10.07 Planetary Magnetism J. E. P. Connerney, NASA Goddard Space Flight Center, Greenbelt, MD, USA

Published by Elsevier B.V.

10.07.1 Introduction 243 10.07.2 Tools 245 10.07.2.1 The Offset Tilted Dipole 245 10.07.2.2 Spherical Harmonic Models 246 10.07.3 Terrestrial Planets 248 10.07.3.1 Mercury 248 10.07.3.1.1 Observations 248 10.07.3.1.2 Models 249 10.07.3.2 Venus 250 10.07.3.2.1 Observations 251 10.07.3.2.2 Discussion 251 10.07.3.3 Mars 251 10.07.3.3.1 Observations 251 10.07.3.3.2 Models 254 10.07.3.3.3 Discussion 256 10.07.4 Gas Giants 256 10.07.4.1 Jupiter 256 10.07.4.2 Observations 257 10.07.4.3 Models 258 10.07.5 Discussion 262 10.07.5.1 Saturn 263 10.07.5.1.1 Observations 263 10.07.5.1.2 Models 264 10.07.5.1.3 Discussion 265 10.07.6 Ice Giants 267 10.07.6.1 Uranus 267 10.07.6.1.1 Models 267 10.07.6.2 Neptune 269 10.07.7 Satellites and Small Bodies 272 10.07.7.1 Moon 272 10.07.7.2 Ganymede 273 10.07.8 Discussion 274 10.07.9 Summary 275 References 275

10.07.1 Introduction nature and dipole geometry of the field and led to an association between magnetism and the interior of pla- Planetary magnetism, beginning with the study of the net Earth. Observations of Earth’s magnetic field geomagnetic field, is one of the oldest scientific disci- gathered over time demonstrated that it varies slowly plines. Magnetism was both a curiosity and a useful tool with time. The orientation of the field was observed to for navigation, the subject of myth and superstition as execute a long-term or secular drift called polar wan- much as scientific study. With the publication of De der. Later, when accurate measurements of the Magnete in 1600, William Gilbert demonstrated that the magnitude of the field could be made, secular variations Earth’s magnetic field was like that of a bar magnet. in the field magnitude were identified. Given the Gilbert’s treatise on magnetism established the global importance of accurate magnetic field maps in

243 244 Planetary Magnetism navigation, global surveys of the magnetic field were Voyager 2’s remarkable tour of the outer solar initiated periodically, at first by ships of discovery and system was made possible by the celestial alignment commerce and later by specialized survey ships built to oftheplanets,thesyzygy,whichoccursevery187years minimize distortion of the magnetic field they sought to or so. measure. In recent times, polar-orbiting, near-Earth Jupiter was visited again, in February 1992, by the satellites such as MAGSAT (Langel et al., 1982), Ulysses spacecraft en route to the high-latitude helio- Orsted, CHAMP, and SAC-C provided the capability sphere and again (albeit at great distance) in 2004. tomapthemagneticfieldovertheentiresurfaceof Ulysses used a Jupiter gravity assist to escape the Earth in a brief period, to capture a snapshot of the field eclliptic plane, but in so doing passed to within 6 at each epoch. By studying the magnetic properties of Rj (Balogh et al., 1992). Additional observations were terrestrial rocks, paleomagnetists can extend the history obtained by the Galileo Orbiter beginning in 1995 of the geodynamo over timescales of hundreds of mil- ( Johnson et al., 1992), but apart from the de-orbit lions of years. For a discussion of the magnetism of the maneuver to send Galileo into Jupiter’s atmosphere Earth see volume 5 of this treatise, for a discussion of for planetary protection (of the Galilean satellites, the geodynamo see Chapters 8.03, 8.08, and 8.09, for a not Jupiter), little additional information regarding discussion of planetary dynamos see Chapter 10.08. Jupiter’s main field was obtained. Instead, Galileo Planetary magnetism is also a recent study, born of surprised us with the remarkable discovery of an the space age and a new era of discovery that began in intrinsic magnetic field of Ganymede (Kivelson the 1960s with the launch of spacecraft to other bodies. et al., 1996) and the induced magnetic fields of The Sun and stars were known to possess magnetic Europa and Callisto (Khurana et al., 1998; Zimmer fields, but one could only speculate on whether the et al., 2000). Today, the Cassini Orbiter orbits Saturn planets and satellites in our solar system were magne- gathering observations of the distant magnetosphere; tized. The planet Jupiter is an exception; its magnetic close in observations must await the polar orbits field was inferred from the detection of nonthermal scheduled for late in the mission. radio emissions (Burke and Franklin, 1955)asearlyas The Mariner 10 spacecraft discovered Mercury’s 1955, before the new age of exploration. In the decades magnetic field in brief flybys in 1974 and 1975 (Ness that followed, the gross characteristics of Jupiter’s mag- et al., 1974a; Ness et al., 1975, 1976) and provided netic field were deduced from variations of the plane of the first indication that slowly rotating Venus was polarization of the emissions or variations in flux den- not magnetized (Ness et al., 1974b). A great many sity (see, e.g., the review by Berge and Gulkis (1976)). spacecraft visited Mars (Connerney et al., 2005), Estimates of the orientation of Jupiter’s field (dipole beginning with the Soviet launch of Mars 1 in 1962, tilt)weremoresuccessfulthanthoseofitsmagnitude; but Mars did not relinquish his secrets until the Mars the detailed nature of Jupiter’s field was established by Global Surveyor (MGS) spacecraft entered orbit direct measurement, by spacecraft. about Mars in September of 1997. MGS measure- In little more than three decades, spacecraft have ments demonstrated that Mars does not have a global visited nearly every large body in the solar system. The magnetic field of internal origin, but its crust is first in situ observations of the Jovian magnetosphere intensely magnetized (Acun˜a et al., 1998). So Mars were obtained by the Pioneer 10 and 11 spacecraft in once had an internal magnetic field, for at least as December 1973 and December 1974, respectively long as it took the crust to acquire remanence. (Smith et al., 1974, 1975; Acun˜a and Ness, 1976). The Perhaps one-day paleomagnetic measurements will Pioneer 11 spacecraft continued to make the first obser- reveal something of the history of that dynamo. The vationsofSaturn’smagneticfieldaswell(Smith et al., only traditional planet (setting aside the debate on 1980a, 1980b; Acun˜a and Ness, 1980). Voyagers 1 and 2 the definition of ‘planet’) not yet visited by spacecraft followed, passing through the Jovian magnetosphere in is the Pluto–Charon system, which is scheduled for a March and July of 1979, respectively (Ness et al., 1979a, visit by the New Horizons spacecraft in July 2015. 1979b). Voyagers 1 and 2 continued onward to Saturn, The New Horizons spacecraft is not instrumented to obtaining additional observationsofSaturn’smagnetic measure magnetic fields, so no direct measurement is field in November 1980 and August 1981 (Ness et al., possible, but the presence of a magnetic field may 1981, 1982).Voyager2continuedonits‘grandtour’of be inferred from measurements made by other the solar system, with the discovery of the magnetic instruments. field of Uranus in January 1986 (Ness et al., 1986)and Our knowledge of the magnetic fields of the pla- that of Neptune in August 1989 (Ness et al., 1989). nets is, in large part, based upon the planetary flybys Planetary Magnetism 245 that occurred decades ago. Mars is the exception, application and/or the availability of observations. having been mapped thoroughly by the polar- Simple representations include dipole models of orbiting MGS spacecraft at a nominal altitude of one form or another and a potential field representa- 400 km; elsewhere the observations are sparse in tion as a series of spherical harmonics. External fields, both space and time, particularly considered in light or those arising from currents outside the planet, are of the data available for the study of the geomagnetic often accommodated by explicit models or spherical field. They are, however, sufficient to describe a harmonic methods. The latter approach is useful only diverse group of planetary magnetic fields and pro- in regions free of currents. vide clues to guide the continued development of dynamo theory. 10.07.2.1 The Offset Tilted Dipole 10.07.2 Tools Dipole models have found use in the interpretation of magnetic field observations, dating to Gilbert’s ana- A planet with an intrinsic magnetic field stands as an lysis of Earth’s magnetic field. The dipole is the obstacle to the solar wind, the high-velocity stream of simplest approximation to a localized source. The plasma emanating from the sun. The interaction of the vector magnetic field B(r) of a dipole at the origin planetary field and the solar wind forms a multitiered is given by interaction region, often approximated as a set of conic m 3ðm ? rÞr sections. The supersonic solar wind forms a shock BðrÞ¼ – þ r 3 r 5 upstream of the obstacle (‘bow shock’). The slowed solar wind flows around the obstacle within the ‘mag- where m is the magnetic moment in units of B r3 netosheath’, bounded by the bow shock and the and r ¼ jrj. The field of a dipole located near the ‘magnetopause’, often approximated by a paraboloid origin is computed by translation of the origin of the of revolution about the planet–Sun line. Within the coordinate system. Offset tilted dipole (OTD) magnetopause is a region dominated by the planetary models are found using forward modeling techniques field, called the ‘magnetosphere’, a term introduced by to compare in situ observations to the OTD model Tom Gold in the post-war era of rocketry that field. The dipole offset (xo, yo, zo) is not linearly provided access to space in the early 1950s. The related to the computed field, so an iterative proce- magnetospheric magnetic field extends well down- dure is often used to find the optimal dipole position stream in the anti-sunward direction, as if stretched (e.g., Smith et al., 1976). Alternatively one may per- like an archer’s bowstring, to form the ‘magnetotail’. form a spherical harmonic analysis (see next section) The observed magnetic field can be regarded as the of degree and order 1 centered upon each of a large sum of contributions from several sources, dominated number of candidate dipole positions, selecting the by the planetary dynamo, sometimes referred to as the offset which minimizes the model residuals. In either ‘main field’. Other relatively minor sources include case, the result is the OTD which most closely currents flowing on the magnetopause and tail approximates the field measured along the spacecraft currents arising from the solar wind interaction and trajectory. distributed currents (‘ring currents’) due to the motion The simple OTD representation provides a con- of charged particles within the magnetosphere. Field- venient approximation to the field, particularly aligned currents, called ‘Birkeland currents’, flow useful at larger distances. It is useful in visualizing between the magnetosphere and the planet’s electri- the gross characteristics of the field and it is often cally conducting ionosphere, particularly during used to chart the motion of charged particles magnetospheric storms, leading to intense auroral dis- throughout the magnetosphere. However, the simpli- plays. All of these currents produce magnetic fields, city of the OTD is also a limitation, in that complex often relatively small when compared to the planetary field geometries cannot be adequately represented field, particularly close to the planet’s surface. with such a limited parametrization. In general, a However, if an accurate model is to be obtained from dipole representation can be expected to closely limited or distant observations, these sources can be a approximate the field for radial distances r a, significant source of errors if not modeled. where a is a characteristic source dimension. At lesser The planetary field is most often characterized by radial distances, an accurate description of the field one of a very few simple models, depending on the requires more flexibility in parametrization, for 246 Planetary Magnetism example, consideration of higher-degree and -order external Schmidt coefficients, respectively. These are moments. most often presented in units of Gauss or nanoteslas A logical extension of the simple OTD model is (1 G ¼ 105 nT) for a particular choice of equatorial one of many dipoles. Earth’s field has been approxi- radius a of the planet. Different values of the equa- mated by adding one or more smaller dipoles to a torial radius have been used and should be noted in ‘main dipole’ and treating the field as a summation the comparison of various field models. The angles over distinct sources; this provides a simple means of and are the polar angles of a spherical coordinate introducing an anomaly, or departure from dipole system, (co-latitude) measured from the axis of geometry. The Earth’s field has been approximated rotation and increasing in the direction of by an ensemble of many dipoles located on the sur- rotation. The three components of the magnetic face of a sphere of radius 0.5 Re, the fluid core radius. field (internal field only) are obtained from the In addition to the field generated deep within Earth, expression for V above: induced and remanent magnetization in the crust can X1 Xn nþ2 be modeled with another set of dipoles, scattered qV a m Br ¼ – ¼ – ðn þ 1Þ gn cos ðmÞ about a sphere of radius 1.0 Re to approximate sources qr r n¼1 m¼0 in the crust (Mayhew and Estes, 1983). A similar m m approach has been taken to model the crustal mag- þ hn sin ðmÞ Pn ðcos Þ netic field of Mars (Purucker et al., 2000). X1 Xn qV a nþ2 B ¼ – ¼ – gm cos ðmÞ rq r n 10.07.2.2 Spherical Harmonic Models n¼1 m¼0 dPmð cos Þ þ hm sin ðmÞ n In the absence of local currents (Ñ B ¼ 0), the n d magnetic field may be expressed as the gradient of a X1 Xn – 1 qV 1 a nþ2 scalar potential V ðB ¼ – rV Þ: It is particularly B ¼ – ¼ m gm cos ðmÞ r sin q sin r n advantageous to expand the potential V in a series n¼1m¼0 of functions, called spherical harmonics, which are – hm sin ðmÞ Pmð cos Þ solutions to Laplace’s equation in spherical coordi- n n nates. This approach, introduced by Gauss in 1839, The leading terms in the series (through degree 4) has been very popular in studies of the geomagnetic may be computed using the Schmidt quasi- field, and subsequently those of the planets. The normalized Legendre functions listed in Table 1. traditional spherical harmonic expansion of V is Observations are often rendered in a west long- given by (e.g., Chapman and Bartels, 1940; Langel, itude system, in which the longitude of a stationary 1987) observer increases in time as the planet rotates. West X1 r n a nþ1 longitudes are simply related to the angle by V ¼ a T e þ T i n n ¼ 360 – . Longitudes for the terrestrial planets n¼1 a r may be assigned by reference to surface features. where a is the planet’s equatorial radius. The first For the outer planets, the rotation period is inferred series in increasing powers of r represents contribu- from observations of episodic radio emissions, which, tions due to external sources, with by assumption, are locked in phase with the rotation Xn of the planet’s magnetic field and hence the electri- e m m m Tn ¼ Pn ðcos Þ Gn cos ðmÞþHn sin ðmÞ cally conducting deep interior of the planet. For m¼0 these planets, longitudes must be assigned with The second series in inverse powers of r represents knowledge of the rotation rate and time. For contributions due to the planetary field or internal Jupiter, observation of high-frequency radio emission sources, with (penetrating Earth’s ionosphere) over several decades Xn led to an accurate determination of the planet’s rota- i m m m Tn ¼ Pn ðcos Þ gn cos ðmÞþhn sin ðmÞ tion period, although one must be cognizant of the m¼0 occasional update (e.g., III(1957) vs. III(1965)). m The Pn ðcos Þ are Schmidt quasi-normalized These two systems result in significantly different associated Legendre functions of degree n and order longitudes when observations of the Pioneer era are m m m m m, and the gn ; hn and Gn ; Hn are the internal and compared with those of the Voyager era, so one must Planetary Magnetism 247

