JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 90, NO. A2, PAGES 1755-1757, FEBRUARY
1, 1985
Revised Ion Temperatures for Voyager Plasma Measurements
in the Io Plasma
Torus
FRANBAGENAL,
1 RALPHL. MCNUTT,JR.,JOHNW. BELCHER,
HERBERT
S. BRIDGE,ANDJAMES
D. SULLIVAN
2
Centerfor Space Research,MassachusettsInstitute of Technolo•ly,Cambrid•le
We have discoveredthat an error was made in computing ion temperatures for some of the results
derived from the positiveion data from the plasma science(PLS) experiment on the Voyager spacecraft.
The reported resultsdirectly affectedby this error are the ion temperaturesin the inner magnetosphereof
Jupiter given by Bagenal et al. (1980) and Bagenal and Sullivan (1981) plus a single ion temperature
calculatedfrom Voyager 1 data obtained in Saturn'smagnetosphereand quoted by Bridge et al. (1981).
The ion temperaturesquoted for the torus region in the original Jupiter Sciencearticle (Bridge et al.,
1979) and all of the ion temperaturesin the middle magnetosphereof Jupiter (McNutt et al., 1981) were
derived independentlyand are unaffectedby the error.
DISCUSSION OF ION TEMPERATURE
MEASUREMENTS
We are currently reanalyzingmuch of the positive ion data
obtained by the Voyager plasma science(PLS) experiment
during the Jupiter encounters.In the courseof that analysisit
becameapparentthat someion temperaturesobtainedin previous work
were a factor of 2 lower than those derived
from
the current analysisprogram. This discrepancywas traced to
tour plots given by Bagenalet al. [1980] and Bagenal and
Sullivan[1981] are incorrect.In addition, values of the flux
tube contentper unit L times the L shell parametersquared
(NL2),derivedusingthesetemperatures,
are underestimates
by
abouta factorof (2)•/2. The followingsectioncontainsa summary of publishedresultsaffectedby this error in calculating
the ion temperatures.
an error which affected some but not all of the earlier results.
The error, which causedthe ion temperature to be quoted
at half of the correct value, was introduced because.the "ion
thermalspeed"wasdefinedinconsistently
in separateparts of
the analysisof the torus data. The energy-per-charge
spectra
obtainedby one of the PLS detectorsduring the inbound
traversalof the Io torus are shown in Figure 5 of Bagenaland
Sullivan[1981]. In the initial analysisof thesespectra,each
ionicspecieswas assumedto havean isotropicreduceddistribution functionin velocityspacewhich could be describedfor
a specifieddirection(suchas alongthe detectornormal) by a
Maxwellian
function
f(v) = nw-'(2r0-1/2exp{-(v-
V)2/(2w2)}
(1)
involvingthreeindependentparameters'the bulk speedof the
ions in the specifieddirection V, the total number densityn,
and the thermal speedw. For the above form of f(v), w is
relatedto the ion temperatureby w = (kT/m)1/2,wherem is
the mass of ion. The error occurred when the values of the ion
thermal speedderivedfrom the data in this way were later
convertedto ion temperaturesusingthe more commondefini-
tion of (2kT/m)•/2 for the thermalspeed.Thusthe ion temperaturesthat emergedfrom the analysiswerea factor of 2 lower
than they shouldhave been.Althoughthe valuesderivedfor
localdensityand bulk speedare obviouslynot affectedby this
error, the underestimate of the ion temperatures has two
major effects.First, the incorrection temperatureswere used
to calculatescaleheightsfor differentionic species.Sincethese
scaleheightsform the basisfor the two-dimensionalplots of
plasmadensityin the torus(as a functionof cylindricalradial
distanceand distancefrom the centrifugalequator, z), the con• Now at ImperialCollege,London.
2 Now at Plasma Fusion Center, Massachusetts
Institute of Technology, Cambridge.
Copyright 1985 by the American GeophysicalUnion.
Paper number 4A8310.
0148-0227/85/004A- 8310502.00
1755
SUMMARY OF THE EFFECTS ON PUBLISHED RESULTS
The ion temperatures derived for the Io torus region by
Bridge et al. [1979] and for the middle magnetosphereof
Jupiter outside of 10 Rj by McNutt et al. [1981] are correct as
given. The ion temperaturesderived by Bagenal and Sullivan
[1981] and shown in Figure 7 of that paper should be increasedby a factor of 2, as should the ion temperaturesin
Figure 1 of Bagenal et al. [1980] (however, see the following
section for a discussion
of the inherent
uncertainties
in the ion
temperaturedetermination).The temperaturesinside of 10 Rj
only, shown in Figure 11 of McNutt et al. [-1981], should also
be increasedby a factor of 2. With regard to the single incorrect estimate in Saturn's magnetosphere,the thermal speeds
quoted in Figure 5 of Bridge et al. [1981] for ions with mass-
to-chargeratios of 1 and 16 shouldbe 38 and 28 km s-•,
respectively,
wherethermalspeedis definedas(2kT/m)•/2.
