Airglow on Mars: Some model expectations for the OH Meinel bands and the O2 IR atmospheric band

Icarus 176 (2005) 75–95 www.elsevier.com/locate/icarus

Airglow on Mars: Some model expectations for the OH Meinel bands and the O2 IR atmospheric band A. García Muñoz a,∗ , J.C. McConnell a , I.C. McDade a , S.M.L. Melo b a Department of Earth and Space Science and Engineering, York University, Toronto, ON M3J 1P3, Canada b Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada

Received 2 July 2004; revised 31 December 2004 Available online 11 March 2005

Abstract This work presents model calculations of the diurnal airglow emissions from the OH Meinel bands and the O2 IR atmospheric band in the neutral atmosphere of Mars. A time-dependent photochemical model of the lower atmosphere below 80 km has been developed for this purpose. Special emphasis is placed on the nightglow emissions because of their potential to characterize the atomic oxygen profile in the 50–80 km region. Unlike on Earth, the OH Meinel emission rates are very sensitive to the details of the vibrational relaxation pathway. In the sudden death and collisional cascade limits, the maximum OH Meinel column intensities for emissions originating from a fixed upper vibrational level are calculated to be about 300 R, for transitions v  = 9 → v 
8, and 15,000 R, for transitions v  = 1 → v  = 0, respectively. During the daytime the 1.27 µm emission from O2 (a 1 ∆g ), primarily formed from ozone photodissociation, is of the order of MegaRayleighs (MR). Due to the long radiative lifetime of O2 (a 1 ∆g ), a luminescent remnant of the dayglow extends to the dark side for about two hours. At night, excited molecular oxygen is expected to be produced through the three body reaction O + O + CO2 . The column emission of this nighttime component of the airglow is estimated to amount to 25 kR. Both nightglow emissions, from the OH Meinel bands and the O2 IR atmospheric band, overlap in the 50–80 km region. Photodissociation of CO2 in the upper atmosphere and the subsequent transport of the atomic oxygen produced to the emitting layer are revealed as key factors in the nightglow emissions from these systems. The Mars 5 upper constraint for the product [H][O3 ] is revised on the basis of more recent values for the emission probabilities and collisional deactivation coefficients.  2005 Elsevier Inc. All rights reserved. Keywords: Atmospheres, composition; Mars, atmosphere; Photochemistry

1. Introduction On Mars, vibrationally excited OH is thought to be primarily produced via the Bates–Nicolet mechanism (Bates and Nicolet, 1950) of hydrogen and ozone, H + O3 → OH + O2 , at about 60 km. On Earth, the overall kinetics of vibrational relaxation of OH is still somewhat uncertain, and the extent of the role played by collisional deactivation of OH has not been unequivocally assessed (McDade, * Corresponding author. Graduate Program in Earth and Space Science, 354 Chemistry Building, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada. Fax: +1-416-736-5817. E-mail address: [email protected] (A. García Muñoz).

0019-1035/$ – see front matter  2005 Elsevier Inc. All rights reserved. doi:10.1016/j.icarus.2005.01.006

1997, and references therein). In the 70s, the Mars 5 mission attempted to observe nightglow in the martian atmosphere with no success. Krasnopolsky and Krys’ko (1976) reported upper limits of about 50 R both in the vertical and at the limb. No additional attempts to detect OH nightglow have been made since then. Dayglow from the a 1 ∆g → X 3 Σg− electronic transition of molecular oxygen at 1.27 µm was first detected on Mars by Noxon et al. (1976). From then, its study has proven useful in the tracing of daytime ozone in the martian atmosphere (Traub et al., 1979; Krasnopolsky, 1997, 2003; Krasnopolsky and Bjoraker, 2000; Novak et al., 2002). During the daytime, O2 (a 1 ∆g ) is formed in the lower atmosphere of Mars from ozone photodissociation

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at wavelengths shorter than the threshold for O3 + hν → O2 (a 1 ∆g ) + O(1 D) near 3100 Å. At night, excitation of O2 is thought to occur in the 50–80 km region directly or indirectly through the three body reaction O + O + CO2 leading to the reformation of molecular oxygen. So far, the nightglow emission from the O2 IR atmospheric band at 1.27 µm on Mars has never been measured. This situation might change soon, as the SPICAM instrument onboard the Mars Express is equipped with an IR spectrometer with detection capabilities in the spectral range 1.0–1.7 µm (Bertaux et al., 2000). Krasnopolsky (2003) has discussed the possibilities and difficulties of detection of O2 IR 1.27 µm nightglow from the existing ground based facilities and space platforms. The observation of the nightglow emissions from the OH Meinel bands and the O2 IR atmospheric band at 1.27 µm will provide a clearer picture of the odd oxygen, Ox (O and O3 ), profile on Mars. Airglow observation might also serve to infer temperatures and wind velocities (Ward et al., 2003) and observe gravity waves (Melo et al., 2004). The mechanisms for vibrational excitation of OH and electronic excitation of O2 represent parts of the more general problem of the atmospheric composition of Mars. The variations in the airglow emission rates occur in response to diurnal, seasonal and latitudinal changes in the dynamics and photochemistry of the atmosphere. Given our interest in the nighttime component of airglow, we have employed a timedependent photochemical model of the martian atmosphere. Diurnal variations in the composition and airglow emissions are integrated in a self-consistent way. The results reveal significant diurnal variations in the density of some short-lived species, and in turn, in the diurnal airglow emission rates. We limit the scope of this work to low latitudes under equinox conditions and altitudes below 80 km. The present work does not aim to explain the disagreement between models and observations for CO, O3 , and O2 (a 1 ∆g ).

2. Photochemical model 2.1. Formulation Mass conservation of minor species in the one-dimensional approach to the atmospheric composition problem is governed by the continuity equation: ∂ni ∂φi + = Pi − Li , ∂t ∂z where the vertical diffusion flux is given by:

1 1 ∂T ∂ni φi = −K + ni + ∂z H T ∂z

 ∂ni 1 1 ∂T + ni − Di + (1 + αi ) ∂z Hi T ∂z and ni , Pi , and Li stand for number density, chemical production and chemical loss of the ith species, respectively.

T is temperature and H is the scale height of the background atmosphere. Hi and αi are the scale height and the thermal diffusion factor of the ith species respectively. Di represents the molecular diffusion coefficient of the ith species. K is the so-called eddy diffusion coefficient. Turbulence and large scale winds contribute to the make-up of K. Below the homopause, at about 120 km on Mars, diffusion by molecular transport is far less efficient than eddy diffusion, Di  K, and may be neglected. The model of the lower atmosphere of Mars presented herein is built on the simplified formulation:

 1 ∂ ∂ni 1 ∂T ∂ni − K + ni + = Pi − Li ∂t ∂z ∂z H T ∂z and solved between 0 and 80 km. The COSPAR mean temperature profile has been adopted (Seiff, 1982). No temporal variation of temperature, within the planetary boundary layer or higher up as a result of gravity waves or other dynamical disturbances, has been considered. In our model, the thermal structure of the atmosphere shapes the water profile throughout most of the lower atmosphere, and in turn, the abundance of odd hydrogen, HOx (H, OH, HO2 ), and other active species. Clancy and Nair (1996) explored this effect with temperature and water profiles dependent on the local season and concluded that active species can undergo seasonal changes by factors as large as one order of magnitude in regions of varying temperature. Hence, comparisons between models and observations must take careful account of the local water content and temperature profile. Critical comments on the values of K inferred for the martian atmosphere can be found in Krasnopolsky (1986, 1993) and Rodrigo et al. (1990a, 1990b). However, in the lower and middle atmosphere the eddy diffusion coefficient remains poorly known. In our model a piecewise profile has been adopted. K = 106 cm2 s−1 from 0 to 40 km, and follows a linear variation in log10 (K), ranging from 106 to 107 cm2 s−1 between 40 and 80 km. This profile, which is meant to represent time averaged conditions, is consistent with the known observational constraints (see also Korablev, 2002, and references therein). A simple scheme of precipitation and sublimation of water has been implemented, which renders it unnecessary to prescribe the water profile. The distributions of vapor and ice are additional outputs from the model. Wherever the atmosphere becomes supersaturated (relative humidity, q, larger than one) the excess of water vapor precipitates out at the rate:
 nH2 O,v − nsat (T ) nH2 O,v q − 1 = . τsat τsat q Sublimation is allowed to occur in any condition where ice exists via a first-order reaction with a time constant τsubl . The saturation vapor pressure over ice has been taken from 273.16 Houben et al. (1997), psat (T ) = 6.11e(22.5(1− T )) mbar. Sedimentation of ice has not been directly considered, but

Martian airglow models

Table 1 Photodissociation and radiative emission reactions Reaction

Rate

(R1) (R2) (R3)

CO2 + hν → CO + O(1 D)

CO2 + hν → CO + O O3 + hν → O2 (a 1 ∆g ) + O(1 D)

0–3.5 × 10−9 3.0 × 10−12 –3.5 × 10−9 3.1 × 10−3

(R4) (R5) (R6) (R7) (R8) (R9) (R10) (R11) (R12) (R13) (R14) (R15)

O3 + hν → O2 + O(1 D) O3 + hν → O2 + O O3 + hν → 3O O2 + hν → O + O(1 D) O2 + hν → 2O H2 O2 + hν → 2OH H2 O2 + hν → HO2 + H HO2 + hν → OH + O H2 O + hν → H + OH H2 O + hν → H2 + O(1 D) H2 O + hν → 2H + O O2 (a 1 ∆g ) → O2 + hν (1.27 µm)

