Download Longitudinal Asymmetry of the Jovian Magnetosphere

VOL. 81, NO. 19
JOURNAL
OF GEOPHYSICAL
RESEARCH
JULY 1, 1976
Longitudinal Asymmetry of the Jovian Magnetosphere
and the Periodic Escapeof EnergeticParticles
T. W. HILL 1 AND A. J. DESSLEn
Departmentof SpacePhysicsand Astronomy,Rice University,Houston,Texas 77001
We utilize an earlier model of the Jovian magnetosphere
in which the centrifugalstressof corotating
plasmadistendsthe outer magnetosphereand opensthe tail field. Becauseof a longitudinalasymmetryin
the ionosphericplasma sourcestrength,causedprincipally by the nonaxisymmetricsurfacefield, the
closed field region in the tail expands and contractswith the rotation period, resulting in a 10-hour
modulationof the flux of energeticparticlesescapingfrom the magnetosphere
into interplanetaryspace.
The most striking evidenceof the effect of the rotation of
Jupiter on its magnetosphericdynamicsconsistsof the energetic particle measurementsmade with Pioneers 10 and 11.
For example,the encounterof Pioneer 10 with Jupiter revealed
energeticparticle fluxes within the magnetospherethat were
strongly modulated at the 10-hour rotation period of Jupiter
[e.g., McKibbenand Simpson,1974].Theseinitial observations
were interpreted as being indicative of a particle distribution
pulled open to let the plasma escape [Michel and Sturrock,
1974].The openingof the field will take placepreferentiallyon
the night side becausethe restraining pressureof the solar
wind is absentthere [Hill et al., 1974a]. Thus while the magnetic field is closedthroughout most of the day sidemagnetosphere[Smith et al., 1975], the field openson the night sideto
form a planetary wind escapingdown the tail.
Second,the magnetosphericplasma distribution should rethat was confined near the current sheet of a distended field
flect any longitudinal asymmetrythat existsin the ionospheric
configurationthat oscillateddiurnally about the ecliptic plane plasma source.This longitudinally asymmetricdistributionof
(and hencepast the spacecraft),owing to the tilt angle between magnetosphericplasma produces a 10-hour variation in the
the spin axis and the magnetic axis of Jupiter (Figure 1). degree of field distortion observed at a given point in the
However, the same 10-hour modulation was subsequentlyre- nonrotating referenceframe. In particular, the distanceto the
ported to be a feature of relativisticelectron fluxesobservedin last closedfield line on the night side, and hencethe extent of
interplanetary space, well outside the Jovian magnetosphere the trapping region for energeticparticles, will vary with the
[Chenette et al., 1974]. Furthermore, the phase of the flux rotation period [Hill et al., 1974b].The open field line region
maxima was found to be the same for the two Pioneer encounwill penetrate closest to Jupiter when the strongestplasma
ters, separatedin time by a full year [Simpsonet al., 1975]. sourceregion facesthe night side and vice versa.
The diurnal variation of the distance to the last closed field
Thus a dynamic 10-hour time variation in the structure of the
Jovian magnetospheremust be responsible.for the observed line implies a diurnal variation of the flux of energeticelectrons that escapefrom the trapping region into the magnetovariations in particle fluxes.
spherictail and henceto the magneticallyconnectedregionsof
LONGITUDINAL ASYMMETRY OF THE MAGNETOSPHERE
interplanetary space.Thus although the particlesescapeprinWe propose that the observed 10-hour variations in ener- cipally on the night side of Jupiter, they may be observedon
geticparticle fluxesobservedboth in the magnetosphereand in the day side on interplanetary field lines that connect to the
interplanetaryspaceare causedby a grosslongitudinal asym- tail, as is shown in Figure 2.
roetry of the distribution of corotating plasma in the magnetoASYMMETRY OF THE SURFACE FIELD
sphere.This asymmetryis not a day-night asymmetry,fixed
with respectto the sun as is the caseof the magnetosphereof
We argue here that the required asymmetry of the ionothe earth, but rather a corotatingasymmetrythat is fixed in the sphericplasmasourcestrengthcan be producedsolelyby the
rotating frame of Jupiter. The source of this asymmetry is observed asymmetries in the surface magnetic field due to
proposed to be the nonaxisymmetric magnetic field at the
nondipolar sources.The essentialargumentis that a given
surface of the planet.
