JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, 1–9, doi:10.1002/2013JA019155, 2013
The magnetosphere under the radial interplanetary magnetic field:
A numerical study
B. B. Tang,1 C. Wang,1 and W. Y. Li1
Received 26 June 2013; revised 18 November 2013; accepted 23 November 2013.
[1] We investigate the magnetosphere under radial interplanetary magnetic fields (IMF)
by using global magnetohydrodynamic simulations. The magnetosphere-ionosphere
system falls into an unexpected state under this specific IMF orientation when the solar
wind electric field vanishes. The most important features that characterize this state
include (1) magnetic reconnections can still occur, which take place at the equatorward of
the cusp in one hemisphere, the tailward of the cusp in the other hemisphere, and also in
the plasma sheet; (2) significant north-south asymmetry exists in both magnetosphere and
ionosphere; (3) the polar ionosphere mainly presents a weak two-cell convection pattern,
with the polar cap potential valued at 30 kV; (4) the whole magnetosphere-ionosphere
system stays in a very quiet state, and the AL index does not exceed –70 nT; and (5) the
Kelvin-Helmholtz instability can still be excited at both flanks of the magnetosphere.
These results imply the controlling role of the IMF direction between the solar wind and
magnetosphere interactions and improve our understanding of the solar
wind-magnetosphere-ionosphere system.
Citation: Tang, B. B., C. Wang, and W. Y. Li (2013), The magnetosphere under the radial interplanetary magnetic field: A
numerical study, J. Geophys. Res. Space Physics, 118, doi:10.1002/2013JA019155.
1. Introduction
Suvorova et al., 2010], and this unusual magnetopause location under radial IMFs is caused by the pressure reduction
in the subsolar region [Samsonov et al., 2012]. However,
many features of the magnetosphere under the radial IMF
still remain open.
[3] The orientation of IMF plays a crucial role in the
interaction between the solar wind and magnetosphere. The
magnetospheric behaviors significantly differ from different IMF orientations. During the southward IMF period,
magnetic flux is first eroded by dayside reconnection and
then transported to the magnetotail. After the nightside
reconnection, the newly closed magnetic flux returns to the
dayside magnetosphere to form a complete circle [Dungey,
1961]. During northward IMF period, reconnection at the
tailward of the cusp region in both hemispheres controls
the global magnetospheric convection: the newly closed
magnetic flux becomes part of the low-latitude boundary
layer (LLBL) and convects to the nightside magnetosphere
[Maezawa, 1976; Song et al., 1999]. Therefore, when the
IMF is radial, meaning the solar wind electric field (nearly)
vanishes under frozen-in conditions (E = –v B ' 0),
the associated magnetospheric response will naturally attract
researcher’s interests.
[4] Using data obtained from the Polar, Defense Meteorological Satellite Program spacecrafts, and Super Dual
Auroral Radar Network (SuperDARN) radars, Farrugia et
al. [2007] characterized the state of the magnetosphere during the recovery phase of the magnetic storms on 24–25
October 2001 when the angle between the IMF and flow vectors is less than 15ı . They concluded that (1) generally weak
low-latitude dayside reconnection or reconnection poleward
[2] The radial interplanetary magnetic field (IMF), which
means the magnetic field is (nearly) flow aligned (parallel
or antiparallel), is different from the averaged Parker’s spiral [Parker, 1958] and can be found in the regions where
the solar wind speed is gradually decreased (e.g., the trailing region of coronal mass ejections) [Watari et al., 2005;
Gosling and Skoug, 2002, and references therein]. Wang et
al. [2003] found that a noticeable low-speed plateau of limited duration in solar wind speed near the Sun can produce
radial field events in the heliosphere. The specific effects
of this IMF orientation brought to the bow shock, magnetopause, and magnetosheath have been studied by many
researchers. For instance, the foreshock region reforms in
the front of the dayside magnetosheath when IMF is parallel
to the flows [Blanco-Cano et al., 2009]; the magnetosheath
becomes more turbulent, and sunward magnetosheath flows
can even be found at the subsolar magnetopause region
[Shue et al., 2009]; the magnetopause subsolar location will
move sunward to make the magnetosheath thinner than usual
[Merka et al., 2003; Dusik et al., 2010; Jelinek et al., 2010;
1
State Key Laboratory of Space Weather, Center for Space Science and
Applied Research, Chinese Academy of Sciences, Beijing, China.
