The Locations and Shapes of Jupiter’s Bow Shock
and Magnetopause
Raymond J. Walker1,2, Steven P. Joy1,2, Margaret G. Kivelson1,2 , Krishan
Khurana1, Tatsuki Ogino3, Keiichiro Fukazawa3
1
Institute of Geophysics and Planetary Physics,
University of California, Los Angeles, CA. 90095-1567
2
Department of Earth and Space Science,
University of California, Los Angeles, CA 90095-1567
3
Solar Terrestrial Environment Laboratory,
Nagoya University, Toyokawa, Aichi, Japan
Abstract. The shape and location of the Jovian bow shock and magnetopause
have been studied by using magnetic field observations and global
magnetohydrodynamic (MHD) simulations. MHD simulations in which the
interplanetary magnetic field (IMF) was set to zero were used to define the
boundary shapes and positions and how they depend on solar wind dynamic
pressure. Polynomial fits to the simulated boundaries along with spacecraft
observations were used to determine the probability of a given position being
outside of the bow shock or inside of the magnetopause. The magnetopause and
possibly the bow shock have two preferred locations, one representing a
compressed magnetosphere and the other an expanded magnetosphere. Variations
in the solar wind parameters near Jupiter also show a bimodal distribution but the
changes in the solar wind dynamic pressure are not sufficient to account for the
observed bimodal distribution of observed magnetopause positions. Internal
pressure changes at Jupiter are required. The interplanetary magnetic field also
influences the location and shape of the boundaries. In particular, when the IMF is
in the By direction or northward magnetopause reconnection acts to reduce polar
flattening. Higher internal pressure at dusk leads to a dawn-dusk asymmetry in the
magnetopause position with the boundary being farther from Jupiter on the dusk
side. For all the simulations the ratio of the bow shock stand-off distance to that of
the magnetopause was less than that at the Earth.
INTRODUCTION
Solar wind plasma is heated and diverted around planetary obstacles by bow shocks
that form upstream of the planets. Studies of the Earth’s bow shock indicate that the solar
wind magnetosonic Mach number, the interplanetary magnetic field (IMF) and plasma
beta influence both the strength and location of the shock [Farris and Russell, 1994].
Many years ago Spreiter and colleagues [Spreiter et al., 1966; Stahara et al., 1989] used
gas dynamic calculations to demonstrate that the shape of the Earth’s bow shock depends
on the shape of the obstacle. At the Earth the magnetospheric obstacle is determined by
pressure balance at the magnetopause between the solar wind and the Earth’s magnetic
field. At Jupiter on the other hand the magnetospheric obstacle is dominated by an
azimuthal equatorial current sheet containing a hot plasma sheet with flows that are
atmospherically driven toward corotation. As a result at Jupiter the thermal and dynamic
plasma pressures also are important at the magnetopause [Huddleston et al., 1998]. The
presence of the equatorial current sheet stretches dayside magnetic field lines [Engle and
Beard, 1980] leading to a more sharply pointed magnetopause at Jupiter than at the Earth.
This is thought to result in Jupiter’s bow shock being relatively much closer to the
magnetopause than is the case at the Earth [Slavin et al., 1985; Stahara et al., 1989]. The
Jovian magnetopause and bow shock locations are highly variable [Smith et al., 1978;
Slavin et al., 1985].
Jupiter provides us with a relatively handy example of a rapidly rotating
magnetospheric obstacle that is very different than that at Earth. Seven spacecraft
(Pioneer 10 and 11, Voyager 1 and 2, Ulysses, Galileo and Cassini) have provided
observations of Jupiter’s magnetopause and bow shock. Together they provide us with a
substantial database with which to study the Jovian boundaries. Joy et al. [2002] used all
of the observations available up to that time to develop probabilistic models of the bow
shock and magnetopause. The models were based on a combination of this large data
base with results from magnetohydrodynamic (MHD) simulations of the effects of
different solar wind dynamic pressures on the bow shock and magnetopause shapes and
locations. Surprisingly both the bow shock and the magnetopause had bimodal
distributions of location with two most probable positions. In this paper we will review
both the simulation and data studies used to determine the probabilistic models of the
bow shock and magnetopause shapes and locations. We also will use results from
additional simulations to evaluate the possible effects of IMF parameters not included in
the previous simulations. In section 2 we briefly review the MHD simulation model and
in section 3 we examine simulated boundaries as a function of solar wind dynamic
pressure. We review the probabilistic model in section 4. Section 5 contains the
simulations of the effects of the IMF on the boundaries. Finally in section 6 we
summarize our understanding of the overall configuration of the Jovian magnetopause
and bow shock.
