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 The Cassini-Huygens mission has been observing Titan since October 2004, resulting in over 70 targeted flybys. Titan's thermosphere is sampled by the Ion and Neutral Mass Spectrometer (INMS) during several of these flybys. The measured upper atmospheric density varies significantly from pass to pass. In order to quantify the processes controlling this variability, we calculate the nitrogen scale height for a variety of parameters related to the solar and plasma environments and, from these, we infer an effective upper atmospheric temperature. In particular, we investigate how these calculated scale heights and temperatures correlate with the plasma environment. Measured densities and inferred temperatures are found to be reduced when INMS samples Titan within Saturn's magnetospheric lobe regions, while they are enhanced when INMS samples Titan in Saturn's plasma sheet. Finally the data analysis is supplemented with Navier-Stokes model calculations using the Titan Global Ionosphere Thermosphere Model. Our analysis indicates that, during the solar minimum conditions prevailing during the Cassini tour, the plasma interaction plays a significant role in determining the thermal structure of the upper atmosphere and, in certain cases, may override the expected solar-driven diurnal variation in temperatures in the upper atmosphere.
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 Saturn's largest moon Titan has a dense, extended atmosphere consisting primarily of nitrogen and methane. When Titan is immersed within Saturn's magnetospheric plasma, it experiences characteristic electron temperatures and densities of approximately 100–1000 eV and 0.1–1 cm−3, respectively [Coates, 2010]. This plasma is composed primarily of oxygen ions, protons, and electrons. Titan is a solid, conducting obstacle with no significant internal magnetic field to deflect the oncoming plasma flow, giving the plasma direct access to the upper thermosphere/exobase region. The plasma environment near Titan has been observed to be highly variable, depending on the moon's location within Saturn's magnetosphere [Rymer et al., 2009]. Occasional excursions out of Saturn's magnetosphere expose Titan to shocked solar wind plasma [Bertucci et al., 2008]. Saturn's magnetospheric configuration is described as a magnetodisk containing a warped plasma sheet, which moves in and out of Titan's orbit depending on several factors including: (1) solar wind parameters, (2) an asymmetry in Saturn's magnetosphere causing a thicker and generally more dense plasma sheet on the dayside, and (3) the periodic perturbations or flapping of the current sheet [Arridge et al., 2008; Bertucci et al., 2008]. Given this dynamic plasma environment, the Titan plasma interaction is currently suspected to play a significant and highly variable role in the upper atmospheric energetics, dynamics, and composition [De La Haye et al., 2007a; Bell et al., 2010a; Johnson, 2009; Johnson et al., 2009].
 The thermosphere of Titan is the uppermost region of Titan's collision-dominated atmosphere, lying below the quasi-collisionless exosphere. On most planetary bodies, the thermosphere is characterized by a positive thermal gradient with altitude; however, Titan's thermal structure is poorly constrained [cf. Bell et al., 2010a] and, because of this, thermosphere configurations that exhibit positive, negative, and flat temperature gradients have been proposed [cf. Bell et al., 2010b; Yelle et al., 2006; Müller-Wodarg et al., 2008; Strobel, 2008, 2009].
 Measurements of the atmospheric density made by the Cassini Ion and Neutral Mass Spectrometer (INMS) suggest a nearly isothermal region extending from ∼1100 km up to the exobase at ∼1500 km [Waite et al., 2005]. Temperatures inferred from individual flyby data range from 116 K to 200 K and exhibit large deviations between similarly oriented flybys [Waite et al., 2005, 2007]. Temperatures obtained from the Cassini Ultraviolet Imaging Spectrograph (UVIS) instrument yielded a temperature between 148 K and 151 K in the thermosphere [Shemansky et al., 2005]. Reanalysis of the Voyager Ultraviolet Spectrometer (UVS) data yielded effective temperatures of 152.9 K and 157.7 K for the dusk and dawn flanks, respectively [Vervack et al., 2004]. The Huygens probe measured thermospheric temperatures ranging between 140 K and 160 K with large wave-like perturbations [Fulchignoni et al., 2005]. Studies of Titan's thermospheric thermal structure in the northern hemisphere have also proposed zonal, meridional, and diurnal dependencies [Müller-Wodarg et al., 2008; Cui et al., 2009].
