submitted to the Astrophysical Journal Photolytic Hazes in the Atmosphere of 51 Eri b 1 K. Zahnle 2 NASA Ames Research Center, Moffett Field, CA 94035 3 [email protected] 4 M. S. Marley 5 NASA Ames Research Center, Moffett Field, CA 94035 6 [email protected] 7 and 8 C. V. Morley 9 Department of Astronomy and Astrophysics, University of California, Santa Cruz, CA 95064 10 [email protected] 11 and 12 J. I. Moses 13 Space Science Institute, 4750 Walnut Street, Suite 205, Boulder, CO 80301 14 [email protected] 15 ABSTRACT 16 We use a 1D model to address photochemistry and possible haze formation in the 17 irradiated warm Jupiter 51 Eridani b. The intended focus was to be carbon, but sulfur photochemistry turns out to be important. The case for organic photochemical hazes is intriguing but falls short of being compelling. If they form, they are likeliest to do so if vertical mixing in 51 Eri b is weaker than in Jupiter, and they would be found below the regions where methane and water are photolyzed. The more novel result is that photochemistry turns H S into elemental sulfur, here treated as S . In the cooler 2 8 models, S is predicted to condense in optically thick clouds of solid sulfur particles, 8 whilstinthewarmermodelsS remainsavaporalongwithseveralothersulfurallotropes 8 that are both visually striking and potentially observable. For 51 Eri b, the division between models with and without condensed sulfur is at an effective temperature of – 2 – 700 K, which is within error its actual effective temperature; the local temperature where sulfur condenses is between 280 and 320 K. The sulfur photochemistry we have discussed is quite general and ought to be found in a wide variety of worlds over a broad temperature range, both colder and hotter than the 650-750 K range studied here, and we show that products of sulfur photochemistry will be nearly as abundant on planets where the UV irradiation is orders of magnitude weaker than it is on 51 Eri b. Subject headings: planetary systems — stars: individual(51 Eri b) 18 1. Introduction 19 The star 51 Eridani is a pre-main-sequence F dwarf that is only 20 million years old. Direct- 20 imaging observations with GPI (Gemini Planet Imager) reveal that the star is orbited by a self- 21 radiant young Jupiter, designated 51 Eri b, that emits with an effective temperature on the order 22 of T = 700±50 K (Macintosh et al. 2015). Thermal evolution models predict that a 20 Myr old 23 eff jovian planet with 51 Eri b’s luminosity will have mass ∼ 2M and radius ∼ 1R (Macintosh 24 Jup Jup et al. 2015). 25 Comparison by Macintosh et al. (2015) of the available spectral and photometric data to 26 spectral models reveal that while the planet shows methane in absorption, methane is depleted 27 compared to thermochemical equilibrium. Carbon monoxide is therefore expected to be abundant 28 but available data do not yet constrain it. Spectral matching with radiative transfer models also 29 stronglysuggestthatclouds,possiblypatchy,arepresentintheatmosphere(Macintoshetal.2015). 30 However, the planet is cool enough that silicate clouds if present would be confined to levels deep 31 beneath the photosphere and thus unlikely to affect what can be seen. Clouds of salts like Na S 32 2 and NaCl are possible, but even these would be expected to be confined to levels beneath the 33 photosphere by the low temperature of the planet (Morley et al. 2012). 