Meridional variations of temperature, C and C …griffith/cgweb/eprints/Greathouse05.pdf · Meridional variations of temperature, C2H2 and C2H6 abundances in Saturn’s stratosphere

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Icarus 177 (2005) 18–31www.elsevier.com/locate/icaru

Meridional variations of temperature, C2H2 and C2H6 abundancesin Saturn’s stratosphere at southern summer solstice

Thomas K. Greathousea,1,∗, John H. Lacyb,1, Bruno Bézardc, Julianne I. Mosesa,Caitlin A. Griffith d, Matthew J. Richtere,1

a Lunar and Planetary Institute, 3600 Bay Area Boulevard, Houston, TX 77058-1113, USAb University of Texas at Austin, Department of Astronomy, Austin, TX 78712, USA

c Observatoire de Paris, Section de Meudon, 92195 Meudon cedex, Franced Lunar and Planetary Laboratory, Tucson, AZ 85721, USA

e University of California Davis, Davis, CA 95616, USA

Received 22 September 2004; revised 11 February 2005

Available online 22 April 2005

Abstract

Measurements of the vertical and latitudinal variations of temperature and C2H2 and C2H6 abundances in the stratosphere of Saturnbe used as stringent constraints on seasonal climate models, photochemical models, and dynamics. The summertime photochtimescale for C2H6 in Saturn’s middle and lower stratosphere (∼40–10,000 years, depending on altitude and latitude) is much greaterthe atmospheric transport timescale; ethane observations may therefore be used to trace stratospheric dynamics. The shorter chemfor C2H2 (∼1–7 years depending on altitude and latitude) makes the acetylene abundance less sensitive to transport effects and moto insolation and seasonal effects. To obtain information on the temperature and hydrocarbon abundance distributions in Saturn’s shigh-resolution spectral observations were obtained on September 13–14, 2002 UT at NASA’s IRTF using the mid-infrared TEXEspectrograph. At the time of the observations, Saturn was at aLS ≈ 270◦, corresponding to Saturn’s southern summer solstice. The obsspectra exhibit a strong increase in the strength of methane emission at 1230 cm−1 with increasing southern latitude. Line-by-line radiattransfer calculations indicate that a temperature increase in the stratosphere of≈10 K from the equator to the south pole between 100.01 mbar is implied. Similar observations of acetylene and ethane were also recorded. We find the 1.16 mbar mixing ratio of C2H2 at−1◦and−83◦ planetocentric latitude to be 9.2+6.4

−3.8 × 10−7 and 2.5+1.8−1.0 × 10−7, respectively. The C2H2 mixing ratio at 0.12 mbar is found t

be 1.0+0.5−0.3 × 10−5 at −1◦ planetocentric latitude and 2.6+1.3

−0.9 × 10−6 at −83◦ planetocentric latitude. The 2.3 mbar mixing ratio of C2H6

inferred from the data is 7.5+2.3−1.7 × 10−6 and 1.0+0.3

−0.2 × 10−5 at −1◦ and−83◦ planetocentric latitude, respectively. Further observatiocreating a time baseline, will be required to completely resolve the question of how much the latitudinal variations of C2H2 and C2H6 areaffected by seasonal forcing and/or stratospheric circulation. 2005 Elsevier Inc. All rights reserved.

Keywords:Infrared observations; Saturn; Atmosphere; Abundances

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* Corresponding author. Fax: +1 281 486 2162.E-mail address:[email protected](T.K. Greathouse).

1 Visiting Astronomer at the Infrared Telescope Facility, which is op
ated by the University of Hawaii under cooperative agreement NCC 5-538with the National Aeronautics and Space Administration, Office of SpaceScience, Planetary Astronomy Program.
0019-1035/$ – see front matter 2005 Elsevier Inc. All rights reserved.doi:10.1016/j.icarus.2005.02.016

1. Introduction

Saturn, like the Earth, undergoes seasonal variationsto an axial tilt of≈27◦ to its orbital plane. Changes in insolation with latitude over a saturnian year cause latitu
nal variations of temperature and photochemistry. Saturn’sstratosphere is very similar to Jupiter’s, where it has recentlybeen shown that C2H2 and C2H6 are the dominant coolants
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(Yelle et al., 2001). These molecules are photochemical bproducts of methane photolysis, so their abundance velatitude may be tied to seasonally varying insolation.understand how seasons affect the meridional temperprofile and photochemical production and loss rates requknowledge of the temperature and abundances of thesephotochemical molecules as a function of latitude and tim

In 1973, spatially resolved N/S scans of Saturn, take12 µm in theν9 band of ethane, showed a gradual increin emission from north to south and a substantial peaemission over the south pole during Saturn’s southern smer (Gillett and Orton, 1975; Rieke, 1975). Variations inethane emission could be attributed to either temperatuabundance variations. Later, in 1975 and 1977,Tokunaga etal. (1978)made spatially resolved N/S scans at other walengths, including within theν4 band of methane at 7.9 µmThey observed a similar increase in emission with increing southern latitude in the methane band as was seen ein the ethane-band observations. Because it is controllediffusion and transport rather than by photochemistry,methane vertical distribution is not expected to exhibitticeable variations in abundance with latitude. Therefore,variable emission observed in the CH4 ν4 band providedevidence that the emission enhancement was causedtemperature increase towards high-southern latitudes.Cessand Caldwell (1979)constructed a stratospheric seasomodel attempting to describe the physics behind the vable emission seen in these early observations. Their msuccessfully accounted for the emission trends observeTokunaga et al. (1978), with the predicted stratospheric temperature being higher at the south pole than at the equHowever, the model indicated the temperature at the spole should be lower than that at the equator during the 1observations, whereasGillett and Orton (1975)and Rieke(1975)observed enhanced 12-µm emission at the southCess and Caldwell (1979)therefore suggested that the oserved south polar enhancement of 12-µm emission in 1could have been caused by enhanced ethane abundrather than enhanced temperatures.

During the Voyager missions in 1980 and 1981, shoafter Saturn’s northern spring equinox,LS ≈ 0◦, the in-frared spectrometer IRIS provided spatially and spectrresolved measurements of thermal emission (e.g.,Hanel etal., 1981, 1982). Using temperatures retrieved from theversion of Voyager infrared spectra,Conrath and Pirraglia(1983)showed that Saturn’s tropospheric temperature a150-mbar level exhibited a warming trend from northsouth, but this trend was not present at the 290- or 7mbar levels. They explained that this difference was cauby the variation in thermal inertia with altitude producia phase lag in the thermal response. Due to observatlimitations (seeHanel et al., 1981, 1982), stratospheric temperature maps have never been derived from the Voy
IRIS data. Similarly, although latitudinal variations in hy-drocarbon emissions were observed by IRIS, no analysis ofthe abundance variations has ever been published, perhap
ndances of C2H2 and C2H6 19

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because of the difficulty in separating the individual roof temperature and abundance in contributing to the esion (seeCourtin et al., 1984; Bjoraker et al., 1985). Usingthe Voyager IRIS data as a constraint,Bézard and Gautie(1985) improved upon previous seasonal models by incporating a radiative transfer treatment and including rshadowing effects on the insolation of Saturn. By calculalatitudinally dependent heating and cooling rates modulaby the saturnian season, they showed that at 5-mbar seavariations of insolation could produce peak temperature vations from pole to pole of 30 K, three to five years followithe solstices.

