A simulation study of currents in the Jovian magnetosphere

A simulation study of currents in the Jovian magnetosphere

Available online at www.sciencedirect.com Planetary and Space Science 51 (2003) 295 – 307 www.elsevier.com/locate/pss A simulation study of currents...

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Available online at www.sciencedirect.com

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 a Institute

of Geophysics and Planetary Physics, and Department of Earth and Space Science, University of California, Los Angeles, Los Angeles, CA 90095-1567, USA b Solar 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 :eld-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 :eld-aligned currents are associated with aurora at the Earth they may be associated with aurora at Jupiter. The upward :eld-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 :eld-aligned currents (both were slightly stronger for higher pressures). The interplanetary magnetic :eld 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 A thin equatorial azimuthal current sheet characterizes Jupiter’s magnetosphere. This current sheet is found at all local times and on the day side extends from near Io’s orbit to within a few tens of RJ of the magnetopause (Smith et al., 1974; Ness et al., 1979; Balogh et al., 1992; Kivelson et al., 1997). On the night side the current sheet merges with the magnetotail current system. The current sheet is located near the magnetic equatorial plane and undergoes a quasi-sinusoidal north–south motion as Jupiter rotates because Jupiter’s magnetic dipole is tilted 10◦ from the spin axis (see Khurana (1992) and references therein). The region containing the current sheet is dominated by rotating 2ows. That part of the magnetosphere that contains the current sheet, plasma sheet and rotating 2ow and extends ∗

Corresponding author. E-mail address: [email protected] (R.J. Walker).

from about 20RJ to 60RJ or 70RJ is frequently called the middle jovian magnetosphere. Plasma originating at the moon Io that is energized by planetary rotation is thought to carry the equatorial currents (Hill et al., 1983; Vasyliunas, 1983). The current sheet has been estimated to be 2–8RJ (Jupiter radii) in thickness. Jupiter’s intrinsic magnetic :eld decreases as r −3 while the current sheet :eld decreases as r −1 or r −2 so the magnetic :eld from the current sheet is dominant in the middle magnetosphere. (See Bunce and Cowley, (2001a) for a recent and detailed review of the properties of the current sheet.) Connerney et al. (1981) suggested that the current sheet is thicker on the day side than the night side while Jones et al. (1981) and more recently Bunce and Cowley (2001a) and Khurana (2001) have argued that the current sheet :eld is weaker on the day side than the night side. The observed day night asymmetry in the azimuthal current implies a radial equatorial current with :eld-aligned 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

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current sheet in order to maintain current continuity. Goertz (1978) noted that on the day side rotating 2ux tubes are constrained by the solar wind dynamic pressure but on the night side they are free to expand. As the 2ux tubes move from the day side to the night side they are stretched resulting in stronger azimuthal currents. Radial currents that 2ow away from Jupiter on the dawn side of the magnetosphere and toward Jupiter on the dusk side will maintain current continuity. An outward radial current bends the magnetic :eld lines in the direction of corotation “lag” (see Fig. 9 of Khurana (2001)). On the dawn side corotation lag bends the magnetic :eld in the same direction as the solar wind interaction while on the dusk side the bending is opposite to that expected from the solar wind. Corotation lag has been observed near Jupiter at all local times, however, nearer the dusk side magnetopause the observed bending is in the opposite direction (Dougherty et al., 1993; Khurana, 2001; Kivelson et al., 2002). In the jovian ionosphere collisions between ions and neutral particles in the Pedersen-conducting layer create a frictional torque on the magnetic 2ux tubes that accelerates them toward corotation. Hill (1979) showed that this ionospheric torque was suLcient to maintain near-corotation in the middle magnetosphere. The ionospheric torque is transmitted to the magnetosphere via :eld-aligned currents. These currents close in the ionosphere and the equatorial current sheet. The resulting ˜J × ˜B force in the ionosphere is directed to balance the viscous torque and slow the rotation of Jupiter’s ionosphere (or atmosphere) while in the equatorial magnetosphere the ˜J × ˜B force is in the direction of corotation and accelerates the plasma (Hill, 1979; 2001; Vasyliunas, 1983). The :eld-aligned currents are away from Jupiter at lower latitudes and toward Jupiter at higher latitudes closing through equatorward Pedersen currents in the ionosphere and outward 2owing radial currents in the equatorial magnetosphere. The outward radial current frequently is called the corotation enforcement current. Recently, Bunce and Cowley (2001b) and Khurana (2001) have used near-equatorial magnetic :eld observations to infer the :eld-aligned currents. Bunce and Cowley (2001b) used Pioneer and Voyager observations in the middle magnetosphere (20RJ –50RJ ) and found currents away from Jupiter along the early morning trajectories of Voyager 1 and 2 outbound and currents toward Jupiter along the Pioneer 10 outbound trajectory at ∼ 0500 LT and the Pioneer 11 inbound trajectory at ∼ 0900 LT. The inferred current densities were between 10−13 and 10−12 Am−2 nT−1 . Khurana (2001) used Galileo orbiter observations to map the distribution of :eld-aligned currents throughout much of the middle magnetosphere. He found :eld-aligned currents 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 30RJ . The radial extent of the currents is poorly known on the dayside because of poor Galileo data coverage. That the largest outward currents were on the dusk side and