34 In this study we use a 1D chemical kinetics model to ask whether, and under what conditions, 35 photochemical hazes are likely to form in the atmosphere of 51 Eri b and perhaps be the agent 36 responsible for the observed particulate opacity. We consider two candidates, one familiar, the 37 other more novel. The familiar candidate is an organic photochemical haze loosely analogous to 38 the hazes seen over Titan, Pluto, or Beijing. Such hazes have been proposed by many workers, but 39 to date the case for them has been inconclusive (Moses 2014). We will find here that a reasonable 40 case for a photochemical organic haze in 51 Eri b can be made, but we do not follow the chain of 41 polymerization reactions to molecules big enough and refractory enough that we can prove that 42 condensates actually form. The novel candidate is sulfur. With sulfur we can follow a much shorter 43 chain of polymerization to the point where sulfur condenses. We will show here that a good case 44 can be made for the presence of photochemical sulfur clouds in the atmosphere of 51 Eri b. 45 This paper begins with a brief review of some related previous work. We next reprise our own 46 – 3 – model. In section 4 we present results for models that span the parameter space in which 51 Eri 47 b probably resides. We will find that for some of these parameters organic hazes might form, and 48 for some parameters sulfur clouds will form, for some parameters both might form, and for some 49 parameters neither kind of haze is likely to form. The important role of sulfur raises the issue that 50 much of the sulfur chemistry is very poorly known. In section 5 we perform a series of sensitivity 51 teststoexaminehowthemodelrespondstoalternativeassumptionsaboutsulfur’sphotochemistry. 52 2. Previous Models 53 The possibility that photochemical organic hazes might be important in irradiated brown 54 dwarfs was first raised by Griffith et al. (1998). It remains an open question. 55 Thefirstexoplanetphotochemicalmodelsshowedthatsmallhydrocarbonswouldnotcondense 56 in the solar composition atmospheres of hot Jupiters (Liang et al. 2003, 2004). Line et al. (2010, 57 2011) confirmed this result for hot Jupiters. They predicted the flowering of a rich disequilibrium 58 non-methane hydrocarbon (NMHC) photochemistry in the cooler (∼ 800 K) and presumptively 59 metal-rich warm Neptune GJ 436b, but stopped short of concluding that the chemistry would 60 necessarilyleadtosmogs. Mosesandcoworkers(Mosesetal.2011;VisscherandMoses2011;Moses 61 et al. 2013a,b; Moses 2014) extended this model to bigger molecules, concluding that “complex 62 hydrocarbons and nitriles might produce high-altitude photochemical hazes” (Moses 2014). On the 63 other hand, as Moses (2014) also points out, methane has not yet been seen in GJ 436b. 64 There are several other models of exoplanet thermochemistry and photochemistry that have 65 been used to address a variety of hydrogen-rich exoplanets, from Jupiters to Neptunes to super- 66 Earths, but none of them go as far as predicting the photochemical production of organic hazes. 67 Venot et al. (2012) examined C-N-O photochemistry on HD 189733b and HD 209458b; Kopparapu 68 et al. (2012) explored the effect of the C/O ratio on the hot Jupiter WASP-12b; Venot et al. (2013) 69 usedhigh-temperatureUVcrosssectionstostudytheeffectofCO photolysisonthewarmNeptune 70 2 GJ 436b; Hu and Seager (2014) addressed temperature and elemental abundances in super-Earths 71 and mini-Neptunes, with application to GJ 1214b, HD 97658b, and 55 Cnc e; Agu´ndez et al. 72 (2014b) added tidal heating and metallicity variations to GJ 436b; Venot et al. (2014) looked at 73 temperature, metallicity, UV flux, tidal heating, and atmospheric mixing in warm Neptunes, with 74 applicationtoGJ3470bandGJ436b; MiguelandKaltenegger(2014)tookintoaccountstellartype 75 and orbital distance; Miguel et al. (2015) focused on Lyman α irradiation of GJ 436b and other 76 warm Neptunes; Koskinen et al. (2013) and Lavvas et al. (2014) addressed ion chemistry; Agu´ndez 77 et al. (2012, 2014a) used a 2D model to address the horizontal quenching that occurs when winds 78 carry hot air to cold places; and Benneke (2015) combined photochemistry with retrievals from 79 exoplanet transit spectra to mine for C/O ratios in several planets. 