Icarus 143, 397–406 (2000)
doi:10.1006/icar.1999.6252, available online at http://www.idealibrary.com on
Interaction of Mercury with the Solar Wind
K. Kabin, T. I. Gombosi, D. L. DeZeeuw, and K. G. Powell
University of Michigan, Ann Arbor, Michigan 48109
E-mail: [email protected]
Received April 7, 1999; revised August 11, 1999
We present the structure of the hermean magnetosphere obtained
by a global three-dimensional MHD simulation. The magnetic field
of Mercury is strong enough to form a permanent magnetosphere
under typical solar wind conditions. Mercury does not have a substantial atmosphere or ionosphere which makes the magnetosphere
unique in the solar system. We study in detail the hermean magnetosphere for the typical solar wind parameters at perihelion and
the nominal Parker spiral interplanetary magnetic field (IMF). Although the magnetosphere of Mercury is qualitatively similar to
Earth’s magnetosphere, its much smaller size results in many quantitative differences. For example, the magnetic field lines of Mercury are closed only for latitudes less than ≈50◦ , while for Earth
the similar latitude will be ≈75◦ . We find that a direct interaction
of the solar wind with the surface of the planet and the formation
of a “bald” subsolar spot become possible if the solar wind speed
is increased by a factor of 2.5 of if density is increased by a factor
of 9 as compared with the nominal values. We present the results
of our simulation for this case as well, although our conclusion is
that direct interaction of Mercury with the solar wind is a rare phenomenon. °c 2000 Academic Press
Key Words: Mercury; magnetospheres.
1. INTRODUCTION
Mercury is a very unusual planet in the solar system. It is
the one closest to the Sun, it has the largest mass density of all
the terrestrial planets, and the eccentricity of its orbit (0.206)
is the second largest (after Pluto). Mariner 10 is the only spacecraft to have visited the vicinity of the planet. It was launched on
November 2, 1973, and had three flybys of Mercury: March 29,
1974, September 21, 1974, and March 16, 1975. Because of the
features of the Mariner 10 trajectory, all of the flybys occurred
when Mercury was close to its aphelion, in an almost identical
position with respect to the Sun. During the first encounter the
spacecraft passed through the wake behind the planet with a
closest approach distance of 707 km (0.3RM ) from the surface.
The highest measured magnetic field intensity during this pass
was about 100 nT and the structure of the wake suggested the existence of an intrinsic magnetic field. During the outbound part
of this passage the magnetic field fluctuated very rapidly, making it hard to estimate the strength of the dipole. This dynamic
behavior of the magnetic field is usually interpreted as substorm
activity (Siscoe et al. 1975). The second passage of Mariner 10
was a remote one with a distance of about 50,000 km upstream
of the planet, well beyond its magnetosphere. The third flyby of
Mariner 10 was specifically aimed at confirming the existence
of the intrinsic magnetic field of Mercury. During this pass the
solar wind conditions were much quieter than during the first
flyby and high-quality magnetic field measurements were obtained. The spacecraft trajectory crossed the high latitudes of
Mercury, with the closest approach being 327 km. During this
flyby the magnetic field peaked at about 400 nT and it clearly
displayed its intrinsic character (Ness et al. 1975). The origin of
the internal field is still uncertain; see Schubert et al. (1988) for
a review.
Soon after the Mariner 10 data were obtained. Ness et al.
(1975) estimated the dipole moment of Mercury to be between
3
284 and 358 nT RM
. Mercury’s magnetic moment has the same
polarity as the present terrestrial one and it is apparently more
or less aligned (within 20◦ ) with the rotation axis of the planet.
Later, a number of authors tried to infer further information
about the magnetic field of Mercury using more sophisticated
models (e.g., Jackson and Beard 1977, Whang 1977, Ng and
Beard 1979). The available estimates for the magnetic moment
of Mercury differ by almost a factor of 2. This uncertainty arises
because the magnitudes of the magnetospheric currents are unknown and because of the very limited spatial coverage provided
by the Mariner 10 flybys. Although we do not attempt a direct
comparison with the Mariner 10 data in this paper, our MHD
model may be used to gain a better understanding of the currents
in the hermean magnetosphere and to improve the estimates for
Mercury’s magnetic field.
