A Simulation Study of Currents in the Jovian Magnetosphere Raymond J

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Planetary and Space Science 51 (2003) 295–307 www.elsevier.com/locate/pss

A simulation study of currents in the Jovian magnetosphere Raymond J. Walkera;∗, Tatsuki Oginob

aInstitute of Geophysics and Planetary Physics, and Department of Earth and Space Science, University of California, Los Angeles, Los Angeles, CA 90095-1567, USA bSolar Terrestrial Environment Laboratory, Nagoya University, Toyokawa, Aichi, Japan Received 23 April 2002; accepted 8 January 2003

Abstract

We have used a global magnetohydrodynamic simulation of the interaction of Jupiter’s magnetosphere with the solar wind to investigate the e/ects of the solar wind on the structure of currents in the jovian magnetosphere. A thin equatorial current sheet with currents 2owing around Jupiter dominates Jupiter’s middle magnetosphere. However, in our simulations this current is not uniform in azimuth. It is weaker on the day side than the night side with local regions where the current density decreases by more than 50%. In addition to this ring current the current sheet contains strong radial “corotation enforcement” currents. Outward radial currents are found at most local times but there are regions with currents directed toward Jupiter. The current pattern is especially complex in the local afternoon and evening regions. In the near equatorial magnetosphere the ÿeld-aligned current pattern also is complex. There are regions with currents both toward and away from Jupiter’s ionosphere. However, when we mapped the currents from the inner boundary of the simulation to the ionosphere we found a pattern more like that expected for the ionosphere to drive corotation with currents away from Jupiter at lower latitudes and currents toward Jupiter at higher latitudes. Since upward ÿeld-aligned currents are associated with aurora at the Earth they may be associated with aurora at Jupiter. The upward ÿeld-aligned currents map to larger distances on the night side (40RJ to 60 RJ) than on the day side (20RJ to 30RJ). In the simulations changing the solar wind dynamic pressure did not make major changes in the current sheet or ÿeld-aligned currents (both were slightly stronger for higher pressures). The interplanetary magnetic ÿeld had a stronger e/ect on the currents with the strongest currents for northward IMF. However, it took a very long time for the magnetosphere to respond to the changes in the IMF. ? 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Jupiter’s magnetosphere; Field-aligned currents; Current sheet; MHD simulation

1. Introduction from about 20RJ to 60RJ or 70RJ is frequently called the middle jovian magnetosphere. Plasma originating at the moon A thin equatorial azimuthal current sheet characterizes Io that is energized by planetary rotation is thought to carry Jupiter’s magnetosphere. This current sheet is found at all the equatorial currents (Hill et al., 1983; Vasyliunas, 1983). local times and on the day side extends from near Io’s or- The current sheet has been estimated to be 2–8RJ (Jupiter bit to within a few tens of RJ of the magnetopause (Smith radii) in thickness. Jupiter’s intrinsic magnetic ÿeld de- et al., 1974; Ness et al., 1979; Balogh et al., 1992; Kivelson creases as r−3 while the current sheet ÿeld decreases as r−1 et al., 1997). On the night side the current sheet merges or r−2 so the magnetic ÿeld from the current sheet is domi- with the magnetotail current system. The current sheet is nant in the middle magnetosphere. (See Bunce and Cowley, located near the magnetic equatorial plane and undergoes (2001a) for a recent and detailed review of the properties of a quasi-sinusoidal north–south motion as Jupiter rotates the current sheet.) Connerney et al. (1981) suggested that because Jupiter’s magnetic dipole is tilted 10◦ from the the current sheet is thicker on the day side than the night spin axis (see Khurana (1992) and references therein). The side while Jones et al. (1981) and more recently Bunce and region containing the current sheet is dominated by rotat- Cowley (2001a) and Khurana (2001) have argued that the ing 2ows. That part of the magnetosphere that contains the current sheet ÿeld is weaker on the day side than the night current sheet, plasma sheet and rotating 2ow and extends side. The observed day night asymmetry in the azimuthal cur- ∗ Corresponding author. rent implies a radial equatorial current with ÿeld-aligned E-mail address: [email protected] (R.J. Walker). currents carrying the current north and south away from the

