JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL. 88, NO. A7, PAGES 5537-5550, JULY
1, 1983
Energetic Oxygen and Sulfur Ions in the Jovian Magnetosphere
and Their
Contribution
to the Auroral
Excitation
N. GEHRELSx AND E. C. STONE
California Institute of Technology,Pasadena,California 91125
Observationsof 1 to 20 MeV/nuc oxygen, sodium, and sulfur ions in the Jovian magnetosphereare
reported. Measurementsmade by the cosmicray subsystemon Voyager 1 and 2 are used to calculate
abundancesand energyspectrain the regionfrom 5 to 20 Jovian radii (Rj). The phasespacedensityof the
oxygenions calculatedfrom the spectrahas a positiveradial gradientbetween6 and 17 Rj, indicatingan
inwarddiffusiveflow.The upperlimit for the diffusioncoefficient
D at 9 R• is ~ 10-s s-•. This limit,
combinedwith the analysisof Voyager plasma observationsby Siscoeet al. (1981), implies an upper limit
to theproduction
rateof oxygenandsulfurionsfromIo of ~ 1028ions/s.If D(9Rj)is ~4 x 10-6 s-•, then
-• 2 x 1024oxygenand sulfurionswith > 70 MeV/nuc-Gare lostper secondastheydiffuseinwardfrom
12to 8 R•. Assuming
theseionsarescattered
intothelosscone,theydeliver~4 x 10•2 W to theJovian
atmosphere.
Extrapolations
to lowermagnetic
moments
suggest
thatthe 10• 3-10•4W requiredto produce
theobserved
ultravioletauroralemissions
couldresultfromtheprecipitation
of ~ 1026oxygenandsulfur
ions/swith magneticmoments •> 10 to 30 MeV/nuc-G (•> 35 to 100 keV/nuc at 10 R•). The ions with •>70
MeV/nuc-G deposittheirenergybetween~67 øand ~ 72ømagneticlatitudeat an averagedepthof ~ 1019
cm-2 of H 2 (~500-km altitude),whichis abovethe homopause.
If the extrapolatedspectrumextends
downto ~ 10 MeV/nuc-G,then10 timesmoreenergy(~ 1013W) is carriedinwardacross10 R• by the
energeticoxygenand sulfurions than flows outward with the plasma,indicatingthe presenceof an energy
sourcein the middle or outer magnetosphere.
INTRODUCTION
1982] instead of torus electrons.Thorne [1981a] has further
suggested
that auroral secondaryelectronsmay be responsible
The auroral activity on Jupiter, discoveredwith the ultraviolet spectrometeron Voyager 1 [Broadfoot et al., 1979-1,is for heatingthe torus.In this case,the energyis suppliedby the
one of the most energetic phenomena associated with the process that acceleratesthe energetic particles in the outer
Jovian magnetosphere,requiring a continuouspower input of magnetosphereand by the adiabaticaccelerationof the ions as
1023to 10•4 W into the auroralzone [Broadfootet al., 1981; they diffuseinward. If, for instance,the accelerationin the outer
Yunq et al., 1982]. There has been wide interest [Thorne and magnetosphere occurs via a magnetic pumping process
Tsurutani, 1979; Goertz, 1980; Eviatar and Siscoe, 1980; She- [Goertz, 1978; Borovskyet al., 1981], then the ultimate energy
mansky,1980a, b; Thorne, 1981a, b, 1982; Sullivanand Siscoe, sourceis Jupiter'srotational energy.One of the goals of the
1981] in determining the source of this power. A possible presentstudy is to determinethe power deliveredto the Jovian
energysource that has been consideredis the accelerationof atmosphereby the precipitationof inwardly diffusingenergetic
Iogenicoxygenand sulfurionsto corotation speedsby Jupiter's oxygenand sulfur ions.
This paper is basedon observationsof oxygen,sodium,and
magneticfield. This energywould be transportedto the Jovian
atmosphereby the local heating of torus electrons,followed by sulfur ions with MeV/nuc energiesmade inside ~20 Jovian
(CRS) on board Voyager
pitch angle scattering of the electrons into the loss cone radii (Rs)by the cosmicray subsystem
[Thorne and Tsurutani, 1979]. Newly ionized oxygen and 1 and 2. In previousreports [Vogt et al., 1979a,b; Gehrelset al.,
sulfurionsacquire260 and 520 eV, respectively,in the corotat- 1981, hereafterreferred to as paper 1] it was found that the
ing frame,so that •>2 x 1029ions/swouldhaveto be created dominant energeticspecieswith nuclearchargegreater than 2
in the inner magnetosphere
are oxygenand sulfur,with sodium
(the massloading rate) in order to producethe auroral power.
also
present.
These
abundances
suggestthat Io is the sourceof
Other observationsof the Io plasmatorus,however,indicate
the
ions.
The
radial
gradient
of
the
oxygenphasespacedensity
a lower massinjectionrate. For example,in situ plasmaobservations [Baqenal and Sullivan, 1981] indicate that the torus between5 and 17 Rs was found to be positive indicating an
containsN ~ 5 x 1034ions,while the ionization statesof the inward diffusive flow in this region. It was postulated from
ionsindicatethat their diffusivelifetimezaiffis in the rangefrom theseobservationsthat plasmaionsdiffuseoutward from the Io
9 to 600 days, with a nominal value of 100 days [Shemansky, torus, are nonadiabatically acceleratedin the outer mag1980b;Shemanskyand Sandel,1982]. Thus the Io sourcerate
whichisN/zaifrisin therange102?• Si • 6 x 1028ions/s,with
a nominalvalueof 6 x 102?ions/s.Thusthemassloadingrate
is apparently too low to provide the required power for the
netosphere, and then diffuse inward and outward from the
accelerationregion as energeticions. In the presentanalysis,
the oxygen phase spacedensity is calculatedWith improved
radial
resolution
and is used to set limits
on the diffusion
coefficientbetween 5 and 20 Rs and thereby on the mass
aurora.
Another possible energy source is the precipitation of in- loading rate of ions from Io. The inward diffusive flow rate of
wardly diffusingenergeticions [Goertz, 1980; Thorne,1981a,b, both oxygen and sulfur ions is determined,and the observed
lossrate of the ions is usedto calculatethe power they deliver
• Currently at NASA Goddard SpaceFlight Center,Greenbelt, to the Jovian atmosphere.
Maryland 20771.
THE INSTRUMENT
Copyright 1983by the AmericanGeophysicalUnion.
The data used in this analysis were obtained with CRS
low-energytelescopes(LET's) [Stoneet al., 1977; Stilwell et al.,
Paper number 3A0564.
0148-0227/83/003A-0564505.00
5537
5538
GEHRELSAND STONE'OXYGEN,SULFUR,AND THE JOVIANAURORA
150 -
i
i
i
i
-5 Rj
VOYAGER
3p.m
I
'\,• ,• ALFOIL
LOW-ENERGY
TELESCOPE
(LET)
'..
SO
o
0
100
6oo
3•)o
2OO
E3 (MeV)
Fig. 1. Theenergylossin detectors
L2 andL3 of individualionsdetected
by LET D fromday64,0936to 1405UT (the
4.9and5.3Rj regions
in Table1).Theoxygen,
sodium,andsulfurtracksareindicated.
Eventsin thebottomleft-handcorner
havenot beenplotted.The insetis a schematic
diagramof a LET.
1979]. The instrumentcommandstate and telescopeorientations in this region are describedin paper 1, with the one
differencethat only data from LET B were usedin that study,
whilethis analysisincludesdata from both LET B and LET D.
A schematicdiagramof a LET is shownin the insetof Figure 1.
