Modeling the effect of atmospheric gravity waves on Saturn’s ionosphere

Icarus 224 (2013) 32–42

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Modeling the effect of atmospheric gravity waves on Saturn’s ionosphere Daniel J. Barrow a, Katia I. Matcheva b,⇑ a b

Buchholz High School, Gainesville, FL 32606, United States Department of Physics, University of Florida, Gainesville, FL 32611-8440, United States

a r t i c l e

i n f o

Article history: Received 12 July 2012 Revised 15 January 2013 Accepted 31 January 2013 Available online 16 February 2013 Keywords: Atmospheres, Composition Atmospheres, Dynamics Ionospheres Saturn, Atmosphere

a b s t r a c t Cassini’s radio occultations by Saturn reveal a highly variable ionosphere with a complex vertical structure often dominated by several sharp layers of electrons. The cause of these layers has not yet been satisfactorily explained. This paper demonstrates that the observed system of layers in Saturn’s lower ionosphere can be explained by the presence of one or more propagating gravity waves. We use a two-dimensional, non-linear, time-dependent model of the interaction of atmospheric gravity waves with ionospheric ions to model the observed periodic structures in two of Cassini’s electron density profiles (S08 entry and S68 entry). A single gravity wave is used to reproduce the magnitude, the location, and the shape of the observed peaks in the region dominated by H+ ions. We also use an analytical model to study small-amplitude variations in the S56 exit electron density profile. We identify three individual wave modes and achieve a good fit to the data. Both models are used to derive the properties (horizontal and vertical wavelengths, period, amplitude, and direction of propagation) of the forcing waves present at the time of the occultations. Ó 2013 Elsevier Inc. All rights reserved.

1. Introduction Information about the structure of Saturn’s ionosphere has increased dramatically since the arrival of the Cassini spacecraft yet our understanding of the underlying processes that maintain its structure has not improved significantly. The bulk of the information comes from radio occultations which return the vertical distribution of electrons. There are 37 electron density profiles available in the literature with 31 of them coming from the Cassini Radio Experiment (Nagy et al., 2006; Kliore et al., 2009). The maximum electron density, the location of the electron density peak as well as the total electron content of the ionosphere show strong variability both with latitude and local time (dusk versus dawn). Despite the observed variability the following trends have been identified: (1) The maximum electron density and the total electron content (TEC) increase with latitude with a maximum in the polar regions and a minimum at the equator (Moore et al., 2010). (2) At low latitudes the dawn electron density peak is smaller than at dusk and occurs at higher altitudes (referred to as dawn/dusk asymmetry) (Nagy et al., 2006; Kliore et al., 2009). (3) A complex system of sharp layers of enhanced electron density is observed in the lower ionosphere at most latitudes. (4) Some profiles exhibit large vertical regions of near depletion of electrons (referred to as bite-outs). Additional information about the structure of the ⇑ Corresponding author. Address: Department of Physics, University of Florida, P.O. Box 118440, Gainesville, FL 32611-8440, United States. E-mail addresses: [email protected] (D.J. Barrow), [email protected]fl.edu (K.I. Matcheva). 0019-1035/$ - see front matter Ó 2013 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.icarus.2013.01.027

ionosphere at middle latitudes is provided by the detection and the monitoring of Saturn’s Electrostatic Discharges (SEDs) which constrain the value of the maximum electron density and show its variation with local time (Fischer et al., 2011). Modeling of Saturn’s ionosphere and fitting of the observed electron density profiles proves to be challenging. The pre-Voyager photochemical models overestimate the maximum electron density and predict the location of the peak to be much lower in the atmosphere than later observed. McElroy (1973) notes that a charge exchange reaction of the dominant H+ ions with vibrationally excited H2 molecules decreases the H+ lifetime. Subsequent models use this mechanism to reduce the predicted electron density peak assuming a range of values for the vibrational temperature of the H2 molecules (Majeed and McConneell, 1996; Moses et al., 2000a,b; Moses and Bass, 2000; Moore et al., 2004, 2006, 2010, 2012). The H2 vibrational temperature remains unconstrained. Oxygen containing compounds (H2O and OH) of ring or meteoritic origin are also shown to have an impact on the ionospheric structure (Moses et al., 2000b; Moses and Bass, 2000; Moore et al., 2006). Vertical plasma drifts as a result of neutral winds or electric fields are used to move the electron density peak to higher altitudes (McConnell et al., 1982; Majeed and McConnell, 1991). More recent models employ updated chemical reaction constants, include realistic modeling of influx of external material (H2O, metallic ions and dust particles) (Moses and Bass, 2000; Moore and Mendillo, 2007), and use an improved parameterization of the effect of secondary photoelectrons on the ion production rate (Moore et al., 2010).

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2. Neutral atmosphere The ionospheric model as well as the wave propagation model used in this work require knowledge of the vertical structure of the neutral atmosphere. The neutral atmosphere is modeled as a superposition of a steady state which is a function of altitude only and a small amplitude perturbation representing a linear gravity wave. Fig. 1 presents a summary of the thermal structure and the chemical composition of the neutral atmosphere in the absence of atmospheric waves (steady state). Throughout the paper we use the 1 bar pressure level as a reference altitude (1 bar is at 0 km altitude). The structure of Saturn’s thermosphere is probed both by Voyager and Cassini observations using stellar and solar UV

Temperature (K) 3000

0 100 200 300 400 H2 He H CH4 Temperature

2500

Altitude (km)

