A Simple Empirical Model of the Equatorial Radial Field in Jupiter's

Planetary and Space Science 50 (2002) 789–806 www.elsevier.com/locate/pss A simple empirical model ofthe equatorial radial ÿeld in Jupiter’s middle magnetosphere, based on spacecraft *y-by and Galileo orbiter data E.J. Bunce ∗, P.G. Hanlon1, S.W.H. Cowley Department of Physics & Astronomy, University of Leicester, Leicester LE1 7RH, UK Received 31 May 2001; received in revised form 5 December 2001; accepted 28 March 2002 Abstract In this paper we consider empirical models ofthe radial ÿeld and azimuthal current in Jupiter’s middle magnetosphere region, at distances in the range 20–45 RJ. We ÿrst ofall compare the model derived previously by Bunce and Cowley (Planet. Space Sci. 49 (2001) 261) using Pioneer, Voyager and Ulysses *y-by data, with a combined data set that now also incorporates data from the ÿrst twenty orbits of the Galileo orbiter. The overall RMS fractional residual is found to be 12.7%, such that the model does provide a good description of the combined data set. In particular, it is shown that the Galileo data also exhibit the same local time asymmetry as found in the *y-by data, in which the radial ÿeld (and azimuthal current) are stronger at a given radial distance on the nightside compared with the dayside. However, it is also shown that ifthe combined data are separated into 2 h bins oflocal time and then ÿtted to individual power law curves, the overall RMS fractional residual is reduced to 7.7%, thus showing scope for improvement in the empirical model. Based on the combined data set, in our revised model the ÿeld is taken as asymmetric outside of14 :5RJ, and to fall with radial distance with an exponent which is taken to vary sinusoidally with local time, varying between −1:5 at noon and −1:0 at midnight, such that the ÿeld becomes increasingly asymmetric with increasing distance. The overall RMS residual for this four-parameter model is found to be 9.7%, only slightly higher than that ofthe free-ÿtsto the 2 h MLT binned data, and representing a worthwhile improvement over the original Bunce and Cowley −2 model. The implied divergence ofthe azimuthal current forthe revised model peaks at ∼ 15 kA RJ near the dawn-dusk meridian at a radial distance of ∼ 23 RJ. The implied diBerence in the total azimuthal current *owing in the current sheet between 20 and 50 RJ at midnight compared with noon is 19 MA, in a total (at dawn and dusk) of59 MA. ? 2002 Published by Elsevier Science Ltd. 1. Introduction signiÿcantly distorts the planetary ÿeld lines at distances of ∼ 10 RJ and beyond (Smith et al., 1974, 1975, 1976; Ness Gledhill (1967) was the ÿrst to postulate that Jupiter’s et al., 1979a, b). However, they also showed that the prin- near-planet equatorial magnetic ÿeld lines would be radially cipal plasma source for the current sheet was not Jupiter’s distended, due to centrifugal forces associated with rapid ionosphere, but the moon Io, which orbits at a jovicentric planetary rotation and ionospheric plasma loading. Subse- distance of ∼ 5:9RJ (Krimigis and Roelof, 1983). The next quently, the ÿrst in situ measurements ofJupiter’s mag- spacecraft to *y past Jupiter was Ulysses in 1992 (Balogh netic environment, made during the Pioneer-10 and -11 and et al., 1992), and more recently the Galileo orbiter arrived in Voyager-1 and -2 spacecraft *y-bys in the 1970s, indeed 1995 to commence a long-term study ofthe Jovian system showed the signatures ofthe radial distension ofthe mag- (Kivelson et al., 1992). The magnetic eBects ofthe equa- netic ÿeld. The earliest studies based on the data from these torial current sheet, or magnetodisc, have been found to be *y-bys demonstrated the existence ofa thin equatorial az- present at all local times investigated by these spacecraft. imuthal current sheet *owing in an eastward direction, which The local time coverage ofthe ÿve Jupiter *y-bys men- tioned above, and the ÿrst 20 orbits ofthe Galileo mission (between 1996 and 1999) are shown in Fig. 1a, where ∗ Corresponding author. Tel.: 0044 116 223 1302; fax: 0044 116 252 the spacecraft trajectories are shown in Jupiter Solar Or- 3555. bital (JSO) coordinates, i.e. X (R ) is positive sunwards, and E-mail address: [email protected] (E.J. Bunce). J 1 Now at Blackett Laboratory, Imperial College, London SW7 2BZ, Y (RJ) is orthogonal to X and in the plane ofJupiter’s orbit. UK. The Pioneer and Voyager *y-bys covered the dawn sector of 0032-0633/02/$ - see front matter ? 