Phase relation of oscillations near the planetary period ...Apr-Jun).Journal... · 03/06/2009 ·...

Phase relation of oscillations near the planetary period of Saturn’s

auroral oval and the equatorial magnetospheric magnetic field

G. Provan,1 S. W. H. Cowley,1 and J. D. Nichols1

Received 13 December 2008; revised 1 February 2009; accepted 11 February 2009; published 11 April 2009.

[1] Previous analyses of Hubble Space Telescope (HST) images of Saturn’s southernauroras obtained during two campaigns, in January 2007 and February 2008, haverevealed that the auroral oval oscillates at a period close to the planetary rotation period,with its center describing an elongated ellipse of semimajor axis �2� colatitude alignedalong the prenoon to premidnight direction. Previous analyses of Cassini magneticfield data from Saturn’s near-equatorial quasi-dipolar magnetosphere have also establishedthe presence of a rotating pattern of magnetic field perturbations near the planetary period,a phase model which has been derived from data over the interval from mid-2004 tothe end of 2007, whose extrapolation is verified here for use during the February 2008HST campaign. In this paper we compare the phases of these oscillatory phenomena andshow that the southern oval displacement was directed approximately opposite to therotating equatorial perturbation field during both HST campaign intervals. We alsoexamine the relation of the southern oval oscillations to the periodic power modulationsin Saturn kilometric radiation (SKR) and show that the southern oval was displacedsunward at SKR maxima. It is suggested that the oval displacements are related tomagnetospheric field line distortions associated with the rotating magnetic fieldperturbations, this picture also being consistent with recently reported periodic tilting ofthe equatorial plasma sheet. We note, however, that this picture provides no immediateexplanation for the significantly elliptical nature of the observed oval motion.

Citation: Provan, G., S. W. H. Cowley, and J. D. Nichols (2009), Phase relation of oscillations near the planetary period of Saturn’s

auroral oval and the equatorial magnetospheric magnetic field, J. Geophys. Res., 114, A04205, doi:10.1029/2008JA013988.

1. Introduction

[2] Oscillations close to the planetary period (�10.8 hours)are omnipresent in Saturn’s magnetosphere, having beenobserved in the magnetic field, plasma parameters, and radiowave emissions. Such oscillations were first discovered inVoyager observations of Saturn kilometric radiation (SKR)emissions, which were found to undergo ‘‘clock-like’’modulations in intensity, independent of the position ofthe observer, with a period of �10.66 hours [Desch andKaiser, 1981; Warwick et al., 1981]. This modulation wastaken to be produced by some rotating anomaly (e.g.,magnetic) at the planet, such that this period became theofficial International Astronomical Union value for therotation period of Saturn. Subsequently, however, investi-gations using Ulysses and Cassini radio data have shownthat the SKR period varies over yearly intervals by as muchas 1%, such changes being far too large to be associateddirectly with the planet itself [Galopeau and Lecacheux,2000; Gurnett et al., 2005; Kurth et al., 2007, 2008].

[3] Oscillations near the planetary period have also beenobserved in magnetospheric charged particle and magneticfield data, initially using data from Pioneer-11 and theVoyager spacecraft [Carbary and Krimigis, 1982; Espinosaand Dougherty, 2000; Espinosa et al., 2003a, 2003b], andsubsequently from Cassini [Krupp et al., 2005; Cowley etal., 2006; Giampieri et al., 2006; Clarke et al., 2006;Gurnett et al., 2007; Carbary et al., 2007a, 2007b, 2008a,2008b]. Unlike the clock-like SKRmodulation, these plasmaand field perturbations rotate around the planet with asidereal period which is close to the SKR period, therotation resulting in Doppler shifts in the observed signalsdue to the azimuthal motion of the spacecraft [Cowley et al.,2006; Giampieri et al., 2006; Gurnett et al., 2007; Carbaryet al., 2007c; Southwood and Kivelson, 2007]. Within thelow-latitude quasi-dipolar ‘‘core’’ region of the magneto-sphere, inside radial distances of �12 RS, the perturbationfield takes the form of a rotating quasi-uniform equatorialfield of a few nTamplitude, such that the radial and azimuthalfield components oscillate in quadrature with comparableamplitudes, with the radial component leading the azimuthalin phase. An oscillating colatitudinal component is alsopresent, in phase with the radial component [Andrews etal., 2008]. (Here RS is Saturn’s radius, equal to 60,268 km.)The phase of these magnetic oscillations was determined byAndrews et al. [2008] for the initial near-equatorial period

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1Department of Physics and Astronomy, University of Leicester,Leicester, UK.

Copyright 2009 by the American Geophysical Union.0148-0227/09/2008JA013988$09.00

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of the Cassini mission, and was extended to cover theinterval from Saturn orbit insertion (SOI) in mid-2004 tothe end of 2007 by Provan et al. [2009]. These studies showthat the variations of the magnetic phase lie within the scatterof the SKR phase data determined by Kurth et al. [2007,2008], such that these oscillations share the same slowlyvarying period to within the accuracy of the measure-ments (corresponding to a fraction of one oscillation over�3.5 years). Their relative phase is such that SKR powermaxima occur when the equatorial perturbation field pointsradially outward at �0200 LT. Provan et al. [2009] alsodemonstrated that related oscillations are present on openfield lines at high latitudes, and determined their polarizationcharacteristics and phase relative to the equatorial oscilla-tions. They suggested that the overall pattern of field pertur-bations may be produced by a rotating longitudinallyasymmetric ring current system, with field-aligned closurecurrents flowing principally to and from the southern summerionosphere. Khurana et al. [2009] have also discussed thesephenomena in terms of a rotating asymmetric ring currentsystem, but instead ascribe the oscillatory field effects to theseasonal action of the solar wind flow relative to the planet’smagnetic axis.[4] Most recently it has also been shown that the location

of Saturn’s auroral oval undergoes oscillations close to theplanetary period. Nichols et al. [2008] analyzed ultraviolet(UV) images of Saturn’s southern aurora obtained duringtwo recent Hubble Space Telescope (HST) campaigns, during13–26 January 2007 and 1–16 February 2008, and showedthat the center of the oval executes small-amplitude oscilla-tions at close to the planetary period. Specifically, the centerdescribes an elongated ellipse of semimajor axis �2� colat-itude, aligned along the prenoon to premidnight direction.Nichols et al. [2008] suggested that these oscillations couldbe due to the presence of a rotating external current systemwhich is similar in form to that discussed by Provan et al.[2009] but is based on the theoretical discussion ofGoldreich and Farmer [2007].[5] Clearly a significant step in determining the physical

origin of the oscillations in the auroral oval is to establishtheir phase relative to other oscillatory phenomena, partic-ularly the magnetic field oscillations and SKR powermodulations. This is the principal purpose of the presentpaper. We note, however, that the SKR modulation phasewas determined by Kurth et al. [2008] to mid-2007, whilethe equatorial magnetic oscillation phase was determined byProvan et al. [2009] to the end of 2007, such that both phasemodels cover only the interval of the first HST campaignstudied by Nichols et al. [2008]. In section 2 we thus firstdiscuss the equatorial magnetic phase model, and use newphase data from the relevant interval of 2008 to verify thatthe model of Provan et al. [2009] can be extrapolated fromthe end of 2007 to cover the second HST campaign inFebruary 2008. In section 3 we similarly discuss the phaseof the southern auroral oval oscillations during each HSTcampaign, following Nichols et al. [2008], and comparethem with the equatorial magnetic field phase in section 4.In section 5 we specifically discuss the auroral oval oscilla-tion phase relative to the SKR modulation given by Kurth etal.’s [2008] phase model, but only for the first HSTcampaignin this case. In section 6 we briefly discuss the physical

origins of the oval oscillations, before finally summarizingour findings in section 7.