Table 1 Schmidt quasi-normalized Legendre functions currents, so in practice the external expansion is often truncated at N ¼ 1 and local currents are Legendre functions max modeled with the aid of explicit models. The domi- 0 P1 ¼ð1Þ cos nant contribution from local currents may be 1 P1 ¼ð1Þ sin described as a large-scale equatorial current system 3 0 2 (Connerney et al., 1981). Field-aligned, or Birkeland P2 ¼ cos – 1=3 2 currents, may also play a role in addition to induction P 1 ¼ 31=2 2 cos sin effects, but thus far have not been included in such 1=2 2 3 2 P2 ¼ sin analyses, excepting those of Earth (e.g., Backus, 1986; 2 5 Sabaka et al., 2002). It is very important to adequately 0 2 P3 ¼ cos cos – 9=15 treat the fields of local currents, because even small 2 ! 53ðÞ1=2 errors accumulating along the spacecraft trajectory P 1 ¼ sin 2 3 1=2 cos – 3=15 can lead to rather large errors in the spherical har- 22ðÞ ! 1=2 1=2 monic coefficients deduced from observations. 2 ðÞ3 ðÞ5 2 P3 ¼ cos sin 2 The maximum degree and order required of the ! internal field expansion depends on the complexity ðÞ5 1=2 3 3 of the field measured. In usual practice, the series P3 ¼ 1=2 sin 22ðÞ above is truncated at a maximum degree Nmax, where 0 35 4 2 P4 ¼ cos – ðÞ30=35 cos þ ðÞ3=35 Nmax is large enough to follow variations in the field 8 ! at the orbital altitude of the measurement. The num- 75ðÞ1=2 1 2 P4 ¼ 1=2 cos sin cos – 3=7 ber of free parameters grows rapidly with increasing 22ðÞ 2 ! Nmax,asnp ¼ (Nmax þ 1) 1. If the observations are 1=2 2 75ðÞ 2 2 P4 ¼ sin cos – 1=7 well distributed on a sphere, the spherical harmonics 4 ! do not covary, and the coefficients obtained are inde- 1=2 1=2 3 ðÞ7 ðÞ5 3 pendent of the truncation of the series. However, if P4 ¼ 1=2 cos sin 22ðÞ ! the observations are poorly distributed or sparse, as is ðÞ7 1=2ðÞ5 1=2 often the case for a planetary flyby, the usual sphe- P 4 ¼ sin4 4 8 rical harmonics covary, so it is advisable to construct new orthogonal basis functions. Furthermore, if an The leading term (in parentheses) converts the functions from Gaussian normalization, convenient for recursive computations, arbitrarily small choice of Nmax is imposed upon the to Schmidt quasi-normalized form. model in order to obtain a manageable linear system, large errors in low-degree and -order terms will result from the neglect of higher-order terms. To address these problems, Connerney (1981) intro- duced a method of analysis based on the singular- be careful to transform earlier results to a current value decomposition (SVD) of Lanczos. The method coordinate system. A detailed description of Jovian involves the construction of partial solutions to the coordinate systems is given by Dessler (1983). For generalized linear inverse problem to obtain esti- Saturn, Uranus, and Neptune the rotation periods mates of those parameters which are constrained by and longitude system in current use are derived the observations. The model parameters which are from Voyager observations of radio emissions not constrained by the data are readily identified and (Desch and Kaiser, 1981; Desch et al., 1986; exploited in characterization of model nonunique- Warwick et al., 1989). In practice (e.g., Saturn) this ness. One advantage of this approach is that the can lead to significant ambiguity in longitudes and physical model of the planetary field (expansion to great confusion in reconciliation of observations degree Nmax) does not depend on the completeness or taken over a lengthy span of time. extent of the available observations. Partial solutions, The expansion in increasing powers of r, repre- and estimates of the model parameters that result, senting external fields, is often truncated at may be interpreted within the context of the n ¼ Nmax ¼ 1 corresponding to a uniform external ‘resolution matrix’ for the particular solution field due to distant magnetopause and tail currents, (see Connerney, 1981; Connerney et al., 1991). The that is, sources well beyond the region of interest. No close flyby of Neptune in 1989 serves to illustrate this potential field can represent the field of local concept well. 248 Planetary Magnetism

10.07.3 Terrestrial Planets spacecraft approached the planet from a local time of approximately 1900 h and departed near 0700 h. 10.07.3.1 Mercury Given the brevity of these encounters, the relatively Mercury, the smallest (Rm ¼ 2439 km) and least mas- slow planetary rotation rate, and the orbital commen- sive (Mm ¼ 0.056Me) planet in the solar system, surabilities, each encounter approximates a shot past occupies the pole position in its race about the Sun, a stationary object, the major difference being the with a semimajor axis of 0.39 AU. Due to its large altitude and subspacecraft latitude of the point of orbital eccentricity (0.206), in one orbit about the Sun closest approach. The first and third of these encoun- (88 days) its orbital radius varies from 0.31 to ters provided observations within the Hermean 0.47 AU. It is locked in a spin-orbit resonance magnetosphere (Figure 1); the second was targeted (Pettengill and Dyce, 1965; Goldreich and Peale, well above the sunlit hemisphere and beyond the 1966) rotating once every 58.65 days or three times reach of the Hermean magnetosphere in the every two orbital periods. It is difficult to observe upstream direction of the solar wind. from Earth, due to its proximity to the Sun, and little Mariner 10’s first flyby was relatively close, as was known about Mercury prior to observation by planetary flybys go, with a periapsis of 1.29 Rm over spacecraft on 29 March 1974, the first of three encoun- the darkened hemisphere (anti-sunward direction), ters with the Mariner 10 spacecraft. Discovery of passing from dusk to dawn behind the planet as the intrinsic magnetic field of Mercury was a bit viewed from the Sun. Mariner 10 traveled from bow surprising since it was widely assumed that a body as shock (inbound) to bow shock (outbound) in a mere small as Mercury would have completely solidified, 33 min, 17 of which were spent within the confines of ruling out generation of a magnetic field by dynamo a Hermean magnetosphere (Figure 2). These obser- action (but see Chapter 10.09). Here we describe only vations are best understood in terms of the field the Mariner 10 observations of Mercury, the only in external to the planet, even at such a close distance. situ observations obtained in the first four decades of The field increased in magnitude from about 45 nT space exploration. As this chapter is being written, the just inside the magnetopause to approximately Messenger spacecraft is on its way to Mercury 100 nT, all the while maintaining the anti-sunward (Solomon et al., 2001; Gold et al., 2001), in part to better understand the internal magnetic field and its origin. It will enter orbit in March 2011, after a series of flybys Mercury flybys of Earth, Venus (two flybys), and Mercury (three 2 flybys: January and October 2008, and September 2009). This mission may be expected to rewrite the M3 (1975) book on Mercury and its magnetic field. A more ambitious mission to Mercury, ‘BepiColombo’, is in development by the European Space Agency (ESA) and the Institute of Space and Astronautical Science in Tail Japan (ISAS) for launch in the near future (Anselmi Z 0 Currents and Scoon, 2001).

M1(1974)

10.07.3.1.1 Observations Mariner 10, known pre-launch as the Mariner Venus–Mercury spacecraft, was launched on 3 Mariner 10 November 1973. The spacecraft used a close flyby –2 01234 of Venus on 5 February 1974 (for gravity assist) to ρ (R ) achieve three close encounters with Mercury m (29 March 1974, 21 September 1974, and 16 March Figure 1 Mariner 10 trajectory in Mercury-centered 1975) before it exhausted its expendibles. The orbital cylindrical coordinates for the first (M1) and third (M3) period of Mariner 10 after the Venus gravity assist encounters. The spacecraft distance from the equator (z)as a function of distance from the z-axis () is given in units of was 176 days, very nearly commensurate with Mercury radius. The part of the trajectory within the Mercury’s orbital (and rotation) period, providing Hermean magnetosphere is indicated by the thick line three very similar close encounters. Each time the segment. Planetary Magnetism 249

Mariner 10 Mercury l encounter Mariner 10 Mercury lII encounter 29 March 1974 16 March 1975 6 s averaged field vectors 6 s averaged field vectors

ZME ZME View from the Sun

ZME –2 2 YME MP MP YME 2 View from the Sun

Magnetopause XME (Sun) 100 nT Mariner 10 BS 500 nT Bow shock MP r 10 Marine MP Mercury –2 2 YME

YME 2 View onto Mercury ecliptic plane e us pa XME (Sunward) to ne k ag Figure 2 M1 encounter trajectory and magnetic field M observations in Mercury eclliptic coordinates, viewed from Bow shoc View onto the Sun (top) and viewed along Mercury’s rotation axis ecliptic plane (bottom). The vector magnetic field observed along the XME Mariner 10 trajectory is illustrated by vector projection onto Figure 3 M3 encounter trajectory and magnetic field the z–y (top) and x–y (bottom) planes; vectors originate at observations in Mercury eclliptic coordinates, viewed from the spacecraft position in ME coordinates at the time of the Sun (top) and viewed along Mercury’s rotation axis observation. Observed bow shock (BS) and magnetopause (bottom). The vector magnetic field observed along the (MP) positions are shown along with scaled nominal bow Mariner 10 trajectory is illustrated by vector projection onto shock and magnetopause boundaries. the z–y (top), x–z (middle), and x–y (bottom) planes; vectors originate at the spacecraft position in ME coordinates at the time of observation. Observed magnetopause (MP) positions are shown along with scaled nominal bow shock orientation characteristic of a planetary magnetotail. and magnetopause boundaries. As Mariner 10 crossed the equator plane, the field decreased in magnitude precipitously, as if crossing a current sheet, after which it was much smaller in magnitude and chaotic, lacking the smooth variation of the magnetosphere (14 min) the field increased and consistent orientation that characterized the from about 20 nT to a maximum of 402 nT observed inbound pass. These observations indicated that just after closest approach at 1.14Rm radial distance 3 Mariner 10 passed through a small magnetosphere, (1Rm ¼ 2439 km). The approximate 1/r dependence sized just large enough to contain the solid body of of the observed field on spacecraft radial distance the planet under nominal solar wind conditions (Ness establishes the internal origin of the field, and initial analysis (Ness et al., 1976) suggested a dipole moment et al., 1975). To form such a magnetosphere, Mercury 3 must have an internal magnetic field, albeit one with of approximately 342 nT ? Rm , aligned with the Z a modest dipole magnitude. axis (normal to the Hermean orbital plane). Mariner 10’s second flyby was upstream of Mercury in the solar wind, and too distant to pene- trate the small Hermean magnetosphere. However, 10.07.3.1.2 Models the third flyby was targeted to pass closely over the Models of Mercury’s magnetic field fall largely into northern pole (Figure 3), in an effort to gather mea- two groups, distinguished by their treatment of exter- surements optimized for characterization of the nal fields. The first group used a spherical harmonic Hermean field. During the spacecraft’s brief traversal expansion for both internal and external fields and 250 Planetary Magnetism

Table 2 Mercury magnetic field models

a 0 3 Model g1 (nT-Rm ) Data Reference Comments

I1 227 I(1/2) Ness et al. (1974a) No external field modeled I1E2 350 I(1/2) Ness et al. (1975) External field model improves internal fit I1E1 342 15 III Ness et al. (1976) III data better suited for modeling internal field I1E1 330 18 III Ness (1979a) III subsets modeled to estimate errors aII denotes internal expansion of degree/order 1; En denotes external field expansion of degree/order n.

were limited to the dipole (n ¼ 1) terms for internal Hermean magnetosphere fields. Initial analyses used the inbound Mercury I Z observations through to the tail current sheet crossing SM (1/2), while later analyses benefited from the Mercury III observations obtained crossing the pole. The latter are better suited to internal field estimation by virtue III of improved signal-to-noise magnitude relative to external fields. These are listed in Table 2. Another set of models were obtained using a spherical harmonic expansion for the internal X Tail field, augmented by explicit models of the external SM I field. These included more detailed models of the fields due to magnetopause and tail currents, the latter being of great importance in interpretation of Noon–midnight meridian plane the Mercury I encounter. An explicit model of the external field allows one to extend analyses through regions of local currents (e.g., tail current Magnetopause sheet), accommodating nonpotential fields more Figure 4 Magnetic field lines of a model Hermean readily. A number of these models (Whang, 1977; magnetosphere (blue) in meridian plane projection (x–z Jackson and Beard, 1977; Ng and Beard, 1979; plane) compared with the vector magnetic field observed Bergan and Engle, 1981) allowed for the possibility along the M1 passage through the magnetotail. of internal field through degree 2 or 3, but only in the zonal harmonic (m ¼ 0) coefficient, for example, 0 0 and g2 and g3. Models allowing for axisymmetric quadrupole (n ¼ 2) or octupole (n ¼ 3) terms are 10.07.3.2 Venus characterized by a reduced dipole magnitude, rela- tive to models allowing dipole terms only. This Venus is similar to Earth in size (Rv ¼ 6051 km), mass applies to all such models, regardless of author or (Mv ¼ 0.815 Me), and density, and probably composi- method of analysis or even the details of the expli- tion as well. Venus orbits the Sun once every 225 cit models chosen to represent fields of external days at a mean orbital radius of 0.723 AU. Proximity origin. This curious effect was shown to be related to Earth has invited a relatively large number of to model nonuniqueness, a consequence of the missions, particularly in the early decades of space limited spatial extent of the data (Connerney and exploration (Colin, 1983; Russell and Vaisberg, 1983). Ness, 1988). At the present time, that is, pending However, unlike Earth, Venus has no measureable arrival of Messenger, there is no evidence for (or internal magnetic field; spacecraft have detected only against) a nonzero axisymmetric quadrupole or weak magnetic fields associated with the solar octupole. Until then, a simple dipole model (e.g., wind interaction (Russell and Vaisberg, 1983). Ness, 1979a) provides the best description of Venus also rotates very slowly, with a period of 243 Mercury’s magnetic field. The internal field is days. The relatively slow rotation in itself does just sufficient to keep the dayside magnetopause not explain the lack of a dynamo, as it is easily above the planet’s surface under nominal solar enough to make Coriolis forces dynamically impor- wind conditions (Figure 4). tant (Stevenson, 2003). Planetary Magnetism 251

