JOURNAL OF GEOPHYSICAL RESEARCH, VOL. ???, XXXX, DOI:10.1029/,

Horizontal structures and dynamics of Titan’s thermosphere

I. C. F. Muller-Wodarg,1, R. V. Yelle2, J. Cui2 and J. H. Waite3

Abstract.

Observations by the Cassini Ion Neutral Mass Spectrometer (INMS) measure the lat-itude and height structure of N2 and CH4 densities in Titan’s thermosphere between 1000and 1600 km altitude. We have used the observations to construct an empirical modelthat describes the mean state of the thermosphere in the northern hemisphere, ignor-ing local time and longitude changes. The principal features in the INMS data are wellreproduced by this simple latitude-height model. We find a pronounced oblateness in thethermosphere, with densities above 1100 km altitude increasing by around 70% from thenorthern (winter-) pole to the equator, resulting in isobaric surfaces being '45 km higherover the equator than at the northern pole. Thermospheric temperatures derived fromthe densities are nearly isothermal above 1200 km at 146±13 K but near 1000 km al-titude reach 167±6 K at the equator and 132±6 K near the pole. Using our Thermo-sphere General Circulation Model with this thermal structure imposed, we derive ther-mospheric horizontal wind speeds reaching 200 m s−1, with primarily poleward flow atequatorial latitudes which, northward of around 60◦N, is accompanied by a band of pro-grade zonal winds of up to 150 m s−1. At high latitudes diverging horizontal winds gen-erate regions of strong subsistence with vertical velocities of up to -30 m s−1. We findthermospheric dynamics to be sensitive to coupling from below. CH4 abundances are en-hanced in the northern polar region, which may result from transport by thermosphericwinds.

1. Introduction

Before the arrival of Cassini/Huygens at the Saturniansystem, the most detailed observations of Titan’s thermo-sphere were made by the Voyager 1 Ultraviolet Spectrome-ter solar occultation experiment and dayglow measurementsin November 1980 [Broadfoot et al., 1981], yielding thermo-spheric densities of N2, CH4 and C2H2 in the morning andevening terminators at near-equatorial latitudes, from whichexospheric temperatures of 196±20 K and 176±20 K wereinferred, respectively [Smith et al., 1982]. A comprehen-sive reanalysis of these data by Vervack et al. [2004] re-vised the original density values by Smith et al. [1982] andinferred lower temperatures of 153-158 K. On January 14,2005, the Huygens probe descended through Titan’s atmo-sphere, with its Atmospheric Structure Instrument (HASI)measuring total atmospheric density below 1400 km alti-tude by recording the decelaration of the probe by atmo-spheric drag. These measurements were carried out at near-equatorial latitudes, giving the first continuous profile of at-mospheric density from the thermosphere to the troposphereof Titan. The derived pressure scale heights yielded at-mospheric temperatures which in the thermosphere rangedfrom around 140-200 K, with strong oscillations of up toaround 10 K amplitude around a mean temperature valueof ∼175 K [Fulchignoni et al., 2005]. In December 2004the Cassini Ultraviolet Imaging Spectrometer (UVIS) ob-served two stellar occultations and derived vertical profiles

1Space and Atmospheric Physics Group, Imperial CollegeLondon, London, UK.

2Lunar and Planetary Laboratory, University of Arizona,Tucson, Arizona, USA.

3Center for Excellence in Analytical Mass Spectrometry,Southwest Research Institute, San Antonio, Texas, USA.

Copyright 2007 by the American Geophysical Union.0148-0227/07/$9.00

of CH4 and minor hydrocarbon species between around 450and 1600 km altitude near latitudes of 36◦S and 35-75◦N[Shemansky et al., 2005].

On October 26, 2004, the Cassini spacecraft carried outits first in-situ measurements of Titan’s upper atmospheredown to a closest approach altitude of 1174 km. Duringthis and the following targeted low altitude flybys the Ion-Neutral Mass Spectrometer (INMS) instrument on boardthe spacecraft [Waite et al., 2004] measured altitude profilesof neutral atmospheric constituents at an unprecedentedlevel of detail, both in terms of species characteristics andspatial resolution. Analyses of the two earliest flybys in-ferred exospheric temperatures of 149±3 K near 39◦N at theevening terminator [Waite et al., 2005; Yelle et al., 2006] andbetween 154–162 K near 74◦N close to midnight local time[Muller-Wodarg et al., 2006; De La Haye et al., 2007]. Theseearly analyses of the INMS measurements suggested an un-expected trend of temperatures in Titan’s thermosphere,with larger values in locations of lower solar EUV energydeposition. As pointed out by Muller-Wodarg et al. [2006],these analyses of density profiles from any single flyby werehowever potentially affected by horizontal structures in Ti-tan’s thermosphere, introducing an uncertainty in the tem-perature determination that could not be resolved with theavailable datasets.

Between 2005 and 2007, the INMS measured thermo-spheric densities during 13 targeted flybys, a dataset thatallows for the first time a more comprehensive determinationof horizontal structures on Titan. This study will present ananalysis of the INMS dataset available to date, constructingan empirical model that describes the latitude-height pro-files of N2 and CH4 densities between 1000 and 1600 kmaltitude in Titan’s northern hemisphere. We will use thisinformation to constrain dynamics in the thermosphere andinvestigate how winds affect the distribution of constituentssuch as CH4. Section 2 will describe the data reduction andempirical model, in Section 3 we will analyze the latitudinalstructures of density and temperature, Sections 4 and 5 willpresent calculations of thermospheric winds and investigatehorizontal variations of CH4 mole fractions. Our results arediscussed in Section 6.

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2. Observations and empirical model

2.1. The Titan flyby trajectories

The INMS measurements used in this study were takenduring 13 targeted Titan flybys which occurred betweenApril 16, 2005 (T5) and June 13, 2007 (T32). Main char-acteristics of the flybys are shown in Figure 1 and listedin Table 1. All flybys considered here sampled only thenorthern hemisphere of Titan. Altitudes of closest approach(C/A) ranged from 950 km (T16) to 1025 km (T5), latitudesat C/A ranged from 30.36◦N (T25) to 85.50◦N (T16). Asshown in the top left panel of Figure 1, 5 of the closestapproaches occurred in the daytime sector, but most solarzenith angles (bottom right panel) are larger than 90◦, im-plying that the majority of measurements were taken dur-ing dusk or night conditions. Due to the uneven coverage ofdayside and nightside passes, we will in this study not in-vestigate local time changes in the thermosphere. Similarly,the majority of flybys occurred within the 60◦E to 60◦Wlongitude sector (bottom left panel), so we will not attemptto study longitude variations.

Figure 1 illustrates the geographic coverage of INMS mea-surements considered in this study. At altitudes abovearound 1300 km most latitudes from the equator to around80◦N are well sampled, whereas below that height the re-gions equatorward of 15-20◦ are poorly sampled. In thisstudy we consider only data taken below 1600 km altitude.

2.2. Data Reduction

In this paper, we examine Cassini Ion Neutral Mass Spec-trometer (INMS) data obtained in the Closed Source Neu-tral (CSN) mode, which is specifically designed for measure-ments of unreactive neutral species detected in the atmo-sphere of Titan or other INMS targets [Waite et al., 2004].The data consists of a sequence of ratios of counting rate ver-sus mass-to-charge ratio, m/z, from m/z=1 to 99 amu perelectron charge. In all flybys and for all channels relevantto this work, the INMS samples Titan’s upper atmospherewith a time resolution of ∼0.9 sec, corresponding to a spa-tial resolution of ∼5.4 km along the spacecraft trajectory,for a typical flyby velocity of 6 km s−1 relative to Titan.

