JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 107, NO. A12, 1490, doi:10.1029/2001JA005071, 2002
Resistive MHD simulations of Ganymede’s magnetosphere
1. Time variabilities of the magnetic field topology
Andreas Kopp and Wing-Huen Ip1
Max-Planck-Institut für Aeronomie, Katlenburg-Lindau, Germany
Received 27 August 2001; revised 15 January 2002; accepted 11 April 2002; published 31 December 2002.
[1] The time-variable structure of Ganymede’s magnetosphere is studied by means of
resistive MHD simulations. Using the magnetometer measurements of the Galileo
spacecraft in the first few Ganymede flybys as examples, we find that the plasma flow
pattern inside the Ganymedian magnetosphere could be subject to significant changes.
Furthermore, the boundary of the polar cap dividing the open magnetic field region from
the closed magnetic field region could expand or contract as the Jovian magnetic field
swings inward and outward. Such an effect could be related to the Hubble Space
Telescope observations of large time variability of the atomic oxygen airglow near the
INDEX TERMS: 2732 Magnetospheric Physics: Magnetosphere
polar regions of Ganymede.
interactions with satellites and rings; 5737 Planetology: Fluid Planets: Magnetospheres (2756); 6218
Planetology: Solar System Objects: Jovian satellites; 7827 Space Plasma Physics: Kinetic and MHD theory;
7843 Space Plasma Physics: Numerical simulation studies; KEYWORDS: Ganymede, Jupiter, magnetosphere,
MHD simulations, polar caps, satellite magnetosphere interactions
Citation: Kopp, A., and W.-H. Ip, Resistive MHD simulations of Ganymede’s magnetosphere, 1., Time variabilities of the magnetic
field topology, J. Geophys. Res., 107(A12), 1490, doi:10.1029/2001JA005071, 2002.
1. Introduction
[2] The Galilean satellites of Jupiter have been found to
have very interesting properties and interaction processes
with the Jovian magnetosphere by the Galilean Orbiter
mission [Neubauer, 1998]. Of these, Ganymede occupies
a special place because of its strong intrinsic magnetic field
[Kivelson et al., 1996, 1997, 1998]. Close flyby measurements by several other instruments have indicated the
presence of a hydrogen plasma outflow [Frank et al.,
1997] (but cf. also the reinterpretation by Vasyliunas and
Eviatar [2000]) and the absorption effects of energetic
charged particles at the polar region [Williams et al.,
1997]. Furthermore, the Ultraviolet Spectrometer (UVS)
experiment showed the existence of an extensive halo of
atomic hydrogen [Barth et al., 1997]. This atmospheric
emission in Lyman a complemented by the Hubble Space
Telescope (HST) observations of the oxygen airglow features in 1304 Å and 1356 Å [Hall et al., 1998; Feldman et
al., 2000] suggested that the icy surface of Ganymede must
be subject to intense sputtering processes by energetic ions
[Ip et al., 1997; Cooper et al., 2001]. The atomic hydrogen
halo and the oxygen emissions are hence likely generated
partly by surface sputtering and partly by thermal sublimation [Spencer, 1987]. This effect is consistent with the
difference in the color ratios between the high- and lowlatitude regions [Hillier et al., 1996; Denk et al., 1999]. This
suggests that the polar caps of Ganymede could be the result
1
Now at Institute of Astronomy and Institute of Space Science, National
Central University, Chung-Li, Taiwan.
Copyright 2002 by the American Geophysical Union.
0148-0227/02/2001JA005071$09.00
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of plasma precipitation along the open field lines [Johnson,
1997].
[3] In the most recent HST observations by Feldman et
al. [2000], significant orbit-to-orbit variations in the oxygen
emission were found. These authors made the interesting
suggestion that such time variations could be related to the
changes in the boundary (termed separatrix) dividing the
open magnetic field region (with magnetic field lines
connected to the Jovian magnetosphere) from the closed
magnetic field region (with magnetic field lines anchored to
the northern and southern hemispheres of Ganymede). That
is, the topology of Ganymede’s magnetosphere could be
substantially altered by the external Jovian magnetic field
and the warped current sheet. In order to explore this issue,
a series of MHD simulations with different plasma parameters were performed for the Ganymede-Jupiter interaction.