This paper focuses on the effects of atmospheric gravity waves on the ionospheric structure of Saturn’s lower ionosphere. A large fraction of the available electron density profiles show a system of narrow layers of high electron concentration. They are present at all latitudes, both at dawn and dusk conditions, and are usually confined to the region below the main electron density peak. In a related paper Matcheva and Barrow (2012) analyze all 31 electron density profiles published to date by the Cassini Radio Science team (Nagy et al., 2006; Kliore et al., 2009) for presence of smallscale vertical variability. They use a wavelet analysis to identify discrete modes of periodicity in the vertical structure of Saturn’s ionosphere. The wavelet analysis alone does not make any assumptions about the nature of the observed periodicity and the origin of the layers is open for debate. Matcheva and Barrow (2012) do make a point that the properties of the spectral modes derived from the wavelet analysis are consistent with atmospheric gravity waves being present in Saturn’s upper atmosphere. Similar systems of multiple layers are also observed in Jupiter’s ionosphere (Kliore et al., 1980; Warwick et al., 1981, 1982; Lindal et al., 1985; Hinson et al., 1997). Barrow and Matcheva (2011) successfully fit the observed layered structure of the Galileo J0-ingress electron density with a gravity wave model and demonstrate that atmospheric gravity waves can easily drive large fluctuations in the ion/electron distribution. The generation of the waves and their propagation through the strong zonal jets of the stratosphere are yet to be adequately modeled. Alternative explanations present in the literature for the origin of the multiple electron density layers in the lower ionosphere of giant planets include layers of different hydrocarbons (Kim and Fox, 1994), layers of metallic ions of meteoritic origin (Moses and Bass, 2000; Kim et al., 2001), and plasma instabilities, but it is yet to be demonstrated how well they can fit Cassini’s observations. This paper has two goals: (1) to demonstrate that atmospheric gravity waves provide a plausible explanation for the origin of the layers in Saturn’s ionosphere and (2) to derive the spectral characteristics of the inferred wave modes (vertical and horizontal wavelengths, wave period and amplitude). Ultimately we are interested in studying the impact that atmospheric gravity waves have on Saturn’s upper atmosphere and to do so we need to quantify the properties of the waves. The paper uses two different approaches in modeling the effect of atmospheric gravity waves on the vertical distribution of ions and electrons. In Section 5 we use a fully non-linear model to simulate the large-amplitude response of Saturn’s ionosphere to traveling gravity waves and to fit the observed sharp peaks with individual wave modes. In Section 6 we then use an analytical approach to study small-amplitude variations in the Cassini electron density profiles. The non-linear simulations provide a realistic treatment of the chemical and dynamical processes involved, whereas the analytical method allows us to study in detail the properties of the underlying gravity waves.

2000

1500

1000

500 1

100000

1e+010

1e+015

1e+020

-3

Number Density (m ) Fig. 1. Steady state neutral atmosphere: composition (bottom axis) and temperature (top axis) profiles.

occultations (Festou and Atreya, 1982; Smith et al., 1983). Near IR observations of Hþ 3 emission from the aurora regions provide information about the temperature of the atmosphere at high latitudes at the altitude of Hþ 3 peak abundance. The available observations show a significant difference in the derived values for the thermospheric temperature as well as for the location of the homopause (Nagy et al., 2009). The temperature at 2500 km varies by more than 100 K and the location of the homopause is quoted to be between 500 and 900 km above the 1 bar pressure level. This hints either to a strong variability in Saturn’s upper atmosphere or to a systematic error in the observations and/or data analysis. In any case this leaves us with a difficult choice for the thermal structure in the current model for Saturn’s upper atmosphere. The temperature profile that we use closely resembles the profile suggested by Moses et al. (2000a) which is based on compilations from ground based and space observations (Festou and Atreya, 1982; Smith et al., 1983; Hubbard et al., 1997) as those are the only profiles which are currently published in peer reviewed journals. At the bottom of the modeled region the atmosphere is almost isothermal with T = 137 K followed by a fast temperature increase between 800 km and 1300 km and topped by an isothermal layer at T = 417 K. Subsequently we keep in mind that the temperature in the thermosphere is likely to vary from latitude to latitude as well as with time. The structure of the neutral atmosphere (temperature, density and wind profiles) impacts the propagation of waves as well as the distribution of ions. The temperature profile is incorporated in a one dimensional diffusive model to calculate the vertical distribution of atmospheric species. The location of the hydrocarbon homopause is determined by the eddy diffusion coefficient and is at about 900 km above the 1 bar pressure level. We use the eddy diffusion model presented in Moses et al. (2000a). The eddy diffusion coefficient varies with altitude in order to satisfy observational constrains both in the lower and upper stratosphere. At the homopause the eddy diffusion coefficient in the model is 2.1  103 m2/s. The neutral densities are calculated by fixing the mixing ratios for He and CH4 at the bottom boundary of the model (z0 = 500 km) and are taken from Conrath and Gautier (2000). The resulting density profiles for the neutrals are in good agreement with the composition model from Moses and Bass (2000). 3. Atmospheric gravity waves Atmospheric gravity waves are modeled as two dimensional (one vertical and one horizontal) linear small-amplitude perturba-

D.J. Barrow, K.I. Matcheva / Icarus 224 (2013) 32–42

tions superimposed on the background steady state of the neutral atmosphere. Atmospheric gravity waves are easily excited in a planetary atmosphere and can propagate over a large distance provided that the atmosphere is stably stratified and that the waves do not get absorbed, reflected, or dissipated along the way (Hines, 1974). In a non-dissipative atmosphere the wave amplitude grows exponentially with height with a growth rate proportional to q1/2, where q is the atmospheric mass density. As a result a wave generated at the 1 bar level will have an amplitude that grows about 3000 times in magnitude by the time it reaches Saturn’s ionosphere (roughly at 900 km or 104 mbar). Clearly even a small-amplitude, tropospheric wave would result in a thermospheric wave with a dramatic amplitude which can easily drive observable signatures in the temperature and the wind structure of the neutral atmosphere. These fluctuations would inevitably impact the dynamics and the chemistry of the ionospheric plasma. The atmospheric gravity wave model used in this work is presented in Matcheva and Barrow (2012) as well as in previous publications (Matcheva and Strobel, 1999; Matcheva et al., 2001; Barrow and Matcheva, 2011; Barrow et al., 2012). This is a linear, hydrostatic, quasi-Bussinesque model that allows for slow variations in the background temperature. It includes the dissipative effect of eddy and molecular viscosity and heat conduction on the wave motion. The dissipative effect of the ion drag on the neutral wave motion is not included though it might have a significant effect and would result in dissipation of the waves at lower altitudes. Higher frequency waves would be required to fit the observations. Above the homopause, molecular dissipation processes are dominant. They become increasingly important with height and effectively prevent the waves from reaching very high altitudes as they limit the wave growth. The exact altitude of wave dissipation depends on the wavelength and the period of the wave. Matcheva and Barrow (2012) demonstrate that Saturn’s lower ionosphere (900–2500 km above the 1 bar) coincides with the region of wave dissipation for a large range of gravity wave parameters. In the numerical implementation of the wave model we use a single linear wave which is imposed at the bottom of the simulated region (z0 = 500 km) by defining the wave vertical and horizontal wavenumbers (kz and kh, respectively), vertical velocity amplitude DW(z0) and phase. We subsequently solve for the temperature, the horizontal, and the vertical velocities throughout the rest of the region using the corresponding polarization and dispersion equations (Matcheva and Strobel, 1999). The wave field is calculated with a 1 km vertical resolution with a time step of 50 s. The horizontal phase is calculated at 20 points along a single wavelength. The output of the gravity wave model (vertical and horizontal winds) is used to force the ion motion in both the non-linear simulations and the analytical calculations.

