Sulfur Hazes in Giant Exoplanet Atmospheres: Impacts on Reflected Light Spectra

Observations of exoplanets have revealed a ubiquity of clouds and hazes that impede understanding of their composition. The presence of these clouds and hazes is typically shown by a flattening of spectral features in transmission spectra, resulting from the inability of stellar photons to reach depths in the atmosphere below the cloud and haze layers (Gibson et al. 2012, 2013; Deming et al. 2013; Jordán et al. 2013; Mandell et al. 2013; Sing et al. 2013; Chen et al. 2014; Fukui et al. 2014; Schlawin et al. 2014; Wilkins et al. 2014; Mallonn & Strassmeier 2016). Such flat transmission spectra have been seen across many exoplanets of different sizes, effective temperatures, and stellar irradiation levels (e.g., Crossfield et al. 2013; Knutson et al. 2014a, 2014b; Kreidberg et al. 2014; Sing et al. 2016), suggesting that the processes governing cloud and haze formation in exoplanet atmospheres are as complex as they are ubiquitous. Clouds and hazes have also been inferred from optical phase curves, where higher-than-expected albedos have been attributed to reflective clouds (e.g., Demory et al. 2013), and dust clouds have been invoked to fit spectra of directly imaged exoplanets (Barman et al. 2011; Madhusudhan et al. 2011; Marley et al. 2012; Currie et al. 2014; Skemer et al. 2014; Chilcote et al. 2015; Macintosh et al. 2016).

One key unknown is whether the aerosols blocking the stellar photons are part of a cloud, which condenses from atmospheric gases and is typically supported in an atmosphere by turbulent mixing, or part of a haze, whose particles are usually produced by photochemistry and often found at high altitudes. Morley et al. (2013) showed that, for the super-Earth GJ 1214 b, photochemical hazes may be preferred as a solution to its flat transmission spectra, as they are formed high up in the atmosphere. By contrast, cloud particles must be lofted by turbulent mixing, and high metallicity may be required to ensure that enough material gets to the pressure levels probed by transmission spectroscopy.

The composition and vertical structure of atmospheric aerosols, whether clouds or hazes, are also of first-order importance for understanding the reflected light spectra of a planet (see Marley et al. 2013, for a review). Cloudless extrasolar giant planets, for example, are expected to be relatively bright at blue wavelengths but dark in the red optical and near-infrared, where molecular absorption dominates over Rayleigh scattering; cloudy planets, by scattering more photons before they can be absorbed, can be much brighter (Marley et al. 1999; Sudarsky et al. 2000). Likewise for terrestrial planets, Morley et al. (2015) and Charnay et al. (2015) showed that there are large differences in the reflected light spectra of super-Earths depending on whether the planet is cloudy or hazy and what kind of aerosols are present. Specifically, cooler planets with KCl and water clouds may be more reflective than clear planets in the near-infrared, while ZnS clouds, forming at similar temperatures, are more absorbing. In contrast, planets with complex hydrocarbon, "soot" hazes resulting from methane photolysis and polymerization could be very dark, whereas hazes composed of tholins—nitrogen-rich organics thought to comprise Titan's hazes (Khare et al. 1984)—are dark at the blue end of the visible range and more reflective at the red end.

The reflectivity of clouds and hazes also impacts the amount of compositional information that can be retrieved from direct imaging, as reflected light is only able to sample the atmosphere above the cloud/haze deck. If the cloud/haze deck is at high altitudes, then the column optical depth of absorbing gases that direct imaging can sample is small, thereby reducing the magnitude of their spectral features in these planets' reflected light spectra (Marley et al. 1999; Sudarsky et al. 2000). Meanwhile, if the cloud/haze is absorbing, then very few photons can sample the chemical composition of the atmosphere and escape. Such considerations are particularly relevant, as NASA is now studying future space-based telescopes capable of characterizing extrasolar planets through high-contrast direct imaging (Krist et al. 2007; Boccaletti et al. 2015; Robinson et al. 2016).

An alternative set of compounds that are known to form hazes in planetary atmospheres are those derived from sulfur chemistry. In oxidizing atmospheres, SO₂, OCS, and H₂S from volcanic outgassing are transformed into sulfuric acid through photolysis and reactions with water. Condensation of sulfuric acid can then form clouds and hazes, such as the global cloud deck of Venus (Hansen & Hovenier 1974) and the Junge layer in the upper stratosphere of Earth (Junge 1963). In reducing atmospheres, photolysis of H₂S can lead to the formation of elemental sulfur. For example, the existence of sulfur aerosols has been proposed for the Venus atmosphere, especially in regions depleted in oxidants (Toon et al. 1982; Zhang et al. 2012). Precipitation of elemental sulfur is the leading hypothesis for the preservation of mass-independent fractionation of sulfur isotopes found in sediments on Earth older than 2.4 billion yr (Pavlov & Kasting 2002). Hu et al. (2013) showed that terrestrial exoplanets with H₂-dominated atmospheres could be enveloped in optically thick sulfur hazes resulting from volcanic outgassing of H₂S.