In section 2, the numerical procedure and the general
property of the Ganymedian magnetosphere will be
described. In section 3, we will discuss the time variations
of the magnetospheric configuration of Ganymede under
different plasma conditions – using the G2, G7 and G8
encounters of the Galileo observations as examples. The
results are summarized briefly in the discussion section.
2. MHD Simulations
[4] The numerical method has been described for the
application to Titan in Kopp and Ip [2001]. For the
application to Ganymede, this model has been adapted, in
particular taking into account that Ganymede has a much
less dense atmosphere and a significantly (about three
orders of magnitude) smaller mass-loading effect (actually
mostly sputtering). The numerical code integrates the basic
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41 - 2
KOPP AND IP: TIME VARIABILITIES OF GANYMEDE’S MAGNETOSPHERE
Table 1. Physical Parameters
Bz ¼ BðzO6Þ þ Baz þ Bbz =r:
Quantity
Symbol
Value
Magnetic field (background)
Particle density
Temperature
Length scale
Average mass number
Mass loading rate
Flow velocity
Plasma beta
Alfvén Mach number
Sound Mach number
B0
n0
T0
L
A
112 nT
50 cm3
200 eV
2634 km
1
1.0 1026 s1
120 km s1
0.65
0.35
0.47
Q_
v0
b
MA
MS
ð7Þ
The additional field is used to represent the Jovian current
sheet. Obviously, a current-free field cannot be more than an
approximation of the current-sheet, but has the advantage to
a
equations of the resistive MHD which read in normalized
form:
@r
¼ r ðrvÞ þ Qc ;
@t
ð1Þ
@ ðrvÞ
1
¼ r ðrv vÞ rP þ j B þ Qs ;
@t
2
ð2Þ
@B
1
¼ r ðv BÞ ðrh j þ hBÞ;
@t
S
ð3Þ
@P
h
¼ r ð PvÞ þ ðg 1Þ Pr v þ j2 þ QE :
@t
S
ð4Þ
Here, r denotes the plasma density, v is the flow velocity,
and P is the gas pressure. The plasma is assumed to be an
ideal gas with the adiabatic index g = 5/3. B is the magnetic
field, j denotes the electric current density and h is the
resistivity with the Lundquist number S. The source terms
arising from mass loading (with the plasma source term r_ ) in
the three balance equations are Qc = r_ , Qs = r_ v and QE = (r_ /
r)P, respectively. Because of the smallness of r_ (cf. the
parameters given below), the source terms Qs and QE were
neglected. The balance equations are integrated by a
leapfrog scheme, the induction equation (3) by a DufortFrankel scheme. The coordinate system is a cylindrical
system with Jupiter at the origin, r points radially outward,
j is the direction of corotation, and z is parallel to Jupiter’s
spin axis. For a more convenient representation, we use in
the figures the usual Cartesian coordinate system with x
pointing into the direction of corotation and y pointing
towards Jupiter, z is the same direction as above.
[5] The initial magnetic field configuration is described
by Jupiter’s dipole field, where the O6 model by Connerney
[1993] was used. The most accurate model for the nondipole part of the Jovian magnetic field, in particular near
the orbits of the satellites and within the Jovian current
sheet, was given by Khurana [1997]. Additional models for
the field near Ganymede can be found in Cooper et al.
[2001] and Stone and Armstrong [2001]. However, for
numerical reasons, we cannot use the model by Khurana
[1997]. Instead, the O6 field was modified by the addition of
a current-free field:
Br ¼ BðrO6Þ þ B0r =r þ B0x cos j þ B0y sin j;
ð5Þ
Bj ¼ BðjO6Þ þ B0j =r B0x sin j þ B0y cos j;
ð6Þ
b
Figure 1. (a) Ganymede’s magnetic field configuration in
the x-z-plane for the simplified case of two aligned dipole
fields. The dashed lines show the unperturbed magnetic
field lines (initial state of the simulations), the solid lines
show the influence of the magnetospheric plasma flow
(final state). Note also the reconnection taking place at the
upstream (and probably also at the downstream) side of
Ganymede. (b) The flow pattern in the equatorial plane of
Ganymede for the final state. The solid and dashed circle
indicate Ganymede’s surface and mass loading region,
respectively.