0032-0633/03/$ - see front matter ? 2003 Elsevier Science Ltd. All rights reserved. doi:10.1016/S0032-0633(03)00018-7 296 R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307 current sheet in order to maintain current continuity. Goertz the largest Jupiterward currents were on the dawn side led (1978) noted that on the day side rotating 2ux tubes are Khurana (2001) to conclude that solar wind e/ects were constrained by the solar wind dynamic pressure but on the important well inside the jovian magnetosphere. night side they are free to expand. As the 2ux tubes move Jovian aurorae have been observed in infrared, ultravio- from the day side to the night side they are stretched result- let and visible light (e.g. Clarke et al., 1996; 1998; Satoh ing in stronger azimuthal currents. Radial currents that 2ow et al., 1996, PrangÃe et al., 1998; Vasavada et al., 1999). By away from Jupiter on the dawn side of the magnetosphere analogy with the Earth’s aurorae, we would expect discrete and toward Jupiter on the dusk side will maintain current jovian aurorae to be associated with ÿeld-aligned currents continuity. An outward radial current bends the magnetic directed away from Jupiter since precipitating electrons ÿeld lines in the direction of corotation “lag” (see Fig. 9 cause discrete aurorae. Southwood and Kivelson (2001) and of Khurana (2001)). On the dawn side corotation lag bends Cowley and Bunce (2001) have presented theories on the the magnetic ÿeld in the same direction as the solar wind relationship between jovian currents and the aurorae. They interaction while on the dusk side the bending is opposite to argue that the strength of the ionospheric ÿeld-aligned cur- that expected from the solar wind. Corotation lag has been rents and the luminosity of the aurora depend on the struc- observed near Jupiter at all local times, however, nearer ture of the magnetic ÿeld in the middle magnetosphere and the dusk side magnetopause the observed bending is in the on the angular velocity proÿle of the equatorial plasma. In opposite direction (Dougherty et al., 1993; Khurana, 2001; particular, they argue that the auroral oval maps to the part Kivelson et al., 2002). of the middle magnetosphere where the velocity of the In the jovian ionosphere collisions between ions and neu- rotating 2ows falls below the corotation velocity. Both tral particles in the Pedersen-conducting layer create a fric- papers conclude that aurorae will respond mainly to changes tional torque on the magnetic 2ux tubes that accelerates them in solar wind dynamic pressure in contrast to the Earth toward corotation. Hill (1979) showed that this ionospheric where changes in the interplanetary magnetic ÿeld (IMF) torque was suLcient to maintain near-corotation in the mid- and reconnection are dominant. For instance they argue that dle magnetosphere. The ionospheric torque is transmitted if the magnetosphere is compressed by the solar wind, the to the magnetosphere via ÿeld-aligned currents. These cur- 2ow in the magnetosphere will increase toward rigid coro- rents close in the ionosphere and the equatorial current sheet. tation thereby decreasing the lag in the ÿeld and the corota- The resulting ˜J × ˜B force in the ionosphere is directed to tion enforcement current. This will lead to dimming of the balance the viscous torque and slow the rotation of Jupiter’s aurorae. Conversely a decrease in solar wind dynamic pres- ionosphere (or atmosphere) while in the equatorial magne- sure will lead to increased ÿeld-aligned currents and more tosphere the ˜J × ˜B force is in the direction of corotation intense aurorae. Both Southwood and Kivelson (2001) and and accelerates the plasma (Hill, 1979; 2001; Vasyliunas, Cowley and Bunce (2001) argue that these changes in the 1983). The ÿeld-aligned currents are away from Jupiter at rotation and currents should hold during dynamic changes lower latitudes and toward Jupiter at higher latitudes clos- in the pressure while Cowley and Bunce (2001) argue that ing through equatorward Pedersen currents in the ionosphere they should hold for the steady-state magnetosphere as well. and outward 2owing radial currents in the equatorial mag- In this paper, we use our three-dimensional global magnetosphere. The outward radial current frequently is called netohydrodynamic simulation of the interaction of Jupiter’s the corotation enforcement current. magnetosphere with the solar wind (Ogino et al., 1998; Recently, Bunce and Cowley (2001b) and Khurana Walker et al., 2001) to model the jovian current structure (2001) have used near-equatorial magnetic ÿeld observa- and its dependence on solar wind parameters. We mainly tions to infer the ÿeld-aligned currents. Bunce and Cowley concentrate on the formation and structure of the equatorial (2001b) used Pioneer and Voyager observations in the mid- current sheet and the ÿeld-aligned currents that connect it dle magnetosphere (20RJ–50RJ) and found currents away to the jovian ionosphere. In Section 2 we brie2y discuss the from Jupiter along the early morning trajectories of Voyager global MHD code. In Section 3 we examine the structure 1 and 2 outbound and currents toward Jupiter along the Pi- of the jovian currents in detail by considering the simple oneer 10 outbound trajectory at ∼ 0500 LT and the Pioneer case in which an unmagnetized solar wind interacts with the 11 inbound trajectory at ∼ 0900 LT. The inferred cur- magnetosphere. Then in Section 4 we examine how the current densities were between 10−13 and 10−12 Am−2 nT−1. rents change when we change the solar wind dynamic pres- Khurana (2001) used Galileo orbiter observations to map sure and interplanetary magnetic ÿeld (IMF). Finally, we the distribution of ÿeld-aligned currents throughout much summarize our results and compare them to observations of the middle magnetosphere. He found ÿeld-aligned cur- and other theoretical models of the jovian current system. rents away from Jupiter in an arc from about 1330 LT to about 0730 LT and currents toward Jupiter from about 0730 to 1330 LT. These currents extend from ∼ 10RJ to at least 2. Simulation model 30RJ. The radial extent of the currents is poorly known on the dayside because of poor Galileo data coverage. That We have presented our Jupiter simulation model in detail the largest outward currents were on the dusk side and previously (Ogino et al., 1998), so we will just review its R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307 297 main features here. Initially, we ÿlled the simulation domain Table 1 with plasma and ÿelds from a simple model of a rotating Solar wind parameters jovian magnetosphere. At time t = 0 we placed an image Solar wind dynamic pressure (nPa) dipole upstream of Jupiter to help form a magnetospheric cavity. The image dipole helped assure that there were no 0.045 0.09 0.18 0.37 0.75 IMF Bz (nT) 0.0 0.0 0.0 0.0 0.0 parallel 2ows in the initial solar wind. It hastened the forma- −0:84 −0:84 tion of a magnetopause and helped assure that the magnetic +0.84 +0.84 ÿeld (˜B) remains divergenceless (·˜B = 0) throughout the −0:42 simulation box (Watanabe and Sato, 1990). +0.42 The simulations used in this study had a 452 × 302 × 152 point Cartesian grid with grid spacing of 1:5RJ. The grid spacing was chosen as a compromise between reasonable (Ogino et al., 1992). The free boundary conditions work well resolution in the middle magnetosphere and computational provided the magnetopause exits the simulation box through time. For very long runs (hundreds of hours in real time) the rear boundary. This condition is met for all of the sim- we found only minor changes when we increased the grid ulation runs used in this study except for the case with a 2 spacing by a factor of 2 to Ox=3RJ. In general, we found that solar wind dynamic pressure of vsw =0:045 nPa. For this the bow shock and magnetopause boundaries were resolved case the magnetopause got within 10RJ of the side bound- much better with Ox =2RJ or Ox =1:5RJ. We launched the ary tailward of about x ≈−280RJ. However, since we are solar wind from the upstream boundary of the simulation primarily concerned with currents in the middle magne- 2 box, and solved the resistive magnetohydrodynamic (MHD) tosphere and since the results from the vsw =0:045 nPa equations as an initial value problem by using the numerical simulation are consistent with those from the other runs approach described in Ogino et al. (1992). We use an explicit we have included them in the paper. Note the bow shock resistivity that enters the equations through Faraday’s law passes through the side and top boundaries in all of the (@˜B=@t = ∇×(˜v × ˜B)+Á∇2˜B where ˜v is the velocity and Á simulations. For all but one of the simulations in this study is the resistivity). The normalized resistivity is set equal to (the southward IMF case discussed in Section 4) the shock 0.002. This corresponds to a magnetic Reynolds number of crosses the simulation boundary tailward of the dawn-dusk about 500. It is uniform in value throughout the simulation meridian. box and is kept constant throughout each simulation run. We modeled the magnetosphere for a number of com- During the simulations the magnetic ÿeld (˜B), the velocity binations of solar wind dynamic pressure and IMF magni- (˜v), the mass density () and the pressure (p) were main- tude and direction. The values of the solar wind dynamic tained at solar wind values at the upstream boundary (usually pressure and IMF for which we have simulated Jupiter’s x = 225RJ) while free boundary conditions through which magnetosphere are listed in Table 1. The ÿve dynamic pres- waves and plasmas can freely enter or leave the system were sures used are listed in the ÿrst row. These values of the used at the downstream (x = −450RJ), side (y = ±225RJ), dynamic pressure span a range somewhat smaller than that 2 and top (z =225RJ) boundaries. Symmetry boundary condi- observed at Jupiter (0:01 nPa 6 vsw 6 1:0 nPa) (Smith tions were used at the equator (z=0) (Ogino et al., 1992) and et al., 1978; Bridge et al., 1979a, b; Phillips et al., 1993). The the dipole tilt was set to zero. At the inner boundary all the median solar wind dynamic pressure at Jupiter is 0:1 nPa ˜ simulation parameters (B;˜v; ; p) were ÿxed for r¡15RJ. (Slavin et al., 1985; Huddleston et al., 1998; Joy et al., For r¡21RJ each parameter (’) in the simulation was 2002). All ÿve dynamic pressures were run without an IMF calculated by using (second row). For two dynamic pressures northward and southward interplanetary magnetic ÿelds were included. For ’(r; t)=f’ (r; t)+(1− f)’ (r); EX IN 0:09 nPa two values of the IMF were used (±0:84 nT and where ’EX (r; t) is the value from the simulation and ’IN(r) ±0:42 nT). The mean IMF at Jupiter’s orbit is 0:8nT(Joy is the value from the initial model. The value of f depends et al., 2002). In this study we will present results for so- only on the radial position and is given by lar wind pressures between 0:045 nPa and 0:37 nPa. For a h2 0:09 nPa we will also show results for IMF values of f ≡ 0 a h2 +1 ±0:84 nT. For all of the simulations vsw = 300 km=s and 0 the temperature of the solar wind was 2 × 105 K. The solar where a0 = 30 and wind was held constant for up to 600 h in these runs in r2 order to obtain quasi-steady magnetospheric conÿgurations. h ≡ − 1;r¿ r 2 a It has long been realized that Io and its plasma torus can ra supply most of the plasma needed to populate the jovian h ≡ 0;r¡r a system. Hill et al. (1983) estimated that transport from the 28 with ra =15RJ. Io source was 3 × 10 ions/s of mass ∼ 20 AMU. In an The outer boundary conditions have been used suc- explicit MHD code it is diLcult to include Io and the Io cessfully in our simulations of the Earth’s magnetosphere torus in the calculation. The numerical stability criterion is 298 R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307

