ANGEOAnnales GeophysicaeANGEOAnn. Geophys.1432-0576Copernicus PublicationsGöttingen, Germany10.5194/angeo-34-303-2016A statistical study on the shape and position of the magnetotail neutral
sheetXiaoSudongZhangTielongtielong.zhang@oeaw.ac.atGeYasongWangGuoqiangBaumjohannWolfganghttps://orcid.org/0000-0001-6271-0110NakamuraRumiCAS Key Laboratory of Geospace Environment, University of Science and
Technology of China, Hefei, ChinaSpace Research Institute, Austrian Academy of Sciences, Graz, AustriaInstitute of Geology and Geophysics, Chinese Academy of Sciences,
Beijing, ChinaTielong Zhang (tielong.zhang@oeaw.ac.at)26February20163423033112July201517January201610February2016This work is licensed under a Creative Commons Attribution 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/3.0/This article is available from https://angeo.copernicus.org/articles/34/303/2016/angeo-34-303-2016.htmlThe full text article is available as a PDF file from https://angeo.copernicus.org/articles/34/303/2016/angeo-34-303-2016.pdf
We study the average shape and position of the magnetotail
neutral sheet based on magnetic field data obtained by Cluster, Geotail,
TC-1, and THEMIS from the years 1995 to 2013. All data in the aberrated GSM
(geocentric solar magnetospheric) coordinate system are normalized to the
same solar wind pressure 2 nPa and downtail distance X∼-20RE. Our results show characteristics of the neutral
sheet, as follows. (1) The neutral sheet assumes a greater degree of curve
in the YZ cross section when the dipole tilt increases, the Earth dipole
tilt angle affects the neutral sheet configuration not only in the YZ cross
section but also in the XY cross section, and the neutral sheet assumes a more
significant degree of tilt in the XY cross section when the dipole tilt
increases. (2) Counterclockwise twisting of the neutral sheet with 3.10∘
is observed, looking along the downtail direction, for the positive interplanetary magnetic field (IMF)
BY with a value of 3 to 8 nT, and clockwise twisting of
the neutral sheet with 3.37∘ for the negative IMF
BY with a value of -8 to -3 nT, and a northward IMF can
result in a greater twisting of the near-tail neutral sheet than southward.
The above results can be a reference to the neutral sheet model. Our large
database also shows that the displaced ellipse model is effective to study
the average shape of the neutral sheet with proper parameters when the
dipole tilt angle is larger (less) than 10∘ (-10∘ ).
Magnetospheric physics (magnetotail)Introduction
The neutral sheet of the magnetotail is located in the middle of the plasma
sheet, lying between two lobes (Ness, 1965; Baumjohann and Treumann, 2012).
It is characterized by a weak magnetic field, strong cross tail current, and a
reversal of the magnetic field direction across it. The neutral sheet is
important for the formation of the magnetotail, and the dynamics of the
Earth's magnetosphere are greatly influenced by physical processes that
occur near the neutral sheet. The exact position of the neutral sheet is
variable with time. The shape of the neutral sheet is known to be warped
because of the tilting of the Earth's magnetic dipole. Figure 1 illustrates
the neutral sheet elliptical shape as controlled by the dipole tilt angle,
χ. The dipole tilt is defined as the angle between the Earth's north
dipole axis and the Z axis in the GSM (geocentric solar magnetospheric) coordinate system and is positive when the
north magnetic pole is tilted toward the Sun.
Therefore, it is essential to have a reliable estimate of the average
position of the neutral sheet. Several shape models of the neutral sheet are
proposed in early studies. For example, a step model is proposed by Murayama (1966),
and a standard ellipse model is proposed by Russell and Brody (1967). While the step model stands against theory and observation, the
standard ellipse model gives unequal cross-sectional areas for north and
south lobes. That would yield different average magnetic field magnitudes in
the two lobes, inconsistent with the observations.
A 3-D diagram of the magnetotail neutral sheet. The sketch
illustrates the geomagnetic neutral sheet as the tailward projection of an
ellipse which is tilted at angle χ, which is the dipole tilt
angle, to the solar magnetospheric plane. The solid line is above the plane
and the dotted line is under the plane. The angle between the XY plane and
the magnetic equatorial plane also equals the dipole tilt angle χ. The hinging point is indicated in this figure, and the hinging distance
H0 is the distance from the Earth's center to the hinging
point, as shown in this figure.