During the Mariner 10 flybys, measurements of thermal plasma electrons were also made (Ogilvie et al. 1977). The interpretation of these data was complicated by a number of technical
difficulties. However, Ogilvie et al. (1977) provide estimates for
the standoff distances of the bow shock and the magnetopause
which are consistent with the results inferred from the magnetometer measurements of Ness et al. (1975). Electron data
allowed Oglivie et al. (1977) to conclude that Mercury’s magnetosphere is similar to a scaled version of that of Earth in a
number of aspects. The electron distribution in the hermean
magnetosphere was found to be similar to that near Earth by
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KABIN ET AL.
Christon (1987), who also pointed out that the electron distribution is nonthermal and can be better described by a lorentzian
distribution function than by a maxwellian. This means that our
simulation results should be considered with care, since thermal
equilibrium is one of the assumptions of the MHD formalism.
We also do not consider in our model turbulence which may be
rather high in the vicinity of the planet according to Roux et al.
(1997) and may be the cause of the lorentzian distributions (Ma
and Summers 1998).
A tenuous atmosphere of Mercury was reported by Broadfoot
et al. (1976) based on Mariner 10 observations of airglow and
occultation measurements. They positively identified helium,
atomic hydrogen, and oxygen as the constituents of the atmosphere. Later, Potter and Morgan (1986) discovered sodium and
potassium emissions coming from the atmosphere of Mercury.
For a review of different issues related to the hermean atmosphere one is referred to Hunten et al. (1988).
The thin atmosphere of Mercury cannot produce a classic
highly conducting ionosphere. However, the estimates of Cheng
et al. (1987) and Ip (1993) suggest that heavy atom (mostly
sodium) pickup may be important close to the planet. Glassmeier
(1997) discusses the role of pickup currents, surface conductivity, and tenuous ionosphere on the magnetospheric interaction
of Mercury.
From the Mariner 10 measurements, Slavin et al. (1997) inferred a field-aligned current on the order of 106 A, which is
comparable to typical values in Earth’s magnetosphere. The existence of such a high field-aligned current requires a sufficiently
conducting layer close to the surface of Mercury, which is unlikely to be provided by the rarefied ionosphere of the planet.
Alfvén waves (Glassmeier 1996) and a photoelectron sheath
(Grard 1997) were considered as possible conducting mechanisms, but neither of these theories has yet been tested. We
neglect the effects of both pickup currents and a possible conducting layer in the present model since the global features of the
magnetosphere are probably determined by the magnetic field
of Mercury.
Mariner 10 discovered dynamic variations of the magnetic
field, plasma, and energetic particle data during the outbound
part of the first flyby. This activity has many characteristics
of a substorm (e.g., Siscoe et al. 1975, Eraker and Simpson
1986, Slavin et al. 1997), although alternative suggestions have
been made as well (Luhmann et al. 1998). This phenomenon
is a very attractive possible application of MHD modeling, because of the lack of significant ionosphere and short temporal scales (on the order of 1 min) in the hermean magnetosphere. Substorms on Mercury may give a clue to the external
triggering, which is much more obscure in Earth’s magnetosphere because of its very large inertia. Understanding the possible substroms on Mercury requires, however, further observations and a reliable model of the basic states of the hermean
magnetosphere. Therefore, in this work we consider only steadystate solutions, applicable in the case of quite solar wind
conditions.
The magnetic field of Mercury is large enough to keep the solar wind away from the surface of the planet under normal conditions. Thus, a magnetosphere is formed. Siscoe and Christopher
(1975) studied the magnetopause standoff distance for Mercury
using a simple pressure balance between the solar wind and an
intrinsic dipole. A very interesting question is whether the magnetopause can be pushed within a typical ion gyroradius from
the surface, when a direct interaction of the solar wind with
the surface begins. Siscoe and Christopher (1975) concluded
that the solar wind can strike the surface of Mercury only on
very infrequent occasions. On the other hand, Slavin and Holzer
(1979) pointed out that dayside magnetic reconnection can significantly reduce the magnetopause standoff distance at Mercury compared with the predictions of Siscoe and Christopher
(1975). They concluded that the magnetopause will erode due to
reconnection and the direct interaction of the solar wind with the
surface becomes much more frequent. At the same time, Hood
and Schubert (1979) noted that the dynamic compression of the
dayside magnetosphere by the solar wind may be effectively opposed by induction currents in the mantle. Goldstein et al. (1981)
attempted to combine all these effects and arrived at probabilities
which are intermediate among the preceding works.
