The Resp onse of s Magnetosphere to an

Outburst on

Michael E Brown and Antonin H Bouchez

Division of Geological and Planetary Sciences

California Institute of Technology

Pasadena California submitted to Science April

BrownBouchez

Abstract

Loss of material from the satellite Io provides the ma jor source of material for

Jupiters magnetosphere b ombardmentby particles in Jupiters magnetosphere

is the ma jor cause of loss of material from Io Though this basic outline is clear

the tightly coupled interaction b etween Io and Jupiters magnetosphere has

long resisted understanding Wehave conducted a sixmonthlong campaign

of intensive monitoring of the Io plasma torus and neutral so dium clouds to

use the timevariable b ehavior of the system to determine the characteristics

of the interaction During the observations a large outburst of material from

Io whichwehyp othesize to b e caused by the eruption of a massivevolcanic

plume on the satellite caused a transient increase in the neutral cloud and

plasma torus masses The resp onse of the plasma torus to this outburst clearly

shows that the interaction b etween Io and Jupiters magnetosphere is stabilized

by a feedbackmechanism in which increases in the plasma torus mass cause a

nonlinear increase in loss from the plasma torus limiting plasma buildup

Jupiters magnetosphere is lled with plasma mostly derived from Io the

innermost of the large satellites of Jupiter and the most volcanically activebody

in the solar system The magnetospheric plasma and the on Io are

coupled in a complex interaction the volcanos feed material primarily

and oxygen atoms and comp ounds to the atmosphere and surface frosts of Io

b ombardmentby magnetospheric plasma removes the atmosphere and frosts

into an extended cloud of gas surrounding the satellite this gas is ionized

by collisions with the magnetospheric plasma b ecomes incorp orated into the

Io plasma torus the inner dense p ortion of the Jovian magnetosphere and

returns to further b ombard Io in a tightly coupled lo op

Although the situation as describ ed ab ove sounds inherently unstable ob

servations haveshown that the plasma density in the Io plasma torus remained

roughly constantover at least a year p erio d even though volcanic activity

on Io is presumably sp oradic Stability of the system in the face of such

varying volcanic input must b e achieved through some feedbackmechanism

either through the regulation of supply to the extended gas clouds surrounding

Io or through regulation of loss from the plasma torus We will refer to

these twotyp es of feedbackmechanisms as supplylimited and losslimited

resp ectively

The typ e of stabilizing mechanism op erating is determined by the detailed

characteristics of the interaction b etween Io and the plasma torus and of the

plasma transp ort pro cesses in the Jovian magnetosphere a knowledge of the

stabilitymechanism thus provides insightinto these two p o orly understo o d

phenomena The system will b e supplylimited if supply to the extended neu

tral gas clouds do es not increase linearly with increasing plasma b ombardment

Two atmospheric mo dels which lead to supplylimitation include an ionospheric

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buering mo del where an increase in plasma b ombardment increases Ios iono

