JOURNAL
OF GEOPHYSICAL
RESEARCH,
VOL.
93, NO. A6, PAGES
5487-5504, JUNE
1, 1988
Dual Periodicity of the Jovian Magnetosphere
B. R. SANDEL
Lunar and Planetary Laborr•ory, University o! Arizona, Tuc•o•
A. J. DESSLER
$po•e Physics and Astronomy Department, Rice University, Houstor• Tezas
Jupiter's magnetic field, like that of the Sun, and perhaps Saturn, exhibits a clear, persistent
dual periodicity, the two Jovian periods differing by almost exactly 3%. We offer a provisional
definitionof a newJovianlongitudesystem(whichwe call systemIV) to organizemagnetospheric
data that are not stationary in system III. We show that available, independent data sets, covering a time interval of 4 years, which either drift in system III or show no particular organization
in system III, fit mutually consistent patterns in system IV. All of the data sets covering several rotations of the planet that are presently available to us, including Voyager observations
of ultraviolet and narrow-band kilometric emissions and ground-based optical observations, are
organized in either system III, system IV, or both. Using these data, we derive provisional val-
uesfor a tramformationbetweensystemsIII and IV: ;kiv = ;kiii + 338- 25.486(t- 2443874.5)
where t is the Julian day and fractional day of the observation. There are pronounced 14.1-day
variations in a number of Jovian magnetospheric phenomena. One possible interpretation of the
system IV modulation is that it is a sideband resulting from the 14.1-day amplitude modulation
of system III phenomena. Alternately, the 14.1-day period could be explained if we assume the
existenceof an activesectorthat is fixed in systemIV but drifts approximately25.5ø/d relative to
the active sector in system III. When the system III and system IV activity maxima are aligned,
magnetospheric activity, such as radio emissions and torus asymmetries, is enhanced, and when
the activity maxima are anti-aligned, magnetospheric activity is subdued. The interval between
alignments(or anti-alignments)is 14.1 days. Finally, we note that, in developingsystemIV, we
have utilized only a small number of data sets. System IV needs to be tested against additional
data before its durability is assured.
1.
INTRODUCTION
distinct periodicity in torus brightness was new and unex-
Magnetospheric
phenomena
arecommonly
organized
into peered.
Theobservation
ofRoesler
et al.wasconfirmed
by
oneof twolongitude
coordinate
systems:
eithera systemSandel
[1983],
whoalsonotedthepresence
of a system
III
thatremains
fixedrelative
to theSun(e.g.,localtimecoor- periodicity
in the brightness
of thetorus.Finally,Pileher
dinates),
ora system
thatrotates
withtheplanet
anduti- andMorgan
[1985]
andPileher
eted.[1985]
present
observalizesa planetary
coordinate
grid(e.g.,universal
timecoordi-tionsthattheyinterpret
asrequiring
plasma
sources
in the
nates).
Mighty
Jupiter
isdifferent.
It wasearlyrecognized
Io torus
rotating
withsystem
III orat a 1%slower
rate.
that tworotatinglongitude
systems
wererequired
to con-
Thetwomagnetospheric
periods
cannotbe described
in
veniently
describe
cloud
motions
(system
I forlowlatitudestermsofa single,
broadband
period
thatencompasses
both
andsystem
II forhighlatitudes).
Later,anadditional
ro- of theobserved
periods.Theperiods
aredistinct,
sepatatinglongitude
system
wasadded
to trackmagnetospheric
rate,andpersistent.
Threeconcepts
havebeenadvanced
radiophenomena
(system
III). It nowappears
that,aswith to account
forthepresence
ofthese
twoperiodicities
in the
theproblem
oftracking
clouds
thatmovewithoneof two magnetosphere
ofJupiter.
angular
velocities,
system
III is notenough
to trackvar- 1. Several
suggestions
utilizeHill's[1979,
1980;Poniousmagnetospheric
phenomena.
Anadditional
longitude
tiusandHill,1982]theory
ofslippage
ofthetorusplasma
grid that rotates with an angular velocity differentfrom sys- relativeto systemIII. For example,KaiserandDesch[1980],
temIII isneeded.
Brown[1983],Roeslet
et al.[1984],
Pileheret al. [1985],
and
The first magnetosphericphenomenonfound to have a pe- PileherandMorgan[1985]interprettheir data in termsof
rioddifferent
fromsystem
Ill wastheJovian
narrow-band
plasma
slippage.
kilometric
radio
emission
[Kaiser
andDesch,
1980],
which 2.
W.Horton
andR.A. Smith
(Solitary
vortices
in
theyconcluded
rotates
3%to 5%slower
thansystem
III. theIo plasma
torus,submitted
to Journal
of Geophysical
Then,
RoeHer
etal.[1984]
discovered
thatthebrightness
of Research,
1987)
propose
alocalized,
long-lived
vortex
within
theIoplasma
torus
varies
witha periodicity
having
a corn-thetorus,
thevortex
being
energized
bytheradial
gradient
ponent
thatis3 + 1%longer
thanthesystem
III period.in plasma
slippage.
Theyargue
thatthevortex
willlag
Persistent
system
III longitudinal
variations
in brightness
system
III corotarion,
andit isthisvortex
thataccounts
for
hadbeen
reported
earlier
ITration,
1980;
Pileher
andMot- thelonger
periodicity.
gan,
1980;
Trauger
etal.,1980],
sotheexistence
ofasecond 3. Dessler
[1985]
suggests
thatJupiter's
magnetic
field,
like the Sun's, possessesmore than one rotation period.
He postulates a high-latitude, magnetosphericallysignificant
Copyright
1988bytheAmerican
Geophysical
Union.
Papernumber
7A9322
magnetic
featurein Jupiter'sinternalfieldthat hasa rotationperiod3% longerthan the systemIII period,andit is
0148-0227/88/007A-9322505.00
this feature that determinesthe new, longer periodicity.
5487
5488
SANDEL AND DESSLER: JOVIAN MAGNETOSPHERIC
TABLE 1. Comparisonof SystemsIV(1979) and III(1965)
System IV
Sidereal
rotation
rate*
845.05
4- 0.09
System III
870.536
4- 0.001
(deg/day)
CML
at 0000
UT
on
126.
148.0
Jan. 1, 1979, deg
PERIODICITIES
ordinary24-hourterrestrialday.) The rotationrate •]IV is
assumed
to be exactby definition(as is the valuefor fiiii).
Zerotime (to) for the startingof the systemis arbitrarily
set to be 0000 UT on the first day of the year of closest
approachof the Voyagersto Jupiter (January1, 1979,Julian day 2443874.5). In order that the bright portion of
the torus be at a system IV longitude of Aiv • 180ø, the
(JD 2443874.5)
Siderealperiodt
1013:27
0955:29.71
(10.224hours)
(9.9249hours)
* The rotation rates are to be regarded as exact by definition.
The stated uncertainty is an indication of how much they might
be changed in some future revision.
systemIV CentralMeridianLongitude(CML) at 0000UT
on January 1, 1979 is set at Air - 126ø. The conversion
between system III and system IV is presented in the form
Aiv(1979)= AIII(1965)+ 338.- 25.486[t- 2443874.51
(1)
t Approximatevaluesderivedfrom rotation rates.
Our purpose in this paper is to provide a more extensive analysis concerning the nature of the second magnetospheric periodicity and to define a matching coordinate
system, which we refer to as systemIV. We use principally
data from the 1979 Voyager fiybys of Jupiter. In order to
lengthen the time base and thereby improve the determination of the system IV rotation rate, we also utilize two
available sets of ground-basedobservationsof the Io torus.
where Af• = -25.486 is the difference between f•iii and •]IV,
and t is the Julian day and decimal day for the day and
time correspondingto the value of Alii. The two coordinate
systems are compared in Table 1.
The rotation rate for system IV is, at this time, not determined well enough to assurethat phenomena will not drift
in longitudeby asmuchasabout35ø/year.Fortunately,observationsof system IV torus periodicity can be made from
the Earth [e.g.,Roesletet al., 1984].H the variousphenomThe data usedare from (1) the Voyager2 ultravioletspec- ena associatedwith system IV do share a common, identical
trometer(UVS), covering100 rotationsof Jupiterbetween rotation period that is durable over time intervals of years,
April 26 andJune7, 1979,(2) the Voyager1 and2 Planetary as we explicitly assume,improvementsin the value of f•iv
Radio Astronomy experiments, coveringnearly a full calen-
and the initial CML will be forthcoming. In that case, we
dar year,January2 to December31, 1979,(3) ground-based shouldfollowthe exampleof Marth [1888,p. 88] and reset
observationsby Brown and Shemansky, data obtained be-
the rotation rate and move the prime meridian as neces-
tweenFebruary23 andApril 27, 1981,and(4) ground-based sary to keep the phenomenaof interest from drifting in an
observationsby Roesler et al. between April 12 and 30, 1982.
The data base, with interruptions, spans a period of just 3.3
years, and we have usedonly the three time intervalslisted
in sets 2 through 4 above. We do not regard the following
analysis as definitely establishingsystem IV. The reality of
the proposedsystem IV must be verified by demonstrations
of its persistenceoutside of the 1979-1982 interval.
We will not present the data in the iterative manner in
which we worked. Rather, we begin by introducing system IV, which was developed to fit the data describedin
sections
3-5.
2.
SYSTEM
IV
improperly defined coordinate system and to keep the phenomena in a convenient part of the longitude scale. If, on
the other hand, other observationsshow the bright portion
of the torus moves about erratically in system IV, or if the
data do not show order as in the cases we have examined,
system IV will be of little utility, and the present values
defining system IV will be adequate.
3.