2. Equatorial Magnetic Field Phase Model

[6] Following the results of Espinosa et al. [2003a,2003b], Southwood and Kivelson [2007], Andrews et al.[2008], and Provan et al. [2009] discussed briefly above,the oscillatory equatorial perturbation magnetic field withinthe low-latitude quasi-dipolar core region of Saturn’s mag-netosphere may be expressed in spherical polar componentsreferenced to the planet’s spin axis as

Br 8; tð Þ ¼ Bo cos FM tð Þ � 8ð Þ ð1aÞ

and

B8 8; tð Þ ¼ Bo sin FM tð Þ � 8ð Þ; ð1bÞ

where 8 is the azimuth angle from noon increasing in thedirection of planetary rotation, equivalent to local time. Wenote that in the equatorial plane this represents a spatiallyuniform magnetic field lying in that plane that rotates in thesense of planetary rotation with a slowly changing synodicperiod given by

tM tð Þ ¼ 360

dFM tð Þdt

� � ; ð2Þ

where (as employed throughout this paper) phase angles areexpressed in degrees. At any time t the azimuthal angle ofthe perturbation magnetic field relative to the solar directionat each point in the plane (again taken positive in thedirection of planetary rotation) is given simply by

8M tð Þ ¼ FM tð Þ: ð3Þ

The oscillating colatitudinal field component, which is inphase with the radial component, may also be representedby the form given by the right side of equation (1a).[7] To determine the orientation of the rotating equatorial

field relative to the displacements of Saturn’s auroral oval,we thus need to analyze magnetic field observations withinthe low-latitude magnetospheric core region (defined forsimplicity to be inside dipole L values of 12), to determinethe magnetic phase function FM(t) during the HST campaignintervals. However, since Cassini generally spends only asmall portion of its time during each �10–30 day orbitwithin the core region, and none at all during the January2007 HST campaign because of the expanded high-inclination nature of the orbit then occurring, the magneticphase during the HSTcampaigns must be determined from anoverall model fitted to values determined from core regiondata obtained from orbit to orbit over the mission. Themethod adopted by Andrews et al. [2008] and Provan et al.[2009] employs the empirical SKR modulation phase,FSKR(t), as an exact ‘‘guide phase’’ relative to which thephase of the magnetic oscillations is determined. That is, wewrite

FM tð Þ ¼ FSKR tð Þ � yM ; ð4Þ

A04205 PROVAN ET AL.: SATURN’S AURORAL OVAL OSCILLATION PHASE

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where FSKR(t) is the SKR modulation phase determined byKurth et al. [2008] from SKR data obtained over the intervalfrom the beginning of 2004 to mid-2007, as employed byProvan et al. [2009], and yM is the relative phase of themagnetic oscillation. The SKR phase is represented by theempirical formula

FSKR tð Þ ¼ 360t

tSKRo�DFSKR tð Þ degrees; ð5aÞ

where t is the epoch time in days since the start of 1 January2004, ‘‘baseline’’ period tSKRo is exactly 0.4497 days(10.7928 hours), and DFSKR(t) is given by the polynomial

DFSKR tð Þ ¼ k0 þ k1t þ k2t2 þ k3t

3 þ k4t4 þ k5t

5; ð5bÞ

where the coefficients ki have the values

k0 ¼ 86:6681 deg

k1 ¼ �2:7537 deg day�1

k2 ¼ 4:7730� 10�3 deg day�2

k3 ¼ �4:8755� 10�6 deg day�3

k4 ¼ 3:5653� 10�9 deg day�4

k5 ¼ �9:1485� 10�13 deg day�5:

ð5cÞ

We note that the SKR phase is defined such that maxima inthe radio power output occur at times t given by

FSKR tð Þ ¼ 360N deg; ð6Þ

where N is any integer, a condition we employ in section 5 toexamine the relation of the auroral oval oscillation phase tothe SKR modulation.[8] For each Cassini periapsis pass through the core region

we then determine the relative phase yM in equation (4) tomodulo 360� by cross correlation between the model fieldsgiven by equation (1) and suitably filtered residual magneticfield data from which the internal planetary field has beensubtracted. (The internal planetary field employed through-out is the ‘‘Cassini SOI’’ model of Dougherty et al. [2005],consisting of centered dipole, quadrupole, and octupoleterms.) This procedure thus assumes that yM can be treatedas an approximate constant during each periapsis pass, whileslow variations with time are revealed through the changesin yM from pass to pass. In principle the analysis yields yM

values for each of the three magnetic field components foreach pass, but as discussed by Andrews et al. [2008] andProvan et al. [2009], some of the phase determinations arenot included in the analysis due, e.g., to field variations atthe spacecraft produced by the ring current entering thefilter band (5–20 hours), thus affecting the phase determi-nations. A cubic polynomial was then least squares fitted tothe remaining phase data to yield an empirical model foryM(t), and hence for the magnetic oscillation phase throughequation (4), derived from data from the SOI pass in mid-

2004 to the periapsis pass of Rev 54 at the end of 2007.This fit is given by

yM tð Þ ¼ kM0 þ kM1t þ kM2t2 þ kM3t

3; ð7aÞ

where the coefficients kMi have the values

kM0 ¼ 209:2� 41:9 deg

kM1 ¼ �0:5718� 0:1719 deg day�1

kM2 ¼ 1:1446� 0:2160ð Þ � 10�3 deg day�2

kM3 ¼ �0:5995� 0:0836ð Þ � 10�6 deg day�3:

ð7bÞ

Results for the magnetic oscillation phase covering theintervals of the twoHSTcampaigns are presented in Figure 1,where we show phase yM versus time t over the intervalt = 1000–1600 days (since 0000 UT on 1 January 2004 asin equation (5)), corresponding to late 2006 to early 2008.Year boundaries are indicated in red at the bottom ofFigure 1, while spacecraft periapsis times and Rev numbersare shown along the top. The intervals of the two HSTcampaigns are shown by the blue vertical bars in the plot.Phase data derived from Revs 30 to 54 using the cross-correlation method outlined above are reproduced fromFigure 5a of Provan et al. [2009]. Using the same dataformat as the latter paper, the red and green solid circlesshow the phases determined from the radial and colatitudinalfield components, respectively, while the blue crosses showthe values determined from the azimuthal component. Thered line shows the cubic polynomial fit to these data(including data from the earlier epoch extending to the SOIpass at t 180 days), given by equation (7). The overallRMS deviation of the data from the fitted line is �30�. Asshown by Andrews et al. [2008], however, much of thisscatter is due to physical ‘‘jitter’’ in the magnetic phasesdetermined from pass to pass, rather than being due tomeasurement uncertainties. We also note with Provan et al.[2009] that both the scatter and the overall model variationsof yM(t) lie wholly within the (substantial) scatter of theSKR phase data over the interval to mid-2007 covered bythe latter data.[9] The magnetic phase model derived in this manner by