The INMS data can be analyzed in two ways. For majorconstituents in Titan’s atmosphere (N2, CH4), density pro-files can be obtained directly from counts in relevant masschannels (usually the channels of main peaks in their crack-ing patterns) as a function of altitude [Yelle et al., 2006].In contrast, analysis of minor constituents (C2H2, C2H4,etc.) requires careful modeling of mass cracking patterns inthe observed full mass spectrum. The full mass spectrumis usually obtained by integrating the counts in all channelsover a particular altitude range. The spectral analysis usedto determine minor species densities is described elsewhere[Waite et al., 2005; Cui et al., 2007]. Here, we present themethodology used in determination of major species densi-ties.

The INMS flight unit (FU) was calibrated prior to launchwith a small number of reference gases, including N2 andCH4. In our analysis, these sensitivities are used to infernumber densities from count rates. However, the N2 andCH4 gases are mixtures of their isopotes and isotopic ratiosmay differ in the atmosphere of Titan and Earth and mayvary with altitude. It is therefore necessary to determinesensitivities for N2,

14N15N, CH4 and 13CH4 separately, al-lowing for the possibility of different isotope ratios on Titan.Details of the procedure are described in Cui et al. [2007].Here, we concentrate exclusively on the main isotopes.

The INMS has both a high gain counter (C(1)) and a lowgain counter (C(2)). The C(1) counts in channels m/z=28,29 and 16 are used to determine the densities of N2,

15N14N,

CH4 and 13CH4 when possible. However, the C(1) counterfor channel 28 becomes saturated below ∼1,300 km in allflybys and is likely to be saturated for channels 14, 15, 16and 29 at low altitude passes. When this happens we de-termine densities either from C(2) counts of the main peakchannel or alternatively from C(1) counts in other channelswhere the cracking pattern of the species shows sufficientlylarge counts. For the former case, the C(2)/C(1) conversionfactor has to be determined. For the latter case, calibrationbetween density values determined from different channelsis required to ensure consistency. This may be associatedwith the fact that the dissociative ionization of a moleculeimparts the dissociation fragments with excess kinetic en-ergy which may affect the way that the fragment ions aretransmitted through the ion optics of the INMS. In all cases,we assume that the densities inferred from the main peakchannel of a given species are correct, to which we calibratedensities determined from other channels.

The cracking pattern of N2 has peaks at m/z=28 and 14,produced by N+

2 and N+ ions. To derive N2 densities, weuse C(2) counts in channel 28 below 1,100 km (where C(1)

counts in channels 14 and 28 are both saturated), we use C(1)

counts in channel 28 above 1,300 km where it is not satu-rated, and we use C(1) counts in channel 14 between 1,100and 1,300 km (where C(1) counts are saturated in channel28 but not in channel 14). The switch to counts in channel14 for the density determination at intermediate altitudes isbased on the consideration that C(1) counts in channel 14are always much higher than C(2) counts in channel 28 andtherefore have a higher signal-to-noise ratio.

For calibration of N2 densities determined from differ-ent channels, we calculate the ratio of the N2 density de-termined from channel 28 to that determined from channel14 between 1,300 and 1,600 km for each flyby. The lowerboundary is selected to ensure that C(1) counts are not af-fected by saturation. Counts of channel 14 are contributedby both N2, CH4, and 14N15N, and the contributions fromCH4 and 14N15N have to be subtracted for an accurate de-termination of N2 densities from this channel. Here CH4

densities are calculated from C(1) counts in channel 16, and14N15N densities from C(1) counts in channel 29. Based onthe above procedure, we obtain a N2 scaling factor for chan-nel 14, which varies by 5% from flyby to flyby and has anaverage value of 0.79.

The C(2)-C(1) conversion factor for channel 28 can inprinciple be determined by taking the average ratio of C(1)

counts to C(2) counts at the same altitudes where the C(1)

counter is not saturated for channel 28. However, C(2)

counts are very low in regions where C(1) counts are notsaturated, making it difficult to estimate the conversion fac-tor from counts in channel 28 directly. Instead, we use theprocedure described above to determine N2 densities above1,100 km from C(1) counts in channel 14, and then predictthe corresponding C(1) counts in channel 28. Here the N2

scaling factor for channel 14 as determined above has beenused for calibration. With the predicted C(1) counts andmeasured C(2) counts in channel 28, the C(2)-C(1) conver-sion factor can be calculated accurately, assuming that it isa constant for each flyby. This conversion factor varies by6% from flyby to flyby, with an average value of 5,470.

As an example, we show in Figure 2 the altitude profileof N2 densities calculated from C(1) (black crosses) and C(2)

(blue squares) counts of channel 28, as well as C(1) counts(red plus signs) of channel 14, for the inbound measure-ments taken at the T16 flyby (July 22, 2006). The dottedlines mark where the determination of N2 densities switchfrom one algorithm to another.

The cracking pattern of CH4 has peaks at m/z=12, 13,14, 15 and 16, produced by CH+

x ions where x ranges from0 to 4. In most cases, the CH4 densities can be determinedaccurately from C(1) counts in channel 16. The contribution

MULLER-WODARG ET AL.: HORIZONTAL STRUCTURES AND DYNAMICS ON TITAN X - 3

from 13CH4 to m/z=16 has to be subtracted, with 13CH4

densities easily obtained from C(1) counts in m/z=17. How-ever, the C(1) counter of channel 16 becomes saturated be-low ∼1,100 km, and the CH4 densities have to be calculateddifferently in that region. C(2) counts in channel 16 can-not be used since they are too noisy. Since C(1) counts inchannels 14 and 15 may also be saturated at low altitudesand have large contributions from N2 and 15N14N, we useC(1) counts in channels 12 and 13 to determine CH4 densi-ties below 1,100 km. Counts in channels 12 and 13 are alsocontributed by C2H2 and C2H4 and for channel 13, 13CH4

provides an additional contribution. All these minor contri-butions have to be subtracted. While 13CH4 densities areeasily obtained from C(1) counts in channel 17, an estimateof C2H2 and C2H4 is uncertain since these two species havecomplex cracking patterns. Counts in channels 24, 25 and 26can in principle be used to constrain densities of C2H2 andC2H4, with minor contributions from other hydrocarbons(C2H6, C3H8, C6H6, etc.) ignored. However, the crackingpatterns of C2H2 and C2H4 are very similar for channels 24,25 and 26, in the sense that the branching ratios of C2H2

are approximately a factor of 3 higher than those of C2H4

for all these channels but the relative signals are the same.This implies that counts in these channels can only be usedto constrain the linear combination of C2H2 and C2H4 den-sities, in the form of nC2H2 + 1

3nC2H4.

Assuming pure C2H2, counts in each of the channels 24,25 and 26 give an independent estimate of the C2H2 den-sities. At any given altitude, the mean value is adoptedand used to calculate the contribution from C2H2 to chan-nels 12 and 13. With contributions from C2H2 and 13CH4

subtracted, the remaining counts in these two channels canthen be used to determine CH4 densities. In the alternativeextreme case in which we assume pure C2H4, we obtain sim-ilar densities of CH4, consistent with the results for the pureC2H2 case within 1-sigma uncertainties. This similarity ismainly due to the fact that the contributions from C2H2 andC2H4 to channels 12 and 13 are small.

As for N2, CH4 densities determined from different chan-nels have to be corrected to ensure consistency among densi-ties in different altitude ranges. The scaling factors for CH4

for channels 12 and 13 are obtained similarly to the adjust-ments to N2 for channel 14 as described above. This resultsin a smooth CH4 density profile for each flyby, which doesnot show any discontuinity at 1,100 km where the densitydetermination switchs from channel 16 to channels 12 and13. In our analysis, the average value of CH4 density deter-mined from channels 12 and 13 is used at any given altitudebelow 1,100 km.