SIMULATION MODEL
Our simulation model of Jupiter's magnetosphere has been described in Ogino et al.
[1998]. In this section we briefly review the simulation model and discuss the runs used
to support this study. Starting from a model of the plasma and field configuration near
Jupiter, at time t = 0 we placed an image dipole upstream of Jupiter to hasten the
formation of the magnetopause and help assure ∇ • B = 0 throughout the simulation box
[Watanabe and Sato, 1990]. We launched an unmagnetized solar wind with a dynamic
2
= 0.75 nPa ( v sw =300 km s-1) and a temperature of 2 × 105 K from the
pressure of ρv sw
upstream boundary of the simulation box and solved the resistive MHD equations as an
initial value problem by using the Modified-Leap Frog Method described by Ogino et al.
[1992].
The Jovian magnetosphere was modeled on either a 602 × 402 × 202 point,
602 × 402 × 402 point or 452 × 302 × 152 point Cartesian grid with grid spacing of 1.5RJ
2
(1RJ = 71,492km). In the simulation the magnetic field (B), velocity (v), mass density (ρ)
and thermal pressure (p) are maintained at solar wind values at the upstream boundary (x
= 300RJ or 225RJ) while free boundary conditions through which waves and plasmas can
freely leave the system are used at the downstream, side, and top boundaries. Symmetry
boundary conditions are used at the equator (z = 0) for the simulations with zero,
northward and southward IMF. For the case with an IMF y-component a full three
dimensional box was used and free boundary conditions were used at the bottom
boundary. The dipole tilt is set to zero in all of the calculations. At the inner
magnetosphere boundary all of the simulation parameters (B, v, ρ , p) are fixed for r <
15RJ. The simulation quantities are connected with the inner boundary through a smooth
transition region (15<r<21RJ). The numerical stability criterion is v gmax ∆t / ∆x < 1 where
v gmax is the maximum group velocity in the calculation domain and ∆t is the time step.
Since the Alfvén velocity becomes very large near Jupiter we placed the inner boundary
of the simulation at 15RJ in order to keep the time step from getting too small. The
simulation parameters are fixed at the inner boundary. In particular the azimuthal velocity
is set to corotate and the pressure and density are set to values determined from the
Voyager 1 flyby of Jupiter [Belcher, 1983]. This reservoir of plasma provides a source
for the Jovian magnetosphere. Typically about 1 × 1030 AMU s-1 pass through a surface at
22.5 RJ and enter the Jovian magnetosphere. The source values for each of the
simulations are given in Table 2 of Walker and Ogino [2003]. We have not included mass
loading terms in the MHD equations for these simulations. The magnetic field is fixed to
values from Jupiter's internal dipole.
THE EFFECTS OF SOLAR WIND DYNAMIC PRESSURE ON
THE LOCATION AND SHAPE OF THE BOW SHOCK AND
MAGNETOPAUSE
In Figure 1 we have plotted the thermal pressure in the noon-midnight meridian plane
(left) and dawn-dusk meridian plane (right) for four different solar wind dynamic
pressures. The IMF was set to zero for these simulations. The pressures range from
0.045nPa to 0.36nPa and were selected by scaling the mean dynamic pressure at Jupiter’s
orbit, 0.092nPa [Slavin et al., 1985; Huddleston et al., 1998; Joy et al. 2002], by factors
of two. Both the bow shock and magnetopause move toward Jupiter with increasing
pressure. We have used the sharp pressure gradients at the boundaries to tabulate their
positions in Table 1. In both the observations and the simulations the distance to the
magnetopause and bow shock vary with pressure as a power law between PDyn-1/4 and
PDyn-1/5 [Slavin et al., 1985; Huddleston et al., 1998; Ogino et al., 1998; Joy et al., 2002].
At noon the ratio of the bow shock distance to the magnetopause distance is between 1.31
and 1.24. It decreases with increasing pressure. The magnetopause has a marked dawndusk asymmetry in which the boundary is closer to Jupiter at dawn than at dusk. The
asymmetry increases (Ydawn/Ydusk decreases) with increasing pressure. Within the
magnetosphere the equatorial plasma sheet is much thinner at dawn than dusk. This is
reflected in an irregularly shaped magnetopause in the X=0 plane (Figure 1, right).