4. Ionosphere The ionospheric model for Saturn is an adaptation of the Jupiter ionospheric model from Barrow and Matcheva (2011). It accounts for the chemistry and dynamics of six major ion species, þ þ þ þ Hþ ; Hþ 2 ; H3 ; He ; HeH , and CH4 and models the ionospheric chemistry on Saturn above the homopause (about 900 km) where H+ and Hþ 3 are the dominant ion species. Below the homopause hydrocarbon chemistry dominates and this model does not represent the chemistry at these altitudes well. Similar to the wave model, the ionospheric model ranges from 500 km to 3000 km in altitude with a vertical step size of 1 km. The horizontal grid is dependent on the wavelength of the propagating wave; it has 20 grid points along the horizontal direction with periodic boundary conditions. An increase of the number of

grid points does not significantly alter the solution however greatly increases the computational time. The model computes the photoproduction of ions due to solar EUV radiation as well as incorporates secondary electron ionization via the parameterization scheme of Moore et al. (2009). The ionosphere assumes no steady-state winds. The only winds in the system are imposed by the propagating gravity waves. The steady state ionosphere is horizontally homogenous representing the vertical ion distribution in absence of waves at a given latitude and time of the day. Throughout the paper we use planetocentric latitudes. The resulting ionospheric structure for average midlatitude conditions is shown in Fig. 2. It assumes a solar zenith angle of 89° (typical dusk conditions). The distribution of H2 molecules in the excited vibrational states is calculated following Majeed and McConnell (1991) using a scaling factor of 83% for the vibrational temperature. We use the EUVAC solar flux model and the corresponding photoionisation cross-sections from Schunk and Nagy (2009) for solar minimum conditions at Saturn distance from the Sun. Above 1100 km the H+ ions are dominant whereas below 1100 km the Hþ 3 ions dominate the ionosphere. The calculated background ionosphere is in good agreement with the ionospheric model of Moses and Bass (2000). The lifetime of the main ion constituents is an important factor in determining to what extent gravity waves can affect the ionospheric structure. If the lifetime of the major ions is very short with respect to the period of the passing wave, the ions and electrons recombine before they can be significantly displaced from equilibrium. In this instance the perturbations from a gravity wave is small since it cannot transport ions a great distance. Conversely, if the lifetime of the major ions is very long (longer than the period of the passing wave) then they are subject to motion along with any large-scale dynamics (Barrow and Matcheva, 2011). The lifetime of the major ions in Saturn’s ionosphere varies dramatically from about 1 min for Hþ 3 at the homopause (900 km) to about 4 Saturn days for H+ at the peak of the electron density (z = 1500 km). Gravity waves with periods as short as 15 min (the buoyancy period at 900 km) and as long as a Saturn day are capable of disturbing the local chemical equilibrium and producing layers of electrons in the region above 1000 km. Below 1000 km the ion lifetime is too short for a typical gravity wave to result in a significant signature in the electron density.

3000

H+ H3+ H2+ He+ CH4+ HeH+

2500

Altitude (km)

34

2000

1500

1000

500 1

100

10000

1e+006

1e+008

1e+010

Number Density (m-3) Fig. 2. Steady state ionospheric model: vertical ion distribution for average dusk midlatitude conditions. The solar zenith angle is 89°. We use Majeed and McConnell (1991) model to calculate the H2 vibrational population scaled by 83%. We adapt the EUVAC solar flux model and photoionisation cross-sections (Schunk and Nagy, 2009) for solar minimum conditions at Saturn distance from the Sun.

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Another factor that affects the extent to which a gravity wave can perturb the ionosphere is the ratio of the ion gyro-frequency to that of the ion–neutral collision frequency. Where the ion gyro-frequency is greater than the ion–neutral collision frequency the ions are constrained to move along the magnetic field lines. In this case the gravity wave induces regions of ion compression and rarefaction. In locations where the ion gyro-frequency is much less than the ion–neutral collision frequency the ions can move perpendicular to the magnetic field lines and are not as efficient in layering the ionosphere. Fig. 3 shows the ion gyro-frequency of H+, the H+ ion–neutral collision frequency, as well as the plasma diffusion time-scale. The ion gyro-frequency in the ionosphere becomes greater than the collision frequency at altitudes above 1100 km. The gravity wave-induced perturbations in the electron density can be significant above this altitude and are mitigated below this altitude by the neutrals dragging ions across magnetic field lines. Cassini’s observations of Saturn’s ionosphere cover a broad range of latitudes over a couple of seasons at different times of the day (dawn/dusk). During this time the ionosphere is exposed to varying flux of incoming charged/neutral particles (not included in the model) and it is impacted by seasonal changes and different illumination conditions. Therefore each observation requires a unique set of model parameters. Past attempts to explain the observed latitudinal and time variations include mechanisms such as: H+ quenching via vibrationally excited H2 (McElroy, 1973; Majeed and McConneell, 1996), vertical plasma drifts driven by neutral winds and/or electric fields (McConnell et al., 1982; Majeed and McConnell, 1991), H2O chemistry via influx from Saturn’s rings (Moses and Bass, 2000), inclusion of secondary photo electrons and ring-shadowing effects (Moore et al., 2004, 2010), and electron/ion precipitation. Unfortunately each of these models depends on unconstrained parameters and so it is unclear to what extent each mechanism affects the ionosphere. The goal of this paper is not to try to explain the structure of the background ionosphere and its latitudinal and diurnal variability. Rather, we are interested in the effects of a wave on the ionosphere during typical Saturn conditions. To this end we vary the vibrational temperature of H2, in effect changing the lifetime of H+ and thus the electron density, in order to produce a representative background ionosphere which matches the overall structure of the observed electron density at a given location. It is this ionosphere in which we propagate a gravity wave. The large number of free 2500

Gyro Ion Collision Plasma Diffusion Buoyancy Saturn Day

Altitude (km)

2000

1500

1000

500

10 -8

10 -6

10 -4

10 -2

10 0

10 2

10 4

10 6

Frequency (1/s) Fig. 3. Relevant dynamical time (frequency) constants: H+ gyro frequency (black solid line); H+ collisional frequency (black dashed line); 1/td, where td is the H+ diffusion time constant (black dotted line); buoyancy frequency of the atmosphere (gray dotted line); 1/tS, where tS is the length of one Saturn day (gray solid line). The model reflects midlatitude dusk conditions.

parameters certainly allows for an exact match to the background ionosphere with the observations though this does not lead to any particular illumination about what exactly controls the structure of the ionosphere. In this respect we make no attempt to exactly fit the observations but rather try to capture the main characteristics of the observed dramatic system of layers in the lower ionosphere.