1.1. Overview of Titan's Plasma Environment
 Plasma from Saturn's magnetosphere deposits energy through collisional processes that occur between the energetic ions and electrons and the neutral atmosphere of Titan. This interaction is very complex and varies significantly with spatial location around Titan [see, e.g., Sittler et al., 2009; Coates, 2010]. Magnetospheric electron distributions are observed to be highly variable in density and temperature as classified by Rymer et al.  using the Cassini Plasma Spectrometer's Electron Spectrometer (CAPS-ELS) data. This investigation, covering the flybys TA-T55, identified four broad interaction types: plasma sheet, magnetosheath, bimodal, and lobe-like electron distributions. The plasma sheet and bimodal distributions generally contained the highest-electron energies and densities. The magnetosheath interactions occur when Titan is out of Saturn's magnetosphere and exposed to shocked solar wind plasma, exhibiting high-density low-temperature electron distributions. The lobe electron distributions are similar in energy to the plasma sheet distributions but are generally an order of magnitude lower in density; these occur when Titan is above or below the plasma sheet but still within Saturn's magnetosphere.
 A magnetic field investigation of the near-Titan plasma environment extending from TA-T62 has been performed, concentrating on the ±8 h around the Titan encounter [Simon et al., 2010]. Portions of the flybys are characterized as being within either lobe or plasma sheet type fields with distinctions made for northern and southern lobe regions. Encounters occurring during Saturn Local Times (SLTs) of 0900 UT to 1500 UT, or within the noon sector magnetosphere, were found to be embedded in a broad, highly perturbed current sheet regime, while those occurring within the midnight sector magnetosphere (SLT of 2100 UT to 0300 UT) were found to be in a significantly thinner, more transient current sheet prone to large vertical fluctuations. Thus, the electron distribution analysis by Rymer et al.  and the magnetic field analysis by Simon et al.  shows consistency in their identification of the plasma environment during the targeted Titan flybys relevant to the INMS.
 Plasma sheet electrons are characterized by peak electron energies of 120 to 600 eV and fluxes at the peak energy of 3.5 × 105 to 1.2 × 106 cm−2 s−1 sr−1. In contrast, the lobe plasma consists of similar peak electron energies (150 to 820 eV) but are generally an order of magnitude lower in flux (5.3 × 104 to 2.4 × 105 cm−2 s−1 sr−1). A systematic study of the ion populations within the various plasma regimes has indicated that the classification schemes in the electron data correspond to the ions as well [Nemeth et al., 2009]. The heavy ion populations, which are likely dominated by O+ ions, in the plasma sheet are similar in energy to those in the lobe flybys but are in general an order of magnitude greater in flux [Nemeth et al., 2009]. Bimodal flybys appear to contain a significant amount of heavy ions while the magnetosheath flybys appear to consist primarily of lighter ions such as H+. The O+ ions have been suggested previously by Shah et al.  to be the dominant source of energy for the upper atmosphere.
 The regions in which plasma has access to the atmosphere are dependent on the flow direction, electric fields, and magnetic fields. Titan is tidally locked to Saturn meaning that the same side of Titan faces Saturn at all times during its orbit. Therefore, longitude on Titan corresponds directly to the region of the plasma interaction as shown in Figure 1. The flow overtakes Titan causing the heavy ions such as oxygen to deposit their energy primarily on the side in which the faster corotating plasma impacts Titan which is referred to as the ram side or trailing hemisphere with some spreading to the Saturn-facing flank [Sillanpää et al., 2007]. The convection electric field is expected to point radially away from Saturn when the magnetic field is roughly dipolar in shape. In this configuration, the convection electric field forces the pickup ions into the atmosphere on the Saturn-facing side and away from the atmosphere on the anti-Saturn-facing side [Hartle et al., 2006; Michael and Johnson, 2005; Tseng et al., 2008]. Also, as discussed by Coates  and Sittler et al. , the wake region of Titan is most likely experiencing electron precipitation along the near radially draped field lines in that region.
1.2. Solar EUV/UV Influence
 Solar EUV/UV photons are absorbed in the thermosphere, resulting in heating from excitation, dissociation, and ionization of the neutral atmosphere. Solar influence varies with several well-known parameters: (1) the time of day on Titan, (2) the solar zenith angle, (3) obliquity of Titan and the instantaneous distance between Titan and the Sun (i.e., seasonal effects), and (4) the solar activity. Calculations by De La Haye et al.  showed that solar processes were dominant over electron precipitation below 1150 km. This study did not consider magnetospheric ions which have been shown to penetrate much further into the thermosphere [Cravens et al., 2008]. The resulting modeled temperature profiles varied from 127.9 K to 156.3 K with the majority of the deviation due to day/night asymmetries. The majority of the Cassini INMS mission to date has occurred during solar minimum conditions, meaning that the solar influence over Titan's upper atmosphere has been at its relative weakest during the observations.
