 2013). This explanation is applicable for CH₄ as well; at high CO₂ or CH₄ partial pressure, water vapor levels decrease in the stratosphere (Figure 3(c)), as well as total water vapor levels decreasing in the atmosphere (Figure 3(d)). The surface temperature decreases from a diminished greenhouse effect combined with a higher planetary albedo due to scattering (Figure 3(b)). We note that, in Figure 3, there is a region in which the stratospheric water vapor mixing ratio and the column density of water vapor do not correlate with each other. When this occurs, it is because the total atmospheric pressure also changes and the increase of (in this case) p_CO is larger than that of water vapor. Thus, while the total amount of water vapor in the column increases when CO causes warming, the relative increase of water vapor compared to CO is actually lower (Figures 3(c) and (d)).

Furthermore, the influence of CH₄ has slight changes depending on the partial pressure of CO. When p_CO ≳ 10 bars, the addition of methane will cause warming from as low as ${p}_{{\mathrm{CH}}_{4}}\sim 1{0}^{-6}\,\mathrm{bars}$ and no longer causes cooling (Figure 3(a)). At high ${p}_{{{\rm{CH}}}_{4}}$ , we find that the addition of CH₄ causes warming instead of cooling as it did when p_CO was low. In this region, the pressure broadening from CO offsets the cooling effect of CH₄. However, the overall behavior of CH₄ does not change.

As was discussed briefly in Section 1, organic haze might form and cool the surface at ${f}_{{{\rm{CH}}}_{4}}/{f}_{{{\rm{CO}}}_{2}}\gtrsim 0.1$ (A. A. Pavlov et al. 2000; J. D. Haqq-Misra et al. 2008). Thus, the surface temperature shown in Figure 3(a) needs to be regarded as an upper limit, and the cooling with increasing ${p}_{{{\rm{CH}}}_{4}}$ can start around ${p}_{{\mathrm{CH}}_{4}}\sim 1{0}^{-3}\,\mathrm{bars}$ . We revisit this issue in Section 4.

3.3. Dependence on CO₂ Partial Pressure

With higher levels of CO₂, the parameter space where increasing CO and CH₄ causes warming expands. We show results with ${p}_{{{\rm{CO}}}_{2}}=1\,{\rm{bar}}$ in Figure 4. The overall temperature of the atmosphere across the parameter space increases due to an increased greenhouse effect from CO₂ and the corresponding increase in water vapor levels (Figures 4(a) and (d)) compared to the ${p}_{{\mathrm{CO}}_{2}}=0.01\,\mathrm{bar}$ case (Figure 3(a)). In contrast to the low ${p}_{{{\rm{CO}}}_{2}}$ case, increasing CO always leads to warming in the p_CO and ${p}_{{{\rm{CH}}}_{4}}$ parameter space studied here, suggesting that the transition from cooling to warming depends on both ${p}_{{{\rm{CO}}}_{2}}$ and ${p}_{{{\rm{CH}}}_{4}}$ .

Figure 4. Refer to the following caption and surrounding text. — **Figure 4.** Same as Figure 3 but showing the results with ${p}_{{\mathrm{CO}}_{2}}=1\,\mathrm{bar}$ .
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The transition to warming is believed to be driven by the dominance of pressure broadening and increased H₂O content (Figure 4(d)) over the increase in albedo due to scattering (Figure 4(b)). We also found that increasing ${p}_{{{\rm{CO}}}_{2}}$ from 0.01 to 1 bar has a greater impact on the transition between CO cooling and warming than changing ${p}_{{{\rm{CH}}}_{4}}$ by the same magnitude (Figures 3(a) and 4(a)). Because CO₂ is a more potent greenhouse gas than CH₄, the transition is more dependent on changes in CO₂ than it is on CH₄.

Cooling with increasing CH₄ at high ${p}_{{{\rm{CH}}}_{4}}$ is no longer present in the ${p}_{{\mathrm{CO}}_{2}}=1\,\mathrm{bar}$ case (Figure 4(a)). Carbon dioxide dominates the greenhouse effect in this case and prevents inhibition of H₂O from CH₄. Above 10 bars of ${p}_{{{\rm{CH}}}_{4}}$ , albedo decreases with increasing ${p}_{{{\rm{CH}}}_{4}}$ (Figure 4(b)). H₂O decreases in the stratosphere but not the entire atmosphere (Figures 4(c) and (d)). Therefore, as was the case with ${p}_{{{\rm{CH}}}_{4}}$ < 10 bars in the low- ${p}_{{{\rm{CO}}}_{2}}$ case (Figure 3(a)), increasing CH₄ results in an increase in the surface temperature even for higher ${p}_{{{\rm{CH}}}_{4}}$ .

