JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 103, NO. A1, PAGES 225-235, JANUARY 1, 1998

A global magnetohydrodynamic simulation of the Jovian magnetosphere

Tatsuki Ogino Solar Terrestrial Environment Laboratory, Nagoya University, Toyokawa, Aichi, Japan

Raymond J. Walker, Margaret G. Kivelson • Institute of Geophysics and Planetary Physics, University of California, Los Angeles

Abstract. We have developed a three-dimensional global magnetohydrodynamic simulation of the interaction between the solar wind and a rapidly rotating magnetosphere and applied it to Jupiter. For fixed solar wind dynamic pressure the rotating model Jovian magnetosphere extends farther toward the Sun and has greater extent in the east-west direction than a model without rotation but is little different in the north south direction. There is a pronounced dawn-dusk asymmetry with the dawn magnetopause displaced farther from Jupiter. The middle Jovian magnetosphere contains a thin plasma sheet dominated by rotating plasmas. On the dayside this plasma sheet thickens near the magnetopause. Near the dawnside magnetopause where rotating Jovian convection is opposed to the solar wind induced flow, a pressure ridge forms where the magnetospheric flow slows and forms a stagnation region. In the magnetotail the rotating flow is diverted tailward. For x < -100Rj x-type and o-type neutral lines form. When the solar wind pressure was decreased, the boundaries moved away from Jupiter and the dayside field lines became stretched into a more tail-like configuration. A flow vortex formed in the evening middle magnetosphere.

1. Introduction

Five spacecraft have flown through Jupiter's magnetosphere and in December 1995 a sixth, Galileo, was placed into Jovian orbit. On their inbound legs all five flybys sampled the midmorning (-0900 LT) magnetosphere at low latitudes. Outbound Pioneer 10 and Voyager 1 and 2 provided observations near the equatorial plane in the early morning hours (0300 to 0600 LT). Pioneer 11 exited the magnetosphere at high northern latitudes at noon while Ulysses sampled the dusk magnetosphere at high southerly latitudes. These observations have presented a picture of a vast and highly dynamic system. For example, the magnetosphere size changes drastically when the solar wind pressure changes. At -1000 LT the dayside magnetopause was encountered as far out as 100Rj (Jovian radii ---71,400 km) by Pioneer 10 and Ulysses and as far in as 45Rj later in the Pioneer 10 flyby. Within the magnetopause the system is controlled by a still not understood combination of the effects of plasma whose ultimate source is the moon Io, atmospherically driven corotation and the solar wind. (Articles in Journal of Geophysical Research, 79, 3487-3695, 1974; Journal of Geophysical Research, 86, 8123-8841, 1981; Gehrels, 1976; Dessler, 1983; Journal of Geophysical Research, 98, 21111-21252, 1993; and Planetary and Space Science, 41, 797-1108, 1993 describe results from the five flybys.)

A goal of the Galileo mission is to provide the first global view of the Jovian system. Its 22-month-long tour will provide synoptic observations over much of the magnetosphere including the first observations of the distant magnetosphere near midnight. To help place these observations into a global context, we have developed a three-dimensional magnetohydrodynamic simulation

•Also at Department of Earth and Space Science, University of California, Los Angeles.

Copyright 1998 by the American Geophysical Union.

Paper number 97A02247. 0148-0227/98/97JA-02247509.00

of a rapidly rotating magnetosphere. To our knowledge this is the first self-consistent simulation of Jupiter's magnetosphere. In section 2 we describe how the model was constructed. We

present the results from the model calculation in section 3. Finally, we compare our simulation results with the observations from the Pioneer 10/11, Voyager 1/2, and Ulysses flybys. We also make predictions for Galileo observations and indicate future improvements in the model.

2. Model

The simulation was approached in two stages. First, we developed a model for a steady state spinning magnetized plasma, and then we used that model as the initial state for a global magnetohydrodynamic simulation of the interaction of the solar wind with a rotating magnetosphere. In this section we will first describe the initial configuration and then the simulation.

The initial pressure, density, and temperature of plasmas from the ionosphere and inner magnetosphere were determined by assuming a hydrostatic equilibrium in the absence of a magnetic field and rotation:

l dp+go p dr -•-=0 where go is the coefficient of gravity, p is the pressure,/9 is the

mass density, and r is the radial distance from Jupiter in jovian radii. If we assume T = To/ and rn =mo r'k where I and k are positive, then hydrostatic solutions such as p = Po exp 0//+k and P = Po exp 0 are obtained by using p = p T/m = Po P/+•/Po where m is the effective mass per ion, T is the temperature, 0-- o((1/rt+n+•)-l) and cr-- pogo/Po(l+k+l). The density has been normalized by no = 1 so that Po = mono = mo. The functional forms for T(r) and m(r), and therefore p(r) and p(r) were chosen so the model temperature and mass density had a radial dependence like that observed in the inner magnetosphere on Voyager 1. The model parameters were adjusted to fit the

225

226 OGINO ET AL.: BRIEF REPORT

Table 1. Parameters for Internal Jovian Plasma

Parameter Value

I 0.378

k 0.493

mo 7.04 ½y 9.41

Voyager 1 observations and by assuming pressure balance between the Jovian plasma and the solar wind ram pressure (0.75 nPa) at rmp = 52.5Rj beyond which p, and p, were set to solar wind values. The parameters used for the internal jovian plasma are given in Table 1.