Provan et al. [2009] thus covers the January 2007 HSTcampaign, but must be modestly extrapolated to cover theFebruary 2008 campaign interval. Here we therefore wish toverify the appropriateness of the extrapolation throughexamination of magnetic field data from early 2008. InFigure 1 we have first added phase data from Rev 55 earlyin 2008 derived using the same cross-correlation techniqueas used by Provan et al. [2009], and shown using the samesymbol types. These data can be seen to be in reasonableagreement with the phase model. However, following Rev 55the Cassini orbit was modified from near-equatorial inclina-tions to a near-polar orbit with a relatively small periapsisradius of a few RS, such that the spacecraft typically spentonly�4–6 hours crossing the core region from north to southduring each periapsis pass. Since such intervals representonly half an oscillation period or less, the above cross-correlation procedure can no longer be used to determine


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phase values. Instead, we have here determined the magneticoscillation phase from Revs spanning the February 2008HST campaign by examining the times at which the azi-muthal magnetic field component B8 in low-latitude coredata passes through zero. We focus specifically on theazimuthal field component since it is the only componentnot strongly affected by the field of the symmetric ringcurrent. We also focus on zero crossings (rather than, e.g.,maxima or minima), since these will be unaffected by theessentially unknown variation of the oscillation amplitudewith latitude away from the equator. We can, however,distinguish two types of zero crossing, those in which B8

increases with time from negative to positive values, andthose in which B8 decreases with time from positive tonegative values. From equation (1b) we note that in theformer case we have FM(t) � 8 = 360N deg for integer N,where 8 is the spacecraft azimuth at the time of the zerocrossing, while in the latter case we similarly have FM(t) �8 = 360N + 180 deg for integer N. Using whichever of theseexpressions is appropriate to a given periapsis interval thatcontains a B8 zero crossing, according to whether the fieldis rising or falling with time across the zero, these expres-sions can be combined with equation (4) to determine

‘‘instantaneous’’ values for yM to modulo 360�. We havecontinued to use the SKR phase defined by equation (5) asan exact guide phase in equation (4), as used by Provan etal. [2009], though now lying rather beyond the interval (tomid-2007) in which it is constrained by fits to SKR data.[10] An example of this procedure is given in Figure 2,

where we showCassini magnetic field data from the periapsispass of Rev 58, specifically for the 12 hour interval startingat 1200 UT on day 39 of 2008. This pass therefore occurrednear the center time of the second HST campaign interval.Figures 2a–2c show the residual field components inspherical polar coordinates referenced to Saturn’s spin andmagnetic axis, from which the internal planetary field hasbeen subtracted, again employing the Cassini SOI model ofDougherty et al. [2005]. We note, however, that theazimuthal component of the model planetary field is zero,so the azimuthal field shown in Figure 2c is as measured.Figures 2d–2f show the position data of the spacecraft,namely the radial distance r (RS), the latitude (degrees), andthe local time (hours). The dashed line in Figure 2d alsoshows the dipole L value of the spacecraft. It can be seenthat during the interval shown the spacecraft passed from thenorthern premidnight sector to the southern postmidnight

Figure 1. Plot showing magnetic phase yM versus time t over the interval t = 1000–1600 days,where t = 0 corresponds to 0000 UT on 1 January 2004. Year boundaries are indicated in red at thebottom, while Periapsis times and Cassini Rev numbers are shown along the top. The times of the twoHST campaigns considered here are shown as blue vertical bars. The data shown for Revs 30–54 arereproduced from Figure 5a of Provan et al. [2009], where red and green circles were derived from ther and q components of the magnetic field, while the blue crosses were obtained from the 8 component.The red line shows the cubic polynomial fit of Provan et al. [2009] to these data (extending from SOIto Rev 54). Here we add data from Rev 55 using the same analysis technique, shown using the samesymbol types, together with data for Revs 58–63 determined from zero crossings of B8 observed duringPeriapsis passes as described in the text, shown by the blue stars.


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Figure 2. Cassini magnetic field data illustrating the method of determining field oscillation phase valuesfrom zeros of the azimuthal magnetic field component observed on Periapsis passes in the low-latitudemagnetosphere. The plot shows 12 hours of data spanning the Periapsis pass of Rev 58, starting at 1200 UTon day 39 of 2008. The residual field components in spherical polar coordinates referenced to Saturn’s spinand magnetic axis (a) DBr, (b) DBq, and (c) DB8 (nT); (d) spacecraft radial distance r (RS); (e) latitude(degrees); and (f ) local time (hours). The residual field components have been obtained by subtracting theinternal planetary field, where the Cassini SOI model of Dougherty et al. [2005] has been employed.However, the azimuthal component of the model planetary field is zero, so the azimuthal field shown inFigure 2c is as measured. The black dashed line in Figure 2c shows the model field given by equation (1b)with an arbitrary amplitude of 4 nT, using the phase model of Provan et al. [2009] given by equations (4),(5), and (7). The dashed line in Figure 2d shows the dipole L value of the spacecraft. The vertical long-dashed lines bracket the low-latitude region where the spacecraft lay within ±30� latitude of the equator,while the vertical dotted line marks the point within this region where the azimuthal field component passedthrough zero from negative to positive values. The magnetic oscillation phase yM is derived from the timeand azimuth of this event as described in section 2 of the text.


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sector, with periapsis occurring south of the equator at1923 UT, at a radial distance of 3.276 RS. The vertical long-dashed lines drawn on either side of the equator indicatethe low-latitude region inside ±30� where the residual fieldsare smoothly varying compared with the structured fieldsat higher latitudes. Within the central low-latitude regionthe residual radial and colatitudinal fields in Figures 2aand 2b exhibit perturbations associated with the equatorialring current within the inner magnetosphere, namely acolatitudinal field that is negative and slowly varying acrossthe equator, and a radial component that reverses sense frompositive in the north to negative in the south. The azimuthalfield component in Figure 2c, which is expected to bedominated by the oscillatory field within this region, showsa rising value which passes through zero from negative topositive at the point indicated by the vertical dotted line.This occurs at �1729 UT, at a local time of 23 hours. Thussubstituting appropriate values of t and 8 into FM(t) � 8 =360N deg then yields yM = �83.6� to modulo 360� at thistime. The black dashed line in Figure 2c shows the modelazimuthal field given by equation (1b) using Provan et al.’s[2009] phase given by equations (4), (5), and (7), with anarbitrary amplitude of 4 nT. It can be seen that this curvepasses through zero from negative to positive close to theobserved position, showing that the yM value derived fromthis pass is close to that predicted at the relevant time byProvan et al.’s [2009] phase model. In fact the model phaseyM at the time of the zero obtained from equation (7) is�96.2� to modulo 360�, which thus differs from the abovevalue by only �13�.[11] Phase data derived using this technique from five

periapsis passes between Revs 58 and 63 to the end ofMarch 2008, are shown in Figure 1 by the blue stars. It canbe seen that these data are in good overall agreement with thephase model of Provan et al. [2009] given by equation (7)shown by the red line in Figure 1. A cubic polynomial fitto the whole data set including the new phase data pointsis found to differ insignificantly from the published model.On this basis we thus continue to use Provan et al.’s [2009]phase model given by equation (7) to estimate the magneticphase values during the February 2008 HST campaigninterval.