sphere which then b egins to deect the plasma b ombardment and reduce the

supply of material to the neutral clouds and a constantsource mo del where

supply to the neutral clouds is a characteristic solely of Ios atmosphere and

do es not change with changing plasma b ombardment We currently lack

sucientknowledge of Ios atmosphere to b e able to evaluate these mo dels

The system will b e losslimited if loss from the plasma torus dep ends non

linearly on plasma mass such that an increase in plasma mass causes an even

larger increase in plasma loss The only plasma transp ort mo del currently de

velop ed whichwould lead to losslimitation hyp othesize that depletion of the

plasma torus is driven bycentrifugallydriven diusion a nonlinear diusion

caused by the fast rotation of the Jovian magnetosphere In such a system the

diusion rate is prop ortional to the square of the plasma density rather than

to the rst p ower of the density for linear diusion so the diusion rate and

thus mass loss dep end nonlinearly on mass Another p ossible losslimiting

mechanism could b e plasma transp ort initiated by largescale plasma instability

where the onset and growth of the instabilitywould lead to a nonlinear

plasma loss Currently few observational constraints on the plasma transp ort

mechanism are available

The resp onse of the system to variable volcanic input dep ends strongly on

the typ e of feedback op erating Fig thus determination of the timevariable

behavior of the system would provide signicant insightinto p o orly understo o d

asp ects of Io its atmosphere the Jovian magnetosphere and their interactions

To determine this timevariable b ehavior we monitored emission from the Io

plasma torus and from the extended neutral cloud of material surrounding Io for

months in A ma jor p erturbation to the system o ccurred in March

We rep ort here on this p erturbation most likely due to a massivevolcanic

outburst on Io and on the implications for Ios atmosphere and volcanos and

for the interaction of Io with the Jovian magnetosphere

Observations We observed the Io plasma torus and the extended neutral

cloud on clear nights b etween Decemb er and June using the

Lick Observatory meter coude auxiliary telescop e connected to the Hamilton

echelle sp ectrograph Light from a slit arcminutes long by arcseconds

wide was passed through the sp ectrograph and disp ersed to a resolution of

of ab out A The slit was centered on the p osition of Jupiter and

aligned with either the plasma torus plane for observations of plasma torus ion

emissions or the Io orbital plane for observations of the extended neutral cloud

The arcminute extent of the slit gave a spatial resolution of ab out R for

J

a distance of ab out R on the east dawn and R on the west dusk side

J J

of Jupiter An R isaJovian radius  km Each of the almost

J

observations consisted of a minute CCD integration centered at a wavelength

of either A to record the plasma torus S emission lines at and A

or A to record the extended neutral cloud Na lines at and A

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Figure Mo dels of the resp onse of the extended neutral clouds of Io and the

Io plasma torus to a volcanic outburst on Io The dotted line indicates the

volcanic input including a twostep day outburst The dashed line shows

the neutral cloud mass and the solid line shows the plasma torus mass In b oth

mo dels the neutral cloud mass resp onds quickly to the outburst b ecause the

lifetime in the neutral clouds is less than a day The plasma torus mass

resp onds more slowly b ecause the plasma lifetime is of the order of days

a The supplylimited case In this mo del the stabilityoftheinteraction

is maintained b ecause an increase in the plasma density reduces the supply of

material to the neutral clouds by for example increasing the ionosphere on

Io and deecting the plasma After the volcanic outburst ends the high

plasma torus mass causes the supply rate to the neutral clouds to drop b elow

its preoutburst value The decrease in supply to the plasma torus causes the

magnetospheric mass to slowly decline until the equilibrium value is reached

Note that whenever the neutral cloud mass is greater than its equilibrium value

the mass of the plasma torus must increase b The losslimited case In

this mo del stabilityismaintained b ecause the plasma loss rate dep ends non

linearly on the plasma mass as exp ected for centrifugallydriven diusion

for example Note the fast decay of the plasma torus p erturbation compared

to the supplylimited case whichbeginseven as the volcanic input is ab oveits

preoutburst value

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From these sp ectra we extract emission intensity as a function of distance from

Jupiter along the entire slit These two sp ecies were chosen b ecause they have

the brightness emission intensities in the visible wavelength range for a plasma

torus ion and neutral cloud atom resp ectively So dium is approximately

times less abundant than sulfur or oxygen in the neutral clouds but we will

attempt to use it as a tracer of the ma jor sp ecies though its eectiveness as

such a tracer has yet to b e demonstrated

The plasma torus sp ectra and neutral cloud sp ectra are analyzed separately

To examine the longterm b ehavior of the plasma torus intensities werstre

move shortterm p erio dic mo dulations The twoobserved mo dulations in the

data o ccur at p erio ds of hours the System I I I rotational p erio d of Jupiter

