Key reactions in the photochemistry of hydrocarbons in Neptune's stratosphere

Planetary and Space Science 58 (2010) 1555–1566

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Key reactions in the photochemistry of hydrocarbons in Neptune’s stratosphere M. Dobrijevic a,b,, T. Cavalie´ c, E. He´brard a,b, F. Billebaud a,b, F. Hersant a,b, F. Selsis a,b a

Universite´ de Bordeaux, Laboratoire d’Astrophysique de Bordeaux CNRS/INSU, UMR 5804, BP 89, F - 33271 Floirac CEDEX c Max-Planck-Institut f¨ ur Sonnensystemforschung, 37191 Katlenburg-Lindau, Germany b

a r t i c l e in fo

abstract

Article history: Received 22 March 2010 Received in revised form 20 July 2010 Accepted 24 July 2010 Available online 13 August 2010

We studied the propagation of uncertainties carried by the reaction rate coefficients in the photochemistry of Neptune’s stratosphere. We showed that the uncertainties on the mole fractions of main hydrocarbons are equal to or larger than the estimated uncertainties on abundances gathered from observations. From a global sensitivity analysis study, we determined a list of 26 key reactions and discussed the 7 main key reactions that should be studied in priority to lower the uncertainties in the mole fractions computed from a photochemical model. This methodology is essential to improve the predictivity of photochemical models and, consequently, to better understand the physical and chemical processes that govern the composition of giant planet atmospheres. & 2010 Published by Elsevier Ltd.

Keywords: Neptune Photochemistry Hydrocarbons Uncertainty propagation Sensitivity analysis Key reactions

Recent detections of methylacetylene (CH3C2H) and diacetylene (C4H2) in the atmosphere of Neptune made by Spitzer provide new constraints on the abundances of hydrocarbons in this planet (Meadows et al., 2008). This confirms for instance that organic photochemistry is less active in Neptune’s atmosphere than in Jupiter’s and Saturn’s (Moses et al., 2005). Photochemical models are expected to be a powerful tool to understand the origin and the evolution of these compounds and to help us to constrain some physical processes (like vertical transport, escape, influx from interplanetary environment, etc.), which are not well constrained in these atmospheres. It seems legitimate, therefore, to re-investigate the photochemistry of hydrocarbons in the atmosphere of Neptune with regard to these new detections. However, He´brard et al. (2006) showed that the kinetic data of hydrocarbons at low temperature (below 200 K) are very uncertain. In particular, they showed that few rate constants have been measured in experiments or inferred from theoretical works. Among those that are known, very few have been measured at conditions (temperature, bath gas, pressure) representative of outer planet atmospheres. As a consequence,

most of the rates used in models are estimated or extrapolated from measurements made at 300 K. He´brard et al. (2007) studied the effect of the photochemical kinetic uncertainties in modeling Titan’s atmosphere. Their uncertainty propagation studies showed that the uncertainties on most of the computed abundances are much larger than the estimated uncertainties on abundances gathered from observations. Dobrijevic et al. (2008), using 0D and 1D models, showed that uncertainties in some rate constants are the source of an epistemic bimodality1 in the abundances of some compounds in the high atmosphere of Titan. As a consequence, the understanding of the physical and chemical processes occurring in the outer planet atmospheres is currently limited by our poor knowledge of the kinetics of hydrocarbons at low temperature. Thus, it is of prime importance to better quantify the chemical uncertainties and the model output uncertainties in order to improve photochemical model predictions. Recently, He´brard et al. (2009) have presented a methodology to improve photochemical models. In particular, they identified some key reactions for which a measurement of the rate constant at low temperature would significantly improve the predictivity of their photochemical model of Titan’s atmosphere and they gave

 Corresponding author at: Universite´ de Bordeaux, Laboratoire d’Astrophysique de Bordeaux. Tel.: + 33 5 5777 6124; fax: + 33 5 5777 6110. E-mail address: [email protected] (M. Dobrijevic).

1 Epistemic uncertainty is an uncertainty that is due to a lack of knowledge of the reaction rates. This can lead to a bimodal distribution in the abundance of some compounds with two different modes in their probability density function.