the largest Jupiterward currents were on the dawn side led Khurana (2001) to conclude that solar wind e/ects were important well inside the jovian magnetosphere. Jovian aurorae have been observed in infrared, ultraviolet and visible light (e.g. Clarke et al., 1996; 1998; Satoh et al., 1996, PrangMe et al., 1998; Vasavada et al., 1999). By analogy with the Earth’s aurorae, we would expect discrete jovian aurorae to be associated with :eld-aligned currents directed away from Jupiter since precipitating electrons cause discrete aurorae. Southwood and Kivelson (2001) and Cowley and Bunce (2001) have presented theories on the relationship between jovian currents and the aurorae. They argue that the strength of the ionospheric :eld-aligned currents and the luminosity of the aurora depend on the structure of the magnetic :eld in the middle magnetosphere and on the angular velocity pro:le of the equatorial plasma. In particular, they argue that the auroral oval maps to the part of the middle magnetosphere where the velocity of the rotating 2ows falls below the corotation velocity. Both papers conclude that aurorae will respond mainly to changes in solar wind dynamic pressure in contrast to the Earth where changes in the interplanetary magnetic :eld (IMF) and reconnection are dominant. For instance they argue that if the magnetosphere is compressed by the solar wind, the 2ow in the magnetosphere will increase toward rigid corotation thereby decreasing the lag in the :eld and the corotation enforcement current. This will lead to dimming of the aurorae. Conversely a decrease in solar wind dynamic pressure will lead to increased :eld-aligned currents and more intense aurorae. Both Southwood and Kivelson (2001) and Cowley and Bunce (2001) argue that these changes in the rotation and currents should hold during dynamic changes in the pressure while Cowley and Bunce (2001) argue that they should hold for the steady-state magnetosphere as well. In this paper, we use our three-dimensional global magnetohydrodynamic simulation of the interaction of Jupiter’s magnetosphere with the solar wind (Ogino et al., 1998; Walker et al., 2001) to model the jovian current structure and its dependence on solar wind parameters. We mainly concentrate on the formation and structure of the equatorial current sheet and the :eld-aligned currents that connect it to the jovian ionosphere. In Section 2 we brie2y discuss the global MHD code. In Section 3 we examine the structure of the jovian currents in detail by considering the simple case in which an unmagnetized solar wind interacts with the magnetosphere. Then in Section 4 we examine how the currents change when we change the solar wind dynamic pressure and interplanetary magnetic :eld (IMF). Finally, we summarize our results and compare them to observations and other theoretical models of the jovian current system. 2. Simulation model We have presented our Jupiter simulation model in detail previously (Ogino et al., 1998), so we will just review its