More recent work by Zahnle et al. (2016) showed that rich sulfur photochemistry could potentially take place in the atmospheres of temperate giant exoplanets (250 K < T_eq < 700 K), generating sulfur allotropes that may condense to form hazes at lower temperatures. As these planets are the targets of current and planned direct imaging campaigns, it is essential that the optical characteristics of elemental sulfur hazes be known in order to inform these future observations. In this paper we investigate the geometric albedo spectra of giant planets hosting elemental sulfur hazes and their variations with haze properties, such as the location of the haze in the atmosphere and the haze optical depth. We also address the observability of a sulfur haze and its impact on inferences of atmospheric composition for the upcoming space-based direct imaging campaigns of the Wide Field Infrared Survey Telescope (WFIRST; Spergel et al. 2013). In future publications, we will evaluate the impact of sulfur hazes on transmission spectroscopy and thermal emission, particularly from temperate, young, directly imaged planets.

In Section 2, we give an overview of the sulfur chemistry elaborated on in Zahnle et al. (2016), with a focus toward the formation of sulfur hazes, as well as sulfur's optical properties. In Section 3 we describe in brief the suite of models used in this study. In Section 4 we present our results showing how the geometric albedo varies with different haze properties and whether a clear planet can be distinguished from a hazy planet using proposed instruments on board WFIRST. Finally, in Section 5 we discuss the impact of our assumptions, the implications of our results, and potential avenues of investigation for future missions and observation campaigns.

H₂S is the dominant reservoir of sulfur in giant exoplanet atmospheres under equilibrium chemistry for the temperatures and pressures considered here (T_eq ∼ 250–700 K, P ∼ 0.1–100 mbar). At temperatures below ∼200 K NH₃ condenses and reacts with H₂S to form NH₄SH (Atreya et al. 1999; Loeffler et al. 2016), whereas above ∼1500 K (at P < 1 bar) it dissociates into SH and S (Visscher et al. 2006). The stability of H₂S is disrupted by disequilibrium processes, however, as upward transport of H₂S to the tropopause by turbulent mixing and advection results in its destruction by photolysis and reactions with atomic H released from photolysis of CH₄, NH₃, and H₂O (Zahnle et al. 2016):

$$\begin{eqnarray}&&{{\rm{H}}}_{2}{\rm{S}}+{\rm{H}}\longrightarrow \mathrm{HS}+{{\rm{H}}}_{2}.\end{eqnarray} \tag{ R1 }$$

The resulting HS radical quickly reacts to free sulfur and forms S₂:

$$\begin{eqnarray}&&\mathrm{HS}+{\rm{H}}\longrightarrow {\rm{S}}+{{\rm{H}}}_{2},\end{eqnarray} \tag{ R2 }$$

$$\begin{eqnarray}&&\mathrm{HS}+{\rm{S}}\longrightarrow {\rm{H}}+{{\rm{S}}}_{2}.\end{eqnarray} \tag{ R3 }$$

This begins the polymerization process to form higher sulfur allotropes, eventually creating the stable allotrope, S₈. Transport of S₈ into the deep atmosphere then results in its destruction via thermal decomposition

$$\begin{eqnarray}&&{{\rm{S}}}_{8}+{\rm{M}}\longrightarrow 2{{\rm{S}}}_{4}+{\rm{M}},\end{eqnarray} \tag{ R4 }$$

the products of which go on to decompose further before reforming H₂S, thus completing the cycle. In the event that the equilibrium S₈ partial pressure is above the saturation vapor pressure P_sat of S₈ somewhere in the atmosphere, given by (Zahnle et al. 2016)

$$\begin{eqnarray}{P}_{\mathrm{sat}}=\left\{\begin{array}{ll}\exp (20-11800/T) & T\lt 413\,{\rm{K}}\\ \exp (9.6-7510/T) & T\gt 413\,{\rm{K}}\end{array}\right.,\end{eqnarray} \tag{ 1 }$$

then an S₈ haze may form.

Figure 1 shows the temperature profile (blue), saturation mixing ratio of S₈ (saturation vapor pressure divided by total atmospheric pressure, in yellow), and the equilibrium mixing ratios of numerous chemical species in a temperate giant exoplanet atmosphere (see Section 3.1) as a result of photochemistry and transport by eddy diffusion. The equilibrium mixing ratio of S₈ peaks at ∼1 ppmv and crosses the S₈ saturation mixing ratio curve between 100 and 1 mbar (the yellow region). This allows for a rough estimate of the total mass of the haze, assuming that all S₈ that is supersaturated condenses. For example, 1 ppmv of S₈ at the 100 mbar level with T ∼ 250 K results in a number density of S₈ molecules of ∼3 × 10¹² cm⁻³. Assuming a column height equaling one scale height (∼20 km at 100 mbar for this atmosphere), the column integrated number density of S₈ is ∼6 × 10¹⁸ cm⁻², which translates to a haze particle column number density of ∼3 × 10¹¹ cm⁻² assuming a particle size of 0.1 μm and a mass density of 2 g cm⁻³.