The LET's providemultiparameteranalysisof individualnuclei
with MeV/nuc energiesand nuclearchargeZ greaterthan 2,
with an rms charge resolution in the inner Jovian magnetosphere
of az • 0.2 chargeunits.Figure 1 showsthe energy
loss in detectors L2 and L3 of individual
ions detected near 5
called the Z > 2 rate, which is primarily the rate of particles
losing more than 9.6 MeV in L1 (paper 1). In regionswhere
oxygenand sulfurare the dominantenergeticspecies,
this rate
is approximatelyan integralmeasurement
of oxygenand sulfur
ions with energiesgreater than • 1.1 and •0.9 MeV/nuc, respectively(energylossin the 3-#m aluminumwindow of the
LET is includedin thesethresholds).Thereforeif the sulfur to
oxygenratio can be determined,the Z > 2 rate can be usedas
an additional point in the integral energy spectraof either
species.
Rj. The largeabundance
of oxygenandsulfurandthe presence
of sodiumin this regioncanbe clearlyseen.
In addition to the analysisof individual ions,the LET's also
provide measurements
of the countingrate of Z > 2 ions,
ENERGY SPECTRA AND ABUNDANCES
Energyspectraweredeterminedfrom the analyzedeventsin
the 12 regionslisted in Table 1. The regionswere chosento
TABLE 1. RegionDefinitionsand MagneticField ValuesUsedin SpectralAnalysis
Region,*
Rj
Voyager
4.9
5.3
1
1
5.9
1
7.9
10.1
12.2
1
2
2
13.0
13.7
1
2
16.8
1
2
2
1
16.9
20.0
20.9
Spacecraft
Event
Time,9UT
day
day
day
day
day
day
day
day
day
day
day
day
64, 1106 to day
64, 0936 to day
64, 1235 to day
64, 0842 to day
64, 1405 to day
64, 0546 to day
190, 2214 to day
190, 1235 to day
63, 2328 to day
190, 0907 to day
63, 1818 to day
190, 0312 to day
64, 1235
64, 1106
64, 1405
64, 0936
64, 1443
64, 0659
191,0016
190, 1440
64, 0110
190, 1109
63, 2022
190, 0517
...
Magnetic Equatorial
B Field at
PlaneCrossingTime,
UT
Crossing,•:
G
day 64, 1200
3.26x 10- 2
day 64, 1034
day 64, 1341
day 64, 0905
2.79 x 10 -2
day64,1428
2.08
x 10-2
day 64, 0608
day 190,2300
day 190,1338
day 64, 0008
day 190,1008
day 63, 1920
day 190,0415
day 189,2238
day 63, 1415
7.18x
3.34 x
1.74x
1.32x
1.20x
4.85 x
6.11x
3.2 x
2.6 x
10- 3
10-3
10-3
10-3
10-3
10-4
10-4
10-4
10-4
*Distancebetweenthe spacecraftand the dipole centerat the time of the magneticequatorialplane
crossing.
Exceptions
are5.3and5.9R• wheretherewereno crossings;
thelistedvaluesaretypicaldistances
and timesin thesetwo regions.
9Spectrabasedon analyzedeventsare not usedat 20.0 and20.9 R• owingto thedifferencein Voyager1
and 2 Z > 2 fluxesat theseradial distancesand beyond(paper 1).
,Magnetic fieldvaluesfrom N. F. Ness(privatecommunication,
1980).
GEHRELS
AND STONE'OXYGEN,SULFUR,ANDTHEJOVIANAURORA
5539
102
include all magnetic equatorial plane crossingsof both spacecraft inside •, 20 Rs. In addition, there are two regionsat 5.3
and 5.9 Rs which do not include plane crossingsbut are at
timeswhenVoyagerwaswithin •, 1 Rs of the plane.The benefit
of calculatingspectranear the magneticequatorial plane will
be explainedin the next section.
The differentialoxygenand sulfurspectrain the 5.3 Rs region
and the sodium spectrumin the combined 4.9 and 5.3 Rs
regionsare shown in Figure 2. The oxygen and sulfur spectra
both have a maximum at • 5 MeV/nuc which is most likely due
to preferentiallow-energylossesnear Io (paper 1). For energies
greater than •, 7 MeV/nuc, these two spectra are well representedby power laws of index -6. The sodium spectrumis
softer, with a power law index of -9. Figure 3 shows the
differential oxygen spectra observedin the 7.9 and 10.1 Rs
regions.In theseregionsthe spectraare well representedby a
powerlaw of index -7 between6 and 15 MeV/nuc.
In order to use the Z > 2 rate point to extend the measured
spectrumof a givenspeciesto lower energies(•, 1 MeV/nuc), it
is necessaryto know the fraction of the rate countsthat are due
to that species.A study was thereforemade of the elemental
abundancesinside •, 25 Rs using analyzed events.The abun-
Oxygen
7.9 Rj
I0.1R d
E-7
104
E (MeV/nuc)
Fig. 3. Differentialoxygenspectrafrom 7.9and 10.1Rs.
Sulfur
(x20)
dance ratios S/O, C/O, and Na/O were calculated in several
radial ranges by summingevents above a given energy-pernucleon
5.3 Rj
_
_
_
_
Oxygen
_
_
_
_
_
Sodium
_
4.9- 5.3 Rj
_
_
-6
E (MeV/nuc)
Fig. 2. Differential oxygen,sodium,and sulfurenergyspectranear
Io. The oxygenand sulfurspectraare from the 5.3 Rs region,and the
sodiumspectrumis from the combined4.9 and 5.3 Rs regions(Table 1).
Note that the sulfur spectrumis multipied by 20. The oxygen point
with dashed error bars at 2.2 MeV/nuc was derived from the Z > 2
rate.
threshold.
The
threshold
was then
converted
to a
particlemagneticmomentthresholdM = pl2/2mB,the first
adiabatic invariant, using M = E/B, where E is the measured
kinetic energyof the ions and B is the measuredlocal magnetic
field strength [Ness et al., 1979a, b; N. F. Ness, private communication, 1980]. It is not strictly correct to calculate the
magneticmoment thresholdsusing M = E/B becauseLET B
and D werenot pointingexactlyperpendicularto the magnetic
field direction throughout the region. However, using the
actual pointing directionsand estimatesof the particle pitch
angledistributions,we find that, on average,the calculatedM is
within •, 30% of the real magneticmoment threshold.
The abundanceratios are shown in Figure 4 as a function of
M. The CRS points are thosewith horizontal error bars,which
representthe range of magneticfield valuesobservedin each
radial range. The points with open symbols were calculated
using data obtained between 10 and 60 Rs inbound with the
low-energychargedparticle (LECP) instrumenton Voyager 2
[Hamilton et al., 1981]. The approximateenergyrangesfor the
measurementsare 6 to 15 MeV/nuc for CRS and 0.6 to 1.2
MeV/nuc for LECP. (The exact energyrange for each point is
givenin the figurecaption.)Althoughthe plotted valuesare not
true integral measurementsbecauseof the upper energylimits,
they are a reasonablerepresentationbecausethe spectra decreaserapidly with energy.
The agreementbetweenthe CRS and LECP data in Figure 4
indicates that the relative abundances of carbon, oxygen,
sodium, and sulfur at a given magneticmoment are approximately the same throughout the daysidemagnetosphere.The
lines shown in the figure are power law fits to the combined
data sets.S/O and Na/O are seento increasetoward smaller
magneticmomentswhile C/O decreases.Therefore an instrument measuringabundanceratios in a fixed energyrange will
detect increasingsulfur and sodium and decreasingcarbon
5540
GEHRELSAND STONE'OXYGEN,SULFUR,AND THEJOVIANAURORA
]•
I I { I I I 11
[
I [ I I I I II}
I I I I_
o
diffusion theory. If it is assumedthat particles conservetheir
first and secondadiabatic invariants in the diffusion process,
but violate their third invariant (see,e.g.,Schulzand Lanzerotti
[ 1974]),then the radial diffusionequationis
ß
L
+s(L)-
_
_-
(b)
0.5-
i
0.2_ .•
o
-
o.i
-
wheref is the phase spacedensity at constant first adiabatic
invariant (M), D is the diffusioncoefficient,L is the McIlwain
parameter,and $(L) and œ(L)representlocal sourcesand sinks,
respectively.