1. Introduction

0032-0633/$ - see front matter & 2010 Published by Elsevier Ltd. doi:10.1016/j.pss.2010.07.024

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a method to quantify this improvement. The present study puts this methodology into practice for the photochemistry of hydrocarbons in the atmosphere of Neptune. In particular, the emphasis is done on the abundance of hydrocarbons that have been detected in the atmosphere so far. This work is principally aimed at astrochemists (experimenters and theoreticians) interested in the study of planetary atmospheres. Our objective is to give a list of key reactions that should be studied in priority in order to lower the uncertainty factors of their rate constants. We also show, quantitatively, how these new measurements can decrease the uncertainties in the model output and will consequently improve the predictivity of the photochemical models of hydrocarbons in Neptune’s atmosphere. In Section 2, the photochemical model is presented. Section 3 summarizes our methodology to study the propagation of uncertainties in the model and to determine the key reactions. Results are given in Section 4. Uncertainties in the model output are presented and a list of key reactions is established. An example of how new rate constants measurements can improve Neptune’s photochemical models is given in Section 5.

levels (z and z þ Dz) are separated by a distance smaller than H(z)/5, where H(z) is the atmospheric scale height at altitude z. We summarize hereafter the boundary conditions of the model. At the lower boundary, we set the mole fraction of He, CH4 and H2 respectively to yHe ¼ 0.19, yCH4 ¼ 5:0  104 and yH2 ¼ 1yHe yCH4 . All other compounds have a flux given by the maximum diffusion velocity v ¼  K/H where K is the eddy diffusion coefficient and H the atmospheric scale height at the lower boundary. At the upper boundary, zero fluxes are assumed for all the species except for atomic hydrogen, which is produced by photochemical processes at higher altitudes in the thermosphere. We assume a fixed downward flux for atomic hydrogen at the upper boundary equal to FH ¼ 4:0  107 cm2 s1 (Romani and Atreya, 1989). The photochemical model results are not particularly sensitive to this value (Moses et al., 2005). The eddy diffusion coefficient K(z) (in cm2 s  1) is given by the following equation: !0:5 103 3 KðzÞ ¼ 1:5  10  ð1Þ pðzÞ

2. Photochemical model

where p(z) is the pressure (in mbar) at altitude z. This coefficient, together with the methane mole fraction at the lower boundary, gives a satisfactory profile of methane in comparison with Voyager data (see Fig. 2).

2.1. Atmospheric model

2.2. Choice of numerical solver

Our photochemical 1D model uses a constant background atmosphere with constant boundary conditions. The temperature and density (cm  3) profiles synthesized by combining various observations are presented in Fig. 1. We use a non-uniform altitude grid with 86 levels from 38 km (pressure level P  100 mbar) to 1280 km ðP  1:13  107 mbarÞ. The altitude reference (z¼ 0 km) correspond to P¼ 1 bar. Two consecutive

The present model is globally similar to the model used in He´brard et al. (2007, 2009). The main difference lies in the numerical solver we used to solve the set of continuity equations. In the previous model of He´brard et al. (2007), we used a Crank-Nicholson method. We now use the ODEPACK library, which implements Hindmarsh’s solvers for ordinary differential equations (Hindmarsh, 1983). Atmospheric chemical rate systems are known to be very stiff with wide ranges

Fig. 1. Temperature (solid line) and total number density (cm  3; dashed line) profiles of Neptune’s atmosphere adopted in the present photochemical model, as a function of pressure p. This atmospheric structure is inferred from various sources: recent AKARI data (Fletcher et al., 2010) for 10  4 mbar o p o 104 mbar, Yelle et al. (1993) for p o 104 mbar, and an extrapolation from the adiabatic profile for p 4 104 mbar.