80 Two recent models do include heavier organic molecules (Rimmer and Helling 2016; Venot et 81 al. 2015). Rimmer and Helling (2016) compile an extensive reaction network that includes both 82 – 4 – neutral and ion chemistry; they pay particular attention to the formation of prebiotic molecules 83 like glycine, but they do not yet address photochemical hazes. Venot et al. (2015) have expanded 84 their reaction network to include selected hydrocarbons with as many as eight carbon atoms. A 85 plus is that their reaction network has been tested against combustion experiments. On the other 86 hand, it should be borne in mind that complex models of complex systems often achieve empirical 87 agreement by cancellation of errors, and that things can go awry when the model is applied to new 88 conditions. Venot et al. (2015) compute that cyclohexadiene (cC H , an obscure but reasonably 89 6 8 stablemolecule)isamajorphotochemicalproductin500Kstratospheres, exceedingevenacetylene 90 (C H ) and CO in abundance. Although Venot et al. (2015) do not mention photochemical hazes, 91 2 2 it is obvious that cyclohexadiene is well along the path to building a heavy smog. However, the 92 stated pathway for cC H formation goes through 93 6 8 C H +C H → nC H +H, (R60r) 2 2 2 2 4 3 averyendothermicreactionthatwewillencounteragaininsection4.1.1whenwediscussitsreverse. 94 We estimate that the rate for R60r is k = 3×10−13e−33000/T cm3/s, which at 500 K is very close 95 60r to never. It is hard to imagine how a reaction with such a huge activation energy could actually 96 be a major factor in a planetary atmosphere. 97 We have used our own code to address photochemistry and thermochemistry in giant planets 98 and brown dwarfs Zahnle et al. (1995, 2009); Zahnle and Marley (2014). Early versions of this 99 code (2011 and earlier) had some issues with the implementation of thermochemical equilibrium 100 that were corrected after consultations with Channon Visscher. Miller-Ricci Kempton et al. (2012) 101 and Morley et al. (2013, 2015) used the corrected code to address photochemistry in the warm 102 (T ≈ 550 K) super earth GJ 1214b and similar planets. They suggested that hazes should form 103 eff when reduced organic radicals like CH (building blocks of bigger organic molecules) were more 104 3 abundant than OH. If so, NMHCs can be abundant enough that organic hazes show potential to 105 provide a viable alternative to clouds of other condensible substances such as Na S. However, as 106 2 with GJ 436b, methane has not been seen in GJ 1214b. 107 3. Model Details 108 We use a vanilla 1D kinetics code to simulate atmospheric photochemistry. Such codes param- 109 eterize vertical transport as a diffusive process with an “eddy diffusion coefficient,” denoted K 110 zz [cm2/s]. Volume mixing ratios f of species i are obtained by solving continuity 111 i ∂f ∂φ i i N = P −L Nf − (1) i i i ∂t ∂z and diffusion 112 (cid:16)m g m g(cid:17) ∂f a i i φ = b f − −(b +K N) (2) i ia i ia zz kT kT ∂z equations for each species. In these equations N is the total number density (cm−3); P −L Nf 113 i i i represent chemical production and loss terms, respectively; φ is the upward flux; b , the binary 114 i ia – 5 – diffusioncoefficientbetweeniandthebackgroundatmospherea, describestruemoleculardiffusion; 115 and m and m are the molecular masses of a and i. 116 a i For the base model we use 481 forward chemical reactions and 42 photolysis reactions for 78 117 chemical species made from H, C, O, N, and S. We supplement these with 12 additional reactions 118 and two additional species for sensitivity tests. Every forward chemical reaction (e.g., CO+OH → 119 CO + H) is balanced by the corresponding reverse reaction (e.g., CO + H → CO + OH) at a 120 2 2 rate determined by thermodynamic equilibrium. We have not included reverses of the photolysis 121 reactions; that is, we include reactions such as H O + hν → H + OH, but we do not include 122 2 H+OH → H O+hν because radiative recombination of small molecules is typically slow, and our 123 2 chemical system does not include large molecules for which radiative attachment can be important 124 (Vuitton et al. 2012). 