EUV
OBSERVATIONS
AND ANALYSIS
The Voyager 2 UVS is an objective-grating spectrometer
coveringthe wavelengthrange from about 50 to 170 nm with
126 contiguous
channels[Broadfoot
eta/., 1977,1981]. The
data used in this investigation were obtained from scans
In order to be able to conveniently intercompare various of Jupiter's satellite system between days 116 and 158 of
relevant magnetosphericobservations,we provisionally de- 1979, or between 75 and 33 days prior to encounter. These
finea coordinatesystem(calledsystemIV(1979)) that par- scans, made with the 0.1ø x 0.86ø UVS slit approximately
allels systemsI, II, and III, but whoserotation rate is chosen perpendicular to the satellite plane, produced measurements
to match the apparent angular motion of the magnetospheric of the intensity of the plasma torus over a period covering
phenomena that seem to share the new, longer periodic- 100 rotations of Jupiter. The brightness used here refers
ity as described in the introduction. We follow the prece- to the most intense feature of the EUV spectrum at 68.5
dent of the establishment of systemsI and II by placing the nm, which includes emission from one O III and three S
zero or prime meridian so the phenomenon being observed III multipiers. These data have already been reported by
is conveniently
placed[Marth,1881,p. 367]. Specifically, Sandeland Broadfoot[1982a],but they are analyzedhere
the rotation rate and initial rotational phase are chosen to
keep the maximum brightnessof the torus in the vicinity of
Aiv:
180 ø.
The basic system IV rotation rate is obtained from Voya-
from a different perspective.
The basic data consist of 235 scansacrossthe torus, which
measuredthe brightnessof the approaching
(east) and receding(west) ansae. The intervalbetweenmeasurements
was nonuniform. The observational sets usually consisted
of a sequenceof seven or eight samples of both ansae sepabaseddata. As shownin section5, the systemIV{1979) rated by approximately 2 hours followed by a gap of 12 or
sidereal rotation rate that best fits all the data is fliv =
10 hours, repeated once per day. This sampling does not
845.05ø/d,as comparedwith the systemIII{1965) sidereal suit the data to analysis by the powerful techniques develrotationrate fliii = 870.536ø/d. {By •day," we meanthe oped for searchingfor periodic modulation of a signal that is
ger 1 and2 narrow-band
kilometric(nKOM} radiodata and
Voyager 2 UV spectrometer data and refined with ground-
SANDEL
AND DgssngR:
JOVIAN
i•[AGNETOSPHERIC
PERIODICITIES
5489
PERIOD (HOURS)
70
50
4-0
50
25
20
15
12
10
I
I
i
i
I
I
i
I
i
12
10
tø
o3,o
,
8
APPROACH
I NG (EAST) ANSA
-
g
-
o
L
2
J
4
6
8
10
12
14
16
18
ANGULARRATE(RADIANS/DAY)
•i•, 1. 8c•r•ie'• mo•ifie•perio•o•r•mcompu•e•Cot•oy•r
•be •o-correi•e•
mo•ul•io•
•
i•i Mi•ei
•re •e
U•8 me•ureme• o½•be685-• b•i•e•
moi• promi•e•
sampled at equal intervals. In the appendix we summarize
two techniques that are useful in the analysis of nonuniformly sampleddata such as these. The first is basedon the
classicalperiodogram, with modifications and extensionsby
feature.
•e
perio•o•r•m
• •e
i• •e
units of Piii, the systemIII period (Figure 3). Modulation of the EUV brightness at the system III period has not
beenreportedprior to this investigation
[SandeiandBroadfoot,1982a;Shernanskll
andSandel,1982],but ground-based
$½argi½
[1982],permittinga straightforward
statisticalinter- measurements of visible emissions show persistent correlapretation of the results. The second technique described tion with systemIII longitude[e.g., Piicher and Morgan,
for evidence
in the appendix, essentially a superposed-epochanalysis, is 1985].Thereforewe examinethe periodograms
useful as a cross check.
of power at Piii, the system III rotation period. At the reThe strongest feature in periodograms computed by $½ar- ceding ansa, the amplitude of the periodogram is low near
gl½'s[1982]methodfor the approaching
and recedingansae the system III rotation period, but the approaching ansa
of the torus is a componentat Io's orbital frequency(Fig- showsa small peak at (1.000 4-0.002) x PIll. We must
ures l a (approaching)and 2a (receding)). This is simply estimate the noise power •r0 to calculate confidence levels.
the Io-related modulation of the torus brightness described
Because the measurement error and periodic variations are
by Sandeland Broadfoot[1982b]. Becausewe wish to fo- small comparedwith (apparently)aperiodicfluctuationsin
cus on periods near the system III period, it is helpful to
remove this component from the data before proceeding
further. Subtraction of the third-order Fourier-series approximations to the Io modulation in Figure 2 of Sandel
brightness, we find •r directly from the scatter of the data
points about their mean, after the Io modulation is subtracted. This is consistent with the procedure described by
andBroadfoot
[1982b]leavesthe substantially
simplifiedpe-
garding the interpretation of the variance of the data. We
riodograms in Figures lb and 2b. Dominant in the receding
Horne and Baliunas[1986]and with their admonitionre-
find •r2 (approaching)=0.11 and •r2 (receding)= 0.17.
ansais a componentat 14.75 tad/d, and in the approach- Analysis of synthetic data that were generated using these
ing ansa are strong components both at this angular rate values has verified that they are appropriate. Using (5)
and at 15.19rad/d. Severalprominentyet spuriousfeatures from the appendix, we find a probability of 0.003 that the
marked in the plot were identified by analyzing control sam- observedpower of 0.631 at the null at 1.005 Pill (nearest
frequency.
plea of synthetic data. The spuriousfeatures are not statis- the peak) is presentby chanceat this preselected
tically significant according to Scargle's criteria. Some of
the nonspuriousfeatures are harmonica or beat frequencies
between systems III and IV and a 14.1-day modulation period.
To concentrate on components near the system III rotation rate, it is convenient to replot the portion of the
periodogram marked by the bars in Figures 1 and 2 in
This is evidence for modulation of the brightness of the approaching ansa at the system III period.
Periodograms for both ansae have peaks near 1.03 Pnl.
Optical observations have revealed brightness variations
near this period, but the period was not precisely deter-
mined [Roesletet al., 1984]. Thereforein evaluatingour
confidence in these peaks, we make the most cautious es-
5490
SANDEL AND DESSLER: JOVIAN MAGNETOSPHERIC
PERIODICITIES
PERIOD (HOURS)
5040
12
I
I
25
I
I
I
20
9
I
I
I
I
I
•1o
10
8
- G
i
RECEDING(WEST) ANSA
-
6
2•'-"•1o
--
.
o
2•"1'•,o
o
•_.
2
0
4
-
2
0
2
4
6
8
10
12
1½
16
18
ANGULAR
RATE(RADIANS/DAY)
Fig. 2. Sameas Figure 1 for the receding(west) ansa. The remainingmodulationin the bottom panelis again
near Jupiter's rotation rate.
timateby using(6) fromthe appendix,
whichis appropri- cycles
with different
randomnoisesequences
(but thesame
ate whenmany(u) frequencies
are examined
for significant amplitudeA in (8)), and with differentstartingpointsfor
power. For No evenly spaceddata points, the periodogram computation of the periodogram have shown that a two-
is usuallyevaluatedat No/2 independentfrequencies,
cor- sigmauncertaintyof 0.002PIiI is a better estimate.This is
respondingto u = 117 for the EUV data. A numerical. the uncertaintywe have adoptedin Table 2.
investigationby Horne and Baliunas[1986]suggests
that,
The amplitudesof the modulationestimatedfrom (7) are
for 235 evenly sampled points, a more appropriate value is shown in the first line of Table 2. The quoted uncertainties
p •, 300 (their equation(13)). However,theynotethat this werederivedusingGroth's[1975]Figure 1 as describedin
is an overestimate in the caseof unevenly sampled data such the appendix. As a consistency check, the data synthesis
as we considerhere. Again we take a cautious approach and technique can be applied by adjusting the amplitudes until
adopt• = 300for our computation.The valueof Pr(Z > z) the synthetic periodogram is acceptably similar to the pe-
so obtained representsthe probability of finding by chancea riodogram computed from the data. A potential pitfall in
powergreater than that observedhere at any of the indepen- this approach is that it may underestimate the uncertainty
dent periods accessiblethrough this data set. These proba- in the amplitude. This is becausesmall variations in the ran-
bilitiesare3 x 10-s (approaching)
and4 x 10-•s (receding),dom noise component can materially
affect the amplitude of
implying a significantidentification of modulation near 1.03 the periodogram, even for a prominent and statistically sigPiiI at both ansae. These probability estimates are conser- nificant feature. To avoid this di•culty,
we have computed
vatively large becausethe value of • that we have adopted periodograms from data synthesizedusing several sequences
is an upper limit to the true value. We have searchedfewer of random numbers to describe the noise in the data. The
than the full set of independentfrequencies,and the number uncertainties quoted with the amplitudes in the second line
of independentfrequencies
is overestimated
by using(13) of of Table 2 reflectthe resultsof this investigation.
Horne and Baliunas.
Plots of the brightness at the approaching and reced-
The bestestimateof the periodof the modulationis the ing ansaeas a functionof systemIV longitude(Figure4)
peak in the oversampledperiodogram. These peaks are showan obviousmodulationof the brightnessof the recedat 1.000 PiII and 1.030 PiiI at the approaching ansa and
ing ansa, and a weaker but nonetheless detectable modu-
at 1.030 PiiI at the recedingansa. Using (14) of Horne lation at the approachingansa. Fitting low-orderFourier
andBaliuna8[1986],we estimatea two-sigmauncertaintyof seriesto thesedata givesan objectivemeasureof amplitude
0.001 Piii in the period. However, our analysisof synthetic
data has shown that the location of the peak in the periodogram is sensitiveto the random noise componentand
more weakly sensitive to the starting point for the cornputation of the periodogram. Many synthesisand analysis
and phase. The amplitudes of the modulations estimated in
this way are included in the third line of Table 2. We have
assignedno uncertaintiesbecausethere is no obviousanalytical procedure to estimate uncertainties by this technique.
Instead, we rely on the other techniques.
