Journal of Geophysical Research: Planets

The CH4 structure in Titan's upper atmosphere revisited

Authors


Corresponding author: J. Cui, School of Astronomy and Space Sciences, Nanjing University, Nanjing 210093, China. (jcui@nju.edu.cn)

Abstract

[1] In this study, we reanalyze the CH4 structure in Titan's upper atmosphere combining the Cassini Ion Neutral Mass Spectrometer (INMS) data from 32 flybys and incorporating several updates in the data reduction algorithms. We argue that based on our current knowledge of eddy mixing and neutral temperature, strong CH4 escape must occur on Titan. Ignoring ionospheric chemistry, the optimal CH4 loss rate is ∼3 × 1027 s−1 or 80 kg s−1 in a globally averaged sense, consistent with the early result of Yelle et al. (2008). The considerable variability in CH4 structure among different flybys implies that CH4 escape on Titan is more likely a sporadic rather than a steady process, with the CH4 profiles from about half of the flybys showing evidence for strong escape and most of the other flybys consistent with diffusive equilibrium. CH4 inflow is also occasionally required to interpret the data. Our analysis further reveals that strong CH4escape preferentially occurs on the nightside of Titan, in conflict with the expectations of any solar-driven model. In addition, there is an apparent tendency of elevated CH4 escape with enhanced electron precipitation from the ambient plasma, but this is likely to be a coincidence as the time response of the CH4 structure may not be fast enough to leave an observable effect during a Titan encounter.

1. Introduction

[2] Among the major species in Titan's neutral upper atmosphere, CH4 is the most elusive. The CH4 density structure as measured by the Cassini Ion Neutral Mass Spectrometer (INMS) implies a large escape flux of ∼3 × 109 cm−2 s−1 referred to the surface, or equivalently a loss rate of ∼2.5 × 1027 s−1, according to Yelle et al. [2008] (hereafter referred to as Y08). However, no convincing mechanism has been proposed so far that drives such a large CH4 outflow. At the range of temperature in Titan's upper atmosphere (∼110–190 K [Westlake et al., 2011]), the thermal Jeans escape rate of 1013–1020 s−1 is far from sufficient. Strobel [2008, 2009] has argued that CH4 loss from Titan is of hydrodynamic nature, but this was not confirmed by the Direct Simulation Monte Carlo (DSMC) results of Tucker and Johnson [2009] and Schaufelberger et al. [2012]. Current estimates of the nonthermal escape rates fall short by 2 orders of magnitude [e.g., De La Haye et al., 2007]. Finally, Bell et al. [2010a] have proposed an alternative mechanism of aerosol trapping to interpret the CH4 distribution with a negligible CH4 escape rate, but later, Strobel [2012] has argued that this mechanism is operative well below the altitude range probed by the INMS and does not reduces the CH4 escape rate significantly.

[3] The motivations for this study are twofold. First, there is still controversy on the interpretation of the INMS CH4 data. The recent analysis of Bell et al. [2011] has obtained an optimal homopause level of ∼1000 km on Titan and a typical CH4 escape flux at least 2 orders of magnitude smaller than those of Y08 and Strobel [2008, 2009]. Since the early INMS works were published, the data from significantly more Titan flybys have now become available, and the data reduction algorithms have also been improved. These call for a reanalysis of the INMS CH4 structure to solve the discrepancy between existing works. Second, the INMS investigations of the CH4structure so far primarily focus on the globally averaged situation. An analysis of the flyby-to-flyby variability is currently lacking and will be attempted here. This allows an assessment of the response of the CH4 structure to varying solar and/or magnetospheric conditions.

[4] The organization of the paper is as follows. In section 2, we describe briefly the INMS sample included in this work, followed by a detailed description of the improvements in data reduction over previous works such as that by Müller-Wodarg et al. [2008] (hereafter referred to as MW08) and Cui et al. [2009] (hereafter referred to as C09). We present the main results of this paper in section 3, where several distinctive questions on the CH4 structure in Titan's upper atmosphere are raised and their answers provided based on the reanalysis of the INMS data. Especially, we conclude that with the current knowledge of the eddy mixing profile and neutral temperature, strong CH4 escape must occur on Titan. Finally, we give conclusions in section 4.

2. Data Reduction Algorithms

[5] The CH4 densities in Titan's upper atmosphere have been extensively measured by the INMS during the Cassini encounters with Titan [Waite et al., 2004]. Systematic analyses of the INMS CH4 data have been presented in various works [e.g., Yelle et al., 2006; Y08; MW08; C09; Magee et al., 2009; Bell et al., 2010a, 2011]. For this study, we combine the INMS neutral measurements from 32 Titan flybys, from T5 to T71. The data are obtained from the Planetary Plasma Interactions (PPI) node of the NASA Planetary Data System (PDS) public archives (http://ppi.pds.nasa.gov) and are reduced in a way similar to MW08 and C09. Nevertheless, several improvements in the INMS data reduction algorithms have been implemented in this study, which we detail in sections 2.12.3. A comparison with results from previous analyses is given in section 2.4.

2.1. Sensitivities and Wall Effects

[6] The conversion from the INMS raw count rates to number densities relies on the choice of the sensitivity values. For a given neutral species, the sensitivity values used for the data analysis are usually parameterized with a peak sensitivity and a cracking pattern (C09). Preliminary sensitivity values have been reported in C09, based on the calibrations made with either the flight unit (FU) or the refurbished engineering unit (REU) [see also Magee et al., 2009]. Later, the REU sensitivities have been recalculated following updated REU calibration campaigns, but reporting peak values only (D. A. Gell et al., Characterization of the Cassini Ion Neutral Mass Spectrometer (INMS): Revision of sensitivity values and implications for previous publications of INMS neutral densities and mixing ratios, manuscript in preparation, 2012, hereafter referred to as G12).

[7] Throughout this study, we adopt FU peak sensitivities and cracking patterns for all species with FU calibrations. For other species, we use the updated G12 peak sensitivities but still use the C09 cracking patterns. The updated REU calibrations do not necessarily affect the analysis of major neutral species such as N2 and CH4, since their sensitivities are based on FU calibration (C09). The situation for 40Ar is more complicated, though the FU calibration results are used for this species. As illustrated in Y08, a proper determination of the 40Ar densities requires a decoupling between 40Ar and other minor species, especially CH3C2H. However, we will show below that in practice the decoupling depends on the CH3C2H cracking pattern rather than its peak sensitivity (see sections 2.3 for details). This means the updated REU calibrations do not affect the 40Ar density determination as well. The 40Ar density profile is critical for this study since as an inert and nonescaping species, it is useful for separating eddy mixing and molecular diffusion.

[8] An additional multiplicative factor, which is not implied by the updated REU calibrations, has to be adopted to account for the difference in total density between INMS and other instruments. This factor is assumed to be common to all species, but its exact value is subject to uncertainty. A comparison between the INMS total densities and the Cassini Ultraviolet Imaging Spectrograph (UVIS) values for the T41 flyby suggests a multiplicative factor of 2.9 [Koskinen et al., 2011], whereas a slightly lower value of 2.6 is inferred by matching the INMS total densities to the values from the Huygens Atmosphere Structure Instrument (HASI) and the Cassini Attitude and Articulation Control Subsystem (AACS) [Strobel, 2010]. A calibration factor of 2.9, common to all species, is adopted throughout this study (thus, all INMS peak sensitivities are divided by 2.9), but in practice, any value in the range of 2.6–3.2 is acceptable.

[9] Some portions of the INMS densities should be used with caution due to wall contamination, which primarily influences outbound densities but leaves inbound densities almost unaffected. Such an instrumental effect refers to adsorption/desorption or surface chemistry occurring on the INMS chamber walls [Vuitton et al., 2008; C09]. Accordingly, throughout this study we focus on the N2 and CH4 densities from inbound only. For 40Ar as a nonreactive species, wall contamination is not relevant, and both the inbound and outbound data are used.

2.2. Extraction of the N2 and CH4 Density Profiles

[10] For a given mass channel, the INMS records count rates in a primary counter (C1) as well as a low gain secondary counter (C2) [Waite et al., 2004]. The latter is used only when the counts in the former are saturated. Due to dissociative ionization of neutral molecules by the INMS electron guns [Waite et al., 2004], the density of a given species could be derived simultaneously from several channels. Specific strategies have to be designed to ensure that the densities from different channels are consistent and that the counts used are not affected by saturation [e.g., MW08; C09; Magee et al., 2009].

