PHOTOCHEMISTRY IN TERRESTRIAL EXOPLANET ATMOSPHERES. II. H₂S AND SO₂ PHOTOCHEMISTRY IN ANOXIC ATMOSPHERES

We have developed a comprehensive photochemistry model to investigate atmospheres of terrestrial exoplanets, and validated the model by simulating the atmospheric compositions of current Earth and Mars (see Paper I). We now describe briefly the main features of the photochemistry model and the specifics for this work.

The purpose of the photochemistry model is to compute the steady-state chemical composition of an exoplanetary atmosphere. The system is described by a set of time-dependent continuity equations, one equation for species at each altitude. Each equation describes: chemical production, chemical loss, eddy diffusion and molecular diffusion (contributing to production or loss), sedimentation (for aerosols only), emission and dry deposition at the lower boundary, and diffusion-limited atmospheric escape for light species at the upper boundary. Starting from an arbitrary initial state, the system is numerically evolved to the steady state in which the number densities no longer change. Because the removal timescales of different species are very different, the implicit inverse Euler method is employed for the numerical time stepping. The generic model computes chemical and photochemical reactions among 111 molecules and aerosols made of O, H, N, C, S elements, and formation of sulfur (S₈) and sulfate (H₂SO₄) aerosols. The numerical code is designed to have the capacity of treating both reducing and oxidizing atmospheres. For the chemical and photochemical reactions, we use the reaction rates data from both the NIST database (http://kinetics.nist.gov) and the JPL publication (Sander et al. 2011). We have also adopted relevant reaction rates from Kasting (1990), Yung & DeMore (1999), and Moses et al. (2002). Sulfur polymerization reaction rates still lack consistent experimental measurements, and we adopt the reaction rates proposed by Kasting (1990) and those proposed by Moses et al. (2002). Both sets of sulfur polymerization reaction rates are speculative and they are widely discrepant, the effect of which will be discussed later in Section 3.1. Ultraviolet and visible radiation in the atmosphere is computed by the δ-Eddington 2-stream method, with molecular absorption, Rayleigh scattering and aerosol Mie scattering contributing to the opacity. For the stellar input spectrum we used the Air Mass Zero (AM0) reference spectrum produced by the American Society for Testing and Materials⁵ for Sun-like stars, and used the simulated non-active M star spectrum from Allard et al. (1997) for quiet-M stars.

In this paper, we use the photochemistry model to study the sulfur chemistry in atmospheres ranging from reducing to oxidizing on terrestrial exoplanets. We use H₂-dominated atmospheres as the representative cases for reducing atmospheres, and we use N₂- and CO₂-dominated atmospheres as the representative cases for oxidized atmospheres that could be both reducing and oxidizing. With the photochemistry model, we simulated the chemical composition of H₂-, N₂-, and CO₂-dominated atmospheres, with sulfur compounds emitted from the surface at various rates. Parameters of the atmospheric models are tabulated in Table 1 and details of water, carbon, and oxygen chemistry have been described in Paper I. We will focus on the sulfur chemistry and photochemistry in terrestrial exoplanet atmospheres in this paper.

We consider in our atmospheric chemistry models the O, H, and S bearing species and a subset of C bearing species. The gaseous molecules considered in this paper are H, H₂, O, O(¹D), O₂, O₃, OH, HO₂, H₂O, H₂O₂, CO₂, CO, CH₂O, CHO, C, CH, CH₂, ¹CH₂, CH₃, CH₄, CH₃O, CH₄O, CHO₂, CH₂O₂, CH₃O₂, CH₄O₂, C₂, C₂H, C₂H₂, C₂H₃, C₂H₄, C₂H₅, C₂H₆, C₂HO, C₂H₂O, C₂H₃O, C₂H₄O, C₂H₅O, S, S₂, S₃, S₄, SO, SO₂, ¹SO₂, ³SO₂, SO₃, H₂S, HS, HSO, HSO₂, HSO₃, H₂SO₄, and S₈, and the aerosols considered are S₈ aerosols and H₂SO₄ aerosols. This set of species is comprised of common H, O, and C bearing species and photochemical products of H₂S and SO₂ emission. We assume a constant H₂O relative humidity at the surface of 60% to mimic the supply of water vapor from a liquid water ocean. To reduce the stiffness of the system and improve the numerical stability, "fast" species with relatively short chemical loss timescales are computed directly from the photochemistry equilibrium. We consider in this work O(¹D), ¹CH₂, C₂H, ¹SO₂, and ³SO₂ as fast-varying species. As such, the photochemistry model rigorously finds steady-state composition of the atmosphere starting with initial compositions without any sulfur compounds. Once the model converged to the steady state, we checked explicitly the mass conservation of O, H, C, N, S atoms and verified the choice of fast species to have been appropriate. We have required all models to balance mass flux within 10⁻³ for convergence and typically our models balance mass flux to 10⁻⁶. We have also explicitly checked the redox (i.e., hydrogen budget) balance (see our definition of the redox number, flux, and balance in Paper I) and required the models to balance redox flux to 10⁻³.

