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2 Icarus 191 (2007) Chemical kinetic model for the lower atmosphere of Venus Vladimir A. Krasnopolsky Department of Physics, Catholic University of America, Washington, DC 20064, USA Received 26 December 2006; revised 28 March 2007 Available online 17 May 2007 Abstract A self-consistent chemical kinetic model of the Venus atmosphere at 0 47 km has been calculated for the first time. The model involves 82 reactions of 26 species. Chemical processes in the atmosphere below the clouds are initiated by photochemical products from the middle atmosphere (H 2 SO 4,CO,S x ), thermochemistry in the lowest 10 km, and photolysis of S 3. The sulfur bonds in OCS and S x are weaker than the bonds of other elements in the basic atmospheric species on Venus; therefore the chemistry is mostly sulfur-driven. Sulfur chemistry activates some H and Cl atoms and radicals, though their effect on the chemical composition is weak. The lack of kinetic data for many reactions presents a problem that has been solved using some similar reactions and thermodynamic calculations of inverse processes. Column rates of some reactions in the lower atmosphere exceed the highest rates in the middle atmosphere by two orders of magnitude. However, many reactions are balanced by the inverse processes, and their net rates are comparable to those in the middle atmosphere. The calculated profile of CO is in excellent agreement with the Pioneer Venus and Venera 12 gas chromatographic measurements and slightly above the values from the nightside spectroscopy at 2.3 µm. The OCS profile also agrees with the nightside spectroscopy which is the only source of data for this species. The abundance and vertical profile of gaseous H 2 SO 4 are similar to those observed by the Mariner 10 and Magellan radio occultations and ground-based microwave telescopes. While the calculated mean S 3 abundance agrees with the Venera observations, a steep decrease in S 3 from the surface to 20 km is not expected from the observations. The ClSO 2 and SO 2 Cl 2 mixing ratios are in the lowest scale height. The existing concept of the atmospheric sulfur cycles is incompatible with the observations of the OCS profile. A scheme suggested in the current work involves the basic photochemical cycle, that transforms CO 2 and SO 2 into SO 3,CO,andS x, and a minor photochemical cycle which forms CO and S x fromocs.theneteffect of thermochemistry in the lowest 10 km is formation of OCS from CO and S x. Chemistry at km removes the downward flux of SO 3 and the upward flux of OCS and increases the downward fluxes of CO and S x. The geological cycle of sulfur remains unchanged Elsevier Inc. All rights reserved. Keywords: Venus, atmosphere; Photochemistry; Atmospheres, composition; Atmospheres, chemistry; Abundances, atmospheres 1. Introduction Photochemical modeling is a powerful tool to study chemical structure and composition of an atmosphere. Chemical processes in the planetary atmospheres are usually driven by the solar ultraviolet photons that dissociate and ionize atmospheric species and initiate numerous reactions. However, this is not the case for the atmosphere of Venus below the cloud layer which is a subject of modeling in this paper. By chemical kinetic modeling we mean modeling of atmospheric chemistry in regions where photolysis is relatively unimportant. * Corresponding address: 6100 Westchester Park Dr. #911, College Park, MD 20740, USA. address: vkrasn@verizon.net. Many efforts have been made to study the chemical composition of the lower atmosphere of Venus. Results from the Venera and Pioneer Venus landing probes were reviewed by Moroz (1983), von Zahn et al. (1983), and Krasnopolsky (1986). Later the problem was discussed by Taylor et al. (1997), Esposito et al. (1997), Fegley et al. (1997), De Bergh et al. (2006), and Krasnopolsky (2006b). The important achievements in this field are related to the ground-based near-infrared spectroscopy of the Venus night side. Strong nightside emissions at 1.74 and 2.3 µm were discovered by Allen and Crawford (1994). Krasnopolsky (1986, p. 181) argued and Crisp et al. (1989) proved that these emissions originate from the hot surface and the lower atmosphere of Venus in the CO 2 transparency windows. Observing absorption bands of other gases in these windows, it is possible to de /$ see front matter 2007 Elsevier Inc. All rights reserved. doi: /j.icarus

3 26 V.A. Krasnopolsky / Icarus 191 (2007) termine their abundances. High-resolution spectroscopy of the emissions revealed absorption lines of CO 2,CO,H 2 O, HDO, OCS, HCl, and HF (Bezard et al., 1990), and OCS was unambiguously detected for the first time on Venus. The D/H ratio and the SO 2 mixing ratio were extracted from the observed spectra (De Bergh et al., 1991; Bezard et al., 1993). Nightside emissions in the transparency windows at 1.27, 1.18, and 1.1 µm were discovered as well, a composite analysis of the observations by a few teams was made by Pollack et al. (1993), and the latest observations of CO and OCS at 2.3 µm were made by Marcq et al. (2005, 2006). Currently the European Venus Express orbiter is studying the atmosphere of Venus. Recently NO was detected in the lower atmosphere of Venus (Krasnopolsky, 2006a), unambiguously confirming lightning on Venus. Strong vertical gradients of OCS and CO retrieved from the nightside spectroscopy at 2.3 µm (Pollack et al., 1993) indicate active chemical processes in the atmosphere. Sulfur allotrope S 3 also varies with height in the Venus lower atmosphere (Sanko, 1980; Krasnopolsky, 1987; Maiorov et al., 2005). H 2 SO 4 vapor is another species which varies both vertically and horizontally on Venus. Its variations were studied using the Mariner 10 and Magellan radio occultations and microwave observations with the Very Large Array (Kolodner and Steffes, 1998; Butler et al., 2001; Jenkins et al., 2002). The objective of this work is a self-consistent chemical kinetic model for the lower atmosphere of Venus from the surface to 47 km, which is near the lower cloud boundary. The results will be compared with the existing data on its chemical composition. This type of modeling has never been applied to the lower atmosphere of Venus. A simplified