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The ultimate haze mass will depend on the microphysics of haze formation (see Section 5) and the degree to which S₈ is supersaturated, which in turn depends on the equilibrium S₈ mixing ratio and the S₈ saturation vapor mixing ratio. Zahnle et al. (2016) showed that, for a wide range of stellar UV fluxes and eddy diffusivities, the peak equilibrium S₈ mixing ratio remained close to 1 ppmv to within a factor of 2, though its vertical profile became more extended/compressed when the eddy diffusivity increased/decreased, respectively. The S₈ mixing ratio is largely independent of stellar UV fluxes because the fluxes experienced by temperate giant exoplanets are such that the photochemistry is limited by H₂S upwelling, rather than the supply of UV photons. The S₈ mixing ratio is also independent of the eddy diffusivity because, in the event that S₈ does not condense, the upward mixing of H₂S is balanced by the downward mixing of S₈, and thus changing the rate of mixing should not change the size of the reservoirs from which material is exchanged by mixing. Note, however, that as precipitation of sulfur becomes important, the mass of haze will begin to reflect the UV flux and the vertical mixing; we will revisit this topic in future work. Furthermore, as Figure 1 shows, changing the temperature does not greatly alter the S₈ mixing ratio because to first approximation all the sulfur is in the form of S₈ molecules. The reason S₈ is favored is that all other S-containing molecules are easily photolyzed by abundant 200–300 nm UV photons. S₈ is also subject to photolysis, but it is a ring molecule, which means that after photolysis it becomes a linear S₈ molecule that is rather likely to grab its tail and reemerge as a ring. In other words, though varying the temperature changes the rates of reactions, all reactions eventually lead to the transformation of H₂S to S₈ above the tropopause.

Given the stability of the equilibrium S₈ mixing ratio, the S₈ supersaturation will largely depend on the saturation vapor mixing ratio, which is a function of temperature. Figure 2 shows the S₈ saturation vapor mixing ratio as a function of temperature and pressure level in the atmosphere, where the range in pressure level denotes where S₈ tends to be abundant (Zahnle et al. 2016). The solid line indicates a saturation vapor mixing ratio of 1 ppmv, while the dashed lines to the left and right sides of it indicate 0.1 and 10 ppmv, respectively. Thus, if an exoplanet atmosphere contains 1 ppmv of S₈, then condensation can occur (S₈ is supersaturated) for temperatures and atmospheric pressure levels to the left of the 1 ppmv line, while to the right the abundance of S₈ is too low to condense. As previously indicated, however, NH₄SH clouds are expected to form at temperatures <200 K (when NH₃ may condense), which removes H₂S from the atmosphere and arrests the photochemical production of S₈. Therefore, we can conclude that sulfur hazes may arise on temperate giant exoplanets with stratospheric temperatures <325 K but warmer than Jupiter, assuming that their metallicity is solar. Increasing the metallicity leads to an increase in the high-temperature limit for sulfur haze formation (and vice versa for lower metallicity), due to the increased sulfur mixing ratio in the atmosphere, i.e., if the equilibrium S₈ mixing ratio is 10 ppm rather than 1 ppm, then sulfur hazes can form up to ∼350 K. The situation at the low-temperature limit is more uncertain, however, due to the unknowns in the formation of NH₄SH clouds.

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The effect of a sulfur haze on a planet's geometric albedo depends heavily on sulfur's optical properties, stemming primarily from its complex refractive index. Figure 3 shows the real (n) and imaginary (k) indices of refraction for orthorhombic crystals of sulfur, a form of solid sulfur composed mainly of S₈. Orthorhombic sulfur is the most thermodynamically stable form of solid S₈ for the temperatures relevant here and is therefore the most likely composition of sulfur hazes on giant exoplanets, with other forms converting to orthorhombic sulfur on finite timescales that tend to decrease with increasing temperatures (Fuller et al. 1998). Above 368 K, an alternative form, monoclinic sulfur, becomes thermodynamically preferred (Meyer 1976). A key feature of orthorhombic sulfur's complex refractive index is the increase in k at shorter wavelengths caused by vibrational modes in the S₈ molecules, which tend to become more populated at higher temperatures, thereby shifting the increase in k to longer wavelengths (Meyer et al. 1972). Increased absorption at shorter wavelengths will lead to sulfur-haze-enveloped exoplanets being yellowish to reddish in color.