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Fig. 2. Abundance profiles of CH4 obtained after 1000 runs. Observation data: Yelle et al. (1993) (square), Orton et al. (1992) (cross), Be´zard et al. (1999) (triangle) and Fletcher et al. (2010) (diamond).

of characteristic timescales. The LSODE (Livermore Solver for Ordinary Differential Equations) routine in the ODEPACK package produces highly accurate solutions of systems of stiff ODE using backward difference multistep formulas. LSODES (where the last S stands for Sparse) exploits the sparsity of the associated Jacobian matrix to obtain an extensive reduction in CPU time, compared to LSODE, without any loss in accuracy. For instance, Saylor and Ford (1995) showed that LSODES provides accurate solutions to photochemical problems with less computational effort. Nejad (2005) made a comparative study of stiff ODE solvers for astrochemical kinetic problems and concluded also on the superior performance of LSODES for solving astrochemical kinetic systems. LSODES uses a mixed error control tolerance algorithm, which is a function of both relative and absolute tolerances. These tolerances define the allowed error per step and hence specify the accuracy requirement. Comparison of LSODES and our previous Crank-Nicholson method gives very similar results within the relative tolerance used (typically 10  3). The main advantage we found concerns the computational time. With the Crank-Nicholson method, we have to limit the time-step in order to prevent numerical instabilities. With LSODES, the time step in our code increases continuously allowing to reach long integration time (greater than 1011 s if necessary, while it rarely exceeds 1010 s with a Crank-Nicholson method). This is particularly interesting regarding our Monte-Carlo procedure to study the propagation of uncertainties. Indeed, the modification of rate constants at each run can alter significantly the chemistry and long integration times may be necessary to reach a steady state. In the model of He´brard et al. (2007), the integration time was limited to 109 s to obtain reasonable computation times, which did not guarantee them to reach a steady state. In the present model, the integration time is limited to 1011 s (more than 3000 years of simulated time of evolution), which is more than 1 order of magnitude greater than the time needed to reach the steady state in the nominal model. LSODES also allows us to implement condensation without any numerical instability. Such instabilities are present in numerous photochemical models. For instance, Summers and Strobel (1989) introduced a parameterization of the loss rate of condensing species in the atmosphere of Uranus and showed that numerical

difficulties arose in their iterative procedure when they tried to lower the supersaturation of the condensing gas. In the present model, we do not assume any supersaturation since there is no observational, nor theoretical evidence that such a process occurs for hydrocarbons in the atmosphere of Neptune. So we assume that species condense as soon as their abundances reach the saturation value. This limits the numbers of additional parameters accounting for this process. Thus, the continuity equation of a given compound, at a given altitude, is not solved as soon as its mole fraction exceeds its saturation profile. This means that we then set fi(z)¼0 in the continuity equation @yi ðzÞ=@t ¼ fi ðzÞ, where yi(z) is the mole fraction at altitude z. This forces the mole fraction profile to perfectly follow the saturation profile.

2.3. Chemical model The overall precision of photochemical models is highly sensitive to the uncertainties in the rates used in the chemical scheme. Previous uncertainty propagation studies dedicated to Neptune (Dobrijevic and Parisot, 1998) and Saturn (Dobrijevic et al., 2003) were made with estimated uncertainty factors of reaction rates (Fk) and photodissociation rates (FJ) since no critical review of the literature were available at this time. Basically, these authors used Fk ¼2 for all reactions (usually the best educated guess) and FJ ¼ 1.5 for photodissociation processes. In the present study these factors are determined from an up-to-date review of the hydrocarbon chemistry at low temperature described in He´brard et al. (2006, 2009) for Titan’s atmosphere. The chemical scheme and associated rate constants are extracted from these two papers. The chemical scheme includes 75 compounds (hydrocarbons plus H, H2 and He), 381 reactions and 50 photodissociation processes. The list of reactions can be provided upon request and will soon be included in the KIDA database (http://kida.obs.u-bordeaux1.fr/). The photodissociation rates are computed for average conditions (at equator and equinox) and account for both solar irradiance and the Ly-a sky glow from the local interstellar medium. Their uncertainty factors are set to FJ ¼ 1.5 (see Dobrijevic and Parisot, 1998). Nitrogen and oxygen compounds are not included in the present study, because they have little

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influence on the abundance of hydrocarbons. The influx (and/or ˜ s atmosphere is actually production) of nitrogen atoms in NeptuneO very low, since the most abundant nitrogen compound is HCN with a mole fraction around 10  9 above its saturation level (Marten et al., 2005). The influence of water influx on the photochemistry of hydrocarbons in giant planets is low as long as the influx of water is low (Moses et al., 2000), which is the case in Neptune’s atmosphere (Moses et al., 2005).