To obtain an observational model of the neutral sheet, three major studies
have been done in the last several decades, i.e., Fairfield (1980), Hammond
et al. (1994), and Tsyganenko and Fairfield (2004). Fairfield (1980)
proposed a displaced ellipse neutral sheet model as shown in Fig. 2, given
by
Z=H0-D1-Y2Y02-DsinχY<Y0-DsinχY≥Y0,
where H0 is the magnetotail hinging distance from the Earth to the
hinge point shown in Fig. 1, D is a factor of the displacement of ellipse,
and Y0 is the semi-major axis of the model ellipse, as Fig. 2 shows.
This model accounts for asymmetrical areas of north and south lobes via a
displacement along Z. For eliminating the aberration effect caused by the
Earth's orbital motion, also called the windsock effect, all data were
rotated to the aberrated GSM (AGSM) coordinate system. The AGSM coordinate
system has its X axis antiparallel to the average direction of the solar
wind, aberrated from the Sun–Earth line. As with the GSM coordinate system,
the XY plane contains the Earth magnetic dipole axis with a Z axis chosen to
be in the same sense as the northern magnetic pole, and the Y axis completes
the right-handed Cartesian coordinate system.
Similar to Fairfield (1980), Hammond et al. (1994) also chose the displaced
ellipse neutral sheet model and the AGSM coordinate system, but with a more
exact aberration angle of 4∘. In addition, all data in the
magnetosphere were normalized to the same solar wind dynamic pressure (3.8 nPa)
using OMNI solar wind data with the equation of R, the magnetotail radius,
given as
R∝Pobs-16,
and a cross section (X=-25RE) given by the flaring magnetopause
model equation of Howe Jr. and Binsack (1972) as
R∝arctan10-XAGSM15.9.
Different from Fairfield (1980), Hammond et al. (1994) counted data to bins
on a cross section, and then obtained parameters via fitting the points
where the X component of the magnetic field changes sign. Tsyganenko and
Fairfield (2004) developed an analytical approximation for the shape of the
nightside tail current sheet with a semi-empirical model as a function of
the Earth's dipole tilt angle, solar wind ram pressure, and the
interplanetary magnetic field (IMF). The model of Tsyganenko and Fairfield (2004)
was developed for covering a downtail distance from 0 to 50 RE,
containing the region of the dipolar magnetic field.
The displaced ellipse neutral sheet model shown on the cross
section of the magnetotail. The blue line indicates the neutral sheet. The
parameters of the model are marked in this figure and “-Dsinχ”
is the displaced degree.
The shape of the neutral sheet can be greatly affected by the solar wind
parameters, the IMF, and the dipole tilt angle (Russell, 1972; Sibeck et al.,
1985; Tsyganenko and Fairfield, 2004). Russell (1972, 1973) predicted that
the IMF BY can twist the magnetotail neutral sheet. Sibeck et al. (1985)
found that the neutral sheet can be twisted left- or right-handed by
the positive or negative IMF BY, respectively. Further observations
found that a northward IMF can result in a greater twisting (e.g., Owen et
al. 1995). Later, Tsyganenko and Fairfield (2004) found that an increase in
solar wind dynamic pressure results in a decrease in the hinging distance
H0. Recently, based on the model of Tsyganenko and Fairfield (2004),
Tsyganenko et al. (2015) developed a new quantitative model of the shape of
the magnetospheric equatorial current sheet as a function of the dipole tilt
angle, solar wind dynamic pressure, and IMF, and the model covers all local
time, including the dayside sector.
A mass of data can now be obtained by spacecraft, such as Cluster, TC-1 and
THEMIS, and a new comprehensive and intuitive observation of the magnetotail
neutral sheet is expected. In this study, we investigate the average shape
of the neutral sheet affected by the dipolar tilt angle, the neutral sheet
configuration in the XY cross section, and the IMF twisting effect on the
neutral sheet.
Orbital coverages of Geotail during the 19-year (1995–2013)
tail period, Cluster 1–4 during the 10-year (2001–2010) tail period, TC-1
during the 4-year (2004–2007) tail period, and THEMIS P1–P5 during the 7-year
(2007–2013) tail period. The bin size is 2.5 RE× 2.5 RE. In each group, the left image
indicates the orbital coverage in the XY plane and the right panel indicates
the orbital coverage in the ZY plane. The residence times of the satellites
are given in days.