Corresponding author: C. Wang, State Key Laboratory of Space Weather,
Center for Space Science and Applied Research, Chinese Academy of Sciences, 1 Nanertiao, Zhongguancun, PO Box 8701, Beijing 100190, China.
([email protected])
©2013. American Geophysical Union. All Rights Reserved.
2169-9380/13/10.1002/2013JA019155
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TANG ET AL.: MAGNETOSPHERE UNDER RADIAL IMF
electrostatic ionosphere shell is imbedded, allowing an electrostatic coupling process introduced to map field-aligned
current and potential between the ionosphere and the inner
boundary of the magnetosphere which is set at 3 RE .
The ionospheric conductance contains two parts: the dayside conductance contributed from EUV radiation, which
depends on the solar flux F10.7 and solar zenith angle [Moen
and Brekke, 1993], and the auroral conductance, which is
empirically calculated from ground magnetic disturbances
[Ahn et al., 1998]. This self-consistent conductance model
has been successfully applied in producing the ionospheric
equivalent current systems of the substorm event on 8 March
2008 [Wang et al., 2011].
[8] To study the effect of the radial IMF on the magnetosphere, we set IMF restricted to the x component at 5 nT, and
the solar wind along the Sun-Earth line at 400 km/s; thus,
the IMF is exactly antiparallel to the flows. Other parameters
for the solar wind are typical: The proton number density
is 5 cm3 and temperature is 105 K. All parameters are kept
unchanged in the entire simulation runs. With keeping generality, the dipole tilt angle is set to 0, so that we can focus
on the effect of radial IMFs only.
of the cusp may exist; (2) the cross-polar cap potential is
20–30 kV, and many flows can be described as a weak
two-cell pattern; (3) no systematic north-south asymmetry is
presented, though some evidences like the polar cap precipitations have been showed; (4) the Kelvin-Helmholtz (K-H)
instability is probably absent from the ground magnetometer
records; and (5) no substorm activity is observed, meaning the activity of the magnetosphere stays in a quite low
level. These results provide key information of the magnetosphere under radial IMFs. However, due to the limitation of
observation methods, a global picture of the magnetosphere
under radial IMFs is still lacking, and some discussions for
the details on associated physical phenomena are left for
future explorations.
[5] Later on, based on in situ Wind observations, Farrugia
et al. [2010] revisited the case above and found vortexlike structures at the dawnside magnetopause. Although
these vortex-like structures can be excited differently [e.g.,
Tkachenko et al., 2008] in the Earth’s magnetospheric environment, they examine various-generating mechanisms and
suggest that the most likely cause is the K-H instability. In
another case, when magnetosphere encounters a discontinuity of Bx component, much of evidence of “substorm-like”
phenomena due to this IMF discontinuity passage were provided [Nowada et al., 2012]: Simultaneous dipolarization
and negative bay variations with Pi2 waves are observed
by GOES and the ground observatories, while global auroral activities are absent. Furthermore, surface waves induced
by K-H instabilities are also observed by Time History
of Events and Macroscale Interactions during Substorms
(THEMIS)-A/C probes at dawnside magnetopause, while
the amplitude of these surface waves reaches several Earth
radii at the maximum [Nowada et al., 2012]. All these in situ
observations suggest that K-H waves are not very occasional
at the flank of the magnetopause when radial IMF is present.
[6] In this study, we obtain a global view of the magnetosphere under the radial IMF by using global magnetohydrodynamic (MHD) simulations, which are particularly well
suited to investigate the solar wind-magnetosphere interactions on a macroscale. The general magnetic reconnection
properties, the following responses in the magnetosphere
and ionosphere, and a profile of K-H vortex at the magnetopause are mainly focused. The paper is organized as
follows. Section 2 describes the simulation model and settings for simulation runs. Section 3 presents a detailed
analysis of the magnetospheric activities based on the simulation result. At last, the discussions and conclusions are
given in sections 4 and 5.