3. Uncertainty propagation and sensitivity analysis The methodology used to improve photochemical models has been described in He´brard et al. (2009) and will not be presented in details here. It can be summarized as follows:

Step 1 Global Uncertainty Propagation study (using Monte-Carlo approach in the present case) to compute model uncertainty output (abundances). Step 2 Global Sensitivity Analysis to determine the key reactions of the chemical scheme. Step 3 Laboratory measurements (or theoretical calculation) of the key reaction rate constants in conditions relevant to planetary atmospheres. Step 4 Go back to step 1 until the model reaches a precision (global or specific to a given compound) in agreement with the scientific objective (for instance, a constraint on a physical parameter). The improvement of model precision is then an iterative process between modelers and experimentalists (and theoreticians).

Fig. 3. Top: abundance profiles of C2H4 obtained after 1000 runs. Bottom: distribution of C2H4 profiles corresponding to 68% (dark grey), 95% (medium grey) and 100% (light grey) of the total range of profiles calculated at a given pressure level. Observation data: Yelle et al. (1993) (square); Schulz et al. (1999) (triangle); Fletcher et al. (2010) (cross).

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At the end of each cycle (sequence of steps 1 to 4), the precision of the model is improved for selected compounds. In the present paper, steps 1 and 2 are presented and a list of key reactions is given to encourage step 3. Several hydrocarbons have been detected so far in the atmosphere of Neptune: CH3, CH4, C2H2, C2H4, C2H6, CH3C2H, C4H2 and C6H6 (Mahmud et al., 2008). The goal of the present paper is to quantify the uncertainty in the abundances that are computed for these compounds by a 1D photochemical model and determine the key reactions that could lower significantly these uncertainties, if new laboratory measurements (or theoretical studies) were performed. Hereafter, the nominal results correspond to mole fraction profiles obtained with the nominal values of the rate constants.

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4. Results 4.1. Uncertainty propagation The method presented in He´brard et al. (2007) is used to study the uncertainty propagation in the 1D photochemical model. In order to have statistically significant results, we generated randomly 1000 runs using, as an initial condition, the steady state composition obtained with the set of nominal constant rates. The basic way to present the results of the uncertainty propagation study is to plot all the profiles generated this way. Fig. 3 (top) shows the set of C2H4 mole fraction profiles. However, the overlap of the profiles doesn’t show where the majority of the profiles are concentrated. From this figure, we have generated

Fig. 4. Densities of the profiles of CH3, C2H2 and C2H6 obtained after 1000 runs. Observation data: Yelle et al. (1993) (square) for C2H2 and C2H6; Be´zard et al. (1999) (triangle) for CH3; Orton et al. (1992) (cross) and Be´zard et al. (1991) (plus) for C2H2 and C2H6; Kostiuk et al. (1992) (diamond) and Fletcher et al. (2010) (cross) for C2H6.

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Fig. 4. (Continued)

another figure with the density of profiles (Fig. 3, bottom). At a given pressure level, the dark grey area holds 68% of the profiles (1s if the distribution of mole fractions is log-normal), dark grey and intermediate gray holds together 95% of the profiles ð2sÞ and the whole shaded area encompasses 100% of the profiles. All the densities of profiles generated this way are presented in Figs. 3–5 for the 7 compounds considered here (except CH4 for which uncertainties in its mole fraction are low). The dispersion of profiles is quite important even for C2-compounds, especially between 1 mbar and 10  2 mbar. For higher hydrocarbons, the various profiles span over several orders of magnitude. However, the mole fraction of CH4 has a very low uncertainty factor and can be used to constrain the eddy diffusion coefficient around the homopause and the abundance of CH4 at the lower boundary. This latter result differs strongly from what happens in the atmosphere of Titan, where the propagation of uncertainties in the model do not allow to put any precise constraints on the eddy diffusion coefficient (He´brard et al., 2007). Indeed, in the case of Titan, CH4 is lighter than N2 (the background atmosphere) and its mole fraction increases with altitude by molecular diffusion above the homopause. Uncertainties in the photochemistry of methane lead to profiles that span over a wide range. In the case of Neptune, molecular diffusion in H2 confines the profiles of methane in a narrow range. This shows the influence of diffusion in the propagation of uncertainties in photochemical models (see also Carrasco et al., 2007). Assuming that the distribution of profiles at a given altitude is roughly a log-normal distribution, we can write that: logðyi Þ ¼ logðyi Þ 7 logðFyi Þ