3. Southern Auroral Oval Phase Model

[12] We now similarly discuss the oscillations of Saturn’ssouthern auroral oval determined by Nichols et al. [2008]from the January 2007 and February 2008 HST campaignimages, before relating them to the equatorial magnetic fieldoscillations in section 4. Nichols et al. [2008] fitted theequatorward boundary of the UV auroral oval to a circle,and determined the position of the center of the circle relativeto the southern spin (and magnetic) pole of the planet in aCartesian system in which X points toward the Sun (within�2�) and Y toward dusk, both coordinates being expressedin length units corresponding to one degree of colatitude fromthe pole. The set of these positions for each campaign intervalwas then subject to Lomb periodogram analysis to determinewhether significant oscillations were present in either ofthese coordinates, and if so their period. Oscillations werefound near the planetary period in both X and Y coordinates

during both campaign intervals. Nichols et al. [2008] thendetermined the amplitude and phase of the oscillations bycross-correlation analysis assuming a common period tOvfor the X and Yoscillations during each campaign on the basisof the mean of those obtained from the Lomb analysis ofthe X and Y data. The oscillations are then expressed bythe formulae

X 0 ¼ X � xo ¼ a sin360t

tOv� 8xo

� �and

Y 0 ¼ Y � yo ¼ b sin360t

tOv� 8yo

� �;

ð8Þ

where xo and yo are the mean coordinate values about whichthe oscillations take place, t is the time since the start of theyear of the corresponding HST campaign (e.g., time since0000 UTon 1 January 2007 for the January 2007 campaign),and, as above, phase angles are expressed in degrees. Themean periods tOv, mean positions (xo, yo), amplitudes (a, b),and phases (8xo, 8yo) for each campaign data set determinedfrom this analysis and employed here are given in Table 1.Wenote that equivalent Table 1 of Nichols et al. [2008] givessome of these values in truncated form, depending on theuncertainty estimates. In particular, although we quote andemploy the derived mean oscillation periods tOv to threedecimal places, 10.764 hours for the January 2007 campaignand 10.765 hours for the February 2008 campaign as given inour Table 1, we note that the uncertainty in these valuesestimated from the width of the Lomb spectral peak isapproximately ±0.15 hours, such that they are quoted byNichols et al. [2008] only to two decimal places. Alsorecorded in our Table 1 for ease of reference are the periods ofthe magnetic field oscillations corresponding to the center ofeach campaign interval, determined from equation (2) and themagnetic phase FM(t) given by equations (4), (5) and (7).These values, 10.822 hours for the January 2007 campaignand 10.826 hours for the February 2008 campaign (withuncertainties about 2 orders of magnitude smaller than forthe oval oscillations), are each a little larger than thosedetermined from the oval position data, by about�0.06 hours(�3.5 min), but it is clear that these values are consistentwithin the uncertainties, principally of the periods deter-mined from the oval data. We also note from Table 1 thatthe oval oscillation amplitudes (a, b) in theX and Y directionsare typically �1�–2� of colatitude about a mean position(xo, yo) that is shifted by �2� from the planet’s pole toward�0300 LT (i.e., toward the nightside and dawn).[13] As discussed by Nichols et al. [2008], a point whose

motion is governed by equation (8) in general describes anellipse in the X-Y plane about (xo, yo) as center, with periodtOv. We may then define a new coordinate system centeredon (xo, yo) and rotated through angle 8R (again taken positivefrom noon in the direction of planetary rotation) such that theX* and Y* axes are aligned with the semimajor and semi-minor axes of the ellipse, respectively. The required angle ofrotation is given by

8R ¼ 1

2tan�1 2ab cos d

a2 � b2

� �; ð9Þ


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where d = 8xo � 8yo. In this shifted and rotated coordinatesystem the motion is then described by

X* ¼ a cos360t

tOv� 8*o

� �and Y* ¼ b sin

360t

tOv� 8*o

� �; ð10aÞ

where semimajor axis a and semiminor axis b are given by

a ¼ 1ffiffiffi2

p a2 þ b2� �

þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2 � b2� �2 þ 4a2b2 cos2 d

q 1=2ð10bÞ

and

b ¼ 1ffiffiffi2

p a2 þ b2� �

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffia2 � b2� �2 þ 4a2b2 cos2 d

q 1=2;

ð10cÞ

and phase angle 8*o is given by

8*o ¼ tan�1a sin8R sin8xo � b cos8R sin8yo

a sin8R cos8xo � b cos8R cos8yo

!: ð10dÞ

The oscillation parameters so determined from the January2007 and February 2008 campaign data are also given inTable 1. As indicated by Nichols et al. [2008], the motion isfar from circular in each case, instead describing an elongatedellipse whose semimajor axis is inclined by �36� from theX0 axis toward dawn. From equation (10a) the oval oscillationphase angle with respect to the rotated coordinates (X*, Y*) isgiven by

8*Ov tð Þ ¼ 360t

tOv� 8*o ; ð11Þ

where 8*o is given by equation (10d). The oval oscillationphase angle with respect to the unrotated coordinates (X0, Y0)is then given by

8Ov tð Þ ¼ 8*Ov tð Þ þ 8R ¼ 360t

tOv� 8*o þ 8R; ð12Þ

where 8R is the rotation angle between these coordinatesystems given by equation (9). We note, however, that theazimuthal angle of the oval displacement vector itself in thesecoordinates, given by

8OvD tð Þ ¼ tan�1 Y 0 tð Þ=X 0 tð Þð Þ; ð13Þ

is only exactly equal to that given by equation (12) (tomodulo 360�) when the vector lies on either the semimajor orthe semiminor axes of the ellipse (unless themotion is exactlycircular, a = b, in which case these azimuthal angles areidentical to modulo 360� at all times). These results, togetherwith the data given in Table 1, will now be used to comparethe oscillatory displacement of the oval derived from theHST images with the direction of the rotating equatorialmagnetic field discussed in section 2.

4. Phase Relation of Magnetic Field and AuroralOval Oscillations

[14] Results from the above analyses are shown inFigures 3 and 4 for the January 2007 and February 2008campaigns, respectively. These first show the oscillationellipses described by the center of the southern auroral ovalin (X0, Y0) coordinates (i.e., relative to the mean positions(xo, yo)) given by equation (8), where we recall that the X0

axis points toward the Sun and Y0 toward dusk. The view inFigures 3 and 4 is thus from the north looking ‘‘through’’the planet onto the southern polar region, such that thecenter of the oval moves around this ellipse in the directionof planetary rotation, anticlockwise in these plots, at theperiod tOv given in Table 1 in each case. The circles oneach ellipse show the position of the oval center at specifictimes during each HST campaign interval as given byequation (8), chosen here for definiteness such that thedisplacement is located on the sunward-displaced semimajoraxis of the ellipse. From equation (10a) the sequence of timesat which this occurs in each campaign is given by putting

360t

tOv� 8*o ¼ 360N ; ð14Þ

where N is any integer. For the January 2007 campaign wehave chosen three such times with N = 27, 42, and 57, sothat using the data from Table 1 and equation (14) we obtain

Table 1. Parameters Describing the ‘‘Planetary Period’’ Oscillations of the Center of Saturn’s Southern Auroral Oval During the Two

HST Campaigns as Employed in This Study, Together With the Corresponding Periods of the Magnetic Oscillations at the Center Time of

the HST Campaigns

Parameter

January 2007 HST Data February 2008 HST Data

X Y X Y

Magnetic field period, tM (hours) 10.822 10.822 10.826 10.826Mean oval oscillation period, tOv

a (hours) 10.764 10.764 10.765 10.765Mean position of oval center, (xo, yo)

a (degrees) �1.5 �0.9 �1.7 �1.4Amplitude of oscillation, (a, b)a (degrees) 1.20 0.94 1.81 1.31Oscillation phase, (8xo, 8yo)

a (degrees) 331 110 356 158Ellipse rotation angle, 8R

a,b (degrees) �36.0 �36.0 �35.5 �35.5Semimajor axis, aa (degrees) 1.4 1.4 2.2 2.2Semiminor axis, ba (degrees) 0.5 0.5 0.33 0.33Oscillation phase angle, 8*o (degrees) 46.4 46.4 79.9 79.9

aValues given in Table 1 of Nichols et al. [2008] (where some were shown in truncated form depending on uncertainty estimates).bAngle 8R is relative to the sunward direction, while the ‘‘ellipse orientation’’ quoted by Nichols et al. [2008] is relative to dawn-dusk.