However the dawn-dusk asymmetry and irregular shape of the magnetopause are much
3
less evident in the bow shock. The dawn-dusk asymmetry may actually reverse for small
dynamic pressure (Table1).
Table 1. Distances to the bow shock and magnetopause for the case Bz = 0.
PDyn
Magnetopause
(nPa)
0.045
0.090
0.180
0.360
X
90
76
67
58
Yavg
136
112
92
78
Z
125
107
92
80
Z/Yavg
0.919
0.951
1.000
1.026
Standoff
Ratio
Bow Shock
Ydawn/
Ydusk
0.985
0.940
0.906
0.867
X
118
100
84
72
Yavg
207
174
146
124
Z
204
173
145
123
Z/Yavg
0.986
0.994
0.990
0.988
Ydawn/
Ydusk
1.029
1.012
1.007
0.992
Xb/Xm
1.311
1.316
1.254
1.241
At Jupiter in addition to the magnetic field, hot internal current sheet plasma and
magnetospheric flows contribute to the pressure balance at the equatorial magnetopause.
Thus we would expect the magnetopause to be relatively further from Jupiter at the
equator than at the poles. This is frequently called polar flattening. We have listed the
ratio of the boundary locations along the z-axis to the average value along the y-axis. For
low dynamic pressure the simulated magnetopause exhibits polar flattening (Z/Yavg <1).
However this effect goes away for higher pressure (Z/Yavg ~1). Again the bow shock
shape is not sensitive to the structure found in the magnetopause.
EMPIRICAL MODELS OF THE BOUNDARY SHAPES AND
POSITIONS
There have been several attempts to model Jupiter’s bow shock and magnetopause
empirically. One approach is to fit actual boundary crossings by assuming that the
boundaries are conic sections of revolution [Lepping et al., 1981a; Slavin et al., 1985;
Huddleston et al., 1998]. The conic section models are symmetric about the x-axis. In Joy
et al. [2002] we used the simulation results to argue that observable dawn-dusk
asymmetry and polar flattening were probable. We argued even with Galileo orbiter data
there are too few boundary crossings to make reliable fits to the data including
asymmetries. However, spacecraft collect more information about the boundary locations
than just the locations of the actual boundary crossings. For instance if a spacecraft is in
the magnetosheath, the bow shock must lie further from the planet and the magnetopause
must lie closer to the planet. Therefore we developed probabilistic models of the
boundaries that include all of the observations.
In Joy et al. [2002] we used the global MHD simulations to organize the boundary
model. First we identified the boundary locations in the simulations for different solar
wind dynamic pressures. We then fit the boundary shapes to a functional form
( z 2 = A + Bx + Cx 2 + Dy + Ey 2 + Fxy ) that does not assume dawn-dusk or x-axis
symmetry. We assumed that the parameters A through F were functions of dynamic
pressure (Pdyn). A linear function of Pdyn-1/4 gives an excellent fit to A, B and C while D, E
and F are well fit with a linear function of Pdyn. We fit this functional form to boundary
positions determined from the simulation results plotted in Figure 1. A number of
parameters (the magnetic field, the current density, velocity, pressure etc.) can be used to
determine the bow shock and magnetopause positions from the simulations. All of these
4
worked well for the bow shock but the gradient of the speed worked slightly better for the
magnetopause along the flanks of the magnetosphere. The boundary fits were optimized
for the dayside and within 50RJ of the equator. The fits should not be used for x<-250RJ
[Joy et al., 2002]. Figure 2 shows the results of the fits to the simulation. The plot
contains views in the XY, XZ and YZ planes of both boundaries for three dynamic
pressures (0.02nPa, 0.098nPa, 0.227nPa). These represent the 10th, 50th and 90th
percentiles of the observed solar wind dynamic pressure at Jupiter’s orbit. The plots show
the extreme variability in the boundary locations at Jupiter. For instance the
magnetopause the standoff distance at the subsolar point varies from over 100RJ to ~50RJ.