SANDEL AND DESSLER: JOVIAN MAGNETOSPHERIC
PERIODICITIES
5491
Aft (degrees/day)
20
0
-20
-40
10
'
8
6
õ
o
'
' I I I I I I ii I 103'
' -
_ RECED
INS
ANSA
1.
O0
- • '
--
2
s
s
o
APPROACHING
0.90
ANSA
0.95
1.00
1.05
1.10
PERIOD(UNITSOf SYSTEMili PERIOD)
Fig. 3. Periodograms of UVS measurements at approaching and receding ansae expanded from the regions
marked by the bars in Figures 1 and 2. These have been replotted in terms of period rather than frequency to
ease later references. The circles mark the amplitude of the periodogram at nulls in the spectral window, the set
of natural periods for evaluation of the periodogram. The smooth curve is the highly oversampled periodogram.
Significant modulation at 1.03 PIII is present at both ansae, and the brightness of the approaching ansa is
modulated at the system III period as well.
Because the modulation at the approaching ansa is dif•cult to detect by eye, we have investigated means of making it more obvious. We have found that the EUV brightness,like the nKOM emissionprobability, is modulated more
strongly when the system III and IV peaks in the nKOM
probability are near alignment. An example is shown in
Figure 5, where we have plotted EUV brightness of the two
ansae as a function of Air, having selected those observations within 3.5 days of the times of alignment and of antialignment as described in section 4. In Figure 5a the modulation at the receding ansa is more prominent than in Figure
4, and modulation at the approaching ansa is apparent as
emission
confirm
as it moves
with
the
nor rule out an EUV
torus.
Thus
enhancement
we can neither
that
rotates
with
system IV to drive the observed modulation. Although a rotating bright spot such as implied by S II images may seem
to be the most natural interpretation of the EUV variations
as well, we note in section 6 that variations in the dawn-dusk
electric field that have the system IV period could account
for the observations in an equally natural way.
The curves of brightness versus Air in Figure 4 have a
characteristic shape. The brightness of the receding ansa
gradually increases to a maximum, then decreases more
rapidly. This shape is similar to the shape that Sandel and
well.
Figures 4 and 5 show that the brightness of an ansa is
greatest when the ansa is near Air = 180ø, that is, the
brightnesscurves of the two ansae are about 180ø out of
TABLE
2.
Amplitude of the Modulation
Approaching
Approaching
Receding
Ansa
Ansa
Ansa
1.00 x P*III
1.03 X PIII
1.03 X PIII
phase. At least two physical phenomena are consistent with
this behavior. The first involves a region of enhanced EUV
Method
emissionthat is fixed near A•v = 180ø, and that rotates
through one ansa and then the other as system IV rotates.
Equation
(7)
0.•4•,
+ø'øst
---v--0.06
0.161+0-05
n
---0.06
..... .2g?+0.06
--0.07
Synthesis
0.23
0.15
0.393
Phaseplots
0.24it
0.15$
0.375
The second involves periodic out-of-phase brightening and
dimming of the ansae, driven by a mechanism other than a
bright spot fixed in system IV. We cannot chose between
these two possibilities solely on the basis of the EUV observations, because time coverage and spatial resolution do
not permit us to follow a putative enhancement in EUV
*PIII
is the system III period, 0955:29.71
t Uncertaintiesrepresent95% confidence.
t Fourierfit (withcomponent
at 1.03x PIII removed).
at 1.03x PIII removed).
tt ]l(max-min) (withcomponent
5492
SANDEL
AND D•SSn•R:
JOWAN
MAGN•?OSPH•RIC
6
•
PERIODICITIES
'
Approaching
I
'
I
'
I
'
I
'
I
Approaching
o
--
W'
øoøo•
o
oø
oo
oøo
too"o.O
o
?
•
o oooø o•. o
o
o
2•
I
'
I
'
I
''
I
'
I ''
Receding
o :
•
•
o
o
0,0o
;o :.:{.o:r
ø..,oo.•o
0,oo
oo;0
o,,i,o
o o
0
'
o
oOO
o o
ß,oo.•o
•, .oo•
o:,,
ooO•,,,
o.o
oO,•
ø ': o'COo _o
2
6
o
E
,
I
'
I
,
I
,
I
I
'
I
'
I
i
5•
oOO-
I
I
6
.•
'
I
Receding
,,.;to
o•,, o
•
•
. .• •o•-•o
o
•o
oo o m
oo
o
•
•
o
•.O•o •o . .• •o •_•
•o o -:oOoO•.%0
,..o•O.j:o
o o.
;o
o%o0
.
•o o•_• 5 •
•o oooo•,ojoOo
o •OOøoO."ø8ø
øø
tooøOo
q,oO•A•o
•:øo
o
oo :;%0
oo
o
o
18o
90
0
S•tem •
270
180
90
0
2•
o
E
Longitude(degrees)
o
18o
,
I
gO
,
I
0
,
I
2?0
,,
I
180
,,
$•tem T•' Longitude(degrees)
Fig. 4. Relativebrightnessof the (top) approaching
and (bottom) recedingansaof the plasmatorusfrom UVS data as a func-
Fig. 5a
tion of system IV longitude. We show the brightnessof the S III
685-]• feature, the brightestin the EUV spectrumof the torus.
The abscissa refers to the system IV longitude of the observed
ansa. The solid curves below the data points are sliding averages
of the data displaced downward by two units. The brightness
at both ansae is modulated at the system IV period, with the
modulation at the receding ansa stronger than at the approaching, where the modulation is barely apparent in this figure. The
dashed curve in the bottom panel is a scaled and phase-shifted
plot of nKOM probability from Figure 8b. The EUV brightness
and the nKOM probability change with system IV in qualitatively
6
" '
I
'
Approaching
I
'
I
o 80o o øø
'
I
oO
'
i
'
I
o 80o o
,_o
O,•o
ø%
Oq,
ooo%
o ooøo•øo
8o.
•:•_oeq,
o
Oq,
o
o,0
_o
eo
'•'
•o•5 •"'
ßo
"6o øo oOOoo•e
8 uo
'"68 o_'l c
, e oø•e•• •0
the same way.
Broadfoot
[1982b]foundfor the Io-correlated
brightness
enhancement, when brightnessis plotted against the orbital
phase of Io. In spite of the similarity in the shapes, the
mechanismdescribedby Sandel and Broadfoot is not applicable to the system IV modulation described here. Their
mechanism involves heating of the plasma electrons as they
are awept past Io. Subsequentcooling of the plasma by
EUV radiation as the plasma is carried further downstream
6
'
I
'
I
'
I
i,
I
'
I
I
I
'
I
I
I
'
I
,
Receding
from Io leads to the observed dependence of brightness on
the azimuthal separation from Io. The key to the successof
the model is the relationship between the radiative cooling
rate and the angular velocity of the plasma relative to the
energysourceat Io, about28ø/h. The difference
in angular
velocitiesbetweensystemsIII andIV is onlyaboutlø/h, so
cooling would take place near a source fixed in system IV.
Furthermore, if the concept of plasma slippageis considered
[Hill, 1980],the torusplasmashouldbe virtuallystationary
in system IV. We would therefore expect a brightnesscurve
more symmetrical than observed if the curve represented
heating and radiative cooling versus time.
The shape of the azimuthal variation in the SIII EUV
emissions that we infer here is similar to that reported by
o
18o
,
I
90
,
0
270
180
90
E
,
0
2m
System:I• Longitude(degrees)
Fig.
Fig. 5. Relative brightness of the ansae as a function of system IV longitude. These observationsfrom the half-periods about
(a) alignmentand (b) anti-alignmentof the probabilitypeaksin
III and IV show that modulation of the EUV is enhanced
PileherandMorgan[1985]for the SIII 953-nmbrightness. systems
near times of alignment, particularly in the receding ansa. Near
Both sets of observations show a steeper brightness gradient
toward the high-longitude side of the peak. This behavior
may also be characteristic of the SIII 953-nm observations
alignment, modulation is apparent in the approaching ansa, with
peaks in each ansa near ),Iv = 180ø. The solid curves are sliding
averagesof the data displaced downward for clarity.
SANDE). AND DESSnER:
JoviAN
]•,•AONETOSPHERIC
PERIODICITIES
5493
the system III period at the approaching ansa. However,
this modulation has already been demonstrated to a high
degree of confidence by the periodogram analysis. We use
this plot rather to learn the phase of the modulation and to
verify that the amplitude inferred from the other techniques
is reasonable. The plot shows that the minimum brightness
occurs when the approaching ansa is near •zzz -- 5ø. The
phase curve is again asymmetric, with the maximum when
the approachingansa is near •z• - 80ø. Becauseof the discontinuous phase grouping, the amplitude is best defined as
half the difference of maximum and minimum group means,
or 0.24 as shown
•
in the last line of Table
2.
For both ansae, the amplitudes of the modulation at
1.03 Pi• determined by the three methods and shown in
Table 2 are in excellent agreement. For the modulation at
Receding
1.00 Pz•, (7) givesa value significantlylowerthan that dem
4.
-'•3
0
180
•,o Ooo
•
•
I
90
,
I
0
S•tem •
Fig. 6.
•
I
270
oo
o
•
I
180
i
I
90
0
Longitude(degrees)
Same as Figure 4 computed for a period of 1.00 Pzzz.
rived from the other two methods, which are in agreement
with each other. This inconsistency may be related to the
asymmetry in the brightness variation. But, in any case,
it is the existence of the modulation, rather than its exact
amplitude, that is of central importance in this paper.
The amplitude of the periodogram at P•z is not an artifact of the sampling sequence, even though the sequence
leads to phase grouping at a period of Pz•z. This possibility
is ruled out on several grounds. First, no significant amplitude is present in the receding ansa at 1.00 P•iz, even though
the sampling sequence was exactly the same. Second, periodograms computed from data synthesized including re-
alisticrandomnoise(but no periodiccomponents)
haveno
of Roederet al. [1984],but there it is certainlylesspro- significant amplitudes near P•. As a control, we have exnounced(seesection5). Pilcherand Morgansuggestthat amined plots of brightness versusphase for periods at which
this structure may arise from a plasma sourcethat lags coro-
the periodograms have no significant amplitude and found
tarion.
no indication
of modulation.