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3.1. Model Atmosphere

3.2. Cloud Model and Haze Treatment

The PT profile of our model atmosphere is such that KCl and ZnS can potentially condense and form clouds (Morley et al. 2012). To include clouds in our model, we use the approach of Ackerman & Marley (2001), where the cloud mass and mean particle size are determined by balancing vertical mixing due to eddy diffusion and sedimentation of cloud particles

$$\begin{eqnarray}&&{K}_{{zz}}\displaystyle \frac{\partial {q}_{{\rm{t}}}}{\partial z}+{f}_{\mathrm{sed}}{{wq}}_{{\rm{c}}}=0,\end{eqnarray} \tag{ 2 }$$

where q_t is the total mixing ratio of the condensing species, q_c is the mixing ratio of the condensed form of the condensing species only, w is the convective velocity, f_sed is a tunable parameter and a measure of the sedimentation efficiency of the cloud particles that we set to 3, appropriate for Jupiter-like words (Ackerman & Marley 2001; Saumon & Marley 2008; Morley et al. 2012), and K_zz is the eddy diffusion coefficient, calculated by assuming that the convective mass transport is equivalent to convective heat transport. A minimum value ${K}_{{zz}}^{\min }$ = 10⁵ cm² s⁻¹ is set in regions that are convectively stable, as eddy diffusion does not only represent convective turbulence. Parameter w is then calculated via mixing length theory: w = K_zz/L, where L is the mixing length given by

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

where H is the atmospheric scale height, Γ and Γ_ad are the local and dry adiabatic lapse rates, respectively, and 0.1 is the minimum scaling for L when the atmosphere is convectively stable.

For both the clouds and sulfur haze, we assume that the particle size distribution dn/dr is lognormal, given by

$$\begin{eqnarray}&&\displaystyle \frac{{dn}}{{dr}}=\displaystyle \frac{N}{r\sqrt{2\pi }\mathrm{ln}\sigma }\exp \left[-\displaystyle \frac{{\mathrm{ln}}^{2}(r/{r}_{g})}{2{\mathrm{ln}}^{2}\sigma }\right],\end{eqnarray} \tag{ 4 }$$

where N is the total number density of particles, r is the particle radius, r_g is the mean particle radius, and σ is a measure of the width of the distribution and is fixed to 2 in the cloud model. This choice of σ is motivated in Ackerman & Marley (2001), as it is broad enough to account for both freshly condensed particles and those that have grown by coagulation. We plan to explore sulfur particle growth and sedimentation more fully in a future study.

We position our nominal sulfur haze layer at the 10 mbar level in the model atmosphere, consistent with the results of Zahnle et al. (2016) and our Figure 1; the column number density of haze particles is set to 10¹¹ cm⁻², in agreement with our calculations of the haze mass in Section 2; and the mean particle radius is set to 0.1 μm, similar to mode 1 particles in the clouds of Venus, which may be composed of elemental sulfur (Knollenberg & Hunten 1980). We will test the sensitivity of geometric albedo spectra to these parameters.

The optical properties of the clouds and the sulfur haze, such as their optical depth, single scattering albedo, and asymmetry parameter (a measure of their degree of forward scattering), are calculated by the cloud model using Mie theory assuming homogeneous spheres. As with the sulfur haze, the optical properties of the clouds are determined by their complex indices of refraction, which for KCl and ZnS are provided by Querry (1987).

In a self-consistent atmosphere, the formation of clouds and hazes would perturb the PT profile, which will in turn lead to different molecular abundances. However, for this exercise we do not ensure this self-consistency. Instead, the PT profile is fixed to that of a clear atmosphere (though the molecular abundances do reflect condensation), with condensate clouds and the prescribed sulfur haze layer added to it afterward. We discuss the consequences of this assumption in Section 5.

3.3. Geometric Albedo Model

3.4. WFIRST Noise Model

WFIRST is a planned NASA mission to be launched in the mid-2020s. It is a space-based, coronagraph-equipped observational platform with a 2.4 m diameter primary aperture, an operational wavelength range from ∼0.4 to 1 μm, and a spectral resolution of 70 (Spergel et al. 2013). Robinson et al. (2016) showed that, given a coronagraph capable of achieving a planet–star contrast ratio of 10⁻⁹ and expected levels of read noise, dark current, leaked stellar light, and zodiacal light from the solar system and the exoplanetary system (noise terms that can be comparable to, or even dominate, the planetary signal itself), a giant exoplanet located at 2 au from a Sun-like star is readily detectable and characterizable with integration times of several tens of hours, provided that the exoplanetary system is located within about 10 pc and that the planet–star angular separation is within the coronagraph inner and outer working angles. Lupu et al. (2016) expanded beyond these constraints and gave a preliminary target list for WFIRST (see their Figure 1), which showed several objects (∼1/3) within the temperature range given in Section 2. Therefore, we can expect a significant fraction of WFIRST targets to exhibit atmospheric conditions favorable to sulfur haze formation.