R.J. Walker, T. Ogino / Planetary and Space Science 51 (2003) 295 – 307

main features here. Initially, we :lled the simulation domain with plasma and :elds from a simple model of a rotating jovian magnetosphere. At time t = 0 we placed an image dipole upstream of Jupiter to help form a magnetospheric cavity. The image dipole helped assure that there were no parallel 2ows in the initial solar wind. It hastened the formation of a magnetopause and helped assure that the magnetic :eld (˜B) remains divergenceless ( · ˜B = 0) throughout the simulation box (Watanabe and Sato, 1990). 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 resolution in the middle magnetosphere and computational time. For very long runs (hundreds of hours in real time) we found only minor changes when we increased the grid spacing by a factor of 2 to Ox=3RJ . In general, we found that the bow shock and magnetopause boundaries were resolved much better with Ox = 2RJ or Ox = 1:5RJ . We launched the solar wind from the upstream boundary of the simulation box, and solved the resistive magnetohydrodynamic (MHD) equations as an initial value problem by using the numerical approach described in Ogino et al. (1992). We use an explicit resistivity that enters the equations through Faraday’s law (@˜[email protected] = ∇ × (˜v × ˜B) + ∇2 ˜B where ˜v is the velocity and is the resistivity). The normalized resistivity is set equal to 0.002. This corresponds to a magnetic Reynolds number of about 500. It is uniform in value throughout the simulation box and is kept constant throughout each simulation run. During the simulations the magnetic :eld (˜B), the velocity (˜v), the mass density () and the pressure (p) were maintained at solar wind values at the upstream boundary (usually x = 225RJ ) while free boundary conditions through which waves and plasmas can freely enter or leave the system were used at the downstream (x = −450RJ ), side (y = ±225RJ ), and top (z = 225RJ ) boundaries. Symmetry boundary conditions were used at the equator (z=0) (Ogino et al., 1992) and the dipole tilt was set to zero. At the inner boundary all the simulation parameters (˜B;˜v; ; p) were :xed for r ¡ 15RJ . For r ¡ 21RJ each parameter (’) in the simulation was calculated by using ’(r; t) = f’EX (r; t) + (1 − f)’IN (r); where ’EX (r; t) is the value from the simulation and ’IN (r) is the value from the initial model. The value of f depends only on the radial position and is given by f≡

a0 h2 a0 h2 + 1

where a0 = 30 and h≡

r2 − 1; ra2

h ≡ 0;

r ¿ ra

r ¡ ra

with ra = 15RJ . The outer boundary conditions have been used successfully in our simulations of the Earth’s magnetosphere

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Table 1 Solar wind parameters

Solar wind dynamic pressure (nPa) IMF Bz (nT)

0.045 0.0

0.09 0.0 −0:84 +0.84 −0:42 +0.42

0.18 0.0 −0:84 +0.84

0.37 0.0

0.75 0.0

(Ogino et al., 1992). The free boundary conditions work well provided the magnetopause exits the simulation box through the rear boundary. This condition is met for all of the simulation runs used in this study except for the case with a 2 solar wind dynamic pressure of vsw = 0:045 nPa. For this case the magnetopause got within 10RJ of the side boundary tailward of about x ≈ −280RJ . However, since we are primarily concerned with currents in the middle magne2 tosphere and since the results from the vsw = 0:045 nPa simulation are consistent with those from the other runs we have included them in the paper. Note the bow shock passes through the side and top boundaries in all of the simulations. For all but one of the simulations in this study (the southward IMF case discussed in Section 4) the shock crosses the simulation boundary tailward of the dawn-dusk meridian. We modeled the magnetosphere for a number of combinations of solar wind dynamic pressure and IMF magnitude and direction. The values of the solar wind dynamic pressure and IMF for which we have simulated Jupiter’s magnetosphere are listed in Table 1. The :ve dynamic pressures used are listed in the :rst row. These values of the dynamic pressure span a range somewhat smaller than that 2 observed at Jupiter (0:01 nPa 6 vsw 6 1:0 nPa) (Smith et al., 1978; Bridge et al., 1979a, b; Phillips et al., 1993). The median solar wind dynamic pressure at Jupiter is 0:1 nPa (Slavin et al., 1985; Huddleston et al., 1998; Joy et al., 2002). All :ve dynamic pressures were run without an IMF (second row). For two dynamic pressures northward and southward interplanetary magnetic :elds were included. For 0:09 nPa two values of the IMF were used (±0:84 nT and ±0:42 nT). The mean IMF at Jupiter’s orbit is 0:8 nT (Joy et al., 2002). In this study we will present results for solar wind pressures between 0:045 nPa and 0:37 nPa. For 0:09 nPa we will also show results for IMF values of ±0:84 nT. For all of the simulations vsw = 300 km=s and the temperature of the solar wind was 2 × 105 K. The solar wind was held constant for up to 600 h in these runs in order to obtain quasi-steady magnetospheric con:gurations. It has long been realized that Io and its plasma torus can supply most of the plasma needed to populate the jovian system. Hill et al. (1983) estimated that transport from the Io source was 3 × 1028 ions/s of mass ∼ 20 AMU. In an explicit MHD code it is diLcult to include Io and the Io torus in the calculation. The numerical stability criterion is