125 Organicphotochemistrybeginswithphotolysisofmethane. Methanefragmentscanreactwith 126 each other to make more complicated organic molecules. Non-methane hydrocarbons (NMHCs) 127 with unsaturated bonds are in turn prone to polymerizing to form chains, rings, PAHs (polycyclic 128 aromatic hydrocarbons), and soots (disorganized agglomerations of PAHs and sheets of PAHs). In 129 this study we truncate NMHC chemistry at C H , with the exception of C H . How we handle 130 2 n 4 2 C H asaproxyforpolymerizationisdiscussedindetailinsection4.1.1below. Themoreabundant 131 4 2 NMHC species in this model are C H , C H , C H , C H , H CO, CH OH, and HCN. The total 132 2 2 2 4 2 6 4 2 2 3 NMHC abundance is assessed as the total number of carbon atoms in the NMHCs and reported in 133 several figures below. 134 Sulfur photochemistry is the important new thing here. Sulfur photochemistry begins with 135 photolysis of, or chemical attack on, H S. Sulfur can be successively oxidized by OH (from H O 136 2 2 photolysis) to SO, SO , and SO or H SO . Sulfuric acid (H SO ) is a major aerosol on Venus and 137 2 3 2 4 2 4 Earth worth looking for generally. Sulfur can also react with hydrocarbons to make CS, CS , and 138 2 OCS. All three were abundant in the wake of the impacts of Comet Shoemaker-Levy 9 into Jupiter 139 in 1994 (Harrington et al. 2004). Finally, sulfur can polymerize, condense, and precipitate as the 140 element. The S molecule was seen as a strong signature in the SL9 plumes (Moses et al. 1995; 141 2 Zahnle et al. 1995) and it has been seen in volcanic plumes over Io (Spencer et al. 2000). There is 142 strong circumstantial evidence in sulfur’s isotopic record in Archean sediments that precipitation 143 of elemental sulfur was commonplace in the anoxic atmosphere of early Earth (Pavlov and Kasting 144 2002). Here we use a simplified system consisting of S, S , S , S , and S . As there is considerable 145 2 3 4 8 uncertainty in sulfur’s reactions, we have listed our choices for key reactions in Table 1. Most of 146 the key reaction rates will be varied — and in one case, created — in sensitivity studies in section 147 5 below. All small sulfur-bearing molecules are rather easily photolysed but the sulfur rings — 148 here gathered together under the master ring S — are more stable to UV (Young et al. 1983; 149 8 Kasting et al. 1989; Yung et al. 2009). Thus, as we shall see, there is a strong tendency for sulfur 150 to polymerize to S under UV radiation. 151 8 Thebackgroundatmosphereisassumedtobe84%H and16%He. Therelativeabundancesof 152 2 – 6 – C, N, O, and S are presumed solar and to scale as a group according to metallicity; scavenging of O 153 and S by silicates and chalcophiles is taken into account (Lodders and Fegley 2006). For simplicity 154 we assume solar metallicity in the base models (the star 51 Eridani itself is very slightly subsolar, 155 [Fe/H] = −0.027). We consider one set of models with metallicity that is a Jupiter-like 3× solar. 156 It is not immediately obvious that higher metallicity always favors haze formation, despite the 157 greater abundance of haze-forming elements. Indeed, in atmospheres where CH is less abundant 158 4 thanCO,raisingmetallicityreducestheCH /COratio,andhencecanmakeorganichazeformation 159 4 less favorable. Here we will find that raising the metallicity from solar to 3× solar in 51 Eri b has 160 a negative effect on NMHC formation. 161 51 Eridani is a bright star that was observed decades ago by the International Ultraviolet 162 Explorer (IUE). We use the observed UV spectrum for 115 < λ < 198 nm, the range of wavelengths 163 for which data are available. For λ > 198 nm we use a standard stellar model photosphere for an 164 F0IV star of radius 1.6R , which makes the star’s luminosity appropriate to 51 Eridani itself. We 165 (cid:12) note in passing that the UV irradiation of 51 Eri b is about twice what it is at Earth today, or 166 about 200× what it is at Titan. 