One of the most significant controlling factors that determine the steady-state composition of atmospheres on terrestrial exoplanets is the dry deposition velocities of emitted gases and their major photochemical byproducts. Of particular importance in this paper is the dry deposition velocities of H₂S and SO₂, which could vary by orders of magnitude (see Table 1 for the fiducial values of key dry deposition velocities). The dry deposition velocities depend on the properties of the lower atmosphere and the surface. For example, in a model of the early cold Martian atmosphere, the deposition velocities are assumed to be reduced by artificial factors of up to 1000 compared with those in warm current Earth (e.g., Tian et al. 2010), in order to account for less efficient deposition at a lower temperature. For another example, in modeling the early Martian atmosphere, because the putative Mars ocean is believed to be saturated with dissolved SO₂ and other sulfur species, SO₂ deposition is assumed to be balanced by an equivalent return flux from the ocean (e.g., Halevy et al. 2007; Tian et al. 2010) and then V_DEP of SO₂ is assumed to be zero. In this paper, we explore the effect of varying the dry deposition velocities of H₂S and SO₂, which can be scaled down by a factor of 100 if the surface is saturated with sulfide or sulfite.

Another important factor that strongly influences the atmospheric sulfur chemistry is the formation and sedimentation of aerosols. Photochemically produced H₂SO₄ and S₈ may condense to form aerosols if their concentrations exceed their vapor saturation concentrations. The parameterization of condensation and sedimentation of aerosols in our photochemistry model is described in detail in Paper I. Saturation vapor pressure of H₂SO₄ is taken as recommended by Seinfeld & Pandis (2006) for atmospheric modeling, with a validity temperature range of 150–360 K. S₈ is the stable form of elemental sulfur because the S₈ molecule has a crown-shape ring structure that puts the least strain on the S–S bond among sulfur allotropes and the crown structure allows for considerable cross-ring interaction between nonbonded atoms (Meyer 1976). The saturation pressure of S₈ is then taken as the total sulfur saturation pressure against liquid sulfur at T > 392 K and solid (monoclinic) sulfur at T < 392 K tabulated by Lyons (2008). We consider the average aerosol particle diameter, a key parameter that determines the aerosols' dynamical and optical properties, to be a free parameter. On Earth, the ambient aerosol size distribution is dominated by several modes corresponding to different sources. The "condensation submode," formed from vapor condensation and coagulation, has an average diameter of ∼0.4 μm (Seinfeld & Pandis 2006). On Venus, the Mode 1 particles with an average diameter of ∼1.0 μm dominate the upper cloud (e.g., Carlson et al. 1993). On Titan, the photochemical aerosols in the stratosphere have mean diameters in the range of 0.1–1 μm (Rages et al. 1983). We treat the particle diameter as a free parameter and explore the effects of varying the particle diameter from 0.1 to 10 μm. The dry deposition velocity of aerosols is assumed to be 0.2 cm s⁻¹, a sensible deposition velocity of particles having diameters between 0.1 and 1 μm (Sehmel 1980; Seinfeld & Pandis 2006).

Before leaving this section we provide the physical rationale of specifying temperature–pressure profiles and eddy diffusion coefficients for our atmospheric photochemistry models.

We modeled the atmospheric composition from the 1 bar pressure level up to the altitudes of about 10 scale heights. We chose appropriate vertical resolution for each scenario so that there are four layers per scale height. We adopted a temperature profile for our atmosphere models, without considering feedback on temperature of the atmospheric composition. The surface temperature is assumed to be 288 K. The semi-major axis of a terrestrial exoplanet around a Sun-like star implied by this surface temperature is 1.6 AU, 1.0 AU, and 1.3 AU, for H₂-, N₂-, and CO₂-dominated atmosphere, estimated based on a similar procedure as Kasting et al. (1993). The temperature profiles are then assumed to follow an appropriate dry adiabatic lapse rate (i.e., the convective layer) until 160 K (H₂ atmosphere), 200 K (N₂ atmosphere), and 175 K (CO₂ atmosphere) and to be constant above (i.e., the radiative layer). The adopted temperature profiles are consistent with significant greenhouse effects in the convective layer and no additional heating above the convective layer for habitable exoplanets. We did not consider the climate feedback of SO₂ or sulfur aerosols in the atmosphere, which could be important to determine the surface temperature (e.g., Halevy et al. 2007; Tian et al. 2010). While not ideal, these temperature profiles yield the same results discussed below as temperature profiles varied by several tens of kelvin. The precise temperature–pressure structure of the atmosphere is less important than photochemistry for the investigation of sulfur chemistry because the most important photolysis and chemical reactions are not significantly affected by minor deviations in the temperature profile. We found that variation of temperature profiles by a few tens of kelvin has minor impact on the atmospheric composition.

