a re-analysis of the 1971 beta scorpii occultation by ... › perso › bruno-sicardy › biblio ›...

s

y

s. 29,lculate newwledge offluctuationstmospherict modes of

Icarus 168 (2004) 324–335www.elsevier.com/locate/icaru

A re-analysis of the 1971 Beta Scorpii occultation by Jupiter:study of temperature fluctuations and detection of wave activity

Elisabeth Raynaud, Katia Matcheva,1 Pierre Drossart,∗ Françoise Roques, and Bruno Sicard

LESIA, CNRS–UMR 8109, Observatoire de Paris, 5 place Jules Janssen, 92195 Meudon CEDEX, France

Received 19 March 2003; revised 26 August 2003

Abstract

Data from the 13 May 1971β Scorpii occultation by the southern polar region of Jupiter (Vapillon et al., 1973, Astron. Astrophy135–149) are re-analyzed with current methods. We correct the previous results for an inacurrate background estimation and catemperature profiles, that are now consistent with the results of other observers of this occultation, as well as with the current knothe jovian atmosphere. The characteristics of the profiles of temperature gradient and the spectral behavior of the temperatureare found to be similar to the results of previous investigations of planetary atmospheres and in agreement with the presence of apropagating gravity waves in the jovian atmosphere. We use a wavelet analysis of the temperature profiles to identify the dominanwave activity and compare the reconstructed temperature fluctuations to model-generated gravity waves. 2003 Elsevier Inc. All rights reserved.

Keywords:Jupiter; Occultations; Atmospheres, structure; Dynamics

rnthis

s: itstialnts

das a

op-as

ione

ere-

lding

d bynd

’ ledell

lta-

ub-andup-73;

ordsevedturefiles

baredto

boute-uesatio

theques

1. Introduction

On 13 May 1971,β Scorpii was occulted by the southehemisphere of Jupiter. The two brightest components ofmulti-star system areβ ScoA(V = 2.76) andβ ScoC(V =2.94), separated by 13 arcsec in position angleP = 64◦ (theposition angle express the relative position of two staris the angle between the line joining them and the celenorth direction). The occultations by the two componecould be observed separately. The starβ ScoA is an unre-solved spectroscopic binary of spectral typeB0.5V and pe-riod 6.8 days, and has a fainter companionβ ScoB(V ∼ 10),at 0.5 arcsec in position angleP = 24◦. The starβ ScoC isof spectral typeB2V . The 1971 occultation by Io revealethat it is a double star (Bartholdi and Owen, 1972) and hfainter companion at 0.1 arcsec.

Theβ Scorpii occultation provided an unprecedentedportunity to study the jovian upper atmosphere. This wthe first time in nearly twenty years (since the occultatof σ Arietis, with V = 5.5, observed by Baum and Codin 1953) that such an important event took place. Th

* Corresponding author.E-mail address:[email protected] (P. Drossart).

1 Present address: Department of Astronomy, Space Sciences BuiCornell University, Ithaca, NY 14853, USA.

0019-1035/$ – see front matter 2003 Elsevier Inc. All rights reserved.doi:10.1016/j.icarus.2003.10.021

,

fore it was observed from various locations and analyzethree groups: the ‘Meudon group’ led by M. Combes aJ. Lecacheux (Combes et al., 1971), the ‘Texas groupby W.B. Hubbard (Hubbard et al., 1972) and the ‘Corngroup’ led by J. Veverka (Veverka et al., 1974). Occutions of the unresolvedβ ScoA system, andβ ScoC allowedthe different groups to constrain the radius of Jupiter (Hbard and Van Flandern, 1972; Lecacheux et al., 1973),to retrieve density and temperature profiles of the jovianper atmosphere (Hubbard et al., 1972; Vapillon et al., 19Veverka et al., 1974). However, although the probed chon the planet were rather close, the different teams retrivery different results concerning the derived temperaprofiles. The Meudon group obtained temperature prowith a very large negative gradient, close to−1.5 K km−1,and temperatures of 350 K at a pressure level of 1 m(Vapillon et al., 1973). The Texas group has publishonly refractivity profiles, but the temperatures relatedthese profiles show a smaller negative gradient, of a−0.6 K km−1 (Hubbard et al., 1972). The Cornell group rtrieved a quasi-isothermal profile, with temperature valaround 200 K (Veverka et al., 1974), depending on the rof helium to hydrogen that was uncertain at that time.

In this paper, we re-analyze the Meudon data usingknowledge acquired since 1971, as well as new techni

http://www.elsevier.com/locate/icarus

Re-analysis ofβ Sco 1971 occultation data 325

re-ingunde-

in

id-er oles

thethatere

es.ndem-evelefor

ud eentanderethethsves

peileoitermlay-adiohasrav-magest

ter-seneup

ry touse

eatngthrse

fluc-o th.

y,

71).data

taandal.

f theet

the

for occultation data study. Section 2 is devoted to dataanalysis with modern tools. In Section 3, after discussthe importance of an accurate estimation of the backgroflux, we fit isothermal lightcurves to the data in order to drive the scale heightH , and perform an inversion to obtatemperature profiles.