10.07.3.2.1 Observations 10.07.3.3 Mars The first measurements of the magnetic field near Mars is about half the size (R ¼ 3394 km) of Earth Venus were obtained in December 1962, by the m and much less massive (M ¼ 0.108M ). Mars resides Mariner 2 spacecraft, on a flyby trajectory with a m e at a mean orbital distance of 1.52 AU, orbiting the closest approach of 6.6 planet radii. Magnetic field Sun once in 687 days. It has also been an attractive measurements obtained by the triaxial fluxgate mag- target for planetary exploration, playing host to netometer (FGM) aboard Mariner 2 provided no more than 30 attempted missions since 1960 evidence of an intrinsic planetary field (Smith et al., (Connerney et al., 2004). At present, the Mars 1963; Smith et al., 1965) at this distance. Venus could Exploration Rovers (MERs) continue to explore the not have an internal magnetic field with a moment surface (Crisp et al., 2003), while MGS (Albee et al., exceeding 0.05 that of the Earth. 1998), Mars Odyssey (Saunders et al., 2004), Mars The 1960s and 1970s saw the arrival of the Venera Express (Chicarro et al., 2004), and the Mars 4 (1967) and Venera 6 (1969) entry probes and the Reconnaisance Orbiter (Graf et al., 2005) all continue Mariner 5 (1967) and Mariner 10 (1974) spacecraft on to acquire observations from orbit. It is the most fly by trajectories with close approach distances of 1.7 impressive armada of active spacecraft ever and 1.96 Rv. These were followed by the Venera 9 assembled for planetary exploration. and 10 orbiters in 1975 and the pioneer Venus Orbiter (PVO) in 1978. The Veneras were placed in highly elliptical orbits with an orbital period of 10.07.3.3.1 Observations approximately 48 h, periapsis at 1545 and 1665 km After five unsuccessful attempts (four by the USSR; altitude, respectively, and apoapses of approximately one by the USA), Mariner 4 became the first mission to return data from Mars on 15 July 1965. Mariner 4’s 18.5Rv. Throughout this period the existence of an intrinsic magnetic field was debated (see Russell and fly by trajectory brought the spacecraft to within 4Rm Vaisberg, 1983) amid ever-decreasing estimates, or of the planet, from which vantage point it observed upper limits on, the Venus dipole moment. The PVO the near-Mars environment. The magnetic field was indistinguishable from the interplanetary environ- was placed in a highly elliptical orbit with an orbital ment; on bow shock, no magnetopause, no period of 24 h, periapsis at 140–170 km altitude, and magnetosphere was observed. If Mars had an intrinsic apoapsis at approximately 12R . This orbit geometry v magnetic field, it had to be very small in magnitude, afforded observation of, and a better understanding less than 3 104 M (M , the magnetic dipole of, the interaction of the solar wind with a planetary e e moment of Earth, is 8 1025 Gcm3), to remain atmosphere. These observations led to an upper limit unseen (Smith et al., 1965). This upper limit is equiva- on the Venus dipole moment of 4105 that of lent to an equatorial surface field of 100 nT, well less Earth’s (Russell et al., 1980), which was reduced than Earth’s (30 000 nT) but not so much less than the further (to 1 105 ) by a more exhaustive ana- Me as yet undiscovered magnetic field of Mercury lysis (Phillips and Russell, 1987) that also (330 nT). demonstrated a lack of evidence for magnetic fields In the following three decades, numerous space- associated with crustal remanence. craft visited Mars, but no spacecraft, probe, or lander instrumented to measure magnetic fields would pass close enough to the surface to establish the presence of an intrinsic magnetic field. The US missions 10.07.3.2.2 Discussion following Mariner 4, Mariner 9 (1971), and Viking One concludes that Venus does not currently have an 1 and 2 (1975), were not instrumented to measure active dynamo; at present, little can be said of the magnetic fields. Additional magnetic field observa- possibility that Venus once sustained a dynamo. One tions were obtained by the Soviet Mars 2, 3, and 5 would like to understand why this Earth-like planet spacecraft (Russell, 1979; Ness, 1979a) in the early does not have an active dynamo, and there are many 1970s and the Soviet Phobos 2 mission in 1988. These possibilities (Stevenson, 2003). The favored explana- observations fueled a great deal of debate regarding tion is that sufficient convection in the fluid outer the existence of a putative Mars dipole (with equa- core is lacking at present, owing perhaps to the inef- torial surface field in the range 20–65 nT) but no ficiency of heat transport (relative to Earth, where convincing evidence of an intrinsic field was found plate tectonics helps cool the core, see Chapter 10.09). (Riedler et al., 1989). 252 Planetary Magnetism

Thus it was the MGS spacecraft (Albee et al., magnetic field measured at 3 s intervals along the tra- 1998), launched in 1996 as a (partial) replacement jectory. From this image one can see that the intrinsic for the unsuccessful Mars Observer, which provided field is not global in scale, as it would necessarily be if it the first unambiguous detection of the intrinsic weregenerateddeepwithintheplanet,forexample,by magnetic field of Mars. On 11 September 1997, the dynamo action. Instead, the field is localized to a small MGS spacecraft was inserted into a highly elliptical part of the trajectory, with a characteristic length scale polar orbit from which it would transition to a comparable to the altitude of observation. This is the circular polar mapping orbit (nominal 400 km alti- signature of a strong and localized magnetic source in tude) via a series of aerobraking maneuvers (Albee the crust of Mars, just beneath the spacecraft orbit et al., 1998). Aerobraking uses atmospheric drag to track. This particular source produces a field of nearly slow the spacecraft, reducing apoapsis by repeated 400 nT at 110 km altitude, requiring a very large passage through the atmosphere; trim maneuvers volume of intensely magnetized material, with a 16 2 are used to raise or lower the altitude at closest moment of 1.6 10 Am (Acun˜a et al., 1998). approach (periapsis) to obtain the desired drag. The MAG-ER investigation on MGS acquired Each aerobraking pass brought the spacecraft over magnetic field observations on over 1000 aerobraking the surface of Mars, to altitude <100 km, about as passes during the transition to mapping orbit. On each close to the surface as any orbiting platform can such pass the crustal field was sampled at low altitude achieve. During each aerobraking pass, the MGS along a limited ground track centered on the latitude and longitude of periapsis and extending approximately magnetometer/electron reflectometer (MAG-ER) investigation (Acun˜a et al., 1992) acquired measure- 25 in latitude north and south of closest approach. ments of the vector magnetic field along the orbit Periapsis passes were distributed more or less randomly track at varying altitudes above the surface. in longitude, as the orbit period was shortened by aerobraking, and over the course of aerobraking, the Periapsis pass 6 (day 264, 1997) provided a wealth of latitude of periapsis slowly evolved from 30 north scientific insight in a few minutes time: lacking a sig- latitude to 87 south. Thus MGS was able to sample nificant field of global scale, Mars has no active crustal fields over nearly the entire planet surface, dynamo but must have had one in the past when the which led to a map of the global distribution of mag- crust acquired intense remanent magnetization (Acun˜a netic sources in the Mars crust (Acun˜a et al., 1999). This et al., 1998). These observations are illustrated in map, reproduced here (Figure 6), is compiled by color Figure 5, showing the spacecraft trajectory and vector coding the (largely north–south) subspacecraft trajec- tory using the radial magnetic field component measured at that latitude and longitude. No correction for spacecraft altitude, which varies along the track Mars global surveyor from periapsis (100 km) to 200 km, is attempted. The most significant magnetic sources are distributed nonrandomly, largely confined to the older, heavily cratered terrain south of the dichotomy boundary; vast regions of the smooth northern plains are relatively nonmagnetic, as are the Argyre and Hellas impact craters and prominent volcanic edifices (Acun˜a et al., Day 264 1999). This led Acuna et al. to conclude that the Mars view from sun dynamo likely operated for a brief (few 100 My) period following accretion (4.5 Ga) and had ceased to oper- 400nT atebythetimeofthelatelargeimpacts,about3.9Ga. In March of 1999, MGS completed the transition to Figure 5 Mars Global Survey or trajectory and magnetic circular, polar mapping orbit with nominal altitude of field observations in an orbit plane projection for day 264, 400 km, from which it would begin its mapping mission. 1997. The vector magnetic field observed along the MGS The orbit is fixed in local time (2 a.m.–2 p.m.), and trajectory is illustrated by vector projection onto the orbit subsequent orbits cross the equator 28.6 westward of plane; vectors originate at the spacecraft position at the time of observation. From Connerney JEP, Acun˜ a MH, Ness the previous orbit. Each ‘mapping cycle’ of 28 days NF, Spohn T, and Schubert G (2004) Mars crustal duration provides uniform sampling of the globe with magnetism. Space Science Reviews 111(1–2): 1–32. track-to-track separation of about 1 (59 km) at the Planetary Magnetism 253

Mars crustal magnetism MGS MAG/ER 90°

–1500 0 1500

BR (nT) 60° Arcadia Utopia planitia Olympus ° mons 30 Elysium Isidis

0°

TharsisSinai montes

–30°

Hellas Argyre –60°

–90° 180° 150° 120° 90° 60° 30° 0° 330° 300° 270° 240° 210° 180° West longitude Figure 6 Global distribution of the most intense magnetic sources in the Mars crust. Magnitude of the radial magnetic field measured during the Mars Global Survey or aerobraking passes below 200 km altitude (to 100 km minimum altitude). Most intense sources are found in the heavily cratered southern highlands, south of and near the dichotomy boundary (thin line). From Acun˜ a MH, Connerney JEP, Ness NF, et al (1999) Global distribution of crustal magnetism discovered by the Mars Global Surveyor MAG/ER Experiment. Science 284: 790–793.

equator. Subsequent cycles increase the density of which ÁBr falls below a minimum threshold of ground tracks, providing complete global coverage 0.3 nT per degree latitude. The threshold is chosen with track-to-track spacing of 3 km at the end of 1 well above the noise background, so little noise Mars year (687 days). Thus MGS passes over the appears in the figure to obscure the context image. same position on Mars many times; the vector magnetic The extraordinary signal fidelity of this map can be field at satellite altitude can be mapped with extraor- appreciated by recognizing the pixels adjacent in long- dinary signal-to-noise (Connerney et al., 2001). This itude are statistically independent, by virtue of the map was compiled with observations obtained over the way MGS orbits accumulate. The map spans over nightside, where time-variable fields due to the solar two orders of magnitude of signal dynamic range. wind interaction are minimized, to improve the signal The electron reflectometer (ER) instrument of the fidelity of the crustal field. The crustal field at mapping MAG/ER investigation (Acun˜a et al., 1992; Acun˜a altitude reaches a maximum of 220 nT over the inten- et al., 1998) provides another means of sensing, remo- sely magnetized southern highlands. This and other tely, the magnitude of the magnetic field between the compilations of MGS observations are available online. spacecraft and atmosphere (Lillis et al., 2004; Mitchell A much improved map of the field produced by et al., 2007). The technique is similar to that used in crustal sources was obtained by using a more effective lunar orbit to infer surface magnetic field magnitudes means to remove residual external fields (Connerney (Anderson et al., 1975; Lin et al., 1998; Mitchell et al., et al., 2005). This map (Figure 7)isa360 180 pixel 2007) from the properties of the (reflected) electron ‘image’ of the filtered radial magnetic field, each pixel distribution; however, at Mars, the presence of an representing the median value in a 1 1 latitude– absorbing atmosphere must be taken into account longitude bin. This map represents the change in (Lillis et al., 2004). Application of this technique at radial field, or ÁBr, in nT per degree latitude, as the Mars is particularly effective in sensing weaker fields spacecraft moves north to south over the darkened at an altitude of about 170 km above the surface. A hemisphere. The map is superposed upon a Mars global map of field magnitudes at this altitude Orbiter Laser Altimeter (MOLA) shaded topography (Mitchell et al., 2007), with a spatial resolution of map (Smith et al., 1999), which appears in any pixel for 150 km and using a minimum B threshold of 254 Planetary Magnetism

Δ Mars crustal magnetismBr Mars global surveyor MAG/ER 90°

60°

30°

0°

–30°

–60°

–90° 0° 90° 180° 270° 360° East longitude ΔB /ΔLat (nT/deg) r –30 –10 –3 –1 –.3 +.3 131030 Figure 7 Map of the magnetic field of Mars observed by the Mars Global Survey or satellite at a nominal 400 km (mapping) altitude. Each pixel is colored according to the median value of the filtered radial magnetic field component observed within the 1 1 latitude/longitude range represented by the pixel. Colors are assigned in 12 steps spanning two-orders-of- magnitude variation. Where the field falls below the minimum value a shaded MOLA topography relief map (Smith et al., 1999)and contours of constant elevation (4, 2, 0, 2, 4 km elevation) are shown. From Connerney JEP, Acun˜ a MH, Ness NF, et al (2005) Tectonic implications of Mars crustal magnetism. Proceedings of the National Academy of Sciences 102(42): 14970–14975.