In Figure 1 we have plotted the solution for the density as a function of distance along with the density observed on Voyager 1 inbound [Belcher et al., 1983]. Three solutions corresponding to values of the power law in the density equation have been displayed. For the simulation we used J = 1. In the simulation domain (r > 15Rj) the initial model density is lower than the peak observed values but is consistent with the trend in the data.

Similarly the power law for the temperature models the observed radial dependence in Figure 3.13 of Belcher [1983].

The initial conditions on the velocity were determined by developing a steady state model of a rapidly rotating magnetospheric configuration. This calculation was carried out in two dimensions since in the absence of a solar wind the

configuration has azimuthal symmetry. We have found that starting with these initial steady state models reduces start up fluctuations and helps us to more rapidly attain a quasi-steady configuration for the magnetosphere when we begin the simulation.

In cylindrical coordinates (R,½,z) with v = v½0 the momentum equation becomes

c) p JzB½ =0 - pro2R + .._jcB z+ c•R

Starting from the plasma and field configuration described here, at time t = 0 we placed an image dipole upstream of Jupiter to hasten the formation of a magnetopause and help assure V. B =0 throughout the simulation box [Watanabe and Sato, 1990]. We launched an unmagnetized solar wind with a dynamic pressure v 2 0.75 nPa (V.,w 300 km/s) and a temperature of 2 P o,'14' • • x 105 K from the upstream boundary of the simulation box, and we solved the resistive magnetohydrodynamic equations as an initial value problem by using the numerical approach described by Ogino et al. [1992]. The approach used in this calculation does not guarantee that V.B = 0; therefore we monitor the divergence of B at several locations during the simulation. The error in V. B is given by E = IzSx(V.B)/BI where zS• is the grid spacing. E is typically -10 '4 and never gets larger than -10 -3. The jovian magnetosphere was modeled on a 302 x 202 x 102 point Cartesian grid with grid spacing of 1.5Rj. The simulation parameters (B, v, p, p) are maintained at solar wind values at the upstream boundary (x = 150R j) while free boundary conditions through which waves and plasmas can freely enter or leave the system are used at the downstream (x = -300Rj), side (y = +150Rj), and top (z = 150Rj) boundaries. Symmetry boundary conditions are used at the equator (z = 0) [Ogino et al., 1992]. At the inner magnetosphere boundary all of the simulation parameters (B, v, p, p) are fixed for r < 15Rj For r < 15Rj the code was advanced one time step before the values were fixed. Like the density in Figure 1 all of the parameters (B, v, p, p) were frozen at values which differ little from the initial model values.

As we discuss in section 5, by setting the parameters constant in time for r < 15Rj we maintain input from an Iogenic source. For r < 21Rj (the shaded region in Figure 1) each parameter ½ was calculated by using

qo (r,t) = f cEx (r,t) + (1-f)tpm(r)

where qoEx (r,t) is the value from the simulation and ½m (r) is the value from the initial model. The value off depends only on the radial position and is given by

- •/p ( JzBR - J RBz ) = O

3 z J RB½ + JcBR = 0 where to is the rotation frequency of Jupiter, J is the current density, and B is the magnetic field. We assume that the magnetic field can be expressed as

B R

where • is the magnetic flux. In (1), Br and B z are dipole. Since we have assumed time independence the induction equation (•/3 t = V x (v x B) = 0) •d the • component of the momentum equation are smisfied if v•/R = • •) and RB• = I(•). Since o must be a function of • for time independence, we selected velocities of the form v½ = WoR•/(• + •o•), where M is • integer, oo = 1.76 x 10 '4 is the corotation frequency, •, is the value of • at Ro and Ro = 35Rj comes from pv• = Bz 2 for the initial confi•ration. At the equator, • can be found from • = Ro /R•o. In this paper we present the results from the simulation for which the M = 2 model was used as the initial state for our MHD

simulations. This gives

M = 2: v½ = Røø = o o R>> R o (2) 1+(•o) 2 [ OoRR<<R o

Equation (2) approximates Hill's [1979] solution based on uniform radial outflow in a dipole field at large R (see Figure 2 of Htll[ 1979]).