Vertical transport of gases in the atmosphere is parameterized by eddy diffusion, and the coefficients are assumed to be those of Earth's atmosphere scaled by the atmospheric scale height to account for H₂, N₂, and CO₂ being the dominant species. The current Earth's eddy diffusion coefficient profile has been derived from mixing ratio profiles of several long-lived gases (Massie & Hunten 1981; also shown in Figure 1 of Paper I). We use the empirical eddy diffusion coefficient profile for current Earth as a template, and scale the coefficient inversely with the mean molecular mass for H₂-, N₂-, and CO₂-dominated atmospheres. The justification for such scaling is that the eddy diffusion coefficient is proportional to the mixing length which is in turn a portion of the atmospheric scale height (e.g., Smith 1998). The pressure surface to pressure surface projection also ensures that the eddy diffusion coefficient profile features an eddy diffusion minimum near the tropopause for atmospheres with different mean molecular masses. Our approach to parameterize vertical transport is of course an approximation. An accurate representation of vertical transport would likely involve circulation on the global scale (e.g., Holton 1986). We explore the effect of eddy diffusion coefficients ranging one or two orders of magnitude from the nominal value in a sensitivity study (see Section 4.1).

We compute synthetic spectra of the modeled exoplanet's atmospheric transmission, reflection, and thermal emission with a line-by-line radiative transfer code (Seager & Sasselov 2000; Seager et al. 2000; Miller-Ricci et al. 2009; Madhusudhan & Seager 2009). The sources of opacities include molecular absorption with cross sections computed based on the HITRAN 2008 database (Rothman et al. 2009), molecular collision-induced absorption when necessary (e.g., Borysow 2002), Rayleigh scattering, and aerosol extinction computed based on the Mie theory (e.g., Van de Hulst 1981). The transmission is computed for each wavelength by integrating the optical depth along the limb path, as outlined in Seager & Sasselov (2000). The reflected stellar light and the planetary thermal emission are computed by the δ-Eddington 2-stream method (Toon et al. 1989). We used the refractive index of S₈ aerosols from Tian et al. (2010) for the UV and visible wavelengths and from Sasson et al. (1985) for infrared (IR) wavelengths. We used the refractive index of H₂SO₄ aerosols (assumed to be the same as 75% sulfuric acid solution) from Palmer & Williams (1975) for UV to IR wavelengths, and Jones (1976) for far-IR wavelengths.

The particle size distribution of aerosols controls their optical properties. We adopt the lognormal distribution as

$$\begin{equation} \frac{dN}{dD} = \frac{N_t}{\sqrt{2\pi }D\ln \sigma }\exp \left [-\frac{(\ln D - \ln D_0)^2}{2\ln ^2\sigma }\right ], \end{equation} \tag{ 1 }$$

where dN is the number of particles per volume in the diameter bin dD, N_t is the total number density of particles, D₀ is the median diameter of the particles, and σ is the particle size dispersion (defined as the ratio of the diameter below which 84.1% of the particles lie to the median diameter). The lognormal distribution is a reasonable assumption because it provides a good fit to the particle size distribution measured in Earth's atmosphere (e.g., Seinfeld & Pandis 2006), and a sensible particle size dispersion parameter for photochemically produced aerosols is in the range of 1.5–2.0 (Seinfeld & Pandis 2006). What is important for the radiative transfer model and the photochemistry model is the surface area mean diameter D_S and the volume mean diameter D_V, respectively. The mean diameters are related to the median diameter as

$$\begin{equation} D_S = D_0 \exp (\ln ^2\sigma), \end{equation} \tag{ 2 }$$

$$\begin{equation} D_V = D_0 \exp \left (\frac{3}{2}\ln ^2\sigma \right). \end{equation} \tag{ 3 }$$

We use the surface area mean diameter D_S (referred to as "mean diameter" in the following) as the free parameter for specifying a particle size distribution, as it is relevant to the radiative properties of the particle population. The volume mean diameter D_V is useful in the conversion from mass concentration of the condensed phase (computed in the photochemistry model) to the number of aerosol particles for radiative transfer computation. The extinction cross sections of H₂SO₄ and S₈ molecules in aerosols for various mean particle diameters are shown in Figure 1.