The subject of wave activity in Jupiter’s upper and mdle atmosphere has been a topic of discussion in a numbprevious investigations. Analyzing the temperature profiresulting from the inversion of theβ Sco lightcurves of theCornell group, French and Gierasch (1974) pointed outpresence of small amplitude variations. They concludedthe observed quasi-periodic temperature fluctuations wconsistent with the propagation of internal gravity wavThey determined a typical vertical wavelength of 13 km aan amplitude of 5 K for the waves present in the egress tperature profile of the jovian stratosphere, at a density lof 1013 cm−3. The 1999 occultation of HIP 9369 by thnorthern polar region of Jupiter also showed evidencepropagating waves in the same pressure regime (Raynaal., 2003). The occultation was observed from four differlocations. Correlation studies of the resulting lightcurvesa wavelet analysis of the retrieved temperature profiles wused to identify a single wave mode propagating alongplanetary meridian with vertical and horizontal wavelengof respectively 3 and 70 km. Signatures of gravity wahave been also detected at lower pressure levels. The temature profile derived from the deceleration rate of the Galprobe during its entry stage in the thermosphere of Jupshows a variability with a typical scale from 90 to 150 k(Young et al., 1997). The presence of regularly spaceders of enhanced electron density observed during the roccultations of the Voyager and the Galileo spacecraftalso been attributed to the propagation of atmospheric gity waves and their interaction with the ionospheric plas(Matcheva et al., 2001). The electron density profiles suga typical vertical scale of 75 km for the present waves.

In the current study we use a wavelet analysis to demine the parameters of the dominant wave modes prein the upper stratosphere of Jupiter, as revealed by thβ

Scorpii stellar occultation observed by the Meudon gro(Section 4). In that respect our results are complementathe wave analysis of French and Gierasch (1974). Theof the forward wavelet transform allows us to study in grdetail the amplitude, the phase and the vertical wavelebehavior of the present waves. We then utilize the invewavelet transform as a tool to reconstruct temperaturetuations at selected scales and compare the results tproperties of model-generated gravity waves (Section 5)

2. Re-analysis of the 1971 Meudon data

The Meudon group observed theβ Sco occultation in theCa II K line (λ = 0.3934 µm) from Radcliffe Observatorsituated in South Africa (28◦13′43.7′′ E, 25◦47′16.9′′ S).

f

t

r-

t

e

Observational details can be found in Combes et al. (19The star path on Jupiter, recalculated from Hipparcosand the JPL ephemeris calculation site,2 is shown in Fig. 1.We digitalized the occultation lightcurves from the dacharts of 1971. The scanning procedure was checkedyielded curves identical to those published by Vapillon et(1973) (see Fig. 2).

Fig. 1. Star path in reference to the planet. Upper panel: path ofβ ScoA,in the sky plane, centered at the center of Jupiter. The position angle opoles’ axis in this frame is 11.32◦ . Lower panel: stellar path on the planon a polar view. Half-light points for ingress and egress are plotted onstellar path, their jovian coordinates are respectively (58.69◦ S, 322.38◦ W)and (56.24◦ S, 197.67◦ W) with system III longitudes.

2 http://ssd.jpl.nasa.gov/horizons.html.

http://ssd.jpl.nasa.gov/horizons.html

326 E. Raynaud et al. / Icarus 168 (2004) 324–335

light-

twoin

at-elianusere-andorelate

lted

s ofoiseet

rater tocalehts

bers

aredtion

ned

lar

d inten-

rr,enceuredro-sionnt

x-surefile,ivityem-

areal.

ns.eeds

eralestlev-eiffures

ISthe

at isrvede isvel,ril-

audpen-ltedalf-

tomtionthehaveck-tric

w-t theeacies

Fig. 2. Ingress (top panel) and egress (bottom panel) normalizedcurves.

We analyze the data presented in Fig. 2 using theclassical methods for occultation lightcurves, reviewedWasserman and Veverka (1973): lightcurve fitting withmospheric models on the one side, and numerical abinversion on the other side. These methods were alsoby the Meudon group in 1971 to obtain the publishedsults. However, today’s progress in numerical analysisthe improved computing capabilities allow us to obtain maccurate results. For ingress and egress, we first calcudimensionless measure of the noiseε

√v⊥/H , whereε is

the rms variance per second of the normalized unoccuflux, v⊥ the star speed perpendicular to the limb, andH thescale height (French et al., 1978). We obtain noise value0.018 for ingress and 0.021 for egress, showing that the nlevel is sufficiently low for an accurate inversion (Youngal., 2001). Following Baum and Code (1953), we genemodel lightcurves for an isothermal atmosphere in ordeobtain the best fit to the data, and thus estimate the sheightH of the atmosphere. Our best fit yields scale heigof H = 34.9± 1.6 km for ingress, andH = 34.6 ± 0.9 kmfor egress (the errors are fitting errors only). These numare consistent with the 1971 estimation ofH = 30± 5 km(Combes et al., 1971). However, they are large compto the values derived from the 1989 equatorial occultaby Hubbard et al. (1995) (yieldingH = 27.2 km at ingressand H = 30 km at egress), as well as to those obtaiby Raynaud et al. (2003) (24.8 < H < 29.7 km for eightlightcurves) for the 1999 occultation by the northern poregion.

