STABILITY OF CO₂ ATMOSPHERES ON DESICCATED M DWARF EXOPLANETS

We use the Caltech/JPL one-dimensional Photochemical model (Allen et al. 1981), as modified by Nair et al. (1994) for the Martian atmosphere. The model calculates the steady state distributions of 27 chemical species: O, O(¹D), O₂, O₃, N, N(²D), N2, N₂O, NO, NO₂, NO₃, N₂O₅, HNO₂, HNO₃, HO₂NO₂, H, H₂, H₂O, OH, HO₂, H₂O₂, CO, CO₂, O⁺, ${{{{\rm O}}}_{2}}^{+}$, ${{\mathrm{CO}}_{2}}^{+}$, and CO₂H⁺. We refer the reader to Allen et al. (1981) for a detailed description of the general photochemical model and Table 2 of Nair et al. (1994) for the full list of reactions and associated rate constants (with minor updates) considered in our model. Table 1 gives a subset of Nair et al. (1994)'s reactions that are significant to this work.

Table 1.  Important Reactions Involved in CO₂ Destruction and Regeneration

	Reaction	Rate Constant
R1	${\mathrm{CO}}_{2}+{hv}\to \mathrm{CO}+{{\rm O}}$	$1.025\times {10}^{-8}$
R2	${{\rm H}}+{{{\rm O}}}_{2}+{{\rm M}}\to {\mathrm{HO}}_{2}+{{\rm M}}$	${k}_{0}=7.3\times {10}^{-29}{T}^{-1.3}$
		${k}_{\infty }=2.4\times {10}^{-11}{T}^{0.2}$
R3	${{\rm O}}+{\mathrm{HO}}_{2}\to \mathrm{OH}+{{{\rm O}}}_{2}$	$3.0\times {10}^{-11}{e}^{200/T}$
R4	$\mathrm{OH}+\mathrm{CO}\to {\mathrm{CO}}_{2}+{{\rm H}}$	$4.9\times {10}^{-15}{T}^{0.6}$
R5	$\mathrm{CO}+{{\rm O}}+{{\rm M}}\to {\mathrm{CO}}_{2}+{{\rm M}}$	$1.6\times {10}^{-32}{e}^{-2184/T}$
R6	${{{\rm H}}}_{2}{{{\rm O}}}_{2}+{hv}\to 2\mathrm{OH}$	$1.273\times {10}^{-6}$
R7	$2{\mathrm{HO}}_{2}\to {{{\rm H}}}_{2}{{{\rm O}}}_{2}+{{{\rm O}}}_{2}$	$3.0\times {10}^{-13}{e}^{460/T}$
R8	${\mathrm{HO}}_{2}+{{{\rm O}}}_{3}\to 2{{{\rm O}}}_{2}+\mathrm{OH}$	$1.0\times {10}^{-14}{e}^{-490/T}$
R9	${{{\rm O}}}_{3}+{hv}\to {{{\rm O}}}_{2}+{{\rm O}}$	$2.898\times {10}^{-6}$

Notes. The rate constants are updated from those of Nair et al. (1994) using Sander et al. (2011) and references therein. Rate constants for photolysis reactions are for the top of the atmosphere. Units for photochemical, two-body, and three-body reactions are s⁻¹, cm³ s⁻¹, and cm⁶ s⁻¹, respectively. k₀ and ${k}_{\infty }$ are the low- and high-pressure limit rate constants, respectively.

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Figure 1 shows a comparison between the solar spectrum (WMO 1985), and a spectrum of the M dwarf GJ 436 from France et al. (2013) that we use for our model, scaled such that the total flux of each star is equal to the total solar flux at 1 AU, ∼1360 W m⁻². In addition, we show the wavelengths at which photolysis of CO₂, O₂, O₃, and H₂O₂ is most efficient. It is clear that the GJ 436 spectrum features a much higher FUV/NUV ratio than Sun-like stars, and as a result the photolysis rates of the four aforementioned species will differ between the two cases. The entire spectral range used in the model is ∼100–800 nm. We assume that the spectrum of the star is fixed throughout the duration of our simulations. This ignores the effects of major flaring events or quiet periods, which we assume to be irrelevant on long time scales.