[11] The N2 and CH4 densities are calculated following the scheme of MW08. In that work, the N2 densities at most altitudes were obtained from C1 counts of either channel 28 or channel 14, depending on where C1 counts of channel 28 become saturated. Near the closest approach (CA) where C1 counts are saturated for both channels, C2 counts of channel 28 were used instead. The CH4 densities were obtained from C1 counts of channel 16, but near CA where they become saturated, C1 counts of channel 12 were used. Channel 12 was chosen because it is not contaminated by 13CH4.

[12] There are a few potential problems with the above approach. First, the transition level for the limit of saturation was set to where the count reaches 105 per integration period (IP, 0.031 s) or 3.2 × 106 s−1based on visual inspection of the INMS data from individual flybys, but a more careful inspection combining the data from all 32 flybys reveals that the C1 counter becomes saturated at a significantly lower level. However, this does not necessarily mean that the C1 count rates should be used in a more conservative manner. In contrast, we will show below that the transition level can in practice be extended to higher count rates by allowing for nonlinear conversion. Second, assuming a clear-cut transition between different channels usually leads to a rapid change in the characteristics of the INMS data at the specified transition levels, and consequently a discontinuity in the derived N2 or CH4 density profile. This naturally introduces an artificial jump in the neutral temperature profile, which is derived from the density gradient. It will be shown below that these artificial density jumps can be largely removed by introducing continuously varying weighting functions for different channels. The improvements that we apply to the data reduction algorithms in this study are detailed as follows.

[13] First, we extend the transition levels to higher count rates by applying a correction for counter saturation in the region where the saturation is slight. An example is shown in Figure 1a where we plot the C1 count rate of channel 14, inline image, as a function of the C1 count rate of channel 28, inline image, both with dead time correction for detector fatigue [Magee et al., 2009]. The INMS data from all 32 flybys have been included. The contributions of CH4 and 14N15N to channel 14 have been subtracted, so both count rates in Figure 1a should measure the N2 densities. For inline image < 2 × 106 s−1, the two count rates are linearly correlated, suggesting that the C1 counters for both channels are not saturated and give reasonable measurements of the N2 density. Above ∼2 × 106 s−1, inline image curves up, indicative of counter saturation in channel 28. Up to ∼(4–5) × 106 s−1, the relation between the two count rates can be described empirically by C1(14) = a0C1(28) exp { tan image } , with a0, a1 and a2 being free parameters to be constrained by the data. The C1 count rates of channel 28 corrected for saturation, inline image, should satisfy inline image as long as inline image is not saturated. Thus, we get

display math

where we have dropped the superscript (28) because similar expressions are used to correct for the saturation of the C1 count rates of channels 14 and 16, as illustrated in Figures 1b and 1c, respectively.

Figure 1.

(a) The C1 count rate of channel 14 ( inline image) as a function of the C1 count rate of channel 28 (C1(28)), both contributed by N2 only. (b) The C2 count rate of channel 28 ( inline image) as a function of the C1 count rate of channel 14 ( inline image), both contributed by N2 only. (c) The C1 count rate of channel 12 ( inline image) as a function of the C1 count rate of channel 16 (C1(16)), both contributed by CH4 only. The INMS data from all 32 flybys have been included. In Figures 1a–1c, the dashed line gives the linear correlation obtained from regions where both count rates are not saturated, and the solid line represents the nonlinear empirical relation used to correct for saturation up to the cutoff level given in Table 1. (d) The weighting functions for count rates in C1 of channel 28 ( inline image, solid), C2 of channel 28 ( inline image, dotted) and C1 of channel 14 ( inline image, dashed), as a function of time from CA. These weighting functions are used for calculating the N2 densities without instantaneous transition near the cutoff levels.

[14] The free parameters, a0, a1 and a2, are listed in Table 1 for reference. Note that a0 is not used for correcting for saturation but instead used for ensuring that the densities derived from different channels and/or counters are consistent (see also section 2.4). These issues have been discussed in sections A3 and A1.2 of C09 in terms of the C1/C2 ratio and the calibration of the N2/CH4 cracking patterns. In previous analyses, the values for each of the above parameters were different from flyby to flyby, whereas in the present study, they are taken to be constant (see section 2.4 for details). The cutoff levels listed in Table 1 refer to the highest count rates for which equation (1)is applicable. Count rates above these cutoff levels are not used in our analysis. In practice, all C1 count rates of channel 16 can be safely used so that no cutoff level is given for this channel. By utilizing the count rates that are slightly saturated, the above procedure increases the signal-to-noise ratio of the density data near the transition regions as compared to early INMS analysis works.

Table 1. Empirical Relations Between the Count Rates From Two Different Channels/Counters but Associated With the Same Ambient Species (N2 or CH4)a
SpeciesEmpirical Relationa0a1a2Cutoff Level
  • a

    Also shown are the free parameters in these relations. Specifically, a1 and a2 are used to correct for saturations, whereas a0 is used to ensure that the densities from different channels/counters are consistent. The cutoff level refers to the highest count rate for which the empirical expression is applicable. N/A, not available.

N2 inline image0.03001.27 × 10−7 s3.054.2 × 106 s−1
N2 inline image0.005361.12 × 10−7 s2.234.2 × 106 s−1
CH4 inline image0.007911.54 × 10−7 s2.77N/A

[15] Second, the clear-cut transition at 4.2 × 106 s−1 from one channel to another (see Table 1) may cause density discontinuities in the derived N2 profiles. To remove such features, the N2 densities are calculated with inline image where inline image, inline image and inline image represent N2 densities from C1 of channel 28, C1 of channel 14 and C2 of channel 28, respectively, inline image, inline image and inline image are predefined weighting functions constructed from hyperbolic tangents

display math
display math
display math

In equations (2)(4), t is time from CA, inline image ( inline image) and inline image ( inline image) correspond to where inline image ( inline image) reaches 4.2 × 106 s−1 during the inbound and outbound portions of a given flyby, and Δt is the timescale for the transition taken to be 10 s in this work. An example of these weighting functions is given in Figure 1d, assuming inline image = −225 s, inline image = +225 s, inline image = −100 s and inline image = +100 s. The choice of the timescale for the transition, Δt, is not unique. Several values have been tested, but give identical N2 density profiles.

[16] Finally, we note that the sampling of the INMS data is nonuniform. The data points from an individual flyby are often grouped in batches covering a very small time interval but with sequential groups separated by a much larger gap. Therefore as a third improvement, we average together all data points obtained within 1.5 s of each other, since they are expected to sample essentially the same portion of Titan's atmosphere. With a typical spacecraft velocity of 6 km s−1, this time interval covers a length scale of ∼9 km along the spacecraft trajectory. In practice, the procedure described above replaces each tightly packed group with a single data point with higher precision.

2.3. Extraction of the 40Ar Density Profile

[17] As an inert and nonescaping species, the density profile of 40Ar is unique for constraining the eddy mixing coefficients on Titan, which can then be used to infer the CH4 escape flux [e.g., Y08; Bell et al., 2011]. The 40Ar atoms produce peak signals at mass channel 40, but the counts in this channel are also contributed significantly by CH3C2H. To illustrate the necessity of decoupling their cracking patterns, an example is provided in Figure 2 for the T18 flyby. We show with the solid circles the total count rate in channel 40 as a function of time from CA. The contributions from 40Ar and CH3C2H are given separately by different symbols. The algorithm used for estimating these contributions is based on our nominal choice, which is explained in detail below. Figure 2 shows that without a proper decoupling, the outbound 40Ar densities would be overestimated by a factor of ∼2.

Figure 2.

The count rate in mass channel 40 as a function of time from CA for the T18 flyby. Different symbols stand for the total count rates, the count rates contributed by 40Ar and CH3C2H, respectively. The relative contributions of different species are calculated with the nominal algorithm (see text for details). The apparent asymmetry in CH3C2H is an indication of the wall chemistry effect.