3. Numerical Result
3.1. Magnetic Reconnection
[9] When the IMF orientation is flow aligned, a significant difference compared with the general cases is that
the solar wind electric field vanishes under frozen-in conditions. But it does not mean that no reconnection happens
at this scenario. In contrast, when the diverted solar wind
contacts with the magnetosphere of the Earth, the antiparallel magnetic field (component) between these two distinct
domains can be found, which leads to various magnetic
reconnections. To search for possible reconnection locations,
we detect the magnetic nulls in the entire numerical domain
by applying the Poincaré index method, which calculates
the topological degree at every grid [Greene, 1992] and
then examine if there is a reconnection. It is noted that the
magnetic nulls have two different types, which depend on
whether the magnetic field line converges (A) or diverges
(B) from the null point. Figure 1a shows such an example (adapted from Pontin [2011]): Around an isolated type
B null, the spine consists magnetic field lines pointing toward the null in both directions, while in the † fan
plane, the magnetic field lines diverge from the null. We
also show another example in Figure 1b for zoomed in picture of a single type A null and the surrounded magnetic
field lines as seen in the northern cusp region obtained from
the simulation result (see Figure 2a in details). In addition, in 3-D separator reconnections, these two nulls always
appear or disappear in A-B pairs [Priest and Forbes, 2000].
For instance, cusp reconnection occurs at both hemispheres
under northward IMF conditions, and meanwhile, two magnetic nulls (type A null in the north cusp region and type B
in the south) can be found and are joined by a separator line
[Dorelli et al., 2007].
[10] Figure 2 displays the location of the identified magnetic nulls under radial IMF conditions (type A showed
in black plus signs and type B in red diamond signs),
which are projected into the noon-midnight meridian plane
2. Simulation Method
[7] The global MHD simulation model, developed by Hu
et al. [2007], is on the basis of an extension of the piecewise
parabolic method with a Lagrangian remap [Colella and
Woodward, 1984] to MHD. The model solves the ideal MHD
equations over a stretched Cartesian coordinate box which
takes the Earth as the origin center and lets the x, y, and z
axes point to the Sun, dusk, and the northward directions,
respectively. The size of this numerical box extends from
30 RE to –300 RE along the Sun-Earth line and from –150 RE
to 150 RE in y and z directions, with 240 240 240
grid points and a minimum grid spacing of 0.2 RE . An
2
TANG ET AL.: MAGNETOSPHERE UNDER RADIAL IMF
local A-B pair of magnetic nulls just locating at poleward
of the southern cusp region, and the reconnected open field
lines (the green line for example) extending very far tailward. Furthermore, the single type B null, which is assumed
to form an A-B pair with the north cusp null mentioned
above, is also absent in this figure. All these can be caused by
the tailward moving of the reconnection site. In the simulation, the adjacent magnetosheath flow of the local magnetic
null pair is found to be super-Alfvénic, and thus, the reconnection site has to move tailward [Gosling et al., 1991].
Figure 3 presents the location of magnetic nulls minutes
after Figure 2: The magnetic null pairs have already convected more than 5 Earth radii tailward, and at the same time
the structure of a magnetic island can be identified. As the
magnetic nulls continue to move tailward, the newly generated open field lines can extend more tailward accordingly.
Finally, a new pair of magnetic nulls reappears at its original position, and this process repeats again. Therefore, it
is reasonable to speculate the assumed single type B null
has already moved to approximate infinity under prolonged
steady radial IMF conditions. Meanwhile, it is also worth
40
Z( RE)
20
Figure 1. (a) An isolated type B null and potential magnetic field lines nearby (adapted from Pontin [2011]). (b)
The single type A null, located at (5.71, –0.01, 9.22) RE in
the north cusp region, is marked by a yellow spot, and
the around magnetic field lines under radial IMFs are also
presented. Background is the contour of the logarithmic values of the plasma number density in the noon-midnight
meridian plane.
2.72
2.08
1.45
0
0.81
0.18
-20
-0.46
-1.09
-1.73
-40
(a)
-60
-40
-20
X( RE)
0
20 log(N)
40
and the equatorial plane, respectively. The background contour, whose color shows the logarithmic values of the
plasma number density, and magnetic field lines show
the basic structure of the solar wind-magnetosphere system. In Figure 2a, a single type A null, locating at
(5.71, –0.01, 9.22) RE , is detected just at the equator side
of the northern cusp region, where the magnetic field in
the bypassed solar wind turns to be antiparallel to the
dayside magnetospheric field. In other words, low-latitude
dayside magnetic reconnection occurs at north hemisphere.