4

2

c

c• o •o

10 '2

+

tik t = 225 h ....... t = 375 h

J=6

5 15 25 35 45

R(Rj) Figure 1. Density versus radial distance in the equatorial plane from the initial plasma model. Three values of the power law (J = k + l ) are shown with solid lines. The pluses give the density observed by the plasma instrument on Voyager i during the inbound leg of its pass by Jupiter [Belcher et al., 1983]. The line with the long dashes gives the density from the simulation at t = 225 hours along the projection of the Voyager trajectory into the equatorial plane. The corresponding curve from the simulation at t = 375 hours was plotted with the short dashes. The shading for 15Rj < r < 21Rj indicates the region over which the inner magnetosphere boundary condition was applied (see text).

OGINO ET AL.: BRIEF REPORT 227

": Y 100R

Plate 1. Magnetic field lines at t = 149.4 hours in the M = 2 simulation. Positive x is toward the Sun, positive y is toward dusk, and positive z is northward. Green field lines are closed, blue field lines have one 1hot at the Earth and the other exits the simulation box, red field lines cross the equator twice, and gold field lines cross the equator once with both ends exiting the back boundary.

-150

150

300 km/s c•

150 0

X(Rj)

lO

-300

Plate 2. Pressure with superimposed plasma flow vectors in the equatorial plane at t = 225 hours. The color bar gives the pressure values. The dark blue region in the center of the plate is inside the inner magnetosphere boundary of the simulation and is not included in the calculation. The number of flow vectors has been decimated by a factor of 8 in both directions.

Table 2. Bow Shock

Earth-like (Rj), Jupiter (R./), Jupiter (R./),

p v 2 =0.75 nPa p v 2 =0.75 nPa p v 2 = 0.18 nPa Noon-equator 62 68 92

Polar 103 109 150* Dawn 103 121 175' Dusk 103 114 165'

*Estimate.

228 OGINO ET AL.' BRIEF REPORT

150

100 km/s

150 0 -150

Dusk Dawn Y(Rj)

10

Plate 3. The same as Plate 2 in the dawn-dusk meridian (yz) plane. Note that the apparent outflow through the magnetopause and bow shock results from using large arrows to represent the projected flow. The actual flow streamlines are parallel to the flared boundaries (see Plate 2). The flow vectors have been decimated by a factor of 8.

-150

Z(Rj) 75

150

-150 (Rj)

T= 225 hrs •

-75 -lOO

T= 375 hrs - v

x

lOO

- 1 oo o 1 oo

Dawn Y(Rj) Dusk

Plate 4. Three-dimensional view of magnetic field lines which cross the equator along the dawn-dusk meridian (x = 0, z = 0). The blue field lines were calculated starting from the equator at y = -20, -40, -60, -80, 20, 40, 60, 70 Rj in the t = 225 hours magnetic field. The intercepts of these field lines at Jupiter were determined. The red field lines were calculated starting from those Jupiter intercepts by using the magnetic field at t = 375 hours. The insert shows the field lines at t = 225 hours projected onto the xy plane.

OGINO ET AL.' BRIEF REPORT 229

150 0 -300

X(Rj) Plate 5, The same as Plate 2 in the noon-midnight meridian (xz) plane at t = 225 hours. The flow vectors have been decimated by a factor of 8.

-150 • •-•'• •

150

150

300 km/s

150 o

,- X(Rj)

Plate 6. The same as Plate 2 for t = 375 hours.

-300

10

0 1 150

Dusk

-.,. ,,,

Y(Rj) Plate ?, The same as Plate 3 for t = 375 hours.

-150

Dawn

230 OGINO ET AL.: BRIEF REPORT

-150

150

Bz>0 Bz<0 300 km/s

........

• •_ ;• ........

•• • • • / .... ,

•• '. •. - ......... . , , , •;'• • - .. ß .... - , ..........

'•%• • ..... ß ......

150 0 -300

X(Rj)

Plate 8. Equatorial regions with Bz < 0 in black and Bz > 0 in red at t = 375 hours. The boundary between red and black gives the location of x- and o-type neutral lines (see text). Flow vectors in gold and the trajectory of Galileo in white have been superimposed.

-lOO

Y(Rj)

Z(Rj) 50

Time Rotation No Rotation

225 hrs .......

300 hrs ........

-50

lOO

X(Rj)

Plate 9. Three-dimensional view of the magnetic field lines which cross the equator along the dawn meridian. The blue field lines were calculated starting from the equator at y =-60R/ for the rotating simulation (dashed line) and the simulation with no rotation (solid line). The red lines were calculated starting from the Jupiter intercepts of the blue field lines by using the magnetic field 75 hours (t = 300 hours) after the solar wind dynamic pressure was reduced.