N2 and CH4 density profiles are extracted from INMSdata with the procedures described above, for both inboundand outbound measurements. The outbound measurementsof some minor species are strongly affected by absorptionfrom the walls of the instrument [Vuitton et al., 2007]. How-ever, this is not an issue for N2 and CH4 at lower altitudes.A comparison between the inbound and outbound densityprofiles averaged over all flybys to smooth out horizontalvariations shows that the inbound and outbound averageprofiles are nearly identical below ∼ 1800 km for both N2

and CH4, implying that the wall chemistry effect is not aconcern for this study.

2.3. Empirical model of Titan’s thermosphere

2.3.1. Construction of model

A major difficulty in deriving atmospheric propertiesfrom any single flyby is the fact that the spacecraft movesboth horizontally and vertically through Titan’s atmo-sphere. Typically the horizontal distance covered in Titan’satmosphere is at least a factor of 5 larger than the sam-pled height range. While density measurements from singleflybys are often displayed as a function of altitude, it is dan-gerous to interpret such figures as height profiles because

horizontal structures in the atmosphere also affect the mea-sured profiles. In order to overcome this difficulty, we haveused measurements from all flybys shown in Figure 1 to con-struct an empirical atmosphere model, allowing separationof the horizontal and vertical structures.

The INMS measures the densities of N2 and CH4, but weuse mass densities (ρ) and CH4 mixing ratios (χ(CH4)) inorder to construct the model and derive the N2 and CH4

densities from them. This is done as mass density is theimportant quantity for hydrostatic equilibrium, an impor-tant constraint assumed in the model for ρ. In constructingthe model we define an altitude grid from 1000 to 1600 kmwith a step size of 10 km and a latitude grid from 0 to 90◦Nwith a step size of 2◦. Since INMS measurement heights inmost cases do not coincide with the initial chosen altitudelevels, we carry out log-linear interpolations in altitude ofsurrounding values of ρ and χ(CH4) from relevant flybys onto the grid levels. Examples of resulting profiles are shownin Figures 3, 4 and 5 for altitudes 1030 km, 1200 km and1590 km, respectively.

At each height level we fit the latitude variations withfourth order Legendre polynomials, shown as dashed linesin Figures 3, 4 and 5. Since measurements are limited tothe northern hemisphere, only symmetric Legendre func-tions P0, P2 and P4 are used. We thus obtain at eachaltitude a set of 3 Legendre polynomial amplitude valueseach for ρ and χ(CH4). These amplitudes are plotted ver-sus height in Figures 6 and 7. The left panels in both figuresshow the P0 amplitudes, the middle and right panels are am-plitudes of P2 and P4, respectively, plotted as fractions ofP0.

In order to obtain a model that can be used for any arbi-trary altitude, we fit altitude dependent functions throughthe Legendre polynomial amplitudes, as shown in Figures6 and 7. For P0 amplitudes of ρ and χ(CH4) we usedthird order polynomial functions of the form P0 = A +Bz + Cz2 + Dz3, where z the altitude (in km). The ver-tical profiles of P2/P0 in ρ and χ(CH4) as well as P4/P0

in ρ were fit with a hyperbolical function of the formx = A + (B − A) · tanh{(z − C)/D}, where x =P2/P0

and P4/P0 [ρ]. We fit P4/P0 [χ(CH4)] with a simple lin-ear function P4/P0 [χ(CH4)] = A + Bz. The values forcoefficients A-D are given in Table 2. These sets of coeffi-cients define a simple model for the N2 and CH4 densitiesin Titan’s thermosphere. Since we used only INMS datafrom Titan’s northern hemisphere in constraining the Leg-endre polynomials, the model should not be applied to thesouthern hemisphere.

It should be noted that in constructing the empiricalmodel we did not consider any changes with time in Titan’satmosphere. The Cassini flybys used in this study occurredover a period of around 2.5 years, which allows for changesin season, solar EUV radiation and magnetospheric forcingto be visible in Titan’s thermosphere. Titan’s solar declina-tion angle changed from -23.34◦ (Oct 26, 2004) to -12.71◦

(Apr 10, 2007), so any seasonally induced variations will besmoothed in our model. To assess the variability of solarEUV flux, Table 1 lists the F10.7 cm flux (at 1 AU) for eachflyby. The values show that we sampled Titan mostly at so-lar minimum conditions, at an average F10.7 cm flux valueof 80 with a standard deviation of 21%. The solar EUVfluctuations, therefore are small and likely to cause minorvariations in Titan’s thermosphere over the time span ofthe observations.2.3.2. Atmospheric variability and model uncertain-ties

The empirical atmosphere model described in the previ-ous section is an average representation of Titan’s thermo-sphere as a function of altitude and latitude. We see in

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Figures 3, 4 and 5 the typical scatter of data points at dif-ferent altitudes around the Legendre fit curves. Also shownin the figures are the standard deviations, calculated fromthe differences between data points and the fitted functions.Figure 8 shows the standard deviations of mass density andCH4 mixing ratio as a function of altitude. While mass den-sity uncertainties range from 10 to 50% between 1000 and1600 km, those of CH4 lie between 20 to 25%. Solid anddashed lines are third degree polynomial fits to the stan-dard deviations, with coefficients listed as σρ and σCH4 inTable 2.

Two types of uncertainties affect the model, those inher-ent in the INMS measurements and those due to time andspatial variations in the atmosphere. Measurement errorsby the INMS are due to counting statistics as well as overallcalibration uncertainties and typically lie below 20%, im-plying that the deviations are due predominantly to localtime, longitude or univeral time variations not included inthe model. Spatial variations in Titan’s atmosphere notcaptured by the empirical model include local time and lon-gitude changes. As can be seen from Figures 3, 4 and 5, nosystematic trend with solar zenith angle is apparent in thedata, but this may in large part be due to the uneven statis-tics, with most measurements having been made at zenithangles larger than 110◦. Similarly, longitude coverage of themeasurements is at present insufficient to identify any lon-gitudinal trends, which could result from standing waves orthe magnetosphere interaction around Titan. As more mea-surements are made, future studies need to investigate thesepossible variations.

Calculations by Muller-Wodarg et al. [2000], using a 3-DGeneral Circulation Model (GCM) of Titan’s thermosphere,found diurnal and hemispheric variability of up to 10-20 K inthermospheric temperatures resulting from solar EUV heat-ing, largest above 1300 km. This is consistent with ourfinding here that the standard deviations of ρ increase withaltitude (Figure 8), so a large part of the spread may be dueto diurnal changes in Titan’s thermoshere driven by solarEUV heating on the dayside.

The presence of strong waves in Titan’s atmosphere isdiscussed by Fulchignoni et al. [2005] and Muller-Wodarget al. [2006]. Amplitudes of pressure and density perturba-tions in the thermosphere reached around 4-12%, consistentwith the standard deviation of measurements near 1000 km,but much smaller than those higher up. Waves such as thoseidentified by Muller-Wodarg et al. [2006] may therefore onlypartly explain the variability we find here. It should benoted, though, that the P2 amplitudes of χ(CH4) in Figure7 appear to contain wave-like variability with height, despiteconsisting of datasets scattered irregularly over time, whichwould be expected to ’wash out’ many of the wave features.

Variability in Titan’s upper atmosphere may in part alsobe caused by changes in solar and magnetospheric forcing.In their calculations of Titan’s thermal structure for solarminimum and maximum conditions, Muller-Wodarg et al.[2000] found that thermospheric temperature increased byup to 20 K at solar maximum. As seen in Table 1, the datawe used in our study here were taken at low solar activity,making it unlikely that any of the variability we see in thedata is linked to solar forcing. More observations are neces-sary to identify any magnetospheric forcing effects in Titan’supper atmosphere.2.3.3. Validation of model

To validate the empirical model, Figure 9 shows compar-isons between modeled densities of N2 and CH4 (lines) andINMS observations (dots) for 3 representative flybys. In-bound values are shown in blue, outbound values in red.The modeled densities were extracted from the empiricalmodel along the trajectories of T5, T19 and T26. We chosethese particular flybys since they cover the widest combinedrange of latitude and altitude, as can be seen also from Fig-ure 1. The model uncertainty error bars are also shown inFigure 9.

