Determination of the orientation of CME flux ropes for frontside full halo CMEs

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Determination of the orientation of CME flux
ropes for front-side full halo CMEs

• Xuepu Zhao
• Stanford University
• LWS-CDAW Conference
• Melbourne, FL March 7, 2007

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1. Purpose of the work

• The magnetic configuration of most of CMEs is
  believed to be the magnetic flux rope since the
  free magnetic energy that drives CME is believed
  to be stored in field-aligned electric currents.
• It is the direction and strength of the central
  axial field of CME flux ropes that basically
  determines the duration and intensity of
  ICME-associated Bs events. Especially, if the
  central axial field is pointed northward, there
  would be no ICME-associated Bs event. (Zhao
  Hoeksema, 1998 Zhao, Hoeksema Marubashi,
  2001).
• To determine the central axial field direction we
  need both the orientation and the helicity of CME
  flux ropes. The Stanford SDO/HMI plans to study
  the helicity of CME flux ropes using HMI vector
  magnetograms.

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• The orientation of CME flux ropes have been
  approximately determined using the orientation of
  Ha filaments, the inclination of the local HCS,
  and the orientation of magnetic arcade. It is
  suggested recently that the orientation of the
  major axis of full halo CMEs (the halo major
  axis) may be used to determine the orientation
  of CME flux ropes (Cremade, 2005 Yurchyshyn et
  al., 2007).
• Halo CMEs can be produced by projecting the base
  (or the cross-section) of the elliptic cone
  model onto the plane of the sky (Cremade, 2004
  Zhao, 2004). To see if the projection effect can
  be neglected, we first show the effect of various
  elliptic cone parameters on the orientation of
  the halo major axis, then compare the orientation
  of major axis of 10 S-type disk full halo CMEs
  (see the Master Data Table of 79 events) with the
  associated EIT arcades.

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2. Comparison of the orientation between modeled
halo and base major axes

• The shape of CME ropes may be approximated by
  the elliptic cone model. The observed halo may be
  reproduced by the base (cross-section) of the
  cone model.
• To define the orientation of the elliptic cone
  base, we set a cone coordinate system XcYcZc
  with its Xc axis aligned with the central axis
  of the cone, and the YcZc plane parallel to the
  elliptic cone base. The Semi-axes, SAy SAz, of
  the elliptic base are located near the Yc and Zc
  axes, respectively.
• The angle ? between Yc and SAy (or between Zc
  SAz) denotes the orientation of the elliptic base
  (see Fig. 1)

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The elliptic cone in XcYcZc, the cone coordinate
system ?y, ?z The half angular width ? the
angle from Ye to Yc. Positive
counter-clockwise
SAy
SAz
Figure 1. The central axis of the cone is aligned
with Xc axis. The cone base is located at Rc from
the origin with two semi-axes, SAy SAz, located
near Yc Zc axes, respectively. The angle ?
characterizes the orientation of the base.
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1. Yc Axis is located on both plane XhYh and
YcZc. 2. The orientation of both cone base halo
is measured relative to Yc axis.
The heliocentric ecliptic coordinate system XhYhZh
Zh
Xc
Xc (?,f) or (ß,a)
Yh (west)
Yc,Yc
Rc
ß
a
The plane of the sky
?
The ecliptic
f
3. The projection of cone base onto the POS
depends mainly on ß and the Zc component of the
rim of base
Xh, Zc (To Earth)
Figure 2. The Xc direction (?,f) or (ß,a) in
XhYhZh. The base on YcZc plane is first projected
onto XcYc plane via ß, then rotating a to YhZh
plane.
Zc
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?
?
0
a
Figure 3. The orientation of elliptic halos is
measured by angle ? between Yeo and Yc(Yc) or
between Xeo and Xc. Here Xc axis is in the
direction from the disk center to the halo
center, the projection of Xc onto YhZh.
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Black line with 0 projection of the base major
axis that is located near Yc axis Red line with
0 halo major axis
Figure 4. The effect of changing ? (-20, 0, 20
from left to right) and ß (90, 70, 50 from top to
bottom) on the angle ?. When ?0 or ß90 there is
no shift between red and black lines. For ? lt
and gt 0, the shift is slightly toward Yc axis.
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Figure 5. The same as Figure 4 but ? increase
from 0, 20 to 40 degrees. The shift of red line
with 0 relative to black line increases as ?
increases.
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When base major axes are located near Yc axis,
the halo major axes move toward Yc. The shft
relative to the projection of base major axes is
less than a few tens deg. When base major axes
are located near Zc axis, the projection effect
is more significant than near Yc axis, halo
major axes may even correspond to base minor axes.
Figure 6. The same as Figure 5 but the base major
axis is located near Zc axis. The shift is away
from Xc axis and greater than Figures 4 5.
When ß 50 degrees (see bottom row) the halo
major axes correspond to the base minor axes !!!
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3. Comparison of the orientation of halo major
axis with that of EIT arcades