[18] There are several complexities. First, the CH3C2H densities are usually obtained from counts in channels 37–39, but these channels are also contributed by C6H6 and CH3CN (C09). Their densities can be determined from counts in channels 77–78 and 41, respectively. Second, another relevant species is C3H6 that has not been included in our previous works. This can be seen from Figure 3 of C09, showing that the singular value decomposition (SVD) analysis has underpredicted the count rate in mass channel 42, the main peak of the C3H6 cracking pattern. Finally, it is also important that the contributions from background signals are subtracted before the count rates are converted to densities [C09; Magee et al., 2009]. The background counts are estimated in a way similar to C09.

[19] Among the neutral species mentioned above, CH3C2H and C6H6 have not been calibrated preflight. The updated REU calibration has inferred their peak sensitivities ∼30% lower than the C09 values. For C3H6, neither FU nor REU calibration is available, leading to considerable uncertainty in evaluating its contributions to channels 37–39. Using the cracking pattern from the chemistry reference data of the National Institute of Standards and Technology (NIST, http://webbook.nist.gov/chemistry/) suggests that the C3H6 contribution to channel 39 is relatively small as compared to the other two channels. Therefore for our nominal choice, we derive the CH3C2H densities based on counts in channel 39 only, to minimize the uncertainty in the C3H6 cracking pattern. Especially, we notice that the CH3C2H densities from channels 37 and 38 are sometimes negative even near CA, implying that the NIST sensitivities of C3H6 for these two channels are probably higher than those appropriate to the INMS.

[20] We compare in Table 2 the 40Ar number densities derived with several different algorithms. For each case, we combine the data from all 32 flybys in our sample, and the results for three different altitude ranges are presented. The first case corresponds to our nominal choice, i.e., with C3H6, C6H6 and CH3CN included, with background subtracted, and with CH3C2H densities from channel 39 only. Alternative algorithms in Table 2 include the case without background subtraction, the case without C3H6, the case without both C3H6 and C6H6, the case without CH3CN, and the case with CH3C2H densities calculated as the average results of channels 37–39. The other aspects of these alternative algorithms remain the same as the nominal case.

Table 2. The 40Ar Number Densities Calculated From Different Algorithms (See Text for Details) and Averaged Over Several Selected Altitude Bins Including All Flybys in Our Sample
Algorithm960–980 km (cm−3)980–1000 km (cm−3)1000–1100 km (cm−3)
Nominal3.5 × 1052.4 × 1051.0 × 105
No background subtraction3.8 × 1052.6 × 1051.1 × 105
No C3H63.3 × 1052.3 × 1059.5 × 104
No C3H6 and C6H63.0 × 1052.0 × 1058.8 × 104
No CH3CN3.5 × 1052.5 × 1051.1 × 105
CH3C2H from mean of channels 37–393.8 × 1052.5 × 1059.7 × 104

[21] As compared to the nominal algorithm, the 40Ar densities are overestimated by ∼5%–10% if the background counts are not subtracted, underestimated by ∼6% if C3H6 is not included, and underestimated by nearly ∼15% if neither C3H6 nor C6H6 is included. We emphasize that we consider C3H6 and C6H6 in our nominal analysis not because their direct contributions to channel 40 counts are significant. Instead, they are included to calculate more accurately the CH3C2H densities, thus representing an indirect influence to the 40Ar density extraction as illustrated in Figure 2. Table 2 also shows that ignoring CH3CN does not make any appreciable change to the derived 40Ar densities. Finally, different channels used for determining the CH3C2H densities may lead to an uncertainty in 40Ar at the level of ∼5%–10%.

[22] As mentioned in section 2.1, 40Ar is a chemically inert species and not contaminated by any wall chemistry effect. This implies that the globally averaged inbound and outbound density profiles of 40Ar should be roughly identical as long as the sample is sufficiently large [e.g., C09]. This fact could be used to evaluate a specific 40Ar extraction algorithm since any imperfect decoupling of 40Ar from other species, all of which are subject to wall contamination, may lead to an 40Ar asymmetry between inbound and outbound. Several examples are given in Figure 3. For our nominal choice, the symmetry between inbound and outbound is maintained at all altitudes. This is also true for the case without background subtraction but more likely because the background signals are themselves symmetric about CA [see C09, Figures 33 and 34]. In contrast, there are clear differences between the inbound and outbound 40Ar densities for the case without C3H6 and C6H6 included, as well as the case with CH3C2H densities from the averages of channels 37–39. The above comparison justifies, though indirectly, our nominal choice of the 40Ar extraction algorithm in this study.

Figure 3.

A comparison between the globally averaged inbound (solid) and outbound (dashed) density profiles of 40Ar, obtained from several algorithms including (a) the nominal case, (b) the case without background subtraction, (c) the case without both C3H6 and C6H6, and (d) the case with CH3C2H densities from the averages of channels 37–39. For a reasonable scheme of 40Ar density extraction, an asymmetry between the inbound and outbound profiles is not expected as 40Ar is an inert species and is free from any wall chemistry effect.

2.4. Comparisons With Previous Results

[23] We present in this section a comparison between the N2, CH4 and 40Ar densities obtained here and those from previous works [e.g., MW08; C09] multiplied by the additional calibration factor of 2.9 (see section 2.1).

[24] In the N2/CH4 data reduction algorithms described in section 2.2, we have adopted a correcting function that varies for different channels (see Table 1). In contrast, it has been assumed in our previous analysis (C09; Y08; MW08) that the saturation is due to the overload of the INMS detector system and thus the saturation characteristics are species independent. The early assumptions are incorrect as revealed by Figure 4, where we show the C2 count rates as a function of the C1 count rates for different channels. The data points from all 32 flybys have been included. The C1-C2 relations for channels 15 and 16, which are primarily contributed by CH4, are nearly identical and both are indicated by blue in Figure 4. Another group of relations, black for channel 14, red for channel 28 and green for channel 29, all of which are primarily contributed by N2 or 14N15N, is different from the relations for CH4. This strongly suggests that saturation is species dependent, though a rigorous interpretation based on physical arguments is currently lacking.

Figure 4.

The C2 count rates as a function of the C1 count rates, for channels 14, 15, 16, 28 and 29. The data points from all flybys in our sample have been included. The C1-C2 relations indicate that the saturation characteristics are species dependent.

[25] When compared with MW08 and C09, the improvements in data reduction adopted here do not significantly alter the N2 and CH4 densities in regions where the C1 counts of channels 28 and 16 are not saturated, but the density differences in the saturated regions are not negligible. If we considered the T16 flyby (on 22 July 2006) as an example, we find that the N2 densities reported here are ∼3%–5% higher than C09 near CA, and the CH4 densities are higher by ∼15%–20%. These differences could be explained with the following arguments: The a0's parameters in Table 1 are related to the C1/C2 ratio and the calibration factors of channels 14 and 12 (C09). The latter were introduced in C09 to ensure that the N2 and CH4 densities from different channels are consistent. It is easily verified that the C1/C2 ratio is identical to the inverse of the multiplication of a0's for channels 28 and 14, which is ∼6219 based on Table 1. The same ratio has been derived in our previous works as ∼5976 for T16. The lower C1/C2 ratio in previous works, due to an overestimated saturation level, accounts for the N2 density difference reported above. Similarly, the CH4 calibration factor for channel 12 is identical to the inverse of the multiplication of a0 for channel 16 in Table 1 and 0.00636, the ratio of the channel 12 to channel 16 sensitivities for CH4. This factor is ∼0.683 for T16 from our previous analysis and ∼0.804 here which is common to all flybys. The difference of ∼18% for this calibration factor is responsible for the CH4 density difference between this work and C09.

[26] The underestimates of the C09 and MW08 N2 densities at relatively low altitudes are primarily associated with the early choice of the transition level (3.2 × 106 s−1), which was based on an investigation of the inline image relation for any given flyby. In practice, when including the data from only one flyby, the relatively large scattering of the inline image relation makes it uncertain to characterize counter saturation, especially based on visual inspection. The improperness of the early choice of the transition level is clearly revealed by Figure 1a, which indicates that the inline image relation shows noticeable deviation from linearity for inline image < 3.2 × 106 s−1. In this work, it is the combination of the data from all flybys that helps to constrain better the saturation characteristics. The underestimates of the C09 and MW08 CH4 densities at low altitudes can be explained in a similar way. It is also worth emphasizing that the definition of the transition level here is different from that in previous works. In C09 and MW08, the transition level refers to where saturation occurs. In contrast, the definition of the transition level in this work is based on where the nonlinear relation, as described in section 2.2, starts to deviate from the data points. In both cases, the transition level corresponds to where the C1 counts can no longer be reliably used.