3.4. Dependence on Spectral Type of the Host Star

For planets orbiting M-type stars, warming with increasing CO is more dominant. Figure 5 shows the results with the host star being the M dwarf GJ 876 and the fiducial ${p}_{{\mathrm{CO}}_{2}}=0.01\,\mathrm{bar}$ . Even at this lower ${p}_{{{\rm{CO}}}_{2}}$ level, CO acts as an indirect greenhouse gas, especially when p_CO ≳ 1 bar (namely, ${p}_{{\rm{CO}}}\gt {p}_{{{\rm{N}}}_{2}}$ ; Figure 5(a)). The radiation from M-type stars is weaker than G types in the visible range (see our Figure 1, C. E. Harman et al. 2015; G. N. Arney et al. 2017). Since the Rayleigh scattering cross section is inversely proportional to the fourth power of wavelength (D. C. Catling & J. F. Kasting 2017), Rayleigh scattering by CO becomes weaker compared to the case of a G-type host star, as indicated by the limited increase in albedo with increasing p_CO (Figure 5(b) versus Figure 3(b)). However, the indirect warming by pressure broadening and the corresponding high water vapor levels remain unchanged. Thus, warming dominates over cooling.

Figure 5. Refer to the following caption and surrounding text. — **Figure 5.** Same as Figure 3 but showing the results with GJ 876 being the host star.
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In terms of CH₄, increasing ${p}_{{{\rm{CH}}}_{4}}$ always causes warming in the ${p}_{{{\rm{CO}}}_{2}}$ and ${p}_{{{\rm{CH}}}_{4}}$ parameter space studied (Figure 5(a)). This result is in contrast to the case of a G-type host star (Figure 3(a)), where cooling with increasing ${p}_{{{\rm{CH}}}_{4}}$ was seen for ${p}_{{\mathrm{CH}}_{4}}\gtrsim 10\,\mathrm{bars}$ . Such contrasting results between G- and M-type host stars have been reported again for CO₂, as shown in R. D. Wordsworth & R. T. Pierrehumbert (2013; their Figure 7 versus Figure 11). Reduced Rayleigh scattering and absorption of stellar light by CH₄ inhibit the increase in albedo even for the high ${p}_{{{\rm{CH}}}_{4}}$ (Figure 5(b)). The resultant higher temperature results in higher stratospheric mixing ratios and H₂O column densities (Figures 5(c) and (d)).

3.5. Case of Fixed Total Carbon Content

For situations in which the carbonate–silicate cycle is inactive, which is likely for planets without global tectonism, we adopt a model whereby the total carbon content of the atmosphere system does not change. This allows us to mimic systems in which there is no transfer into and out of the system for carbon and nitrogen, though we do not fix the total amount of hydrogen or oxygen. We found that increasing ${p}_{{\rm{CO}}}/{p}_{{{\rm{CO}}}_{2}}$ cools the surface (Figure 6(a)), as expected from decreasing a greenhouse gas, CO₂. The cooling is also attributed to CO Rayleigh scattering, as indicated by the increasing albedo (Figure 6(b)). Pressure broadening cannot compensate for the cooling in this system, since the total pressure of the atmosphere is kept constant.

Figure 6. Refer to the following caption and surrounding text. — **Figure 6.** Same as Figure 3 but showing the dependence on p_CO/ ${p}_{{{\rm{CO}}}_{2}}$ and ${p}_{{{\rm{CH}}}_{4}}$ / ${p}_{{{\rm{CO}}}_{2}}$ with a fixed p_Ctotal = 0.1 bar.
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When we change ${p}_{{{\rm{CH}}}_{4}}$ / ${p}_{{{\rm{CO}}}_{2}}$ , the surface temperature peaks at ${p}_{{{\rm{CH}}}_{4}}$ / ${p}_{{{\rm{CO}}}_{2}}\sim 1$ (Figure 6(a)). These greenhouse gases have strong absorption bands in different wavelengths: for instance, ≃13 μm and ≃8 μm for CO₂ and CH₄, respectively (D. C. Catling & J. F. Kasting 2017). Thus, mixing with a roughly 1:1 ratio maximizes the net greenhouse effect, although the precise value will be dependent on the relative strength of their absorption and the surface temperature, which determine the blackbody spectrum.

Furthermore, we found that H₂O levels, both stratospheric mixing ratios and column densities, peak at ${p}_{{{\rm{CH}}}_{4}}$ / ${p}_{{{\rm{CO}}}_{2}}\sim 1$ (Figures 6(c) and (d)). Like the previous cases, the water vapor levels as a result of changes in temperature amplify the already existing warming or cooling effects.

