PHOTOCHEMISTRY IN TERRESTRIAL EXOPLANET ATMOSPHERES. III. PHOTOCHEMISTRY AND THERMOCHEMISTRY IN THICK ATMOSPHERES ON SUPER EARTHS AND MINI NEPTUNES

Figure 1 schematically show the architecture of our photochemistry–thermochemistry kinetic-transport model for thick atmospheres on exoplanets. We design our model to have two levels of sophistication: the first level is a thermochemical equilibrium model to compute the atmospheric composition at thermochemical equilibrium, with the temperature–pressure profile computed by a coupled radiative–convective model; the second level, beyond the thermochemical equilibrium model, is a kinetic-transport model that treats the effects of vertical mixing and photochemical processes on the molecular composition, with the temperature–pressure profile self-consistently computed based on the molecular composition from disequilibrium chemistry. The first-level thermochemistry model provides appropriate initial conditions, including the atmosphere's thermal structure and molecular composition, for the second-level kinetic-transport model.

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A unique feature in our photochemistry–thermochemistry model for non-H₂-dominated thick atmospheres is that the model does not require specification of the main component of the atmosphere (nor the mean molecular mass), and instead, the model takes the elemental abundances as the input parameters. All previous photochemistry models assume a specific dominant gas (and therefore mean molecular mass) and seek steady-state abundances of trace gases in the fixed background atmosphere. However, for applications to super Earths, one cannot assume any specific dominant gas, and the mean molecular mass needs to be self-consistently determined. We provide for the first time such a feature in our photochemistry–thermochemistry code. In the first-level thermochemistry model that includes a thermochemical equilibrium routine and a radiative–convective routine, we use a pressure level grid so that the mean molecular mass is no longer required. The mean molecular mass is synthesized from the thermochemical equilibrium composition profile and then used to transform the pressure grid to an altitude grid. In the second-level photochemistry–thermochemistry model, we perform kinetic-transport simulation on a pressure–temperature–altitude profile which itself is updated by the radiative–convective calculation. Our approach eliminates the need to specify a background atmosphere for kinetic-transport simulations of thick atmospheres, which makes our model uniquely suitable for applications in the study of super Earths and mini Neptunes.

2.1.1. Thermochemistry Model

2.1.2. Kinetic-transport Model

The kinetic-transport model solves the one-dimensional continuity-transport equation for the steady state, viz.,

$$\begin{equation} \frac{\partial n}{\partial t} = P - L - \frac{\partial \Phi }{\partial z}, \end{equation} \tag{ 1 }$$

where n is the number density for a certain species (cm⁻³), z is the altitude, P and L are the production and loss rates of the species (cm⁻³ s⁻¹), and Φ is the vertical transport flux of the species (cm⁻² s⁻¹). The production and loss rates are the summary of all contributions from relevant chemical and photochemical reactions in the atmosphere. The transport flux that couples different layers of the atmosphere is parameterized by eddy diffusion and molecular diffusion, i.e.,

$$\begin{equation} \Phi =-K_{\rm zz}N\frac{\partial f}{\partial z} - DN\frac{\partial f}{\partial z} +Dn\left (\frac{1}{H_0}-\frac{1}{H}-\frac{\alpha _{\rm T}}{T}\frac{dT}{dz}\right), \end{equation} \tag{ 2 }$$

where K_zz is the eddy diffusion coefficient (cm² s⁻¹), D is the molecular diffusion coefficient (cm² s⁻¹), N is the total number density of the atmosphere, f ≡ n/N is the mixing ratio of the species, H₀ is the mean scale height, H is the scale height of the species, T is the temperature (K), and α_T is the thermal diffusion factor. The first term of Equation (2) represents eddy diffusion, and the last two terms represent molecular diffusion. Equations (1) and (2) are solved numerically by the inverse-Euler method with the lower boundary condition set by thermochemical equilibrium.

Physical processes presented by P, L, and Φ in Equation (1) are competing and which one dominates depends on the temperature and pressure, i.e., altitude. Deep in the atmosphere, P and L are the dominant terms, because they increase with pressure and temperature, and the steady-state condition becomes P = L, i.e., thermochemical equilibrium. Near the top of the atmosphere, photochemical processes contribute dominantly to the P and L terms. The effect of photochemical processes confines to pressure levels above 0.1 bar, because ultraviolet photons that could dissociate atmospheric molecules usually only penetrate to the pressures of 0.1 bar due to Rayleigh scattering and absorption by molecules in the upper atmosphere. In the intermediate pressure levels, the transport flux Φ can be the major source and sink for species as compared with photochemical and chemical reactions. The reason is that the reactive radicals produced by photochemistry are usually not abundant because of the lack of photons that penetrate to these altitudes and that the temperature and pressure (and therefore reaction rates) are usually not high in the intermediate pressures. In all, when all production and loss mechanisms are properly taken into account in P, L, and Φ, Equation (1) is the governing equation for molecular compositions in any atmosphere.

We have extended the photochemistry model described in Hu et al. (2012) to the pressure regime in which thermochemical equilibrium holds. To make the model applicable to the pressure regime of thermochemical equilibrium, we include the contribution of the reverse equation for each forward equation into the production and loss terms in Equation (1). The reverse reactions are the reversal of the chemical reactions whose kinetic rates have been measured or computed for the studies of Earth and planetary atmospheres (chosen as forward reactions). The kinetic rates of reverse reactions (k_r) and forward reactions (k_f) are linked by the difference in the Gibbs free energy of formation (Δ_fG°) of the reactants and the products as

$$\begin{eqnarray} &&k_r = k_f \exp {\left [\frac{\Delta _fG^{\circ }({\rm products})-\Delta _fG^{\circ }({\rm reactants})}{RT}\right ]} (k_b^{\prime }T)^{n_p-n_r}, \nonumber \\ \end{eqnarray} \tag{ 3 }$$

where R is the gas constant, T is the temperature (K), $k_b^{\prime }=1.38065\times 10^{-22}$ bar cm³ K⁻¹ is the Boltzmann constant, and n_p and n_r are the number of products and reactants, respectively (Visscher & Moses 2011).

Using Equation (3), we calculate the rates of the reverse reaction of each forward reaction in the reaction list of Hu et al. (2012) that includes bimolecular reactions, termolecular reactions, and thermodissociation reactions. The Gibbs free energies of formation are taken from the NIST-JANAF database (Chase 1998), Burcat & Ruscic (2005), and Visscher & Moses (2011). For a number of reactions, there are empirical measurement for both forward and reverse reactions, which provide an opportunity of validating this computation scheme. Whenever possible, we adopt the empirical kinetic rate that has the widest temperature range (i.e., define as the forward reaction), compute the reverse reaction rate, and compare the reverse rate with its empirical measurements. For all tested reactions, we find agreement within one order of magnitude, which validates our calculation of reverse reaction rates.

Another update to our reaction network so that the model is applicable to high pressures is that we have included the high-pressure limit rates for all three-body reactions and dissociation reactions. In the reaction list of Hu et al. (2012), many three-body reactions only have low-pressure limit rates, which are appropriate for applications to thin atmospheres. We have added the high-pressure limit rates for the three-body reactions and thermo-dissociation reactions, based on recommended rates of the NIST Kinetics database,⁶ Baulch et al. (1994, 2005), Jasper et al. (2007), and Moses et al. (2011).

We have coupled our kinetic-transport model to the gray-atmosphere radiative–convective model. Since the composition (and therefore the mean molecular mass) might change as the photochemistry code steps forward, the temperature–pressure profile and the pressure–altitude conversion need to be updated to keep the atmosphere in radiative equilibrium and hydrostatic equilibrium. We therefore iteratively run the kinetic-transport routine and the radiative–convective routine for this update. In practice, the altitude grid is not re-calculated for each time step in kinetic-transport simulations. Instead, as chemistry only has secondary dependency on the atmospheric temperature, we run the kinetic-transport code to convergence and use the radiative–convective code to calculate a temperature–pressure–altitude profile based on the converged kinetic-transport result. Then, the new atmospheric profile, with the new mean molecular mass incorporated, is provided to the kinetic-transport code for another run. Starting from the atmospheric structure profile provided by the first-level thermochemistry model, we find that the temperature profile typically converges with the disequilibrium chemistry composition within three iterations. Here, by convergence, we practically mean that the variation of temperature between two successive iterations is within 2%. The end results of atmospheric composition and temperature profile satisfy radiative–convective equilibrium, hydrostatic equilibrium, and the detail balance between production and loss by chemical and photochemical processes and vertical transport.

For the current model, we focus on thick atmospheres on warm and hot super Earths/mini Neptunes, in which water vapor will not condense. Table 1 tabulates the critical temperatures of common gases in planetary atmospheres. Water vapor, having a critical temperature of 647 K, stands out as having a much higher critical temperature than any other common volatiles made of C, H, O, and N elements. Therefore, it is possible that, for a certain class of planets that have equilibrium temperatures lower than 647 K, water vapor could condense to form oceans, and then the planets could be potentially habitable. For this paper, we focus on the atmospheres in which water remains in its gas phase. We emphasize that most of the transiting super Earths and mini Neptunes discovered so far fall within our consideration. Note that some minor constituents of the atmosphere, not included in our photochemistry–thermochemistry model, might condense out to form layers of cloud or haze. In fact, for super Earth/mini Neptune GJ 1214 b and perhaps other loss-mass exoplanets potential layers of condensates could mask molecular features in their transmission spectra and affect interpretation of the spectra (e.g., Fortney 2005; Benneke & Seager 2012; Morley et al. 2013).

Table 1. The Critical Temperature and Critical Pressure for Common Building Blocks for Planetary Thick Atmospheres

Substance	Critical Temperature	Critical Pressure
	(K)	(bar)
H2	33.2 ± 0.2	13.00 ± 0.01
H2O	647 ± 2	220.64 ± 0.05
CH4	190.6 ± 0.3	46.1 ± 0.3
CO	134.5 ± 0.4	35.0 ± 0.3
CO2	304.18 ± 0.04	73.80 ± 0.15
O2	154.58 ± 0.0015	50.43 ± 0.005
C2H2	308.3 ± 0.1	61.4 ± 0.1
C2H4	282.5 ± 0.5	50.6 ± 0.5
C2H6	305.3 ± 0.3	49 ± 1
N2	126.19 ± 0.01	33.978 ± 0.007
NH3	405.4 ± 0.1	113.00 ± 0.05

Note. The data are compiled from the NIST Chemistry WebBook (http://webbook.nist.gov/chemistry/).