Ground-based infrared images obtained byGezari etal. (1989) have revealed a latitudinal gradient in 7.8-µmethane emission increasing from the equator to the npole. This reversal of the emission gradient from the e1973 and 1975 observations was successfully predictethe seasonal climate models ofBézard and Gautier (1985,Bézard et al. (1984), andCess and Caldwell (1979). Morerecent observations of seasonal effects on Saturn wertempted byOllivier et al. (2000). The observations, taken1992 during Saturn’s northern summer, exhibited brightnvariations in their mid-infrared circular-variable-filter (CVFimages similar to those observed byGezari et al. (1989).Ollivier et al. (2000)attempted retrievals of temperature aabundances of C2H2 and C2H6. However, their observationcould not constrain the temperature at the 2-mbar level inpendently from the abundance of C2H2 or C2H6.

In this paper we attempt to derive the stratosphtemperature using independent information from that uto derive the abundances of C2H2 and C2H6 in Saturn’sstratosphere. We use high-resolution spectra of theν4 bandof methane to derive stratospheric temperatures. Methathe most abundant trace molecule in Saturn’s atmosphhowever, its mixing ratio is still uncertain due to thderivations being somewhat model dependent. Using reCassini CIRS observations of CH4 pure rotational linesFlasar et al. (2004)determined the methane troposphemixing ratio to be 4.5 ± 0.9 × 10−3. This result is in ex-cellent agreement with that ofCourtin et al. (1984)whoderived a constant mixing ratio of 4.5+2.4

−1.9 × 10−3 for thelower stratosphere using Voyager IRIS observations. Odeterminations have ranged from∼1.7 × 10−3 to ∼4.2 ×10−3 (Tomasko and Doose, 1984; Trafton, 1985; Kille1988; Karkoschka and Tomasko, 1992; Kerola et al., 19Lellouch et al., 2001). The CH4 mixing ratio is expectedto remain roughly constant in the lower stratosphere undeclines due to diffusive separation above the methanemopause (e.g.,Festou and Atreya, 1982; Smith et al., 1983).In addition, the methane abundance is affected primaby diffusion and not by chemistry in the middle and lowstratosphere. The methane distribution is therefore expeto be homogeneous with latitude and longitude through

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much of the stratosphere, and variations in the strength of itsemission lines must then be due to thermal variations. Thisassumed uniformity, along with the fact that CH4 emits on

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the Wien side of Saturn’s blackbody curve, makes metha very sensitive temperature probe. After deriving tempatures from the methane data, we use those temperprofiles to derive abundances of C2H2 and C2H6, the keyhydrocarbon coolants and main photochemical producSaturn’s stratosphere.

2. Observations

We measured spectra along Saturn’s central meridiaSeptember 13 and 14, 2002, UT at NASA’s Infrared Tescope Facility to look for variations in the emission of CH4,C2H2, and C2H6 with latitude. The slit was oriented alonthe celestial N/S direction. Saturn’s rotational axis was tilby −5.29◦ to celestial N/S, and the sub-Earth and sub-spoint were both near planetocentric latitude−26◦. Saturn’sequatorial diameter was 18.2 arcsec. Our spatial resolualong the slit, due to diffraction and seeing, was 1.1 asec, allowing 16 independent latitudinal bins to be probHowever, due to the extinction of the rings and the weness of the methane emission near the equator, weunable to derive reliable temperature information fromnorthern hemisphere. Only the southern hemisphere wicovered in this paper. We achieved a resolving power,R =ν̃/�ν̃ ≈ 80,000, using TEXES(Lacy et al., 2002)in high-resolution cross-dispersed mode with a 1.4 arcsec wideSpectrally separated emission lines from theν4 band of CH4,between 1228 and 1231.6 cm−1 (Fig. 1), were used to deriveinformation on the stratospheric temperature profile. Obvations of theν5 Q branch of C2H2 at 730 cm−1 (Fig. 2)and theν9 band of C2H6 at 820 cm−1 (Fig. 3) were usedto derive their respective mixing ratios. In each of the abspectral settings13C isotopic variants of the respective mocules were seen along with a few CH3D emission lines in themethane observations. A small number of lines are asunidentified in our C2H6 spectrum (see the residuals plottin Fig. 3). We include plots of the integrated line fluxes frovarious emission lines versus latitude to aid in compaour observations to previous spectrally unresolved obsetions. We normalized the peak of the integrated fluxesfor ease of comparing the trends between different molecand lines of differing opacities (seeFig. 4).

Due to the fact that Earth exhibits strong methane featin its spectrum, we were required to observe Saturn asquadrature as possible, to maximize the Doppler shift forseparation of Saturn’s CH4 emission from Earth’s CH4 ab-sorption. We observed when Saturn exhibited a−28 kms−1

Doppler shift (Fig. 1). The need for a large Doppler shreduced the amount of time per night that Saturn was obsable. This, along with the fact that Saturn is extremely faat 1230 cm−1, forced us to spend all of the first half-nigobserving CH4 to acquire the S/N required for our anal
sis. Due to the long integration time required, the methanespectrum at a given latitude is an average over≈100◦ inlongitude. Therefore, after modeling of the data, we retrieve
arus 177 (2005) 18–31

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Fig. 1. A methane spectrum taken at−80◦ planetocentric latitude. The dapoints (crosses) have been overplotted by the model (solid line). The daline is the atmospheric transmission (divided by 5). The high spectral rlution of TEXES allows us to observe the strong methane emission lin1228.8 cm−1 Doppler shifted by the Earth/Saturn motion to 1228.91 cm−1,cleanly separating it from the telluric methane absorption.

Fig. 2. A spectrum of the C2H2 Q branch taken at−80◦ planetocentriclatitude. The data points (crosses) have been overplotted by the m(solid line). The dashed line is the atmospheric transmission (multipby 4). Note the C2H2 hot bandl′ = 0 ν4 + ν5 − ν4 at 731.15 cm−1 hasmany closely spaced lines making what looks like a squared-off shoto the Q(20) line at 731.11 cm−1. Gaps in the data exist due to opaqatmospheric absorption, e.g., 731.6 cm−1, and because of the incomplespectral coverage of TEXES beyond 11 µm, e.g., 729.4 and 730.75 cm−1.

an approximately longitudinally averaged temperature pfile for each latitude probed. However, little integration timwas required for the C2H6 observations since ethane emin a very clear part of the atmosphere and the emission fSaturn is exceedingly strong at 820 cm−1. As a result, theethane observations are averaged over only≈6◦ in longi-tude. In addition, the methane data and C2H2 and C2H6 data
were taken on consecutive nights; the temperatures werefound using an average methane observation≈180◦ in lon-gitude away from the other hydrocarbon observations. If the

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thermal structure is variable with longitude, the temperatusampled from the methane data may differ from those spled by the ethane and acetylene data. We have assum

Fig. 3. An ethane spectrum taken at−80◦ planetocentric latitude. The dapoints (crosses) have been overplotted by the model (solid line). The daline is the atmospheric transmission (multiplied by 3). This is theν9 band ofC2H6 along with theν12 band of13C12CH6 at 821.63 cm−1. A plot of theresiduals of our model fit compared to the data is included at the bottoeach plot offset by−0.5. Most of the wiggles seen are due to a slight streof the spectrum. Small gaps existing at 816.83, 817.5, 818.18, etc., ar

Q(9) and Q(21) lines at 729.55 and 731.22 cm−1, respectively, whereas the doQ branch at 731.08 cm−1. The solid and dashed vertical lines through all thrWavenumbers quoted here are the rest frame values.