Figure 1b illustrates the detailed structure of magnetic lines
near the marked magnetic null: Two groups of magnetic field
lines along the spine are separated by the † fan, which is
lying on the magnetopause. At the magnetic null region, the
previous closed field line reconnects with the solar wind field
line, and two open field lines are generated. One of these
newly generated magnetic field lines, as shown in Figure 2a,
is plotted in black color, and its root is in the south polar
region. Meanwhile, the other open field line is rooted in
the north polar region and dragged tailward by the solar
wind flows.
[11] The scenario of magnetic reconnection is more complicated in the Southern Hemisphere. Figure 2a shows a
Y( RE)
20
2.72
2.08
1.45
0
0.81
0.18
-20
-0.46
-1.09
(b)
-1.73
-40
-60
-40
-20
X( RE)
0
20
log(N)
Figure 2. The projection of detected magnetic nulls in
(a) the noon-midnight meridian plane and (b) the equatorial plane, where two different types of magnetic nulls
are shown by the black plus signs and red diamond signs.
The background contour of the logarithmic plasma number
density and black magnetic field lines illustrate the basic
structure of solar wind-magnetosphere system. Two newly
generated open magnetic lines by north and south cusp
reconnection are selected and shown in black and green
color, respectively.
3
TANG ET AL.: MAGNETOSPHERE UNDER RADIAL IMF
magnetic field lines that are rooted in the north hemisphere
are dragged tailward directly by the solar wind flows. Meanwhile, the convection of open field lines from the south
hemisphere is more complex. Figure 5a displays the flows
of these magnetic field lines in the dayside equatorial plane,
where the red color again indicates the open field line
regions, and the flow vectors that are larger than 20 km/s in
this plane are presented. We find this situation has some similarity to that of north IMF conditions: reconnections take
place tailward of the cusp region, and then the reconnected
magnetic flux tubes will move nightward along the magnetopause in the equatorial plane, which form LLBL that
separates the magnetosheath and the magnetosphere [Song
et al., 1999]. In Figure 5a, except for the part that extends
to the solar wind region, the rest of the red region is contacted with the magnetopause, and the flow within is also
in the antisunward direction. That is to say, the LLBL can
also be formed under radial IMF conditions. However, significant differences still exist. When IMF is northward, the
flux tubes in the LLBL are generated by cusp reconnection at two hemispheres, and the flux tubes can be closed.
While under radial IMF conditions, the LLBL is formed
only by reconnections in one hemisphere, and thus, the flux
tubes inside are always open and may have a southward
velocity component.
[15] When these open magnetic lines rooted in the different hemispheres move to the nightside magnetosphere,
they also behave differently. Figure 5b shows the pressure contour near x = –20 RE plane and the flow vectors in this plane. In the northern lobe region, the flows
have a general tendency that compress the plasma sheet,
which is indicated by the light green arrow, while in
the southern lobe region, there is another kind of flow:
plasma moves from flanks of the magnetopause to the
central regions as shown by two red arrows, implicitly
suggesting that the magnetosheath plasma is transported
by K-H instability from the flankside magnetopause, and
then nightside reconnection occurs. Therefore, a systematic north-south asymmetry of plasma flows is present in
the magnetosphere.
-17
X(RE)
1.5
1.0
-18
0.5
0.0
-19
-0.5
-1.0
-1.5
-20
-6
-5
-4
-3
log(N)
X(RE)
Figure 3. The local magnetic null pairs in the Southern
Hemisphere. Comparing with Figure 2a, they have moved
several Earth radii tailward.
noting that similar tailward moving of high-latitude magnetic reconnection location under northward IMFs has been
revealed by Omidi et al. [1998] in the simulations.
[12] Many magnetic nulls are detected broadly in the
equatorial plane, which are located from x = –20 RE to further tail. Closed field lines are thus generated, which convect
to the dayside magnetosphere to form an entire circulation.
Readers will note that the location of the nearest X-line still
may be not far enough from Earth, but comparing with the
result of southward IMF simulation runs, the X-line location
has already shifted tailward.