Overall, the match between the model and observations isgood. The difference between model and data is well withinthe model uncertainties, and the main features in the N2

densities are reproduced. In particular, the difference be-tween the inbound (blue) and outbound (red) values at T19are well captured by the model. This shows that many of theobserved differences between inbound and outbound densityprofiles can be explained reasonably well by latitudinal vari-ations in Titan’s thermosphere. The average trends of CH4

are reasonably well captured, but some of the differences be-tween inbound and outbound profiles are not present in themodel. The empirical model can be regarded as a reasonablerepresentation of Titan’s average thermospheric structure inthe winter hemisphere at low solar activity.

While the empirical model agrees reasonably well withmeasurements at most flybys so far, there are considerabledifferences at T18, T25 and T32, where discrepancies above1100 km can reach up to a factor of 7. Interestingly, the T25flyby has a trajectory very similar to that of T26 through Ti-tan’s atmosphere, but the measured densities differ consider-ably. Near 1500 km altitude N2 densities are [N2] ∼ 7.1×106

cm−3 (T26) and [N2] ∼ 1.7 × 107 cm−3 (T25), roughly afactor of 2 larger at T25. Corresponding CH4 mixing ratiosat that height are 18% (T26) and 15% (T25). The cause ofthis discrepancy is not certain but the similarity in geometrystrongly suggests that it must be a temporal variation. How-ever, as seen from Table 1, the solar F10.7 cm flux was verysimilar during both flybys (74 and 70×10−22 W/m2/Hz).Thus, this could be evidence for a thermospheric responseto a variable magnetospheric or wave forcing, but at thepresent time we have insufficient data on magnetosphericconditions or wave sources to investigate this further.

3. Latitudinal structures in Titan’s thermosphere

3.1. Mass densities

The empirical model allows us to quantify latitudinalstructures of density in Titan’s thermosphere. Figure 10shows vertical and latitudinal profiles of mass density. Thevertical density profiles (left panel) are shown for latitudes0◦N (solid), 55◦N (dashed-dotted) and 80◦N (dashed) be-tween altitudes 1000 and 1600 km. Near 1000 km (solid line)the latitudinal density variations are below 15% and therebywithin the model uncertainties (see Figure 8), while a dis-tinctive latitude shape evolves at higher altitudes. Near 1070km (dashed-dotted curve) equatorial densities are roughly40% larger than those near 80◦N. This latitudinal differ-ence increases to around 70% above 1100 km and remainsunchanged up to the upper boundary of our range (dashedcurve). Model uncertainties between 1100 km and 1590 kmrange from 20 to 50% (see the error bars and Figure 8), sothe latitudinal structures are larger than the model uncer-tainties, particularly in the lower thermosphere.

The Huygens Atmospheric Structure Instrument (HASI)measured decelerations of the probe during its descentthrough Titan’s themosphere on Jan 14, 2005, from whichmass densities have been inferred [Fulchignoni et al., 2005].The Huygens probe flew through thermospheric heights atequatorial latitudes of 9◦S. We find for the equatorial lat-itude of HASI observations that our densities at 1000 kmaltitude are 2.3 times the HASI values, while at the upperboundary of HASI observations (1380 km) our densities are0.6 times the HASI values. Our empirical model mass den-sities agree with HASI near 1300 km. This comparison isvalid for latitudes within around 20◦ of the equator, so anylatitudinal motion of the probe along its descent trajectorywill not affect the comparison. The differences, if real, may

MULLER-WODARG ET AL.: HORIZONTAL STRUCTURES AND DYNAMICS ON TITAN X - 5

be signatures of strong local variations in Titan’s thermo-sphere not captured by the empirical model, such as waves,or other temporal changes in the thermosphere.

The mass density profiles of our empirical model showan oblateness to be present in Titan’s thermosphere, clearlydominating the horizontal variations detected by INMS. Us-ing observations only from the TA and T5 flybys, Muller-Wodarg et al. [2006] inferred the presence of this bulge, butderived a factor of 3 decrease in density from 30◦N to 70◦N,around 4 times more pronounced than we found in thisstudy. Given the improved statistics of this study and theuncertainties in separating horizontal variations from verti-cal variations in the study by Muller-Wodarg et al. [2006],we expect our new value to be more reliable. However, acontributing factor to the smaller bulge found in this studymay be time variations in Titan’s thermosphere, given thatthe bulk of data used in this study were taken more than 1year after those used by Muller-Wodarg et al. [2003] (see Ta-ble 1). The density bulge will be accompanied by a thermalbulge and vigorous dynamics, as discussed in the following.

3.2. Temperatures

Temperatures are not measured directly in Titan’s ther-mosphere, but can be derived from the INMS density mea-surements. The procedure consists of first deriving verticalprofiles of atmospheric pressure followed by calculations oftemperatures from the ideal gas law, using the calculatedpressure and measured density. Pressures are calculated byintegrating the weight of the atmosphere from the top down[Muller-Wodarg et al., 2006]. An upper boundary conditionis needed for the temperature determination. We calculatedthis by evaluating the average density scale height between1500 and 1600 km at each latitude.

The technique for calculating pressures assumes a ver-tical column integration in the atmosphere. The inherentdifficulty in calculating pressures and temperatures for anygiven flyby lies in the fact that measurements are carried outalong horizontal trajectories along which density changesnot only with altitude but also horizontally. As a result,calculation of pressure from densities taken along any singletrajectory have an error associated with them, which will af-fect the inferred temperatures [Muller-Wodarg et al., 2006].Construction of the empirical model, as described in section2.3 overcomes this problem. By combining the data frommany flybys, we succeed in separating latitudinal from ver-tical variations, removing a significant source of uncertaintyfor the derived temperatures.

Temperature error bars are derived using the same proce-dure as Muller-Wodarg et al. [2006]. We derived a series of10000 pressure and temperature profiles using the techniquedescribed above, each time allowing ρ to vary randomly, as-suming a Gaussian distribution with a standard deviationequal to the error bar (Figure 8). At each location, thisgenerates 10000 different pressure and temperature values,for which we calculate the standard deviations for the tem-perature profile.

Figure 11 shows temperatures of Titan’s thermosphere,as derived from the empirical model densities. The up-per panel shows temperatures as a function of latitudeand altitude. The bottom left panel shows vertical tem-perature profiles at latitudes 20◦N (solid), 50◦N (dashed-dotted) and 70◦N (dashed). The bottom right panel showstemperatures at fixed altitude levels of 1030 km (solid),1200 km (dashed-dotted) and 1590 km (dashed) with errorbars super-imposed. Temperatures close to 1000 km varystrongly with latitude, reaching 167±6 K at the equator and132±6 K near the pole. In contrast, Titan’s thermosphereappears nearly isothermal above 1200 km with an averagetemperature of 146±13 K. Exospheric temperature values

are in good agreement with the previously derived value of149±3 K for the TA flyby [Waite et al., 2005; Yelle et al.,2006]. For the latitude range covered by TA (∼25-42◦N be-low 1600 km), we obtain an average value of Texo=144±13K. The good agreement of these values is due to the fact thatTA covered a latitude and altitude range where atmospherictemperatures are virtually constant and latitudinal densityvariations were relatively small, below 8%. As a result, thecontribution of horizontal variations in TA flyby data wassmall and derivation of temperatures from the flyby datadirectly was accurate.