167 An important simplification is that we treat vertical mixing by an eddy diffusion parameter 168 K that does not vary with height. What K should be in a stratified atmosphere like that of 169 zz zz 51 Eri b is not well-constrained (Freytag et al. 2010). Values ranging from 103 cm2/s at the top 170 of the troposphere to 106−107 cm2/s at the top of the stratosphere seem to be useful for Jupiter 171 (Moses et al. 2005), and values as high as 1010 cm2/s have been suggested for hot Jupiters. Here 172 we consider 105 ≤ K ≤ 1010 cm2/s. 173 zz We set surface gravity to g = 32 m/s2 in the nominal model. To test the response of the model 174 to different gravities we consider g = 56 m/s2 as a variant. These bracket what is expected for 51 175 Eri b; g = 32 m/s2 is not better than g = 56 m/s2. The higher gravity models are cooler at a given 176 pressure and thus are more favorable to CH and to sulfur condensation. 177 4 The pressure-temperature profile is computed by a radiative-convective equilibrium model 178 assuming a cloud-free atmosphere. In the troposphere these assumptions produce a relatively cool 179 model. Unlike the thermal structure of the troposphere, which is governed by the planet’s own 180 luminosity, temperatures at very high altitude depend also on heating by the star. Here we simply 181 extend an isothermal atmosphere to altitudes above the top of the radiative-convective model. 182 This is an important limitation on our models: we don’t know the temperature well enough to 183 categorically state that sulfur does or does not condense in 51 Eri b. The temperature structure of 184 a sulfurous atmosphere is a big enough topic that it is best deferred to a future study. 185 4. Results 186 We begin with a particular model that illustrates the general features of 51 Eri b photochem- 187 istry. We then look at how the models respond to parameter variations. 188 – 7 – 4.1. Nominal 51 Eri b models: two kinds 189 −8 K =107 700 K g=32 m=1 −8 K =107 700 K g=32 m=1 10 zz 10 zz 10−6 O2 10−6 S ] ] s OH s S condenses ar ar SO 8 b b [10−4 [10−4 CS e C H e r 2 2 r su H CH4 CO su S8 s −2 s −2 e10 e10 Pr "C4H2" CO2 Pr OCS S 1 1 S 2 4 S condenses 2 H S HS 2 2 2 10 10 −10 −8 −6 −4 −8 −7 −6 −5 −4 10 10 10 10 10 10 10 10 10 Volume mixing ratio Volume mixing ratio 10−8 Kzz=107 700 K g=32 m=1 10−8 Kzz=107 700 K g=32 m=1 S 10−6 O2 10−6 rs] OH C4H2 rs] S8 condenses a a SO b b [10−4 C2H2 [10−4 CS e e r r su CH4 CO su S8 s −2 s −2 e10 e10 Pr CO2 Pr H OCS S 1 1 S 2 4 S condenses 2 H S HS 2 2 2 10 10 −10 −8 −6 −4 −8 −7 −6 −5 −4 10 10 10 10 10 10 10 10 10 Volume mixing ratio Volume mixing ratio Fig. 1.— Photochemistry in a nominal 51 Eri b model (T = 700 K, g = 32 m s−2, solar metallicity, eff cloud-free atmosphere, K = 107 cm2s−1). The top and bottom rows differ in how C H is treated. How zz 4 2 C H is treated has little effect on the more abundant molecules. Left. Carbon and oxygen. In the top 4 2 panel, “C H ” is treated as the gateway to C H polymerization. Where “C H ” is more abundant than 4 2 2 2 4 2 acetylene (C H ), our chemical scheme has broken down. In the bottom panel, C H is chemically recycled. 2 2 4 2 Right. Sulfur shows a rich photochemistry that tends to build toward the relatively photolytically stable S 8 molecule. This particular model is about 5 K too warm for S to condense. Abundances of SO, CS, and S 8 in the upper stratosphere will be smaller than shown here if sulfur condenses. Note that S is abundant at 4 the interface between H S and S . 2 8 The particular model documented in Figure 1, which we call the nominal model, assumes an 190 – 8 – effective temperature T = 700 K, an eddy diffusivity of K = 107 cm2s−1, constant gravity 191 eff zz g = 32 m/s2, solar metallicity m = 1, and a cloud-free atmosphere. Figure 1 plots volume mixing 192 ratios of selected carbon-, oxygen-, and sulfur- bearing species as a function of altitude (pressure). 