1.3. The Purpose of This Study
 This study compiles the INMS atmospheric mass density measurements from the TA-T61 flybys to assess the impact of the plasma environment on the thermal structure of the upper atmosphere. Within this study we compare to previous work to evaluate assertions made regarding the parameters controlling the thermal structure, however we focus on the effect of the plasma environment. Specifically we assess how the upper atmospheric thermal structure responds to the presence or absence of the plasma sheet. The Titan Global Ionosphere Thermosphere Model (T-GITM) of Bell et al. [2010a] is used to further interpret the results. Furthermore, this study aims to assay the relative importance of the solar and plasma influences on Titan's upper atmosphere.
2. Instrumentation and Methodology
 From October 2004 to January 2010 the INMS sampled Titan's atmosphere during many targeted flybys. Table 1 summarizes the data analyzed in this study which are taken from the closed source of the Cassini INMS for 29 flybys. The method used for reducing the INMS data to obtain the N2 and CH4 densities is detailed by Magee et al. . The geospatial details and conditions during the flybys considered in this study are detailed in Table 1 with trajectories shown in Figure 1. The INMS densities are corrected by a factor of 3 to account for a cross calibration factor between the INMS, NAV, and AACS [Bell et al., 2010a].
Table 1. The Details of the Flybys Considered in This Studya
The altitude, latitude, west longitude, and solar zenith angle is given at the closest approach to Titan. The F10.7 cm solar flux refers to that observed at 1 AU and is given in solar flux units (sfu) which are equivalent to 10−22 W m−2 Hz−1. The plasma classifications are the following: plasma sheet (PS), bimodal (BM), lobe, and magnetosheath (MS). The starred plasma identifications are preliminary CAPS-ELS observations and are consistent with Simon et al. .
26 Oct 2004
16 Apr 2005
22 Jul 2006
23 Sep 2006
09 Oct 2006
12 Dec 2006
13 Jan 2007
22 Feb 2007
10 Mar 2007
10 Apr 2007
26 Apr 2007
12 May 2007
13 Jun 2007
02 Oct 2007
20 Dec 2007
05 Jan 2008
22 Feb 2008
25 Mar 2008
12 May 2008
05 Dec 2008
21 Dec 2008
07 Feb 2009
27 Mar 2009
21 May 2009
06 Jun 2009
22 Jun 2009
08 Jul 2009
24 Jul 2009
25 Aug 2009
 The N2 densities are analyzed using the following procedure. Assuming that the atmosphere is hydrostatic and in diffusive equilibrium the number density of a major neutral species is then determined by
where ns(z) is the number density of species s, z0 is the reference altitude, Ts is the species temperature, and Hs is the scale height of species s. Assuming that the scale height is invariant with the altitude, linear fits to the logarithm of the N2 density are performed. To restrict the fits to be within the thermosphere the altitude of the exobase is estimated by equating the mean free path with the scale height. The mean free path for species s within a gas mixture containing several other gases i is estimated as
 Where σij is the collision cross section of species i interacting with species j which is estimated using the hard sphere radii of the molecules in the following expression
where ri and rj are the hard sphere radii of the gases i and j, respectively [Chapman and Cowling, 1952]. The exobase is calculated considering the atmosphere to consist of N2, and CH4, whose hard sphere radii were taken to be 2.07 × 10−8cm and 2.34 × 10−8cm. N2 is the dominant species in the thermosphere, therefore we calculate its exobase and use it to set the upper boundary of the fit.
 This method produces a scale height which is averaged over a few hundred kilometers in altitude. Within this region the gravitational acceleration is decreasing with altitude. To account for the decline in g the altitude is replaced with a surface referenced geopotential altitude defined as
where r0 is the reference height, in this case the radius of Titan and h represents the physical altitude above the reference [Banks and Kockarts, 1973]. Placing the reference h0 at the surface then accounts for the nonnegligible (∼20%) decrease in gravitational acceleration over the altitude range. This geopotential altitude, z, then directly replaces the physical altitude and is used in the fits.
 The effective temperature, Teff is then derived from the scale height as
where k is Boltzmann's constant, ms is the mass of species s, and g0 is the gravitational acceleration at the reference surface, in this case the surface of Titan. N2 is relatively inert and due to its dominance in the upper atmosphere its effective temperature can in general be regarded as a good indicator of the effective temperature of the atmosphere as a whole.
 The scale height determination is solely dependent on the change in density, therefore the absolute calibration of the INMS is irrelevant and only the precision of the measurement becomes important. This model is based upon the simple assumptions of a hydrostatic, isothermal, and N2 dominated atmosphere and is in general not susceptible to uncertainties due to systematic density perturbations occurring outside of the altitude range studied. For example if a heating process occurred a few scale heights below the boundary of the model it is plausible that the increased density and upwelling would become a factor in the upper atmosphere. This effect is studied in Appendix A in which simulated Cassini flybys are produced considering a simplistic model atmosphere. The results from Appendix A show that the effective temperature deviations caused by geospatial density perturbations are of the order of a few degrees Kelvin. Furthermore, this study does not assume that horizontal density deviations are greater than temporal deviations.