OGINO ET AL.' BRIEF REPORT 231

where ao = 30 and

ao h2 ao h2 +1

2

h----T-1 ra

r> r a

h--O r<ra

with ra = 15Rj.

We ran the simulations starting from the initial states given by the plasma model for p and p, (1) for B and (2) for v until a quasi-steady magnetospheric configuration resulted ( t = 225 hours for the M = 2 case). After 225 hours the solar wind dynamic pressure was reduced to 0.18 nPa by reducing the density and the simulation was run for an additional 150 hours. A second case without the rotation but all other parameters unchanged was run to give an Earth-like case for comparison. As before an image dipole was applied at the start to help establish a magnetopause.

3. Magnetospheric Configur•ation for High Solar Wind Dynamic Pressure pv' = 0.75 nPa

Plate 1 shows magnetic field lines from the M = 2 simulation at t = 149.4 hours for a high solar wind dynamic pressure of pv 2 = 0.75 nPa. There are four types of field lines present. Closed field lines with both ends linked to Jupiter are green. Field lines with one end at Jupiter and the other extending outside of the simulation box are blue. Field lines that cross the equator twice are red, and field lines that cross the equator once with both northern and southern ends exiting the downstream end of the simulation box are gold.

Plate 2 gives the plasma pressure in the equatorial (x-y) plane with flow vectors plotted on top of the color shading for the simulation at t = 225 hours. Plate 3 provides the analogous plot in the dawn-dusk meridian plane (yz plane at x = 0). The dark blue region near Jupiter is inside of the inner magnetosphere boundary and was not included in the calculation. The magnetopause pressure gradient, the change in the flow pattern, and the last closed magnetic field lines can be used to identify the locations of the bow shock and magnetopause. Tables 2 and 3 give key points on these surfaces for several versions of the simulation including the Earth-like case. For Jupiter simulations the columns labeled pv 2 = 0.75 nPa give the boundary positions at t = 225 hours, while the columns labeled pv 2 = 0.18 nPa give the values after the pressure had been reduced at t = 375 hours. In Tables 2 and 3, noon-equator refers to distance along the x axis at 1200 LT, dawn is along the y axis at 0600 LT, dusk is along the y axis at 1800 LT, and polar is along the z axis.

Compared to an Earth-like model with the same solar wind Conditions both the bow shock and the magnetopause extend farther from Jupiter in units of planetary radii, in the equatorial plane, but the difference is much smaller out of the equator. Note that corotation causes a dawn-dusk asymmetry in the magnetosphere with the magnetopause and bow shock extending farther from Jupiter on the dawnside than on the duskside.

The rotation causes an equatorial current sheet to develop in the middle magnetosphere. In Plate 4 we have plotted in blue field lines calculated by starting at the equator along the dawn dusk meridian at t = 225 hours. They map to between 79 ø and 86 ø in latitude. The field lines are stretched from a dipole configuration in the region between 20Rj and 70Rj although they remain more dipolar than observed and twist out of the meridian plane by an angle that increases with distance to the equatorial crossing. The twisting out of the meridian plane can be seen in the insert in which the xy plane projection of some field lines at t = 225 hours has been plotted. The stretching is greater on the dawnside than on the duskside. The field lines crossing the equator inside of 65Rj are stretched relative to the dipole field, but beyond about 65Rj near the magnetopause they have a more dipole like shape. These field lines near the magnetopause are twisted much farther out of the meridian than the stretched current sheet field lines.

Rotating flows dominate the middle magnetosphere equatorial current sheet (Plate 2) although there is weaker flow (--50-100 krn/s) away from Jupiter on both the dawnside and duskside (Plate 3). The outward flow near the dusk magnetopause has an equatorward component as it merges with the tailward solar wind induced flow. This equatorward and outward flow occurs when relatively inflated afternoon field lines like those at dusk in Plate 4 convect into the nightside (Plate 1).

The flow in the outer dawnside magnetosphere is greatly reduced (Plate 2) and stagnates in the equatorial plane near the magnetopause on the dawnside. The flow near the dawn magnetopause is field aligned and away from the equator (in Plate 3 v,-- (50 - 100) km/s at y -- -65Rj). A pressure ridge dominates the equatorial morning magnetosphere (Plate 2). In Plate 3 this ridge is the outer peak at y -- -65Rj in the dawnside pressure distribution. Although not readily visible beyond x -- -60Rj in the color shading of Plate 2 the ridge extends to x -- -100Rj in the dawnside magnetotail.

For x < -85Rj the flow turns tailward. The tailward flows extend in y from the dusk magnetopause to the dawn stagnation region with the strongest flows near midnight.