ð2Þ

where Fyi is the uncertainty factor of the mole fraction of compound i and logðFyi Þ is the 1s uncertainty attached to log(yi). Uncertainty factors attached to the abundance distribution are given in Table 1 for the 8 compounds we have considered in this study. Another way to present the results is to give the C2H6/C2H2, C2H6/C2H4 and C2H2/C2H4 ratios. These ratios are used by Moses et al. (2005) to test their photochemical model since observations show that these ratios are different in the four giant planets. Many

parameters (like temperature, eddy diffusion and photolysis rates due to the change in distance from the Sun) might be responsible for these different values. Assuming that there are no uncertainties in the chemical scheme, Moses et al. (2005) stated that their chemical reaction scheme did not reproduce the relative abundances of these compounds. We see in Fig. 6 that model uncertainties can potentially impact there ratios significantly (for Neptune and surely for the other giant planets). For comparison, recent results of Fletcher et al. (2010) showed that the logarithm of these three ratios at 0.2 mbar are equal respectively to 1.30, 2.83 and 1.48. They are in very good agreement with our model, taking uncertainties of the model and observations into account.

4.2. Sensitivity analysis The method to determine the key reactions is described in He´brard et al. (2009) and in Dobrijevic et al. (2010). It is based on the calculation of Rank Correlation Coefficients (RCC) between a given compound and the set of reactions. A key reaction is a reaction that has a strong influence on the uncertainty of the model outputs. Table 2 presents the reactions for which the RCC have the greatest absolute values, for the 8 compounds considered here. Key reactions for a given compound correspond to reactions with absolute values of RCC greater than 0.2 at a given altitude. This choice is arbitrary but it allows one to select a short list of key reactions. Compounds in italic highlight the main key reactions (defined as having absolute values of RCC greater than 0.5) at each pressure level. Key reactions For some compounds like C2H2, all the key reactions contribute to almost the same degree. With the exceptions of photodissociations, results suggest that only 7 reactions should be measured with priority among the 26 key reactions (reactions R51, R81, R135, R360, R362, R364, R387, see Table 2). He´brard et al. (2009) published a list of key reactions in the photochemical modeling of Titan’s atmosphere. Some key reactions which they found are also pointed out in the present study, like reactions R51, R53, R362 and R387, and

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photodissociation of CH4 via R2 and R4. Reactions with propadienylidene radicals (C3H2), which play a key role in Titan, are not pointed out here. Most of the key reactions for Neptune involve atomic hydrogen or molecular hydrogen as a reactant. One noticeable result of our sensitivity analysis is that few photodissociation processes appear as major key reactions for many compounds, in contrast with what had been previously found for Titan. Assuming that our estimation of their uncertainty factor is not too much underestimated, this means that most of the uncertainties in the model outputs are controlled by neutral reactions. Our results especially highlight, from the original point of view of uncertainty propagation, the obvious role played by the primary radicals produced from molecular hydrogen H2 and methane CH4 photodissociations (atomic hydrogen H, methyl

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CH3, excited methylene 1CH2, and methylidene CH radicals) in the formation of lighter hydrocarbons in Neptune’s atmosphere. Future photochemical models of Neptune’s atmosphere would thus greatly benefit from a much closer investigation of the rate constants attached to the key reactions identified here, as it would help to improve significantly their predictivity. A short review of the main key reactions is given in the following paragraphs. R51: Hþ CH-Cþ H2 . Amongst the set of thermal reactions identified, the H + CH reaction has a strong influence at high altitude. This reaction was already identified in recent works concerning the bimodality in the density profiles of some species in the atmosphere of Titan (Dobrijevic et al., 2008) and the lack of low-T measurements on model predictivity (He´brard et al., 2009). In Neptune’s stratosphere, this reaction has a strong influence on

Fig. 5. Densities of the profiles of CH3C2H, C4H2 and C6H6 obtained after 1000 runs. Observation data: Meadows et al. (2008) for CH3C2H and C4H2.