Table 2 ideal the inner boundary condition provides a reasonable Source rates from the inner boundary (AMU/s) approximation to the Io source for studies of the middle and outer jovian magnetosphere. To further investigate how Bz Dynamic pressure (nPa) magnetic 2ux is conserved in a system with net out2ow 0.045 0.09 0.18 0.37 we calculated the E˜ · dl along a path enclosing Jupiter. 07:0 × 1030 8:6 × 1029 7:6 × 1029 6:4 × 1029 −0:84 5:0 × 1030 In general 2ux is removed in the noon, dawn and midnight +0.84 3:4 × 1030 quadrants and returned in the dusk quadrant.

3. Currents in the jovian magnetosphere max max vg Ot=Ox¡1 where vg is the maximum group velocity in the calculation domain, Ox is the grid spacing and Ot is In the top panel of Fig. 1 we have plotted the thermal the time step. Since the AlfvÃen velocity (vA) becomes very pressure and 2ow vectors in a plane 0:75RJ above the equa- 2 large near Jupiter (approaching the speed of light at 1RJ)we tor for a solar wind pressure vsw =0:37 nPa. The bottom placed the inner boundary of the simulation at 15RJ. This panel contains the speed. The IMF was set to zero. The enabled us to model time-dependent phenomena without us- simulation was run for 300 h by which time a quasi-steady ing an extremely small time step. Unfortunately, this means magnetospheric conÿguration had formed. The solid black that the important Io interaction must be handled by the in- circle shows the position of the inner simulation boundary ner boundary condition. As we discuss further, we carried (15RJ). The magnetosphere was not simulated in this re- out a series of tests to evaluate how well our boundary con- gion. A circle has been drawn at r ≈ 60RJ to help the reader dition has modeled the Io source. As noted above the simu- judge distances in the middle magnetosphere. Rotation and lation parameters were ÿxed at the inner boundary. In partic- the equatorial plasma sheet dominate near Jupiter. Although ular, the velocity was purely rotational and the pressure and the plasma density and pressure are spherically symmetri- density were set to values determined from the Voyager 1 cal inside the 15RJ boundary the equatorial plasma sheet 2yby of Jupiter (Belcher, 1983). The magnetic ÿeld was forms self-consistently within a few grid spaces outside the ÿxed to values from Jupiter’s internal dipole. boundary (see Plate 3 of Ogino et al. (1998) for an exam- As a test of the behavior of the inner boundary con- ple). The plasma sheet pressure varies as a function of local dition we examined the results from a simulation during time with the largest values in a band extending from ap- which the code was run for 600 h with a southward IMF proximately 1700 LT past midnight. Actually there are two and then for 150 h with a northward IMF. We calculated peaks (not shown) in the pressure one centered at about the mass 2ux through a surface at 22:5RJ. For the southward 1800 LT and the other centered at about 2300 LT. The 2ow IMF case the inner boundary provided 5:0 × 1030 AMU=s pattern is complex. In the middle magnetosphere rotational to the jovian system. For the northward IMF case the out- 2ows dominate but the velocity varies with local time. The 2ow was 3:4 × 1030 AMU=s. These values are somewhat largest rotating 2ows are found pre-dawn while the smallest higher than the estimate by Hill et al. (1983). Other simu- 2ows are found pre-dusk. The 2ow is small nearer both the lation runs gave values as low as 2 × 1029 AMU=s(Ogino dawn and dusk magnetopause. There is out2ow at all local et al., 1998). Table 2 contains the source rate values for each times in the magnetotail but the tailward velocity is great- of the runs used in this study. Although the exact regions of est in a channel extending dawnward from midnight. The out2ow and in2ow vary from run to run in general there is out2ow in the tail is an inertial e/ect. On the day side the out2ow on the dawn side of the magnetosphere and in2ow outward 2owing plasma is constrained by the solar wind. on the dusk side. These results are qualitatively consistent However, as the plasma rotates past dusk into the night side with recent determinations of the 2ow direction based on it is no longer constrained by the solar wind. Tailward 2ow energetic ion 2ux anisotropies (Krupp et al., 2001). near the dusk magnetopause stretches the ÿeld lines. Just As noted above the out2ow is not uniform and there are tailward of the dusk meridian the tension on these stretched regions of both out2ow and in2ow. As a second test we ÿeld lines causes some of them to snap toward Jupiter. Near calculated the magnetic 2ux through the closed surface at midnight the stretched-closed ÿeld lines reconnect causing 22:5RJ and examined its change as a function of time. In the the tailward 2ow (Ogino et al., 1998). case discussed above the 2ux increased between t =600 and Flow streamlines provide another way to visualize the 750 h by 2:8 × 109 W or about 0.5%. To determine whether convection pattern in the equatorial jovian magnetosphere this value is signiÿcant it is necessary to understand the (Fig. 2). In the top panel the 2ow streamlines have been uncertainty in the numerical calculation. As a check of the color coded with the thermal pressure while in the bottom accuracy of our integration we increased the grid spacing by panel the color-coding gives the density. As the plasma 2ows a factor of two and repeated the calculation. This changed around dusk from the day side to the night side it 2ows ÿrst the results by 3:6 × 109 W or approximately 0.7%. Thus away from Jupiter then toward Jupiter before reaching the to the uncertainty in the calculation there was no change tail. Both the density and pressure reach a maximum at about in the magnetic 2ux during the test interval. Although not 2100 LT. The pressure and density decrease as the plasma R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307 299