Figure 3 contains the trajectories of 35 Galileo orbits and the Pioneer 10 and 11,
Voyager 1 and 2, Ulysses and Cassini flybys. We used magnetometer and plasma wave
observations to determine the times at which the Galileo satellite crossed the boundaries
while for the other spacecraft we used published crossing times [Intrilligator and Wolfe,
1976; Bame et al., 1992; Lepping et al., 1981b; Achilleos et al., 2004]. Then we shaded
the trajectories according to whether the spacecraft was in the solar wind (blue), the
magnetosheath (green) or the outer magnetosphere (red). Trajectories from which data
are not available are black. Even with orbiter data there are relatively few boundary
crossings. Despite the relatively few boundary crossings, the Galileo orbiter observations
significantly improve the probabilistic determination of the boundary locations. However,
spacecraft collect more information about the boundaries than just the location of the
actual crossings. For instance if a spacecraft is in the magnetosheath, the shock must lie
further from the planet and the magnetopause must lie closer. All of the data can be used
to establish the probability of finding the bow shock or magnetopause at different
locations.
Ten minute samples of the data from all of the spacecraft were collected into bins
whose shapes were determined by the fits to the simulation results in Figure 2 and whose
subsolar standoff distances varied by 4RJ. The fraction of data inside or outside of a
boundary was determined for each bin. In Figure 4 the fraction of observations outside
the bow shock is plotted in the left column while the fraction inside the magnetopause is
plotted on the right. The error bars mark the actual data points. The error bars that are
closest together give the probable error of the mean. The outer error bars were
determined by randomly selecting 10 subsets of the data each with 10% of the data and
repeating the analysis. The error bars give the spread in the results from these
calculations. Surprisingly both the bow shock and magnetopause positions have bimodal
distributions with two preferred boundary positions. Fits to a bimodal distribution (sum
of two Gaussian distributions) give peaks in the bow shock position at 73RJ and 108RJ
with a standard deviation of 10RJ in both cases. The magnetopause positions are 63RJ and
92RJ with standard deviations of 4RJ and 6RJ respectively. Single Gaussian fits were used
to create the solid lines. An F-test was used to compare the variances of the deviations
from the Gaussian distribution to those of the bimodal distribution. For the magnetopause
the improvement in the fit of the bimodal distribution over the Gaussian distribution was
at the 99.9% confidence level while for the bow shock it was at the 89.8% confidence
level. We have plotted the equatorial intercepts of the model boundaries in Figure 3. The
dark shading shows the region between the 25 and 75 percentile contours of being in the
solar wind. The lightly shaded regions denote one sigma (standard deviation) bands about
the two peaks in the magnetopause distribution.
5
Finally we analyzed all of the solar wind observations (interplanetary magnetic field,
dynamic pressure and Alfvén Mach number) near Jupiter [Joy et al., 2002]. We found a
bimodal distribution of solar wind parameters however the magnitude of the bimodal
solar wind pressure distribution was too small to account for the bimodal distributions in
the boundary positions. Internal pressure changes also are required.
THE EFFECT OF THE IMF ON THE SHAPES AND POSITIONS
OF THE BOUNDARIES
By the time the solar wind reaches Jupiter the spiral of the IMF has wound up so
tightly that the magnetic field is mainly in the Jovicentric Solar Equatorial (JSEq) ydirection. However, to simplify our investigation of the influence of the IMF on the
Jovian boundaries we will start by assuming that the IMF is oriented in the north-south
direction. In Figure 5 the thermal pressures for weak southward (Bz=-0.105nT) and
northward (Bz= 0.105nT) IMF have been plotted in the Y=0 (top two panels) and X=0
(bottom two panels) planes. The locations of the magnetopause and bow shock are
tabulated in Table 2. Recall in the following that Jupiter’s intrinsic magnetic field is
opposite to that of the Earth. For northward IMF reconnection at the dayside
magnetopause moves both it and the bow shock closer to Jupiter than when BIMF=0.
Conversely for southward IMF the boundaries move away from Jupiter. However the
bow shock is relatively closer to the magnetopause for both southward and northward
IMF than for the zero IMF case. For northward IMF the dawn magnetopause is closer to
Jupiter than the dusk magnetopause while the opposite is true for southward IMF. In both
cases Yavg>Z but it is less so for the northward IMF case. In Figure 5 the high latitude
magnetosheath for BZ>0 has a “hat” like region of increased thermal pressure. A close
examination of the magnetic field lines in the “hat” shows that this region is on field lines
that have been opened by dayside reconnection.
