GEOPHYSICAL RESEARCH LETTERS, VOL. 12, NO. 5, PAGES 299-302, MAY 1985 DIFFERENTIAL ROTATION OF THE MAGNETIC FIELDS OF GASEOUS PLANETS A. J. Dessler Space Science Laboratory, NASA Marshall Space Flight Center Abstract. We argue that, with regard to the about 3%. This difference in repetition period is spin rate of magnetic field structure as a func- commonly attributed to the effect of slippage of tion of latitude, the behavior of the magnetic plasma within the magnetosphere first described by fields of gaseous planets is more analogous to the Hill (1979). The slippage predicted by Hill un- Sun than the Earth. Certain Jovian magnetospheric doubtedly does occur, as first reported by McNutt phenomena differ in repetition period by 3%. In et al. (1979). However, there is no obvious way order to explain Jupiter's two distinct periodici- this slippage can account for the observations of ties, it is hypothesized that the spin period of two separate, distinct magnetospheric periodici- the planet's magnetic features is a function of ties. (These phenomena are described below.) both latitude and the size of the feature, with The observed plasma slippage follows Hill's smaller high-latitude features rotating slower (1979) theory; the magnetospheric plasma increas- than either low-latitude features or the dominant ingly slows relative to corotation as the Jovicen- dipole moment. Similarly, the low-latitude tric distance increases outward from the Io plasma planetary spin period of Saturn is shorter than torus. The primary periodicity is easily account- the presently accepted single value because the ed for as being due to either the rotation of a present value is based on a high-latitude magnetic major magnetic anomaly in Jupiter's surface field phenomenon. We should also expect differential or the rotation of its tilted dipole (see Section rotation of surface magnetic features at both 10.7 of Hill et al., 1983). To get a distinctly Uranus and Neptune if they prove to have internal different period utilizing the slippage of magne- dynamo-generated magnetic fields. tospheric plasma, one would have to suppose the existence of a physically unrealistic, longitudi- Introduction nally confined, long-lived blob that (a) slips relative to corotation, (b) does not change its Our conceptual ideas concerning the spin period Jovicentric distance, and (c) is continually re- of planetary magnetic fields are based on our supplied with either plasma or energy. This is familiarity with the Earth's magnetic field. not to say that there exists no possible explana- Thus, we might expect magnetic features at the tion based on appeal to plasma slippage, but I do surface of other planets to corotate (isorotate) not see how to do it. with that planet if we were to argue by analogy with the Earth. The purpose of this Letter is to Jovian Narrow-Band Kilometric Radio Emission suggest that for the giant gaseous planets, the (nKOM) behavior of the solar magnetic field provides a better analogy. Differential rotation of the System III coordinates are fixed relative to a Earth's magnetic field is constrained; only the rather precisely known periodicity in decametric slow secular variations are relatively unimpeded. radio emissions that originate in the innermost In contrast, the Sun's magnetic field exhibits portion of the magnetosphere and decametric emis- differential rotation. Magnetic features near the sions from low to mid-latitudes (Dessler, 1983). equator rotate with a sidereal period of 25 days, Kaiser and Desch (1980) were the first to find a while at high latitudes the period increases to spin-periodic magnetospheric phenomenon that was about 30 days. Furthermore, Howard et al. (1984) not fixed in System III coordinates. They found a report that sunspot groups and larger sunspots narrow-band emission (called nKOM) that rotates 3- rotate 1-2% more slowly than small sunspots; and 5% slower than System III. They concluded that sunspots and coronal holes, which are created by the radio emissions originate in a longitudinally specific magnetic structure in the Sun's photo- restricted region of the Io plasmas torus at a sphere, commonly drift in longitude relative to radial distance of 8-9 R . If we were to define a one another (Krieger, 1977). newcoordinate system (•ich weprovisionally label "System IV") that spins 3.1% slower than Evidence of Magnetic Differential Rotation System III, the longitude of the nKOM emission would presumably (aside frcm some longitudinal There is a body of experimental evidence to "jitter") remain fixed in the new coordinate sys- support the hypothesis that polar magnetic fea- tem. (Longitudinal jitter is common to all of tures on Jupiter and Saturn spin more slowly than Jupiter's radio emissions, including the emissions the equatorial magnetic field. The data for Jupi- used to establish System III.) ter are particularly compelling in that they indi- The nKOMmust be