[13] The open field lines generated by reconnections at
north and south hemispheres can extend into upstream solar
wind (as plotted in Figure 2a, black and green lines for
example), but they are all rooted into the south ionosphere.
To confirm this result, we draw magnetic field lines from
upstream solar wind at x = 20 RE to check where they are
pointing. As illustrated in Figure 4, only two kinds of magnetic fields are found: The white region of the solar magnetic
field lines and the red region where the magnetic field lines
are connected to the south hemisphere. Besides these two
types, no other type of magnetic lines is present. Thus, the
signature of polar rain detected by the Polar spacecraft is
much clearer [Farrugia et al., 2007], when the IMF is also
almost in the sunward direction. Under this special geometry of the open field lines, the polar cap precipitation in the
north hemisphere is very weak, and sometimes absent, while
in the south hemisphere, much more intense precipitation
is showed in the observation. Therefore, the observations
present a north-south asymmetry, though Farrugia et al.
[2007] also addressed that it may be not so obvious during
different polar region passes. In addition, the open field lines
in the solar wind also show a north-south geometric asymmetry: The red area in the z < 0 region is much larger. The
reason of this asymmetry is partly because the latitude of
south hemisphere reconnection is higher and partly because
these magnetic field lines have to convect to the nightside
along both flanks of the magnetopause.
Figure 4. The location of different kinds of magnetic field
lines in the upstream solar wind (x = 20 RE ). The regions
of solar wind magnetic field lines are shown in white; open
field lines that are rooted in the south ionosphere are shown
in red.
3.2. Magnetospheric State
[14] After reconnection, the convection of the magnetosphere is almost determined. The newly generated open
4
TANG ET AL.: MAGNETOSPHERE UNDER RADIAL IMF
the white lines, and the black vectors depict the distribution
of field-aligned current (FAC), the boundary of polar cap
region, the ionospheric potential, and the horizontal ionospheric current, respectively. First, the size of the polar cap,
whose dayside boundary is located at 78–80ı , and the
nightside boundary is 73ı , is relatively small comparing
with substorm active periods when its nightside boundary
usually decreases to less than 70ı [Carbary, 2005]. This
means that the open field magnetic flux generated by reconnections under radial IMFs is correspondingly less and is
in good agreement with the Polar spacecraft observations
[Farrugia et al., 2007]. Second, region 1 and 2 FACs can
easily be identified, and their location in latitude is higher
accordingly, while they are rather weak in magnitude. In
the simulation, the total amount of region 1 current in the
north ionosphere is about 0.63 MA, which is weaker than
Figure 5. Simulation result of the magnetospheric flows
under radial IMF conditions. (a) The flow of open field lines
(shaded in red color) in the dayside magnetosphere; (b) the
flow vectors near x = –20 RE plane, and background contour
is filled by thermal pressure. The length of the flow vectors
in both panels indicates the flow speed, and in Figure 5a,
only the flow vectors larger than 20 km/s are presented.
[16] It is also noted that the position of plasma sheet
(Figure 5b, the cyan strip) shifts about 2 RE southward at
x = –20 RE , which is different from usual cases. One may
guess the plasma sheet is flapping, and it could shift southward occasionally. We check the result at different time steps
and find the plasma sheet flapping range is only about 0.4 RE
(2 grid spacings) in the simulation. Therefore, we believe
that we observe a steady southward plasma sheet displacement rather than its flapping. Based on this plasma sheet
behavior, we are able to interpret that a larger amount of the
reconnected flux tubes is piled up in the northern lobe than
in the southern lobe due to the dayside reconnection equatorward of the north cusp region. Resultant imbalance of
compressions between the north and south lobes causes the
southward shifting of the plasma sheet.
Figure 6. The physical state of the (a) north and (b) south
ionosphere. Dashed circles show latitude of 60ı , 70ı , and
80ı . The background color contour shows the distribution
of field-aligned current (FAC), with red/white color contours
for downward FAC and green/black colors for upward FAC.
The yellow line, the white lines, and the black vectors depict
the boundary of polar cap region, the ionospheric potential,
and the horizontal ionospheric current, respectively.