The relationshipbetweenthe integral particleflux J, and the
phasespacedensityis given by
_
•,(M, L) J•_(M, L)
_
0.05 •
-
f(M,L,•z=90
ø)- 2mM•
' B•.(L)
(2)
_
0.02
ß
_
_
O.O5
No
0
0.02
0.001
_
_
_
_
10z
103
104
M (MeV/nuc
•i8. 4. Abundanceratioswith respectto oxysenof (•) $uffur,(b)
carbon,and (½)$odiu• as functionsoœthe particle•asneti½ •o•ent$.
The opensymbolswerecalculatedu$in8publishedLECP data [H•ilw• s½M., •98•]. The symbolsin the plot are dennedas Collows:
plain
cross,Voyaser • 6.6-•7.3 MeV/nuc' solid circle,Voyaser 2 7.•-•.0
MeV/nuc; solid s•uare, Voyaser • 4.7-•4.8 MeV/nuc; soliddiamond,
su• o½solid circle and solid s•uare; o•n circle, L•CP Voyaser 2
0.60-•.•5 MeV/nuc. The verticalerror barsrepresemstatisticaluncertaimies.The linesare powerlaw •ts to the combinedCRS and
data.
abundancesrelative to oxygen as it moves toward smaller
radial distances(smaller M). Also, an instrument at a fixed
radial positionwill measurea sulfurto oxygenand sodiumto
oxygenratio that increases
toward lower energiesand a carbon
to oxygen ratio that decreases,sincethe sulfur and sodium
spectraare softer than the oxygenspectrumand the carbon
spectrumis harder. If the approximation is made that the
energyspectraof theseelementsare proportionalto E -y, then
the fits shown in the figure indicate that •'s= •'o + 0.2, •c = •'o
-0.6, and •'Na= •'O+ 0.1. The harder carbon spectrummay
reflect a solar wind origin for carbon [Hamilton et al., 1981],
whereasthe other speciesare Iogenic.
In the next section,oxygenintegralspectraare calculatedfor
each of the regionsin Table 1 and are usedto determinethe
radial profileof the oxygenphasespacedensityinside • 20 Rs.
The data in Figure 4 will be used to calculate the oxygen
fraction of the Z > 2 rate so that the spectracan be extended
down to • 1 MeV/nuc.
PHASE SPACE DENSITY
DETERMINATION
In order to comparespectralmeasurements
madeat different
locationsin a magnetosphere,
it is usefulto relate them to a
(paper 1), where •zis the particle pitch angle and •, = -[d log
(J•_)]/[d log (M)]. Equation (2) showsthat in order to calculate
f, one must measure the integral flux perpendicular to the
magnetic field direction (i.e., the flux of mirroring particles).
Also, implicit in the diffusionequationis the requirementthatf
be determinedalong the dynamic path that particlesfollow in
the diffusion process.To satisfy these two requirements,we
have restrictedanalysisto ions mirroring at the magneticequatorial plane. Since LET B and D were not in general oriented
perpendicularto the field linesat the time of the planecrossing,
the mirroring flux J•_was calculatedfrom the measuredfluxes
by applying a pointing correction factor. The correction is
basedon estimatesmade of the pitch angle distribution of the
energeticheavyionsinside20 Rs.The telescopepointingdirectionsand the pointingcorrectionfactorin eachregionare listed
in Table 2. Also listed are the live time correction
factors for the
Z > 2 rate, the analyzedeventrate as determinedby laboratory
measurements,
and the effectiveenergythresholdsof the Z > 2
rate for oxygenions(paper 1).
The oxygen fraction of the Z > 2 rate was also used to
calculateJ•_.This number was determinedfrom the data in
Figure 4 and, owing to the offsettingeffectsof a decreasing
carbon abundanceand an increasingsulfurabundancetoward
smallerradial distances,is approximatelyconstantand equal to
1/2 throughoutthe regionbetween6 and 17 Rs. Note that this
number is not an oxygenabundancefraction,sincethe energy
thresholdof the Z > 2 rate (in energyper nucleon)is different
for different elements.
The quantityJ•/B 2, usedin calculatingthe phasespace
density(equation(2)), is shown as a function of M in Figure 5
for the regionslistedin Table 1. The magneticfield strengthfor
eachregion(Table 1) is the valuethat wasmeasuredat the time
of the magneticequatorial plane crossing.The continuoussteplike part of eachspectrumis basedon analyzedevents,and the
solid symbol with an error bar is calculatedfrom the Z > 2
rate. The long-dashedcurvesjoining the two is an interpolation. The event portions of the Voyager 1 13.0 and 16.8 Rs
spectraare representedby singlepoints(opencircles)insteadof
by completespectraowing to the few eventsobtainedin these
regions.These two measurements,as well as the Z > 2 flux
measurementsin the two regions,are important, becausethey
showthat to within a factor of 2, the Voyager 1 and 2 fluxesof
energeticoxygenionswerethe samebetween12 and 17 Rj.
The short-dashed and dash-dotted curves in Figure 5 are
extrapolations of the measured spectra to smaller magnetic
moments. The error bars associatedwith these parts of the
GEHRELSAND STONE:OXYGEN, SULFUR,AND THE JOVIANAURORA
5541
TABLE 2. QuantitiesUsed to Calculate
Region,
R•
LET*
PointingAngle
With Respect
to
FieldLine,deg
4.9
5.3
5.9
B
B
B
68
62
60
7.9
10.1
12.2
13.0
13.7
16.8
16.9
20.0
20.9
Pointing
Correction
Factor•
1.1
1.2
1.3
Z > 2 LiveTime
Correction
Factor;[
EventLiveTime
Correction
Factor•
1.3
1.2
1.3
1.5
1.5
1.5
EffectiveOxygen
Z > 2 Threshold,{}
MeV/nuc
1.4
1.4
1.5
B
55
1.3
1.7
1.5
D
53
1.4
1.6
1.5
1.5
B
65
1.2
1.4
1.6
1.3
1.6
B
77
1.1
1.2
D
41
1.6
1.2
1.6
B
78
1.1
1.1
1.6
D
36
1.8
1.1
1.6
B
57
1.2
1.1
1.6
D
44
1.6
1.1
1.6
B
49
1.4
1.0
1.6
D
50
1.4
1.0
1.6
B
75
1.1
1.0
1.6
D
53
1.4
1.0
1.6
B
D
B
D
71
42
90
48
1.1
1.6
1.1
1.5
1.0
1.0
1.0
1.0
...
-..
...
..-
1.2
1.1
1.1
1.1
1.1
1.1
1.1
*In the 4.9, 5.3,5.9,and 10.1Rj regions,
onlyLET B wasusedbecause
it providedadequate
statistics
by'itselfand wasmorenearly
perpendicularto the magneticfieldthan LET D.
'{'ACompton-Getting
correction
ofmagnitude
•<0.05isincluded
in these
factors.
Thecorrection
factors
for5.3and5.9R• takeintoaccount
the
nonzeromagneticlatitudeof the spacecraft
in theseregions.
$1.0 impliesno correction.
ôThe4.9,5.3,and5.9R• spectra
haveanadditional
pulsepileupcorrection
thathasbeenapplied
to theeventportions,
ofmagnitude
1.4for
E •< 7 MeV/nuc (paper 1).
{}The
nominal
oxygen
threshold
is 1.1MeV/nuc(sulfur
is0.9MeV/nuc,carbon
is1.2MeV/nuc).
These
thresholds
include
theparticle
energy
loss
in the telescopewindow.
spectrarepresentthe uncertaintyin the extrapolations.