The ion temperaturesin the inner magnetosphereof Jupiter
were used to extrapolate the local measurementsof ion density away from the spacecraftlocation along magnetic field
lines' these extrapolated values of ion density describe the
spatialdistribution of plasmain the Io torus and were given in
the form of density contour plots by Bagenalet al. [1980] and
by Bagenaland Sullivan [1981].
Correction of the ion temperaturesresultsin a torus which
is more extendedin latitude than that shown in thesepapers.
If we approximate the density distribution along a field line as
a Gaussian function,
n(z)- n(z= 0) exp{-(z/H) 2}
(2)
wherethe scaleheightH oc(T) •/2, it is evidentthat the twofold increase in temperature means that the torus should be
•40% more extended in the z direction. The spatial distribution of torus plasma has been recalculated in the same
manner as that of Bagenal and Sullivan [1981] using temperaturescorrectedby a factor of 2. The resultingmap of positive
ion charge density (in elementary chargesper cubic centimeter) is shown in Figure 1.
1756
BAGENAL
ETAL.'BRIEFREPORT
CHARGE
DENSITY(CM-3)
•
INBOUND
125
•' ,.I
•
Y••W
• •_
• I CENTRIFUGAL
3OO
the PLS ion measurementswas the Alfv6n speedin the torus.
Since the Alfv6n speed is inversely proportional to only the
square root of the local mass density, the correctedion temperaturesproducelittle changein the contour map of Alfv6n
speedshownin Figure 15 of Baoenaland Sullivan[1981]. The
average time taken by an Alfv6n wave to travel along field
linesbetweenIo and the ionosphereof Jupiter [Baoenal, 1983]
shouldbe increasedby --•20% to 400 s owing to the extension
of the torus. The range in travel times due to the variation in
Io's positionin the torus becomesabout 200 to 800 s.
UNCERTAINTIES IN THE MEASUREMENTS
OUTBOUND •
-2l
I
I
I
OF ION TEMPERATURES
I
The ion data obtained inside --•5.7 Rj allowed accurate
determination of the temperaturesof the major ionic species
RADIALDISTANCE
(Rj)
[Baoenal and Sullivan,1981; Bagenal,1985]. In this cold inner
FJ•. 1. Revised
Jsode•sJt•
co.tourmapo[ positive
c•ar•ede•sJt• torus, then, the factor of 2 correction to temperatures dis(inelementary
charges
percubiccentimeter)
asa function
of centrifu- cussedabove reflects the physical conditions in that region.
galdistance
andheightabovethecentrifugal
equator.
However, outside of --•5.7 R j, in the warm torus, there are
If we take the boundaryof the plasmatorusto be definedas inherent difficultiesin the determination of ion temperatures.
We currently feel that an increaseof a factor of 2 in published
the 250 cm-3 contour of the electron density map, the total
volumewasestimatedto be 7.7 x 103zcm3 (212 R• 3) before ion temperaturesin that region, although mathematicallycorrect, probably is not physically realistic; on physical grounds
correctingthe temperature.Usingthe correctedcontourmap
an increasein publishedvalues of a factor around 1.5 is probin Figure1,thevolume
isincreased
by30%to 1.0x 103•cm3 ably more appropriate in the warm torus for the following
(287R• 3)andis equivalent
to a uniformtoruswith majorand
reasons.First, the broad velocity distributions of the warm
minor radii of 6.0 and 1.56R•, respectively.
Only 3.0% (27%)
plasma produce a very flat energy-per-chargespectrum in
of this volume is occupiedby chargedensitiesof over 20•
which the individual peaks of the ionic speciescannot be re(1000)cm-3, while theseregionsof high densitycontribute
solved.Thus the parameters V, n, and w for each speciesare
9% (48%)of thetotalof 9.1 x 103½
elementary
charges.
Asan
not well constrainedby the data. Imposing the condition that
aside,wenotethattheaverage
density
is only875cm-3. this
all the ions should have the same temperature would reduce
is considerably
lessthan valuesgenerallyusedin the literature
the number of freeparametersand improve the fit.
for the Voyager1 epochin studiesof the torus.