Table 2. Boundary positions for southward and northward IMF
BZ(nT)
0.105
-0.105
0
X
117
130
119
Magnetopause
Yavg
Z
Z/Yavg Ydawn/Ydusk
159 149
0.94
0.95
178 152
0.85
1.0
170 137
0.81
0.98
X
144
165
155
Yavg
231
280
261
Bow Shock
Z
Z/Yavg
250
1.08
245
0.88
250
0.96
Ydawn/Ydusk
0.96
1.0
1.0
Standoff
Ratio
Xb/Xm
1.23
1.27
1.30
Since some of the most dramatic changes occurred when the IMF was northward we
have carried out a pair of numerical experiments in order to quantify better the effects of
the IMF. In the first experiment we set the dynamic pressure to the mean at Jupiter
(0.09nPa) and modeled the magnetosphere by assuming that the mean IMF (0.8)nT, Joy
et al., [2002]) was entirely northward. In Table 3 we have listed the distances to the
boundaries from this experiment and from one with the same dynamic pressure but half
the magnetic field. For the larger IMF the subsolar magnetopause is further eroded while
the distance to the northern magnetopause increases dramatically. For the simulation with
BZ=0.84nT the bow shock exits the top of the simulation box just sunward of X=0 so the
Z value is a lower limit. The most dramatic change with larger IMF is that Z/Yavg.>1 for
6
both the magnetopause and the bow shock. This is a direct result of increased dayside
reconnection and the addition of open flux to the magnetosheath.
Table 3. Boundary locations for constant dynamic pressure and decreasing northward IMF.
BZ(nT)
0.42
0.84
X
Yavg
90
87
137
110
Magnetopause
Z
Z/Yavg
119
117
0.87
1.06
Ydawn/
Ydusk
0.91
0.92
X
114
106
Bow Shock
Yavg
Z
Z/Yavg
181
199
191
>225
1.05
>1.13
Ydawn/
Ydusk
0.98
0.91
Standoff
Ratio
Xb/Xm
1.31
1.23
Next we held the northward IMF constant at 0.42nT and decreased the dynamic
pressure by a factor of ~4 from 0.09nPa to 0.02nPa. The boundary locations can be found
in Table 4. The largest effect of lowering the pressure for constant magnetic field is to
increase Z/Yavg. at both the magnetopause and bow shock.
Table 4. Boundary locations for constant IMF and decreasing dynamic pressure.
PDyn
(nPa)
0.02
0.09
X
84
90
Yavg
124
137
Magnetopause
Z
Z/Yavg Ydawn/Ydusk
150
1.24
0.90
119
0.87
0.91
X
110
114
Bow Shock
Yavg
Z
Z/Yavg
200 245
1.23
181 191
1.05
Ydawn/Ydusk
0.93
0.98
Standoff
Ratio
Xb/Xm
1.31
1.31
In Figure 6 we have plotted the pressure in the YZ plane from a simulation for which
the IMF was in the Y-direction (By=0.42nT) pointing toward dusk. The solar wind
dynamic pressure was 0.09nPa. The corresponding fits to the BIMF=0 bow shock and
magnetopause positions are shown with solid and dashed lines respectively [Joy et al.,
[2002]. The entire magnetosphere rotates about the sun-Jupiter line for BY ≠ 0 . At high
latitudes the boundaries are farther from Jupiter than for BIMF=0 while nearer the equator
they are closer to Jupiter. Reconnection can occur near the equator on the flanks of the
magnetopause when the IMF points in the y-direction. This can change the shape of the
obstacle. The addition of IMF By does not change the standoff distance at the bow shock
or the magnetopause. The standoff ratio remains 1.31.
SUMMARY AND DISCUSSION
We have used a combination of global magnetohydrodynamic simulations and
observations to form models of Jupiter’s magnetopause and bow shock. Rather than
fitting observed boundary crossings, we used all of the spacecraft observations at Jupiter
to determine the boundary positions in terms of the probability of being outside of the
bow shock or inside of the magnetopause. We used the global MHD models to define
boundary models, to define the boundary shapes and locations and to determine how they
vary with solar wind dynamic pressure.
The magnetopause at Jupiter and possibly the bow shock have two preferred locations,
one representing a compressed magnetosphere and the other an expanded magnetosphere.
The solar wind dynamic pressure in the neighborhood of Jupiter during the time interval
7
under study also has a bimodal distribution. While this contributes to the bimodal
distribution observed in the boundary positions the dynamic pressure changes are too
small to account for the large variation in the magnetopause position [Joy et al., 2002].
Internal pressure changes also are required. The bimodal distribution is less clear for the
bow shock. The speed with which the bow shock can adjust to changes in either the solar
wind or the obstacle will smear out the observed distribution.