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The choice of boundary conditions strongly affects the resulting atmospheric composition. The major processes that are typically modeled include hydrogen escape, volcanic outgassing, and surface deposition of oxidants. The rates of these processes, especially the latter two, are highly uncertain. For example, the outgassing flux of water for Earth is 10¹¹–10¹² cm⁻² s⁻¹ (Fischer 2008), while on Venus it could be as low as 5.5 × 10⁵–10⁷ cm⁻² s⁻¹ (Walker et al. 1970; Grinspoon 1993). This is likely due to the hydrodynamic loss of water in Venus's past (Hamano et al. 2013), similar to the conditions experienced by our modeled M dwarf exoplanet. Likewise, the deposition velocity of oxidants, such as O₂ and O₃, is strongly tied to surface composition and water content. On Earth and Mars, aqueous reactions of molecular oxygen and ozone with ferrous iron, sulfides, and other reducing species act as significant sinks for oxidants, but deposition velocities on Mars could be 10–100 times lower than on Earth due to the reduced surface humidity and differences in surface composition (Zahnle et al. 2008). Therefore, given that our modeled planet could be drier still, and that the crust and upper mantle may already be heavily oxidized, the deposition of oxidants could be severely limited.

If hydrogen escape is in the diffusion-limited regime, then the flux can be expressed as

$$\begin{eqnarray}&&{\phi }_{\mathrm{lim}}={f}_{{{\rm H}}}(z){b}_{{{\rm H}}/{{{\rm H}}}_{2}}^{{\mathrm{CO}}_{2}}\left(\displaystyle \frac{1}{{{{\rm H}}}_{{\mathrm{CO}}_{2}}}-\displaystyle \frac{1}{{{{\rm H}}}_{{{\rm H}}/{{{\rm H}}}_{2}}}\right)\end{eqnarray} \tag{ 1 }$$

(Zahnle et al. 2008) where ${\phi }_{\mathrm{lim}}$ is the diffusion-limited escape flux, f_H is the total mixing ratio of all hydrogen species at the homopause, ${b}_{{{\rm H}}/{{{\rm H}}}_{2}}^{{\mathrm{CO}}_{2}}$ is the binary diffusion coefficient of hydrogen (H or H₂) escaping through CO₂, and ${H}_{{{\rm x}}}$ is the scale height of species x, where x = H or H₂ and CO₂. As M dwarfs emit abundant XUV (λ < 121 nm) radiation and highly charged particles that can cause hydrodynamic escape and sputtering, the rate of hydrogen loss could readily reach the diffusion-limited regime (Cohen et al. 2015), though sputtering could be reduced if a strong planetary magnetic field exists (Lammer et al. 2007). On the other hand, the abundance of hydrogen above the homopause is strongly tied to the rate of production from photolysis of water and H₂O₂, as well as chemistry in the ionosphere (Nair et al. 1994). Thus, in the limit of low atmospheric hydrogen content, the hydrogen escape flux could be much lower than the diffusion-limited flux.

Given the possibility that the outgassing, deposition, and escape fluxes may be low, we will simplify the problem and focus strictly on the effects of high UV flux, low water content, and high CO₂-content by assigning zero fluxes to all species for our upper and lower boundary conditions. We make an exception for ions, which have a zero flux upper boundary condition and a fixed concentration of 0 cm⁻³ at the lower boundary to simulate recombination with electrons at the surface (Nair et al. 1994). This is equivalent to hydrogen escape being balanced by the outgassing of water, with the outgassed oxygen atoms being lost through surface deposition of oxidants. These simplified boundary conditions, which are potentially representative of desiccated terrestrial exoplanets orbiting M dwarfs, will be evaluated in Section 4.1.

In order to model a CO₂-dominated atmosphere we simulate Mars-like atmospheric composition with a surface atmospheric pressure of 1 bar for an Earth-sized planet with Earth's surface gravity. We keep the same (Martian) mixing ratios of atmospheric species as Nair et al. (1994). The pressure P, temperature T, and eddy diffusion coefficient K_zz profiles are shown in Figure 2. The model atmosphere extends from the surface to 100 km altitude with an altitude bin thickness of 1 km. The pressure profile is calculated assuming an ideal gas atmosphere in hydrostatic equilibrium.