Except
ments.Inside 7.9 Rs the lines connectingpoints of the same
at 10.1 Rs, the upper and lower limits for each error bar were
magneticmomentare dotted to indicatethat there may be
discontinuities
in theshapeof thephasespacedensityprofilein
determinedby extendingthe spectrafromthe Z > 2 point with
linesof slope•'z>2 and•'z>2/1.4,respectively,
where•'z>2 is the
slopeat the Z > 2 point(seeFigure6). The •;z>2 and •'z>2/1.4
this region due to discontinuitiesin the diffusion coefficient
[Siscoeet al., 1981].
extrapolation limits were chosenas reasonableestimatesbased
on the LECP spectralshape and observedfluxes of 0.6-1.15
As was previouslyobserved[Vogt et al., 1979b;paper 1],
thereis a positiveradialgradientin thephasespacedensityof
MeV/nuc-Goxygen(• 250 MeV/nuc-Gat 11Rs).At 10.1Rs a theenergetic
oxygenionsbetween5.6and 17 Rs,indicatingan
longerextrapolationwas performedthan in other regionsin inward diffusiveflow in this region.The objectivein the next
order to extendthe spectrumto 70 MeV/nuc-G. In this case, sections
will beto estimatethediffusioncoefficient
in theregion
the shapeof the spectrumwascalculatedusingthe energy-per- and to determinethe rate at whichionsand energyflow into
chargespectrummeasuredat thesemagneticmomentsby the inner magnetosphere.
LECP at • 16 Rson Voyager2 [Hamiltonet al., 1981].
LECP observations
werealsousedasa consistency
checkon
the slopesof the spectraat the Z > 2 points.Figure 6 shows
theseslopes(/• = 7z>2 + 1) comparedwith thosemeasuredin
the energyrangefrom0.60to 3.17MeV/nuc between10 and 25
Rs by LECP [Hamiltonet al., 1981]. The valuesfrom the two
instrumentsare the same within statistics,and both show the
sametrendof softerspectratowardincreasingradialdistance.
The oxygen phase spacedensity at severalvalues of M,
calculatedusing(2) and the spectrain Figure 5, is shownin
Figure 7 as a function of L. Since these measurementswere
obtainednear the magneticequatorialplane,L is definedto be
LIMITS ON THE DIFFUSION COEFFICIENT
AND MASS LOADING RATE
The measuredradial dependence
of the oxygenphasespace
density(Figure 7) can now be usedto obtain solutionsto the
diffusionequationand therebysetlimits on the diffusioncoefficient.The diffusionequation(1) for a steadystateconditionin
a region in which there are no sourcesand the lossterm is of the
form œ(L)= f/•:, where• is the particlelifetime,is
L2• • • = -(3)
the spacecraft-dipole
centerdistanceat the time of the plane
crossing.
The uncertainties
shownfor eachmeasurement
representuncertaintiesin the magneticfield strength(• 3%), in the In this analysisthe phasespacedensityprofileat a given
oxygenfractionof the Z > 2 rate (• 15%),in 7(M, L) (• 15%), magneticmomentis approximatedas a seriesof powerlaw
and in the pointingcorrectionfactor (• 10%) and statistical lines(foc/_5)connecting
the measurements.
Comparison
with
counting uncertaintiesin the number of events in the event the smoothedcurvesin Figure7 indicatesthat thisis a reasonportionsof the spectra.An additional• 15% systematic
uncer- ableapproximation.
Table3 liststhe valuesof the powerlaw
tainty in the live time correctionfactorappliesto all measure- indicesq that will be used.
5542
GEHRELSAND STONE:OXYGEN, SULFURAND THE JOVIANAURORA
I
I
I
I • I Ill
I
I
I
I I I II I
I
I
I
I I I I l[
I
I
I
I010:-
_
Oxygen
_
_
_
_
io9 _
\
\
\
\
io8
•o7
106
105
_
_
-
_
_
io4 ß Voyager I
ß Voyager 2
I1
I0•0I I I I I I IIll
I02 I I I I I 11
I03 I I I i I II1[
10
4 I I I I I II1
10
5
M (MeV/nuc-G)
Fig. 5. Integral oxygenspectrafrom all regionslisted in Table 1 divided by the squareof the local magneticfield
strengths,as functionsof magneticmoment.The solid line portion of each spectrumis basedon pulse-height-analyzed
events,exceptat 4.9 Rs wherea dottedlineis usedto distinguish
thespectrum
fromthat at 5.3Rs.Because
veryfewanalyzed
eventswereobservedby Voyager1 at 13.0and 16.8Rs, thosedata are represented
by opencircleswith error barsratherthan
by integralspectra.The solid symbolswhich indicatethe integralfluxesobtainedfrom the Z > 2 rate are connectedby
long-dashed
linesto thecorresponding
spectrum
of analyzedeventsobserved
at 4.9,5.3,5.9,7.9,10.1,12.2,13.7,and 16.9Rs.
AdditionalZ > 2 fluxesobservedat 13.0,16.8,20.0.and 20.9Rs are shownfor comparison.
The short-dashed
curvesand the
dash-dottedcurverepresentextrapolationsbasedon data from the Low-EnergyChargedParticleExperimentas discussed
in the text.The error barsat the lowerlimit of the extrapolationsindicatethe uncertainties
in the extrapolations.
Note that
theseare not true integralspectra,sinceoxygennucleiwith >•23 MeV/nuc are not analyzed[Gehrelset al., 1981].Thusthere
is an unmeasured
additivecontributionto thesespectra.For example,if the differentialspectrumin Figure2 at 5.3 Rs
extends
to higherenergies
asE -6, theadditionalcontribution
wouldbe • 103cm-2 s-1 sr- 1G-2
of lessthan -5 to give the observedradial dependenceof the
oxygenphasespacedensityif thereare no lossesin the region.
A large negativeindex such as this is inconsistentwith other
D ocL3-q s-•
(4) determinationsof n made usingobservationsof energeticelectrons and protonsand of plasmain the region [Thomseneta!.,
Between5.9 and 12.2 Rj, q is greaterthan 8 (Table 3), so that
the diffusion coefficientwould have to have an index n (D oc/_2) 1977; Goertz et al., 1979; Froidevaux, 1980; Siscoeet al., 1981],
We first considerthe caseof no losses(z --• oo)between6 and
17 Rs. In this limit,
GEHRELSAND STONE:OXYGEN, SULFUR,AND THE JOVIAN AURORA
6
[
I
]
[
[
•
I
]
]
[
[
I
]
•-• cC
E
[
[
]
I
[
[
]
[
$$43
denceof the plasma densityin the region, and we will therefore
usen = 4 in (6) between8 and 9 Rs.
The diffusion coefficientupper limit calculated at L- 8.9
with (6) usingn = 4, q from Table 3, and Zsfrom (5) is shownfor
severalmagneticmomentsin Figure 8. Theselimits are not very
sensitiveto the value usedfor n as is indicatedby the dashed
I
'l MeV/nuc
5-
error bar which representsthe range of D, for 9.4 x 102
MeV/nuc-G as n varies between 0 and 12. The solid lines
between 8 and 9 Rs in Figure 8 are the plasma diffusion
coefficient
for Si = 1027,1028,and1029ions/s.It isseenthatthe
upper limits imposedon the diffusioncoefficientat 8.9 Rs by
the energetic oxygen observations,when combined with the
plasmaanalysisof Siscoeet al. [1981], placean upper limit on
ß CRS
o LECP
5
I0
15
20
themassloadingrateof • 1028ions/s.
25
At radial distanceslarger than 9 Rs, the diffusioncoefficient
upper limits were obtained from the value at 8.9 Rs using a
Fig. 6. A comparison
of the logarithmicslopeof the oxygenspectrum at the Z > 2 point (• 1 MeV/nuc) observedby CRS and the finitedifferencesolutionof the diffusionequation(3). For example,D(11.4Rs)wascalculatedusing
powerlaw index between0.60 and 3.17 MeV/nuc measuredby LECP
r (Rj)
[Hamilton et al., 1981]. Note that /• is the power law index for a
differentialspectrum
(dJ/dE ocE-•), sothat for theCRS observations,
/• = •:>2 + 1, where•z>2 is the slopeof the integralspectrumat the
Z > 2 point.
