How to Identify Exoplanet Surfaces Using Atmospheric Trace Species in Hydrogen-dominated Atmospheres

While our modeling is designed to represent generic sub-Neptunes, we adopt the properties of K2-18b for our models. K2-18b is an intermediate-sized sub-Neptune (radius 2.71 R_Earth; Cloutier et al. 2019) in the habitable zone of a moderately active early M-dwarf star (M2.5 ± 0.5; Cloutier et al. 2017), with an equilibrium temperature of 255 ± 4 K (assuming an albedo of 0.3). The atmosphere of K2-18b has been characterized by the Kepler Space Telescope (K2) in the 0.4–0.9 μm range, the Hubble Space Telescope (HST) Wide Field Camera 3 (WFC3) in the 1.1–1.7 μm range, and the Spitzer Telescope at 3.6 and 4.5 μm (Benneke et al. 2017, 2019b; Tsiaras et al. 2019). In contrast to the flat spectra observed for most sub-Neptunes (Knutson et al. 2014a, 2014b; Kreidberg et al. 2014; Chachan et al. 2020; Guo et al. 2020; Libby-Roberts et al. 2020), the observations of K2-18b reveal a significant absorption feature at 1.4 μm, possibly due to water (H₂O) or methane, assuming an H₂/He-dominated atmosphere (Tsiaras et al. 2019; Bézard et al. 2020; Scheucher et al. 2020), albeit with some evidence for water ice/liquid clouds (e.g., Benneke et al. 2019b; Charnay et al. 2020; Piette & Madhusudhan 2020; Blain et al. 2021).

Even though a high mean molecular weight atmosphere (H₂O dominated) with some N₂ and/or H₂/He cannot be ruled out given the current HST/WFC3 data (Tsiaras et al. 2019), photoevaporation models and Lyα observations (e.g., dos Santos et al. 2020; Mordasini 2020) suggest that K2-18b could have retained a large percentage of any primordial H/He atmospheric envelope owing to the combination of its moderate size and relatively low stellar irradiation levels. The mass and radius of K2-18b (Cloutier et al. 2019) are also fully consistent with an H₂-rich, Neptune-like atmosphere. On the other hand, atmosphere and interior models (Madhusudhan et al. 2020; Piette & Madhusudhan 2020) suggest that K2-18b could have a cool, habitable liquid water surface (T < 400 K) with pressure as low as 1 bar. However, identifying the existence of a surface and retrieving the surface pressure of K2-18b would likely be difficult with solely JWST/ARIEL transit observations (Changeat et al. 2020).

Here we use an established one-dimensional (1D) thermochemical and photochemical kinetics and transport model, based on the Caltech/JPL KINETICS code (Allen et al. 1980; Moses et al. 2011, 2013, 2016; Moses 2014), to simulate the atmospheric evolution of K2-18b. This model bridges the photochemistry-dominated upper atmosphere and the thermochemistry-dominated deep atmosphere seamlessly and considers potential disequilibrium chemical processes such as transport-induced quenching and photochemistry (Moses et al. 2011), allowing us to investigate the effect of different surface pressure (P_surf) levels on the chemical evolution of major observable species containing C, H, O, and N in the atmosphere of K2-18b. We run the model with surfaces located at four different pressure levels (1 bar, 10 bar, 100 bar, and deep/no surface). The model runs until a steady state is reached for a convergence criterion of 1 part in 1000.

The required inputs to the model include (1) the assumed bulk elemental composition of the atmosphere; (2) the atmospheric pressure–temperature profile (P–T profile); (3) the initial atmospheric composition along this P–T profile, which is assumed to be in thermochemical equilibrium throughout; (4) the stellar spectrum; (5) the vertical profile of eddy diffusion coefficients K_zz ; (6) constituent boundary conditions; and (7) chemical inputs such as species' ultraviolet cross sections and reaction rate coefficients.

We assume a hydrogen-dominated but metal-rich atmosphere for the sub-Neptune K2-18b, with a metallicity of 100 times solar (where the "solar composition" is defined from the protosolar abundances of Lodders 2010), which is within the metallicity range of the best-fit HST data (Bézard et al. 2020; Charnay et al. 2020; Blain et al. 2021) and is plausible from formation models (Fortney et al. 2013). The P–T profiles in our model are generated with a well-established 1D radiative-convective model (Marley & McKay 1999; Fortney et al. 2005, 2008; Morley et al. 2012). The model accounts for both incident radiation from the parent star and thermal radiation from the planet's atmosphere and interior. The radiative transfer scheme is described in Toon et al. (1989) and McKay et al. (1989), with further model details and methods described in McKay et al. (1989).