In the left column of Figure 7 we have shaded the region between the 25 and 75
percentiles of being in the solar wind from the probabilistic model along with Galileo
observations from orbits not included in the original study and observations from the
Cassini flyby of Jupiter. Most of the magnetosheath observations are from the region
between the 25% and 75% curves. However, some of the observations especially those
from the Galileo G29 orbit suggest that the bow shock may extend farther from Jupiter
than in the MHD simulations. In the right panel we have plotted two bands of
magnetopause positions. The shaded areas are centered on the two preferred locations of
the magnetopause. The shading extends plus or minus one sigma (standard deviation)
about the two preferred locations. Here the models seem to be in reasonable agreement
with the new observations.
The boundary shapes on which the probabilistic models are based did not include the
IMF. We have examined simulations with both a purely north-south IMF and with an
IMF in the y-direction. Although the dynamic pressure has the largest effect the inclusion
of a non-zero IMF can make smaller changes in the location of the boundaries. For
instance for northward IMF dayside reconnection erodes the position of the
magnetopause and as a result the bow shock moves toward Jupiter as well. For southward
IMF the reconnection site moves to high latitudes and the boundaries move away from
Jupiter. However for all of the simulations the ratio of the standoff distances remains
significantly less than the typical values at the Earth. Both the solar wind Mach number
and the shape of the obstacle can influence the standoff distance. We compared
simulations of the Earth and Jupiter at the same Mach number and found that the ratio at
Jupiter (1.23-1.31) was smaller than at Earth (1.4-1.5). This indicates that the obstacle
shape is responsible for the differences in the standoff ratio and that Jupiter’s
magnetopause is less blunt than the Earth’s.
We would expect Jupiter’s boundaries to have strong polar flattening because of the
equatorial current sheet. However, the simulations suggest that this is not always the case.
Clear polar flattening is evident in zero IMF simulations for below average dynamic
pressure and when the IMF is southward. For above average dynamic pressure the
flattening decreases. For northward IMF dayside reconnection adds flux to the lobes
thereby moving the boundaries in the z-direction away from Jupiter reducing or
eliminating the polar flattening. At Jupiter’s orbit the IMF is primarily in the y-direction.
For an IMF in the y-direction we also find that the polar flattening is reduced.
In the simulations the magnetopause is generally found closer to Jupiter at dawn than
at dusk. This effect becomes smaller for smaller dynamic pressure when the
magnetopause is farthest from Jupiter. The dawn-dusk asymmetry seems to be related to
higher thermal pressure on the dusk side of the magnetosphere (Figure 1, Figure 5 and
Figure 6).
The bow shock shape and position also are influenced by the IMF. The largest effect
seems to be related to changes in the obstacle shape caused by reconnection. This can be
8
seen most dramatically in Figures 5 and 6 and Table 3. The addition of open magnetic
flux to the tail lobes and magnetosheath caused the “hat” in Figure 5 and the large
increase in the z position of the shock in Table 3. Similarly the inclusion of an IMF By
caused the magnetopause to twist (Figure 6) and that resulted in a twisted bow shock.
For given solar wind dynamic pressure and IMF conditions we have analyzed the
bow shock and magnetopause locations and shapes by assuming steady-state conditions.
In particular we ran the simulations until quasi-steady configurations resulted. However,
the Jovian magnetosphere in the simulations can be very dynamic [Fukazawa et al. 2005].
Changes in the dynamic pressure and IMF lead to large amplitude waves which distort
the boundary shapes as the system responds to the changes.
Acknowledgements: We would like to thank Mr. Joseph Mafi for help with the data
processing and display. Helpful comments by Lee Bargatze are gratefully acknowledged.
The work at UCLA was supported by grant NAG5-12769. 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.
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Geophys. Res., 90(A7),6275, 1985.
15. Smith, E. J., R. W. Fillius, and J. H. Wolfe, Compression of Jupiter’s magnetosphere
by the solar wind, J. Geophys. Res., 83, 4733, 1978.
16. Spreiter, J. R., A. L. Summers, and A. Y. Alksne, Hydromagnetic flow around the
magnetosphere, Planet. Space Sci. 14, 223, 1966.
17. Stahara, S. S., R. R. Rachiele, J. R. Spreiter, and J. A. Slavin, A three dimensional gas
dynamic model for the solar wind past non-axisymmetric magnetospheres:
Application to Jupiter and Saturn, J. Geophys. Res., 94(A10), 13,353, 1989.
