Magnetic Fields of the Outer Planets

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. El0, PAGES 18,659-18,679, OCTOBER 25, 1993

J. E. P. CONNERNEY

Laboratory for Extraterrestrial Physics,NASA Goddard Space Flight Center, Greenbelt, Maryland

It is difficultto imaginea groupof planetarydynamos more diversethan thosevisited by the Pioneer and Voyager spacecraft.The magneticfield of Jupiteris largein magnitudeand hasa dipole axis within 10ø of its rotation axis, comfortably consistent with the paleomagnetic history of the geodynamo. Saturn's remarkable(zonal harmonic) magneticfield has an axis of symmetry that is indistinguishable from its rotation axis (<<1 ø angular separation);it is also highly antisymmetricwith respect to the equatorplane. Accordingto one hypothesis,the spin symmetrymay arisefrom the differentialrotation of an electrically conductingand stably stratified layer above the dynamo. The magnetic fields of Uranus and Neptune are very much alike, and equally unlike those of the other known magnetized planets. These two planets are characterized by a large dipole tilts (59ø and 47ø, respectively) and quadrupole moments (Schmidt-normalizedquadrupole/dipole ratio -•1.0). These properties may be characteristicof dynamo generationin the relatively poorly conducting"ice" interiors of Uranus and Neptune. Characteristicsof these planetary magneticfields are illustrated using contour maps of the field on the planet's surfaceand discussedin the context of planetary interiors and dynamo generation.

INTRODUCTION Jupiter's magnetic field [Ness et al., 1979a, b]. Voyagers 1 and 2 would both continue onward to Saturn, obtaining The study of the geomagnetic field had progressed for additional observations of Saturn's magnetic field in Novem- many years before the landmark publication of De Magnete ber 1980 and August 1981 [Ness et al., 1981, 1982]. Voyager in 1600, in which William Gilbert demonstrated that the 2 continued on its "grand tour" of the solar system, with the Earth's magnetic field was like that of a bar magnet. Obser- discovery of the magnetic field of Uranus in January 1986 vations of the terrestrial magnetic field have been gathered [Ness et al., 1986] and that of Neptune in August 1989 [Ness for hundreds of years, recorded by mariners and explorers et al., 1989]. Voyager 2's remarkable tour of the outer solar on voyages to distant lands as well as by students of system was made possible by the celestial alignment of the magnetism. Such direct measurements quickly demon- planets, the syzygy, which occurs every 187 years or so. strated that the Earth's magnetic field varies slowly with Very few additional opportunities to add to our present time. Global surveys of the magnetic field were initiated knowledge of outer planet dynamos will be forthcoming in periodically, at first by ships and more recently by polar- the near future. For the planet Jupiter, these include the orbiting near-Earth satellites such as MAGSAT [Langel et encounter of the Ulysses spacecraft in February 1992 [Ba- al., 1982] which provide a wealth of observations of the field, logh et al., 1992] and observations to be obtained by the acquired during a brief interval of time and well distributed Galileo Orbiter, now en route to Jupiter, beginning in 1995 over the globe. In addition, by studying the magnetic prop- [Johnson et al., 1992]. Neither of these missions was de- erties of terrestrial rocks, paleomagnetists can extend the signedwith an emphasis on mapping the planetary magnetic history of the geodynamo over time scales of hundreds of field of Jupiter. New observations of Saturn's magneto- millions of years. sphere will be available early in the next century if the In contrast, prior to 1955, one could but speculate on the Cassini Orbiter remains on schedule. nature of extraterrestrial dynamos (excepting those of the Our knowledge of the magnetic fields of the outer planets Sun and stars). The existence of Jupiter's magnetic field was is thus confined to one or more flyby encounters, separated inferred from the detection of nonthermal radio emissions by at most a few years (summarized in Table 1). The associatedwith the planet [Burke and Franklin, 1955]. In the observationsare sparsein both spatial distribution and time, decades that followed, numerous estimates of the gross particularly considered in light of the data available for the characteristicsof Jupiter's magneticfield (e.g., the dipole tilt study of the geomagneticfield. They are, however, sufficient and phase) were deduced from variations of the plane of to provide a surprisingly comprehensive understanding of polarization of the emissions or variations in flux density the magnetic fields of the outer planets and provide fresh (see, e.g., the review by Berge and Gulkis [1976]). The first new constraints to guide the continued development of in situ observations of the Jovian magnetosphere were dynamo theory. obtained by the Pioneer 10 and 11 spacecraft in December 1973 and December 1974, respectively [Smith et al., 1974, OFFSET TILTED DIPOLE MODELS 1975; AcutTa and Ness, 1976]. The Pioneer 11 spacecraft Various dipole models have found use in the interpretation continued on to make the first observations of Saturn's of magnetic field observations, dating to Gilbert's analysis of magnetic field as well [Smith et al., 1980a, b; Acu•ia and the Earth's magnetic field. The vector magnetic field B(r) of Ness, 1980]. On the heels of the Pioneers came Voyagers 1 a dipole at the origin is given by and 2, passing through the Jovian magnetosphere in March and July of 1979, providing yet another set of observationsof This paper is not subject to U.S. copyright. Published in 1993 by [ m3(m.r)r.] r the American Geophysical Union. wherem is themagnetic moment in unitsof B-r 3 andr = Paper number 93JE00980. The field of a dipole located near the origin, at x0, Y0, z0, is

18,659 18,660 CONNERNEY' MAGNETIC FIELDS OF THE OUTER PLANETS

TABLE 1. Planetary Encounters mum along a field line), multiple dip equators (where B ßn = 0; n is the surface normal vector), and complex field geom- Year Jupiter Saturn Uranus Neptune etries, require a model with more comprehensive parameter- 1971 ization. 1972 1973 Pioneer 10 1974 Pioneer 11 SPHERICAL HARMONIC MODELS 1975 1976 1977 The observed magnetospheric magnetic field can be re- 1978 garded as the sum of contributions from several sources, 1979 Voyagers 1, 2 Pioneer 11 dominated by that due to the planetary dynamo (interior 1980 Voyager 1 source) which is of primary interest. The interaction of the 1981 Voyager 2 planetary field with the solar wind generates magnetopause 1982 1983 surface currents and tail currents which can be regarded as 1984 external sourcesif they are located well outside of the region 1985 of measurement. The relatively small field due to these 1986 Voyager 2 sourcesmust in general be modeled along with the planetary 1987 field if an accurate model is to be obtained from limited or 1988 1989 Voyager 2 distant observations. In the absence of local currents (V x B 1990 = 0), the magnetic field may be expressedas the gradient of 1991 a scalar potential V (B = -VV). It is particularly advanta- 1992 Ulysses geous to expand the potential V in a series of functions, 1993 1994 called spherical harmonics, that are solutionsto Lapiace's 1995 Galileo equationin sphericalcoordinates. This approach, introduced 1996 by Gauss in 1839, has been overwhelmingly popular in 1997 studies of the geomagnetic field. The traditional spherical 1998 1999 harmonic expansion of V is given by [e.g., Chapman and 2000 Bartels, 1940; Langel, 1987]

computed by translating the origin of the coordinate system. V=a n• 1 Tne+ The offset tilted dipole (OTD) models of planetary magnetic fields are found using forward modeling techniques to com- where a is the equatorial radius of the planet. The first series pare in-situ observations of the field to the OTD model field. in increasing powers of r represents contributions due to Since the dipole offset is not linearly related to the computed external sources, with field, an iterative solution to the linearized system is often n used to find the optimal dipole position [e.g., Smith et al., 1976]; this method is sometimes referred to as a "walking Tne= Z (pnm(cos O)[Gn mcos (mtb)+ Hn m sin dipole." Another approach is to perform a spherical har- m=O monic analysis (see next section) of degree and order 1 centered upon each of a large number of candidate dipole The second series in inverse powers of r represents contri- positions in the vicinity of the origin, selecting the offset butions due to the planetary field or internal sources, with which minimizes the model residuals. In either case, the n result is the OTD which most closely approximates the field measured along the spacecraft trajectory. T•= Z {pnm(cøsO)[gn mcos (mtb)+hn msin The simple OTD representation provides a convenient rn=O approximation to the field, particularly useful at larger radial distancesfrom the planet. It is useful both in visualizing the The Pnm (cos 0) are Schmidt quasi-normalizedassociated gross characteristics of the field and in describing, in an Legendrefunctions of degree n and order m, and the t7nm , approximate way, the motion of charged particles through- hnm and Gnm , Hnm are the internal and external Schmidt out much of the planet's magnetosphere. However, the coefficients,respectively. These are most often presented in simplicity of the OTD representation is also a limitation, in unitsof Gaussor nanoteslas(1G = 105nT) for a particular that complex field geometries cannot be adequately repre- choice of equatorial radius a of the planet. Distances are sented with such a limited parameterization. If we assume mostoften given in unitsof theplanet radius R e , sothat one that the magnetic field is produced by currents within a may set a = 1 above. For some planets, slightly different volume characterized by the spatial scale a, then in general, values of the equatorial radius have been used and shouldbe a dipole representation can be expected to closely approxi- noted in the comparisonof various field models. The angles mate the field for radial distances r >> a. At lesser radial 0 and qbare the polar anglesof a sphericalcoordinate system distances, an accurate description of the field requires con- 0 (co-latitude) measured from the axis of rotation and qb sideration of higher degree and order moments. Many of the increasingin the direction of rotation. The three components features that make a planetary magnetic field interesting, of the magnetic field of the planet (internal field only) are e.g., warpedmagnetic equators (where IBI reachesa mini- obtained from the expression for V above' CONNERNEY:MAGNETIC FIELDS OF THE OUTER PLANETS 18,661

TABLE 2. Schmidt Quasi-Normalized Legendre Functions

Br= Or Legendre Function -•=n•= • m=0 • (n+1) [gnmcos(mo) P1ø=(1) cos0 +h•m sin (m•b)]P• m(cos 0)} P• = (1) sin0