Comparison of the EUV spectra from times of maximum
and minimum brightness shows that the brightness varia4.
NARROW-BAND
KILOMETRIC
P,•DIATION
tion is consistent with the inferred change in electron temHere we consider observations
of the narrow-band
kiloperature. This analysis is based on the ratio of the SIII
68.5-nm and 102.0-nm features, as described by Shemansky metric radiation in the context of system IV and of the
andSandel[1982],for the caseof the dawn-dusk
EUV asym- EUV measurements. Using catalogs of Voyager nKOM obmerry. Changes in electron temperature are also responsible servations kindly supplied to us by M. L. Kaiser and Y.
for the Io-relatedenhancement
in EUV emission[Sandeland Leblanc, we have investigated the nKOM periodicity reported by Kaiser and Desch[1980]and DaigneandLeblanc
Broadfoot,
1982b].
The azimuthal extent of the enhancement in EUV bright[1986]to help in establishingthe systemIV longitudesysness is difficult
to determine
from
these data.
Because
we
are limited in this data set to samples at the ansa, this extent can be determined only in the case of a bright spot
that revolves at the system IV period, and is therefore carried through the ansa. By using simple models of azimuthal
tem and to determine the phaserelationship of the EUV and
nKOM modulations. We have also verified the system III
modulationreportedby DaigneandLeblanc[1986].
The nKOM
data
used here are the recorded
times
of the
beginning and end of intervals during which nKOM emisvariationsin brightness[SandelandBroadfoot,
1982b],we sions were detected. The polarization of the radiation was
estimate that such a bright region probably would have a recorded as well, but has not been included in this analywidth between 60 ø and 150 ø in azimuth.
sis. Near closest approach to Jupiter, nKOM was detected
To investigate the system III modulation at the approach- almost continuously. Therefore nKOM observations from
ing ansa, it is desirable to remove the effects of the modu- these times are not helpful in defining periods, and nKOM
lation in system IV. This can be done to first order by observations within two days of closest approach have been
subtracting from each data point the Fourier fit derived omitted from consideration. The remaining 381 separate
from the phase curve calculated for the system IV varia- episodesof nKOM detected by both Voyagers I and 2 span
tion. The plot soderived(Figure6) showsstronggrouping a full year, from January 2, 1979, to December 31, 1979.
of the points in phase because the observing sequencewas
We use a simple modification of superposedepoch analyclosely synchronized with Jupiter's rotation rate. Neverthe- sis to study the data. The nKOM catalog does not include
less a weak modulation in the brightness of the approaching explicit information on the detected signal strength, so that
ansa in system III is apparent. The mean and standard de- the usual techniquesare not directly applicable. Instead, we
viation for each of the groups are indicated by the bars to plot the probability of detecting nKOM as a function of the
the right of each group. All the groups overlap at the one system IV longitude of the central meridian of Jupiter as
sigmalevel,sothisparticularpresentation
of the datadoes seen from Voyager. To compute this probability, we record
not demonstrate that significant modulation is present at the number of times nKOM is detected in 360 azimuth bins,
5494
SANDEL AND DESSLER: JOVIAN MAGNETOSPHERIC
3.0
PERIODICITIES
3.0
2.0
•.0
1.0
(degrees/day)
(degrees/day)
3.0
oL
>, :2.0
•
].0
0.0
-60
-50
-40
-30
-20
- 10
0
10
Aft (degrees/day)
Fig. 7. The ordinate measures the degree of organization in plots of the probability of detecting nKOM as a
function of azimuth, when azimuth is computed using the value All on the abscissa. The range of All in the lower
panel corresponds
to periodsfrom 1% lessthan the systemIII periodto 7% greater. The smallerplots showthe
two dominantpeaksnear All = 0.0 and -2õ.õø/d at higherresolution.Comparewith Figure 95 of Dai•e arid
Leblane
[1986].
each 1ø wide in ,•IV. For the plots shown here, we have
summed these bins in groups of five to 10 for smoothing.
Using a similar technique, we have also computed the probability of finding the center of an nKOM episode in a particular range of Air. The two procedures yield consistent
results. Because the first procedure preserves information
about the duration of each episode while the second does
not, we prefer the first and rely on it here.
This technique can reveal periodicities in the occurrence
of nKOM. If the nKOM is modulated at the trial period
used to compute the azimuthal binning, then the probability distribution will vary markedly in azimuth. To define
periodicities in the nKOM, we have searched a number of
trial periodsnear the systemIII period and near a period3%
greater that is consistent with earlier determinations of the
nKOM period and with the EUV period determined here.
Figure 7 showsthe results. In each panel, the ordinate measures the degree of modulation found when the probability
of detecting nKOM is computed at the value of All along
the abscissa. Maxima are clearly defined at periods corre-
spondingto All = 0.0 (that is, the systemIII period) and
at All = -25.4ø/d, corresponding
to a periodabout 3%
Figure 8 shows the probability of observing nKOM as a
function of longitude for system III and for system IV. In
computing the latter, we have used the definition of system IV in section 2. Modulation at a period compatible
with system IV has already been demonstrated by Kaiser
andDesch[1980]. DaigneandLeblanc[1986]showedthat
the emissionsare also modulated at the system III period.
Figure 8 is therefore a verification of these earlier findings.
Daigne and Leblanc point out that considering the polarization of the signal resolvesthe structure in Figure 8a into
two separate peaks. The stronger, which is in right-hand
polarized emission, falls near AIII= 40ø and is the main
contributor to the maximum in Figure 8a.
There is no significant modulation if other periods are
randomly selected. For example, Figure 9 shows the same
probability plotted in a system defined by a value of All
for which only weak modulation is expected on the basis of
Figure 7. The striking differences in modulation with azimuth between Figure 9 and Figure 8 show that the periods
usedin Figures8 (i.e., the systemIII and IV periods)do
in fact organize the nKOM probability better than do other
periods.
greater than the system III period. The latter is in close
The shapesof the probability curvesin the two coordinate
agreement with the period inferred from the analysis of the systems are similarly asymmetric, with maxima separated
EUV data. The peaks are rather broad because of scatter from minima by about 130ø, measuring in the direction of
in the nKOM episodes about their mean, because at least increasinglongitude. That is, as seenfrom Voyager, the time
two periods are present, and because many of the nKOM
from maximum probability of detecting nKOM to minimum
episodesare lengthy. Figure 7 also showspeaks near All =
probability is about 3.6 hours, while the time from minimum
--23.3and-27.5ø/d. Althoughthepeakat All = -23.3ø/d to maximum is about 6.4 hours. Also, the nKOM probabilis quitestrong,both it and the oneat -27.5ø/d are outside ity curve has the same asymmetry as the EUV brightness
curve as shown in Figure 4.
the range of periods that is acceptable,based on the EUV
analysis. For this and other reasonsdiscussedin section5,
The presence of modulation at these two similar periwe rule out these periods and focuson the valuesof All near ods suggests that some aspect of the nKOM should vary
as these two systems rotate relative to one another. Ev-25.4ø/d for systemIV.
SANDEL AND D•ssL•l•:
JOVIAN
]%•AGN]DTOSPHER, IC PERIODICITIES
5495
nKOM Probobili•y
180'
180'
I
O
SystemIII
i'"":'"::•:
'
' '.•....'%'....'.••:.• i
'
i
b
270'
SystemIV
O'
Fig. 8.
•
.••-............
- -:...•;:,•;.;.;.:.
, ,
O'
Relative probability of observing nKOM as a function of the longitude of the central meridian of Jupiter
asseenfrom Voyager.(a) Probabilityin systemIII. (b) Probabilityin systemIV. In both systemsthe probability
has well-defined peaks and varies by more than a factor of 2 with longitude. In this and the following three figures,
the radial coordinate is only a rough estimate of the absolute probability. This coordinate properly represents
changes in the relative probability under the different conditions of the four figures.
ery 14.125 days, when the maxima in the two systems are
aligned, nKOM emissionsshould be particularly strong, and
particularly strongly modulated. At times for which the
maximum at about 40ø in ,XIIi is anti-aligned with the maximum at about 67ø in •Iv, nKOM emissionshouldbe weak.
The period should be the time required for the two systems
to return to alignment of maximum probabilities. To test
this idea, we divided the nKOM episodesinto two portions,
with about half the episodesin each. The first includes the
episodesobserved within 3.5 days of alignment of the maxima in the two systems, and the secondincludes the episodes
detected within 3.5 days of the times at which the maxima
in the two systems are 180ø apart in •Iv.
The times of
(2)
and times of anti-alignment
2443865.52-t-n(14.125)
rotations of system III. In summary, the duration of a typical nKOM event does not depend on the relative alignment
of the system III and IV longitude grids, but the probability of detecting nKOM at all is strongly dependent on this
alignment, and hence exhibits a period of approximately 14
days.
Kurth et aJ.[1980]describeda 14-dayseparationbetween
severalminima in the bKOM emission(which originates
froma differentpart of the magnetosphere
thanthe nKOM),
but they attributed this periodicity to changes in the sector structure of the magnetic field of the solar wind. The
minima reported by Kurth et al. were at days 162,176, 188,
and 204 of 1979. Using(3) for timesof anti-alignment,we
alignment in Julian days and fraction are given by
ta!ignment
-- 2443872.58
+ n(14.125)
tions. The 14-dayperiodicityin (2) corresponds
to 34.2
find that expected minima in nKOM activity in systemsIII
and IV fall at days 161.5, 175.6, 189.8, and 203.9 of 1979,
in agreement with the times reported by Kurth et al. We
(3)
where n is an integer. Figure 10a shows the probability of
detecting nKOM in the window about time of alignment,
and Figure 10b showsthe correspondingprobability for the
window about time of anti-alignment. Comparison of these
and Figure 8b showsthat nKOM is more likely during times
near alignment of the maxima, and the nKOM emission
probability is more strongly modulated at the system IV
period. Calendar dates for the times in 1979 corresponding
nKOM Probability
180'
90'
270'
to (2) and(3) are givenin Table3.