Here we assume a moderate 100 times solar metallicity and use two end-member intrinsic fluxes from the planetary interior (${F}_{\mathrm{int}}=\sigma {T}_{\mathrm{int}}^{4}$), parameterized by the intrinsic temperature T_int of 0 and 70 K, respectively, to calculate the P–T profile. The intrinsic flux depends on the size, age, and composition of the planet. T_int values for Neptune and Saturn are 53 and 78 K, respectively (Pearl & Conrath 1991). Lopez & Fortney (2013) suggest that T_int values of ∼30 K could be appropriate for a planet with K2-18b's properties, so the T_int = 0 and 70 K end-member cases should bracket the likely range of possibilities. Because the model-generated P–T profiles only go to 1 μbar at high altitudes, and important photochemistry occurs at altitudes above that level, we extended the profiles to lower pressures by assuming an arbitrary power-law expression that extends to a nearly isothermal profile at pressures <1 μbar. The thermo/photochemical kinetics model also requires that the deep atmosphere extends to temperatures of ∼2600 K to accurately capture the quench points for all species so they can reach thermochemical equilibrium at depth. For the T_int = 70 K case, we extended the model-derived temperature profile to deeper levels assuming an adiabat. The T_int = 0 K profile reaches a deep isothermal temperature that is cooler than 2600 K and so was not extended to greater depths; thus, some species (e.g., nitrogen species N₂–NH₃) cannot achieve full thermochemical equilibrium at any point in the atmosphere for this T_int = 0 K case. To examine a phase space for warmer sub-Neptune planets, we also generated a warmer P–T profile for a hypothetical hotter sub-Neptune by halving the current orbital distance of K2-18b, resulting in a factor of four increase in the solar insolation the planet receives. The final P–T profiles, shown in Figure 1(a), extend to pressures of 10^-11 bar. For the model runs with different surface pressure levels, we simply cut the P–T profiles at each corresponding surface level (1 bar, 10 bar, or 100 bar).

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Once the P–T profiles for the different cases are established, we generate an equilibrium initial composition for the atmosphere using the NASA CEA thermochemical equilibrium model of Gordon & McBride (1984). We adopt a stellar UV flux relevant to a young, active M dwarf because much of the photochemical evolution occurs in the first ∼1 million years, when the UV flux from the star was greater than it is today. At wavelengths less than 70 nm, the flux is derived from EUVE spectra of Gliese 411 ⁵ ; at wavelengths from 115-173 nm, the flux derives from Au Mic from the CoolCat database ⁶ ; at wavelengths from 173-198 nm, the flux derives from IUE spectra of Gliese 867 A ⁵ ; and at 198-320 nm, the flux derives from IUE spectra of Gliese 229 A ⁵ .

The eddy diffusion coefficient profiles are shown in Figure 1(b) for the nominal K2-18b and the hotter sub-Neptune variant. The K_zz in the deep, convective portion of the atmosphere is estimated using the free-convection and mixing-length theories (e.g., Stone 1976). For the upper atmosphere, K_zz is assumed to vary inversely with the square root of atmospheric pressure, with a scaling that depends on the atmospheric scale height H(z) and the equilibrium temperature T_eq, using the empirical formula described in Moses et al. (2020). The temperature profiles predicted from the radiative transfer models exhibit a detached convective region lying between two radiative regions. Based on the inferred K_zz values for Earth and the solar system planets (e.g., Yung & Demore 1999), we assume a K_zz of 10⁶ cm² s⁻¹ for the detached upper-tropospheric convective region in the cooler nominal model and a K_zz of 10⁵ cm² s⁻¹ for the deeper radiative region in the upper troposphere. For the hotter planetary model, we assume K_zz = 4 × 10⁶ cm² s⁻¹ for the detached upper-tropospheric convective region and K_zz = 4 × 10⁵ cm² s⁻¹ for the radiative region below it. However, given the large expected uncertainties in the K_zz profile, we also test the sensitivity of our results to two additional K_zz profiles for the nominal case, by multiplying and dividing the nominal K_zz profile by a factor of three, hereinafter called the large and the small K_zz cases, respectively.

We assume zero flux for all species at both the top and bottom boundaries, which essentially assumes no sources or sinks at the surface (if there is one in the model) and no escape or influx at the top of the atmosphere. Although some atomic H and potentially other gases will be escaping under conditions relevant to K2-18b, dos Santos et al. (2020) demonstrate that the expected loss of H over the age of the system amounts to <1% of the mass of the planet. Although volcanism, interior outgassing, and other geological or biological sources can provide potential nonzero flux terms to introduce new material to the atmosphere, and although chemical weathering, dissolution in oceans, sequestering of condensates, and other surface–atmosphere interactions could provide potential sinks for atmospheric gases, the magnitude of such processes is unknown for exoplanets. The zero-flux boundary conditions therefore provide a good first-order prediction of the influence of the surface on the atmospheric composition in the absence of geological/biological sources and sinks. We return to this point in the Discussion section.

The fully reversed chemical reaction list of Moses et al. (2013) is adopted for this work. The model considers 92 neutral species that interact with each other through ∼1650 kinetic reactions, including hydrocarbons with molecular weight up to benzene (C₆H₆), nitriles and other nitrogen-bearing species with two or fewer N atoms, and oxygen species with three or fewer oxygen atoms. The non-photolysis reactions are fully reversed, allowing thermochemical equilibrium to be reproduced kinetically in the deep atmosphere when temperatures are large enough. However, when vertical transport is faster than the kinetic reactions can maintain that thermochemical equilibrium, certain constituents can have their mixing ratios "quenched" (e.g., Prinn & Barshay 1977; Lodders & Fegley 2002; Moses et al. 2011; Venot et al. 2012) at values not representative of the local thermochemical equilibrium abundances. Photochemistry can further alter the abundances. Condensation is not included in this version of the model, which could potentially impact both the steady-state gas abundance profiles (e.g., H₂O would be overestimated at any altitudes where it condenses) and the time-variable atmospheric evolution (e.g., the oxygen tied up in the condensed H₂O could slow the speed of conversion of that oxygen into other gas-phase species, such as CO). Further details of the chemical model can be found in Moses et al. (2005, 2011, 2013, 2016).