In contrast, the T5 flyby covered a latitude range (60◦N-76◦N) where horizontal density variations reach around 30%,so derivation of temperatures by either fitting vertical den-sity curves to the observations or calculating pressures bydownward integration becomes more problematic. For T5,Muller-Wodarg et al. [2006] derived an isothermal temper-ature value of 155 K. The study by De La Haye et al.[2007] derived T5 temperatures of 162 K (ingress) and 154 K(egress). When extracting temperatures of Figure 11 alongthe T5 trajectory we find values to range between 136-150K, clearly lower than the previously derived values, whichconsidered the T5 densities only. This illustrates the effectsof horizontal density variations on derived temperatures. Inaddition, it shows that we cannot necessarily assume isother-mal conditions along any given flyby.

Vertical profiles of temperature derived from the ac-celerometer measurements by HASI have suggested consid-erable variability of temperature with altitude on Titan.Large amplitude (10 K) waves around an average tempera-ture value of 170 K dominate the structure between around800 and 1000 km altitude, followed at higher altitudes by asharp decrease to around 150 K near 1200 km [Fulchignoniet al., 2005]. While uncertainties remain at those altitudesdepending on the choice of boundary conditions in thosederivations, the general trend appears remarkably similarto our derived temperatures. Near-equatorial temperaturesin our model at latitudes of the HASI measurements rangefrom 170±6 K at 1000 km to 152±10 K at 1200 km. Thesharp temperature gradient that we find at low latitudes be-tween 1000-1200 km appears consistent with that detectedby HASI.

The INMS measurements used in this study were takenduring southern hemisphere summer conditions on Titan,the solar declination angle ranging from -23.34◦ (Oct 26,2004) to -11.79◦ (June 13, 2007), so solar zenith angles in-crease towards the northern pole. Solar EUV heating, whichforms one of the important energy sources in Titan’s thermo-sphere, will therefore be stronger at the equator than pole.Using a General Circulation Model of Titan’s thermosphere,Muller-Wodarg et al. [2003] calculated global temperaturesin Titan’s thermosphere, assuming solar EUV heating asthe only energy source. Their calculated dayside exospherictemperature decrease at solstice conditions from equator tothe winter pole by 10 K above 1300 km and less at lower alti-tudes. As shown in Figure 11, the thermosphere above 1200km appears to be nearly isothermal, but the uncertainty of±15 K allows for seasonal variations with latitude consistentwith those modeled. The TGCM calculations suggest thatthe observed temperature structure below 1200 km is likelynot to be caused by solar EUV heating.

4. Dynamics of Titan’s thermosphere

The temperature and density structure derived in theprevious section can be used to infer dynamics in Titan’sthermosphere. The thermal wind equation is used to de-rive wind speeds from the thermal structure, but this ig-nores some non-linear acceleration terms in the momentumequation and molecular viscosity, which have been shownto play an important role in Titan’s thermosphere [Rishbeth

X - 6 MULLER-WODARG ET AL.: HORIZONTAL STRUCTURES AND DYNAMICS ON TITAN

et al., 1999; Muller-Wodarg et al., 2000]. We therefore usea numerical rather than analytical approach to derive thedynamics consistent with the thermal structure.

We use a simplified version of the General CirculationModel by Muller-Wodarg et al. [2003] by imposing the ther-mal structure of Figure 11 and numerically solving the full3-D momentum and continuity equations, but not the en-ergy equation. Our vertical range is 960 km (2.67×10−5

Pa) to around 1700 km (5.7×10−10 Pa), with isothermalconditions assumed above 1590 km. In order to avoid anyhorizontal boundary discontinuities, we solve the equationspole-to-pole and assume the same thermal profiles in thenorthern and southern hemispheres, even though at presentwe have no observational constraints from INMS for thesouthern hemisphere. The full gas continuity equation issolved with molecular and eddy diffusion of the two maingases N2 and CH4 as well as optional gas transport by winds.We assume fixed mixing ratios at the lower boundary andoptional escape flux for CH4 at the upper boundary (seeSection 5). The other details of the model are describedby Muller-Wodarg et al. [2003]. Because the momentumequation needs to be solved in 3 dimensions, we extend the2-dimensional temperatures of Figure 11 to 3 dimensionsby assuming equal temperatures at all local times for anylatitude/height location. While the thermal structure thusvaries with altitude and latitude only, the equations are stillsolved in 3 dimensions. The resulting winds are, of course,local time independent. We ran the model to steady state,which typically takes 1 Titan rotation for the dynamics and10 Titan rotations for the composition.

In Figures 12 and 13 we show the three calculated windcomponents (meridional, zonal, vertical) as a function of al-titude and latitude. The two figures show results from sim-ulations for different assumed lower boundary conditions.Figure 12 shows a simulation assuming zero winds at 960km, whereas Figure 13 shows a case of non-zero winds atthe lower boundary.

When assuming zero winds at 960 km, and hence co-rotation of the atmosphere at that height with Titan’s sur-face, the dynamics in our simulation are entirely driven bythe latitude and altitude gradients of pressure in the at-mosphere. We see from the upper panel of Figure 12 thatmeridional winds are poleward, reaching maximum valuesof 200 ms−1 above 1100 km near 75◦N. Above this heightmeridional winds are virtually constant with height and de-crease below that, reaching zero values at 960 km due to ourboundary condition. The latitudinal pressure gradients, viathe large meridional winds, effectively drive a super-rotatingeastward jet at high latitudes which varies little with alti-tude above 1000 km and peaks near 80◦N with 130 m s−1.Zonal winds decrease towards the equator. Zonal winds arenot driven by accelerations from zonal pressure gradients(which are zero in our simulations) but primarily by curva-ture and Coriolis forces. The small radius of Titan and itsatmosphere result in a more curved geometry than on plan-ets like Earth and Venus, and thereby in enhanced curvatureforces, whereas the slow rotation rate of Titan reduces theimportance of the Coriolis term.

The divergence of the horizontal winds generates upwardwinds of 2 m s−1 near equatorial latitudes which turn tosubsistence near 50◦N, increasing towards the pole with ver-tical wind speeds of -30 m s−1 poleward of 80◦N. Seen inthe latitude-height plane, therefore, a large circulation cellis formed with upwelling over the equator, poleward flowand subsistence over the pole. A weak equatorward returnflow at low altitudes (not seen in Figure 12) closes the flow.

A considerable uncertainty is whether the base of thethermosphere super-rotates, as does Titan’s stratosphere[Hubbard et al., 1993; Flasar et al., 2005; Sicardy et al., 2006].No direct observational constraints are currently availablefor the dynamics above 500 km. Upward propagating waves

may considerably affect the momentum balance [Muller-Wodarg et al., 2006; Strobel , 2006] and either maintain theatmospheric super-rotation up to thermospheric altitudesor suppress it. To assess the influence of possible super-rotation on dynamics of the thermosphere, we carried outanother simulation with our model, where we implementeda profile of super-rotating zonal winds at our bottom bound-ary (near 960 km). We adopted for our lower boundary thestratospheric winds derived by Achterberg et al. [2007] fromobservations by the Cassini Composite Infrared Spectrome-ter (CIRS) for around 500 km altitude. While zonal windsare likely to change between 500 and 1000 km altitude, ouruse of the profile by Achterberg et al. [2007] is sufficient toassess the sensitivity of thermospheric winds to the lowerboundary condition.