10 nT at 170 km altitude, compares very well with (Purucker et al., 2000; Langlais et al., 2004) to chose the map (Figure 7) compiled from magnetic field from. These models can be obtained from the authors measurements. The broad regions that appear in in electronic form. They offer a means of extrapolating shaded topography in Figure 7, in which the mag- the field from the measurement surface (400 km) and netic field falls below threshold, are nearly identical volume spanned by aerobraking passes to nearby to the weak-or zero-field regions (to an accuracy of a points; however, neither can be expected to accurately few nanoteslas) mapped by the ER. predict the field near the source region. Mars crustal magnetism is amenable to study using 10.07.3.3.2 Models many of the methods and tools developed for inter- The representations routinely employed throughout pretation of magnetic surveys on Earth. In ‘Source the solar system – dipoles and spherical harmonic modeling’, one attempts to fit the observed vector expansions – lose much of their appeal when applied field using one or more magnetized sources, for exam- to the crustal field on Mars. Such global models require ple, a collection of thin plates and prisms, often guided an awkward number of model parameters or coeffi- by constraints suggested by local geology and material cients to represent the crustal field. For example, properties. General techniques of ‘continuation’ of a Cain’s (Cain et al., 2003) spherical harmonic model potential field may also be applied to extrapolate the 2 extends to Nmax ¼ 90, requiring Nmax þ 1) 1 ¼ 8280 field away from a surface upon which the vector field is model coefficients to calculate the field at one point known. Downward continuation (toward the source) above the surface. Likewise, Purucker’s many-dipole must be done with caution, as it is essentially a differ- model (Purucker et al., 2000)uses11500dipolesdis- encing operation that amplifies short-wavelength tributed on a spherical surface (1 Rm) to represent the random noise (exponentially in z). Source modeling field by superposition. There are a variety of spherical mustalsobedonewithcaution,asitisnotpossibleto harmonic (Cain et al., 2003; Arkani-Hamed, 2001a; uniquely determine crustal magnetizations using Arkani-Hamed, 2002) and equivalent source models measurements external to the source. Planetary Magnetism 255

Connerney et al., (1999) used a source model to fit 1500 B observations obtained during several aerobraking 1999 day 20 P7 x passes over the intensely magnetized southern high- 1000 lands(TerraCimmeriaandTerraSirenum).These 500 quasi-parallel features appear lineated in the east– west (cross-track) direction; many can be traced over 0 1000 km in length. The model consisted of multiple –500 uniformly magnetized parallel thin plates, aligned (and extending to infinity) in the east–west direction. –1000 Altitude 400 The volume magnetization of each strip was deter- 200 –1500 mined using a linear inverse methodology to best fit –3000 –2000 –1000 0 1000 2000 3000 the vector observations along one or more aero- braking passes (Figure 8). The observations could be 20 J fit well with a model characterized by strips of alter- 0 x –1 A m nating polarity and volume magnetizations of as much –20 20 1 J as 20 A m (assuming a 30 km-thick plate). This z 0 figure is likely a lower bound, since only the product –20 of thickness and volume magnetization is constrained by the observations (Connerney et al., 1999). If the 1000 magnetization is borne in a thin layer, say 3 km, then 1999 Bz 1 day 20 P7 volume magnetizations of 200 A m would be 500 required. Connerney et al., (1999) found the magnetic lineations on Mars sufficiently reminiscent of the pat- 0

tern of magnetization associated with seafloor nT nT spreading on Earth that they proposed a similar –500 mechanism – crustal spreading in the presence of a reversing dynamo – for the evolution of the Mars crust. –1000 Sprenke and Baker (2000) modeled crustal magne- tization in the southern highlands using the same –1500 –3000 –2000 –1000 0 1000 2000 3000 aerobraking observations and inverse methods used x (km) by Connerney et al. (1999). Their models imposed Figure 8 Vector magnetic field measured by MGS during constraints on the direction of magnetization aerobraking on calendar day 20, 1999. Periapsis occurred (‘normal’ and ‘reversed’) and allowed for a variation in at 68.0 S, 181.2 W, and 106 km altitude. The x (north) and z the intensity of magnetization in the cross-track direc- (down) components of the vector field sampled every 3 s tion. They found similar magnetization intensities and (crosses) are compared with a model fit (solid line). Altitude variation in kilometers is indicated with a dashed line. found a good fit to the observations with a seafloor Observations plotted as a function of distance x north and spreading model, allowing for variation of magnetiza- south of an origin at 53 S and at the longitude of periapsis. tion intensity (but not direction) along the stripes. The Model consists of 20 uniformly magnetized slabs aligned more uniformly distributed observations obtained at with the y-axis (east–west) and infinite in extent along y. The mapping altitude over the same region were downward x and z-components of the model crustal magnetization per unit volume (A m1) are indicated in the bar graphs between continued using the Fourier transform method (Jurdy the two panels. From Connerney JEP, Acun˜ a MH, and Stefanick, 2004). Continuation to a 100 km-altitude Wasilewski PJ, et al. (1999) Magnetic lineations in the surface allowed a favorable comparison with the aero- ancient crust of Mars. Science 287: 794–798. braking observations, and revealed abrupt lateral changes in field direction and magnitude suggestive of, but not requiring, reversed lineations. There is great interest in identifying a Mars Frawley and Taylor, 2004). A large number of putative paleopole, and a number of authors have sought to paleopoles have been proposed but as yet no concensus determine ancient pole position(s) on Mars by fitting has emerged. A general consideration of nonuniqueness various magnetized sources to MGS magnetic in the interpretation of potential fields would suggest field observations (Hood and Zakharian, 2001; that without additional constraints the problem remains Arkani-Hamed, 2001b; Sprenke and Baker, 2000; intractable (Connerney et al., 2004). An alternative 256 Planetary Magnetism approach, based on a statistical analysis of many sources are unique to plate tectonics, so if these features are (Sprenke, 2005), suggests a preference for paleopoles indeed transform faults then the Mars crust formed via near 17 N, 230 E, and 17 S, 50 E, near those pro- seafloor spreading as on the Earth (Connerney et al., posed earlier based on geomorphology and analysis of 1999; Sleep, 1990). The interpretation of this map is not grazing impacts (Schultz and Lutz, 1988). without controversy, however, and one may expect much more from these observations as the analyses 10.07.3.3.3 Discussion mature. Mars has no global field, therefore no dynamo at pre- Magnetic mapping is an even more powerful tool sent, but must have had one in the past when the crust on Mars than on Earth, where it has been indespen- acquired intense remanent magnetization. (see also sable in understanding the evolution of the Earth, Chapter 10.09) It is likely that a molten iron core especially in the development of the unifying theory formed early, after, or during hot accretion 4.5– of plate tectonics. On Earth, magnetic surveys are 4.6 Ga, and for at least a few hundred million years, a complicated by the presence of the main field, substantial global field was generated by dynamo which makes measurement of crustal anomalies action in the core. The chronology proposed by challenging (limited signal to noise) and more diffi- Acun˜a et al. (1999) attributes the global distribution of cult to interpret (induced or remanent field?). Mars is magnetization to an early demise of the dynamo, prior free of such complications; the global map of its to the last great impacts (4Ga).Schubert et al. (2000) crustal field is unique, affording an opportunity to argued in favor of a late onset of the dynamo, and apply the methods of exploration geophysics on a propose that the southern highlands crust acquired global scale. It is clear that the crust of Mars retains magnetization from local heating and cooling events a magnetic imprint of its formation and subsequent that postdate the era of large impacts and basin forma- evolution. That history may be read with increasing tion. Early onset and cessation of the dynamo is resolution as magnetic surveys are conducted at difficult to reconcile with the notion of a dynamo lower altitudes. One may anticipate great insights driven by solidification of an inner core (Schubert from such surveys as well as Mars paleomagnetism et al., 1992), the preferred energy source for the when that field develops. Earth’s dynamo. Alternatively, an early dynamo can be driven by thermal convection, with or without plate tectonics, for the first 0.5–1 Gy (Breuer and Spohn, 10.07.4 Gas Giants 2003; Schubert and Spohn, 1990; Stevenson et al., 10.07.4.1 Jupiter 1983; Connerney et al., 2004), persisting as long as the core heat flow remains above a critical threshold for Jupiter, the largest (Rj ¼ 71 372 km) and most massive thermal convection (Nimmo and Stevenson, 2000). (Mj ¼ 318 Me) planet in the solar system, resides at a After more than 2 full years of mapping operations, mean orbital distance of 5.2 AU from the Sun. Jupiter, MGS has produced an unprecedented global map of capturing much of the gas component of the solar magnetic fields produced by remanent magnetism in nebula, is largely a solar mix of H and He, possibly the crust (Connerney et al., 2005). This map (Figure 7) with a rock and ice core of some tens of Earth masses. reveals cotrasts in magnetization that appear in associa- The Jovian system (see also Chapter 10.13 for a dis- tion with known faults; variations in magnetization that cussion of the gaint planets) has been visited often by are clearly associated with volcanic provinces; and spacecraft, both as a destination and as a waypoint for magnetic field patterns that appear shifted along vessels destined to travel onward. A passing space- small circles in the manner of transform faults at craft can use Jupiter’s considerable mass and orbital spreading centers (Connerney et al., 2005). Connerney velocity to advantage, acquiring a boost to greater et al. proposed that the entire crust acquired a magnetic radial distances (e.g., Cassini, New Horizons to imprint via spreading in the presence of a reversing Pluto) or to achieve higher solar latitudes (e.g., dynamo and that erasure of this imprint occurred Ulysses), than would otherwise be possible. Thus, where the crust was buried (thermal demagnetization) Jupiter’s orbit serves as a crossroads for travelers to by flood basalts to depths of a few kilometers. In the other worlds as well. remaining magnetic imprint one can identify the tell- Jupiter was known to have a magnetic field long tale signature of transform faults, in Meridiani, and the before the first in situ observations were obtained. signature of craters that formed both before and after Burke and Franklin (1955) had detected nonthermal thedemiseofthedynamo.Ofcourse,transformfaults decameter-wavelength emissions (22 MHz) from Planetary Magnetism 257

Jupiter, leading to speculation that Jupiter possessed direction of Io’s orbital motion from geocentric a magnetic field of internal origin. Observations at superior conjunction). Io’s influence on Jovian radio decimetric (1 GHz) wavelengths subsequently emissions was attributed to an electrodynamic inter- revealed synchrotron radiation, emitted by high- action (Goldreich and Lynden-Bell, 1969) that drives energy electrons trapped in a Jovian Van Allen belt. currents along magnetic field lines to and from This emission, as observed, is modulated by the rota- Jupiter’s magnetosphere. tion period of the planet (9.925 h). Since synchrotron radiation is narrowly beamed in a direction perpen- dicular to the magnetic field guiding the electron 10.07.4.2 Observations motion, the modulation can be used to infer the Pioneer 10, the first spacecraft to enter the Jovian geometrical properties of the field. Thus, the tilt magnetosphere, passed within 2.8 of the planet at Rj (9.5 ) and phase (200 III) of the Jovidipole were closest approach in December 1973. Pioneer 10’s deduced (Morris and Berge, 1962), and estimates of flyby trajectory carried it through the Jovian system the dipole offset (from the origin) were made at relatively low magnetic latitudes (Figure 9). This (Warwick, 1963), well before the first spacecraft region, near the equator, is home to a large-scale arrived at Jupiter. The magnitude of the field, how- system of azimuthal currents (ring currents) extend- ever, remained in doubt. ing from about 5 Rj to the outer reaches of the Continued observations of Jovian radio emission magnetosphere (100Rj). This current system at decameter wavelength revealed yet another peri- imparts a disk-like geometry to the magnetic field, odicity in the occurrence of radio storms, one that with field lines at great distances stretched nearly matched the orbital period (42.46 h) of the innermost parallel to the equator (leading to the descriptive Galilean satellite, Io (Bigg, 1964). The intensity and ‘Jovian magnetodisc’). Precisely 1 year later, occurrence rate of radio storms varies dramatically Pioneer 11 approached to within 1.6 Rj on a retro- with Io’s orbital phase, as well as Jovian central mer- grade III trajectory. The Pioneer 11 trajectory idian longitude (CML). Activity peaks when Io’s provided measurements over a wide range of planet orbital phase is near 90 and 240 (measured in the latitudes (Figure 9) and longitudes.

Z II M ULY (1992)

P10 (1973) P11 (1974) 5

a

10 Europ Magnetodisc – – – Current sheet V1 (1979) ymede Gan

–5

Pioneers 10 and 11 Voyager 1 and Ulysses

15 10 5 0 5ρ 10 15 (RJ)

Figure 9 Spacecraft flybys (Pioneer 10 and 11, Voyager 1, and Ulysses) of Jupiter in a magnetic equatorial (cylindrical) coordinate system. The z-axis is aligned with Jupiter’s magnetic dipole axis. The spacecraft distance from the magnetic equator (z) as a function of distance from the z-axis () is given in units of Jupiter radius. The Galilean satellites Io, Europa, and Ganymede trace out arcs (not shown) in this coordinate system crossing the equator at the radial distances indicated. The shaded region approximates the washer-shaped system of azimuthal ring currents that gives rise to the magnetodisc configuration of the Jovian magnetosphere. 258 Planetary Magnetism

The Pioneer 10 and 11 spacecraft were instru- much like that of Voyager 1, in that for much of the mented to measure magnetic fields with a vector time nearest closest approach the spacecraft was helium magnetometer (VHM) provided by the Jet immersed in the local currents of the Jovian Propulsion Laboratory (Smith et al., 1975). This magnetodisc. instrument could measure a maximum of 1.4 G in The recently completed Galileo mission to the the highest of its eight dynamic ranges. Pioneer 11 Jovian system was designed to deliver an atmospheric also carried a small high-field triaxial FGM provided probe, explore the distant magnetosphere, and provide by the Goddard Space Flight Center (Acun˜a and opportunities for many satellite encounters (Johnson Ness, 1976). The FGM was added as a precaution, et al., 1992). It did not provide appreciable additional to extend measurement capability to a field of 10 G information on the planetary field. Likewise, the along each axis (Earth’s field magnitude 0.6 G at Cassini spacecraft encounter was a distant flyby, engi- the pole). The magnitude of Jupiter’s field was neered to speed the spacecraft onward to its unknown at the time of launch, and the concern destination (Saturn) in the outer solar system. was that without a high-field instrument Pioneer 11 might not have the dynamic range needed to make observations throughout the encounter. Fortunately, 10.07.4.3 Models the maximum field experienced by Pioneer 11 was 1.12 G, observed just as the spacecraft went into The large number of Jovian magnetic field models occultation on its way to closest approach at 1.6 Rj. available is a result of several factors, interest in the There are small but significant differences between Jovian system undoubtably foremost among them. the two data sets that have not been fully resolved, so There is a wealth of observations of Jovian phenom- most analyses have tended to use data from one or ena, many of which (e.g., radio emission, aurorae) the other but not both. depend critically on details of the magnetic field The two Voyager encounters followed in March near the planet where few direct observations exist. and July of 1979. Like Pioneer 10, the Voyagers The need is great. In addition, techniques for model- remained near the Jovigraphic equator, confined to ing the field have evolved, and improved, in part in relatively low magnetic latitudes. Voyager 1 was response to the challenges of separating the planetary targeted for a close flyby of Io and the Io flux tube field from that produced by external currents. (IFT); its closest approach to Jupiter was 4.9 Rj, just Techniques have also evolved to take advantage of inside the orbit of Io (5.95 Rj). The maximum field new observations (e.g., emission from the foot of the measured by Voyager 1 was just 3330 nT. The IFT) that serve as valuable constraints on the field Voyager 2 flyby was relatively distant, with a closest near the surface. Here we describe a subset of the approach distance of 10Rj. In this region of the mag- available models, intended to illustrate the develop- netosphere, the measured magnetic field has a ment of new approaches. significant contribution due to the magnetodisc The first models of Jupiter’s planetary field were currents. These will tend to reduce the component the OTD approximations (D2 and D4) obtained of the planetary field near the equator and introduce from the Pioneer 10 and 11 VHM observations a component of the field in the radial direction (Smith et al., 1976). Analyses of the Pioneer 11 which changes sign in crossing the magnetic equator. FGM observations suggested that a more capable Local currents cannot be modeled with potential parametrization was needed, leading to development fields and if present, may lead to large errors in of the O4 model (Acun˜a and Ness, 1976), the first of estimates of the planetary field if not accounted for many spherical harmonic models of Jupiter’s internal (Connerney, 1981). field. This model and the SHA model of Smith et al. Jupiter was not visited again until the Ulysses (1976) allowed spherical harmonics of degree and flyby on 8 February 1992, more than two decades order 3 (octupole) for the internal field and approxi- after the Voyager flybys. Ulysses was designed to mated external fields with external harmonics of study the heliosphere at high solar latitudes; the degree 1 or 2. Table 3 gathers together the spherical Jupiter flyby was used to kick the spacecraft into a harmonic coefficients of several models, fit to various high-inclination orbit about the Sun. The spacecraft subsets of data and using a variety of methods. approached Jupiter at relatively high northern lati- Estimated errors are given for some of these models, tude, measuring a maximum field of 2372 nT just but not reproduced here, for brevity. The original after closest approach at 6.3 Rj. This encounter was publication should be consulted. Planetary Magnetism 259