Zoom In Zoom Out Reset image size

Elemental sulfur aerosols and sulfuric acid aerosols have different optical properties at the visible and infrared (IR) wavelengths. In the visible, S₈ aerosols have a larger cross section than H₂SO₄ aerosols (Figure 1). For wavelengths less than 400 nm S₈ aerosols are both reflective and absorptive. In the infrared, the cross section of S₈ aerosols drops significantly with increasing wavelength unless the mean diameter is in the order of 10 μm. In contrast, H₂SO₄ aerosols have an enhancement of absorption at the MIR wavelengths (5–10 μm) for all particle sizes (Figure 1).

Both H₂S and SO₂ emitted from the surface are efficiently converted into elemental sulfur in reducing H₂ atmospheres. The major chemical pathways for sulfur compounds in the H₂-dominated atmosphere and the results of photochemistry model simulations are shown in Figure 2. Atomic hydrogen produced from photodissociation of water vapor and H₂S itself is the key reactive species that converts H₂S and SO₂ into elemental sulfur. The primary chemical loss for H₂S in the atmosphere is via

$$\begin{equation} {\rm H_{2}S + h\nu \longrightarrow HS + H}, \end{equation} \tag{ C1 }$$

and

$$\begin{equation} {\rm H_{2}S + H \longrightarrow HS + H_{2}}. \end{equation} \tag{ C2 }$$

The HS produced can then react with H again or with itself to produce elemental sulfur. HS can also react with S to produce S₂. The primary chemical loss for SO₂ in the atmosphere is photodissociation that produces SO. SO can be either photodissociated to elemental sulfur, or be further reduced to HS via HSO by H or CHO and then converted to elemental sulfur (see Figure 2).

Zoom In Zoom Out Reset image size

The S and S₂ molecules produced in the atmosphere will polymerize to form S₈, and S₈ will condense to form aerosols if it is saturated in the atmosphere. Due to its ring structure, S₈ is stable against photodissociation. S₈ is a strong UV absorber (Kasting 1990). Therefore, S₈ aerosols, if produced in the atmosphere, can effectively shield UV photons so that H₂S and SO₂ may accumulate beneath the aerosol layer (see the case for a sulfur emission rate 300 times higher than Earth's current volcanic sulfur emission rate shown in Figure 2).

The primary source of atomic hydrogen is the photolysis of H₂O, which occurs above the altitudes of ∼10³ Pa pressure level. The atomic hydrogen can be then transported by eddy diffusion to the pressure level of ∼10⁴ Pa to facilitate the removal of H₂S and SO₂ and the production of elemental sulfur. Additional numerical simulations show that an increase of the eddy diffusion coefficient by one order of magnitude can increase the yield of elemental sulfur by about 20%, because the transport of atomic hydrogen becomes more efficient. A secondary source of atomic hydrogen is photolysis of H₂S (reaction (C1)). This secondary source for atomic hydrogen is particularly important when the host star is a quiet M dwarf, because a quiet M dwarf produces few photons that could dissociate water.⁶ For planets around quiet M dwarfs the photolysis of H₂S could be the main source of atomic hydrogen in their atmospheres. Additional numerical simulations show that in the habitable zone of a quiet M dwarf having an effective temperature of 3100 K, H₂S photolysis alone can produce enough atomic hydrogen to drive the formation of elemental sulfur in the atmosphere.

We here comment on the uncertainty of photochemistry models regarding the yield of S₈. In our model, we have assumed polymerization of elemental sulfur proceeds via

$$\begin{equation} {\rm S + S \longrightarrow S_{2}}, \end{equation} \tag{ C3 }$$

$$\begin{equation} {\rm S + S_{2} \longrightarrow S_{3}}, \end{equation} \tag{ C4 }$$

$$\begin{equation} {\rm S + S_{3} \longrightarrow S_{4}}, \end{equation} \tag{ C5 }$$

$$\begin{equation} {\rm S_{2} + S_{2} \longrightarrow S_{4}}, \end{equation} \tag{ C6 }$$

$$\begin{equation} {\rm S_{4} + S_{4} \longrightarrow S_{8}}. \end{equation} \tag{ C7 }$$

We also include photodissociation for S₂, S₃, and S₄. However, the reaction rates of sulfur polymerization (reactions (C3)–(C7)) have not been well established by laboratory studies, and previous authors have adopted different rate constants for these reactions. In particular, Kasting (1990) and Pavlov & Kasting (2002) have used three-order-of-magnitude lower rates for reactions (C3) and (C4) and one-order-of-magnitude lower rates for reactions (C5)–(C7), compared with Moses et al. (2002). In this work, we have adopted the reaction rates of Moses et al. (2002) for elemental sulfur reactions. Our sensitivity tests show that adopting the reaction rates of Kasting (1990) would result in about 3–10 times less S₈. We have chosen higher sulfur polymerization rates for nominal models because: (1) the chemical pathways of reactions (C3)–(C7) are probably not complete and there may be other pathways to form S₈; (2) S₂, S₃, and S₄ may condense as suggested by Lyons (2008) and the polymerization may still proceed in the condensed phase to S₈. Experimental studies are encouraged to settle this important uncertainty.