[27] As compared to the C09 results (multiplied by the calibration factor of 2.9), the 40Ar densities reported here are generally decreased by ∼10%. The difference partly comes from the additional inclusion of C3H6 in this work. Also, the previous algorithms relied on a simultaneous fitting of counts in channels 37–39, whereas in this study we use channel 39 only, for the reason addressed in section 2.3. The recalibration of the REU sensitivities is not an issue since in both works the FU peak sensitivity is used for 40Ar and the same cracking patterns are used for the other species involved, thus not changing their relative contributions to mass channel 40. To illustrate the update in 40Ar density, we repeat our analysis on a sample identical to that of C09, i.e., up to T37, and we obtain at an altitude of 980 km an average 40Ar density of ∼3.9 × 105 cm−3 for the nominal case and ∼4.2 × 105 cm−3 for the case without C3H6 and with CH3C2H densities from the average results of channels 37–39. The latter is identical to the value quoted by C09 when multiplied by 2.9.

[28] The INMS densities have also been calculated independently by Magee et al. [2009]. Their average values are ∼8.9 × 109 cm−3 for N2, ∼2.0 × 108 cm−3 for CH4 and ∼1.2 × 105 cm−3 for 40Ar between 1000 and 1100 km when multiplied by 2.9. Taking into account the difference in peak sensitivities, the Magee et al. [2009] N2, CH4 and 40Ar densities are about 15%, 10% and 20% lower than our nominal values obtained from an identical sample, i.e., from T18 to T43. The 1000–1100 km altitude range is typically where the C1 counts of channels 14 and 16 start to be saturated; thus, the difference in N2 and CH4 densities must be due to the respective methods used to correct for the saturation characteristics. The difference in 40Ar densities cannot be traced back easily, as some of the details in their data reduction are not available to us. But we do note that for the algorithms listed in Table 2, the case without C3H6 and C6H6 reproduces the Magee et al. [2009] value most closely. It is also noteworthy that despite of the 10–20% difference in absolute density, the 40Ar mixing ratios from the two works are consistent.

[29] To end this section, we summarize the key issues of the updated N2/CH4/40Ar data reduction algorithms: (1) comparisons with the total densities from other Cassini/Huygens instruments suggest that the absolute densities of all species have been underestimated by a factor of ∼2.9 in previous analysis [e.g., C09; Y08; MW08; Cui et al., 2008; Magee et al., 2009]; (2) the N2 and CH4 densities near CA have been revised due to a more appropriate treatment of the saturation characteristics; (3) the instantaneous transitions in N2 and CH4 density profiles near regions where saturation occurs have been carefully removed in this study; and (4) the 40Ar densities have been updated by including C3H6 in the decoupling and by restricting CH3C2H density extraction to channel 39 only.

[30] Finally, it should be remembered that the Cassini measurements of Titan's lower atmosphere have revealed seasonal variations [e.g., West et al., 2011]; thus, the change in the globally averaged density profile of any species observed by the INMS is partly due to Titan's long-term thermospheric evolution over the time when the data were acquired. For example, with our updated data reduction algorithms and an averaging between 1000 and 1100 km, the N2, CH4 and 40Ar densities drop by about 15%, 10% and 25% from the C09 sample (from 16 April 2005 to 19 November 2007) to the present sample including all available flybys (from 16 April 2005 to 7 July 2010).

3. Reanalysis of the CH4 Structure in Titan's Upper Atmosphere

[31] Based on the improved reduction of the INMS data presented in section 2, several distinctive questions on the CH4 structure in Titan's upper atmosphere are discussed below. In particular, our aim is to solve the discrepancy in the interpretation of the CH4 data between existing works [e.g., Y08; Bell et al., 2011].

[32] The mixing ratio profile of a minor species, i, in Titan's atmosphere is readily modeled with the one-dimensional, steady state diffusion equation:

display math

to derive the eddy mixing coefficient and the diffusion flux (Y08). In equation (5), Fi, Xi, Hi, Di, and αi are the flux, mixing ratio, density scale height, and molecular diffusion coefficient of species i; na and Ha are the number density and density scale height of the background atmosphere; T is the neutral temperature; K is the eddy mixing coefficient; and r is the radial distance from Titan's center. In equation (5), we implicitly assume a common temperature profile for all atmospheric constituents.

[33] The results presented throughout this section are obtained within the framework of the fluid approach through equation (5), but we also note that the validity of such an approach has recently been questioned when compared to results from kinetic model calculations [e.g., Tucker and Johnson, 2009; Tucker et al., 2012; Volkov et al., 2011], especially in the transition region between strong collisional and collisionless.

3.1. How Important Is Eddy Mixing on Titan?

[34] It has been shown by Yelle et al. [2006, 2008] that the INMS CH4 density profile can be interpreted by either the combination of diffusive equilibrium (i.e., Fi = 0) and an eddy mixing profile significantly larger than in any other solar system body or the combination of a large escape rate and an ordinary eddy mixing profile. To separate the above two effects, we first derive the eddy mixing coefficient as a function of altitude from the 40Ar data.

[35] Eddy mixing in Titan's atmosphere is the summed effect of large-scale mixing by dynamics and small-scale mixing by turbulence [Müller-Wodarg and Yelle, 2002]. The former can only be obtained from time-dependent, full three-dimensional global circulation models [e.g.,Müller-Wodarg et al., 2000; Bell et al., 2010b], and the latter is usually not resolved in these calculations. The analysis presented in this section is based on the steady state, one-dimensional calculations to be compared with the globally averaged40Ar data. This has the advantage of parameterizing the summed effect of all mixing processes, irrespective of the detailed mechanisms driving it.

[36] We adopt the empirical eddy mixing profile given by equation (4) of Y08, i.e., inline image,where p is atmospheric pressure, p0 = 1.43 × 105 dyn cm−2 (note the value of 1.43 dyn cm−2 given by Y08 is erroneous), K0 = 3 × 102 cm2 s−1, γ = 0.9 and K is the asymptotic value of the eddy mixing coefficient. Such a functional form treats K as the only free parameter to be constrained by the data with a diffusive equilibrium model for 40Ar. To constrain rigorously the eddy mixing profile, we combine the INMS 40Ar data obtained above ∼950 km and the tropospheric 40Ar mixing ratio of ∼3.39 × 10−5 measured by the Huygens Gas Chromatograph Mass Spectrometer (GCMS) below ∼140 km [Niemann et al., 2010].

[37] The interpolation of the 40Ar mixing ratio profile to low altitudes using equation (5)requires a background model atmosphere to be constructed all the way from the top of the atmosphere down to the lower stratosphere. Several post-Cassini background models are available from the literature, including the model based on the HASI measurements made during the Huygens descending phase [Fulchignoni et al., 2005], the model from Y08, and the standard chemical model of Strobel [2012]. These background models are denoted as HASI, RVY08, and DFS12, respectively. The HASI densities above 1000 km are systematically higher than the actual globally averaged values due to the oblateness of Titan's upper atmosphere (MW08), as the HASI data were acquired at the equatorial regions. The RVY08 model, which is based on previous INMS results, clearly underestimates the true atmospheric densities in the upper thermosphere by a factor of ∼2.9 due to the uncertainty in absolute calibration (see section 2.1). The DFS12 model is the favored one for this study, as it is consistent with both the updated INMS total density profile and the range of Titan's average thermospheric temperature [e.g., C09; Westlake et al., 2011].

[38] In Figure 5 we show the globally averaged INMS 40Ar mixing ratio as a function of altitude. Such a profile is obtained by interpolating to a common altitude grid the observed 40Ar mixing ratios based on the nominal data reduction algorithm described in section 2.3, which are then averaged over all flybys in our sample, both inbound and outbound. Also shown in Figure 5 is the best fit diffusive equilibrium model, with K ≈ 2 × 107 cm2 s−1, as well as models calculated with other choices of K. Especially, the dash-dotted line gives the model withK ≈ 2.2 × 109 cm2 s−1, required by the condition of CH4 being in diffusive equilibrium (see below). This model shows considerable departure from the INMS data. For all cases, the background atmosphere is taken from the DFS12 standard chemical model, and the lower boundary condition is taken to be consistent with the GCMS result [Niemann et al., 2010]. Detailed in Table 3 are the K values for several test runs with different choices of the background model atmosphere and different inputs of the INMS 40Ar mixing ratio. These test runs give K in the range of ∼(1–6) × 107 cm2 s−1, comparable to the values in the upper atmospheres of other solar system bodies such as Mars [e.g., Rodrigo et al., 1990] and Venus [e.g., von Zahn et al., 1979]. For all cases the corresponding CH4 homopause level is well below the 1000 km level suggested by Bell et al. [2011]. Our calculations indicate that above ∼1200 km, the eddy mixing coefficient is at least 2 orders of magnitude lower than the molecular diffusion coefficient for CH4. In section 3.2 we show that this has important impacts on the inference of CH4 escape on Titan.