We invert the lightcurves using the method describeVapillon et al. (1973). We calculate the pressure equipotials of the planet with the following equation:

U(r, θ)= −GM

r

[1−

∑n=2,4,6

Jn

(a

r

)n

Pn(cosθ)

]

(1)− 1ω2r2 sin2 θ,

2

d

a

wherePn are Legendre polynomials,ω the rotating angulaspeed of the planet,Jn the gravitational moments of Jupiteanda the equatorial radius. The gravitational field is thobtained byg = −∇U . The value of the helium abundanratio well below the homopause is set to the value measby the Galileo probe (von Zahn et al., 1998). A vertical pfile of helium abundance is then generated using a diffuequation, with the value of the eddy diffusion coefficiefixed toK = 2×106 cm2 s−1, (Drossart et al., 2000) and etrapolated at the latitudes of occultation along the presequipotentials. From the helium abundance vertical prowe then obtain the molecular mass and specific refractprofiles needed for a correct inversion. The inverted tperature profiles obtained for both ingress and egressdisplayed in Fig. 3 and agree with those of Vapillon et(1973).

These profiles are highly unlikely for several reasoFirstly, the very large negative temperature gradient excthe adiabatic gradient(∂T

∂z

)ad

= −Γ = −g/cp = −1.81 K km−1

(wherecp is the specific heat at constant pressure) in sevpoints (marked with crosses in Fig. 3). That would suggthat the atmosphere is convectively unstable at theseels, a result which is not supported by observations (Set al., 1996). Secondly, the high temperatures at pressP > 100 µbar (Fig. 3) are not compatible with the CH4 emis-sion in theν4 band at 7.8 µm, as observed by Voyager/IR(Hanel et al., 1979). Such temperatures extrapolated to10 mbar pressure level lead to a methane emission th70 (270) times higher for ingress (egress) than the obsevalue (Orton et al., 1991). Thirdly, the jovian atmosphernow known to be roughly isothermal below the 10 µbar ledue to radiative equilibrium between CH4 emission and solaflux absorption (Yelle et al., 2001). The profiles from Vaplon et al. (1973), shown in Fig. 3, are thus not credible.

3. Estimation of the background flux

It has been shown before (Roques et al., 1994; Raynet al., 2003) that the inverted temperature profiles are dedent on the photometric quality of the data: the unoccustellar flux influences the shape of the profile above the hlight level, and the background level changes the botvalue of the temperature profile. An inaccurate estimaof the background flux during the occultation could because for the inconsistencies in the inversion results wepointed out. Berezne et al. (1975) explained how this baground flux was calculated and claimed a 1% photomeaccuracy for the lightcurves of Vapillon et al. (1973). Hoever, their calculation was based on the hypothesis thacontribution of the jovian limb is only proportional to thdisk area seen by the photometer and that the inaccur


l li
Fig. 3. Temperature profiles obtained by inversion of the lightcurves in Fig. 2, for a background flux equal to 0. Ingress temperature profile is in fulne, andegress profile is in dashed line. Crosses on the profiles mark the points where the temperature gradient is super-adiabatic.
undre

le-ess

eeninel

reeves

,

isnow).

es.yedoreainera-tentat-

wasure.ck-weturet of

Fig. 4. Inverted temperature profiles, for ingress, for values of backgroflux going fromφ0 = 0 toφ0 = 0.1, with a 0.01 step. The darker curves athe ones with smallerφ0.

of the manual guiding were negligible. To check the revance of their background estimation, we invert the ingrlightcurve imposing different background levelsφ0, fromtheir estimated valueφ0 = 0 to φ0 = 0.1. The results areshown in Fig. 4. We can see that a background flux betw0.08 and 0.09 gives a nearly isothermal profile. To determa more accurate value ofφ0, we perform new isotherma

fits to the lightcurves, leaving the background flux as a fparameter. Fitting only the external parts of the lightcur(i.e., for t < 18h42 UT at ingress, and fort > 19h46 UTat egress), we obtain good fits forφ0 = 0.087± 0.004,H = 26.8 ± 1.7 km, andt1/2 = 67002.5± 0.4 s at ingressand φ0 = 0.068± 0.004, H = 24 ± 0.2 km, and t1/2 =71337.1 ± 0.4 s at egress. The isothermal fit for ingressdisplayed in Fig. 5. The values for the scale heights aremore in the range of previous measurements (see above

We set the background flux atφ0 = 0.087 for ingress andφ0 = 0.068 for egress and invert the resulting lightcurvWe accordingly obtain quasi-isothermal profiles, displain Fig. 6. The temperature profiles in Fig. 6 are now mconsistent with those of Veverka et al. (1974). They remconvectively stable, and the corresponding bottom temptures of 190 K for ingress and 150 K for egress are consiswith the observations of methane emission lower in themosphere (Orton et al., 1991).

The only need to re-analyze the temperature profilesto obtain a realistic profile of the atmospheric temperatThis goal has been achieved with a correction of the baground stellar flux. In the remaining part of the paper,shall focus on the analysis of the small scale temperavariations in the retrieved profiles, which are independenthe background flux estimation.


d

Fig. 5. Isothermal fit (plain solid line) of the observed ingress lightcurve (dotted line) forφ0 = 0.087± 0.004,H = 26.8± 1.7 km, andt2 = 67002.5± 0.4 s.The level of background flux for the best fit is indicated with a dash-dotted line.