Figures 11 a and 11 b illustrate these effects more dramatically. These plots include nKOM episodeswithin one day
of alignment and anti-alignment. The most striking difference is in the number of episodesdetected during the two
windows: 71 in the window near alignment, and only 34 in
the window about anti-alignment. In contrast, there is no
significant difference in the averagedurations of episodesin
the two windows. This nKOM modulation has been pointed
out by DaigneandLeblanc[1986],whonotethe existence
of
long-term fluctuations with a period of 30-40 Jovian rota-
Fig. g. Relative probability of observing nKOM as a function
of central meridian longitude, with longitude computed for a pe-
riod corresponding
to All -- -26.46ø/d. The modulationat this
period is weak, as expected on the basis of Figure 7.
5496
SANDEL
AND DESSLER:
JOVIAN
MAGNETOSPHERIC:
PERIODIC:ITIES
nKO• Probobility
180'
Fig.
10.
180'
Relative nKOM probability as a function of the system IV longitude of the central meridian.
The
observations
havebeen dividedinto two portions,(a) the 7-dayhalf-periodaroundthe time of alignmentof the
peaksin systemsIII and IV shownin Figure8, and (b) the otherhalf-periodabout anti-alignmentof the peaks.
The probability is more strongly modulated at times near alignment of the peaks in systems III and IV.
suggest that their observations are most naturally explained
as a beat period between system III and system IV.
As a consistencycheck we have used two other techniques,
computation of the Fourier power spectrum and Scargle's
periodogram, to search for periodicities in the nKOM. We
find results that are in accord with those already described.
Both of these techniques are intended to look for periodic
structure in the amplitude of a signal that depends on time.
Because the nKOM data available to us include no explicit
measure of signal amplitude, it was necessaryto provide amplitude information in some way. For the Fourier analysis,
we divided the time spanned by the data into 10-min intervals, corresponding approximately to the time resolution of
TABLE 3.
reasonable
because
and falls below the detection
of the event
Day of 1979
threshold.
Thus the duration
strongest
peakslie nearA• = 0 and A• = -25.5ø/d, with
Times of Anti-Alignment
Date of 1979
Julian Date
Day of 1979
Date of 1979
6
Jan.
20
34
49
63
77
Jan.
Feb.
Feb.
March
March
20
3
18
4
18
2443964.4
2443978.5
2443992.6
2444006.8
2444020.9
91
105
119
133
147
April
April
April
May
May
1
15
29
13
27
2444035.0
2444049.1
162
176
July 2
July 16
July 30
Aug. 13
Aug. 27
Sept. 10
Sept. 24
2444063.3
2444077.4
2444091.5
2444105.6
2444119.8
2444133.9
2444148.0
190
204
218
232
246
260
Oct.
Oct.
Nov.
Nov.
Dec.
Dec.
2444162.1
2444176.3
2444190.4
2444204.5
2444218.6
2444232.8
13
27
41
56
70
Jan.
Jan.
Feb.
Feb.
March
13
27
10
25
11
2443893.8
2443907.9
2443922.0
2443936.1
2443950.3
2443957.3
2443971.5
2443985.6
2443999.7
2444013.8
84
98
112
126
140
March
April
April
May
May
25
8
22
6
20
2444028.0
2444042.1
154
169
June 3
June 18
2444056.2
2444070.3
2444084.5
2444098.6
2444112.7
2444126.8
2444141.0
183
197
211
225
239
253
267
2444155.1
2444169.2
2444183.3
2444197.5
2444211.6
2444225.7
282
296
310
324
338
352
9
23
6
20
4
18
is measured
of the episodemay be expected to be related to the amplitude of the detected signal. With both methods, the two
2443879.6
2443886.7
2443900.8
2443915.0
2443929.1
2443943.2
the duration
between the times at which the nKOM amplitude exceeds
Times of Alignment and Anti-Alignment in 1979
Times of Alignment
Julian Date
the nKOM catalog. To each of these intervals we assigned
an amplitude of 1 or 0, depending on whether nKOM was
or was not detected during that interval. These data were
used to compute the Fourier power spectrum. To compute
the Scargle periodogram, times were taken as the center of
each nKOM episode, and the corresponding amplitude was
taken to be the duration of the episode. This is physically
6
June 11
June 25
275
July
July
Aug.
Aug.
Sept.
Sept.
Oct.
9
23
6
20
3
17
2
289
303
317
331
345
359
Oct.
Oct.
Nov.
Nov.
Dec.
Dec.
16
30
13
27
11
25
SANDEL
AND DESSLER:
JOVIAN
MAGNETOSPHERIC
PERIODICITIES
5497
nKOM Probabflity
180'
180'
System
IV
0"
Fig.
11.
b
System
IV
0"
Relative probability of detecting nKOM as a function of the system I¾ longitude of the observer's
centralmeridian. This figureis similarto Figure 10, exceptthat only data from 2-dayperiodsabout (a) alignment
and (b) anti-alignment
of the peaksin systemsIII and IV havebeenincluded.Detectionof nKOM is morelikely
during times of alignment.
the formerbeingsharper.The broaderpeaknear -25.5 ø/d
modulation of the EUV brightness of the receding ansa. We
has three relative maxima, as in Figure 7. The locations of
these peaks are shown in Figure 12 for comparison with the
range of Aft acceptable for the EUV data.
The modulation in the EUV and the nKOM probability have a fixed relationship in system IV. The system IV
phase has been chosen to place the EUV bright spot near
Aiv = 180ø, as shown in Figure 4. The source of the nKOM
is believed to lie near the central meridian plane at the
find a time that agreeswith the time givenin (2) within0.5
day, which is near the resolution of the determination. The
EUV and nKOM modulations are therefore related not only
in having the same 10.2-hour period, but also the amplitude
of their modulations varies synchronouslywith a 14-day period.
5.
GP•OUND-BASED
OBSEP•VATIONS
The EUV and nKOM observations show that both phetimeswhenthe nKOM is detected[KaizerandDezch,1980].
The minimumin nKOM probability(near centralmeridian nomena are modulated at a period of about 10.2 hours, but
,•iv = 180ø) is approximatelythe systemIV longitudeof from these data alone the period cannot be determined precisely enough to permit comparisons of observations several
the EUV bright spot. Details of the shape of the nKOM
probability curve and of the EUV brightness enhancement years apart. The fractional uncertainty of 0.002 in the period inferred from the EUV measurements correspondsto a
are similar, as shown in Figure 4.
Other evidence argues that the nKOM and EUV phenom- drift of 1.74ø/d, or 180ø in about 100 days. The nKOM obena that we describe here are related in a fundamental way. servations help to reduce this uncertainty because they span
a longer period of time. However, we can define this quanFigures 5a and 5 b show the result of dividing the EUV data
into two groups, one including data near times of alignment tity more accurately if we turn to ground-basedobservations
as givenby (2), and the otherneartimesof anti-alignment of the torus that do not share the limited temporal coverasgivenby (3). Modulationof the EUV brightness
at both age inherent in the Voyager observations. To be most useful
ansae is more pronounced near alignment. We have also in this context, observations should span a number of rotasearchedfor the time of alignment that yields the strongest tions of the planet, should have time resolution better than
Preferred
Value
-25.4•6
FRo•sl•r
etel.
1982L•984
...O OOOOOOO
..... d •9s2
... O D D D O
1981I-.
bSh,•on,•y.
1980
•
1979
• EUV
OO0O0000-..I Inferred
from
combination
with
EUV and nKOM
DD
DDD
I
i
nKOM
I
-28
i
,
F
I
-27
•
-26
I•
•
I
I
-25
,
i
-2•
'• Measurements
Independent
,
I
-25
,
I
-22
AD (degrees/d•y)
Fig. 12. Ranges of values of All that are acceptable on the basis of several subsets of the data. The ranges
determined from the EUV and nKOM observations are independent. Neither the data of Roesler et al. nor of
Brown and Shemansky limit All within the range of the abscissa. The ranges shown for those sets of observations
were inferred by combining them with the EUV and nKOM measurements.
5498
SANDEL AND DESSLER: JOVIAN MAGNETßSPHERIC
ß
800
'
Roesler
I
'
et ol., 1984
number of complete rotations in the 1000 days between the
Voyager and the ground-based observations. Discrete ranges
of periods are acceptable, and the centers of these ranges fall
I
ß
600
e•e
at Af• = --25.4864- a(0.337)ø/d. The width of the rangeis
_
edi• ß
determined from our estimate of the uncertainty in the location of the peak 953-nm brightness in system IV, 4-45ø.
These ranges are shown in Figure 12. Four of them are
at least marginally consistent with the full data set exam-
400
inedso far, with the two at -25.149 and -25.486ø/d being
200
,
0
180
I
,
90
I
,
0
I
,
270
I
,
I
180
preferable to the two more extreme values.
To discriminate among these possible periods, we add the
observationsof the plasma torus reported by Brown and She-
,
90
0
manskil[1982]. They measured
dramaticvariationsin the
System3• Longitude(degrees)
Fig. 13. Measurementsof the SIII 9531-J• brightnessof the
recedingansaof the torus obtainedin 1982 [Roeslet
eta/., 1984].
The abscissa refers to the longitude of the ansa. The brightness
is strongly modulated at the system IV period, with a peak near
AIV = 180 ø.
1 hour, and should show modulation at a period consistent
with those determined from the Voyager observations.
Such observations have been reported by Roeslet et al.
[1984].Theseauthorsmeasured
the brightness
of the IS III]
953-nm emissionfrom the receding ansa of the plasma torus,
accumulating 71 observations in the time period of April 12
to 30, 1982. They identified a modulation in the brightness
of the ansa that had a period of 10.2 + 0.1 hours, corre-
spondingto Af• = -23 4-8ø/d. The extent of the bright
region was about 90ø in azimuth, and the amplitude of the
modulation
The
PERIODICITIES
was a factor
observations
of about
of Roeslet
2.
et
al.
relate
to the
same
brightness of S II 673-nm emission from both ansae of the
torus in February and April of 1981. They reported that
their search for a dependence of brightness in system III revealed none, although system III variations are reported by
others[e.g.,Pilcheret al., 1985].However,wefindthat their
data are organized in system IV. We have added their S II
673-nm brightnessesplotted against Air, as computed from
the definition given in section 2, to those of Roesler et al.