1.1 × 10−5 5.5 × 10−4 –5.6 × 10−4 1.7 × 10−9 –7.9 × 10−7 0–2.1 × 10−7 3.1 × 10−10 –4.6 × 10−8 3.8 × 10−5 –4.0 × 10−5 4.1 × 10−7 –9.8 × 10−7 2.2 × 10−4 –2.3 × 10−4 2.0 × 10−10 –2.3 × 10−6 0 − 1.1 × 10−7 0–1.1 × 10−7 2.237 × 10−4

Rates in s−1 . See Appendix A for references on cross sections and quantum yields. A15 = 2.237 × 10−4 s−1 from Lafferty et al. (1998).

precipitated water can diffuse driven by eddy diffusion. This implementation does not preclude supersaturation in some regions. The excess water vapor depends roughly upon the ratio τsat /τsubl . Time constants τsat = 30 min and τsubl = 15 sols prevent supersaturation from becoming larger than 30% at any altitude in the present conditions. Given its importance in the budget of HOx compounds, the effect of the water cycle in the lower atmosphere should be further explored in more realistic terms. We plan to do this in the investigation of the martian atmosphere with a General Circulation Model (GCM) which is being carried out in parallel with this work. 2.2. Photochemistry The system of continuity equations has been solved for an atmosphere composed of 13 gaseous species: CO2 , CO, O2 , O2 (a 1 ∆g ), O3 , O, O(1 D), H2 , H, H2 O(vapor), OH, H2 O2 , and HO2 , and H2 O(ice). A summary of the sources for the photoabsorption cross sections and quantum yields employed in the photochemical model has been included in Appendix A. Table 1 lists the set of photochemical reactions. Photodissociation rates are evaluated on-line at each time step. Scattering has not been taken into account for this study. Table 2 shows the set of bimolecular, termolecular and phase change reactions considered. The employed actinic solar fluxes are taken from Torr and Torr (1985) (50–1050 Å), Mount and Rottman (1983) (1150–1750 Å), and WMO (1985) (1754–8525 Å), and have been scaled by the mean Sun–Mars distance (1.52 AU). In order to represent mean solar activity, the actinic fluxes at solar maximum and nearly solar minimum conditions have been arithmetically averaged. As it is CO2 that primarily absorbs above 80 km, the exponential factor e−τupper /µ(t) 80→TOA σ 80→TOA . may be readily estimated by τupper  NCO CO2 2 µ(t)  cos φ cos h near the equinox, with φ and h stand-

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ing for latitude and hour angle, respectively. The column abundance of CO2 between 80 km and the top of the at80→TOA = 1.9 × 1019 cm−2 , has been determosphere, NCO 2 mined in a separate calculation of the atmosphere in hydrostatic equilibrium up to the exobase. At short wavelengths the CO2 photoabsorption cross sections are weakly temperature-dependent, and hence, the estimated absorption thickness τupper is nearly unaffected by the temperature para80→TOA . For σ 80→TOA , the values at 298 K meterization of σCO CO2 2 have been employed. The calculations are carried out at a latitude of 20◦ . 2.3. Numerical method The system of time-dependent partial differential equations is solved by means of the Strang operator splitting method (Strang, 1968). The diffusion and chemical operators are treated separately in intermediate stages within each time step. The chemistry is solved by a 2nd order Rosenbrock 2 method, which allows for time steps of up to one hour to be handled without instabilities (Verwer et al., 1999). The temporal evolution of the diffusion operator has been solved with a Crank–Nicholson scheme, also second-order accuracy in time. A finite volume formulation has been implemented for this operator, with evaluation of the fluxes at the edges of the cells. In this way, the spatial accuracy of the scheme turns out to be 2nd order. The ordered composition of both operators is aimed to guarantee the second-order accuracy in time of the complete solution. The 0–80 km domain is covered by a uniform grid of 80 cells. The computations were run with progressively refined time steps. Large time steps of up to one hour were used in the initial stages of the run to accelerate the convergence. At the final stage of the computation a time step of 24.62 s was utilized. A total of 3600 such time steps comprises one sol. Some tests were performed after further halving the time step or doubling the number of cells and no significant change in the solution was observed. 2.4. Boundary and initial conditions In a model of the lower atmosphere the effect of the upper atmosphere is introduced through the boundary conditions at the top of the computational domain. In a study on the uniqueness and minimal constraining of solutions to photochemical steady state models, Krasnopolsky (1995) put forward a series of recommendations intended to ensure the uniqueness of a numerical steady solution while preventing its overdetermination. The idea behind the concept of overdetermination is that flux type boundary conditions determine less rigidly the atmospheric composition, and that this is a suitable approach at interfaces of photochemical models (atmosphere-ground and lower atmosphere-upper atmosphere). The application of these directions requires, for an atmosphere composed of three elements (C, H, and O), that only three number densities or diffusion velocities be

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Table 2 Bimolecular, termolecular and phase change reactions. Rate coefficients in cm s units Reaction

Rate coefficient

Reference

(R16) (R17) (R18) (R19) (R20) (R21) (R22) (R23) (R24) (R25) (R26) (R27) (R28) (R29) (R30) (R31) (R32) (R33) (R34) (R35) (R36) (R37) (R38) (R39) (R40) (R41) (R42) (R43) (R44) (R45) (R46) (R47) (R48)

CO + OH → CO2 + H O + O3 → 2O2 O(1 D) + CO2 → O + CO2 O(1 D) + H2 → OH + H O + H2 → OH + H O(1 D) + H2 O → 2OH O(1 D) + O3 → 2O2 O(1 D) + O3 → O2 + 2O O(1 D) + O2 → O + O2 H + O3 → OH + O2 O + OH → O2 + H O + HO2 → OH + O2 HO2 + OH → H2 O + O2 H + HO2 → H2 + O2 H + HO2 → H2 O + O H + HO2 → 2OH 2HO2 → H2 O2 + O2 O + H2 O2 → OH + HO2 HO2 + O3 → OH + 2O2 H2 + OH → H + H2 O H2 O2 + OH → HO2 + H2 O OH + O3 → HO2 + O2 2OH → H2 O + O O2 (a 1 ∆g ) + CO2 → O2 + CO2 CO + O + CO2 → 2CO2 O + O2 + CO2 → O3 + CO2 2O + CO2 → O2 + CO2 2O + CO2 → O2 (a 1 ∆g ) + CO2 H + O2 + CO2 → HO2 + CO2 2OH + CO2 → H2 O2 + CO2 2H + CO2 → H2 + CO2 2HO2 + CO2 → H2 O2 + O2 + CO2 H2 O → H2 O(ice)

1.5 × 10−13

a

(R49)

H2 O(ice) → H2 O

a b c d

8.0 × 10−12 exp(−2060/T ) 7.4 × 10−11 exp(120/T ) 1.1 × 10−10 2.26 × 10−20 2.2 × 10−10 1.2 × 10−10 1.2 × 10−10 3.2 × 10−11 exp(70/T ) 1.4 × 10−10 exp(−470/T ) 2.2 × 10−11 exp(120/T ) 3.0 × 10−11 exp(200/T ) 4.8 × 10−11 exp(250/T ) 6.48 × 10−12 1.62 ×10−12 7.29 × 10−11 2.3 × 10−13 exp(600/T ) 1.4 × 10−12 exp(−2000/T ) 1.0 × 10−14 exp(−490/T ) 5.5 × 10−12 exp(−2000/T ) 2.9 × 10−12 exp(−160/T ) 1.7 × 10−12 exp(−940/T ) 4.2 × 10−12 exp(−240/T ) 2.0 × 10−20 5.92 × 10−33 exp(−2031.4/T ) 1.216 × 10−27 T −2.4 8.16 × 10−35 exp(900/T ) 1.59 × 10−34 exp(900/T ) 1.205 × 10−27 T −1.6 4.76 × 10−28 T −1 2.7 × 10−31 T −0.6 3.91 × 10−33 exp(1000/T ) q−1 qτsat (if q > 1), or 0 (if q < 1) 1 τsubl

a a a b a a a a a a a a a* a* a* a a a a a a a a c a** d** d** a** a** e*** a**

See text See text

Sander et al. (2003); * : Keyser (1986); ** : Lindner (1988). Balakrishnan (2003); 200 K. Slanger et al. (1972). Fit between 2.3 × 10−37 cm6 s−1 at 200 K and 6.2 × 10−36 cm6 s−1 at 296 K. Tsang and Hampson (1986). See text for net yields of O2 and O2 (a 1 ∆g ). ** : Lindner (1988).

e Baulch et al. (1992); *** : uncorrected for CO as third body. 2

imposed, and that each element be present in at least one of these boundary conditions. The remaining boundary conditions must be of the flux type. In our model, number densities of CO2 , O2 , H2 , and H2 O have been assigned on the ground and diffusion fluxes elsewhere. Krasnopolsky’s recommendations would require the replacement of the number density of either H2 or H2 O for a flux type boundary condition. However, the major sink of H2 is located in the upper atmosphere, above the top boundary of the present model, and Krasnopolsky’s recommendations show a very slow convergence in the numerical solution of the lower atmosphere. The convergence is greatly accelerated by fixing the number density of H2 , at the cost of formally overdetermining the problem. At the surface the pressure reported by Seiff (1982), 6.36 mbar, has been scaled by 0.9532 to account exclusively for the partial pressure of CO2 . Relative abundances of the

