Comparison of Simulated and Observed Interplanetary Flux
Ropes
M. Vandas , S. Watari† and A. Geranios
Astronomical Institute, Academy of Sciences, Boční II 1401, 14131 Praha 4, Czech Republic
†
Communications Research Laboratory, 4-2-1 Nukuikita, Koganei, Tokyo 184-8795, Japan
Physics Department, Nuclear and Particle Physics Section, Athens University, Panepistimioupoli-Kouponia,
Athens 15771, Greece
Abstract. Three dimensional magnetohydrodynamic numerical simulations of propagating interplanetary flux ropes are presented and compared with “in-situ” spacecraft measurements. Flux ropes are injected near the Sun with various inclinations.
Specific features followed from simulations, as double-peak magnetic field profiles or a possibility to observe one flux rope
two times by the same spacecraft, are searched in observational data.
INTRODUCTION
Several years ago we have performed [7] MHD simulations of a propagating flux rope in the inner heliosphere
in two dimensions. The flux rope was perpendicular to
the computational domain and was introduced by perturbations of quantities at the inner boundary, which was supermagnetosonic. A model of the flux rope was a cylinder with a constant-α force-free field inside. For three
dimensional simulations we used the same way, only the
cylinder was replaced by a toroid; initially, a constantα force-free field was inside the toroid and the external field was a potential field around a toroid, described
in [8]. During injection of the toroid, only the magnetic
field was perturbed at the inner boundary, other quantities
remained unchanged. When a half of the toroid emerged,
its feet were kept at the inner boundary and shifted westward to simulate the solar rotation. The magnetic field
strength in the computational domain was one fifth of a
typical value to suppress numerical diffusion (i.e., 1 nT
at 1 AU).
More details on these simulations are given in [9]. The
simulations were made for several inclinations of the flux
rope to the ecliptic plane.
Interplanetary flux ropes are a subject of many studies
(e.g., [1, 2, 3, 4, 5, 6]). The most distinct interplanetary
flux ropes are magnetic clouds, defined by [1] as regions
in the solar wind with higher and smoothly rotating
magnetic fields and with lower proton temperatures, with
spatial extents of the order of 0.1 AU near 1 AU.
RESULTS OF SIMULATIONS
Figure 1 shows a shape of a flux rope when its leading
edge (apex) crossed 1 AU. The flux rope was injected
with 0Æ inclination to the ecliptic plane. Labels in Figure 1 identify parts of the flux rope, the apex and two
legs (western and eastern). The points A and L (bullets)
are located in the apex and the western leg, respectively.
FIGURE 1. Flux rope in the ecliptic plane as a result of
numerical simulations. The dashed line shows 1 AU distance.
CP679, Solar Wind Ten: Proceedings of the Tenth International Solar Wind Conference,
edited by M. Velli, R. Bruno, and F. Malara
© 2003 American Institute of Physics 0-7354-0148-9/03/$20.00
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FIGURE 2. Simulated observations at 1 AU of a flux rope with an inclination 20Æ . Hypotetic spacecraft were located in places
with the same longitude, the first one 4Æ below the ecliptic plane (a), the second one in the ecliptic plane (b), and the third one 4Æ
above it (c). B is the magnetic field magnitude, Bx , By , and Bz are the solar ecliptic components of the magnetic field, V , N, and T
are the velocity, density, and temperature of the solar wind, respectively.
the apex may be identified as a magnetic cloud. Contrary,
in the leg, variations of the density and temperature are
not so pronounced and they have even higher values near
the leg’s center. A saddle in B profile may develop at a
leg (Figure 2c).
Figure 3 displays the different spatial behaviors of
quantities at an apex and legs where distribution of B and
N on planes perpendicular to the flux rope at points A
and L (Figure 1) are shown. The black lines give projections of magnetic field lines, approximately indicating a
boundary of the flux rope. The apex has an oblate shape,
the shape of the leg is more circular. The leg has an increase in density (and temperature) near the center. We
understand this fact by different external conditions for
the apex and the leg. The leg moves more radially and
its central part does not expand so much as the diverging
Simulations give us temporal profiles of solar wind
quantities at various locations. Inspection of these profiles reveals that they are highly variable and depend on
which part of the flux rope was observed. A hypothetic
spacecraft sitting in A (Figure 1) will observe the flux
rope two times, its apex and its eastern leg (imagine a
radial line connecting A with the Sun).
Figure 2 shows simulated observations of a flux rope
with an inclination 20 Æ by three hypothetic spacecraft
at 1 AU, which are located quite close together. The
first spacecraft observed only an apex, the second one
both the apex and a leg, and the third one only the
leg. Rotation of the magnetic field vector is pronounced
in both the apex and the leg. But behaviors of plasma
parameters are different in these parts. There are distinct
decreases in the density and temperature in the apex, so
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FIGURE 3. Spatial distribution of the magnetic field magnitude B and density N at the cross-section of the flux rope at the apex
(A) and the leg (L). The temperature has a similar behavior as the density. A local Xc axis lies in the ecliptic plane.
ambient solar wind.
The simulations show that when a double-peak in
B (Figure 2c) develops, the saddle in the B profile is
located where the B z component changes its sign (for
low inclined flux ropes, B z has a profile like the sin
function, see again Figure 2c). And this is really the
case which is met in observations. Figure 4b documents
this fact. The flux rope of September 25–26, 1982, has
been analyzed by [4], who determined ϑ c
10Æ and
Æ
ϕc 111 . Another example could be the case of May
25-26, 1975, analyzed by [1], who estimated ϑ c 31Æ
and ϕc 206Æ.
Any clear example of two subsequent crossings of
one flux rope was not found. A flux rope should be low
inclined and have two subsequent increases in B z with
the same polarity (see Figure 2b). One suspicious case
is the event of June 2–4, 1998, with ϑ c 9Æ . A real
situation may disfavored this possibility: a larger B and
COMPARISON WITH OBSERVATIONS
Simulations show that candidates for a leg would have
relatively lower inclinations ( 30Æ ) and would be more
radially aligned (the last item is not always the case for
eastern legs, see Figure 1). Figure 4a displays a flux rope
of June 8–9, 1997, which might be a candidate for a
leg observation. The magnetic field and plasma behavior
look similar to simulated profiles. An estimated inclination of the flux rope is ϑ c 4Æ and its azimuthal angle
ϕc 201Æ. The density and temperature have increases
in the center of the rope. Another example could be the
interplanetary flux rope of February 18, 1998, where the
density and temperature are enhanced inside the rope.
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FIGURE 4. “In-situ” observations of interplanetary flux ropes by (a) the Wind and (b) IMP-8 spacecraft. The quantities have the
same meaning as in Figure 2, Tp is the proton temperature.
faster motion than they are in the simulations, may cause
a flux rope is not so bended; or magnetic field rotation is
not very distinct in some parts of legs.
Sciences of the Czech Republic.
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CONCLUSIONS
1.
Simulations show a variety of profiles through interplanetary flux ropes and may help to understand what part of
a rope is observed by spacecraft. In particular, they suggest a distinction in plasma parameters in an apex and
legs.
2.
3.
4.
5.
6.
ACKNOWLEDGMENTS
7.
The observational data were provided by the computer
services of the National Space Science Data Center
(WDC-A-R&S); PIs are: R. P. Lepping for magnetic field
data, and J. T. Gosling and K. W. Ogilvie for plasma
data. This work was supported by grant A3003003 and
projects S1003006 and K3012103 from the Academy of
8.
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