constantflux of plasmaaway from the Jovian ionospherewill
The effect of such an asymmetryon the energeticparticle produce a variable plasma concentration in the magnetofluxesis illustratedin Figure 2. The planetaryfield is distended sphericequatorialplane becauseof the nonuniformityof the
outward perpendicular to the spin axis of Jupiter by the cen- surface magnetic field strength. Thus a longitudinal asymtrifugal force of corotating plasma [Hill et al., 1974a]. The metry of the plasma sourceflux as suggestedby Hill et al.
plasma is assumedto be of ionosphericorigin [Ioannidisand [1974b]is not a necessary
conditionfor producinga longitudiBrice, 1971; Michel and Sturrock, 1974].
nally asymmetricplasma distribution in the outer magnetoThe fact that the plasma has its source in the Jovian iono- sphere.
spherehas two important consequences.First, the plasma in
The effect of a nonaxisymmetricsurface field is schematthe outer magnetospherewill eventually accumulate until it ically illustratedin Figure 3. The two flux tubesillustratedin
can no longer be confinedby the field, and the field will be the figure crossthe equator at the same radial distanceand
• Now at Environmental Research Laboratories, NOAA, Boulder,
Colorado
80302.
Copyright¸ 1976by the AmericanGeophysicalUnion.
therefore have the same equatorial value of field strength,
providedthat the equatorialcrossingpoint is sufficientlydistant that the nondipolarfield componentsare negligible(i.e.,
beyond L = 3, where L is the radial distance measured in
Jovian radii). The flux tube A intersectsthe ionospherein a
3383
3384
HILL AND DESSLER;JUPITERCONFERENCE
........... ; '-
plane
Fig. 3. Schematic
illustrationof the effectof a nonaxisymmetric
surfacemagneticfieldstrengthon theionospheric
sourceof plasmato
the outermagnetosphere.
The two flux tubescrossthe equatorat the
same distance and have the same cross section there. In the iono-
sphere,flux tubeB hasa smallerfieldstrengththanfluxtubeA and
torial
plane
Fig. 1. Illustration of the field distortion causedby corotating
plasmain the Jovianmagnetosphere
[from Hill et al., 1974a].The
rotation of the tilted magneticaxis M about the rotation axisw causes
the current sheetto oscillatediurnally about the eclipticplane.
region of enhanced surface field strength, and flux tube B
intersectsthe ionospherein a region of lower field strength,
owing to the nondipolar terms in the surfacefield. Thus the
two flux tubes having the same equatorial crosssection will
have differentcrosssectionsin the ionosphere.Flux tube B has
a larger ionosphericcrosssectionand therefore a larger collecting area, i.e., a larger plasma sourcestrengthfor a given
source flux, than flux tube A. We therefore expect that the
activehemisphere,i.e., the hemispherethat facesthe tail during the periodsof enhancedescapeof energeticparticles,will
be the hemispherethat has a minimum in the longitudinal
profile of field strengthon the surfaceof the planet.
In Figure 4 we have plotted as a function of longitudethe
surfacefield strengthaveragedover all latitudes. These plots
were derived from the contour maps of Acur•aand Ness [1976]
(solid curve) and Smith et al. [1975] (dashed curve). As is
expectedon the basisof the abovearguments,we find that the
hemisphereof Jupiter that faces the tail during the interplanetaryparticleflux maxima observedby the Pioneerspacecraft, which is centerednear 300ø longitude[Vasyliunas,1975],
correspondsreasonablywell with the longitudinalsectorhaving the minimum value of surfacemagneticfield strength(and
henceproviding the strongestionosphericplasma source).
thereforehas a largercrosssectionfor collectingionospheric
plasma
particles.
energy density of corotating plasma be comparable to the
magneticenergy density [Hill et al., 1974a]:
pc02r
2 • B2/#o
(1)
wherep is the equatorial value of the plasma massdensity,B is
the equatorialvalue of the magneticfield strength,cois the
rotationfrequencyof Jupiter,and r is the distancefrom the
rotation axisof Jupiter.A more convenientcriterion [Hill and
Michel, 1976] is that cotoration becomesunstablebeyond the
distanceat which the centrifugal force of corotation balances
the centripetal force provided by the tension in the magnetic
field:
crco2r
• B2/2#0
(2)
where e is the plasma massdensityper unit area in the equatorial plane, i.e., the volume massdensityintegratedacrossthe
equatorial current sheet.