approach to the problem is based on the assumption of local thermochemical equilibrium at each altitude in the atmosphere. This problem can be easily solved using thermodynamic properties of the atmospheric species and the law of constancy of elemental composition with height (Krasnopolsky, 1986). However, Krasnopolsky and Pollack (1994) proved that this approach does not work and results in absurd values for some species on Venus. Fegley et al. (1997) combined thermodynamics with some kinetic consideration to study the chemical composition in the lowest 10 km on Venus. Krasnopolsky and Pollack (1994) considered a partial chemical kinetic problem for OCS, CO, H 2 SO 4, and SO 3 that included five reactions and provided a reasonable agreement with the observations. However, all partial chemical problems neglect some consequences of processes under consideration and therefore are at risk to be in error. Specifically, a significant production of free sulfur in the model by Krasnopolsky and Pollack (1994) may affect densities of CO and OCS, and this was beyond the scope of that partial model. Contrary to the partial chemical models, each chemical reaction changes densities of all species involved in this reaction in the self-consistent models making them more adequate. Krasnopolsky and Pollack (1994) developed two basic models for the H 2 O mixing ratios of 30 and 90 parts per million (ppm) in the lower atmosphere. All references to Krasnopolsky and Pollack (1994) below are addressed to the model with 30 ppm. 2. Sulfuric acid concentration in Venus clouds Though this problem is beyond the basic task of this paper, we will consider it because of a wide-spread confusion on this subject. Sulfuric acid aerosol was identified in the upper cloud layer from polarimetric observations at 0.365, 0.55, and 0.99 µm (Hansen and Hovenier, 1974); the recommended concentration was 75% based on the extracted refractive indices. Polarimetric observations refer to a level where the cloud optical depth τ 1 which is at 68 km. Using the Venus International Reference Atmosphere (VIRA, Seiff et al., 1985) and the H 2 SO 4 H 2 O phase equilibrium (Giauque et al., 1960; Tabazadeh et al., 1997), the H 2 O mixing ratio required for the concentration of 75% is 25 ppm at 68 km. Dayside spectroscopic observations refer to a level τ(1 g) 1 where g 0.75 is the aerosol scattering asymmetry factor. This level is at 62 km where the H 2 SO 4 concentration of 75% corresponds to the H 2 O mixing ratio f H2 O 50 ppm. Both H 2 O mixing ratios are unrealistically high. The Krasnopolsky and Pollack (1994) model for the H 2 SO 4 H 2 O system in the Venus clouds results in a constant concentration of 85% in the upper cloud layer increasing to 98% at the lower cloud boundary. This concentration corresponds to the H 2 O abundance of 1 ppm at 68 km and 2.5 ppm at 62 km, in accord with the observations. Spectroscopic observations by Pollack et al. (1978) also showed the concentration of 85% at the cloud tops. Palmer and Williams (1975) pointed out that refractive indices of sulfuric acid with concentrations of 75 and 85% are essentially the same at 0.55 and 0.99 µm and differ by 0.01 at µm. This difference is smaller than the uncertainty of in the refractive indices extracted by Hansen and Hovenier (1974). Though the values of 75 and 85% look rather similar, they correspond to H 2 SO 4 1.8H 2 O and H 2 SO 4 H 2 O, respectively. Absorption and scattering by the sulfuric acid aerosol are also different for these concentrations in the infrared. We strongly recommend avoiding the widespread error in the concentration of sulfuric acid in the upper cloud layer. 3. Sources of energy Chemical processes may proceed if there is disequilibrium in the system. Temperature varies in the atmosphere from 735 K near the surface to 360 K at 47 km. Thermal decomposition (thermolysis) of some species may be efficient near the hot surface. The products may be delivered by mixing into the higher levels of the atmosphere and drive chemistry there. Products of photochemistry above the clouds may be transported into the lower atmosphere and initiate chemistry there. The basic photochemical products are H 2 SO 4, CO, and free sulfur S x ; their fluxes are cm 2 s 1 in Krasnopolsky and Pollack (1994). Oxidation of reduced atmospheric species by SO 3 from H 2 SO 4 is another major source of chemistry in our model. Prior the Pioneer Venus and Venera missions Prinn (1978) pointed out that photolysis of S 3 by the visible light

4 Chemical model for lower atmosphere of Venus 27 Table 1 Chemical composition of the Venus atmosphere near the surface Species CO 2 N 2 SO 2 H 2 O HCl HF NO OCS CO Mixing ratio Species given by densities at the lower boundary in the model are shown bold. should affect chemistry of the lower atmosphere on Venus. We will consider this process in our model. It was also suggested that the S atoms formed by photolysis of S 3 might have kinetic energy of ev and react with other species. However, the Venera spectra (Golovin et al., 1982; Moshkin et al., 1983) show a steep decrease near the S 3 dissociation limit at 461 nm (the so-called blue absorption). Our calculation using those spectra results in a mean energy of the fresh S atoms of 0.2 ev at 16 km assuming that the excess photon energy is completely released as kinetic energy. This energy is even smaller if the rotation and vibration of S 2 are taken into account. Anyway it is too low to initiate specific hot atom chemistry. Cosmic ray ionization is also a source of chemistry of the lower atmosphere of Venus. Calculations by Upadhyay et al. (1994) show that ionization by muons dominates in the lower atmosphere with a peak rate of 300 cm 3 s 1 at 20 km and a column rate of cm 2 s 1. This rate is smaller than the flow of photochemical products from the middle atmosphere by three orders of magnitude, and this source will be neglected in our model. 