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t = 12.168, 18.895, and 25.623 days (since 0000 UT on1 January 2007), corresponding to the start, middle, andend of the campaign interval spanning t = 12–26 days(13–26 January inclusive). Plots for these times are shown inFigures 3a–3c, respectively. Similarly, for the February 2008campaign we have chosen N = 69, 87, and 104, such that weobtain t = 31.049, 39.122, and 46.747 days (since 0000 UTon 1 January 2008), which are again near the start, middle,and end of the campaign interval spanning t = 31–47 days(1–16 February inclusive). Plots for these times are shownin Figures 4a–4c.[15] The straight solid lines drawn from the center of each

plot in Figures 3 and 4 show the direction of the rotatingmagnetic field in Saturn’s equatorial magnetosphere deter-mined from equations (3)–(5), at the same instants as forthe circles. In deriving these directions we recall that t inmagnetic field equations (1)–(5) corresponds to time indays since 0000UTon 1 January 2004, such that to the valuesof t given above for the two campaigns we add 1096 daysfor the January 2007 campaign interval, and 1461 days forthe February 2008 campaign. If the model rotation periodsof the oval and magnetic field were exactly the same, thesame phase relationship would be maintained over theinterval of each campaign, such that the field directions inFigures 3a–3c and in Figure 4a–4c would be the same.However, as noted above this is not quite the case, so that therelative phase drifts with time. Figures 3a–3c and Figure 4a–4cthus show how the orientation of the magnetic field, deter-mined at times when the model oval displacement is locatedon the sunward semimajor axis, varies over each campaigninterval. We emphasize, however, that physically we expectthe true periods of these two phenomena to be essentiallyidentical (which is certainly the case within errors), such thatthis phase drift is not a real physical effect, but insteaddemonstrates the uncertainty range associated with the phasemodels. During the January 2007 campaign the anglebetween the magnetic field direction marked by the solidline and the oval displacement vector marked by the dashedline (taken anticlockwise from the latter to the former)decreases from 207� in Figure 3a at the start of the campaign

Figure 3. Plots showing the ellipse described by the centerof the southern auroral oval relative to the mean values(xo, yo) during the January 2007 HST campaign (i.e., in(X0, Y0) coordinates), obtained from equation (8) and thevalues in Table 1. The view is from the north looking downonto the southern polar region, with X0 pointing towardthe Sun and Y0 toward dusk. These Cartesian coordinateshave length units equivalent to 1� of colatitude from the spin(and magnetic) pole. The circle on the oval (joined to thecenter by the dashed line) shows the position of the center ofthe oval at a specific time, chosen such that it lies in each caseexactly on the semimajor axis of the ellipse on the sunwardside at a time given by equation (14). The specific timeschosen are t = (a) 12.168, (b) 18.895, and (c) 25.623 dayssince 0000 UT on 1 January 2007, corresponding to timesnear the start, middle, and end of the January 2007 HSTcampaign interval (t = 12–26 days). The line drawn from theorigin then shows the direction of the rotating equatorialmagnetic field at the same instants of time, given byequation (3).


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interval, to 178� in Figure 3b near the middle of thecampaign, and to 149� in Figure 3c near its end. Thedecreasing angle is a consequence of the smaller modelperiod of the oval oscillation, such that the circle in theFigure 3 rotates anticlockwise once around the ellipse in aslightly shorter time than the line representing the fielddirection rotates once about the origin. Similarly, for theFebruary 2008 campaign the corresponding angle decreasesfrom 204� in Figure 4a at the start of the campaign, to 167� inFigure 4b near its middle, and to 133� in Figure 4c at its end.Although the model angular variations during each campaignare thus quite large,�60� for the January 2007 campaign and�70� for the February 2008 campaign, it can be seen that thedisplacement of the southern auroral oval from its meanposition is directed generally opposite to that of the oscilla-tory equatorial field in both cases.[16] A less graphic but more general presentation of these

results can be obtained by considering the angular differencebetween the azimuth of the equatorial magnetic field direc-tion and the phase of the southern oval oscillation given by

D8 tð Þ ¼ 8M tð Þ � 8Ov tð Þ; ð15Þ

where 8M(t) is given by equation (3) and 8Ov(t) byequation (12) (at appropriately defined common times t). Wenote that angle D8(t) corresponds directly to those quotedabove in relation to Figures 3 and 4 (valid at times when theoval is displaced along either the semimajor or semiminoraxes of the ellipse). The solid lines in Figure 5 thus showD8versus time over the intervals of each HST campaign (only),for the January 2007 (Figure 5 (top)) and February 2008(Figure 5 (bottom)) campaigns, respectively. It can be seenthatD8 falls slowly with time over both intervals for reasonsalready discussed above. However, the value passes through180� (horizontal dashed lines) during both intervals, closeto the center time for the January 2007 campaign (as inFigure 3), and nearer the beginning of the interval for theFebruary 2008 campaign (as in Figure 4). More exactly, forthe January 2007 campaign the model phase differencefalls from �208� at the beginning of the campaign to�148� at its end, with an averaged value of �178�, whilefor the February 2008 campaign the difference falls from�204� at the beginning to�132� at its end, with an averagedvalue of �168�. Again we emphasize that these variationsin essence represent uncertainty ranges rather than a realphysical variation. Overall, however, the results confirm theconclusion based on Figures 3 and 4, that the displacementof the southern auroral oval from its mean position isdirected nearly opposite to the direction of the rotatingmagnetic field in Saturn’s equatorial plane.

5. Relation to SKR Modulation

[17] In addition to considering the relation of the ovaloscillations to the rotating equatorial field, we can also use

Figure 4. As for Figure 3, but for the February 2008 HSTcampaign. The specific times chosen are t = (a) 31.049,(b) 39.122, and (c) 46.747 days since 0000 UT on 1 January2008, corresponding to times near the start, middle, and endof the February 2008 HST campaign interval (t = 31–47 days).