We investigate the observability of a sulfur haze and its impact on the detectability of various atmospheric chemical species using an updated version of the noise model described in Robinson et al. (2016), which includes specific coronagraph designs that have been proposed for WFIRST, such as the Shaped Pupil Coronagraph (SPC; capable of both broadband imaging and spectroscopy; Kasdin et al. 2004) and the Hybrid Lyot Coronagraph (HLC; imaging mode only; Trauger et al. 2016). The baseline telescope and instrument parameter values corresponding to these coronagraphs are different from that of Robinson et al. (2016; see their Table 3). We show these updated values in Table 1.

Table 1.  Changes to Telescope and Instrument Parameter Values

		Value from	Value of	Value of
Parameter	Description	Robinson et al. (2016)	Current Work (HLC)	Current Work (SPC)
D	Telescope diameter	2 m	2.4 m	2.4 m
${R}_{e-}$	Read noise counts per pixel	0.1	0.2	0.2
${ \mathcal T }$	Telescope and instrument throughput	0.05	0.074	0.037
θIWA (λ/D)	Coronagraph inner working angle	2	2.8	2.7

Note. Only parameters updated for this work are shown.

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To fully characterize the impact of sulfur hazes on the geometric albedo spectrum, we position our exoplanetary system, composed of the K1IVe subgiant host star and the warm giant exoplanet at 8 pc distance, so that the full wavelength range under consideration can be observed without going beyond the inner or outer working angles (the real Gamma Cephei Ab is located 13.79 pc away (Hatzes et al. 2003), such that wavelengths longer than ∼0.6 μm would not be observable owing to the planet–star on-sky separation for those wavelengths being within WFIRST's inner working angle). In addition, we assume that (1) the exozodi brightness is the same as zodiacal light in our own solar system and (2) our model planet has the same radius as Jupiter. As the observation would likely be made while the exoplanet is at quadrature rather than at full phase, we multiply the contrast ratio calculated from the (full phase) geometric albedo by a correction factor 1/π, roughly simulating the drop in brightness at quadrature versus full phase. However, this does not take into account the changes in geometric albedo due to nonuniform scattering phase functions of the clouds and hazes in the atmosphere. It should also be noted that the real Gamma Cephei A is part of a binary system, which would reduce WFIRST's ability to reach its designed planet–star raw contrasts. For simplicity, we assume that our model host star does not have a stellar companion.

4.1. Geometric Albedo Spectra

Figure 4 shows the geometric albedo spectra of a clear Gamma Cephei Ab atmosphere (gray), an atmosphere with KCl and ZnS clouds included (blue), and our nominal hazy model including both the aforementioned clouds and a sulfur haze (black). Absorption features due to H₂O and CH₄ can be clearly discerned at longer wavelengths in the clear case, which makes the planet especially dark there. At shorter wavelengths Rayleigh scattering increases the geometric albedo, with absorption dominated by alkali metals such as potassium and sodium (Cahoy et al. 2010; Morley et al. 2015). Adding condensation clouds darkens the albedo by ∼5% as a result of ZnS absorption, even though the metallicity is not high enough to produce optically thick KCl and ZnS clouds.

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In contrast, adding a sulfur haze layer drastically alters the geometric albedo spectrum. The CH₄ and H₂O absorption bands are now mostly absent save for some small dips longward of 0.7 μm, where the planet is much brighter owing to the purely scattering sulfur haze there, while at wavelengths <0.45 μm the albedo drops precipitously owing to increased sulfur absorption, and all traces of alkali metal absorption are gone as a result of their depletion in the upper atmosphere from KCl and ZnS cloud formation deeper in the atmosphere. These features are strongly reminiscent of the geometric albedo spectrum of Venus, where sulfuric acid provides the high albedo at long wavelengths and an unknown UV absorber decreases the albedo shortward of ∼0.45 μm, though not as severely as what is seen here (the albedo shortward of 0.45 μm and longward of the SO₂ absorption band at 0.3 μm is ∼0.5; Pollack et al. 1980). While S₈ has been proposed as a candidate for the unknown absorber (Hapke & Nelson 1975; Young 1977), atmospheric models that included S₈ as one of the cloud particle modes were unable to fit the observations (Pollack et al. 1979). However, these studies do not rule out more complex scenarios that incorporate S₈. For example, the "gumdrop model" supposes that the Venus cloud particles may be layered spheres with cores of sulfuric acid surrounded by a thin shell of sulfur arising from collisions with small sulfur aerosols or direct condensation of sulfur onto the cores (Young 1983; Markiewicz et al. 2014; Petrova et al. 2015). Furthermore, reactions between sulfur and sulfuric acid can yield compounds of intermediate redox states that absorb UV, such as thiosulfates in the oxidizing Venus atmosphere and sulfanes in reducing atmospheres.