P• = (31/2)COS 0 sin0 = - n cos (mqb) Bø=rO0 n•l= m=0Z [gm

dPn +h nm sin (m•b)] rndO(COS '5(3)1/2• -1 ov P3•= ,2(2)m/]sin0(cos 20- 3/15) rsin 0 O0 = COS0sin 2 0 sin0n•• = m=0• m [gnmsin (mqb) p32 ((3) 1/2(5)2 1/2•) -hnmcos (m•b)]Pn m(cos 0)) P33=•2(2)•/2 ] sin30 The leading terms in the series may be computed using the Schmidt quasi-normalized Legendre functions listed in Table P•=(•)[cos4 0- (30/35)cos2 0+ (3/35)] 2. (7(5),/2• Observations of the outer planets are most often rendered P]= •2(2)m ) cos0 sin 0(cos 20 - 3/7) in a west longitude system, in which the longitude of a = sin2 0 (cos2 0- 1/7) stationary observer increases in time as the planet rotates. p•(7(5)m) 4 West longitudesare simply related to the angle & by • = 360 /(7)1/2(5) 1/2• - qb.For Jupiter, the most recent version of this coordinate =[, 0 30 systemis •iii(1965), which reflects the most recent revision to the planet's rotation rate. For each of the outer planets, = sin4 0 8 the rotation period of the planet is inferred from observa- p•((7) 1/2(5)1/2 ) tions of episodic radio emissions, which, by assumption, are locked in phase with the rotation of the planet's magnetic The leading term (in parentheses) converts the functions from field and hence the electrically conducting deep interior of Gaussian normalization, convenient for recursive computations, to the planet. An earlier version of this coordinate system Schmidt quasi-normalized form. (•iii(1957)), based on a slightly different rotation rate, was used for observations obtained during the Pioneer era. These two systems result in significantly different longitudes when external fields such as that encountered at Jupiter. Space- observations of the Pioneer era are compared with those of craft traversing the Jovian magnetosphere have all encoun- the Voyager era, so one must be careful to transform earlier tered the ubiquitous presence of a large-scale equatorial results to a current coordinate system. A detailed descrip- current system associated with the Jovian magnetodisc tion of the evolution of Jovian coordinate systemsis given by [Connerney et al., 1981]. This disc-like system of eastward Dessler [1983]. Similarly, for Saturn, Uranus, and Neptune, azimuthalcurrents extends from the orbitof Io (at 5.9 Rj) to the rotation periods and longitude system in use are derived beyond50 Rj. Sincethe magneticfield producedby these from Voyager observations of radio emissions [Desch and local currents cannot be represented by the gradient of a Kaiser, 1981; Desch et al., 1986; Warwick et al., 1989]. As scalar potential function, the representation of B described the time base of available observations at each planet grew, above is augmented with a small field of external origin, b, more precise determinations of the rotation period were due to local currents (within the region of measurement). available. In the case of Neptune, the Voyager Project This latter contribution has been modeled explicitly with Steering Group ultimately adopted a definition of the zero both empirical models and fully self-consistent magnetohy- longitude in such a way as to minimize differences in drodynamic models [Connerney, 1981; Connerney et al., longitudes during the Voyager encounter resulting from 1982a; Caudal and Connerney, 1989], allowing the simulta- changesin the assumedrotation period. neous determination of planetary field parameters and those The expansion in increasing powers of r, representing of the magnetodisc. A more general modeling approach to external fields, may be truncated at n = Nmax = 1 corre- the analysis of poloidal and toroidal magnetic fields has been spondingto a uniform external field due to distant magneto- proposed by Backus [ 1986] but has not yet found application. pause and tail currents. On rare occasions,expansion of the The maximum degree and order required of the internal external field to degree and order 2, representingan external field expansion depends on the complexity of the field field that grows linearly with r, has been utilized [e.g., Smith evidenced in the region of measurement. The traditional et al., 1976] as a means of approximating more complex (i.e., terrestrial) application of spherical harmonic analysis 18,662 CONNERNEY'.MAGNETIC FIELDS OF THE OUTER PLANETS

exploitsthe orthogonality of theLegendre functions over the x0 = a(L1 - g•T)/3m2 unit sphere.If the availableobservations are suitablydis- tributedon the surfaceof a sphere,the SchmidtcoeffÉcients Yo= a(L2- h•T)/3m2 canbe estimatedindependently. In usualpractice, the series aboveis truncatedat somemaximum degree and order Zo= a(Lo- g•øT)/3m2 Nmax, whereNma x is sufficientlylarge to wellrepresent the observedfield, but not so large as to introducemore free wherem 2 = (91ø)2 + (gl1 )2 + (h•)2 and parameters than can be determined from the observations. L0 = 290lg2 0 + 3 1/2(g 1921 1+ h 1h2 1 ) (Thenumber of freeparameters grows rapidly with increas- ingNmax, as rtp= (Nmax + 1)2 - 1.)If, onthe other hand, L1= -g•g21 0 + 31/2( 9192 0 1+ g•g• + h•h22) theobservations are poorly distributed or sparse,this prac- ticecan lead to largeerrors. Each of theouter planets has L2 = -hlg1 20 + 31/2( glh2- 0 1 hlg1 2 + g•h22) beenvisited by one or morespacecraft on flyby trajectories, someapproaching close to the planet,others remaining T= (Lo.q•+ Lig• + L2h• )/4m2 relativelydistant. The Legendre functions are not orthogo- This translationresults in a new set of sphericalharmonic nal on the trajectoryof the spacecraft,so in general,esti- coefficients(g•',g•',h•'=gl ø,g•,h• ;g20'=g•' =h2•' matesof the Schmidtcoefficients cannot be independently= o; g22' , h22' = gi, forthe quadrupole; thedipole determined.Furthermore, if an arbitrarilysmall choice of coefficientsremain unchanged. Ignoring the quadrupole m = Nmax is imposedupon the model (in order to obtain a 2 terms,and any higher degree and order terms, one may manageablelinear system), large errors in low degreeand associatewith anyspherical harmonic expansion an "eccen- orderterms will resultfrom the neglect of higher-orderterms tric dipole" modelapproximation, much like the OTD dis- with whichthey covary. To addressthese problems, Con- cussedpreviously, consisting of a dipole(g•0, g•, h•) nerneyintroduced a method of analysisbased upon the use locatedat x0, Y0, z0 as givenabove. The dipoletilt and of the singularvalue decomposition of Lanczos.The method offsetvector of theeccentric dipole may be expectedto be involvesthe construction of partial solutions to thegeneral- similarto that of the OTD, but in general,they are not izedinverse problem [Connerney, 1981] to obtainestimates equivalent.The former is a simpleabstraction of anyspher- of thoseparameters which are constrainedby the observa- icalharmonic model, which remains well-defined regardless tions.The model parameters which are not constrained by of hownondipolar the field is or howthe sphericalharmonic the dataare readilyidentified and exploited in characteriza- coefficientswere determined.The OTD is the OTD which tion of modelnonuniqueness. One advantage of thisap- bestfits a givenset of observations;it may only be used proachis that the physicalmodel of the planetaryfield (e.g., fit to observations)where the field is reasonably dipolar,at somedistance from the planet. Like the OTD, the (expansionto degree and order Nmax) is not dependent upon the completenessor extent of the availableobservations. A eccentricdipole approximation provides a meansof easily visualizingthe gross characteristicsof the field. partialsolution constructed in thismanner, and estimates of themodel parameters that result, must be interpreted within the contextof the "resolutionmatrix" for the particular JUPITER solution[see Connerney, 1981; Connerney et al., 1991]. Jupiter,the largest (Rj = 71,372km) andmost massive (Mj -- 318 M e) planetin the solarsystem, resides at a mean "ECCENTRIC DIPOLE" MODELS orbitaldistance of 5.2 AU fromthe sun.Jupiter's consider- It is customaryto chosethe gravitationalcenter of the able mass and orbital velocity can be used to boost a planetas the originof the sphericalharmonic expansion of spacecraftto muchgreater radial distances from the sun,or themagnetic field, but it is notnecessary to do so.Expan- to achievehigher solar latitudes(Ulysses), than would sion abouta centeroffset from the originwill resultin otherwisebe possible. For thisreason, Jupiter's orbit serves quadrupole(degree n = 2) coefficientsthat differfrom those asa crossroadsfor travelersto theouter planets (Table 1). It is themost frequented magnetic planet in the solarsystem obtainedby expansionabout the origin; quadrupole param- (excepting Earth). eterscovary with the parameters(x0, Y0, z0) of the offset Long before the first in situ observations of the Jovian vectorto the new origin.By suitablechoice of origin,it is magnetospherewere obtainedby Pioneer10 in 1973[Smith possibleto minimizethe mean squared amplitude of thefield et al., 19741,the magnetic field of Jupitermade its presence dueto termsof degreen - 2 averagedover the surfaceof a known via escapingnonthermal radio emissions.Burke and sphere (R2): Franklin[1955] first detecteddecameter wavelength emissions(22 MHz) fromJupiter, which could readily be identi- n fiedas nonthermal in origin.This discovery led to specula- Rn=(n+ 1) • {(gnm)2+(hnm) 2} tion that Jupiterpossessed a significantmagnetic field of m=0 internalorigin and motivatedsynoptic observations of Jo- vianradio emissions at a varietyof wavelengthsby Earth- Thisnew origin, often referred to asthe "magneticcenter" boundobservers and spacecraft alike (reviewed by Berge of the planet,can be foundfrom the sphericalharmonic andGulkis [1976] and Carr et al. [1983]).Not untila large coefficientsofthe expansion about the origin (e.g., Chapman bodyof observationsat decimetric(of order1 GHz) wave- andBartels [1940], Smith et al. [1976],and Langel [1987]; lengthshad accumulateddid it become clear that this latter notesign errors in the firstand third reference): emissionwas synchrotron radiation, emitted by high-energy CONNERNEY' MAGNETIC FIELDS OF THE OUTER PLANETS 18,663 electrons trapped in a Jovian Van Allen belt. At the often 240 ø 270 ø 300 ø observed wavelengths of 6-30 cm, the emitting region ex- / tendsover a distanceof a few Rj, confinedto a region JUPITER extending along the Jovigraphic equator [Radhakrishnan and Roberts, 1960; de Pater, 1980, 1981]. From models of 210 ø 330 ø this synchrotron radiation, it was possible to infer the tilt (9.5ø) and phase (200ø Aiii) of the Jovidipole [Morris and Hr9 Berge, 1962], the dipole offset from the center of the planet, Hr0 the sense of orientation of the magnetic field [Warwick, 180 ø 6 1963b], and the approximate dipole moment, all prior to (1965) Pioneer 10's arrival. However, only the tilt of the dipole and the sense of the field was well established prior to the Pioneer 10 encounter. The magnitude of the field could not be determined accurately, nor was there agreement on the 150 ø 30 ø offset of the dipole from the planet's center. For example, Warwick's analysis of decameter radiation (in the frequency range 8-41 Mc/s) led him to concludethat the Jovian dipole / 120 ø 90 ø 60 ø hada momentof11.7 G-R• and was offset from the center of I i i I I the planet by as much as 0.75 of the planet's radius [War- 10 5 0 5 10 wick, 1963a, b], mostly along the axis of rotation. These RADIAL DISTANCE (Rj) predictionswould not be confirmedby Pioneer 10, but serve Fig. 2. System III longitude (Aiii) of Pioneer 10 and 11 space- to remind us that this type of low-frequency radio emission craft as a function of radial distance throughout the close encounter can be very difficult to interpret unambiguously. interval. Pioneer 1l's retrograde trajectory provided a very favor- Pioneer 10, the first spacecraft to enter the voluminous able spatial distribution of observations for internal field modeling. Jovianmagnetosphere, passed within 2.8 Rj of theplanet at closest approach in December 1973. A year later, Pioneer 11 approachedto within1.6 Rj of theplanet at closestapproach secondis better suited to analyses of the planetary magnetic on a retrograde trajectory. Of these two encounters, the field. There are two major reasons for this; the fact that Pioneer 11 approached closer to the planet than Pioneer 10 is not one of them. The first advantagethat Pioneer 11 enjoyed 20 was the relatively good (for a flyby) spatial distribution of the observations, as is illustrated in Figures 1 and 2. The Pioneer JUPITER 11 trajectory provided measurements over a wide range of planet latitudes (Figure 1) and longitudes (Figure 2). Pioneer