The results are shown in Figure 14. The brightest points
fall in the range Air = 180ø 4- 90ø, with most of them closer
to 180ø. The ambiguity in Af• described for the 953-nm
observations is present in this case as well, and the acceptable values of Af• are shown in Figure 12. The spacing
of the values is different
because 637-nm
observations
were
made about 700 days after the Voyager measurements, and
the uncertainty is larger becauseof the larger scatter in the
637-nm brightness values.
Taking all these data into account, we find that one of
the discrete ranges of Af• fits better than any of the oth-
species, SIII, as the EUV measurements and, within the
uncertainty, show the same periodicity. Therefore we explicitly assume that the two sets of data are manifestations
of the same underlying physical mechanism, and we further
assumethat the bright regions at the two wavelengthswould
ers. The centerof this rangeis Af• = -25.486ø/d, and this
have been coincident
alternative to -25.486ø/d.
had the two sets of measurements
been
performed at the same epoch. We adjust the value of Aft
is the value that we have adopted in section 2. This selection hinges on the weight given to the 673-nm observations.
Relaxing the requirement for compatibility with these mea-
surements
wouldleavethe Af• = -25.149ø/d an acceptable
Af•
=
--25.486
Nevertheless,we believe that
is the correct
choice because it is closer to
and A0sothat the regionof enhanced
IS III] 953-nmemission falls at Aiv = 180 ø.
In Figure 13 we have used our preferred value for Aft
,, o Brown and Shemansky, 1982
ß
of -25.486ø/d to plot the data of Roesleret al. in system IV. These data were kindly supplied to us in a form
useful for this investigation by F. Scherb. This figure, which
is analogous to Figure 2 of Roesler et al., shows an unmistakable modulation at the system IV period, with a peak at
Air = 180ø. The 953-nm observationsspan a time interval
that includes periods of both alignment and anti-alignment
of the sectors of maximum activity in systems III and IV.
We find that the amplitude of the azimuthal variation in the
953-nm brightness tends to be greater at times near alignment than at times near anti-alignment. The data are not
extensive enough to permit an unambiguous identification
of this trend, but we note that such behavior is common
to the EUV
and nKOM
emissions
as well.
800
ality suggestsa close relationship among the sourcesof the
Several values of Aft are consistentwith the nKOM, the
EUV, and the 953-nm observations,becauseof the ambiguity introduced by the possibility of increasing or decreasing
the rotation of system IV relative to system III by an integral
I
'
I
'
I
'
I
'
I
'
•'
_
• 600._
•
):
400
•½ 200 _
- oß
o o
N
•
o
500
.-
o•
-- 0
-
O
0
180
,
I
90
,
I
0
S•tem •
Such common-
emissions.
Roesler et ol., 1984
'
,
I
270
,
1
180
90
0
Longitude(degrees)
Fig. 14. Ans• brightnessd•t• of Bm• • $he•ky
[1982]
(opensymbols),superposed
on the d•t• shownin Figure 13 (solid
circ]es).The obse•tio• of Roes]eret •]. wereof on]ythe receding •ns•, while those of Brown •nd Shem•nsky invo]v•
The d•
•re p•r•icu]•r]y
we]] org•ized
d•t• •re consid•ed (i.e., ignoretri•]es).
both the
if only reced•g
SANDEL AND DESSLER: JOVIAN MAGNETOSPHERIC
the value preferred on the basis of the nKOM and the other
phenomenathat fit naturally into the system IV so defined.
Other ground-based observations of S II emissions have
shown azimuthal asymmetries that are consistently fixed in
6.1.
PERIODICITIES
6.
THEORETICAL
General
Considerations
5499
IMPLICATIONS
The principal finding of two persistent, discrete periodic-
systemIII [PilcAereta/., 1985;Morgan,1985;Trafion,1980]. ities in the Jovian magnetosphere can be addressed in sevSampling of a structure correlated with system IV at different times when, by chance, the relationship between the two
systems is nearly constant would cause the structure to appear fixed in system III as well. This is apparently not the
case with the S II observations. For the two nights' obser-
eral ways. We are aware of the three listed in the intro-
duction:(1) plasmaslippagein the Io torus,(2) a localized
vortexwithin the torus,and (3) a differentialrotationwithin
Jupiter's magnetic field.
SuggestionI is the most conspicuouspossibility. Unfortunately,
it has no obvious merit. As pointed out by Desder
vationsshownin Figures12 and 13 of PileActet al. [1985],
[1985],•To get a distinctlydifferentperiodutilizingthe slipthe offset between systemsIII and IV changed by only 20ø,
page of magnetosphericplasma, one would have to suppose
so any structure would be stable in both systems. However,
Figure6 of Morgan[1985]showsthe samestructurein sys- the existence of a physically unrealistic, longitudinally contem III at a time when the offset between the two systems
differed by about 180ø from that of the earlier measurements. We conclude that these variations are well organized
in system III, but not in system IV.
PilcherandMorgan[1985]observedpeaksin the brightnessesof both SIII and S II emissionsto drift toward higher
•i•i by 25ø in about 50 hours. This drift is in the correct
sensefor a phenomenon fixed in system IV, but the rate is
a factor of about 2 smaller than our preferred value of Ate.
However, ours is a time-averaged value of Ate, and each of
the data sets used in defining it is compatible with intermittent departures by a factor of 2 from this average value.
Thus the short-term drift rate observedby Pilcher and Morgan may be consistent with other system IV phenomena.
Pilcher and Morgan's Figure 3 suggeststhat peaks in the
brightnessof both S II and SIII emissionsshifted by roughly
the same amount in 2 days. If this correlation is typical,
then we face a difficulty in understanding the relationship
fined,long-livedblobthat (a) slipsrelativeto corotarion,(b)
doesnot changeits Jovicentricdistance,and (c) is continually resupplied with either plasma or energy3 The period
of a magnetosphericphenomenonis determined by the periodicity of the sourcethat powers that phenomenon. Simple
plasma slippage shifts the phase of a spin-modulated phenomenon, but it cannot change the period. For example,
although the solar wind slips rather excessively relative to
solar rotation, the period of solar wind activity remains the
nominal 270day rotation period of the Sun. There is a phase
shift, however,asreceding(west)limb activity at the Sunis
often moreimportantterrestriallythan approaching
(east)
limb activity.
Suggestion2, the formation of a vortex within the torus, is
a clever and sophisticatedvariant of suggestion1. W. Hor-
ton and R. A. Smith (Solitary vorticesin the Io plasma
torus, submittedto Journalof Geoph•tsical
Research,1987)
propose that the velocity shear in the torus that is caused
by the predicted and observed increase of plasma slippage
of the 953-nm SIII measurements
of Roesleret al. (which
are organizedin systemIV), to the 673-nm S II emissions with increasingradial distance[Hill, 1979; McNutt et al.,
(whichshowpersistentorganization
in systemIII). However, 1979] can providea continuoussourceof powerto a vortex (or solitoh)within the torus. This suggestion
immediwe note that the SIII 953-nm peak in Pilcher and Morgan's
ately overcomes
difficulties(a) and (c) quotedin the previFigure 3 falls at •iv N 230ø, near its expected position in
system IV. More information on the conditions under which
the S II and SIII
emissions
are correlated
is needed.
All the phenomena used in the definition of system IV
show a 14-day modulation, with maximum amplitude at
times near alignment of the sectors of maximum activity
in systems III and IV. We find a suggestion of this behavior in the S II emissions as well. All the data plotted
ous paragraph. The lifetime of a solitoh in the torus is not
addressed. However, we can see that this is an important
issue. The rotation period of a solitoh must remain constant
within rather narrow limits for months to account for, say,
the nKOM data, which requires, presumably, that the Jovi-
centticdistanceof a solitohcannotchange(difficulty(b)).
Also, becausethere is no evidence for two or more sources
in the figuresof Pileher andMorgan[1985]wereobtained within the torus, the birthrate of solironsin the torus must
near times of alignment, and show pronounced azimuthal
variations.Morgan[1985]showsdata acquirednear alignment (hisrun 1, Figure4), midwaybetweenalignmentand
anti-alignment(run 3, Figure 5), and near anti-alignment
(runs 2 and 4, Figure 4, $• and 6). Run 1 (aligned)shows
be low so that only one solitoh is present at any time. Another potential difficulty for the solitoh model is that it does
not seem to explain the observed14-day periodicity in magnetosphericactivity. Finally, the solitoh model is specificto
Jupiter and the Io plasma torus. As pointed out by Desder
the strongest and best organized modulation in both S II
[1985],dualperiodicitymaybe a commonfeatureof gaseous
emissions of all four data sets. This is similar
planets. A model with wider applicability would be prefer-
•o the behav-
ior of the 953-nm emissionsdescribed earlier, the EUV, and
able.
the nKOM emissions.Near anti-alignment(runs 2 and 4,
particularlyFigure6) the brightness
is moreuniformin az-
Suggestion3 is the most complex, and it has the broadest
applicability. We begin by calling the reader's attention to
the observationsof the Sun's magnetic field, showing that its
dipole field rotates with two discrete periods that are present
imuth than the data from his run 1 and in Figures 1, 2,
and 3 of Pilcher and Morgan, especially in view of the point
near •iii = 10ø in his Figure 6. Although we cannot draw
firm conclusionsfrom this limited sampling, it seems plausible that the azimuthal asymmetry in the S II emissionsis
modulated in a way analogous to the EUV, the nKOM, and
the SIII 953-nm brightness measured by Roesler et al.
simultaneously
[Hoeksema
andScherrer,1987].The two periods, 26.9 days and 28.1 days, differ by 4.5%. There is
indirect
evidence
that
Saturn
exhibits
the same sort of duM
periodicity behavior in the rotation of its magnetic field. For
Saturn, if we accept the commonly held view that the forma-
5500
SANDEL
AND DESSLER:
JOVIAN
MAGNETOSPHERIC
coincidence, and weakened, as they move to opposing longitudes. This effect is illustrated in Figures 5, 10, and 11.
o Brown and Shemansky, 1982
ß
Roesler ef al., 1984
800
Lß,
I ' I ' I ' I' I '_
ßß
•00 I ß
ß
½
O
a
ß
Oo
eee
•
ßlz2
A
ß •
ß
__ 1000
½
ß
•
Oo
_•
o•
•-
erty of the Jovian magnetospherein terms of a modulation
-
of corerating convection.