Most of the ionospheric plasma source is confined to the
innermost L shells of the magnetosphere.For exarrtple,the
latituderangeIxl -< 60ø covers87% of the sourcearea but
corresponds(for an aligned dipole) to the relatively small
range of L _< 4. Therefore the plasma must be transported
radially outward in order to drive the centrifugal instability,
which apparently beginsat about L = 30 [Hill et al., 1974a].
We assumethat the outward transport takesplace by flux tube
interchange motions [Gold, 1959; Ioannidis and Brice, 1971].
Such interchangemotionsmay be driven by an unstableradial
distribution of plasma density that results from the ionospheric source, in a way analogous to the Rayleigh-Taylor
MODULATION AMPLITUDE OF ESCAPING PARTICLE FLUX
instability [Ioannidisand Brice, 1971], or they may be driven by
We estimatehere the degreeto which the escapingenergetic a diurnal systemof meridional winds in the dynamo region of
particleflux can be modulatedby the effectof the nonuniform the atmosphereof Jupiter [Brice and McDonough, 1973]. In
surface field discussedabove. The appropriate condition for either casethe interchangemotion has the property of presercentrifugalinstabilityin the outer magnetosphere
is that the vation of the plasma content of a given flux tube; thus the
quantityr• -- e/B is conservedin the outward transportprocDIURNAL
TRAPPING
PSEUDO[ STABLE DIURNAL
RAPPIN•G
ESCAPE
ess.
The sourcestrength,expressedas the time rate of changeof
r/(denoted by r/'), is
78' = mF/Bj
(3)
where F is the upward flux of photoelectronsand ions from the
WN%
SHOCK
Fig. 2. Sketch of the Jovian magnetosphereshowingthe diurnal
trapping region [Hi// eta/., 1974/)] wherein energeticparticles arc
trappedduring part of eachJovianday but escapealongtail field lines
into interplanetaryspaceduring the other part of the day. The 10-hour
variation in the size of the diurnal trapping region is causedby a
longitudinallyasymmetricdistributionof the cotoratingplasma that
forcesthe field open on the night side.
ionosphereof Jupiter,m is the massof the ions,and Bj is the
vertical componentof the surfacemagneticfield.
The lossrate, similarly expressedin terms of r/', is proportional to the value of r/at the openingradius,whichis obtained
from equation (2):
n•' c• wn(Lo) --we(Lo)/B(Lo)=
B(Lo)/(2#owR•Lo) (4)
whereL0 is the opening radius expressedin units of 1 R• (the
radius of Jupiter). (We can obtain the same expressionfrom
•'=
p(Lo)va(Lo)/B(Lo)
(5)
HILL AND DESSLER:JUPITERCONFERENCE
I
between
I
AVERAGE
--
Smithetal
•
OVER
r and r + fir is
N = 4•r•r•firn
ALL LATITUDES --
_
3385
_
(12)
wherel• is a geometryfactorof the orderof unity.The opening
area throughwhichparticlesescapecan be approximatedby
the surface area of the night side half of the drift shell:
A • 2•r//r•
(13)
(The openingarea givenby (13) is an upper limit, but the effect
of a smaller opening area should be compensatedfor by the
6
0
90 ø
180 ø
270 ø
:360 ø
expansion
of the fluxtubeas the Particles
escape
to interplanetaryspace;seeFigure 2.) The escapetime is taken to be
escapeflux is
Fig. 4. The mean surfacemagneticfield strengthof Jupiter aver- At ,-, •r/co- • Jovianday. Thusthe average
aged over latitude, including both the northern and the southern
Es = N/(AAt) • (coAr/c)Fv= (coaa/c)ALoFv (14)
hemisphere,
plottedas a functionof System3 longitude(epoch1974).