15 11's retrograde trajectory enabled it to complete a full sweep of 360ø in planetary longitude in a short 4.5-hour time span, during which the radial distance of the spacecraft remained 1 ß in the range4 Rj > r > 1.6 Rj. A secondfull 360ø longitude coverage was provided at somewhat greater radial distances, 10 but still within 10 Rj of the planet.The secondadvantage provided by the Pioneer 11 trajectory is its avoidance of the ß15 Jovian current sheet, a large-scale system of azimuthal currentsextending from about5 Rj radialdistance to well '• •2 PIo ,• .,. over 50 Rj (Figure1). It is this currentsystem which gives I the Jovian magnetosphere its disclike magnetic field geome- / , try andname "magnetodisc." Approximately 300 x 106A of current flows in this system of ring currents, contributing significantlyto the magnetic field measured in situ by space- / - :•:•.•::•::•::•::•?:CU R R E N T ::•::•::f:•::•?•,.•:•j•.•9.•.:.•:.•.:•i•: craft [Connerney et al., 1981; Connerney, 1981]. Spherical harmonic analyses of Pioneer 11 observations were rela- Hr3 • • • ...... tively successful because the region of current flow lies outside the region of measurement. The Pioneer 10 observa- -5 ß ,. , tions were obtained at lower latitudes, largely within the Hr0 region of current flow (Figure 1), where potential field - ' methods alone are not sufficient to model the observed field. These two encounters provided two OTD models of -10 I I I Jupiter's magnetic field (D2 and D4), shown in Table 3, and 0 5 10 15 20 a host of spherical harmonic models (reviewed by Smith et 0 (Rj) al. [1976]) obtained from the Vector Helium Magnetometer (VHM) observations. Note that these models were rendered Fig. 1. Projection of the Pioneer 10 and 11 spacecrafttrajecto- ries in a cylindrical coordinate system aligned with the dipole axis. in a coordinate system (Am(1957)) that differs from that The magnetodisc current sheet occupies an extensive region (Am(1965)) in general use today. Comparison of models boundedby z -< 2.5 Rj andp -> 5 Rj. obtained from the Pioneer 10 and Pioneer 11 VHM observa- 18,664 CONNERNEY: MAGNETIC FIELDS OF THE OUTER PLANETS

TABLE 3. OTD Magnetic Field Models

Jupiter P10 Jupiter P11 Saturn Uranus Neptune

M 4.00 4.23 0.20 0.23 0.13 0, deg 10.6 10.8 0.0 60.0 46.8 •b, deg 195. 201. N/A 48. 79.5 Irl 0.11 0.10 0.04 0.31 0.55 r x -0.11 -.10 0.00 -0.02 0.17 ry 0.00 0.00 0.00 0.02 0.46 r z 0.03 0.01 0.05, 0.04 -0.31 -0.24 Model D 2 D 4 N79D, OTD OTD OTD

N/A, not applicable' D2, D 4 [Smith et at., 1976], N79D [Smith et at., 1980b], Saturn OTD [Acut•a et at., 1980], Uranus OTD [Ness et at., 1986], Neptune OTD [Ness et at., 1989]. Angle •brendered in west longitude system. tions left open the possibility of a secular changeof up to 5% between the Pioneer 11 encounter in 1973 and that of of the total field in a year's time [Davis and Smith, 1976]. Voyager 1 in 1979. A spherical harmonic expansion of the The Pioneer 11 spacecraft was also instrumented with a planetary field to degree and order 6 was combined with an high-field vector fluxgate magnetometer which obtained ob- explicit model of the magnetodisc, as in previous studies, to servations throughout the inner Jovian magnetosphere. represent the field due to magnetodisccurrents. The param- Analyses of these observations suggested that the limited eters of the planetary field through and including the octu- parameterization of the OTD models was not sufficient to pole (n = 3) were obtained by construction of a partial describe Jupiter's magnetic field; ultimately, this investiga- solution; terms of higher degree and order cannot be re- tion provided the 04 sphericalharmonic model [Acutia and solved (with the available data). Construction of partial Ness, 1976] which is in widespread use today. solutions via the singular value decomposition method si- The two Voyager encounters followed in March and July multaneously minimizes the residual (difference between of 1979 on trajectories comparable to that of Pioneer 10 in model and observation) as well as the magnitude of the that both remained near the Jovigraphic equator throughout parameter vector. The expectation (a priori information) that encounter, confined to low magnetic latitudes. Voyager 1, the magnitude of harmonic terms decreaseswith increasing targeted for a close flyby of the Io flux tube, approachedto degreewas introduced by weighting harmonic terms with the within 4.9 Rj of Jupiter;Voyager 2 remainedrelatively weight(rc/a) n+2 where rc, thecore radius, was taken to be distant(r -> 10Rj) andwould measure a fieldgreatly altered 0.7a, where a is the planet radius. The Schmidt coefficients by the magnetodisc currents. At Voyager 2's closest ap- of the resultingmodel ("06" model) are listed in Table 4. proach, the 0 component of the planetary field is decreased The "06" model of Jupiter's magneticfield benefitsfrom by about 30%, and the radial field component increased by a the inclusion of two sets of spacecraft observations in its similar amount. These trajectories are ideal for studying the derivation, which provides better spatial distribution of magnetodisc currents [Connerney et al., 1981] but are less observations, and consequently more tightly constrained well suited in some respects for constraining the planetary model coefficients.Unlike all previous models, the 06 model field. Initial spherical harmonic analyses of the Voyager 1 observationsyielded a considerably reduced dipole moment, which was attributed to the presence of magnetodisc currents which were not adequately modeled [Ness et al., EARTH JUPITER 1979a]. Subsequentanalyses of the Voyager 1 observations, glO in which the magnetodisc currents were explicitly modeled, resulted in a partial octupole model of the planetary mag- (nT) (nT) netic field [Connerney et al., 1982a]. Allowing the param- 30,400 421,800 eters of the magnetodisc current sheet model and the parameters of the planetary field to be determined simultaneously provided a means of separating the fields of external origin 30,300 420,300 from those generated in Jupiter' s core. The Voyager 1 model of the field, as it was observed in 1979, could be compared 30,200 418,800 with the Pioneer 11 model (GSFC 04) of the field appropriate to the year 1973 to greatly constrain any possible Jovimag- 30,100 417,300 netic secularvariation (of g•0) to no morethan 0.2%/yr [Connerney and Acutia, 1982]. By comparison, the present- day decreasein the terrestrialg•0 term is about0.075%/yr 30,000 415,800 (Figure 3). I A new octupole model of Jupiter's magnetic field, ob- 1965 1970 1975 1980 1985 1990 tained using suitably weighted observationsfrom both Pio- YEAR neer 11 and Voyager 1, and a priori information about Fig. 3. Seculardecrease of theEarth's main g •0term (left scale) Jupiter's harmonic spectrum, has recently been introduced comparedwith the two available estimatesof Jupiter's main dipole [Connerney, 1992]. This model was derived under the as- term (right scale). One vertical division represents0.033% of the sumptionthat the magneticfield has not changedappreciably main dipole term in each case [from Connerney and Acut•a, 1982]. CONNERNEY:MAGNETIC FIELDS OF THE OUTER PLANETS 18,665 derivation provides for the possibility of the existence of I i i contributions of higher degree than octupole (n = 3). The . NEPTUNE 06 model is characterized by smaller quadrupole and octu- 1.0 pole moments, relative to the comparable 04 model of URA ' ""'. Acut•a and Ness [1976], and in that regard is more Earth-like in harmonic content (Figure 4). The similarity is also evident upon inspection of the "eccentric dipoles" (Table 5) computed for both planets. After preliminary analyses of the Ulysses encounterobservations, Balogh et al. [1992] report close agreement between the observed magnetic field and that predicted using a model magnetospherebased upon the 0.1 ••'"\• JUPITER '04 MODEL - 06 planetary field augmentedwith the magnetodisccurrent sheet model [Connerney et al., 1981]. Since the Ulysses close approach observationswere obtained in the immediate - • 06 MODEL vicinity of the inner edge of the current sheet, estimation of the planetary magnetic field parameters presupposes an \\ e• /e effective separation of the observed field into internal and external components. This is a difficult task that will require further analysesbefore the intriguingpossibility of Jovimag- 0.01 netic secular variation can be examined anew. The magnitudeof the surfacefield for the 06 model ranges from just over 3 G in the equatorial region to slightly over 14 2 3 4 G in the north polar region. This is similar to the range of DEGSEE N field magnitudespredicted by the 04 model of Acut7a and Ness [1976]. The variation of magnetic field magnitude on Fig. 4. Relative magnetic spectrum of the planets Jupiter, Sat- urn, Uranus, and Neptune, compared with that of the Earth. For the surfaceof Jupiteris illustratedin Figure 5, which depicts Jupiter the magnetic spectrum is computed for the 04 model of contours of constant field magnitude on the dynamically Acut7a and Ness [1976] and an alternate model (06) which mini- flattenedsurface of Jupiter,computed using the 04 model.A mizes the quadrupole and octupole moments. prominent north-south asymmetry in the field is evident upon comparison of the maximum field in the northern hemisphere(14 G) with that of the southernhemisphere (11 nitude on the surface of each planet. Field magnitudes are G). Figure 5 also illustrates the foot of the Io flux tube ("Io color coded using the color bar shown between the two foot"), which is the path traced out on the planet's surface planets, which represents fields ranging in magnitude from by the field lines which pass through the satellite Io as the 0.2 G to 0.7 G in the case of the Earth, and 2.0 G to 14.0 G planet rotates. The foot of the Io flux tube passesthrough the for Jupiter. Both planets are viewed from a central meridian region of highest field strengthin the northern hemisphereat longitude (CML) of 180ø, but the projection of the Earth's a longitude of about 150ø AiiI. The maximum surface mag- magnetic field is shown (uncharacteristically) with south netic field magnitude present along the Io foot is consistent latitudes at the top of the figure, a view which increases the with the maximum frequency extent (39.5 MHz) of Jovian apparent similarity of the magnetic fields of Earth and decameter radio emission (DAM), assumingthat the emis- Jupiter. sion occurs at the local electron gyrofrequency and at the foot of the Io flux tube (fc[MHz] = 2.8 B[G]). In Plate 1 we SATURN compare the magnetic field of Jupiter with that of the Earth, viewing a sinusoidalequal-area projection of the field mag- Saturn, the second largest (Rs = 60,000 km) and most massive(Mj = 95 Me) planetin the solarsystem, resides at a mean orbital distance of 9.5 AU from the sun, nearly twice the distanceof Jupiter' s orbit. Unlike Jupiter, Saturn did not TABLE 4. Jupiter 06 Magnetic Field Model Schmidt- Normalized Spherical Harmonic Coefficients reveal the existence of its magnetic field prior to the first (Jupiter Radius of 71,372 km) spacecraftreconnaissance, the Pioneer 11 flyby in Septem- ber 1979. Saturn is both too weak a radio source and too n rn gnm h•n distant to be easily detected from Earth. Saturn radio