O2 molecule of about 0.11% have been reported by numerous authors (Krasnopolsky, 1993, and references therein). Hence, a mixing ratio of 1.1 × 10−3 is assumed for O2 at the surface. Recently Krasnopolsky and Feldman (2001) reported an estimated H2 mixing ratio of 15 ppm in the lower atmosphere based on their observations of the upper atmosphere with the Far Ultraviolet Spectroscopic Explorer (FUSE). Since H2 is expected to be well mixed in this region, the mixing ratio 1.5 × 10−5 has been taken as the boundary condition on the surface. Regarding the water vapor content, an abundance of 240 ppm at the surface has been adopted. The suitability of this choice is discussed later. The surface is assumed passive for all other species, or equivalently, φi = 0 for them. Fluxes of H and H2 at the top may be taken from the analysis of Anderson (1974), φH = −4 × 108 cm−2 s−1 and φH2 = 3 × 108 cm−2 s−1 , or from the work of Krasno-

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79

polsky (2002) for medium solar activity, φH = −0.35 × 108 cm−2 s−1 and φH2 = 1.3 × 108 cm−2 s−1 . They correspond to net escapes of 2 × 108 and 2.25 × 108 H atoms from the exosphere, respectively. Our nominal results are calculated with the set of fluxes provided by Anderson (1974). For completeness, the effect of adopting the alternative set is also explored. Since there is little chemical loss above the 80 km level, the downward fluxes of CO and O may be approximated by the column photodissociation rate of CO2 above 80 km. For globally averaged conditions, the fluxes of CO and O are −1.05 × 1011 cm−2 s−1 , which are largely determined by the total solar flux for wavelengths shortward of 1600 Å. For all other species zero fluxes are adopted. Rodrigo et al. (1990a) reported no significant diurnal fluctuations of CO, O, H or H2 at 80 km. This conclusion coincides with the time-dependent analysis of Nair et al. (1994) for O at 60 km and our work. The model is run to the steady state of the long-lived species, defined as the moment when the following relations: 80 km , φC∗ = φCO

φH∗ = φH80 km + 2 × φH802 km ,

80 km φO∗ = φO80 km + φCO

are satisfied throughout the domain. The elementary flux φC∗ is the total flux of carbon atoms, made up of the contribution of all carbon containing compounds. Likewise, the fluxes φH∗ and φO∗ are the total fluxes of hydrogen and oxygen atoms. Strictly, this criterion of convergence is valid exclusively for steady problems. However, it turns out that only the locally stable species contribute significantly to the elementary fluxes φ ∗ , and therefore, the criterion indicated above suffices to state the numerical convergence of the problem.

3. Atmospheric composition The photochemistry of Mars has been reviewed by Barth (1985) and Krasnopolsky (1986). More recent photochemical models (Rodrigo et al., 1990a; Krasnopolsky, 1993; Atreya and Gu, 1994; Nair et al., 1994; Clancy and Nair, 1996) have also furnished valuable insights into the understanding of the lower atmosphere and the stability issue. Since the early 70s, it has been realized that water plays an important role in the catalytic recombination of CO and O2 into CO2 in the martian atmosphere. Viking observations with the Mars Atmospheric Water Detectors (MAWD) indicated that its content is globally and seasonally variable (Jakosky and Farmer, 1982). The measurements carried out with the Thermal Emission Spectrometer (TES) onboard the Mars Global Surveyor have confirmed this variability (Smith, 2002, 2004). Recently, Fedorova et al. (2004) have revised the MAWD results and corrected them to account for aerosol scattering, neglected in the original work by Jakosky and Farmer (1982). The corrected water abundances reveal an apparent similarity between the MAWD and TES sets of observations. Clancy and Nair (1996) pointed out that

Fig. 1. Top: Concentration of major and odd oxygen species. Bottom: Concentration of hydrogen compounds.

the seasonal change of temperature in the atmosphere, and in turn of the vertical distribution of water vapor, drives large seasonal variations in the abundance of ozone and related short-lived species. Similar behavior can be expected on time scales of hours, in response to the diurnal cycle of temperature in the lowest scale height of the atmosphere. In the present work a moderately moist scenario has been considered, with a water vapor mixing ratio at the surface of 2.4 × 10−4 . The modeled water vapor column abundance results 14.5 pr-µm (1 pr-µm = 3.34 × 1018 cm−2 ), consistent with an annual average of both the corrected MAWD and TES retrievals. The noon and midnight number densities calculated by our model are shown in Fig. 1. O2 (a 1 ∆g ) is not included in this figure, but its number density can be inferred readily from the volume emission rates of O2 (a 1 ∆g ) 1.27 µm airglow in Fig. 12, to be commented on later. Figure 2 shows the diurnal variation of OH, H, O3 , and O at selected altitudes. Given its long lifetime, CO is expected to be well mixed in the lower atmosphere. However, photochemical models yield a non-constant vertical profile of the CO mixing ratio, as shown in Fig. 1. Atreya and Gu (1994) suggested

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Fig. 2. Diurnal variation of OH, H, O3 , and O at selected altitudes.

heterogeneous chemistry as a means of slowing down the reformation of CO2 in the lower atmosphere, and so reconcile the CO theoretical expectations and model calculations. Clancy and Nair (1996) pointed out that the permanent state of non-equilibrium of long-lived species affects their vertical distribution, and in consequence, the profile of active species. Figure 3 shows the modeled water vapor profile, along with the saturation vapor curve for the prescribed temperature profile. For our temperature profile the atmosphere becomes supersaturated by up to 30%. Water is well mixed below the saturation level and controlled by saturation above this point. While crucial in the photochemistry of other species, water is largely unaffected by photochemical processes in the current model domain. In the planetary boundary layer water undergoes a diurnal cycle of saturation–sublimation and transfer with the regolith. Amounts of the order of a few pr-µm can be drawn from the subsurface into the atmosphere after sunrise (Titov, 2002, and references therein). An unsteady model of the martian atmosphere must necessarily account for these means of conversion and transfer of moisture. However, the effect of these mechanisms is less important at altitudes where the

Fig. 3. Saturation curve of water vapor (solid line) and water vapor profile in the model (dashed line).

considered nightglow emissions are expected to peak. For simplicity we have omitted them from the present work. Molecular hydrogen, H2 , is mostly produced between 20 and 40 km via H + HO2 → H2 + O2 . Dissociation of H2 in the thermosphere by ion–molecule reactions is an efficient

Martian airglow models

81

Fig. 4. Production rates of HOx at noon.

regulator of its distribution in the entire atmosphere. In the current model, the flux of H2 towards the upper atmosphere must be prescribed at the top of the model domain. The resulting mixing ratio of H2 is nearly constant from the ground up to 80 km. For molecular oxygen, the mixing ratio is fixed at the surface and eddy diffusion keeps it well mixed from 0 to 80 km. 3.1. HOx compounds In the daytime odd hydrogen compounds HOx are formed in the lower atmosphere directly, via photodissociation of water, or indirectly by photodissociation of H2 O2 or reaction of O(1 D) with either H2 O or H2 , as shown in Fig. 4. At night, the HOx production decays and the odd hydrogen compounds tend to disappear, Fig. 1. The downward flux of H, the product of the H2 dissociation in the thermosphere, towards the lower atmosphere is important to the HOx budget. However, this effect is limited in depth and the layers below 50 km run out of H shortly after dusk. HO2 also has a diurnal cycle, but its nighttime concentrations do not drop to such low densities as those of H and OH. To date there are no measurements of odd hydrogen compounds in the martian lower atmosphere and only the constraint of [H][O3 ]
1015 cm−6 at 60 km has been set from the upper limit to the OH Meinel airglow in the Mars 5 observations (Krasnopolsky and Krys’ko, 1976). The validity of this constraint is reviewed later, on the basis of a more recent set of kinetic parameters for the OH Meinel bands airglow. The production of OH is governed by R27: O + HO2 → OH + O2 throughout the lower and middle atmosphere, Fig. 5. At about 60 km the Bates–Nicolet mechanism, R25: H + O3 → OH + O2 , becomes competitive and an important contributor to the total production of OH. The Bates–Nicolet mechanism peaks at night as a result of the greater amount of O3 at high altitudes in the nighttime. Below 40–50 km the behavior of OH mimics the diurnal variation of H and O and decreases rapidly after sunset. It is interesting to compare

Fig. 5. Top: Production rates of OH at noon. Production of OH by R25 and R27 at midnight is included for comparison. Bottom: Loss rates of OH at noon.

our OH production rates with those from other models. Table 3 shows the R25 and R27 OH production rates calculated by several photochemical models at 60 km altitude. Number densities have been estimated visually from the original publications. It can be seen that there are serious differences amongst the models. The discrepancies reflect the sensitivity of the models to the input conditions and uncertainties in some parameters, such as the eddy diffusion coefficient and the water vapor profile. No general conclusion can be drawn on the relative importance of R25 and R27 or their net productions of OH. In terms of OH production, we obtain values which are similar to those of Nair et al. (1994). Hydrogen peroxide may be regarded as another member of the HOx family due to its rapid convertibility. Only very recently have attempts to detect H2 O2 in the martian atmosphere been successful, as reported by Clancy et al. (2004) and Encrenaz et al. (2004). The measurement by Clancy et al. (2004) was carried out at perihelion and revealed a mixing ratio of 18 ppb in the lowest 30 km, when the water abundance was about 15–20 pr-µm. This is in reasonable agreement with the mixing ratio of 1.3 × 10−8 obtained with our model for a water abundance of 14.5 pr-µm.