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Table 2 Source rates from the inner boundary (AMU/s)

Bz

Dynamic pressure (nPa)

0

0.045 7:0 × 1030

−0:84

+0.84

0.09 8:6 × 1029 5:0 × 1030 3:4 × 1030

0.18 7:6 × 1029

0.37 6:4 × 1029

vgmax Ot=Ox ¡ 1 where vgmax is the maximum group velocity in the calculation domain, Ox is the grid spacing and Ot is the time step. Since the AlfvMen velocity (vA ) becomes very large near Jupiter (approaching the speed of light at 1RJ ) we placed the inner boundary of the simulation at 15RJ . This enabled us to model time-dependent phenomena without using an extremely small time step. Unfortunately, this means that the important Io interaction must be handled by the inner boundary condition. As we discuss further, we carried out a series of tests to evaluate how well our boundary condition has modeled the Io source. As noted above the simulation parameters were :xed at the inner boundary. In particular, the velocity was purely rotational and the pressure and density were set to values determined from the Voyager 1 2yby of Jupiter (Belcher, 1983). The magnetic :eld was :xed to values from Jupiter’s internal dipole. As a test of the behavior of the inner boundary condition we examined the results from a simulation during which the code was run for 600 h with a southward IMF and then for 150 h with a northward IMF. We calculated the mass 2ux through a surface at 22:5RJ . For the southward IMF case the inner boundary provided 5:0 × 1030 AMU=s to the jovian system. For the northward IMF case the out2ow was 3:4 × 1030 AMU=s. These values are somewhat higher than the estimate by Hill et al. (1983). Other simulation runs gave values as low as 2 × 1029 AMU=s (Ogino et al., 1998). Table 2 contains the source rate values for each of the runs used in this study. Although the exact regions of out2ow and in2ow vary from run to run in general there is out2ow on the dawn side of the magnetosphere and in2ow on the dusk side. These results are qualitatively consistent with recent determinations of the 2ow direction based on energetic ion 2ux anisotropies (Krupp et al., 2001). As noted above the out2ow is not uniform and there are regions of both out2ow and in2ow. As a second test we calculated the magnetic 2ux through the closed surface at 22:5RJ and examined its change as a function of time. In the case discussed above the 2ux increased between t = 600 and 750 h by 2:8 × 109 W or about 0.5%. To determine whether this value is signi:cant it is necessary to understand the uncertainty in the numerical calculation. As a check of the accuracy of our integration we increased the grid spacing by a factor of two and repeated the calculation. This changed the results by 3:6 × 109 W or approximately 0.7%. Thus to the uncertainty in the calculation there was no change in the magnetic 2ux during the test interval. Although not

ideal the inner boundary condition provides a reasonable approximation to the Io source for studies of the middle and outer jovian magnetosphere. To further investigate how magnetic 2ux is conserved in a system with net out2ow  ˜ · dl along a path enclosing Jupiter. we calculated the E In general 2ux is removed in the noon, dawn and midnight quadrants and returned in the dusk quadrant. 3. Currents in the jovian magnetosphere In the top panel of Fig. 1 we have plotted the thermal pressure and 2ow vectors in a plane 0:75RJ above the equa2 tor for a solar wind pressure vsw = 0:37 nPa. The bottom panel contains the speed. The IMF was set to zero. The simulation was run for 300 h by which time a quasi-steady magnetospheric con:guration had formed. The solid black circle shows the position of the inner simulation boundary (15RJ ). The magnetosphere was not simulated in this region. A circle has been drawn at r ≈ 60RJ to help the reader judge distances in the middle magnetosphere. Rotation and the equatorial plasma sheet dominate near Jupiter. Although the plasma density and pressure are spherically symmetrical inside the 15RJ boundary the equatorial plasma sheet forms self-consistently within a few grid spaces outside the boundary (see Plate 3 of Ogino et al. (1998) for an example). The plasma sheet pressure varies as a function of local time with the largest values in a band extending from approximately 1700 LT past midnight. Actually there are two peaks (not shown) in the pressure one centered at about 1800 LT and the other centered at about 2300 LT. The 2ow pattern is complex. In the middle magnetosphere rotational 2ows dominate but the velocity varies with local time. The largest rotating 2ows are found pre-dawn while the smallest 2ows are found pre-dusk. The 2ow is small nearer both the dawn and dusk magnetopause. There is out2ow at all local times in the magnetotail but the tailward velocity is greatest in a channel extending dawnward from midnight. The out2ow in the tail is an inertial e/ect. On the day side the outward 2owing plasma is constrained by the solar wind. However, as the plasma rotates past dusk into the night side it is no longer constrained by the solar wind. Tailward 2ow near the dusk magnetopause stretches the :eld lines. Just tailward of the dusk meridian the tension on these stretched :eld lines causes some of them to snap toward Jupiter. Near midnight the stretched-closed :eld lines reconnect causing the tailward 2ow (Ogino et al., 1998). Flow streamlines provide another way to visualize the convection pattern in the equatorial jovian magnetosphere (Fig. 2). In the top panel the 2ow streamlines have been color coded with the thermal pressure while in the bottom panel the color-coding gives the density. As the plasma 2ows around dusk from the day side to the night side it 2ows :rst away from Jupiter then toward Jupiter before reaching the tail. Both the density and pressure reach a maximum at about 2100 LT. The pressure and density decrease as the plasma