The pressure and flows in the noon-midnight meridian plane are given in Plate 5. The plasma sheet on the nightside has a form like the plasma sheet in the Earth's magnetotail. The Jovian model differs t¾om an Earth-like model in the dayside magnetosphere where a plasma sheet like region extends from about x = 30Rs to the magnetopause. The noon plasma sheet becomes thicker with distance from Jupiter.

4. Magnetospheric Configuration for Low Solar Wind Dynamic Pressure pv z = 0.18nPa

At t = 225 hours the solar wind pressure was decreased by a factor of 4. Following the reduction in pressure, the bow shock and magnetopause moved away from Jupiter as expected (Tables 2 and 3). The values with asterisks in Tables 2 and 3 are estimates since the bow shock passed through the simulation boundary slightly sunward of the dawn-dusk meridian. However, since the bow shock crossed the boundary so near the dawn-dusk meridian these should be accurate estimates. The thermal

pressure and flows in the equatorial and noon-midnight meridian plmaes at t = 375 hours are plotted in Plate 6 and 7. The magnetopause expanded so much that tailward of x - -110Rj the

Table 3. Magnetopause Earth-like (R.0, Jupiter (R.O, Jupiter (R j),

p v 2 = 0.75 nPa p v 2 = 0.75 nPa p v 2 = 0.18 nPa Noon-Equator 48 57 77

Polar 78 62 99

Dawn 58 80 124

Dusk 58 70 104

232 OGINO ET AL.' BRIEF REPORT

magnetopause moved beyond the simulation boundary at y = +150Rj. For x < -110R• the results near the simulation boundary may not be valid. However, the results nearer Jupiter and in the center of the tail should be reliable since at earlier time steps the results in these regions were not greatly affected by processes at the distant magnetopause. In the dawn magnetosphere and tail the flow and pressure patterns are very similar at both times, with the decelerated flow on the dawnside and antisunward flow in the

magnetotail. In both cases the decelerated flow occurs near a dawnside pressure ridge. However, the biggest change in the flow pattern at t = 375 hours occurs in the middle dusk side magnetosphere. At t = 225 hours there is a small Jupiterward flow perturbation at about 2200 LT for 50R• < r < 80R• (Plate 2). By t = 375 hours (Plate 7) this structure has grown and evolved into a flow vortex centered at about 2100 LT and extending from 50Rj to 120R•. Now the plasma sheet flow in the dusk meridian is toward Jupiter rather than away from JuPiter (compare Plate 7 with Plate 3). As the flux tubes convect from the afternoon into the evening sector, the field lines become stretched. This stretching results from the reduction in the constraining effects of the magnetopause currents and the outflow. Eventually, the field lines can become so distorted that the magnetic tension is sufficient to restore the distended field. This caused the

jupiterward motion on the duskward edge of the flow structure. On the edge of the structure nearest midnight outflow (100 km/s < v < 200 km/s) again stretches the field lines. The structure is more pronounced at t = 375 hours when the field lines become more stretched than they were at t = 225 hours as we will see in section 5.

In the magnetotail the flow in Plate 6 is tailward in a narrow channel. In Plate 8 the equatorial flow pattern has been superimposed on a plot of the sign of B z. The flow turns tailward where Bz changes sign. This is the location of an x-type neutral line in the tail. The neutral line is displaced toward dawn (-72R• < y < 20R•). The duskward and dawnward boundaries are part of the magnetic o line and do not impose flow rotation. The magnetic o line extends beyond the tail boundary and closes in the more distant tail.

5. Discussion

We have plotted the density from the simulation along the equatorial projection of the Voyager 1 inbound trajectory as the dashed lines in Figure 1. The densities from the simulation are higher then those from the initial model. The simulated values are closer to the peak Voyager values that occurred when the spacecraft passed through the equatorial region. We evaluated the net transport across the outer edge of the inner magnetosphere boundary by calculating lnv.dS over the sphere at r = 21R• where n is the number density and dS is an element of area. At t = 225 hours the transport is equivalent to --1028 particles/s moving from the inner magnetosphere to the outer magnetosphere. This outflow is not uniform. There is net outflow in the region from -2100 to --1500 LT and net inflow near dusk. The outflow is

primarily at low latitudes in the plasma sheet where the density is high. The flow is convective at low latitudes, but parallel flows become more important at higher latitudes where the density is low. For the simulation discussed in this paper the density and pressure at the inner boundary were set to Voyager 1 values and the velocity was set to the values from (2). The values selected at the inner boundary determine the transport across that boundary. We have not yet run the simulation with other initial models. This outward transport is comparable to estimates of transport from the Io source to the magnetosphere (3 x 1028ions/s) [Hill et al., 1983].