In this paper we present the first global MHD model of the
hermean magnetosphere and discuss our results for several interplanetary magnetic field (IMF) configurations and solar wind
parameters. In general, the magnetosphere has a complicated
essentially three-dimensional structure, with the magnetic field
lines being very strongly twisted. We find that the magnetic field
lines of Mercury are closed only for latitudes less than ≈50◦
which means that results obtained by scaling Earth’s magnetosphere for Mercury must be treated very carefully. We also
present a calculation in which the solar wind reaches the surface of Mercury directly; however, we conclude that it is a rare
phenomenon.
2. MODEL
We apply an ideal single-species MHD model to describe the
interaction of the solar wind with Mercury. Similar models have
been developed for the interaction of comets with the solar wind
(Gombosi et al. 1996); plasma flow past Venus (DeZeeuw et al.
1996), Io (Combi et al. 1998), and Titan (Kabin et al. 1999); and
global simulation of the heliosphere in the magnetized very local
interstellar medium (Linde et al. 1998). The numerical aspects
of the method are discussed at length in the above papers and in
DeZeeuw and Powell (1993) and Powell (1994).
In many space physics applications the usage of ideal MHD
is somewhat restricted by finite gyroradius effects (Kabin et al.
1999). Fortunately, the gyroradius of a solar wind proton based
on a typical thermal speed near Mercury is just about 20 km.
This is less than 1% of Mercury’s radius, which means that ideal
MHD is a reasonably good approximation. Gyroradius can be
much larger for heavier ions, such as sodium, which is likely
to be a significant component in the hermean magnetospheric
399
MAGNETOSPHERE OF MERCURY
plasma. For example, Cheng et al. (1987) estimated that the
fraction of sodium atoms in the magnetosphere can be as large
as 50%. A recent work of Othmer et al. (1999) suggests a smaller
percentage of 14% which is rather close to the estimates of Ip
(1986). Our first modeling attempt neglects completely both the
multifluid and finite gyroradius effects which certainly affect
the details of Mercury’s interaction with the solar wind. Other
non-MHD effects, such as deviation from thermal equilibrium
(Christon 1987), may be also important, but we expect the global
structure of the hermean magnetosphere to be well described by
our model.
The conservative form of the dimensionless single-fluid ideal
MHD equations is



ρu
ρ
∗



∂ 
ρu + ∇ ·  ρuu + p I − BB  = 0,




uB − Bu
∂t B
E
u(E + p ∗ ) − B(B · u)

where ρ is mass density, u is plasma velocity, p is pressure, B
is magnetic field vector, and γ is the specific heat ratio. In addition we use p ∗ = p + B 2 /2, E = ρu 2 /2 + p/(γ − 1) + B 2 /2.
Finally, I is a unit 3 × 3 matrix. We neglect the pickup process
at Mercury; therefore, there is no source term in the MHD equations.
This system is solved using a higher-order Godunov-type
finite-volume method on an unstructured Cartesian grid with
adaptive mesh refinement. The cell structure (“octree”) provides
very good resolution in the interaction region, while allowing the
total simulation box to be very large. The adaptive grid structure
is an important advantage, because in this problem we have a
number of thin interfaces, such as bow shock and contact discontinuity (magnetopause), which ought to be well resolved for
our simulation to produce a correct solution.
The boundary conditions on the surface were imposed by using cut cells (DeZeeuw and Powell 1993), which allow secondorder (piecewise linear) reproduction of the geometry of the
boundary. The physical properties of the surface of Mercury
determine how the fluxes through the cut faces are treated in
the code. We assumed no change in the magnetic field across
the surface (zero gradient boundary condition). Plasma inflow
was allowed into the surface of Mercury, but no outflow was
permitted. Thus, Mercury in our simulation was approximated
by an absorbing nonmagnetic (electrical isolator) sphere; its radius was taken to be 2440 km. We did not include Mercury’s
rotation because it is very slow (rotation period is about 60
days) and no plasmasphere exists around the planet (Glassmeier
1999).
Because the hermean magnetosphere is immersed in a dynamic solar wind, time-dependent effects may play a very important role. However, in this first simulation we restrict ourselves to steady-state solutions. Because of this, we also do not
need to consider induction in a conductive mantle of the planet
(Hood and Schubert 1979) or magnetospheric reconfiguration
currents (Glassmeier 1999), which will be important if the IMF
conditions change with time.