18. Walker, R. J., and T. Ogino, A simulation study of currents in the Jovian
magnetosphere, Planet. Space Sci., 51, 295, 2003.
19. Watanabe, K., and T. Sato, Global simulation of the solar wind-magnetosphere
interaction: The importance of its numerical validity, J. Geophys. Res., 95, 75, 1990.
10
Figure 1. Pressure contours in the noon-midnight merdian plane (left) and dawn-dusk meridian
plane (right) for solar wind dynamic pressures of 0.045nPa, 0.09nPa, 0.18nPa, and 0.36nPa. The IMF
was set to zero for these simulations.
11
200
Bow Shock
200
a
100
Y0
Y0
-100
-100
-200
400
-200
-100
X
0
-200
100
Z
Z
100
100
200
X
0
100
e
200
-200
-100
X
0
0
100
-200
-100
400
c
300
Z
Z
100
100
200
X
0
100
f
Dawn-Dusk
300
0
-200
-100
200
-100
0
Y
100
200
0
-200
Noon-Midnight
b
300
400
-200
400
300
0
Equatorial
100
Magnetopause
d
-100
0
Y
100
200
figure 4
Figure 2. Fits to the bow shock and magnetopause shapes in Figure 1 evaluated at the 10th (outer),
50th(middle) and 90th percentiles (inner) of the observed solar wind dynamic pressure in the three
axis planes (rows). The distances are in Jovian radii. [Joy et al., 2002].
12
300
28
ULY O
CAS
200
29
32
30
27
100
31
(Y 2 + Z2)1/2
33
0
P11 O
VG1 i
VG2 i
ULY i
-100
P10 i
1
P11 i
Solar Wind
VG2 O
Magnetosheath
-200
VG1 O
-300
Magnetosphere
Joy 25/75
BS
Joy ±1-σ
MP
0
-200
P10 O
-100
JA
0
X
100
Figure 1
Figure 3. Trajectories of spacecraft near Jupiter shaded to show the region through which the
spacecraft were traveling. Trajectory segments in the solar wind are blue, those in the
magnetosheath are green and those in the magnetosphere are red. Trajectories for which data were
not available at the time of the Joy et al. [2002] study are black. The dark gray shading shows the
region between the 25 and 75 percentile probabilistic models for the bow shock. The light gray
regions on the right show plus or minus one standard deviation about the two preferred locations of
the magnetopause. (After Joy et al. [2002].)
Figure 4.The fraction of observations outside of the bow shock boundary surfaces (left column) and
the fraction of observations inside of the magnetopause boundary surfaces (right column). Solid lines
are single distribution fits and the dashed lines are bimodal distribution fits. The error bars are
discussed in the text. (After Joy et al., [2002])
13
Figure 5. Pressure contours in the noon-midnight meridian plane (top two plots) and the dawn-dusk
meridian plane (bottom two plots) from simulations with the northward and southward IMFs of
0.105nT and dynamic pressure of 0.011nPa.
14
Figure 6. Pressure contours in the dawn-dusk meridian plane for a simulation with a 0.42nT IMF in
the y-direction and solar wind dynamic pressure of 0.09nPa. The solid line gives the bow shock
position and the dashed line gives the magnetopause position from the fit to the MHD simulations for
0.09nPa and zero IMF.
G29
200
Solar Wind
Solar Wind
G29
200
Magnetosheath
Magnetosheath
Magnetosphere
Magnetosphere
150
150
Cassini
Cassini
I32
I32
100
(Y 2 + Z2)1/2
(Y 2 + Z2)1/2
C30
100
C30
I31
I31
50
50
I33
I33
J35
J35
0
0
A34
-50
0
50
X
100
Figure 7
1
A34
-50
0
50
X
100
Figure 7
1
Figure 7. Trajectories of spacecraft near Jupiter not included in the Joy et al. [2002] study. The
trajectories have been labeled to indicate the region in which the spacecraft was flying. Trajectory
segments in the solar wind are blue, those in the magnetosheath are green and those in the
magnetosphere are red. There were no data along the black trajectory segments. The gray shading
on the left shows the region between the 25 and 75 percentile probabilistic models for the bow shock.
The gray regions on the right show plus or minus one standard deviation about the two preferred
locations of the magnetopause. Distances are in Jovian radii.
15