and hours an unexplained mo dulation termed System IV

The measured intensities are divided by the slidingaverage of the mo dulation at

these p erio ds to removethevariations of ab out and for System I I I and

IV resp ectively The corrected plasma torus intensityversus Julian date for a

point R the approximate orbital distance of Io on the dawn side of Jupiter

J

is plotted in Figure a The longterm intensity b ehavior at other lo cations in

the plasma torus is qualitatively similar The emission intensity is prop ortional

to the pro duct of the electron and ionized sulfur densities approximately pro

p ortional to the square of the S density as the emission is due to the electron

impact excitation of the sulfur

Analysis of the emission intensities from the neutral so dium cloud suers the

complication that the emission seen is from the resonant scattering of sunlight

the emission intensitythus dep ends on the received solar ux at the wavelength

of the atomic transition and therefore on the helio centric velo city of the so dium

atoms This eect is dep endent mostly on Io phase so we correct by

removing the slidingaverage mo dulation of the data at Ios orbital p erio d The

total mo dulation by Io phase is No System I I I or System IV mo dulations

are seen in the so dium data The so dium intensities summed along the entire

slit and corrected for viewing at Io elongation are shown in Figure b The

emission intensity is linearly prop ortional to the column densityofsodium

An Io outburst The most striking feature of the data is a sudden increase

in the brightness and thus mass of the neutral so dium cloud starting around

Julian date February hereafter only the last three digits

of eachJuliandatewillbegiven followed by a more gradual increase in the

plasma torus emission intensity Figure shows an expanded view of the p erio d

of the outburst with b oth the neutral so dium and sulfur plasma torus emission

intensities plotted relative to the medians of their values b efore dayThe

so dium cloud mass increases byanaverage of ab out a factor of two for at least

days with transient increases of higher than a factor of The plasma

torus mass increases by almost over this time p erio d and drops backtoits

previous value after the so dium outburst has ended The timing of the neutral cloud and plasma torus p erturbations is strong

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Figure The intensityofAS emission from the plasma torus and A

so dium emission from the neutral clouds as a function of Julian date The

observations b egin on Decemb er whichisJDIntensities are in

 photons cm sec sterad Rayleighs dened as R

evidence that an increase in mass injection from Io causes the neutral cloud

p erturbation which then causes the plasma torus p erturbation For example

on day the so dium mass has already increased by a factor of while all

observations show that the plasma torus remains undisturb ed The simplest

explanation for this observation is that the mass supply to the neutral clouds

has suddenly doubled The plasma torus intensityslowly b egins increasing

around this time and a backwards linear extrap olation of the increasing phase

of the plasma torus p erturbation suggests a starting time around day Such

behavior is precisely that exp ected from an increase in injection of material

from Io starting around day The link b etween the neutral so dium and

ionized sulfur p erturbations suggests that so dium can b e used to trace at least

the basic b ehavior of the more abundant sulfur We discuss this p oint further

below

The detailed resp onse of the neutral clouds and plasma torus to this injection can b e used to determine if the system is supplylimited or if it is losslimited

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Figure A direct comparison of the neutral so dium and ionized sulfur emission

intensities Both are plotted relative to the median of their preoutburst values

The data are connected by lines going through the median values of the seven

separate clusters of data Note that b etween days and the plasma

torus mass decreases slightly while the neutral cloud mass remains ab oveits

preoutburst value Such b ehavior can o ccur only in a losslimited system

One simple yet p owerful diagnostic is that in a purely supplylimited system

the plasma torus mass must increase any time the neutral cloud mass is ab ove

its equilibrium value see Fig This requirement results b ecause supply to

the plasma torus is prop ortional to the ionization and chargeexchange rates

which are prop ortional to the pro duct of the plasma and neutral densities while

loss is prop ortional only to the plasma density Figure clearly shows that the

system do es not resp ond in this purely supplylimited manner from day

until day the neutral so dium cloud is ab out twice as massiveasitwas pre

outburst but the plasma torus decreases in mass by Such b ehavior

can b e achieved only in a losslimited system

This losslimited b ehavior shows that the system maintains stabilitybya

large increase in plasma loss as the plasma torus mass increases This increased

loss overcomes the supply rate increase caused by the higher plasma density

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Figure Spatial proles of the lineofsight emission intensity of the plasma