The plasma flow conditions around Mercury vary greatly depending on the position of the planet along its orbit and on solar
activity. As one of the extreme cases we consider Mercury at perihelion, at the distance of about 5.8 × 107 km from the Sun. The
average solar wind parameters at this position are: plasma density 73 cm−3 , plasma temperature 14 eV, magnetic field 46 nT,
solar wind speed 430 km/s, ion-acoustic sound speed 74.2 km/s,
Alfvén speed 120 km/s, mean molecular mass ∼1 amu, specific heat ratio 1.67. The corresponding Mach number is 5.8 and
Alfvénic Mach number 3.6. Parker’s spiral magnetic field forms
an angle of 20◦ with the solar wind direction. We assumed the
intrinsic magnetic moment of the planet to be a dipole of 350 nT
3
aligned with the Z axis.
RM
3. RESULTS AND DISCUSSION
Both Earth’s and Mercury’s magnetospheres result from the
interaction of the solar wind with a dipole roughly perpendicular
to the direction of the solar wind. This is the explanation for the
similarities in the basic structure of the two magnetospheres.
The differences arise because the typical solar wind parameters
are different and the magnetic field of Mercury is much smaller
than that of Earth.
Because of the high eccentricity of Mercury’s orbit, the variability of the mean solar wind parameters near Mercury is very
large. Unlike the magnetospheres of giant planets which have
much larger spatial scales and significant ionospheres which
slow down magnetospheric convection, even small changes in
the solar wind parameters will have a nearly immediate effect
on Mercury’s environment (Luhmann et al. 1998). In this paper we study only several steady-state solutions, which are the
“basic states” of the hermean magnetosphere to which it would
relax if the conditions in the solar wind were steady for a long
enough time. This is, of course, a simplified approach. We do
not present here solutions for northward and southward IMF for
which a typical structure of a magnetosphere is reasonably well
understood (e.g., Dungey 1961, Song et al. 1999). Although
these are important benchmark calculations, the corresponding
conditions in the solar wind occur too seldom to be statistically
important at Mercury.
First, we present the results for a nominal Parker spiral (Fig. 1).
This case is to a certain degree analogous to that considered for
Earth by White et al. (1998), although differs from it by a strong
positive Bx component. In this case, the solar wind goes through
a fast shock approximately 2.2 Mercury radii upstream from the
center of the planet. At approximately 1.6RM in the subsolar direction there is a magnetopause, which appears in our simulation
as a steep density gradient. We note that just like in any other
MHD simulation, our magnetopause is not a nonpenetrable surface, although the flow across it is relatively small as it can be
concluded from the streamlines in the Fig. 1. Behind it there is a
magnetic cavity, in which the plasma is controlled by Mercury’s
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KABIN ET AL.
FIG. 1. The X –Z (north–south) and X –Y (equatorial) cuts through the simulation showing density (color code) and plasma streamlines (upper panels) and
logarithm of the normalized magnetic field intensity (color code) and field lines (lower panels) for the nominal Parker spiral. The flow is along the X axis from left
to right. The upstream magnetic field is in the equatorial plane tilted 20◦ with respect to the X axis. The dipole moment of Mercury is along the Z axis.
magnetic field. The bow shock and magnetopause distances in
our simulation are somewhat larger than those estimated from
the Mariner 10 flybys as 1.8RM and 1.4RM , respectively, by
Ogilvie et al. (1977) who used a scaled model of Earth’s magnetosphere. We believe that these differences can be attributed
to the change in Alfvénic Mach number from Earth to Mercury,
which cannot be accounted for in a scaled model.
The general structure of the hermean magnetosphere may be
inferred from Fig. 1, which shows the plasma density and magnetic field intensity in the equatorial and north–south planes.