Data and methods
More data and satellites have become available since the work of Tsyganenko and
Fairfield (2004). In total, 10 years (2001–2010) of Cluster 1–4 (Balogh et
al., 2001), 19 years (1995–2013) of Geotail (Kokubun et al., 1994),
4 years (2004–2007) of TC-1 (Carr et al., 2005), and 7 years
(2007–2009 for P1/P2; 2007–2013 for P3–P5) of THEMIS (Auster et al., 2008)
magnetometer data are used in our study, with an original resolution of 4,
64, 60, and 3 s, respectively. The data from Cluster and THEMIS are
averaged over 1 min intervals. In addition, the concurrent solar wind and
IMF data from OMNI (5 min resolution) are combined to normalize the
magnetotail neutral sheet model. To obtain symmetric images, the data are
converted into the AGSM coordinate system with an average aberration angle
of 4∘.
This work focuses on the near-Earth and middle tail. The hinging distance
can serve as an indication of the range of the dipolar magnetic field of the
Earth. Based on prior studies, the hinging distance is less than 10 RE,
so we consider the area with a downtail distance beyond 10 RE.
Furthermore, in consideration of the satellite orbits, the observation
region is set as -35 RE < X < -10 RE, -20 RE < Y < 20 RE,
and -10 RE < Z < 10 RE (in AGSM, which is used throughout the paper unless mentioned
otherwise). Figure 3 shows orbit coverage of the magnetic field data
obtained from Geotail, Cluster, TC-1, and THEMIS satellites projected onto
the XY and YZ plane with bin size 2.5 × 2.5 RE. One can find
that THEMIS and Geotail have a large number of data and extensive spatial
coverage. Cluster provides a large number of data, but the coverage is
concentrated in the area with a near-to-middle tail distance. The orbit of
TC-1 is lower than Cluster, providing more data nearer to the Earth.
In order to combine all data from different satellites to study the average
shape and position of the neutral sheet, the data should be merged into one
unified data set. Similar to Fig. 3, the unified data set is plotted in the
XY (left panel) and YZ (right panel) plane. As shown in Fig. 4, combining
the data from different satellites provides better coverage, in space and
time.
Orbital coverage of all satellites in the XY and ZY plane
in the AGSM coordinate system. The bin size is 2.5 RE× 2.5 RE. The left panel indicates the
orbital coverage in the XY plane and the right panel indicates the
orbital coverage in the ZY plane. As this figure shows, a better coverage in space and time can be obtained by merging the data of
different satellites.
The data are normalized to the same conditions to eliminate the effect of
the solar wind dynamic pressure and the flaring of the magnetotail with the
same method used by Hammond et al. (1994). The solar wind dynamic pressure
corresponding to the magnetic data used in this study is shown in Fig. 5a. The
mean value of the solar wind dynamic pressure is ∼ 2 nPa. Thereby, all data are normalized to a reference solar wind dynamic
pressure of 2 nPa. As a reference, Fig. 5b shows the statistics of the
solar wind dynamic pressure data obtained from OMNI for years 1995 to 2013,
which also have a mean value of ∼ 2 nPa. Because of the
flaring of the magnetotail, the cross section varies with downtail distance,
even at fixed solar wind dynamic pressure. In order to eliminate this
effect, all data are normalized to the same downtail distance with the
magnetopause model of Howe Jr. and Binsack (1972). Considering the data
distribution from X∼-10 RE to X∼-35 RE,
a reference value of a downtail distance of 20 RE is chosen in
this study.
The next step is to obtain images of the cross section of the magnetotail
containing the average shape and position of the neutral sheet. In order to
investigate the effect of the dipole tilt on the neutral sheet, the data are
divided into 14 sets with a dipole tilt angle interval of 5∘.
Magnetic field data in each set are binned into 0.5 × 0.5 RE
bins in a plane of |Y| < 20 RE and |Z| < 10 RE. Bins are ignored if they contain fewer than 10
data points. We count the number of data with a positive BX in each bin
and calculate the percentage. A percentage of more than 50 % indicates
that BX in the corresponding bin is positive, and a percentage of less
than 50 % indicates a negative BX.
Histograms of the solar wind dynamic pressure. The panels
show the results of the concurrent solar wind dynamic pressure when the
magnetosphere data are available and analyzed in this study (a) and the OMNI
data spanning the years 1995–2013 (b). The blue dashed lines show the mean
values of the solar wind dynamic pressure, at about 2 nPa.
