University of Kansas Cassini Studies

(DRAFT) Model of Titan's Ionosphere with Detailed Hydrocarbon Ion Chemistry C. N. Keller, V. G. Anicich, and T. E. Cravens

The ionospheric models we used need to have as inputs neutral atmosphere density profiles, ion production rate profiles (both from solar EUV and from Saturnian magnetospheric electrons), an electron temperature profile (to determine temperature dependent electron recombination reaction rates), and the relevant ion-neutral reaction rates. Most of this information for the current paper was taken from the same sources as it was in the KCG model. Major changes were made only in the neutral atmosphere used and in some of the ion-neutral reaction rates.

2.1 Neutral Atmosphere

In this work we developed ionospheric models using the neutral atmospheric models of Yung et al. (1984, 1987) and Toublanc et al. (1995). In both of these cases we constructed a nitrogen density profile based on Voyager 1 data (cf. KCG), then used the mixing ratios from either the Yung or the Toublanc model to obtain the neutral densities for all other species up to an altitude of 1195 km (the upper limit of the Yung model). For altitudes higher than this (well above the homopause) we used the hydrostatic equation to compute neutral densities for all the species except for the hydrogen species (H and H2). These two species were treated differently (cf. KCG) because they are of low enough mass to escape from Titan's atmosphere.

Our models included the twenty-one major species from Yung's and from Toublanc's models. Table 1 displays the neutral densities from both of these models at two altitudes of interest: 1055 km, the ionospheric peak region; and 1655 km, near the upper limit of the chemically controlled ionosphere. The density profiles from both these model atmospheres are shown in Figures 1, 2, and 3.

One notes that at an altitude of 1055 km the Toublanc model atmosphere is enhanced over Yung's model in methane, water and propane (C3H8), but depleted in the higher mass hydrocarbons (ethane, ethylene, and acetylene) and in the nitrile species (HCN and HC3N). The differences in the hydrocarbons and in the HCN densities affect the resulting ion-neutral chemistry in this region. Toublanc et al. (1995) stated that the differences in their heavier hydrocarbon profiles from that of Yung et al. (1984) are likely due to: 1) the way in which attenuation of solar radiation due to aerosols in the lower atmosphere was treated; and 2) differences in the eddy diffusion coefficients used in each model. The differences in the other hydrocarbon species are likely produced by the way the two models handled the eddy diffusion coefficient (Toublanc et al., 1995, page 21). They also state that the lower density of HCN (a key player in the ion-neutral chemistry) is "a direct result of the lower influx of N in their model" (Toublanc et al., 1995, page 19). The considerable differences in the oxygen species (water and carbon monoxide) between the two models does affect the chemistry of the water species but has little impact on the major ion chemistry. Toublanc et al. (1995) stated that they still need to work on the oxygen species in their model.

It is not our purpose to extensively compare and contrast these two models of Titan's atmosphere or to express a preference for one or the other. It seems more reasonable to treat these differences as an estimate of the uncertainty inherent in our current understanding of the neutral upper atmosphere.

2.2 Ion Production Rates

Ion production rates for both of our models (using Yung's and Toublanc's atmosphere models) were computed as in KCG. Photoionization cross sections obtained for nitrogen and methane were integrated with the solar EUV flux, and ion production rates were computed at each altitude grid point. The production of ions from the other neutral species were computed by using ionization rates (given at 1 AU for optically thin and solar minimum conditions by Heubner et al., 1992). These rates were scaled by factors to account for solar maximum conditions at the time of the Voyager encounter with Titan (a factor of 3); and to account for the increased distance from the sun (9.5 AU); and to account for attenuation of the solar EUV flux by the major neutral species in the atmosphere (cf. KCG for details of this procedure).

When including the eleven new neutral species in this model we used the ionization rate (again from Huebner et al., 1992) for water, then estimated ionization rates for the species C3H2, C3H4, C3H6, C3H8, and C4H2. We estimated ionization rates for these species comparable to those of the acetylene, ethylene, and ethane series. The rates we used in our models are given in equations 2a - 2j below. These rates were scaled by the same factors as for the other minor ions as explained above. Electron impact ionization rates are species dependent as well as being functions of the geometry of the particular model being used. In KCG we found that near the ionization peak most of the ratios of the electron impact ionization to photoionization for the hydrocarbon species were in the range from 0.5 - 1.5. Therefore, in our current model we used the approximation that electron impact ionization would produce ions at a rate equal to the photoionization production rate. Using our estimated rates, we found that production of the daughter ions from these new neutral species was mostly (90% - 99%) from ion-neutral reactions, not from direct photoionization or electron impact ionization. We neglected any direct ionization of the neutral species C3HN, CO, C2N2, C4N2, and CH3.