The shape and position of the bow shock and magnetopause from the simulation are similar to those inferred from

observations. The range of solar wind dynamic pressures observed in the neighborhood of Jurfiter is large (0.01 nPa to >

1 nPa) [Smith et al., 1978; Bridge et al., 1979a, b; Phillips et al., 1993]. Since the pressure in the initial stage of the simulations (0.75nPa) was at the high end of the observed range, we would expect the boundary positions to be more like those observed during the higher-pressure Pioneer and Voyager encounters than the lower-pressure Pioneer 10 and Ulysses encounters. That the magnetopause extends further sunward than the Earth-like model in Tables 2 and 3 is consistent with the shape determined from tbrce balance calculations by Engle and Beard [1980]. The model boundaries tall well within the range of observed values [Intriligator and Wolfe, 1976; Bridge et al., 1979a, b; Bame et at., 1992; Kivelson et al., 1997]. This can be seen by comparing the magnetopause and bow shock positions in Tables 2 and 3 with Figure 2 of HuddleStøn et al. [1997] (H97) in which they have plotted the observed bow shock and magnetopause positions in the equatorial plane.

H97 have normalized the observed boundary positions fbr solar wind dynamic pressure using crude estimates of the latter parameter. Since the Pioneer and Voyager spacecraft were launched in pairs, one spacecraft was in the outer solar system but not within Jupiter's magnetosphere when the twin was passing through the magnetosphere. Thus, for Pioneer and Voyager pressure estimates were available. Observations from spacecraft near Earth were mapped to Jupiter's orbit to normalize

_ _

the Jovian boundary observations from Ulysses and Galileo. H97 adjusted the boundaries by assuming that the position depends on the solar wind dynamic pressure (P,•.v,,) as ptiyn 'ø'25. When we applied the same normalization procedure to the simulation results we found that the simulation boundaries extend farther

from Jupiter than a model fit to the observations. However, the simulated boundary positions are within the scatter in the range of observed positions (cf. Tables 2 and 3 with Figure 4 of H97). H97 find that the bow shock and magnetopause are closer together at the subsolar point at Jupiter than at the Earth. They find Ra4/RBs = 0.88 at Jupiter versus Ra4/RBs= 0.75 at Earth, where RM is the distance from the center of Jupiter to the magnetopause and R•s is the distance to the bow shock, We find Ra4/R•s = 0.84 in the Jupiter simulation. We also find that the position of the subsolar magnetopause ¾aries as pay. n -ø'2t close to the P•tyn 'ø'22 found by H97. Finally, H97 found evidence for flattening of the Jovian magnetosphere in which the distance from Jupiter to the polar magnetopause is less than the distance to the equatorial magnetopause at dawn and dusk. This effect suggested by Hill et al. [1974] also is seen in the simulation.

Within the magnetosphere the simulation demonstrates many features deduced from the flybys. The plasma sheet and current sheet dominate the middle magnetosphere (30R• <_ r < 70Rj) [Acuna et al., 1983]. In Plate 4 the red curves were calculated at t = 375 hours by starting at the Jupiter intercepts of the blue field lines calculated at t = 225 hours. In the middle and outer

magnetosphere the red field lines extend farther from Jupiter. The effect of reducing the solar wind pressure and moving the magnetopause away from Jupiter is to increase the effects of the equatorial current sheet especially in the outer regions of the middle magnetosphere. This can be seen in Plate 9 where we compare the change in the 60R• field line in Plate 4 with the change following an identical solar wind pressure reduction in the case with no rotation. The field line in the rotating case responds to the pressure reduction by becoming much more stretched while the change in the case without rotation is relatively small. In Plate 10 we have plotted the field lines in the midmorning magnetosphere near the region in which Pioneer 10 and 11, Voyager 1 and 2, and Ulysses entered the Jovian magnetosphere. That the equatorial current sheet extends to the postdawn magnetosphere is evident as is the region of dipole like field lines nearer the magnetopause. In many ways the magnetic configuration in Plate 10 resembles that deduced from Pioneer magnetic field observations by Smith et al., [1976] (compare their Figure 2) with extended field lines in the middle magnetosphere and rather dipolar field configuration in the outer magnetosphere. Reducing the solar wind dynamic pressure

OGINO ET AL.' BRIEF REPORT 233

10

* Galileo Inbound

o + Pioneer 10 Outbound P -0.75 nPa

• ß (T=225 hrs.)

