THE ATMOSPHERIC CHEMISTRY OF GJ 1214b: PHOTOCHEMISTRY AND CLOUDS

We calculate atmospheric abundances for the transiting super-Earth GJ 1214b that result from non-equilibrium chemical processes (photolysis and vertical mixing) using the photochemistry model developed in Zahnle et al. (2009b) and Zahnle et al. (2009a) for hot Jupiter exoplanets. This model is based on the one-dimensional photochemical kinetics code initially described in Kasting et al. (1989) and Kasting (1990). While GJ 1214b is not a hot Jupiter, this code is generally applicable to exoplanets with hydrogen-rich atmospheres. Since Zahnle et al. (2009a), the code has been completely re-written in the C programming language. Updates have been made to further generalize the code for calculating the composition of any given exoplanet atmosphere. Specific improvements include functionality for using an arbitrary temperature–pressure (T–P) profile and increased flexibility in the altitude step size, along with a generalized treatment of UV photolysis. We use the photochemical kinetics code to calculate chemical abundances for 61 atomic and molecular species in GJ 1214b's atmosphere as a function of height (parameterized within the code in terms of atmospheric pressure) by simultaneously solving the equations of continuity and flux. In this study, we solve for 698 chemical reactions including 33 photolysis reactions. The reaction rates and photolysis cross sections employed in this work are listed in Zahnle et al. (2009a, their Tables 2 and 3). Reverse reaction rates are calculated using the method outlined in Visscher & Moses (2011) as outlined below.

For reactions of the form A + B → C + D with forward reaction rate k_f, the reverse rate (i.e., the rate for C + D → A + B) is k_r = k_fexp (− ΔG/RT), where ΔG, the Gibbs free energy, is obtained from enthalpies and entropies of the of the reactants and products, ΔG = H_A + H_B − H_C − H_D − T(S_A + S_B − S_C − S_D). Associative reactions of the form A + B → AB, the rate for the reverse reaction (dissociation of AB) is k_r = k_f(kT/P_○)exp (− ΔG/RT), where P_○ = 10⁶ dynes cm⁻² is one atmosphere. This must be done in both the low pressure and high pressure limits. Similarly, the associative reverse of a dissociative reaction is given by k_r = k_f(P_○/kT)exp (− ΔG/RT). For this code, we have fit the reverse reaction rates to the standard Arrhenius form k = AT^bexp (− T/C). This maximizes code flexibility and exploits the thermodynamic limit as an error check. The fits can be quite good, although the asymptotic match to the thermodynamic equilibrium limit is imperfect.

For all of our calculations, we employ an underlying T–P profile for GJ 1214b's atmosphere that was presented in Miller-Ricci & Fortney (2010) for solar composition gas in chemical equilibrium and assuming planet-wide redistribution of heat (shown also in Figure 7). The effective temperature and surface gravity for this model are T_eff = 555 K and g = 8.95 m s⁻¹, respectively. We do not include feedback on the T–P profile based on the changes in atmospheric composition that result from the photochemical modeling.

Due to the fact that the vertical eddy mixing rate and the atmospheric metallicity are unknown for GJ 1214b, we generate a grid of models in both of these parameters. For the eddy diffusion coefficient, we calculate models with constant mixing rates of K_zz = 10⁶, 10⁷, and 10⁹ cm² s⁻¹. For metallicity, we choose values ranging from solar composition to metal enhanced at 1, 5, and 30 times solar. For all of our calculations, we use a stellar zenith angle of θ = 30°. We have done some additional tests with higher values of θ corresponding to longitudes closer to the terminator, and we have found the effects to be minimal, although a slightly lower level of photodissociation is found.