Fig. 1. Pressure contours and 2ow vectors (top) and 2ow speed contours (bottom) in the Z =0:75RJ plane from the simulation with solar wind dynamic pressure of 0:37 nPa and no interplanetary magnetic ÿeld. These snapshots of the results were taken 300 h after the solar wind entered the upstream boundary. By this time the magnetosphere had reached a Fig. 2. Flow streamlines for the simulation in Fig. 1. The streamlines have quasi-steady conÿguration. The black dots indicate the region Jupiterward been color coded with the plasma pressure (top) and density (bottom). of the inner boundary of the simulation. The black circles are at r ≈ 60RJ.

2ows from the night side to the day side. The smallest values are found in the midafternoon. We determined the currents throughout the jovian magnetosphere by numerically calculating ∇×˜B. In the simulation the equatorial current sheet forms self-consistently with the plasma sheet. It is found primarily near the equator and the north–south distribution is very much like that for the density and pressure. The current pattern is slightly more di/use since it results from taking a numerical derivative. The currents just north of the equator are shown in more detail in Figs. 3 and 4. We have separated the perpendicular currents into radial and azimuthal components in Fig. 3 while in Fig. 4 they are plotted with green arrows that are proportional to the current density. The current sheet currents are not uniform. The azimuthal currents are largest on the night side where they merge with the cross magnetotail currents. The azimuthal currents are weaker across the day side and have minima at about 1300 LT and at about 1900 LT. There are regions of intense radial currents both away from Jupiter and toward Jupiter. However, throughout most of the middle magnetosphere the radial currents are away from Jupiter. These away currents merge with Fig. 3. Radial and azimuthal currents in the Z =0:75RJ plane for the the away currents in the tail and the dawn magnetosphere. simulation in Fig. 1. In the top panel warm colors represent currents that However, there are four regions with radial currents toward are away from Jupiter. In the bottom panel warm colors represent 2ow Jupiter. Three of these are most likely real since they cover in the corotation sense. The black circles are at r =60RJ. large regions of the magnetosphere and extend well away 300 R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307

Fig. 5. Parallel currents in the X = 0 (top) and Y = 0 planes for the Fig. 4. Perpendicular and parallel currents in the Z =0:75RJ plane for the simulation in Fig. 1. The parallel currents are given by the color shading simulation in Fig. 1. while the arrows give the perpendicular currents. Warm colors represent currents along the magnetic ÿeld while cold colors represent currents 2owing opposite to the direction of the magnetic ÿeld. The circle is at r ≈ 60RJ.

from the inner boundary. The one near dawn is very small and is conÿned to a region only a few grid points from the inner boundary. It is probably related to the inner boundary condition and is not real. Between approximately 1100 and 1500 LT the radial currents are toward Jupiter at all radial distances. These currents merge continuously into the dusk 2ank current structure. The parallel currents near the equator also are highly structured (Fig. 4). The currents in the middle magnetosphere nearer the inner boundary are mostly away from Jupiter (warm colors indicate currents away from the ionosphere and blue indicates currents toward the iono- Fig. 6. Parallel currents calculated at a radial distance of 21RJ (just outside sphere) except in the late morning and early afternoon in the inner boundary) and mapped along dipolar ÿeld lines into Jupiter’s ionosphere. Warm colors indicate currents away from Jupiter while cold local time. These away ÿeld-aligned currents are found colors indicate currents toward Jupiter. This calculation was carried out over a region extending 10’s of RJ from Jupiter. Right at for the same simulation as Fig. 1. The green traces give the ionospheric the inner boundary there are very small regions with both end points of ÿeld lines calculated starting at 20RJ,40RJ, and 60RJ in the away and toward currents. These are most likely noise since equatorial magnetosphere. The 180 points in each trace were calculated they are conÿned to the immediate neighborhood of the from points that were uniformly spaced in the equatorial plane. boundary in the region r¡21RJ. The expected pattern with away currents in the near primarily toward Jupiter. As noted above the current struc- Jupiter part of the middle magnetosphere and toward tures conÿned to grid points immediately adjacent to the currents further out is not clearly evident in Fig. 4.In inner boundary are suspect. Some of the high latitude cur- Fig. 5 we have plotted the parallel currents in the dawn-dusk rents 2owing toward the ionosphere connect to the magne- meridian (x =0; top) and noon-midnight meridian planes topause. In the tail the main parallel current system is away (y =0; bottom). In the dawn-dusk plane the parallel current from Jupiter nearer Jupiter and toward Jupiter further out. pattern is as expected. Near Jupiter the currents are away In Fig. 6 the parallel currents just outside the inner sim- from the ionosphere and further out the return currents go ulation boundary have been mapped along magnetic ÿeld toward Jupiter on both sides. The parallel currents are dis- lines to the ionosphere. The values were calculated at 21RJ tributed over tens of jovian radii. At high latitudes on the at the point where the smoothing discussed in Section 2 is dawn side some of the currents toward Jupiter merge with turned o/. We have superimposed three green curves on the currents on the magnetopause. Along the noon-midnight current contours. They show the ionospheric intercepts of meridian the pattern is a bit more complex especially at magnetic ÿeld lines calculated starting at the equator at 20RJ, noon. Near the inner boundary there are regions with both 40RJ and 60RJ. At lower latitudes the parallel currents are upward and downward currents while those further out are primarily away from Jupiter as expected. A band of upward R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307 301 currents extends from about 1700 LT through the night side to about 1000 LT. The peak current densities are approximately 10−7 A=m2. Patches of downward currents are found at lower latitudes on the night side but they are over an order of magnitude smaller than the upward currents. We believe these are spurious and are caused by the inner boundary condition. Between 1000 and 1700 LT the upward currents are much weaker. The upward currents mostly map to the equatorial region between 20RJ and 40RJ. However, they map farther out (40RJ–60RJ) pre-dawn. The most intense away currents are found between 1800 and 2100 LT. As expected the high latitude currents are primarily toward Jupiter. The most intense toward currents also are in the 1800–2100 LT region. They map beyond 40RJ everywhere except a narrow region between 1000 and 1300 LT. In the late morning the inward currents extend all the way to the inner simulation boundary. We repeated the mapping in Fig. 6 by calculating the currents on spheres at 25RJ and 30RJ. The pattern and magnitude of the parallel currents were virtually unchanged. The only di/erence was the elimination of currents at lower latitudes.