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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 :eld. 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 quasi-steady con:guration. The black dots indicate the region Jupiterward 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 the away currents in the tail and the dawn magnetosphere. However, there are four regions with radial currents toward Jupiter. Three of these are most likely real since they cover large regions of the magnetosphere and extend well away

299

Fig. 2. Flow streamlines for the simulation in Fig. 1. The streamlines have been color coded with the plasma pressure (top) and density (bottom).

Fig. 3. Radial and azimuthal currents in the Z = 0:75RJ plane for the simulation in Fig. 1. In the top panel warm colors represent currents that are away from Jupiter. In the bottom panel warm colors represent 2ow in the corotation sense. The black circles are at r = 60RJ .

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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 while the arrows give the perpendicular currents. Warm colors represent currents along the magnetic :eld while cold colors represent currents 2owing opposite to the direction of the magnetic :eld. The circle is at r ≈ 60RJ .

from the inner boundary. The one near dawn is very small and is con:ned 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 ionosphere) except in the late morning and early afternoon in local time. These away :eld-aligned currents are found over a region extending 10’s of RJ from Jupiter. Right at the inner boundary there are very small regions with both away and toward currents. These are most likely noise since they are con:ned to the immediate neighborhood of the boundary in the region r ¡ 21RJ . The expected pattern with away currents in the near Jupiter part of the middle magnetosphere and toward currents further out is not clearly evident in Fig. 4. In Fig. 5 we have plotted the parallel currents in the dawn-dusk meridian (x = 0; top) and noon-midnight meridian planes (y = 0; bottom). In the dawn-dusk plane the parallel current pattern is as expected. Near Jupiter the currents are away from the ionosphere and further out the return currents go toward Jupiter on both sides. The parallel currents are distributed over tens of jovian radii. At high latitudes on the dawn side some of the currents toward Jupiter merge with currents on the magnetopause. Along the noon-midnight meridian the pattern is a bit more complex especially at noon. Near the inner boundary there are regions with both upward and downward currents while those further out are

Fig. 5. Parallel currents in the X = 0 (top) and Y = 0 planes for the simulation in Fig. 1.

Fig. 6. Parallel currents calculated at a radial distance of 21RJ (just outside the inner boundary) and mapped along dipolar :eld lines into Jupiter’s ionosphere. Warm colors indicate currents away from Jupiter while cold colors indicate currents toward Jupiter. This calculation was carried out for the same simulation as Fig. 1. The green traces give the ionospheric end points of :eld lines calculated starting at 20RJ , 40RJ , and 60RJ in the equatorial magnetosphere. The 180 points in each trace were calculated from points that were uniformly spaced in the equatorial plane.