The solidcurveis derivedfrom Figure4 of AcudaandNess[1976],and
the dashedcurveis derivedfrom Figure 4 of Smithet al. [1975].The SettingL0 = 30 for the averageopeningradiusgives
hemispherethat faces the tail during the maxima of the 10-hour
Fe/Fv • 10-aALo/Lo
(15)
variationsin interplanetaryelectronflux is centerednear 300ø longitude [Vasyliunas,1975].Note that thislongitudinalsectorcorresponds We have estimated above (in (10)) that ALo/Lo • •, so
reasonablywell to the minimum in the longitudinal distribution of
that the escapingflux of relativisticelectronsaveragedover 6
surfacemagneticfield strength.
Jovian day should be of the order of 10-4 times the trapped
flux at 30 Ra. This estimategivesa lower limit to the instantawhereVAis the Alfv6n speed,usingp(Lo)from (1).) Equating neous value of the escape flux and should be a reasonable
estimatefor the averageenhancementof the escapeflux during
the loss rate (4) to the sourcerate (3), we find
the half of each Jovian day when the active hemispherefaces
B(Lo)/Lo ecrls' ec 1/Ba
(6) the tail. This ratio appearsto be consistentwith the counting
We assumethat the equatorial field strength falls off as an rates 0[6- to 30-MeV electronsobservedby the University of
Chicagoexperimenton Pioneer10;countingratesof •102/s
inversepower of distance:
were reported inside the magnetosphereat a 25 Ra distance
B(Lo) cr Lo-"
(7) from Jupiter [McKibbenand Simpson,1974],and the counting
rates in interplanetaryspacefor the samedetectorwere 10-•/s
where
[Chenetteet al., 1974].
l<n<3
(8)
CONCLUSION
The limit n = 3 correspondsto a dipole field, and the limit n =
The surface magneticfield strength of Jupiter has large
1 correspondsto a radially extendingdiscfield configuration.
longitudinal asymmetries,with longitudinal variations of a
Combining (6) and (7) gives
factor of 2 at a given latitude and a longitudinalvariation of
Lo o: Bfi/n+•
(9) about 50% in the field strengthaveragedover all latitudes.This
asymmetry causesa longitudinal asymmetry in the sourceof
Thus as was noted above,the openingradiusis smaller on the ionosphericplasmafilling the outermagnetosphere
and thusa
sideof the planet havingthe smallervalueof surfacemagnetic 10-hour variation in the degreeof distortion of the magnetofield strength.From Figure 4 we take the minimum value of Ba sphereas viewed in the noncorotatingframe.
(averagedover latitude) to be Ba• = 6.0 G and the maximum
Becauseof this longitudinal asymmetrythe radial distance
value to be Ba2 = 10.1 G (from the Acur•aand Ness [1976] at which the field is pulled open on the night side variesby
data). Thus the ratio of maximum to minimum values of the 10-20%
duringtheJovianday,causing
a 10-hour
mo•lulation
opening radius is
of the flux of relativisticelectronsescapingfrom the Jovian
Lo2/Lo•= (10.1/6.0)1/"+•• 1.30
n= 1
Lo2/Lo•= (10.1/6.0)1/'•+•
• 1.14
n= 3
(10)
magnetosphere.The escapeflux is estimatedto be of the order
of 10-4 timesthe trappedflux at a 30 Ra distancefrom Jupiter.
This mechanismappearsto be capableof explainingthe observed 10-hour modulations
of relativistic electron fluxes ob-
Thus a 14-30% modulation of the openingradiusoccursas a
servedin interplanetaryspaceduring the Pioneers10 and 11
result of the longitudinal variation in the surfacemagnetic
approachesto Jupiter.
field strength.Similarly, if we adopt the data of Smith et al.
[1975], we obtain a smaller (but still significant)variation of
Acknowledgments.We wish to thank JamesCarbary for several
9-19%.
usefulcomments.This work was supportedin part by the National
Following the procedureof Hill et al. [1974b], we can estimate the resultingflux of escapingparticles in terms of the
trapped flux. The trapped flux of relativisticelectronsis
Aeronauticsand SpaceAdministrationgrant NGR44-006-137 and the
National ScienceFoundation grant DES74-21185.
nc
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