KOPP AND IP: TIME VARIABILITIES OF GANYMEDE’S MAGNETOSPHERE
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41 - 3
Figure 2. The components and the amount of the magnetic field for flyby G2. The measurements by
Kivelson et al. [1998] are shown in grey, the results of the numerical simulations are shown in black.
be self-consistent, so that the initial configuration is an
analytical equilibrium. For the computation of the six
parameters B0r, B0j, B0x, B0y, Baz, and Bbz, the model field is
fit to the Galileo data in all three components at two points
along the trajectory, near the beginning and the end of the
respective flyby. To this field, Ganymede’s internal dipole
field according to Kivelson et al. [1996] was added. For the
normalization of the MHD equations, we used the following
quantities for Ganymede’s immediate environment, which
are listed in Table 1 [Frank et al., 1997; Kivelson et al.,
1996, 1997, 1998]:
[6] The initial configuration is a current-free, isorotating
magnetosphere. During the simulation, the plasma is slowed
down to zero velocity within Ganymede by means of a timedependent function similar to that used by Kopp and Ip
[2001] for Titan. The simulations were continued until a
steady state was achieved, which of course is no longer
current-free. For better illustration, the first figure shows
results for the case of the superposition of two vacuum
parallel dipole fields which magnetic moments have only
z-components.
[7] The magnetic field and the velocity for this configuration are shown in Figure 1. Figure 1a shows the change of
Ganymede’s magnetic field configuration from a symmetric,
dipolar structure to a slightly bent structure under the influence of the corotating plasma flow. In this simplified case, the
polar cap boundary separating the open and closed field
regions is located at about 20 degrees latitude. Within the
polar cap region where the magnetic field lines coming out of
Ganymede are connected to the Jovian field lines, the plasma
flow velocity is highly reduced to a value of about 40 km/s (as
it turned out in the computation), compared to the background
value of 120 km/s. Such a decrease of the flow velocity and
hence of the corotating electric field therein is consistent with
the Galileo energetic particle detector’s (EPD) observations
by Williams et al. [1997]. Strictly speaking, the authors
performed loss cone measurements of energetic particles,
but we use their values here only for a rough estimate.
[8] The pattern of plasma flow convection in the equatorial plane is illustrated in Figure 1b. As expected, the
equatorial plasma flow inside the magnetopause is in
opposite direction to the corotation. The flow pattern
basically traces the velocity field of the cold plasma. For
charged particles of higher energy injected from the Jovian
magnetosphere, their trajectories will be determined by the
drift motion under the influence of the magnetic field
gradient effect [Volwerk et al., 1999].
3. Time Variations
[9] Because of the tilting of the Jovian current sheet at
Ganymede’s orbital distance of about 15 Jupiter radii, the
corresponding magnetospheric interaction could be strongly
modulated by the changing ambient magnetic field geometry. This phenomenon was amply demonstrated by the
magnetometer measurements in the first four Ganymede
flybys [Kivelson et al., 1998]. The effect of induced
magnetic fields [Neubauer, 1998, 1999] will be neglected
here due to the presence of Ganymede’s strong internal
dipole field of about 750 nT at the equator, but will be
important for the other Galilean satellites, in particular for
Europa where no intrinsic field is present. As an example,
the superposition of the numerical results and the magnetic
field measurements by Kivelson et al. [1998] is shown for
flyby G2 in Figure 2. The comparison shows a very good
agreement between measurements and simulations. A comparison of the different flybys shows the time variability of
Ganymede’s magnetosphere. For example, the Jovian field,
assumed locally as homogeneous, was about 120 nT and
oriented by about 50 degrees outward during the G2
encounter while it was of similar magnitude but the tilting
was 50 degrees inward instead during the G7 flyby. On the
other hand, the Jovian field was pointing almost vertically at
G8 [Kivelson et al., 1998]. Figure 3 shows the simulation
results for the Galileo flybys G2 (left column), G7 (central
column), and G8 (right column). The first two panels
summarize the topological behaviors of the magnetic fields
in two perpendicular planes, the y-z-plane in Figure 3a and
the x-z-plane in Figure 3b, for the magnetic field model of
Jupiter as described above. The third panel (Figure 3c)
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KOPP AND IP: TIME VARIABILITIES OF GANYMEDE’S MAGNETOSPHERE
(a)
(b)
(c)
Figure 3. (a) Magnetic field lines for the model field for the three encounters G2 (left), G7 (center) and
G8 (right), projected onto the y-z-plane. (b) same, but projected onto the x-z-plane. (c) Flow patterns in
the equatorial plane. The length scale is 5 Ganymede radii in each direction.