The sign of BX (in AGSM) in 0.5 RE× 0.5 RE
bins for a 40 RE× 20 REYZ cross
section in 5∘ intervals of dipole tilt angle. All data are
normalized to X=-20 RE and a solar wind dynamic
pressure of 2 nPa. Red (blue) indicates more positive (negative) values of
BX in each bin. The neutral sheet is located between the
red and blue areas.
Fitting the neutral sheet locations in the YZ cross sections
for different dipole tilt angles. The blue points give the positions
BX= 0 (in AGSM), and the red lines are the best
fits to these points.
An illustration of the neutral sheet in the XY cross section
for 5∘ intervals of dipole tilt angle. Data of -5 RE < Y < 5 RE are chosen. To
increase the data coverage, the negative dipole tilt angle data are combined
with the positive angle data, and the data for a tilt greater than
25∘ are combined also. The ratio of the Z axis to the X axis in
data units is set as 2.
Global shape of the magnetotail neutral sheet
Figure 6 shows the shape of the neutral sheet under different dipole tilt
angle. Red indicates that BX is positive and blue indicates negative
BX. The position between the two colors is considered the neutral
sheet. As Fig. 6 shows, the neutral sheet is curved more with increasing
dipole tilt. The neutral sheet curves toward north for positive dipole tilts
and toward south for negative dipole tilts. The correlation between the
dipole tilt and the curvature of the neutral sheet can be expressed as a
sine function. The points where the sign of BX changes are recorded in
Fig. 7, and the points where data are lacking are ignored. Our study focus
on the average shape and position of the neutral sheet; therefore an
empirical model of the displaced ellipse model is chosen to fit the shape of
the neutral sheet. The average position and shape of the neutral sheet can
be parameterized by fitting these points using the displaced ellipse model.
The fitted curves are also plotted in Fig. 7. We calculate the correlation
coefficient (R2) for each best-fitted curve, labeled on each panel.
Figure 8 shows the neutral sheet configuration in the XY cross section with
the data of -5 RE < Y < 5 RE. The fitting angle
of slope and the uncertainty are labeled. While the neutral sheet has a
displacement along Z, it tilts slightly along the tailward direction when
the dipole angle increases. The larger the dipole tilt angle is, the more
the neutral sheet tilts. Therefore, the dipole tilt angle affects not only
the neutral sheet warping in the YZ cross section but also the tilting of
the neutral sheet in the XY cross section.
For a small dipole tilt, the shape of the neutral sheet on the cross section
is almost a straight line, and the fitting will make little sense.
Therefore, the four sets of parameters, where |θ| is
less than 10∘, are ignored. The final parameters can be obtained
by taking the average of the remaining 10 sets of parameters listed in Table 1, and the final parameters are listed in
Table 2.
The parameters listed in Table 2 have been normalized to eliminate the
effect of solar wind dynamic pressure and magnetotail flaring. Thereby, the
model function contains a scaling factor as follows:
Z=H0′+D′1-Y2Y0′2-D′sinχY<Y0′-D′sinχY≥Y0′,H0=9.98,Y0=18.44,D=15.10,H0′=H0⋅ksp,Y0′=Y0⋅ksp⋅kmf,D′=D⋅ksp,ksp=2Pobs1/6,kmf=1.06arctan10-XAGSM15.9,
where H0′, Y0′, and D′ are the three parameters of the
displaced ellipse model. The parameters of kspand kmf are the
correction factors of solar wind dynamic pressure and magnetotail flaring,
respectively. H0, Y0, and D are the normalized parameters under
the solar wind dynamic pressure of 2 nPa and the downtail distance of 20 RE.
A comparison with three prior studies is given in Fig. 9. All model curves
are shown for a dipole tilt of 30∘. The result of this study is
shown by the blue line. The green, red and brown lines indicate the models
of Fairfield (1980), Hammond et al. (1994), and Tsyganenko and Fairfield (2004),
respectively. Except for the model of Fairfield (1980), which did not
consider the effect of solar wind dynamic pressure and downtail distance,
the other three models are shown for a downtail distance of 20 RE and a
solar wind dynamic pressure of 2 nPa. As Fig. 9 shows, at the center,
where the Y axis value is zero, the height of the neutral sheet in this
study is close to the prior models, a little lower than Fairfield (1980) and
a little higher than Hammond et al. (1994) and Tsyganenko and Fairfield (2004). The difference becomes less when the dipole tilt decreases. Our hinging
distance is a little greater than that of Hammond et al. (1994) and less
than that given by Fairfield (1980). Our result is very similar to the
result of Tsyganenko and Fairfield (2004), which indicates that the
displaced ellipse model with suitable parameters are reliable to study the
average of the neutral sheet shape.