As a lower boundary condition, we assume that GJ 1214b resides in a state of chemical equilibrium at the base of the atmosphere. Generally speaking, deep in the atmosphere of a planet at sufficiently high temperatures and pressures the chemistry should approach thermal equilibrium. However, this may not be valid if the atmosphere is thin, in which case interactions between the planet's surface and its atmosphere should be taken into account. For GJ 1214b, the minimum mass of its hydrogen envelope corresponds to an atmosphere of at least 450 bars, and the temperature at the base the atmosphere should exceed 1175 K based on calculations of the T–P profile. We calculate equilibrium abundances at the base of the atmosphere using the Gibbs free energy minimization code described in Miller-Ricci et al. (2009), which is in turn based on the method outlined in White et al. (1958). Some of the 61 species considered in the photochemistry code are not included in the equilibrium chemistry code because they are not predicted to be present in any significant quantities in equilibrium. For these molecules, we set their initial abundances at the bottom of the atmosphere to an arbitrary low value of 10⁻⁴⁰. We place our lower boundary for all of our models at a pressure of 1000 bars, where the atmospheric temperature is predicted to be T ≈ 1400 K from the T–P profile that we employ in this work. We have performed limited tests to determine the sensitivity of our results to the pressure that we choose as the bottom boundary of the atmosphere, and we do not find any strong dependences for pressures greater than 100 bar. We have additionally assured that our lower boundary lies below the height where CO–CH₄ quenching takes place (around 100 bar). Below this height we find that the abundance profiles for the carbon-bearing species follow their equilibrium values. We do not attain quenched abundances for N₂ and NH₃ even at the 1000 bar lower boundary of our atmosphere, but we show in subsequent sections that this does not have a strong effect on our results.

As an upper boundary condition, we set a zero flux lid at 1 μbar with no flow allowed into or out of the top of the atmosphere. From theoretical calculations, GJ 1214b is thought to be potentially undergoing atmospheric mass loss at a rate of ∼9 × 10⁸ g s⁻¹ (Charbonneau et al. 2009), however this rate is unconstrained by observations and we therefore choose to ignore the effects of mass loss in our photochemical calculations.

To calculate photolysis rates, it is necessary to know the amount of stellar UV flux that is absorbed by the planet's atmosphere; however, the UV spectrum of GJ 1214 has not been measured. Generally, M-stars such as GJ 1214 tend to be relatively more active than early-type stars, with stellar activity decreasing as a function of stellar age. In theory, we can place GJ 1214 on a stellar type versus age diagram (such as from Selsis et al. 2007) to determine its expected level of UV flux. However, given the large uncertainty in the star's age (6 ± ⁴₃ Gyr; Charbonneau et al. 2009), the constraints that we can place on its UV flux are essentially meaningless. For this reason, we choose to include UV flux as an additional parameter in our grid of photochemical models. We choose stellar spectra that represent two bounding cases of a low and high UV flux as shown in Figure 1. It is our assumption that the actual UV spectrum for GJ 1214 falls somewhere in between these two extremes. For our low UV case, we employ a stellar model with the same T_eff and g_surf as GJ 1214, which we calculate by interpolating between bracketing models by Hauschildt et al. (1999). The stellar model does not include sources of UV emission due to stellar activity, so it produces a spectrum that drops off precipitously in the UV following the stellar blackbody, which is almost certainly an underestimate for the actual UV flux from GJ 1214. For our high UV case, we take the observed time-averaged spectrum of the active M4.5V flare star AD Leo from Segura et al. (2005) (T_eff = 3400 K), which is one of the most active known M-stars. The incident stellar spectrum is then calculated at the orbital distance of GJ 1214b, from 100 to 1000 nm, and this flux is used for calculating photodissociation rates for the 33 photolysis reactions included in the photochemical kinetics code.

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Using the chemical abundances profiles that we obtain from the photochemical modeling, we calculate transmission spectra using the model outlined in Miller-Ricci et al. (2009) for super-Earth exoplanets. We calculate absorption of stellar light along chords through the planet's upper atmosphere and then integrate to determine the total absorption over the entire projected annulus of the planet's atmosphere in transit. This results in a wavelength-dependent transmission spectrum, which we calculate from 0.3 to 30 μm. As with the photochemical modeling, we employ the T–P profile from Miller-Ricci & Fortney (2010) for a solar composition atmosphere when calculating the spectra.

To calculate the transmission spectra, we include opacities for the major molecular absorbers in the optical and IR including H₂O (Freedman et al. 2008; Partridge & Schwenke 1997), CH₄ (Freedman et al. 2008; Karkoschka 1994; Strong et al. 1993), NH₃, CO (Freedman et al. 2008, and references therein), and CO₂ (Rothman et al. 2005). We additionally include absorption from a number of non-equilibrium carbon-bearing species—HCN (Harris et al. 2008), C₂H₂, C₂H₄, and C₂H₆ (Rothman et al. 2005)—that have significant IR cross sections and are predicted to be present at high abundances in some of our photochemical calculations. We caution that some of the opacity lists, especially those for C₂H₂, C₂H₄, and C₂H₆, along with the short-wavelength CH₄ data may be incomplete. Atomic species with large opacities in the optical—Na and K—are predicted to be condensed out of the atmosphere of GJ 1214b at the heights probed by transmission spectroscopy and are not included in our calculations. We do however include the effects of Rayleigh scattering in the optical for the most abundant molecules in the atmosphere (H₂, He, H₂O, CH₄, NH₃, CO, CO₂, and N₂). We calculate Rayleigh scattering cross sections for each molecule individually according to