1 0 4.24202 emission is largely confined to lower frequencies (a few 1 1 -0.65929 0.24116 kilohertz to 1 MHz), well below the critical frequency 2 0 -0.02181 required to penetrate the Earth's ionosphere, and thus 2 1 -0.71106 -0.40304 cannot be monitored using terrestrial radio receivers. While 2 2 0.48714 0.07179 several attempts had been made to detect Saturn radio 3 0 0.07565 3 1 -0.15493 -0.38824 emissionsprior to the Pioneer 11 encounter, it appears that 3 2 0.19775 0.34243 none were successful [see Kaiser et al., 1984]. 3 3 -0.17958 -0.22439 The discovery of Saturn's magnetic field was thus left to visiting spacecraft, the first of which was Pioneer 11. The These coefficients are referenced to Jupiter System III (1965) coordinates;coefficients given (Gauss)to five decimalplaces not as particle and fields investigations on board Pioneer 11 ob- an indication of parameter uncertainty but as an aid in conversionto tained observations along a spacecraft trajectory that re- nanoteslas(ignore decimal point). mained within approximately 6ø of the equator (Figure 6). 18,666 CONNERNEY: MAGNETIC FIELDS OF THE OUTER PLANETS

TABLE 5. Eccentric Dipole Models

Earth Jupiter Saturn Uranus Neptune

M 0.306 4.300 0.2154 0.228 0.142 0, deg 11.2 9.4 0.0 58.6 46.9 •b, deg 70.8 200.1 N/A 53.6 72.0 Irl 0.076 0.119 0.038 0.352 0.485 rx -0.060 -0.103 0.000 -0.157 0.047 ry 0.039 -0.059 0.000 0.025 0.483 r z 0.027 0.003 0.038 -0.314 0.002 Parentmodel GSFC1283 06 Z3 Q3 08

Eccentric dipole model parametersare derived from sphericalharmonic models as describedin the text. The referencesfor the parent(spherical harmonic) models are as follows:GSFC1283 [Langel, 1987], 06 [Connerney,1992], Z3 [Connerneyet at., 1982b],Q3 [Connerneyet at., 1987], 08 [Connerney et at., 1991]. Angle •brendered in west longitude system.

The two magnetic field investigations determined that Sat- southern latitudes [Ness et al., 1981, 1982]. The three urn's magneticfield was well approximatedby a dipole with encounter trajectories are compared in Figure 6, which a momentof 0.20G-Rs 3 , slightlyoffset to thenorth of the shows the subspacecraft latitude as a function of longitude planet's center [Smith et al., 1980a; AcuKa and Ness, 1980; throughout the near encounter interval. The radial distance Acuffa et al., 1980] by about 0.04 or 0.05 Rs. The most of each spacecraftis also indicated numerically at regular remarkablefeature of Saturn's magneticfield proved to be intervalsalong the trajectory. Pioneer 11 approachedclosest the close alignmentof the magneticdipole and rotation axes, to the planet but sampleda very limited range of planetary alsonoted by the chargedparticle investigations [Simpson et latitudes and longitudes. In contrast, Voyagers 1 and 2 al., 1980; Van Allen et al., 1980]. The simple northward- remainedmore distant, but provided a greater spatialdistri- offsetdipole model was affirmedby independentanalyses of bution of observations, of great benefit in constraining charged particle absorption signatures[Chenette and Davis, models of the magnetic field. These observations were not 1982]. These Pioneer 11 OTD models are listed in Table 3. consistentwith the field of a simpledisplaced dipole, nor did Analysesof the Pioneer 11 high-fieldfluxgate magnetometer these observationsreveal any measurable departure from observations[Acuffa et al., 1980]found no departureof the spin-axisymmetry.An axisymmetric, zonal harmonic model field from axisymmetry; however, in Saturn's relatively of degree 3 was found to be both necessaryand sufficientto weak field, the resolution of this instrument was quite describethe magnetic field of Saturn as measuredby Voy- limited. Working with higher resolution observations ob- ager 1 and 2 [Connerney et al., 1982b]. This three- tained by the helium magnetometer, Smith et al. [1980b] parameter model is referred to as the Z3 model (zonal averred that a dipole tilt of the order of 1ø was experimen- harmonic of degree 3) and it is listed in Table 6; the tally well established,although the orientationof the dipole nonaxisymmetricterms (m > 0) are explicitly shown in this could not be determined. table to emphasizethe high degree of axisymmetry of the The Voyager 1 encounter in November 1980 and the field. Independentanalyses of the Voyager 1 and 2 observa- Voyager 2 encounter in August 1981 provided the first tions suggeststhat the Z 3 coefficientsare known to an observationsof Saturn's magneticfield at high northernand accuracy of about 100 nT (0.001 G). The magnetic and

TOTALSURFACE FIELD INTENSITY GSFC04 MODEL 90 ø

L A T I T U D E

Fig. 5. Contours of constantmagnetic field magnitude(gauss) on the dynamicallyflattened (1/15.4) surfaceof Jupiter, computed using the 04 model of Acutia and Ness [1976]. The foot of the Io flux tube is indicated with dots which map alongfield lines to equally spaced(20 ø longitudeincrements) points along Io's orbit. CONNERNEY: MAGNETIC FIELDS OF THE OUTER PLANETS 18,667

MAGNETIC FIELD OF JUPITER AND EARTH and Smith [1985, 1986] obtained a zonal harmonic model in substantialagreement with the Z3 model listed in Table 6. The Z3 model leads to field magnitudeson the surface of a dynamically flattened Saturn (flattening 1/10.6) ranging from JUPITER 06 MODEL a minimum of 0.18 G at the equator to maxima of 0.65 G at the south pole and 0.84 G at the north pole (Figure 7). Note that Saturn is the most dynamically flattened of all the planets, and the magnitude of the field in the polar regions is substantially increased by the decreased radial distance to the surface of the planet at the poles (0.9 Rs). The Z3 equatorial field magnitude is less than that of a simple dipole or offset dipole, and the Z3 polar field magnitudes (both north and south) those of the centered or offset dipole. An eccentricdipole representationof the Z3 model (Table 5) has a northward displacementof the dipole of 0.038 R s along the 2.0 6.0 10.0 14.0 rotation axis, in agreement with the Pioneer 11 OTD repre- IBI GAUSS sentations.However, the ratioof #30/#20is too largeby a

0.2 0.3 0.4 0.5 O.6 0.7 factor of 30 to be attributed to a dipole offset. The Z3 model's large antisymmetry with respect to the equator plane cannot be removed by a simple coordinate system translation. Saturn is unique among the magnetized planets with regard to the high degree of spin axisymmetry of its magnetic field. This unanticipated symmetry is somewhat disquieting from both a theoretical and an observational perspective.

MAGNETIC FIELD OF URANUS AND NEPTUNE

EARTH GSFC 12/83

Plate 1. Sinusoidal equal-area projection of the magnitudeof the URANUS Q3 MODEL magnetic field on the surface of Jupiter and Earth, computed using the 06 model magneticfield of Jupiter and the GSFC1283 model of the terrestrial magnetic field. Colors are assignedto field magnitudes 270 according to the color bar shown. Note that the magnitude scalesfor Earth and Jupiter differ and that the Earth's field is shown with south latitudes toward the top of the figure. Both planets are viewed from a CML of 180 ø.

rotation axes are indistinguishable, aligned to within approximately 0.1 ø. A series of analyses followed which supported the accu- lEVI(GAUSS) racy of the Z 3 model and the high degree of axisymmetry of the field (reviewed in Connerhey et al. [ 1984b]). Acut•a et o 0.5 1 .o al. [1983a] showed that the charged particle absorption signaturesobserved in Saturn's magnetosphere were consistent with the Z 3 model. A reanalysis of the absorption signaturesstudied by Chenette and Davis [1982], but allow- O•,W ing for the presenceof a nonzero#30 term, foundthese N• signatures to be best fit by a zonal harmonic model which was indistinguishablefrom the Z 3 model [Connerneyet al., 1984b]. A retrospective analysis of the Pioneer 11 vector helium magnetometer observations was performed which demonstrated that these measurements were consistent with the Z3 model field, and axisymmetry, to better than the level NEPTUNE •-• os MODEL of accuracy of the measurement [Connerney et al., 1984a]. Connerney et al. identified in those observations a spacecraft Plate 2. Sinusoidal equal-area projection of the magnitude of the roll attitude error (of 1.4ø in magnitude) as the primary magnetic field on the surface of Uranus compared with that on the source of the discrepancy between the Pioneer and Voyager surface of Neptune. Colors are assignedto field magnitudes according with the color scale shown between the two planets, from a results. The roll attitude error was subsequently verified by minimum of 0 G (black) to a maximum of 1 G (red). Neptune, viewed independent analysis of Pioneer 11 imaging photopolarime- from a CML of 150ø, appears much like Uranus, viewed from 180ø ter data. After correcting for the roll attitude error, Davis CML. 18,668 CONNERNEY'MAGNETIC FIELDS OF THE OUTER PLANETS

40*

4 I • VOYAGœR 2

20* --7--•*•• ,o z.?'. • -'--'---•+I--L-_ Io PIONEER"

0 o •CCULTATION:• EARTH• • 4 1.3R s .•0• b••• ••• -20'

-40' 3 I• 180 ø 90 • 360 • 270 • 180• 90 ø 0 ø WEST LONGITUDE

Fig. 6. Close flyby trajectories of Pioneer 11 (dashedline), Voyager 1 (light solid line), and Voyager 2 (bold line) in Saturnographiccoordinates. The variation of subspacecraftlatitude, SLS longitude, and planetocentric radial distance(in Rs) is shown for each encounter.