5. Ionospheric response to large amplitude perturbations Most of the observed electron density profiles of Saturn’s lower ionosphere have a very complex structure. Matcheva and Barrow (2012) perform a wavelet analysis on 31 Cassini electron density profiles to study the spectral characteristics of the present scales of vertical variability. The results reveal a broad range of discrete scales (200–450 km) at most latitudes with the 300 km scale being most commonly present. A gravity wave model is used to demonstrate that the characteristics of the detected variability (the location of the peaks and their relative magnitude) is consistent with the properties of gravity waves expected to be present in Saturn’s upper atmosphere. In this section we use the wave properties derived from the wavelet analysis as an input to our two-dimensional, time-dependent, non-linear model of the interaction of gravity waves with ionospheric plasma to study their effect on Saturn’s ionosphere. The simulations are run for two of Cassini’s profiles: S08 entry, a dusk observation at 3°S, and S68 entry, a dusk observation at 28°S (see Table 1). The profiles are selected for two reasons: (1) the vertical scale of variability detected by the wavelet analysis (Figs. 2 and 3 in Matcheva and Barrow (2012)) is consistent with a gravity wave mode and (2) the variability is dominated by a single vertical scale. Our ionospheric model (Barrow and Matcheva, 2011) allows only for a single propagating wave and cannot accurately reproduce the ionosphere with multiple waves present. It is certainly possible for more than one wave to be present in the ionosphere at the same time. A good example for a multiple wave system detected in a single observation is the S56 exit observation which we model in Section 6. Figs. 4 and 5 compare the observed electron density profile (blue dotted line) to the modeled electron density profile in the presence of atmospheric gravity waves (thick red line). The waves used in the model have the same vertical wavelength as the scales derived from the wavelet analysis. The parameters of each of the simulated waves are shown in Table 2 and the amplitudes are presented in Fig. 6. In Table 2, zmax is the altitude of maximum variability in the data for a given scale s and z⁄ is the altitude, at which the temperature amplitude of the wave is maximum. The altitude at which molecular dissipation becomes significant and the damping of the wave exceeds the natural exponential growth of the wave is wave-dependent and it is about 1380 km for the current choice of wave parameters. This is the altitude at which the amplitude of the vertical velocity is maximum (see Fig. 6). Note that in a non-isothermal atmosphere the location of the maximum velocity and temperature amplitudes can be different. The results from the ionospheric simulations are shown after five wave periods have elapsed to ensure that any initialization ef-

Table 1 Observation parameters for the Cassini radio occultations used in this paper (Nagy et al., 2006; Kliore et al., 2009). The magnetic field inclination is based on the Gombosi et al. (2009) model of Saturn’s magnetic field. Observation

Latitude (°S)

Dawn/dusk

SZA (°)

~ B inclination (°)

S08 entry S68 entry S56 exit

3.1 27.7 71.7

Dusk Dusk Dusk

85.2 83.8 89.6

12 43 77

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3000 Background Electron Density Observed Electron Density Model Electron Density

Altitude (km)

2500

2000

1500

1000

500

0

5e+009

1e+010

1.5e+010

2e+010

Number Density (m-3) Fig. 4. Large amplitude simulation for the S08 entry occultation (3.1°S latitude). Dotted line – observed electron density; thin black line – initial steady state electron density (no waves); thick solid red line – wave-perturbed electron density after five wave periods. Observational parameters are listed in Table 1. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

3000 Background Electron Density Observed Electron Density Model Electron Density

Altitude (km)

2500

2000

1500

1000

500

0

2e+010

4e+010

6e+010

8e+010

Number Density (m-3) Fig. 5. Same as Fig. 4 but for S68 entry (27.7°S latitude). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

fects have dissipated and that the ionosphere has reached a quasiequilibrium state. The initial background electron density profile used in the model is also shown (thin black line). Note that the initial electron density profile can be significantly different from the mean profile after the wave has been propagating for several periods. This is an expected effect due to a wave driven ion flux along the magnetic field line (Matcheva et al., 2001). The wave-induced electron flux is negative (downward) for an upward propagating

wave. The wave transport results in plasma removal at high altitudes and plasma accumulation at lower altitudes. In the lower ionosphere (below 1000 km) chemical processes dominate over the dynamical transport and the newly deposited H+ ions quickly react with a variety of hydrocarbons producing short lived hydrocarbon ions. As a result, the total electron content of the ionosphere decreases until a new equilibrium is established and the original electron density profile can be significantly different from the newly established background density in the presence of waves. This effect is particularly well illustrated in Fig. 5 where the initial steady state electron density in the model is a factor of three larger than the observed one in order for the final profile to fit the observations (after five periods of wave propagation). For both sets the observed electron density and the gravity wave perturbed electron density profile bear striking similarities. The spacing between peaks, the locations of the peaks, and the relative amplitude of perturbations are very similar in both cases. The S08 entry data contains three peaks: one at 1700 km, one at 1300 km, and one just below 1000 km. The model recreates the location, spacing, and size of the two higher peaks. It also demonstrates a remarkable similarity in the overall shape for this profile. The third peak in the model fails to match the size, location, spacing, and shape of the lowest peak. The S68 entry data contains four peaks: a small peak just below 2000 km, one at 1600 km, one around 1100 km, and another near 850 km. The model recreates the two upper peaks in location, spacing, and relative size. The model produces a peak at the same location as the third peak at 1100 km though this peak’s shape and amplitude fail to match the observation. The fourth peak near 850 km is not seen in the simulation. The wavelet analysis of the S68 entry profile shows a significant power at a second, shorter scale (210 km) in the region below 1100 km, which gives rise to the bottom peak at an altitude of 850 km. This may explain the lack of a peak in our simulated results at this altitude. In summary, for both simulations the upper peaks are reproduced well while the modeled lower peaks are not. This is an expected shortcoming of the model. As described in the previous section the model does not contain a robust hydrocarbon model and so the chemistry at these lower heights is not well represented. Further, the ion–neutral collision frequency becomes comparable to the ion-gyro frequency at around 1100 km so the perturbing mechanism itself is not as effective below. Both the hydrocarbon chemistry and relative frequencies reduce the accuracy of the model at the bottom of the ionosphere. We also study the effect of gravity waves on the electron density in the hypothetical case where Saturn’s ionosphere is dominated by Hþ 3 ions throughout most of the main ionospheric peak (Fig. 7). In the case of the S08 exit occultation we increase the vibrational temperature of the H2 molecules so that the H+ ions become relatively short lived and allow for the Hþ 3 ions to become dominant. Note that this leaves the ionosphere with an electron density significantly smaller than the observation requires. We then use the same wave parameters (amplitude, wavelength, and period) as in Fig. 4 to evaluate the effect of the wave. The result