Table 2 and Figure 2 give the results of the scale height fits over the entirety of the INMS data. When considering the complete data set the effective temperature is found to be 153.0 ± 1.2 K. This corresponds to a scale height of about 74 km in physical altitude and 35 km in geopotential altitude. The dayside and nightside sampling appears to be roughly uniform, producing a mean solar zenith angle of the measurements is 97.0 which is roughly consistent with a diurnal mean of 90.0. The average F10.7 cm solar radio flux for this investigation was 76 s.f.u indicating that the solar flux was well within solar minimum conditions throughout the study. The longitude coverage of the orbit synchronous satellite is mostly on the Saturn and anti-Saturn facing sectors with 30% and 38% of the coverage, respectively, and the corotational ram and wake sectors containing 17% and 15%, respectively.
Table 2. Presented are the Effective Temperatures and Exobase Heights for the Listed Groupingsa
Exobase Height (km)
The fits are taken over the altitude range 1050 km to the calculated exobase height.
153.0 ± 1.2
160.7 ± 1.0
131.7 ± 1.2
145.1 ± 1.9
144.3 ± 1.8
3.1. Global Plasma Influence
 Based on only a few data sets, De La Haye et al. [2007a] suggested that there was evidence for a plasma effect. Here we show using an extensive data set and Cassini data on the plasma that a magnetospheric effect is likely as can be seen in Figure 3 and Table 2. The high-density high-energy plasma sheet flybys show an effective temperature of 160.7 ± 1.0 K while the low-plasma density, low-energy lobe flybys show an effective temperature of 131.7 ± 1.2 K. The 29.0 K effective temperature increase observed between the plasma sheet encounters versus the lobe encounters is indicative of the large magnitude of the heating and was the largest deviation observed between data groupings used in this work. Furthermore, the density decrease results in a roughly 135 km reduction in the exobase height. The bimodal and magnetosheath bins constitute two flybys each and thus have insufficient geospatial and solar coverage to draw any conclusions from. However, it does appear that these plasma environments are in between the heating provided by the plasma sheet and the decreased heating of the lobe type flybys.
Figure 4 shows the temperatures derived on a flyby by flyby basis. The mean effective temperature of the flybys is 140.4 K, a result significantly lower than that obtained by fitting the entirety of the data in a single profile. The difference is likely due to the nonlinearity of the temperature extraction process; the inferred temperature of the mean data set is not equivalent to the mean of the inferred temperatures from each flyby. The presence or absence of the plasma sheet defines the outliers of the temperatures with plasma sheet flybys being the highest in temperature and lobe flybys being the lowest. The mean effective temperature of the plasma sheet flybys is 143.8 K while that of the lobe flybys is 118.2 K, a 25.6 K difference. No solar or geophysical trend is apparent in the observed temperatures.
 Two flyby groupings show significant changes in effective temperatures on timescales of 1 Titan day (about 16 Earth days). The T25/T26 and the T55/T56/T57 grouping are nearly identical in flyby trajectory, solar condition, and local plasma configuration and differ only in the identified plasma regime. T25 was identified to be mixed plasma sheet and lobe conditions while T26 was bimodal. The effective temperatures were 171.9 ± 1.7 K and 142.9 ± 1.3 K for the T25 and T26 flybys, respectively. Simon et al.  classify the time before the T26 flyby to be within the southern lobe while the entirety of the T25 flyby was within the plasma sheet. The T55/T56/T57 flyby grouping is nearly identical in trajectory with a slight deviation in latitude ranging from 21°S to 42°S. Again, the solar conditions were nearly identical and only the plasma regime differs. The obtained effective temperatures were 147.2 ± 6.4 K, 127.3 ± 2.5 K, and 140.8 ± 1.5 K for T55, T56, and T57, respectively. T55 and T57 were classified as plasma sheet while T56 is a lobe flyby. These two groupings are separated by 1 Titan day. The T36, T39, and T49 flybys present outliers in the plasma sheet data. The T39/T40 and T48/T49 flybys, though only 1 Titan day apart have very different flyby trajectories and are therefore not expected to isolate the plasma influence. The magnitude of the temperature differences observed between these flybys further indicates that Titan's thermosphere reacts globally on a timescale which is less than 1 Titan day, however some portion of the observed difference may be due to nonplasma related effects.