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Table 3 Comparison of R25 and R27 as sources of OH in recent photochemical models at 60 km altitude At 60 km

[H]

[O3 ]

k25 [H][O3 ]

[O]

[HO2 ]

k27 [O][HO2 ]

Rodrigo et al. (1990a) Krasnopolsky (1993) Nair et al. (1994) Atreya and Gu (1994) Present model

∼3 × 106

∼108 /106

∼2 × 103 /∼20

∼7 × 109

∼4 × 106 ∼4 × 107 ∼108 ∼2 × 108

∼107 ∼4 × 107 ∼4 × 106 ∼3 × 107 /7 × 106

∼2 × 102 ∼104 ∼2 × 103 ∼3 × 104 /8 × 103

∼5 × 1010 ∼2 × 1010 ∼4 × 1010 ∼2.4 × 1010

∼100 104 ∼2 × 103 104 ∼6 × 103

∼80 6 × 104 ∼5 × 103 5 × 104 ∼2 × 104

When available nighttime/daytime values are provided, otherwise the values refer to daily averaged conditions. Number densities are estimated visually from the cited references. Number densities in cm−3 . Production rates in cm−3 s−1 .

3.2. O(1 D) and Ox compounds The O(1 D) excited state of atomic oxygen is formed from photodissociation of O3 below 3750 Å, as indicated by Bauer et al. (2000), and to a lesser extent from photodissociation of O2 and CO2 . Although present in very small amounts, it is an important source of odd hydrogen after reaction with H2 and H2 O, thereby triggering the reformation of CO2 . O(1 D) is rapidly lost by collisional deactivation with CO2 . Large amounts of O are formed in the upper atmosphere as a result of CO2 photodissociation. This source of O is accounted for in our model by an imposed downward flux at the top of the model domain. Below 80 km, O is chiefly produced by photodissociation of CO2 , although O2 also contributes significantly. After sunset its production is cut-off and the O concentration drops rapidly below 50 km. Above this altitude eddy diffusion is more efficient than chemical conversion at determining the O density. The diffusion time to draw the atomic oxygen produced in the thermosphere above 80 km down to the 50 km altitude region is of the order of a few days, which explains the lack of diurnal variations in the O density in the region in between. The vertical extent of this process is controlled by dynamical activity. Only one reaction in the photochemical scheme, R41: O + O2 + CO2 → O3 + CO2 , forms ozone. Because of its fast interconvertibility, ozone can be regarded as a temporary state of O. During the daytime ozone is primarily lost by photodissociation. At the higher altitudes, the Bates–Nicolet mechanism is also an important sink of ozone. The competition between these two processes and R41 determines its daytime balance. At night the drop in O results in the decrease of O3 in the lower atmosphere. However, production of O3 goes on all day above 50 km, which explains the nocturnal rise in ozone in the middle atmosphere after sunset. Figure 6 shows the main sinks of odd oxygen in the region of study. The column abundance of ozone peaks at noon, with 0.55 µm-amagat (1 µm-amagat = 2.69 × 1015 cm−2 ) (see Fig. 13 to be commented on later). Espenak et al. (1991) and Clancy et al. (1996, 1999) have mapped the ozone column abundance on Mars. Only the values at equinox (Ls = 10◦ ) of Clancy et al. (1999) yield column abundances comparable to what we obtain. For all the other measurements, our calculations are at least a factor of 2–3 lower than the reported values. Heterogeneous chemistry, for instance the surface

Fig. 6. Loss rates of Ox at noon.

loss of HOx on aerosols, could modify the O3 abundance and account for the discrepancies between observations and model results. Given the short lifetime of ozone at the altitudes where the atomic oxygen density peaks, approximate chemical equilibrium expressions for the ozone concentration can be inferred. Thus, for the nighttime: k41 [O][O2 ][CO2 ] . (1) k25 [H] Similarly, during the sunlit hours and in the same altitude range: [O3 ] 

k41 [O][O2 ][CO2 ] . (2) J3+5 + k25 [H] Ozone is directly involved in the production of vibrationally excited OH in the nighttime and O2 (a 1 ∆g ) in the daytime. Equations (1) and (2) clearly describe the behavior of the high altitude ozone concentration throughout the day. [O3 ] 

4. OH Meinel band airglow 4.1. Formulation The OH Meinel band system consists of fundamental and overtone vibrational–rotational transitions from the v  = 1 through v  = 9 vibrational levels of the ground state of the hydroxyl radical, OH(X, v  → X, v  ).

Martian airglow models

83

Table 4 Adopted OH Meinel bands transition probabilities A(v  , v  ) (s−1 ) v

v  0

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9

2.274(1) 0 0 0 0 0 0 1.342(1) 3.242(1) 0 0 0 0 0 1.082(0) 3.860(1) 3.078(1) 0 0 0 0 1.327(−1) 4.082(0) 7.187(1) 2.146(1) 0 0 0 2.429(−2) 5.882(−1) 9.431(0) 1.083(2) 9.288(0) 0 0 5.680(−3) 1.212(−1) 1.529(0) 1.690(1) 1.416(2) 1.072(0) 0 1.498(−3) 3.111(−2) 3.510(−1) 3.237(0) 2.627(1) 1.669(2) 1.582(0) 4.354(−4) 9.309(−3) 9.793(−2) 7.432(−1) 5.264(0) 3.658(1) 1.815(2) 1.336(−4) 2.979(−3) 3.153(−2) 2.230(−1) 1.334(0) 9.809(0) 4.460(1)  AT (v  ) = v  A(v  , v  ). Powers of 10 in parentheses. For instance, A(9, 1) = 2.979(−3) s−1 = 2.979 × 10−3 s−1 .

The postulated vibrational excitation of OH(v
6) via reaction R27 of the perhydroxyl radical, HO2 , and O: k27

O + HO2 −→ OH(v
6) + O2 has long been a controversial issue. It is now generally accepted that R27 does not contribute significantly to the Earth’s OH Meinel bands nightglow (Meriwether, 1989). Thus, in the absence of clearer evidence we consider that the Bates–Nicolet mechanism, R25: k25

H + O3 −→ OH(v
9) + O2 is the only source of vibrationally excited OH on Mars. It is also worth noting that about one third of the OH produced at nighttime above 50 km in the martian atmosphere is supplied by R27, as shown in Table 3 and Fig. 5. Loss of vibrationally excited OH proceeds via either spontaneous emission in the Meinel bands: A(v  ,v  )

OH(v  ) −→ OH(v  ) + hν or collisional deactivation: k Q (v  ,v  )

OH(v  ) + Q −→ OH(v  ) + Q, where A(v  , v  ) and k Q (v  , v  ) are the transition probabilities and deactivation coefficients between levels v  and v  , respectively. Q can be any collisional partner capable of deactivating OH(v  ). 4.2. Transition probabilities The determination of accurate transition probabilities for the Meinel bands has been the subject of numerous works (for instance, Murphy, 1971; Mies, 1974; Turnbull and Lowe, 1989; Langhoff et al., 1989; Nelson et al., 1990). The controversy on the accuracy of the different sets, which differ by more than 100% in some bands, is still open, and may be traced to the shape of the electric dipole moment function (EDMF) of the OH molecule. At separations close to the internuclear equilibrium distance, the EDMF is strongly non-linear and difficult to resolve theoretically or

7

8

AT

0 0 0 0 0 0 0 1.354(1) 1.829(2)

0 0 0 0 0 0 0 0 3.693(1)

22.74 45.85 70.48 97.56 127.7 161.3 198.4 237.8 275.9

Table 5 Band origins of the Meinel bands in air (Å) v  v  0

1

2

3

4

5

6

7

8

1 28007 2 14336 29369 3 9788.0 15047 30854 4 7521.5 10273 15824 32483 5 6168.6 7911.0 10828 16682 34294 6 5273.3 6496.5 8341.7 11433 17642 36334 7 4640.6 5562.2 6861.7 8824.1 12115 18734 38674 8 4172.9 4903.5 5886.3 7274.5 9373.0 12898 19997 41409 9 3816.6 4418.8 5201.4 6256.0 7748.3 10010 13817 21496 44702 Taken from Chamberlain (1961).

experimentally. The transition probabilities in the fundamental and lower overtone sequences are very sensitive to the non-linearity, which has caused the large scattering of the available transition probability sets. For this work, the relative transition probabilities of Murphy (1971), calculated from an empirical EDMF for 
8, have been all the possible transitions v 
9 and v  adjusted to the total values, AT (v ) = v  A(v  , v  ), of Turnbull and Lowe (1989) for each emitting level. The empirical EDMF of Turnbull and Lowe (1989) was designed to reproduce the observed emissions from a number of atmospheric and laboratory experiments. The entire set of absolute transition probabilities, as employed herein, is listed in Table 4. For completeness, the wavelength of each band transition is shown in Table 5, as reported by Chamberlain (1961). More recent assignments, including rovibrational and purely rotational transitions, can be found in the HITRAN database (Rothman et al., 2003). 4.3. Collisional deactivation coefficients Quenching of OH(v  ) by CO2 has been the subject of much laboratory work. In Table 6 we list the deactivation coefficients adopted for our calculations based on the measurements of Dodd et al. (1991), Knutsen et al. (1996), Dyer et al. (1997), and Chalamala and Copeland (1993). To date there are no measurements for v  = 5 and 6. Figure 7 shows

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Table 6 Adopted fractional yields, f (v), of the production of vibrationally excited OH in the H + O3 reaction and total collisional removal rate coefficients, CO kT 2 , with CO2 as collider (cm3 s−1 ) v 1 2 3 4 5 6 7 8 9

f (v  )

kT

0 0 0 0.05 0.05 0.07 0.19 0.29 0.35

1.8 × 10−13

CO2

(v  )

4.8 × 10−13 1.4 × 10−12 2.8 × 10−12 7.8 × 10−12 2.0 × 10−11 6.7 × 10−11 6.4 × 10−11 5.7 × 10−11

Ref. Dodd et al. (1991) Dodd et al. (1991) Dodd et al. (1991) Dodd et al. (1991) Extrapolated, see text Extrapolated, see text Knutsen et al. (1996) Dyer et al. (1997) Chalamala and Copeland (1993)

Collisions of vibrationally excited OH with CO2 can occur with vibration to translation (V–T) or vibration to vibration (V–V) energy transfer in the OH molecule. The possibility of multi-quantum collisional deactivation of vibrationally excited OH in V–V collisions has been reported by Dodd et al. (1991) for v 
4 and is expected to occur also at higher vibrational levels. In their study of the terrestrial Meinel band emission, McDade and Llewellyn (1987) introduced the concept of sudden death and collisional cascade to bracket the possible paths of collisional deactivation. In the sudden death model, vibrationally excited OH is completely deactivated after colliding with the quencher molecule: OH(v  ) + CO2 → OH(0) + CO2 . Thus, in this model k CO2 (v  , 0) = kTCO2 (v  ) and zero otherwise. Hence, the deactivation of one level is not a source for a lower level. In the collisional cascade model the excited OH molecule relaxes a single quantum level at each collision: OH(v  ) + CO2 → OH(v  − 1) + CO2 .