Figure 5.

The diffusive equilibrium model fitting of the INMS and GCMS 40Ar mixing ratios (solid circles) as a function of altitude throughout Titan's atmosphere. The INMS values are derived with the nominal choice of the 40Ar data reduction algorithm (see section 2.3 for details). For illustrative purpose, the GCMS result is placed at 200 km, but the actual measurements were made at ∼75–140 km [Niemann et al., 2010]. The best fit model is given by the solid line, with an asymptotic eddy mixing coefficient, K ≈ 2 × 107 cm2 s−1. Models with other choices of K are also indicated, including the case with K ≈ 2.2 × 109 cm2 s−1 that implies globally averaged CH4 distribution under diffusive equilibrium.

Table 3. Asymptotic Eddy Mixing Coefficient, K, and the CH4 Homopause Level, zhom (CH4), Calculated From Several Different Choices of the Background Model Atmosphere and the Input INMS 40Ar Density Profile
Background AtmosphereINMS 40Ar InputK (cm2 s−1)zhom (CH4) (km)
DFS12Nominal2.0 × 107855
No C3H6/C6H61.6 × 107845
No background subtraction2.2 × 107860
RVY08Nominal5.0 × 107875
No C3H6/C6H64.1 × 107865
No background subtraction5.5 × 107880
HASINominal1.6 × 107840
No C3H6/C6H61.3 × 107825
No background subtraction1.8 × 107850

[39] Bell et al. [2011] used a simultaneous fitting to the 14N15N and 40Ar density data to constrain the eddy mixing profile, but we will not attempt this because the change in K has a larger impact on the 40Ar mixing ratio than on the 14N15N mixing ratio, which makes 40Ar a more sensitive diagnostic of eddy mixing. This could be seen from Bell et al. [2011, Figure 6], who show that enhanced eddy mixing leads to a factor of 2 increase in 40Ar mixing ratio but only a 5% decrease in 14N/15N ratio at 1200 km.

[40] For further illustration, we use equation (5) to calculate the 14N/15N ratio as a function of altitude in Titan's upper atmosphere, with different choices of the temperature profile and eddy mixing coefficient. A fixed lower boundary condition of 167.7 is adopted, based on the updated GCMS result of Niemann et al. [2010]. For the DFS12 temperature profile and over the K range of 1 × 107 to 1 × 108 cm2 s−1 (i.e., from 1/5 to 5 times the nominal value), we find a range in 14N/15N of ∼200–220 at 1200 km. For the RVY08 and HASI temperature profiles, the corresponding ranges are ∼210–230 and ∼190–210, respectively. Thus, it is clear that 40Ar is a more powerful and preferred constraint on eddy mixing as a combined result of (1) the uncertainty in temperature and (2) the insensitivity of 14N/15N ratio to K.

3.2. Does Strong CH4 Escape Occur on Titan?

[41] As soon as the eddy mixing profile is known, the CH4 distribution is readily modeled with equation (5), treating the CH4 escape rate as the only free parameter. For a preliminary test of the model validity, we show with the light solid line in Figure 6 the model profile obtained by integrating equation (5) upward from the lower stratosphere where the CH4 mixing ratio is set as 1.48% based on the GCMS result [Niemann et al., 2010]. A CH4 loss rate, L(CH4), of 3.8 × 1027 s−1 is used for constructing the model. The neutral temperature profile is taken from the DFS12 background atmosphere, and K ≈ 2 × 107 cm2 s−1is adopted for self-consistency (seeTable 3). The model adequately reproduces the INMS CH4 data in the 1200–1600 km altitude range but systematically overestimates the data both below and above.

Figure 6.

The CH4 diffusion model profiles in Titan's upper atmosphere compared with the globally averaged INMS CH4 densities from the updated data reduction algorithms. The density uncertainties due to counting statistics are too small to be visible at the scale shown. Five models are indicated, falling into two groups: (1) The gray and blue lines represent models calculated throughout the entire atmosphere and match the GCMS CH4 mixing ratio of 1.48% deep in the lower stratosphere [Niemann et al., 2010]. The former gives the best fit model with a loss rate of 3.8 × 1027 s−1 and the latter gives the diffusive equilibrium (DE) model. (2) The red, magenta and green lines represent models calculated in the 1200–1600 km altitude range, matching the INMS CH4 mixing ratio of 4.6% at the lower boundary. The red line gives the best fit model with a loss rate of 3 × 1027 s−1, and the remaining two represent diffusive equilibrium models with different input background atmospheres (either DFS12 or isothermal at 140 K).

[42] The departure below ∼1200 km comes from the fact that the chemical destruction of CH4 molecules has been ignored. In Titan's upper atmosphere, CH4 photolysis typically peaks at ∼850 km [Lavvas et al., 2011]. and the effects of magnetospheric destruction may vary considerably in response to the plasma environment [e.g., Rymer et al., 2009]. Strobel [2009] has recently shown that the CH4 loss rate derived from the INMS data may differ by ∼20% with or without ionospheric chemistry included. It is also likely that the specific functional form of the eddy mixing profile adopted in this study has some impact on the model CH4 mixing ratios below ∼1200 km. We note that in the analysis of Y08, the lower boundary for CH model fitting is placed at ∼950 km, which is the lowest altitude probed by the INMS. The choice of the lower boundary at 1200 km is in fact a quite significant difference between the two works. The present choice lessens the sensitivity of the model results to both CH4 photochemical destruction and eddy mixing, whose influences tend to diminish with increasing altitude.

[43] Above ∼1600 km, the Knudsen number, Kn, defined as the ratio between the particle mean free path and the atmospheric scale height, becomes sufficiently high that a kinetic model should be used instead [e.g., Volkov et al., 2011]. Bird [1994] argued that the fluid description is only valid with Kn < 0.2, which corresponds to a typical altitude of ∼1400 km for CH4 on Titan. However, Figure 6 indicates that the diffusion model can in practice be extended upward by at least 200 km and still with satisfactory results.

[44] Based on the above discussions, we use the INMS CH4densities in the 1200–1600 km range for the data-model comparison to ensure that the effect of chemical destruction is negligible, that the exact form of the eddy mixing profile is not important, and that the fluid description is valid. The corresponding best fit CH4 diffusion model is indicated by the red line in Figure 6, with a CH4 loss rate of ∼3.0 × 1027 s−1 or a CH4 upward flux of ∼3.6 × 109 cm−2 s−1 referred to the surface, in agreement with the early results of Y08 and Strobel [2008, 2009]. Here the DFS12 background atmosphere and a nominal eddy mixing coefficient of K ≈ 2 × 107 cm2 s−1 have been used. The CH4 flux inferred above accounts for ∼65% of the CH4 limiting flux well below Titan's homopause.

[45] Table 4 lists the results from model runs with different input profiles of the eddy mixing coefficient and neutral temperature. All models are calculated with a fixed CH4 mixing ratio of 4.6% at the lower boundary (1200 km), based on the updated INMS data reduction algorithms. For models 1–2, the temperature profile is taken from the DFS12 background atmosphere, whereas for the other models isothermal condition is assumed. The diffusive equilibrium solutions for several model inputs are illustrated in Figure 6 for comparison. The change in the best fit CH4 loss rate with continuously varying eddy mixing coefficient, K, and isothermal temperature, T, is illustrated in Figure 7. Some extreme models are able to reproduce the INMS CH4 data without invoking a large CH4 loss rate. If we restrict temperature in the 140–150 K range as implied by existing INMS analyses, the eddy mixing coefficient, K, has to be ∼(2–3) × 109 cm2 s−1 to suppress the CH4 loss rate below the typical nonthermal level [e.g., De La Haye et al., 2007]. If we use K values consistent with the INMS and GCMS 40Ar data, the neutral temperature has to be ∼165 K to maintain CH4 diffusive equilibrium. Occasionally the neutral temperature in Titan's upper atmosphere reaches such a high level [Westlake et al., 2011], but this only occurs for particular flybys and cannot be used as the globally averaged value.