Figure 13 shows thermospheric winds calculated with thesuper-rotating lower boundary condition. The circulationdiffers considerably from the previous calculation withoutlower boundary forcing (Figure 12), but some common fea-tures are present in both. Peak meridional (poleward) windspeeds occur roughly 25◦ equatorward of those in the un-forced case, near 55◦N, reaching around 80 m s−1, a factorof 2 smaller. Poleward of 55◦N we now obtain a broad regionof near-zero meridional winds. As expected, zonal winds aregenerally more strongly eastward than in the unforced case,but their peak values in the zonal jet are similar to the un-forced case. The zonal jet is now broader in latitude andhas moved equatorward by around 15◦ to 65◦N. The regionof strong polar subsistence found in our unforced calcula-tions (Figure 12) has become weaker, with vertical windslower than -10 ms−1. The region of strongest subsistenceno longer occurs over the pole but at 60-70◦N.

In essence, the super-rotating lower boundary conditionsplits the single circulation cell we had found in the un-forced case of Figure 12 into two cells. Upwelling occursover the equator, with poleward flow and downwelling near65◦N. A second circulation cell is located poleward of that,with weak upwelling in the polar cap region and weak equa-torward flow. The two circulation cells are thus oppositeto one another and converge in the downwelling zone near65◦N. Eastward winds are above the diurnal rotation speedof the thermosphere (around 18 m s−1) everywhere except inthe polar region, so in this calculation Titan’s thermosphereis super-rotating everywhere.

Both circulation patterns shown in Figures 12 and 13 arephysically consistent with the thermal profile of Figure 11.The numerical calculations illustrate that thermospheric dy-namics are not fully constrained by the thermal profile alone,but depend on the vertical coupling from below. We haveinvestigated the influence of super-rotation from below, but,in addition, dynamics may be driven by accelerations due todissipating waves. Observations by Cassini/Huygens havedetected strong waves in Titan’s thermosphere [Fulchignoniet al., 2005; Muller-Wodarg et al., 2006] and model calcula-tions have suggested potentially strong wave forcing to occurin the thermosphere [Muller-Wodarg et al., 2006; Strobel ,2006]. Since the problem of wave forcing is currently under-constrained by observations, we have not yet attempted toinclude it in our calculations, but the principle introducesanother degree of freedom to dynamics. We will in the fol-lowing explore additional possible observational constraintson thermospheric dynamics.

5. Latitude variations of CH4

Methane is one of the principal gases in Titan’s atmo-sphere and important for the chemistry and energy balance.In Titan’s thermosphere CH4 undergoes photolysis princi-pally by solar Lyα radiation. As shown by Yelle et al. [2007],the time scale for Lyα photolysis of CH4 at the height of

MULLER-WODARG ET AL.: HORIZONTAL STRUCTURES AND DYNAMICS ON TITAN X - 7

strongest absorption (near 850 km) is around 2×107 sec.The diffusion time scale at that altitude is around 3×106

sec. Assuming the horizontal and vertical wind velocitiesderived in Section 4, we find transport time scales of up to1×104 sec. The numbers illustrate that the photolysis timescale for CH4 in Titan’s thermosphere is significantly largerthan dynamical time scales. We may therefore in the contextof this study treat CH4 as chemically inert and expect it tobe redistributed in Titan’s thermosphere by the winds anddiffusion. Inert constituents lighter than the mean molecularmass (∼28 to 25 amu at 1000 to 1600 km altitude) such asCH4 will accumulate in regions of subsistence. The responseof the CH4 distribution to transport by solar driven ther-mospheric winds on Titan was calculated by Muller-Wodarget al. [2003] using their Thermospheric General CirculationModel. The study showed an accumulation of CH4 on thenightside and winter hemisphere which resulted from thesubsistence of winds there. We can therefore regard CH4

as a tracer for atmospheric dynamics, so investigating itslatitudinal distribution may help constrain thermosphericwinds.

The upper panels of Figures 3, 4 and 5 show CH4 molefractions as a function of latitude. A clear trend is seenwith CH4 abundances increasing towards polar latitudes byup to around 60%. However, it is important to note thatthese values include the effect of the atmosphere’s oblate-ness, whereby isobar levels are at lower altitudes towardsthe pole. We find isobaric levels to decrease in altitude byup to around 45 km from equator to pole between 1200 and1600 km. This implies that along a level of constant alti-tude we sample regions of lower pressure at polar latitudes,and hence of larger CH4 abundances due to the diffusiveseparation. This alone does not constitute a real change incomposition. Rather, we need to investigate whether CH4

mole fractions vary with latitude on an isobar surface.In order to compensate for the atmospheric oblateness,

dotted lines in the upper panels of Figures 3, 4 and 5 showthe CH4 mole fractions from the empirical model on levelsof constant pressure located close to the plotted altitudes.The mole fractions on a constant pressure level vary lesswith latitude, by up to around 45%, which is smaller thanthe error bars. While the implication of this is that the cur-rent dataset does not allow us to identify a clear increaseof CH4 abundances towards the northern pole, there nev-ertheless remains a suggestive trend that CH4 accumulatesin the northern (winter-) polar region in Titan’s thermo-sphere. Such an accumulation of CH4 would most likely becaused by subsiding winds, in agreement with our calculateddynamics, which showed downwelling at the northern polarlatitudes.

In 1-D diffusion models the eddy coefficient is commonlytreated as a free parameter which represents small-scaleturbulence and larger-scale dynamics not resolved by themodel. Previous studies of Titan’s atmosphere have de-rived the eddy coefficient by adjusting its value in orderto match particle densities with observations, assuming zeroor thermal escape flux at the top boundary. This yieldedan eddy coefficient for Titan’s thermosphere of a few times108 cm2s−1, orders of magnitude larger than that derivedfor any other planet in our solar system. Yelle et al. [2006]points out that the effects of an upper boundary conditionof non-zero vertical flux in the continuity equation is similarto that of a large eddy coefficient, and combinations of largeeddy coefficient with low escape flux or low eddy coefficientwith large escape flux can produce the similar vertical dis-tributions of constituents, introducing an uncertainty in thedetermination of the true eddy coefficient and escape rates.On Titan, the CH4 measurements alone cannot solve thisambiguity, and an independent determination of the eddydiffusion coefficient is necessary. Recently, Yelle et al. [2007]from analysis of 40Ar data from Cassini/Huygens derived an

eddy coefficient in Titan’s thermosphere of 3×107 cm2s−1,an order of magnitude smaller than the value previously as-sumed.

Figure 14 shows CH4 mole fractions in Titan’s thermo-sphere at latitude 60◦N. The plot shows measurements bythe INMS during flybys T5, T16, T18, T19, T21, T27, T28,T30 and T32 alongside values from our empirical model.Also shown in the figure are values from our diffusion modelwhich we ran to steady state assuming an eddy coefficientof K=3×107 cm2s−1 and escape flux of Φesc=2.77×109

cm−2s−1 (relative to Titan’s surface). There is very goodagreement between the empirical and diffusion models aswell as the measurements. Given that no assumptions weremade when constructing the empirical model, this goodmatch represents an independent validation of the empir-ical model. Our diffusion calculations confirm the result byYelle et al. [2007] and show that a large CH4 escape flux isnecessary to reproduce the observed distribution.

Recently, Strobel [2007] showed that hydrodynamic es-cape in Titan’s atmosphere could account for such loss rates,while both Jeans escape and nonthermal escape processesare insufficient by orders of magnitude. Hydrodynamic es-cape on Titan is driven primarily by the energy absorbedthrough solar EUV absorption and possibly by energy de-posited in the thermosphere through magnetosphere cou-pling processes. No calculations have to-date been carriedout to characterize the latitude variation of hydrodynamicescape on Titan. The high equatorial temperatures below1200 km altitude could enhance hydrodynamic escape atthose latitude, but the larger solar zenith angles in the north-ern (winter-) hemisphere imply that solar EUV absorptionthere occurs at higher altitudes, which could increase theproportion of absorbed energy driving escape. It is there-fore at this stage unclear how the CH4 escape rates on Titanchange with latitude.