4. Changing the interplanetary magnetic ÿeld and the Fig. 7. Parallel and perpendicular currents in the plane Z =0:75RJ for solar wind dynamic pressure southward (top) and northward (bottom) interplanetary magnetic ÿeld. The format is the same as Fig. 4. The IMF was held constant at BZ =−0:84 nT for 600 h for the top plot and then rotated northward for 150 h. A We have examined results from other simulations in quasi-steady magnetospheric conÿguration had evolved in the ÿrst case Table 1 to determine the dependence of the jovian current but the magnetosphere was still slowly evolving even after 150 h in the systems on the interplanetary magnetic ÿeld and the so- second case. lar wind dynamic pressure. The parallel and perpendicular current densities at Z =0:75RJ are plotted for two IMF found just pre-dawn for the southward IMF case has no ob- orientations in Fig. 7. For these simulations the code was vious counterpart in the BZ ¿ 0 calculation. Near Jupiter run with a southward IMF for 600 h and then for 150 h the largest di/erence is that the region of parallel currents with a northward IMF. For the southward IMF simulation 2owing toward Jupiter is larger for the northward IMF case the magnetosphere had reached a very steady conÿguration extending from ∼ 0900 to ∼ 1800 LT. while for the northward IMF case the conÿguration was The radial currents from these two simulations are plot- slowly changing (Walker et al., 2001). For southward IMF ted in Fig. 8. Although there are detailed di/erences in the reconnection tailward of the polar cusp removes tail lobe middle magnetosphere there are also similarities. The largest magnetic 2ux (Walker et al., 2001) thereby reducing the tail di/erences are near the magnetopause, in the magnetosheath currents. The dominant currents are those associated with and in the more distant parts of the tail. The strong radial the current sheet in the middle magnetosphere. The paral- currents in the tail for the northward IMF case are related lel currents are basically similar to those for the BIMF =0 to the tail reconnection. The magnetosheath currents have case with currents away from Jupiter dominant from late opposite signs. In both simulations radial currents are away afternoon to the late morning but lots of structure. from Jupiter in the morning and toward Jupiter in the after- When the IMF is northward reconnection occurs at the noon. The signatures in the evening are complex with re- subsolar magnetopause and in the near jovian tail (Walker gions of both away and toward currents. Not too surprisingly et al., 2001). The thin tail current sheet and reconnection the currents mapped from the inner boundary of the simu- give much stronger currents across the tail in this simula- lation to Jupiter also are very similar (Fig. 9). The magni- tion. The largest di/erences in the perpendicular currents tude of the current density is larger and the currents map to between the three cases considered so far are in the strength slightly larger radial distances for the northward IMF case. of the tail current (cf. Figs. 4 and 7). The bright band of The purple curve in Fig. 9 gives the position of the bound- away ÿeld-aligned currents in the jovian tail is associated ary between open and closed ÿeld lines (the polar cap bound- with the tail reconnection. In the middle magnetosphere the ary). The polar cap is only about 10◦ in extent. For the parallel current pattern is similar to that for the southward northward IMF case a second band of away currents formed IMF simulation although there are some di/erences. For in- at higher latitudes between 0400 and 1300 LT near the polar stance the away and toward Jupiter ÿeld-aligned current pair cap boundary. This second band of away currents crosses 302 R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307

Fig. 8. Radial currents in the equatorial plane for the simulations in Fig. 7. Warm colors represent currents that are away from Jupiter. The format is the same as in top panel of Fig. 3. onto open ÿeld lines in the polar cusp region. All of the other ÿeld-aligned currents are on closed ÿeld lines. In order to investigate the in2uence of the solar wind dynamic pressure on the jovian current sheet we carried out a numerical experiment during which the solar wind pressure was reduced in a series of steps. Starting with the magnetospheric conÿguration presented in Section 3 we re- Fig. 9. Parallel currents projected into the ionosphere for the southward duced the dynamic pressure by a factor of two and ran the (top) and northward IMF cases. The format is the same as in Fig. 6 simulation until a quasi-steady magnetosphere resulted. except that the purple curve outlines the polar cap for the northward IMF case. Polar cap ÿeld lines were deÿned as open ÿeld lines with one end We repeated this procedure two more times each time using closing in Jupiter and one end in the IMF. half the pressure in the previous simulation. The resulting currents for three of the pressures are shown in Fig. 10. The current patterns in these three cases and that in Fig. 4 are and a few surprises. In all of our simulations the azimuthal very similar. Both the perpendicular currents and the paral- ring current of the equatorial current sheet dominates the lel currents are strongest for the high-pressure compressed region of corotating plasma or the middle magnetosphere. magnetosphere. Similarly the radial current pattern is virtu- However, this current is not uniform in azimuth. It is weaker ally the same for all the decreasing pressure runs (Fig. 11). on the day side than the night side with local regions where The largest radial currents occur for the highest solar wind the current density decreases by more than 50% (e.g. Fig. pressure. Finally, the ÿeld-aligned currents mapped to the 5, bottom). In addition to the ring current the jovian middle ionosphere also have very similar patterns for all pressures magnetosphere contains strong radial currents. Outward ra- (Fig. 12). In general the amplitude of the current density is dial currents dominate most of the middle magnetosphere, largest for the high-pressure case for most longitudes. How- however, there are regions where the radial currents are to- ever, between noon and ∼ 1600 LT the upward currents ward Jupiter. are slightly stronger for the lowest pressure case. The structure of the afternoon and evening magnetosphere is very complex. In all of the simulations there is a region in the afternoon where the plasma 2ow velocity, the 5. Discussion plasma density and pressure decrease (e.g. Figs. 1 and 2). In this region the ring current becomes smaller and the radial The jovian magnetospheric currents from our simulation currents 2ow toward Jupiter at all radial distances (Fig. 3). have many of the properties expected for a rotating planet Closer to dusk the 2ow turns toward Jupiter and accelerates R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307 303