Parameters of the displaced ellipse model of the neutral sheet
for 5∘ intervals of dipole tilt, with a downtail distance of 20 RE
and a solar wind dynamic pressure of 2 nPa.
Final parameters of the displaced ellipse model of the
neutral, with a downtail distance of 20 RE and a solar
wind dynamic pressure of 2 nPa.
ParameterHammondPresent studyet al. (1994)H09.579.98Y021.4818.44D13.5815.10IMF dependence of the magnetotail neutral sheet
The IMF has a bearing upon the shape of the neutral sheet (Russell, 1972, 1973). The IMF BY can lead to a twisting of the magnetotail (Cowley,
1981), as well as the neutral sheet. The IMF BY-related twisting effect
has been observed in prior studies (e.g., Slavin et al., 1983; Sibeck et al.,
1985). Previous works (e.g., Owen et al., 1995; Maezawa and Hori, 1998) have also
found that the IMF BY-related twisting becomes much larger during the
periods of northward IMF.
Comparison of the curves in the YZ cross section of the
neutral sheet of three similar studies. Four neutral sheet models from three
previous studies and this study are shown for a dipole tilt of 30∘.
The blue line shows the result of this study. The green line indicates the
model of Fairfield (1980). The red line indicates the model of Hammond et
al. (1994). The brown line, which is close to the blue line, represents the
model of Tsyganenko and Fairfield (2004). Except for Fairfield (1980), the
neutral sheet models are shown with a downtail distance of 20 RE and a solar
wind dynamic pressure of 2 nPa.
Illustration of the IMF-BY related
twisting effect on the neutral sheet for (a) IMF-BY < -3 nT, (b)-1 nT < IMF-BY < 1 nT, and (c) IMF-BY > 3 nT. The white belt
between red and blue indicates the shape of the neutral sheet. The black
dotted lines are the fitting results of the neutral sheet, and the twisting
angles are marked in the respective panel. In order to obtain a more
pronounced visual effect, the ratio of the Z axis to the Y axis in data
units is set as 2. It is shown that a counterclockwise (clockwise) twisting of
the neutral sheet is observed, along the downtail direction, when the
IMF-BY is positive (negative).
Summary of previous studies and comparison with the present study.
Fairfield (1980)Hammond et al. (1994)Tsyganenko andFairfield (2004)Present studySatellitesIMP-6 IMP-7 IMP-8IMP-7 IMP-8 ISEE-2 OMNIGeotail Polar ACE WIND IMP-8Cluster 1–4 Geotail TC-1 THEMIS 1–5 OMNIMagnetic fielddataIMP-6 1971–1973 9–12 IMP-7 1972.10–1973.3 IMP-8 1973.11–1974.11IMP-7 1973 IMP-8 1978–1986 ISEE-2 1978/1979/1984/1986Geotail 1994–2002 Polar 1999–2001Cluster 1–4 2001–2010 Geotail 1995–2013 TC-1 2004–2007 THEMIS P1–P2 2007–2009 P3–P5 2007–2013Solar wind dataNoOMNIACE WIND IMP-8OMNIScalingNoSolar wind dynamicpressure Flaring of the magnetotailNoSolar wind dynamicpressure Flaring of the magnetotailModelThe displaced ellipsemodelThe displaced ellipsemodelA semi-empiricalmodelThe displaced ellipsemodelObtainingparametersMinimizing the number of mismatches between the observed and predicted orientation of the magnetic field on two sides of the modelFitting the points between bins with different sign of BXMinimizing the number of mismatches between the observed and predicted orientation of the magnetic field on two sides of the modelFitting the points between bins with different sign of BXCoordinate systemAGSMAGSMGSWAGSM
Illustration of the IMF-BZ effect on the
neutral sheet twisting for (a1) IMF-BY < -3 nT
and IMF-BZ > 0 nT, (b1) IMF-BY > 3 nT
and IMF-BZ > 0 nT, (a2) IMF-BY < -3 nT and
IMF-BZ < 0 nT, and (b2) IMF-BY > 3 nT and IMF-BZ < 0 nT. It is shown that a
northward IMF can result in a larger twisting angle of the near-tail neutral
sheet.