Vertical winds in the thermosphere add another layer ofcomplexity to the problem since they also generate a ver-tical CH4 flux in the thermosphere. Our derived verticalwinds are weakly upward in the equatorial and low latituderegions, depleting CH4 abundances there, while the subsis-tence at polar latitudes enhances CH4 abundances. Thecombined effects of atmospheric dynamics and escape willdetermine the latitudinal distribution of CH4, but at presentthe problem is still not sufficiently constrained to allow de-riving thermospheric winds from the latitudinal variationsof CH4. We intend to further address this problem in futurestudies.

6. Discussion

Using the combined in-situ observations of thermosphericN2 and CH4 densities by the INMS during 13 Cassini flybys,we have constructed an empirical model of Titan’s thermo-spheric densities and temperatures. The reasonable agree-ment between observations and the model allow us to con-clude that most features found to-date in the INMS along-trajectory densities of N2 and CH4 are well explained bylatitude and height variations in Titan’s thermosphere. Themost striking feature we find is the considerable oblatenessof Titan’s thermosphere. Despite uncertainties in the de-rived dynamics, we find that this oblateness is likely to drivestrongly super-rotating prograde jets at high latitudes in thenorthern (winter) pole. No consistent trend has to-date beenidentified with local time and longitude, which may in partbe a result of the zonal winds which can ”wash out” zonalvariations. However, local time and longitude sampling issparse to date, and definite conclusions on the variabilitywith these coordinates is not possible.

Another important consequence of the horizontal windsis the possibly strong subsistence in the polar regions. This

X - 8 MULLER-WODARG ET AL.: HORIZONTAL STRUCTURES AND DYNAMICS ON TITAN

may via adiabatic processes have important effects on thethermal structure there. The combined effects of polewardwinds and subsistence can accumulate lighter gases (includ-ing CH4 and HCN) in the winter polar region. An enhancedpresence of HCN in the winter polar region, if real, wouldlead to very effective radiative cooling in the region due toemissions in the rotational bands which play a key role inTitan’s thermosphere [Yelle, 1991]. Recalculating the ther-mal structure of Titan’s thermosphere will be important alsoat equatorial latitudes, where we found temperatures muchlarger than at the northern polar latitudes. This will helpdetermine whether the latitudinal thermal structure that wefind is a result of latitudinal variations in the net radiativeheating rate.

Recent analyses of INMS densities have identified thepresence of large atmospheric waves in Titan’s thermosphere[Fulchignoni et al., 2005; Muller-Wodarg et al., 2006]. Thesemay through dissipation in the thermosphere deposit signif-icant amounts of momentum there, altering thermosphericwinds [Strobel , 2006; Muller-Wodarg et al., 2006]. Our cal-culations of dynamics did not consider waves as a source ofmomentum. This adds another uncertainty to the wind pro-files we calculated from the density and temperature struc-ture since our calculations assumed winds to be driven pri-marily by pressure gradients. While it is likely that presentand future Cassini observations will not be able to furtherconstrain this problem, future studies can explore the pos-sible parameter space for thermospheric winds, taking intoaccount also horizontal variations of composition.

Our calculations in Section 4 have shown thermosphericwinds to be sensitive to the dynamics of the lower atmo-sphere. Recent measurements by the Cassini Composite In-frared Spectrometer (CIRS) through nadir and limb sound-ing of the atmosphere have obtained latitudinal tempera-ture maps from around 5 mbar to 0.005 mbar, from whichwinds could be inferred via the gradient wind equation upto around 500 km altitude [Flasar et al., 2005; Achterberget al., 2007]. These studies found zonal jets which peak be-tween around 30-60◦N near 0.1 mbar with values of up to190m s−1, in reasonable agreement with stratospheric windsderived from ground-based observations of two stellar oc-cultations in 2003 [Sicardy et al., 2006]. The CIRS windmaps show a decrease of wind speeds above the 0.1 mbarlevel, but nothing is known of wind speeds between around500 and 1000 km altitude on Titan. This introduces anuncertainty into our derived horizontal wind profiles thatcannot currently be resolved. We found the vertical windvelocities to be particularly sensitive to this lower bound-ary condition (Figures 12 and 13), which may importantlyaffect transport of constituents (CH4, HCN) in the polarregions and adiabatic heating rates there. Our understand-ing of the high latitude thermosphere on Titan will thus beparticularly sensitive to coupling from below.

In some cases, as discussed in Section 2.3.3, the matchbetween our empirical model and observations is poor. Par-ticularly interesting are the differences between T25 and T26flybys. The spacecraft followed almost an identical trajecto-ries through the atmosphere, the solar activity in both caseswas similar (see Table 1), and furthermore the position of Ti-tan relative to Saturn was almost identical. Data from theCassini Magnetometer instrument (MAG) have shown lit-tle difference of the overall magnetic field configuration andvariability in the vicinity of Titan during these two flybys(C. Bertucci, personal comm. [2007]), suggesting that theforcing from Saturn’s magnetosphere was comparable duringT25 and T26. A more comprehensive analysis of magneto-spheric conditions during these flybys, including the char-acteristics of energetic electrons and ions (measured by theCassini Plasma Spectrometer and Magnetospheric ImagingInstrument) will be important to determine any differencesin magnetospheric forcing during these flybys. In the ab-sence of evidence for an external forcing mechanism that

could cause differences in the atmosphere as observed be-tween T25 and T26, a further possibility is the presence oflarge scale waves in the atmosphere which might cause suchbehavior. Further studies are needed to investigate this.

Our study suggests Titan’s thermosphere to be domi-nated by strong dynamics which are accompanied by anoblate shape of the atmosphere at those heights. This pic-ture diverges considerably from the global structure pre-dicted in the pre-Cassini era by General Circulation modelswhich considered solar heating alone [Muller-Wodarg et al.,2000]. Much of this results from vertical coupling to loweraltitudes, illustrating that the thermosphere of Titan cannotbe regarded as an isolated system. Furthermore, we cannotat present evaluate the relative importance of various energysources upon the thermosphere, solar EUV absorption, mag-netospheric heating or vertical wave propagation. Furtherobservations in the years to come are expected to enhanceour understanding of Titan’s atmosphere as a strongly cou-pled entity.

Acknowledgments.IM-W is funded by a University Research Fellowship of the

British Royal Society. RVY and JC have been supported byNASA grant NAG5-12699 to the University of Arizona. JHWis funded by NASA and the Jet Propulsion Laboratory contract1283095 with Southwest Research Institute.

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Table 1. Summary of Titan flybys used in this study. Al-titudes at closest approach (C/A) are given in km, Latitude,longitude and solar zenith angles (SZA) are given in degrees.Longitudes are defined as positive west. The local times ofC/A are given in Titan local solar time (LST). The F10.7 cmsolar flux is given in units of 10−22 W/m2/Hz for 1 AU. Thelocation of Titan around Saturn is given in hours of SaturnLocal Time (SLT), where for 12.00 SLT Titan is positionedbetween Saturn and the Sun and for 0.00 SLT Titan is posi-tioned on the anti-sunward side of Saturn.