In Figure 2, we summarize the main chemical pathways for the net production and loss of key species in the deep-surface/no-surface case and a shallow-surface case for K2-18b. For the no-surface case (Figure 2(a)), the atmosphere can be divided into three sections that are dominated by different chemical processes. The upper region of the atmosphere (pressures less than a few bars, depending on the thermal structure) is dominated by photochemistry and vertical diffusion, and the deepest, hottest part of the atmosphere is dominated by thermochemical equilibrium (the pressures at which equilibrium dominates depend on the thermal structure of the atmosphere). The composition in the rest of the atmosphere is mainly controlled by species diffusion and transport; in this intermediate region, a process called transport-induced quenching, which occurs when transport timescales are shorter than the chemical kinetic reaction timescales, can act to prevent the constituents from achieving thermochemical equilibrium (e.g., Lodders & Fegley 2002; Visscher & Moses 2011). The P–T point at which the transport timescale is equal to the chemical kinetic conversion timescale of a particular constituent is called that species' quench point. At altitudes below the quench point, the mixing ratio of a species will be governed by thermochemical equilibrium. At altitudes above the quench point, the mixing ratio of a species will remain constant with altitude at the thermochemical equilibrium value it reached at the quench point, unless other disequilibrium chemical processes such as photochemistry act upon it.

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For the no-surface case, all three chemical processes conspire to determine the abundance profiles of species. In this scenario, species with weak bonds such as NH₃, CH₄, and H₂O are readily broken apart (photolyzed) by ultraviolet photons. The photolysis products undergo further chemical reactions that act to either reform the original "parent" species or form new photochemical products, such as N₂, hydrocarbons, nitriles, carbon monoxide (CO), and carbon dioxide (CO₂). When they are transported to the deep, hot part of the atmosphere, the photochemically formed species will be converted back in part to NH₃, CH₄, and H₂O and transported back to the upper atmosphere. If a surface is located below the quench point of a species, thermochemistry can act to fully recycle this species back to the upper atmosphere as if there were no surface. However, if there exists a cold and shallow surface vertically above the point at which thermochemical equilibrium would have been achieved kinetically, then the chemical reactions do not work effectively to recycle the photochemical products back into the parent molecules. Thus, over time, the shallow-surface case would evolve to have decreased abundances of photochemically fragile species (NH₃, CH₄, and H₂O, marked in blue in Figure 2(b)) and increased abundances of more photochemically stable species (N₂, CO, and CO₂, marked in red in Figure 2(b)) compared to the no-surface case.

In Figures 3 and 4, we show the converged VMR profiles of the main chemical species for the nominal K2-18b and the hotter variant (both with T_int = 70 K). Different surface levels with different surface pressures and temperatures are shown to have significant impacts on the final chemical makeups of the atmosphere. For the no-surface cases (Figures 3(a) and 4(a)), large amounts of hydrocarbon and nitrile species are produced photochemically—the main ones shown here include ethane (C₂H₆), acetylene (C₂H₂), and hydrogen cyanide (HCN)—and other significant atmospheric species include H₂O, CH₄, CO, CO₂, NH₃, and N₂. Species such as H₂O and CH₄ have abundances close to their expected equilibrium values, whereas CO, CO₂, and N₂ are considerably enhanced and NH₃ is depleted in the upper atmosphere over equilibrium expectations, as a consequence of transport-induced quenching and (for the case of CO₂) related chemistry involving quenched species. The species for the 100 bar surface cases (Figures 3(b) and 4(b)) have similar VMR profiles to the no-surface cases, as the surface temperatures at 100 bar (>1300 K) are already hot enough for thermochemistry to be effective, as if there were no surface.

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The 10 bar surface cases (Figures 3(c) and 4(c)) start to deviate from the no-surface cases, as the surface level is now well above the original deep quench point for the key nitrogen-containing species N₂, NH₃, and HCN, and chemical kinetics at these cooler temperatures no longer lead to efficient exchange of nitrogen between N₂ and NH₃. Some exchange of nitrogen between NH₃ and HCN still occurs, but the nitrogen lost from NH₃ photolysis largely ends up in the photochemically stable N₂, so NH₃ becomes depleted, and then the coupled NH₃-CH₄ kinetics that produces HCN operates less efficiently. The 10 bar surface cases therefore exhibit decreased VMRs of NH₃ and HCN compared to the no-surface and 100 bar surface cases, whereas N₂ (with its strong triple N–N bond that makes it less susceptible to UV photolysis) exhibits an increase in its VMR. The 10 bar surface is also above the original quench point for CO–CH₄–H₂O, but surface temperatures are high enough that the photochemically produced complex hydrocarbons remain in equilibrium with CH₄ in the lower atmosphere, such that the photochemically produced C₂H_x hydrocarbons and other species are recycled back to CH₄, preventing a significant depletion in atmospheric methane.

For the shallowest 1 bar surface cases tested in our model (Figures 3(d) and 4(d)), the surface level is located well above the quench point for most species, leading atmospheric compositions to deviate significantly from the no-surface case. Instead of being tied to an equilibrium abundance at depth, the species vertical profiles represent a steady-state balance between photochemical production and loss and vertical transport. The column densities of photochemically fragile H₂O, CH₄, and NH₃ drop significantly compared to the no-surface case, while those of the more photochemically robust species CO, CO₂, and N₂ increase, as they become the major end products for the oxygen, carbon, and nitrogen released from the photochemistry of H₂O, CH₄, and NH₃. However, CO, CO₂, and N₂ and other key photochemical products can themselves be photolyzed by high-energy photons, and some of that oxygen, carbon, and nitrogen ends up back in H₂O, CH₄, and NH₃, so these original "parent" species are not completely lost from the atmosphere. Instead, the vertical profiles of all the species evolve to reflect this complex chemical coupling and steady-state balance mentioned above. The resulting atmospheres end up being much "cleaner" in terms of fewer complex, refractory, photochemical products compared to the no-surface cases. Most hydrocarbons and nitriles are depleted to VMR < 10⁻⁶ in this shallow 1 bar surface case.