Fig. 6. Temperature profiles obtained with the background levels given in the text, for ingress (left) and egress (right). The mean profiles calculatefrom thewavelet reconstruction forλz > 70 km (see text) are plotted in dash-dotted line.

ate

ilo-e ofandtructhe

e isn bewithstel-03)t al.,rdytingient

e gra-

4. Temperature variations

4.1. Temperature gradient

From the temperature profiles in Fig. 6, we calculthe vertical temperature gradient∂T /∂z, shown in Fig. 7.From now on, our vertical scale will be expressed in kmeters above the half-light level, situated at a pressurP ∼ 2.8 µbar. One can see in Fig. 7 that both ingressegress gradients are very asymmetric. Round shaped stures appear on the negative side, with values close to

-

adiabatic gradient when the global temperature profilessentially isothermal, whereas sharp, large peaks caobserved on the positive side. Temperature gradientssimilar properties have now been observed in severallar and radio occultations, by Jupiter (Raynaud et al., 20or other planetary bodies such as Neptune (Roques e1994), Venus (Hinson and Jenkins, 1995), or Titan (Sicaet al., 1999). It is interpreted as a signature of propagagravity waves, breaking whenever the temperature gradreaches the adiabatic value (here−Γ = −1.81 K km−1), andthus causing the rounded appearance of the temperatur


Fig. 7. Temperature gradients for ingress (left) and egress (right). The adiabatic gradient is shown for comparison in dashed line.

samrdy

isi-averti-the

eser-ingthe

theby

uren

rmpose

byon

aly-d et

thecut-ed

uc-

r

dc-r

tua-d to,um’ro-lsoe

tua-hericmi-eters.inu-thee all

po,ans-sig-

but. Ineri-eletionwooef-ale

dients at negative values. Ray crossing could cause thekind of asymmetric structures at the lowest altitudes (Sicaet al., 1999), but would provide no explanation for the vble cut-off precisely at the adiabatic value. The gravity winterpretation is also consistent with the fact that the vecal scale of the structures is larger in the upper part ofatmosphere (∼ 10–15 km) than at the bottom of the profil(∼ 1 km). This dependence of the structures’ minimum vtical scale with altitude cannot be explained by the flattenof the smoothing star’s diameter only: as a matter of fact,diameter of the unresolved binaryβ ScoA is of the order of4 km before the occultation (Hubbard et al., 1972) andvertical resolution at the bottom of the profiles is limited

the Fresnel scale (√λobsDJup−Earth= 0.5 km).

4.2. Spectral behavior of temperature fluctuations

To extract the small scale fluctuations of temperatfrom the inverted profileT (z), we need to calculate a meaprofile 〈T 〉(z). We use the continuous wavelet transfo(Farge, 1992; Torrence and Compo, 1998) and decomthe temperature profile onto the different scales allowedthe length of the data set. For more detailed informationthe continuous wavelet transform and its use for the ansis of occultation data, we refer the reader to Raynaual. (2003). The mean temperature profile〈T 〉(z) is definedas the reconstruction of the temperature profile usinginverse wavelet transform for scales larger than a givenoff scale λmean

z . The calculated mean profiles are plottin Fig. 6 in dash-dotted line (λmean

z = 70 km for a totallength of the profile equal to 140 km). The small scale fltuations, of wavelengths smaller thanλmean

z , are then givenby δT (z) = T (z) − 〈T 〉(z). We calculate the wavelet powe

espectrum of the fluctuations,PδT (z)(λz), as a function of thevertical wavelengthλz of the structures in the profiles, anplot it in Fig. 8. A straight line, corresponding to a spetrum P(mz) = m−3

z , wheremz is the vertical wavenumbe(mz = 2π/λz), is plotted for comparison. This−3 spectralindex has been observed on Earth for temperature fluctions caused by saturated gravity waves, and is referrein atmospheric science literature, as the ’universal spectrfor gravity waves (Smith et al., 1987). For the inverted pfiles in this work, the spectra of the fluctuations have aslopes close to−3, which is likely to be a signature of thpresence of propagating gravity waves.

4.3. Determination of dominant wave modes

The observed power spectra of the temperature fluctions entails the presence of a broad spectrum of atmospwaves. We now focus our attention on identifying the donant modes present in the atmosphere and their paramFor this analysis we use a modified version of the contous wavelet transform. In the classic wavelet transform,scaled and translated versions of the mother function arnormalized to have the same energy (Torrence and Com1998). Hence the results from the continuous wavelet trform visualize the energy repartition in the decomposednal between the different scalesλz for each altitude point. Asa result, two monochromatic waves of equal amplitudesdifferent wavelengths have different wavelet coefficientsthis work we want to compare the amplitudes of the podic structures and not their energy. In the modified wavtransform we relax the condition for energy normalizatof the individual wavelet functions and require that any twaves with the same amplitude result in equal wavelet cficient. This modification allows us to study the small sc


).
Fig. 8. Power spectra ofδT (z) (see text) for ingress (full line) and egress (dashed). A line of slope−3 has been plotted for comparison (dash-dotted line
fluc-

and-nd

ps iam-enof

tkedthe

eret thedatpa-

ofileuxtlyp ofare

pro-

e at-andtheex-turenen

nser-calic),

f dis-sion,theen-Butdis-d/orn theex-andtifyture

esaveKBtionddyindar isd inofilero-

lfitsap.

structures without being overpowered by the large scaletuations. The non-normalized wavelet coefficientsA(z,λz)

are proportionnal to the amplitude of the fluctuationsvary accordingly with the altitudez and the vertical wavelengthλz. The results from the analysis of the ingress aegress temperature profiles are shown as contour maFig. 9. The lowest dark line in Fig. 9 represents a zeroplitude. A cut-off value for the large amplitudes has beimposed for better viewing. We calculate the locationsthe local maxima ofA(z,λz) in the(z, λz) plane and detec5 maxima for ingress and 4 for egress, which are marby black stars in Fig. 9. The locations of the maxima in(z,λz) plane determine the vertical wavelengthsλobs

z of thewave modes present in the data, and the altitudes whmaximum amplitude is achieved. In order to ensure thadetected wave modes are not due to artefacts of theinversion and that they are independent of the modelrameters, we repeat the analysis using temperature prinverted for different values of the background stellar fl(with 0.1> φ0 > 0.06). Only the modes that are persistenpresent in all wavelet maps are retained for the next steour analysis. The vertical wavelengths of these modes22.5, 13.9, 9.3, and 2.9 km for the ingress temperaturefile, and 10.5, 5.9, and 1.9 km for the egress profile.