3.3. Ionospheric State
[17] Figure 6 displays the state of the north (a) and south
(b) ionosphere. Dashed circles show latitudes of 60ı , 70ı ,
and 80ı . The background color contour, the yellow line,
5
TANG ET AL.: MAGNETOSPHERE UNDER RADIAL IMF
asymmetry can be found between these two ionospheres,
being most obviously expressed by the polar cap potential.
The south ionospheric potential is 36 kV, which is nearly
20% larger than the north ionospheric potential, and thus, the
calculated AE/AL from the south ionosphere is 108/ – 63 nT,
also larger than that in the north ionosphere.
3.4. K-H Vortex
[19] Some clues of the vortex-like structure at the flank of
the magnetopause have been provided in the previous figures
(such as Figure 5a). In this section, we will give a more
detailed analysis to show it is induced by K-H instability.
The K-H instability can be excited more frequently under
northward IMF conditions than other IMF orientations, since
the propagating direction of the K-H waves is almost perpendicular to the magnetic field either in the magnetosphere
or in the magnetosheath, being the most K-H unstable condition in a shear flow region. Under radial IMFs, if the
region of the flank magnetopause is K-H active, the direction of the magnetosheath field is nearly parallel to the K-H
wave propagating, which will generate a magnetic tension
force tending to stabilize the distorted magnetic flux. Nevertheless, the K-H instability can still be excited. Figure 7a
displays the dusk flank magnetopause by VX contours, with
sunward/antisunward velocity plotted by solid/dot lines, and
also the boundary of open/closed magnetic field lines, which
is showed by a solid black curve. The magnetopause is rather
wavy/wave like, characterized by the dense/sparse VX contour lines. Across the magnetopause of dense contour lines,
the flow shear is corresponding larger, where a K-H vortex
may lie therein. Here, we select such a region and show a
zoom picture in Figure 7b. The drawn background contour
of Figure 7b is the plasma number density, and vectors illustrate the plasma flows in the plane. A well-developed vortex
can be identified. We select two points that are located at
the magnetosheath and magnetospheric sides of this vortex,
which are marked by the cyan cross, and find the linear criterion for the onset of K-H instability [Chandrasekhar, 1961]
is satisfied. Thus, this vortex is considered as a K-H vortex.
Meanwhile, similar vortex structures have also been found
at the dawnside magnetopause, and therefore, the K-H vortex can be well excited at both flanks of the magnetopause
under radial IMF conditions. This result accords with Wind
spacecraft observations, which also present K-H wave signatures when crossing LLBL at x = –13 RE [Farrugia et al.,
2010]. However, due to stabilizing effect of the radial IMF,
the K-H vortex here occurs at more tailward location (the
first vortex is at x = 3 RE ) than that under north IMF conditions, where the first K-H vortex can appear as early as at
LT 1400 sector [Li et al., 2012; Taylor et al., 2012].
[20] Since K-H vortex is identified, whether it shows a
north-south asymmetry at higher latitude (20ı ) is an interesting question to answer. Here we are not intending to study
such a localized problem. But some asymmetry may accordingly exist to address the formation of LLBL. For instance,
the perturbation amplitude of K-H waves will decrease
faster to higher latitude in the north hemisphere than in the
south hemisphere.
Figure 7. (a) VX contours of the magnetosphere in
the dusk equatorial plane, with solid/dot lines for sunward/antisunward flows. The black curve indicates the
boundary of open/closed magnetic field lines. (b) Zoom in
of the box selected in Figure 7a. The background contour
shows the plasma number density, and arrows illustrate the
flow vectors in the plane.
that either in the substorm expansion phase (1.8 million
amperes (MA)) or in the substorm growth phase (0.8 MA)
simulated by the same model [Tang et al., 2011], suggesting the whole magnetosphere-ionosphere system stays in a
quiet state. The region 2 current is about 0.46 MA, i.e.,
about 73% of region 1 current. Also, we find polar cap current is lying in the latitude just higher than the region 1
current in the dayside region, while it is very weak, only
about 0.08 MA. Third, the polar cap potential is about 29 kV
in the north ionosphere, which is much smaller than south
IMF situations. But a two-cell pattern, which is an identical
convection pattern under south IMF conditions, is mainly
revealed: the positive one in the dawn sector, while the negative one in the dusk sector. Finally, the ionospheric current
vectors are plotted. A weak westward/eastward electrojet
appears in the morning/afternoon sector, with the maximum
value of 0.28 A/m, while very small current is found in the
midnight ionosphere sector. Ground magnetic disturbances
can be approximately calculated from its toroidal part, which
shows the AE/AL index is 78/ – 44 nT, suggesting a quiet
magnetosphere-ionosphere system.