In order to find the species that can be used for probing the existence of surfaces, in this section we examine the sensitivity of several key species to the existence of surfaces at different surface pressures.

Based on our results shown in Figures 3 and 4, here we group the key chemical species into four categories (Table 1 and Figures 5–8), and each category of species is affected by the existence of a surface differently. The first category includes NH₃ and HCN, whose abundances are very sensitive to different surface levels (e.g., our 1 bar and 10 bar cases), such that their abundances decrease with decreasing surface pressure. The second category includes CH₄, other hydrocarbons (only C₂H₆ and C₂H₂ are included in the table here), and H₂O; this category of species is only sensitive to very shallow cool surfaces (e.g., our 1 bar case), such that the mixing ratios of these species decrease in comparison to all other surface scenarios. The third category includes CO and CO₂, whose abundances are most sensitive to the very shallow cool 1 bar surface as well, but whose mixing ratios increase in the 1 bar surface case compared to all other surface scenarios. The last category includes species that are not very sensitive to the existence of surfaces; they are mostly nonpolar or relatively inert species such as hydrogen, nitrogen, and helium (He).

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Figure 5 shows mixing ratio profiles for the species in the first category for the nominal K2-18b case (T_int = 70 K) with different surface levels at convergence. The thermochemical equilibrium profile of NH₃ has the highest VMR in the observable part of the atmospheres (10⁻⁴–1 bar). When vertical transport and photochemistry are included in the model, the NH₃ VMR for the no-surface case decreases from its expected equilibrium value by more than one order of magnitude in the observable region of the atmosphere, as a result of transport-induced quenching. At pressures less than ∼100 bar, the atmosphere is simply too cold for the thermochemical kinetics reactions to efficiently exchange nitrogen between different major species, and vertical transport is faster than the chemical reactions can maintain thermochemical equilibrium. However, at pressures greater than ∼100 bar, temperatures are high enough that the kinetic reactions dominate over transport, and thermochemical equilibrium can be kinetically maintained. As on Jupiter, any NH₃ lost by photolysis at higher regions of the atmosphere can be recycled at depth in these assumed hydrogen-dominated sub-Neptune atmospheres, and the NH₃ can be transported back throughout the atmosphere (see Figure 2). Because the N₂–NH₃ quench point lies close to 100 bar, adding a surface at 100 bar does not cause significant changes in the NH₃ mixing ratio compared with the no-surface case; essentially, the 100 bar, ∼1300 K conditions near the surface allow the thermochemical kinetics reactions to efficiently recycle the NH₃ that is lost from photochemical processes higher up in the atmosphere, and NH₃ is not permanently lost.

Ammonia is, however, very sensitive to surfaces located at lower pressures—both the 10 bar surface case (T_surf ∼ 1000 K) and the 1 bar surface case (T_surf ∼ 600 K) exhibit a decrease in the NH₃ mixing ratio of ∼2 and ∼4 orders of magnitude, respectively, compared to the no-surface case. In the upper atmospheres of our shallow-surface models, some of NH₃ is irreversibly destroyed and converted mainly to N₂ and HCN, as the nitrogen in these two species forms strong triple-bonded structures that make them less chemically reactive and only able to be photolyzed by high-energy, extreme-ultraviolet photons. Note that hydrazine (N₂H₄), a major NH₃ photochemical product on Jupiter, is not synthesized in large quantities in these warmer sub-Neptune atmospheres, as numerous competitors for the NH₂ radicals exist to impede its production, and the produced N₂H₄ does not condense, which allows other chemical loss mechanisms to operate.

In the shallow-surface models, without the thermochemistry that would occur deeper in the atmosphere, NH₃ cannot be recycled as efficiently, leading to the depletion of NH₃ in favor of N₂ compared to the no-surface and 100 bar surface cases. The fate of NH₃ on K2-18b is similar to that on Titan, where it is irreversibly converted to nitrogen, leading to a nitrogen-dominated atmosphere (∼94%–98% N₂). However, because the atmosphere near our shallow-surface K2-18b cases is still relatively hot (∼600 K for the 1 bar surface and ∼1000 K for the 10 bar surface) and because the background atmosphere is abundant in H₂, some NH₃ can still be recycled after it is photolyzed, either from NH₂ (through temperature-dependent reactions such as NH₂ + H₂ → NH₃ + H) or from N₂ (through N₂ photolysis and subsequent reactions in the uppermost atmosphere or through schemes initiated by H-atom addition to N₂ at high pressures; Moses et al. 2010, 2011). At convergence, NH₃ is not completely lost from the atmosphere. However, the lower the temperature and pressure at the surface, the less the NH₃ is able to be recycled. Being so sensitive to various surface levels less than 100 bar, NH₃ can be used as a key species to determine whether an exoplanet has a surface or not.