primarily toward Jupiter. As noted above the current structures con:ned to grid points immediately adjacent to the inner boundary are suspect. Some of the high latitude currents 2owing toward the ionosphere connect to the magnetopause. In the tail the main parallel current system is away from Jupiter nearer Jupiter and toward Jupiter further out. In Fig. 6 the parallel currents just outside the inner simulation boundary have been mapped along magnetic :eld lines to the ionosphere. The values were calculated at 21RJ at the point where the smoothing discussed in Section 2 is turned o/. We have superimposed three green curves on the current contours. They show the ionospheric intercepts of magnetic :eld lines calculated starting at the equator at 20RJ , 40RJ and 60RJ . At lower latitudes the parallel currents 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 eld and the solar wind dynamic pressure We have examined results from other simulations in Table 1 to determine the dependence of the jovian current systems on the interplanetary magnetic :eld and the solar wind dynamic pressure. The parallel and perpendicular current densities at Z = 0:75RJ are plotted for two IMF orientations in Fig. 7. For these simulations the code was run with a southward IMF for 600 h and then for 150 h with a northward IMF. For the southward IMF simulation the magnetosphere had reached a very steady con:guration while for the northward IMF case the con:guration was slowly changing (Walker et al., 2001). For southward IMF reconnection tailward of the polar cusp removes tail lobe magnetic 2ux (Walker et al., 2001) thereby reducing the tail currents. The dominant currents are those associated with the current sheet in the middle magnetosphere. The parallel currents are basically similar to those for the BIMF = 0 case with currents away from Jupiter dominant from late afternoon to the late morning but lots of structure. When the IMF is northward reconnection occurs at the subsolar magnetopause and in the near jovian tail (Walker et al., 2001). The thin tail current sheet and reconnection give much stronger currents across the tail in this simulation. The largest di/erences in the perpendicular currents between the three cases considered so far are in the strength of the tail current (cf. Figs. 4 and 7). The bright band of away :eld-aligned currents in the jovian tail is associated with the tail reconnection. In the middle magnetosphere the parallel current pattern is similar to that for the southward IMF simulation although there are some di/erences. For instance the away and toward Jupiter :eld-aligned current pair

Fig. 7. Parallel and perpendicular currents in the plane Z = 0:75RJ for southward (top) and northward (bottom) interplanetary magnetic :eld. 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 quasi-steady magnetospheric con:guration had evolved in the :rst case but the magnetosphere was still slowly evolving even after 150 h in the second case.

found just pre-dawn for the southward IMF case has no obvious counterpart in the BZ ¿ 0 calculation. Near Jupiter the largest di/erence is that the region of parallel currents 2owing toward Jupiter is larger for the northward IMF case extending from ∼ 0900 to ∼ 1800 LT. The radial currents from these two simulations are plotted in Fig. 8. Although there are detailed di/erences in the middle magnetosphere there are also similarities. The largest di/erences are near the magnetopause, in the magnetosheath and in the more distant parts of the tail. The strong radial currents in the tail for the northward IMF case are related to the tail reconnection. The magnetosheath currents have opposite signs. In both simulations radial currents are away from Jupiter in the morning and toward Jupiter in the afternoon. The signatures in the evening are complex with regions of both away and toward currents. Not too surprisingly the currents mapped from the inner boundary of the simulation to Jupiter also are very similar (Fig. 9). The magnitude of the current density is larger and the currents map to slightly larger radial distances for the northward IMF case. The purple curve in Fig. 9 gives the position of the boundary between open and closed :eld lines (the polar cap boundary). The polar cap is only about 10◦ in extent. For the northward IMF case a second band of away currents formed at higher latitudes between 0400 and 1300 LT near the polar cap boundary. This second band of away currents crosses

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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 :eld lines in the polar cusp region. All of the other :eld-aligned currents are on closed :eld 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 con:guration presented in Section 3 we reduced the dynamic pressure by a factor of two and ran the simulation until a quasi-steady magnetosphere resulted. We repeated this procedure two more times each time using 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 very similar. Both the perpendicular currents and the parallel currents are strongest for the high-pressure compressed magnetosphere. Similarly the radial current pattern is virtually the same for all the decreasing pressure runs (Fig. 11). The largest radial currents occur for the highest solar wind pressure. Finally, the :eld-aligned currents mapped to the ionosphere also have very similar patterns for all pressures (Fig. 12). In general the amplitude of the current density is largest for the high-pressure case for most longitudes. However, between noon and ∼ 1600 LT the upward currents are slightly stronger for the lowest pressure case.