4. Discussion

4.1. Climate-photochemistry Feedback

When the influence of photochemistry is coupled with the findings from the climate calculations, feedback that initiates in the atmospheres of these target terrestrial planets will cause different forms of atmospheric evolution. The feedback we are referring to is given by Figure 7. Positive feedback is shown in Figure 7(a), where the addition of CO or CH₄ causes cooling in the atmosphere, and Figure 7(b) shows negative feedback that occurs when CO or CH₄ cause warming in the atmosphere.

Figure 7. Refer to the following caption and surrounding text. — **Figure 7.** Qualitative climate-photochemistry feedback in the atmospheres of Earth-like planets considered in this study. A barbed arrow represents a positive coupling, where an increase (decrease) in the source component yields an increase (decrease) in the target component. A circular arrow represent a negative coupling, where an increase (decrease) in the source component yields a decrease (increase) in the target component.
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First, in the fixed ${p}_{{\mathrm{CO}}_{2}}=0.01\,\mathrm{bar}$ case (Section 3.2), we expect both positive and negative feedback. Positive feedback exists in the parameter region where p_CO > 1 bar and ${p}_{{{\rm{CH}}}_{4}}$ < 1 bar (Figure 3(a)). In this region, increasing CO causes cooling because of Rayleigh scattering. The cooling then decreases water vapor levels, because the saturation vapor pressure is temperature-dependent, as discussed above. Thus, there is less OH in the atmosphere and therefore a slower oxidation rate of CO (e.g., J. F. Kasting 1990), because OH is a product of H₂O photodissociation. This helps CO to build up, assuming that there is CO supply to the atmosphere from outgassing, photochemical reactions, or both (Figure 7(a)).

There is more positive feedback in the region of the parameter space where ${p}_{{\mathrm{CH}}_{4}}\gtrsim 10\,\mathrm{bars}$ and p_CO ≲ 1 bar (Figure 3(a)). In this region, rising CH₄ levels, assuming there is also a flux from, for example, hydrothermal systems or photochemistry, would result in a temperature decrease, because of a decrease in the H₂O greenhouse effect (Figures 3(c) and (d)). The decrease of water vapor leads to less oxidation of CH₄ with OH, allowing further CH₄ buildup.

The remaining region of the parameter space, ${p}_{{{\rm{CH}}}_{4}}$ < 10 bars and p_CO < 1 bar, contains negative feedback. Both CO and CH₄ have this feedback with H₂O. In these remaining spaces, increasing either CO or CH₄ will lead to the warming of the atmosphere, which subsequently raises the water vapor content (see column density figures). As was discussed previously, this would raise the oxidation rate of these gases through reactions with OH produced via H₂O photodissociation, preventing further increase in CO or CH₄ levels (Figure 7(b)). This negative feedback may put upper limits on p_CO and ${p}_{{{\rm{CH}}}_{4}}$ .

Our results suggest that worlds with low CO₂ abundances are favorable for the buildup of other reducing compounds. The high- ${p}_{{{\rm{CO}}}_{2}}$ case shows warming trends with increasing CO and CH₄ (Section 3.3, Figure 4(a)). This suggests that the parameter space for negative feedback expands compared to the low- ${p}_{{{\rm{CO}}}_{2}}$ case, which may limit the buildup of other reducing compounds.

For planets orbiting M-type stars (Section 3.4), our results suggest dominance of negative feedback. We found that CO and CH₄ only act as warmers in the atmosphere (Figure 5(a)). Here, the greenhouse and indirect greenhouse effects of CH₄ and CO, respectively, would lead to increased water vapor levels. The warming leads to an increase in the H₂O mixing ratio, and consequently, OH production. Then, increased oxidation rates of CO and CH₄ with OH may limit further buildup of these reducing species.

However, we also note that low near-UV fluxes of M-type stars support the buildup of CO and CH₄. Around M-type stars, the dissociation of water vapor is slower because UV radiation is less intense in the part of the spectrum relevant to H₂O dissociation (≤200 nm) compared to G-type stars (F. Tian et al. 2014; C. E. Harman et al. 2015). Additionally, between 200 and 240 nm, HO₂ and H₂O₂ are photodissociated and produce OH. With a weaker spectrum from the host star, these species are dissociated to OH less. Even in situations where carbon species cause warming and thus negative feedback, the necessary flux of reducing species to overcome such feedback would be lower compared to that for planets orbiting G-type stars. Because of this, it is possible that these worlds can be rich in CO or CH₄ at lower reducing fluxes than worlds orbiting G-type stars. This suggests that CO runaway (C. E. Harman et al. 2015; Y. Watanabe & K. Ozaki 2024) can happen even when CO causes warming. Furthermore, we also expect that flaring of active M dwarf stars (R. O. P. Loyd et al. 2018) specifically would enhance the negative feedback because of the increased UV flux shortward of 120 nm, where H₂O photodissociates and provides the OH used in oxidation of CO and CH₄ (Y. Chang et al. 2021).