Chemical production of HCN is tied closely to NH₃ kinetics, so HCN is affected in a similar way to NH₃ to the presence of a surface at different pressure levels. As a result, HCN is also a key species for determining whether an exoplanet might possess a surface or not. Thermochemical equilibrium predicts minimal amounts of HCN in the observable atmospheres of K2-18b, while photochemistry and vertical transport significantly enhance the mixing ratio of HCN in those regions. The enhancement is largely the result of the coupled NH₃−CH₄ photochemistry, initiated by reactions such as CH₃ + NH₂ + M → CH₃NH₂ + M, where M is any third atmospheric molecule or atom, followed by reactions with atomic H to eventually form HCN (see Moses et al. 2010, 2011). The peak HCN mixing ratio at high altitudes in Figure 5 is a signature of this strong photochemical source. Similar to NH₃, the VMR profile of HCN is not affected by a 100 bar surface. This lack of sensitivity results from NH₃ being the main photochemical source of HCN—because the ammonia profile is not affected, neither is HCN. Thermochemical kinetics at the surface conditions of 100 bar and ∼1300 K can fully recycle the HCN and NH₃ back to their larger equilibrium abundances at depth. The existence of a shallow, cool surface, however, drastically decreases the abundance of HCN by 1–2 orders of magnitude for the 10 bar surface case and by 3–4 orders of magnitude for the 1 bar surface case compared to the no-surface case. Again, because HCN is the photochemical product of NH₃ and CH₄, when NH₃ is decimated in favor of N₂, the HCN abundance is also decreased. However, since HCN is expected to have a smaller column abundance than ammonia and thus is potentially harder to observe, it may not be as useful in predicting the existence of surfaces as NH₃.

Figure 6 shows the species in the second category, whose abundances in our models are only sensitive to very shallow, cool 1 bar surfaces. These species include H₂O, CH₄, and most heavier hydrocarbons (C_x H_y ), of which only the most abundant ones, C₂H₆ and C₂H₂, are shown in Figure 6. The thermochemical equilibrium model and the no-surface model produce similar amounts of H₂O and CH₄ in the observable part of the atmosphere owing to the fact that these species are already the dominant oxygen and carbon carriers at the quench point in the no-surface model. Compared to the no-surface model, the very shallow 1 bar surface makes the mixing ratio of H₂O drop by a factor of ∼6 and the mixing ratio of CH₄ drop by almost 2 orders of magnitude. Similar to NH₃, some CH₄ is irreversibly converted to hydrocarbons photochemically in the upper atmosphere, with inefficient recycling of the complex hydrocarbons back to CH₄ at the surface conditions of 1 bar and 640 K. H₂O and CH₄ together are also photochemically converted to CO₂ and CO in the upper atmosphere via pathways involving O + CH₃ → H₂CO + H (among others), with no efficient thermochemical recycling at the 1 bar surface conditions, causing CO and CO₂ to eventually supplant CH₄ and H₂O as the dominant carbon and oxygen species in the atmosphere. Thus, we have the interesting result that a cool, shallow surface could lead to a reduced abundance of CH₄ and H₂O in favor of CO and CO₂ in sub-Neptune atmospheres, even when atmospheric metallicities are not high enough to favor CO and CO₂ in equilibrium.

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Note that CH₄ and H₂O do not become as depleted as NH₃ because they are more efficiently recycled by thermochemistry and because their main photochemical products can be converted back to CH₄ and H₂O at lower temperatures than the main nitrogen-bearing photochemical products (HCN and N₂) can be converted back to NH₃. Photolysis of the complex hydrocarbons, for example, leads to pathways that can recycle methane in H₂-dominated atmospheres (see Moses et al. 2005). CO and CO₂ kinetics can also recycle the H₂O and CH₄ through reaction schemes such as H + CO₂ → OH + CO, followed by OH + H₂ → H₂O + H, or by

• H + CO + M → HCO + M
• HCO + H₂ → H₂CO + H
• H + H₂CO + M → CH₂OH + M
• H + CH₂OH → OH + CH₃
• OH + H₂ → H₂O + H
• CH₃ + H₂ → CH₄ + H
• ——————————————–
• Net: CO + 3H₂ → H₂O + CH₄,

which occur more efficiently at higher temperatures and pressures but are still effective at atmospheric conditions relevant to the 1 bar surface cases. The final vertical profiles of the key species H₂O, CH₄, CO, and CO₂ represent a steady state between their coupled chemical production, loss, and vertical transport. Note that the case with CH₄ for K2-18b with a 1 bar surface is different from Titan (with a 1.5 bar surface), where CH₄ will be completely depleted, because (1) there is hardly any oxygen in Titan's atmosphere to permanently convert the carbon from CH₄ into CO and CO₂, and (2) Titan, with T_eq ∼ 80 K, is much colder compared to K2-18b (T_eq ∼ 255 K), and lots of the photochemically produced hydrocarbons are condensable and would deposit on the surface of Titan to irrevocably deplete the atmospheric CH₄ over time (e.g., Anderson et al. 2018), unless geological or biological source mechanisms are available to replenish the methane (e.g., Atreya et al. 2006).

The warmer 10 bar and 100 bar surface (T_surf > 1000 K) models produce similar abundances of CH₄ and H₂O compared to the no-surface model. Under these surface pressure and temperature conditions, the photochemically produced hydrocarbons and to some extent the CO and CO₂ are readily converted back to CH₄ and H₂O in the lower atmosphere and thus replenished, similar to the no-surface case. For the 10 bar surface case, CO₂ and CO are not completely in equilibrium with CH₄ and H₂O, but their mixing ratios have increased until a steady-state exchange of carbon and oxygen is maintained at a near-equilibrium situation, without a significant loss of H₂O and CH₄. In contrast, the lower atmosphere in the 1 bar surface case remains well out of thermochemical equilibrium.