H₂S and SO₂ gases emitted from the surface can be converted into both elemental sulfur (S₈) and sulfuric acid (H₂SO₄) in the oxidized (but anoxic) atmospheres such as N₂- and CO₂-dominated atmospheres. The major chemical pathways that lead to the formation of both elemental sulfur and sulfuric acid and the results of photochemistry model simulations are shown in Figure 3. The production of elemental sulfur aerosols involves UV photons and atomic hydrogen, as does in reducing H₂ atmospheres; whereas the production of sulfuric acid requires oxidizing species, notably OH and O₂. These reactive species, either reducing or oxidizing, are produced from photolysis of water and CO₂. In particular, the source of OH, responsible for converting SO₂ to sulfuric acid in the atmosphere, is the photodissociation of H₂O. As a result, the amount of UV photons that are capable of dissociating water controls the yield of H₂SO₄. For example in the habitable zone of a quiet M dwarf the yield of H₂SO₄ is much reduced compared with solar-like stars by at least one order of magnitude.

Zoom In Zoom Out Reset image size

The photochemically produced S₈ and H₂SO₄ may condense to form aerosols in the atmosphere if saturated. As a result, aerosols in the atmospheres provide a UV shield that enables the accumulation of H₂S and SO₂ beneath the layer of aerosols. In particular for an Earth-sized planet in the habitable zone of a Sun-like star, when the surface emission rate is more than two orders of magnitude higher than the current Earth's volcanic sulfur emission rate, photochemical aerosols in the atmosphere lead to substantial UV shielding for accumulation of H₂S and SO₂, as shown in Figure 3. We find that only when sulfur emission is highly elevated with respect to current Earth could H₂S or SO₂ accumulate to the order of parts per million mixing ratio in the N₂ and CO₂ atmospheres.

The relative yield between elemental sulfur and sulfuric acid is controlled by the redox power of the atmosphere. In general, more sulfuric acid aerosols and less elemental sulfur aerosols are anticipated in a more oxidizing atmosphere. The redox power of the atmosphere, in turn, is determined by both the main constituent and the reducing gas emission. CO₂-dominated atmospheres are more oxidizing than N₂-dominated atmospheres as photodissociation of CO₂ leads to atomic oxygen. Therefore, the primary sulfur emission is more likely to be converted to sulfuric acid in CO₂-dominated atmospheres than in N₂-dominated atmospheres (see Figure 3). Surface emission of reducing gases, including H₂, CH₄, CO, and H₂S, alters the redox budget of the atmosphere and therefore increases the relative yield of elemental sulfur versus sulfuric acid aerosols (e.g., Zahnle et al. 2006). As shown in Figure 3, when the sulfur emission rate increases, both N₂ and CO₂ atmospheres become more and more reducing (because H₂S is reducing), which results in a dramatic increase of elemental sulfur production in the atmosphere. Furthermore, the H₂S/SO₂ ratio in the sulfur emission affects its contribution to the redox power of the atmosphere and then the relative abundances of the two types of aerosols in the atmosphere significantly. As a result of the increase in the H₂S/SO₂ emission ratio, the amount of S₈ aerosol in the atmosphere increases, and the amount of H₂SO₄ in the atmosphere decreases dramatically (see Figure 4). For an Earth-like planet having an N₂ atmosphere, if the H₂S/SO₂ emission ratio is less than 0.1 (as is the case for current Earth; Holland 2002), the dominant type of aerosols in the atmosphere is sulfate; whereas elemental sulfur aerosols become the dominant type if the H₂S/SO₂ emission ratio is larger than 1.

Zoom In Zoom Out Reset image size

The main finding is that on terrestrial exoplanets having atmospheres ranging from reducing to oxidizing, the primary sulfur emission from the surface (e.g., H₂S and SO₂) is chemically short-lived. The sulfur emission leads to photochemical formation of elemental sulfur (S₈) and sulfuric acid (H₂SO₄), which would condense to form aerosols if saturated in the atmosphere. In reducing atmospheres (e.g., H₂ atmospheres), S₈ aerosols are photochemically formed based on H₂S and SO₂ emission; and in oxidized atmospheres (e.g., N₂ and CO₂ atmospheres), both S₈ and H₂SO₄ aerosols may be formed (see Figure 5). In general, the higher the surface sulfur emission, the more aerosols exist in the atmosphere (see Figure 5).