In the case without a carbonate–silicate cycle (fixed total carbon content in the atmosphere; Section 3.5), we suggest that CO buildup is promoted by positive feedback, whereby cooling should decrease water vapor levels and the oxidation rate of CO, allowing for it to build up, given a certain reducing flux from outgassing. There may exist a limit on CH₄ growth from positive feedback. If the ratio of CH₄ to CO₂ were to exceed unity because of disequilibrium chemistry, then it is possible for CH₄ to build up in the atmosphere.

4.2. Water Loss

In addition to the various photochemical reactions in the atmosphere that influence a planet’s evolution, the loss of hydrogen from water vapor may result in the loss of water in both the atmosphere and ocean. The escape of hydrogen is thought to be regulated by two limiting factors: diffusion efficiency and the available energy (D. C. Catling & J. F. Kasting 2017).

The amount of water vapor at the cold trap determines the rate at which it diffuses to the upper atmosphere (D. C. Catling & J. F. Kasting 2017). This diffusion of hydrogen to the upper atmosphere (ϕ_l) is calculated via the following equation:

where c is a constant calculated based on atmospheric scale height and the diffusion coefficient, given to be (2.5 × 10¹³ cm⁻² s⁻¹), and f_T(H) is the total mixing ratio of hydrogen in all forms above the cold trap.

Then the XUV radiation from the host star determines the escape rate of diffused hydrogen (ϕ_el; D. C. Catling & J. F. Kasting 2017), calculated with the following equation:

where S_EUV is the incoming globally averaged extreme-UV (EUV) flux, G is the universal gravitation constant, M is the mass of the planet, m is the hydrogen atom mass, and r is the relevant radius for atmospheric escape. Next, we calculate the area-integrated escape rate from the Earth’s surface area, divide by the mass of hydrogen in the Earth’s oceans, and convert to the desired units of M_EO Gyr^–1 (where M_EO is the amount of water equal to the mass of hydrogen in the Earth’s ocean). From these two equations, we set the escape of hydrogen equal to whichever rate is slower. This gives us the amount of hydrogen a planet can lose relative to the Earth’s oceans over the course of 1 Gyr (Figure 8).

Figure 8. Refer to the following caption and surrounding text. — **Figure 8.** Dependence of water loss on the partial pressures of CO₂, CO, and CH₄; spectral type; and active carbon transfer for an Earth-like terrestrial planet. The relationship for a Sun-like host star with 0.01 bar CO₂ is shown in (a), the relationship for a Sun-like host star with 1 bar CO₂ is shown in (b), the relationship for a GJ 876 host star with 0.01 bar CO₂ is shown in (c), and the relationship for a Sun-like host star with 0.1 bar p_Ctotal is shown in (d).
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The relationship between the water vapor mixing ratio and the diffusion-limited escape is linear, and the energy limit in our study is dependent only on spectral type (in reality, it also depends on the age of the star, the distance of the planet from the star, and the planet mass and radius, but all of those are fixed in our model to be consistent with a planet receiving the same flux as the modern Earth that would yield modern surface temperatures). Thus, at some point, an increase of water vapor in the atmosphere will cause the diffusion limit to exceed the energy limit, and no additional hydrogen can be lost regardless of the water vapor mixing ratio. For the case in which the Sun is the host star, the upper limit on water loss in one Earth lifetime from the energy-limited escape is 136 M_EO, and for the M-type star case, it is 391 M_EO (see Figure 8), owing to a stronger XUV flux that allows for higher escape rates.

In the case of the Sun as the host star (Figures 8(a) and (b)), increasing the methane concentration will cause water loss equivalent to ≳1 M_EO Gyr^–1, peaking at ${p}_{{{\rm{CH}}}_{4}}$ = 1 bar. Above this value, as was discussed earlier, the amount of water vapor in the stratosphere is diminished, and thus the supply of hydrogen to the upper atmosphere is lower. A similar behavior occurs for the cases of fixed carbon content when ${p}_{{{\rm{CH}}}_{4}}$ / ${p}_{{{\rm{CO}}}_{2}}$ is increased (Figure 8(d)). However, the decrease in water loss above the peak at ${p}_{{{\rm{CH}}}_{4}}$ / ${p}_{{{\rm{CO}}}_{2}}$ = 1 is due to a decrease in CO₂ levels that lower temperatures and thus water vapor mixing ratios. In the M-type case, there is no CH₄ peak. Instead, increasing methane increases the amount of water that will subsequently be lost (Figure 8(c)).