• The orientation of EIT or Soft-X arcades is
  believed to be aligned with the orientation of
  CME flux ropes near the Sun.
• In the table of 79 major geostorms, there are 17
  geostorms associated with single halo CMEs. Among
  them, 10 are S-type, disk full halo CMEs with
  rather clear outline. Figures 8 -- 12 display
  the major axes of halos and EIT arcades.

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EIT 19970512_1455 N13W08
C3 19970512_1451

Figure 7.1.
C3 20000714_1142
EIT 20000714_1155 N22W07
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EIT 19970512 N13W08
C319970512_1451
Figure 7.2
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EIT 20000714 N22W07
C3 20000714_1142
Figure 7.3
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EIT 20000809_1954 N11W11
C3 20000809_2018
Figure 8.1.
C3 20001025_1242
EIT 20001025_1250 N06W61
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EIT 20000809 N11W11
C3 20000809_2018
Figure 8.2
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(No Transcript)
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EIT 20001025 N06W61
C3 20001025_1242
Figure 8.2
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C320020415_0742
EIT 20020415_0750 S15W01
C320020417_1038
EIT 20020417_1106 S14W34
Figure 9.1.
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EIT 20000415 S15W01
C3 20020415_0742
Figure 9.2
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EIT 20020417 S14W34
C3 20020417_1038
Figure 9.3
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C3 20031028_1142
EIT 20021028_1154 S16W02
Figure 10.1.
C3 20031029_2142
EIT 20031029_2154 S15W02
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EIT 20031028 S16W02
C3 20031028_1142
Figure 10.2
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EIT 20031029 S15W02
C3 20031029_2142
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C3 20040725_1718
EIT 20040725_2006 N04W30
Figure 11.1.
C3 20050513_1742
EIT 20050513_2352 N12E11
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EIT 20040725 N04W30
C3 20040725_1718
Figure 11.2
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EIT 20050513 N12E11
C3 20050513_1742
Figure 11.3
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4. Summary

• The prediction of the orientation of halo major
  axis presented above shows that when the base
  major axis located near Yc axis, the halo major
  axis exhibts a shift from a few to 30 degrees
  toward the Yc axis relative to the base major
  axis. The shift increases as ? increases and ß
  decreases.
• When the base major axis located near Zc axis,
  the shift is away from Xc axis with greater
  value than when the base major axis near Yc axis.
  If ß is small enough, the modeled halo major
  axis may even correspond to the base minor axis.
• The comparison of the orientation of observed
  halo major axes with the orientation of EIT
  arcades supports the above conclusion.

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• Therefore, when an observed halo major axis is
  located near Xc axis, it may be used to
  approximately determine the orientation of CME
  flux ropes, though the shift may not be
  neglected. If the halo major axis is located near
  Yc axis, it must be careful to make any
  inference because in this case the halo major
  axis sometime may correspond to the base minor
  axis, instead of the base major axis or the
  orientation of CME flux rope.
• To more accurately determine the orientation of
  CME flux ropes it is necessary to invert the cone
  parameters ß, ?, ?y and ?z and to find the
  orientation of the base major axis. The new
  inversion algorithm for the elliptic cone model
  that uses STEREO observations of halo CMEs (Zhao,
  2006) will be useful in this study.