Differential Rotation of the Magnetic Fields of Gaseous Planets

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 persistence 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 persistent, 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). Gauss (Voyager 1), and 0. I Gauss (Voyager 2). Finally, Pilcher et al. (1985) provide evidence Thus, we could have a magnetic anomaly in the for the presence of two localized plasma sources northern hemisphere of Saturn that could not be for the Io torus, one that rotates with System III detected by any of the passing spacecraft, cover- and the other that has a longer period (presumably ing a region about 0.1 R in radius with a field the System IV period). Although they interpret s strength of about 0.1 Gauss that either adds to or their data in terms of plasma slippage relative to System III, their data are consistent with differ- subtracts from Saturn's north polar field of 0.84 Gauss (Connerney et al., 1984). ential rotation of the planetary magnetic field as proposed here. If we assume the solar analogy applies to Saturn, then the high-latitude magnetic field must have a longer period than that at low latitudes. Saturn Cloud Motions We can then take the analysis of Allison and Stone as a supporting argument to the effect that the The concept of magnetic differential corotation low-latitude spin period, 10.557 hours according eases an otherwise sticky problem in the dynamics to Allison and Stone (1983), is shorter than the of Saturn tneteorology. The periodic kilometric high-latitude radio period ( 10.657 hours) reported radio emissions frcm Saturn (SKR) (Kaiser and by Desch and Kaiser (1981). There is, unfortu- Desch, 1980) have been used to establish a Saturn nately, no known radio phenomenon to provide a Longitude System (SLS) with a spin period of measure of the spin period at low latitude. We 10.657_+0.002 hours. In this coordinate system, conclude that, as for Jupiter, the magnetospheric all cloud motions are either prograde or station- spin period of Saturn should be described by a ary; no significant retrograde motions are ob- low- and a high-latitude magnetic coordinate sys- served (Smith et al., 1982). Allison and Stone tem, viz., SLS I (low latitude) and SLS II (high (1983) argue that this may be an artifact of the latitude) with respective periods of 10.557 and SLS coordinate system. They present meteorologi- 10.657 hours. Dessler: Magnetic Differential Rotation 301

Discussion and Conclusions analogy should not be taken too far; analogies are not identities. There are some additional theoretical conse- One might worry that differential rotation of quences to the magnetic differential rotation the internal magnetic field leads to twisting of hypothesis. The differential rotation proposed the magnetospheric magnetic field lines that have for Jupiter may not be consistent with the theory their feet in regions of differing rotation rates. of a 10-hour "clock" in Jupiter's magnetosphere Such twisting does not occur because the insulat- proposed by Dessler and Hill (1975). Their model ing layer of gas between the ionosphere and the could as well produce a 10.2-hour System IV modu- dynamo region decouples plasma motions in the lation. However, an alternate model for the clock ionosphere from those of the deeper interior. modulation by Goertz and Baker (1985) is There are some additional consequences that controlled by the System III period. follow frc• the concept of differential rotation. The reduction by 0.95% in the low-latitude spin For Jupiter, the subcorotational plasma flow in rate of Saturn proposed by Allison and Stone the torus and magnetodisc may not all be caused by (1983), and defended here as being consistent with plasma mass loading as described by Hill (1979) the differential rotation hypothesis, has other and Pontius and Hill (1982). Differential rota- possible theoretical consequences. Northrup and tion causes the corotation speed to be less, so Hill (1982) have advanced a theory of a specific the deviation frc• corotation is smaller than for structure in Saturn's B ring that is related to rigid-body magnetic field rotation. As a result, the magnetic geostationary distance. (The geosta- the mass loading required to produce the remaining tionary distance is defined as the distance at subcorotational flow may be less than previously which an object in a circular, equatorial e s timated. Keplerian orbit remains at a given longitude. For The polar field maps that have been drawn for the SLS longitude system, the geostationary dis- Jupiter on the basis of the Pioneer 11 flyby, tance is 1.86 R ; for the new, shorter period it $ although largely time-stationary, must have some is 1.85 R .) The rings are close enough to Saturn $ magnetic features that rotate with the 10.2-hour to be threaded by low-latitude