The shape of the geometric albedo spectrum, as produced by a sulfur haze, also contrasts with those produced by hazes composed of other materials. Hydrocarbon hazes such as soots, for example, darken the planet across the entire wavelength range studied here, while tholins are more similar to sulfur in that they also brighten a planet at long wavelengths while darkening it at short wavelengths, though the transition from high to low albedo for a tholin haze is considerably more gradual (Morley et al. 2015). Neither of these types of hazes is relevant for the kind of planets considered here, however, as hydrocarbon hazes are likely in low abundance at the relevant pressure levels owing to reactions between haze precursors with OH (Zahnle et al. 2016).

Figure 5 shows the variations in the geometric albedo spectrum as the sulfur haze layer is placed at different pressure levels in the atmosphere, within the range of pressure levels where S₈ is abundant. The location of the sulfur haze layer can be variable since it depends on where the S₈ mixing ratio curve intercepts the S₈ saturation vapor mixing ratio curve, which in turn is a function of the atmospheric temperature structure and intensity of vertical mixing. There is very little difference between the different cases, with the only variations due to increased absorption by CH₄ and H₂O as the haze is lowered in the atmosphere, thereby increasing the optical depth of these gases above the haze.

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Figure 6 shows the changes in the geometric albedo spectrum as the column number density of sulfur haze particles is varied. The column number density is strongly related to the degree of supersaturation of S₈ vapor and is controlled largely by the microphysics of sulfur haze formation. Increasing the column number density from our nominal case does not change the geometric albedo spectrum to any large degree, indicating that the effect of the sulfur haze has already "saturated" for our nominal haze abundance. This is not surprising since the optical depth of our nominal case is already >1. Decreasing the column number density past an optical depth of 1 reduces the effect of the haze on the geometric albedo. In particular, the brightness of the planet is reduced significantly longward of 0.45 μm until it begins to match the clear case. By contrast, the geometric albedo shortward of 0.45 μm remains largely unchanged even at very low sulfur haze optical depths, only approaching the clear case for optical depths 1000 times less than that of the nominal case.

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Figure 7 shows the changes in the geometric albedo spectrum as the mean sulfur haze particle size is varied, while keeping the total haze mass the same (i.e., increasing particle size leads to a lower column particle number density). Like the column number density, the particle size depends on the microphysics of sulfur haze formation and growth by condensation of S₈ vapor. Varying the particle size is seen to have different effects depending on whether the particles are mostly scattering (longward of 0.45 μm) or absorbing (shortward of 0.45 μm). In the scattering region, decreasing the particle size such that it becomes much smaller than the wavelength results in a Rayleigh slope developing at longer wavelengths, darkening the planet slightly. Increasing the particle size past the considered wavelength range leads to a decrease in the geometric albedo due to the decrease in haze optical depth. This results from the consolidation of haze mass in larger particles, since optical depth is proportional to the square of the particle radius, while particle mass is proportional to the cube of the particle radius, and the scattering efficiency is largely independent of the particle radius for radii much greater than the wavelength (van de Hulst 1957). The geometric albedo is largely unchanged in the absorbing part of the spectrum. This can be explained by the roughly linear relationship between particle size and the absorption efficiency (van de Hulst 1957); in other words, the decrease in haze optical depth due to consolidating mass in larger particles is balanced by an increase in absorption by those larger particles. In addition, the wavelength at which the geometric albedo drops abruptly moves to longer wavelengths with increasing particle size. This is because larger particles are more absorbing and smaller particles are more Rayleigh scattering, which increases the albedo at shorter wavelengths.

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4.2. Impact on WFIRST Observations

We can assess whether the drastic changes to a giant exoplanet's geometric albedo caused by a sulfur haze layer are detectable using the updated WFIRST noise model. Figure 8 shows the low-resolution (R = 70) planet–star flux ratio for the clear atmosphere case (blue) and the nominal hazy case (red). Superimposed on the spectra are synthetic observations taken by the SPC in imaging (teal) and spectroscopy (gray) mode and by the HLC (magenta), each with a 20 hr integration time per observation. Note that the SPC in spectroscopy mode requires three exposures to capture its full wavelength range, so the full observation time to obtain SPC spectra is 60 hr. The larger error bars near 1 μm are due to the dropping quantum efficiencies of the detector (∼90% at 0.6 μm versus ∼10% at 1 μm; Robinson et al. 2016; Traub et al. 2016). The top panel shows our idealized case, where the star system is placed at 8 pc to ensure that all wavelengths under consideration can be observed. The bottom panel shows the case where the star system is placed at its actual distance of 13.79 pc (Hatzes et al. 2003).