In order to show a flat neutral sheet, only data with a low dipole tilt
angle (absolute value less than 5∘) are used. To statistically
study the effect of large angle twisting on the neutral sheet under different levels of
the IMF BY, the data with IMF BY-8 to -3 nT (negative), -1 to 1 nT (zero),
and 3 to 8 nT (positive) are used in this section. Figure 10
shows the twisting effect of the IMF BY on the neutral sheet (in order
to obtain a more pronounced visual effect, the ratio of the Z axis to the
Y axis in data units is set as 2). The white belt between red and blue area
indicates the shape of the neutral sheet. As expected, looking along the
downtail direction, the neutral sheet is twisting clockwise for a negative
IMF BY and counterclockwise for positive IMF BY. Here we find a
clockwise twist of 3.37∘ for the IMF BY between -8 and -3 nT
and a counterclockwise twist of 3.10∘ for the IMF BY between
3 and 8 nT. Furthermore, the IMF BZ also plays a significant role in
the neutral sheet twisting. As shown in Fig. 11, we separate Fig. 10a
and c into positive and negative IMF BZ periods. For the IMF BY
between -8 and -3 nT, one can find a clockwise twist ∼ 4.40∘
for positive IMF BZ, and ∼ 2.73∘ for negative IMF BZ; for the IMF BY between 3
and 8 nT, a counterclockwise twist ∼ 3.37∘ is found
for positive IMF BZ, and ∼ 2.20∘ for negative
IMF BZ. This indicates that a northward IMF can result in a greater twisting
of the neutral sheet in the near tail.
Discussion and conclusions
Our results show that the displaced ellipse model of the neutral sheet has a
greater degree of curve than that of Hammond et al. (1994) and is close to
the model of Tsyganenko and Fairfield (2004). The position of the hinging
point in this study is close to the findings in the prior studies (Hammond
et al., 1994; Tsyganenko and Fairfield, 2004). As shown in Fig. 9, the
curves in the cross section of YZ are plotted with a very large dipole tilt of
30∘ to make the difference clearer. The curves will be closer to
each other for a smaller dipole tilt. Fairfield (1980) did not normalize the
data, which have a significant effect on the result, so the curve of
Fairfield (1980) is just for reference.
As listed in Table 3, there are some comparisons of this work with prior
works. In the past few decades, more satellites have become available and more
data can be obtained. We define a satellite year as the number of years of
data. However, satellites with similar orbits are counted only once. For
this study, the four Cluster satellites count as one, and THEMIS P3–P5 should
be counted as one, too. Thereby, our study spans 46 satellite years, containing
10 years of Cluster, 19 years of Geotail, 4 years of TC-1, and 3 + 3+ 7
years of THEMIS (compared with 9 satellite years in the study of Fairfield, 1980,
14 satellite years in the study of Hammond et al., 1994, and 12
satellite years of Tsyganenko and Fairfield, 2004). As in the investigations of
Fairfield (1980) and Hammond et al. (1994), the data are converted
to the AGSM coordinate system in this work. Tsyganenko and Fairfield (2004)
converted the data to the GSW (geocentric solar wind) coordinate system. The difference between the
AGSM coordinate system and the GSW coordinate system is the direction of the
X axis. The X axis in the AGSM coordinate system is antiparallel to the
average solar wind flow, while the X axis in the GSW coordinate system is
antiparallel to the observed solar wind flow.
The effect of solar wind dynamic pressure and magnetotail flaring on the
shape of the neutral sheet is substantial. Thus all data are scaled to the
same solar wind dynamic pressure and downtail distance to eliminate their
effects. We use a statistical method to investigate the average position of
the neutral sheet with grids (bins) in the YZ cross section, instead of
simply recording where the X component of the magnetic field changes sign.
The bin method offers a superb solution to solve the problem of
undersampling and increases the accuracy of the result. Fairfield (1980)
parameterized the model by minimizing the number of mismatches between the
observed and predicted orientation of the magnetic field on two sides of the
neutral sheet, same as Tsyganenko and Fairfield (2004). The method of
Fairfield (1980) can also solve the problem of undersampling effectively,
but it is hard to produce visualized images like Figs. 6, 7, and 8.
Therefore, the bin method is a good choice.
Figure 6 illustrates the change in the average shape of the neutral sheet
with different dipole tilt angle. Obviously, a positive dipole tilt leads to
a northern curve and a negative dipole tilt leads to a southern curve. In
addition, the larger the dipole tilt is, the greater the curvature is. As
Fig. 6 shows, the shape of the curve of the neutral sheet in the YZ cross
section is almost a semi-ellipse, and the flanks of the neutral sheet extend
under the XY plane. The results are consistent with expectations. To balance
the magnetic pressure in two lobes, the neutral sheet has a displacement
along Z with curving.