[18] The physical picture in the south ionosphere is almost
symmetry to the north ionosphere, but interhemispheric
4. Discussions
[21] In this paper, we have discussed the magnetosphereionosphere system under the condition of the radial IMF.
6
TANG ET AL.: MAGNETOSPHERE UNDER RADIAL IMF
Magnetopause
original formula. Although ˆpc value in the simulation is
about 30 kV and is larger than the fitted observation value,
it still shows the treatment of an offset value for ˆpc is reasonable, leaving the only concern whether the term ˆ0 is
constant for even changeable reconnection rate under radial
IMF conditions.
[23] Although MHD simulations have revealed many
interesting features of magnetosphere under radial IMF conditions in a qualitative view, it remains unclear whether
simulations capture these features accurately. For instance,
the smallest grid spacing in this simulation run is 0.2 RE ,
which may be larger than the separation of a local magnetic
null pair (it can be less than 1000 km in Cluster observations [Xiao et al., 2006]). Thus, we may miss some magnetic
nulls in the simulation, but as an assist method to find reconnection locations, it still works well. Second, the nightside
reconnection location is at x = –20 RE that seems not
distant enough from the Earth. If the X-line location can
shift more tailward, the magnetosphere can be much quieter.
Third, in this simulation, the subsolar position of magnetopause is at x = 10.7 RE , which does not move outward
significantly as observations suggested [Merka et al., 2003].
Samsonov et al. [2012] take this outmoving location of magnetopause as a result of the reduction of total pressure at the
subsolar magnetopause, and also, they pointed out that the
MHD simulation with isotropic temperatures may underestimate this pressure reduction. Here we carry out a similar
pressure balance analysis as shown in Figure 8, and the pressure reduction at the subsolar magnetopause is about 15%.
Assuming that this reduced pressure is balanced by the magnetospheric magnetic pressure at the subsolar magnetopause,
the magnetopause can only move sunward about 3%, which
is not enough if comparing with observations. Thus, whether
the MHD simulation is capable for this issue and how to
improve the result still needs more explorations.
[24] At last, in the real solar wind, the Bx component in
IMFs is observed much more frequently than pure radial
IMFs. In this situation we can still suspect some impacts
of this Bx component to magnetosphere if we have a good
understanding of magnetospheric responses to radial IMFs.
For instance, during Cluster summer seasons when Earth’s
dipole tilts toward the Sun, plasma can enter into the Southern Hemisphere more easily under north IMF conditions
with a simultaneous sunward Bx component [Shi et al.,
2013]. That is because reconnection tailward of the cusp
region is more favorite in this case, which has been suggested in our numerical study.
Bow shock
1.4
1.2
P/PSW
1.0
0.8
0.6
0.4
Pb
0.2
0.0
8
9
Pt
10
11
Pdyn
12
13
14
15
X(RE)
Figure 8. Magnetic ( pb ), thermal ( pt ), and dynamic ( pdyn )
pressures along Sun-Earth line under radial IMF. The two
vertical lines show the location of the magnetopause and the
bow shock. We can find the total pressure is reduced at the
subsolar magnetopause.
Signatures of reconnection at the equatorward of cusp region
in one hemisphere, and at poleward of cusp region in the
other hemisphere are given even when the solar wind electric field vanishes. Meanwhile, the nightside reconnection
features are also presented. A two-cell convection pattern
is formed in both ionospheres, but the AL index in the
simulation does not exceed –70 nT. This means the whole
magnetosphere-ionosphere system falls into a quiet state,
even though slow and weak convections still occur. In the
observation of Farrugia et al. [2007], a 28 h substorm-free
interval is showed, also remarkably suggesting low level
activities of the magnetosphere. Furthermore, during these
28 h, the magnetosphere stays in the recovery phase of the
previous magnetic storm occurred before this substormless
interval, which is indicated by the quasi-linear recovery of
the Dst index; however, the size of the polar cap shows no
clear tendency to shrink or expand during this period. Why
does not the polar cap shrink during the recovery phase?