500
•
•
&-o
200 -••o øøø%oo o ½o % •
0
•
180
'
[
90
'
e,
•
0
'
•
270
•
180
'
•
90
-
øøo%o'
6.2.
Modulated Corotstint! Convection
Corerating convection,as originally suggestedby Vasllli-
_
0
'
The timesof alignmentand anti-alignmentare givenby (2)
and (3). We canoffera tentativeexplanationof this prop-
_
_
400
ßo -
PERIODICITIES
0
SystemllT Longitude(degrees)
Fig. 15. The same data as in Figure 14, except plotted in system III coordinates. The data are not ordered as they are in
Figure 14, although persistent system III ordering is reported by
unas[1978],is drivenby the effectof centrifugalstresson an
azimuthal mass imbalance in the inner portion of the torus.
(SeeHill et al. [1983,pp. 392-393]and Vasllliunas
[1983,pp.
450-451]for a descriptionof this particularviewof corerating convection.)The systemIII longituderangefromwhich
the convection is expected to be outward is the active sec-
tor. The longituderangeof the activesector(from about
Aiii = 150ø to 320ø) containsnearlyall the Jovianmagnetospheric phenomena that show a grossazimuthal asymmetry
(seeFigure10.10of Hill et al. [1983]).
To account for the system IV longitudinal asymmetries
that have been described in this paper, we propose a second
active sector, this one fixed in system IV. This active sector
tion of spokesin its ringsis somehowa magnetospheric
phe- appears to influence the outer part of the torus where there
nomenon,
then the discovery
by PortoamdDamielso,[1984] is organization in system III and system IV, depending on
of a dual periodicity in spoke activity leads us to suspecta the phenomenon being observed. For example, the EUV
Tr./to• [1980],P•l½her
.rid Mo•g.• [1980],and Tm,
ugeret al. [1980].
dual periodicityin the rotation of Saturn'smagneticfield.
This dual periodicityin spokeactivity has beenverifiedby
recentmoreextensiveanalysis(C. Porco,privatecommunication,1987). Porcoand Danielsonpo•n"•
out that the two
periodicitiesof spokeactivity are approximatelycoincident
(Figure6), the ground-based
data of BrownandShemanskll
[1982],andof Roesletet al. [1984](Figure15) arenot well
ordered in system III.
The organi•.ation of the nKOM in
systemIII (Figure8) maybe duein part to the wobblingof
the torus causedby its 7ø tilt relative to Jupiter's spin axis.
with the SKIt (Saturnkilometricradiation)period•nd the The nKOM showsbeamingin magneticlatitude[Daigneand
of the nKOM may
SED (Saturnelectrostatic
discharge)
period(seeFigure1 of Leblanc,1986]. Thusthe Ain dependence
be
to
some
unknown
degree
a
viewing
angle
effect and not
PorcoandDanielson).
Theseperiodsdifferby nearly5.0%.
Ileturning to the case of the Sun's magnetic field, for
which Hockseros
and Scherrer[1987]detail compellingevidencefor two periodicities,Howardet al. [1984]showthat
larger magnetic structuresrotate more slowly than small
solely a system III longitudinal asymmetry.
If we assume for the moment
that
there
are two active
sectors, one in each coordinate system, that drift relative
to one another, we could well expect a modulation of the
strength of the corerating convectionpattern. The period
magnetic
structures
(suchassmallsunspots).
Sheelell
et al.
[1987]presenta solarmodelto accountfor the observationsof the modulationwouldbe 14 days,as shownin (2) and
betweenthe
of rigid-bodyrotation of coronalholesand other large-scale (3). We have alreadynoted the coincidence
solar/magnetic
fieldpatternswhilesmall-scale
magnetic
fea- hulling of the kilometric radio emissionsfrom Jupiter retures,suchas sunspotsand X ray bright spots,showingthe portedby Kurth et al. [1980]and the timesof minimum
convection
that wewouldpredictusing(3).
long-observed
latitude-dependentdifferentialrotation, drift magnetospheric
Also, we find in data presented by several observersthat
through the larger structureswithout disturbingthem.
Magnetized,rotating gaseous
bodiesthat are heatedfrom Jupiter's decametricradio emissionis modulated with a 14[e.g.,Barrow,1979;Cart et al.1983,p. 256].
within oughtto have similar magneticbehavior[Hathaway dayperiodicity
andDessler,1986].Magneticdualperiodicityis established Although these modulations are usually attributed to a twofor the Sun. The conceptof dual periodicity may be appli-
sector structure in the solar wind, we note several difficulties
with the solar wind interpretation. First, a quantitative mismain pulseand a drifting subpulseare alsoexhibitingsome match lies in the synodic period of solar rotation, which as
sort of magneticallycontrolleddual periodicity.Thus what seen from Jupiter is approximately 25 days, not the 27-day
we are finding for Jupiter has precedencein observations period seen from Earth. Thus if a two-sector structure in
of other rotating fluid bodies with active internal magnetic the solar wind were to produce a modulation at Jupiter, it
fields.
would have periods centered on 12 to 13 days, not the obThere are numerousphenomena that show persistent az- served 14-day period. Second, we are not aware of a mechaimuthal asymmetriesin systemIII. (For a graphicalcom- nism that would connect the solar wind to the deep interior
pilation,seeFigure 10.10of Hill et al. [1983]and references of a magnetosphere such as Jupiter's, which is dominated
citedtherein.)Wehaveseenin sections
3, 4, and5 that some by plasma processesrelated to the rapid spin of the planet
cable to Saturn. We also note that those pulsars that have a
of the same, or at least similar, phenomenahave persistent
azimuthal asymmetriesin system IV. Becausesystem IV
slipsnearly 11ø relative to systemIII during one systemIII
period, a given phenomenonwill be periodicallyreinforced,
as the system III and IV active sectorscome into spatial
and the Io torus. Finally, we remindthe readerthat (3),
which was derived from other data sets, and is not related
to solar wind phenomena, sucessfullyaccounts for the times
of the four nulllngeventsobserved
at 56.2kHz [Kurthet al.,
1980].
'
SANDEL AND DEss,.E•t-
6.3.
JOVIAN MAGNETOSPHERIC
Dusk Quadrant Modulation
PgRIODICITIES
•
--H
0
transmitted to lower latitudes. But again, mighty Jupiter
(whichis on the dusksidefor Voyager2 inbound)showsa
clear spin-modulation signature.
of the difference
in character
of
the modulation on the dusk side is shown in Figure 17. We
seea largerangeof motionof the dusk (receding)ansanearlya full Jupiterradius--whilethe dawn (approaching)
ansa, except for the singular point at 5.25 Rj which we discuss below, is normally restricted to a movement of 0.3 Rj,
or just 1/3 of the motionof the duskansa.
The radial position of each ansa is determined in part by
plasmadrift in the localconvection
electricfield [Goertzand
lp, 1984;lp and Goertz,1983;BarbosaandKiuelson,1983].
Because this electric field is modulated at the system IV
period on the dusk side, the UVS instrument on Voyager 2
inbound saw large radial motions and brightness variations
in the receding ansa and correspondingly small effects in
the approaching ansa where the electric field shows little
spin modulation.
The case marked by the triangle in Figure 17 is an interesting exception. At the time that measurement was made
•
O0
is different.Vas•lliunas
[1983]haspointedout that the neutral x-line(which,for the Earth at magnetically
quiettimes,
extendsthe full width of the tail) in Jupiter'scaseis likely
to cross only part of the tail. This is illustrated in Figure
16. We propose that the flow of plasma from the Io torus
into the outflow region on the dusk side is modulated at
the system IV period. A consequenceof this unsymmetrical
outflow is seen in Figure 4, where only the receding ansa
t--
0 T,
cap ionosphere,from whence global convectioneffects are
demonstration
Brighter
6.5
The convection electric field across the Earth's magnetotail is uniform to first order, and except for substorm
intervals, it is rather smoothly impressed acrossthe polar
Another
5501
ø1
0 %0
5.0
5.5
5.0
6.0
Dipoleto Approaching
Peak (Rj)
Fig. 17. Distances from Jupiter's magnetic dipole to the peak
in brightness at the two ansae, inferred from UVS measurements
of the torus location combined with information on the position
of the dipole. Each symbol shows the distance to both ansae,
measured at nearly the same time. The dispersion in the location of the receding ansa is larger by a factor of approximately
3, if the point marked with a triangle is regarded as atypical, as
explained in the text. We interpret this plot as confirming Figure 16 in which a spin-modulated electric field is usually applied
principally across the receding ansa. Dipole-ansa distance correlates inversely with brightness as indicated. The arrows show
the averagedistanceof the approaching
and recedingansae(the
point markedwith a triangleis againneglected).
and from the Voyagerlog and (1), the activesectorswere
in the sunlit hemisphere(Jupiter'ssubsolarlongitudewas
,•iii • 200ø, and ,•iv • 220ø). Outwardplasmaflowon the
dayside is normally inhibited by solar wind pressure, as is
suggestedin Figure 16. However, this is not the case on 1979
day 41 when the magnetosphere was expanding at an aver-
agerate of 7.4 R•/d, with sporadicintervalsof faster (and
slower)expansion.We believethat at this time there was
(1979,day 41, 13 hours),the sizeof the magnetosphere
was transient sunward flow out of the aligned active sectors. The
expanding from about 62/?• on day 39 to 114/?• on day 46
convection electric field was reversed and impressed across
[Goodrich
et al., 1980].Using(2), wefindthe systemIII and the approaching ansa. Thus the approaching ansa moved inIV active sectorswere aligned at the time of the observation,
Subcorotational
Plasma
Flow
Quasisteady
X
and
•'•
//•
'r½•
F Bd;b
• cNø
Magnetic
Electric
Field
onnecUon
ward and brightened, while the receding ansa was located at
approximately the radial distance one usually finds the approaching ansa. The normal dawn to dusk brightening was
observed to reverse. We conclude therefore that the point
plotted as a triangle in Figure 17 is a special case wherein
the plasma flow from the active sectors was not as shown
in Figure 16, but instead was temporarily directed sunward
instead
o o
%
%%
•
•
Regionof
øøøø
•agneUc Field
Spin-Modulated
Plasma
FIo•
and
Fig.