3.2. Model Results
 Next, we employ the Titan Global Ionosphere Thermosphere Model (T-GITM) [Bell et al., 2010a] in order to test whether or not plasma heating can lead to the variations found in the INMS data. We emphasize that we are not attempting to reproduce the exact N2 density variations identified by the data analysis of the previous sections, but instead we are merely using T-GITM to test whether or not the temperature variations from the data can be reproduced by the model in a gross sense. In order to accomplish this, we employ the one-dimensional (1-D) version of the three-dimensional (3-D) T-GITM framework, which calculates the coupled energetics, dynamics, and composition of Titan's upper atmosphere. In the work given by Bell et al. [2010a, 2010b, 2010c], the 1-D model was validated by self-consistently reproducing the average INMS major neutral densities and mixing ratios between TA and T40. T-GITM itself is a nonhydrostatic 3-D Navier-Stokes Global model for the Ionosphere-Thermosphere region of Titan's atmosphere, based upon the Earth Global Ionosphere-Thermosphere Model (GITM) of Ridley et al. .
 The T-GITM consists of 15 neutral species and 5 ion species that interact chemically through a reduced ion-neutral chemical scheme focused on the production of HCN, C2H4, HCNH+, and C2H5+. Moreover, the T-GITM includes a self-consistent calculation for the thermal structure using solar EUV/UV forcing, HCN rotational cooling, thermal conduction, and plasma heating. We assume, for the purposes of this study, that we can approximate the plasma influence on Titan's upper atmosphere through the precipitation of O+ and H+ ions from Saturn's magnetosphere as well as pickup ions. We adopt the vertical heating profiles from Shah et al.  for O+, from Smith et al.  for H+, and from Michael and Johnson  for pickup ions. The vertical heating rates from all species are shown alongside that of the solar EUV/UV photons and the HCN rotational cooling in Figure 5. Above 1200 km, the heating rates for the plasma processes are of the same magnitude as the solar EUV/UV heating. We know that the plasma heating by precipitating ions is located mostly on the corotational ram-side of Titan while the pickup ions deposit their energy primarily on the Saturn-facing side of Titan [Tseng et al., 2008; Sillanpä et al., 2007]. For the moment, we ignore this spatial dependence and utilize a global mean heating rate, scaled so that the column integrated orbit-averaged energy deposition is roughly 6 × 108 eV cm−2 s−1. Furthermore, the impact of magnetospheric electrons is neglected as the field configurations around Titan in which the electron precipitation is highly dependent are very complex and are likely significantly different for each pass [Bertucci et al., 2008]. It is also possible that other effects are contributing to the plasma heating such as Joule heating will be treated in subsequent work. The results here are suggestive of the net effect of the thermal response of the thermosphere to a plasma-induced heating process of the magnitude assumed for ion precipitation.
 We use two models for Titan's upper atmosphere, one model with plasma heating and one model without plasma heating, as shown in Figures 6 and 7. For each model, the most salient settings and boundary conditions are as follows: (1) F10.7−cm = 80.0 × 10−22 W m−2 Hz−1, (2) latitude = 0.0°N (equator), (3) subsolar latitude = ∼5.0°S, (4) T0 = 165.0 K, and (5) N0 = 8.7 × 1019 molecules m−3.
 In the above list, we note that Latitude stands for the latitude of the 1-D model, subsolar latitude is that latitude directly below the Sun, T0 is the temperature adopted at the model lower boundary at 500 km, and N0 is the total density adopted at 500 km. Thus, the only difference between the two models is that one includes plasma heating and one does not; all other parameters are held constant.
Figure 6 contains the resulting diurnally averaged temperature structures from T-GITM. From Figure 6, we note that the plasma heating has a profound impact on the overall thermal structure of the upper atmosphere, as was found previously by Bell et al. [2010a]. Exospheric temperatures range from 160 K (heating included) to 141 K (without heating), producing a temperature deviation on the order of 19.0 K between the two models. This is similar the thermal structure deviations of 29.0 K identified between the plasma sheet and lobe flybys.
 The diurnally averaged total densities in the upper atmosphere from both models are presented in Figure 7, which shows the wide dichotomy in neutral densities produced by the thermal structures of Figure 6. Upon inspection, one notes that the model that includes plasma heating is consistent with the INMS mass densities during plasma sheet conditions. Similarly, when we exclude plasma heating from T-GITM, we generate the blue curve in Figure 7, which is similar to the INMS densities that occur during the lobe conditions. The heating versus nonheating model results produce a similar dichotomy in effective temperatures and density structures as the plasma sheet versus lobe observations.