Table 4. The Best Fit CH4 Loss Rates for Different Input Parameters of the Asymptotic Eddy Mixing Coefficient, K, and Isothermal Neutral Temperature, Ta
ModelK (cm2 s−1)T (K)L(CH4) (s−1)
  • a

    Diffusive equilibrium (DE) is obtained for some extreme choices of the model input.

12 × 107DFS123.0 × 1027
22.2 × 109DFS12DE
32 × 1071404.5 × 1027
42 × 1071502.7 × 1027
52.6 × 109145DE
62 × 107165DE
Figure 7.

(left) The best fit CH4 loss rate as a function of asymptotic eddy mixing coefficient, K, and isothermal neutral temperature, T. (top right) The variation of the CH4 loss rate with K when T is fixed to 145 K (bottom right) the CH4 loss rate with T when K is fixed to 2 × 107 cm2 s−1. The inference of strong CH4 escape on Titan is based on the optimal range of these two parameters, as constrained by our current knowledge of the N2 and 40Ar density structures.

[46] We conclude that strong CH4 escape does occur on Titan, with a globally averaged loss rate of ∼3 × 1027 s−1 which is many orders of magnitude higher than the Jeans rate. We reach this conclusion by combining our knowledge of (1) the 40Ar structure throughout the entire atmosphere based on the INMS and GCMS data and (2) the CH4 structure in the 1200–1600 km range based on the INMS data only. The inclusion of the GCMS 40Ar data (obtained well below the homopause) is essential for constraining the eddy mixing profile since the INMS 40Ar mixing ratio (obtained well above the homopause) is not sensitive to K when K ≪ Di. In contrast, we do not require that the CH4 model profiles reproduce the GCMS CH4 mixing ratio of 1.48% [Niemann et al., 2010]. For example, the gray solid line in Figure 6, when extrapolated downward with equation (5), approaches asymptotically 1.25% in the lower stratosphere. We expect that the difference in the stratospheric CH4 mixing ratio could be compensated for by including chemical destruction terms in the model calculations [Strobel, 2012].

3.3. How Variable Is CH4 Escape on Titan?

[47] In this section, we investigate the variability of CH4 escape and search for potential trends with solar and/or magnetospheric conditions. We derive for each flyby the best fit CH4loss rate with the one-dimensional, steady state diffusion model based on a common eddy mixing profile withK ≈ 2 × 107 cm2 s−1. Using different K values gives very similar results as eddy mixing is unimportant at the altitudes involved in the model fitting. This is justified by Figure 7 (top right), which shows that over the range of possible K values (several 107 cm2 s−1), the impact of eddy mixing is small. The neutral temperature is obtained from the hydrostatic fitting to the N2 densities for each flyby, assuming isothermal.

[48] More specifically, we evaluate the best fit temperature and CH4 loss rate, as well as their uncertainties, with a Monte Carlo approach [e.g., Pang, 2006]. For a given flyby, we obtain the large-scale trends for N2 and CH4in Titan's upper atmosphere based on the third-order polynomial fittings to the logarithmic N2/CH4 densities as a function of altitude. We then generate 1000 random realizations of the N2 and CH4profiles of this flyby that encompass the apparent wiggles in the INMS data around the large-scale trends. This is accomplished by artificially placing random fluctuations around the polynomial fits with altitude dependent magnitudes equal to the measured density variations along the spacecraft trajectory. For each random realization, we apply isothermal fitting to N2 and diffusion model fitting to CH4. The averages (standard deviations) of the random temperature and loss rate values are then taken to be their respective best fit values (uncertainties). The wiggles in the data are contributed not only by counting statistics but also by gravity wave perturbations which are persistently seen in Titan's upper atmosphere [e.g., Fulchignoni et al., 2005; Müller-Wodarg et al., 2006; Koskinen et al., 2011]. Variations due to counting statistics are ∼(1–2)% at a reference altitude of 1400 km (C09) and the wave amplitudes are typically 10% of the mean densities [Müller-Wodarg et al., 2006]. In practice, the uncertainty due to density wiggles is more important than that due to counting statistics and that due to finite temperature gradient. The latter justifies the isothermal assumption adopted throughout this section.

[49] The best fit CH4 loss rates and neutral temperatures are detailed in Table 5. Nearly 1/3 flybys have been excluded either due to the insufficient coverage of the INMS data in the 1200–1600 km altitude range, or due to large variations of the INMS densities around the empirical trend that lead to significant uncertainties in the derived temperatures and loss rates. The former is primarily caused by INMS ram angles too large to allow accurate density determination, and the latter, as seen in the T37, T48 and T61 flybys, might be indicative of large amplitude wave structures in the ambient atmosphere. Since Table 5 only gives a portion of the available INMS sample, the average of the listed CH4 loss rates is not exactly identical to the value of 3.0 × 1027 s−1 reported in section 3.2. Also note that the neutral temperatures listed in the table are not exactly equal to those of Westlake et al. [2011] due to different altitude ranges used for isothermal fitting.

Table 5. The Best Fit CH4 Loss Rate Calculated From the Diffusion Model Fitting to the Updated INMS CH4 Data for Each Flyby in Our Samplea
FlybyDate (Earth Day)LAT LONSZALSTT(K)L(CH4) (1027 s−1)e 0.6 eV to 5 MeVIons 1 eV to 50 keVp* 27–255 keV
  • a

    Also listed are the date of observation in units of Earth days before (indicated by negative) or after (indicated by positive) equinox (on 11 August 2009), latitude (LAT), longitude (LON), solar zenith angle (SZA), local solar time (LST), as well as the characteristics of the ambient plasma following the classification schemes of Rymer et al. [2009], Németh et al. [2011] and Garnier et al. [2010]. Heavy-riched means events enriched with heavy ions. The geophysical parameters are given for a reference altitude of 1400 km;p* indicates energetic protons. The uncertainties of T and L(CH4) as well as the upper limits for L(CH4) are evaluated with a Monte Carlo approach which takes into account the effects of both counting statistics and density fluctuations due to wave structures.

T5−157867°N355°108°17:40156 ± 23.8 ± 0.5Plasma sheetPlasma sheetMedium
T18−105375°N111°102°06:50121 ± 2<1.9Lobe-likeLobe-likeHigh
T21−97360°N229°132°22:41157 ± 22.0 ± 0.5MixedMixedHigh
T23−94152°N20°67°12:34147 ± 2<1.2Plasma sheetPlasma sheetMedium
T25−9015°N25°172°23:58171 ± 32.2 ± 0.3UnidentifiedUnidentifiedLow
T26−8857°N11°166°00:52143 ± 22.4 ± 0.2BimodalHeavy-richedMedium
T28−85425°N13°164°00:41143 ± 2<0.9MixedMixedHigh
T29−83834°N14°157°00:32157 ± 32.0 ± 0.4Plasma sheetPlasma sheetMedium
T30−82242°N17°150°00:19155 ± 22.5 ± 0.3MixedMixedMedium
T32−79057°N24°135°23:47131 ± 2<0.9MagnetosheathMagnetosheathHigh
T36−67949°S63°93°19:10180 ± 42.9 ± 0.2Plasma sheetPlasma sheetHigh
T39−60075°S71°83°18:31120 ± 3<0.7Plasma sheetPlasma sheetHigh
T40−58420°S104°63°16:16138 ± 21.2 ± 0.3BimodalHeavily enrichedMedium
T42−50439°S127°46°14:32158 ± 21.5 ± 0.4MagnetosheathMagnetosheathHigh
T43−4563°N114°50°15:15107 ± 3<2.2Lobe-likeMixedHigh/Medium
T50−18658°S328°120°00:17138 ± 3−2.5 ± 0.8MixedMixedHigh
T56−677°S164°160°22:47122 ± 6<1.6Mixed-High
T57−5117°S163°155°22:48151 ± 54.1 ± 1.0Mixed-High/Medium
T58−3527°S162°148°22:48149 ± 45.7 ± 0.7Plasma sheet-Medium
T59−1936°S161°140°22:52141 ± 1−1.2 ± 0.3Mixed-Medium
T6515358°S20°112°03:17146 ± 2<1.9---
T7132944°S341°105°04:58140 ± 12.5 ± 0.3---