For the hydrocarbons, the equilibrium model predicts minimal amounts in the observable part of the atmosphere. The no-surface model ends up with lots of hydrocarbons in the same region because of methane photochemistry (e.g., Moses et al. 2005). The 100 bar and 10 bar surface results are similar to the no-surface case, as all the hydrocarbons (including methane) at these surface temperatures can be efficiently and thermochemically converted back and forth between each other. The 1 bar surface model ends up with significantly fewer hydrocarbons at convergence, predominantly because of the lower final abundance of CH₄. Actually, a lot of hydrocarbons are produced at the beginning of the 1 bar surface case (<0.1 Myr model runtime). However, because the photochemically produced triple-bonded CO is less subject to photolysis and attack by atomic hydrogen compared to the photochemically produced hydrocarbons, with time evolving, CH₄ and the photochemically produced hydrocarbons are eventually converted to CO and then to CO₂.

The species in group 2 are very sensitive to very shallow, cool surfaces (P_surf of a few bars or surface temperature T_surf < 800–900 K) but are not sensitive once the surface becomes too hot. Together with the group 1 species (which are sensitive to deeper, hotter surfaces), we can potentially identify not only the existence of surfaces but also the environmental conditions of the surfaces, such as pressure and temperature.

In Figure 7, we summarize VMR profiles for the species in the third category, CO₂ and CO—both are also very sensitive to very shallow 1 bar surfaces, but their abundances increase in comparison with the no-surface case. At equilibrium, CO₂ and CO have minimal abundances in the observable part of the atmosphere in this H₂-dominated, 100× metallicity atmosphere. With photochemistry and transport, the no-surface case produces significant amounts of CO₂ and CO. By adding a 1 bar surface, which significantly reduces thermochemistry in the deep hot part of the atmosphere, the oxygen in water and the carbon in methane are eventually converted to CO and CO₂, making them the dominant carrier of carbon and oxygen. As described in the previous category 2 species discussion, with CH₄ being inefficiently recycled from the photochemically produced hydrocarbons at 1 bar surface conditions, CO outcompetes the hydrocarbons over the long term because it is less prone to photolysis or permanent destruction by reactions with atomic hydrogen. CO₂ also has increased abundance, as it is readily produced from CO and H₂O kinetics. The 10 bar case is really interesting, as both CO₂ and CO are slightly less abundant compared to the no-surface case. The 10 bar surface is above the quench point of CO, and because the equilibrium abundance of CO increases with depth, the final quenched CO mixing ratio in the no-surface case is greater than the steady-state CO abundance in the 10 bar surface case. The decreased CO abundance for the 10 bar surface then leads to less kinetically produced CO₂. The 100 bar surface case is very similar to the no-surface case, as by putting a surface at this higher temperature and pressure, thermochemical reactions can fully recycle CH₄ and H₂O from CO₂ and CO.

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Figure 8 includes species that are not very sensitive to the existence of surfaces, including H₂, He, and N₂. These species are all very abundant but are not readily observable in exoplanet atmospheres. Note that plotting the results case on a magnified linear scale makes it more obvious that the VMR profiles of H₂, He, and N₂ deviate slightly from the no-surface case. For the 1 bar surface model, H₂ has increased in VMR, and He and N₂ have decreased VMRs compared to the no-surface case (see the insets of Figure 8). The increase in H₂ for the 1 bar case is caused by the loss of hydrogen from water and methane (Figure 6) and the increased sequestration of the carbon and oxygen into CO and CO₂, which allows the released hydrogen to end up mostly in H₂, accompanied by a corresponding increase in the total number of molecules per unit volume at any pressure (at which point the mixing ratios are renormalized in the model). The increase in the atmospheric density caused by the increase in H₂ causes the VMRs of the other species to be correspondingly reduced. Thus, even though He is an inert species that does not participate in the chemical cycle, its mixing ratio is reduced compared to the no-surface case. The concentration of N₂ (number of molecules per unit volume) is increased compared to the no-surface case, but because the increase in H₂ concentration and total atmospheric density is more significant, the mixing ratio of N₂ in the 1 bar surface model ends up decreasing compared to the no-surface model. For the 10 bar surface model, the concentration of N₂ also increases compared to the no-surface case, but because H₂O and CH₄ are not lost as readily to H₂ at this surface level, the atmospheric density increase is minimal; thus, N₂ has increased mixing ratio compared to the no-surface case.

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In the previous sections, we identified a few species that can be potentially used as proxies for determining the existence of surfaces and surface conditions. Here we test the robustness of our results to different model assumptions, by changing planetary parameters such as the atmospheric thermal structure and strength of vertical mixing. Overall, our main qualitative conclusions in Section 3.2 remain true for species with various changed planetary parameters. In the following paragraphs, we will discuss the detailed effects of individual planetary parameters on the abundance profiles of key species listed in Table 1.