Table 2 Parameters of the gravity waves used in the large and small amplitude simulations in Sections 5 and 6. The vertical wavelength kz and the wave temperature amplitude Tmax are quoted at the altitude of wave maximum amplitude z⁄. The scale s is given at the altitude of maximum wavelet coefficient zmax. a is the angle between the direction of the wave number vector and the magnetic field in the horizontal plane. Occultation

s

zmax

z⁄ (km)

kz(z⁄) (km)

kh (km)

s (min)

Tmax(z⁄) (K)

a (°)

S08 entry S68 entry S56 exit

380 430 165 250 500

1250 1350 1200 1000 1500

1102 1102 1050 1090 1526

244 244 93 225 652

7000 7000 791 7792 11,987

470 470 120 550 573

8 4 23 12.5 2.2

0 0 108 120 0

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Temperature [K] 3000

0

2

4

6

Temperature [K]

8

3000

Vertical Velocity Amplitude Horizontal Velocity Amplitude Temperature Amplitude

4

6

8

2500

Altitude [km]

Altitude [km]

2

Vertical Velocity Amplitude Horizontal Velocity Amplitude Temperature Amplitude

2500

2000

1500

2000

1500

1000

1000

500

0

0

5

10

15

20

25

30

35

Velocity [m/s]

500

0

5

10

15

20

25

30

35

Velocity [m/s]

Fig. 6. Vertical amplitude profiles of the temperature T, the horizontal velocity V, and the vertical velocity W of the forcing waves in the case of S08 entry occultation (left panel) and the S68 entry occultation (right panel).

is shown in Fig. 7 (right panel) and compared to the S08 exit electron density. The wave–ion interaction again results in a multi-layered structure of the lower ionosphere. The magnitude of the wave effect though is diminished (1) because of the smaller background electron density and (2) because the major ion (Hþ 3 in this case) has a shorter life time than the major ion in the H+ dominated ionosphere in Fig. 4. To increase the magnitude of the wave-induced peaks one can increase the amplitude of the propagating wave keeping the rest of the wave parameters the same. The critical amplitude for a gravity wave with a vertical wavelength of 380 km at an altitude of 1250 km is 46 K. This is more than five times the amplitude used in the simulations shown in Figs. 4 and 7, where the temperature amplitude does not exceed 8 K. Overall, our model of Saturn’s ionosphere in the presence of atmospheric gravity waves recreates the general structure of the observed electron density profiles. These results support the

hypothesis that the observed layers in Saturn’s lower ionosphere during the S08 entry and S68 entry observations are each driven by a single atmospheric gravity wave present at the time and location of the occultation. 6. Small amplitude simulations The wavelet analysis of the Cassini electron density profiles shows that the present variability is of diverse scale and magnitude. In addition to the well defined sharp layers that sometimes dominate the entire vertical profile (for example S08 entry and S68 entry) the variability in the electron density often has a rather small-amplitude. These small-amplitude fluctuations can be traced as coherent structures for several scale heights. Because of their small amplitude these fluctuations can be modeled as linear perturbations superimposed on the background ionospheric state.

Fig. 7. A case study for an Hþ 3 dominated ionosphere. Left panel: steady state ionosphere for S08 entry conditions with no waves present. The vibrational temperature is the same as in Majeed and McConnell (1991). Right panel: results from the wave–ion interaction model for the same wave as in Figs. 4 and 6 (left panel). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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Small-amplitude ionospheric fluctuations induced by traveling atmospheric gravity waves can be modeled analytically (Barrow and Matcheva, 2011). The analytical approach provides a better understanding of the forcing waves and the ionospheric response avoiding large non-linear effects like wave-induced vertical ion fluxes. The electron density profile obtained during the high latitude S56 exit occultation (71.9°S) is a very good example of a profile which has a detectable small-scale periodicity of modest amplitude. The detected scales are at s1 = 165 km, s2 = 250 km, and s3 = 500 km each peaking at 1200 km, 1000 km, and between 700 and 1800 km above the 1 bar pressure level respectively (Matcheva and Barrow, 2012). Fig. 8 shows the S56 exit electron density profile (left panel) together with the identified scales of variability (right panel). The vertical structure of the individual scales is obtained by using a wavelet analysis (central panel) to decompose the original Ne profile and to subsequently reconstruct the selected scales by using the inverse wavelet transform. A detailed discussion of the wavelet analysis and its application to the S56 exit electron density profile is presented in Harrington et al. (2010) and Matcheva and Barrow (2012), respectively. We use our analytical model for wave-driven small-amplitude ion oscillations to fit the observations and to extract information about the properties of the forcing waves. In the case of a single dominant long-lived ion the resulting electron density perturbation N 0e is described by the following formula (Matcheva et al., 2001; Barrow and Matcheva, 2011)

     ~0  ^lb  Ne0 U n 1 @N e0 1 ~ ^ ^ kr  ^lb  i N0e ðx; y; z; tÞ ¼ þ   kzi ðlb  lz Þ : Neo @z 2H x0 ð1Þ In the equation above Ne0 is the background steady state electron density which is a function of height only, H⁄ is the density scale height, and ~lb is a unit vector in the direction of the local magnetic field. The unit vector ~lz points up. The forcing wave is given by the