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2.1.3. Synthetic Spectrum Model

For a super Earth/mini Neptune with known stellar irradiation level, the controlling factors for the molecular composition of its thick atmosphere are the elemental abundance, the efficiency of vertical mixing, and the internal heat flux. The elemental abundance determines the molecular composition at thermochemical equilibrium, the efficiency of vertical mixing determines to which extent vertical transport brings up gases from the thermochemical equilibrium regime, and internal heat flux determines the temperatures at high pressures that affect the compositions at thermochemical equilibrium. The elemental abundance rather than the background molecular composition is a fundamental parameter in our models for thick atmospheres, because an arbitrary combination of molecules may not be chemically stable in thick atmospheres (a point that will be discussed later in Section 5).

We emphasize the uniqueness of the photochemistry–thermochemistry solution. In mathematical terms, the mixing ratio profiles at the steady state obey the continuity equation, a second-order ordinary differential equation whose solution is uniquely determined by the boundary conditions at both ends. For the upper boundary conditions, we place a zero-flux lid at the pressure level of 10⁻³ Pa for all gases except H and H₂, for which we apply the diffusion-limited escape rates. As such, our solutions of atmospheric chemical composition, for a certain planetary scenario with an assigned value for the eddy diffusion coefficient, are uniquely determined by the lower boundary conditions, for which we apply the thermochemistry equilibrium compositions. We have run a number of test cases to verify the uniqueness from model simulations. For example, for an H:O:C ratio of 2:2:1, the molecular composition can be either 50% H₂ 50% CO₂ or 50% H₂O 50% CO. Under thermochemical equilibrium, the deep atmosphere will be composed of 50% H₂ and 50% CO₂; in a separate simulation, we start with 50% H₂O 50% and CO as the initial condition, and the system naturally evolves to the steady-state composition of 50% H₂ 50% CO₂ at high pressures, i.e., the unique solution. The photochemistry–thermochemistry solution of the atmospheric chemical composition on an exoplanet is the only steady-state solution for a certain elemental abundance, vertical mixing rate, and internal heat flux.

We have validated our photochemistry–thermochemistry model in pressure regimes for different physical processes. The model is applicable to the low pressures where photochemistry dominates, the intermediate pressures where vertical transport dominates, and the high pressures where thermochemical equilibrium dominates. For the low pressures where photochemistry dominates, the model in this paper reduces to the photochemistry model for thin atmospheres, which has been validated in Hu et al. (2012). For the high pressures where thermochemical equilibrium dominates, we find that our kinetic model that balances all forward and reverse reactions gives identical results compared with direct minimization of the global Gibbs free energy (Figures 2 and 3). This straightforward mathematical validation implies that our calculation of reverse reaction rates is correct and that our model is applicable for the regime of thermochemical equilibrium.

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For the intermediate pressures in which vertical transport dominates, direct mathematical validation is not possible because the steady-state solution is unknown. Instead, we seek to validate our model in this regime by reproducing the results of observations of planets and other models. We have simulated the atmosphere of Jupiter and the atmosphere of hot Jupiter HD 189733 b to compare with observations. We focus on reproducing the effect of vertical transport on the $\mathrm{CO \rightleftharpoons CH4}$ conversion in these atmospheres that have very different temperatures (Figures 2 and 3). We describe the details of these model tests below.

For the deep atmosphere of Jupiter, the most important feature relevant for this investigation is the enhancement of the CO mixing ratio in the observable parts of the atmosphere due to vertical transport. Our model correctly predicts this enhancement in comparison with the observed mixing ratio of CO (Figure 2). We have also compared our simulated CO mixing ratios with those of the latest model for Jupiter's deep atmosphere (Visscher et al. 2010) and found agreement within a factor of two. The remaining discrepancy may be due to updated kinetic rates of several reactions that we have adopted. Compared with reaction rates used in Visscher et al. (2010) and Moses et al. (2011), we found that the rates for reaction $\mathrm{CH_3O \longrightarrow CH_2O + H}$ have updated recommended values and that the discrepancy in these rates can account for the minor discrepancy in the $\mathrm{CO \rightleftharpoons CH4}$ conversion rates between our models and the models of Visscher et al. (2010). We have taken for this reaction the low-pressure limit rate from Baulch et al. (1994) and the high-pressure limit rate from Curran (2006); both recommended values are based on extensive literature reviews.

To test the $\mathrm{CO \rightleftharpoons CH4}$ conversion computation for a warmer planet than Jupiter, we have simulated the H₂-dominated atmosphere on hot Jupiter HD 189733 b and compared our predictions with the molecular compositions derived from observations (Figure 3). We find agreement in the amounts of CH₄ and CO₂ at the pressure levels of 0.001–1 bar between our models and the interpretation of observations of Madhusudhan & Seager (2009). Because of limited data available for exoplanets including HD 189733 b, the observational constraints on the molecular composition are poor. To further test our model, we have compared our results with a similar suite of simulations by Visscher & Moses (2011) and found agreement to within a factor of two. The efficiency of vertical mixing affects the steady-state mixing ratios of methane and other hydrocarbons significantly in the observable parts of the atmosphere. In particular, the eddy diffusion coefficient needs to be no greater than 10⁸ cm² s⁻¹ to produce a methane mixing ratio consistent with the observationally derived upper limit.

Furthermore, we have also compared our results with the main features of H₂-dominated atmospheres simulated by Miller-Ricci Kempton et al. (2012) for super Earth/mini Neptune GJ 1214 b. For a solar elemental abundance, we simulate the steady-state atmosphere on GJ 1214 b with C, H, O, N chemistry. Our simulations compare nicely with Miller-Ricci Kempton et al. (2012) in both qualitative and quantitative behaviors of H₂O, CH₄, NH₃, and N₂. We see also photochemical HCN formation in the upper part of atmosphere, similar to Miller-Ricci Kempton et al. (2012); however, we find 1-order-of-magnitude higher concentration of HCN and 1-order-of-magnitude lower concentration of C₂H₂ and C₂H₄ than Miller-Ricci Kempton et al. (2012). We suspect that this is because we have included a more complete set of chemical and photochemical reactions that allows the formation of C-N bond as Moses et al. (2011), and then a larger fraction of CH₃ from methane photolysis is converted into HCN instead of forming C₂H₂ and C₂H₄. In summary, we find our model is able to simulate H₂-dominated thick atmosphere of irradiated exoplanets; and we here extend the analysis to irradiated thick atmospheres that are not H₂-dominated.

With the photochemistry–thermochemistry model, we simulate the molecular composition of thick atmospheres on super Earths and mini Neptunes for wide ranges of temperature and elemental abundance. We focus mostly on exploring different temperatures and elemental abundances as they are the most important parameters for the bulk compositions of the thick atmospheres. Furthermore, we also explore the effect of stellar spectrum and eddy diffusivity. For each scenario, we use the thermochemistry–photochemistry model to compute the steady-state molecular composition from 10⁴ bar to 10⁻⁸ bar. We verify that the lower boundary at 10⁴ bar is sufficient to maintain thermochemistry equilibrium at the lowest atmosphere layer for each simulation. Typically, we find it suitable to assign O(¹D), C, and ¹CH₂ to be "fast species" in the simulations for H₂-dominated cases, and O(¹D), ¹CH₂, and CH₂O₂ to be "fast species" in the simulations for non-H₂-dominated cases. The specifics and the rationale for exploring the relevant parameters are outlined in the following.

Elemental abundances of the atmosphere. With the photochemistry–thermochemistry model, we simulate thick atmospheres of exoplanets with a variety of C–H–O elemental abundances. We focus on the C–H–O chemistry as they are the most common elements in the universe. In a C–H–O system, the elemental abundance can be characterized by the hydrogen abundance (defined by number, and denoted as X_H) and the carbon versus oxygen ratio (denoted as X_C/X_O). We explore thick atmospheres being hydrogen-rich (X_H ⩾ 0.7), hydrogen-intermediate (0.3 < X_H < 0.7), and hydrogen-poor (X_H ⩽ 0.3); and we also explore the atmospheres with very different C/O ratios ranging from 0.1 to 10. To be specific, the grid for X_H is 0.99, 0.7, 0.5, 0.3, and 0.01; and the grid for X_C/X_O is 10, 2, 1, 0.5, and 0.1. This parameter exploration is reasonable, considering the masses of the elemental building blocks of the thick atmospheres. Taking GJ 1214 b as an example, the mass of a 1000-bar atmosphere is 10⁻³ of the planet's mass. If the atmosphere has X_H = 0.5 and X_C/X_O = 2, the mass of hydrogen, carbon, and oxygen in the atmosphere is 7.3 × 10⁻⁵, 5.8 × 10⁻⁴, 3.9 × 10⁻⁴ of the planet's mass. The masses of these building blocks for the thick atmosphere are reasonable.

Incident stellar irradiation. The incident stellar irradiation is specified in terms of the irradiation temperature (T_irr) for the calculation of temperature profiles. The irradiation temperature is defined as $\sigma T_{\rm irr}^4 \equiv ({L_{\rm star}}/{4\pi a^2})$, where σ is the Stefan–Boltzmann constant, L_star is the star's luminosity, and a is the planet's semi-major axis. We here explore the molecular composition of thick atmospheres having an irradiation temperature of 770 K, 1000 K, 1200 K, 1400 K, 2000 K, and 2754 K: 770 K is the irradiation temperature of GJ 1214 b, and 2754 K is the irradiation temperature of 55 Cnc e. For different types of stars that have different luminosities, an irradiation temperature corresponds to different semi-major axes of the simulated planet. For a Sun-like G2V star as the parent star, our grid of irradiation temperature corresponds to semi-major axes of 0.20, 0.12, 0.082, 0.060, 0.030, and 0.016 AU. For an M star like GJ 1214 as the parent star, our grid of irradiation temperature from 770 K to 1400 K corresponds to semi-major axes of 0.014, 0.0085, 0.0059, and 0.0043 AU. We assume zero planetary albedo and full heat redistribution for the calculation of temperature profiles, so the equilibrium temperature T_eq is related to the irradiation temperature as T_eq = (1/4)^1/4T_irr. The specific choices on the albedo and the heat redistribution fraction do not affect the generality of our results because they are degenerate with T_irr under the gray-atmosphere approximation (Guillot 2010).