[50] Several examples of the INMS CH4 mixing ratio profiles are presented in Figure 8 between 1200 and 1600 km. The diffusive equilibrium models are indicated by the dashed lines for comparison. Figure 8 reveals a large variability in the pattern of CH4 bulk flow. The T5, T29 and T71 plots correspond to cases with strong CH4 outflow at the level of several 1027 s−1. The T23 and T39 plots show cases with CH4 distributions under approximate diffusive equilibrium. The inference of diffusive equilibrium for a specific flyby is made based on the criterion that the actual best fit flux is less than 3 times the flux uncertainty. The T50 plot is an example with the best fit CH4 flux being inward. Cases with CH4 outflow are seen in 12 out of 22 flybys in our sample (∼55%). The diffusive equilibrium cases are seen in eight flybys (∼36%), and for each of them we provide in Table 5 the corresponding 3σ upper limit of the CH4 outflow rate. Finally, cases with CH4 inflow are seen in only two flybys. The variability of CH4 bulk flow revealed by Table 5 is considerably larger than that for H2, which remains roughly constant among different flybys [Cui et al., 2011]. The INMS data used for this study have been acquired primarily under solar minimum conditions, with ∼10% variance in solar activities based on either the F10.7 cm or 121.6 nm solar irradiance, as reported by the space weather prediction center of the National Oceanic and Atmospheric Administration (NOAA). Not surprisingly, it would be difficult to explain the variability of CH4bulk flow as solar-driven only.

Figure 8.

The INMS CH4 mixing ratio profiles for several example flybys and categories with different solar and/or magnetospheric conditions. For comparison, the dashed line gives the diffusive equilibrium (DE) model. A considerable variability inCH4 structure is revealed and suggests that CH4escape on Titan is more likely to be sporadic rather than steady. Specifically, cases with strong escape include T5, T29, T71, T50, the nightside (night) category and the plasma sheet (PS) category, whereas the data from T23, T39, the dayside (day) category and the lobe-like (lobe) category are reasonably described by diffusive equilibrium.

[51] Table 5 also shows that the CH4 flow in Titan's upper atmosphere is preferentially outward. If the flows from individual flybys were eventually associated with horizontal transport rather than escape [Tucker and Johnson, 2009], a considerable portion of the flybys with inward flow would be expected in our sample. But the INMS data do not support this. In the following we will interpret the CH4 flux derived for any individual flyby as an escape flux, except for the two flybys with best fit CH4 flux being negative. This means we assume the true sinks of CH4 molecules reside far away in the interplanetary space rather than some horizontally connected regions on Titan [see also Yelle et al., 2006]. A rigorous evaluation of such an issue will be presented in a future paper (I. C. F. Müller-Wodarg et al., The role of thermospheric winds on the distribution of CH4 and 40Ar in Titan's upper atmosphere, manuscript in preparation, 2012). It is also worth mentioning that the observed variability in CH4 structure could be either spatial or temporal. If the latter is dominant, the variability reported here is not necessarily indicative of horizontal transport.

[52] One of the prominent features revealed by Table 5 is that strong CH4 escape preferentially occurs on the nightside. We note that for the five flybys with dayside trajectories (defined here as SZA < 90° at a reference altitude of 1400 km), three (T23, T39 and T50) show CH4 distributions under approximate diffusive equilibrium, and two of the remaining flybys (T40 and T42) are characterized by relatively small CH4 loss rates of ∼1.2 × 1027 s−1 and ∼1.5 × 1027 s−1. In contrast, all the three flybys with the largest CH4 escape rates (>3 × 1027 s−1) occur deep in the nightside. The above difference is clearly seen in Figure 8 (third column), where we compare the diffusive equilibrium distribution for CH4with the INMS profile averaged over all measurements made on the dayside or nightside. This is obviously in conflict with the expectations of any solar-driven model. Other features consistent with this include the nondetection of appreciable difference in CH4 loss rate between the equatorial region and the polar region, or between preequinox and postequinox. Both meridional and seasonal trends might be present if CH4loss from Titan is primarily solar-driven, analogous to the findings of the variation of N2/CH4 densities and neutral temperature with latitude (MW08), as well as the decrease in altitude of the detached haze layer from before to after the equinox [West et al., 2011].

[53] The above discussions motivate us to investigate the magnetospheric response of CH4 escape on Titan. Ideally, varying plasma conditions are encountered for different zonal sectors. The actual situation is however more complicated, and a better categorization can be made in terms of the varying levels of electron precipitation in the 0.6 eV to 5 MeV range [Rymer et al., 2009], ion precipitation in the 1 eV to 50 keV range [Németh et al., 2011], or energetic proton precipitation in the 27–255 keV range [Garnier et al., 2010]. Following these works, we list in Table 5 the characteristics of Titan's plasma environment for reference.

[54] Table 5 reveals that there is no systematic trend in CH4 loss rate with longitude, and there is no evidence for elevated CH4 escape with enhanced energetic proton precipitation or with the presence of enriched water group ions peaking at ∼4400 eV [Németh et al., 2011]. The latter is indicated by the e classification of bimodal in Table 5. However, we do identify a tentative trend with magnetospheric electron precipitation. This is illustrated in Figure 8 (fourth column), where we compare the INMS CH4mixing ratio profiles averaged over the plasma sheet and lobe-like categories with the respective diffusive equilibrium profiles. It is clear that strong CH4 escape does occur for plasma sheet conditions, characterized by a relatively high peak electron flux of ∼3.5 × 105 to 1.2 × 106 cm−2 s−1 sr−1 in the 120–600 eV energy range [Rymer et al., 2009]. We note that among the six flybys in our sample that belong to this category, four show strong CH4 escape on Titan. Especially, this category includes two of the three flybys with the largest CH4 loss rates in Table 5. In contrast, for each of the two lobe-like flybys in our sample, the INMS CH4 distribution is reasonably described by diffusive equilibrium. According to Rymer et al. [2009], lobe-like conditions are characterized by an incident electron flux a factor of 10 lower than the plasma sheet value in a similar energy range. The magnetosheath category (not shown inFigure 8) also includes two flybys: one under diffusive equilibrium and the other one with a relatively low CH4 loss rate of ∼1.5 × 1027 s−1. The incident electron flux for this category is comparable with the plasma sheet category but shifts to lower energies peaking at ∼50 eV. Thus, if electron precipitation drives CH4 escape on Titan, then the relevant electron energy range is more likely at the level of several hundred eV or above.

[55] In Table 6 we summarize the mean CH4 loss rates for all categories that we consider above, along with the corresponding mean neutral temperatures. These are obtained from the isothermal and diffusion model fittings to the N2 and CH4 density profiles averaged over each category, rather than simply taking the averages over values in Table 5. The interpretation of the results in Table 6 deserves some caution. For most of the categories, the variations in CH4 loss and neutral temperature are so large that comparisons between different categories do not lead to conclusive results. Thus, some of the tendencies revealed by Table 6, such as the preferential occurrence of strong CH4escape at the anti-Saturn side, are not statistically significant. The most rigorous conclusions that we can draw for the variability in CH4escape are probably the diurnal difference and the trend with varying electron precipitation, as the dayside and lobe-like categories are the only two cases inTable 6 with CH4 distribution under diffusive equilibrium. The implications of these features have already been discussed above.

Table 6. Mean CH4 Loss Rates and Neutral Temperatures for Different Categories of Titan Flybysa
CategoryNeutral Temperature (K)CH4 Loss Rate (s−1)Flybys Included
  • a

    Also shown are the flybys included in each category. The diffusive equilibrium (DE) model provides reasonable description of the CH4data on the dayside and for lobe-like plasma conditions.