The well-known Cowling antidynamo theorem [Cowling, helium raindrops results in a stably-stratified conducting 1937, 1957] state that regenerative dynamo action cannot shell which, in differential rotation with respect to the core, occur if the magnetic field and fluid motions are axisymmet- attenuates any nonaxisymmetric fields generated below. ric. This observation, and the observation that the magnetic The axisymmetric field provides no ready explanation for fields of Earth, Jupiter, and Mercury all favor dipole tilts of observationsof periodic magnetosphericphenomena, such approximately 10ø in magnitude, contributed to an expecta- as the rotation modulation of Saturn kilometric radio emis- tion of a similar dipole tilt for all planets. However, the sion [Desch and Kaiser, 1981; Kaiser and Desch, 1982], Cowling antidynamo theorem applies to the field in the optical spoke activity in Saturn's B ring [Porco and Daniel- dynamo region, not to the field observed above the conduct- son, 1982], and auroral ultraviolet intensity [Sandel et al., ing core; axisymmetric magnetic fields are thus not an 1982]. The presence of an undetected magnetic anomaly has insurmountable problem for dynamo theory [e.g., Lortz, been invoked as a possible explanation for each of the 1972]. It is, however, necessary to explain why Saturn's above. However, it is not clear how a necessarily slight magnetic field is so dramatically different from Jupiter's departure of the magnetic field from axisymmetry would magnetic field, given that these planets are similar in size, influence these phenomena, which occur at different mag- composition, and rotation rate. Stevenson has proposed a netic latitudesand as far as 1 or 2 R s above the surfaceof the model of Saturn's magneticfield in which the field is axisym- planet. In the case of the earth, which has a substantially metrized by the differential rotation of an electrically con- nonaxisymmetric magnetic field, there is no demonstrable ducting shell above the dynamo region [Stevenson, 1980, longitudinal variation of terrestrial kilometric radiation 1982; also Kirk and Stevenson, 1987]. This nonconvecting shell forms above the dynamo region as a result of the immiscibilityof helium and hydrogenunder the temperature, pressure conditions in this region (the larger planet, Jupiter, would have no such region). In this model, the formation of

I I I I I 90 ø , i , • : l//•, .: TABLE 6. Saturn Z 3 Magnetic Field Model Schmidt- Normalized Spherical Harmonic Coefficients (Saturn Radius of 60,000 km) c• 60 ø

n m anm hnm <• 30 øI- ••..,<.,•.• SURFACEMAGNETIC fi ELD 1 0 0.21535 1 1 0.0 0.0 I- .•/..,•" MAGNITUDE 2 0 0.01642 o /•1• I , (fliattENlING =' / 'i0'6)I 2 1 0.0 0.0 .2 .3 .4 .5 .6 .7 .8 2 2 0.0 0.0 GAUSS 3 0 0.02743 3 1 0.0 0.0 Fig. 7. Magnetic field magnitude as a function of latitude on the 3 2 0.0 0.0 Saturn's oblate surface (flattening 1/10.6), computed using the 3 3 0.0 0.0 axisymmetricZ 3 model, an offsetdipole model (OD), and a centered dipole model. Field magnitudesat southern latitudes are given by Coefficients given (Gauss) to five decimal places not as an the dashed line, and those appropriate to northern latitudes are indication of parameter uncertainty but as an aid in conversionto indicated by solid lines; the symmetric centered dipole model nanoteslas(ignore decimal point). From Connerney et al. [1982b]. (dotted) curve applies to both hemispheres. CONNERNEY.'MAGNETIC FIELDS OF THE OUTERPLANETS 18,669

[Green and Gallagher, 1985] or auroral brightness [Frank and Craven, 1988]. Nevertheless, Galopeau et al. [1991] • 6o have proposed nonaxisymmetricSaturn magneticfield mod- • 50 els based upon observations of Saturnian kilometric radio emission (see also comments by Connerney and Desch •z 40 [1992] and Ness [1993]). • 30 Another peculiarity of Saturn's magnetic field is evidenced when one examines the radial dependenceof the radial field component. The radial field componentis of interest since it • METALLICH-He. •J• INSULATINGH2-H e is continuousacross the core boundary, and if the frozen flux assumption is satisfied, serves as a tracer of horizontal fluid •o •0 motion at the outer extremity of the dynamo [Backus, 1968; .._fi,•I I I I I i I I I Benton, 1979; Benton and Muth, 1979]. Downward extrap- .2 .3 .4 .5 .6 .7 .8 .9 1.0 olation of the field is fraught with pitfalls, due to uncertain- RADIUS (Rs ) ties in higher-degreeterms (and neglect of the same), but in Fig. 9. Low-latitude (___45ø) unsigned flux on the surface of a the following we will consider the field of a zonal harmonic sphere, as a percentage of total flux, for spheres of radius 0.2-1.0 of degree n = 3 only. In Figure 8 we show the latitudinal Rs, computed using the Z3 model magnetic field (solid line). This variationof IBrl, computedusing the Z3 model, on the quantityis a minimumfor a sphereof radius0.5 R s, coincidentwith surface of a sphere of radius r = 0.5 Rs, which is the the outer radius of the conducting core. approximate outer boundary of the metallically conducting core [Stevenson,1983]. The Z3 model(via the #• term) enhances the field at the poles and reduces the radial field unsignedflux acrossthe core surface. Of course, this may be near the equator, relative to a simple dipole. As a reference, nothing more than a simple coincidence. However, it is note that a dipole has one half of its unsigned flux between interesting to consider whether this characteristic may be an +45 ø latitude and -45 ø latitude, and of course, this is unanticipated consequenceof the differential rotation of the independentof radial distance.But the Z3 model field will outer core envisioned by Stevenson. put a greater or lessor fraction of its unsigned flux between -+45ø latitude, depending on the spherical surface chosen, URANUS AND NEPTUNE due to the (l/r) n+2 dependenceof the field of termsof Uranus and Neptune, residing at a mean orbital distance harmonic degree n. Figure 9 illustrates how the percentage of 19.2 and 30 AU, are the most distant of the Jovian planets. of unsignedflux at low latitudes (between +_45 ø) varies with Very little was known of either of these planets prior to the the radius chosen. For the Z3 model field (solid line), a Voyager 2 encounters with Uranus in January 1986 and choice of r = 0.5 Rs actually minimizes the percentageof Neptune in August 1989. At such a distance, they both unsignedflux at low latitudes. As is illustrated in Figure 9, appear bland and featureless when observed from the Earth this coincides with the outer radius of Saturn's metallically even under the best circumstances. They are known to be conducting core. Alternately, one can assume that the core similar in size (approximately 25,000 km radius), mass radius is indeed 0.5 Rs, and attempt to minimize the (about 15 Earth masses), and presumably composition unsigned flux at low latitudes by suitable choice of zonal (largelylow-temperature condensates, or "ice": H20, NH3, harmonics,as illustratedin Figure 10. The Z3 modelis very CH4). Uranus, however, is unique in that its rotation axis nearly identical to that required to minimize the low latitude lies very nearly in its orbital plane, which is inclined by less

90 ø 50 [• g•O=.21535 x 60 ø

• 40 z g2ø=.o1642 30ø//•o•, •' '•3'MODEL g3ø-- .02743 z oo EQUATOR ' 30

o _30 ø

zI,- 20 _60 ø

I _90 ø I 0 2 4 6 F I I I MINIMUM I (rcUNSIGNED=0.5 IR s)FLUX I GAUSS 0.0 .01 .02 .03 .04 .05 g3ø (gauss-Rs5) Fig. 8. Magnitude of the radial componentof Saturn's magnetic field as a function of latitude on the surfaceof a sphereof radiusr = Fig. 10. Low-latitude unsignedflux on the surface of a sphere of 0.5 R s, computedusing the Z3 magneticfield model (solidline). For radiusr = 0.5 Rs, as a functionof the magnitudeof the#• term. comparison, the radial field of the dipole term only is also shown The Z3 model coefficientsare very nearly identical to those which (dashed line). minimize this quantity. 18,670 CONNERNEY'MAGNETIC FIELDS OF THE OUTER PLANETS