10.12(
D(
ll'4)(c3f/•L)(11'4)/11'42
- D(8'9)(c3f/•L)(8
ß
11.4 -
8.9
f(lO. 1)
which can be summarized
as n = 4 + 2. We therefore
conclude
that there must be lossesbetween6 and 12 Rs, and hencewe
will now considerthe caseof 1ossydiffusion.
It will be assumedthat the lossesare occurringin the strong
pitch anglediffusionlimit. In this limit, there is sufficientpitch
angle scatteringto refill the losscone with particlesas quickly
as it empties,so that the lifetime of the particlesto pitch angle
scatteringis a minimum. The loss cone solid angle at the
magnetic equatorial plane (both directions)is approximately
2•0•0t
2,whereSotis theequatorial
lossconeangle,andthetime
requiredto empty it of particlesis approximatelyone quarter of
the bounce period % [Kennel and Petschek,1966]. Therefore
for nonrelativistic particles at constant M, the strong pitch
anglediffusionlifetimezs,assuminga dipolaf Jovianmagnetic
fieldof4 G as3,isgivenby
%/4
• 5M-•/2L•/214- 3/L] •/2 s
ßs- øtot
2/2
(5)
where[M] = MeV/nuc-G. The deviationof the measuredmagnetic field from a dipole [Connerney et al., 1981] tends to
decreaseSotand therebyincreaseZs.The difference,however,is
estimatedto be lessthan ,-•50% between6 and 17 Rs, and in
theanalysisthat follows,(5) will be usedto calculateZs.
Using z = Zsin the diffusionequation(3) and assumingf< O
and D < •, the upperlimit for the diffusioncoe•cient D,is
L:
D,(L, M) =
q(q + n- 3)•(L, M)
s-'
(6)
This representsan upper limit becauseit is basedon the minimum particlelifetime •.
In a recent analysis of Voyager plasma data •Siscoeet al.,
1981], the diffusioncoe•cient between8 and 9 R• wasfound to
'rs(10.1)
(7)
The results are shown in Figure 8. The diffusion coefficient
upper limit that will be used in the analysisthat follows is
representedby the dashedline labeledD,, which is a fit to the
measurements.
The radial dependenceof this fit between9 and
17 Rsis D, c• L•'6.Thereasonable
lowerlimit of • 1027ions/s
for Si (seethe introduction)wasusedto determinea lower limit
for the diffusion coefficient,labeled D t in the figure. The fact
that D t is lessthan a factor of 10 below D, implies that the
particle lifetime is within an order of magnitude of the strong
pitch anglediffusionlifetimein this region.The limits shownat
5.3 Rs were not calculatedfrom the energeticoxygendata but
representthe range of valuesdeterminedfrom energeticproton
and electronmeasurements[Thomsenet al., 1977' Goertz et al.,
1979].
Fits performed on previously published CRS and LECP
phasespacedensitymeasurementsin the inner magnetosphere
[Thorne, 1982] give upper limits to the diffusioncoefficientthat
are similar to those shown in Figure 8. For instance,at 9 Rs
ThornefindsD, to be in therange8 x 10-6 to 3 x 10-• s-•
compared
with • 10- • s- • shownin thefigure.Note,however,
that Thorne's model fits assumedthat D •/Y throughout the
region,so that the resultingradial dependencediffersfrom that
in Figure 8.
Althoughdiffusioncoefficientlimits between5.3 and 8 Rs are
not neededin the analysisthat follows,the radial dependenceof
D in this region,as determinedfrom the plasmadata [Siscoeet
al., 1981] (assumingS•= 1028ions/s),is also displayedin
Figure 8. The discontinuitiesin D are due to observeddiscontinuitiesin the radial dependenceof the plasmadensity.
PARTICLE AND ENERGY FLOW
RATES
be of theformD = 2.6 x 10-37 SiL4 s-•, whereSi (in ionsper
The diffusioncoefficientlimits shownin Figure 8 will now be
usedin combinationwith the measuredphasespacedensities
and energyspectrato determine the inward diffusiveflow rate
indicatethatS•ismostlikelyin therangefrom1027to 6 x 1028 of the energeticoxygenions.The diffusiveflow rate of ions with
ions/s,witha nominalvalueof 6 x 1027ions/s.Thusthemag- magnetic moments greater than M, F(> M) acrossradius r is
nitude of the diffusion coe•cient can only be estimatedfrom
givenby
second)is the ion sourcestrengthfrom Io, also called the mass
loading rate. As discussedin the introduction,previousstudies
the plasmaanalysis.The radial dependence
of D (D < L4) is,
however,directly determinedfrom the measuredradial depen-
F( > M) = n(> M) . 2nr. 2h' va' Rs3 ions/s
(8)
5544
GEHRELS
ANDSTONE:
OXYGEN,
SULFUR,
ANDTHEJOVIAN
AURORA
IO4 _
I
'
I
'
I
'
I
'
I
'
I
'
I
'
-G
• M=7.0x10
• nuc
MeV
ß
/
/
I0 3
ß
//
,,I2.0xl0
•
Oxygen
•1.•,,/,J.,•
4.0
x'02
io2
/././/"
:/
.:f
' /f'
IO
c
"t
-,,,'"'T9.4xl0
2
'}
/•..:.......:...
,,"
1.7x
Io
3
I
i0-1
10-2
/
10-3
10-'; _
_
_
_
_
_
10-5_
_
_
_
_
_
4
5
6
7
8
9
I0
15
20
25
L
Fig. 7. The radial dependenceof the phasespacedensityof the energeticoxygenions at constantmagneticmoment,for
severalvaluesof M. The solidpointsarederivedfrom the measuredportionsof the spectrashownin Figure 5, whilethe open
pointsa•ebasedontheextrapolations.
The4.9and5.3Rj measurements
at 6.9 x 102 MeV/nuc-Gwereaveraged
together
to
improvestatistics.Solidlinesjoin the measurements
at givenmagneticmomentsbetween7.9 and 16.9Rs. The 5.3, 5.9, and
7.9 Rs measurements
areconnected
by dottedlinesto indicatethat theradialprofilesin thisregionmay havediscontinuities
betweenthe points.
where
n(>M)isthenumber
density
(cm3)ofoxygen
ions
with that if the actual diffusioncoefficientis a factor of 3 larger(or
magneticmomentgreaterthanM calculatedfromthespectra,h
smaller),F(> M) will be correspondingly
larger(or smaller).
is the scaleheight(Rs) of the particledistributionrelativeto the
magneticequatorialplane,and VDis the averageradial diffusion
The typical uncertaintyin the calculatedpointsrepresentsuncertaintiesin n(> M) (• 20%), h (• 20%), (1/f)(c•f/t•L)(• 15%),
and D (• 50%). The inward flow rate of >400 MeV/nuc-G
velocity(Rs/s)givenby 19
D-- D(1/f)(•f/•L).(see,e.g.,Schulz
and
Lanzerotti [1974]). Based on measurementsof the latitudinal
dependenceof the energeticZ > 2 fluxes and on estimatesof
the particlepitchangledistributions,h wasfoundto be -• 3 Rs.
Figure 9b shows the radial profile of F(> M) for several
magneticmoment thresholds,assumingD(L), which is the geo-
metricmeanof D,,and Dt (e.g.,D(9 Rs)• 4 x 10-6 s-1). Note
oxygenionsat 10Rsis • 1022ionss- l, somewhat
largerthan,
but consistentwith, the lessaccurateestimatein paper 1 of
5 x 102•e• ions s-•. The inwardflow rate at all magnetic
momentsis approximatelyconstantbetween17 and 12 Rs,
implyingthat few particlesare lost in this region.Between12
and 6 Rs, on the otherhand,the rate steeplydecreases
so that,
GEHRELS
AND STONE:OXYGEN,SULFUR,AND THEJOVIANAURORA
5545
TABLE 3. Power Law Indicesof the OxygenPhaseSpaceDensity
L•-L 2
5.9- 7.9
7.9-10.1
10.1-12.2
12.2-13.7
13.7-16.9
M = 200*
M = 400
M = 690
M = 940
M = 1700
14.5
10.4
8.0
...