16.
Illustrative
Electric
Field
sketch of Jovian magnetospheric convec-
of anti-sunward.
7.
CONCLUSION
We have shown that a number of separate phenomena can
be fit into a newJovianlongitudegrid (systemIV) havinga
presentlydefinedrotationrate of 845.05ø/d. However,until
more independent data are obtained, it is not established
that all the phenomena we have plotted will remain fixed
in system IV. In a sense,we have forced a fit among three
data sets. Study of Figure 12 should show that, with two
independent,adjustableconstantsin (1), namely,,•o and
A•, we would have found an acceptablefit even if, contrary
tion in the outer magnetosphere(adapted from Figure 11.19 of
Va•li•n• [1983]).The view is of the magneticequatorialsurface to our explicit assumption, the phase of the 1981 and 1982
points were not fixed in a rigidly rotating longitude system.
as seen from above the north pole with the solar wind incident
from the left. The flow of plasma on the dawn side tends to be
The test of the validity and utility of system IV will be to
steady, so the electric field impressed across the dawn polar cap
place more independently acquired data from different times
tends to be steady. We propose that the electric field on the dusk
into this system.
side is modulated at the 10.2-hour, system IV spin period by the
The question of beat frequencies and sidebands has not
outflowing plasma. The electric field that is mapped down to the
dusk polar cap is similarly modulated at the system IV period.
been investigated. At this point it is possiblethat the sys-
5502
SANDEl, AND DESSl,ER: JOVIAN MAGNETOSPHtgRIO PERIODIGITIES
tem IV variations reported here are a result of a 14.1-day
amplitude modulation of systemIII phenomena.Similarly,
as explained in section 6, the 14.1-day modulation could
follow from the beating of the system III and system IV
periods. Additional analysisis necessary.
If systemIV shouldproveto be a durable descriptionof a
significant portion of the time-dependent behavior of a certain classof Jovian phenomena,a new theoreticalchallenge
will be to find a descriptionof Jupiter's magnetic field that
allowsfor this sort of dual periodicity and to relate this theory to other objects exhibiting dual magnetic periodicities
such as the Sun, and possibly Saturn, and certain pulsars.
APPENDIX:
ANALYSIS TECHNIQUES
The brightnessof the ansae of the Io torus undergo large,
apparently aperiodic, fluctuations in the extreme ultraviolet
that exceed the measurement uncertainty. These fluctuations mask any periodic structure in a simple plot of brightness versus time. To reveal possible periodic structure, we
must rely on detection techniques suited to finding modulations that are weak compared with random fluctuations and
that may be applied to unevenly sampled data. One such
Pr(g > z)= exp(-z)
(5)
Pr(Z > z) is the probabilityof findinga ratio Z greater
than the observedratio z at the preselectedfrequency.Here
z is the ratio of the signal power to the noise power. The
signal power is just the amplitude of the periodogram at
the appropriate frequency, but the noise power must be estimated independently. If we search many frequenciesfor
statistically significant power, the expressionto use is Scargle's equation 14:
Pr(Z > z)= 1- [1- exp(--z)]"
where v is the number of independentfrequenciesexamined.
As v is increasedby testing more frequenciesfor significant
power, the probability of finding by chancea physically unreal, but apparently significant, Z > z is increased. This is
takeninto accountby the exponent• in (6).
The best estimates for the signal frequency and power
come not from evaluating the periodogram at the frequenciesdefinedby the nulls in the spectralwindow, but by over-
samplingto findthe true peakin theperiodogram
[Blackand
Scargie,
1982].The bestestimatefor the signalfrequencyis
techniqueis basedon periodogramanalysis.Scargle[1982] simply the frequencyof the peak in the periodogram. The
has developed a useful formulation of the statistical properties of a slightly modified form of the classicalperiodogram,
including simple expressionsfor the reliability of detections
and for the power at a particular frequency. We have computed periodogramsfrom our data usingScargle'sequations
amplitude of the modulation X0 is Scargle'sequation 7:
10 and
where P is the amplitude of the periodogramat the peak
11:
•/P
x0=• •
(,)
and No is the number of observations.
=
{[
+[•i
--0]
The amplitude of the modulation obtained in this way
is only an estimate, but it is useful to know, at a specified
level of confidence,the range of amplitudes consistentwith
the observations. This range, which dependson the ratio
of signal power to noise power, may be found for several
- }
sin••(ti - r)
confidence
levelsusingcurvesin Groth's[1975]Figure 1 in
conjunctionwith (7).
where r is defined by
A secondmethod of searchingfor periodic modulations,
sometimescalled superposedepochanalysis,is basedon the
idea that a plot of brightnessversusphasewill grouppoints
of similar phaseclosetogether when the correctfrequency
is chosen. Similar techniqueshave been used by Belfort et
sin2wti
cos2wti
tan(2wr) =
a
and X i is the signalmeasuredat time ti (seealsoScargle's al. [1980]andby LafierandKinman[1964].To calculate
AppendixB). For evenlysampleddata, the periodogram
is quality-of-fitdiscriminant,a measureof the groupingof the
usually evaluated at a set of frequenciesw,• given by
2•'f•
co.= T
(4)
where T is the total time spanned by the observations,and
r• = 0, 1,2,...,N0/2
(No is the numberof observations).
For unevenly sampled data, the analogous set of natural
frequencies is the set of nulls in the spectral window function. Although no closed-form expression for this window
exists under the definition of the modified periodogram, a
satisfactory approximation can be derived by computing the
periodogram
of a high-frequency
sinewave(seeScargle's
AppendixD) or of a dc signal[Blackand$cargle,1982].At the
set of frequencies determined in this way, the amplitudes of
the periodogram are independent of each other, and the statistical properties of the periodogram are well understood.
If we wish to evaluate the evidence of modulation at a preselected frequency, the expression to use is
data points, we have averagedbrightnessas a function of
phaseover a number of bins, typically 10. The discriminant
is the sum of the squareddeviation of eachbrightnessfrom
the mean in its phasebin. A plot of the discriminantversusfrequencyhas a minimum at a frequencypresentin the
signal.
Although the two techniquesyield consistentresultswhen
appliedto our data, most of our discussion
is basedon periodogram analysis because its statistical behavior is well
known and becauseit permits an explicit estimate of the
power at a particular frequency.On the other hand, the superposedepochanalysisis conceptuallysimpler and leadsto
an intuitively more satisfyingresult. The signalpower can
be estimatedby generatingand analyzingsyntheticdata,
keepingin mind the dangersmentionedin section3.
Analysisof synthetic data has alsoproven to be a useful
adjunct to the more direct methods described above. Generation and reduction of synthetic data is a sensitivetest of
the functioningof the analysisprogram,andit helpsto iden-
SANDEL AND DESSLER: JOVIAN MAGNETOSPHERIC
tify spuriousfeatures resulting from the sampling schemeor
leakage from other frequencies. Synthetic data were generated for the times of the observations
from
PEP•IODICITIES
5503
tions of the standoff distance of the Jovian bow shock, MITRep.
OSR-TR-80-4, Mass. Inst. of Technol., Cambridge, June 1980.
G•oth, E. J., Probability distributions related to power spectra,
Astrophys.
J. $uppl.,œ9,285, 1975.
S(ti)-' AGi+ Z Bjsin(•0jti)
(8)
Hathaway, D. H., and A. J. Dessler, Magnetic reversalsof Jupiter
and Saturn, Icaras, 67, 88, 1986.
Hill, T. W., Inertial limit on corotation, J. Geoph•ts.
Res., 84, 6554,
1979.
Noise is included through the term AGi, where Gi is a
Gaussian random variable having variance 1.0. Measurement error makes a small contribution to the total "noise,•
but real, aperiodic brightness variations dominate the EUV
data. Therefore the amplitude A cannot be determined from
the measurement error alone. In practice, it is adjusted to
match the random component of the observed brightness
variations as measured by the two analysis techniques already described.
Acknowledgments. We thank M. L. Kaiser, Y. Leblanc, F.
Scherb, and F. L. Roesler for providing their data to us in convenient form and for helpful discussions. We also thank T. W.
Hill, J. S. Morgan, C. B. Pilcher, C. T. Russell, R. A. Smith• and
V. M. Vasyliunas for their comments and suggestions. A.J.D.
acknowledges support by grant NAGW-1151
from the Space
Plasma Physics Branch of NASA's Office of Space Science and
Applications. B.R.S. acknowledges support under NASA contract NAGW-610 to the University of Arizona.
The
editor
thanks
M.
J. Klein
and C. B. Pilcher
for their
as-
sistance in evaluating this paper.
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PERIODICITIES
B. R. Sandel, Lunar and Planetary Laboratory, University of
Arizona, 901 Gould-Simpson Building, Tucson, AZ 85721.
A. J. Dessler, Space Physics and Astronomy Department, Rice
University, P.O. Box 1892, Houston, TX 77251.
(ReceivedSeptember29, 1987;
revised January 12, 1988;
acceptedFebruary4, 1988.)