Zoom In Zoom Out Reset image size

As a result of photochemical production of elemental sulfur and sulfuric acid, terrestrial exoplanets with a habitable surface temperature (e.g., 270–320 K) and substantial sulfur emission from the surface are likely to have hazy atmospheres. In this paper, we use "hazy" to describe an atmosphere that has significant aerosol opacities at visible wavelengths (e.g., 500 nm). We find that even with an Earth-like surface sulfur emission, 1 bar H₂-dominated atmospheres on habitable rocky exoplanets are hazy with S₈ aerosols (see Figure 5). We also find that if the sulfur emission rate is 30–300 times more than Earth's current volcanic sulfur emission rate, photochemical S₈ aerosols become optically thick at visible wavelengths in oxidized atmospheres including N₂ and CO₂ atmospheres (see Figure 5).

The key parameters that determine the aerosol opacity in the atmosphere are the surface sulfur emission rate, the dry deposition velocity, and the aerosol particle size. First, a higher surface sulfur emission rate leads to more sulfur and sulfate aerosols in anoxic atmospheres (e.g., Figures 5 and 6). Second, larger dry deposition velocities of H₂S and SO₂ cause more rapid removal of these sulfur compounds from the atmosphere, which reduces the chance of converting them into condensable molecules (i.e., S₈ and H₂SO₄). Therefore, larger dry deposition velocities of H₂S and SO₂ result in lower aerosol loading and aerosol opacities in the atmospheres, as shown in Figure 7. Third, we find that the particle size has only secondary effects on the chemical composition of the atmosphere (i.e., by increasing the penetration of ultraviolet radiation), but has a primary effect on the aerosol optical depth. For mean particle diameter varying in the range of 0.1–1 μm (i.e., typical particle sizes of photochemical aerosols on Earth (e.g., Seinfeld & Pandis 2006) and Titan (e.g., Rages et al. 1983)), we do not see a notable variation in the yield of elemental sulfur, but we see an enhancement of H₂SO₄ production with large particles (Figure 6). Even with the same aerosol abundances, however, micron-sized particles cause lower opacities at the visible wavelengths and higher opacities in MIR compared with submicron-sized particles (Figure 6).

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We capture the effects of the three key parameters on the aerosol opacity in anoxic atmospheres on terrestrial exoplanets by fitting the following power-law formula, i.e.,

$$\begin{eqnarray} &&\tau = C\left (\frac{\Phi ({\rm S})}{10^{11}\ {\rm cm}^{-2}\ {\rm s}^{-1}}\right)^a\left (\frac{V_{\rm DEP}}{V_{\rm DEP}({\rm Earth})}\right)^{-b}\left (\frac{d_{\rm P}}{0.1\ \mu {\rm m}}\right)^{-c}, \nonumber\\ \end{eqnarray} \tag{ 4 }$$

where τ is the vertical optical depth due to aerosols at 1 bar, Φ(S) is the total sulfur emission rate, V_DEP/V_DEP(Earth) is the dry deposition velocities of H₂S and SO₂ with respect to current Earth values, d_p is the mean particle diameter of aerosols, a, b, and c are positive numbers, and C is a constant that covers other uncertainties. We have fit the empirical relation (4) through an extensive parameter exploration using photochemistry models (see Figures 5–7 for examples) and determined the values of C, a, b, and c for H₂-dominated reducing atmospheres and for N₂- and CO₂-dominated oxidized atmospheres. We summarize graphically the parameter regime in which sulfur emission leads to a hazy atmosphere in Figure 8. Here we use τ_500 nm and τ_7.5 μm as the representatives for aerosol opacities at visible wavelengths and MIR wavelengths; due to the complex nature of the extinction cross sections of aerosol particles (Figure 1), it is not practical to fold the full wavelength dependency into the empirical formula. Also, we find that it is always true that τ_500 nm ∼ 0 for mean particle diameter in the order of 10 μm and τ_7.5 μm ∼ 0 for mean particle diameter in the order of 0.1 μm.