TABLE 7. Uranus Q3 Magnetic Field Model Schmidt- OTD representation of the field (Table 3). The Uranus OTD Normalized Spherical Harmonic Coefficients is characterizedby a dipoleof moment0.23 G Ru3 (1 R u = (Uranus Radius of 25,600 km) 25,600 km), displacedalong the rotation axis by 0.33 Ru and n rn gnm hnm inclined by 60ø with respect to the rotation axis [Ness et al., 1986]. 1 0 0.11893 The very large dipole offset of the OTD is an indication of 1 1 0.11579 -0.15684 2 0 -0.06030 a planetary magnetic field with a large quadrupole, i.e., a 2 1 -0.12587 0.06116 very complex field. Spherical harmonic analysis of the field 2 2 0.00196 0.04759 required an expansion to degree and order 3 (octupole) to adequately represent the measurements [Connerney et al., Coefficients given (Gauss) to five decimal places not as an indication of parameter uncertainty but as an aid in conversion to 1987], which is somewhat surprising in view of Voyager's nanoteslas(ignore decimal point). From Connerney et al. [1987]. relatively large periapsis. The distribution of observations was sufficient to resolve, or determine, only the spherical harmonic terms of degree 1 and 2, the dipole and quadru- than 1ø to the ecliptic plane. The actual inclination of its pole, by partial solution to the underdetermined inverse equatorial plane to that of its orbit is 82ø . Twice during each problem. The resulting model, designated "Q3" (Quadru- orbit about the Sun (84 years), the rotation axis is oriented pole part of an expansion to degree and order 3), is listed in very nearly along the planet-Sun line, so that we on Earth Table 7. As anticipated, the relative magnitude of the qua- look upon the pole. The Voyager 2 encounter in 1986 drupole is quite large (Figure 4); the octupole is likely to be occurred at just such a time. large as well, but cannot be meaningfully constrainedby the Neither planet was known to have a magnetic field prior to Voyager observations.The quadrupoleQ3 model is the best the Voyager encounter. The first radio emissions from representation of the field available, yet it may be limited in Uranus and Neptune were not detected, or recognized, until accuracy near the planet, where lack of knowledge of higher just prior to the entry of the spacecraft into the magneto- degree terms may be an important consideration. This is, of sphere [Desch et al., 1991; Warwick et al., 1989; Gurnett et course, a natural consequenceof the limited data available. al., 1989]. This was due in part to the fact that each is a An eccentricdipole representationbased upon the Q3 model relatively weak radio source, emitting only at lower frequen- coefficients (Table 5) shares many of the same characteris- cies (below about 1 MHz). In the case of Uranus, the tics as the OTD: a large dipole tilt, and a large spatial offset peculiar encounter geometry dictated by the orbital phase of of the magnetic center of the planet. However, the offset of Uranus at the time of encounter also masked radio emissions the eccentric dipole has a sizeable component in the planet's from early detection, as they were beamed away from the equator, whereas the OTD offset is primarily antiparallel to observer. Voyager 2, on a flyby trajectory approaching to the rotation axis. within 4.2 Ru radial distance, provided the first measure- The magnetic field magnitude on the surface of Uranus ments of the magnetic field [Ness et al., 1986]. These reaches a maximum of approximately 1 G at mid-latitudes in measurements led to the rather surprising discovery of the the south, and a minimum of -<0.1 G at middle to high first "oblique rotator," a planet with a large angular separa- northern latitudes (Figure 11). Figure 11 also illustrates the tion between magnetic and rotation axes. Preliminary anal- foot of the Miranda flux tube, which is the path traced out on yses of the Voyager magnetic field observations used an the planet's surface by the field lines which pass through the

SURFACE TOTAL INTENSITY MODEL Q3 • 90

-30

-60

-90 360 270 180 90 0 WEST LONGITUDE Fig. ]]. Contours of constant magnetic field magnitude (gauss) on the dynamically flattened (]/4].6) surface of Uranus, computedusing the Q3 sphericalharmonic model. An estimatedauroral oval (shaded),the foot of the Miranda flux tube, and multiple magnetic dip equators (dashed lines) are shown. For comparison, the locations of the OTD magnetic poles (positive/negative) are indicated by a circled dot and circled cross, respectively [Ness et at., 1986]. Figure is from Connerney et at. [1987]. CONNERNEY: MAGNETIC FIELDS OF THE OUTER PLANETS 18,671 satellite Miranda as the planet rotates. Also shown are TABLE 8. Neptune 08 Magnetic Field Model Schmidt- estimates of the position of the aurorae (stippled regions) and Normalized Spherical Harmonic Coefficients (Neptune Radius of 24,765 km) the paths of multiple-dip equators (where B r = 0). Uncer- tainties in the higher degree and order components of the n rn gnm hnm field, which are substantial, may lead to large differences in the actual surface field, particularly in the weaker field 1 0 0.09732* 1 1 0.03220* -0.09889* regions. For this planet the intuitively appealing conceptu- 2 0 0.07448? alization of a magnetic field with dipolar geometry can be 2 1 0.00664? 0.11230* very misleading, particularly if one is interested in field 2 2 0.04499* -0.00070* geometry near the planet's surface. Note that for Uranus, 3 0 -0.06592 planetary latitudes are taken to be positive over the hemi- 3 1 0.04098 -0.03669? 3 2 -0.03581 0.01791 sphere in which the angular momentum vector resides, i.e., 3 3 0.00484? -0.00770? the hemisphere oriented toward the Sun (and Earth) in 1986, the time of the Voyager encounter. (Be aware that the Coefficients are poorly resolved or unresolved unless noted oth- International Astronomical Union (IAU) latitude convention erwise. From Connerney et al. [1991]. *Coefficient well resolved (Rxx > 0.95). is opposite to that used by the Voyager particles and fields ?Coefficient marginally resolved (0.75 < Rxx < 0.95). investigators. The IAU defines the south pole as the rotation pole south of the ecliptic.) The first evidence of Neptune's magnetic field appeared in radio observations [Warwick et al., 1989] obtained by Voy- moment 0.13 G Rn,3 offsetfrom the center of theplanet by a ager 2 just days prior to its closest approach to the planet on rather surprisingly large 0.55 R n and inclined by 47ø with August 25, 1989. The in situ magnetic field observations respect to the rotation axis [Ness et al., 1989]. revealed a magnetic field of internal origin with characteris- It was necessary for Ness et al. [1989] to exclude from tics not unlike those of the planet Uranus. The most striking their OTD analysis all observations of the field obtained at r difference between the Uranus and Neptune encounterswas < 4 R n. One indication of how nondipolar the field of a difference of our own design: the Voyager 2 flyby trajec- Neptune is can be had by comparison of the actual field tories at each planet. Where Voyager 2 at Uranus remained measured at closest approach (approximately 10,000 nT) to relatively distant from the planet, Voyager 2 at Neptune that one would expect if the field were dipolar (6500 nT, for approachedto within 1.18 R n of the planet. The presenceof the OTD model). In fact, the field measured near closest higher degree and order componentsof the field in the latter approach was quite complex, as is illustrated in Figure 12. observations is overwhelming, simply a consequence of the Two local maxima appear in the magnitude of the field close periapsis. Preliminary analyses of the Voyager mag- observed along the flyby trajectory, instead of the one netic field observations used an OTD representation of the maximum one would observe in a dipolar field. Spherical field, valid at moderatedistances from the planet (4 to 15R n harmonic analysis of the field required an expansion to radial distance; 1 Rn = 24,765 km), and fitted to data in degree and order 8 to adequately represent the measure- excessof 4 R u from the planet only. In this first approxima- ments [Connerney et al., 1991]. The large number of param- tion, the field may be characterized as that of a dipole of eters associated with a spherical harmonic expansion of degree and order 8 (80 Schmidt coefficients) and the rather limited observations leads to a severely underdetermined

SPACECRAFT RADIAL DISTANCE (Rn) inverse problem which has only a partial solution [Conner- 3 2 1.5 1.18 Rn 1.5 2 3 ney et al., 1991]. The distribution of observations is sufficient

lOS_1 , , I I, ' II •PHEF•ICAL'HARMONIC' - to resolve, or determine, all of the spherical harmonic terms iI CONTRIBUTIONSBY ORDER of degree 1 (dipole), some of the terms of degree 2 (quadrupole), and some terms of degree 3 (octupole) and higher. The resulting model, designated "O8" (octupole part of an expansionto degree and order 8), is listed in Table 8. For the Neptune field model, it is necessary to add a measure of the • ,-:.'' ...... ' ,...... resolution of each parameter listed in Table 8. For this we > o•,, use the magnitude of the corresponding diagonal element of m 103 O the resolution matrix, a measure of the uniqueness of the solution, the extent to which an individual model parameter can be represented by the basis vectors included in the partial solution. Note that some of the quadrupole and IBI1844evMODEL - OA=1.18 RN octupolecoefficients of the 08 model are not well resolved, 10 20 30 40 50 0 10 20 30 40 50 MINUTES HOUR 3 HOUR 4 HOUR 5 but included out of necessity (see discussion of parameter DAY 237 resolution in Connerney et al. [1991]). FiB. ]2. •a[nitudc o[ the observed field (crosses) as a [unction As anticipated, the relative magnitude of the quadrupole is o[ time and spacccra[tradial distancecompared with that computed quite large (Figure 4); the octupole is large as well, but can usin8 the pavia] solution (solid line throush data points [see Con- only be loosely constrained by the Voyager observations. •er•e• el •I., ]99]]), the dipole coc•cients o[ the partial solution An eccentric dipole representationbased upon the Q3 model (dashed line), the dipole plus octupolc (dotted line), and the dipole plus quad•pole plus octupolc terms (dot-dashed line). The peculiar coefficients (Table 5) shares many of the same characteris- double peak in the masnetic field masnitude observed near closest tics as the OTD: a large dipole tilt, and a large spatial offset approach illustrates the complexity o[ the field. of the magnetic center of the planet. However, the offset of 18,672 CONNERNEY:MAGNETIC FIELDS OF THE OUTER PLANETS

SURFACETOTAL INTENSITY MODELO 8 901 ' ' I ' • • ' ' .2. ORL 3•-- (50

o / .