5. Wave simulations and interpretations

When an atmospheric wave propagates through thmosphere, the wave amplitude, vertical wavelengthphase are affected by variations in the properties ofbackground atmosphere. A vertically propagating waveperiences a natural exponential growth of its tempera(velocity) amplitude as a direct consequence of the expo

n

a

a

s

-

tial decrease of the atmospheric density and energy covation. If the amplitude becomes large enough for the logradients to exceed the stability criteria (static or dynamthe wave becomes unstable and overturns. A number osipative processes, such as molecular and eddy diffuthermal conduction, or radiative damping, can also limitwave amplitude growth, causing the wave to deposit itsergy in the background atmosphere (Lindzen, 1981).even if the atmosphere is conservative, i.e., there is nosipation, variations in the background temperature anpresence of wind shear will cause observable changes iwave amplitude and vertical wavelength. In our study weploit this dependence of the wave amplitude, wavelengthphase on local atmospheric properties to positively identhe presence of gravity waves in the retrieved temperaprofiles.

We perform a numerical simulation of the wave modidentified in Section 4.3 and compare the simulated wproperties with the observations. We use a hydrostatic Wwave model in a dissipative rotating atmosphere. Dissipais due to molecular viscosity, thermal conduction and ediffusion. Because no information is available for the wstructure at these altitudes we assume that no wind shepresent. A detailed description of the model can be founMatcheva and Strobel (1999). The mean temperature prfor the wave simulations is obtained using the wavelet pcedure we describe in Section 4.2 withλmean

z = 30 km. Theeddy diffusion coefficient isD0 = 300 m2 s−1 at the 1 µbarlevel and decreases asD ∝ ρ−0.5 (Atreya, 1986), whereρ isthe density.

For each of the identified wave modesλobsz , the numerica

simulation is performed with a vertical wavelength thatthe observation at the altitude of the peak in the wavelet m


Fig. 9. Amplitude contour maps of the ingress (top panel) and egress (bottom panel) temperature profiles in Fig. 6. The warm colors represent high amplitudes.The local extrema are marked with stars, and their vertical wavelengthsλobs

z are given in the text. The points subject to the edge effects due to the wavelettransform have been excluded from both maps.


Fig. 10. Brunt–Vaisala frequency for immersion.

ro-ature

of

d byshedsipa-wave

solidr bet

ack-velesengths

h thef the

) forcus-

icalh thee theatedhows.c-

ightsichingr for

edgeter-

Thisatelywsthe

Fig. 11. Analysis of the 13.9 km structure. (a) Vertical wavelength pfile for a simulated gravity wave. (b) Comparison between the temperamplitude of the simulated wave (thick solid line) and the amplitudethe reconstructed temperature fluctuations (thin solid line) for 12 km<

λz < 17 km. The amplitude of the reconstructed wave is representethe envelope of the actual fluctuations and their mirror image. The daline corresponds to the amplitude of the simulated wave when no distion is present. (c) Comparison between the phase of the simulated(thick solid line) and the reconstructed temperature fluctuations (thinline). Here again, both phases have been represented symmetrically foter viewing.

From the simulation we determine the range(λmin, λmax) inwhich the vertical wavelength changes as a result of bground temperature variations. We use the inverse watransform to reconstruct the temperature fluctuations prein the observed temperature profile, using only wavelenλz within the expected range(λmin < λz < λmax). The recon-structed temperature fluctuations are then compared witwave simulations. For completeness, we present a plot obuoyancy frequency in the region of interest in Fig. 10.

We present one figure with three panels (Figs. 11–14each peak in the data wavelet map followed by a dis

-

tt

Fig. 12. Same as Fig. 11 but for the 22 km structure.

sion in the text. The left panels show the simulated vertwavelength behavior of the wave as it propagates througnon-isothermal atmosphere. The middle panels comparreconstructed temperature fluctuations with the simulwave temperature amplitude, and the right panels showwell the phase of the simulated wave fits the observation

Ideally one should be able to follow the wave-like struture over several scale heights with at least two scale hebelow the altitude of wave damping. The region over whthe wavelet analysis returns useful information regardthe present wave modes becomes progressively smallelarger scales, as a result of the increasing importance ofeffects. Therefore large scale structures are difficult to inpret uniquely as a result of propagating waves.