Fig. 10. Parallel and perpendicular currents in the Z =0:75RJ plane for Fig. 11. Radial currents for the three simulations in Fig. 10. The format three solar wind dynamic pressures. The format of each panel is the is the same as that in the top panel of Fig. 3. same as Fig. 4. The simulation was started with a dynamic pressure of 0:37 nPa (the simulation shown in Fig. 1) and then the pressure was The ÿeld-aligned current pattern within the jovian mag- decreased in 3 steps to 0:045 nPa. In each case the simulation was run netosphere also is complex. There are regions with currents until a quasi-steady magnetosphere evolved. both toward and away from Jupiter’s ionosphere. It is not clear from looking at the distribution of parallel currents in and the pressure and density increase (e.g. Figs. 1 and 2). the near-equatorial magnetosphere that these are the con- The radial current again becomes positive. When the 2ow necting currents needed for the ionosphere to enforce coro- is decelerated, the pressure and density become large (e.g. tation. However, when we examined the currents in the Figs. 1 and 2) and the radial current reverses. Goertz (1978) XZ and YZ planes (Fig. 5) and mapped the ÿeld-aligned pointed out that out2owing rotating plasma on the day side currents from a sphere at 21RJ to the ionosphere (Fig. 6) is constrained at the magnetopause until it rotates past noon. we found a pattern more nearly like that expected with a In the afternoon and evening the ÿeld lines can be stretched ring of current away from Jupiter at lower latitudes and a into a more tail like conÿguration. This leads to an asym- region of currents toward Jupiter at higher latitudes. The metric azimuthal current system. Current closure requires ÿeld-aligned currents map to di/erent distances in the equa- either outward radial currents at dawn and inward radial torial magnetosphere at di/erent local times. For instance currents at dusk as discussed by Bunce and Cowley (2001a) the upward ÿeld-aligned currents map to larger distances on or ÿeld-aligned currents toward Jupiter at dawn and away the night side (e.g. 40–60RJ at 0300 LT) than on the day at dusk as discussed by Khurana (2001) or both. In the side (∼ 20–30RJ). Upward ÿeld-aligned currents also are morning and evening both ÿeld-aligned currents and radial much weaker on the day side. The strongest currents map currents seem to be involved in providing current closure to the region where corotation breaks down (Hill, 2001). In (cf. Figs. 3 and 4). However, in the early afternoon the Fig. 13 we have plotted the ratio of azimuthal 2ow veloc- inward radial currents are the dominant closure currents ities to the corotation velocity for the 2ows in Fig. 1. The (e.g. Fig. 3 in the afternoon). The cross magnetosphere 2ow decreases below corotation rapidly at dusk where the magnetotail currents in the equatorial plane (dusk to dawn largest parallel currents are found (Figs. 4 and 6). The 2ow at Jupiter) have an inward radial component on the dusk falls o/ less rapidly in the morning where the currents map side and an outward component on the dawn side. This to a larger region of the magnetosphere. Finally, there are causes the inward currents in the pre-midnight tail and weaker currents (frequently toward Jupiter in Figs. 6, 9 and the outward currents in the post-midnight tail (e.g. Fig. 3, 12) that originate in the region immediately adjacent to the top panel). inner boundary. They most likely are not real. 304 R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307

Khurana (2001) produced maps of the currents in the equatorial plane based on Galileo orbiter observations. The distributions of azimuthal and radial currents in his maps (see Plates 2 and 3 of Khurana, 2001) are very similar to the distributions in Fig. 3. At a given radial distance the largest azimuthal currents occur in the early morning in both the observations and simulations. At the time of Khurana’s study there were no observations in the afternoon where the simulation results suggest the azimuthal currents should be smallest. The radial currents are mostly away from Jupiter with the largest radial currents in the early morning region in both the observations and simulations. In the simulations the radial currents are toward Jupiter in the afternoon and along the dusk 2ank. Khurana (2001) re- ports radial currents toward Jupiter around dusk. Near dusk these inward radial currents extend from the magnetopause to at least 40RJ. Closer to Jupiter it is not clear whether the details of the structure in Jr from the simulation (e.g. in Fig. 3) are observed. Again Khurana did not have observations in the afternoon middle magnetosphere so we cannot compare the radial current pattern there. Khurana (2001) inferred the height-integrated perpendicular current density from the observations. To compare our simulation results quantitatively with his observations we integrated our results over the current sheet. The height-integrated currents from the simulations were smaller by a factor of 2 or 3 than those inferred from the magnetic Fig. 12. Parallel currents mapped to the ionosphere for the three pressures ÿeld observations. There are a couple of possible reasons in Fig. 10. The calculation and the format are the same as in Fig. 6. for this. First inferred current densities may have signiÿcant uncertainty since it is a diLcult model dependent task to infer currents from single spacecraft observations (Khurana, 2001). However, the current strength from the simulations may be too low. In a recent study we compared the magnetic ÿeld observations in the day side magnetosphere with a number of simulation runs and found that although the simulation results were qualitatively consistent with the observations they did not reproduce the extremely strong current sheets observed by Pioneer 10 and Ulysses on their inbound trajectories (Walker et al., 2001). We believe this is caused by our need to apply the inner boundary condition far from Jupiter (15RJ). The real current sheet starts to form well inside of 15RJ. Khurana (2001) also calculated the divergence of the perpendicular currents to obtain a map of the ÿeld-aligned currents. The resulting distribution (Plate 6 of Khurana, 2001) is similar to that found in the simulations with currents away from Jupiter in an arc from early afternoon to past dawn and toward currents in the morning and early afternoon Fig. 13. Contours of the ratio of the azimuthal 2ow velocity to the although the currents in the simulation have much more corotation speed for the simulation in Fig. 1. structure. Khurana argued that the jovian currents were analogous to the region 2 currents in the Earth’s magnetosphere and that they were an indication that solar wind Recently, Bunce and Cowley (2001a, b) and Khurana driven magnetospheric convection was important deep in (2001) have inferred the current sheet currents using space- the magnetosphere. We also found solar wind e/ects in the craft observations. The observed currents like the simulated simulated currents with the strongest e/ects related to the currents are weaker on the day side than on the night side. direction of the interplanetary magnetic ÿeld. R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307 305