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Fig. 5. (Continued)

Table 1 Uncertainty factors Fyi of mole fractions for the 8 compounds detected so far in the atmosphere of Neptune. Pressure (mbar)

10

1

10  1

10  2

10  3

10  4

Altitude (km) CH3 CH4 C2H2 C2H4 C2H6 CH3C2H C4H2 C6H6

76 3.41 1.00 1.28 1.97 1.39 3.03 1.00 32.21

144 2.09 1.00 2.77 4.60 1.43 25.5 10.02 33.11

243 2.12 1.00 5.30 5.58 1.42 35.39 17.46 36.19

349 2.12 1.01 2.15 4.63 1.41 7.06 6.60 20.97

460 1.27 1.06 1.62 1.79 1.33 4.02 7.25 14.26

600 1.18 1.08 1.95 2.05 1.31 5.38 27.98 5  105

Altitude reference (0 km) corresponds to a pressure of 1 bar.

the uncertainties on CH3C2H, C4H2 and C6H6. In their evaluated kinetic data for combustion modeling, Baulch et al. (2005) adopted high temperature measurements with substantial error limits as their preferred values over the range of 1500–2500 K. Taking into account the still-existing discrepancy between experimental and theoretical rate constants at room temperature, He´brard et al. (2006) recommended the use of the room temperature theoretical rate constant (Harding et al., 1993) with higher uncertainty factors when considering the use of this reaction in a temperature range relevant to outer planet atmospheres. R81: CH þ H2 -3 CH2 þ H. This reaction has a strong influence on the uncertainty on C4H2. The importance of the three-body combination counterpart of the CH + H2 reaction at low temperatures and low pressures gives rise to a complex temperature and pressure dependence of the overall rate constant which is difficult to investigate experimentally (Baulch et al., 2005). As a result, there is still no direct measurement of the rate constant nor of the product channels of the CH + H2 reaction. Information on any temperature dependance at conditions representative of Neptune’s atmosphere is thus very limited even

if quite recent studies covering a wide range of temperature (53–800 K) and pressure (1–160 bar) have done much to clarify the relative importance of the two reaction channels (Fulle and Hippler, 1997; Brownsword et al., 1997). R135: 3 CH2 þH2 -CH3 þ H. Like R81, this reaction has a strong influence on the uncertainty on C4H2. In their chemical kinetic database for combustion chemistry, Tsang and Hampson (1986) recommended for the 3 CH2 þ H2 reaction rate an upper limit already given in Laufer (1981) review and based on two different experimental upper limits previously reported at room temperature, with substantial uncertainties (Braun et al., 1970; Pilling and Robertson, 1977). R387: CH3 þ CH3 þ M-C2 H6 þM. Uncertainty on CH3 is strongly influenced by this reaction. Concerning this three-body recombination reaction, a lot of both experimental and theoretical studies have been published in order to investigate its rate constant (see Klippenstein et al., 2006 for a quite exhaustive review). R360: Hþ CH3 þ M-CH4 þ M; R362: H þ C2 H2 þ M-C2 H3 þM; R364: Hþ C2 H4 þM-C2 H5 þ M. Uncertainties on CH3, C2H4, C2H6 and CH3C2H are strongly influenced by these reactions. As in the case of the other three-body recombination reactions pinpointed here, very few of these studies have been performed in conditions appropriate to the study of planetary atmospheres and most of the rate expressions available in the literature still have to be extrapolated to the bath gases and down to the lowest temperatures encountered in outer planet atmospheres. This still-existing scarcity results from both laboratory limitations a nd a wide competiting interest for their studies in conditions more appropriate to hydrocarbon combustion chemistry (Baulch et al., 2005).