4. Chemical composition of the atmosphere near the surface Chemical composition of the Venus atmosphere near the surface is generally poorly known. However, there are some considerations that favor extrapolation of observational data at other altitudes to the surface. The law of constancy of elemental composition in a lower atmosphere without condensation (Krasnopolsky, 1986) is among these considerations. Some of the extrapolations will be confirmed by our model. The recommended chemical composition is shown in Table 1.TheN 2 mixing ratio is taken from the Pioneer Venus gas chromatograph measurements (Oyama et al., 1980), SO 2 is from the Venera 12 gas chromatograph (Gelman et al., 1979) and the nightside high-resolution spectroscopy (Bezard et al., 1993), H 2 O is from Pollack et al. (1993), HCl and HF are from Connes et al. (1967), Bezard et al. (1990), and Pollack et al. (1993), and NO is from Krasnopolsky (2006a). Other measurements of N 2,SO 2, and H 2 O have been discussed in the reviews cited in Section 1 with references to the original papers. There are no reliable measurements of OCS near the Venus surface, and the value in Table 1 is from Krasnopolsky and Pollack (1994). The CO mixing ratio is adopted at 15 ppm, close to 17 ppm measured by the Venera 12 gas chromatograph at 12 km (L.M. Mukhin, personal communication). The mixing ratios in Table 1 are rather similar to those from Fegley et al. (1997) and Krasnopolsky and Parshev (1979). Fegley et al. (1997) involved more sulfur species, H 2, and NH 3 and did not consider HCl, HF, and NO. Some of the mixing ra- Table 2 Bond energies in some species on Venus and S X bond energies Species S CO O SO 2 H SH H Cl H H H OH S O O CO O SO E (ev) Species N O C O S Cl S S 2 S H S S S N S C S SO E (ev) tios from Table 1 will be used as the lower boundary conditions for our model. 5. Reactions and their rate coefficients Bond energies in the main species on Venus are given in Table 2. If a reaction is endothermic, then each ev reduces its rate at K by a factor of Therefore the data in Table 2 help to estimate which reactions may be significant for the model. Evidently thermolysis of OCS is the most probable and may be a source of S atoms. Hydratation of SO 3 (R1 in Table 3) was studied in detail by Loverjoy et al. (1996), and the decomposition of H 2 SO 4 (R2) is calculated using thermodynamic properties of the species involved from Chase (1998). Reactions 2 5 were suggested in Krasnopolsky and Pollack (1994) to explain the observed behavior of CO and OCS. The only change is the higher activation energy for R4. The net effect of R2, R4, and R5 is H 2 SO 4 H 2 O + SO 3, SO 3 + OCS CO 2 + (SO) 2, (SO) 2 + OCS CO + SO 2 + S 2, Net H 2 SO 4 + 2OCS H 2 O + CO 2 + SO 2 + CO + S 2. These reactions transform the downward photochemical flow of H 2 SO 4 and the upward flow of OCS into the chemically neutral species H 2 O, CO 2, and SO 2 and add CO and free sulfur to the photochemical flow of these species from the middle atmosphere. Free sulfur in the lowest scale height is also a source of S atoms. Therefore chemistry of the lower atmosphere is mostly sulfur-driven. S, S 2, and S 3 are the main sulfur allotropes in the lowest 20 km. Their interactions and reactions with CO, OCS, and SO 2 are given in Table 3 as R6 R22. Reactions of S with NO and SNO are exothermic and fast (R23, R24). We have not found the S NO bond energy in the literature and assumed that it is smaller than the S S 2 energy of 2.69 ev; then R25 S 2 + SNO may proceed. The bond energies of H SH, H Cl, and H H are higher than but comparable with that of S H. Reactions of S with these species release SH, H, and Cl. Their reactions are R26 R43. Formation of ClSO 2 and SO 2 Cl 2 on Venus was discussed by DeMore et al. (1985), Mills (1998), and Pernice et al. (2004).

5 28 V.A. Krasnopolsky / Icarus 191 (2007) Table 3 Chemical reactions in Venus lower atmosphere, their rate coefficients and column rates No. Reaction Rate coefficient Column rate 1 SO 3 + H 2 O + H 2 O H 2 SO 4 + H 2 O T e 6540/T a H 2 SO 4 + H 2 O SO 3 + H 2 O + H 2 O e 5170/T / SO 3 + CO CO 2 + SO e 13000/T b SO 3 + OCS CO 2 + (SO) e 10000/T b (SO) 2 + OCS CO + SO 2 + S b SO+ SO SO 2 + S e 1700/T c S+ SO 2 SO + SO e 5200/T CO+ SO 2 CO 2 + SO e 24300/T d SO+ CO 2 SO 2 + CO e 22000/T S 3 + hν S 2 + S exp ( 0.15h h 2) S + S + M S 2 + M (300/T) S 2 + M S + S + M e 50000/T S + S 2 + M S 3 + M (300/T) S 3 + M S + S 2 + M e 29800/T S + CO + M OCS + M e 1000/T OCS + M CO + S + M e 37300/T S + OCS CO + S e 2800/T S 2 + CO OCS + S e 17460/T / S + S 3 S 2 + S e 2800/T S 2 + S 2 S + S e 23000/T CO + S 3 OCS + S e 20000/T e S 2 + OCS CO + S e 25500/T S + NO + M SNO + M e 940/T f S + SNO S 2 + NO g S 2 + SNO S 3 + NO h SH + SH H 2 S + S i S + H 2 S SH + SH e 3620/T / S + SH S 2 + H j H + S 2 SH + S e 8830/T H + SH H 2 + S j S + H 2 SH + H e 10080/T H + OCS CO + SH e 1950/T j / CO + SH OCS + H e 7780/T H + HCl H 2 + Cl e 1770/T c Cl + H 2 HCl + H e 2270/T H 2 S + Cl HCl + SH e 210/T c SH + HCl H 2 S + Cl e 5750/T / Cl + SH HCl + S e 210/T k S + HCl SH + Cl e 9380/T H + SNO NO + SH e 340/T l H + SH + M H 2 S + M (300/T) 2 m H 2 S + M SH + H + M e 44750/T H + S 3 SH + S e 1950/T Cl + SO 2 + M ClSO 2 + M e 940/T n / ClSO 2 + M Cl + SO 2 + M e 10540/T o ClSO 2 + ClSO 2 SO 2 Cl 2 + SO h / SO 2 Cl 2 + SO 2 ClSO 2 + ClSO e 11000/T o ClSO 2 + Cl SO 2 + Cl h ClSO 2 + S SO 2 + SCl h ClSO 2 + H SO 2 + HCl h SO 2 Cl 2 + Cl ClSO 2 + Cl h SO 2 Cl 2 + S ClSO 2 + SCl h SO 2 Cl 2 + H ClSO 2 + HCl h H + Cl 2 HCl + Cl e 416/T p S + Cl 2 SCl + Cl e 300/T q Cl + SCl S + Cl e 650/T S + SCl S 2 + Cl h H + SCl HCl + S h SH + Cl 2 HSCl + Cl e 690/T c HSCl + SH H 2 S + SCl e 500/T r