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the above phase models to address the issue of the relationof the oval displacements to the SKR power modulation.The relationship between the rotating equatorial field andthe SKR modulation has previously been discussed both byAndrews et al. [2008] and Provan et al. [2009], the latterover the interval from Cassini SOI in mid-2004 to the end of2007. Consistent with Andrews et al. [2008], the latterauthors found that SKR maxima as given by equation (6)

occur at equatorial field angles defined by equation (3) of8M = 210� ± 40�, equivalent to the field angle of�150� ± 40�quoted by Provan et al. [2009]. This condition thereforecorresponds to times when the rotating equatorial fieldpoints radially outward at a local time of 2.0 ± 2.5 hoursin the postmidnight sector, the uncertainty range lying withinthe overall scatter of the SKR and magnetic field phase data.Since southern oval displacements from their mean position

Figure 5. Plots of the phase difference D8 versus time (solid lines) between the equatorial magneticfield direction and the displacement of the southern auroral oval relative to its mean position, defined byequation (15). (a) Results for the 14 day interval of the January 2007 HST campaign, where time t isgiven in days since 0000 UT on 1 January 2007. (b) Results for the 16 day interval of the February 2008HST campaign, where time t is given in days since 0000 UT on 1 January 2008. The horizontal dashedlines at 180� correspond to oval displacements that are directed opposite to the equatorial field direction(exactly so when the oval displacement is located on the semimajor and semiminor axes of the oscillationellipse).


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are directed approximately opposite to the orientation of theequatorial field, as established in section 4 above, thisimplies that SKRmaxima should correspond to southern ovaldisplacements that are directed generally sunward. We nowconsider this qualitative conclusion in a little more detail.[18] The empirical model given by equation (5) describes

the phase of the SKR power modulation derived by Kurth etal. [2008] from Cassini radio data between 1 Jan 2004 and10 August 2007 (i.e., t = 0–1318 days), correspondingessentially to N = 0–2929 in equation (6). We may thereforeemploy these equations to estimate the times of SKRmaxima that occur during the January 2007 HST campaign,but not during the February 2008 campaign, and we thusrestrict our attention to the former. Although the SKRemission is a considerably variable phenomenon, examina-tion of relevant spectrograms indicates that equation (6) doesindeed give a reasonable account of the times of periodicSKR maxima over the January 2007 campaign interval.However, Kurth et al. [2008] also report that SKR emissionsare sometimes modulated with a rather shorter period of�10.6 hours in addition to the longer-period modulations at�10.8 hours that are more consistently present and describedby equations (5) and (6). According to Kurth et al. [2008],these shorter-period modulations were indeed present duringthe first HST campaign, though with an amplitude generallyless than that of the longer-period oscillations (see, e.g., theirFigures 5 or 11). Here we therefore continue to concentrateon the phase relations between the oval oscillations and thelonger-period SKR modulations, but will comment on pos-sible relations with the shorter-period modulations at theend of the section.[19] According to equation (6), a total of 31 periodic

maxima in the SKR power are expected during the intervalof the January 2007 HST campaign (t = 12–26 days). Thesestart with N = 2464 in equation (6) at t = 12.198, and endwith N = 2494 at t = 25.729 days, with the ‘‘middle’’maximum corresponding to N = 2479 occurring at t =18.963 days. We note that these times lie between �0.7and �2.5 hours later than those depicted in Figure 3, wherewe recall that the model oval displacement specifically layon the sunward-directed semimajor axis. In Figure 6 wethus similarly show the model location of the auroral ovaldisplacement and the direction of the rotating equatorialfield at the above times of SKR maxima corresponding to thestart, middle, and end of the campaign interval. Because themodel periods of the SKR and magnetic field oscillations arevery close to each other, differing by only �0.003 hours(i.e.,�10 s) during the campaign epoch [Provan et al., 2009],the equatorial field directions shown by the solid straightlines in Figure 6 are essentially the same in Figures 6a–6c.The angles 8M are 194.7�, 196.4�, and 198.1� in Figures 6a,

Figure 6. Plots showing the direction of the rotatingequatorial magnetic field and the displacement of the southernauroral oval from its mean position at times correspondingto SKR power maxima given by equation (6) during theJanuary 2007 HST campaign. The specific times chosenare t = (a) 12.198, (b) 18.963, and (c) 25.729 days since0000 UT on 1 January 2007, corresponding to times nearthe start, middle, and end of the January 2007HSTcampaigninterval (t = 12–26 days). Note that these times occur shortlyafter those shown in Figures 3a–3c in each case.


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6b, and 6c, respectively, such that the field points radiallyoutward at local times of 1.0, 1.1, and 1.2 hours, in confor-mity with the results of Provan et al. [2009] mentionedabove. However, because the model oval period is some-what smaller than both as previously discussed, the derivedphase of the model oval displacement at SKR maximavaries significantly over the campaign. At the start of thecampaign in Figure 6a, the model oval displacement at therelevant SKRmaximum lies just past the sunward semimajoraxis (8*Ov = 24.0� from equation (11)), corresponding to anazimuthal angle of the displacement relative to the X0 axisgiven by equation (13) of �26.9�. In the middle of thecampaign interval as shown in Figure 6b the phase angleincreases to 8*Ov = 54.4�, such that the displacement vectornow lies nearly on the X0 axis with an azimuthal angle relativeto X0 of�9.3�. Finally, at the end of the interval in Figure 6c,the oval displacement now lies nearly on the duskward-directed semiminor axis of the ellipse (8*Ov = 85.1�),corresponding to an azimuthal angle relative to X0 of 40.6�.Again, the phase drift of �60� over the campaign intervalmost likely represents the uncertainty ranges of these quan-tities rather than real physical variations. Overall, theseresults confirm that (the longer-period) SKR maxima duringthe January 2007 campaign correspond to southern ovaldisplacements in the sunward direction approximately alongthe X0 axis, roughly antiparallel to the tailward-pointingrotating equatorial field at these times. Further discussionof this finding is given in section 6 below.[20] We finally briefly discuss possible phase relations

between the oval and magnetic field oscillations and themore intermittent shorter-period (�10.6 hours) SKR powermodulations noted by Kurth et al. [2008]. Because a phasemodel of these modulations equivalent to equation (5) hasyet to be presented, an analysis equivalent to that givenabove for the longer-period SKR modulation cannot beundertaken. Nevertheless a few relevant comments can bemade. The first is that the magnetic oscillations observedwithin the magnetosphere are clearly related to the longer-period SKR modulations and not the shorter-period modu-lations. The overall difference in period between themagnetic oscillations and the longer-period SKR modula-tions is of order �0.001 hours (�4 s [see, e.g., Provan et al.,2009, Figure 5c]. More specifically, at the center of the2007 HST campaign interval the magnetic period given byequations (2), (4), and (5) is 10.822 hours (Table 1), whilethe longer-period SKR period derived from equation (5) is10.825 hours, the difference being �0.003 hours (�10 s)as indicated above. These deviations correspond to a fractionof an oscillation over the�3.5 years of common data studiedto date, as indicated in section 1. By comparison, thedifference in period between the magnetic oscillations andthe shorter-period SKR modulations is typically 2 orders ofmagnitude larger, �0.24 hours (�15 min) during the 2007campaign interval [see Kurth et al., 2008, Figure 5]. Thisdifference corresponds to a phase drift of �180�, from inphase to antiphase, every �10 days. Clearly there can existno consistent relation between the equatorial perturbationfield and the shorter-period SKR modulation over intervalseven as short as the HST campaign intervals.[21] The situation with regard to the oval oscillations is

not quite so clear-cut. Even so, the period of the ovaloscillations estimated by Nichols et al. [2008] (�10.76 ±

0.15 hours) lies rather closer to that of the longer-periodSKR modulation (�10.82 hours) than to the shorter-periodSKR modulation (�10.58 hours during the 2007 HSTinterval), by a factor of about three. The longer SKR periodlies well inside the uncertainty interval of the oval oscilla-tion period, while the shorter period lies just outside.Consequently, the phase drift of �60� between the ovaloscillation and the longer-period SKR modulation over the2007 HST interval noted above increases to �190� inrelation to the shorter-period SKR modulation over thesame interval. Thus, as for the magnetic field oscillations,the phase relation between the oval oscillations and theshorter-period SKR modulation over the 2007 HST cam-paign interval will be significantly less clear-cut than for thelonger-period SKR oscillations depicted in Figure 6.