......
15.4
9.0
8.8
5.9
18.8
9.4
9.9
4.5
6.1
24.2
11.4
9.9
6.4
4.7
...
.-.
12.3
7.2
4.6
Calculatedusingthe data shownin Figure 7.
*Units of MeV/nuc-G.
for example,6 timesmore particleswith M > 200 MeV/nuc-G
are flowinginward at 10 Rj than at 8 Rj. Sincewe are assuming
an equilibrium condition in which the densityof particlesbetween10 and 8 R• is not increasing,the differencein the inward
flow rates is a direct indication of large particle losses.The
10-3
Lossy Diffusion
(r=rs)
From Voyager
Plasma
Data---•
S= IOZ9/
region in which the largest total number of energeticoxygen
ionsis lost is between8 and 12
The likely causeof the lossesis pitch anglescatteringinto the
losscone,as can be seenby the following arguments(seealso
Thorne [1982]). First, a comparison with the plasma charge
densityin Figure 9a [Bagenal and Sullivan, 1981] showsthat
the region wheremost of the ions are lost (8-12 Rj) is outside
the region of maximum plasma density and well outside the
orbit of Io (5.9 Rj). Hence geometric absorption by Io and
energy loss in the plasma torus near Io are ruled out as the
dominant lossmechanisms.Second,the fact that few particles
are lost outside• 12 Rj and that largelossesoccurinside • 10
ions/s--
10-4
•'
iO4
Plasma
Du
'•
103
o
I0a
10-5
10-6
I
i
I
[
I
I
i
I
I
I
I
I
'
'
•
'
I
i
,
,
,
i
,
,
,
Oxygen
1024
__
S=1027
•ons
s
I
>7o MeV
..
..
nuc-G
,
-
-
,,•'
/
-
/
_
10:'3
_
>200
.6
_
.or''
/
_
-
>400
_
/'
E: iO22
''
>690
O
._
>9_4_0_
0
1.7x 103 MeV/nucG
9.4 x I0 z
6.9 x I0 z
4.0 x I0 z
2.0 x I0 z
fie i0 2• o
•
.: /
i ozø_
ß
4
5
6
7
8
9
I0
15
20
c'-
(7). The dashed lines are the diffusion coefficient limits (D,,, upper; Dr,
lower)that will be usedin the analysisthat follows,with the rangeat
5.3 Rs determinedfrom Pioneer measurements
of energeticprotons
and electrons[Thomsenet al., 1977; Goertzet al., 1979]. The diffusion
coefficientshownbetween5.8 and 8 Rs is that obtainedfrom the
plasmaanalysis
[Siscoe
etal.,1981]assuming
S•= 10• ions/s.
uncertainty
ß
.
-
ß
L
Fig. 8. Diffusion coefficientlimits between5.3 and 17 Rs. The
upper limit valuesbetween9 and 17 Rs were calculatedassuming
strongpitch anglediffusion(z = z•, z• beinggivenby (5)).The pointsat
8.9 Rs were determinedusing(6) with n = 4 as indicatedby Voyager
plasmadata between8 and 9 Rs [Siscoeet al., 1981].The dashederror
bar represents
therangeof valuesthat the9.4 x 102MeV/nuc-Gpoint
assumesas n variesfrom 0 to 12. The solid linesin the portion of the
figurebetween8and 9 Rs showthe dependence
of the plasmadiffusion
coefficienton the Io sourcestrengthS of oxygenand sulfur ions.The
pointsat 11.4,13.0,and 14.4Rs werecalculatedusingequationslike
...:
.
.
ß
:
I019 _
.
•,.
ß
_
.
.
.
i0 •e
ß
_
i0 I?
5
6
7
8
9
I
I
20
L
Fig. 9. (a) The plasma chargedensitynear Io [Bagenal and Sullivan, 1981]. (b) The inward flow rate of oxygen ions with magnetic
momentsgreaterthan the indicatedvalues.The points were calculated
using(8). A typicalerror bar is shown.There is, in addition,a factorof
3 absoluteuncertaintythat appliesto all points. Smoothedcurvesare
drawn through pointsof givenmagneticmoment threshold.
5546
GEHRELSAND STONE:OXYGEN,SULFUR,AND THE JOVIANAURORA
i0 a
-
expected,whereasinside-,-10 Rs the oppositeis true, indicating
large losses.The figure also showsthat becauseof the dependenceof rs on M (equation(5)), one expectsions with smaller
magnetic moments to diffuse farther in, on average,before
beinglost than ionswith largerM.
In the analysisthat follows,we will assumethat the predominant particle lossmechanismis pitch angle scatteringinto the
loss cone and thereforethat the energeticions deposit their
energyin the Jovian atmosphere.The power deliveredto the
atmosphereby oxygenionslostin a givenradial rangeis simply
the loss rate of the ions (i.e., the decreasein F(> M) in that
radial rangefrom Figure9) multipliedby their averageenergy.
The averageenergyEM(L) dependson the magneticmoment
thresholdand is givenby
M2 MeV
/
•
= nuc-/•
i0?
\\ TD:I/VD
/
/
Es•(L) =
typical
104
relative
1.7xlO3 MeV/nuc-G
9.4x10z
6.9 xlOz
4.0 xlO2
uncertainhes
T 7.9-
16.9Rj
2.0xlO •
1
103
6
7
8
9
I0
L
Fig. 10. Comparisonof the diffusiontime TD-- 1/VD,where19
D=
D(1/fXOf/OL), with the particle lifetime • in the strong pitch angle
diffusion limit. The diffusion coefficientused to calculate'•D is the
geometricmean of D t and D. in Figure 8. The line connectingthe
calculatedvaluesof '•Dat differentL is showndashedbetween5.3 and
7.9 R• becausethe radial dependence
off in this regionis not known.
The curvesfor %at differentvaluesof M werecalculatedusing(5).
=•/• v dE
dE
=•/• v dE
dE
(9)
where v is the ion velocity,which is includedto transformthe
flux into a number density.
Figure 11a shows the power per unit L (i.e., per Rs),
dP(> M)/dL, deliveredto the atmosphereby oxygenions with
magneticmomentsgreater than the indicated thresholds,as a
function of the radial distanceat which they are lost. Most of
the power comesfrom between7 and 13 R•, as expectedfrom
Figure9. Also,thereis a shiftin the locationof the peakpower,
from -,-10.5Rs for > 1700MeV/nuc-G oxygenionsto --•8.5 Rs
for > 70 MeV/nuc-G ions. This is consistentwith the shift in
the locationof the crossover
point of rsand r• in Figure 10.The
power per degreelatitude has been calculatedfrom the curves
in Figure 1l a and is shownin Figure 1lb as a functionof the
magneticlatitude at whichthe poweris delivered.The mapping
was done usingthe Voyager 1 magneticfield model of Connerney et al. [1981]. The latitude dependenceof the power will be
discussed below.
Rs is consistentwith a particle lifetime near the strongpitch
anglediffusionlimit throughoutthe inner magnetosphere.
This
is illustratedin Figure 10, which comparesthe radial dependenceof rs with that of the characteristic
diffusiontime, r o =
1/VD,where outside --•12 Rs the diffusion time is short in
comparisonwith the particle lifetime so that a low lossrate is
1012
-
I
I
I
I
I
I
I
I
I
I
()
I
I
I
The total powerdeliveredto the atmosphereby oxygenions
with magneticmomentsgreaterthan a givenM wasdetermined
by integratingthe curvesin Figure 1l a and is shownin Figure
12a. The sulfur points in the figure were calculatedfrom the
oxygendata usingthe sulfurto oxygenratios in Figure 4. The
sulfur contributionis approximatelyequal to that of oxygen
-
-
o
Oxygen.'
ioII
..-"
:
•"'--'•.