6 Chemical model for lower atmosphere of Venus 29 Table 3 (continued) No. Reaction Rate coefficient Column rate 61 HSCl + S SH + SCl r HSCl + H H 2 + SCl e 2770/T r HSCl + Cl HCl + SCl e 130/T r SH + SCl S 2 + HCl e 230/T r SH + OH H 2 O + S S + H 2 O OH + SH e 17700/T OH + H 2 H 2 O + H e 1800/T c H + H 2 O OH + H e 9420/T OH + HCl H 2 O + Cl e 350/T c Cl + H 2 O OH + HCl e 8470/T / OH + H 2 S H 2 O + SH e 75/T c SH + H 2 O H 2 S + OH e 14160/T H + H 2 S SH + H e 1470/T j SH + H 2 H 2 S + H e 7930/T / CO + OH CO 2 + H / H + CO 2 CO + OH e 12400/T OH + OCS CO 2 + SH e 1200/T c SH + CO 2 OH + OCS e 19360/T / SO + OH SO 2 + H e 335/T c SO 2 + H SO + OH e 14350/T S + OH SO + rh c SO + H S + OH e 11200/T 293 Rate coefficients are in cm 3 s 1 and cm 6 s 1 for two- and three-body reactions, respectively, and in s 1 for R10. Column rates are in cm 2 s 1, = Differences between column rates of direct and inverse reactions are shown for some reactions. Rate coefficients without reference are either for inverse reactions or discussed in the text. a Loverjoy et al. (1996). b Krasnopolsky and Pollack (1994). c Sander et al. (2006). d Bauer et al. (1971). e Adopted using R8 and CO + NO 2 as analogs. f Goumri et al. (2004) corrected for the higher efficiency of CO 2 than Ar by a factor of 5. g Similar to S + NO 2 from Clyne and Whitefield (1979). h Adopted. i Schofield (1973). j Woodall et al. (2007). k Clyne et al. (1984). l Similar to H + NO 2 from Sander et al. (2006). m Similar to H + OH + M from Baulch et al. (1992). n Mills (1998). o Based on DeMore et al. (1985). p Berho et al. (1999). q Krasnoperov et al. (1984). r Similar to the reaction with O instead of S from Sander et al. (2006). Production and loss of these species are described by R44 R53. Cl 2, SCl, and then HSCl appear in some of these processes. R54 R64 are the interactions and loss of these species. R65 R82 are the reactions of formation and loss of OH. Rate coefficients of the reactions between sulfur allotropes S 1 8 and of those with other species are poorly known. To simplify the problem, we consider four components: S, S 2,S 3, and S x = ns n for n = 4 8. We assume local thermochemical equilibrium between the sum of S + 2S 2 + 3S 3 and S x. Rate coefficients of the inverse reactions in Table 3 are calculated using the adopted rate coefficients of the direct reactions k 0 and constants of thermochemical equilibria K. These constants are calculated using thermodynamical properties of gases from Chase (1998). Properties of S and S 2 are taken from Lide (2006), heat of S 3 formation from Mills (1974), and propertiesofshfromlodders (2004). Thermochemical equilibria are considered for species pressure in bars, therefore a rate coefficient of inverse reaction is k i = k 0 K ( 10 6 kt ) m n. Here k is the Boltzmann constant and m and n are the numbers of the reactants and products, respectively. Values of k i are calculated at 400 and 700 K and then fitted by the Arrenius form k i = a i exp( A i /T). The pre-exponential factor a i for the inverse reactions may significantly exceed the collision rate coefficient cm 3 s 1. Dissociation energy of S 3 is 2.69 ev according to the data of Lide (2006) and Mills (1974) and corresponds to the limiting wavelength of 461 nm. Absorption cross-sections of S 3 are taken from Billmers and Smith (1991). Visible spectra of the solar radiation were observed at various altitudes in the deep atmosphere of Venus by the Venera landing probes

7 30 V.A. Krasnopolsky / Icarus 191 (2007) (Golovin et al., 1982; Moshkin et al., 1983). The Venera 12 spectrometer had problems below 22 km, the Venera 13 and 14 spectra started at 470 nm, and the Venera 11 spectra that began at 435 nm are the best for our purpose. However, the overlapping interval is very small even in those spectra, and a steep decrease in the spectra below 500 nm is not favorable for careful evaluation of the photolysis rate. Therefore the measured spectra at nm were approximated by a function exp(a + bλ + cλ 2 ) and extrapolated below 435 nm to calculate the S 3 photolysis rate as a function of height. This function maybefittedbyj 10 = γ exp(0.15h h 2 ) s 1 with a mean deviation of 17%. The photolysis yield γ = 0.1 is adopted independent of wavelength below 461 nm. This yield has not been measured in laboratory, and the chosen value provides a reasonable fit to the Venera data. Rate coefficients of three-body reactions in Table 3 are poorly known, and there are no data on their high-pressure limits. High-to-low pressure limit ratios may be defined as limiting densities m = k /k 0. We adopt m = cm 3 for all three-body reactions. This value is close to the mean value for the reactions with the known low and high pressure limits in the JPL compilation (Sander et al., 2006). Therefore the effective atmospheric density is m m e =, 1 + m/m and all three-body reactions below 40 km in our model are near their high-pressure limits. Evidently m e refers also to their inverse processes. Rate coefficient of R5 (SO) 2 + OCS at 500 K should exceed cm 3 s 1 to neglect a loss of (SO) 2 in the reaction (SO) 2 + SO SO 2 + S 2 O with a rate coefficient of cm 3 s 1 at 300 K (Herron and Huie, 1980). Rate coefficient of R11 S + S + M was measured at cm 6 s 1 for M = Ar and T = 300 K by Fair and Thrush (1969) and at cm 6 s 1 for M = H 2 S and T = 300 K by Nicholas et al. (1979). The adopted value is k 11 = (300/T) 2 cm 6 s 1. S 3 has a structure S=S=S which is different from the triangle structure of O 3. Therefore while the reaction O + O 2 + M is slower than O + O + M, we assume k 13 = k 11 for R13 S + S 2 + M. R15 S + CO + M is spin-forbidden similar to O + CO + M. However, the conservation of spin is not so restrictive for heavy reactants, and the chosen rate coefficient in Table 3 reflects this consideration. R17 S + OCS was measured by Klemm and Davis (1974) at K and by Shiina et al. (1996) at K. The observed activation energies are very different in these studies. Therefore we adopt the rate coefficient at 400 K from Klemm and Davis (1974) and at 900 K from Shiina et al. (1996) and interpolate the values by the Arrenius form to get k 17 = e 2800/T cm 3 s 1. R19 S + S 3 may be similar to R17 because the bond structures of S 3 and OCS are similar. However, two S atoms are available for the reaction in S 3 and one atom in OCS, the S 2 =S bond is weaker than CO=S, and the adopted value is k 19 = e 2800/T cm 3 s 1. Accordingly, the adopted rate coefficient of R43 H + S 3 exceeds that of R32 H + OCS by a factor of 10. There are no data on the rate coefficient of R65 SH+OH. We adopt k 65 = 0.5(k SH k OH ) 1/2 = cm 3 s 1.Herek SH and k OH are the rate coefficients of SH + SH and OH + OH, and the factor of 0.5 reflects the fact that the branch of SH + OH H 2 S + O is endothermic. R75 CO + OH is a well studied reaction. The rate coefficient in Table 3 is from the JPL compilation (Sander et al., 2006) and corrected to the effective density of the atmosphere. Overall, our model involves 82 reactions of 26 species. 