6. Discussion

[22] As discussed previously by Nichols et al. [2008], itseems most likely that the oscillating oval displacementsinvestigated here are physically related to distortions of themagnetospheric magnetic field and its mapping to theionosphere that are directly associated with the observedrotating system of magnetic field perturbations, which is inturn produced by a rotating external current system. Theoverall system of magnetospheric magnetic field perturba-tions deduced from the study of Provan et al. [2009] issummarized in Figure 7a. In this diagram the dashed linesschematically represent the nonoscillatory ‘‘background’’field produced by the sum of the planetary field and themean ring current and tail-magnetopause current systems,shown in some meridian plane containing the planet withthe line marked ‘‘N–S’’ corresponding to the spin andmagnetic axes. The solid lines then represent the overalldirections of the oscillatory field perturbations at an instantof time when the rotating equatorial field discussed in thispaper points from left to right in this plane. The perturbationfield lines out of this plane can then be visualized bydisplacing the solid lines directly into and out of the planeof the diagram without significant distortion [see Provan etal., 2009, Figure 10b]. With increasing time this overallpattern of magnetic field perturbations rotates about thenorth-south (N–S) axis at the slowly variable period givenby equation (2), giving rise to the oscillatory signalsobserved throughout the magnetosphere.[23] If we then consider the magnetic perturbations in the

quasi-dipolar equatorial magnetosphere shown in Figure 7a,it can be seen that they consist of two components, a north-south (colatitudinal) component that is directed northwardon the left of the diagram and southward on the right, and anequatorial field that is directed from left to right, i.e.,radially inward on the left of the diagram and radiallyoutward on the right (this being the rotating quasi-uniformequatorial field that has formed the primary focus of ourdiscussion). The distortions of the background magneto-spheric field lines produced by these field perturbations areillustrated schematically in Figures 7b and 7c. Figure 7bshows the distortions produced by the north-south fields,which, in the idealized situation envisaged, produces sym-metric outward displacements of the field lines on the left,related to the associated weakening of the southward equa-torial planetary field by the northward perturbation field,


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and symmetric inward displacements on the right, related tothe corresponding strengthening of the equatorial planetaryfield by the perturbation field. Provan et al. [2009] suggestthat these field distortions are produced by the presence ofa rotating asymmetric equatorial ring current that is strongeron the left of the diagram than on the right at the oscillationphase depicted. No significant displacements of the field linefeet occur in the ionosphere, however, where the fieldstrengths are many orders of magnitude larger than theperturbation fields.[24] Figure 7c then shows the field line distortions

associated with the equatorial field directed from left toright. In this case following a field line from a given pointon the equator to the ionosphere shows that on the left of thediagram the field line feet are displaced poleward in thenorthern hemisphere and equatorward in the southern hemi-sphere, and vice versa on the right of the diagram. It cantherefore be seen that the field lines in the southern hemi-sphere are displaced toward the left at the instant depicted,i.e., in the direction opposite to the perturbation field simul-taneously present in the equatorial magnetosphere. This

displacement is therefore in the same sense relative to theequatorial field as found for the southern oval in section 4above, such that we suggest that this effect is directly relatedto the observed oscillations of the southern oval. We notethat the same direction of displacement is implicit in thefield modeling study briefly reported byNichols et al. [2008].With regard to the corresponding behavior in the northernhemisphere, unmeasured to date, we note that the simulta-neous displacement in Figure 7c is to the right at the instantdepicted, i.e., in the same direction as the equatorial pertur-bation field. This discussion therefore suggests that theoscillatory displacements of the oval will be oppositelydirected in the two hemispheres.[25] To put this result in somewhat different but related

terms, the magnetic moment of the rotating current systemthat gives rise to the magnetic perturbations shown inFigure 7a [see, e.g., Provan et al., 2009, Figure 11] isdirected parallel to the equatorial field in the low-latitudemagnetosphere, thus pointing from left to right in Figure 7.When combined with the planetary dipole pointing upwardin the Figure 7, the overall dipole is thus tilted toward the

Figure 7. (a) Sketch showing the nature of the observed perturbation fields associated with themagnetic oscillations near the planetary period. The dashed lines schematically represent the nonoscillatorybackground field principally due to the internal field of the planet, shown in a meridian plane containing theplanet. The line marked N–S (‘‘north’’ and ‘‘south’’) corresponds to the planet’s spin and magnetic axes.The solid lines represent the overall directions of the oscillatory field perturbations at an instant of timewhen the rotating equatorial field points from left to right in this plane. The perturbation field lines out ofthis plane can be visualized simply by displacing the solid lines directly into and out of the plane of thediagram without significant distortion. With increasing time this overall pattern of field lines then rotatesabout the north-south axis at the slowly varying period given by equation (2). (After Provan et al. [2009].)(b) Sketch of the field line distortions in the closed field region associated with the north-south fieldperturbations shown in Figure 7a, directed to the north on the left and to the south on the right, as indicatedby the arrows. The initial field lines are shown by the dashed lines, while the perturbed field lines originatingfrom the same positions in the ionosphere are shown by the solid lines. (c) Sketch of the field line distortionsin the closed field region associated with the equatorial field perturbations shown in Figure 7a, directed fromleft to right on both sides of the planet, as also indicated by the arrows. The initial field lines are again shownby the dashed lines, while the perturbed field lines originating from the same positions in the equatorialplane are shown by the solid lines.

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right, such that the northern oval will also be displaced tothe right, in the direction of the equatorial field, while thesouthern oval will be displaced to the left, opposite to thedirection of the equatorial field as observed. A corollary ofthis picture is that the magnetic equatorial plane where theradial field changes sign will also become tilted relative tothe spin equator in accordance with the tilt of the overalldipole, such that, e.g., the northward normal to the magneticequator is, like the dipole, also tilted to the right in Figure 7c(away from the strong ring current sector), as can be seenfrom the field lines shown. A rotating tilt of the magneticequator relative to the spin equator will therefore also occuras the current system and associated magnetic perturbationsrotate about the north-south axis, leading also to a rotatingtilt of the equatorial magnetospheric plasma populations.Oscillatory tilting of the equatorial plasma sheet in the noon-midnight plane near the planetary period has recently beenreported by Carbary et al. [2008b], using Cassini energeticneutral atom images. A detailed analysis of the phase of theseoscillations has yet to be undertaken, but since we know thatthe equatorial perturbation field and transverse dipole pro-duced by the external current system points approximatelytailward at SKR power maxima (e.g., Figure 6), the northernnormal of the magnetic equator and plasma sheet should alsotilt tailward relative to the spin and magnetic axis at suchtimes. This is indeed the phasing of the plasma sheet tiltfound by Carbary et al. [2008b], such that the rotatingequatorial field perturbations, the tilting plasma sheet, andthe oscillating auroral oval together form a consistent picture.Although this discussion may thus provide an initial basis forunderstanding the relations between these phenomena, wenote that it gives no immediate explanation for the stronglyelliptical nature of the observed oval motions.[26] With regard to the physical origins of these phe-