Intrinsic temperature. We assign an intrinsic temperature (T_int) for the temperature–pressure profile calculation in each scenario to specify the internal heat flux from a planet. The relation between the internal heat flux (F_int) and the intrinsic temperature is $F_{\rm int} = \sigma T_{\rm int}^4$. The parameterization of intrinsic temperature has been widely used for simulating temperature–pressure profile of extrasolar gas giants, and appropriate values for the intrinsic temperatures can vary from a few tens K to a few hundreds K depending on the evolution history of the planet (e.g., Marley et al. 2007; Fortney et al. 2008). For super Earths and mini Neptunes, the intrinsic temperatures are unknown and rely on future observations to be determined. We here consider a fiducial intrinsic temperature of 35 K, which is the intrinsic temperature corresponding to the geothermal heat flux. In addition, we explore the effect of an intrinsic temperature being 90 K (similar to the intrinsic temperature for Jupiter) and 180 K for some scenarios.

Stellar spectral type. For GJ 1214 b models, we use the latest Hubble Space Telescope (HST) measurement of the UV spectrum of GJ 1214 (France et al. 2013) and the NextGen simulated visible-wavelength spectrum of an M star having parameters closest to those of GJ 1214 (i.e., effective temperature of 3000 K, surface gravity log(g) = 5.0, and metallicity [M/H] = 0.5; Allard et al. 1997). We also explore the effect of stellar UV flux by assuming a Sun-like G2V star as the parent star for a GJ 1214 b–like exoplanet. For the Sun-like star we use the standard reference solar spectrum (Air Mass Zero) published by the American Society for Testing and Materials.⁷ For the HD 97658 b and 55 Cnc e models, we use a black body spectrum of effective temperature 5200 K with additional Sun-like chromospheric emission in UV wavelengths.

Eddy diffusivity and molecular diffusivity. We explore eddy diffusion coefficients ranging from 10⁶ to 10⁹ cm² s⁻¹, reasonable values for deep atmospheres according to the free-convection and mixing-length theories (Gierasch & Conrath 1985; Visscher et al. 2010). The eddy diffusion coefficients are assumed to be constant throughout the atmosphere. Such an assumption does not consider the possibility of a temperature inversion that may lower the eddy diffusion coefficients by more than 3 orders of magnitude at ∼0.1 bar (e.g., Gladstone et al. 1996 for Jupiter). Our models may therefore underestimate the amounts of potential photochemical products in the upper atmosphere; however, this paper is mainly concerned with the transport-driven disequilibrium in the deep atmosphere, for which our assumption regarding the eddy diffusion coefficients is sufficient. In addition to eddy diffusion, our model takes molecular diffusion of H and H₂ into account, even though the effect of molecular diffusion for the visible part of the atmosphere (10⁻⁴ to 1 Bar) is quite minimal. For an eddy diffusion coefficient ranging from 10⁶ to 10⁹ cm² s⁻¹, the homopause (defined as where a molecular diffusion coefficient equates to an eddy diffusion coefficient) ranges in 0.2–0.0002 Pa for planets as irradiated as GJ 1214 b, and in 2.3–0.0023 Pa for planets as irradiated as 55 Cnc e. Molecular diffusion is therefore only important for the top layers of the atmospheres on super Earths/mini Neptunes. The effect of molecular diffusion is to enrich H and H₂ and to lower the mean molecular mass above the homopause.

We classify thick atmospheres on super Earths/mini Neptunes broadly into hydrogen-rich atmospheres, water-rich atmospheres, oxygen-rich atmospheres, and hydrocarbon-rich atmospheres, depending on the hydrogen abundance and the carbon to oxygen abundance ratio. The classification is based on the fraction of the gases that have mixing ratios in the order of 0.1 (i.e., the major gases) in the thick atmospheres. If a thick atmosphere is not H₂-dominated, we find that the dominated C–H–O molecule at the potentially observable levels (1 ∼ 100 mbar) can be H₂O, CO₂, CO, CH₄, other hydrocarbons (C₂H₄ and C₂H₂), or even O₂. This is the first complete list of major molecular building blocks made of C, H, O elements for thick atmospheres on super Earths and mini Neptunes, and the proposition that unsaturated hydrocarbons including C₂H₂ and C₂H₄ can be the dominant gases in an exoplanet atmosphere is also the first. Figure 4 summarizes the parameter regimes for each type of atmosphere based on the hydrogen abundance and the carbon to oxygen abundance ratio; Figures 5 and 6 show an example of this classification for super Earth/mini Neptune GJ 1214 b and 55 Cnc e, respectively; and Figure 7 illustrates the dependency of this classification regime on temperature. These figures show the theoretical range of atmospheric chemical composition; different types of atmosphere may not be equally likely in reality.

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Before describing the non-H₂-dominated atmospheres, we first show that if X_H > 0.7, thick atmospheres of super Earths and mini Neptunes contain abundant H₂ and, therefore, have the same chemical behaviors as atmospheres of gas giants. Previous thermochemistry and photochemistry results regarding the thick atmospheres on gas giants are valid in these cases, including the following: CH₄ is the dominant carbon species at equilibrium temperatures lower than ∼1000 K; CO is the dominant carbon species at equilibrium temperatures higher than ∼1000 K (Line et al. 2010; Visscher & Moses 2011; Madhusudhan 2012); and H₂O becomes scarce as X_C/X_O exceeds 1 at the high temperatures that favor CO over CH₄ (e.g., Kuchner & Seager 2005; Kopparapu et al. 2012; Madhusudhan 2012). We confirm all these behaviors in our simulations for super Earths and mini Neptunes having hydrogen-rich atmospheres (see Figure 7). In particular, we observe at the low temperatures, where CH₄ is the dominant carbon carrier and H₂O is the dominant oxygen carrier, that the ratio CH₄/H₂O is equal to the C/O ratio (Figure 7), and in such cases, the eddy diffusion coefficients have no effects on the abundances of CH₄ or H₂O in the observable parts of the atmospheres. At the high temperatures where CO is the dominant carbon carrier, the mixing ratio of H₂O drops dramatically when X_C/X_O exceeds 1 due to the fact that most oxygen atoms have to be bound with carbon atoms. The exact irradiation temperature for the CH₄–CO transition also depends on the internal heat flux; and the exact mixing ratios of trace species, for example, CO at the low temperatures and CH₄ at the high temperatures, depend on the strength of eddy mixing and the UV flux of the parent star.

Now we turn to non-H₂-dominated atmospheres. If the hydrogen abundance (X_H) is lower than 0.7 ∼ 0.8, H₂ is no longer the dominated gas in the atmosphere, and the atmosphere will contain abundant water vapor for low X_C/X_O and hydrocarbons (i.e., CH₄, C₂H₂, and C₂H₄) for high X_C/X_O. The water-rich atmospheres occur when X_C/X_O ⩽ 0.5, and the hydrocarbon-rich atmospheres occur when X_C/X_O ⩾ 2, for an equilibrium temperature ranging from 500 to 2000 K (Figure 7). For the intermediate cases (0.5 < X_C/X_O < 2), the atmosphere will have abundant CO and H₂, and their fractions are sensitive to X_H. In addition, CH₄, CO₂, and H₂O can also take a significant fraction, and their relative abundances depend on the temperature and the elemental abundance of the atmosphere (Figure 7). A general trend in this regime is that CO and C₂H₂ become more and more abundant and CH₄ and CO₂ become less and less abundant with increasing temperatures (Figure 7). If the hydrogen abundance (X_H) is lower than 0.3 (e.g., for an extremely evolved super Earth on which most atmospheric hydrogen has been lost), significant amounts of O₂ will build up in the atmosphere when X_C/X_O < 0.5. We therefore classify super Earth atmospheres according to the hydrogen abundance and the carbon to oxygen abundance ratio, which includes hydrogen-rich atmospheres, water-rich atmospheres, hydrocarbon-rich atmospheres, oxygen-rich atmospheres, and the atmospheres that could have similar amounts of CO, H₂, CH₄, CO₂, and H₂O (Figure 4).

Non-H₂-dominated atmospheres differ from H₂-dominated atmospheres mostly in the dependency on the carbon to oxygen abundance ratio. In general, the composition of a non-H₂-dominated atmosphere is much more sensitive to the carbon to oxygen abundance ratio than that of a H₂-dominated atmosphere (Figure 8). This is because when the atmosphere is not hydrogen-rich, the composition is first and foremost constrained by the limited supply of hydrogen. To better illustrate this point, let us consider how the H₂O versus CO abundance ratio depends on X_C/X_O for an example (see the upper panel of Figure 8). For H₂-dominated atmospheres at the irradiation temperature less than ∼1200 K, the main carbon-bearing species is CH₄, and CO is in equilibrium with H₂O; therefore, the H₂O versus CO abundance ratio only has week dependency on X_C/X_O. However, for non-H₂-dominated atmospheres at similarly low temperatures, CO must serve as one of the carbon carriers and then increasing X_C/X_O will result in more fractions of oxygen to be bound with carbon, and less fractions to be bound with hydrogen to form H₂O. In all, while the carbon to oxygen abundance ratio affects the amounts of minor gases in H₂-dominated atmospheres, the carbon to oxygen abundance ratio controls the abundances of major gases in non-H₂-dominated thick atmospheres.