4.1. Comparison With Previous Results
 Several methods have previously been utilized to determine the effective or inferred temperature of the upper atmosphere from the INMS measurements. The first and most sophisticated method utilizes a diffusion model with the scale height, boundary densities, eddy coefficient, and vertical flux as free parameters [Waite et al., 2005, 2007; De La Haye et al., 2007a; Yelle et al., 2006]. Several assumptions are required when employing this method, including the assumption of either high escape rates or eddy coefficients to fit the spectrum, yielding multiple solutions that are not unique. It should be noted however that the tradeoff between eddy coefficients and escape rates primarily impacts the interpretation of the observed methane mixing ratios and plays a minor role in determining the thermal structures. Top down pressure integration yields temperature profiles below the exobase. This method is susceptible to both the choice of pressure, and hence temperature, at the top of the atmosphere and to horizontal movements in the spacecraft [Müller-Wodarg et al., 2008]. Finally, it is possible to determine the scale height directly from the slope of the measured densities utilizing the hydrostatic equation as performed in this study. This method is not dependent on boundary conditions and relies solely on the assumption that the atmosphere is hydrostatic and isothermal in the upper thermosphere; an assumption which has been shown to be in good agreement locally with the measured N2 densities [Waite et al., 2005]. This method has been used considering the flybys T5-T37 [Cui et al., 2009] and to obtain preliminary results for the spatial variation in coronal heating [Johnson et al., 2009].
 Shown in Table 3 are the fit results for an array of solar and dynamical parameters. The effective temperature was obtained from the mean scale height as fit to the collection of data points which lie in the specified bin in the altitude range between 1050 km and the exobase. Titan's dayside is observed to have an effective temperature of 148.9 ± 0.8 while the night side has an effective temperature of 157.0 ± 0.8. The observation of an 8.1 K greater effective temperature on Titan's nightside is suggestive of significant nonsolar heating sources (i.e., magnetospheric heating and/or global dynamics). A greater fraction of the nightside flybys sampled occur during plasma sheet interactions which are likely the cause of the greater nightside temperatures. Müller-Wodarg et al.  posit that in the northern hemisphere there appears to be a latitudinal temperature and density dependence. This dependency was then likened to an oblateness in the thermosphere. However, the southern hemisphere presents no regular organization like that of the northern hemisphere. Müller-Wodarg et al.  further noted that the observed density structure did not show a systematic trend with solar zenith angle. Our study found that observations during the greatest SZAs yielded the greatest temperatures, a result atypical for a solar driven atmosphere. Furthermore, within the flybys assessed by Müller-Wodarg et al.  (T5-T32) the lowest northern latitude passes (T23, T25, and T26) were within the plasma sheet for most of the time leading up to the flyby [Simon et al., 2010]. The highest northern latitude passes (T5, T16, T18, T32) were more mixed but were more frequently within the southern lobe region. The coincidental correlation between the plasma environment and the latitude may have led to the assessment that the densities and thermospheric structure were latitudinally dependent rather than dependent on the plasma environment. Our study however finds no global correlation with latitude or solar zenith angle that would indicate that the upper thermospheric structure is solar driven.
Table 3. Presented are the Effective Temperatures for the Groupings Listeda
The fits are taken over the altitude range 1050 km to the calculated exobase height. Also shown for comparison are the values from Cui et al. .
153.0 ± 0.6
151.0 ± 1.5
Dayside (0600–1800 UT)
148.9 ± 0.8
142.1 ± 1.4
Nightside (1800–0600 UT)
157.0 ± 0.8
154.8 ± 1.5
152.8 ± 0.8
144.4 ± 0.9
High northern latitude (60N–90N)
142.3 ± 1.4
146.4 ± 1.5
Middle northern latitude (30N–60N)
147.5 ± 1.2
151.2 ± 1.5
Low northern latitude (0–30N)
160.9 ± 1.6
153.4 ± 1.4
Low southern latitude (0–30S)
141.5 ± 1.2
Middle southern latitude (30S–60S)
163.6 ± 1.5
Low SZA (0–60)
153.9 ± 1.1
Mid SZA (60–120)
145.8 ± 1.0
High SZA (120–180
158.2 ± 1.0
4.2. Implications of Plasma Influence on Titan's Upper Atmosphere
 The altitude of maximum energy deposition, as shown in Figure 5, for thermal plasma processes is in general at altitudes above the solar EUV/UV energy deposition. The observation of weak dependence of the upper thermospheric temperature on solar parameters appears to reinforce this. Throughout the flybys covered in this study the Sun was in a particularly quiet solar minimum; the F10.7 cm solar radio flux ranges from 66 to 137 solar flux unit (sfu) with a mean value of 76 sfu which is well within the solar minimum range, and significantly below the robust F10.7 cm value of 183 sfu observed during the Voyager encounter. The solar forcing may therefore be substantially subdued due to its apparent inactivity during the time span of the measurements. Therefore, since solar heating is not expected to dominate in the region investigated and the solar forcing is at its relative minimum the external heating from solar EUV/UV photons would be expected to have a diminished effect on the upper atmospheric density and temperature profiles.