In all situations, increasing the amount of CO, either through p_CO or p_CO/ ${p}_{{{\rm{CO}}}_{2}}$ , will cause the amount of water loss to decrease. In situations where CO can cause significant warming, there is minimal risk of water loss and oxidation of the atmosphere. This suggests that terrestrial planets around M-type stars may retain surface water, potentially being habitable. We also find that high methane concentrations, roughly ${p}_{{{\rm{CH}}}_{4}}$ = 1 bar or ${p}_{{{\rm{CH}}}_{4}}$ / ${p}_{{{\rm{CO}}}_{2}}$ = 1, result in high water vapor mixing ratios that ultimately cause the loss of vast amounts of water, on the order of 10 times more than the current oceans of the Earth and potentially more. This is especially true for planets orbiting M-type stars, where the upper limit from energy escape to bound loss of water is about 3 times higher and where the increase of ${p}_{{{\rm{CH}}}_{4}}$ increases water vapor levels significantly.

From these findings, planets with smaller CH₄ are favorable for water retention, unless p_CO ≳ ${p}_{{{\rm{CH}}}_{4}}$ . CO-rich worlds, possibly the early Earth and Mars or planets orbiting M-type stars, would still be capable of retaining significant amounts of water despite CO warming. However, certain feedback in the atmosphere may prevent these ideal situations from occurring, as was outlined in the previous section.

4.3. Applications to Planets

Various planets likely had or have a combination of these three carbon species and different styles of carbon cycling at some point in their history. In this subsection, we discuss the implications for atmospheric evolution of (potentially) habitable worlds: early Earth, early Mars, early Venus, and habitable exoplanets orbiting M-type stars. We note that atmospheric modeling dedicated to each planet is beyond the scope of this study; here we focus on implications that can be derived from model results for the setting of Earth-like parameters obtained in Section 3.

4.3.1. Early Earth

Early Earth before the Great Oxidation Event sustained a reducing atmosphere with variable amounts of CH₄ and, possibly, CO with a high CO₂ level ( ${p}_{{\mathrm{CO}}_{2}}\,\sim$ 0.01–1 bar; D. C. Catling & K. J. Zahnle 2020). A reducing flux from the mantle (S. Aulbach & V. Stagno 2016; R. W. Nicklas et al. 2019), CH₄ production by methanogens (A. A. Pavlov et al. 2001; E. E. Stüeken et al. 2020), and asteroid impacts (J. F. Kasting 1990; K. J. Zahnle et al. 2020) are thought to have contributed to sustaining the reducing gases. D. C. Catling & K. J. Zahnle (2020) compiled geochemical constraints (K. Zahnle et al. 2006; K. J. Zahnle et al. 2019) and model predictions (M. W. Claire et al. 2006) for the CH₄ level and estimated ${p}_{{{\rm{CH}}}_{4}}\sim 1{0}^{-5}$ –10⁻² bars or even higher. Carbon monoxide is thought to have been a minor species, but a transient high-CO atmosphere (p_CO ∼ 1 bar) is possible after large impacts (J. F. Kasting 1990; K. J. Zahnle et al. 2020).

The early Earth might have had plate tectonics from a young age, though the exact time of the onset of plate tectonics is not widely agreed upon. Studies suggest plate tectonics began sometime between 0.7 and 4.4 Ga, with evidence from ophiolites, blueschists, zircons, and various other supposedly tectonically deformed materials (T. M. Harrison et al. 2005; R. J. Stern 2005; M. Hopkins et al. 2008; J. van Hunen & A. P. van den Berg 2008; B. J. Foley 2018). Earlier onset of plate tectonics was also suggested from the potential accretionary complex in the 3.8 Ga old Isua supracrustal belt (T. Komiya et al. 1999).

For an early Earth with active tectonics (resulting in carbonate–silicate cycling) with a reducing flux to the atmosphere, we can apply our findings in this study to investigate atmospheric evolution. In a theoretical CH₄-rich atmosphere, the transition from CH₄- to CO₂-rich would yield decreased surface temperatures and water vapor mixing ratios, as shown in Figures 3 and 4. Over time, unless ${p}_{{{\rm{CO}}}_{2}}$ increases against the change in ${p}_{{{\rm{CH}}}_{4}}$ , a negative feedback (Figure 7(b)) would self-regulate atmospheric ${p}_{{{\rm{CH}}}_{4}}$ , given a sufficient outgassing flux. In the case of CO, its expected levels would likely not be large enough to incite any feedback in climate through oxidation over time. Early Earth’s atmosphere may potentially (since what we estimate here is a minimum value and thus the true value may be orders of magnitude higher for a reducing atmosphere) have been safe from significant amounts of water loss (Figures 8(a) and (b)), as discussed in Section 4.2.