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One might ask how this classification scheme depends on the parameters other than the elemental abundance and the irradiation temperature, e.g., the internal heat flux that affects the temperature at depth, the eddy diffusivity that determines the efficiency of vertical mixing, and the UV flux that determines the efficiency of photodissociation. Based on our numerical experiments, we find that (1) the effect of the internal heat flux is to increase or decrease the temperature at the quenching pressure, which to a certain extent leads to the same effect as increasing or decreasing the irradiation level; (2) the effect of changing eddy diffusivity and stellar UV flux in reasonable ranges is not critical for the species that has mixing ratios in the orders of 10⁻¹ ∼ 10⁻² but may be critical for other minor species. The properties presented by Figure 7 can therefore be considered to be general, if the irradiation temperature is regarded as a general proxy for the atmospheric temperature that could also contain contribution from internal heating. Because the effects of the internal heat flux, the eddy diffusivity, and the stellar spectrum on minor species depend on specific atmospheric scenarios, we defer the discussion of that aspect to the subsequent sections dedicated to specific types of atmospheres.

Interestingly, for certain endmember scenarios of non-H₂-dominated thick atmospheres, we find that the elemental abundance uniquely determines the amounts of major components in the atmosphere for a wide range of temperatures, and we derive analytical formulae of the molecular compositions for those scenarios. Table 2 tabulates an exhaustive list of parameter regimes of the elemental abundance, and the derived formulae for mixing ratios of major components in these regimes. The fundamental principle that we use here is simply that all H, C, and O atoms in the atmosphere have to be bound to form a limited set of thermochemically stable molecules (e.g., H₂, H₂O, CO₂, CO, CH₄, C₂H₄, C₂H₂, O₂, etc.), to the extent that molecular forms of C, H, and O elements are thermochemically preferred over atomic forms (which typically corresponds to an equilibrium temperature of less than ∼2500 K) and that water vapor does not condense in the atmosphere (which typically corresponds to an equilibrium temperature of greater than ∼300 K). In the cases of X_C ≪ 1 and the cases of X_H ≪ 1, the abundances of major gases in the atmosphere are uniquely determined by the elemental abundance (Table 2).

Table 2. Main Components of Thick Atmospheres on Super Earths and Mini Neptunes as a Function of the Abundances of Hydrogen, Oxygen, and Carbon

Parameter Regime	Main Components	Mixing Ratio Formulae	Corresponding Classification
XH ∼ 1, XO ≪ 1, XC ≪ 1	H2	$X_\mathrm{H_2}\sim 1$	Hydrogen-dominated atmospheres
XH ≪ 1, XO ∼ 1, XC ≪ 1	O2	$X_\mathrm{O_2}\sim 1$	Oxygen-rich atmospheres
XH ∼ 1, XO ∼ 1, XC ≪ 1, XH ⩾ 2XO	H2, H2O	$X_\mathrm{H_2}=1-\frac{2X_\mathrm{O}}{X_\mathrm{H}}$, $X_\mathrm{H_2O} = \frac{2X_\mathrm{O}}{X_\mathrm{H}}$	Water-dominated atmospheres
XH ∼ 1, XO ∼ 1, XC ≪ 1, XH < 2XO	H2O, O2	$X_\mathrm{H_2O}=\frac{2X_\mathrm{H}}{X_\mathrm{H}+2X_\mathrm{O}}$, $X_\mathrm{O_2}=\frac{2X_\mathrm{O}-X_\mathrm{H}}{X_\mathrm{H}+2X_\mathrm{O}}$	Water-dominated atmospheres
XH ∼ 1, XO ≪ 1, XC ∼ 1	H2, CH4, C2H2, C2H4, C2H	Temperature dependent	Hydrocarbon-rich atmospheres
XH ≪ 1, XO ∼ 1, XC ∼ 1, XC ⩽ XO ⩽ 2XC	CO, CO2	$X_\mathrm{CO}=2-\frac{X_\mathrm{O}}{X_\mathrm{C}}$, $X_\mathrm{CO_2} = \frac{X_\mathrm{O}}{X_\mathrm{C}}-1$	CO–CO2 atmospheres
XH ≪ 1, XO ∼ 1, XC ∼ 1, XO > 2XC	CO2, O2	$X_\mathrm{CO_2} = \frac{2X_\mathrm{C}}{X_\mathrm{O}}$, $X_\mathrm{O_2} = 1-\frac{2X_\mathrm{C}}{X_\mathrm{O}}$	Oxygen-rich atmospheres
XH ∼ 1, XO ∼ 1, XC ∼ 1	CO, H2, H2O, CH4, CO2	Temperature dependent

Notes. The table lists all plausible combinations of H, O, and C, in the orders of one-element dominance, two-element dominance, and three-element dominance, except for the case of X_H ≪ 1, X_O ≪ 1, X_C ∼ 1 as elemental carbon is not in the gaseous phase for the temperatures of interest. The main components are stable molecules made of H, O, and C, and the table is valid to the extent that the molecular forms are thermochemically favored over elemental forms and water vapor does not condense in the atmosphere.

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Finally, we outline the key molecules as remote-sensing probes for the atmospheric scenarios of super Earths and mini Neptunes as a cookbook for observers. Note that molecules such as H₂O and CO₂ can typically produce considerable features in an exoplanet spectrum even for very low abundances. For the purpose of the cookbook, we apply a mixing ratio threshold of 10⁻⁶ for considering H₂O, CO₂, and CH₄ to be abundant, and 10⁻⁴ for CO and hydrocarbons. The cookbook is mainly summarized from Figure 7, and the most significant effects of internal heating and photolysis are also included.

• 1.  
  H₂O is generally abundant in any thick atmosphere that has X_C/X_O ⩽ 1 and an irradiation temperature ranging from 700 to 2700 K. H₂O is not expected to have an observable abundance (i.e., a mixing ratio greater than 10⁻⁶) in any thick atmospheres that has X_C/X_O significantly greater than unity, except for those dominated by H₂ and having T_irr ⩽ 1200 K.
• 2.  
  The parameter space for which CO₂ is abundant (i.e., a mixing ratio greater than 10⁻⁶) is similar to the parameter space for H₂O; in other worlds CO₂ and H₂O should be generally expected to coexist. The exceptional parameter regime is H₂-dominated atmospheres with X_C/X_O ⩽ 0.5 and T_irr ⩽ 1200 K; in this regime, the atmospheres have abundant H₂O but not CO₂.
• 3.  
  CO is expected to be abundant (i.e., a mixing ratio greater than 10⁻⁴) in any thick atmosphere that has X_H ⩽ 0.7, X_C/X_O ⩾ 0.5, and an irradiation temperature ranging from 700 to 2700 K. Otherwise CO is not expected to be abundant in the atmosphere, unless the irradiation temperature is greater than 1200 K.
• 4.  
  CH₄ is not expected to have an observable abundance (i.e., a mixing ratio greater than 10⁻⁶) in any atmosphere that has T_irr > 1400 K (or, significant internal heating with T_int > 200 K) and X_C/X_O ⩽ 1, and CH₄ is generally abundant at cooler temperatures. The only scenario in which T_irr ⩽ 1400 K and yet methane is not abundant is the H₂O/CO₂-dominated atmosphere.
• 5.  
  Hydrocarbons (i.e., C₂H₂ and C₂H₄) are expected to be abundant (i.e., a mixing ratio greater than 10⁻⁴) in any atmospheres that have X_H ⩽ 0.7, X_C/X_O ⩾ 2, and an irradiation temperature ranging from 700 to 2700 K. Abundant hydrocarbons can also be expected in the atmospheres that have abundant CH₄ and efficient photolysis.

In the following two subsections, we present the results for the two new types of thick atmospheres on super Earths and mini Neptunes: water-rich atmospheres and hydrocarbon-rich atmospheres. Oxygen-rich atmospheres are described together with water-rich atmospheres as they both correspond to low X_C/X_O scenarios. We focus on the ranges of possible molecular compositions in these atmospheres, because it is the molecular compositions that control the observational properties of these atmospheres.

Water-rich atmospheres are interesting in particular because water is a substance fundamental for life. We have already shown that water-rich atmospheres emerge as an atmosphere with low X_C/X_O loses most of its free hydrogen (Figure 4). For low X_C/X_O, the atmosphere is a mixture of H₂ and H₂O when X_H ⩾ 2X_O and H₂O and O₂ when X_H < 2X_O (Table 2). In this section, we study the possible ranges of mixing ratios for both the main components and the minor components in water-rich atmospheres. The main components are important because they are directly controlled by the elemental abundances and they serve as the background atmosphere; and the minor components are also important because they may lead to significant, if not dominant, spectral features and they provide means to characterize vertical mixing and internal heating of a super Earth exoplanet.

We first consider the main components of water-rich atmospheres. Among the water-rich atmospheres, water-dominated atmospheres are defined as the atmospheres in which water is the most abundant gas. Our atmosphere models show that water-dominated atmospheres only occur when X_H ∼ 2X_O and X_C/X_O ≪ 1, a fairly small part of the parameter space of elemental abundances. Mixture of carbon, even at the solar X_C/X_O, would lead to the removal of most atmospheric water. As shown in Figure 9, when X_H = 0.5, X_C/X_O = 0.1, the atmosphere is dominated by water, with a trace amount of carbon in the form of CO₂. The water vapor abundance decreases dramatically as the atmosphere has more carbon (Figure 8). At the solar X_C/X_O, the atmosphere would be a mixture of H₂, CO, CO₂, CH₄, and H₂O, in which the water vapor mixing ratio is about 10% (Figure 9). Such an atmosphere is not water-dominated, but such an atmosphere shall still be considered water-rich, because a water vapor amount of even less than 10% would be very significant in the spectrum. A conceptual way to understand this sensitivity of water abundance on the carbon content is that for a wide temperature range, oxygen atoms tend to be bound with carbon atoms whenever available. In summary, water-rich atmospheres exist when X_C/X_O ⩽ 0.5, but water-dominated atmospheres exist only when X_C/X_O ≪ 0.5.