torus b efore the start of the so dium outburst and after the start of the out

burst In addition to b ecoming brighter and more dense the dawn side of the

torus moved further out from Jupiter The dusk side moved in towards Jupiter

slightly This shift likely results from an increase in the dawndusk electric eld

across the magnetosphere

preventing a p ositive feedbackwhichwould make the system unstable

Magnetospheric resp onse to an outburst Further evidence for a large

increase in the plasma loss rate is found by examining the magnetospheric re

sp onse to the outburst Previous observations have noted that the plasma torus

app ears oset towards the dawn direction This eect is a predicted conse

quence of a largescale electric eld of ab out mV m across the inner magne

tosphere The eld is thought to b e due to the v  B electric eld set up by

the plasma owing down to the magnetotail with the eld propagated to the

inner magnetosphere in a manner analogous to terrestrial equatorial currents

Our preoutburst observations of the plasma torus show this exp ected dawn

oset the p eak of emission intensity on the dusk side o ccurs at R while

J

the dawn p eak o ccurs at R During the outburst the p eaks of emission

J

of the plasma torus shift even further dawnward Figure This shift is most

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prominent on the dawn side and only marginally visible on the dusk side Figure

a shows average intensity proles for the dawn side for dierent times

preoutburst the rising phase of the torus p erturbation the p eak of the torus

p erturbation and the declining phase of the torus p erturbation The dawnward

shift of the plasma torus increases with each increase in the plasma mass Figure

b plots the fractional dawnward shift of the plasma torus versus the relative

plasma torus mass for these time p erio ds The plasma torus systematically

shifts dawnward with increasing mass of plasma

Adawnward shift in the plasma torus can b e caused byanincreaseinthe

largescale electric eld across the inner magnetosphere Weshow here a sim

plistic mo del that suggests that such an increase can b e caused by an increase

in the plasma outowandthus by an increase in mass loss from the plasma

torus the transition b etween where the magnetospheric motion is domi

nated by corotation and radial transp ort and where the tailward ow b egins

o ccurs around a characteristic distance the Hill length L of

H



L R B M

H

J J

where is the P ederson conductivityoftheJovian ionosphere B is the Jo

J

vian surface magnetic eld strength and M is the total rate of outward mass

transp ort As M increases L decreases and tailward ow b egins closer to

H

Jupiter Closer to Jupiter the magnetic eld strength B is higher and for a

simple dip ole the strength go es as B  R Thus the tailward plasma ow

J

b egins in a region of stronger magnetic eld and assuming that the tailward

owvelo cityiscontrolled by the solar wind sp eed and remains constant the

electric eld E which is prop ortional to v  B increases as

M



E 

M

where M is the initial mass outow rate While this analysis is simplistic and

cannot capture many of the complexities of the real magnetospheric interactions

it likely repro duces the basic b ehavior of the relationship b etween changing

plasma outow rates and the largescale electric eld an increase in the mass

outow will cause an increase in the electric eld thus a dawnward shift in the

Io plasma torus as observed

We see from the data Fig that the dawnward shift and thus the plasma

outow rate increases precipitously as the mass of the plasma torus increases

This b ehavior is precisely that exp ected for a losslimiting mechanism to sta

bilize the interaction b etween Io and the magnetosphere an increase in the

plasma mass causes an even larger increase in plasma loss so the plasma mass

decreases From equation and the measured shift in the plasma torus we

can attempt to estimate the plasma outow rate as a function of the plasma

mass Figure b shows curves for the exp ected dawnward shift assuming

equation is strictly correct for twotyp es of plasma transp ort p ostulated

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Figure Shifts in the plasma torus a The emission intensity prole at time

p erio ds b efore and during the torus p erturbation The torus shifts systemati

cally dawnward with the increase in mass b The p eak of torus emission as a

function of relative torus mass for the four time p erio ds ab ove Also plotted are