Note that these planes are not planes of symmetry for the plasma
flow because the magnetic field is tilted with respect to the velocity. Superimposed on the density color code are shown the
plasma streamlines and, similarly, above the magnetic field intensity the magnetic field lines. We note that these streamlines
and field lines are plotted in the two-dimensional (2D) planes
and completely ignore the component of the vector field perpendicular to the plane. Although 2D field lines do not always reflect
exactly the topology of the 3D field lines and streamlines, many
important features of the magnetosphere of Mercury can be seen
more easily from 2D pictures. For example, in the north–south
cut in Fig. 1, the magnetic field lines show clearly that there is
reconnection on the day side of the planet as well as on the night
side. On the day side it occurs in the southern hemisphere and
on the night side in the northern one. In both instances it is cusp
reconnection; however, for Mercury the cusps are so large that
the reconnection points are in fact not that far from the equatorial plane. One should keep in mind that the actual reconnection
positions are somewhat shifted from the points where they appear in the 2D figures of the north–south plane because of the
component of the magnetic field perpendicular to the XZ plane.
In steady state, the dayside cusp reconnection does not result
in a net transfer of magnetic flux into the tail. Instead, solar
wind-laden flux tubes simply replace older tail flux tubes as is
discussed as more detail later.
Figure 2 shows the actual 3D magnetic field lines. On the left is
a view of the southern hemisphere of Mercury, while on the right
is shown the northern hemisphere. In this figure, the last closed
MAGNETOSPHERE OF MERCURY
401
FIG. 2. Three-dimensional structure of the magnetosphere of Mercury for the nominal Parker spiral. Left: view of the southern hemisphere of the planet; right
view of the northern hemisphere. The background color is the logarithm of magnetic field intensity in a cross-tail plane 8RM downstream. The X axis is shown
by a black line with tick marks every 2RM . On the surface of Mercury are indicated the equator and the subsolar and terminator meridians. The colored lines are
the field lines: brown, open on both ends; magenta, closed; blue, open connected to the northern hemisphere of Mercury; white, open emerging from the southern
hemisphere.
magnetic field lines are shown in magenta; the IMF field lines,
which are open on both ends, are brown; field lines connected to
the northern hemisphere of Mercury are blue; and the field lines
originating from the southern hemisphere of Mercury are white.
On the left both brown and blue field lines start in the equatorial
plane upstream. On the right the blue field lines are uniformly
distributed along the cusp region; they belong to the different
upstream horizontal planes. On the left in Fig. 2 one can clearly
see the magnetic field lines originating in the southern polar cap
(white lines). The color code is the logarithm of the magnetic
field intensity (the same color code as Fig. 5) in the YZ plane
8RM downstream. For easier interpretation, the grid structure in
that plane is also shown. On the surface of Mercury are drawn
the equator and the subsolar and terminator meridians. The X
axis, which is the direction of the solar wind flow, is shown by
a thick black line with ticks marking 2RM increments.
The first open field lines from the northern hemisphere of
Mercury can be traced upstream of the bow shock. By doing
so we can define an area in the YZ plane upstream of the bow
shock to which the polar cap of Mercury is mapped by the magnetic field lines. Figure 3 shows this area in a slice X = 3RM .
The choice of a particular YZ plane is rather arbitrary since the
magnetic field is uniform upstream of the bow shock. Thus, if
another plane were chosen, the area in Fig. 3 would only be
shifted along the Y direction without changing its shape. The
2
, which correstotal area of the region in Fig. 3 is about 22RM
6
ponds to a magnetic flux of 5.5 × 10 Wb. The extent of the area
in Fig. 3 in the Y direction is close to 12RM . The solar wind
direction is perpendicular to the YZ plane; because the IMF is
tilted 20◦ degrees with respect to the solar wind velocity, an IMF
line travels in the YZ plane along the Y direction with the speed
of VSW tan 20◦ . Therefore, it takes for a field line about 3 min
to cross the area in Fig. 3 from left to right. This is the longest
time an IMF line may be connected to the northern polar cap
of Mercury and may be viewed as a characteristic time scale
of the hermean magnetosphere. The circles in Fig. 3 designate
the points where the magnetic field lines entering the northern polar cap of Mercury at particular longitudes cross this YZ
plane (blue lines from the right panel of Fig. 2). Zero marks
the line connected to the subsolar point of the polar cap; the
increment between adjacent circles is 30◦ longitude. Clearly, a
FIG. 3. Mapping of the polar cap on the slice X = 3RM by the magnetic field
lines (bold line). The thin horizontal lines with arrows are the two-dimensional
magnetic fields lines in this YZ plane. The circles represent the positions of the
magnetic field lines originating from the northern polar cap at 30◦ increments
in longitude, 0 being the noon meridian.