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The temperature profile is split into the troposphere, the stratosphere/mesosphere, and the thermosphere. The troposphere is assumed to be a dry adiabat with the heat capacity of CO₂ as a function of temperature taken from McBride & Gordon (1961) and Woolley (1954). The surface temperature is assumed to be 240 K, accounting for the warming due to 1 bar of CO₂ (Kasting 1991). The temperature decreases along the adiabat with increasing altitude until it reaches the planetary skin temperature of 139 K, identical to that of Mars, by assumption (Nair et al. 1994). This places the tropopause of our atmosphere at ∼7.5 km. Above the tropopause the temperature profile is assumed to be isothermal, consistent with previous works (Kasting 1990; Segura et al. 2005, 2007). The temperature increases in the thermosphere above 60 km due to inefficient collisional cooling, and the temperatures are calculated by assuming that the temperature–pressure relationship is identical in the thermospheres of both our model atmosphere and Nair et al. (1994)'s model atmosphere. This assumption is valid given the density (and thus pressure) dependence of collisional cooling (López-Puertas & Taylor 2001). As the pressure profile depends on the temperature profile, we iterate between the two until convergence.

The eddy diffusion coefficient as a function of altitude is calculated assuming free convection (Gierasch & Conrath 1985),

$$\begin{eqnarray}&&{K}_{{zz}}=\displaystyle \frac{H}{3}{\left(\displaystyle \frac{L}{H}\right)}^{4/3}{\left(\displaystyle \frac{R\sigma {T}^{4}}{\mu \rho {C}_{p}}\right)}^{1/3}\end{eqnarray} \tag{ 2 }$$

where H is the scale height given by ${RT}/\mu g$, R is the universal gas constant, σ is the Stefan–Boltzmann constant, μ is the atmospheric molecular weight, which is assumed to be identical to that of CO₂, ρ is the atmospheric mass density, C_p is the atmospheric heat capacity, and L is the mixing length defined with respect to the convective stability of the atmosphere (Ackerman & Marley 2001),

$$\begin{eqnarray}&&L=H\mathrm{max}(0.1,{{\rm \Gamma }}/{{{\rm \Gamma }}}_{{{\rm a}}})\end{eqnarray} \tag{ 3 }$$

where Γ is the lapse rate and Γ_a is the adiabatic lapse rate. As with Ackerman & Marley (2001), we set a lower bound for L of 0.1H in the radiative regions of the atmosphere. Using Equations (1) and (2), we find a surface eddy diffusion coefficient value of 3.4 × 10⁷ cm² s⁻¹, which is more than twice as high as in previous studies where a value of 10⁵ cm² s⁻¹ is often used (e.g., Nair et al. 1994; Segura et al. 2007). This is likely due to the equations' assumption of free convection breaking down in the presence of a solid surface. Therefore, we scale the entire profile by a constant factor such that the surface value is 10⁵ cm² s⁻¹.

The temperature, pressure, and eddy diffusion coefficient profiles are held constant with time throughout the simulation, even when the atmospheric composition changes drastically. We will discuss how a self-consistent atmospheric model may impact our results in Section 4.3.

The hydrodynamic loss of water leads to an atmosphere depleted in hydrogen, which is mostly bound in H₂ and H₂O in our model. To simulate such depletion we decrease the initial water content of the atmosphere such that it is undersaturated at all altitudes. Using the expression of Lindner (1988) for the temperature-dependent saturation vapor pressure of water we find the minimum value of the saturation water vapor mixing ratio of our model atmosphere to be 1.675 × 10⁻⁵ ppm at the tropopause, where the temperature is 139 K. We then vary the H₂ content to investigate the result of different degrees of hydrogen depletion in the atmosphere. We simulate six cases, with total atmospheric H mole fractions $f{({{\rm H}})}_{\mathrm{tot}}$ of (1) 26 ppm, (2) 2.6 ppm, (3) 0.27 ppm, (4) 0.032 ppm, (5) 0.0088 ppm, and (6) 0.0065 ppm. f(H)_tot is defined as the number of hydrogen atoms in the atmosphere divided by the total number of atoms in the atmosphere. By comparison, the H mole fraction of Venus is 14 ppm (Miller-Ricci et al. 2009).

We assume that the excess oxygen produced from water depletion is taken up by the crust and upper mantle during the Runaway Greenhouse phase, when a magma ocean may have formed on the surface that would have acted as an extremely efficient oxygen sink (Hamano et al. 2013; Luger & Barnes 2015). The resulting atmosphere would then be low in oxygen, while the crust and upper mantle compensate by being oxidized.