In this investigation, we find that the dipole tilt angle has a global
influence on the neutral configuration. It affects not only the warping of
the neutral sheet in the YZ cross section but also the tilting in the XY cross section. Furthermore, we observe the IMF BY twisting effect on
the neutral sheet. As shown in Fig. 10, the neutral sheet twists clockwise
for a negative IMF BY and counterclockwise for a positive IMF BY. It
is considered that the farther the distance from Earth, the larger the
degree of the IMF BY twisting (Cowley, 1980; Tsyganenko and Fairfield,
2004). The IMF BY twisting effect in the distant magnetotail has been
observed in some prior studies (Slavin et al., 1983; Sibeck et al., 1985;
Owen et al., 1995; Maezawa and Hori, 1998). In this study, the observation
of the IMF BY twisting effect focused on the near tail, between X=-10 RE and -35 RE. It is observed that the larger the IMF BY, the
larger the twisting angle. However, because of the lack of data for large
IMF BY, it could not be accurate enough to investigate the quantitative
relation between the twisting angle and the IMF BY in this observation.
In the near tail, we can also observe a larger twisting angle for northward
IMF BZ than for southward, as which has been observed in the distant
tail (e.g., Owen et al., 1995; Maezawa and Hori, 1998).
There have been a series of works reporting the model of the magnetotail
neutral sheet (e.g., Fairfield, 1980; Hammond et al., 1994; Tsyganenko and
Fairfield, 2004). Recently, a new quantitative model of the shape of the
magnetospheric equatorial current sheet has been developed, taking the
dipole tilt angle, the solar wind ram pressure, and transverse components of
the IMF into consideration (Tsyganenko et al., 2015). Tsyganenko et al. (2015) defined the current sheet as the location where the observed magnetic
field reverses its radial component. This model provides a global view of
the current sheet. Compared to the model of Tsyganenko et al. (2015), we
provide a reliable average neutral sheet shape and position with a large
database. Our results can be a significant reference to the model of the
neutral sheet.
Acknowledgements
This work was supported by NSFC grants 41574173, 41421063, and 41474144 in
China and by EU FP7 grant 263325 – ECLAT and the Austrian Science Fund FWF
P23862-N16 and Fund P24740-N27 in Austria. We are grateful to the teams and
PIs of all experiments whose data were used in this study. We appreciate
Cluster Active Archive at http://caa.estec.esa.int/ and the THEMIS data
center of Berkeley at http://themis.ssl.berkeley.edu/ for the data used in
this study. The TC-1 FGM and PGP data were provided by the Austrian DSP
Data Center at http://dione.iwf.oeaw.ac.at/ddms/, and the Geotail MGF data
and the interplanetary data of OMNI were obtained from CDAWeb online
facility at http://cdaweb.gsfc.nasa.gov/.
The topical editor, C. Owen, thanks H. Lühr and one anonymous referee for help in evaluating this paper.
ReferencesAuster, H. U., Glassmeier, K., Magnes, W., Aydogar, O., Baumjohann, W.,
Constantinescu, D., Fischer, D., Fornacon, K., Georgescu, E., Harvey, P.,
Hillenmaier, O., Kroth, R., Ludlam, M., Narita, Y., Nakamura, R., Okrafka,
K., Plaschke, F., Richter, I., Schwarzl, H., Stoll, B., Valavanoglou, A.,
and Wiedemann, M.: The THEMIS fluxgate magnetometer, Space Sci. Rev., 141,
235–264, 10.1007/s11214-008-9365-9, 2008.Balogh, A., Carr, C. M., Acuña, M. H., Dunlop, M. W., Beek, T. J., Brown, P.,
Fornacon, K.-H., Georgescu, E., Glassmeier, K.-H., Harris, J., Musmann, G.,
Oddy, T., and Schwingenschuh, K.: The Cluster Magnetic Field Investigation:
overview of in-flight performance and initial results, Ann. Geophys., 19,
1207–1217, 10.5194/angeo-19-1207-2001, 2001.