5. Discussion 5.1. Comparison with observations As a matter of fact, the aim of the present work is not to make an exhaustive comparative study of the model output with

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Fig. 6. Histograms for the logarithm of C2H6/C2H2, C2H6/C2H4 and C2H2/C2H4 ratios at a pressure level of 0.1 mbar. Histograms quoted as ‘‘before’’ correspond to the results obtained in Figs. 3 and 4. Histograms quoted as ‘‘after’’ correspond to the results obtained after reducing the uncertainties of some key reaction rates (see Section 5). For comparison, ratios from the photochemical model of Moses et al. (2005) (black dashed line) and from AKARI observations of Fletcher et al. (2010) (black solid line and grey rectangle for uncertainty) are also given. We have estimated the uncertainty on AKARI ratios from the uncertainties on the mole fractions of ethane and ethylene at 0.3 mbar and 2.8  10  3 mbar respectively.

available observations. New abundance determinations of hydrocarbons are expected from Spitzer and Herschel that will measure precisely the stratospheric CH4 abundance (Hartogh et al., 2009), which will thus give a better opportunity to do this work. The main point here is to make sure that our model is fairly consistent with observations in order to propose a pertinent list of key reactions. Another point is to compare error bars gathered from observations and uncertainties in abundances

inferred from the photochemical model. Our results are compared with several data gathered from different techniques. However, we underline the fact that this is a crude comparison. Indeed, the only correct way to compare these data with the model is to compare the light curves or the spectra computed from the model results directly with the observations. As a first approximation, we consider that these data are representative of a mean composition of the atmosphere of Neptune. We have shown in

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Table 2 Key reactions for the main compounds at different pressure levels. Reaction \ Pressure (mbar)

10

1

10  1

10  2

10  3

10  4

R2 CH4 þ hn-CH3 þ H

C2H6

C2H6

C2H6 C2H6

C2H6 C2H6

CH3; C2H6 CH3; C2H2; C2H6

CH3; C2H6 CH3; C2H2; C2H6

C2H2

C2H2

C2H2 CH3C2H; C4H2

C2H2 C2H2; C2H4; CH3C2H C4H2; C6H6 C2H4; CH3C2H

C2H2 C2H2; C2H4; CH3C2H C4H2; C6H6 CH3C2H; C6H6

C2H2; C4H2; C6H6 CH3C2H

C2H2; C4H2; C6H6 CH3C2H

C2H2; C4H2 CH3C2H C2H2; CH3C2H; C4H2 C6H6 CH3; C2H2; CH3C2H

C2H4; CH3C2H; C4H2 C6H6 C2H4; CH3C2H; C4H2 C6H6

CH3C2H; C4H2; C6H6

R4 CH4 þ hn-1 CH2 þ H2 R10 C2 H4 þ hn-C2 H2 þ H2 R11 C2 H4 þ hn-C2 H2 þ H þ H R12 C2 H6 þ hn-C2 H4 þ H2 R14 C2 H6 þ hn-C2 H2 þ H2 þ H2 R51 H þ CH-C þ H2

R53 H þ 3 CH2 -CH þ H2 R57 H þ C2 H3 -C2 H2 þ H2 R63 H þ C3 H5 -CH3 C2 H þ H2

C2H4 C2H4 C2H4

CH3C2H

R81 CH þ H2 -3 CH2 + H

C2H2

R135 3 CH2 þ H2 -CH3 þ H

C2H2

C4H2 R165 R184 R187 R212

CH3 þ C2 H3 -C3 H5 þ H C2 H þ H2 -C2 H2 þ H C2 H þ C2 H2 -C4 H2 þ H C2 H3 þ H2 -C2 H4 þ H

R234 C2 H3 þ C4 H2 -C6 H4 þ H R360 H þ CH3 þ M-CH4 þ M R362 H þ C2 H2 þ M-C2 H3 þ M