4.3.2. Early Mars

Early Mars is known to have possessed a warm climate and a hydrological cycle, at least transiently (e.g., B. L. Ehlmann et al. 2016; R. D. Wordsworth 2016). Climate models and geochemical and geological constraints suggest ${p}_{{{\rm{CO}}}_{2}}\sim 1{0}^{-1}$ –10⁰ bars around 3.6–4.5 Ga (F. Forget et al. 2013; R. D. Wordsworth & R. T. Pierrehumbert 2013; R. M. Ramirez et al. 2014; E. S. Kite et al. 2017; H. Kurokawa et al. 2018). Because of the low temperature, early Mars is prone to CO runaway (K. Zahnle et al. 2008); the CO runaway might lead to p_CO comparable to ${p}_{{{\rm{CO}}}_{2}}$ . Moreover, recent studies suggest a high background N₂ level ( ${p}_{{{\rm{N}}}_{2}}\,\simeq$ 0.1–0.5 bar; R. Hu & T. B. Thomas 2022).

It is widely believed that Mars has not exhibited plate tectonics through its history. There is a lack of unambiguous evidence to suggest plate tectonics, and a stagnant lid regime is more likely (D. Breuer & T. Spohn 2003).

In a stagnant lid regime, the supply of carbon species to the atmosphere of Mars would be limited. The lifetime of these species would be dictated by photochemical reactions and feedback with climate. The necessary pressure of greenhouse gases (p_GHG) for CO warming increases as the planet’s orbital distance increases, and, based on the likely composition of the ancient Martian atmosphere, CO warming would not have been possible. This puts the atmosphere in the positive feedback regime (Figure 7(a)) for CO (see the high-p_CO, low-p_CH4 region of Figure 3(a)) and would have potentially allowed for CO buildup in the atmosphere. However, the modern atmosphere is depleted in CO, suggesting that some event must have occurred to remove atmospheric CO and convert it to CO₂.

4.3.3. Early Venus

Different models have been proposed for the atmosphere and climate of early Venus. While some studies suggested that water never condensed on Venus (C. Gillmann et al. 2009, 2020; K. Hamano et al. 2013; M. Turbet et al. 2021), others proposed a habitable early Venus scenario (M. J. Way et al. 2016; M. J. Way & A. D. Del Genio 2020). Here we focus on the latter case, where our model results are applicable. Given poor constraints on atmospheric composition in the habitable Venus scenario, M. J. Way et al. (2016) assumed modern-Earth-like CO₂ and CH₄ concentrations (400 ppm and 1 ppm, respectively) with the background 1 bar N₂. Carbon monoxide is not usually considered, because it is not infrared-active. Similar to Mars, Venus likely has always lacked plate tectonics (F. Nimmo & D. McKenzie 1998; H. Lammer et al. 2018).

In this scenario, we expect negative feedback to self-regulate CO₂ and CH₄ levels (Section 4.1), as CH₄ is acting as a greenhouse gas in this situation. However, at higher instellations compared to the Earth, CH₄ might not be capable of cooling the atmosphere, similar to the case in Figure 5(a), where greenhouse processes dominate across the entire parameter space. Therefore, it is unlikely that positive feedback could operate on early Venus and allow for the buildup of CH₄. We do, however, anticipate that an early Venus with abundant CO₂ and CH₄ would be susceptible to large amounts of water loss (Figures 8(a) and (b)).

4.3.4. Exoplanets Orbiting M-type Stars

Though Earth-sized planets orbiting habitable zones of M-type stars are primary targets for studying habitable worlds in exoplanetary systems, their atmospheric compositions are poorly constrained so far. For instance, transmission spectra of habitable-zone Earth-sized planets orbiting TRAPPIST-1 (planets d, e, f, and g) obtained with the Hubble Space Telescope show no clear features of atmospheric gases (J. de Wit et al. 2018), awaiting further constraints from the James Webb Space Telescope (JWST) and future telescopes. The JWST successfully constrained atmospheric pressures for the inner planets TRAPPIST-1 b and c with secondary-eclipse observations (T. P. Greene et al. 2023; S. Zieba et al. 2023), implying a potentially small volatile inventory for this system.