$$\begin{equation} \sigma = \frac{8\pi }{3}\left(\frac{2\pi }{\lambda }\right)^4\alpha ^2, \end{equation} \tag{ 1 }$$

where α is the polarizability obtained from the CRC Handbook for each molecule. We do not include the effects of additional scattering into or out of the beam or refraction, which has been found to have a minimal effect (Hubbard et al. 2001).

The end result is a suite of 18 transmission spectra for possible chemical compositions of GJ 1214b's atmosphere. Spectra are calculated for three values of metallicity: 1, 5, and 30 times solar; three values of K_zz: 10⁶, 10⁷, and 10⁹ cm² s⁻¹; and two stellar UV input spectra.

Results from running the photochemical kinetics code with our suite of 18 permutations on the model parameters are shown in Figure 2 (major atmospheric constituents) and Figure 3 (carbon-bearing molecules). Depending on the input parameters, the resulting atmospheric abundance profiles can differ dramatically from what is obtained from equilibrium chemistry. This is a result of both photochemistry, which breaks apart molecules in the upper atmosphere, and vertical mixing, which redistributes species throughout the atmosphere. Qualitatively, the effect of eddy mixing is to smooth out chemical gradients in the lower atmosphere, resulting in a more evenly distributed chemical composition. In the upper atmosphere, the effects of UV photolysis and molecular diffusion dominate.

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Chemically, the main source of differences between the predictions of equilibrium chemistry and our photochemical modeling is that certain reactions occur so slowly that the chemistry will never converge to equilibrium before photolysis and mixing take over. Specifically, photolysis of both ammonia and methane occurs readily in the upper atmosphere, but reactions that create these molecules are not favored. The end result is that nitrogen and carbon preferentially form into molecules other than methane and ammonia, resulting in lower abundances of both of these species in the upper atmosphere than what is predicted by equilibrium calculations. Nitrogen tends to combine into the very stable N₂ molecule and also forms a smaller amount of HCN. Carbon is redistributed into a wide variety of molecules including CO, CO₂, C₂H₂ (acetylene), C₂H₄ (ethylene), C₂H₆ (ethane), and HCN (hydrogen cyanide), resulting in a complex carbon chemistry as shown in Figure 3.

In our models using the quiet M-star as the UV input spectrum (dashed lines in Figures 2 and 3) very little UV photolysis takes place. These results can therefore be interpreted as showing the effects of vertical mixing in the absence of any significant photochemistry. In these models, the atmosphere is generally well mixed, and abundance profiles for most major constituents are constant with height throughout most of the atmosphere until molecular diffusion takes over at high altitudes. This is in sharp contrast to the predictions of equilibrium chemistry that produce strong gradients in the abundances of several key molecules including CO, CO₂, and NH₃ (dotted lines in Figures 2 and 3). Our model results produce obvious quenched behavior for several molecules at modest depth including CO, CO₂, and HCN. For these molecules, abundance profiles clearly follow their equilibrium values at depth, whereas their abundances are fairly constant above the quench point. All of these molecules also display a gradual transition between the quenched regime and the equilibrium regime, which is a result of atmospheric mixing. In the absence of mixing, the abundance profiles would transition sharply from equilibrium to their constant quenched abundances at the quench point. CO, CO₂, and HCN display fully quenched behavior above 1–10 bar. In contrast, N₂ and NH₃ display quenched behavior even at the very base of the atmosphere for all of our models, which implies that the actual quench point for these species lies deeper than 1000 bar. For this reason, it is possible that the actual abundances of nitrogen-bearing species in GJ 1214b's atmosphere may differ somewhat from the values we report here.

Without high levels of UV irradiation, methane remains the dominant carbon-bearing species throughout the atmosphere and is present at high abundances ranging from 0.1% for solar metallicity atmospheres to 1% when the metallicity is enhanced to 30 × solar. Ammonia and N₂ are expected to be the most abundant nitrogen-bearing molecules with N₂ becoming increasingly abundant at higher metallicities. Some additional carbon-bearing species appear at moderate abundances for models with low K_zz and high metallicity including HCN and C₂H₆. Molecular diffusion allows for heavy molecules to preferentially settle out of the atmosphere at pressures lower than ∼100 μbar for models with K_zz of 10⁶ cm² s⁻¹ and ∼10 μbar for models with K_zz of 10⁷ cm² s⁻¹.