Now, we know when IMF turns to the radial direction, a
quasi-steady convection of magnetic convection induced by
reconnections can be built, albeit in a very low level; thus,
the polar cap can maintain its size for such a long time.
[22] Another interesting point is referred to the polar cap
potential (ˆpc ). Currently, many widely used formula for ˆpc
is the function of solar wind electric field (Esw ) and IMF
clock angle ( ), but when IMF is radial, Esw is 0, and has
no definitions. How to empirically get the value of ˆpc has
not been well considered. Using the data set of ˆpc from
SuperDARN radars, Shepherd et al. [2003] test Hill-Siscoe
model [Siscoe et al., 2002] in a wide solar wind range. They
found if reconnection electric field (written as Esw F( )) is
close to 0, a minimum value of ˆpc seems to exist (about
17 kV). Therefore, they propose a constant term (ˆ0 ) at this
value to indicate other processes not being included in the
5. Conclusions
[25] By applying global MHD simulations, we performed
a numerical study on the general state of magnetosphere
under radial IMFs (antiparallel to the solar wind flows here).
Although the solar wind electric field disappears, magnetic
reconnections are still found, which thus determines the state
of magnetosphere-ionosphere system. The most important
features that characterize this state are summarized below:
[26] 1. Magnetic reconnections take place at the equatorward of the cusp region in one hemisphere and at the tailward of the cusp region in the other hemisphere. The open
magnetic field lines dragged tailward by the solar wind flow
7
TANG ET AL.: MAGNETOSPHERE UNDER RADIAL IMF
are piled up in the magnetotail lobe and then reconnected
into closed field lines again by magnetotail reconnections.
[27] 2. The open magnetic fluxes rooted in the north hemisphere are dragged tailward by the solar wind directly, and
the open magnetic fluxes that are original from the south
hemisphere will flow along the both flanks of the magnetopause to form LLBL. Therefore, the compression to the
plasma sheet from the north lobe is stronger, which makes
the plasma sheet shift somewhat southward.
[28] 3. The polar cap potential presents a two-cell pattern in both ionospheres and its value is about 29/36 kV in
the north/south ionosphere, which indicated that magnetic
convection is slow and weak.
[29] 4. Thus, the whole magnetosphere-ionosphere system stays in a very quiet state, with an AL index of
–44/ – 63 nT in the north/south ionosphere. Also the size of
polar cap region and the amount of total region 1 current are
much smaller if comparing with the south IMF conditions.
[30] 5. Systematical north-south asymmetries have been
revealed. This asymmetry is caused by the interaction
between the specific radial IMFs and the Earth’s dipole.
Thus, the subsequent magnetic reconnections, the magnetospheric flows, the position of the plasma sheet, the ionosphere parameters, and the ground magnetic disturbances are
all asymmetric.
[31] 6. K-H vortex is detected at both flanks of the magnetopause, which is in good agreement with observations.
[32] Many of these features of magnetospheric responses
described above focus on providing physical pictures, while
some in-depth analysis are not involved much. For instance,
the formation of LLBL is an interesting topic. Sonnerup et
al. [2001] simulate the magnetospheric state under zero IMF
conditions, which is another case of zero solar wind electric
field, and they find no reconnection occurs. In their results,
the LLBL is formed by the viscous effect, and the polar cap
potential is about 30 kV under normal solar wind conditions,
which is similar to our result. Therefore, it still needs further
considerations on how to understand this viscous effect, and
how important to compare this mechanism (viscous effect)
with high-latitude magnetic reconnection in forming LLBL
is. But still, the numerical study in this paper can deepen our
understanding about the magnetosphere-ionosphere system,
especially during the recovery phase of magnetic storms,
when the orientation of IMF has a chance to be radial.
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[33] Acknowledgments. This work was supported by NNSFC grants
41231067 and 41204110, 973 program 2012CB825602, and in part by the
Specialized Research Fund for State Key Laboratories of China. The computations were performed by Numerical Forecast Modeling R&D and VR
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stand of Chinese Meridian Project.
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