ß;ø
-
X
.
::'
:
...... :.
x•
:
i!
,t\x:>4øø
_
xMeV/nuc-GI
.."
:....
\,>200
ß'"'"'
""
>400
'"""
/,/••• \',>690•
-
_
_
.:.......
/
' ' : -"
109
"...,'"'
...•,,,
> 200
i /
", >70
• ..... •.x
\
: :
-
.-"'
x >70MeV/nuc-G-
-
Qxx>
690 _
_ ::/.:I 'I uncerta,nty
tynP•Cal
• •>1760
\\•>940:--
:-
'
.
>1700X
..
iO8
I
I
6
I
I
8
I
I
I
I0
I
12
I
I
14
I
I
16
I
18
65
66
67
68
69
70
71
72
L
Latitude, X (degrees)
Fig. 11. The powerdeliveredto theJovianatmosphere
(a)perunit L and(b)perdegreemagneticlatitudeby oxygenions
with magneticmomentsgreaterthan the indicatedvalues.Typical error bars are shown.The curvesin Figure 1la were
calculatedusing(9) and the datain Figure9b.The curvesin Figure1lb werecalculated
fromthosein Figure1la usingthe
Voyager 1 magneticfieldmodelof Connerneyet aL [1981].
GEHRELS
ANDSTONE:
OXYGEN,
SULFUR,
ANDTHEJOVIAN
AURORA
id4 -
(a) -
5547
-
(b) - IO"•
AURORAL
EXCITATION P(>M)
P(>E)
_
_
iC•
:•:-
-
_
-• i0•:•
..
--
•
--
x
\
ß
-
'"
Q_
x'•.\S
- I0'•
0 '\
_
i0 •
J'%".,.
•o
I0 _
o ß Oxygen
,
.......
Sulfur
""....
[[X• -
"-I0•ø
Oxygen + Sulfur
I0
I0a
103
M (MeV/nuc-G)
IO•IC•
a
IC•
I
I
E (MeV/nuc)
I0
Fig. I2. Thetotalpowerdelivered
byoxygen
andsulfurions(a)withmagnetic
moments
greater
thanM and(h)energy
greater
thanE totheJovian
atmosphere.
In Figure12athesolidcircles
arebased
onth•measured
portions
ofthespectra
in
Fi[ur•5,andth• opencircles
ar• based
onth•extrapolated
portions.
Theox•[cnpoints
wcr•d•tcrmin•d
b• inte[ratin[th•
curves
in Fi[ur• ] ]. Thesulfurpointsw•r• calculated
fromthoseof ox•[cnusin[th• datain Fi[ur• 4•. Th• ran[cof
estimates
of th• powerr•quir•dto cxcit•theobserved
auroralactivit•[Bro•oot • M., ]9•]; Y•g • M., ]9•2] is also
shown.
In Fi[ur• ]2hth• ox•[cncurv•wascalculated
fromthedatain Fi[urc] ]•. Thedashed
portions
indicate
•ncr•s at
whichth• calculation
is basedon •xtrapolations
of the measured
data.The sulfurcurv•wascalculated
fromthe ox•[cn
curveusin[ th• data in Fi[urc 4•.
owingto the fact that the sulfurto oxygenratio at constant widthandis in theregionin whichauroraeareseen[Broadfoot
energyper nucleonis •,0.5 and sulfurhas twiceas many et al., 1981].
From the data in Figure 12b,we have estimatedthe atmonucleons.
Oxygenand sulfurionswith > 70 MeV/nuc-Gare
seento deposit
powerin excess
of 10•2W in theJovianatmos- sphericdepth distributionof the oxygenand sulfur energy
deposition,usingthe tablesof NorthcliffeandSchilling[1970]
phere.
The powerabovea fixedmagnetic
momentis usedin this to calculatethe range of oxygenand sulfur ions in the H2
analysis
because
it is thequantitybestrelatedto theparticle
_] >O.6MeV/nuc
>0.3
>O.I
>0.03
>O.Ol
diffusion
andlossprocesses.
However,for atmospheric
studies,
a more usefulquantityis the power abovea fixed energy,
io ! o;' 1õ'"6! '1 Is'
P(> E),sincea particle's
energy
determines
thedepthto which
it penetrates
intotheatmosphere.
Wehavecalculated
P(> E) as
a functionof energyfrom the data in Figure 11a,with the
resultsdisplayedin Figure12b.
I
I
'I
['1
•
I
'
'J
,
,,
DISCUSSION
''o'i ....Ils ' 6•'"• TM ol ' 'l's'"q
''/
I
,
I
''l / ''
i
I
/
,
/t
L•
,'
ø
,o
The auroralactivityobserved
on Jupiteris oneof the most
I
energetic
phenomena
associated
with the magnetosphere,
re-
/
• •
quiringa continuous
powerinputof 10•3-10
• W intothe
auroralzone[Broadfoot
et al., 1981;rung et al., 1982].Extrapolationof the curvesin Figure12a suggests
that oxygenand
sulfurionswith magneticmomentsof •, 10 MeV/nuc-G(•, 35
keV/nucat 10 Rs)maybedelivering
a reasonable
fractionof
thatpower.FromFigurel lb, weseethat thepowerfromM
•>70 MeV/nuc-Gis deposited
in a •,5 ø zonein magnetic
latitude between •,67 ø and -•72 ø, which is •,4 ø poleward of
i0 aø
o
IOIo•9
io•O
IONIZATION
IOa•
ENERGY
IO•S
i0•
DEPOSITION
RATE
ergs(mg/cma)
-I •l
Fig. 13. Illustrativecalculationof the energydepositionin the
Jovianatmosphereby oxygenand sulMr ions with energiesgreater
theIo footprint[Connerney
et al.,1981],whileionswithlower than the indicated values,as a Mnction of depth along the particle
magnetic
moments
mightprecipitate
somewhat
closerto the paths.Thecurveswerecalculated
byextrapolating
theresultsin Figure
footprint.Thisis consistent
with the observed
auroralzone 12bto lower energies.
5548
GEHRELSAND STONE'OXYGEN,SULFUR,AND THEJOVIANAURORA
17
OXx
•,S (>0I)
0•', % S (>0.01MeV/nuc)
x• •
I-Q_ i0m
•
•
- 600---
LLI
C•
tion to lower magnetic moments of the inward flow rate and
power deliveredto the atmosphere.The inward flow rate was
calculatedusing the data in Figure 9 (with the sulfur contributionestimatedfrom Figure4) whilethe poweris from Figure
12. Sincethe flow rate and powerdependon the Io sourcerate
Si, the bands indicate the range of valuescorrespondingto
1027< Si < 1028ions/s.
Z
A numberof interestingfeaturescanbe deducedfrom Figure
15. For example,the observedinward flow rate of oxygenand
0 jO19
sulfurionswith M > 70 MeV/nuc-Gis ,-•10-3 S•.Thoseions
deposit10•2 to 10•3 W in theJovianatmosphere.