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There is a significant difference between the clear and hazy cases. For the wavelength range WFIRST is able to observe in the 8 pc case, the hazy planet is brighter by a factor of ∼6 and thus easier to detect. On the other hand, the minor CH₄ and H₂O absorption features in the hazy spectra are not detectable, thus rendering any effort to retrieve their abundances hopeless (Lupu et al. 2016). This is even more so in the case where the star system is placed at its actual distance, where the molecular features are not even accessible since they are at wavelengths within the inner working angle of the coronagraph. This does not affect the HLC channels at shorter wavelengths, however, which in both cases show an obvious Rayleigh slope for the clear planet. In contrast, the hazy planet has a geometric albedo spectrum that is flat for all observable wavelengths, making clear and hazy atmospheres easily distinguishable even for the actual Gamma Cephei Ab.

Nevertheless, a flat spectrum does not in itself confirm the existence of a sulfur haze, as its defining feature is its strong absorption shortward of 0.45 μm, which WFIRST cannot observe. However, while Morley et al. (2015) and Charnay et al. (2015) showed that high water ice clouds in a colder atmosphere and KCl and ZnS clouds in a warmer atmosphere could also produce flat geometric albedo spectra, the metallicities necessary (>50× solar) are far higher than what has been observed in giant planets. In fact, MacDonald et al. (2017) showed that the geometric albedo spectrum of a giant exoplanet with water clouds is replete with molecular features. Therefore, the existence of sulfur hazes offers a likely explanation for any future observations of temperate giant exoplanets with flat geometric albedo spectra longward of 0.45 μm.

We have demonstrated that sulfur photochemistry in temperate giant exoplanets with solar metallicity inexorably generates ∼1 ppmv of S₈ vapor for large swaths of planetary parameter space. Therefore, a sulfur haze could form if the stratospheric temperature is low enough such that S₈ becomes supersaturated. The effect of such a sulfur haze on the planet's geometric albedo is significant: pure scattering sulfur particles boost the albedo longward of 0.45 μm to ∼0.7, while strong absorption shortward of 0.45 μm lowers the albedo to near zero. This is the opposite trend to a clear atmosphere, where deep molecular absorption darkens a planet at long wavelengths while Rayleigh scattering brightens the planet at short wavelengths. Therefore, the existence of a sulfur haze would drastically change the color of the planet, shifting it from blue to orange. The haze also vastly reduces the detectability of atmospheric chemical species such as methane and water, as most of their absorbing column density lies below the sulfur haze. As a result, WFIRST direct imaging targets that exhibit sulfur hazes are unlikely to provide useful constraints on their atmospheric composition.

Our results depend heavily on the properties of the haze, such as the mean particle size and column particle number density; these are determined by microphysical processes, such as the nucleation of aerosols, growth by condensation and coagulation, loss through evaporation and collisional breakup, and transport by sedimentation, mixing, and advection (Pruppacher & Klett 1978; Marley et al. 1999). Although the modeling of these processes is beyond the scope of this work and will be treated in a future paper, we can speculate on how a sulfur haze subject to microphysics differs from the simple slab model we have used. A major difference would be the vertical profile of the haze. Vertical mixing will loft sulfur particles to higher altitudes, where the lower atmospheric pressure and S₈ mixing ratio may result in evaporation of haze particles and a decrease in mean particle size. A haze layer with a vertical gradient in mean particle size would generate a different geometric albedo spectrum than a layer with the same size distribution at all altitudes.

Given that the sulfur haze would have a source of new particles at or near the altitude where S₈ is photochemically produced, there exists the possibility of multimodal particle size distributions. The situation is similar to that of Venus, where large, ∼1 μm sulfuric acid cloud particles coexist with ∼0.1 μm particles of photochemical origins, possibly composed, at least in part, of elemental sulfur as well (e.g., Knollenberg & Hunten 1980; Imamura & Hashimoto 2001; Gao et al. 2014). In our case, freshly nucleated sulfur haze particles may coexist with larger, "aged" sulfur particles that have grown by the condensation of S₈ and other sulfur allotropes, resulting in more complex geometric albedo spectra than those presented here. Setting the particle size distribution width σ to 2 in our model is an effort to account for this scenario, but a more detailed study is needed.

As discussed in Section 2, the S₈ vapor mixing ratio is largely insensitive to the UV flux and the eddy diffusivity. However, this would no longer be true upon the formation of solid S₈, as it will lead to S₈ rainout. Indeed, while the S₈ supersaturation is important in determining the haze mass, another crucial factor is the difference between the haze loss rate due to rainout and the haze production rate, ultimately dependent on the UV flux. For example, if the UV flux were significantly smaller than the nominal values considered in Zahnle et al. (2016) and the particle transport were dominated by sedimentation rather than mixing, then any haze particles produced would be lost relatively quickly as a result of sedimentation and evaporation, leading to a more diffuse haze and depleted S₈ abundances above the pressure levels where S₈ can condense, much like condensation clouds. On the other hand, if the UV flux and/or eddy diffusivity were high enough such that ample haze particles are produced and are kept aloft in the atmosphere, then we can expect haze masses similar to those shown here. We will examine these processes in more detail in future work.