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The composition of the water-rich but not water-dominated atmospheres can be affected by the temperature, the efficiency of vertical mixing, and the stellar input spectrum (see Figures 7, 9, and 10). The mixing ratio of CH₄ is highly sensitive to the irradiation level and the internal heat flux. With an irradiation temperature of 770–1200 K and a small intrinsic temperature of 35 K, the mixing ratio of CH₄ can be as high as 10⁻² in a water-rich but not water-dominated atmosphere. Increasing the irradiation temperature to above 1200 K or the intrinsic temperature from 35 K to 90 K would decrease the CH₄ mixing ratio by several orders of magnitude (Figures 7 and 10). Therefore, CH₄ can be an effective probe for the temperature in the deep atmosphere. Other major constituents that have mixing ratios greater than 0.1 are not significantly affected by the temperature. The mixing ratios of CH₄ and CO can increase by a factor of a few and the mixing ratios of CO₂ and H₂O can decrease by a few tens of percent when the eddy diffusion coefficient decreases from 10⁹ to 10⁶ cm² s⁻¹ (Figure 9). Interestingly, using the solar spectrum that gives considerably more near UV fluxes than does an M dwarf spectrum, a significant fraction of H₂O and CO can be converted into CO₂ and H₂, while the atmosphere still remains a roughly equal mixture of H₂, CO, CO₂, and H₂O (Figure 9).

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We now turn to consider the minor components in the water-dominated atmospheres. The minor components of interest are, of course, the three stable forms of carbon, CH₄, CO, and CO₂. We here outline an analytical treatment for the carbon speciation in the water-dominated atmospheres, which is also applicable to study the thermochemical speciation of other elements in a given mixture of gases. When X_H ∼ 1, X_O ∼ 1, X_C ≪ 1, we may consider carbon as perturbation on a background atmosphere made of either H₂, H₂O, or H₂O, O₂ (Table 2). For carbon in a H₂–H₂O system, we have the following balanced reactions:

$$\begin{equation} \mathrm{H_2O + CH_4 \rightleftharpoons 3H_2 + CO}, \end{equation} \tag{ C1 }$$

$$\begin{equation} \mathrm{H_2O + CO \rightleftharpoons H_2 + CO_2}. \end{equation} \tag{ C2 }$$

Let K₁ be the equilibrium constant of reaction (C1), and K₂ be the equilibrium constant of reaction (C2). Note that K₁ and K₂ only depend on the temperature. The Law of Mass Action reads

$$\begin{eqnarray} &&\frac{X_\mathrm{CO}}{X_\mathrm{CH_4}} = \frac{K_1}{P^2}\frac{X_\mathrm{H_2O}}{X_\mathrm{H_2}^3}, \end{eqnarray} \tag{ 4 }$$

$$\begin{eqnarray} &&\frac{X_\mathrm{CO_2}}{X_\mathrm{CO}} = K_2\frac{X_\mathrm{H_2O}}{X_\mathrm{H_2}}, \end{eqnarray} \tag{ 5 }$$

in which X denotes the mixing ratio of a molecule and P is the atmospheric pressure in the unit of bar. Similarly for a H₂O–O₂ system,

$$\begin{equation} \mathrm{3O_2 + 2CH_4 \rightleftharpoons 4H_2O + 2CO}, \end{equation} \tag{ C3 }$$

$$\begin{equation} \mathrm{O_2 + 2CO \rightleftharpoons 2CO_2}. \end{equation} \tag{ C4 }$$

We have also

$$\begin{eqnarray} && \frac{X_\mathrm{CO}}{X_\mathrm{CH_4}} = \sqrt{\frac{K_3}{P}\frac{X_\mathrm{O_2}^3}{X_\mathrm{H_2O}^4}}, \end{eqnarray} \tag{ 6 }$$

$$\begin{eqnarray} && \frac{X_\mathrm{CO_2}}{X_\mathrm{CO}} = \sqrt{ K_4PX_\mathrm{O_2} }, \end{eqnarray} \tag{ 7 }$$

in which K₃ is the equilibrium constant of reaction (C3) and K₄ is the equilibrium constant of reaction (C4). The relative abundance of CH₄, CO, and CO₂ in thermochemical equilibrium with a predominantly hydrogen and oxygen atmosphere can be calculated with Equations (4)–(7), for a variety of temperatures and pressures. Figure 11 summarizes the result.

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We find that when the atmosphere is mainly a H₂–H₂O mixture (X_H > 2X_O), the main form of carbon is either CH₄ at low temperatures or CO at high temperatures (similar to gas giant atmospheres); when the atmosphere is mainly a H₂O–O₂ mixture (X_H < 2X_O), the main form of carbon is always CO₂, regardless of temperature (Figure 11; also see Figure 9 for an example). The transition from CH₄ to CO in a H₂–H₂O atmosphere depends on the temperature at the quenching pressure (i.e., the pressure at which the eddy mixing timescale is equal to the thermochemical equilibrium timescale) and the hydrogen abundance (see Figure 11). Therefore, the abundances of CH₄ and CO can probe the efficiency of eddy mixing and the flux of internal heating. A higher quenching pressure (in other words more efficient eddy mixing) would lead to more CH₄ and less CO in the observable atmosphere. When the atmosphere is depleted in molecular hydrogen, however, the dominant form of carbon is always CO₂ to the extent that carbon is a minor constituent in the atmosphere (X_C/X_O ≪ 0.5). In this case, the carbon speciation is insensitive to the effect of eddy mixing or the temperature structure of the atmosphere and, therefore, cannot serve as the probe to these physical quantities. In particular, CH₄ is thermochemically prohibited to exist in abundance in a H₂-depleted water-dominated atmosphere; therefore, nonexistence of CH₄ can be an indicator for water dominance in the atmosphere.

Finally, we comment on the rise of free oxygen in the water-rich atmospheres. Previous discussions have shown that when X_H < 2X_O, one would expect the atmosphere to be a mixture of H₂O, O₂, and CO₂ (see Figure 5). The free oxygen in the atmosphere is basically the left-over oxygen after forming H₂O and CO₂; in other words, free oxygen is expected when X_O > 0.5X_H + 2X_C. The rise of free oxygen we present here is a result of the loss of hydrogen rather than of the photon-driven processes that only affect the upper atmosphere at ∼10⁻⁵ bar (see the upper panel of Figure 9 for an example). The caveat here is that we do not consider any material exchange between the atmosphere and the surface (if there is a surface). The oxygen build-up from hydrogen loss could be prevented by active volcanic release of reduced gases or oxidative weathering of the surface, a process that has been proposed to have operated on Venus (e.g., Kasting 1997). A side point is that the OH radical would be very abundant in such H₂O–O₂–CO₂ atmospheres, with mixing ratios varying between 10⁻⁸ and 10⁻⁴. As OH radicals remove most other gases in the atmosphere rapidly, such a high concentration of OH necessarily implies that the any gas that reacts with OH without reforming pathways is not expected to be able to accumulate in the atmosphere. The H₂O–O₂–CO₂ atmospheres on super Earths are likely to be highly oxidized, with all other elements in their most oxidized form.

Another new type of super Earth atmosphere we find is the hydrocarbon-rich atmosphere. The hydrocarbon-rich atmospheres are the conjugate situation of the water-rich atmospheres; the difference here is that while the only stable "hydro-oxygen" is H₂O, there are many stable hydrocarbons. Based on our simulations, the potentially observable parts of a hydrocarbon-rich atmosphere may be composed of H₂, H, CH₄, C₂H₂, C₂H₄, and other higher-order hydrocarbons (Figures 5 and 6). As the number of possible molecules in hydrocarbon-rich atmospheres exceeds the number of major elements in the atmosphere (2), the main components are not uniquely set by the elemental abundance, and they depend on other factors including the efficiency of vertical mixing and the temperatures in the atmosphere.

For a super Earth/mini Neptune having a carbon-rich atmosphere, unsaturated hydrocarbons can become the dominant carbon-bearing gases in the atmosphere if the atmosphere loses most of its free hydrogen. When the atmosphere has free hydrogen (i.e., X_H > 4X_C), carbon is in the most reduced form, CH₄, if the planet receives a similar degree of irradiation as GJ 1214 b (see Figures 5 and 12). If X_C < X_H < 4X_C, the abundance of hydrogen in the atmosphere is not enough to saturate carbon, and C₂H₄ and C₂H₂ emerge as the main carbon carrier for decreasing hydrogen abundances (see Figures 5 and 12). If the planet receives a similar degree of irradiation as 55 Cnc e, CH₄ and C₂H₄ are not expected to exist in abundance in the atmosphere in any cases as they are thermochemically unstable at high temperatures, instead C₂H₂ would be the main carbon carrier (see Figures 6 and 12). For highly evolved carbon-rich atmospheres with X_H < X_C, high-order hydrocarbons with more than two carbon atoms should form in the atmosphere. Our chemistry model stops at C₂H_x and produces abundant C₂H in the atmosphere. This is a model artifact, and C₂H should be regarded as the precursor for more complex organics. It has been known that C₂H can be attached to existing hydrocarbons to form higher-order hydrocarbons and therefore hazes (e.g., Yung et al. 1984). We identify this caveat as an important aspect of further studies.

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The scarcity of hydrogen is the main driver for the formation of unsaturated hydrocarbon in oxygen-poor, carbon-rich, thick atmospheres of super Earths and mini Neptunes. We systemize the speciation of carbon in hydrocarbon-rich atmospheres in Figure 12, for which we have used thermochemistry simulations (i.e., minimizing global Gibbs free energy) to compute the relative abundance of hydrocarbons for different hydrogen abundances X_H and temperatures and pressures. For an intermediate X_H, significant, even dominant, amounts of C₂H₄ and C₂H₂ would be present in the atmosphere. For smaller and smaller X_H, the hydrocarbons in the atmosphere become less and less saturated (Figure 12). Interestingly, C₂H₆ cannot be the dominant carbon species in any cases. This is in contrast with the photochemical formation of unsaturated hydrocarbons (mostly in C₂H₆) in Jupiter's atmosphere (e.g., Gladstone et al. 1996) and Titan's atmosphere (e.g., Yung et al. 1984), which is driven by the photon-initiated dissociation of methane and is confined to pressures lower than 0.1 bar (i.e., the stratosphere). Here, the formation of unsaturated hydrocarbon is no longer a photochemical perturbation, but an inevitable result of hydrogen loss of the atmosphere. Unsaturated hydrocarbons can be the dominant gases in evolved carbon-rich atmospheres on super Earths, and they lead to spectral features that allow unique identification of carbon-rich atmospheres.