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this paper that the variations of temperature and hydrobon abundances with longitude are much smaller thanvariations with respect to latitude.

All the spectra were sky subtracted, flat fielded and flcalibrated by an ambient temperature blackbody followthe procedure inLacy et al. (2002). To remove the effectof telluric absorption we divided the Saturn observationsobservations of the asteroid Ceres.

3. Radiative transfer

We modeled the data with a line-by-line radiative trafer code assuming a plane-parallel 75-layer atmosphereequal log(P ) spacing between 1.8 and 1× 10−7 bar. Localthermodynamic equilibrium (LTE) was assumed throuout. The variation of saturnian airmass and gravity for eobserved latitude was included in the calculation. Linesitions, intensities and energies for NH3, CH3D, 12C2H2,12C13CH2, 12C2H6 and 12C13CH6 were taken from theGEISA databank(Jacquinet-Husson et al., 1999), and thosefor 12CH4 and 13CH4 come from the TDS spectroscopdatabank(Tyuterev et al., 1994). H2 and He mole fractionswere 0.877 and 0.118, respectively(Conrath and Gautier
2000). The H2–H2 and H2–He collision-induced transitions
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to incomplete coverage of the spectral orders at wavelengths longer than11 µm, by TEXES. The weak emission lines observed between 820.8 and821.1 cm−1 and between 818.1 and 818.4 cm−1 have yet to be identified.

were calculated following the formalism ofBorysow et al.(1988). The mean molecular mass was set to 2.226 g mo−1.

Fig. 4. Plots of the normalized integrated flux of selected emission lines. Due to Saturn’s axial tilt at the time of our observations, all longitudes atlatitudes southof −80◦ were visible. The region north of 7◦ latitude was obscured by Saturn’s rings. In the CH4 plot the solid line represents the emission at 1228.81 cm−1,the dashed line is the moderate strength CH4 line at 1229.47 cm−1, and the dot-dashed line is the optically thin13CH4 line at 1229.71 cm−1. In the C2H6plot the solid line represents the peak of emission at 822.34 cm−1. At this wavelength the C2H6 becomes optically thick at high airmass, causing the emisto slightly decrease between the−80◦ observation and the−83◦ latitude bins which straddle the south pole but are at different airmasses. This is in coto the other two lines plotted, which correspond to the emission from 821.06 cm−1 and the peak of theν12 band of13C12CH6 at 821.56 cm−1. These linesare optically thin, causing them to peak near the saturnian limb where the airmass is largest. In the C2H2 plot the solid line and the dashed line represent

t-dashed line is the integrated flux over a few blended lines of theν4 + ν5 − ν4ee plots represent the sub-solar point at−26◦ and the south pole, respectively.

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Fig. 5. The mixing ratio profiles of CH4 (solid line), C2H2 (dashed line),and C2H6 (dot-dashed line) fromMoses et al. (2000). We derive temper-atures using the CH4 mixing ratio profile as it is plotted here. We vathe entire mixing ratio profile of C2H6 by a multiplicative factor to fit the820 cm−1 data, and the mean and slope of the entire C2H2 profile in orderto fit the 730 cm−1 data.

The ratio of the abundances of12C–13C hydrocarbon speciewas set to the terrestrial value appropriate for a12C–13C ra-tio of 89 (Sada et al., 1996), and the D/H ratio in methanwas set to 1.7 × 10−5 (Lellouch et al., 2001). These iso-topic values were not allowed to vary. The model spewere calculated with a sampling of 25 times the resoluof the data, i.e., a velocity resolution of≈0.16 kmsec−1, andthen convolved with a measured line profile taken from lopressure gas-cell data measured on the same observinas the data presented here. A Lorentzian convolution wFWHM of 1.5 km sec−1 was used to mimic the effect of thconvolution of our beam profile across the slit and Saturotation.

4. Modeling and results

The strength of stratospheric emission from Saturnpends predominantly on the vertical distribution of the emting molecule and the temperature profile of the stratosphThe effects of the temperature and abundance of the emmolecule on the observed molecular emission are oftenficult if not impossible to separate. This was the case inwork byOllivier et al. (2000), where they were unable to drive a unique solution; that is their derived abundancesC2H2 and C2H6 were dependent on their assumed tempture profiles. However, we describe here a method to dethe stratospheric thermal profile independently from anysumptions regarding the abundances of C2H2 and C2H6.

Because methane has a long photochemical lifetimthe middle and lower stratosphere of Saturn and has nopreciable destruction pathway in the observable atmosp
we assume that its mixing ratio does not vary with latitudeor longitude. Eddy and molecular diffusion do affect its alti-tude variation, however, especially in the upper stratosphere
arus 177 (2005) 18–31

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Fig. 6. A plot of the temperature profile fromMoses et al. (2000)shownwith symbols and line. The initial temperature profile for the modelprogram is the long-dashed line. We include the derived temperaturefiles for planetocentric latitudes of−83◦ (solid),−69◦ (dashed), and−29◦(dot-dashed).

Thus, it is possible that coupling between meridional cirlation and vertical gradients could cause the methaneing ratio in the upper stratosphere to vary with latitude,our data cannot simultaneously constrain both the methmixing ratio and the stratospheric temperature. For ourculations we adopt the methane mixing ratio profile fromphotochemistry/diffusion model ofMoses et al. (2000)witha CH4 mixing ratio of 4.5× 10−3 at 10 mbar (Fig. 5). Hav-ing fixed the methane abundance in our line-by-line radiatransfer model, we can derive the temperature at eachtude by producing synthetic spectra that reproduce our hresolution spectra taken in theν4 band of methane. Thenholding the derived temperature profiles fixed in the mowe vary the abundances of C2H2 and C2H6 to produce syn-thetic spectra that closely resemble the observed emisspectra near 730 and 820 cm−1, respectively.