We first examine the effect of temperature in the deep atmosphere by testing two end-member cases of the internal heat flux, as represented by an intrinsic temperature T_int of 0 and 70 K (the latter being our nominal case). As shown in Figure 1, changing T_int causes the P–T profile to vary in the deep atmosphere at pressures greater than a few bars, but not at lower pressures. Thus, the 1 bar surface case results are unaltered by the change of T_int, as can be seen in Figure 11. For the 10 bar surface case, the surface temperature is only ∼50 K higher for the T_int = 70 K case compared to the T_int = 0 K case; thus, most species (species in groups 1, 2, and 4) have similar VMR profiles. The only exceptions are the species in group 3, CO and CO₂, whose steady-state kinetics are quite sensitive to temperature and pressure. Although CH₄ and more complex hydrocarbons interact readily with each other at the P–T conditions relevant to the 10 bar surface for both T_int cases, the carbon species as a whole are not in thermochemical equilibrium at any pressure in these atmospheres, and full exchange between CO and CH₄ at depth, for example, is inhibited. However, kinetic reactions still occur, allowing the photochemically produced CO and CO₂ to be destroyed throughout the atmospheric column, including near the surface. The cooler conditions at depth in the T_int = 0 K model favor the kinetic maintenance of CH₄ over CO, so there is less CO in the T_int = 0 K model than in the T_int = 70 K model, and CH₄ is more readily recycled. The decreased CO abundance in the T_int = 0 K model leads to decreased net chemical production of CO₂; thus, its abundance is also decreased.

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For the 100 bar surface case, the carbon and oxygen species are able to eventually follow their equilibrium abundances at depth in the higher-temperature T_int = 70 K model, but these species remain out of equilibrium in the cooler T_int = 0 K model. The kinetics at high pressures in these H₂-rich atmospheres increasingly favors CH₄ over CO, especially at colder temperatures, so VMRs of group 3 species, CO and CO₂, become significantly depleted in the colder T_int = 0 K, 100 bar model in comparison to the T_int = 70 K, 100 bar model. For species in group 2 (CH₄ shown as an example in Figure 11), the 100 bar surface temperature is hot enough for thermochemistry to fully recycle the hydrocarbon photochemical products back to methane and transport CH₄ back to the upper atmosphere. Thus, the abundances of group 2 species show little sensitivity to T_int when the surface is placed at 100 bar.

Similarly, the nitrogen species never achieve thermochemical equilibrium at the surface conditions relevant to the T_int = 0 K, 100 bar model, but they come very close to it in the T_int = 70 K, 100 bar model. This causes the species in group 1 (NH₃ shown as an example in Figure 11) to exhibit sensitivity to T_int in the 100 bar models. Note that at 100 bar the surface temperature is ∼350 K lower in the T_int = 0 K case in comparison to the T_int = 70 K case. Thermochemical kinetics in the lower atmosphere cannot fully recycle the NH₃ that was lost photochemically in the upper atmosphere in the T_int = 0 K model, in contrast to the warmer T_int = 70 K model, leading to lower NH₃ abundances in the T_int = 0 K case. Because HCN is generated predominantly from ammonia photochemistry, the decreased NH₃ abundance in the T_int = 0 K model leads to less HCN as well.

We also test the sensitivity of our results to orbital distance, creating a model of a hotter sub-Neptune with K2-18b's physical parameters, except the orbital distance is half that of K2-18b (i.e., the incident stellar flux is increased by a factor of four), while keeping the same T_int (70 K) but increasing the strength of vertical mixing (K_zz ) by a factor of 4, in keeping with the enhanced energy input. The full results for the hot case are shown in Figure 4. Comparison between the nominal and the hotter variant for selected species is shown in Figure 12. Note that we did not test a colder variant because our current model does not include condensation, and water would condense over a large pressure range in the colder sub-Neptune atmosphere, leading to drastic changes in its abundance profiles and subsequent photochemical processes.

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The temperature difference between the hot case and the nominal case remains relatively constant in the upper atmosphere down to ∼1 bar, at which point the difference becomes smaller until the two P–T profiles coincide with each other at around ∼100 bar. Hotter temperatures lead to more effective thermochemical kinetics, allowing chemical reactions to better compete with vertical transport, in general, although vertical transport is also enhanced in the hot model. The net result is that, in the no-surface case, thermochemical equilibrium persists to slightly lower pressures in the hot model than in the nominal model. For example, the quench point for CH₄–CO–H₂O is at ∼10 bar for the hot case and ∼30 bar for the nominal case. At these respective quench points, the hot model has smaller equilibrium mixing ratios of CH₄ and H₂O and larger equilibrium mixing ratios of CO and CO₂ than the nominal model, and transport-induced quenching then preserves these differences as the quenched species are transported to the upper atmosphere. However, because the quench point for N₂–NH₃ is located deeper in the atmosphere (near ∼100 bar), where the thermal structure converges for the two models, the quench points and quenched mixing ratios of ammonia and N₂ are similar for the nominal and the hot cases, leading to similar N₂ and NH₃ VMR profiles when no surface is present. Note that we did not include the 100 bar surface case results in Figure 12, as the abundance profiles for these models overlap with the no-surface case for all species for both the nominal and the hot models, because thermochemical kinetics is efficiently operating at 100 bar conditions to recycle the parent molecules and transport them back to the upper atmosphere.