The mixing ratios of CH₄, C₂H₂, and C₂H₄ in the hydrocarbon-rich atmospheres also depend on the internal heat flux and the efficiency of vertical mixing. First, the internal heat flux can directly affect the abundance of hydrocarbons through controlling the temperature at the quenching pressure. The lower panel of Figure 10 shows a case of X_H = 0.5 and X_C/X_O = 2. This atmosphere is mainly composed of CO and CH₄, but also has a great deal of C₂H₂ and C₂H₄. Increasing T_int from 35 K to 180 K, the mixing ratio of C₂H₂ increases from 5 × 10⁻³ to 5 × 10⁻², and the mixing ratio of C₂H₄ decreases from 10⁻¹ to 5 × 10⁻². While the temperature changes dramatically by thousands of K at 10³ Bar when T_int increases from 35 K to 180 K (i.e., the planet's internal heat flux increases by 700 folds), the effect on the mixing ratios of the major components at the observable pressure levels is rather small. This is because elevating the internal heat flux moves up the quenching level and diminishes the effect of internal heating. Second, the internal heat flux affects the manner that the mixing ratios of hydrocarbons depend on the eddy diffusivity. When the eddy mixing is more efficient, the quenching pressure becomes higher. If the planet has negligible internal heat flux, the atmosphere below the radiative layer would be close to isothermal, and then as a result of increasing pressure and constant temperature, a greater eddy mixing coefficient would lead to more CH₄ in the observable part of the atmosphere. If the planet has significant internal heat flux, the atmospheric temperature would increase with pressure adiabatically at depth, and then the mixing ratio of C₂H₂ should increase with more efficient vertical mixing (Figure 12; also see the upper-right panel of Figure 9). In all, CH₄, C₂H₂, and C₂H₄ have distinctive spectral features; and their relative abundance may provide a probe to the processes of eddy mixing and internal heating in the deep atmosphere of a super Earth that are otherwise not measurable.

The results above are valid for hydrocarbon-rich atmospheres, which typically requires X_C/X_O ⩾ 2. If we loosen this requirement and consider the cases with X_C/X_O ⩾ 1, we find that the atmosphere is most likely to be dominated in CO. For X_C/X_O ∼ 1, the abundance of unsaturated hydrocarbons in the non-H₂-dominated thick atmosphere of an exoplanet having similar temperatures as HD 97658 b would be at the level of 1000 ppmv in the observable part of the atmosphere, which is also significant in terms of driving spectral features. More efficient photolysis and less efficient vertical mixing would favor formation and accumulation of hydrocarbons. In all, we find that unsaturated hydrocarbons are abundant in non-H₂-dominated, carbon-rich, thick atmospheres on super Earths and mini Neptunes, and therefore, they should be considered as one of the basic building blocks for super Earth/mini Neptune atmospheres.

Finally we turn to the minor components in hydrocarbon-rich atmospheres. The main form of oxygen in hydrocarbon-rich atmospheres is invariably CO. For a non-H₂-dominated carbon-rich oxygen-poor atmosphere (i.e., X_H ⩽ 0.7, X_C/X_O ⩾ 2), we always find that $X_\mathrm{H_2O}/X_\mathrm{CO}<0.1$, and $X_\mathrm{H_2O}/X_\mathrm{CO}$ becomes even smaller for higher temperatures or higher X_C/X_O (Figures 7 and 8).

Current observations of the super Earth/mini Neptune GJ 1214 b have shown a flat spectrum in transmission (Bean et al. 2010, 2011; Crossfield et al. 2011; Désert et al. 2011; Berta et al. 2012; de Mooij et al. 2012). The observed flat transmission spectrum has ruled out the scenario that the planet has a H₂-dominated clear atmosphere but can be explained by an atmosphere having a mean molecular mass larger than 15, or an atmosphere having thick layers of haze (e.g., Bean et al. 2010; Miller-Ricci Kempton et al. 2012; Howe & Burrows 2012; Benneke & Seager 2012; Morley et al. 2013). Using the photochemistry–thermochemistry model and focusing on atmospheric scenarios without haze or clouds, we find that as long as X_H ⩽ 0.7, the mean molecular mass of the observable part of the atmosphere is greater than about 15, and such an atmosphere would be consistent with current observations (Figure 13). All models with X_H ⩽ 0.7, regardless of the carbon to oxygen ratio, provide an adequate fit to the current observations of GJ 1214 b (Figure 13). The acceptable scenarios based on the transmission spectrum include a water-dominated atmosphere (upper-left panel of Figure 9), a H₂–CO dominated atmosphere (lower-left panel of Figure 9), a CO–CH₄ dominated atmosphere (upper-right panel of Figure 9), and a C₂H₂–C₂H₄ dominated atmosphere (lower-right panel of Figure 9).

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How could future observations distinguish these scenarios? Figure 14 shows the transmission spectra and the thermal emission spectra of the planet if its atmosphere is non-H₂-dominated. A number of diagnostic features indicating hallmark molecules for different atmospheric scenarios stand out, and these features will allow for future characterization of super Earth/mini Neptune GJ 1214 b and other transiting super Earths and mini Neptunes with similar temperatures yet to be discovered. Out of a number of spectral features labeled in Figure 14, we highlight the following three points.

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First, a hydrocarbon-rich atmosphere (i.e., the case of X_C/X_O ⩾ 2) can be uniquely identified by detecting the absorption bands of C₂H₂ at 1.0 and 1.5 μm in transmission and the absorption bands of C₂H₂ and C₂H₄ at 9–14 μm in thermal emission. In particular, the C₂H₂ feature at 1.0 μm is not contaminated by other potential constituents in the atmosphere and is as sizable as the water features nearby (Figure 14). The photochemistry–thermochemistry models show that C₂H₂ is expected to be abundant in a carbon-rich atmosphere of GJ 1214, and we suggest C₂H₂ as a main component and hallmark molecule for carbon-rich atmospheres on a GJ 1214 b–like exoplanet. To complicate the matter, transmission spectroscopy is often interfered with by haze in the atmosphere (Fortney 2005; Howe & Burrows 2012; Benneke & Seager 2012; Morley et al. 2013). Although we do not treat photochemical haze in this paper, we expect non-H₂-dominated carbon-rich atmospheres to be ideal environment to form photochemical haze, and therefore, the transmission spectra produced by such kind of atmospheres are likely to be affected by haze.

Second, measurements of the thermal emission of this planet in the mid-infrared wavelengths yields a great deal of knowledge of its atmosphere. A hydrocarbon-rich atmosphere has little H₂O or CO₂, so its thermal emission spectrum should be dominated by the absorption bands of CH₄, C₂H₄, and C₂H₂ (Figure 14). A water-rich atmosphere has little methane or other hydrocarbons, so its thermal emission spectrum should only show the prominent absorption bands of CO₂ on top of the pseudo-continuum of H₂O absorption (Figure 14). Recent observations with Spitzer have constrained the planet's thermal emission at 4.5 μm to be 70 ± 35 ppm of stellar emission and at 3.6 μm to be not greater than 205 ppm. Figure 14 shows that these constraints rule out the cloud-free scenarios with a very high or very low carbon to oxygen ratio (X_C/X_O = 0.1 or X_C/X_O = 10), and permits all other scenarios with X_C/X_O ranging from 0.5 to 2. The thermal emission spectrum is likely to be observed by future infrared telescopes in space, as the planet to star flux ratio will be within the reach of the JWST.

Third, a water-dominated atmosphere may be inferred from the nonexistence of methane absorption features. With transmission and thermal emission spectroscopy, a water-rich atmosphere (i.e., the case of X_C/X_O ⩽ 0.5) may be inferred based on the detection of water vapor absorption bands in the near-infrared. However, it would be very hard to establish that the atmosphere is mostly composed of water vapor based on water vapor features alone. Figure 14 shows that the atmosphere scenarios with X_C/X_O ranging from 0.1 to 1, which have the water vapor mixing ratio ranging from 70% to 5%, have almost identical water vapor features in transmission at 0.6–1.5 μm and in thermal emission. The water vapor features would allow for detection of water-rich atmospheres but not water-dominated atmospheres. The photochemistry–thermochemistry models show that an H₂-depleted water-dominated atmosphere must have CO₂ as the carbon carrier and must not have any significant amounts of CH₄. Therefore, a confirmed nonexistence of methane feature in either transmission or thermal emission (see Figure 14), in combination with a detection of water features, will provide sufficient evidence for a water-dominated atmosphere on a GJ 1214 b–like super Earth.

HD 97658 b is a $2.34^{+0.18}_{-0.15}$ R_⊕ super Earth/mini Neptune discovered recently (Dragomir et al. 2013). Orbiting a very bright star, the transiting super Earth/mini Neptune is one of the prime target for follow-up observations to determine its atmospheric properties in the near future. The planet receives stellar radiation flux of T_irr = 1030 K, making it warmer than GJ 1214 b and cooler than 55 Cnc e. The measured mass and radius of the planet implies that the planet must have a significant gas envelope which can be either H₂-dominated or non-H₂-dominated (Dragomir et al. 2013). Using our photochemistry–thermochemistry models, we compute self-consistent atmosphere models for this planet and show synthetic spectra in Figure 15.

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The transmission spectrum of HD 97658 b will be dominated by the combined feature of water and methane in the near-infrared wavelengths if the planet has an H₂-dominated cloud-free atmosphere. For the temperature of the planet, methane should be the dominant form of carbon, and water should be the dominant form of oxygen in the H₂-dominated atmosphere. Since the mixing ratios of CH₄ and H₂O only have linear dependency on X_C/X_O, it will be difficult to distinguish a carbon-rich atmosphere versus an oxygen-rich atmosphere.