We start our discussion with the best wave candidate.is the 13.9 km ingress structure that peaks at approxim−45 km below the mid-occultation level. The peak shoa significant power and is well situated in the middle of


es.gth

ctu

uc-

ica-vetal

rdeon-ytheec-thelt o

herepa-the

sim-

thetua-ree-ith a

vedindour

icaluctu-esstinge iskmicalb-metry

at-y innaud

kmn seerva-ase

oveItrgeer

alel.ree-not

kelyavity

is-wellmu-fileree-ob-all

ions

es-

mcurs



sampled region, with no significant influence from the edgThe simulation shows (Fig. 11) that the vertical wavelenof a gravity wave that fits the observations atz = −45 kmvaries betweenλmin = 12 km andλmax = 17 km throughoutthe observed region. The reconstructed temperature fluations for wavelengths 12 km< λz < 17 km is comparedwith the simulation of the wave amplitude. The reconstrtion indicates a global maximum atz = −40 km with sev-eral smaller local maxima at−90, −5, and 27 km. Thepresence and the location of a global maximum is indtive for wave dissipation at this altitude. The level of wadissipation is determined by both vertical and horizonwavelengths. At this point the horizontal wavelengthλh isundetermined and is treated as a free parameter. In oto be able to fit the reconstructed amplitude, the horiztal wavelength should beλh = 750 km for the chosen edddiffusion coefficient. The results show an excellent fit toobserved amplitude. Most notably the locations of the sondary maxima and minima are very well predicted bysimulations. These secondary peaks are entirely a resu

-

r

f

the non-isothermal structure of the background atmospand cannot be artificially adjusted by varying the modelrameters. The same amplitude variations are visible intemperature profile when no dissipation is present in theulations.

The next step is to compare the phase behavior ofsimulated wave and the reconstructed temperature fluctions (Fig. 11c). Once again we have a rather good agment between the observations and the simulations wmore notable discrepancy at about−15 km below the mid-occultation level where we also over-predict the obseramplitude. This discrepancy could be a result of a small wshear at this altitude, an effect which we do not include insimulations.

Based on our analysis of the wave amplitude, vertscale and phase, we conclude that the temperature flations responsible for the 13.9 km structure in the ingrtemperature profile are most likely a result of a propagaatmospheric gravity wave. The maximum wave amplitudabout 1 K. If the actual vertical wavelength is indeed 14this wave is not in a saturated regime. The actual vertwavelength however might differ significantly from the oserved one as a result of the slanted phase plane geoof the wave and the non-radial stellar path through themosphere. For more detailed discussion of this ambiguitthe actual wave parameters we refer the reader to Rayet al. (2003).

The results from our analysis for the 22, 9, and 3peaks are presented in Figs. 12–14, respectively. One cathat we are not able to achieve such a good fit of the obsetions as for the 14 km structure. The amplitude and the phof the simulated 22 km wave fit well the observations abz = −60 km but fail to explain the data below that level.is possible that the significant power contained in the lascales belowz = −60 km reflects stationary features raththan propagating waves.

It is also difficult to reconcile the reconstructed verticprofile of the 9 km structure with a gravity wave modAlthough the predicted phase looks in reasonable agment with the observations the simulated amplitude doesfit the observed temperature fluctuations. It seems unlithat these fluctuations are caused by an atmospheric grwave.

Our simulations of the 3 km structure look more proming. The predicted behavior of the wave phase agreeswith the phase of the reconstructed fluctuations. The silated wave amplitude profile also captures the overall proof the observed temperature fluctuations although the agment is more qualitative than quantitative. Because theserved vertical wavelength of this wave mode is very smthere is a concern about the resolution of the observat(∼ 3 km in the upper part of the profiles,∼ 0.5 km at thebottom) and our capability to properly resolve the wavepecially at higher altitudes.

It is difficult to apply a similar analysis to the 10.5 kstructure in the egress temperature profile. The peak oc


ichhin-

be-ve-at-

e isifi-des.gree

allave-

surelta-outat-

eddycalay

estinedlsoruc-lta-ionfi-

thamave

i-

he

re-able(2)with

cur-nta

r.

ture

eighthetionsratedthelta-l asointeric

es inThetua-thatpro-heschodethe

erefilessi-schetectem-ouldn theern,

s-d-ellethel deon.mu-n-ro-RL:

ts and

iter

lta-

very close to the bottom of the atmospheric region for whdata is available (see Fig. 9), and the wavelet analysis isdered by strong edge effects.

To summarize the results from the simulations, welieve that the temperature fluctuations with a vertical walength of about 14 km are a result of a vertically propaging gravity wave. The temperature amplitude of the wavabout 1 K and is damped by eddy diffusion which signcantly exceeds molecular diffusion effects at these altituThe wave does not appear to be saturated which is in ament with the observed vertical wavelength and the smtemperature amplitude. The corresponding horizontal wlength is 750 km and the wave period is 263 min.

The wave reaches a maximum amplitude at a preslevel of 11.5 µbar, about 40 km below the half-light occution level. By the time the wave reaches this altitude, ab63% of the wave energy is deposited in the backgroundmosphere as a result of wave dissipation dominated bydiffusion. Assuming no significant wind shear, the vertienergy flux of the wave at the level of generation, awfrom the region of dissipation, is about 0.1 erg cm−2 s−1.Once again, the exact wave parameters and therefore themated energy flux carried by the wave cannot be determuniquely from a single temperature profile. A question aarises about the detectability of periodic atmospheric sttures of a relatively short horizontal scale with an occution technique. As a matter of fact, most of the refractof the stellar light during an occultation occurs within anite horizontal regionL = √