Table 3 Jovian magnetic field models: spherical harmonics

1992.1: 1979.2: 1979.2: Pioneer 11 Coefficient Ulysses Voyager 1

Number Coefficient VIT 4: VIP 4: 17ev O6 17ev O4 SHA

0 1 g1 428077. 420543. 410879. 424202. 420825. 421800. 409200. 1 2 g1 75306. 65920. 67885. 65929. 65980. 66400. 70500. 1 3 h1 24616. 24992. 22881. 24116 26122. 26400. 23100. 0 4 g2 4283. 5118. 7086. 2181. 3411. 20300. 3300. 1 5 g2 59426. 61904. 64371. 71106. 75856. 73500. 69900. 2 6 g2 44386. 49690. 46437. 48714. 48321. 51300. 53700. 1 7 h2 50154. 36052. 30924. 40304. 29424. 46900. 53100. 2 8 h2 38452. 5250. 13288. 7179. 10704. 8800. 7400. 0 9 g3 8906. 1576. 5104. 7565. 2153. 23300. 11300. 1 10 g3 21447. 52036. 15682. 15493. 3295. 7600. 58500. 2 11 g3 21130. 24386. 25148. 19775. 26315. 16800. 28300. 3 12 g3 1190. 17597. 4253. 17958. 6905. 23100. 6700. 1 13 h3 17187. 8804. 15040. 38824. 8883. 58000. 42300. 2 14 h3 40667. 40829. 45743. 34243. 69538. 48700. 12000. 3 15 h3 35263. 31586. 21705. 22439. 24718. 29400. 17100 0 16 g4 22925. 16758. 1 17 g4 18940. 22210. 2 18 g4 3851. 6074. 3 19 g4 9926. 20243. 4 20 g4 1271. 6643. 1 21 h4 16088. 7557. 2 22 h4 11807. 40411. 3 23 h4 6195. 16597. 4 24 h4 12641. 3866.

Magnetodisc

R0 7.1 5.(UR) R1 128. (UR) 56. D 3.3 3.1

0I0/2 137. 185. Y0 8.2 6.5 È 200. 206.

Schmidt normalized spherical harmonic coefficient in gauss, referenced to Jupiter system III (1965) coordinates, and 1 Rj ¼ 71 398 km for Ulysses; 1 Rj ¼ 71 323 km for Voyager 1. Voyager 1 17ev model from Connerney et al. (1982a). The notation ‘UR’ refers to unresolved parameters. Pioneer 11 O4 model coefficients as tabulated for system III (1965) by Acun˜ a et al. (1983b) (originally (1957 system III) from Acun˜ a and Ness (1976)). Pioneer 11 SHA model originally (1957 System III) from Smith et al. (1976).

The Pioneer 11 VHM and FGM observations external fields – can lead to large errors among the have proved to be most useful for studies of the internal field coefficients. Pioneer 11 also remained planetary field, in large part due to the relatively largely outside of the region of current flow (equa- good spatial distribution of observations afforded by torial magnetodisc) near closest approach so external that spacecraft’s trajectory. The problem of inverting fields are less of a problem. flyby observations to obtain estimates of the spherical The Voyager 1 observations yielded a consider- harmonic coefficients has been posed as an eigenva- ably reduced dipole moment, upon preliminary lue problem and solved using the SVD method analysis, which was attributed to the presence of (Connerney, 1981). This technique allows partial magnetodisc currents that were not adequately mod- solutions to underconstrained linear inverse pro- eled (Ness et al., 1979a). Subsequent analyses of the blems and can be used to show how even small Voyager 1 observations used an explicit model of the measurement errors – such as noise or unmodeled magnetodisc (Connerney et al., 1981) in combination 260 Planetary Magnetism with a spherical harmonic model for the planetary fields of higher degree and order than octupole might field. An inversion scheme that allowed for variation be present in the observations (particularly those of of the parameters of the magnetodisc along with Pioneer 11, passing to within 1.6 Rj). This model those of the internal field resulted in a partial octu- represents a partial solution to an underdetermined pole model (V1 17ev) of the planetary magnetic field inverse problem (spherical harmonic expansion to (Connerney et al., 1982a). The Voyager 1 model of degree and order 6) combined with an explicit the field (epoch 1979) could be compared with the model of the magnetodisc. Another distinguishing Pioneer 11 model (GSFC O4) of the field (epoch feature of this model was the application of a weights 0 nþ2 1973) to limit Jovimagnetic secular variation (g1)to (rc/a) to parameters of degree n, where rc, the core 1 no more than 0.2% yr (Connerney and Acun˜a, radius, was taken to be 0.7Rj. This weighting 1982). By comparison, the present-day decrease in encourages a model solution with terms of degree 0 1 the terrestrial g1 term is about 0.075% yr . n contributing equally to the mean-squared field Preliminary analysis of the Ulysses encounter amplitude on the (presumed) core boundary, as is observations (Balogh et al., 1992) suggested good observed for Earth, through degree 13 or so agreement with the magnetic field calculated using (Langel, 1987). The Schmidt coefficients of this the O6 planetary field augmented with a magnetodisk model (‘O6’ for octupole part of a degree 6 expansion) current sheet model (Connerney et al., 1981)ifone are listed in Table 3. The O6 model is characterized allowed for variations of the external field during the by smaller quadrupole and octupole moments, rela- encounter. The Ulysses close approach observations tive to the comparable O4 model of Acun˜a and Ness were obtained in the immediate vicinity of the inner (1976), and in that regard is more Earth-like in har- edge of the current sheet, so some attention to exter- monic content (Figure 10). nal fields is required. Dougherty et al. (1996) found The discovery of infrared emission at the foot of the the data consistent with Connerney’s O model, 6 IFT in Jupiter’s ionosphere (Connerney et al., 1993) allowing for a reduction of the g0 coefficient (main 1 provided an entirely new and extremely valuable dipole term), from 4.242 to 4.059 G. Connerney et al. constraint on magnetic field models. This emission (1996) derived an octupole model of the field occurs in Jupiter’s polar ionosphere where field lines (Ulysses 17ev), also with a reduced dipole g0 coeffi- 1 threading the satellite Io (or its conducting ionosphere) cient (4.109 G), and demonstrated that the internal at an orbital distance of 5.95R intersect the Jovian iono- zonal harmonic coefficients covary with the para- j sphere. The feature is observed to move across the disk meters of the current disk, complicating attempts to of Jupiter in concert with Io’s orbital motion, tracing a separate internal and external fields. The magneto- path around each magnetic pole ( ). This path disk current system was considerably weaker during Figure 11 the Ulysses epoch, relative to that observed during serves as a fiducial marker, providing an unambiguous the Pioneer and Voyager epochs. Connerney et al. reference on Jupiter’s surface through which magnetic (1996) quote a figure of 20% less total integrated field lines with an equatorial crossing distance of 5.95Rj magnetodisk current at the time of Ulysses encoun- must pass. Thus, observations of the location (latitude, ter, Dougherty et al. (1996) quoting a 28% reduction. longitude) of the footprint offer a unique constraint on Differences among the Ulysses era (Ulysses 17ev) magnetic field models, precisely where it is most model and those of Voyager (Voyager 1 17ev) and needed, on the surface of the planet, and otherwise unavailable. This emission is observable from Earth Pioneer (O4) appear within, or comparable, to esti- mated parameter errors (Connerney et al., 1996); so with ground telescopes (e.g., Infrared Telescope there is little evidence of secular variation of the Facility on Mauna Kea) in the infrared region of the main field as yet. spectrum (Connerney et al., 1993; Connerney and The O6 model of Jupiter’s magnetic field used Satoh, 2000), and with the Hubble Space Telescope observations from both Pioneer 11 (1973) and in the ultraviolet (Clarke et al., 1995, 1996, 2005; Prange Voyager 1 (1979), assuming that the magnetic field et al., 1996). Emission has now been detected at the foot has not changed appreciably between encounters, of the Europa and Ganymede flux tubes as well (Clarke and adds a constraint on Jupiter’s harmonic spectrum et al., 2002). These observations are less useful con- (Connerney, 1992). This model was designed to straints on the internal field because these field lines benefit from the better spatial distribution of obser- pass through the equator at greater radial distance (9.4 vations afforded by combining trajectories. It was also and 15Rj, respectively) where relatively large and vari- designed to allow for the possibility that unmodeled able external fields are encountered. Planetary Magnetism 261

1.0 n IRTF NSFCAM ∑ m 2 m 2 29 Jun 1995 Rn = (n + 1) {(gn ) + (hn ) } m = 0 .5

tor ua eq tic .2 ne ag M

.1 04 PH SHA V1 17ev Rn GSFC 06 VIP4 JUPITER io-6 Rj ULY17ev 89° CML .05 Φ ° 10 = 90 VIT4_16ev 30 Rj

Figure 11 Image of Jupiter at 3.4 mmobtainedatNASA’s IRTF at Mauna Kea, Hawaii, using the NSFCAM facility þ .02 imager. At this wavelength, bright H3 auroral emissions originating above the homopause appear again as a planetary disc darkened by methane absorption. Magnetic field lines Earth

Satrun are drawn in meridian plane projection to illustrate where field lines crossing the equator at 30R and 6R (Io’s orbit) intersect .01 j j Jupiter’s surface. A bright emission feature at the foot of the Io Flux Tube (IFT) can be identified near the dawn limb, as well as faint emission extending along the Io L-shell downstream of the instantaneous IFT. From Connerney JEP and Satoh T .005 1 2 3 4 (2000) The H3þ ion: A remote diagnostic of the Jovian n magnetosphere. Philosophical Transactions of the Royal Society of London A 358: 2471–2483. Figure 10 Relative harmonic content (Lowe’s spectrum) of spherical harmonic models of the Jovian field, compared with that of Earth and Saturn. model. All that is needed is a means of constraining the Over 100 determinations of the location of the IFT magnitude of the field. The final model in Table 3 lists footprint were combined with in situ magnetic field a model derived using over 500 IFT footprint locations observations (Pioneer 11 VHM and Voyager 1 FGM) (Connerney et al., 1998). This model constrains the field to obtain a partial solution to a fourth degree and order magnitude using a minimum of in situ magnetic field expansion of the internal field (Connerney et al., 1998). data: the component, only, of the Voyager 1 closest This model is referred to as the ‘VIP4’ model approach data obtained within 7Rj. The Voyager 1 data (Table 3), reflecting use of Voyager 1, IFT, and was chosen as the most accurate (0.1%) available and Pioneer observations; and an internal spherical har- the component, ranging from 1036 nT to a maximum monic expansion to degree and order 4. This model of 3280 nT, as the least influenced by external fields was designed to fit the position of the IFT footprint (larger in magnitude than the radial component of the very well (within 1 latitude), so it has proven parti- external field but easily modeled). This model (‘VIT4’, cularly useful in analyses of satellite interactions and reflecting use of IFT observations, Voyager compo- aurorae. However, no one model fits the IFT foot- nent, degree and order 4) is essentially a product of prints and ‘all’ of the in situ magnetic field observations remote observation, using just enough in situ data to to within their expected errors (Connerney et al., constrain the magnitude of the field. In principal, any 1998), although the IFT observations can be so fit constraint on the field magnitude – such as the field with any ‘one’ set of flyby observations. magnitudeonthesurface,deducedfromthemaximum Surprisingly, the IFT footprint observations are frequency of radio emission at the electron cyclotron nearly sufficient ‘by themselves’ to yield a useful field frequency – would serve as well. 262 Planetary Magnetism

10.07.5 Discussion magnitude on the dynamically flattened surface of Jupiter, computed using the VIT4 model. This model The magnitude of the surface field for the O6 model has a less prominent north–south asymmetry in the ranges from just over 3 G at low latitudes to just over magnetic field magnitudes, compared to earlier models; 14 G at high (northern) latitudes. This is similar to the the maximum field in the Northern Hemisphere range of field magnitudes predicted by the O4 model of (13.9 G) is comparable to that of earlier models Acun˜a and Ness (1976). The variation of magnetic field (see Acun˜a et al., 1983b), but the maximum field in magnitude on the surface of Jupiter is illustrated in the Southern Hemisphere (13.2 G) is considerably lar- Figure 12, which depicts contours of constant field ger. The estimated uncertainty in the surface field

Jupiter 4 Ganymede 6 Europa 6 180 8 8 0 10 150 210 30 330 4 lo 10

8 12 120 2406 60 12 300

10 4

90 270 90 8 270 6

60 300 120 10 8 60 –60 6 4 30 330 150 0 180 M 4 6 ag net 30 ic equa –30 4 tor 6 North South