lation results support the idea by Khurana (2001) that solar wind driven magnetospheric convection can in2u- ence the currents in the middle magnetosphere. How- ever, we should keep in mind that Jupiter responds slowly to changes in the solar wind and IMF. In this case it took approximately 70 hours from the time the northward IMF reached the subsolar magnetopause until a solar wind driven near tail neutral line formed. Although this was an extreme case because of the length of time the IMF was southward before the northward turning, in other simulation studies it still took at least 30 h for tail reconnection to start. Walker et al. (2001) used solar wind observations near Jupiter to show that long intervals during which the IMF was either northward or southward were fairly common. During the period in their study, intervals during which the IMF north–south component had one sign for at least 10 h made up over half the time at Jupiter’s orbit. We would expect solar wind driven convection to have a signiÿcant in2uence only during those intervals. Southwood and Kivelson (2001) and Cowley and Bunce (2001) have suggested that the solar wind dynamic pressure may have an important in2uence on the middle magneto- Fig. 14. Flow speed contours for the southward IMF (top) and northward sphere. They invoke conservation of angular momentum to IMF (bottom) simulations in Fig. 7. The format is the same as in the argue that when the dynamic pressure increases the plasma bottom panel of Fig. 1. in the middle magnetosphere will rotate more rapidly. This in turn will require weaker corotation enforcement currents and weaker ÿeld-aligned currents. Conversely when the The ÿeld-aligned currents inferred from Galileo obser- dynamic pressure decreases they predict that the 2ow vations correspond to currents of 3–6 × 10−8 A=m2 when velocity will decrease and the enforcement currents and mapped to Jupiter’s ionosphere (Khurana 2001; Hill, 2001). ÿeld-aligned currents will increase. We are unable to in- Based on Pioneer and Voyager observations Bunce and vestigate the size of any temporal changes associated Cowley (2001b) inferred currents as strong as 10−6 A=m2. with the pressure changes since we did not save the sim- The simulated parallel currents (typically 6 10−7 A=m2) ulation results with suLcient time resolution. However, are consistent with the Galileo values but never reach the we can investigate how the steady-state middle magneto- much larger values inferred from the Pioneer and Voyager sphere changes for various solar wind and IMF parame- data. ters. In Fig. 15 we have plotted the 2ow speed for three Magnetic reconnection mainly drives convection in solar wind pressures. The corresponding ÿeld-aligned cur- the Earth’s magnetosphere. The numerical experiment in rents and radial currents are given in Figs. 10–12. Recall Figs. 7–9 provides an extreme example of the e/ects of re- that for this experiment we decreased the pressure from connection at Jupiter. Recall that the simulation was run with 0:37 nPa and each case was run until a quasi-steady mag- a southward IMF for 600 h and then the IMF was turned netosphere resulted. There are virtually no changes in northward for 150 h. Walker et al. (2001) have discussed the 2ow speed in the inner parts of the middle magneto- the changes in convection during this simulation in detail. In sphere (¡ 10%) as the pressure changes. The most dra- the southward IMF case high latitude polar cusp reconnec- matic changes occurred nearer the dayside magnetopause tion removed tail lobe 2ux. The middle magnetosphere was beyond the region where the ionospheric ÿeld-aligned dominated by rotating plasma. When the IMF was turned currents map. In Figs. 10–12 both the equatorial radial northward the magnetopause reconnection site moved to currents and the ÿeld-aligned currents are slightly larger the subsolar magnetopause and this was followed by tail for the high-pressure simulations. In the simulations the reconnection (see Fig. 2 of Walker et al., 2001). In Fig. 14 pressure changes do not cause very dynamic changes in the we have plotted the 2ow speed in the equatorial plane from steady-state middle magnetosphere. In the steady state we these two simulations. Following the northward turning of ÿnd no evidence that lower pressures correspond to larger the IMF the 2ow speed in the middle magnetosphere on the ÿeld-aligned currents as suggested by Cowley and Bunce dawnside increased by at least a factor of 2 while the 2ow (2001). We have begun a study of the e/ects of dynamic speed on the dusk side decreased. The magnitude of the changes in the solar wind by simulating the response of the radial and ÿeld-aligned currents also increased (Figs. 8 magnetosphere to pressure pulses and will report on these and 9) but not as dramatically. In general our simu- results in the future. 306 R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307

Computing support was provided by the Computer Center of Nagoya University and by the National Partnership for Advanced Computing Infrastructure (NPACI).