193 For carbon and oxygen we plot CO and CH , the major oxidized photochemical product CO , the 194 4 2 reduced photochemical products acetylene (C H ) and C H , the bleaching agents OH and O , and 195 2 2 4 2 2 atomic H. For sulfur we plot most of the species that are abundant, although CS and SO are not 196 2 2 labeled and S , which is coincident with S but less abundant in these models, is omitted entirely 197 3 4 for clarity. We do not plot H O (the most abundant molecule other than H ), atomic O, other 198 2 2 hydrocarbons, nor any N-bearing species. 199 Figure 1 illustrates the vertical structure of chemical products. The top of the atmosphere is 200 relatively oxidized by OH from H O photolysis, but it is also where CH is photolyzed by Lyman 201 2 4 α, and so the top is also the primary source of small hydrocarbon radicals. Reactions with OH 202 are the chief competition to hydrocarbon polymerization because the CO bond once formed is 203 effectively unbreakable in the haze-forming region. Thus NMHC production is possible only when 204 OH is suppressed. OH is controlled by reaction with H to reconstitute H O, or with CO to make 205 2 2 CO ; this is why CO is always a major photochemical product in all 51 Eri b models. Conditions 206 2 2 are more reduced at greater depth. 207 4.1.1. Alternative carbon polymerizations 208 It is self-evident that hydrocarbon polymerization can ramify without any known limit, espe- 209 cially in the presence of nitrogen and a little oxygen. In the bigger picture this is obviously a good 210 thing, but our modeling effort cannot ramify without limit. We must either be able to show that 211 abundances go to zero for molecules with more than a few carbon atoms, or we must artificially 212 truncate the system. If the atmosphere is sufficiently oxidized, the first option is workable. The 213 system will stop at CO without much of interest happening — this has historically been the bane 214 2 of terrestrial prebiotic atmospheric chemistry models (Abelson 1966; Pinto et al. 1980). But here 215 wearedealingwithH -richatmospheresanditisnotobviousa priorithatthechemistryconverges. 216 2 In this study we truncate the system at C H , the first molecule to form as the product of two 217 4 2 C H molecules. The state of the art in exoplanets takes the chemistry up to C H (Moses 2014; 218 2 n 8 n Venot et al. 2015; Rimmer and Helling 2016), but only a tiny fraction of all possible C H (m ≤ 8) 219 m n can be taken into account, and the combinatorial nature of the chemistry rapidly approaches or 220 exceeds the limit of what can be done with a detailed chemical kinetics model. Further progress 221 requires working with a limited number of generic or representative species. We consider two 222 extreme assumptions that might bound the problem. 223 In one set of numerical experiments we treat C H as a bucket in which polymerizing carbon 224 4 2 accumulates, ratherthanasanactualchemicalspecies. Theonlylossisthereverseoftheformation 225 – 9 – reaction, 226 C H+C H → C H +H. (R57) 2 2 2 4 2 The underlying idea is that C H is destined to grow into ever larger C H N O S molecules by 227 4 2 m n x y z the addition of free radicals. When used in this way, we will from here forward put quotes on 228 “C H ” to indicate that we are treating it as a representative species rather than as the real C H 229 4 2 4 2 molecule. This is the case documented by the upper left-hand panel of Figure 1 and in most other 230 spaghetti plots in this paper. 231 In the other set of numerical experiments we add three chemical reactions with H to crack 232 C H : first an addition, 233 4 2 C H +H+M → C H +M (R58) 4 2 4 3 followed either by H-abstraction 234 C H +H → C H +H (R59) 4 3 4 2 2 or by fission 235 C H +H → C H +C H . (R60) 4 3 2 2 2 2 Reaction R58 is a fast reaction that has been studied both theoretically and experimentally (Eite- 236 neer and Frenklach 2003; Klippenstein and Miller 2005); we use rates for k from the latter. The 237 58 other two reactions are inventions. For R59, we assume that k = 5×10−11exp(−500/T) cm3/s, 238 59 which is not unusual for an H-abstraction, if perhaps a bit fast. For R60, the unusual reverse 239 reaction R60r discussed above with respect to cyclohexadiene suggests that there ought to be a 240 considerable activation barrier and a rather small collision factor to the reverse reaction to account 241 for the special geometry that would seem required. We assume that 242 k = 5×10−11exp(−2000/T) cm3/s. (3) 60 The lower left-hand panel of Figure 1 shows that adding reactions R58-R60 to the network reduces 243 the peak abundance of C H and restricts the molecule to the photochemical region. Not shown is 244 4 2 that if k is reduced by a factor of 30, the C H altitude profile reverts to the “C H ” profile seen 245 60 4 2 4 2 in the upper left panel of Figure 1. 