the shifts exp ected for plasma transp ort by simple diusion and bycentrifugally

driven diusion using the mo del in equation The shifts are b est t bya

mo del where plasma outow is prop ortional to the seventh p ower of the mass

of the plasma torus shown as a dashed line

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for the Jovian magnetosphere linear diusion where the plasma loss is

directly prop ortional to the plasma density and centrifugally driven diusion

where the diusion is prop ortional to the square of the density The b est

p olynomial t to the data is given by a mo del where plasma outow is prop or

tional to the seventh p ower of the plasma mass We place no signicance on

the sp ecic p olynomial t the critical characteristic suggested by these data

is that plasma outow increases quickly with increase in plasma mass Even

the nonlinearity of centrifugallydriven diusion cannot account for the large

increase in plasma outow with increasing plasma mass if our simplistic mo del

of the relationship b etween the plasma torus shift and the plasma outowis

approximately correct Another even more nonlinear mechanism suchas

transp ort through largescale plasma instability is required in this case

Magnitude of the outburst Using our knowledge of the b ehavior of the

system we can now attempt to estimate the magnitude of the outburst from Io

In a purely losslimited system p erturbations to the neutral cloud mass directly

reect p erturbations to the source from Io During the outburst the neutral

so dium cloud mass increases by ab out a factor of for days and a factor of

more than for at least a day p erio d thus the so dium supply from Io must

have increased by at least that amount

But is the mass increase in so dium a minor sp ecies in the neutral clouds

indicative of the b ehavior of the dominant sulfur and oxygen The subsequent

increase in the sulfur plasma mass following the so dium outburst shows that

atomic sulfur must have increased in mass at the same time as atomic so dium

but the total amount of the sulfur increase remains unknown We can esti

mate the increase in atomic sulfur by the magnitude of the increase in sulfur

plasma mass if we know the plasma outow rate We calculate a lower limit

to the atomic sulfur increase by assuming the minimum plasma outow consis

tent with the observed losslimited b ehavior This minimum outowisgiven by

centrifugallydriven diusion where plasma outow increases with the square

of the plasma mass Using the simple mo del of the interaction b etween the

neutral clouds and plasma torus describ ed earlier we nd that small p er

turbations such as that seen in the plasma torus require a mass input increase

of approximately the same amount as the p erturbation Thus for the minimal

plasma outow the increase in plasma torus mass requires a increase

in neutral cloud mass As the so dium mass increases by a factor of so dium

would havetobe times more abundant in the outburst than sulfur in this

case

Assuming however that the much larger increase in plasma outow with

increased plasma mass inferred from the plasma torus shift is correct a much

larger atomic sulfur increase is required to account for the increase in sulfur

plasma mass For this case we nd that the observed increase in plasma

torus mass requires a factor of increase in supply to the neutral clouds in

approximate agreement with the factor of increase in the neutral so dium

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cloud mass Thus the data are consistent with the hyp othesis that the mass of

so dium is a direct tracer of the mass of the more dominant sulfur and presum

ably oxygen comp onents

The precise relationship b etween the mass in the so dium outburst and the

mass in the sulfur and oxygen would b e quickly determined bycontemp oraneous

observations of neutral sulfur or oxygen during the so dium outburst Unfortu

natelynosuch observations were obtained during these observations Future

monitoring of the Io plasma torus system should put sp ecial emphasis on ob

taining suchobservations

Cause of the outburst It is not p ossible to directly determine the cause

of the increase in gas supply from Io but with volcanic activitya know transient

phenomenon on the satellite the eruption of a volcanic plume on the satellite is

a natural explanation The only conclusive supp orting evidence would b e direct

images of a new large plume on Io Such images are currently p ossible only

from remote observations taken by spacecraft in the Jovian system No such

spacecraft was inside the Jovian system during these observations Groundbased

infrared observations are able to monitor hotsp ot activityonIo but we

have no reason to exp ect that these are asso ciated with plumes on Io nor

were any observations obtained during the outburst We therefore conclude

that although no pro of of the hyp othesis will ever b e p ossible the eruption of