tied to a surface magnetic cate that different spin-periodic phenomena con- feature of the Jovian magnetic field. Simple trolled by the magnetic field of the planet have slipping of a longitudinally uniform distribution one of two distinct periodicities that differ by of plasma in the torus and outer magnetosphere would not lead to the observed longitudinal per- sistence of the radio emissions with a 3% longer This paper is not subject to U.S. copyright. Pub- period. If the nKOM were generated by some chance lished in 1985 by the American Geophysical Union. longitudinal variation in either the number den- sity, temperature, or current flow in the torus, Paper number 5L6451. one would expect radial diffusion or radial out- 299 300 Dessler: Magnetic Differential Rotation flow to destroy the source region in just a few cal arguments to the effect that the energetics of planetary rotations (Siscoe and Summers, 1981; the Saturnian atmosphere would be better accom- Hill et al., 1981, 1982; Summers and Siscoe, modated if the underlying rotation period of the 1982). Instead, the longitudinal persistence of planet were 1% shorter than the radio period. the nKOM source is reported to continue for at Using the shorter rotation period, Allison and least 40-50 rotations (Kaiser and Desch, 1980). Stone show cloud motions have the more typical In order that a specific volume of torus plasma east-west alternating flow bands; see their Figure maintains its identity while increasing its System 1 and the discussion in Section IV.A of Ingersoll III longitude by approximately 11ø each rotation, et al. (1984). it must be continuously renewed by contact with Saturnian radio emissions have been shown by some magnetic feature associated with the planet Kaiser and Desch (1982) and Lecacheux and Genova that rotates 3% slower than System III. In this (1983) to arise from latitudes of 75¸ or greater. interpretation, a magnetic feature (a magnetic Kaiser et al. (1980) have suggested that the spin anomaly) a few tenths of Jupiter's radius below modulation of the SKR is caused by the rotation of its surface controls the longitude of the nKOM a magnetic anomaly in Saturn's near-surface field source. This magnetic feature has a spin period (see also Carbary and Krimigis, 1982). of 10.23 hours (which we propose defines a new For Saturn, we accept the hypothesis of Kaiser System IV coordinate system) as compared with the et al. (1980) that a high-latitude magnetic anoma- 9.925 hour System III period. ly in Saturn's surface field modulates the SKR emissions. Although the magnetometers on Pioneer Brightness Periodicities in the Io Torus 11 and Voyagers 1 and 2 did not detect one, a surprisingly large magnetic anomaly could be pres- Although a persistent System III longitude ent and not be seen by any of the magnetometers. variation of brightness in the cold torus (i.e., For ease of calculation, let us assume the magnet- the portion of the torus well inside 5.9 Rj) has ic anomaly can be represented by a magnetized been documented (Trafton, 1980; Pilcher and spherewith a radius 0.1 Rs, its magneticmoment Morgan, 1980; Trauger et al., 1980) no similar parallel to the planetary radius vector, centered System III longitudinal asymmetry is seen in the at 0.7 Rs , latitude 80¸ north, andSLS longitude hot torus (Sandel and Broadfoot, 1982; Brown and 115¸. Althoughat closest approachPioneer 11 was 1.3 R from the center of Saturn, it came within Shemansky, 1982). However, Roeslet et al. (1984) discovered a distinct 10.2-hour periodicity in the only•.5 R of the anomalybecause, at closest approach, the spacecraft was slightly south of the hot torus at distances beyond5.9 Rj. Their data equator while the anomaly is in the northern hemi- set covers more than 40 rotations of Jupiter. This finding of a variation in torus brightness sphere and displaced 65¸ from the spacecraft lon- having a periodicity that is distinctly different gitude. The two Voyagers did not approach the from System III has been confirmed and refined by anomaly as closely as Pioneer 11; Voyager 1 came within 3.6 R and Voyager 2 came within 2.7 R . Sandel (1983) who, using Voyager data, obtained a s rotation period of 10.23+0.04 hours. His Voyager For an upper limit, we assume the magnetic data cover more than 100 consecutive rotations of field of the anomaly at the spacecraft is 0.2% of Jupiter. Both optical data sets are consistent the maximum field strength at closest approach (Connerney et al., 1984), which is 16 nT for with the idea that the Io torus contains a per- sistent, longitudinally restricted bright sector Pioneer and 2 nT for the Voyagers. At the surface that rotates with a period that is 3% longer than of Saturn (which has a polar radius of 0.9 R ), the respective field strengths produced by the the System III period (i.e., the bright sector above anomalies are: 0.13 Gauss (Pioneer 11), 0.23 stays fixed in System IV coordinates).