4.1. Approach to fitting the spectra

To derive the temperature profile at each latitude, wethe radiative transfer model using an initial guess therprofile created by using the thermal profile fromMoses etal. (2000)below the 10 mbar level and assuming a constemperature above this level (Fig. 6). The program measurethe goodness of fit of our model spectrum to an obserCH4 spectrum, producing aχ2 given by:

χ2 =n∑

i=1

[(data(i) − model(i)

)( τ(i)

[1.1− τ(i)]1/2

)]2

,

where data(i) is the measured radiance in erg s−1 sr−1 cm−2

per cm−1, model(i) is the radiance at theith pixel in the

.

same units as the data, Doppler shifted to account for the ra-dial velocity of Saturn, andτ(i) is the telluric transmissionat spectral pixeli. The sum is over all spectral pixels, i.e.,

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Fig. 7. Contribution functions illustrating the pressure levels that are ressible for the observed flux at a given wavenumber. These functionscalculated assuming the temperature and mixing ratio profiles fromMoseset al. (2000), a latitude of−60◦, and a saturnian airmass of 1.0. When moeling the TEXES data, we take advantage of all the different contribufunctions in the observed spectrum by minimizing theχ2 between data andmodel with respect to all the spectral points in a given spectrum. Theplots contain a few contribution functions from separate resolution elemshowing the range and variation of pressure levels probed by the diffspectral regions. Due to the high-spectral resolution achieved by TEXwe begin to resolve the wings of the strongest emission lines in the4and C2H2 spectral regions. The double peak contribution functions exha high-altitude peak due to the Doppler core and a low altitude peak dthe pressure broadened wings of the emission lines. Using the largeber of spectrally separated lines in the CH4 setting, their various intensitieand energies, we are able to derive mean stratospheric temperatureand curvature of the temperature profile between 10 and 0.01 mbar. Usimilar information found in the C2H2 and C2H6 spectral settings plus thderived temperature profiles from the CH4 data, we were able to retrievthe mean and slope of the C2H2 and the mean of the C2H6 mixing ratioprofiles.

over all observed̃ν. The quotient at the end of the equatiis a measure of how the noise in the spectrum varieswavelength. By including this term, we give higher weigto spectral regions exhibiting low telluric absorption. In tthermal infrared, the dominant noise is photon noise frsky and telescope emission. After dividing the source sptrum by an asteroid spectrum to remove the effects of tellabsorption on the spectrum, the noise in the source specis equal to the square root of the telluric emission dividedthe telluric transmission. We approximate the telluric emsion by 1.1—the telluric transmission since the combinaof the instrument window and the telescope have an emisity of ≈10%.

After finding theχ2 of the initial model (χ20 ), the pro-

gram adjusts the temperature profile with a constant�T ,whereT is in Kelvin, above 10 mbar (seeFig. 7 for sensi-tivity information) and derives a newχ2 for both a positiveand negative�T shift. The slope of theχ2 surface can thenbe found by

∂χ2

∂T= χ2+ − χ2−

2�T.


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Fig. 8. A contour plot of stratospheric temperature derived from radiatransfer modeling of theν4 band of CH4. The sub-solar latitude is indicated by the vertical line at−26◦ latitude. The temperature is assumedbe constant above 0.01 mbar. Between 0.01 and 10 mbar, only thetemperature and its first and second derivatives with log(P ) were allowedto vary at each latitude.

We also derive the second difference by

∂2χ2

∂T 2= χ2+ + χ2− − 2χ2

0

(�T )2.

If the second difference is positive, the attempted changthe original temperature profile in order to improve the fi

T = Tprev− ∂χ2

∂T

/∂2χ2

∂T 2

between 10 and 0.01 mbar, i.e., the temperature is chaby the first derivative divided by the second derivative, whshould adjustT to the value whereχ2 is minimized if otherparameters are kept fixed. The methane data are instive to temperature variations at altitudes below the 10-mlevel and at altitudes above the 0.01-mbar level (Fig. 7).Thus, the temperature below the 10-mbar level is not alloto vary and the temperature above the 0.01-mbar level i

equal to that of the 0.01-mbar level. If∂2χ2

∂T 2 is negative thetemperatures are changed by±5 K, whichever is in the di-rection of decreasingχ2. Using this new temperature profila new model is run and a newχ2 derived. Ifχ2 increasesthe original profile is changed by only half of the previocorrection, and the new profile is tested. Onceχ2 is found todecrease the whole process is repeated, taking the last mas the initial guess and looking for a better solution. Onceprogram’s suggested temperature change becomes lesthe test step,�T equal to 0.005 K in this work, the prograis assumed to have converged.

The next step is to try not only a constant shift of ttemperature profile, but also a change in slope. We tespermutations of a positive and negative change in slope

a positive and negative constant offset. We derive the∂χ2

∂T,

∂χ2

∂M, ∂2χ2

∂T 2 , ∂2χ2

∂T ∂M, and∂2χ2

∂M2 , whereM is the slope of the tem-

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perature profile (M = dT/d(logP)). The second derivativvalues are placed into a matrix

S =

∂2χ2

∂T 2

∂2χ2

∂T ∂M

∂2χ2

∂M∂T

∂2χ2

∂M2

.

The terms ∂2χ2

∂T ∂Mand ∂2χ2

∂M∂Tare equal. The slope and consta

offset are then adjusted by

δT = S−1 · (−∇χ2),

where in this case the elements of the arrayδT areδT1 = δT

and theδT2 = δM . If δT · ∇χ2 is greater than zero then thsuggested move is along the gradient rather than opposIf this occurs or if the inversion of the matrixS produces asingular matrix, the gradient approach is applied, where

δT = −5K × ∇χ2

|∇χ2|and the 5K is an arbitrary constant. The adjustment totemperature profile between 10 and 0.01 mbar wouldbe

T = Tprev+ (δT2) × log(P ) + δT1.

The program can use this methodology with any numof free parameters. After running a series of sensitivity tewe found that the methane data could constrain the mslope, and curvature of the temperature profile betweeand 0.01 mbar. Higher-order terms were not considered

To derive the abundances of C2H2 and C2H6, we followthe same procedure as outlined above with a few minornotable, variations. First, we vary the abundances by mplicative factors instead of additive variations as was dfor the temperature. Instead of changing the fitting progrwhich works in linear temperature space versus log psure space, we converted the mixing ratios into the logthe mixing ratio. By operating in log mixing ratio versus lopressure space, an additive constant to the mixing ratlog space is the same as a multiplicative change in linmixing ratio space. Secondly, we only allowed variationsthe mean and slope of the entire C2H2 mixing ratio profile,and only the mean of the entire C2H6 mixing ratio profile tominimize χ2. For our initial guess, we used the abundaprofiles for C2H2 and C2H6 derived inMoses et al. (2000from globally averaged ISO observations (Fig. 5).

The error analysis of the model fit to the data was carout using theχ2 values the program derived after haviconverged on the final solution to the temperature or mixratio profile it was modeling. We assume that theχ2 space iscontinuous and can be described by a quadratic functionrespect to each free parameter. Using the minimum v

of χ2, the ∂2χ2, and the number of free parameters (Np),

∂xi∂xj

we solve forχ2 over a broad range of allxi andxj valuesto derive aχ2 surface. The value ofχ2 for a given set of

arus 177 (2005) 18–31

.

,

Fig. 9. A line plot taken fromFig. 8. The vertical solid line marks the postion of the sub-solar latitude. The sloping solid lines are linear regressto the 3 pressure levels, excluding the 3 points nearest the sub-solar ladisplaying the general trend of temperature versus latitude. The interioror bars represent the 1-sigma uncertainties due to the possible variatthe mean, slope and curvature parameters in fitting each individual spe(Section4.1). The exterior error bars include the modeling, flux calibratiatmospheric division and methane abundance uncertainties (Section4.2).

parameters can be found by

χ2 = 1

2

[ Np∑i=1

Np∑j=1

(δxi)(δxj )

(∂2χ2

∂xi∂xj

)]+ min(χ2).