2πrH ≈ 3600 km, wherer isthe planetary radius. Sicardy et al. (1999) demonstratedthe amplitude of the stellar flux fluctuations resulting frothe presence of a monochromatic atmospheric gravity wwith a vertical wavelengthλz and a projection of the horzontal wavelength along the line of sightl = λh/cosθl , isnot significantly reduced if

(2)l

λz> η, η =

(r

4H

)0.5

,

whereθl is the angle of the line of sight with respect to thorizontal direction of wave propagation(0◦ < θl < 90◦)and for Jupiterη ≈ 25. Therefore, as long as the abovequirement is satisfied, a wave structure is well detecteven if the horizontal wavelength is very small. Equationalso suggests that waves propagating at a large anglerespect to the line of sight are easier to detect. In therent study we have no means to determine the horizodirection of wave propagation andθl is a free parameteNevertheless it is easy to see that for a wave withλz = 14 kmandλh = 750 km

(3)l

λz� λh

λz= 53> η

and (2) is satisfied for any angle of wave propagation.

-

i-

t

l

6. Conclusion

A new estimate of the background flux in the 1971β Scooccultation data has allowed us to obtain new temperaprofiles for the high southern latitudes (∼ 60◦) in the jovianatmosphere. The updated value for the pressure scale h(H = 24± 1.5 km) brings the observational results of tMeudon group into a better agreement with the observaof the Texas and the Cornell groups. We have demonstthe usefullness of the continuous wavelet transform foranalysis of small scale structures in the inverted occution profiles. The temperature gradient profiles, as welthe spectral behavior of the temperature fluctuations, pto the presence of gravity waves in the probed atmosphregion. We have been able to detect several wave modthe wavelet decomposition of the temperature profiles.detailed comparison of the observed temperature fluctions with model-generated gravity waves demonstratesat least one of the identified wave modes in the ingressfile (λz = 13.9 km) shows a remarquable similarity with tproperties of an inertia-gravity wave. French and Giera(1974) pointed out the presence of a 13 km wave-like min the egress temperature profile that resulted fromlightcurves of the Cornell group (Veverka et al., 1974). Thwas however no information on the exact vertical proof the wave amplitude and vertical wavelength. It is poble that the 13 km wave identified by French and Giera(1974) corresponds to the 10.5 km wave mode that we din our egress wavelet map. A wavelet analysis of the tperature profiles of the Texas and the Cornell groups callow a comparison between the present wave modes idifferent profiles, and in the case of a common wave pattthe determination of the exact wave parameters.

Acknowledgments

We thank F. Arenou for his efforts to improve the atrometry of theβ Sco system, and L. Vapillon for his avice on the 1971 data charts. We are grateful to R. Yand an anonymous referee for their help in improvingmanuscript. We thank the French Programme NationaPlanétologie (CNES/INSU) for support in data reductiKM acknowledges the support by the European Comnity through the Marie Curie Fellowship Program (cotract HPMF-CT-2000-01005). Wavelet software was pvided by C. Torrence and G. Compo and is available at Uhttp://paos.colorado.edu/research/wavelets/.

References

Atreya, S.K., 1986. Atmospheres and Ionospheres of the Outer Planetheir Satellites. Springer-Verlag, Heidelberg, New York.

Bartholdi, P., Owen, F., 1972. The occultation of Beta Scorpii by Jupand Io. II. Io. Astron. J. 77, 60–64.

Baum, W.A., Code, A.D., 1953. A photometric observation of the occution of σ Arietis by Jupiter. Astron. J. 58 (1208), 108–112.

http://paos.colorado.edu/research/wavelets/


. Theic

ulta-

aite,fromiter.

nce.

here

cul-33,

P.,rva-

ure-

Cit-eta

.J.,09.

tidal

e byon-

vityere.

.H.,F.,M.,ime

252

.B.,, D.,hen of61.het,T.,F.,

990:files.

.,.S.,robe

evo,, W.,E.,is,

28

ated04–

ysis.

per

ationere.

light

n

y

1.tion.

er’sEx-

Berezne, J., Combes, M., Laporte, R., Lecacheux, J., Vapillon, L., 1975occultation ofβ Scorpii by Jupiter III. Discussion of the photometrresults. Astron. Astrophys. 40, 85–90.

Combes, M., Lecacheux, J., Vapillon, L., 1971. First results of the ocction of β Sco by Jupiter. Astron. Astrophys. 15, 235–238.

Drossart, P., Sicardy, B., Roques, F., Widemann, T., Gladstone, R., WJ.H., Vincent, M., 2000. The methane homopause of Jupiter seenthe IR spectroscopy of star HIP 9369 during its occultation by JupBull. Am. Astron. Soc. 32, 1013.

Farge, M., 1992. Wavelet transforms and their application to turbuleAnnu. Rev. Fluid Mech. 24, 395–457.

French, R.G., Gierasch, P.J., 1974. Waves in the jovian upper atmospJ. Atmos. Sci. 31, 1707–1712.

French, R.G., Elliot, J.L., Gierasch, P.J., 1978. Analysis of stellar octation data: effects of photon noise and initial conditions. Icarus186–202.

Hanel, R., Conrath, B., Flasar, M., Herath, L., Kunde, V., Lowman,Maguire, W., Pearl, J., Pirraglia, J., Horn, H., 1979. Infrared obsetions of the jovian system from Voyager 2. Science 206, 952–956.

Hinson, D.P., Jenkins, J.M., 1995. Magellan radio occultation measments of atmospheric waves on Venus. Icarus 114, 310–327.