shows the flow patterns, which also show a strong variation
with the Jovian magnetic field. It is therefore clear that these
three magnetic field configurations cover a wide range of
possible magnetospheric conditions.
[10] With regard to the issue of the oxygen airglow
observed by HST, the large swing of the polar magnetic field
lines is expected to bring about significant changes in the
shape of the polar cap. The latitudinal locations of the polar
cap for the G2, G7 and G8 encounters are displayed in
Figure 4. It can be seen that the largest difference exists
between G2 and G7 at j 180 degrees (opposite to the
Jupiter-facing side) with J 20 degrees. The expansion
and contraction of the polar cap as Ganymede moves around
Jupiter should therefore facilitate temporal changes of the
effective area and location of magnetospheric particle precipitation. A direct comparison with observations is, at least
in the present state, difficult to perform, but will be a topic of
subsequent investigations. As a rough estimate we can
compare the size of the polar cap detected by Feldman et
al. [2000] for the flyby G2 with the numerical results and see
that in both cases we obtain a value around J = 45 near j =
270, indicating that our numerical results are at least in the
correct range.
4. Discussion
[11] In this paper, we report how the magnetic field
configuration of Ganymede’s magnetosphere could change
under different external plasma conditions. Our simulation
results show how the polar cap region of Ganymede mainly
shifts around in surface position but could also expand or
KOPP AND IP: TIME VARIABILITIES OF GANYMEDE’S MAGNETOSPHERE
Figure 4. The boundaries between open and closed field
lines for the three configurations shown in Figure 3: G2:
thin, G7: thick, and G8: dotted. J and j are angular
coordinates on Ganymede’s surface, where j is in Western
longitude with j = 0 representing the Jupiter-facing part of
Ganymede.
contract as a function of the orientation of the Jovian
magnetic field. If the same process could modulate the
ion sputtering rate, the large variations of the atomic oxygen
emission at the polar regions discovered by Feldman et al.
[2000] might be partially explained. It is, however, possible
that the observed emission changes could be localized in
nature and that field-aligned particle acceleration energies of
in the keV range driven by nonstationary magnetic field
reconnection could have a role to play.
[12] Acknowledgments. The authors would like to thank Andreas
Lagg and Norbert Krupp for useful discussions, and Andreas Lagg
especially for providing the trajectories of the Galileo spacecraft. This
project was supported by the Bundesministerium für Bildung und Forschung (BMBF) through the German Space Agency, DLR (Bonn, Germany), under 50 QJ 94010 and the National Council of Taiwan under NSC
89-2111-M-008-017.
[13] Michel Blanc and Lou-Chuang Lee thank Martin Volwerk and
John F. Cooper for their assistance in evaluating this paper.
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41 - 5
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W.-H. Ip, Institute of Astronomy and Institute of Space Science, National
Central University, Chung-Li, 320, Taiwan. ([email protected])
A. Kopp, Max-Planck-Institut für Aeronomie, Max-Planck-Straße 2,
37191 Katlenburg-Lindau, Germany. ([email protected])