For the highly irradiated models, the upper atmosphere chemistry is further complicated by UV photolysis. In these atmospheres, the chemistry is driven by photolysis of methane and ammonia. Ammonia has an appreciable photolysis cross section throughout the UV, making it unstable in the upper atmosphere (see Figure 4). Methane only has a large UV cross section shortward of 1400 Å, but it experiences significant photolysis from Lyα photons at 1216 Å. The heights at which CH₄ and NH₃ are removed from the atmosphere have a strong dependence on the amount of vertical mixing. At higher values of K_zz, methane and ammonia are lofted higher into the atmosphere, which results in a replenishing source that counteracts the effects of photolysis. As the models increase in metallicity, both methane and ammonia also maintain higher abundances to higher altitudes. This results from the overall higher abundance of each of these molecules at high Z. Ammonia photodissociates at pressures ranging from 0.1 mbar for high metallicity and high K_zz, to several millibars for solar metallicity and low K_zz. Methane is stable to somewhat higher altitudes corresponding to pressures of ∼10 μbar for high metallicity and high K_zz, to ∼100 μbar for low metallicity and low K_zz. Despite methane's propensity to remain stable even at fairly high altitudes in GJ 1214b's atmosphere, the combination of methane being converted into other carbon-bearing molecules at altitude along with downward transport produces a complex carbon chemistry throughout the atmosphere. For all of the models with high UV irradiation, CO and CO₂ abundances steadily increase as a function of altitude until reaching the region of the atmosphere that is affected by molecular diffusion. HCN, C₂H₂, C₂H₄, and C₂H₆ all demonstrate similar behavior with abundances increasing in the upper atmosphere due to photochemical production before tailing off again at the very top of the atmosphere due to molecular diffusion and UV photolysis. The abundance gradients for each of these species are highly dependent on metallicity and vertical mixing. At high metallicity, HCN, C₂H₄, and C₂H₆ achieve modest abundances even at the very base of the atmosphere. Here again the effect of mixing is to smooth out vertical chemical gradients, which results in the non-equilibrium carbon species becoming increasingly well mixed at higher values of K_zz.

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Aside from methane and ammonia, other molecular species such as H₂O, C₂H₂, C₂H₄, C₂H₆, and HCN experience significant UV photolysis in the upper atmosphere in all of our highly irradiated models. As a result, the abundances of these molecules diminish rapidly at high altitude (P ∼ 10⁻⁶ bar), even for our models with high K_zz. Conversely, for the highly irradiated high K_zz models, photochemical production of N₂, CO, and CO₂ leads to increasing abundances of these molecules at altitude given their negligible photolysis cross sections over the wavelength range where UV photons readily penetrate the atmosphere. Atomic species along with the OH radical also become increasingly abundant at high altitude as products of photolysis reactions. At low values of K_zz, molecular diffusion plays a significant role high in the atmosphere, and in this case heavy molecules are not present at altitude due to gravitational settling. For these low K_zz models, the upper atmosphere chemistry is driven by a combination of both molecular diffusion and photolysis.

We take the abundance profiles from our photochemical modeling and use these to produce theoretical transmission spectra for GJ 1214b for each of our 18 models. These results are shown in Figure 5 for the highly irradiated atmosphere and Figure 6 for models using the quiet M-star as the input stellar spectrum. In these figures, all of the spectra have been normalized so as to reproduce the observed transit depth of 1.35% in the MEarth filter bandpass spanning 675–1050 nm (Charbonneau et al. 2009).