Hubbard, W.B., Van Flandern, T.C., 1972. The occultation ofβ Scorpii byJupiter and Io III. Astrometry. Astron. J. 77, 65–74.

Hubbard, W.B., Nather, R.E., Evans, D.S., Tull, R.G., Wells, D.C., vanters, G.W., Warner, B., Vanden Bout, P., 1972. The occultation of BScorpii by Jupiter and Io. I. Jupiter. Astron. J. 77 (1), 41–59.

Hubbard, W.B., Haemmerle, V., Porco, C.C., Rieke, G.H., Rieke, M1995. The occultation of SAO 78505 by Jupiter. Icarus 113, 103–1

Lecacheux, J., Combes, M., Vapillon, L., 1973. Theβ Scorpii occultationby Jupiter I. The jovian diameter. Astron. Astrophys. 22, 289–292.

Lindzen, R.S., 1981. Turbulence and stress owing to gravity wave andbreakdown. J. Geophys. Res. 86, 9707–9714.

Matcheva, K.I., Strobel, D.F., 1999. Heating of Jupiter’s thermospherdissipation of gravity waves due to molecular viscosity and heat cduction. Icarus 140, 328–340.

Matcheva, K.I., Strobel, D.F., Flasar, F.M., 2001. Interaction of grawaves with ionospheric plasma: implications for Jupiter’s ionosphIcarus 152, 347–365.

Orton, G.S., Friedson, A.J., Caldwell, J., Hammel, H.B., Baines, KBergstrahl, J.T., Martin, T.Z., Malcolm, M.E., West, R.A., Golish, W.Griep, D.M., Kaminsky, C.D., Tokunaga, A.T., Baron, R., Shure,1991. Thermal maps of Jupiter: spatial organisation and tdependence of stratospheric temperatures, 1980–1990. Science537–542.

.

,

Raynaud, E., Drossart, P., Matcheva, K., Sicardy, B., Hubbard, WRoques, F., Widemann, Th., Gladstone, G.R., Waite, J.H., NadeauBastien, P., Doyon, R., Hill, R., Rieke, M.J., Marley, M., 2003. T10 October 1999 HIP 9369 occultation by the northern polar regioJupiter: ingress and egress lightcurves analysis. Icarus 162, 344–3

Roques, F., Sicardy, B., French, R.G., Hubbard, W.B., Barucci, A., BoucP., Brahic, A., Gehrels, J.A., Gehrels, T., Grenier, I., Lebertre,Lecacheux, J., Maillard, J.P., McLaren, R.A., Perrier, C., Vilas,Waterworth, M.D., 1994. Neptune’s upper stratosphere, 1983–1ground-based stellar occultation observations III. Temperature proAstron. Astrophys. 288, 985–1011.

Seiff, A., Kirk, D.B., Knight, T.C.D., Mihalov, J.D., Blanchard, R.CYoung, R.E., Schubert, G., von Zahn, U., Lehmacher, G., Milos, FWang, J., 1996. Structure of the atmosphere of Jupiter: Galileo pmeasurements. Science 272, 844–845.

Sicardy, B., Ferri, F., Roques, F., Lecacheux, J., Pau, S., Brosch, N., NY., Hubbard, W.B., Reitsema, H.J., Blanco, C., Carreira, E., BeiskerBittner, C., Bode, H.-J., Bruns, M., Denzau, H., Nezel, M., Riedel,Struckman, H., Appleby, G., Forrest, R.W., Nicolson, I.K.M., HollA.J., Miles, R., 1999. The structure of Titan’s stratosphere from theSgr occultation. Icarus 142, 357–390.

Smith, S.A., Fritts, D.C., VanZandt, T.E., 1987. Evidence for a saturspectrum of atmospheric gravity waves. J. Atmos. Sci. 44 (10), 141410.

Torrence, C., Compo, G.P., 1998. A practical guide to wavelet analBull. Am. Meteor. Soc. 79, 61–78.

Vapillon, L., Combes, M., Lecacheux, J., 1973. Theβ Scorpii occultationby Jupiter. II. The temperature and density profiles of the jovian upatmosphere. Astron. Astrophys. 29, 135–149.

Veverka, J., Wasserman, L.H., Elliot, J., Sagan, C., 1974. The occultof β Scorpii by Jupiter I. The structure of the jovian upper atmosphAstron. J. 79, 73–84.

Wasserman, L., Veverka, J., 1973. On the reduction of occultationcurves. Icarus 20, 322–345.

Yelle, R.V., Griffith, C.A., Young, L.A., 2001. Structure of the joviastratosphere at the Galileo probe entry site. Icarus 152, 331–346.

Young, L.A., Yelle, R.V., Young, R., Seiff, A., Kirk, D.B., 1997. Gravitwaves in Jupiter’s thermosphere. Science 276, 108–110.

Young, L.A., Bosh, A.S., Buie, M., Elliot, J.L., Wasserman, L.H., 200Uranus after solstice: results from the 1998 November 6 occultaIcarus 153, 236–247.

von Zahn, U., Hunten, D.M., Lehmacher, G., 1998. Helium in Jupitatmosphere: results from the Galileo probe Helium Interferometerperiment. J. Geophys. Res. 103, 22815–22829.

a re-analysis of the 1971 beta scorpii occultation by ... › perso › bruno-sicardy › biblio ›...

Documents