246 We note that neither R59 nor R60 are likely to be important in reality. Much more likely is 247 that the reaction with H will be another addition (Harding et al. 2007) and the hydrocarbon will 248 continue to grow, 249 C H +H+M → C H +M, (R61) 4 3 4 4 with no natural truncation point in the photochemical region where C-bearing radicals are also 250 abundant; that is, additions and ramifications will continue, and there is no obvious end to this. 251 Fromthisperspective“C H ”isagatewayspecies. Atgreaterdepthinahydrogen-richatmosphere, 252 4 2 hydrogenation will probably focus on the unsaturated carbon bonds until what is left is an alkane 253 or alkanes, and in the end the alkanes will be hydrogenated to CH and H , completing the cycle. 254 4 2 In most figures that follow we will show “C H ” profiles computed with the high C H because 255 4 2 4 2 these are more interesting to look at. 256 – 10 – 4.1.2. Sulfur photochemistry and sulfur condensation 257 The righthand panels of Figure 1 line up the sulfur chemistry with the carbon and oxygen 258 chemistry in the nominal model. Several things stand out. The first is that H S — sulfur’s stable 259 2 form in the abyss — barely makes it past the tropopause. Although H S is susceptible to UV 260 2 photolysis, that is not what is happening here. Rather, H S is being destroyed by atomic H flowing 261 2 down from the high altitude photochemical source region, 262 H S+H → HS+H . (R23) 2 2 The HS radical reacts quickly with H to free S, 263 HS+H → S+H , (R9) 2 and atomic S reacts with HS to make S , 264 2 HS+S → S +H, (R8) 2 and the polymerization of sulfur has begun, which is the second thing to stand out: S is very 265 8 abundant, generally at a lower altitude than the NMHCs and under more reduced conditions. 266 The high predicted abundance of S suggests that it might condense. Sulfur vapor is compli- 267 8 cated by the presence of several allotropes. Our first simplification is to lump S and S together 268 6 7 with the more abundant S . Lyons (2008) gives simple curve fits to many allotropes above the liq- 269 8 uid, and then describes a scheme for extrapolating these to lower temperatures above solid sulfur. 270 A complication is that the vapor pressure curves given by Lyons (2008) are discontinuous by nearly 271 a factor of two at sulfur’s melting point (T = 398 K). We use a blended approximation in which 272 m the vapor pressure over the solid is extended to higher temperature until it intersects the reported 273 vapor pressure over the liquid, 274 p (S ) = exp(20−11800/T) T < 413 K v 8 275 p (S ) = exp(9.6−7510/T) T > 413 K (4) v 8 where the vapor pressure is in bars. In Figure 1, the S mixing ratio is ∼ 2×10−6 for atmospheric 276 8 pressure levels between 100 µbars and 10 mbars. At these partial pressures, 2×10−10 < p(S ) < 277 8 2×10−8, sulfur’s condensation temperature is between 280 and 310 K. The uncertainty in Eq 4 278 in this temperature range is probably less than a factor of two (the coldest datum is at ∼ 310 K), 279 which is insignificant compared to the uncertainty in the temperature in our models. For context, 280 the corresponding condensation temperatures for water are between 170 and 200 K at the same 281 altitudes. At higher metallicity both condensation temperatures are ∼ 20log (m) K higher. 282 10 The vapor pressure of S over solid or liquid sulfur is tiny (Lyons 2008), 283 2 p (S ) = exp(27−18500/T) T < 413 K v 2