If the planet has a non-H₂-dominated atmosphere, the size of the features in its transmission spectrum will be quite small, but its thermal emission spectrum is expected to have prominent features of CO₂ for an oxygen-rich atmosphere or C₂H₂ and C₂H₄ for a carbon-rich atmosphere (Figure 15). Therefore, a carbon-rich atmosphere and an oxygen-rich atmosphere can be distinguished by thermal emission spectroscopy in the future if transmission spectroscopy finds the planet's atmosphere to be non-H₂-dominated. In both warm Spitzer bands, the planet's flux is within 10 ppm of the stellar flux, making the planet's emission very difficult to be observed by Spitzer. In the future, it will be promising to perform detailed atmosphere characterization for this planet by mid-infrared spectroscopy with JWST because different atmosphere scenarios (H₂-dominated versus non-H₂-dominated, carbon-rich versus oxygen-rich) have distinctive molecular features (see Figure 15).

The measured radius of super Earth 55 Cnc e (2.2 ± 0.1 R_⊕) implies a volatile envelope on the planet (Gillon et al. 2012). For the measured mass of the planet, the planet's radius would be 1.5 R_⊕ if it was completely composed of iron, or 1.9 R_⊕ if it was completely composed of MgSiO₃ (estimated using of the models of Zeng & Sasselov 2013); that is to say, the room for a potential atmosphere is maximally ∼4000 km thick, or 30% of the observed planet radius. The planet's radius has also been measured by Winn et al. (2011) in the visible wavelengths to be ∼2 R_⊕ (based on the reanalysis by Gillon et al. 2012). Recently, the detection of the thermal emission of the planet in the Spitzer 4.5 μm band indicates a relatively high dayside brightness temperature (2360 ± 300 K; Demory et al. 2012).

We simulate the transmission spectra and thermal emission spectra of a 55 Cnc e–like super Earth, assuming a thick atmosphere on the planet (Figure 16). Current observations of the thermal emission of 55 Cnc e in the Spitzer 4.5 μm band is likely to contain absorption features of either CO₂ in oxygen-rich scenarios, or CO in carbon-rich scenarios, if the planet has an atmosphere. Assuming poor heat redistribution, all our atmosphere models are consistent with the Spitzer 4.5 μm observation at 1σ. Interestingly, the Spitzer 3.6 μm band (not yet observed), where the main CH₄ band falls into, is likely to probe deep into the atmosphere and has a higher brightness temperature than the 4.5 μm band, because methane is not expected to exist in significant amounts in such a high-temperature atmosphere according to our photochemistry–thermochemistry simulations.

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For future observations of 55 Cnc e, a water-rich atmosphere can be detected in thermal emission with the absorption bands of H₂O and CO₂, and by transmission spectroscopy if the mean molecular mass is low (Figure 16). This is similar to the case of GJ 1214 b that has a much lower temperature. A hydrocarbon-rich atmosphere on 55 Cnc e would result in prominent absorption bands of CO and C₂H₂, potentially detectable via thermal emission and transmission if the mean molecular mass is low (Figure 16). Note that unlike the case of GJ 1214 b, the nonexistence of methane features cannot be interpreted as water dominance. On 55 Cnc e, the methane features are expected to be suppressed due to the high temperature.

The transmission spectroscopy of 55 Cnc e, if the planet has an extended H₂-rich atmosphere, is within reach of current observation facilities including Very Large Telescope and Hubble. Especially, the diagnostic features of water-rich atmospheres (H₂O features) and the diagnostic features of hydrocarbon-rich atmospheres (C₂H₂ and CO features) are well separated in the near-infrared wavelengths in transmission spectra (Figure 16), which would enable straightforward characterization of the chemical compositions of the atmosphere.

Water-dominated atmosphere, if discovered, would be an exciting environment in our interstellar neighborhood because of its reminiscence of a habitable world. In fact, one of preferred scenarios for the super Earth/mini Neptune GJ 1214 b is that the planet has a significant fraction of its mass as water based on mass-radius constraints (Rogers & Seager 2010b; Nettelmann et al. 2011) and that the planet has a water-dominated atmosphere or a H₂–H₂O atmosphere (Nettelmann et al. 2011) based on the flat transmission spectrum (Bean et al. 2010, 2011; Berta et al. 2012). We study the range of atmospheric composition of GJ 1214 b in detail using our photochemistry–thermochemistry, and find that the water-dominated atmosphere exists at a carbon to oxygen ratio much smaller than the solar value. For a range of carbon to oxygen ratios, we show a range of possible scenarios and their transmission and thermal emission spectra, and we outline a number of possible ways to distinguish them by future observations in Section 4.1.

For a more general discussion beyond GJ 1214 b, we suggest that identifying a water-dominated atmosphere may be harder than previously expected. There are two reasons for this suggestion. The first reason is that water vapor features in the transmission spectra are not effective in distinguishing a water-dominated atmosphere versus a water-rich atmosphere. This has been shown by Benneke & Seager (2012) with a quantitative retrieval method for super Earth transmission spectra. This is also shown in Figure 14 as an example, in which atmospheric scenarios with water vapor mixing ratios ranging from 1% to 70% have similar sizes of water vapor features in the transmission spectra. The second reason is that the mixing ratio of water vapor in a non-H₂-dominated atmosphere is highly sensitive to the carbon to oxygen ratio (Figure 8). In particular, for a solar carbon to oxygen ratio, a non-H₂-dominated atmosphere is not water-dominated, but such an atmosphere will have prominent water vapor features in its spectrum (Figures 9 and 14). Therefore, identifying a water-dominated atmosphere not only involves measuring the water vapor features, but it also requires evaluating the carbon to oxygen ratio of the atmosphere, which warrants measurements of other gases in the atmosphere.

Moreover, a water-dominated atmosphere might be indigenously rare in nature. For a planet to have a water-dominated atmosphere, the planet has to start with an almost pure water ice envelope, with the fraction of methane ice of no more than 20% by weight. We show in Section 3.2 that the carbon to oxygen ratio has to be less than 0.2, much smaller than the solar ratio, for a thick atmosphere to evolve into a water-dominated atmosphere. Such a condition on the planet's forming environment is quite confining, which might only be possible close to the snow line of a protoplanetary disk with a solar-like carbon to oxygen ratio. Studies of the condensation sequence of volatile ices from protoplanetary nebula gases have shown that the ice compositions sensitively depend on the carbon to oxygen ratio of the nebulae (e.g., Marboeuf et al. 2008; Johnson et al. 2012). Even for a planet-forming nebula with a solar carbon to oxygen ratio, the ice mixture should have ∼20% carbon by weight (Marboeuf et al. 2008); and the carbon content in ice increases with increasing carbon to oxygen ratios of the nebulae, in particular for those with cold midplanes (Johnson et al. 2012). To summarize, one could expect the super Earths that are born as mini Neptunes to have a wide range of carbon to oxygen ratios in their atmospheres, and a water-dominated atmosphere is one of many plausible atmospheric scenarios. This finding suggests that water-dominated atmospheres might be rare.

One useful application of our photochemistry–thermochemistry model is to verify the chemical stability of atmospheric gases. The "million model" approach has been developed to interpret the observations of exoplanet atmospheres (e.g., Madhusudhan & Seager 2009; Benneke & Seager 2012). These methods seek best-fitted model spectra of planetary emission and transmission by exploring the full parameter space of molecular compositions. We have shown in this paper that not all combinations of gases are chemically stable in thick atmospheres on super Earths and mini Neptunes. For example, we find that methane is not compatible with water-dominated atmospheres on GJ 1214 b. Therefore, our photochemistry–thermochemistry model can be used in conjunction with the "million model" approach to eliminate a significant part of the parameter space, in terms of ruling out the unstable atmospheric scenarios and strengthening the interpretation of spectra.

As a general study on the stability of gases in thick atmospheres, we additionally simulate atmospheres initially composed of all possible 50%–50% molecular binary combination of H₂, H₂O, CH₄, CO, and CO₂ for an exoplanet like GJ 1214 b. For each scenario, we derive the elemental abundance from the initial composition for the model input. For example, to simulate a 50% H₂ 50% CO atmosphere, we use an H:O:C ratio of 2:1:1. The thermochemistry–photochemistry model result is then compared with the initial molecular composition, to determine whether such an initial state is chemically stable.

We find that H₂ is compatible with all major stable gases of C, H, O elements, but H₂O is not compatible with equal amount of CH₄ and CO. An atmosphere mainly composed of H₂O and CO or CH₄ is not stable for GJ 1214 b because of the following reactions:

$$\begin{equation} \mathrm{H_2O + CH_4 \longrightarrow 3H_2 + CO}. \end{equation} \tag{ C5 }$$

$$\begin{equation} \mathrm{H_2O + CO \longrightarrow H_2 + CO_2}. \end{equation} \tag{ C6 }$$

For the elemental abundance of the H₂O–CO or H₂O–CH₄ combinations, we find that CO and CH₄ can always reduce most of H₂O to H₂ (see Figure 17). Similarly, the CH₄–CO₂ combination has the same elemental abundance as the H₂–CO combination; the atmosphere will have the composition of H₂ and CO at the steady state, and the CH₄–CO₂ combination is not stable (and therefore not a plausible scenario). These results imply that chemical stability has to be taken into account when deriving atmospheric molecular compositions from spectra of super Earths and mini Neptunes.

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One might ask whether a kinetic-transport simulation is necessary for the study of super Earths and mini Neptunes, considering the fact that observations of their atmospheres will remain disk-averaged and have low spectral resolution for a long time. Here, our two-level model framework (Figure 1) provides an opportunity to compare thermochemical equilibrium calculations to kinetic-transport calculations for a wide range of exoplanet thick atmospheres.