Zoom In Zoom Out Reset image size

For H₂ atmospheres, and mean particle diameter d_P in the range of 0.1–1 μm,

$$\begin{eqnarray} \tau _{500 \,\rm {nm}} &=& 1\hbox{--}20\left (\frac{\Phi ({\rm S})}{10^{11}\ {\rm cm}^{-2}\ {\rm s}^{-1}}\right)^{0.5}\left (\frac{V_{\rm DEP}}{V_{\rm DEP} ({\rm Earth})}\right)^{-0.4} \nonumber\\ &&\times \left(\frac{d_{\rm P}}{0.1\ \mu {\rm m}}\right)^{-0.6}, \end{eqnarray} \tag{ 5 }$$

and for d_P in the range of 1–10 μm,

$$\begin{eqnarray} \tau _{7.5 \,\rm {\mu m}} &=& 0.1\hbox{--}1\left (\frac{\Phi ({\rm S})}{10^{11}\ {\rm cm}^{-2}\ {\rm s}^{-1}}\right)^{0.7}\left (\frac{V_{\rm DEP}}{V_{\rm DEP} ({\rm Earth})}\right)^{-0.4} \nonumber\\ &&\times \left (\frac{d_{\rm P}}{1.0\ \mu {\rm m}}\right)^{-1.5}. \end{eqnarray} \tag{ 6 }$$

For N₂ and CO₂ atmospheres, and d_P in the range of 0.1 and 1 μm,

$$\begin{eqnarray} \tau _{500 \,\rm {nm}} &=& 0.1\hbox{--}3\left (\frac{\Phi ({\rm S})}{10^{11}\ {\rm cm}^{-2}\ {\rm s}^{-1}}\right)^{0.7}\left (\frac{V_{\rm DEP}}{V_{\rm DEP} ({\rm Earth})}\right)^{-0.3} \nonumber\\ &&\times \left(\frac{d_{\rm P}}{0.1\ \mu {\rm m}}\right)^{-0.7}, \end{eqnarray} \tag{ 7 }$$

and for d_P in therange of 1–10 μm,

$$\begin{eqnarray} \tau _{7.5 \,\rm {\mu m}} &=& 0.01\hbox{--}0.1\left (\frac{\Phi ({\rm S})}{10^{11}\ {\rm cm}^{-2}\ {\rm s}^{-1}}\right)^{0.8}\left (\frac{V_{\rm DEP}}{V_{\rm DEP} ({\rm Earth})}\right)^{-0.5} \nonumber\\ &&\times \left (\frac{d_{\rm P}}{0.1\ \mu {\rm m}}\right)^{-1.6}. \end{eqnarray} \tag{ 8 }$$

The constant C in Equations (5)–(8) spans about one order of magnitude, which covers the variation of the following model inputs.

• 1.  
  The H₂S/SO₂ ratio in the surface sulfur emission, ranging from 0.01 to 10.
• 2.  
  Temperature profiles deviating from the adopted temperature profile by ±30 K that controls the mixing ratio of water vapor in the atmosphere by the cold trap.
• 3.  
  Stellar ultraviolet radiation received by the planet, ranging from the habitable zone of solar-like stars to the habitable zone of quiet M dwarfs with an effective temperature of 3100 K.
• 4.  
  Eddy diffusion coefficients ranging from 0.1 to 100 times the values of Earth's atmosphere.
• 5.  
  Sulfur polymerization reaction rates (reactions (C3)–(C7)) ranging by one order of magnitude.

To summarize, we find that the emission of H₂S and SO₂ from the surface is readily converted into sulfur (S₈) and sulfate (H₂SO₄) in anoxic atmospheres of terrestrial exoplanets. The photochemical sulfur and sulfate would condense to form aerosols if saturated in the atmosphere, which is likely to occur on a planet in the habitable zone of either a Sun-like star or a quiet M star. The aerosol layer is optically thick at the visible and NIR wavelengths if the surface sulfur emission is comparable to Earth's volcanic sulfur emission in the H₂ atmosphere, and more than 30–300 times Earth's volcanic sulfur emission in other anoxic atmospheres, depending on the dry deposition velocities of sulfur compounds and particle size of the aerosols.

The sulfur emission from the surface shapes the spectra of terrestrial exoplanets at the visible and NIR wavelengths, mostly through the photochemical formation of S₈ and H₂SO₄ aerosols. We use the model outputs from the photochemistry models to compute the transmission, reflection, and thermal emission spectra of a terrestrial exoplanet with various levels of sulfur emission, and show examples of the computed spectra in Figure 9. We see that submicron-sized S₈ aerosols dominate the transmission and reflection spectra at wavelengths from visible up to 3 μm, if the sulfur emission is more than about two orders of magnitude higher than Earth's volcanic sulfur emission. In general, an atmosphere with high sulfur emission and therefore high aerosol loading generally exhibits a flat transmission spectrum (the H₂O features at NIR muted), and a high visible albedo (see Figure 9). Notably, S₈ aerosols are purely reflective at 500 nm but absorptive at 300 nm. The absorption edge of S₈ aerosols in 300–400 nm is evident in the reflection spectra for planets with enhanced sulfur emission (Figure 9), which is a potential diagnostic feature for S₈ aerosols.