36O 27O 18O 9O 0

WEST LONGITUDE

Fig. 13. Contours of constantmagnetic field magnitude(gauss) on the dynamicallyflattened (1/47.6) surfaceof Neptune, computedusing the 08 sphericalharmonic model. An estimatedauroral oval (shaded)and multiple magnetic dip equators(dashed lines) are shown.For comparison,the locationsof the OTD magneticpoles (positive/negative) are indicated by a circled dot and circled cross, respectively [Ness et al., 1989]. From Connerney et al. [1991]. the eccentric dipole is more nearly confined to the planet's temperature, and gravitational zonal harmonics, it is not equator, whereas the OTD offset has a large component possible to infer the composition and state of a planet's antiparallel to the rotation axis. interior without appeal to a theory of formation of the The magnetic field magnitude on the surface of the planet planets. It is, however, possibleto construct a reasonable,if rangesfrom approximately 0.9 G at southernmid-latitudes to nonunique, scenario of planet formation that produces outer -<0.1 G near the equator and at northern mid-latitudes planets with the required characteristics, and lends some (Figure 13). Figure 13 also shows estimated auroral zones insight into how or why it is that the magnetic fields of these (stippled regions) which differ greatly in size as a result of the planets differ so (for a review of planetary interiors and hemispherical asymmetry in field magnitudes.In this repre- dynamos, see Stevenson [1983]). sentation, it must be recognized that only the low degree and It is generally assumed that the outer planets condensed order part of the field is portrayed on the surface of the out of a primitive solar nebula as it cooled, each planet planet, and the likely presence of higher degree and order incorporating a mix of high-temperature condensates terms may be expected to significantlyalter the surfacefield. ("rock") and low-temperature condensates("ice"), each of A comparison of the magnetic fields of Uranus and Neptune solar composition [e.g., Hubbard and MacFarlane, 1980; appears in Plate 2, which is a sinusoidal equal-area projec- Podolak and Reynolds, 1981; Torbett and Smoluchowski, tion of the surface field magnitude. In this figure, Neptune is 1979]. The rock component consists largely of iron and viewed at a central meridian longitude (CML) of 150ø and magnesiumsilicates, most often forming a central core as the Uranus is viewed at a CML of 180 ø. The same color bar is heavier elements sink to the planet's center. The ice com- used for field magnitudes on both planets, with weak field ponent is a mixture of H20, NH3, and CH4 in solar magnitudes appearing black or dark blue, and strong field proportions. To this mixture of ice and rock, a captured regions appearing yellow and red in color. In this presenta- gas-phasecomponent consistingof H and He, again in solar tion, it is clear that the magneticfields of Uranus and Neptune proportions, must be added. The massive gas giants Jupiter are quite similar in the range of surfacefield magnitudes,the tilt and Saturn must have captured the bulk of the available gas of the dipole, and the appearanceof one strongpole at southern phase component, for reasonsthat are not clear, and exhibit mid latitudes. Both Uranus and Neptune have extendedweak- the characteristics expected of a condensed object of solar field regions, multiple-dip equators, and multipolar structurein proportions (i.e., largely H-He). Uranus and Neptune have evidence at the surfaceof the planet. average densitiesgreatly exceeding that expected of such an object, so it is assumed that they captured only a modest DISCUSSION low-density envelope of the gas phase component, which The necessary (but not sufficient) conditions for a self- now resides above a rock and ice core. To first order, Jupiter sustaining dynamo include the motion of an electrical con- and Saturn have similar interiors, dominated by the behavior ductor in a magnetic field and the supply of energy to the of the gas component at high temperatures and pressures, system. These key requirements link dynamo theory with illustrated in Plate 3. For Jupiter and Saturn, the presenceof the study of planetary formation and the behavior of mate- the rock and ice componentsis largely irrelevant. Similarly, rials under extremes of temperature and pressure. Given the Uranus and Neptune have similar interiors, dominated by number of observables, e.g., planet mass, radius, surface the ice component, illustrated in Plate 4. CONNERNEY'MAGNETIC FIELDS OF THE OUTERPLANETS 18,673

SATURN

hlOLEGU•\R

METALLIC H- He ..e e,:...(l• eel...... ]•;u•\'rt• J•'•:) .' ':"'0eeee.eß'•½ e '.o "0 ROCK' (",i, '-'].' '" CORE • . -...... , ,, . ..

1.0 Rj .8 .6 .4 .2 0 .2 .4 .6 .8 1.0 RS (71,372 km) RADIALDISTANCE (60,000 km)

Plate 3. Schematic of the model interiors of Jupiter and Saturn. Each has an outer envelope of convecting molecular H2-He, a metallically conducting and at least partially convecting H-He outer core, and an inner rock core. Saturn is depicted with a nonconvectingbut still metallically conducting region atop the outer core according to Stevensoh's [1983] model interior.

URANUS AND NEPTUNE INSULATOR H2 ,He ,CH4 ? IONIC CONDUCTION

FLUID ICE H20,NH 3 ,CH4 ? (+ ROCK AND GAS?) METALLIC?

ROCK CORE IRON-SILICATE

1.0 Rp .8 .6 .4 .2 0 (Ru - 25,600Km) (Rn = 24,765Km)

Plate 4. Schematicof the modelinteriors of Uranus and Neptune. Each has an outer envelopeof H2, He, and CH 4 above an ice mantle [after Stevenson, 1983]. A model with a centrally condensedrocky core is indicated, but a model with a more heterogeneousmixture of ice and rock is equally acceptable. 18,674 CONNERNEY:MAGNETIC FIELDS OF THE OUTER PLANETS

The model interiors of Jupiter and Saturn each have an outer envelope of fluid, convecting H-He above a pressure levelof a few 106bars. At greaterdepth and pressure, the NEPTUNE (.75) 2.0 hydrogen becomes a metallic conductor; by virtue of its greatermass, Jupiter has a largermetallic core (0.75 Rj) than URANUS (.75) 1.0- Saturn (0.50 Rs). Plate 3 illustrates Stevenson's[1980, 1982] model of Saturn's interior, in which the uppermost part of the metallically-conducting core is maintained stable against :2) 0.5 SATURN .5) convection by a helium gradient resulting from the immisci- bility of H and He at the corresponding temperature and • JUPITER .75)- 04 MODEL • 0 2 • .:':•.... pressure. The proposed presence of this layer within the "' ' • .... > • cooler Saturn, and not within Jupiter, provides a much- <1: Ol I needed means of distinguishingbetween these two interiors. LLI I EARTH(. 55) Indeed, Stevenson has suggested that the axisymmetry of "" \ t Saturn's magnetic field is due to the differential rotation of 0.05 \, I this metallically conducting but non-convecting layer above v the dynamo region. The Uranus and Neptune interior model illustrated in Plate 4 depicts a centrally condensed object consistent with O,O2(n+l) * /Rp/(2n+4)• *m=0 ,• {(gn m)2"F(hnm)2t 0.01 I I I I I early modeling efforts, but a wide range of alternate possi- 1 2 3 4 5 6 7 bilities exists [Podolak et al., 1990; Podolak and Reynolds, HARMONIC DEGREE n 1987; Hubbard and Marley, 1989]. For example, one highly Fig. 14. Relative magnetic spectrum of the planets Jupiter, differentiated model appropriate for both planets [Podolak et Saturn, Uranus, Neptune, and Earth, normalized to an assumed al., 1990] consistslargely of ice ("ice-to-rock" ratio of 15 to core radius for each planet, as indicated in parenthesesfollowing 30), with a relatively small rock core of about 1 Earth mass, each labeled curve. Two Jovian harmonic spectra are computed and a comparable mass of gaseous envelope (which may be using two models (04 and 06) which illustrate a range of possible Jovian fields. The Neptune octupole (n = 3) is poorly constrained, enriched with heavier constituents). However, the observ- and the Uranus octupole is unconstrained. ables can also be satisfied with an undifferentiated mixture of ice and rock of roughly solar (2.7 to 1) proportions[Hubbard and Marley, 1989; Podolak et al., 1991]. In either case, we assume for the following discussion a Uranus or Neptune core-mantle boundary [e.g., Lowes, 1974]. It is assumed that interior consisting mostly of the ice component, enriched, the core-mantle boundary, the location of which is very perhaps with appreciable rock and/or gaseouscomponent. accurately known, represents the outer boundary of the A convenient measure of the complexity of a planetary geodynamo. magnetic field, often used in studies of the magnetic field of If one assumesthat a white spectrum is a common feature the earth and planets, is the "harmonic spectrum," some- of all planetary dynamos [Elphic and Russell, 1978], the times referred to as a "Lowes spectrum," defined as follows results in Figure 4 can be partially reconciled with a larger [Lowes, 1974; Langel and Estes, 1982]: dynamocore radiusfor Jupiter(•0.75 Rj) and a smaller core radiusfor Saturn (•0.5 Rs). This would place the outer boundary of each near the surface at which the pressure- Rn -- (n+ 1) • {(9nm)2+ (hnm)2} induced transition from molecular to metallic hydrogen is m=0 expected to occur on each planet. This suggests that a comparison of the harmonic spectra of the planets might be This quantity is equal to the mean squared magnetic field more illuminating if we renormalize the magnetic spectrum intensity over the planet' s surface produced by harmonics of shown in Figure 4 to the assumed core surface for each degree n. The variation of R n with increasingdegree n, planet, as is presented in Figure 14. For each planet, the shown in Figure 4 for the Earth and outer planets, is but one assumedcore radius is shown in parentheses on the figure. of several quantities of interest in the comparison of plane- For Jupiter and Saturn, we assume that the core radius is tary fields [e.g., Riidler and Ness, 1990; Schulz and Pauli- near the radius of the metallically conducting hydrogen core, kas, 1990]. In Figure 4, R n is calculated using the GSFC approximately 0.75 and 0.5 planet radius, respectively [e.g., 12/83 model for the Earth [Langel and Estes, 1985], the Z3 Stevenson, 1983]. For Uranus and Neptune, we take r c = model for Saturn [Connerney et al., 1982b], and the Q3 0.75 Re with the expectationthat the dynamofor these model for the magnetic field of Uranus [Connerney et al., planets operates in the ice mantle, where ionic conduction 1987]. For Jupiter both the 04 model [Acura and Ness, 1976] prevails. If the dynamo is confined to the deep mantle, where and 06 models [Connerney, 1992] are shown, illustrating a theconductivity is greatest,a valueof r c = O.5 Re mightbe range of possible values for the quadrupole and octupole. more appropriate. We adopt the former value for this pre- For Uranus, no estimate of the magnitude of higher degree sentation and note that the latter would but exaggerate the (n > 2) moments can be made, while for Neptune, terms of magnitude of the higher-degree terms for Uranus and Nep- higher degree are appreciable, but quite uncertain. The tune. In this presentation, the planets fall into two distinct Earth's field is well known to high degreeand order (Nmax = groups, one in which the core surface field is dominated by 23). Scaled to the core-mantle boundary with the factor the dipole (Earth, Jupiter, Saturn) and one in which the core (a/re)2n+4, the spectrumbecomes almost flat for n -< 14, surface field is dominated by higher-degree contributions suggesting a "white" spectrum for the dynamo at the (Uranus and Neptune). However, in recognition of the CONNERNEY: MAGNETIC FIELDS OF THE OUTER PLANETS 18,675