5. Discussion The jovian magnetospheric currents from our simulation have many of the properties expected for a rotating planet

Fig. 9. Parallel currents projected into the ionosphere for the southward (top) and northward IMF cases. The format is the same as in Fig. 6 except that the purple curve outlines the polar cap for the northward IMF case. Polar cap :eld lines were de:ned as open :eld lines with one end closing in Jupiter and one end in the IMF.

and a few surprises. In all of our simulations the azimuthal ring current of the equatorial current sheet dominates the region of corotating plasma or the middle magnetosphere. However, 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% (e.g. Fig. 5, bottom). In addition to the ring current the jovian middle magnetosphere contains strong radial currents. Outward radial currents dominate most of the middle magnetosphere, however, there are regions where the radial currents are toward Jupiter. 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 plasma density and pressure decrease (e.g. Figs. 1 and 2). In this region the ring current becomes smaller and the radial currents 2ow toward Jupiter at all radial distances (Fig. 3). Closer to dusk the 2ow turns toward Jupiter and accelerates

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Fig. 10. Parallel and perpendicular currents in the Z = 0:75RJ plane for three solar wind dynamic pressures. The format of each panel is the 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 decreased in 3 steps to 0:045 nPa. In each case the simulation was run until a quasi-steady magnetosphere evolved.

and the pressure and density increase (e.g. Figs. 1 and 2). The radial current again becomes positive. When the 2ow is decelerated, the pressure and density become large (e.g. Figs. 1 and 2) and the radial current reverses. Goertz (1978) pointed out that out2owing rotating plasma on the day side is constrained at the magnetopause until it rotates past noon. In the afternoon and evening the :eld lines can be stretched into a more tail like con:guration. This leads to an asymmetric azimuthal current system. Current closure requires either outward radial currents at dawn and inward radial currents at dusk as discussed by Bunce and Cowley (2001a) or :eld-aligned currents toward Jupiter at dawn and away at dusk as discussed by Khurana (2001) or both. In the morning and evening both :eld-aligned currents and radial currents seem to be involved in providing current closure (cf. Figs. 3 and 4). However, in the early afternoon the inward radial currents are the dominant closure currents (e.g. Fig. 3 in the afternoon). The cross magnetosphere magnetotail currents in the equatorial plane (dusk to dawn at Jupiter) have an inward radial component on the dusk side and an outward component on the dawn side. This causes the inward currents in the pre-midnight tail and the outward currents in the post-midnight tail (e.g. Fig. 3, top panel).

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Fig. 11. Radial currents for the three simulations in Fig. 10. The format is the same as that in the top panel of Fig. 3.

The :eld-aligned current pattern within the jovian magnetosphere also is complex. There are regions with currents both toward and away from Jupiter’s ionosphere. It is not clear from looking at the distribution of parallel currents in the near-equatorial magnetosphere that these are the connecting currents needed for the ionosphere to enforce corotation. However, when we examined the currents in the XZ and YZ planes (Fig. 5) and mapped the :eld-aligned currents from a sphere at 21RJ to the ionosphere (Fig. 6) we found a pattern more nearly like that expected with a ring of current away from Jupiter at lower latitudes and a region of currents toward Jupiter at higher latitudes. The :eld-aligned currents map to di/erent distances in the equatorial magnetosphere at di/erent local times. For instance the upward :eld-aligned currents map to larger distances on the night side (e.g. 40–60RJ at 0300 LT) than on the day side (∼ 20–30RJ ). Upward :eld-aligned currents also are much weaker on the day side. The strongest currents map to the region where corotation breaks down (Hill, 2001). In Fig. 13 we have plotted the ratio of azimuthal 2ow velocities to the corotation velocity for the 2ows in Fig. 1. The 2ow decreases below corotation rapidly at dusk where the largest parallel currents are found (Figs. 4 and 6). The 2ow falls o/ less rapidly in the morning where the currents map to a larger region of the magnetosphere. Finally, there are weaker currents (frequently toward Jupiter in Figs. 6, 9 and 12) that originate in the region immediately adjacent to the inner boundary. They most likely are not real.

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Fig. 12. Parallel currents mapped to the ionosphere for the three pressures in Fig. 10. The calculation and the format are the same as in Fig. 6.

Fig. 13. Contours of the ratio of the azimuthal 2ow velocity to the corotation speed for the simulation in Fig. 1.

Recently, Bunce and Cowley (2001a, b) and Khurana (2001) have inferred the current sheet currents using spacecraft observations. The observed currents like the simulated currents are weaker on the day side than on the night side.

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) reports 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 :eld observations. There are a couple of possible reasons for this. First inferred current densities may have signi:cant 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 :eld 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 :eld-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 although the currents in the simulation have much more 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 driven magnetospheric convection was important deep in the magnetosphere. We also found solar wind e/ects in the simulated currents with the strongest e/ects related to the direction of the interplanetary magnetic :eld.

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Fig. 14. Flow speed contours for the southward IMF (top) and northward IMF (bottom) simulations in Fig. 7. The format is the same as in the bottom panel of Fig. 1.