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For the low-irradiation models, the spectra that we obtain look virtually identical to the spectra calculated using equilibrium chemistry (gray lines in Figure 6). For these models, photodissociation does not play a strong role in perturbing the atmospheric chemistry. While the overall atmospheric chemistry is expected to be more well mixed from our calculations than what is obtained from equilibrium chemistry, there is very little effect on the species that produce most of the opacity in our models. Water, methane, ammonia, and to a lesser extent CO and CO₂ all have significant opacities between 0.3 and 20 μm. Of these, the spectral features of water and methane dominate the transmission spectrum, and the abundances of these two species do not differ substantially from their predicted equilibrium values at the height probed by transmission spectroscopy (generally ∼1 mbar, but can vary between 0.1 and 500 mbar). The CO and CO₂ abundance profiles from Figures 2 and 3 do differ dramatically from their equilibrium abundances above ∼100 bars, however this is difficult to discern from looking at the transmission spectra. One reason for this is that the CO and CO₂ abundances remain low throughout all of our low-irradiation models with CO and CO₂ abundances not exceeding 10⁻⁴ and 10⁻⁵, respectively. Additionally, most of the predicted CO spectral features overlap with stronger absorption features from H₂O and CH₄, which essentially swallow up the spectral signature of what would otherwise be an excellent tracer molecule for the presence of atmospheric mixing and photochemistry. For ammonia, we tend to predict somewhat higher abundances than what is obtained from equilibrium predictions, and this has a small effect in increasing the ammonia absorption in features at 1.5 and 10.5 μm. However, we note that this result is somewhat dependent on the quenching behavior of ammonia at depth and may not be accurate since our photochemical models do not extend down to the NH₃/N₂ quench point. We also tend to see very slightly decreased methane absorption in some of the models, but once again, this is a very small effect and is unlikely to be observable.

Perhaps more surprising is the appearance of the spectra using the high UV irradiation models (Figure 5). Despite markedly different overall atmospheric chemistry than what is predicted from equilibrium expectations, the effect on the transmission spectra here is also fairly minimal. Methane and ammonia photodissociation lead to slightly weaker spectral features for both of these molecules. Additionally, for models with high levels of CH₄ photolysis, HCN contributes significant opacity around 14 μm, and increased abundances of CO₂ also add spectral features at 4.3 and 15 μm for the high-metallicity models. It has been previously pointed out that CO and CO₂ abundances increase strongly with metallicity (Zahnle et al. 2009a). We find the same result here, and note that we see increasing absorption from CO₂ in the transmission spectra as a function of metallicity. Generally, the abundance of CO₂ needs to exceed 1 part in 10⁵ for this molecule to be apparent in the transmission spectrum of GJ 1214b. Overall, while the changes in the transmission spectra relative to equilibrium expectations are noticeable, they are not dramatic. The largest effects are seen at low K_zz and high metallicity. Given the current quality of observational transmission data, it is likely that it will be difficult to distinguish between the different possibilities with observations. We explore this question further in Section 4.

As a note of caution, it is important to point out that transmission spectroscopy specifically probes the region of the atmosphere at the planet's day–night terminator (around the 1 mbar pressure level), since this is where all absorption of stellar light will take place. It is possible that the terminator chemistry is more complex than what we have modeled here for a number of reasons. Since GJ 1214b is expected to be tidally locked to its host star, it is likely that chemical gradients exist between the day and night side of the planet. Observations of the planet in transmission may therefore be sensitive to the presence of longitudinal winds that carry material from the day side to the night side of the planet, or vice versa. These winds could be an additional contributor to non-equilibrium chemistry that we are unable to address here using our one-dimensional model (e.g., Cooper & Showman 2006). Three-dimensional models of atmospheric dynamics on hot Jupiters show that strong winds that advect heat from the day side to the night side of the planet should be present at the heights probed by transmission spectroscopy at both the eastern and western terminators (Showman et al. 2008; Dobbs-Dixon et al. 2010; Rauscher & Menou 2010). In this case, the chemistry at the terminator should resemble that of the planet's day side, and our use of a dayside chemistry model is justified in calculating transmission spectra for GJ 1214b (e.g., Fortney et al. 2010). However, we caution that it is unclear how to scale the dynamical models for hot Jupiters to a super-Earth like GJ 1214b, and therefore the atmospheric circulation for this planet is unconstrained at this point in time.

Clouds would further complicate the appearance of the planet's transmission spectrum by efficiently scattering starlight at short wavelengths. At longer wavelengths in the mid-IR, the spectrum of GJ 1214b should remain mostly unaffected by clouds. Qualitatively, in the optical and near-IR, clouds can flatten the planet's transmission spectrum by scattering light at higher altitudes than where spectral features in transmission are expected to originate. For GJ 1214b, we have previously found that clouds at pressures greater than 200 mbar can explain the observations of a flat transmission spectrum from 780 to 1000 nm by Bean et al. (2010). This value was determined by cutting off transmission at different heights in the planet's atmosphere to simulate the effects of an optically thick gray cloud deck. Clouds deeper in the atmosphere than 200 mbar would have only a minimal effect on the transmission spectrum at the wavelengths of the Bean et al. (2010) observations. If clouds are present, the exact shape of the transmission spectrum at short wavelengths is determined by whether the scattering is occurring within the Rayleigh or Mie regime, which will produce different power-law slopes for the scattering opacity. Unfortunately, self-consistently modeling the cloud opacity requires knowledge of the cloud particle size and height distributions, which are currently unknown for GJ 1214b. Here, we offer up some suggestions for what the cloud composition could be.