TABLE 9. Summary of Dynamo Parameters

Saturn 0.0017 1.64 x 10-4 1 4 x 102 2000 0.001 Jupiter? 0.169 1.76x 10-4 0.5 (1 x 105) 5400 0.084 Jupiter 0.169 1.76x 10-4 0.5 (1 x 106) 5400 0.837 Earth 0.199 0.73 x 10-4 10. 2 x 104 62 1.0 Neptune 1.11 1.08X 10-4 1.2 1 X 106 430 4.96 Uranus 1.66 1.01 X 10-4 1.3 1 X 106 42 23.04

From Connerhey et al. [1991]. F = 42 - 40 [Pearl et al., 1990]. *Earth 5 1, all R m equal. ?ForJupiter 105 < Am < 106cm 2 s-1 peculiarity of Saturn's axisymmetric field, one might better dipole tilt in a variety of ways. Following Parker's [1969] think in terms of three classifications. The former group suggestion that the dipole tilt (radians) is related to the includes the planets with near alignment of dipole and numberof convectivecells nc by 0a • 1/(n•)•/2 Connerney rotation axes (%10), whereas the latter includes the oblique et al. [1991] related the dipole tilt to the inverse of the rotators Uranus (59ø) and Neptune (47ø), those with a very Rossby number R b - v•/f•L, where f• is the angular large angular separation of the dipole and rotation axes. rotational frequency. The Rossby number is a measureof the Connerney et al. [1987, 1991] attributed the unusual tilt importance of rotation on the fluid motion, comparing the and offset of the magnetic field of Uranus and Neptune to the time (L/v•) it takes a fluid element with velocity v• to relatively poor electrical conductivity of their icy interiors. traverse a path of length L with a period of rotation of the The electrical conductivity of the ice componentranges from fluid core (1/f•). This measureis effectively dominated by the about2 to 20 (ohmscm)-•, underthe appropriatepressure large variation of electrical conductivity (magnetic diffusiv- and temperature conditions [Smoluchowski and Torbett, ity) among the planets. 1981], as a result of pressure-inducedionization of H20 The magnetic Rossby number (Rb = v c/f•L) can be [Mitchell and Nellis, 1982; Nellis et al., 1988]. This is orders rewritten in terms of the magnetic Reynolds number (R m = of magnitude less than that of an iron-rich terrestrial core or vcL/Am),using a convectivefluid velocity v c 3 = F/p, where a metallically conducting hydrogen core. Dynamo action in F is the internally generated planetary heat flux and p is the an ice interior would require a much larger characteristic density [e.g., Stevenson, 1983; Smoluchowski and Torbett, scale length L to satisfy the necessary (but not sufficient) 1981; Curtis and Ness, 1986]. This approximation for the conditionthat the magneticReynolds number R m = vcL/Am fluid velocity assumesthat the scale length of the convective exceed 10 or so in order to sustain the magnetic field against cells and the scale length of the fluid region are equal, for ohmic diffusion;v c is a characteristicvelocity of convective lack of a better approximation. We then have motions and Am is the magnetic diffusivity, inversely pro- F2/3 portional to the electrical conductivity. Early conceptual Rb-- models of the geodynamo and secular variations [Parker, p2/3•AmRm 1955, 1969, 1971; Elsasser, 1946; Levy, 1972] attributed the tilt of the geodynamo to the number of convective cells. which may be computed for the planets Jupiter, Saturn, Similarly, Connerhey et al. [1987] suggestedthat dynamo Earth, Uranus, and Neptune, in a relative sense(Earth = 1), generation in an icy body would result in a large dipole tilt if we assume that a similar magnetic Reynolds number and a large quadrupole component, due to the large scale characterizes dynamo action in each case. The relevant lengths required for dynamo action. Alternate proposals for parameters are summarized in Table 9; the magnetic diffu- the generation of such a field, which appealed to unique sivities and densities are as given by Stevenson [1983], and conditions such as a magnetic field reversal [Schulz and the observed heat fluxes are from Pearl et al. [1990] and Paul&as, 1990] or a large orbital obliquity [Stevenson, 1986], Pearl and Conrath [1991] (note that the value quoted for appear less likely with the discovery of a second such Uranus is effectively an upper limit). For Jupiter, we con- planetary magnetic field, that of Neptune [also Hide, 1988]. sider the possibility of dynamo action in the outer molecular Ruzmaiken and Starchenko [1991] attribute the large tilt and H2 regionwith 10 5 --

10.000 the field. These currents may close in the conductive region beneath the shell (dynamo region), and give rise to an azimuthal field contained within the meridional current 1.000 NEPTUNE,'//URANUS-- loops, again with antisymmetry about the magnetic equator plane. One way to produce a radial field component with this interaction is suggestedby Parker' s [ 1969] proposed dynamo ...... , JUPITER EARTH reversal mechanism: allow the azimuthal field (due to the 0.100 --(METALLIC) (MOLECULAR H2) interaction of the radial field and the conductive shell) to reduce the azimuthal field from which the dynamo generates the large-scale meridional field. This process is illustrated in 0.010 • -- Plate 5, an illustration of the Parker dynamo reversal mechanism. The evolution of the field in time is represented from SATURN• 9 left to right in the figure. The left half of the meridian plane 0.001I • •,• I I I • I • • I • I I I I shows a dipole field geometry, the net result of the merged 10-4 10-3 10'2 10-• 10ø 10 102 small meridional loops (blue) created by the action of up- Inverse Rossby Number (normalized) welling convective cells on the (initial) azimuthal field (red). Fig. 15. Dipole tilt (tan Od)of the magneticplanets as a function Differential rotation acts upon the small meridional field of inverse Rossby number, estimated using parameters of Table 9 loops, drawing the field into azimuthal loops (dark blue to and assuming each dynamo is characterized by the same magnetic light blue, left to right) which either align parallel to the Reynolds number. Saturn's dipole tilt is an upper limit. Jupiter is indicated in two positions (stippled) appropriate to either of two original azimuthal field, as at high latitudes, or antiparallel possibilities: a dynamo operating in a highly conducting metallic with the original field, as at low latitudes. In Parker' s model, core or in a molecular hydrogen envelope (rightmost entry) above the reversal in the sign of the low-latitude azimuthal field the metallic core. leads to a reversal in sign of the low-latitude meridional field loops (to the right of the figure, in green), and eventual reversal in sign of the entire field. The field geometry planets with large dipole tilt (Uranus and Neptune) are likely depicted on the right half of the meridian plane would be an to have large nondipolar fields, e.g., harmonic spectra with intermediate configuration in Parker's reversal, since only greater field amplitudes in the quadrupole and/or octupole the low latitude field has reversed. However, it is this than the dipole. Schulz and Paulikas [1990] take note of this intermediate state that closely resembles Saturn's present and argue that we might better consider Uranus and Neptune day field geometry. as deficientin aligneddipole (# •0) only.Indeed, one could That is not to say that Saturn's field is in the process of construct an earthlike field for these planets simply by reversing, like the Earth's field does at a rate of a few increasing the aligned dipole by about an order of magnitude reversals per million years (as of late). Indirect evidence, or so. Figure 15 would also imply that Saturn's magnetic based upon a theory of formation of Saturn's rings [Northrop field is characterized by a small dipole tilt comparable in and Connerney, 1987], suggeststhat Saturn's magnetic field magnitude to the current upper limit of approximately 0.1 ø. has been locked in its present configuration for at least the Saturn's high degree of axisymmetry would then be attrib- past 60 m.y. Rather, it is suggested that the differential uted to characteristically small length scales of metallic rotation of an outer conductive shell above the dynamo hydrogen dynamos. However, Saturn appears to be some- could interact with the dynamo in producing a field config- what of a special case. In Stevensoh's [1982] model, differ- uration which minimizes the low latitude unsigned flux on ential rotation of an outer conductive shell attenuates the the core boundary, in a manner analogous to the Parker nonaxisymmetric components of the dynamo within, dynamo reversal model. thereby reducing the observed tilt by an order of magnitude or more from the "nominal" value. This model has an SUMMARY appealing physical basis (material properties of the H-He fluid) and appears to satisfy other constraints, e.g., helium We are fortunate to find such a diverse group of planetary depletion of the gaseousouter envelope and a relatively high dynamos among the recently explored planets of the outer planetary heat flux. solar system. The study of the terrestrial dynamo is a few Saturn's magnetic field is unusual with regard to its high centuries old. It is a difficult problem made more so by the degree of axisymmetry. It appears as well that Saturn's inability to construct planetary-scale dynamos for laboratory magnetic field is constructed in such a way as to minimize study. The magnetic planets of the solar system provide at the low-latitude unsigned flux across the core boundary. Can least a few alternative objects of study of relevance to this observation also be reconciled with the differential dynamo theory. In Jupiter and Saturn, we have two planets rotation of Stevenson's [1982] conducting shell above the of nearly the same compositionand comparable size but with dynamo region? Consider the action of such a shell on the magnetic fields that are worlds apart. Jupiter's dynamo axisymmetric radial and theta components of the field. A produces a magnetic field resembling Earth' s, while Saturn' s conductor moving in the & direction acting upon the 0 is uniquely spin-axisymmetric and peculiar, suggestively so, component of the field will establish a radial electric field in the distribution of flux across the core boundary. Steven- which simply polarizes the shell, as no radial currents are son's account of Saturn's internal structure and magnetic allowed to flow across the outer radius of the conducting field is both appealing and promising, as it provides a vehicle shell. The same motion will produce an electric field and for understanding the differences between these giant plan- currents in meridian planes (antisymmetric about the mag- ets. In Uranus and Neptune we have again two planets of netic equator) via interaction with the radial component of similar composition and size, this time with similar magnetic CONNERNEY.'MAGNETIC FIELDS OF THE OUTER PLANETS 18,677

DYNAMO REVERSAL MODEL- E.N. PARKER

Plate 5. Schematic of Parker's [ 1969] dynamo reversal model. The evolution of the field in time is represented from left to right. The left half of the meridian plane shows a dipole field geometry, the net result of the merged small meridional loops (in blue) created by the action of upwelling convective cells on the (initial) azimuthal field (in red). Differential rotation acts upon the small meridional field loops, drawing the field into azimuthal loops (dark blue to light blue, left to right), which either align parallel to the original azimuthal field, as at high latitudes, or antiparallel with the original field, as at low latitudes. In Parker's model the reversal in the sign of the low-latitude azimuthal field leads to a reversal in sign of the low-latitude meridional field loops (to the right, in green), and eventual reversal in sign of the entire field.

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