We have assumed zero-flux boundary conditions for all neutral species in our model atmosphere in order to simplify the problem and focus on the effects of high UV flux, low water content, and high CO₂-content. This is equivalent to assuming that all fluxes are nonzero, but are in balance with each other. In this section we evaluate this assumption by introducing explicit, balanced fluxes into our model with the goal of determining what surface and escape fluxes are necessary to reproduce our zero-flux results, and thus what planets may possess these atmospheric compositions. The fluxes modeled are the outgassing of H₂O, the escape of H and H₂ into space, and the surface deposition of O₃. O₂ deposition is assumed to be zero due to its relatively low reactivity and solubility in water compared to O₃ (Sonntag & von Gunten 2012), though its high abundance in the drier cases may increase its significance (see below). Comparisons between the zero-flux and explicit flux models are done using our wettest and driest cases, Cases 1 and 6, respectively. All other run parameters of the models are identical to the corresponding zero-flux cases.

Figure 7 shows the comparison between the mixing ratios derived from the explicit flux model (dashed curves) and that derived from our nominal model (solid curves), for Cases 1 (red) and 6 (blue). There is satisfactory agreement between the two models for almost all of the species, including those vital to the catalytic cycles outlined in Section 3. The major difference between the two models is the reservoir of atmosphere hydrogen. For the zero-flux case, the reservoirs are H₂ and H₂O₂, while in the explicit flux model the hydrogen reservoir is water. This is understandable since water is being actively replenished by outgassing, and the production of H and H₂ is dependent on the H₂O abundance. This leads to a slight decrease in H and H₂ mixing ratios, which further leads to the minor differences in the abundances of the other species.

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Table 2 shows the escape velocities/fluxes, outgassing fluxes, and surface deposition velocities/fluxes for Cases 1 and 6 of the explicit flux model. The hydrogen escape velocities, which were derived using Case 1 and then applied to Case 6, are consistent with the diffusion-limited escape velocity of hydrogen at Earth's homopause (Hunten 1973). We found that greater escape velocities led to the depletion of hydrogen in the upper atmosphere with respect to the zero-flux results, while lower velocities led to excesses of H and H₂ without any changes in the shapes of their profiles. The hydrogen escape flux for Case 1 is consistent with that of Venus (Grinspoon 1993), which is unsurprising given their similar atmospheric hydrogen mole fractions (Miller-Ricci et al. 2009), while Case 6 has much lower escape fluxes, in accordance with its lower atmospheric hydrogen content. The same pattern holds for water outgassing: The flux for Case 1 is similar to that of Venus (5.5 × 10⁵–10⁷ cm⁻² s⁻¹), while that of Case 6 is an order of magnitude lower than the given lower limit of the Venus water outgassing flux (Walker et al. 1970). By analogy this could mean that volcanism rates, and thus heat fluxes, are relatively high, but the water content of the lava is much lower. This is consistent with a desiccated upper mantle that lost its hydrogen during the early runaway greenhouse-induced magma ocean phase (Hamano et al. 2013; Luger & Barnes 2015).

The deposition of oxidants is crucial in determining the oxidative state of the atmosphere. For example, in the work of Zahnle et al. (2008), where H₂O₂ and O₃ are lost to aqueous reactions with ferrous iron and sulfides, the atmosphere tends to be converted entirely to CO. As O₃ and H₂O₂ are crucial to the catalytic cycles we have outlined, it is not surprising that losing them to the surface would result in high CO concentrations, as the efficiency of CO₂ regeneration would be vastly decreased. Zahnle et al. (2008) used an O₃ deposition velocity of 0.02 cm s⁻¹ for the surface of Mars, which is 3 and 8 orders of magnitude greater than that of our explicit flux results for Cases 1 and 6, respectively. Such low deposition velocities may be consistent with a surface much drier than that of Mars. Zahnle et al. (2008) used a surface relative humidity of water of 17% for their Mars model, which is 320 times higher than the relative humidity for our Case 1 results, and 8.5 × 10⁵ times higher than that of our Case 6 results. Therefore, it is plausible that our deposition velocities are low due to the lack of an aqueous medium within which oxidation can proceed quickly. However, the exact relationship between O₃ deposition velocity and relative humidity is unknown, especially for very low water abundances. Alternatively, the planetary surface may be low in ferrous iron and sulfides due to the oxidation resulting from burial of hundreds of bars of oxygen during the aforementioned magma ocean phase.