Clouds are formed by condensation processes, which will occur if the partial pressure of a species surpasses its vapor or condensation pressure. To determine whether cloud formation will occur in the atmosphere of GJ 1214b, we compare the planet's T–P profile against the condensation curves of various molecules that are predicted to condense in hot planet and cool star atmospheres from Lodders & Fegley (2006). The only molecules that we find whose condensation curves intersect the predicted T–P profile of GJ 1214b are KCl and ZnS, as shown in Figure 7, although we caution that the T–P profile of GJ 1214b is unconstrained by observations, so its exact shape is somewhat uncertain. If the T–P profile from Figure 7 is correct, then both KCl and ZnS should condense at pressures of ∼500 mbar in GJ 1214b's atmosphere at solar composition. For higher metallicities, a number of effects come into play that can shift the condensation to either higher or lower pressure in GJ 1214b's atmosphere. These effects are (1) the abundances of condensate materials tend to be higher at higher Z, (2) the condensation curves for condensate species tend to shift to higher temperature, i.e., to the right on Figure 7, due to the increased vapor pressure of the heavy elements in the gas phase, and (3) the T–P profile tends to shift up and to right on Figure 7 due to the increased opacities from higher metal abundances at high metallicity. The first two of these effects will push condensation to higher pressures where a deeper and more massive cloud layer will form. The third effect (shifting the T–P profile) will have the opposite effect of pushing condensation to higher in the atmosphere at lower pressure. KCl and ZnS are both predicted to be present at very low abundances under the assumption of equilibrium, so it is unclear if either of these species could be present in large enough quantities to form an optically thick cloud. The predicted equilibrium abundance for KCl at 500 mbar and 800 K is only 8.5 × 10⁻⁹ at solar metallicity and 1.5 × 10⁻⁶ at 30 × solar metallicity. We do not calculate abundances for ZnS in our equilibrium chemistry code since we only include the 22 most abundant atomic elements from the Sun. Zinc's abundance in the Sun is only 1.5 × 10⁻⁸ (Asplund et al. 2005), and ZnS is likely to be present in even lower amounts in GJ 1214b's atmosphere. However, due to the fact that GJ 1214b is viewed in transmission along a slant optical path, even low abundances of condensate particles can form an optically thick cloud. Fortney (2005) explored this issue and found that condensed KCl may form a cloud with an optical depth of ∼0.18 in a solar composition hot Jupiter atmosphere, whereas ZnS should only form a cloud of optical depth ∼0.09.

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Another possibility is that GJ 1214b may form photochemical hazes in its atmosphere. The composition of any such hazes is unconstrained due to the complex nature of the photochemical processes that would lead to their formation. However, we can look to solar system objects to inform our understanding of possible haze formation mechanisms for GJ 1214b. Photochemically induced hazes are common in the atmospheres of solar system planets and planet-sized moons. Among the nearby planets, Venus possesses a sulfuric acid haze layer in its atmosphere. Additionally, a number of solar system objects including Jupiter, Neptune, and Titan have hazes composed of complex hydrocarbons. Hazes may be common in exoplanet atmospheres as well. The transiting hot Jupiter HD 189733b has an optical transmission spectrum that is consistent with a high-altitude haze (Sing et al. 2011; Pont et al. 2008), although its composition is currently unconstrained. Of the solar system haze scenarios, it is most likely that GJ 1214b forms hydrocarbon hazes in its atmosphere, given the high abundance of methane that we predict. Many of our photochemical models from Section 3.1 produce large amounts of the second-order hydrocarbons C₂H₂, C₂H₄, and C₂H₆, which are the first byproducts in the sequence of chemical reactions to form the high-level hydrocarbons that would make up a Titan-like haze. Unsaturated hydrocarbons such as C₂H₂ have a propensity to polymerize, eventually forming complex molecules such as polycyclic aromatic hydrocarbons, tholins, and soots (e.g., Yung et al. 1984). Unfortunately, our photochemical code does not include reactions for hydrocarbons of higher order than C₂H_X, so we cannot predict the exact composition or abundance profiles for the haze layer. We can however state that GJ 1214b should be amenable to forming hydrocarbon haze in its atmosphere.