In addition to the microphysics of the haze itself, the effect of the haze on the rest of the atmosphere must be considered. The chemical abundances presented in Figure 1 do not take condensation into account. Indeed, if S₈ condenses, then all other sulfur allotropes may condense on the S₈ particles as well, as their saturation vapor pressures are all significantly lower (Lyons 2008; Zahnle et al. 2016). This will have the effect of not only changing the sulfur chemistry in the atmosphere, possibly removing all sulfur species above the haze layer, but also introducing/increasing contamination of the haze particles by smaller sulfur allotropes such as the metastable S₃ and S₄. Spectra of these species in the vapor phase have shown absorption bands at 400 nm (S₃) and 550 nm (S₄), which would push the UV absorption edge to longer wavelengths compared to what we have shown. This would make giant exoplanets with sulfur hazes redder still, and it may allow WFIRST to detect hints of their existence provided that there is a sufficient degree of contamination (Meyer et al. 1972; Meyer 1976). Finally, as H₂S is key in forming sulfide clouds in exoplanet atmospheres (Morley et al. 2012), including the ZnS clouds in our model, and sulfur haze particles can potentially form condensation nuclei for cloud formation, perturbations to the sulfur chemistry and emergence of sulfur hazes could impact condensation clouds as well.

The strong absorption of UV photons by sulfur hazes is also likely to affect the rest of the atmosphere. On Venus, absorption of UV by the unknown agent in the mesosphere leads to several K day⁻¹ of heating (Crisp 1986; Haus et al. 2015, 2016). Such heating in a giant exoplanet atmosphere may increase temperatures, affecting the sulfur haze abundance. Increasing the haze temperature also increases the wavelength of sulfur's UV absorption edge, though the change is small over the temperature range of relevance (∼0.23 nm K⁻¹; Meyer et al. 1972). On the other hand, the high albedo generated by the haze at longer wavelengths could decrease atmospheric temperatures by reflecting away more of the stellar flux. Calculating the equilibrium temperature profile due to haze heating and cooling will require a more sophisticated model.

The current configuration of WFIRST cannot observe the strong absorption of sulfur hazes shortward of 0.45 μm, which is its defining feature between 0.3 and 1 μm. Future telescopes capable of direct imaging (Dalcanton et al. 2015), such as the LUVOIR (Bolcar et al. 2016) or HabEx (Mennesson et al. 2016) mission concepts, as well as ground-based facilities, could potentially probe down to such short wavelengths. Alternatively, sulfur hazes may be discernible by thermal emission spectroscopy in the infrared, which has been conducted on young, bright giant exoplanets by ground-based observational campaigns (e.g., Kenworthy et al. 2016; Macintosh et al. 2016; Wagner et al. 2016) and will be especially powerful in the era of the James Webb Space Telescope (JWST). The refractive index of sulfur is essentially featureless between 1 and 2 μm, and a gap exists in the imaginary component between 2 and 7 μm, likely indicating that it was too low to be measured precisely. However, at wavelengths longer than 7 μm, k increases steadily from 10⁻⁶ to 10⁻², with punctuating spikes up to as high as 0.1 (Fuller et al. 1998), thereby offering possible features by which a sulfur haze could be characterized. In addition, the haze will become optically thin at wavelengths significantly greater than the particle size, such that important molecular features may be detectable in the infrared. We will investigate the effectiveness of JWST and other future telescopes at characterizing giant exoplanets with sulfur hazes in transmission and thermal emission in a future publication.

M.S.M. acknowledges the support of the WFIRST preparatory science program and the NASA XRP program. P.G. acknowledges the support of the NASA Postdoctoral Program. In addition, we acknowledge and thank the Kavli Summer Program in Astrophysics and its sponsors for providing the opportunity and funding to conduct this research. We thank the Scientific Organizing Committee (J. Fortney, D. Abbot, C. Goldblatt, R. Murray-Clay, D. Lin, A. Showman, and X. Zhang) for putting together an enlightening series of lectures and activities that bolstered our research efforts both at Kavli and at home. We thank P. Garaud, the program coordinator, and others in the Local Organizing Committee (J. Scarpelli, Z. Kornberg, and S. Nasab) for ensuring that our stay at UC Santa Cruz was an amazing experience, being both conducive to research and fun. We thank the senior participants in the Kavli program, in particular D. Catling, K. Menou, and J. Bean, for giving such illuminating and interesting talks to start off our days. Last but far from the least, we thank the Kavli Fellows, A. Baker, C. Leung, C. Cadiou, D. Powell, G. McDonald, K. Feng, K. Ohno, L. Mayorga, M. Malik, N. Batalha, N. Espinoza, R. Garland, F. Ryan, R. MacDonald, T. Komacek, T. Louden, and Y. Kawashima, for creating an incredible atmosphere of camaraderie, friendship, adventure, and cake by the ocean.

Software: FORTRAN, Python, IDL.