Extrapolations to lower magneticmoment suggest,for example,that
,-•10-2 S• oxygenand sulfurions/smay flow inward with
> i0aø
I0
400
I
10•2
IONIZATION
ENERGY
PER CENTIMETER
10•$
10•4
DEPOSITION
RATE
OF ALTITUDE
(ergscm-ls-I)
Fig. 14. Illustrativecalculationof the altitude dependence
of the
oxygen and sulfur energy deposition(per centimeter)in the Jovian
atmospherefor two lower limitsof the extrapolatedoxygenand sulfur
energyspectra.The curveswere calculatedfrom thosein Figure 13
usingthe atmosphericmodelof Atreyaet al. [ 1981].
region of the upper Jovian atmosphere.The actual spectral
forms assumedfor the oxygen and sulfur fluencesare F0(>
E) = 1 x 1023 E-2'• oxygen ions s-• and Fs(>E) = 6
x 1022E- 2.3sulfurionss- •. For purposes
ofillustration,
it has
been assumedthat these spectral forms, which are based on
observationsfrom ,-•0.6 MeV/nuc to 4 MeV/nuc, extend to
lower energies.Figure 13 showsexamplesof the oxygen and
sulfur energy deposition as a function of depth for casesin
which the flueneespectraextend down to lower energylimits
rangingfrom 0.6 MeV/nuc to 0.01 MeV/nuc. The plotted depth
is that along the particlepath.
As a further illustration,we have calculatedthe energydeposition as a function of altitude insteadof depth, employingthe
atmospheric model of Atreya et al. [1981] for the number
density of molecularhydrogen,as a function of altitude. The
effectsof the approximatelyisotropicincidentflux on the top of
the atmospherehave been taken into accountby assumingall
particles are incident at 60ø. The calculated altitude distribution of deposited energy is shown in Figure 14 for two
different energylower limits to the flueneespectrawhich were
M > 30 MeV/nuc-G. It is also apparentthat with the assumed
extrapolations,
a depositionpowerof 10•3 to 10TMW could
resultfroman inwardflowrate of energetic
ionsof • 1026s
- •.
The bulk of theseions would have M ,-• 10 to 30 MeV/nuc-G,
correspondingto ,-•35 to 100 keV/nuc at 10 R• and ,-•1.5 to 5
keV/nuc (,-• 30 to 100 keV total kinetic energy)at 40 R•.
Ions of theseenergiesare also observedat distancesgreater
than 150 R• in the magnetotail,streamingaway from Jupiter.
The total outward flow rate of this oxygen and sulfur rich
magnetosphere
wind is estimatedto be ,-•2 x 1027ions/s
[Krirnigis et al., 1981], indicatingthat the accelerationprocess
operatingin the outer magnetosphereheatsa large fraction of
the plasma ions that diffuse into the region from Io. It is
thereforepossiblethat enoughions are acceleratedin the outer
magnetosphere
to supplythe ,-•1026ions/sinwarddiffusion
rate requiredto power the aurorae.
As a final point, we comparethe energycarriedinto the inner
E (MeV/nuc)at
-2
I
I0
9R
I0-
I
I0
I
I
I
I
1028
J
103
I J
EXCITATI
)•)•
io
• 1026
LLI
I014
io
i0 m
1027
chosen
to illustratethedeposition
of ,-•10•3to ,-•10•4 W.
The figureshowsthat for the assumedspectralextrapolation,
J 24
most of the energydepositionoccursbetween2 x 10•8 and
5 X 1019cm-2 of H2, corresponding
to an altituderangeof
LL I0
-
approximately450-550 km. The location of the peak depends
on the minimum energy of the spectrum but is above the
homopausefor either of the two representativelower limits
shownin the figure.In their studyof the observedwavelength
dependenceof the ultraviolet auroral emission, Yung et al.
[1982] find that the energy deposition must occur between
•
_
5 x 10•? and 2 x 1020 cm-2, which is consistentwith the
oxygenand sulfurdepth profilesin Figure 14.
The rate at which oxygenions with > 70 MeV/nuc-G diffuse
into theinnermagnetosphere
is ,-•1024ions/s(Figure9),which
is smallin comparison
with the 1027-1028
ions/screatednear
Io. However, Figure 12a showsthat, in order for oxygenand
sulfur to drive the aurora, the bulk of the power must come
from ions with ,-•10 MeV/nuc-G. Since these ions have less
energythan thoseat larger M, relativelymore are neededfor a
comparable contribution of power. To estimate the total required particle flow rate, we show in Figure 15 the extrapolao
Power
i0•o
0
•)
EL
10
cJ
iO22-
-
I02ø
i08
I
I
I
IO
I
I02
I
I03
Flow
irate
]JO
?
I0 4
i06
M (MeV/nuc - G)
Fig. 15. The inward flow rate of oxygen and sulfur ions across
• 15 Rs (outsidethe 1ossyregion)and the total powerdeliveredto the
atmosphereby theseions,as functionsof magneticmomentthreshold.
The energyof the particlesat 9 R•, which is the typical distanceat
whichthe lossesoccur,is shownon the top axis.The bandsindicatethe
rangeof valuescorresponding
to an Io sourcestrengthof 10:: to 10:8
ions/s. As in Figure 5, the dot-dash region is derived from LECP
spectralshape,while the dashedregionsare extrapolations.The auroral excitationpower requirementis alsoindicated.
GEHRELS
AND STONE:OXYGEN,SULFUR,AND THEJOVIANAURORA
5549
magnetosphereby the energeticoxygen and sulfur ions with
that flowing outward with the plasma.The inward energyflow
depths derived from the observedwavelengthdependenceof
the ultraviolet emissions[Yung et al., 1982]. This corresponds
rate across10 Rj due to • 1026ions/sof • 10 MeV/nuc-G to a height in the atmosphereof -,•500 km, which is above the
oxygenandsulfurionsis • 1013W. Thenumberofplasmaions homopause.
diffusingoutwardacross10Rj is • 5 x 1027ions/s,and their
6. If the spectrumextendsdown to -,•10 MeV/nuc-G, then
average energy is approximately the corotation energy of an 10timesmoreenergy(• 10•3 W) is carriedinwardacross10Rj
ion with mass 21 amu (the mean atomic mass of the dissocia- by the energeticoxygen and sulfur ions than flows outward
tion productsof SO2), which is 1.7 keV. The outward energy with the plasma.Thus the main sourceof energyfor powering
flow is therefore-,•1012W. Thusif the particlespectrumex- the aurora and torus would have to be suppliedby an accelertends to lower energiesas suggestedby the extrapolation in ation processoccurringin the middle or outer magnetosphere.
Figure 15, then there is a net flow of energy into the inner'
Acknowledgments.We greatly appreciatethe efforts of R. E. Vogt,
magnetosphere.The inward energyflow is in fact even larger
than 10•3 W, sincethe contributions
fromenergetic
electrons
and protons were not included.
CONCLUSIONS
The principal conclusionsof this study of Z > 2 ions with
energiesin the range 1 to 20 MeV/nuc between5 and 20 R• in
the Jovianmagnetosphereare asfollows:
1. The elemental abundancesof carbon, sodium, and sulfur
relative to oxygen vary as a function of particle magnetic
moment but are to first order the same throughout the mag-
netosphereat a given M. For ions with 103 MeV/nuc-G
both in his capacity as CRS Principal Investigator and as a colleague
who has provided useful discussions.We are also indebted to our
colleagueJ. H. Trainor for his contribution to this analysis.We are
gratefulto the California Institute of Technologyand Goddard groups
who have supported the investigation,with special thanks to W. E.
Althouse, R. Burrell, W. R. Cook, and D. E. Stilwell. We also thank D.
L. Chenette for helpful discussions.N. F. Ness and his colleagueson
the Voyagermagnetometerteam providedthe magneticfield data used
in this analysis,which we gratefully acknowledge.We thank Y. L.
Yung and G. R. Gladstonefor usefuldiscussions
concerningthe Jovian
atmosphereand its auroral emissions.
This work wassupportedin part
by NASA under grants NAGW-200 and NGR 05-002-160 and contract NAS7-918 (formerly NAS7-100).
The Editor
thanks D. Hamilton
and C. K. Goertz
for their assistance
in evaluatingthis paper.
(E • 3.5 MeV/nuc at 10 Rj) the followingabundanceratios are
found: S/O = 0.5, C/O = 0.1, and Na/O • 0.05. The sulfur and
sodium energy spectraare softer than the oxygen spectrum,
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