JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 98, NO. El0, PAGES 18,659-18,679, OCTOBER 25, 1993 Magnetic Fields of the Outer Planets 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.