 Complex chemical feedback systems within the thermosphere are likely to contribute to the heat budget of Titan. HCN is linked to the thermal balance through not only diffusion processes but also through photochemical processes. Electron recombination of the primary ionospheric ion, HCNH+ whose abundance is largely solar controlled [Agren et al., 2009], is the major production pathway for HCN. The cooling ability of HCN is unmatched in Titan's thermosphere and is the major controller of the thermal structure [Yelle, 1991]. The production of HCN seems to effectively mitigate the solar heating through a chemical feedback system. This proceeds in the following fashion: increased solar EUV/UV produces enhanced HCNH+, which then increases the abundance of HCN, finally HCN radiates away the heat. This process will reduce the local effect of the solar heating while atmospheric convection will quickly distribute any localized heating source throughout the atmosphere. The impact of oxygen ion deposition is not expected to drastically influence the chemistry of the upper atmosphere [Hörst et al., 2008]; therefore chemical regulation feedbacks may be less important for this particular heating process. Pickup ions are expected to chemically react in the upper atmosphere, possibly leading to a thermal feedback. The absence of feedbacks leading to cooling may result in the observed thermal structures. Further studies of the effect of minor species on solar or plasma heating are needed.
 It is observed that Titan's thermosphere reacts to the plasma environment on a timescale of the order or less than 1 Titan day (16 Earth days). This is evident from the large deviations between the T25/T26 and T55/T56/T57 flyby groupings. The northern hemisphere T25/T26 show a 29.0 K effective temperature difference. The trajectory and solar conditions were nearly identical for these two flybys, although the plasma was observed to deviate. Müller-Wodarg et al.  note that the T25 and T26 flybys differ in density structure by roughly a factor of 2. Rymer et al.  state that T25 is a mixed flyby with plasma sheet and lobe portions while T26 is bimodal; Simon et al.  show that the ingress of T26 occurs within the southern lobe which is expected to be the region of least plasma influence. The T55/T56/T57 flyby grouping contains three flybys which are identical in nearly every respect and take place 1 Titan day apart. Effective temperatures of 147.2 ± 3.2 K, 127.3 ± 2.5 K, and 140.8 ± 1.5 K are observed for T55, T56, and T57, respectively. T55 and T57 were identified as a plasma sheet flybys while T56 is a lobe flyby. The temperature differences between these flybys are likely indicative of the plasma heating occurring when Titan is influenced by the plasma sheet. These flyby groupings suggest the relatively fast response of the thermosphere to the change in plasma conditions.
 Other processes linked to the plasma environment such as Joule heating and pickup ion deposition will likely contribute to the thermospheric heating. It is likely that Titan will experience substantial amounts of Joule heating due to the variable plasma and magnetic environment in addition to the observed ion precipitation. The extent of the effect of Joule heating on the thermosphere is currently unknown.
 Titan's thermospheric structure can, in principle, be influenced by Saturn's magnetospheric plasma [Johnson, 2009]. Dense, energetic plasmas observed within the plasma sheet have been shown to heat the thermosphere possibly through O+ and H+ ion precipitation. Such processes could account for effective temperatures found here to be on average 29.0 K greater than those observed in the sparse, cold lobe plasmas. The propensity of Saturn's magnetospheric plasma to deposit heat into Titan's thermosphere is most clearly shown when assessing INMS data with respect to the plasma environment during the flyby. The plasma influence on Titan's upper atmosphere first suggested by the analysis of the earlier results from the INMS instrument [De La Haye et al., 2007a] is now evident in the large effective temperature difference observed between the dense, energetic plasma sheet encounters and the sparse lobe encounters. The magnitude of the temperature deviation is significantly greater than those obtained by grouping the flybys by solar parameters. Navier-Stokes modeling utilizing the T-GITM model further illustrated that the observed density differences can be replicated with appropriate plasma parameters based on CAPS observations. The plasma influence has therefore likely been the driver of the upper atmospheric thermal structure throughout the Cassini mission to date.