Fig. 7. Deactivation coefficients for OH(v 
12) + CO2 collisions. The values adopted for this work, v  = 1–9, are shown in Table 6. The values for the higher vibrational levels are taken from Dyer et al. (1997) (v  = 10, 11), Sappey and Copeland (1990) (v  = 12), and Lacoursière et al. (2003) (v  = 10 at 223 and 300 K).

the additional deactivation coefficients up to v  = 12. Dyer et al. (1997) suggests that resonance enhancement could be the cause of the relative increase of the deactivation coefficient for levels v  = 7–9 respect to v  = 10 and 11. In the present work, we have assumed that levels v  = 5 and 6 are unaffected by resonance enhancement, and thus, have extrapolated the deactivation coefficients at v 
4 up to v  = 5 and 6 with a log10 (kTCO2 ) − v  law. Unexpectedly, the assumed law seems to represent reasonably well the entire range v  = 1–7. The extrapolated values are also shown in Table 6. We label these deactivation coefficients as kTCO2 (v  ), irrespective of the lower vibrational level v  , for reasons that will become clear below. As the temperature dependence of the deactivation coefficients for v 
9 remains unresolved, we are forced to use the only available values, measured at ambient temperature. For v  = 10, Lacoursière et al. (2003) have reported a rise of nearly 40% when going from 300 to 223 K, what suggests that the rate at which vibrationally excited OH is quenched in the atmosphere is fairly sensitive to temperature.

Thus, in this model k CO2 (v  , v  − 1) = kTCO2 (v  ) and zero otherwise. Atomic oxygen is thought to be an efficient quencher of the terrestrial OH Meinel bands nightglow. However, little is known about the actual rates of OH(v  ) + O and only the removal rates for v  = 0 and v  = 1 have been measured, k O (v  = 0) = 4 × 10−11 cm3 s−1 and k O (v  = 1) = 1.05 × 10−10 cm3 s−1 , as reported by Howard and Smith (1981) and Spencer and Glass (1977), respectively. McDade and Llewellyn (1987) determined an empirical upper limit for the quantity (k O (v  )/AT (9))([O]/[O2 ]) from observations of the terrestrial nightglow. Their uppermost limit, when combined with a ratio of 0.01 for [O]:[O2 ] at the peak of the terrestrial airglow layer and our present value of AT (9), yields k O (v  ) = 1.65 × 10−10 cm3 s−1 . More recently, Makhlouf et al. (1995) modeled the collisional removal of excited OH with a vibrationally dependent set of k O (v  ). They adopted the experimental values for v  = 0 and 1 and k O (v  = 2–9) = 2.5 × 10−10 cm3 s−1 for the higher levels. Adler-Golden (1997) assumed a single value of k O (v  ) = 2 × 10−10 cm3 s−1 irrespective of the vibrational level. In order to explore this issue, we have set upper and lower limits for the total rate of collisional deactivation of OH(v  ) by O: k O (v  )

OH(v  ) + O −→ OH(0) + O of 1.65 × 10−10 cm3 s−1 and zero respectively for all levels. To the best of our knowledge, no measurements of quenching by CO exist, and so, its effect has been omitted from the calculations. Quenching by other relatively abundant species, for instance, N2 , Ar, O2 , is of minor importance and may be ignored. The overall OH kinetics proceeds at a much slower rate than vibrational deactivation, which allows us to separate the

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85

OH airglow mechanisms from the photochemical scheme that determines the atmospheric composition. Assuming chemical equilibrium for the concentration of OH(v), we obtain:
   BN OH(v) = f (v)POH A(v ∗ , v) + k CO2 (v ∗ , v) + 9
v ∗ >v



  × [CO2 ] OH(v ∗ ) −1  × AT (v) + kTCO2 (v)[CO2 ] + k O (v)[O] . (3) BN ≡ k [H][O ] and f (v) is the fracIn this expression POH 25 3 tional yield of level v in reaction R25. The values of f (v) are taken from Ohoyama et al. (1985) and, for consistency, have been adjusted to the transition probabilities shown in Table 4. The adjusted values of f (v) are shown in Table 6. The volume emission rate for each Meinel band is given by:   V (v  , v  ) = A(v  , v  ) OH(v  ) .

Likewise, the total volume emission from each level is given by:   VT (v  ) = AT (v  ) OH(v  ) . 4.4. Results and discussion Figure 8 shows the calculated OH Meinel volume emission profiles at midnight with no quenching of OH(v  ) by atomic oxygen for both the sudden death and collisional cascade models. The diurnal variation in the column intensities for emissions from fixed upper vibrational levels v  is shown in Fig. 9, with maximum values of about 300 and 15,000 R (1 Rayleigh = 106 ph cm−2 s−1 ) for the sudden death and collisional cascade models, respectively. At the altitude of peak emission all the vibrational levels of OH are strongly quenched for both models. The quenching frequency is greatest for v  = 7 and becomes smaller for the lower vibrational levels. At 60 km, the losses of OH(v = 7) and OH(v = 1) due to radiative emission and quenching are in proportions 1:135 and 1:3, respectively. Clearly, the choice of deactivation model, i.e., sudden death versus collisional cascade, has a major impact on the predicted OH Meinel emission rates. Recalling the expression for the equilibrium concentration of vibrationally excited OH(v), Eq. (3), and the fractional yields and deactivation coefficients of Table 6, one can show after some algebraic manipulations that in the collisional cascade model the sequential gain of vibrationally excited OH satisfies: [OH(v)] >1 [OH(v + 1)] for all the vibrational levels. With the same reasoning it can be shown that the profiles of OH(v) densities have all a similar shape, peaking at a common altitude. Radiative cascade becomes important only at the lower levels, v
3,

Fig. 8. Volume emission rates of OH Meinel airglow at midnight. No quenching by atomic oxygen. Top: Sudden death model. Bottom: Collisional cascade model.

and barely affects the shape of the density profiles of OH(v), as seen in Fig. 10. In contrast, in the sudden death model it is apparent from Figs. 8 and 10 that the altitude of the peak emissions and peak densities may be v-dependent for the lower vibrational levels. For v > 3, in the sudden death model, Eq. (3) is well approximated by:   OH(v) =

BN f (v)POH

kTCO2 (v) × [CO2 ]

and hence, the vertical profiles of OH(v > 3) have a common shape. However, for v
3 only the radiative relaxation of the upper levels contributes to the numerator of Eq. (3), which results in the shift of the peak emission to higher altitudes for the lower vibrational levels. The differences in the emission rates between both models are attributable to the relatively high density of the martian atmosphere in the emitting layer as compared to the situation for Earth. For analysis purposes, it is useful to split the volume emission rate, with the help of Eq. (3), into the contribution from direct production in the R25 reaction and the contribution from radiative and collisional cascade. So, a normalized volume emission rate of the OH Meinel bands

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Fig. 9. Integrated OH Meinel airglow intensities vs. local time. Each curve contains the integrated emissions from all the transitions whose upper level is indicated by v  : v  → v  − 1, v  − 2, . . . , 0. No quenching by atomic oxygen. Top: Sudden death model. Bottom: Collisional cascade model.

airglow, F (v), can be defined as: VT (v) BN POH  = F f (v ∗ ), A(v ∗ , v ∗∗ ) + k CO2 (v ∗ , v ∗∗ ) × [CO2 ] (4)

F (v) =

if quenching by atomic oxygen is neglected. F (v) operates upon f (v ∗ ) and A(v ∗ , v ∗∗ ) + k CO2 (v ∗ , v ∗∗ ) × [CO2 ], with the indexes v ∗ and v ∗∗ running within the intervals v
v ∗
9 and v
v ∗∗
8. Function F (v) takes explicit account of the composition of the atmosphere only through the density of the main quencher, [CO2 ]. The values of F (v) at levels v = 1, 3, 5, 7, and 9, have been plotted versus [CO2 ] in Fig. 11 for the sudden death and collisional cascade models. It is apparent that high quencher densities result in large differences between the collisional cascade and sudden death model. On Earth, the OH Meinel nightglow peaks at about 87 km (McDade, 1997). At that altitude, the equivalent atmospheric density of O2 , taking into account the lower deactivation coefficients of O2 , amounts to less than 1013 cm−3 . As seen in Fig. 11, the two deactivation models differ by less than one order of magnitude at densities of 1013 cm−3 , which is in agreement with past models

Fig. 10. Density of the vibrationally excited states of OH at midnight. No quenching by atomic oxygen. Top: Sudden death model. Bottom: Collisional cascade model.

of terrestrial nightglow (McDade et al., 1987). On Mars the atmospheric density at the location of the peak emission is about 4 × 1014 cm−3 . Dominance of quenching, especially for the higher vibrational levels, causes the large deviation in the output of the two deactivation models in the martian atmosphere. At nighttime, Eq. (1) indicates that the production of vibrationally excited OH may be written in terms of the atomic oxygen density: BN POH = k41 [O][O2 ][CO2 ].