0 246810 12 14 IBI Gauss

Ganymede 10 Europa Io 8 12 60

6 8 30 8 6 or 6 10 quat 4 tic e gne Ma 0

4

4 –30 6 6 8 8 –60 10 8 10 12 10 12

12 –90 360 330 300 270 240 210 180 150 120 90 60 30 0 System lll longitude Figure 12 Contours of constant magnetic field magnitude (Gauss) on the dynamically flattened (I/15.4) surface of Jupiter, computed using the VIT4 model field (see text). The top panel shows the field magnitude in orthographic projections viewed from the north (left) and south (right); below the color bar is a rectangular latitude–longitude (System III west longitude) projection. A trace (dashed) indicates the position of the magnetic equator. Solid lines join points on the surface that trace along field lines to the orbits of the Galilean satellites Io, Europa, and Ganymede, with filled circles for increments of 30 in the satellite’s System III longitude. Planetary Magnetism 263 magnitude is about 1G(Connerney, 1981, 1992), but kilohertz to 1 MHz) than Jupiter, well below the could be appreciably greater if higher-degree and critical frequency required to penetrate the Earth’s -order harmonics are larger than expected. Figure 12 ionosphere. Thus, Saturnian radio emissions cannot also illustrates the foot of the IFT (‘Io foot’), which is be monitored using terrestrial radio receivers. the path traced out on the planet’s surface by the field lines which pass through the satellite Io as the planet rotates. The foot of the IFT passes through the region 10.07.5.1.1 Observations of highest field strength in the Northern Hemisphere at The discovery of Saturn’s magnetic field was thus left to Pioneer 11, arriving in September 1979, following a longitude of about 150 III. The maximum surface magnetic field magnitude present along the Io foot is its Jupiter swingby. The particle and fields investiga- consistent with the maximum frequency extent tions on broad Pioneer 11 obtained observations (39.5 MHz) of Jovian decameter radio emission along a spacecraft trajectory that remained within (DAM), assuming that the emission occurs at the local approximately 6 of the equator (Figure 13). The electron gyrofrequency and at the foot of the IFT most remarkable feature of Saturn’s magnetic field proved to be the close alignment of the magnetic (fc(MHz) ¼ 2.8 B (G)). dipole and rotation axes (Smith et al., 1980a; Acun˜a and Ness, 1980; Acun˜a et al., 1980), also noted by the charged particle investigations (Simpson et al., 1980; 10.07.5.1 Saturn Van Allen et al., 1980). Pioneer 11 approached to Saturn, the second largest (Rs ¼ 60 000 km) and most within 1.35Rs, measuring a maximum field of massive (Mj ¼ 95 Me) planet in the solar system, 8200 nT at 6 latitude (Smith et al., 1980a). resides at a mean orbital distance of 9.5 AU, nearly The Voyager 1 encounter in November 1980 and twice as far from the Sun as Jupiter. Like Jupiter, the Voyager 2 encounter in August 1981 provided the Saturn exhibits the characteristics of a condensed first observations of Saturn’s magnetic field at high object of solar composition. Saturn was assumed to northern and southern latitudes (Ness et al., 1981, be much like its larger companion before Pioneer 11 1982). Voyager 1 sampled relatively high latitudes arrived. However, unlike Jupiter, Saturn as a radio (40 ) at close radial distance (3.07Rs) but remained source was quiet. Saturn is too weak a radio source in the Southern Hemisphere while inside of 6Rs radial and too distant to be easily detected from Earth. In distance. Voyager 1 measured a maximum field of addition, Saturn emits at lower frequencies (a few 1093 nT at 40 latitude and 184 SLS longitude,

Saturn flybys 5

Zˆ II M II W Voyager 2 (1981) Ring current

as Pioneer II (1979 ) Mim EnceladusTethys Dione 0 a SOI (2004) Rhe Cassini Voyager 1 (1980)

–5 10 5 0 5 10 ρ (Rs)

Figure 13 Spacecraft flybys (Pioneer 11, Voyager 1 and 2, and Cassini) of Saturn in a cylindrical coordinate system in which the z-axis is aligned with Saturn’s magnetic dipole axis and rotation axis. The spacecraft distance from the equator plane (z) as a function of distance from the z-axis () is given in units of Saturn radius. The positions of satellites Mimas, Enceladus, Tethys, Dione, and Rhea are indicated. The shaded region approximates the innermost portion of a washer-shaped region of azimuthal ring currents. 264 Planetary Magnetism just prior to closest approach (Ness et al., 1981). dipole model was affirmed by independent analyses of Voyager 2’s closest approach of 2.69Rs occurred at charged particle absorption signatures (Chenette and 323 longitude, diametrically opposite those of Davis, 1982) which serve as a probe of the geometry of Pioneer 11 and Voyager 1. Voyager 2 sampled rela- the field. Analyses of the Pioneer 11 high-field fluxgate tively high latitudes in both hemispheres and measured magnetometer observations (Acun˜a et al., 1980)found a maximum field of 11:7 nT just prior to closest no departure of the field from axisymmetry; however, approach (Ness et al., 1982). in Saturn’s relatively weak field, the resolution of the More than two decades passed before the arrival of high-field fluxgate was quite limited. Working with Cassini at Saturn. The Cassini spacecraft has been in higher-resolution VHM observations, Smith et al. orbit about Saturn since its orbit insertion (SOI) on 30 (1980b) proposed a dipole tilt of 1, although the June 2004, and has remained relatively distant subse- orientation of the dipole could not be determined. quent to the orbit insertion maneuver (Dougherty et al., The combined Voyager 1 and 2 magnetic field 2005), targeting multiple satellite flybys from the van- observations were not consistent with the field of a tage point of a near-equatorial orbit. During SOI, the simple displaced dipole, nor did these observations spacecraft periapsis was just 1.33 Rs;thisistheclosest reveal any measurable departure from spin-axisym- CassiniwillcometoSaturn throughout its mission. metry (of the internal field). An axisymmetric, zonal Cassini is instrumented with two magnetometers, a harmonic model of degree 3 was found to be both vector fluxgate and a helium magnetometer, the latter necessary and sufficient to describe the magnetic operated in a mode to measure field magnitudes near field of Saturn (Connerney et al., 1982b). This three- the planet (Dougherty et al., 2004). However, a large parameter model is referred to as the Z3 model (zonal number of orbits have been executed, many with peri- harmonic of degree 3) and it is listed in Table 4;the apses <4Rs. The spacecraft is just now executing a nonaxisymmetric terms (m > 0) are insignificant. series of maneuvers designed to increase the inclination Independent analyses of the Voyager 1 and 2 observa- of the orbit, which will provide a more favorable dis- tions suggested an estimated uncertainty of 100 nT tribution of observations for internal field analysis, for the Z coefficients. The magnetic and rotation axes particularly near the end of mission, with many orbits 3 are indistinguishable, aligned to within 0.1. plannedwithperiapses<3R . s A series of analyses followed to test the high degree of axisymmetry of the Z3 model (reviewed in 10.07.5.1.2 Models Connerney et al. (1984b). Acun˜a et al. (1983a) showed The Pioneer 11 magnetic field observations were con- that the charged particle absorption signatures 3 observed in Saturn’s magnetosphere were consistent sistent with a dipole field of moment 0.20 G ? R S, slightly offset to the north of the planet’s center (Smith with the Z3 model. A reanalysis of the absorption et al., 1980a; Acun˜a and Ness, 1980; Acun˜a et al., 1980) signatures studied by Chenette and Davis (1982), 0 by about 0.04 or 0.05 Rs. The simple northward-offset allowing for the presence of a nonzero g3 term, found

Table 4 Saturn magnetic field models

Voyager Cassini Pioneer 11 g Epoch 2004.5 (V1þV2) 1980.9 1981.6 1979.7 Model SOI Z3 VI V2 P11A Zonal harmonics 0 g1 21084. 21184. 21224. 21084. 21180. 0 g2 1544. 1606. 1678. 1607. 1980. 0 g3 2150. 2669. 2613. 2513. 2350. External field 0 g1 10 11 8 10 1 g1 101 1 h1 002

Schmidt normalized zonal harmonic coefficients in nT, SLS coordinate system: 1Rs ¼ 60 330 km for Voyager and Pioneer 11 models. Cassini model uses 1Rs ¼ 60 268 km. Voyager and Pioneer model coefficients provided in this table have been adjusted for a reference radius of 60 330 km; see Connerney et al. (1982b) for coefficients referenced to 60 000 km as originally published. Planetary Magnetism 265 these signatures to be best fit by a zonal harmonic 90° Offset model which was indistinguishable from the Z3 model dipole 60° Z3 (Connerney et al., 1984b). A reanalysis of the Pioneer 11 VHM observations (Connerney et al., 1984a) identified 30° a spacecraft roll attitude error (of 1.4 in magnitude) as the primary source of the discrepancy between the 0°

Pioneer and Voyager results. After correcting the Latitude ° spacecraft roll attitude, these authors demonstrated –30 that the Pioneer 11 measurements were consistent –60° with the Z3 model field, and axisymmetry, to better than the accuracy of measurement (Connerney et al., –90° 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 1984a). The roll attitude error was subsequently inde- Field magnitude (G) pendently verified by analysis of Pioneer 11 imaging photopolarimeter data. After correcting for the roll Figure 14 Magnetic field magnitude (Gauss) as a function of planetocentric latitude on the dynamically flattened attitude error, Davis and Smith (1985, 1986) obtained (1/10.6) surface of Saturn computed using the axisymmetric a zonal harmonic model in substantial agreement with Z3 (zonal harmonic of degree 3) model of Saturn’s magnetic the Z3 model (Table 4). field (Connerney et al., 1982b), compared with that of a Analysis of the Cassini fluxgate magnetometer simple offset dipole. observations obtained during SOI confirmed (to the level of accuracy, approximately 0.1% and 0.1) too large by a factor of 30 to be attributed to a dipole the spin-symmetry of Saturn’s magnetic field offset. The Z3 model’s large antisymmetry with (Dougherty et al., 2005). A command error prevented respect to the equator plane cannot be removed by the helium magnetometer from making measurements a simple coordinate system translation. during SOI. A zonal harmonic model of degree 3 was ThehighdegreeofspinaxisymmetryofSaturn’s obtained (Table 4) from the fluxgate observations: it is magnetic field is unique among the planets. This unan- very similar to the earlier zonal harmonic models ticipated symmetry is somewhat disquieting from an derived from Voyager and Pioneer observations, but observational perspective, as it lends no simple expla- 0 for a smaller g3 term. The Cassini mission now enters a nation for observations of periodic magnetospheric phase in which the orbital inclination increases, provid- phenomena, for example, periodicities in magnetic ing observations of the magnetic field at progressively field and particle observations in the distant magneto- higher latitudes, although not as close to Saturn as SOI. sphere (Galope´au et al., 1991; Connerney and Desch, With better spatial coverage, and as more observations 1992; Giampieri and Dougherty, 2004; Giampieri et al., accumulate, one may expect some refinement of the 2006; Cowley et al., 2006;seealsoKaiser et al., 2005 and spherical harmonic models derived from Cassini. Giampieri et al., 2005), the modulation of Saturn kilo- metric radio emission (Desch and Kaiser, 1981; Kaiser 10.07.5.1.3 Discussion and Desch, 1982), optical spoke activity in Saturn’s B Magnetic field magnitudes (Z3 model) on the surface ring (Porco and Danielson, 1982), and ultraviolet aur- of a dynamically flattened Saturn (flattening 1/10.6) orae (Sandel et al., 1982). All of these phenomena would range from a minimum of 0.18 G at the equator of presumably be easier to explain if a magnetic anomaly maxima of 0.65 and 0.84 G at the southern and north- could be found. However, it is not clear how such a ern poles, respectively (Figure 14). Note that Saturn slight departure (e.g., the 0.1 limit of detection) from is the most dynamically flattened of all the planets, axisymmetry might so dramatically influence these and the polar magnetic field is substantially increased phenomena, which occur at different magnetic lati- by the decreased radial distance (0.9 Rs at the poles. tudes and as far as 1 or 2RS above the surface. The equatorial field magnitude is less than that of a The uncertainty regarding the origin of Saturn’s simple dipole or offset dipole, and polar field magni- quasi-periodic magnetospheric phenomena has spilled tudes (both north and south) exceed those of either a over into a related topic: Saturn’s rotation period. centered or offset dipole. An eccentric dipole repre- Accurate measurement of the rotation period of gas- sentation of the Z3 model has a northward eous planets relies on the long-term observation of displacement of the dipole of 0.038 Rs along the magnetospheric radio emissions, which are assumed rotation axis, in agreement with the Pioneer 11 to be locked in phase with the magnetic field and 0 0 OTD representations. However, the ratio of g3/g2 is interior of the planet. Long-term observation of 266 Planetary Magnetism