avolcanic plume on Io is the most likely source of the sudden transientgas

injection

Voyagers and imaged active plumes on Io thus even if the neu

tral clouds are supplied solely by an atmospheric comp onentcausedby active

plumes a typical plume should aect the supply rate by only a small amount

All plumes except one however were active during b oth Voyager encounters

months apart so short term variability is not necessarily exp ected for these

plumes the largest observed plume was that only plume observed to have

turned o b etween the Voyager and encounters In addition b etween the

two encounters a plume with dimensions similar to Pele resurfaced a large area

around Surt It thus app ears that the largest plumes are the most variable

and that a plume with duration of only days might b e exp ected to b e

quite large If the neutral clouds are fed by sputtering of atmospheres lo cal to

active plumes we exp ect that the contribution of each individual plume should

b e roughly prop ortional to the surface area covered by the plume Based on

Voyager measurements of observed plume widths we nd that the surface

area covered byPele was almost times greater than the surface area covered by

all of the other plumes taken together Thus the factor of or more increase in

the supply of so dium to the neutral clouds suggested by the data is reasonable

for the largest observed plumes on Io

Implications for the system We prop ose the following scenario to ex

plain the observations presented here Starting on approximately daya

large plume of dimensions similar to those of the Pele plume b egan erupting

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This eruption greatly increased the surface area of plume material available to

b e sputtered into the neutral clouds and the neutral cloud mass quickly ad

justed to this increase in mass input The plume remained active for ab out

days and its output was highly variable during this time The increase in mass

of the neutral clouds caused an increase in the supply of ions to the plasma

torus so the mass of the plasma torus b egan to increase The increase in mass

of the plasma torus then led to a highly nonlinear increase in plasma outow

causing the plasma torus mass to fall to its equilibrium value quickly after the

cessation of plume activity

This scenario suggests the following implications for Io and the plasma torus

The stability of the magnetosphereIo interaction is controlled not by Io and

the details of its atmosphere and mass pickup but by the magnetosphere and

the metho d of plasma transp ort An increase in plasma mass causes a very

strong increase in plasma loss from the torus as suggested by mo dels where the

plasma transp ort is driven by largescale plasma instability So dium is a

go o d tracer of plume activity on Io and the resp onse of the sulfur plasma torus

to the observed so dium outburst is consistent with that exp ected if so dium and