Temperature profile. To what extent the temperature profile calculated under the assumption of thermochemical equilibrium would differ from the profile consistent with the chemical composition that resulted from the kinetic-transport modeling? We find that among all models we have run, the variation of temperature caused by disequilibrium processes (i.e., photochemistry and vertical transport) is maximally 10% with respect to the temperature profile that one would get assuming thermochemical equilibrium. In fact, for more than 90% of the cases, the effect of disequilibrium chemistry on the temperature is within 5%. For most cases, the temperature would increase when considering disequilibrium processes like vertical transport, and the magnitude of such temperature variation increases with increasing eddy diffusivity. The most significant variation for the GJ 1214 b simulations happen for X_H = 0.9 and 0.5 < X_C/X_O < 2, and X_H = 0.7 and X_C/X_O = 1. In these scenarios, the increase of temperature is mostly due to H₂O and CH₄ brought up by vertical transport to the pressure levels of 1–100 mbar.

Mean molecular mass and atmospheric structure. The same question can be asked for the mean molecular mass of the atmosphere. We find that the most significant variation in the mean molecular mass caused by disequilibrium processes is a decrease of the mean molecular mass above the pressure level of ∼0.1 Pa due to lift of light species by molecular diffusion. Other than this, we also find that the fraction of major components of the atmosphere (and therefore the mean molecular mass) can vary significantly due to vertical transport only in the middle regime of Figure 4 where H₂, CH₄, CO, CO₂, and H₂O can coexist. The main effect is that vertical transport may homogenize the atmosphere and remove the dependency of mean molecular mass on pressure under thermochemical equilibrium, when the temperature is not too high. One such example is shown in Figure 18. In this example, the difference between the true mean molecular mass and the mean molecular mass consistent from thermochemical equilibrium is up to 40% in the observable part of the atmosphere. Similar effects occur, but to a lesser extent, for other scenarios in the parameter regime of 0.3 < X_H < 0.7 and 0.5 < X_C/X_O < 2. This finding demonstrates the necessity of the kinetic-transport computation for a self-consistent modeling of thick atmospheres on warm super Earths and mini Neptunes.

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Planetary spectrum. The question of how disequilibrium chemistry would affect the emergent spectrum of a super Earth/mini Neptune is fairly involved, because the planetary spectrum depends on both the atmospheric thermal structure and the atmospheric chemical composition. We did not find a definitive trend comparing the spectra calculated for thermochemical equilibrium compositions and the spectra calculated for disequilibrium compositions. For the transmission spectrum, our exploration of elemental abundances and temperatures shows that the error induced by assuming thermochemical equilibrium is in general within 1% of the planet's radius, and this error is mostly due to mean molecular mass differences. For the thermal emission spectrum, we find that in some cases disequilibrium processes can cause very significant variation, for which an example is shown in Figure 18. In this example, the synthetic spectrum based on thermochemical equilibrium would significantly under-predict absorption of methane, which is expected to be enhanced by vertical transport. Therefore, we suggest that self-consistent models are needed for understanding the physics and chemistry of thick atmospheres on super Earths and mini Neptunes.

Molecular compositions of a thick atmosphere at the pressure levels relevant to observations are controlled by vertical transport and chemical reactions at a deeper level. The idea of disequilibrium chemistry driven by vertical transport was originally proposed to explain the overabundance of CO and the deficit of NH₃ in Jupiter's atmosphere (Prinn & Barshay 1977; Prinn & Olaguer 1981) and was used to explain chemical composition of Solar-System giant planets (e.g., Fegley & Prinn 1985; Yung et al. 1988; Fegley & Lodders 1994). Similar processes have also been suggested to operate on brown dwarfs and hot Jupiters (e.g., Fegley & Lodders 1996; Griffith & Yelle 1999; Cooper & Showman 2006; Line et al. 2010; Madhusudhan & Seager 2011; Visscher & Moses 2011; Moses et al. 2011). In general, the chemical timescale of a certain molecule decreases with increasing pressure and temperature. At the pressure levels where vertical transport timescale is shorter than the chemical kinetic timescale, the molecule is well mixed; at deeper levels in which the chemical timescale becomes shorter than the vertical transport timescale, the molecule's abundance is set by thermochemical equilibrium. Therefore, the molecule's abundance at observable pressure levels is set by thermochemical equilibrium at the level at which the vertical transport timescale equals the chemical kinetic timescale, i.e., the quenching level.

The most significant effects of vertical mixing are on the second most abundant carrier of major elements, and the most abundant carrier of minor elements. The abundances of the most abundant carriers of major elements, like H₂, H₂O, and O₂ in water-rich atmospheres, are determined by the constraints of elemental abundances. Indeed, the elemental abundance could uniquely determine the abundances of major components in some super Earth thick atmospheres (see Table 2). Based on the major composition set by the elemental abundance, relatively minor constituents in the atmosphere are indicators of the effects of eddy mixing and disequilibrium chemistry. The minor constituents can be either the carriers of minor elements, like carbon species in a water-rich atmosphere (Figure 9) and oxygen species in a hydrocarbon-rich atmosphere (Figure 9), or the second most abundant carriers of major elements, like C₂H₂ in a CO–CH₄ atmosphere (Figure 9).

Determining the major components and some of the minor components in atmospheres of super Earths and mini Neptunes like GJ 1214 b via spectroscopy may offer a window to their deep atmospheres that are otherwise not detectable and may potentially enable the study of vertical mixing and internal heating on these planets. For a warm exoplanet like GJ 1214 b, we find that for a wide range of composition, and an eddy diffusion coefficient ranging from 10⁶ ∼ 10⁹ cm² s⁻¹, the quenching pressure is 10 ∼ 100 bar. This is true for almost all types of atmospheres. What determines the abundance of the minor species is the interplay between eddy mixing, which determines the quenching pressure, and the internal heat flux, which determines the temperature at the quenching pressure. The so called "minor species," although low in absolute amounts, may have significant imprints in spectra and may therefore be detectable. For example, C₂H₂ in a CH₄-dominated atmosphere leads to prominent C₂H₂ features in both transmission and thermal emission (Figure 14). For a very hot super Earth like 55 Cnc e (equilibrium temperature higher than ∼2000 K), however, the atmosphere is very close to thermochemical equilibrium at all relevant pressure levels. For these planets, thermochemical equilibrium calculations would be efficient and adequate for studying the chemical properties of their atmospheres.

A cumulative loss of hydrogen from atmospheres on super Earths would result in the build-up of oxygen, unsaturated hydrocarbons, and other thermochemical and photochemical products. In this study, we neglect the possible material exchange between the atmosphere and the surface of a super Earth. How would active atmosphere–surface exchange affect the atmospheric composition of a super Earth?

First, surface emission of reduced gases (e.g., H₂, CH₄, H₂S) and exposure of unoxidized minerals (e.g., FeO) by volcanism can consume atmospheric oxygen and potentially prevent the formation of O₂-rich atmospheres. Without atmosphere–surface exchange, we predict that some super Earths that form in oxygen-rich nebulae will have O₂-rich atmospheres due to a loss of atmospheric hydrogen into space (Section 3.2). Such O₂-rich atmospheres may be short-lived due to atmosphere–surface exchange. A Solar-System example reminiscent of this process is Venus. If Venus starts with an ocean and loses its ocean during the runaway greenhouse phase, a scenario supported by the detection of an atmospheric D/H ratio ∼160 times higher than the terrestrial value (e.g., Donahue et al. 1982), a massive O₂-rich atmosphere up to 240 bars must have existed on Venus (Kasting 1997). However, today's Venus atmosphere only has trace amounts of oxygen, which means that that much of the oxygen has to be consumed over the history of Venus. Volcanic eruptions can release reduced gases (e.g., H₂, CH₄, H₂S) and expose unoxidized lithosphere (e.g., FeO), which can consume atmospheric oxygen. It has been estimated that volcanic eruption rates on Venus has to be a few times higher than the current volcanic eruption rate of Earth to consume the left-over O₂ in 100 million years (Fegley 2008). For a super Earth to prevent the O₂ build up due to hydrogen loss, the level of volcanic activity would need to be at least comparable to Earth's, depending on how fast the hydrogen loss is.

Second, surface emission of hydrogen and other reduced gases to the evolved atmosphere on a super Earth will be quickly removed by thermochemical reactions that yield energy. For example, in an oxygen-rich atmosphere, emitted hydrogen would react with free oxygen to form water, a process that yields chemical energy. For another example, in an evolved carbon-rich atmosphere, emitted hydrogen would react with unsaturated hydrocarbons to form more saturated forms of carbon, a process that also yields chemical energy. As shown in Figures 11 and 12, the scarcity of hydrogen, driven by atmospheric loss, is the controlling factor for the major components in water-rich atmospheres and hydrocarbon-rich atmospheres. Therefore, hydrogen escape to space could potentially result in a large chemical gradient between the atmosphere and the interior of the planet. Such a chemical gradient could be exploited by chemotrophs (organisms that obtain energy through chemical process; see Seager et al. 2012), and if the temperature is suitable, it could lead to potential biosignature gases.

Photochemically produced species in the upper atmosphere. This paper is mostly concerned with transport-driven disequilibrium chemistry deep in the atmosphere of low-mass exoplanets. However, one should note that photochemical processes can have a large effect on emission and especially transmission spectra, since these spectra are sensitive to the molecular abundances high up in the atmosphere. One example is shown in Figure 9. In this example, C₂H₂ is produced by photochemical processes above the pressure level of 1 mbar, and the photochemical source can increase the C₂H₂ mixing ratios to 10⁻². In general, a higher UV flux or a lower eddy diffusivity would favor the formation of such photochemical derivatives. Further research to quantify the effects of these photochemical products is warranted.

Chemistry of high-order hydrocarbons and haze formation. Our current chemical scheme for hydrocarbon chemistry stops at C₂H_x. For an atmosphere with high X_C/X_O, it is possible to form hydrocarbons with more than two carbons, with the chemical paths shown in Yung et al. (1984) for Titan's atmosphere. One might also speculate that for suitable temperatures the photochemically produced hydrocarbons may condense and form haze layers in the atmosphere. In fact, such a process has been proposed to occur on some hot Jupiters (Zahnle et al. 2009a) and as one of the explanations for the flat transmission spectrum of GJ 1214 b (Morley et al. 2013). However, it is highly complex to model the hydrocarbon chemistry and potential haze formation in planetary atmospheres, because most of the chemical kinetic rates remain unknown.