However, for the isothermal approximation to be valid the
Valuesof the quantityNL • have beenderivedusingthe
time scalefor thermal equilibrium betweenthe different heavy
scaleheightapproximationfor the densitydistributiongiven
ion speciesmust be appreciablyless than the characteristic
in (2) and integratingover z to obtain
time for diffusiveloss.For the thermal (,-•60 eV) multispecies
NL• = • 2n3/: R•• L3ni(z
= O)Hi
(3) torus plasma ions the time for equilibrationvia ion-ion Coui
lomb collisionsis about 5 days, and the diffusion time scaleis
Thustheerroneous
ion temperatures
caused
thevalueof NL •
10 to 100 days. Thus the isothermal assumptionis probably
4
6
8
I0
to beunderestimated
by a factorof •(2) •/:.
Values of NL • derived from the Voyager data have been
reasonable for the bulk of the ions. However, new ions are
continuouslycreatedat pickup energiesof 300 to 600 eV, and
usedby variousauthorsto calculateratesof plasmadiffusion these ions maintain a high-energytail in the ion distribution
in the torus region[Richardsonet al., 1980' Richardson
and at energieswell above the peak of the thermal distribution.
Siscoe,1981' Siscoeet al., 1981' Richardsonand Siscoe,1983a'
Chenoet al., 1983]. Tokar et al. [1982a] usedthe plasma
distributionderivedby Baoenaland Sullivan[1981] to calcu-
This hot componentwill broaden the energy-per-chargespectra and increasethe ion temperaturesderived under the assumptionof thermal equilibrium.A preliminary inspectionof
late the dispersionthat would be expectedif the whistlers the high-energytail of the spectrumsuggests10-20% of the
observedby the Voyagerplasmawave experimenthad trav- ions are hotter than the thermal population. These numbers
eled from the ionosphereof Jupiterto the spacecraft.
The are consistent with both theoretical studies [Barbosa et al.,
1983; Richardsonand Siscoe,1983b] and spectralobservations
electronsaccompanyingthe torus ions were insu•cient to
from S+ ionsreportedby Brown[1982].
producethe observeddispersion,and Tokar et al. [1982b] of opticalemissions
A study of the ionic composition of the warm torus using
inferredthat light ions, suchas protons,had e•capedfrom
Jupiter'sionosphere
and populatedthe mid-latitudesbetween data from both the PLS detector and the Voyager ultraviolet
spectrometeris in progressand it is hoped that, as a result of
reducingthe number of free parameters,the ion temperature
ion temperatures
by a factor of 2 in the warm toruswould can be better constrained.Meanwhile, the original analysisof
increasethe total plasmacontentby •40% whichmay pro- Bagenaland Sullivan[1981] probably overestimatedthe width
ducefar greaterfrequencydispersionof the whistlersthan of the velocity distributions becauseof the presenceof nonobserved(however,seethe discussion
concerning
temperature thermal tails, and hence we believe the temperature of the
below).Withoutrepeatingthe work of Tokaret al. [1982a,b] thermal ion population outside 5.7 R• to be only a factor
it is not possibleto accuratelydeterminethe constraintplaced ,-•1.5 greaterthan their resultsand not the full factor of 2. We
by the observedwhistlerdispersions
on the total flux tube must be cautiousin comparing local measurementsmade by
content.
Voyager 1 in 1979 with remote observationsmade using
over a period of severalyears.NeverFinally, another important quantity that was derivedfrom ground-basedtelescopes
the torus and the ionosphere,contributinga further 1•20%
to the total electron content of these L shells.Correcting the
BAGENAL
ET AL.: BRIEFREPORT
1757
theless,
we suggest
that theion temperatures
reportedhereare
T. P. Armstrong,Energeticion lossesnear Io's orbit, J. Geophys.
consistentwith the temperaturesof S+ and S2+ ions obtained
fromspectralmeasurements
of line emissions
by Traugeret al.
[1980],Brown[1981,1982],andRoederet al. [1982].
McNutt, R. L., Jr., J. W. Belcher,and H. S. Bridge,Positiveion
observations
in the middlemagnetosphere
of Jupiter,J. Geophys.
Acknowledgments.
Thiswork wassupported
by NASA undercontract953733to MIT fromtheJetPropulsionLaboratory.
The Editor thanks W. S. Kurth and G. L. Siscoefor their assistance
in evaluatingthis paper.
Res., 88, 3936, 1983.
Res., 86, 8319, 1981.
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86, 8485, 1981.
Richardson,
J. D., and G. L. Siscoe,
The problemof coolingthe cold
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Richardson,
J. D., and G. L. Siscoe,
The non-Maxwellian
energy
distributionof ionsin the warmIo torus,J. Geophys.
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1983b.
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J. W. Belcher,
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(ReceivedSeptember4, 1984;
acceptedOctober4, 1984.)