Lat = 71.7 S, (S56 exit) 4000

~0 , where the subscript n stands for ‘‘neutrals’’, wave velocity field U n by the frequency of the wave x0, and by the wave number vector ~ k with a real component k~r . The vertical component of the wave number is complex and has a real kzr and an imaginary part kzi. Eq. (1) assumes that the ionosphere is dominated by a single long-lived ion which basically means that the ion chemistry is ignored and the electron density is equal to the density of the dominant ion. This assumption is well justified for short period waves above 1100 km where the H+ ions are thought to dominate. The bottom of the ionosphere is complicated by the presence of Hþ 3 and CHþ 4 ions and therefore the use of Eq. (1) is not expected to produce reliable results below 1100 km. This region is also complicated by the negative values for the electron density derived from the occultation data (Kliore et al., 2009). The wavelet analysis and the reconstruction of the small-scale variations is not affected by this nor by the exact choice of background Ne0 as long as the averaging is done over scales longer than 700 km. Fig. 8 (left panel) shows two choices of background electron density obtained by filtering out scales shorter than 700 km (blue line) and shorter than 2000 km (red line) using the inverse wavelet transform. The 700 km line retains the general shape of the observed profile better, though it does not avoid the negative values for the electron density at the bottom of the ionosphere. For our analytical model we use the profile that smoothes out all variations with scales shorter than 2000 km. This ensures positive electron density throughout the modeled region. We then proceed with a selection of atmospheric gravity wave parameters to fit the identified scales of variability in the data. The vertical wavelength of the waves is already determined by the wavelet analysis. The period and the amplitude of the waves, however, are not directly constrained by the data. They rely on modeling of the wave propagation and dissipation. Figs. 9–11 show the results from our best fits (left panel) and the amplitude profiles of the forcing wave (right panel). The parameters of the gravity waves are summarized in Table 2. Note that the altitude at which the temperature amplitude of the wave is maximum z⁄ does not

Amplitude of Ne’/Nemax [%]

Reconstructed scales 4000

4000

2000 km 700 km

14

3500

s1

s2

s3

3500

3500 12

3000

3000

3000

Altitude [km]

10 2500

2500

2500 8

2000

1500

1500

1000

1000

500 -10 -5

2000

2000

0

5

10 15 20

Ne [10 9 m-3 ]

500

6

4

2

0

200

400

600

800 1000

Vertical Scale S [km]

0

1500

1000

500 -5

0

5

10 9

15

-3

Ne’ [10 m ]

Fig. 8. S56 exit radio occultation. Left panel: observed electron density profile (black line); wavelet reconstruction for scales longer than 700 km (blue line); wavelet reconstruction for scales longer than 2000 km (red line). Central panel: wavelet decomposition map for the S56 exit observation. The amplitude of the vertical variations in the observed Ne profile is shown as a function of scale and altitude. Contours (solid black lines) are drawn at 5% increments. Right panel: reconstruction of the detected scales s1 = 165 km, s2 = 250 km, s3 = 500 km. The reconstructed scales are shifted on the horizontal axis for clarity. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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D.J. Barrow, K.I. Matcheva / Icarus 224 (2013) 32–42

Wave Amplitudes

Best fit for Scale 1

2500

2500

reconstruction model fit

W T V

Altitude [km]

Tcritical

2000

2000

1500

1500

1000

500

1000

-4

-2

0 9

2

4

500

-3

Ne’ [10 m ]

0

20

40

60

80

100

T [K], V [m/s], W [m/s]

Fig. 9. Best fit for scale 1. Left panel: wavelet reconstruction for scale 1 (s1 = 165 km) (black line) and the best fit to the data (green line) based on our analytical smallamplitude model of a gravity wave interaction with the ionosphere. Right panel: vertical amplitude profiles of the temperature T, horizontal velocity V, and vertical velocity W of the forcing wave. The critical temperature Tcr is shown as a blue line. Note that this wave is close to breaking conditions. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

coincide with the location of maximum ionospheric response zmax (where N 0e is largest) and hence the discrepancy between the vertical wavelength kz(z⁄) and the identified wavelet scale s. The vertical wavelength varies significantly around 1000 km because of the large temperature gradient at the homopause. In addition to the vertical and horizontal wavelength the response of the ionosphere depends also on the horizontal orientation of the wave with respect to the magnetic field as indicated by the ~ kr  ^lb term in Eq. (1). In other words the same wave can have very different effect on the ionosphere as it propagates in a North/ South or in a East/West direction. This dependence can result in an

ambiguity in the derived wave parameters but also can be exploited to deduce information about the horizontal direction of the wave propagation. To illustrate our fitting procedure we will discuss the modeling of the shortest scale s1 = 165 km. Fig. 12 shows the amplitude of the ionospheric response to a 93 km wave with a maximum temperature amplitude 23 K. Each panel shows the footprint of the electron density perturbation (green shaded area) and the reconstruction of the 165 km scale (red solid line). The figure is organized like a table with each row corresponding to a given wave period and each column showing results for a given horizontal orientation of the wave number vec-

Wave Amplitudes

Best fit for Scale 2 2500

2500 reconstruction model fit

W T V

Altitude [km]

Tcritical

2000

2000

1500

1500

1000

500

1000

-4

-2

0

2

Ne’ [109 m-3 ]

4

500

0

10

20

30

40

50

60

T [K], V [m/s], W [m/s]

Fig. 10. Same as in Fig. 9 but for scale 2 (s2 = 250 km). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

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D.J. Barrow, K.I. Matcheva / Icarus 224 (2013) 32–42

Wave Amplitudes

Best fit for Scale 3 3000

3000

reconstruction model fit

W T V

Altitude [km]

Tcritical

2500

2500

2000

2000

1500

1500

1000

1000

500 -2 -1.5 -1 -0.5

0

0.5

1

1.5

Ne’ [109 m-3 ]

2

500

0

2

4

6

8 10 12 14 16 18

T [K], V [m/s], W [m/s]

Fig. 11. Same as in Fig. 9 but for scale 3 (s3 = 500 km). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

tor with respect to the magnetic field. The period (in minutes) is given in the bottom left corner and the angle (in degrees) is specified in the top right corner of the first column and row respectively. Note that 23 K is just under the critical amplitude for this vertical wavelength and the results therefore show the largest response for a given period and geometric orientation. One can scale the amplitude of the response down but cannot increase the predicted ionospheric perturbation without exceeding the wave critical amplitude. From the figure it is clear that the ionospheric response to short period waves (30 < s < 60 min) peaks higher than

the observed wavelet maximum for s1. We also note that the response to these waves does not depend much on the angle a. In contrast, waves with periods longer than 180 min cause the maximum effect to be too low in the ionosphere. We obtain a best fit with a wave that has a period of 120 min. The fit to the shape of the reconstructed scale is improved as we vary the angle at which the wave propagates. The bottom right corner of the table is eliminated from the potential options as the amplitude of the response is too small. From the shown combinations of wave periods s and angles a the best fit to the observation is s = 120 min and a = 90°.