nomena, we note that both Provan et al. [2009] andKhurana et al. [2009] have invoked the presence of arotating asymmetric ring current as a central feature, asmentioned previously in section 1. However, while Provanet al. [2009] attribute the above effects to a seasonal hemi-spheric asymmetry in the field-aligned currents that closethe ring current through the ionosphere, Khurana et al.[2009] instead invoke the seasonal dependence of the solarwind flow direction relative to the tilted spin and magneticaxis of the planet. Interestingly, these two pictures lead toopposite predictions as to the sense of the equatorial tiltingrelative to the strong ring current sector, which may providea means to distinguish between them. For example, underthe southern summer conditions which have prevailedduring the initial phase of the Cassini mission, Khuranaet al.’s [2009] model predicts that the northward normal tothe magnetic equator is tilted toward the sector containingthe enhanced ring current, while Provan et al.’s [2009] modelpredicts that it is tilted away. Both effects would reverse insense under northern summer conditions.[27] We finally comment on the relation between the

oscillatory field and oval tilting phenomena discussed hereand the modulation of the emitted SKR power. In the modeldiscussed by Provan et al. [2009] it is suggested that themodulated emissions are produced by accelerated electronsflowing down the field lines in the rotating system ofupward-directed field-aligned currents that are connectedto the enhanced sector of the equatorial ring current. The

phasing of the SKR modulation then suggests that theelectron acceleration and radio power output are at a maxi-mum when the upward-directed current region is centered inthe postdawn sector, with the enhanced ring current on thedayside. The equatorial perturbation field and effectivetransverse dipole then point tailward for southern summerconditions (as observed to date), or sunward for northernsummer conditions. The reason that the dawn sector isfavored for maximum radio output (and by implicationmaximum field-aligned current density) is not presentlyunderstood, but it has long been known that SKR emissionfavors the prenoon sector [e.g., Lecacheux and Genova,1983; Galopeau et al., 1995]. Further, in Provan et al.’s[2009] picture (unlike that of Southwood and Kivelson[2007]) the senses of the field-aligned currents in the twohemispheres at a given local time are always the same as eachother, either outward or inward, though stronger in thesummer than in the winter hemisphere. Thus it is plausiblewithin this picture that radio emissions from the northern andsouthern hemispheres are modulated in phase with eachother, as is also well established to occur [e.g., Lamy et al.,2008], though again possibly being stronger in the summerthen the winter hemisphere. If the configuration describedabove with upward-directed field-aligned currents in thedawn sector is the key feature of SKR power maxima, thenthe relationship to the auroral oval displacement is simplythat the summer oval is displaced sunward and the winteroval displaced tailward at SKR maxima. Thus while theresults in section 5 show that under southern summer con-ditions the southern oval is displaced sunward at SKR powermaxima, in conformity with this discussion, we then expectthat under northern summer conditions the northern ovalwould instead be displaced sunward at SKR power maxima.

7. Summary

[28] In this paper we have examined the phase relation-ship between the oscillations of Saturn’s southern auroraloval determined by Nichols et al. [2008] from UV imagesobtained during two HST campaigns, in January 2007 andFebruary 2008, and the rotating equatorial magnetic fieldperturbations studied by Provan et al. [2009] over theinterval 2004–2007. The magnetic phase model derivedin the latter study thus encompasses only the first HSTcampaign interval, but field data from the first quarter of2008 have been used to verify that the model may appro-priately be extrapolated to the February 2008 HST campaigninterval. We have also examined the relationship of the ovaloscillation phase to the SKR power modulation phase deter-mined by Kurth et al. [2008] from 2004 to mid-2007, butonly for the January 2007 HST campaign in that case. Ourprincipal findings are as follows.[29] 1. The displacement of the southern auroral oval

from its mean position was found to be directed approxi-mately opposite to the direction of the rotating magneticfield in the equatorial plane for both HST campaigns.Specifically, the phase difference between these oscillationswas found to be �180� ± 30� during the January campaign,and �170� ± 35� during the February 2008 campaign, thequoted uncertainties arising primarily from the slight dif-ference in periods deduced for the oval and magnetic fieldoscillations during the campaign intervals.


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[30] 2. Since periodic SKR maxima occur at times whenthe rotating equatorial field points approximately tailward,as previously determined by Andrews et al. [2008] andProvan et al. [2009], the displacement of the southern ovalat these times is directed approximately sunward. Exami-nation of the SKR phase model of Kurth et al. [2008]during the January 2007 HST campaign interval indicatesthat the oval displacement from its mean position at SKRmaxima is directed within �±35� of the sunward direction.Possible relations with the shorter-period SKR modulationsduring the campaign interval reported by Kurth et al.[2008] are less clear-cut by a factor of three.[31] 3. It is suggested that the oscillating oval displacement

is related to magnetospheric field line distortions associatedwith the observed rotating magnetic field perturbations. Inparticular, the presence of a rotating quasi-uniform equatorialfield in the near-equatorial magnetosphere will lead torotating shifts in the feet of closed field lines in the southernionosphere in the sense determined. The correspondingrotating shift in the northern hemisphere, as yet unobserved,is directed opposite to that in the south, thus being in thesame sense as the rotating equatorial field. This picture isconsistent with the periodic tilting of the equatorial plasmasheet reported recently by Carbary et al. [2008b]. However,the picture provides no immediate explanation for thesignificantly elliptical nature of the observed oval motion,which indicates a significantly greater response of thesouthern oval in the prenoon to premidnight direction thanin the orthogonal direction. The general relation to the SKRmodulation is suggested to be one in which the summer ovalis displaced sunward at SKR power maxima.

[32] Acknowledgments. This work was supported by STFC grantPP/E000983/1. We thank M. K. Dougherty, S. Kellock, and the Cassiniteam at Imperial College London for access to the processed magnetic fielddata. We also thank W. S. Kurth for access to Cassini RPWS spectrogramsfor the January 2007 HST campaign interval and for helpful comments andD. L. Talboys for aid with the display of these data. We also thank A. F.Farmer for helpful comments on the field line displacements in themodeling study reported by Nichols et al. [2008].[33] Wolfgang Baumjohann thanks James F. Carbary and another

reviewer for their assistance in evaluating this manuscript.

ReferencesAndrews, D. J., E. J. Bunce, S. W. H. Cowley, M. K. Dougherty, G. Provan,and D. J. Southwood (2008), Planetary period oscillations in Saturn’smagnetosphere: Phase relation of equatorial magnetic field oscillationsand SKR modulation, J. Geophys. Res., 113, A09205, doi:10.1029/2007JA012937.

Carbary, J. F., and S. M. Krimigis (1982), Charged particle periodicity inthe Saturnian magnetosphere, Geophys. Res. Lett., 9, 1073 – 1076,doi:10.1029/GL009i009p01073.

Carbary, J. F., D. G. Mitchell, S. M. Krimigis, and N. Krupp (2007a),Electron periodicities in Saturn’s outer magnetosphere, J. Geophys.Res., 112, A03206, doi:10.1029/2006JA012077.

Carbary, J. F., D. G. Mitchell, S. M. Krimigis, D. C. Hamilton, and N. Krupp(2007b), Charged particle periodicities in Saturn’s outer magnetosphere,J. Geophys. Res., 112, A06246, doi:10.1029/2007JA012351.

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��S. W. H. Cowley, J. D. Nichols, and G. Provan, Department of Physics

and Astronomy, University of Leicester, University Road, Leicester LE17RH, UK. ([email protected])


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