Baumjohann, W. and Treumann, R. A.: Basic Space Plasma Physics (Revised
Edition), Imperial College Press, London, UK, 2012.Carr, C., Brown, P., Zhang, T. L., Gloag, J., Horbury, T., Lucek, E., Magnes,
W., O'Brien, H., Oddy, T., Auster, U., Austin, P., Aydogar, O., Balogh, A.,
Baumjohann, W., Beek, T., Eichelberger, H., Fornacon, K.-H., Georgescu, E.,
Glassmeier, K.-H., Ludlam, M., Nakamura, R., and Richter, I.: The Double Star
magnetic field investigation: instrument design, performance and highlights
of the first year's observations, Ann. Geophys., 23, 2713–2732,
10.5194/angeo-23-2713-2005, 2005.
Cowley, S. W. H.: Magnetospheric asymmetries associated with the y-component
of the IMF, Planet. Space Sci., 29, 79–96, 1981.Fairfield, D.: A statistical determination of the shape and position of the
geomagnetic neutral sheet, J. Geophys. Res., 85, 775–780,
10.1029/JA085iA02p00775, 1980.Hammond, C. M., Kivelson, M. G. and Walker, R. J.: Imaging the effect of dipole
tilt on magnetotail boundaries, J. Geophys. Res., 99, 6079–6092,
10.1029/93JA01924, 1994.Howe Jr., H. C. and Binsack, J. H.: Explorer 33 and 35 plasma observations
of magnetosheath flow, J. Geophys. Res., 77, 3334–3344,
10.1029/JA077i019p03334, 1972.
Kokubun, S., Yamamoto, T., Acuña, M. H., Hayashi, K., Shiokawa, K.,
and Kawano, H.: The GEOTAIL magnetic field experiment, J. Geomagn. Geoelectr.,
46, 7–21, 1994.Maezawa, K. and Hori, T.: The Distant Magnetotail: Its Structure, IMF
Dependence, and Thermal Properties, in New Perspectives on the Earth's
Magnetotail, American Geophysical Union, Washington, D.C., USA, 1–19, 10.1029/GM105p0001, 1998.Murayama, T.: Spatial distribution of energetic electrons in the geomagnetic
tail, J. Geophys. Res., 71, 5547–5557, 10.1029/JZ071i023p05547,
1966.Ness, N. F.: The Earth's magnetic tail, J. Geophys.
Res., 70, 2989–3005, 10.1029/JZ070i013p02989, 1965.Owen, C. J., Slavin, J. A., Richardson, I. G., Murphy, N., and Hynds, R. J.: Average motion,
structure and orientation of the distant magnetotail determined from remote
sensing of the edge of the plasma sheet boundary layer with E >35 keV ions, J. Geophys. Res.-Atmos., 100, 185–204,
10.1029/94JA02417, 1995.
Russell, C. T.: The configuration of the magnetosphere, in: Critical Problems
of Magnetospheric Physics, edited by: Dyer, E. R., p. 1, IUCSTP Secretariat,
National Academy of Sciences, Washington DC, USA, 1972.Russell, C. T.: Comments on the paper “The internal structure of the
geomagnetic neutral sheet”, by K. Schindler and N. F. Ness, J. Geophys. Res.,
78, 7576–7579, 10.1029/JA078i031p07576, 1973.Russell, C. T. and Brody, K. I.: Some remarks on the position and shape of
the neutral sheet, J. Geophys. Res., 72, 6104–6106,
10.1029/JZ072i023p06104, 1967.Sibeck, D. G., Siscoe, G. L., Slavin, J. A., Smith, E. J., Tsurutani, B. T.,
and Lepping, R. P.: The distant magnetotail's response to a strong
interplanetary magnetic field By: Twisting, flattening, and field line
bending, J. Geophys. Res., 90, 4011–4019, 10.1029/JA090iA05p04011,
1985.Slavin, J. A., Tsurutani, B. T., Smith, E. J., Jones, D. E., and Sibeck, D.
G.: Average configuration of the distant (<220 Re) magnetotail:
Initial ISEE-3 magnetic field results, Geophys. Res. Lett., 10, 973–976, 10.1029/GL010i010p00973, 1983.Tsyganenko, N. A. and Fairfield, D. H.: Global shape of the magnetotail
current sheet as derived from Geotail and Polar data, J. Geophys. Res., 109,
A03218, 10.1029/2003JA010062, 2004.Tsyganenko, N. A., Andreeva, V. A., and Gordeev, E. I.: Internally and
externally induced deformations of the magnetospheric equatorial current as
inferred from spacecraft data, Ann. Geophys., 33, 1–11,
10.5194/angeo-33-1-2015, 2015.