• •ø P10 Galileo

hrs3 '• '...._." '• ,._.. , (m = 375 .... ' ? "-•' 'œ•X,' • ' •,

0 50 100 150

R(Rj)

Figure 2. Magnetic field magnitude in the equatorial plane (z = 0) on the dawnside for x ---0. The solid line gives the simulation results at t = 225 hours, while the dashed line is from the lower pressure cage at t = 375 hours. Asterisks give values observed on Galileo inbound, and pluses give values from Pioneer 10 outbound. The observed values were determined by taking the minimum B during each current sheet crossing. The dotted lines give the location of the first magnetopause crossing of Pioneer 10 and the Galileo boundary crossing. The simulated magnetopause was at r = 80R•, at t = 225 hours and at r = 124Rj at t = 375 hours.

allowed increased stretching of the field lines on the dayside (Plate 10). Pioneer 10 and Ulysses inbound detected the dayside magnetopause over t00Rj from Jupiter. The magnetic field observed in the middle magnetosphere and off the equator on the Ulysses inbound trajectory was nearly radial [Balogh et al., 1992]. However the solar wind pressure prior to the Ulysses encounter was 0.01 nPa [Phillips et al., 1993] more than an order of magnitude smaller than the lowest pressure (0.18 nPa) we have used in our simulations. This suggests that the dayside field lines become even more stretched than those at t = 375 hours in Plate 9 as the solar wind dynamic pressure decreases.

The magnetic field magnitude at dawn for z = 0 has been plotted in Figure 2. Since we have not included the dipole tilt in the simulation we plotted only equatorial field (minimum B during each current sheet crossing) values along the Galileo inbound trajectory and the Pioneer 10 outbound trajectory. The simulation results at t = 225 hours track the scattered Galileo values reasonably well, but the Pioneer 10 values fall much below the simulation results. The simulation values at t = 375 hours (lower solar wind dynamic pressure) are closer to the Pioneer 10 observations but still give too large magnetic field magnitude for 5.0Rj < r < 100Rj. They follow the trend of the Galileo results but fall below most of those measurements. Kivelson et al. [1997] suggested that after Galileo encountered the magnetopause at 118Rj the solar wind pressure increased and the magnetopause moved toward Jupiter. They argued that the difference between the Pioneer and Galileo values could be understood if Galileo's pass through the middle magnetosphere occurred at high solar wind pressure while Pioneer encountered the middle magnetosphere during an interval with low pressure. This explanation is consistent with the simulation results provided the pressure assumed at t = 375 hours was lower than that relevant to Galileo's pass and higher than that for Pioneer 10 outbound. We also plan to run the simulation for a tilted dipole. This will allow us tO compare the timing of Galileo and Pioneer

entries into the current sheet with the simulation. In the middle magnetosphere azimuthal flow dominates in

both observations and model [Belcher, 1983; Krimigis and Roelof 1983]. On the duskside the corotating magnetospheric flow merges with the tailward flow as observed on Ulysses [Phillips et al., 1993]. On the dawnside where the corotarion and magnetosheath flow are in opposite directions the corotating magnetospheric convection stops and a pressure ridge forms. The flow in the stagnation region is along the magnetic field. Southwood [ 1995] suggested the presence of a stagnation region in the dawn magnetosphere. The stagnation region moved outward with the boundary when the solar wind pressure was reduced (cf. Plates 2 and 6). The location of this region may be sensitive to changes in the interplanetary magnetic field (IMF) orientation. This will be investigated in future simulations. Observations from Galileo will allow us to study the flows in the outer dawn magnetosphere and test our simulation results.

In Figure 3 we have plotted an equatorial projection of field lines calculated at 45" intervals around Jupiter. Between ~2100 and -1400 LT the field lines bend out of the meridian plane in the sense consistent with corotarion lag. However, those in the local afternoon and evening do not. In the simulation the field lines are bent tailward much like they are in the Earth's magnetosphere. Balogh et al. [1992] reported similar bending from Ulysses magnetic field observations at dusk while Simpson et al, [ 1992] used energetic particle data to infer corotation lead and therefore field lines which are bent tailward.

Flow in the magnetotail is generally tailward. In the simulation the tailward flow can result from a viscous interaction between the solar wind and the magnetosphere, pressure gradient effects and the inertia of corotating flows (which are tailward on the duskside of the magnetosphere). The simulation algorithm was designed to be minimally diffusive and tested in simulations of the Earth's magnetosphere [Ogino et al., 1992, 1994]. The sharply defined magnetopause and bow shock in Plates 2,3,6, and

234 OGINO ET AL.: BRIEF REPORT

-8O

-4O

4O

0 , i i i i i i i

-80 -40 0 4O 8O

Dawn Y(Rj) Dusk

Figure 3. Equatorial projection of magnetic field lines calculated at 45 ø intervals in local time in the magnetic field from the simulation at t = 225 hours. The field lines were calculated at equatorial crossing distances of r = 20, 40, 60Rj except at 1200 LT where the farthest field line was started at the position of the magnetopause (r = 57Rj).