magnetic fields. System IV rate, thus producing a time-varying If the spin period is decreased by 0.95%, the polar field whose pattern repeats approximately theoretically expected distance of the specific every 32 rotations. The gross shape of the auro- ring boundary noted by Northrup and Hill moves ral zone, being largely determined by the main closer to Saturn by 2/3%, or 0.010 R from 1.625 s dipole, stays fixed in System III, but the differ- R to 1.615 R . The ring boundary explained by s ential rotation of smaller magnetic features their theory is placed experimentally between through the auroral zone causes the location of 1.605 to 1.625 R and 1.633 R . Thus, the shorter s s the zone to meander somewhat and show time, spa- spin period proposed here for the low-latitude cial, and brightness variations that might be magnetic field leads to a somewhat worse but not consistent with those reported by Skinner and Moos unacceptable fit between observation and theory. (1984). In particular, the passage of a magnetic Also, if the low-latitude field is truly axisym- anomaly through the auroral zone would cause the metric, the relevant spin period is determined by active sector (where the auroral brightness is a ionospheric winds and not the underlying magnetic maximum) to move in longitude. This might explain dynamo region that is separated from the why Skinner and Moos found the longitude of maxi- ionosphere by an insulating atmospheric layer. mum brightness covers a larger longitude range Also possibly relevant to the differential than expected on the basis of the stationary rotation hypothesis on Saturn is the finding by magnetic-anomaly model. Porco and Danielson (1982) of a correlation be- One of the outstanding features of solar mag- tween the formation of spokes in the B ring and netism is a broad array of rotation periods for 115¸ SLS longitude (the longitude of the nKOM various magnetic surface structures, e.g., large radio emission). The B ring is threaded by low- sunspots, small sunspots, sunspot groups, coronal latitude magnetic fields while nKOM is a high- holes. Not only are their rotation periods dif- latitude phenomenon. Thus, one might expect spoke ferent at different latitudes, but the rotation activity to have a shorter periodicity than the periods of these different magnetic classifica- nKOM period. Porco and Danielson do, in fact, tions can differ, even if they are at the same report a short period for modulation of spoke latitude. We see this happening in the cloud activity ( 10.35+_0.37 hours, as compared to the SLS structure of Jupiter where small clouds overtake II period of 10.657 hours). But the uncertainty the Great Red Spot, are spun around it, and are in spoke statistics, as well as a lack of theoret- then flung off to continue their earlier longitu- ical understanding of the relationship between dinal drift. The principal point of this Letter spoke formation and nKOM, make it necessary to set is that something similar happens to the magnetic this observation aside for the time being. fields of Jupiter and Saturn (and presumably The magnetic fields of the Sun, Jupiter, and Uranus and Neptune). probably Saturn, originate near the surfaces of these bodies (Hide and Stannard, 1976; Acknowledgments. I am grateful to Dr. Lyle Smoluchowski, 1975; Hubbard and Stevenson, 1984), Broadfoot and his staff at the Lunar and Planetary while the magnetic field of the Earth originates Laboratory for their help and hospitality during in or near its central core. It seems appropri- the initial writing of this paper. I benefitted ate, therefore, to look at the solar magnetic from conversations with Bill Sandel, and Doug field, rather than the Earth's, to obtain a first- Rautenkranz assisted in solving some c•nputer order approximation of the behavior of the magnet- problems. I also wish to thank John Clarke, Ernie ic fields of Jupiter and Saturn, as well as those Hildner, David Hathaway, Tom Hill, Ron Moore, Don of Uranus and Neptune, if they have internal mag- Shemansky, and Hunter Waite for their useful sug- netic fields. It is well to state here that the gestions. 302 Dessler: Magnetic Differential Rotation