(5)

Because of its direct impact on the volume emission rate from the OH Meinel bands, and also on the emission from the O2 IR atmospheric band, the sensitivity of the atomic oxygen profile to various input conditions is discussed in a later section. Rodrigo et al. (1990a) previously evaluated the OH Meinel emission on Mars and concluded that it would be very weak under the conditions of their model. This is consistent with their very low OH production rates, listed in Table 3. As noted above, the only known attempt to measure OH Meinel nightglow was carried out on the Mars 5 mission, as

Martian airglow models

Fig. 11. Normalized volume emission rate of OH Meinel airglow, F (v), vs. local density of CO2 . No quenching by atomic oxygen. Thick line: Sudden death model. Thin line: Collisional cascade model.

reported by Krasnopolsky and Krys’ko (1976). Nightglow was not detected, and an upper limit of 1015 cm−6 to the product [H][O3 ] at 60 km was set up using the instrument threshold in the (8, 2) band. Approximately, in the sudden death model the volume emission rate from the (8, 2) band is given by: V (8, 2) 

A(8, 2)/AT (8) BN . f (8)POH CO2 1 + kT (8)[CO2 ]/AT (8)

(6)

The numerator of the fractional expression on the righthand side is identical for both models, as we are using the same set of relative transition probabilities of Murphy (1971). However, the ratio kTCO2 (8)/AT (8) in our parameterization (= 6.4 × 10−11 /237.8 cm3 ) is about two orders of magnitude larger than in Krasnopolsky and Krys’ko’s work (= 5 × 10−14 /12.3 cm3 ), which indicates that quenching has been underestimated in this latter work. Therefore, with the more recent deactivation coefficients and transition probabilities, the sudden death upper constraint at 60 km from the limb observation is replaced by [H][O3 ]
2 × 1017 cm−6 . A more stringent upper constraint is obtained if OH deactivation is assumed to proceed by cascading in single-quantum steps. Because of the strong quenching of the upper vibrational levels, in the collisional cascade model almost all the initial population of level v = 9 is quenched down to v = 8. The corresponding expression for the volume emission rate from the (8, 2) band reads as Eq. (2) after replacing f (8) by f (8) + f (9). Then, the collisional cascade upper constraint [H][O3 ]
1017 cm−6 is inferred. As seen in Table 3, all current photochemical models satisfy these two limits.

87

There is an additional factor that compromises the reliability of this estimate. For OH the first and second overtone sequences are more intense than the fundamental, and that the three of them make up most of the total transition probability for any level v 
9. Table 7 compares the total transition probability from level v  = 8, AT (8), and the ratio A(8, 2)/AT (8) given by several authors. The values for AT (8) vary within a factor of 2. However the uncertainty in the (8, 2) band, and in the high overtone sequences in general, is far larger. Most experimental determinations of the EDMF of the OH molecule rely upon measurements that involve internuclear distances close to the equilibrium position, leaving out the weaker transitions in the high overtone sequences. Thus, the disregard of the high overtone sequences in the experimental determination of the EDMF reduces its accuracy at high internuclear distances, and in consequence, the reliability of the calculated transition probabilities in the respective bands. Being aware of the dubious validity of the EDMFs in the range of high internuclear distances, many authors avoid giving the absolute or relative transition probabilities for high overtone sequences. In the present case, see Eq. (6), the uncertainties in AT (8) and in the ratio A(8, 2)/AT (8) (or simply in A(8, 2), as the emission from the upper vibrational levels are strongly quenched and therefore kTCO2 (8)[CO2 ] AT (8)) significantly affect the accuracy of the upper constraints for [H][O3 ] at 60 km. Only if A(8, 2) is shown to have been seriously underestimated, could the unobserved nightglow emission actually constrain the product [H][O3 ] in photochemical models. Vibrational deactivation of OH by atomic oxygen is of first-order importance in the modeling of terrestrial OH Meinel bands nightglow. However, on Mars, the relative abundance of atomic oxygen in the emitting layer, fO
1 × 10−3 , is lower than in the Earth’s atmosphere. Also the quenching rate of the major atmospheric component, CO2 , is faster than that of its counterpart, O2 . As a result, only the lower vibrational levels, v 
2, exhibit a slight difference when the quenching by atomic oxygen is included.

5. O2 IR atmospheric band airglow 5.1. Formulation The O2 IR atmospheric band system originates from the electronic transition a 1 ∆g → X 3 Σg− of molecular oxygen. The dayglow emission of O2 (a 1 ∆g ) at 1.27 µm in the martian atmosphere has been observed a number of times (see

Table 7 Total transition probability for the v  = 8 vibrational level, AT (8) (s−1 ), and relative transition probabilities for the (8, 2) band, A(8, 2)/AT (8), as given by different authors

AT (8) A(8, 2)/AT (8)

Murphy (1971)

Mies (1974)

Turnbull and Lowe (1989)

Langhoff et al. (1986)

– 4.11 × 10−4

259.7 1.15 × 10−4

237.8 9.67 × 10−4

158.7 –

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Novak et al., 2002, and Krasnopolsky, 2003, for recent updates). The measured emission intensities may be compared with predictions of photochemical models and used to estimate daytime ozone abundances. Ozone and hydrogen peroxide are the only chemically active species in the martian lower atmosphere whose column abundances have been measured. To date the nighttime emission from O2 (a 1 ∆g ) has not been observed. The diurnal cycle of production and loss of O2 (a 1 ∆g ) is accounted for by the photochemical scheme:   O3 −→ O2 a 1 ∆g + O 1 D ,  k43 O + O + CO2 −→ O2 a 1 ∆g + CO2 ,  A15 O2 a 1 ∆g −→ O2 + hν (1.27 µm),  k39 O2 a 1 ∆g + CO2 −→ O2 + CO2 . J3

During the sunlit hours, excited O2 (a 1 ∆g ) is chiefly produced in the lower atmosphere by photodissociation of ozone at wavelengths shortward of 3100 Å with a yield of up to 0.9. Longward of the O3 + hν → O2 (a 1 ∆g ) + O(1 D) threshold, O(1 D) is still produced up to 3750 Å accompanied by other states of O2 that we have assumed in the ground state and grouped in reaction R4. The three body reformation of molecular oxygen is exothermic and results in molecular oxygen in various excitation states. Crisp et al. (1996) have estimated the net yield for the production of O2 (a 1 ∆g ) from this mechanism on Venus to be between 0.6 and 0.75. This net yield encompasses the direct production in this state plus the production of higher excitation states which are rapidly quenched down to O2 (a 1 ∆g ). A general view of the production and deactivation of electronically excited O2 from both laboratory studies and atmospheric observations on Earth and Venus is provided by Huestis (2002) and Slanger and Copeland (2003). At night, this reaction is thought to be the only source of O2 (a 1 ∆g ), and the total nightglow emission is proportional to its efficiency in producing excited O2 . Krasnopolsky (2003) considers a net yield of 0.66 to estimate the total nightglow intensity of an earlier model. For comparison purposes, we adopt the same net yield in the present study. Radiative relaxation of O2 (a 1 ∆g ) extends for about 1.24 h (A15 = 2.237 × 10−4 s−1 , Lafferty et al., 1998). In addition, O2 (a 1 ∆g ) may be collisionally deactivated by CO2 . We have adopted as deactivation coefficient in the collisions with CO2 the upper limit for k39 = 2 × 10−20 cm3 s−1 recommended by Sander et al. (2003). O2 is a much more rapid quencher than CO2 , and may contribute about 10% to the total quenching. For simplicity, we have assumed the effect of this additional collisional deactivation mechanism to fall within the uncertainty of the upper limit of k39 for collisions with CO2 . Quenching by any other species may be ignored. Thus, for our nominal atmospheric model quenching is more rapid than emission in the deactivation of O2 (a 1 ∆g ) at altitudes lower than 30 km. However, this does not imply that

the airglow emission can be ignored in this altitude range. The volume emission rate from the O2 IR atmospheric band at 1.27 µm airglow is given by:    VIR at = A15 O2 a 1 ∆g . The density of the excited molecule is evaluated on-line in the time-dependent model.

6. Results and discussion Figure 12 shows the volume emission rates at selected times above and below 40 km. In spite of the strong quenching in this region, it is apparent that the model predicts the greatest contribution to the total daytime emission in the lowest 30 km. Within the quenching dominated region, the daytime column emission rate scales approximately as the ozone mixing ratio, and in consequence, may be readily related to the ratio of scale heights HO3 /H :

J3 VIR at dz  A15 fO3 dz k39

− z (1−HO3 /H ) J3 g  A15 fO3 e HO3 dz, k39 g

where fO3 is the mixing ratio of ozone on the ground. The last of the foregoing expressions allows the identification of two main situations, as the ratio HO3 /H is smaller or larger than one. If HO3 /H < 1, the bulk of the dayglow column emission originates at the ground. Otherwise, if HO3 /H > 1, the volume emission rate increases with altitude in the quenching dominated region, and the largest contribution to the column emission is likely to originate above the ground. Our model results correspond to the first of these

Fig. 12. Volume emission rates from the O2 (a 1 ∆g ) 1.27 µm airglow at selected times. At sunrise, the situation immediately before and 3 minutes after the ascent of the Sun over the line of horizon are noted by <06:00 LT and >06:00 LT, respectively. Similarly, at sunset, the situation immediately before and 3 minutes after the descent of the Sun below the line of horizon are noted by <18:00 LT and >18:00 LT, respectively.