Similar arguments can be made for O₂ deposition. Zahnle et al. (2008) attributed the surface flux of O₂ on Mars to UV photostimulated oxidation of magnetite in the presence of trace amounts of water. However, this may be insignificant in our case due to the low UV flux at our model planet's surface, as a result of our thicker atmosphere. Therefore, any O₂ flux at the surface is likely due to aqueous reactions with reducing species, as with O₃. An alternative simulation of the explicit flux cases using O₂ deposition instead of O₃ deposition yielded velocities of 3.7 × 10⁻¹² cm s⁻¹ and 3 × 10⁻¹⁵ cm s⁻¹ for Cases 1 and 6, which are 5 and 8 orders of magnitude lower, respectively, than that assumed by Zahnle et al. (2008) for UV photostimulation (4 × 10⁻⁷ cm s⁻¹). Despite the different depositional mechanisms, these differences are similar in magnitude to that of our O₃ deposition results. Therefore, as both UV photostimulation and aqueous chemistry require some water, the reduced relative humidity at the surface of our desiccated planet may inhibit O₂ deposition by either mechanism just as it does O₃ deposition.

These calculations show that terrestrial planets that have experienced severe loss of water and oxidization of the crust and upper mantle, such as planets orbiting in the habitable zones of M dwarfs, can potentially possess an atmosphere similar to our zero-flux results provided that CO₂ is abundant in their atmospheres. Consequently, biosignature false positives may be prevalent for planets orbiting in the habitable zone of M dwarfs, and should be taken into consideration in future studies and observation campaigns, as we discuss below.

Our results show that O₂ mixing ratios of ∼20% and O₃ mixing ratios >1 ppm are achievable on H₂O-depleted M dwarf terrestrial exoplanets due to photochemistry. These values are similar to that of modern Earth (Yung & DeMore 1999), where the abundant O₂ and O₃ are produced by biological photosynthesis. In this section we calculate their spectral signatures and consider their impact as potential false positive biosignatures.

Figure 8 shows the thermal emission spectrum of our model atmosphere for Cases 1 (red), 3 (orange), and 6 (green), as generated by the Spectral Mapping Atmospheric Radiative Model (SMART; Meadows & Crisp 1996). We also plot the spectrum of Earth (black) generated by the extensively validated Virtual Planetary Laboratory (VPL) 3D spectral Earth model (Robinson et al. 2010, 2011, 2014), divided by two for comparison. We see immediately that not only are our three cases difficult to separate, but all three cases are very different from Earth's atmosphere as seen in the mid-IR. This is mostly due to the completely different temperature profile assumed and the lack of water vapor, which absorbs at 6.3 and beyond 18 μm, though there is a slight decrease in flux at 6.3 μm for our wettest case (Case 1). Our model atmosphere also lacks methane, which absorbs at 7.7 μm. All spectra feature a deep 15 μm CO₂ band, though it is deeper for our model atmosphere due to the cooler stratosphere. Finally, there is weak O₃ absorption at 9.7 μm that gets progressively stronger as our model atmosphere becomes drier, but it never approaches the strength of O₃ absorption in Earth's atmosphere. The weakness of this absorption is caused by the emission occurring near the surface, such that the brightness temperature of the O₃ absorption is similar to the surface temperature, which sets the continuum on either side of the absorption feature. Thus, from the thermal emission there is a clear distinction between actual Earth-like planets and those with abundant atmospheric O₂ and O₃ caused by low water content and photolysis.

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Figure 9 shows the normalized reflectance of the same cases as in Figure 8 compared to the reflectance of Earth, again generated by SMART and the VPL Earth model, respectively. A gray surface albedo of 0.15 is assumed for our model planet. We see that the O₃ in our model atmosphere can be detected via deep O₃ absorption in the NUV similar in strength to O₃ absorption in Earth's atmosphere, and our driest case (Case 6) even features a deeper Chappuis band (∼0.6 μm) than Earth. However, whereas all of our cases exhibit a smooth fall-off in reflectance past 0.7 μm, punctuated by CO₂ absorption, Earth's reflectance in this region is dominated by water absorption, and thus water again acts as the discriminating species between Earth and our model planet.

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From these comparisons it is clear that the condition necessary to produce abundant O₂ and O₃ in CO₂-dominated atmospheres—low water content—leads to a clear distinction in planetary spectra from those of Earth-like planets via the disappearance of strong water vapor absorption bands. Thus, biologically active, Earth-like planets can be distinguished from the planetary environments presented here using the 0.95 μm water vapor band, the numerous water bands throughout the nearinfrared, or, in the thermal infrared, the 6.3 μm water band, which are all observable by JWST (Beichman et al. 2014). However, caution must be exercised, as high-altitude cloud cover could potentially mask spectral signatures of water vapor.