The :eld-aligned currents inferred from Galileo observations correspond to currents of 3–6 × 10−8 A=m2 when mapped to Jupiter’s ionosphere (Khurana 2001; Hill, 2001). Based on Pioneer and Voyager observations Bunce and Cowley (2001b) inferred currents as strong as 10−6 A=m2 . The simulated parallel currents (typically 6 10−7 A=m2 ) are consistent with the Galileo values but never reach the much larger values inferred from the Pioneer and Voyager data. Magnetic reconnection mainly drives convection in the Earth’s magnetosphere. The numerical experiment in Figs. 7–9 provides an extreme example of the e/ects of reconnection at Jupiter. Recall that the simulation was run with a southward IMF for 600 h and then the IMF was turned northward for 150 h. Walker et al. (2001) have discussed the changes in convection during this simulation in detail. In the southward IMF case high latitude polar cusp reconnection removed tail lobe 2ux. The middle magnetosphere was dominated by rotating plasma. When the IMF was turned northward the magnetopause reconnection site moved to the subsolar magnetopause and this was followed by tail reconnection (see Fig. 2 of Walker et al., 2001). In Fig. 14 we have plotted the 2ow speed in the equatorial plane from these two simulations. Following the northward turning of the IMF the 2ow speed in the middle magnetosphere on the dawnside increased by at least a factor of 2 while the 2ow speed on the dusk side decreased. The magnitude of the radial and :eld-aligned currents also increased (Figs. 8 and 9) but not as dramatically. In general our simu-

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lation results support the idea by Khurana (2001) that solar wind driven magnetospheric convection can in2uence the currents in the middle magnetosphere. However, 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 signi:cant 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 magnetosphere. They invoke conservation of angular momentum to argue that when the dynamic pressure increases the plasma in the middle magnetosphere will rotate more rapidly. This in turn will require weaker corotation enforcement currents and weaker :eld-aligned currents. Conversely when the dynamic pressure decreases they predict that the 2ow velocity will decrease and the enforcement currents and :eld-aligned currents will increase. We are unable to investigate the size of any temporal changes associated with the pressure changes since we did not save the simulation results with suLcient time resolution. However, we can investigate how the steady-state middle magnetosphere changes for various solar wind and IMF parameters. In Fig. 15 we have plotted the 2ow speed for three solar wind pressures. The corresponding :eld-aligned currents and radial currents are given in Figs. 10–12. Recall that for this experiment we decreased the pressure from 0:37 nPa and each case was run until a quasi-steady magnetosphere resulted. There are virtually no changes in the 2ow speed in the inner parts of the middle magnetosphere (¡ 10%) as the pressure changes. The most dramatic changes occurred nearer the dayside magnetopause beyond the region where the ionospheric :eld-aligned currents map. In Figs. 10–12 both the equatorial radial currents and the :eld-aligned currents are slightly larger for the high-pressure simulations. In the simulations the pressure changes do not cause very dynamic changes in the steady-state middle magnetosphere. In the steady state we :nd no evidence that lower pressures correspond to larger :eld-aligned currents as suggested by Cowley and Bunce (2001). We have begun a study of the e/ects of dynamic changes in the solar wind by simulating the response of the magnetosphere to pressure pulses and will report on these results in the future.

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

Fig. 15. Flow speed contours for the simulations in Fig. 10. The format is the same as the bottom panel of Fig. 1.

In this set of simulations the plasma source rates at the inner boundary were determined by the magnetospheric con:guration. For northward IMF the source rate was 3:4 × 1030 AMU=s (Table 2) while for southward IMF it was 5×1030 AMU=s. These source rates are higher than has been inferred from observations (Hill, 1979). Note that the strongest current densities (:eld-aligned and perpendicular) occurred with the smaller source rate but the di/erence between the source rates is small. The source rates for the cases without an IMF (except the 0:045 nPa case) are closer to the inferred rate. Again the smallest currents occur for the highest source rates. Acknowledgements One of us (RJW) thank Margaret G. Kivelson and Krishan K. Khurana for helpful discussions. We also thank Todd King for help with the simulation diagnostics and Erin Means for help in processing the simulation results. The work at UCLA was supported by Jet Propulsion Laboratory contract JPL 958694 and NASA grant NAG 5-10282. The work at Nagoya University was supported by grants in aid from the Ministry of Education, Science and Culture.

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