Reference s Krieger, A. S., Temporal behavior of coronal holes, in Coronal Holes and High-S•eed Wind Allison, M., and P. Stone, Saturn meteorology: A Streams, edited by Jack B. Zirker, pp. 71-102, diagnostic assessment of thin-layer configura- University of Colorado Press, Boulder, Colo., tions for the zonal flow, Icarus, 54, 296-308, 1977. 1983. Lecacheux, A., and F. Genova, Source localization Brown, R. A., and D. E. Shemansky, On the nature of Saturn kilometric radio emission, J. of SII emission from Jupiter's hot plasma Geophys. Res., 88, 8993-8998, 1983 torus, Astro•hys. J., 263, 433-442, 1982. McNutt, R. L., Jr., J. W. Belcher, J. D. Sullivan, Carbary, J. F., and S. M. Krimigis, Charged parti- F. Bagenal, and H. S. Bridge, Departure from cle periodicity in the Saturnian magnetoshpere, rigid co-rotation of plasma in Jupiter's Geophys. Res. Lett., 9, L1073-L1076, 1982. dayside magnetosphere, Nature, 280, 803, 1979. Connerhey, J.E.P., L. Davis, Jr., and D. L. Northrup, T. G., and Jay Roderick Hill, Stability Chenette, Magnetic field models, in Saturn, of negatively charged dust grains in Saturn's edited by T. Gehrels and M. S. Matthews, pp. ring plane, J. Geophys. Res., 87, 6045-6051, 354-377, University of Arizona Press, Tucson, 1982. Ariz., 1984. Pilcher, C. B., and J. S. Morgan, The distribution Desch, M.D., and M. L. ..Kaiser, Voyager measure- of S[II] emission around Jupiter, Astrophys. ment of the rotation period of Saturn's J., 238, 375-380, 1980. magnetic field, Geo•hys. Res. Lett., 8, L253- Pilcher, C. B., J. H. Fertel, and J. S. Morgan, L256, 1981. S[II] images of the Io torus, Astro•hys. J., in Dessler, A. J., Coordinate systems, in Physics of press, 1985. the Jovian Magnetos•here, edited by A. J. Pontius, D. H., Jr., and T. W. Hill, Departure Dessler, pp. 498-504, Cambridge University from corotation of the Io plasma torus: Local Press, New York, 1983. plasma production, Geo•hys. Res. Lett., 9, Dessler, A. J., and T. W. Hill, High order L1321-L1324, 1982. magnetic multipoles as a source of gross Porco, C. C., and G. E. Danielson, The periodic asymmetry in the distant Jovian magnetosphere, variation of spokes in Saturn's rings, Astron. Geo•hys. Res. Lett., 2, L567-L570, 1975. J., 87, 826-833, 1982. Goertz, C. K., and D. N. Baker, Polar cap Roesler, F. L., F. Scherb, and R. J. Oliversen, photoionization and the 10-hour clock at Periodic intensity variations in S[III] 9531A Jupiter, J. Geo•h•s. Res., in press, 1985. emission from the Jupiter plasma torus, Hide, R., and D. Stannard, Jupiter's magnetism: Geoph•s. R•s. Lett., 11, L128-L130, 1984. Observation and theory, in Jupiter, edited by Sandel, B. R., Corotation lag in the Io plasma T. Gehrels, pp. 767-787, University of Arizona torus--Evidence from Voyager EUV observations Press, Tucson, Ariz., 1976. (abstract), Bull. AAS, 15, 810, 1983. Hill, T. W., Inertial limit on corotation, J. Sandel, B. R., and A. L. Broadfoot, Io's hot Geo•h•s. Res., 84, 6554-6558, 1979. plasma torus--A synoptic view from Voyager, J. Hill, T. W., A. J. Dessler, and L. J. Maher,Co- Geoph•s.Res., 87, 212-218, 1982. rotating magnetosphericconvection, J. Geophys. Siscoe, G. L., and D. Summers,Centrifugally- Res., 86, 9020-9028, 1981. driven diffusion of Iogenic plasma, J. Geophys. Hill, T. W., C. K. Goertz, and M. F. Thomsen, Some Res., 86__,8471-8479, 1981. consequences of corotating magnetospheric con- Skinner, T. E., and H. W. Moos, Comparison of the vection, J. Geoph•s. Res., 87, 8311-8314, 1982. Jovian north and south pole aurorae using the Hill, T. W., A. J. Dessler, and C. K. Goertz, IUE observatory, Geophys. Res. Lett., 11, Magnetospheric models, in Physics of the Jovian Ll107-L1110, 1984. Magnetos•here, edited by A. J. Dessler, pp. Smith, B. A., et al., A new look at the Saturn 353-394, Cambridge University Press, New York, system: The Voyager 2 images, Science, 215, 1983. Howard, R., P. A. Gilman, and P. I. Gilman, Rota- 504-537, 1982. tion of the Sun measured from Mount Wilson Smoluchowski, R., Jupiter' s molecular hydrogen white-light images, Astrophys. J., 283, 373- layer and the magnetic field, Astrophys J. Lett., 200, Ll19-L121, 1975. 384, 1984. Hubbard, W. B., and D. J. Stevenson, Interior Summers, D., and G. L. Siscoe, Solutions to the structure of Saturn, in Saturn, edited by T. equations for corotating magnetospheric Gehrels and M. S. Matthews, pp. 47-87, Univer- convection, Astro•h•s. J., 261, 677-683, 1982. sity of Arizona Press, Tucson, Ariz., 1984. Trafton, L., Jovian SII torus: Its longitudinal Ingersoll, A. P., R. F. Beebe, B. J. Conrath, and asymmetry, Icarus, 42, 111-124, 1980. G. E. Hunt, Structure and dynamics of Saturn's Trauger, J. T., G. Munch, and F. L. Roesler, A atmosphere, in Saturn, edited by T. Gehrels and study of the Jovian [SII] nebula at high M. S. Matthews, pp. 195-238, University of spectral resolution, Astro•hys. J., 2.36, 1035- Arizona Press, Tucson, Ariz., 1984. 1042, 1980. Kaiser, M. L., and M. Desch, Narrow-band Jovian kilometric radiation: A new radio component, Geo•h•s. Res. Lett., 7, L389-L392, 1980. A. J. Dessler, Space Science Lab, NASA Marshall Kaiser, M. L., and M.D. Desch, Saturnian Space Flight Center, Huntsville, AL 35812. kilometric radiation: Source locations, J. Geo•h•s. Res., 87, 4555-4559, 1982. Kaiser, M. L., M. D. Desch, J. W. Warwick, and J. B. Pearce, Voyager detection of nontherml (Received January 29, 1985; radio emission from Saturn, Science, 209, 1238- revised March 10, 1985; 1240, 1980. accepted March 5, 1985.)