Constraining the presence/absence of plate tectonics on extrasolar rocky planets is more challenging. At a statistical level, it has been proposed that a correlation between stellar irradiation and ${p}_{{{\rm{CO}}}_{2}}$ predicted with active carbonate–silicate cycling can be tested with tens of Earth-like exoplanet samples (O. R. Lehmer et al. 2020; B. J. Foley 2024). Theoretical prediction for the plate tectonics on these planets is currently limited by our knowledge of how it depends on planetary parameters (such as water content and thermal history; see R. Wordsworth & L. Kreidberg 2022 and references therein) and by uncertainty in these parameters themselves. Previous studies modeling the atmospheric photochemistry of terrestrial planets orbiting M-type stars practically fixed ${p}_{{{\rm{CO}}}_{2}}$ in their parameter surveys (R. Hu et al. 2020; Y. Watanabe & K. Ozaki 2024), which may correspond to the case with ${p}_{{{\rm{CO}}}_{2}}$ regulation with plate tectonics and an active carbonate–silicate cycle.

CO on these worlds requires lower p_GHG to act as an indirect warmer in the atmosphere (see Figures 3(a) and 5(a)). This occurs because Rayleigh scattering by CO is weaker around M-type stars (Figure 5(b)). This would effectively put most CO-rich worlds in the negative feedback regime, where CO levels would self-regulate themselves and be robust against buildup, unless there is a large reducing flux from the interior. The range for CH₄ cooling would instead occur at lower amounts of ${p}_{{{\rm{CO}}}_{2}}$ , where there is a lessened greenhouse effect to be counteracted.

4.4. Limitations

As stated in previous sections, the understanding and implementation of methane hazes are limited. We note that, in situations where ${p}_{{{\rm{CH}}}_{4}}$ / ${p}_{{{\rm{CO}}}_{2}}$ ≳ 1, methane haze may form. On planets orbiting G-type stars, this may cause warming through the absorption of outgoing planetary radiation or scattering of incoming radiation from the host star. However, around M-type stars, the range where these hazes would potentially absorb or scatter (between 0.4 and 1 μm) is weaker (Figure 1), and the effects of haze is greatly diminished. In such scenarios, they can be ignored (C. E. Harman et al. 2015; G. N. Arney et al. 2017). In the cases where haze would form, we may need to revisit our calculations in the future when our understanding is improved.

There are two potentially critical assumptions made for our treatment of water loss that need to be addressed. First, we assume that the atmosphere is isothermal above the tropopause. In reality, the tropopause and stratospheric temperatures will vary with height and composition (R. D. Wordsworth & R. T. Pierrehumbert 2013), and stratospheric temperatures may be lower than the 200 K isothermal case we have assumed. Because of the dependence of water vapor on temperature, not only would water vapor levels decrease, the amount of water loss would also decrease.

Second, our discussion in Section 4.2 considers only water loss as a result of mechanisms operating in the stratosphere. In reality, the feedback discussed in Section 4.1 also occurs in the lower atmosphere. Increasing tropospheric water content in a reducing atmosphere can lead to oxidation of CO and CH₄. Unless the OH produced from H₂O photodissociation recombines with free hydrogen, OH will be used to oxidize the reducing species, and the remaining H will escape to space. This provides a lower limit on the estimated escape of water from our modeled atmospheres. How this would be counteracted by the limitation of an isothermal stratosphere is something that may need to be revisited in the future.

Our methodology for determining the incoming stellar flux to the top of the atmosphere largely influences the findings made in our study. If the modeled planet were moved closer or farther away (to increase or decrease the stellar TOA flux, respectively), it would change the trends and implications of our study.

Finally, it is necessary to discuss the ability of our model to be applied to synchronous rotators around M dwarf planets, specifically for the global temperature and mixing ratio distribution. The well-mixing of species is dependent on two things: the timescale of advection and the photochemical lifetime of the given species. For an Earth-like terrestrial planet, the advection timescale of carbon species will be faster than their photochemical lifetime, as previous studies have found (J. S. Yates et al. 2020; M. Braam et al. 2022). This will allow the species to be homogeneously distributed globally. Numerous 3D global climate models (GCMs) have been applied to synchronous rotators like the planets of the TRAPPIST-1 system and have investigated the variation of dayside and nightside temperatures, finding significant differences (E. T. Wolf 2017; M. Turbet et al. 2018). In the context of planetary habitability, the assumption of a global mean surface temperature is at times insufficient. A. H. Lobo & A. L. Shields (2024) found that the fractional habitability of synchronous rotators around M dwarfs varied from 16% to 79%, suggesting that the applicability of a global mean surface temperature can vary greatly. Lastly, because the saturation vapor pressure of water is temperature-dependent and thus may vary more globally than our carbon species, it may lead to varying levels of water loss on the day- and nightsides, respectively, which is something a 3D GCM may be able to better model, though we anticipate the trends we find to be robust.