Jupiter’s radio emissions, for example, yield a consistent electrically conducting shell above the dynamo region estimate (Riddle and Warwick, 1976)ofrotationperiod (Stevenson, 1980, 1982;alsoKirk and Stevenson, 1987). (9 h, 55 min, 29.71 s) regardless of frequency of emission This nonconvecting shell forms above the dynamo measured or method of analysis (Carr et al., 1983). Note region as a result of the immiscibility of helium and that the uncertainty associated with this estimate is hydrogen under the temperature, pressure conditions in about 0.02 s (Carr et al., 1983), reflecting observation this region (the larger planet, Jupiter, would have no over many years. Saturn’s rotation period was mea- such region). In this model, the formation of helium sured in the Voyager era (1980–81) using periodicities raindrops results in a stably stratified conducting shell in kilometric radio emissions (SKR), yielding an esti- which, in differential rotation with respect to the core, mate of the rotation period (10 h, 39 min, 24 s) with an attenuates any nonaxisymmetric fields generated below. uncertainty of 7s (Desch and Kaiser, 1981; Kaiser Schubert et al. (2004) treated the more general case of et al., 1984). The larger uncertainty of this estimate is dynamo generation in a convective core within an due to the limited span of time (9 months) over which electrically conducting shell, taking into account the SKR could be monitored. Continued observation of mutual coupling between the two. These authors con- Saturn’s radio emissions, however, in the Ulysses era clude that the observable characteristics of planetary (Galope´au and Lecacheux, 2000) and during the dynamos are largely determined by the nature of the Cassini mission (Gurnett et al., 2005;Kurthet al., (electrically conducting) flow above the dynamo region. 2007) revealed variations of about 1% (6min)in The Z3 model of Saturn’s field can be used (with the apparent radio period – far in excess of that allowed caution) to predict the field inside the planet, but by statistical uncertainties. Likewise, direct measure- above the dynamo (or regions of current flow). The ment of periodicities in the magnetic field (Giampieri radial field component is of particular interest since it and Dougherty, 2004;seealsoKaiser et al. (2005) and is continuous across the core boundary, and if the Giampieri et al., (2005, 2006); Cowley et al., 2006) frozen flux assumption is satisfied, serves as a tracer yielded inconsistent rotation periods. Saturn’s radio of horizontal fluid motion at the outer radius of the emissions are influenced by variations in the solar dynamo (Backus, 1968; Benton, 1979; Benton and wind (Desch, 1982; Desch and Rucker, 1983)andare Muth, 1979). Figure 15 shows the latitudinal variation emittedfromasourceregionfixedinlocaltime(Kaiser of jBrj,computedusingtheZ3 model, on the surface of and Desch, 1982; Kaiser et al., 1984; Galope´au et al., a sphere of radius r ¼ 0.5 Rs, which is the approximate 1995). It has thus been proposed that variations in the outer boundary of the metallically conducting core 0 apparent periodicity of radio emissions are related to (Stevenson, 1983). The Z3 model (via the g3 term) variations in the solar wind (Cecconi and Zarka, 2005). enhances the field at the poles and reduces the radial If so, it is not clear which of the proposed rotation field near the equator, relative to a simple dipole. In periods most closely matches that of the deep interior fact, the Z3 model is very nearly identical to that of the planet. This is the subject of intense activity at required to minimize the low-latitude unsigned flux present, so perhaps a better understanding of Saturn’s across the core surface (Connerney, 1993). This may rotation, and quasi-periodic magnetospheric phenom- be the signature of a dynamo axisymmetrized by ena, will be forthcoming soon. differential rotation of a conductive layer above. The magnetic fields of Earth, Jupiter, and Mercury The high degree of symmetry (about the rotation all favor dipole tilts of approximately 10 in magnitude; axis) of Saturn’s magnetic field is a distinguishing Saturn’s dipole tilt is not yet determined but <0.1 or feature that may have some unexpected conse- so. The high degree of spin axisymmetry is surprising quences throughout the system. For this planet, a but not in and of itself a problem for dynamo theory specific radial distance in the equatorial plane maps (e.g., Lortz, 1972). The Cowling antidynamo theorem (along the magnetic field) uniquely to a correspond- (Cowling, 1933, 1957), which states that regenerative ing latitude on the surface (Connerney, 1986), as is dynamo action cannot occur if the magnetic field and illustrated in Figure 16. Thus, one may associate a fluid motions are axisymmetric, applies to the field in radial distance (ring plane conjugate) with any north- the dynamo region, not the field observed above. It is, ern or southern latitude. Narrow dark bands that however, necessary to explain why Saturn’s magnetic encircle the planet at 44.2 N, 46.3 N, and 65.5 N field is so dramatically different from Jupiter’s, given have been attributed (Connerney, 1986) to an influx the similarity in size, composition, and rotation. of water guided along magnetic field lines from Stevenson proposed a model in which the field is sources in the ring plane: two locations at the inner axisymmetrized by the differential rotation of an edge of the B ring (1.525Rs, 1.62Rs) where high Planetary Magnetism 267

B r on Sphere r = 0.5 Rs charge-to-mass ratio particles (e.g., submicron ice or 90° dust) become unstable (Northrop and Connerney, 1987) and a third (3.95 Rs) at the orbit of Enceladus 60° Saturn and the E ring. The B-ring sources are identified with Model Z3 and electromagnetic erosion mechanism that sculpted the rings (Northrop and Connerney, 1987). 30° The Enceladus/E-ring source may reflect persistent Dipole activity of the recently discovered geysers on Equator 0° Enceladus (Kivelson, 2006; Kargel, 2006). Latitude

–30° 10.07.6 Ice Giants 10.07.6.1 Uranus –60° Uranus, residing at a mean orbital distance of 19.2 AU, was a mystery prior to the Voyager 2 –90° 02468encounter with Uranus in January 1986. The planet Gauss appears bland and featureless when observed from Figure 15 Unsigned magnetic flux computed on a sphere the Earth even under the best circumstances. Uranus of radius 0.5Rs (presumed dynamo core radius) using the Z3 and Neptune are similar in size (approximately magnetic field model, compared to that for a simple dipole. 25 000 km radius), mass (about 15 Earth masses), Saturn’s magnetic field is very nearly that which (with three and presumably composition (largely low-tempera- terms) minimizes the low-latitude (<45) unsigned flux across the core boundary. From Connerney JEP (1993) ture condensates, or ‘ice’: H2O, NH3,CH4). One Magnetic fields of the outer planets. Journal of Geophysical might therefore expect that their magnetic fields Research 98(E10): 18659–18679. would be similar. Uranus is unique in that its rotation axis lies very nearly in its orbital plane, which is within 1 of the ecliptic plane. The actual inclination of its equatorial plane to that of its orbit is 82. Twice during each orbit about the Sun (84 years), the rota- 2 tion axis is oriented very nearly along the planet–Sun

° N line, so that we on Earth look upon the pole. This was 65.5 61.6° N the case during the Voyager 2 encounter in 1986, the 1 Southern Hemisphere was directed toward the Sun. Uranus was not known to have a magnetic field prior to the Voyager encounter, having maintained ‘radio silence’ prior to encounter. It is a relatively C B A Z 0 Mimas s weak radio source, emitting only at lower frequencies Enceladu (below about 1 MHz), making detection from Earth difficult. In addition, the peculiar ‘pole-on’ encounter geometry kept the Voyager spacecraft beyond the –1 –58.3° S reach of radio emissions. Voyager 2, on a flyby tra- –62.7 ° S jectory (Figure 17) approaching to within 4.2Ru, provided the first and thus far only measurements –2 of the magnetic field (Ness et al., 1986). These mea- 0 1 2 34 surements led to the rather surprising discovery of ρ (R ) s the first ‘oblique rotator’, a planet with a large angular Figure 16 Saturn’s magnetic field is very nearly separation between magnetic and rotation axes. symmetric about its rotation axis but not about the equator; all field lines passing through the ionosphere at one latitude 10.07.6.1.1 Models cross the ring plane at a unique radial distance (ring plane conjugate) and map to a corresponding (but different) Preliminary analyses of the Voyager magnetic field latitude in the opposite hemisphere. The magnetic equator observations used an OTD representation of the field. is at 5.9 N (planetocentric) latitude (Connerney, 1986). This model is characterized by a dipole of moment 268 Planetary Magnetism

10 Table 5 Uranus and Neptune magnetic field models

Uranus Neptune

(1Ru ¼ 25 600 km) (1Rn ¼ 24 765 km)

Model Uranus Q3 Neptune O8 0 986) 1 g1 11893. 9732. 1 2 g1 11579. 3220. 5 1 nus (1 3 h1 15684. 9889. 0 4 g2 6030. 7448. 1 V2 Ura 5 g2 12587. 664. 2 6 g2 196. 4499. 7 h 1 6116. 11230. nda 2 8 h 2 4759. 70. Mira Ariel 2 Z 0 0 9 g3 6592. 1 10 g3 4098. Umbriel 2 V2 Neptune (1989) 11 g3 3581. 3 12 g3 484. 1 13 h3 3669. 2 14 h3 1791. 3 15 h3 770. –5 Uranus model from Connerney et al. (1987);seereferenceforparameter uncertainties and resolution. Neptune model from Connerney et al., 1991; see this reference for discussion of parameter resolution.

(Quadrupole part of an expansion to degree and –10 order 3), is listed in Table 5. The relative magnitude 02 46810 of the quadrupole is quite large; the octupole is likely ρ (Rp) to be large as well, but cannot be meaningfully con- Figure 17 Voyager 2 spacecraft flybys of Uranus and strained by the observations. Lack of knowledge of Neptune in a cylindrical coordinate system. The spacecraft higher-degree and-order terms may be an important distance from the equator plane (z) as a function of distance consideration, particularly in estimation of the field from the rotation axis () is given in units of planet radius. The positions of satellites Miranda, Ariel, amd Umbriel in the near the planet. The Q3 model provides a low-degree Uranus system are indicated. and-order approximation only, and it is likely that surface fields are more complex than illustrated here. 3 0.23 G R u (IRu¼25 600 km), displaced along the rota- The magnetic field magnitude on the surface of tion axis by 0.33Ru and inclined by 60 with respect to Uranus reaches a maximum of approximately 1 G at the rotation axis (Ness et al., 1986). Since Voyager mid-latitudes in the south, and a minimum of 0.1 G remained somewhat distant, and OTD representation at middle to high northern latitudes (Figure 18). is expected to be a good approximation to the field, Figure 18 also illustrates the foot of the Miranda and indeed it fits the observations well (Ness et al., flux tube, which is the path traced out on the planet’s 1986). The very large dipole offset of the OTD is an surface by the field lines passing through the satellite indication of a planetary magnetic field with a large as the planet rotates. Also shown are estimates of the quadrupole, and likely higher-degree and-order position of the aurorae (stippled regions) and the terms, that is, a very complex field. paths of multiple-dip equators (where Br ¼ 0). A spherical harmonic analysis of the field required Uncertainties in the higher-degree and-order com- an expansion to degree and order 3 (octupole) to ponents of the field, which are substantial, may lead adequately represent the measurements (Connerney to large differences in the actual surface field, parti- et al., 1987), which is somewhat surprising in view of cularly in the weaker field regions. Note that for Voyager’s relatively large periapsis. The Voyager Uranus, the convention adopted by the Voyager par- trajectory provided a fairly good spatial distribution ticles and fields investigations is at odds with the of observations, sufficient to resolve, or determine, International Astronomical Union (IAU) latitude spherical harmonic terms of degree 1 and 2, the convention. The Voyager system has planetary lati- dipole and quadrupole. This partial solution to the tudes positive over the hemisphere in which the underdetermined inverse problem, designated ‘Q3’ angular momentum vector resides, that is, the Planetary Magnetism 269

0.4 0.4 0.5 Uranus 180 0 150 210 30 0.3 330 r ato qu 0.3 120 240 60 e 300 tic e 0.4 n 0.5 g a

.4 0.2 M 0 0.3 90 270 90 0.6 270 c equa neti tor ag 0 M 0.7 0.4 60 0.2 120 0.5 60 –60 0.1 0.9 0.8 .7 30 150 0 0 180

0.2 30 –30 0.3 0.3 0.5 0.6 North South

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 IBI Gauss

90 0.1 0.2

0.3 60 0.1 Miranda 30 0.4 0.2 0.2 0.3 0 0.3 0.4 0.4 0.7 0.4 0.5 –30 0.8 0.5 0.6 0.6 0.9 M a gne –60 tic equator 0.5 0.6 –90 0.7 360 330 300 270 240 210 180 150 120 90 60 30 0 West longitude Figure 18 Contours of constant magnetic field magnitude (Gauss) on the dynamically flattened (1/41.6) surface of Uranus, computed using the Q3 spherical harmonic model (see text). The top panel shows the field magnitude in orthographic projections viewed from þz (left) and z (right); below the color bar is a rectangular latitude–longitude (west longitude) projection. A trace (dashed) indicates the position of the magnetic equator. Solid lines join points on the surface that trace along field lines to the orbit of the satellite Miranda, with filled circles for increments of 30 in the satellite’s longitude.

hemisphere oriented toward the Sun (and Earth) at temperature condensates, or ‘ice’: H2O, NH3,CH4) the time of the Voyager encounter. The IAU defines to Uranus. Very little was known of Neptune prior the south pole as the rotation pole south of the to the Voyager 2 encounter in August 1989. The first ecliptic, without regard to the direction of rotation. evidence of Neptune’s magnetic field appeared in radio observations (Warwick et al., 1989) obtained by Voyager 2 just days prior to its closest approach to the 10.07.6.2 Neptune planet on 25 August 1989. Neptune, residing at a mean orbital distance of 30 AU, The in situ magnetic field observations revealed a is the most distant of the Jovian planets. It is similar in magnetic field of internal origin with characteristics not size (approximately 25 000 km radius), mass (about 15 unlike those of the planet Uranus (Ness et al., 1989). Earth masses), and composition (largely low- ThemoststrikingdifferencebetweentheUranusand 270 Planetary Magnetism

Neptune encounter was a difference of our own design: trajectory, instead of the one maximum one would the Voyager 2 flyby trajectories at each planet, Where observe in a dipolar field. Spherical harmonic Voyager 2 at Uranus remained relatively distant from analysis of the field required an expansion to degree the planet, Voyager 2 at Neptune approached to within and order 8 to adequately represent the measurements 1.18Rn of the planet (Figure 17). The presence of (Connerney et al., 1991). The large number of para- higher-degree and-order components of the field in meters associated with a spherical harmonic expansion the latter observations is overwhelming, simply a con- of degree and order 8 (80 Schmidt coefficients) and the sequence of the close periapsis. Preliminary analyses rather limited observations leads to a severely under- of the Voyager magnetic field observations used an determined inverse problem which has only a partial OTD representation of the field, valid at moderate solution (Connerney et al., 1991). The distribution of distances from the planet (4 –15Rn radial distance; observations is sufficient to resolve, or determine, all of 1Rn ¼ 24765km),andfittedtodatainexcessof4Ru the spherical harmonic terms of degree 1 (dipole), some from the planet only. In this first approximation, the of the terms of degree 2 (quadrupole), and some terms of field may be characterized as that of a dipole of degree 3 (octupole) and higher. The resulting model, moment 0.13 G Rn, offset from the center of the planet designated ‘O8’ (octupole part of an expansion to degree 3 by a rather surprising large 0.55Rn and inclined by 47 andorder8),islistedinTable 5. For the Neptune field with respect to the rotation axis (Ness et al., 1989). model, it is necessary to consider the resolution of each It was necessary for Ness et al. (1989) to exclude from parameter listed in Table 5. For this we use the magni- their OTD analysis all observations of the field obtained tude of the corresponding diagonal element of the at r 4Rn. One indication of how nondipolar the field of resolution matrix, a measure of the uniqueness of the Neptune is can be obtained by comparison of the actual solution, the extent to which an individual model para- fieldmeasuredatclosestapproach(approximately meter can be represented by the basis vectors included 10 000 nT) to that one would expect if the field were in the partial solution (see Connerney et al., 1991). Note dipolar (6500 nT, for the OTD model). In fact, the field that some of the quadrupole and octupole coefficients of measured near closest approach was quite complex, as is the O8 model are not well resolved, but included out of illustrated in Figure 19. Two local maxima appear in necessity (see discussion of parameter resolution in the magnitude of the field observed along the flyby Connerney et al. (1991)).