References

Balogh, A., et al., 1992. Magnetic ÿeld observations during the Ulysses 2yby of Jupiter. Science 257, 1515. Belcher, J.W., 1983. The low-energy plasma in the jovian magnetosphere. In: Dessler, A.J. (Ed.), Physics of the Jovian Magnetosphere. Cambridge University Press, New York, pp. 68. Bridge, H.S., et al., 1979a. Plasma observations near Jupiter: initial results from Voyager 1. Science 204, 987. Bridge, H.S., et al., 1979b. Plasma observations near Jupiter: initial results from Voyager 2. Science 206, 972. Bunce, E.J., Cowley, S.W.H., 2001a. Local time asymmetry of the equatorial current sheet in Jupiter’s magnetosphere. Planet. Space Sci. 49, 261. Bunce, E.J., Cowley, S.W.H., 2001b. Divergence of the equatorial current in the dawn sector of Jupiter’s magnetosphere: analysis of Pioneer and Voyager magnetic ÿeld data. Planet. Space Sci. 49, 1089. Clarke, J.T., et al., 1996. Far-ultraviolet imaging of Jupiter’s aurora and the Io “footprint”. Science 274, 404. Clarke, J.T., et al., 1998. Hubble Space Telescope imaging of Jupiter’s UV aurora during the Galileo orbiter mission. J. Geophys. Res. 103 (20), 217. Connerney, J.E.P., Acuna, M.H., Ness, N.F., 1981. Modeling the jovian current sheet and inner magnetosphere. J. Geophys. Res. 86, 8370. Cowley, S.W.H., Bunce, E.J., 2001. Origin of the main auroral oval in Jupiter’s coupled magnetosphere-ionosphere system. Planet. Space Sci. 49, 1067. Dougherty, M.K., Southwood, D.J. Balogh, A. Smith, E.J., 1993. Fig. 15. Flow speed contours for the simulations in Fig. 10. The format Field-aligned currents in the jovian magnetosphere during the Ulysses is the same as the bottom panel of Fig. 1. 2yby. Planet. Space Sci. 41, 291. Goertz, C.K., 1978. Energization of charged particles in Jupiter’s outer magnetosphere. J. Geophys. Res. 83, 3145. In this set of simulations the plasma source rates at the Hill, T.W., 1979. Inertial limit on corotation. J. Geophys. Res. 84, 6554. Hill, T.W., 2001. The jovian auroral oval. J. Geophys. Res. 106, 8101. inner boundary were determined by the magnetospheric Hill, T.W., Dessler, A.J., Goertz, C.K., 1983. Magnetospheric models. In: conÿguration. For northward IMF the source rate was Dessler, A.J. (Ed.), Physics of the Jovian Magnetosphere. Cambridge 3:4 × 1030 AMU=s (Table 2) while for southward IMF it University Press, New York, pp. 353–394. was 5×1030 AMU=s. These source rates are higher than has Huddleston, D.E., et al., 1998. The location of the jovian bow shock and been inferred from observations (Hill, 1979). Note that the magnetopause: Galileo initial results. Adv. Space Res. 21 (11), 1463. strongest current densities (ÿeld-aligned and perpendicu- Jones, D.E., Thomas, B.T., Melville II, J.G., 1981. Equatorial disc and dawn-dusk currents in the frontside magnetosphere of Jupiter: pioneer lar) occurred with the smaller source rate but the di/erence 10 and 11. J. Geophys. Res. 86, 1601. between the source rates is small. The source rates for the Joy, S.P et al., 2002. Probabilistic models of the jovian magnetopause cases without an IMF (except the 0:045 nPa case) are closer and bow shock locations. J. Geophys. Res., 107 (A10), to the inferred rate. Again the smallest currents occur for doi:10.1029/2001JA09146. the highest source rates. Kivelson, M.G., et al., 1997. Galileo at Jupiter: changing states of the magnetosphere and ÿrst looks at Io and Ganymede. Adv. Space Res. 20, 129. Kivelson, M.G., Khurana, K.K., Walker, R.J., 2002. Sheared magnetic Acknowledgements ÿeld structure in Jupiter’s dusk magnetosphere. J. Geophys. Res., 107 (A7), doi:10.1029/2001JA000251. One of us (RJW) thank Margaret G. Kivelson and Kr- Khurana, K.K., 1992. A generalized hinged-magnetodisc model of Jupiter’s nightside current sheet. J. Geophys. Res. 97, 6269. ishan K. Khurana for helpful discussions. We also thank Khurana, K.K., 2001. In2uence of solar wind on Jupiter’s magnetosphere Todd King for help with the simulation diagnostics and Erin deduced from currents in the equatorial plane. J. Geophys. Res. 106 Means for help in processing the simulation results. The (A11), 25,999. work at UCLA was supported by Jet Propulsion Labora- Krupp, N., et al., 2001. Local time asymmetry of energetic ion anisotropies tory contract JPL 958694 and NASA grant NAG 5-10282. in the jovian magnetosphere. Planet. Space Sci. 49, 283. Ness, N.F., Acu˜na, M.H., Lepping, R.P., Burlaga, L.F., Behannon, K.W., The work at Nagoya University was supported by grants in Neubauer, F.M., 1979. Magnetic ÿeld studies at Jupiter by Voyager aid from the Ministry of Education, Science and Culture. 1: preliminary results. Science 204, 982. R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295–307 307

Ogino, T., Walker, R.J., Ashour-Abdalla, M., 1992. A global Smith, E.J., et al., 1974. The planetary magnetic ÿeld and magnetosphere magnetohydrodynamic simulation of the magnetosphere when the of Jupiter: Pioneer 10. J. Geophys. Res. 79, 3501. interplanetary magnetic ÿeld is northward. IEEE Trans. Plasma Sci. Smith, E.J., Fillius, R.W., Wolfe, J.H., 1978. Compression of Jupiter’s 20, 6817. magnetosphere by the solar wind. J. Geophys. Res. 83, 4733. Ogino, T., Walker, R.J., Kivelson, M.G., 1998. A global Southwood, D.J., Kivelson, M.G., 2001. A new perspective concerning the magnetohydrodynamic simulation of the jovian magnetosphere. in2uence of the solar wind on the jovian magnetosphere. J. Geophys. J. Geophys. Res. 103 (A1), 225. Res. 106 (A4), 6123. Phillips, J.L., et al., 1993. Ulysses plasma observations in the jovian Vasavada, A.R., et al., 1999. Jupiter’s visible aurora and Io footprint. magnetosphere. J. Geophys. Res. 98 (21), 189. J. Geophys. Res. 104 (27), 133. PrangÃe, R., et al., 1998. Detailed study of FUV jovian auroral features Vasyliunas, V.M., 1983. Plasma distribution and 2ow. In: Dessler, A.J. with the post-COSTAR HST faint object camera. J. Geophys. Res. (Ed.), Physics of the Jovian Magnetosphere. Cambridge University 103 (20), 195. Press, New York, pp. 395–453. Satoh, T., Connerney, J.E.P., Baron, R.L., 1996. Emission source model Walker, R.J., Ogino, T., Kivelson, M.G., 2001. Magnetohydrodynamic + of Jupiter’s H3 aurora: a generalized inverse analysis of images. Icarus simulations of the e/ects of the solar wind on the jovian magnetosphere. 122, 1. Planet. Space Sci. 49, 237. Slavin, J.A., Smith, E.J., Spreiter, J.R., Stahara, S.S., 1985. Solar wind Watanabe, K., Sato, T., 1990. Global simulation of the solar 2ow about the outer planets: gas dynamic modeling of the Jupiter and wind-magnetosphere interaction: the importance of its numerical Saturn bow shocks. J. Geophys. Res. 90 (A7), 6275. validity. J. Geophys. Res. 95, 75.