7 are consistent with minimal diffusion. That the flows in Plates

2 and 6 peak away from the boundary also is inconsistent with ,viscous flow. Viscous convection is small but not zero. Both

pressure driven outflow and corotation driven flows are present in the simulation. If reconnection was the driving mechanism for the tailward flows, we would expect also to have flows away from the x-type neutral line toward Jupiter which are not found in the simulation. Instead, the reconnection seems to channel the tailward flows since they are well organized by the region of northward Bz in Plate 8.

A tail neutral line was suggested by Vasyliunas [1983], who also proposed a magnetic o line along the dusk edge of the reconnected field lines similar to that in Plate 1. In his discussion

as flux tubes move from the dayside into the low-pressure magnetotail plasma outflow causes them to become highly extended and eventually break open as originally suggested by Hill et al.[ 1974]. The extended field lines become detached by forming x-and o-type neutral lines. The formation of the neutral lines in the simulation is more complex. In the simulation the

flux tubes become highly stretched as they con•,ect from the dayside (see Plate 1). For x < -100R• x- and o-type neutral lines form in the simulation (Plate 1). The actual reconnection occurs because of resistivity included in the MHD equations [Ogino et al., 1992]. Without some form of resistivity reconnection cannot occur in MHD.

Outflow qualitatively like that in Plate 2 and 6 was interred from energetic particle anisotropy observed in Voyager data by Krimigis et al. [ 1981 ]. Cheng and Krimigis [ 1989; Cheng, 1992] have used the Voyager observations to suggest a different convection pattern. They propose a region of strong cross-tail (dusk to dawn) flows for r > 70R• (see Figure 1 of Cheng [I,•,•,,• •,J,.,j]. The simulation results show some of the features of this model as well. In Plates 2 and 7 there are strong cross tail flows (v-- 200 km/s) for- 100R• < x < -70R•. However, the simulation does not demonstrate the flows toward Jupiter duskward of the

tailward flow suggested in the Cheng and-Krimigis model. The white lines superimposed on Plate 8 show the Galileo tour plan. Galileo will reach x = -149Rj at midnight near the equator during its ninth orbit (Plate 8). This should be deep enough in the tail to see the flow and magnetic field reversal associated with the neutral line.

In the simulation the temperature (T) is given by T/m = p/kp, where rn is the mass of the ions and k is the Boltzmann constant.

In the plasma sheet we find T/m < 200 eV/amu. Voyager 1 and 2 observations have shown that energetic ions (> 20 keV) frequently dominate the pressure [Krimigis and Roelof 1983; Mauk et al., 1996]. Since the plasma pressures in Plates 2 and 3 are similar to those observed (see Figures 4.20 and 4.22 of Krimigis and Roelof [1983]) this indicates that the plasma temperature is too low in the simulation. There are several possible explanations for this. The density in the MHD model is larger than observed. This is in part a deliberate attempt to reduce the Alfven velocity in regions with low density by maintaining a minimum density. In addition, the MHD model has only a single fluid, while the Voyager observations suggest hot and cold parts to the fluid. In future runs we will reduce the density minimum. We also plan to investigate plasma acceleration in the Jovian system by calculating test particle trajectories in the model electric and magnetic fields from the simulation.

Acknowledgments. One of us (R.J.W.) would like to thank R. Richard for providing simulation analysis software. The work at UCLA was supported by Jet Propulsion Laboratory contract JPL 958694. The work at Nagoya University was supported by grants in aid from the Ministry of Education, Science and Culture. Computing support was provided by the Computer Center of Nagoya University and by the San Diego Supercomputer Center. Pioneer 10 magnetic field data and Voyager 1 plasma observations were provided by the Planetary Plasma Interactions Node of the Planetary Data System.

The Editor thanks T. Tanaka and another referee for their assistance

in evaluating this paper.

T = 225 hrs

T = 375 hrs Z(Rj)

50

235

-lOO Y(Rj)

lOO

X(Rj)

-5O

Plate 10. Magnetic field lines calculated at 0900 LT at equatorial crossing distances of r = 30, 50, 70, 90 Rj. The blue field lines were calculated at t = 225 hours, while the red field lines were calculated at t = 375 hours by starting at the Jupiter intercepts of the blue field lines.

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M. G. Kivel•on and R. J. Walker, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, 6843 Slichter Hall, 405 Hilgard Avenue, Los Angeles, CA 90095-1567. (e-mail: mki velson @ igpp. u cla.edu; rwalker @ igpp. ucla.edu)

T. Ogino, Solar-Terrestrial Environment Laboratory, Nagoya University, Toyokuwa, Aichi, 442 Japan. (e-mail: ogino@stelab.nagoya-u.ac.jp)

(Received September 4, 1996: revised July 7, 1997; accepted July 31, 1997.)