402
KABIN ET AL.
uniform field line distribution over the polar cap maps into a very
nonuniform distribution in the upstream YZ plane. A similar plot
can be made by tracing the open field lines originating from the
southern polar cap for some YZ plane far enough downstream,
where we can consider the plasma flow to be uniform again. In
the steady state, the two areas are the same, which reflects the
conservation of the magnetic flux. The plot of the upstream area
connected to the polar cap may be very useful, for example, for
estimates of the flux of energetic particles reaching the surface of
Mercury, although this calculation is not within the scope of our
paper.
We can think about the evolution of a particular IMF field line
in the following manner. As it is advected by the solar wind, it
travels along a certain horizontal line in Fig. 3. As long as this
line does not cross the bold curve in Fig. 3, the IMF field line
is opened on both ends. When it crosses the curve, it reconnects
with one of the original dipole field lines in the northern hemisphere. The corresponding dipole field line becomes open and
is dragged into the tail, like one of the white lines in Fig. 2 emanating from the southern polar cap. Then, as long as the IMF
field line stays inside the domain in Fig. 3 it is connected to the
planet and follows a certain path in the northern polar cap. Eventually it crosses the closed curve in Fig. 3 once more. At this
moment it reconnects once more with an open field line originating from the southern polar cap and becomes open on both ends
again.
One can see from Figs. 1 and 2 that the magnetosphere of
Mercury is very “open.” Figure 4 shows the boundary of the
polar cap in the northern hemisphere on Mercury. As expected,
FIG. 4. Boundary between open and closed magnetic field lines in the
northern hemisphere.
the polar cap is asymmetric and is significantly larger on the
night side than on the day side. The total area of the northern
2
. Compared with the area in Fig. 3 this
polar cap is about 2RM
gives a compression ratio of 11 for the magnetic flux. The last
closed field lines cross the surface of the planet at about 52◦
north on the day side and at 18◦ on the night side. For comparison, a typical boundary between closed and open field lines is
at 75◦ at Earth and at around 70◦ at Jupiter. Our value fo the
polar cleft latitude is close to, although somewhat larger than,
that suggested by Ness (1979) and Ogilvie et al. (1977) who
estimated it to be around 50◦ –57◦ on the day side and 25◦ –35◦
on the night side. In addition, one can see from the Fig. 2 that
the closed field lines of Mercury are very skewed. For some of
the last closed field lines we find that there is close to 20◦ longitude difference between the magnetically conjugate points in the
northern and southern hemispheres. For the Earth, similar differences are typically on the order of 1◦ (Baker and Wing 1989).
One should be aware of the fact that tracing last closed field
lines is an intrinsically unstable process, since it involves finding
bifurcation points numerically. In all our figures we have determined their positions with a precision slightly better than 1◦ in
latitude.
Figure 5 shows the logarithm of the magnetic field intensity
in the cross section of the wake 3RM downstream of the planet.
The black solid line shows the position of the bow shock in
this plane. One can also see a 2 shaped region of low magnetic
field intensity. This region can also be seen from a different
prospective in the north–south plane in Fig. 1. This region is
rather similar to the magnetospheric “sash” discussed by White
et al. (1998) for Earth. The depression of the magnetic field is
related to its bending (seen in Figs. 1 and 2) and therefore currents, which are the strongest, where the magnetic field lines are
bent most. The black arrow in Fig. 5 indicates the direction of
the current. For this particular IMF configuration, the current
layers are much stronger in the northern lobe of the magnetotail
than in the southern one. The reason for this is that some of the
IMF field lines originating from the Sun are connected to the
northern hemisphere of Mercury. In a very simplified picture,
these IMF lines do not make it into the tail, thus leaving a volume of low magnetic field intensity (“magnetic vacuum”), and
it takes a while for the magnetic field lines originating from the
southern polar cap to fill it in. More realistically, IMF lines connected to the north polar cap are bent strongly: first the filed
lines are dragged by the plasma past the planet and only then
are they twisted back and connect to the polar cap. On the other
hand, the open field lines coming out of the southern hemisphere of Mercury are simply dragged into the tail by the plasma,
which requires much less bending. Thus, almost all cross-tail
currents in Mercury’s magnetosphere close through the northern
lobe.