Zoom In Zoom Out Reset image size

Although opaque at visible wavelengths, the atmospheres with enhanced sulfur emission are likely to be transparent in the MIR wavelengths (λ > 5 μm). The spectral features of aerosols depend on their particle sizes, so we now consider two possibilities: if the particles are submicron-sized, the aerosol molecules have negligible cross sections at MIR (see Figure 1); or if the particles are micron-sized, the falling velocity of aerosol particles is large enough to rapidly remove aerosols from the atmosphere, as implied by Equations (6) and (8) that are applicable for micron-sized particles. Therefore in both cases the aerosol opacities at MIR are minimal even for very high sulfur emission rates (see Figure 9 for examples of N₂ atmospheres, and H₂ atmospheres are qualitatively similar). The only exception, in which aerosols indeed affect MIR spectra, is the case of abundant H₂SO₄ aerosols. The main spectral effect of H₂SO₄ aerosols is absorption at MIR wavelengths (5–10 μm; Figure 9). However, the column-average mixing ratio of H₂SO₄ needs to be larger than 0.1 ppm in order to produce significant aerosol absorption at MIR. We find with numerical exploration that such a high abundance of H₂SO₄ aerosols is only possible in highly oxidizing CO₂-dominated atmospheres without reducing gas emission (see Paper I for an example of such atmospheres). With reducing gas emission (i.e., H₂ and CH₄), it is unlikely that H₂SO₄ mixing ratio exceeds 0.01 ppm in anoxic atmospheres for a wide range of sulfur emission rates (see Figure 5). In summary, we expect the spectral effects of S₈ and H₂SO₄ aerosols to be minimal at MIR for most cases.

We now turn to consider the direct spectral features of H₂S and SO₂. It has been previously proposed that H₂S and SO₂ can be detectable on terrestrial exoplanets by their spectral features (Kaltenegger & Sasselov 2010). However, our photochemistry models show that both H₂S and SO₂ are chemically short-lived in the atmospheres, which implies that substantial surface emission is required to maintain a detectable level of either H₂S or SO₂ in the atmosphere. SO₂ has diagnostic absorption features at 7.5 μm and 20 μm (see Figure 9). For these features to be detectable the mixing ratio of SO₂ needs to be larger than 0.1 ppm, which corresponds to sulfur emission rates 1000 times more than current Earth's sulfur emission rates for H₂, N₂, and CO₂ atmospheres (see Figure 5). The spectral feature of H₂S is the pseudo-continuum absorption at wavelengths longer than 30 μm, which coincides with the rotational bands of H₂O. We find that the only scenario in which H₂S may be directly detected is the case with extremely high sulfur emission rates (i.e., 3000 times higher than the current Earth's sulfur emission rate) on a highly desiccated planet without liquid water ocean so that there is no water vapor contamination. We therefore conclude that direct detection of H₂S and SO₂ is tricky: they are chemically short-lived so that extremely large surface emission is required for a detectable mixing ratio in the atmosphere, and their spectral features may be contaminated by other gases in the atmosphere.

Finally, we suggest that the emission of sulfur compounds might be indirectly inferred by detecting sulfur and sulfate aerosols. Our numerical exploration reveals a monotonic relationship between the abundance of aerosols in the atmosphere and the emission rates of sulfur compounds (see Figure 5), and the composition of aerosols is correlated with the H₂S/SO₂ ratio of the surface emission (see Figure 4). A combination of featureless low atmospheric transmission (large planet radius viewed in transits) and high planetary albedo (large planetary flux at the visible wavelengths viewed in occultations) may establish the existence of aerosols in the atmosphere. In particular, elemental sulfur (S₈) aerosols are absorptive at wavelengths shorter than 400 nm and therefore might be identified by the absorption edge (see Figure 9). Sulfate aerosols (H₂SO₄), if abundant in the atmosphere, lead to absorption features at the MIR wavelengths (λ ∼ 5–10 μm). However, none of these features are uniquely diagnostic of certain types of aerosols. The identification of aerosol composition, therefore, is by no means straightforward. We learn from the solar system exploration that the discriminating piece of information for aerosol identification comes from polarization of reflected stellar light. Historically, the bright clouds on Venus were identified to be mainly composed of H₂SO₄ droplets after the phase curve of the planet in polarized light had been observed (e.g., Young 1973; Hansen & Hovenier 1974). We therefore postulate that aerosol identification on terrestrial exoplanets and the inference of surface sulfur emission might require observation of polarized reflected light as a function of the planetary illumination phase.