For the 10 bar surface case, the carbon and oxygen species in group 2 and 3 have similar abundance profiles to the no-surface case for both the hot and the nominal models, as the surface temperature is warm enough that thermochemical kinetic reactions help drive the C and O species toward their equilibrium abundances, such that the species that have been lost to photochemistry can be recycled (see Section 3.2). The nitrogen species in group 1, in contrast, remain far from thermochemical equilibrium at the temperatures relevant to the 10 bar surface for both the hot and nominal models, so their mixing ratios are not tied to equilibrium at the surface. Instead, the VMR profiles of the nitrogen species are controlled largely by photochemical production/loss and transport. The warmer temperatures throughout the upper atmosphere for the hot case are more conducive to prompt recycling of NH₃ once it is photolyzed, through temperature-sensitive reactions such as NH₂ + H₂ → NH₃ + H, NH₂ + H₂O → NH₃ + OH, and NH₂ + CH₄ → NH₃ + CH₃. Moreover, other non-recycling pathways for NH₂ loss, such as NH₂ + CH₃ + M → CH₃NH₂ + M and NH₂ + NH₂ + M → N₂H₄ + M, compete more effectively against the NH₃ recycling in the nominal model, leading to a lower ultimate steady-state VMR of NH₃ in the nominal model compared with the hot model.

The same scenario with respect to the nitrogen species occurs in the 1 bar surface cases, in terms of enhanced NH₃ in the hotter atmospheric model, as a result of more efficient ammonia recycling in the photochemically active region of the atmosphere when temperatures are higher. Thermochemical equilibrium is not recovered at the surface conditions relevant to the 1 bar surface for either the hot or nominal models, so the oxygen and carbon species in the 1 bar cases are also controlled by photochemical production, loss, and transport. H₂O behaves in a similar manner to NH₃—hotter atmospheric temperatures favor more efficient recycling of water once it is photolyzed, through the temperature-sensitive reactions such as OH + H₂ → H₂O + H—so the hot 1 bar surface model has more H₂O than the nominal model. However, CH₄ is actually depleted and CO enhanced in the hot 1 bar surface case in comparison with the nominal case because the higher UV flux and higher H abundance help fuel the conversion of CH₄ into CO on the hot planet in comparison with the nominal planet. Despite the slightly enhanced CO abundance on the hot planet with the 1 bar surface, the high atmospheric temperatures significantly enhance the rate coefficient for the reaction H + CO₂ → CO + OH, which, when combined with the larger H abundance due to the higher UV flux incident, causes a reduction in the abundance of CO₂ in the hot 1 bar surface case in comparison with the nominal 1 bar surface case.

Our model results are also sensitive to the assumed K_zz profile, which can alter the pressure regions at which photochemistry, transport, and thermochemistry are most effective. Large K_zz values lead to deeper quench points, which makes thermochemistry less effective at shallower pressures. Large K_zz values also lead to more rigorous atmospheric mixing, allowing quenched species to be carried to higher altitudes, leading to photochemistry being initiated at lower pressures. The pressure at which the main parent molecules are photolyzed can change their relative production rate (or recycling rate) and loss rate (conversion to new photochemical species). Large K_zz values in the lower stratosphere can also cause depletion of photochemical products that were produced at higher altitudes, accelerating their transport and conversion back to the parent molecules.

Comparison between the model results using two end-member K_zz profiles (so-called "large" and "small" K_zz profiles) for selected species is shown in Figure 13. In general, the main atmospheric species are not very sensitive to K_zz . The larger K_zz causes a slightly deeper quench point for CO–CH₄–H₂O, which leads to a slight decrease in the quenched mixing ratios of CH₄ and H₂O and a larger increase in the quenched CO mixing ratio for the models whose surface is deep enough to capture this quench point (e.g., surface P ≥ 30 bar). The larger change in CO is caused by the larger vertical gradient of its equilibrium mixing ratio at depth in the atmosphere. A larger K_zz also causes all the species to be carried to higher altitudes before molecular diffusion limits their abundance. This leads to an increase in abundance for some photochemical products (e.g., C₂H₂, C4H₂, C₆H₆, O₂), but the larger K_zz also results in faster transport of photochemically produced species to the hot, deep lower atmosphere, where some of the more stable products are more easily destroyed, so the larger K_zz actually leads to a decrease in the abundance of some species (e.g., C₂H₆, C₃H₈, HCN, CH₃CN, CH₃OH) at observable pressures.

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For the shallower surface cases (1 bar, 10 bar), variations in K_zz have little effect on the overall stability and steady-state abundance profiles of the major parent molecules H₂O, CO, and CH₄ at observable pressure regions. The CO₂ abundance is slightly enhanced by the shift of the photolysis region to higher pressures that occurs with the lower-K_zz case. The higher-pressure photolysis region in the low-K_zz case also enhances the conversion of NH₃ into HCN, so NH₃ is notably depleted and HCN is correspondingly enhanced at observable pressure levels in the low-K_zz case. Although CH₄ also participates in this HCN formation, methane is much more abundant than ammonia to begin with (because of the recycling of hydrocarbons to methane at surface conditions; see Section 3.2), so the loss to HCN has little effect on the CH₄ abundance. Variations in K_zz do not affect our main conclusion that species in group 1 such as NH₃ and HCN are still sensitive to 1 bar and 10 bar surfaces and have different mixing ratios compared to the no-surface case in the observable part of the atmosphere. Species in group 2 and 3 are still only sensitive to 1 bar surfaces.

Overall, our main qualitative conclusions in Section 3.2 remain true for species in different groups with the changed T_int, semimajor axis, and K_zz profiles. A very shallow, cool 1 bar surface would generally lead to decreased levels of NH₃, HCN, CH₄, C_x H_y , and H₂O and increased levels of CO compared to the no-surface case. However, the increased levels of CO₂ for the 1 bar surface case become more muted for the hotter planet at half K2-18b's orbital distance. A 10 bar surface would lead to decreased levels of NH₃ and HCN, but deeper surfaces at pressures beyond 100 bar would lead to the same results as the no-surface case.