Dayside148DET23, T40, T41, T42, T43, T48
Nightside1502.1 × 1027T21, T25, T26, T28, T29, T30, T32, T50, T55, T56, T57, T58, T59
Equatorial1452.1 × 1027T25, T26, T28, T37, T40, T43, T48, T55, T56, T57, T58, T61
Polar1533.1 × 1027T5, T16, T18, T19, T39, T49, T64
Sub-Saturn1522.3 × 1027T5, T23, T25, T26, T28, T29, T30, T32, T50, T64, T65, T71
Anti-Saturn1403.3 × 1027T16, T48, T49, T51, T55, T56, T57, T58, T59, T61
Ramside1572.0 × 1027T21
Wakeside1502.0 × 1027T18, T19, T36, T37, T39, T40, T41, T42, T43
Preequinox1532.3 × 1027all flybys up to T59
Postequinox1392.2 × 1027T61, T64, T65, T71
Plasma sheet1593.3 × 1027T5, T19, T23, T29, T36, T39, T49, T51, T55, T58
Lobe-like115DET18, T41, T43, T61
Bimodal1411.9 × 1027T26, T40
High proton flux1512.0 × 1027T18, T19, T21, T28, T32, T36, T39, T42, T50, T51, T56
Medium proton flux1511.9 × 1027T5, T23, T26, T29, T30, T37, T40, T49, T58, T59
Low proton flux1712.2 × 1027T25

[56] The recent INMS investigation of Westlake et al. [2011] has revealed a trend of enhanced neutral temperature in Titan's upper atmosphere when exposed to elevated electron precipitation. Thus, CH4 escape and neutral heating tend to occur under similar conditions. This may imply a potential correlation between the CH4 loss rate and the neutral temperature, but the scattering of such a relation is quite large, as indicated in Figure 9. Indeed, Table 6 shows that a similar temperature is derived for both the dayside and nightside categories, but the CH4 escape rates for the two categories are significantly different.

Figure 9.

The CH4 loss rate, L(CH4), as a function of the neutral temperature, T, for all flybys with strong CH4 escape confirmed at >3σ significance level (see text for details). No rigorous correlation can be identified between the two quantities.

[57] At the face value, the variability in CH4 escape revealed by Table 6 implies that CH4 escape on Titan is more likely to be magnetospherically driven rather than solar driven. However, one important consideration complicates the above argument: In response to varying solar and/or magnetospheric conditions, the change in CH4 distribution occurs within the diffusion timescale, inline image h, where we have used a CH4 scale height, Hi, of ∼200 km and a CH4 molecular diffusion coefficient, Di, of ∼5 × 1010 cm2 s−1 referred to 1400 km. For comparison, the timescale over which solar inputs vary, τsolar, is about half a Titan day, i.e., τsolar ≈ 200 h. This is significantly longer than τdiff, ensuring that the solar response of CH4 escape on Titan, if present, can in principle be observed in the INMS data. However, this is not necessarily the case for magnetospheric variations. Simon et al. [2010] have shown that on the nightside of Titan, the timescale for magnetic field variability could be as long as 5 h, whereas on the dayside, the timescale is typically 102 s. Thus, the timescale for magnetospheric variations is either comparable with or much shorter than τdiff. For such cases, the time response of the CH4 structure is not fast enough to leave an observable effect during a Titan encounter, and accordingly the apparent trend of CH4 escape with magnetospheric electron precipitation may simply be a coincidence.

4. Concluding Remarks

[58] The inbound INMS data from 32 Cassini flybys with Titan are analyzed in this work, focusing on the CH4 structure in the upper atmosphere of the satellite. Several updates in the data reduction algorithms have been implemented, including the improved treatment of the counter saturation characteristics, the removal of instantaneous transition in the N2 and CH4 density profiles, as well as the appropriate decoupling between 40Ar and other minor species. The analysis presented here is aimed at (1) solving the inconsistency in the interpretation of the CH4 data between existing works [e.g., Y08; Bell et al., 2011] and (2) investigating the variability of CH4 escape among different flybys. Several questions raised in this paper are listed below along with our findings.

[59] 1. How important is eddy mixing on Titan? We use a diffusive equilibrium model to describe the 40Ar mixing ratio profile, combining both the INMS data in the upper atmosphere and the GCMS data in the lower stratosphere [Niemann et al., 2010]. The globally averaged asymptotic eddy mixing coefficient is K ≈ 2 × 107 cm2 s−1, based on the standard chemical model of Strobel [2012] as the input background atmosphere. The corresponding homopause level is at ∼850 km, consistent with the early result of Y08 but in conflict with the 1000 km level suggested by Bell et al. [2011]. Over the altitude range probed by the INMS, molecular diffusion is significantly more important than eddy mixing. This has important impacts on the interpretation of the INMS CH4 data.

[60] 2. Does strong CH4 escape occur on Titan? With the current knowledge of eddy mixing (derived from the 40Ar data) and neutral temperature (derived from the N2 data), we conclude that strong CH4 escape must occur on Titan. The nominal CH4 loss rate is ∼3 × 1027 s−1 or 80 kg s−1 in a globally averaged sense, in general agreement with the early results of Y08 and Strobel [2008, 2009]. The CH4 loss rate is not a linear response of the ambient atmospheric parameters, as revealed by Figure 7. In practice, the CH4 loss rate can only be reliably inferred when it is near or above the level of 1027 s−1. This is fortunately the case for Titan's upper atmosphere, making it possible to constrain the globally averaged CH4 loss rate with a diffusion model. The strong CH4 escape implied by the INMS data makes only a small contribution to the CH4 budget on Titan, with the bulk of the CH4 molecules supplied from Titan's interior photochemically converted to more complex hydrocarbons [Strobel, 2009]. The main uncertainty in the derived globally averaged CH4 loss rate is associated with the choice of the temperature profile. The possible range of CH4 loss rate is ∼(2.7–4.5) × 1027 s−1 in accord with the range of average temperature reported in existing works [e.g., Y08; C09; Westlake et al., 2011].

[61] 3. How variable is CH4 escape on Titan? Cui et al. [2011] have shown that the H2 escape remains roughly stable from flyby to flyby, but the analysis in this work reveals a large variability of CH4 escape on Titan. Specifically, about half of the flybys show evidences for strong CH4 escape at the level of several 1027 s−1, whereas for most of the other flybys, the CH4 structures are reasonably described by diffusive equilibrium. This suggests that CH4 escape on Titan is more likely a sporadic rather than a steady process. CH4 inflow may also occur on Titan, though only occasionally. We search for systematic trends in CH4 escape with varying solar and/or magnetospheric conditions. We find that strong CH4escape preferentially occurs on the nightside, in conflict with the expectations of any solar-driven model. However, no rigorous connection can be identified between the CH4 loss rate and the precipitation of various magnetospheric species, except for an apparent trend of elevated CH4escape for plasma sheet conditions as compared to lobe-like conditions. But this may simply be a coincidence as the time response of the CH4 structure to magnetospheric inputs is not fast enough to leave an observable effect during a Titan encounter. The main uncertainties in the CH4loss rates derived for individual flybys are associated with the density fluctuations around the large-scale trends, presumably due to wave structures in the ambient atmosphere.

[62] In a more general context, how magnetospheric particle precipitation influences the structure of Titan's neutral atmosphere has recently drawn significant attention. This is a highly complicated and variable process, which may leave a variety of observational signatures. Elevated neutral temperature has been found to preferentially, but not always, occur under plasma sheet conditions [Westlake et al., 2011]. Thus, neutral heating and CH4 escape may represent intermediate processes of a complex interaction between Titan's upper atmosphere and magnetosphere, if the enhanced CH4 escape associated with plasma sheet (see section 3.3) is realistic. The relative importance of particle precipitation depends on the depth in the atmosphere, with different magnetospheric species depositing most of their energies at different altitude levels, either above or below where solar EUV/FUV radiation dominates[e.g., Michael and Johnson, 2005; Cravens et al., 2008, Smith et al., 2009]. The access of incident charged particles, especially electrons, into Titan's atmosphere is also strongly controlled by the ambient magnetic field configuration, which could be either a barrier or a gate [e.g., Galand et al., 2006; Ma et al., 2009; Richard et al., 2011]. Due to the above complexities, it is by no means possible to obtain any conclusive result based on a simple comparison between broad categories, as done in this work. Simulations of Titan's plasma-atmosphere interactions on a flyby-to-flyby basis and with realistic model inputs are required to eventually pin down the role of magnetospheric inputs on Titan's neutral atmosphere.

Acknowledgments

[63] J.C. acknowledges support from the National Science Foundation of China through grant NSFC-41174146. D.F.S. was supported by the Cassini-Huygens mission through JPL contract 1353551 and NASA grant NNG05G091G. I.M.W. acknowledges support from the UK Science and Technology Facilities Council (STFC).