Using this equation, we solve for all possible combitions of free parameters that yield a value ofχ2 less thanthe minimum value ofχ2 multiplied by (1 + 1/N), whereN is the number of independent spectral elements inobserved spectrum. This provides an estimate of the untainty in the retrieved parameters at the 1-sigma level.value ofχ2 used here has an unknown scaling factor, siwe only know how the noise varies across the spectrumits absolute value. This derivation of the error does notclude possible observational errors such as flux calibraor the removal of telluric absorption, but it does showrange of values that are possible solutions for the modelfile given the free parameters and the data spectrum usconstrain those parameters.

4.2. Temperature and its variation with latitude

As can be seen inFig. 4, the integrated emission ofnumber of the observed methane emission lines show a gual increase from the equator to≈ −65◦ latitude, at whichpoint the emission ramps up at a significantly faster ratpeak at the south pole. This rise in emission is similathat observed byGillett and Orton (1975)andRieke (1975).They, like us, observed Saturn during or slightly after Surn’s southern summer solstice, except their observat
were taken 30 years earlier. Observations made byGezariet al. (1989)just after northern summer solstice show a sim-ilar variation of brightness with latitude except reversed; i.e.,

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the north pole is bright with emission decreasing to the eqtor. So from the earliest infrared scans of Saturn taken duthe 1970’s, observations have been made of Saturn oversaturnian year. These observations of hydrocarbon emisshow distinct trends with the changes in season, suchthe hydrocarbon emission peaks at the summer polesthe emission decreases towards the equator.

Ollivier et al. (2000)using CVF observations taken1992, found that Saturn still exhibited a north polar pein emission at wavelengths corresponding to the emissof C2H2 and C2H6 ≈5 years after northern summer sostice. This suggests the possibility of a lag in the therresponse in Saturn’s stratosphere, as suggested byTokunagaet al. (1978). Such a lag is in direct agreement with tstratospheric seasonal model produced byBézard and Gautier (1985).

Previous determinations of Saturn’s stratospheric temature profile have come from stellar(Hubbard et al., 1997Cooray et al., 1998)or Voyager occultations(Lindal et al.,1985). The stellar occultations are primarily sensitive toµbar level, which is higher in the stratosphere than our C4observations probe (Fig. 7). The Voyager radio occultatiodata constrain temperature profiles between 0.2 mbar1.3 bar. All of these measurements sample spatially disregions of Saturn giving information on the variation of teperature from place to place on Saturn. However, onfinite number of occultation experiments were carried outhe two Voyager spacecraft, and observers must take whoffered by random stellar occultation events. This makedifficult to carry out a methodic program to unravel the vartions of temperature with latitude. In principle Voyager IRobservations containing CH4 emission could have been usto derive stratospheric temperatures in the mbar regiomany different latitudes and longitudes, but the low brigness temperature of Saturn along with the low sensitivitthe IRIS instruments at 8 µm made this derivation unfeas(Hanel et al., 1981, 1982).

Recently, ISO observations of CH4 were successfullyused byMoses et al. (2000)and Lellouch et al. (2001)toderive the temperature of Saturn in the 0.4–5-mbar regbut these measurements were global averages giving nformation on the latitudinal variations of temperature.

Fig. 8 presents a contour plot of the retrieved tempetures, from our CH4 data, of Saturn’s stratosphere with rspect to latitude and pressure. Line plots of temperaturesgiven pressure level versus latitude are shown inFig. 9. Thedominant trend at pressures between 10 and 0.01 mbar iof increasing temperature with increasing southern latituSuperimposed on this trend is a small perturbation centat the sub-solar latitude seen as a temperature increasethe general trend at pressures larger than 1 mbar anddecrease in temperature relative to the general trend atsures lower than 1 mbar. Fitting a line to the data point
Fig. 9, ignoring the 3 data points centered about the sub-solar point, we find that the temperature variation betweenthe equator and the south pole is+8.7 ± 0.5 K at 3 mbar,

l

t

-

t

ea-

Fig. 10. A plot of the zonal mean winds as a function of latitude and psure. Velocities are in m s−1 with positive corresponding to winds movinfrom west to east. We have assumed zero wind velocity at 10 mbarlatitudes and have integrated the thermal wind equation upward fromlevel. Our data set was insufficient to constrain Saturn’s troposphericperature, which is required in order to integrate the thermal wind equafrom the level of wind measurements derived from cloud tracking aSánchez-Lavega et al. (2004).

+9.7± 0.7 K at 0.3 mbar, and+10.8± 0.5 K at 0.03 mbar.The increase in the temperature variation with decreapressure, although not highly significant, is consistent wthe thermal inertia time scale decreasing with decreapressure. We suggest that the perturbation to this gentrend at the sub-solar latitude is dynamically forced eitheexisting winds below the 10 mbar level or vertically propgating waves. It has been shown byConrath and Pirraglia(1983) that the temperature at the 150 mbar level, derifrom Voyager 1 and 2 IRIS data, displayed a general noto-south thermal gradient, which they believed to be seasin nature. This trend however was overlaid by smaller scvariations which they argued were dynamically forced.

Uncertainties in the derived temperature profiles are dinated by possible errors in flux calibration and the assuCH4 abundance. These errors affect the derived tempture profiles at all latitudes in the same manner. Thus,latitudinal variations shown inFigs. 8 and 9should be un-affected by these errors. Errors in flux calibration tendchange the derived temperatures by increasing or decing the temperature profile by a constant offset, whervariations of the CH4 abundance change the slope oftemperature profile while keeping the mean constant. Ancrease/decrease in the assumed CH4 abundance causes aincrease/decrease of the derived temperature above≈1 mbarand a decrease/increase of the derived temperature b≈1 mbar. The combined effects of the uncertainty in flcalibration, atmospheric correction, and plausible CH4 mix-ing ratios between 3.6×10−3 and 5.3×10−3 give error barsof +1.4/−1.2 K at 0.03 mbar,+1.2/−1.1 at 0.3 mbar, and±1.1 K at 3 mbar.

We have carried out a comparison of the temperature re-trievals described inFlasar et al. (2004)with this data setand a more recent data set taken using TEXES on the IRTF

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Fig. 11. A plot of the derived C2H6 mixing ratio at 2.3 mbar (trianglesversus planetocentric latitude, compared to the 1-D photochemical mpredictions(Moses and Greathouse, 2005)for the mixing ratio at the sampressure level and at southern summer solstice, (solid line). The solidcal line represents the sub-solar latitude at−26◦. The dashed line is a linearegression to the data points. The error bars represent the uncertaintyethane mixing ratio due to uncertainties in flux calibration, atmospherivision and the uncertainties of the temperature profiles (Section4.4). Themodeling 1-sigma statistical errors (Section4.1) on the fit of the mean C2H6abundance to the data have not been plotted since they are smaller thindividual data points.

in October 2004. The temperature profiles fromFlasar etal. (2004)produce CH4 emission lines that are significantstronger and broader than either of the TEXES data setscates. Our data suggest that theFlasar et al. (2004)temper-ature profiles are much too warm in the lower stratosphbetween≈0.4 and 4 mbar at the latitudes tested. It seeunlikely that time variability could explain this effect, espcially regarding the comparison to our October 2004 dat