Spacecraft radial distance (Rn)

3 2 1.5 1.18R n 1.5 2 3 105 Spherical harmonic contributions by order

Quadrupole

104

Dipole

103 Octupole IBIN Observed + lBI 44ev Model – CA = 1.18 R n

102 10 20 30 40 50 0 10 20 30 40 50 min Hour 3Hour 4 Hour 5 Day 237 Figure 19 Magnitude of the observed magnetic field (crosses) as a function of time (lower axis) and spacecraft radial distance (upper axis) for the Voyager 2 encounter with Neptune, compared with a model fit (O8 model) and the relative magnitudes of the dipole (dashed), quadrupole (solid), and octupole (dot-dashed) terms in the spherical harmonic expansion. Planetary Magnetism 271

As anticipated, the relative magnitude of the be recognized that only the low-degree and -order part quadrupole is quite large; the octupole is large as of the field is portrayed on the surface of the planet, and well, but can only be loosely constrained by the the likely presence of higher-degree and -order terms Voyager observations. may be expected to significantly alter the surface field. The magnetic field magnitude on the surface of the It is clear that the magnetic fields of Uranus and planet ranges from approximately 0.9 G at southern Neptune are quite similar in the range of surface field mid-latitudes to 0.1 G near the equator and at north- magnitudes, the tilt of the dipole, and the appearance of ern mid-latitudes (Figure 20). Figure 20 also shows one strong pole at southern mid-latitudes. Both Uranus estimated auroral zones (stippled regions) which differ and Neptune have extended weak-field regions, multi- greatly in size as a result of the hemispherical asymme- ple-dip equators, and multipolar structure in evidence try in field magnitudes. In this representation, it must at the surface of the planet.

0.1 0.2 Neptune 0.1 0.2 0.3 0.4 0.3 0.5 180 0.3 0 0.4 150 210 30 330 0.5 0.6 0.1 M

a 0.7

g

n 240 60 0.8

120 e 300

t i

0.2 c

0.5 e q

0.6 u

a

t o

90 270 90 r 270 0.3 0.2

r

o 0.6 t 0.5 a 0.3 0.4 u 60 300 q 120 0.4 e 0.1

ic t 0.7 60 e 60 n 330 g 30 a 150 0.5 M 0 180

0.2 0.1 300.4 –30 0.3 North South

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 IBI gauss

90 0.3

0.4 0.2 60 0.1 0.3 0.5 0.2

30 0.4 0.4 0.3

0.3 Magnetic equator

0 0.5 0.1 0.6 0.7 0.8 0.2 –30 0.1 0.2 0.3 0.3 0.4 0.5 –60 0.6 0.4 0.6 0.5

–90 360 330 300 270 240 210 180 150 120 90 60 30 0 West longitude Figure 20 Contours of constant magnetic field magnitude (G) on the dynamically flattened (1/47.6) surface of Neptune, computed using the O8 spherical harmonic model (see text). The top panel shows the field magnitude in orthographic projections viewed from þz (left) and z (right); below the color bar is a rectangular latitude–longitude (west longitude) projection. A trace (dashed) indicates the position of the magnetic equator. 272 Planetary Magnetism

10.07.7 Satellites and Small Bodies magnetism evolved from study of the lunar samples returned from the Moon, combined with in situ obser- 10.07.7.1 Moon vations collected both on the surface and in orbit about The Moon, with a radius of 1738 km and a mass of little the Moon. Robotic scientific exploration of the Moon more than 1% that of the Earth (m/Me ¼ 0.0123), is the was rekindled decades after the Apollo Program ended, largest satellite among the terrestrial planets. It is not so beginning with the orbiting Clementine spacecraft in much smaller than Mercury (2439 km) in size, with a February and March of 1994. The Lunar Prospector little more than one-third the volume of Mercury, but spacecraft was in polar mapping orbit from 13 January only about one-fifth of the mass. It is a differentiated 1998 through 31 July 1999, mapping crustal magnetic object similar in composition to the Earth’s mantle. fields via both direct and indirect methods. ESA’s The Moon has been a frequent target of space SMART-1 spacecraft was in orbit about the Moon exploration spanning nearly half a century, beginning from 15 November 2004 through impact on 3 with a series of robotic probes in the 1960s (Ranger September 2006. series of the US space program, Luna and Zond series The most complete Lunar magnetic field map of the USSR program) and culminating in the first (Figure 21) currently available was compiled using missions of human exploration of the Moon, the US 1.5105 estimates of the surface field magnitude Apollo Program. For a brief moment in history, begin- obtained over Lunar Prospector’s 18-month mission ning with Apollo 11 on 20 July 1969, and ending with (Mitchell et al., 2007). This recent map uses the electron Apollo 17 on 14 December 1972, humans walked (and reflection technique corrected for charging of the lunar drove) on the surface of another world, deploying surface and spacecraft (Halekas et al., 2002), signifi- instruments and collecting soil and rock samples for cantly extending (to 0.2 nT) the dynamic range of return to Earth. Much of what we know of lunar field magnitudes mapped relative to previous maps

North pole South pole 180 0

103–250 90 90 90 90 W E W E 42–103 17–42 7–17

3–7 0 Mid-latitudes 180 +60 1–3 0.5–1 +30 0.2–0.5

0–0.2 0 B (nT) –30

–60 0 90 E 180 90 W 0 Figure 21 Magnetic field magnitude on the Lunar surface as measured by the electron reflection technique. Field magnitudes from 0.2 to 250 nT are represented by colors according to the color bar to the left. The top panel shows the field magnitude in orthographic projections viewed from þz (left) and z (right); below is a rectangular latitude–longitude projection. The white circles denote major impact basins, and the black circles are drawn at the antipodal site. From Mitchel DL, Halekas JS, Lin RP, Frey S, Hood LL, Acun˜ a MH, and Binder A (2007) A global mapping of Lunar crustal fields by Lunar prospector. Journal of Geophysical Research (in press). Planetary Magnetism 273

(Halekas et al., 2001). This map is still undersampled, in this magnitude is sufficient to produce a Ganymede the sense that substantially more observations would be ‘mini-magnetosphere’ with all of the characteristics required to obtain complete spatial coverage at the normally associated with a trapped particle resolution implied by the electron gyroradius (about population. Ganymede’s immediate environment 5 km at 300 eV). However, it provides a good sense of (Figure 22) includes field lines with both ends the global distribution of magnetic sources in the Lunar anchored within Ganymede, hosting a local trapped crust and the characteristic scale length of coherent radiation environment; ‘open’ field lines that extend magnetization in the Lunar crust. Where the Lunar to the Jovian ionosphere; and Jovian field lines. crust is magnetized, it is weakly magnetized (on spatial A more comprehensive analysis, performed after the scales of 5 km and greater), compared to the Mars crust, discovery of induced magnetic fields associated with or Earth’s. Lunar crustal magnetization also appears to Europa and Callisto (Neubauer, 1998; Khurana et al., be less coherent at large spatial scales, compared to 1998; Kivelson et al., 1999; Zimmer et al., 2000), allowed Earth and Mars. The large impact basins (e.g., for the presence of an induced field in addition to the Orientale, Imbrium) appear nonmagnetic, implying main field (Kivelson et al., 2002). This analysis demon- that the impact melt cooled in zero field (no lunar strated that Ganymede has both an inductive response dynamo at the time of impact); and yet, the regions of to the time-varying magnetic field (due to currents strongest field magnitude appear ‘antipodal’ to the induced in a hidden global ocean) and an intrinsic largestimpactbasins(Lin et al., 1988). So it seems that field likely due to a dynamo in the deep interior. The Lunar crustal magnetization and large impacts are intrinsic field is a permanent dipole with a surface related; perhaps impacts magnetize the crust not at equatorial field of 719 nT, tilted by 176 with respect the impact site, but on the opposite side of the Moon. to the rotation axis and rotated 24 toward the trailing One theory for how this might occur (Hood and hemisphere from the Jupiter-facing meridian plane. Vickery, 1984; Hood and Huang, 1991)usesthe The permanent field is perhaps the best evidence that impact-generated plasma cloud to intensify the weak Ganymede has a substantial Fe or FeS core in the ambient magnetic field at the antipode, if only briefly interior; dynamo action implies that it is fluid, and (1 day), as it expands from the impact site to envelop the Moon. The expanding plasma cloud, being a good 4 electrical conductor, sweeps up the ambient field as it converges on the antipode, where the crust then acquires remanence via shock magnetization (Fuller et al., 1974; Cisowski et al., 1983). 2

10.07.7.2 Ganymede Ganymede, with a radius of 2634 km, is the largest 0 satellite in the solar system. It is slightly larger than the smallest planet in our solar system, Mercury (Rm ¼ 2439 km), but only about half as massive –2 (Mg ¼ 0.025Me). Ganymede may have an Fe or FeS core extending to as much as half the satellite’s radius, overlain by a silicate mantle and topped with 800 km layer of ice (Anderson et al., 1996). –4 The Galileo spacecraft was targeted for several –4 –2 0 2 4 close flybys of Ganymede, the first of which occurred Figure 22 Magnetic field of Ganymede and its immediate in June of 1996. The first two flyby encounters, with environment in meridian plane projection. Ganymede’s minimum altitudes of 838 and 264 km, demonstrated internal magnetic field moment is indicated with a filled conclusively the presence of an intrinsic dipolar mag- arrow. Low-latitude field lines close within the satellite’s netic field and associated magnetosphere (Kivelson interior; high-latitude field lines (blue) form a flux tube with et al., 1996, 1997; Gurnett et al., 1996). Initial analysis one end rooted in Jupiter’s ionosphere; Jovian field lines (black) are separated from those linking Ganymede by a of the magnetometer observations revealed a dipole sepratrix (heavy black). Adapted from Kivelson MG, Khurana field with equatorial surface field of 750 nT, nearly K, and Volwerk M (2002) The permanent and inductive (within 10) aligned with the rotation axis. A field of magnetic moments of Ganymede. Icarus 157: 507–522. 274 Planetary Magnetism convecting, with sufficient energy input to sustain the dynamo. However, it is possible (but not likely) that Ganymede’s dipolar magnetic field is due to remanent Neptune (.75) magnetism (Crary and Bagenal, 1998). 2.0

? Uranus (.75) 1.0 10.07.8 Discussion 0.5 Saturn (.5) A convenient measure of the complexity of a plane- tary magnetic field, often used in studies of the Jupiter (.75) – 04 model magnetic field of the earth and planets, is the ‘har- 0.2 monic spectrum,’ sometimes referred to as a ‘Lowes Jupiter (.75) – 06, VIT4 Models spectrum,’ defined as follows (Lowes, 1974; Langel magnitude Relative 0.1 and Estes, 1982): Earth (.55)

Xn no 0.05 m 2 m 2 Rn ¼ðn þ 1Þ gn þ hn m¼0

This quantity is equal to the mean-squared magnetic 0.02 R n p m 2 m 2 (n + 1)∗ (2n + 4)∗ Σ {(g ) +(h ) } field intensity over the planet’s surface produced by ()r n n c harmonics of degree n. Scaled to the core–mantle m = 0 2nþ4 0.01 boundary with the factor (a/rc) , this quantity repre- 123 456 7 sents the mean-squared magnetic field intensity at the Harmonic degree n dynamo surface. The Earth’s field is well known to high Figure 23 Relative harmonic content (Lowe’s spectrum) degree and order (Nmax ¼ 23). Scaled to the core–man- of spherical harmonic models of Jupiter, Saturn, Uranus, tle boundary, the spectrum becomes almost flat for n and Neptune, compared with that of Earth, normalized to 14, suggesting a ‘white’ spectrum for the dynamo at the the assumed core radius (in parentheses) for each planet. Two Jovian field models are chosen to illustrate the range of core–mantle boundary (e.g., Lowes, 1974). It is assumed possibilities for that planet. that the core–mantle boundary, the location of which is very accurately known, represents the outer boundary this presentation, the planets fall into two distinct of the geodynamo. Thus, it has often been assumed that a white spectrum is a common feature of all planetary groups, one in which the core surface field is domi- dynamos (Elphic and Russell, 1978), although in the nated by the dipole (Earth, Jupiter, Saturn) and one Earth’s case the quadrupole is considerably less than in which the core surface field is dominated by higher-degree contributions (Uranus and Neptune). expected. In Figure 23, Rn is calculated using the GSFC 12/83 model for the Earth (Langel and Estes, However, in recognition of the peculiarity of Saturn’s axisymmetric field, one might better think 1985), the Z3 model for Saturn (Connerney et al., in terms of three classifications. In Stevenson’s (1982) 1982b), and the Q3 model for the magnetic field of Uranus (Connerney et al., 1987). For Jupiter both the model, differential rotation of an outer conductive shell attenuates the nonaxisymmetric components of O4 model (Acun˜a and Ness, 1976)andO6 models (Connerney, 1992) are shown, illustrating a range of the dynamo within, thereby reducing the observed tilt possible values for the quadrupole and octupole. For by an order of magnitude or more from the ‘nominal’ Uranus, no estimate of the magnitude of higher-degree value. This model has an appealing physical basis (n > 2) moments can be made, while for Neptune, terms (material properties of the H–He fluid) and appears of higher degree are appreciable, but quite uncertain. to satisfy other constraints, for example, helium deple- For Jupiter and Saturn, we assume that the core tion of the gaseous outer envelope and a relatively radius is near the radius of the metallically conducting high planetary heat flux. The dipole-dominated group hydrogen core, approximately 0.75 and 0.5 planet includes the planets with near alignment of dipole and radius, respectively (e.g., Stevenson, 1983). For rotation axes (10); the other includes the oblique Uranus and Neptune, we take rc ¼ 0.75 Rp with the rotators Uranus (59 ) and Neptune (47 ), the planets expectation that the dynamo for these planets operates with a very large angular separation of the dipole and in the ice mantle, where ionic conduction prevails. In rotation axes. Planetary Magnetism 275

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