CH3C2H; C6H6

CH3; C2H4; C2H6 C2H4; CH3C2H; C6H6

R364 H þ C2 H4 þ M-C2 H5 þ M

C2H4

R367 H þ C3 H3 þ M-CH3 C2 H þ M R369 H þ CH3 C2 H þ M-CH3 þ C2 H2 þ M R370 H þ CH3 C2 H þ M-C3 H5 þ M R377 H þ C4 H2 þ M-C4 H3 þ M R387 CH3 þ CH3 þ M-C2 H6 þ M R431 H þ H þ M-H2 þ M

C6H6

CH3C2H C4H2 C4H2; C6H6 C2H2; CH3C2H; C6H6 C4H2; C6H6 CH3; C2H6 CH3; C2H2; C2H4

C4H2 C2H2; C6H6 C4H2; C6H6 CH3; C2H6 CH3; C2H4; CH3C2H

C2H6; CH3C2H; C6H6 C6H6 C2H2; C2H4; C6H6 C2H2; C2H4; C4H2 C6H6

CH3C2H; C4H2; C6H6

C4H2 C4H2

C6H6 C6H6 CH3; C2H6 CH3; C2H2; C2H6 CH3; C2H4; CH3C2H

C2H6

C6H6 CH3; C2H2; C2H4 C4H2

C2H2

C6H6 C2H2; C2H4

CH3C2H CH3C2H

CH3C2H

CH3 CH3; C6H6

CH3; C2H6 C2H2; C4H2; C6H6

CH3C2H C4H2 CH3; C2H6 CH3; C2H2; C2H4 CH3C2H; C4H2; C6H6

CH3C2H C4H2 C2H6 CH3; C2H2; C2H4 CH3C2H

CH3

CH3; C2H6 C6H6

Compounds for which the abundance is highly sensitive to a given key reaction are highlighted in italic. These key reactions are referred as ‘‘main key reactions’’ in the text.

Figs. 2–5 that the model is in good agreement with the observations.

5.2. Model improvement To encourage experimentalists and theoreticians to study in detail some key reactions, it is crucial to show how a new measurement of their rate constants (at conditions relevant of planetary atmospheres) can improve a photochemical model. A concrete example is shown in He´brard et al. (2009) for the atmosphere of Titan. We present here an illustration of what can be expected for Neptune. Let us now assume that future studies will enable a reduction in the uncertainty factors of reactions R81, R135, R234, R362 and R364 to the value of 1.5 (the choice of this value is arbitrary but not to far from what we can expect). We used these new values all together and made a new uncertainty propagation study with 1000 runs. Results are shown in Fig. 7. The new uncertainty factors of the mole fractions of C2H2, C2H4, C2H6, CH3C2H, C4H2 and C6H6 (after evaluation of these reaction rates) are given as a function of the old uncertainty factors (before evaluation of these rates). For C2H6, the improvement is not significant. On the contrary, improvements are quite important for

all the other compounds. For instance, at 1 mbar, the uncertainty factor associated with the C2H4 mole fraction decreases from 4.6 to 2.0. The decrease of the uncertainty factor is even more important for hydrocarbons which bear more than 2 carbon atoms. Another illustration of the model improvement is given in Fig. 6. Our work is limited by the fact that we have implicitly assumed that our chemical scheme (set of reactions) is complete. Of course, this is surely not the case as discussed in Dobrijevic and Dutour (2006). It is possible that the addition, in the future, of some new reactions to the chemical scheme may change the list of key reactions. In addition, the present work might be extended to study the effect of other sources of uncertainties in photochemical models (mainly: eddy diffusion coefficient, atmospheric temperature, vapor pressure, boundary conditions. See Wakelam and Herbst (2010) for a similar study applied to dense interstellar clouds). This means that our methodology is a dynamical one and that the process developed here should be performed again every time the chemical scheme is completed. It is probable that a modication of the scheme might change and/or add key reactions. Nevertheless, the relevance of our work in terms of the need to improve the current reaction rates for the reactions identified in this paper is still expected to hold.

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Fig. 7. Uncertainty factors on mole fractions of some compounds as a function of pressure levels before and after evaluations of some reaction rates (see text). These figures show how new evaluations of a few rate constants affect the uncertainties of the model output.

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