Fig. 12. Response table for scale 1. The modeling is done for a wave with kz(zmax) = 165 km (kz(z⁄) = 93 km). The period of the wave in minutes is shown in the bottom left corner and the angle of propagation a in degrees is given in the top right corner of the most left and top panels. Panels in the same row show a wave with the same period and panels in a given column have the same angle a. Each panel shows the amplitude of the resulting electron density perturbations (the contour of the green shaded area) and the s1 scale (red line), plotted once with a positive and once with a negative sign). From the shown cases the closest fit is achieved for s = 120 min and a = 90°. Our best fit is for s = 120 min and a = 108° (not shown here). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

D.J. Barrow, K.I. Matcheva / Icarus 224 (2013) 32–42

3500 Wave model results Observed profile

Altitude [km]

3000

2500

2000

1500

1000

500 -10

-5

0

5 9

10

15

20

-3

Ne [10 m ] Fig. 13. Comparison between S56 exit observation (black line) and the smallamplitude simulation model (red line). The ionospheric results from the three waves are added together and superimposed on the background electron density profile shown in Fig. 8. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The fit improves a little bit for a = 108° (not shown in this figure). The final fit to the s1 scale is shown in Fig. 9. For all three scales (s1, s2, s3) we are able to get a reasonable fit to the observed fluctuation in amplitude, location of the maximum response, and phase behavior. The quality of the fit deteriorates below 1100 km (as expected). The model also does not fit the phase of the fluctuations at the top of the ionosphere as our wave model starts violating its original assumptions when the waves are strongly dissipated. The wave corresponding to the s1 scale has the largest amplitude and it is very close to breaking. For the long period waves s2 and s3 the required amplitude is more modest. Both s1 and s2 propagate practically in a zonal (East–West) direction. We were not able to discriminate strongly between the different directions of propagation for wave s3. The final comparison between the superposition of all three waves and the S56 exit observation is shown in Fig. 13. In this figure the individual simulated waves are added to the background electron density which retains scales longer than 700 km. The background profile which retains the strong variability present in the data at scales S = 900 km (blue line in Fig. 8) allows for a better comparison with the observation than the 2000 km smoothed curve (red line in Fig. 8). Fig. 13 demonstrates that the model captures the main features of the small-scale structure in the observed electron density profile. 7. Conclusions In this paper we present the results from modeling the ionospheric response of Saturn to atmospheric gravity waves propagating at high altitudes. The purpose of the project is twofold: (1) to demonstrate that gravity waves can create layers in the electron distribution similar to the layers in the Cassini observations and (2) to derive the properties of the waves present at these heights. We focused our work on three of Cassini’s electron density profiles: S08 entry, S68 entry, and S56 exit which represent low latitude, midlatitude and high latitude dusk conditions. We use our two-dimensional, non-linear, time-dependent model of the interaction of atmospheric gravity waves with ionospheric ions to model the observed periodic structures in the S08 and S68 observations and our simplified small-amplitude analytical model to study the S56 observation. The results shown in Figs. 4, 5, and 13 clearly demonstrate that the gravity wave driven variations pro-

41

vide a good fit to the observations. The vertical parameters of the forcing waves are constrained by the data and identified by the use of wavelet analysis (Matcheva and Barrow, 2012). The remaining characteristics of the waves (see Table 2) are derived from our gravity wave propagation/dissipation model and ionospheric interactions. The identified wave modes have relatively modest amplitudes with the 93 km (s1 = 165 km) scale wave in the S56 exit occultation being close to breaking conditions. The rest of the identified waves have rather long vertical wavelengths and are not expected to break. All four of the modeled large scale waves have rather long periods ranging from 8 to 9 h. Our model did not account for a time dependent solar zenith angle which is needed if more realistic simulations are desired in the case of vary long period waves. It is interesting to point out that the S08, the S68 and the s2 wave in S56 profiles have very similar characteristics (vertical wavelength, horizontal wavelength, period and amplitude) although they are propagating at very different latitudes and result in different effects on the ionosphere. In conclusion we find that gravity waves provide a reasonable explanation for the observed layered structure of Saturn’s lower ionosphere as observed by the Cassini spacecraft. References Barrow, D., Matcheva, K.I., 2011. Impact of atmospheric gravity waves on the jovian ionosphere. Icarus 211, 609–622. Barrow, D., Matcheva, K.I., Drossart, P., 2012. Prospects for observing atmospheric gravity waves in Jupiter’s thermosphere using Hþ 3 emission. Icarus 219, 77–85. Conrath, B.J., Gautier, D., 2000. Saturn helium abundance: A reanalysis of voyager measurements. Icarus 144 (Icarus), 124–134. Festou, M.C., Atreya, S.K., 1982. Voyager ultraviolet stellar occultation measurements of the composition and thermal profiles of the saturnian upper atmosphere. Geophys. Res. Lett. 9, 1147–1150. Fischer, G., Gurnett, D.A., Zarka, P., Moore, L., Dyudina, U.A., 2011. Peak electron densities in Saturn’s ionosphere derived from the low-frequency cutoff of Saturn lightning. J. Geophys. Res. 116 (A4), CiteID A04315. Gombosi, T.I. et al., 2009. In: Dougherty, Michele K., Esposito, Larry W., Krimigis, Stamatios M. (Eds.), Saturn from Cassini–Huygens. Springer Science and Business Media B.V., p. 203. Harrington, J., French, R., Matcheva, K.I., 2010. The 1998 November 14 occultation of GSC 0622-00345 by Saturn. II. Stratospheric thermal profile, power spectrum, and gravity waves. Astrophys. J. 716 (1), 404–416. Hines, C.O., 1974. The Upper Atmosphere in Motion, Geophysical Monograph, vol. 18. American Geophysical Union, Washington, DC. Hubbard, W.B., Porco, C.C., Hunten, D.M., Rieke, G.H., Rieke, M.J., McCarthy, D.W., Haemmerle, V., Haller, J., McLeod, B., Lebofsky, L.A., Marcialis, R., Holberg, J.B., Landau, R., Carrasco, L., Elias, J., Buie, M.W., Dunham, E.W., Persson, S.E., Boroson, T., West, S., French, R.G., Harrington, J., Elliot, J.L., Forrest, W.J., Pipher, J.L., Stover, R.J., Brahic, A., Grenier, I., 1997. Structure of Saturn’s mesosphere from the 28 SGR occultations. Icarus 130, 404–425. Hinson, D.P., Flasar, M.F., Kliore, A.J., Schinder, P.J., Twicken, J.D., Harrera, R.G., 1997. Results from the first Galileo radio occultation experiment. J. Geophys. Res. Lett. 24, 2107–2110. Kim, Y.H., Fox, J.L., 1994. The jovian ionospheric E region. Geophys. Res. Lett. 18, 123–126 (February 1991). Kim, Y.H., Pesnell, W. Dean, Grebowsky, J.M., Fox, J.L., 2001. Meteoric ions in the ionosphere of Jupiter. Icarus 150 (2), 261–278. Kliore, A.J. et al., 1980. Structure of the ionosphere and atmosphere of Saturn from Pioneer 11 Saturn radio occultation. J. Geophys. Res. 85 (1), 5857–5870. Kliore, A.J. et al., 2009. Midlatitude and high-latitude electron density profiles in the ionosphere of Saturn obtained by Cassini radio occultation observations. J. Geophys. Res. 114 (A4), CiteID A04315. Lindal, G.F., Sweetnam, D.N., Eshleman, V.R., 1985. The atmosphere of Saturn: An analysis of the Voyager radio occultation measurements. Astron. J. 90, 1136– 1146. Majeed, T., McConnell, J.C., 1991. The upper ionospheres of Jupiter and Saturn. Planet. Space Sci. 39, 1715–1732. Majeed, T., McConneell, J.C., 1996. Voyager electron density measurements on Saturn: Analysis with a time dependent ionospheric model. J. Geophys. Res. 101 (E3), 7589–7598. Matcheva, K., Barrow, D., 2012. Small-scale variability in Saturn’s lower ionosphere. Icarus 221, 525–543. Matcheva, K.I., Strobel, D.F., 1999. Heating of Jupiter’s thermosphere by dissipation of gravity waves due to molecular viscosity and heat conduction. Icarus 140, 328–340. Matcheva, K.I., Strobel, D.F., Flasar, F.M., 2001. Interaction of gravity waves with ionospheric plasma: Implications for Jupiter’s ionosphere. Icarus 152, 347–365.