The thickness of the magnetopause and tail current sheets in
our simulation is about 0.1RM at the typical distances of the
Mariner 10 flybys (about 1.5RM ). This is somewhat thicker than
the measurements suggest [Whang (1977) estimated the width
MAGNETOSPHERE OF MERCURY
of the current layers to be about 150 km] but one should keep
in mind that this thickness is determined by different parameters in the model and in nature. In the model it is controlled by
numerical viscosity and resistivity (proportional to the grid size),
while in nature the width of a current layer is usually on the order of an ion gyroradius. For further discussion of the currents
in the hermean magnetosphere arising from a MHD simulation
see Gombosi et al. (1999). In addition, a brief summary of currents inferred from Mariner 10 measurements and further theoretical conjectures about hermean current systems are given by
Glassmeier (1999).
Because the upstream magnetic field is tilted 20◦ with respect
to the solar wind direction, it has a significant B y component.
Thus, the bow shock in Fig. 5 is asymmetric and is shifted to the
right. For the same reason the upper part of the magnetic field
depression is tilted and curved in a sashlike pattern, behavior
that is often observed in Earth’s magnetosphere (Kaymaz and
Siscoe 1998).
In the equatorial plane shown in Fig. 1, the maximum density
behind the shock is clearly shifted eastward from the subsolar
point. This behavior is explained by the tilt of the magnetic
field with respect to the solar wind velocity. We may understand
this phenomenon simply from the basic physics of conservation
laws described by the Rankine–Hugoniot conditions. For a shock
wave the compression ratio, q, is defined as the ratio of the
density immediately behind the shock to the density upstream of
the shock. Unlike gas dynamics, the equation for q in MHD may
not be solved easily for oblique shocks. In general, q satisfies
the following third-order equation (Kalikhman 1967):
¡
A21
−q
¢2
·
A21
·
− qk12 A21
2q S12
−
q + 1 − γ (q − 1)
¸
¸
2q − γ (q − 1) 2
A1 − q = 0.
q + 1 − γ (q − 1)
√
Here a is the sound speed, Va = Bn / ρ is the Alfvén speed
calculated using only the component of the magnetic field normal to the shock, Vn is the plasma speed normal to the shock
front, A = Vn /Va , S = a/Va , and k = Bt /Bn . The subscript 1 on
S, A, and k indicates that these quantities are based on the parameters upstream of the shock. The equation for q is written
assuming that there is only one tangential component of either
magnetic field or velocity, which may always be achieved by
a simple rotation of the coordinate system. It may be shown
(Kalikhman 1967) that only one root of this equation has physical sense; the other two are either imaginary or describe rarefaction shocks that contradict the second law of thermodynamics.
Figure 6 shows the solution of the above equation as a function
of α, the angle the solar wind velocity forms with the normal
to the shock. The continuous line corresponds to the IMF tilted
20◦ and the dashed line is the case when IMF is parallel to the
solar wind speed. One can see that while for the parallel case the
highest compression ratio is achieved right at the subsolar point,
for the tilted IMF the highest compression point is shifted; now
403
FIG. 6. Compression ratio for different angles between the solar wind
velocity and the shock normal. The solid line corresponds to the nominal Parker
spiral, and the dashed one to the magnetic field parallel to the plasma velocity.
The vertical lines mark the transition from strong to weak shock for the Parker
spiral case.
it occurs at the point where the IMF is normal to the surface of
the shock. For the nominal Parker spiral, the compression ratio
becomes one at −63◦ and at 64◦ . These angles correspond to the
degeneration of the shock into a linear characteristic of the flow,
which occurs far away from Mercury. Finally, the two vertical
lines in Fig. 6 mark −11◦ and 23◦ , the points where the nominal
Parker spiral flow immediately behind the shock stays hyperbolic. These points correspond to the transition from a strong to
a weak shock wave in classic gas dynamics.
A very interesting question is if direct interaction of the solar
wind with the surface of Mercury is possible. To investigate this
possibility we have increased the solar wind speed and pressure
(keeping the Mach number constant) until the solar wind was
able to reach the surface of the planet directly and the whole
day-side magnetosphere was pushed under the surface. In this
case a “bald spot” forms around the subsolar point. As seen in
Fig. 7, the magnetosphere in this case becomes very degenerate.