sulfur are equally abundantinsuch outbursts Observations of neutral oxygen

or neutral sulfur during such an outburst are vital to conrm this suggestion

The large resp onse of the so dium neutral cloud if it is representativeofthe

sulfur and oxygen clouds shows that the Io atmosphere is easily overwhelmed

by the eruption of a single large plume lending supp ort to the idea that the

atmosphere of Io is primarily due to plumes Variable volcanic activity

on Io aects plasma mass plasma transp ort and largescale electric elds in

the Jovian magnetosphere

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References

DB Nash MH Carr J Gradie DM Hunten and CF Yoder in Satel

lites JA Burns and MS Matthews Eds University of Arizona Press

Tucson pp

See review by JR Sp encer and NM Schneider Ann Rev Earth Planet

Sci

HM Mo os TE Skinner ST Durrance MC Festou and JL Bertaux

Astrophys J N Thomas J Geophys Res

RG Strom and NM Schneider in Satel lites of Jupiter D Morrison Ed

University of Arizona Press Tucson pp

see review by NM Schneider MA McGrath and WH Smyth in Time

Variable Phenomena in the Jovian System MJS Belton et al Eds

NASA SP pp AF Cheng J Geophys Res

RE Johnson and M McGrath Geophys Res Let

see for example JK Wilson and NM Schneider J Geophys Res sub

mitted

See for example E Lellouch Icarus

GL Sisco e and D Summers J Geophys Res

DH Pontius and RA Wolf Geophys Res Lett YS Yang

RA Wolf RW Spiro TW Hill and AJ Dessler J Geophys Res

S Vogt Pub Astron Soc Pacic

Details on the observations and the plasma torus data reduction can b e

found in M Brown The StructureandVariability of the Io Plasma Torus

PhD thesis University of California at Berkeley Reduction of the

so dium data followed essentially the same techniques with additional com

plications due to the so dium night sky lines the continuum sp ectrum of

Io and the water absorption features The complete reduction pro cedure

for these sp ectra will b e presented later

BR Sandel and AJ Dessler J Geophys Res

ME Brown J Geophys Res

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JT Bergstralh JW Young DL Matson TV Johnson Astrophys J

L RA Brown and YL Yung in Jupiter T Gehrels Ed

University of Arizona Press Tucson pp

We estimate the total mass increase in the plasma torus by summing all

emission along the slit and taking the square ro ot as the emission intensity

is prop ortional to the pro duct of the ion density and the electron density

whichwe assume scale together Figure app ears to imply an even larger

change in mass only b ecause of the structural changes that o ccur in the

torus at the same time discussed later

An alternative scenario mightbeenvisioned where the increase in mass of

the neutral so dium cloud is caused by an increase in the so dium lifetime

caused for example by a decrease in the electron temp erature We reject

this hyp othesis for two reasons observations of the plasma torus while

not directly sensitive to electron temp erature shownochange in the plasma

torus mass ion temp erature or rotation velo city at the start of the neutral

so dium cloud p erturbation and the increase in mass of the plasma torus

shows that for sulfur at least the supply increases precisely when the

so dium mass increases strongly suggesting that the so dium mass increase

is caused by a so dium supply increase

CB Pilcher JH Fertel and JS Morgan Astrophys J

AJ Dessler and BR Sandel Geophys Res Lett NM

Schneider and JT Trauger Astrophys J

DD Barb osa and MG Kivelson Geophys Res Lett

The fractional torus shift is dened as p  p p p where

dawn dusk dawn dusk

p and p are the p osition of the p eak of plasma torus intensityon

dawn dusk

the dawn and dusk sides resp ectivelyAsabove the relative densityis

estimated by the square ro ot of the total intensityintergrated along the

sp ectral slit

We are indebted to AJ Dessler for the analogy to terrestrial equatorial

currents and for the suggestion of the form of the relationship b etween an

increasing plasma outow and an increasing electric eld

TW Hill J Geophys Res

The curves for simple diusion and for centrifugallydriven diusion are

calculated assuming zero electric eld for a zero mass plasma torus and by

forcing the curves to go through the equilibrium mass p oint relativetorus

mass of

The mo dels of the b ehavior of the neutral cloud and magnetosphere mass are based on the zerodimensional mo dels of TS Huang and G L Sisco e

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J Geophys Res For the supplylimited case supply to the

neutral clouds is prop ortional to the squarero ot of the plasma density and

diusive loss from the magnetosphere is prop ortional to the plasma density

For the losslimited case supply to the neutral clouds is prop ortional to

the plasma density and loss from the magnetosphere is prop ortional to the

fourth p ower of the plasma densityFor b oth cases mo del input parameters

are adjusted to yield a steadystate plasma lifetime of days and an

neutral lifetime of hours

See for example GJ Veeder DL Matson TV Johnson DLBlaney

and JD Goguen J Geophys Res

WH Smyth and MR Combi Astrophys J

DF Strob el in Time Variable Phenomena in the Jovian System MJS

Belton et al Eds NASA SP pp

Wehave b eneted greatly from conversations with AJ Dessler TW Hill

MA McGrath EJ Moyer and DH Pontius This researchwould not

have b een b egun without a generous seed grant from the California Space

Institute and would not have pro ceeded without the reliable help of Tony

Misch and the other sta at Lick Observatory