 The thermosphere was observed to respond to plasma heating on a timescale of 1 Titan day (16 Earth days) or less. Flybys with nearly identical trajectories and solar conditions but different plasma conditions are observed to have large effective temperature differences. Fortuitously these flybys occurred within 1 Titan day. This observation leads to the conclusion that Titan's thermosphere responds to the plasma environment on a timescale less than the time between these flybys. Further investigations using time dependent, coupled models are necessary to further investigate this effect.
 The thermospheric temperatures show little or no correlation with solar parameters. This is possibly due to reduced solar activity and fluxes during the extended solar minimum in which the observations took place, or indicative of the effectiveness of the photochemical feedback mechanism in Titan's upper atmosphere in regulating the heat provided by solar photons. The Cassini solstice mission extending observations of Titan until 2017 will allow for observations of the thermosphere during solar maximum conditions.
Appendix A:: Assessment of Systematic Uncertainties
Müller-Wodarg et al.  noted that the trajectory of the Cassini spacecraft through Titan's upper atmosphere could yield significant horizontal deviations within a vertical density profile. This is due to the large swaths of area transversed by the Cassini spacecraft when near closest approach. If significant horizontal structure exists in Titan's upper atmosphere this would affect the temperature structure obtained through the assumption of purely vertical motions. To ascertain the extent to which systematic density perturbations such as meridional and zonal bulges affect the effective temperature derivation a simplistic model of Titan's upper atmosphere was constructed. The atmospheric mass density was defined as dependent on geopotential altitude by the following:
where z0 is the reference altitude and H0 is the reference scale height, in this case defined as 1000 km with the scale height fixed using an effective temperature of 148 K. The density was then perturbed through the function f(ϕ, λ), creating a confined density variation. Physically the density perturbations correspond to atmospheric changes outside of the observation altitude which modify the isobaric surface. Two models were chosen, one which represented a latitudinal bulge of twice the nominal density at the equator than the pole (Model 1) and another representing a convolution of two density bulges, one in longitude and one in latitude (Model 2). The choice of models is motivated by previous works by Müller-Wodarg et al.  in which it is shown that the INMS data may present systematic density perturbations aligned with geospatial parameters. Model 1 is motivated by the latitudinal bulge reported in the INMS data by Müller-Wodarg et al. ; Model 2 represents potentially aligned forcings from solar and plasma effects. The magnitude of the perturbations were chosen to match those previously published.
 Once the three-dimensional density structure was produced the Cassini INMS targeted flybys were then flown through the model atmosphere. The resulting densities were binned and effective temperatures determined using the same method as presented in section 2. To verify the functionality of the model a flat atmosphere (f(ϕ, λ) = 0) was produced and verified to obtain the 148.0 K temperature.
 Model 1, shown in Figure A1 (top) produces a range of temperatures from 147.2 K to 149.4 K with a mean temperature of 148.4 K. The resulting total temperature deviation of 2.2 K is close enough to the average effective temperature uncertainty to be neglected. Model 2, whose results are shown in Figure A1 (bottom) exhibits a range of binned effective temperatures from 145.1 K to 153.1 K a total difference of 8 K. This effect could possibly mask lower-order heating processes in the upper atmosphere, especially those which result in temperature deviations of less than 10 K. However, it is clear that this effect cannot reasonably account for the magnitude of the deviations observed between the plasma sheet and the lobe flybys.
De La Haye et al. [2007a] noted that a significant population of suprathermal N2 existed near the exobase on some flybys. This population is manifest in the drastic upturn in the density profiles above the exobase and in general results in a 10–20 K temperature increase. De La Haye et al. [2007b] calculated the density of suprathermal N2 to be roughly 5 orders of magnitude less in density than the thermal population and decreases significantly as the atmospheric density increases. We assessed the potential effects of a suprathermal population on the obtained effective temperatures by selecting the TA flyby which De La Haye et al. [2007a] stated had a significant suprathermal population at the exobase and performing the mean scale height fits at various altitudes both above and below the exobase. The results of this study are shown in Table A1. The difference in obtained effective temperatures is at most 1.2 K, or 0.8%. This result shows that when averaged over the upper thermosphere the effective temperature is not affected by the suprathermal populations at the exobase.
Table A1. Shown are the Effective Temperatures Obtained by Various Mean Scale Height Fits on the TA Flybya
Boundary Altitude (km)
The fits varied the upper boundary altitude to either neglect or incorporate exospheric populations.
1597.5 (exobase height)
146.7 ± 1.6
146.7 ± 1.5
146.9 ± 1.5
147.4 ± 1.4
147.9 ± 1.3
 This work was supported by NASA Headquarters under the NASA Earth and Space Science Fellowship Program grant NNX08AW24H.
 Masaki Fujimoto thanks the reviewers for their assistance in evaluating this paper.