There are no closed magnetic field lines, the bow shock sits
right on the surface of the planet, and the magnetic barrier is
completely broken and dragged behind the planet. The regions of
the decrease in the magnetic field and current layers associated
with them, discussed above for the nominal Parker spiral, are
now spread over much larger regions and exist further down in
the tail. Although the Mach number did not change, the Alfvénic
Mach number increased by a factor of 2.6, so that not only is
the bow shock shifted backward, but its shape is changed at the
same time.
The parameters of this simulation are the following: solar
wind speed 1100 km/s, solar wind temperature 100 eV. The
density and the direction and IMF intensity were kept the same
as for the nominal Parker spiral conditions. While cases of a temperature increase in the solar wind by a factor of 7 may be found
404
KABIN ET AL.
FIG. 5. Logarithm of the magnetic field intensity in a cross-tail section 3RM behind Mercury. The black line is the bow shock position in this plane. The black
arrow shows the direction of the current.
FIG. 7. Same as Fig. 1 for the Parker spiral with high speed and pressure of the solar wind, allowing it to penetrate to the surface.
405
MAGNETOSPHERE OF MERCURY
in measurements, the required increase in the solar wind speed
is well above the typical variations. Thus, we may conclude that
direct interaction of the solar wind with the surface of Mercury
is a relatively unusual feature. It is still possible, however, if the
solar wind density increases at the same time as temperature and
speed. A simple equation for pressure balance suggests that if
the density of the solar wind increases by a factor of 9 (which
is not that uncommon) direct interaction may occur even at a
solar wind speed of 430 km/s. We did not perform this kind
of simulation, however. In general, we expect that the typical
features of an exotic magnetospheric interaction in which the
solar wind reaches the surface of Mercury will be similar to
those depicted in Fig. 7. There will be no closed filed lines,
the high-intensity magnetic field near the polar region will be
swept back, and the large domain of low magnetic field will form
further down the tail. The magnetic field will be strongly bent
and there will be strong current sheets in the tail.
We note that if one considers kinetic effects, for the direct
interaction of the solar wind with Mercury’s surface to occur it is
not necessary for the magnetopause to touch the surface. Once it
is within an ion gyroradius from the surface the direct interaction
will start to take place. In addition, southward IMF will bring
the magnetopause closer to the surface for a given upstream
pressure while the induction in the mantle and reconfiguration
currents associated with rapid increases in solar wind pressure
will have the opposite effect.
4. CONCLUSIONS
We have presented and discussed the results of an MHD model
applied to Mercury’s magnetosphere. For the case of the nominal
Parker spiral, we find an essentially three-dimensional structure
of the magnetic field and plasma flow. Under typical conditions,
Mercury possesses a relatively small magnetosphere with a distinct magnetopause. In this case, open field lines cover more than
50% of the surface of the planet, so the hermean magnetosphere
is very “open.” Magnetic reconnection required to sustain such
large volumes of the open field lines takes place on both the day
side and night side.
We have increased the speed and temperature of the solar wind
until it reached the surface of Mercury and showed the results
for this exotic magnetosphere as well. However, the physical parameters that correspond to this kind of interaction are extremely
rare. The possible combinations of the upstream conditions that
may result in the formation of a subsolar “bald” spot on the
surface of Mercury remain to be investigated. A careful study
of these conditions will be a basis of future work. However, regardless of a particular combination of the parameters leading
to a “bald” spot, we expect that the gross features of this “blown
away” magnetosphere will be similar to those presented in this
paper.
In this paper we studied only steady-state solutions while the
dynamic processes are probably very important in the hermean
magnetosphere. Even more, because the magnetosphere is relatively small and the magnetic field is rather weak (and thus
does not lead to such restrictive limits on the Alfvén time step
as for Earth or giant planets), Mercury is a very attractive target
for modeling of time-dependent phenomena, such as reconfiguration currents. Once the data of a Mercury mission become
available, global numerical simulation may be extremely effective in relating the magnetospheric response to the changes in
solar wind conditions, thus providing many physical insights
into the field of general magnetospheric physics.
ACKNOWLEDGMENTS
We thank Dr. Rejean Grard for inspiring us to undertake this work and for
providing input parameters. We are grateful to Dr. Michael Liemohn for the
stimulating discussions. We are indebted to ISSI for their support and hospitality
during the sabbatical leave of T.I.G. and the visit of K.K. This work was also
supported by NSF–NASA–AFOSR Interagency Grant NSF ATM-9318181 and
by NASA HPCC CAN NCCS5-146.
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