We also compare our results with the predictions ofstratospheric radiative seasonal climate model produceBézard and Gautier (1985). We first note that their modewas produced using the Voyager data as constraints,that the model extends to a minimum pressure of 0.1 mwhich is below the altitude where we measure the peak instratospheric temperature. The Bézard and Gautier mpredicts that, at the time of our observations, the tempture at 5 mbar should decrease slightly from the equatothe south pole. In the model, a few years following the souern summer solstice, this trend reverses and the temperincreases from equator to pole. In contrast we observe atinct increase of temperature from equator to pole at soutsummer solstice. The discrepancy between model andservations may be due to the different abundance proof C2H2 and C2H6 derived here compared to those usedBézard and Gautier (1985), and to the fact that the moddoes not include the effects of stratospheric circulation. Tdiscrepancy indicates a need for new and improved seasclimate models for Saturn. Future observations, supplyinmeasure of the temporal variation of the temperature msurements made here, will shed light on the question of
time scale of thermal variations at a given latitude and willhelp constrain the magnitude of the thermal inertia in Sat-urn’s stratosphere.
arus 177 (2005) 18–31

e

l

e-

-

l

4.3. Stratospheric winds

Due to the lack of visible tracers in Saturn’s stratosphdirect studies of zonal winds in Saturn’s atmosphere hbeen restricted to the troposphere where cloud featcan be seen and tracked in visible image data sets(Smithet al., 1981; Smith et al., 1982; Ingersoll et al., 19Sánchez-Lavega and Rojas, 2000; Sánchez-Lavega e2003; Sánchez-Lavega et al., 2004). However, using temperatures along a constant pressure surface and the thwind equation, one can indirectly measure the wind shethe given pressure level. This indirect method was first uon Saturn data byConrath and Pirraglia (1983). By invertingVoyager IRIS measurements,Conrath and Pirraglia (1983were able to derive the variation of temperature with ltude at 150 mbar. Employing the thermal wind equation twere then able to infer the zonal wind shear at the 150 mlevel. They found that the wind shear was in the sensto dampen Saturn’s jet structure. Using a similar approwe derive the zonal wind shear in the southern hemisphBy applying the thermal wind equation (e.g.,Wallace andHobbs, 1977) to our derived temperature map, we infer tzonal wind shear between 10 and 0.01 mbar. We displayresults inFig. 10. In this analysis we have no informatioon the wind shear between the cloud top measurementssented bySánchez-Lavega et al. (2004)at ≈100 mbar andour temperature measurements starting at 10 mbar. Sinclarge gap exists between the two measurements, we makassumption that the wind at 10 mbar at all latitudes is eqto zero. This allows us to display the behavior of the winabove the 10-mbar level by integrating the calculated tmal wind shear from 10 to 0.01 mbar (Fig. 10). The actualwinds will differ from our derived winds by a latitudinalldependent additive factor of the wind velocity at the 10-mlevel.

Two fairly distinct regions are found inFig. 10. The firstconsists of latitudes south of−25◦ where we find wind val-ues that are predominantly negative. This behavior ispected since the southern hemisphere is experiencinsummer, and our measured temperatures show a clearof decreasing from the south pole to the equator. The odistinct region is that north of−25◦ latitude. Here we semultiple reversals of the wind shear with latitude and prsure. A possible explanation is that these are manifestaof vertically propagating waves.

We compare our results with the linear radiative-dynaical model results presented inConrath et al. (1990). Theonly temperature and zonal wind maps of Saturn preseby Conrath et al. (1990)are for Saturn’s northern sprinequinox,LS = 0, and Saturn’s northern summer solstiLS = 90. Since our observations were taken at Satusouthern summer solstice,LS = 270, we will compare ouresults in the southern hemisphere with theLS = 90 results
in the northern hemisphere assuming that the seasonal ef-fects are close to symmetrical. We find a larger latitudinaltemperature gradient from pole to equator (compareFig. 8

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Fig. 12. The photochemical loss time scale for C2H6 (thick lines) and C2H2(thin lines) as a function of pressure atLs = 273◦ (near southern summesolstice) from the photochemical model ofMoses and Greathouse (2005.The solid lines are for−8◦, the dashed lines for−29◦, and the dotted linesfor −81◦ latitude. The vertical dot-dashed line demarks Saturn’s orbitariod and is included for reference. The star represents an estimate of thscale for meridional transport, assuming the effective meridional eddyfusion coefficientKyy on Saturn is similar to that derived from the evolutiShoemaker–Levy 9 gaseous debris on Jupiter. Note that the photochelifetime for C2H6 is greater than both the estimated transport time sand a saturnian season, whereas the lifetime for C2H2 is less than, but othe same order as, both.

in this paper with Fig. 9b inConrath et al. (1990)) and thusa larger wind shear (compareFig. 10in this paper to Fig. 9ein Conrath et al. (1990)) than that found byConrath et al.(1990). This discrepancy implies that the radiative time costant,tr, is less than the orbital time constant,torb, rather thantr = torb inferred byConrath et al. (1990). The discrepancymight also result from their use of latitudinally independabundance profiles for C2H2 and C2H6 and their omission oaerosol heating and ring shadowing effects.

It must be emphasized that the plotted wind speare calculated with the assumption that the wind spee10 mbar is equal to zero everywhere. This assumptioprobably incorrect, but we lack the data to connectstratospheric data set with tropospheric wind measuremHowever, if the wind speed was known at the 10-mbar lefrom some other method, the 10-mbar wind field couldadded toFig. 10 to find the actual zonal wind velocity apressure levels between 10 and 0.01 mbar. Future TEand Cassini observations will help unravel the time vations of the zonal winds. These time variations will constrthe possible forcing mechanisms that are the cause owind patterns we find.

4.4. C2H6 abundance and latitudinal variation

Some of the earliest observations of Saturn in the m
infrared were done in a bandpass containing emission due toC2H6, in large part because the 12-µm region is a very clearportion of Earth’s atmospheric spectrum. Like our observa-

l

.

Fig. 13. A plot of the derived C2H2 mixing ratio at 1.16 mbar (trianglesand 0.12 mbar (diamonds) compared to the 1-D photochemical modedictions (Moses and Greathouse, 2005)for the mixing ratio at the sampressure levels and at southern summer solstice, solid line and dasherespectively, versus planetocentric latitude. The two dot-dashed linelinear regressions of the data to emphasize the dominant trend. Thevertical line is a reference to the sub-solar point at−26◦ latitude. The smallerror bars are the 1-sigma uncertainties in the fit of the model to the(Section4.1). The total uncertainty in the measurements due to modeflux calibration, atmospheric division and errors in the derivation of teperatures are indicated by the large error bars (Section4.5).

tions, the observations ofGillett and Orton (1975), Rieke(1975), Tokunaga et al. (1978), Tokunaga et al. (1979)andSinton et al. (1980)at this wavelength show a general icrease in emission with increasing southern latitude. Ttrend in 12-µm emission was shown byGezari et al. (1989to have reversed with the reversal of the saturnian seaso

Using the temperature profiles derived in Section4.2, wemodeled the C2H6 spectra and inferred mixing ratio profileat multiple latitudes. We found the 2.3 mbar mixing ratioethane at−83◦ planetocentric latitude to be 1.0+0.3

−0.2 × 10−5.A linear regression of the variation of the mixing ratio wlatitude indicates a decrease of the C2H6 mixing ratio fromthe south pole to the equator by a factor of 1.8, shownFig. 11.