Ionization Reaction	Rate at 1 AU, Solar Minimum, Optically Thin Conditions (estimated by authors except for equation 2a)
H2O + hn --> H2O+ + e-	k2a = 3.3 x 10-7 s-1	(2a)
C3H2 + hn --> C3H2+ + e-	k2b = 5.5 x 10-7 s-1	(2b)
C3H4 + hn --> C3H4+ + e-	k2c = 5.5 x 10-7 s-1	(2c)
C3H4 + hn --> C3H2+ + H2 + e-	k2d = 2.0 x 10-7 s-1	(2d)
C3H6 + hn --> C3H6+ + e-	k2e = 5.5 x 10-7 s-1	(2e)
C3H6 + hn --> C3H4+ + H2 + e-	k2f = 2.0 x 10-7 s-1	(2f)
C3H6 + hn --> C3H2+ + 2H2 + e-	k2g = 0.1 x 10-7 s-1	(2g)
C3H8 + hn --> C3H6+ + H2 + e-	k2h = 2.0 x 10-7 s-1	(2h)
C3H8 + hn --> C3H4+ + 2H2 + e-	k2i = 0.1 x 10-7 s-1	(2i)
C4H2 + hn --> C4H2+ + e-	k2j = 2.0 x 10-7 s-1	(2j)

2.3 Electron Temperature Profiles

The electron temperature profiles computed by Gan et al. (1992) and used in KCG were adopted for use in the current models. These temperature profiles are not expected to be very sensitive to changes in minor ion composition as we change from Yung's to Toublanc's atmospheric models.

2.4 Ion-Neutral Reaction Rates

The current model used the table of ion-neutral reactions compiled by Anicich and McEwan (1997). We do not reproduce that table here, but we will point out in our discussion some of the more important reactions used in our model. In addition to the reactions in Anicich and McEwan (1997), we used reactions involving NH from KCG and the reactions listed in Table 2. This table shows reactions in which either branching ratios or the rates were estimated by the authors. The reaction rate constants for reactions 2.2, 2.3, 2.7, and 2.11 are from laboratory data listed and referenced by Anicich and McEwan (1997); only the branching ratios were estimated. All reactions with rate constants of 1.0 x 10-9 were guesses and are somewhat less than the collision rate constants. In all these cases except one, using this rate did not result in these reactions accounting for more than 10% of any of the ions produced by these reactions. The rate constant for reaction 2.1 was the calculated collision rate constant, and the branching ratios for this reaction was patterned after the reaction N2+ + C2H4. The only reaction in Table 2 which produces significant amounts of a daughter ion is reaction 2.4, producing C9H9+ (included in the CnHm+ category). For this reaction we used a rate only 5% of the collision rate constant based on experience with radiative association reactions.

Electron recombination reaction rates were taken from the same sources as in KCG. Recombination rates for the higher mass hydrocarbons and nitriles added since KCG were estimated to be 1.0 x 10-6 (300)1/2 /Te cm3 s-1. Electron recombination rates used for other "new" ions to this model were (from Mendis et al., 1985):

H3O+ + e- --> H2O + H, OH + 2H, OH + H2	k3a = 7.0 x 10-7 (300)1/2/Te cm3 s-1	(3a)
H2O+ + e- --> OH + H, O + H2	k3b = 6.82 x 10-7 (300)1/2/Te cm3 s-1	(3b)

2.5 Photochemical Equilibrium Numerical Model

The neutral atmosphere profiles, ion production rates, electron temperature profiles, and ion neutral reaction rates were incorporated into a model to compute ion density profiles for fifty-one ion species in chemical equilibrium. The coupled nonlinear equations representing the conditions for chemical equilibrium were solved on a 10 km grid from 725 km to 3005 km using a Newton-Raphson iterative algorithm similar to that given by Press et al. (1986). The uncertainties in the densities computed in this model reflect uncertainties in ion neutral reaction rates and our limited knowledge of the exact atmospheric composition. Experimental measurements of ion-neutral reaction rates are typically reported with uncertainties ranging from 30% to 100%. Any reaction rate estimates which the authors have made in this model can be assumed to be no more accurate than the measured rates. While we believe our model gives a qualitatively accurate description of the composition of Titan's ionosphere, one should not expect any specific ion density to be more accurate than a factor of two at best.

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References

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Last modified January 30, 2004 T. Hunt-Ward tizby@ku.edu