6. Background atmosphere and boundary conditions A temperature profile of the atmosphere at 0 47 km and the surface pressure of 92 bar are taken from the Venus International Reference Atmosphere (Chapter I, Seiff et al., 1985). This profile, the calculated density profile, and eddy diffusion adopted from Krasnopolsky and Pollack (1994) are shown in Fig. 1. Photochemistry in the middle atmosphere consumes CO 2 and SO 2 from the lower atmosphere and returns an oxidant H 2 SO 4 and reduced species CO and S x : SO 2 + CO 2 + H 2 O H 2 SO 4 + CO, (1) SO 2 + 2CO 2CO 2 + S. (2) Our model involves OCS and H 2 S, and these species may be delivered into the middle atmosphere by mixing. Net losses of OCS and H 2 S in the middle atmosphere are OCS CO + S, (3) H 2 S + CO 2 H 2 O + CO + S. (4) Krasnopolsky and Pollack (1994) proved that a sulfuric acid flux Φ H2 SO 4 = cm 2 s 1 fits the observed properties of the cloud layer, and we adopt this value. OCS and H 2 S are subjects to photolysis above 60 km, and a convenient form Fig. 1. Temperature, number density, and eddy diffusion profiles.

8 Chemical model for lower atmosphere of Venus 31 of the upper boundary conditions for these species in our model is velocity V = K/2H.HereK is the eddy diffusion coefficient (Fig. 1) and H is the scale height. To balance the oxidation state of CO 2 and SO 2, the following relationships between fluxes at the upper boundary hold: Φ H2 SO 4 = , Φ SO2 = fs, Φ H2 O = [H 2 S] 47 km V, Φ Sx = fs [OCS] 47 km V [H 2 S] 47 km V, Φ CO = fs [OCS] 47 km V [H 2 S] 47 km V, CO2 = fs +[H 2 S] 47 km V. All fluxes are in cm 2 s 1.Herefs is the photochemical production of free sulfur from SO 2 in the middle atmosphere. We adopt fs = cm 2 s 1 for our basic model, and the limiting cases fs = 0 and cm 2 s 1 will be considered as well. CO 2 is the major constituent, and its flux is too small to affect the hydrostatic distribution of this species. Zero fluxes of all other species are assumed at the upper boundary. If all species are given by their fluxes at the upper boundary, then the number of parent species given by their densities at the lower boundary should be equal to the number of chemical elements in the model (Krasnopolsky, 1995). Here the element means a species which is undividable in the model. Our model involves the following elements: CO, NO, S, O, H, and Cl. The following species are given by densities near the surface: CO 2, SO 2,H 2 O, HCl, NO, and OCS. They are shown bold in Table 1. Zero fluxes for all other species are adopted at the surface. We have already discussed in Section 4 that the abundances of some species selected for the lower boundary conditions either have not been measured near the surface (HCl, OCS, NO) or the observational data near the surface are contradictory (H 2 O, SO 2 ). Generally, we could vary the densities at the lower boundary to fit the most reliable observations at the heights they refer to. However, the results would be the same. The balance of fluxes at the upper boundary and the zero fluxes at the lower boundary reflect the conditions of a chemically passive surface. Here we assume that the kinetics of the gas surface interactions is slow compared to that of the gasphase reactions. This assumption agrees with the results of Fegley and Treiman (1992), Fegley et al. (1997), and discussion of the sulfur cycles (see below). Furthermore, while thermodynamics of the surface atmosphere interactions is rather well established, the kinetics of this exchange is poorly known and cannot be used in our model. Actually any species density near the surface chosen as the lower boundary condition reflects the surface atmosphere interaction for this species. The Vega/ISAV observations of the vertical profile of SO 2 (Bertaux et al., 1996) show a gradual decrease in the SO 2 mixing ratio below 30 km. This decrease may be partly explained by a very intense loss of SO 2 in the reaction with carbonate rocks (see below). However, this strong loss should be local and cannot correspond to the global-mean conditions. The model has been computed using a method described in Krasnopolsky and Cruikshank (1999) with a vertical step of 1km. Fig. 2. Profiles of major species in the model. The HCl mixing ratio is constant at and not shown. Fig. 3. Density profiles of minor species in the model. The NO mixing ratio is constant at and not shown. 7. Results The computed density profiles are shown in Figs Column reaction rates from 1 to 46 km (the boundaries are not included) are given in Table 3. These rates help to evaluate relative importance of various processes in balances of species. Some key values from the model are given in Table 4. The model CO mixing ratio varies from 14 ppm near the surface to 39 ppm at 47 km, in excellent agreement with the PV and V12 gas chromatographic data (Table 5). The nightside spectroscopic observations (Pollack et al., 1993; Taylor et al., 1997; Marcq et al., 2006) give lower values for CO at 36 km than the gas chromatographic measurements. While the CO mixing ratios are similar in all nightside observations, the CO gradient is smaller in the results by Taylor et al. (1997) and Marcq et al. (2006) than that in Pollack et al. (1993) by a factor of 2. The CO gradient at 36 km is 0.8 ppm km 1 in our model and just equal to the mean value from the observations. The CO abundance near the surface is not assigned but calculated in the model. The calculated abundance is close to those from