5. Conclusions

We studied the climate effects of CO₂, CO, and CH₄ in the atmosphere of a terrestrial planet orbiting different types of host stars. We also aimed to understand the effects of CO, as recent studies suggest that CO-rich atmospheres may exist on early Mars and extrasolar terrestrial planets, especially those orbiting M-type stars. In this study, we updated a 1D atmospheric climate model of CLIMA/ATMOS to include optical and thermodynamic properties of CO. We calculated the equilibrium temperature and water vapor profiles and the surface temperature for planets with varying levels of atmospheric CO₂, CO, and CH₄ orbiting G- and M-type stars.

We found that, even for a CO-rich atmosphere (p_CO = 1 bar and ${p}_{{\mathrm{CO}}_{2}}=1{0}^{-3}\,\mathrm{bars}$ ), the impact of absorption by CO on the surface temperature is negligible. However, the absorption of stellar light by the given amount of CO increases the stratospheric temperature moderately (20–30 K) and, consequently, the stratospheric water vapor mixing ratio by an order of magnitude. Under Earth-like ${p}_{{{\rm{N}}}_{2}}$ , our parameter survey with fixed ${p}_{{{\rm{CO}}}_{2}}$ showed that increasing p_CO leads to surface cooling on planets orbiting Sun-like stars unless the sum of ${p}_{{{\rm{CO}}}_{2}}$ and ${p}_{{{\rm{CH}}}_{4}}$ exceeds ∼1 bar. This is likely caused by changing the balance between two warming mechanisms (the pressure broadening of absorption lines and increasing H₂O content) and cooling by Rayleigh scattering. Increasing ${p}_{{{\rm{CH}}}_{4}}$ , in contrast, chiefly causes surface warming except for the low- ${p}_{{{\rm{CO}}}_{2}}$ (10⁻² bars) and high- ${p}_{{{\rm{CH}}}_{4}}$ (≳10¹ bars) cases, whereas organic haze formation will lead to a lower ${p}_{{{\rm{CH}}}_{4}}$ for the transition from warming to cooling. Changing the host star to M-type star GJ 876 b leads to the dominance of warming with increasing both p_CO and ${p}_{{{\rm{CH}}}_{4}}$ . This is likely caused by the decrease in the planetary albedo due to reduced Rayleigh scattering and absorption of stellar light by CH₄. Finally, our parameter survey with fixed total carbon content shows that cooling increases with increasing ${p}_{{\rm{CO}}}/{p}_{{{\rm{CO}}}_{2}}$ , and warming peaks at ${p}_{{{\rm{CH}}}_{4}}/{p}_{{{\rm{CO}}}_{2}}$ approaching unity.

The warming and cooling trends with increasing reduced species (CO and CH₄) may induce negative and positive climate-photochemistry feedback, respectively. Warming (cooling) causes an increase (a decrease) in atmospheric water vapor content, which then decreases (increases) the oxidation rates of reduced species by OH radicals. We discussed that such climate-photochemistry feedback may have influenced the evolution of the solar and extrasolar terrestrial worlds.

Moreover, our minimum estimate of water loss based on the obtained water vapor mixing ratio in the stratosphere showed that atmospheres will become significantly oxidized through hydrogen loss when ${p}_{{{\rm{CH}}}_{4}}$ is approximately 1 bar or when the methane-to-carbon-dioxide ratio approaches unity. Around these regions, the water vapor mixing ratio in the stratosphere is at a maximum and thus is readily supplied to the upper atmosphere, where it then escapes. At these peak levels, we find that such planets would lose substantial amounts of water from hydrogen loss, as much as 100 times the mass of water in Earth’s oceans. Planets dominated by CO will not lose much water from their surface or atmosphere, even when CO acts as a warming gas, and planets without active transfer from the carbon cycle are also capable of retaining more hydrogen in the form of H₂O. These findings help us further the understanding we have for Earth-like terrestrial planets with a wide range of possible carbon compound abundances that we now think are both plausible and likely on Earth, Mars, and exoplanets, giving us insight into the environments they might have formed in or evolved through.

Acknowledgments

This study was supported by JSPS Grant-in-Aid Nos. 18K13601, 20KK0080, 21K13983, 22H01290, 22H05150, 21H04514, and 23K22561.

Competing Interests

The authors declare no competing interests.

Footnotes

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