Flyby Flyby C/A C/A C/A C/A C/A F10.7 cm Titan-SaturnName Date Altitude Latitude Longitude LST SZA flux at 1 AU angle (SLT)

T5 Apr 16, 2005 1025 73.75 89.49 23.28 127.54 84 5.29T16 Jul 22, 2006 950 85.50 44.61 17.35 105.44 76 2.43T18 Sep 23, 2006 962 70.85 2.97 14.41 89.76 71 2.26T19 Oct 09, 2006 980 60.85 2.38 14.32 81.02 75 2.20T21 Dec 12, 2006 1000 43.30 95.38 20.34 125.19 99 2.03T23 Jan 13, 2007 1000 30.63 2.12 14.02 53.27 79 1.94T25 Feb 22, 2007 1000 30.36 -16.24 0.58 161.19 74 13.85T26 Mar 10, 2007 981 31.66 2.09 1.76 149.53 70 13.82T27 Mar 25, 2007 1010 41.08 2.13 1.72 143.96 73 13.72T28 Apr 10, 2007 991 50.36 2.03 1.67 137.16 69 13.73T29 Apr 26, 2007 981 59.39 1.65 1.60 129.79 81 13.66T30 May 12, 2007 960 68.58 1.23 1.53 121.73 71 13.64T32 Jun 13, 2007 965 84.52 -1.24 1.31 106.93 71 13.56

Table 2. Coefficients describing the vertical change of am-plitudes of Legendre polynomials P0, P2 and P4 in Titan’sthermosphere between 1000 and 1600 km altitude as well asstandard deviations. For ρ (P0), χ(CH4) (P0) and standarddeviations (σ) the coefficients A-D are for a third order poly-nomial of the form x = A + B y + C y2 + D y3, where x is therespective quantity and y the altitude (in km). For χ(CH4)(P4/P0) coefficients A and B are for a first order polynomialof the form x = A + B y. For ρ (P2/P0), ρ (P4/P0) andχ(CH4) (P2/P0) coefficients A-D are for a hyperbolical func-tion of the form x = A + (B-A)· tanh {(y-C)/D}, where xis again the respective quantity and y the altitude (in km).The fits resulting from these coefficients are shown in Figures6 and 7 as dashed lines. Standard deviations are given asfractions of background values and are plotted in Figure 8 (aspercentages).

A B C D

ρ (P0) -8.3315 -0.0264 6.8348×10−6 -8.9991×10−10

ρ (P2/P0) -0.2724 -0.4488 1060.73 38.21ρ (P4/P0) -0.1003 -0.0485 1157.14 55.43σρ 3.262 -0.0081 6.5577×10−6 -1.6245×10−9

χ(CH4) (P0) 3.3937 -0.0248 2.3514×10−5 -6.1526×10−9

χ(CH4) (P2/P0) 0.2573 0.4336 1075.84 79.53χ(CH4) (P4/P0) 0.0538 -3.3876×10−6 / /σCH4 4.5858 -0.010 7.698×10−6 -1.8792×10−9

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Figure 1. Trajectories of the Cassini spacecraft duringtargeted Titan flybys between Apr 16, 2005 (T5) andApr 10, 2007 (T28). Only the paths of Cassini below 1600km altitude are shown. Solid (blue/black) lines denotethe inbound path, dashed (red/gray) are outbound legs.The points of closest approach to Titan are marked withgreen points. In order to illustrate the coverage of INMSobservations used in this study, only the locations aremarked where measurements were returned from by theINMS.

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Figure 2. The N2 density profile for inbound mea-surements during the T16 flyby (July 22, 2006). Above

1,300 km, N2 densities are determined from C(1) counts inchannel 28 (black crosses); between 1,100 and 1,300 km,

densities are determined from C(1) counts in channel 14(blue squares) and below 1,100 km, densities determined

from C(2) counts in channel 28 (red plus signs). Densi-

ties from both C1 counts in channel 14 and C(2) counts inchannel 28 have been calibrated to those from C1 countsin channel 28 (see text).

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Figure 3. Methane mixing ratios (upper panel) andmass densities (lower panel) at 1030 km altitude, as ob-served by the INMS during multiple flybys (T5-T32) andplotted as a function of latitude. Best fits of Legendrepolynomials, as used in the empirical atmosphere model,are shown as dashed lines. Since measurements from allavailable local times are plotted, markers of data pointsdistinguish the solar zenith angles, with stars indicatingsunlit conditions (SZA<90◦), triangles indicating duskconditions (90◦≤SZA<110◦) and filled circles indicatingconditions of darkness (SZA≥110◦). The standard devi-ations of data points around the fitted curves are shownin both panels. Dotted lines in the upper panel showMethane mole fractions on a level of constant pressureclose to 1030 km determined by the empirical model, dis-cussed in Section 5.

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Figure 4. Same as Figure 3, but for an altitude of 1200 km.

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Figure 5. Same as Figure 3, but for an altitude of 1590 km.

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Figure 6. Amplitudes of the first 3 symmetric Legendrepolynomials that best fit mass density in Titan’s atmo-sphere observed by INMS. Examples of Legendre polyno-mial fits are shown in Figures 3, 4 and 5. The left panelshows amplitudes of P0 (in g/cm3), the middle and rightpanels show amplitudes of the ratios P2/P0 and P4/P0.Also shown as dashed lines are the best fits to the points,using function coefficients given in Table 2 and describedfurther in the text.

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Figure 7. Same as Figure 6, but for CH4 mixing ratios.

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Figure 8. Standard deviations of CH4 mixing ratios(stars) and mass density (dots) as a function of altitude.The values are fluctuations of measurements around thefitted Legendre polynomial curves, also shown in Figures3, 4 and 5 as error bars. Dashed and solid lines are poly-nomial fits through the values, with coefficients given inTable 2. Standard deviations are given as percentages ofthe average background values.

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Figure 9. Examples of comparisons between our em-pirical model and densities of N2 and CH4 observed byINMS in Titan’s upper atmosphere. Dots are the mea-surements and solid lines denote model values. Blue(black) lines/markers are for the inbound trajectory legs,red (gray) lines/markers are along the outbound trajec-tory. Also shown are uncertainty error bars on the modelprofiles.

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Figure 10. Mass densities in Titan’s thermosphere, asgiven by our empirical model. The left panel shows verti-cal profiles at latitudes 0◦N (solid), 55◦N (dashed-dotted)and 80◦N (dashed), illustrating the change with altitudeof latitudinal variations. The right panel shows densitiesat fixed altitudes of 1000 km (solid), 1070 km (dashed-dotted) and 1150 km (dashed), normalized to their aver-age values at each height. The latitudinal density struc-ture is roughly uniform above 1100 km, as can be seenalso in the left panel. Also shown are standard deviationsof densities.

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Figure 11. Temperatures in Titan’s thermosphere, asinferred from the empirical model atmosphere densitiesusing the method described in the text. The upper panelshows temperatures as a function of latitude and alti-tude. The bottom left panel shows vertical temperatureprofiles at latitudes 20◦N (solid), 50◦N (dashed-dotted)and 70◦N (dashed). The bottom right panel shows tem-peratures at fixed altitude levels of 1030 km (solid), 1200km (dashed-dotted) and 1590 km (dashed). While theatmosphere is nearly isothermal above around 1200 kmaltitude, temperatures below 1100 km increase towardsthe equator. Error bars are also shown and smallest atthe lowest heights.

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Figure 12. Horizontal and vertical winds in Titan’sthermosphere, as derived with our General CirculationModel, assuming the thermal structure of Figure 11.The upper panel shows meridional winds (positive north-ward), the middle panel shows zonal winds (positive east-ward) and the lower panel are vertical winds (positiveupward). We assume zero winds at the model’s lowerboundary (960 km).

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Figure 13. Same as Figure 12, but assuming the strato-spheric eastward winds of Achterberg et al. [2007] at thelower boundary (960 km).

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Figure 14. Methane mole fractions in Titan’s ther-mosphere at latitude 60◦N. Dots are measurements bythe INMS during flybys T5, T16, T18, T19, T21, T27,T28, T30 and T32. The dotted line gives values from theempirical model, while the dashed line represents valuesfrom a diffusion model which assumes an eddy coefficientof K=3×107 cm2s−1 and escape flux of Φesc=2.77×109

cm−2s−1 (relative to Titan’s surface).