9 32 V.A. Krasnopolsky / Icarus 191 (2007) thermodynamic considerations by Krasnopolsky and Parshev (1979) and Fegley et al. (1997), 15 and ppm, respectively. Krasnopolsky and Pollack (1994) adopted CO = 1 ppm near the surface to facilitate the high value of the gradient from Pollack et al. (1993). According to the nightside spectroscopy, the OCS mixing ratio is f OCS = 4.4 ± 1 ppm with logarithmic gradient d ln f OCS /dz = 0.36 ± 0.1km 1, both at 33 km (Pollack et al., 1993). Marcq et al. (2005) extend a region of the constant logarithmic gradient for 7 km. Then f OCS = 18 ± 9 ppm at 29 km and 1.5 ± 0.6 ppm at 36 km for the data of Pollack et al. (1993). Marcq et al. (2006) obtained f OCS = 0.55 ± 0.15 ppm at 36 km and the gradient d ln f OCS /d ln p = 5 ± 1. Simple calculations give f OCS = 8 36 ppm at 29 km from these data. It would be better to indicate the OCS mixing ratio in the middle of their sensing interval (33 km) instead of the upper point. Then the uncertainty at the lower point (29 km) would be smaller. The model values of the OCS mixing ratio are 11 ppm at 29 km and 1.3 ppm at 36 km, in a reasonable agreement with the observations. The upward flux of OCS is equal to cm 2 s 1 at 47 km which may be compared with cm 2 s 1 in the photochemical model by Mills (1998). Scaling the fluxes to the OCS mixing ratio of 100 ppb adopted by Mills (1998) at 58 km, the expected OCS abundance is 14 ppb at this height. The average H 2 SO 4 gas mixing ratio at km is 5.6 ppm in our model. The Mariner 10 and Magellan radio occultations and microwave observations using the Very Large Array give very variable but close values (Kolodner and Steffes, 1998; Butler et al., 2001; Jenkins et al., 2002). This is in favor of the H 2 SO 4 flux of cm 2 s 1 obtained in Krasnopolsky and Pollack (1994) and adopted in our model. Although the H 2 SO 4 flux exceeds that of S x by a factor of 4 at the upper boundary in our model, the sulfuric acid mixing ratio is smaller than that of S x by the same factor. This is because flux is proportional to gradient of mixing ratio and not to mixing ratio itself. Using the saturated vapor pressure of sulfur from Mills (1974), thes x density is just 25% below the saturation at the upper boundary, and the bottom of the free sulfur aerosol is near 48 km. It is very close to the bottom of the sulfuric acid aerosol, which was calculated at 48.4 km in Krasnopolsky and Pollack (1994) and observed at 48.4 ± 0.8 km by the Pioneer Venus probes and at 48.7 ± 0.5 km by the Venera probes [see the discussion and references in Krasnopolsky and Pollack (1994)]. If precipitation velocities of sulfuric acid and S 8 are equal in the middle cloud layer, then our boundary con- Table 5 Observations of CO in the lower atmosphere Fig. 4. Density profiles of atoms and radicals. Instrument h (km) CO (ppm) Gradient (ppm km 1 ) PV GC a ± ± 3 V12 GC b ± ± 5 NS c ± ± 0.5 NS d ± ± 0.5 NS e ± ± 0.3 a Pioneer Venus gas chromatograph (Oyama et al., 1980). b Venera 12 gas chromatograph (Gelman et al., 1979; Mukhin, personal communication). c Nighside spectroscopy (Pollack et al., 1993). d Nightside spectroscopy (Taylor et al., 1997). e Nightside spectroscopy (Marcq et al., 2006). Table 4 Model results for various input parameters Model Basic fs = 0 fs = K 2 K = 10 4 k 3 10 k 4 10 k 8,9 10 k 13,14 10 k 15,16 10 k 17,18 10 CO(0) CO(47) OCS(29) OCS(36) S x (0) S x (47) H 2 (0), ppb H 2 (47), ppb H 2 S(0) H 2 S(47) S 3 (0), S 3 (10), H 2 O(47) H 2 SO 4 (43) Mixing ratios of all species except H 2 and S 3 are in ppm, altitudes are in parentheses, and =

10 Chemical model for lower atmosphere of Venus 33 Fig. 5. Reactions with the highest rates in the model. Reaction rates at the boundaries are not involved in the model, and the altitude scale starts at 1 km. ditions correspond to the mass loading ratio of 15:1. This is close to 10:1 observed by the Vega 1 and 2 gas chromatographs (Porshnev et al., 1987). Gaseous sulfur is rather abundant in the atmosphere of Venus with a mixing ratio of sulfur atoms decreasing from 30 ppm at km to 1.5 ppm near the surface. The most abundant sulfur allotropes at 47 km are S 8,S 7, and S 6 (80, 8.5, and 10.5 percent at thermodynamic equilibrium, respectively). Free sulfur consists of S 2 almost entirely in the lowest scale height with a mixing ratio of 0.75 ppm near the surface. The model results are significantly different from those of Sanko (1980) with the S x mixing ratio of throughout the lower atmosphere. Krasnopolsky and Parshev (1979) and Fegley et al. (1997) calculated f S2 = 0.1 ppm and ppm near the surface, respectively. The H 2 S mixing ratio varies in the model (Fig. 3) from 180 ppb near the surface to 68 ppb at 47 km. The H 2 S densities are mostly controlled by R36 37 HCl + SH = H 2 S + Cl that have the highest rates in the model (Table 3, Fig. 5). R26 27 H 2 S + S = SH + SH are also strong but weaker by two orders of magnitude. The gradual decrease of H 2 S to the upper boundary is caused by the H 2 S velocity at the upper boundary which accounts for the photolysis of H 2 S in the middle atmosphere. The upward flux is equal to cm 2 s 1. The model does not support the controversial detections of H 2 S by the Pioneer Venus mass spectrometer (Hoffman et al., 1980) and the Venera gas chromatographs (Mukhin et al., 1983). Krasnopolsky and Parshev (1979) and Fegley et al. (1997) calculated f H2 S = 50 ppb and ppb, respectively, for thermochemical equilibrium near the surface. H 2 slightly varies in the model from 3.2 to 4.5 ppb at 0 and 47 km, respectively. R73 74 H 2 S + H = H 2 + SH and R34 35 HCl + H = H 2 + Cl control the H 2 abundances. The value near the surface agrees with those in Krasnopolsky and Parshev (1979) and Fegley et al. (1997). The model does not support some expectations of significant abundances of ClSO 2 and SO 2 Cl 2 in the lower atmosphere Fig. 6. Balance of the main species in the model. D(S 2 + CO) and D(S + SO 2 ) are differences between the direct and inverse reaction rates. Thin line is D(SO + CO 2 ). Reaction rates at the boundaries are not involved in the model, and the altitude scale extends from 1 to 46 km. (DeMore et al., 1985; Dalton et al., 2000). Their mixing ratios are near the surface (Fig. 3). The global-mean column rate of the CO 2 photolysis in the middle atmosphere is equal to a quarter of the solar photon flux with λ<200 nm at the Venus orbit, that is, cm 2 s 1. Of all reactions in the middle atmosphere, the CO 2 photolysis has the highest rate which, however, is smaller than some reaction rates in the lower atmosphere by two orders of magnitude (Table 3). However, the strongest reactions in the lower atmosphere (Fig. 5) are balanced by the inverse reactions, and their net effects are much smaller than the rates of each component and comparable to those in the middle atmosphere. Reactions that determine the balance of CO, S x, and OCS are shown in Fig. 6. LossofSO 3 in R3 SO 3 + CO is much smaller than that in R4 SO 3 + OCS, and the flux of SO 3 increases the flux of CO because of R4 R5. Therefore the downward flux of CO is Φ CO 2 (Φ H2 SO 4 + fs) cm 2 s 1 below 33 km (see Section 6). Here fs = cm 2 s 1 is the