Martian airglow models

89

as a result of the simultaneous emission of the O2 (a 1 ∆g ) generated from the atomic oxygen recombination reaction R43. The ozone concentration in this region is primarily, although not exclusively, dictated by atomic oxygen. Atomic hydrogen, on its course from the upper atmosphere to reform H2 , is also a determining agent in the O2 IR dayglow emission. In this altitude range, the volume emission rate of the O2 (a 1 ∆g ) 1.27 µm dayglow may be approximated by:    VIR at = A15 O2 a 1 ∆g  J3 [O3 ] + k43 [O]2 [CO2 ] (7)

Fig. 13. Column emissions from the O2 (a 1 ∆g ) 1.27 µm airglow (in MR, solid line) and ozone column (in µm-amagat, dashed line) vs. local time. The lower solid line corresponds to k39 = 2 × 10−20 cm3 s−1 (Sander et al., 2003), whereas the upper solid line corresponds to k39 = 10−20 cm3 s−1 (Krasnopolsky and Bjoraker, 2000).

situations. Clancy and Nair (1996) have shown that the profile of ozone in the lowest atmosphere is very sensitive to the seasonal shift of the hygropause, which indicates the difficulty in isolating unequivocally the dayglow emitting layer. Krasnopolsky (2003) gives a retrospective account of observational evidence pointing to HO3 /H being both smaller and larger than one. These considerations are of practical importance in the interpretation of the total ozone columns retrieved from O2 (a 1 ∆g ) dayglow observations. Figure 13 shows the airglow intensity and the ozone column vs. local time. Both integral amounts exhibit a similar trend during the daytime, peaking shortly after noon with a phase-lag of less than one hour between them. The dayglow column emission is composed of a minor contribution, which is readily identified as coming from the O2 reformation reaction, of about 25 kR and a purely daytime component associated with photodissociation of ozone. In the daytime, the total intensity reaches a maximum of about 0.55 MR. This intensity is strongly dependent on the quenching rate for O2 (a 1 ∆g ). As indicated in Table 2, we have employed the upper limit recommended by Sander et al. (2003), k39 = 2 × 10−20 cm3 s−1 , as the rate for our nominal model. However, Krasnopolsky and Bjoraker (2000) have advocated the smaller value k39 = 10−20 cm3 s−1 . Figure 13 shows the emission intensities obtained with either value of k39 . The corresponding peak dayglow intensities roughly differ by a factor of 1.7, as expected since quenching is the major mechanism of O2 (a 1 ∆g ) deactivation in the region at which the bulk emission is generated. The dayglow emission and ozone column drop by a factor of 2–3 from the midday peak to the values at the beginning and end of the sunlit hours. Krasnopolsky (2003), in the only set of diurnal measurements of O2 (a 1 ∆g ) dayglow emission to date, reports a similar daytime drop. High altitude ozone reaches a daytime maximum at about 55 km, Fig. 1, which is reflected in a local peak of the O2 IR dayglow emission, Fig. 12. Actually, the peak in the O2 IR dayglow emission is slightly shifted to higher altitudes

with [O3 ] given by Eq. (2). After sunset, O2 (a 1 ∆g ) is no longer produced from ozone photodissociation. However, the long radiative lifetime of O2 (a 1 ∆g ) causes the daytime emission to extend for about two hours on the dark side. This is particularly true at the higher altitudes, where quenching is ineffectual at deactivating the O2 (a 1 ∆g ) molecule. The luminescent tail can be observed in Fig. 13. When the remnant daytime emission has faded out, only the O2 (a 1 ∆g ) produced from the O + O + CO2 reaction is present. Then, under conditions of chemical equilibrium for the O2 (a 1 ∆g ) molecule, the volume emission rate of the O2 (a 1 ∆g ) 1.27 µm nightglow is given by:    VIR at = A15 O2 a 1 ∆g  k43 [O]2 [CO2 ]. (8) The production rate of the three body reaction peaks at about 60 km and remains fairly constant throughout the day. The top half of Fig. 12 shows the volume emission rate above 40 km at selected times of the day. Our integrated purely nightglow emission amounts to about 25 kR, Fig. 13. This is in reasonable agreement with the intensity of 50 kR estimated by Krasnopolsky (2003) on the basis of his earlier work Krasnopolsky (1995). The seeming simplicity of Eq. (8) for a prospective retrieval of the atomic oxygen density is flawed by the uncertainties in the reaction rate k43 . In order to assess the correctness of the values for use in photochemical models of Mars, the reaction rate of the three body reformation of O2 should be measured in realistic conditions for the martian atmosphere. Likewise, the overall understanding of the excitation mechanism of O2 should be improved.

7. Further discussion As we have seen earlier, the purely nightglow emissions from the OH Meinel bands and the O2 IR atmospheric band are ultimately related to the concentration of atomic oxygen. At night the disturbances to a nominal profile of atomic oxygen are expressed, for the emission from the OH Meinel bands and the O2 IR atmospheric band, in a linear, Eq. (5), and quadratic fashion, Eq. (8), respectively. On the other hand, during the daytime the production of O2 (a 1 ∆g ) from ozone photodissociation and molecular oxygen reformation in the 60 km altitude region are of compara-

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ble significance. Thus, the corresponding volume emission rates are likely to reflect the relative degree of importance of the two principal channels of ozone destruction, i.e. photodissociation and the Bates–Nicolet mechanism. We have tested the sensitivity of the emissions under study to the water content of the atmosphere, the mixing efficiency by eddy diffusion and the transport of hydrogen between the lower and the upper atmosphere. 7.1. Water content The presence of clouds at the peak of the emitting layer, apparently composed of water ice, has been detected repeatedly at equatorial latitudes, which seems to indicate that saturation is likely in that altitude range (Korablev, 2002). We have made an additional run in unsaturated conditions to quantify the effect of the water content on the atomic oxygen profile, and in turn, on the nightglow emissions. With a water column abundance of 0.05 pr-µm, the local density of water vapor near 60 km is 2.5 times smaller than in the standard saturated case. The relative differences in the O concentrations between the unsaturated and saturated cases converged progressively towards high altitudes and fell within 20% above 60 km. This result suggests that, above a certain critical layer, water abundance plays a minor role in constraining the atomic oxygen, and therefore, in the nighttime emissions from the OH Meinel bands and the O2 IR atmospheric band. 7.2. Eddy diffusion At high altitudes, the atomic oxygen abundance is dictated by the number of photons absorbed in the upper atmosphere and the subsequent transport to the emitting layer. Hence, vertical mixing and solar activity are of paramount importance for the OH Meinel and O2 IR 1.27 µm airglow emissions. The capability of GCMs to resolve the larger scales of the flow and possibly gravity wave structures must shed some light on the mechanisms of transport of atomic oxygen to the emitting layer. We have estimated the sensitivity of the profile of atomic oxygen to the mixing induced by the dynamical activity of the atmosphere. For this purpose, we have considered an additional profile for the eddy diffusion coefficient, which coincides with the standard one below 40 km, but grows exponentially up to 108 cm2 s−1 at 80 km. The imposed downward flux of atomic oxygen at 80 km remains equal to −1.05 × 1011 cm−2 s−1 . The resulting atomic oxygen profiles are represented in Fig. 14 (top, curves labeled AN74 Kstd and AN74 Khigh), which shows the decrease in the peak concentration of atomic oxygen in the high eddy diffusion coefficient case. The increased mixing prevents the atomic oxygen from building up in the diffusion dominated region and shifts the peak in the atomic oxygen profile towards lower altitudes. The peak atomic oxygen density drops by a factor of 2.

Fig. 14. Top: Concentration of atomic oxygen in the emitting layer for different profiles of the eddy diffusion coefficient K and diffusion fluxes of H and H2 at the top of the domain. AN74 Kstd: Standard K and H and H2 diffusion fluxes from Anderson (1974). AN74 Khigh: High K and H and H2 diffusion fluxes from Anderson (1974). KR02 Kstd: Standard K and H and H2 diffusion fluxes from Krasnopolsky (2002). Bottom: Volume emission rates from the O2 (a 1 ∆g ) 1.27 µm airglow at noon and midnight for H and H2 diffusion fluxes from Anderson (1974) (AN74) and Krasnopolsky (2002) (KR02). Standard K in both cases.

For both emissions, the immediate consequence of the decrease in the peak atomic oxygen concentration is the reduction in the corresponding volume emission rates. This effect is larger for the O2 (a 1 ∆g ) IR emission rate because of its quadratic dependence on the atomic oxygen concentration. Additionally, in the specific case of the OH Meinel bands, the shift of the profile to lower altitudes reinforces the effect of collisional deactivation, so that there is less of a difference between the sudden death and collisional cascade deactivation pathways. 7.3. Hydrogen flux The hydrogen fluxes from the lower atmosphere were determined by Anderson (1974) in his analysis of the Lyman α airglow data retrieved on the Mariner 6, 7, and 9 missions. More recently, Krasnopolsky (2002) has analyzed the implications of varying solar activity on the net exospheric hydrogen escape and inferred the H and H2 fluxes at 80 km for conditions of medium solar activity appropriate to his H2 observations with the Far Ultraviolet Spectroscopic Explorer (Krasnopolsky and Feldman, 2001). The two sets provide comparable net escape fluxes of hydrogen. However, the allocation of the net H flux into atomic and molecular hydrogen differs greatly between them. Together, both sets span a wide range of conditions for the hydrogen transport between the lower and the upper atmosphere. The implementation of one set or another does not introduce significant differences in our modeled atomic oxygen profile, and hence, in the nighttime emissions, as shown in Fig. 14. It does, however, affect the H–O3 partitioning, and therefore the daytime

Martian airglow models

emission from the O2 IR atmospheric band in the 60 km region to a somewhat larger extent, as can be seen in Fig. 14 (bottom, curve labeled KR02).