Global average observations of Saturn from ISO indica mixing ratio of 9±2.5×10−6 at the 0.5-mbar level(Moseset al., 2000). Using the updated global-average temperaprofile derived from ISO data byLellouch et al. (2001), theISO-derived ethane mixing ratio fromMoses et al. (2000should be updated to 1.3± 0.3× 10−5. In order to compareour data to that of ISO we averaged the ethane mixing rover all our latitude bins giving us a global average value1.5+0.5

−0.3 × 10−5 at 0.5 mbar, in good agreement within terrors of the updated ISO measurement.

Because we have made a concerted effort to septhe contributions of temperature and abundance in termtheir effects on the emission intensities, these measuremprovide the first quantitative description of the latitudinvariation of C2H6 mixing ratios. No published observation
exist with which we can compare our results. In addition, notwo- or three-dimensional photochemical models are avail-able for comparison.Fig. 11 illustrates how our derived

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ethane mixing ratios compare with the one-dimensionalitudinal/seasonal model ofMoses and Greathouse (2005.This time-variable photochemical model accounts for vations in ultraviolet flux due to orbital position, solar cycring-shadowing effects, and latitude/season. Both the tmal structure and the eddy diffusion coefficient profile inmodel are assumed to be latitude invariant, and windshorizontal eddy diffusion are ignored. Therefore, variatiowith latitude are solely due to changes in solar insolatAt high altitudes, the model predicts that the ethane mixratio will remain roughly constant with latitude in the summer hemisphere due to the nearly constant daily averasolar insolation in the summer hemisphere at solstice. Hever, due to the long vertical diffusion time scales in Satustratosphere, the otherwise dramatic seasonal changespropagate very far into the stratosphere.Fig. 11shows thatthe latitude variation in the lower stratosphere is expectemimic the yearly average solar insolation rather than thesolation of the current season. One would therefore exthe C2H6 mixing ratio to decrease with increasing latituin the summer hemisphere if meridional winds were nofactor (seeFig. 11). The observed increase in the C2H6 mix-ing ratio with increasing latitude at these altitudes proviclear evidence for the importance of meridional transporSaturn.

Ethane is a long-lived photochemical byproduct of meane photolysis; its photochemical loss time scale at−29◦latitude atLs = 273◦ (near summer solstice) is∼2000 yearsat 2 mbar (i.e., the level at which the C2H6 contributionfunction peaks). Although the loss time scale is altitudelatitude dependent, ethane survives longer than the∼29-yearsaturnian year at all pressures greater than the few-micrlevel (seeFig. 12). The photochemical lifetime is relativelshort in its peak production region at∼4×10−4 mbar; how-ever, ethane will take∼40 years to diffuse from its peaproduction region to the 2-mbar level, where it is observGiven the long vertical diffusion time scale and the lophotochemical lifetime of ethane in the middle and lowstratosphere, abundance variations due to seasonally vainsolation are expected to be confined to high altitudes.

There are no current observations that can help ustermine meridional transport time scales at relevant strspheric altitudes on Saturn. On Jupiter, however, meriditransport time scales were determined from observationthe spreading of the Shoemaker–Levy 9 debris after the 1impact of the comet with Jupiter (e.g.,Sánchez-Lavega et a1998; Friedson et al., 1999; Lellouch et al., 2002; Morenoet al., 2003; Griffith et al., 2004). From observations of thspreading of comet-derived gas in the 0.1–0.5 mbar reof Jupiter,Lellouch et al. (2002), Moreno et al. (2003), andGriffith et al. (2004)determined the effective meridioneddy diffusion coefficientKyy to be 2.0–2.5×1011 cm2 s−1.If transport in Saturn’s stratosphere behaves in a sim
manner as on Jupiter with a similarKyy , we estimate themeridional transport time scaleτlat to beL2/Kyy , whereL
is an effective length scale taken to be the equator to pole

arus 177 (2005) 18–31

ot

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distance of∼90,000 km; thus,τlat ≈12 years in Saturn’smiddle stratosphere. Note that our estimatedτlat is muchshorter than the photochemical lifetime of C2H6. We there-fore expect ethane to be strongly affected by meridiotransport on Saturn, and C2H6 should be a good tracer fostratospheric dynamics.

More realistic 2-D or 3-D photochemical models thatclude meridional transport will be needed to addressC2H6 model-data discrepancies shown inFig. 11; observa-tional errors clearly are not large enough to account fordiscrepancies. Possible errors in flux calibration and inderivation of the temperature profiles would lead to unctainties in abundance of a factor of∼1.3 at 2 mbar. Theseerrors should be regarded as affecting an offset for the edata set; they will not alter the latitudinal trend significan

4.5. C2H2 abundance and latitudinal variation

Our observations of the C2H2 ν5 Q-branch show lit-tle variation in emission with latitude except for a minpeak in emission at the south pole (Fig. 4). However, theν4 + ν5 − ν4 hot band, measured in the same spectral seas the Q-branch (Fig. 2) shows substantial variations wilatitude (Fig. 4). Our observations agree with the obsertions taken at wavelengths corresponding to C2H2 emissionby Tokunaga et al. (1978). These early observations did nresolve the weak hot band features and so only exhibitslight peak in emission at the south pole. In their CVFages, taken in late northern summer,Ollivier et al. (2000)observe a slight emission peak at high-northern latitudethe filter settings corresponding to C2H2 emission, but thedata also exhibit a stronger peak between 10◦ and 30◦ lat-itude. This mid-latitude brightening is, to some extent, dto tropospheric thermal effects, not stratospheric, sinceobserve a similar∼17◦ latitude peak in their 10.91-µm observations.

Both,Winkelstein et al. (1983)andCourtin et al. (1984),analyzed their respective ultraviolet and infrared data wC2H2 abundance profiles such that the mixing ratios wassumed constant above 20 mbar, and zero at lowertudes. The derived C2H2 mixing ratios were(9± 3) × 10−8

(Winkelstein et al., 1983)and 2.1 ± 1.4 × 10−7 (Courtinet al., 1984). From the most recent measurements by ISMoses et al. (2000)were not only able to retrieve the abudance of C2H2, but also the slope to the abundance prowith altitude. Their measured values were 1.2+0.9

−0.6 × 10−6

at 0.3 mbar and 2.7± 0.8× 10−7 at 1.4 mbar. Using the updated global-average temperature profile fromLellouch et al.(2001), the ISO-derived acetylene mixing ratio fromMoseset al. (2000)should be updated to 1.4+1.0

−0.7×10−6 at 0.3 mbar

and 3.2+1.0−0.9 × 10−7 at 1.4 mbar. If we again average our d

rived C2H2 abundances over all latitude bins observed,derive a global average at 0.3 mbar of 2.0+1.0 × 10−6 and at
−0.7
1.4 mbar of 4.1+2.9−1.7 × 10−7, in agreement within the errors

with the ISO measurements.