photochemical production of free sulfur from SO 2 in the middle atmosphere. Thermolysis of OCS, R22 S 2 + OCS, and D(SO + O 2 ) add cm 2 s 1 to the production of CO, mostly below 5 km. Here D(SO + CO 2 ) means a difference between the rates of the direct and inverse reactions in SO + CO 2 = SO 2 + CO. The production of CO is balanced by its loss in R15 S + CO + M and D(S 2 + CO) in the lowest scale height. The H 2 O dissociation energy is comparatively high (Table 2); therefore the OH chemistry is rather weak and D(CO + OH) is responsible for 0.4% of the total CO loss. However, D(CO + OH) is the only process that oxidizes CO to CO 2 in the lowest scale height. Except R3 SO 3 + CO and D(SO + CO 2 ), the production and loss of CO are related to the loss and production of OCS, respectively. Accordingly, OCS is formed in the lowest scale height by R15 S + CO + M and D(S 2 + CO). This production (Fig. 6), reduced by 30% by R16 OCS + M and R22 OCS + S 2 below 5 km, forms an upward flux of OCS which is lost in R4

11 34 V.A. Krasnopolsky / Icarus 191 (2007) avoid this depletion if the S 3 photolysis yield is very low. For example, the S 3 mixing ratio does not change from 0 to 10 km for the yield of but equals , exceeding the measured values. An increase of eddy diffusion to K = 10 4 cm 2 s 1 does not help to remove the high gradient of S 3 (see the next section and Table 4). 8. Sensitivity of the model to variations of input parameters Fig. 7. S/S 2 ratio in the model (solid line) is compared with those for thermochemical equilibria S + S = S 2 (thin line) and S + OCS = CO + S 2 (dashed line). S 3 /S 2 ratio in the model is also compared with that from the balance of R10 S + S 2 + MandR7S 3 + hν. SO 3 + OCS and R5 at 35 km. This makes a strong gradient of OCS observed near this height by the nightside spectroscopy (Pollack et al., 1993; Taylor et al., 1997; Marcq et al., 2005, 2006). Production of S 2 in R5 results in the downward flux of S x at fs + 2Φ H2 SO cm 2 s 1 below 33 km. R16 OCS + M and R22 S 2 + OCS (Fig. 6) add to the production of free sulfur which is lost in R15 S + CO + M, D(S 2 + CO), and D(S + SO 2 ). The downward flux of S x results in a positive gradient of S x in the lower atmosphere (Fig. 2). S x consists of S 2 below 15 km (Fig. 2). The S 2 mixing ratio near the surface is very similar to that calculated for thermochemical equilibrium 2OCS = 2CO + S 2.S/S 2 and S 3 /S 2 are shown in Fig. 7. S/S 2 is very different from that expected for thermochemical equilibrium S + S = S 2, though the values coincide near the surface. The calculated S/S 2 ratio is similar to that for the equilibrium S + OCS = CO + S 2. Actually both the direct and inverse reactions of this equilibrium (R17 and R18) are the main loss and production terms for S in our model (Table 3). The model S 3 /S 2 ratio is equal to k 13 [S][M]/J 10 that reflects the equilibrium between the production of S 3 in R13 S + S 2 + M and its loss by photolysis. The visible spectra from the Venera landing probes show a strong blue absorption which is due to the Rayleigh extinction in the dense atmosphere and absorption by S 3 (Sanko, 1980; Moroz et al., 1981). Krasnopolsky (1987) retrieved a S 3 mixing ratio of (8 ± 3) at 5 25 km from the Venera 14 measurements and values lower by more than a factor of 3 for the Venera 11 and 13 data. Maiorov et al. (2005) derived S 3 increasing from at3kmto10 10 at 19 km from the Venera 11 data. Both papers show that the S 3 mixing ratio is at 5 20 km, and this agrees with the model (Fig. 3). (It is easy to adjust the S 3 abundance in the model by changing the photolysis yield which is adopted at 0.1.) However, the model yields a steep depletion of S 3 by two orders of magnitude from the surface to 20 km (Fig. 3). It is possible to Photochemical production fs of free sulfur from SO 2 in the middle atmosphere is one of the main parameters of the model. We adopted fs = cm 2 s 1 for our basic model, and the limiting cases fs = 0 and cm 2 s 1 are compared with the basic model in Table 4. We have discussed in the previous section that fluxes of free sulfur and CO are equal to 2Φ H2 SO 4 fs and 2Φ H2 SO 4 + 2fs, respectively, below 33 km. Then Φ Sx is , , and cm 2 s 1 in the basic model and for the limiting values of fs, respectively. Accordingly, Φ CO = , , and cm 2 s 1 at 33 km. The calculated variations of CO are of a factor of 2 above 30 km, variations of S 3 are of a factor 2 as well but below 10 km, and variations of S x are of a factor of 1.5. The other densities are rather stable. Currently the only chemical scheme to explain the high gradient of OCS is that suggested by Krasnopolsky and Pollack (1994) and adopted in this work. The downward flow of sulfuric acid from the middle atmosphere removes the upward flow of OCS from the atmosphere below 20 km in this scheme. This flow of OCS is proportional to eddy diffusion that should be rather low to balance the flow of H 2 SO 4. K = cm 2 s 1 below 30 km is adopted in Krasnopolsky and Pollack (1994) and our model, smaller than the values of cm 2 s 1 considered by Krasnopolsky and Parshev (1979) and adopted by Fegley et al. (1997). Any significant increase of eddy diffusion below 30 km breaks the scheme and drastically reduces the OCS gradient (Table 4). The proportional increase of the sulfuric acid flow may properly balance the increase in eddy diffusion. However, a significant increase of this flow is not supported by the model of the H 2 SO 4 H 2 O system in Krasnopolsky and Pollack (1994) and disagrees with the observed abundances of H 2 SO 4. We have tested a sensitivity of the model to the chosen reaction rate coefficients by increasing selected values by a factor of 10. Naturally, rate coefficients of the inverse reactions are also increased by the same factor. Surprisingly, changes in the calculated values for the basic species are typically rather low. The highest sensitivity is to the reactions given in Table 4. However, the results of this test do not mean that the model is very certain and well established. The Krasnopolsky and Pollack (1994) scheme still needs confirmation by laboratory studies. The model does not include a detailed chemistry of (SO) 2 S 2 O SO which is poorly known but may affect the model results.