In our calculations we fix the pressure, temperature, and eddy diffusion coefficient profiles. As we have shown, considerable atmospheric evolution occurs over the 10 Gyr duration of each simulation, including the formation of a significant O₃ layer comparable to that of Earth and the conversion of ∼40% of the atmospheric CO₂ into CO and O₂. Furthermore, the liberation of CO and O from CO₂ increases the total number of molecules in the atmosphere, but this should be balanced by the decrease of the molecular weight of the atmosphere from ∼44 to ∼37 g mol⁻¹, thereby increasing the scale height such that local number densities should remain constant. The O₃ layer in the stratosphere should raise the temperature such that a temperature inversion results due to heating by photolysis, much like in Earth's stratosphere (Park & London 1974). The decrease in CO₂ should result in warming of the stratosphere and mesosphere due to lower rates of radiative cooling (Roble & Dickinson 1989; Brasseur & Solomon 2005), as well as a cooling of the troposphere due to decreased greenhouse effects. Finally, the increase in O₂ should result in heating by photolysis in the mesosphere and thermosphere (Park & London 1974). In all, the temperature profile should increase above the tropopause and evolve in shape toward that of Earth, while below the tropopause the temperature will likely decrease.

The reaction rates will change in response to these temperature variations, as most of the reaction rate constants are exponential functions of inverse temperature (Table 1). Of the chemical reactions considered here, R2 (low pressure limit), R3, and R7 have rate constants that are inversely proportional to temperature, while R2 (high pressure limit), R4, R5, and R8 have rate constants that are directly proportional to temperature. Of the photolysis reactions, R1 decreases for decreasing temperatures (Schmidt et al. 2013) and R6 varies negligibly with temperature (Nicovich & Wine 1988). Photolysis of O₂ and O₃ (R9) decrease slightly with decreasing temperatures (Hudson et al. 1966; Lean & Blake 1981).

The combination of the temperature changes and the response of the reaction rates seem to suggest that (1) CO₂ destruction will increase as temperature increases in the stratosphere, (2) CO₂ regeneration via S2 and S3 will decrease due to decreasing temperatures in the troposphere, and (3) CO₂ regeneration via R5 will also decrease, again due to the cooler troposphere. In other words, the atmosphere may lose much more CO₂ if the temperature evolution were taken into account. Quantitatively verifying these hypotheses require running coupled photochemistry and radiative transfer models, which is beyond the scope of this study.

For many of our cases, H₂O is supersaturated in the stratosphere/mesosphere by the end of the 10 Gyr model run due to equilibration among the different hydrogen species. The formation of ice clouds would affect the UV radiation environment in the lower atmosphere, but whether the UV is enhanced or attenuated depends on location above or below the clouds, the solar zenith angle, cloud particle properties and distribution, and cloud optical depth. Typical variations in UV intensity on Earth's surface due to clouds are on the order of 25% in either direction while enhancement tends to occur above the clouds (Bais et al. 2006). Given the degree of supersaturation in our wetter runs, however, attenuation is more likely than enhancement below the clouds. This would decrease the H₂O₂ and O₃ photolysis rates and cause an increase in the number densities of these species, which in turn would decrease the efficiency of S2 and R5 while increasing the efficiency of S3. The magnitude to which these pathways change will depend on how much UV is attenuated as a function of wavelength, as well as the variability time scale of the clouds—if this time scale is sufficiently short, it may be irrelevant for the long time scales considered here.

The existence of water ice clouds may also result in heterogeneous chemistry that impacts the stability of CO₂ (Atreya & Blamont 1990). For example, observations of high O₃ mixing ratios over the northern polar region of Mars during northern spring is likely due to the uptake of HO_x radicals by cloud particles (Lefèvre et al. 2008). If similar processes occurred in our model atmosphere, then the decrease in HO_x species would reduce the efficiency of S2 and S3, while the buildup in O₃ would increase the efficiency of S3 and R5. As S2 is responsible for the highest rate of CO₂ regeneration, inclusion of heterogeneous chemistry will likely result in reduced amounts of CO₂, even when the atmospheric hydrogen content is relatively high. This is consistent with simulations of the Martian atmosphere that included heterogeneous chemistry (Atreya & Gu 1994; Lefèvre et al. 2008). The magnitude of these effects will depend on the reactive surface area of the cloud particles and the amount of condensable water vapor in the atmosphere.

In drier cases, the lack of significant cloud formation and rainout may produce a substantial silicate dust layer, as in the near-surface atmosphere of Mars (Hamilton et al. 2005). These particles may also participate in heterogeneous chemistry and UV attenuation (Atreya & Gu 1994), though the magnitude of the effect is likely less than that of water ice particles (Nair et al. 1994).