8. Conclusions We have studied the composition of the atmosphere of Mars between 0 and 80 km. The results of our timedependent photochemical model reveal the existence of diurnal cycles in the concentration of some short-lived species. Typically, these cycles are more intense in the lowest atmosphere, where collisions with other species are more frequent. At night O, OH, and H are strongly depleted below 50 km, but replenished again after sunrise by the products of the photodissociation of CO2 , H2 O, H2 O2 , and O2 . Higher up, O and H remain nearly unchanged throughout the day. Solar activity and eddy diffusion, as they control the column productions of O and H from photodissociation and ion– molecule processes in the thermosphere and the subsequent transport to the lower atmosphere, are key factors in the actual budgets of Ox and HOx in the 50–80 km region. Ozone can be observed from the Earth, what renders it an optimal tracer of the photochemistry of the martian atmosphere. Our model yields a diurnal variation of O3 of different sign below and above 40 km. In the lower region, O3 follows the fate of O and is slightly depleted at night respect to its daytime levels. Above 40 km, where the reformation of ozone from atomic oxygen is fairly constant all day long, the nighttime ozone concentration is determined by the Bates–Nicolet mechanism of H and O3 . Photodissociation leads to a drop in its daytime concentration. The nocturnal rise in ozone above 40 km is accompanied by a higher production rate of vibrationally excited OH. The radiative emissions from the vibrationally excited levels of OH that constitute the OH Meinel bands have been evaluated for one entire sol. All the vibrational levels of excited OH are rapidly quenched by CO2 . The overwhelming dominance of quenching over radiative cascading results in large differences in the column emissions between the sudden death and collisional cascade models. The peak column intensities for transitions from fixed upper vibrational levels amount to about 300 and 15,000 R for each model, respectively. They occur shortly after sunset from transitions v  = 9 → v 
8 in the sudden death limit and v  = 1 → v  = 0 in the collisional cascade limit. For the calculated concentrations of atomic oxygen in the emitting layer, quenching of vibrationally excited OH by atomic oxygen is of minor importance. We have also reviewed the upper limit for [H][O3 ] inferred from the results of the Mars 5 mission. Based on more recent values of AT (8) and kTCO2 (8), our study indicates that the (8, 2) Meinel band is more strongly quenched than estimated by Krasnopolsky and Krys’ko (1976). We suggest the upper constraints [H][O3 ]
2 × 1017 cm−6 and [H][O3 ]
1017 cm−6 in the sudden death and collisional cascade lim-

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its respectively. The accuracy of these constraints depends on the reliability of the relative transition probability of the overtone (8, 2) band. The sources of excited molecular oxygen in the O2 (a 1 ∆g ) 1.27 µm dayglow and nightglow emissions are easily distinguishable. In the daytime, most O2 (a 1 ∆g ) is produced from the photodissociation of ozone below 30 km. Our results indicate that the bulk of the column intensity is emitted near the ground. At night, O2 (a 1 ∆g ) is produced from the three body reformation of molecular oxygen. Some aspects of this latter mechanism remain uncertain, in particular, the yields for the various states of excited O2 and the possible collisional cascading of these states into O2 (a 1 ∆g ). With the estimated net yield adopted for the calculations, our model provides a midnight column emission of about 25 kR. O2 (a 1 ∆g ) has a long radiative lifetime, and a luminescent tail of O2 (a 1 ∆g ) formed from ozone photodissociation can be observed for about two hours after sunset, especially at the higher altitudes where quenching by CO2 is ineffective. The emitting layer of the nightglow from the OH Meinel bands and O2 (a 1 ∆g ) 1.27 µm band lies at about 50–80 km. The nocturnal emission rates from these systems largely depend upon the local concentration of atomic oxygen. The profile of O in this region is efficiently controlled by the transport of O from the upper atmosphere, and ultimately by the incoming solar flux. The variability in the water content and flux of atomic hydrogen from the upper atmosphere are revealed as factors of minor importance in the profiling of high altitude atomic oxygen. However, these factors may change significantly the H–O3 partitioning in the same region. We intend to explore the dynamical interaction between the lower and the upper atmosphere in the future. The ongoing development of a GCM with online photochemistry may provide an insight into the features of the large scale winds and gravity waves in the emitting layer. Airglow modeling introduces its own specific mechanisms of excitation, deactivation and radiative emission. The poor knowledge of some of these mechanisms may compromise the accuracy of model results. We have listed in Table 8 the parameters relevant to the modeling of airglow from the OH Meinel bands and the O2 IR atmospheric band. The review and update of them to conditions of composition and temperature appropriate to the martian atmosphere is a peremptory task to ensure the reliability of prospective airglow models.

Acknowledgments The authors acknowledge the Natural Sciences and Engineering Research Council for ongoing support. We also want to thank Vladimir Krasnopolsky for his clarification of the Mars 5 results.

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Table 8 Excitation, deactivation and radiative emission parameters relevant to airglow modeling of the OH Meinel bands and the O2 IR atmospheric band in the martian atmosphere OH Meinel

O2 (a 1 ∆g )

k25 k41 f (v) k CO2 (v  , v  ) A(v  , v  )

k42 η k39 A15

η is the net yield of production of O2 (a 1 ∆g ) in atomic oxygen recombination events, k43 = η(k42 + k43 ).

Appendix A Absorption cross sections and branching ratios have been averaged in the intervals where the actinic fluxes are provided, except for Lyman α, in which case the values at 1215.67 Å are used instead. Temperature dependence is implemented where given. CO2 is the major opacity source in the martian atmosphere. Tabulated values of its photoabsorption cross sections are found in Chan et al. (1993): 61–1172 Å (203– 10.58 eV); Lewis and Carver (1983): 1213.5–1926.5 Å; and Shemansky (1972): 1927.5–2050 Å. Values at 1126 Å (11 eV) and 1032.5 Å (12 eV) taken from Hitchcock et al. (1980), and in close agreement with Chan et al. (1993), have been added as well. As proposed by Chan et al. (1993), the fit to their results between 90 and 203 eV has been extended above this latter energy, up to values of 250 eV (50 Å). Longward of 2050 Å Rayleigh scattering dominates the extinction spectrum of CO2 . The values of Shemansky (1972) above this wavelength have not been included. The temperature dependence has been parameterized as indicated in Anbar et al. (1993) above 202 K in the range 1213.5– 1926.5 Å. Below 202 K the cross sections at 202 K are used. CO2 photoionization and photodissociation quantum yields have been obtained from Hitchcock et al. (1980), Berkowitz (2002), Slanger and Black (1978), Okabe (1978), Lawrence (1972a, 1972b), and Stolow and Lee (1993). O2 photoabsorption cross sections have been taken from Kirby et al. (1979): 34–1029 Å; Watanabe (1958): 1029– 1051 Å; Kley (1984): Lyman α; Ogawa and Ogawa (1975): 1087–1750 Å; Ackerman (1971): 1600–1750 Å; Yoshino et al. (1988): 2060–2400 Å. The Schumann–Runge bands (1754–2058 Å) have been parameterized following Murtagh (1988). O2 photoionization and photodissociation quantum yields have been obtained from Kirby et al. (1979), Lee et al. (1977), Lawrence and McEwan (1973), and Okabe (1978). H2 O photoabsorption cross sections have been taken from Haddad and Samson (1986): 100–984 Å; Dutuit et al. (1985): 990–1251 Å; Kley (1984): Lyman α; Yoshino et al. (1996): 1259–1751 Å; Sander et al. (2003): 1755–1893 Å; and Cantrell et al. (1997): 1900–1930 Å. H2 O photoionization and photodissociation quantum yields have been ob-

tained from Haddad and Samson (1986), Stief et al. (1975), Mordaunt et al. (1994), and Okabe (1978). Values for the O3 photoabsorption cross sections have been taken from Ogawa and Cook (1958): 526–1305 Å; Ackerman (1971): 1310–1780 Å; Sander et al. (2003): 1794–2286; Burrows et al. (1999): 2300–7940 Å; Voigt et al. (2001): 7940–8500 Å. O3 photoionization and photodissociation quantum yields have been obtained from Taherian and Slanger (1985), Turnipseed et al. (1991), Hancock and Tyley (2001), Bauer et al. (2000), Wine and Ravishankara (1982), Brock and Watson (1980), Fairchild et al. (1978), and Okabe (1978). H2 O2 cross sections have been taken from Schürgers and Welge (1968): 1250–1900 Å and Sander et al. (2003): 1900– 3500 K. H2 O2 photoionization and photodissociation quantum yields have been obtained from Atkinson et al. (1997), Stief and DeCarlo (1969), Sander et al. (2003), and Lee (1982). HO2 absorption cross sections, between 1900 and 2600 Å, have been taken from Sander et al. (2003). Most bimolecular and termolecular reaction rates are taken from the JPL review, Sander et al. (2003). Rate coefficients of third order reactions have been modified as suggested in Lindner (1988), to take account of their enhanced efficiency with CO2 as third body. k36 has been calculated to fit with an Arrhenius law the values k36 (200 K) = 2.3 × 10−37 cm6 s−1 and k40 (296 K) = 6.2 × 10−36 cm6 s−1 provided in Slanger et al. (1972). k46 was measured in a H2 bath, as reported by Baulch et al. (1992). Lacking additional information on the applicable correction, its value has not been amended.

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