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D.J. Barrow, K.I. Matcheva / Icarus 224 (2013) 32–42

McConnell, J.C., Holberg, J.B., Smith, G.R., Sandel, B.R., Shemansky, D.E., Broadfoot, A.L., 1982. A new look at the ionosphere of Jupiter in light of the UVS occultation results. Planetary and Space Science 30, 151–167. McElroy, M., 1973. The ionospheres of the major planets. Space Sci. Rev. 14 (3–4), 460–473. Moore, L., Mendillo, M., 2007. Are plasma depletions in Saturn’s ionosphere a signature of timedependent water input? Geophys. Res. Lett. 34, L12202. Moore, L.E., Mendillo, M., Mueller-Wodarg, I.C.F., Murr, D.L., 2004. Modeling of global variations and ring shadowing in Saturn’s ionosphere. Icarus 172, 503– 520. Moore, L., Nagy, A., Kliore, A., Mueller-Wodarg, I., Richardson, J., Mendillo, M., 2006. Cassini radio occultations of Saturn’s ionosphere: Model comparisons using a constant water flux. Geophys. Res. Lett. 33, L22202. Moore, L., Galand, M., Mueller-Wodarg, I., Mendillo, M., 2009. Response of Saturn’s ionosphere to solar radiation: Testing parameterizations for thermal electron heating and secondary ionization processes. Planet. Space Sci. 57 (14–15), 1699–1705. Moore, L., Mueller-Wodarg, I., Galand, M., Kliore, A., Mendillo, M., 2010. Latitudinal variations in Saturn’s ionosphere: Cassini measurements and model comparisons. J. Geophys. Res. 115 (A11), CiteID A11317. Moore, L., Fischer, G., Muller-Wodarg, I., Galand, M., Mendillo, M., 2012. Diurnal variation of electron density in Saturn’s ionosphere: Model comparisons with Saturn Electrostatic Discharge (SED) observations. Icarus 221, 508–516.

Moses, J.I., Bass, S.F., 2000. The effects of external material on the chemistry and structure of Saturn’s ionosphere. J. Geophys. Res. 105 (E3), 7013–7052. Moses, J.I., Bezard, B., Lellouch, E., Gladstone, G., Feuchtgruber, H., Allen, M., 2000a. Photochemistry of Saturn’s atmosphere: I. Hydrocarbon chemistry and comparison with ISO observations. Icarus 143, 244–298. Moses, J.I., Bezard, B., Lellouch, E., Gladstone, G., Feuchtgruber, H., Allen, M., 2000b. Photochemistry of Saturn’s atmosphere: II. Effects of an influx of external oxygen. Icarus 145, 166–202. Nagy, A.F. et al., 2006. First results from the ionospheric radio occultations of Saturn by the Cassini spacecraft. J. Geophys. Res. 111 (A6), CiteID A06310. Nagy, A. et al., 2009. Upper Atmosphere and ionosphere of Saturn. In: Dougherty, Michele K., Esposito, Larry W., Krimigis, Stamatios M. (Eds.), Saturn from Cassini–Huygens. Springer Science Business Media B.V., p. 181, ISBN: 978-14020-9216-9. Schunk, R., Nagy, A., 2009. Ionospheres: Physics, Plasma Physics, and Chemistry. Cambridge Atmospheric and Space Science Series, ISBN: 10-052187706. Smith, G.R., Shemansky, D.E., Holberg, J.B., Broadfoot, A.L., Sandel, B.R., McConnell, J.C., 1983. Saturn’s upper atmosphere from the Voyager 2 EUV solar and stellar occultations. J. Geophys. Res. 88, 8667–8678. Warwick, J.W. et al., 1981. Planetary radio astronomy observations from Voyager 1 near Saturn. Science 212 (10), 239–243. Warwick, J.W. et al., 1982. Planetary radio astronomy observations from Voyager 2 near Saturn. Science 215 (29), 582–587.