12 Chemical model for lower atmosphere of Venus Sulfur cycles The nightside spectroscopy of OCS (Pollack et al., 1993) and its kinetic interpretation in Krasnopolsky and Pollack (1994) and in our model are incompatible with a concept of the slow atmospheric cycle of sulfur (Prinn, 1985). Basic processes of this concept are photolysis of OCS and formation of SO 2,SO 3, and (1/x)S x above the clouds and SO 3 + 4CO OCS + 3CO 2, CO + (1/x)S x OCS, below the clouds. Here OCS is formed by the species moving down from the middle atmosphere, and its mixing ratio should be rather constant below the clouds and steeply decreasing in the cloud layer because of the intense photolysis above the clouds. The observed strong gradient of OCS at km rules out this scheme. Furthermore, these processes require a large flux of CO at the upper boundary that exceeds the flux of SO 3 by more than a factor of 4. The latest photochemical model (Mills, 1998) predicts comparable fluxes of CO and SO 3 at 58 km. Here we suggest a new version of the atmospheric cycles of sulfur that removes the above inconsistencies. The major net effect of photochemistry above the clouds maybegivenas CO 2 + (1 + 3α)SO 2 CO + (1 + 2α)SO 3 + (α/x)s x. Here α is the ratio of the fluxes of S and CO. This cycle involves two parameters that are two of the fluxes of CO, SO 3,SO 2, and S; CO and S are chosen in the above formulation. Photochemistry also involves two minor processes: OCS CO + (1/x)S x, OCS + 2CO 2 SO 2 + 3CO. OCS has not been detected above the clouds with an upper limit of 10 ppb (Kuiper, 1969), and these processes are poorly constrained by the observations. The net effect of thermal chemistry in the lowest 10 km is CO + S, S 2 /2 OCS. Chemistry at km balances the effects of the photochemical and thermochemical cycles by SO 3 + 2OCS CO 2 + CO + SO 2 + S 2. This chemistry removes the downward flux of SO 3 and the upward flux of OCS and increases the flow of CO and free sulfur. For the sake of simplicity we do not consider hydration of SO 3 and loss of water by sulfuric acid. The mean lifetime of SO 2 in the middle atmosphere may be estimated as a ratio of the SO 2 column abundance at 58 km to its upward flux. Using the data of the nominal model by Mills (1998), this lifetime is 3 months. The mean lifetime of OCS in the subcloud atmosphere is equal to a ratio of its column abundance to the column rate of SO 3 + 2OCS, that is, 270 years in our model. Therefore the cycling of sulfur in the middle atmosphere may be considered as fast and that in the lower atmosphere as slow. Our model is closed, that is, it does not need any supply of species from the surface rocks. This actually means that the surface-atmosphere interaction is much slower than the atmospheric processes. This interaction is a so-called geological cycle (von Zahn et al., 1983; Prinn, 1985; Fegley and Treiman, 1992): FeS 2 + CO 2 + CO FeO + 2OCS, SO 2 + CaCO 3 CaSO 4 + CO, 2CaSO 4 + FeO + 7CO FeS 2 + 2CaCO 3 + 5CO 2. In the first reaction pyrite FeS 2 forms OCS which evolves into SO 2 by the minor photochemical cycle. SO 2 reacts with carbonate rock to form anhydrite CaSO 4 which may return pyrite in the last reaction and complete the geological cycle. Here we do not consider the H 2 S cycling because its abundance is rather low on Venus. 10. Conclusions We have calculated for the first time a self-consistent chemical kinetic model of the subcloud atmosphere of Venus. 82 reactions of 26 species in the model are initiated by photochemical products from the middle atmosphere (SO 3,CO,S x ), thermochemistry in the lowest 10 km, and photolysis of S 3. The sulfur bonds in OCS and S x are the weakest among the bonds of the other elements in the basic atmospheric species on Venus, and chemistry of the subcloud atmosphere on Venus is sulfur-driven with minor contribution of H, Cl, and OH atoms and radicals. The lack of kinetic data for many reactions in the model has been compensated using some similar reactions and thermodynamic calculations of inverse processes. While column rates of some reactions exceed the highest rates in the middle atmosphere by two orders of magnitude, many reactions are balanced by the inverse processes, and their net rates are comparable to those in the middle atmosphere. The calculated profiles of CO, OCS, and gaseous H 2 SO 4 agree with the existing observational data. While the mean S 3 abundance in the model agrees with the Venera observations, the steep decrease in S 3 from the surface to 20 km is not expected from the observations. The ClSO 2 and SO 2 Cl 2 mixing ratios are low in the model and do not support some expectations regarding to this species. The existing concept of the atmospheric sulfur cycles is incompatible with the observations of the OCS profile and has been significantly changed. The geological cycle of sulfur remains unchanged. The model is based on the chemical scheme suggested by Krasnopolsky and Pollack (1994) to explain the observed profile of OCS. Validation of this scheme by laboratory studies would be of great importance for the problem of chemical composition of the Venus lower atmosphere. New observational data, especially from the Venus Express mission, may result a further progress in the field.