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Fig. 13 shows how the derived acetylene mixing ravaries with latitude in comparison with the photochemimodel ofMoses and Greathouse (2005). The model predictsthat the summer-solstice C2H2 mixing ratio should dropfrom equator to−81◦ latitude by a factor of 1.9 at 1.2 mbaand by a factor of 2.6 at 0.12 mbar. The overall trendsqualitatively similar to what is observed, although the mels clearly underestimate the abundance of C2H2 at highaltitudes, and the overall latitudinal gradient and detastructure of the data differ from that of the model. The quitative shape of the latitudinal gradient for both model adata mimic the average yearly solar insolation at thesetitudes rather than the insolation for the current season.photochemical loss time scale for C2H2 at summer solstice i2–7 years at 1 mbar and 1–6 years at 0.1 mbar, dependinlatitude (seeFig. 12); the results are also dependent on sson. If Saturn’s stratosphere has aKyy similar to Jupiter’s,these time scales are shorter than the estimated meridtransport time scale (∼12 years at 0.1–0.5 mbar) and aslightly shorter than or similar to a saturnian season. Becacetylene is not as long-lived as ethane, its abundance wbe expected to more closely track insolation values, whethe ethane abundance would be less seasonally depeand more sensitive to transport effects. Two predictionscan be made from the current model-data comparisonsthat (1) the seasonal variation of hydrocarbon mixing rawill be more pronounced at high-stratospheric altitudes,(2) the C2H2 abundance should exhibit a greater latitudiand seasonal variation than the C2H6 abundance, unless amospheric transport varies dramatically with season. Nthat the measured mixing ratio at the 1.16 mbar leve2.5+1.8

−1.0 × 10−7 at −83◦ planetocentric latitude and a linefit to the 1.16 mbar data indicates an increase in the ming ratio from south pole to equator by a factor of 2.7 (sFig. 13). The mixing ratio at−83◦ planetocentric latitude aa pressure of 0.12 mbar is 2.6+1.3

−0.9 × 10−6 and is found to in-crease from the south pole to the equator by a factor of 2

Uncertainties in the flux calibration and in our measutemperature profiles due to the uncertainty in CH4 abun-dance combine to give us an overall uncertainty in the aclene abundances at 1.16 and 0.12 mbar of a factor of 1.71.5, respectively. However, these uncertainties do not ethe latitudinal trends inFig. 13.

5. Conclusions

By measuring high-resolution emission spectra inmid-infrared and modeling these spectra using a line-by-radiative transfer code, we have shown that it is possto retrieve detailed information on the latitudinal variatioof temperature, winds, and abundances of C2H6 and C2H2in the stratosphere of Saturn. By automating the mode
process we were able to explore parameter space in an orderly fashion. This automation will allow for the modelingof larger and more complicated data sets in the future. De-

n

l

nt

tailed conclusions about the state of Saturn’s stratospherlisted below.

(1) We find a dominant trend of the stratospheric tempature decreasing from the south pole to the equby ≈10 K between 10 and 0.01 mbar. This confirearly predictions byTokunaga et al. (1978), Sinton etal. (1980)and many others who argued that the increin emission at 7.8 µm from equator to the south pole ding and after the southern summer solstice was a reof the stratospheric temperature increasing with soern latitude.

(2) The sharp peak in methane emission south of−59◦ lat-itude (seeFig. 4) is not due to a sharp increase in tstratospheric temperature there, but to a combinaof the gradual increase in the stratospheric tempture with increasing southern latitude (Fig. 9) and theincreasing angle of incidence of our observations,increasing airmass.

(3) Application of the thermal wind equation to our latudinal- and pressure-dependent map of temperatallows us to make measurements of the zonal wind sin Saturn’s stratosphere. These measurements extwo distinct regions in Saturn’s stratosphere. The wiin the region between the equator and−25◦ latitudeexhibit variations in wind direction and strength wilatitude and altitude, possibly indicating the preseof some sort of dynamical forcing within this latitudrange. The region south of−25◦ latitude is much morequiescent and predominantly displays a trend of eawest winds (assuming that the winds at 10 mbarequal to zero).

(4) The linear fit of C2H6 mixing ratio versus latitude a2.3 mbar decreases by a factor of 1.8 from the sopole to the equator, while the linear fit of mixing ratversus latitude at 1.16 and 0.12 mbar of C2H2 increasesby a factor of 2.7 and 2.3, respectively. The photocheical/seasonal model ofMoses and Greathouse (200does a fairly good job of reproducing the trend of C2H2mixing ratio with latitude, although the predicted vetical slope of the C2H2 mixing ratio profile is possiblytoo shallow in the model. However, the latitudinal vaations in the C2H6 mixing ratio are not explained bthe Moses and Greathouse (2005)model. We believethe latitudinal variation of C2H6 is controlled chiefly bylarge scale stratospheric circulation. The data setwhole suggests that the dynamical time for stratosphcirculation at∼1 mbar lies somewhere in between tchemical loss time of C2H2 at ∼7 years and the chemcal loss time of C2H6 at∼1000 years.

This unambiguous derivation of the variations of teperature, stratospheric zonal winds, and the abundanc
-C2H2 and C2H6 in the stratosphere of Saturn has illumi-nated deficiencies in current stratospheric seasonal modelsof Bézard and Gautier (1985)andConrath et al. (1990)and

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a need for a 2-D photochemical model. These models wbenefit from the creation of a stratospheric global circution model to accurately predict temperatures and latitudvariations of long-lived molecules such as C2H6.

We find that high-resolution observations in the minfrared can be used to constrain temperature, zonal wand abundances of key molecules in the atmospheres ogiant planets. By using high-resolution data, we resolvetelluric spectrum allowing us to ignore the data contanated by Earth’s atmospheric absorption and reducinguncertainties in flux measurements that can often confusinterpretation of lower spectral resolution data. This isportant for planetary observations where the rotation ofplanet is large enough to Doppler shift the observed emisfeatures in and out of telluric absorption features depenon where on the planet one is observing. This positionalpendence of the Doppler shift can modulate the integremission when making observations from the eastern towestern limb of the giant planets. The high resolution aoffers an increase in sensitivity, relative to lower resolutdata, to extremely weak emission lines caused by molecpossessing very low abundances. This sensitivity is duthe fact that the line to continuum ratio increases lineawith spectral resolution until the line is completely resolvThus, we were able to detect very weak unidentified featin the C2H6 emission region (Fig. 3).

It is notable that all of this work may be done from tground, allowing for long observing programs that can msure the temporal variations of key parameters requireunderstand seasonal variations of the outer planets, wis impossible to do with short satellite missions (i.e.,5 year Cassini tour of Saturn) when the time for a full ssonal cycle is approximately 30 years (for Saturn). A secTEXES observing run, where we can repeat these obsetions, will be extremely informative since we will be ablecompare it to this work and derive some limits on the teporal variations of the temperature and abundance latitudvariations. Our data will complement the lower spectralhigher spatial resolution data retrieved from Cassini overnext 5 years. It will be important to make several groubased observing runs during that time so that the datatrieved with TEXES can be directly compared to that froCassini. In this way TEXES observations after Cassinibe used to extrapolate trends observed in the Cassiniwith some level of certainty in their correlations. The crent data set gives a seasonal context with which the Cateam can compare their results.

Acknowledgments

Special thanks to Joe Tufts who had to listen to my echanging explanations of what all this data meant. This w
was supported by USRA Grant 8500-98-008, NSF GrantAST 0205518, and by the Lunar and Planetary Institute,which is operated by the Universities Space Research Asso
arus 177 (2005) 18–31

,e

-

l

a

i

ciation under NASA CAN-NCC5-679. This paper represeLPI Contribution 1235.

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