2002 Published by Elsevier Science Ltd. PII: S 0032-0633(02)00011-9 790 E.J. Bunce et al. / Planetary and Space Science 50 (2002) 789–806 200 G(throughC20) P10 150 P11 U V1 V2 V2 BS 100 V2 MP 50 ) J X (R 0 -50 -100 -150 -200 250 200 150 100 50 0 -50 -100 -150 -200 -250 (a) Y (RJ) 12 RJ 60 40 20 18 06 50 nT (b) 00 Fig. 1. (a) Trajectories ofthe ÿrst 20 orbits ofthe Galileo orbiter along with the ÿve *y-by spacecraftrelative to Jupiter, shown in Jupiter Solar Orb ital coordinates. X points positive sunwards, and Y is orthogonal to X and in the plane ofJupiter’s orbit. The solid line indicates the Galileo orbiter and the dashed lines indicate the *y-by spacecraft. The individual *y-by spacecraft are distinguishable by the varying symbols shown in the key. A heavy dashed line depicts a model bow shock, and a model magnetopause is shown by the heavy solid line. Both model positions are derived from the Voyager-2 data. The region ofinterest forthis paper, 20–45 R J, is highlighted by the grey annulus in the centre ofthe plot. This ÿgure was kindly provided by Joe Maÿ ofthe Planetary Data System, UCLA. (b) Plot ofthe half-houraverages ofthe magnetic components measured outside the current sheet during the ÿrst 20 orbits ofthe Galileo orbiter and the ÿve *y-bys ofPioneer-10 and -11, Voyager-1 and -2, and Ulysses, fromwhich the VIP4 planetary ÿeld model (Connerney et al., 1998) has been subtracted. The averages have been projected onto the magnetic equatorial plane and rotated through 90◦ to indicate the approximate direction and strength ofthe corresponding current. Those ÿelds measured north ofthe current sheet have been rotated 90 ◦ anti-clockwise, while those measured to the south have been rotated in a clockwise sense. Dashed lines indicate the distance from the centre of the planet (RJ), and local time is also shown. The individual spacecraft are identiÿable by comparison with Fig. 1a. At the bottom right of the plot is the scale for 50 nT. the magnetosphere from near noon (Pioneer-11 outbound) to from dawn through to midnight, and some way into the post-midnight (Voyager-2 outbound), while Ulysses passed evening sector. The jovigraphic latitudes ofthese trajecto- through the pre-noon sector inbound and made unique ob- ries were near-equatorial in the main, except for the out- servations ofthe dusk meridian magnetosphere outbound. bound passes ofPioneer-11 and Ulysses, which exited near Presently available data from the Galileo mission extend noon at ∼33◦N and near dusk at ∼37◦S, respectively. Also E.J. Bunce et al. / Planetary and Space Science 50 (2002) 789–806 791 shown in the ÿgure are the positions ofthe magnetopause upon local time. For example, at distances of ∼40–50 RJ and bow shock as modelled from the Voyager-2 data (Ness the current is approximately twice as strong at a given radial et al., 1979b). The shaded region also indicates the domain distance at midnight than at the same distance at noon. This ofinterest forthis study, that is, the middle magnetosphere phenomenon was ÿrst noticed by Goertz (1978) in a com- region between 20 and 50 RJ. On the dayside, the magne- parison ofthe Pioneer-10 inbound and outbound data. The topause extends on average to ∼65 RJ as shown here, but diBering gradients ofradial ÿeld fall-oBwith distance at is highly variable depending upon the upstream solar wind the two local times (∼1000 MLT inbound and ∼0500 MLT conditions. On the nightside the magnetospheric tail extends outbound for Pioneer-10) were discussed in terms of the to ∼3000 RJ and has a diameter of ∼300 RJ (Ness et al., asymmetrical compressive and conÿning eBect the solar 1979c). wind dynamic pressure has on the magnetosphere, com- As indicated above, it is understood that the dynamics of pressing the *ux tubes on the dayside but allowing them to the Jovian middle magnetosphere are governed by the Io stretch out on the nightside. This stretching further distends plasma source, located deep within the equatorial magneto- the magnetic ÿeld lines, hence increasing the azimuthal cur- sphere at ∼5:9RJ. The current in the equatorial magnetodisc rent, on the nightside. Bunce and Cowley (2001a) favour is then carried (a) by the inertia current ofnear-corotating this interpretation, which then indicates that azimuthal cur- cold torus plasma which slowly diBuses outwards, and (b) rent closure is enforced via radial currents *owing wholly by the pressure-gradient current oflow density hot plasma within the current sheet, *owing away from the planet which slowly diBuses inwards (Hill, 1979; Vasyliunas, at dawn and towards the planet at dusk. Khurana (2001) 1983; Caudal, 1986; and references therein). This azimuthal prefers to attribute the divergence of the azimuthal current current sheet deÿnes what has become known as the Jovian to an Earth-like partial ring current closing via “region-2 “middle magnetosphere” region, which extends from ∼5RJ type” ÿeld-aligned currents, *owing towards the planet at (the inner edge ofthe Io plasma torus) to within ∼15 RJ of dawn, closing through the jovian ionosphere and *owing the magnetopause on the dayside.

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