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
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.
• The orientation of CME flux ropes have been
approximately determined using the orientation of
Hα 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.
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 χ between Yc and SAy (or between Zc &
SAz) denotes the orientation of the elliptic base (see Fig.
1)
The elliptic cone
in XcYcZc, the
cone coordinate
system
ωy, ωz: The half
angular width
χ: the angle from
Ye to Yc. Positive
~ counterclockwise
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 χ characterizes the
orientation of the base.
1. Yc Axis is located on
both plane XhYh and
YcZc.
The heliocentric ecliptic coordinate system XhYhZh
X’c
Zh
2. The orientation of
both cone base & halo
is measured relative to
Yc axis.
Y’c,Yc
Xc (λ,φ) or (β,α)
Yh (west)
Rc
α
The plane of
the sky
β
λ
φ
3. The projection
of cone base onto
the POS depends
mainly on β and
the Zc component
of the rim of base
The
ecliptic
Xh, Z’c (To Earth)
Zc
Figure 2. The Xc direction (λ,φ) or
(β,α) in XhYhZh. The base on YcZc
plane is first projected onto X’cY’c
plane via β, then rotating α to YhZh
plane.
ψ
ψ
0
α
Figure 3. The orientation of elliptic halos is measured by angle ψ
between Yeo and Yc(Yc’) or between Xeo and Xc’. Here
X’c axis is in the direction from the disk center to the halo center, the
projection of Xc onto YhZh.
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 χ (-20, 0, 20 from left to right) and β
(90, 70, 50 from top to bottom) on the angle ψ. When χ=0 or β=90 there
is no shift between red and black lines. For χ < and > 0, the shift is
slightly toward Yc axis.
Figure 5. The same as Figure 4 but χ increase from 0, 20 to 40 degrees.
The shift of red line with 0 relative to black line increases as |χ|
increases.
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 X’c axis and greater than Figures 4 & 5.
When β = 50 degrees (see bottom row) the halo major axes correspond
to the base minor axes !!!
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.
C3: 19970512_1451
EIT 19970512_1455 N13W08
C3: 20000714_1142
EIT 20000714_1155 N22W07
Figure 7.1.
EIT: 19970512 N13W08
C3:19970512_1451
Figure 7.2
EIT: 20000714 N22W07
C3: 20000714_1142
Figure 7.3
C3: 20000809_2018
EIT 20000809_1954 N11W11
Figure 8.1.
C3: 20001025_1242
EIT 20001025_1250 N06W61
EIT: 20000809
C3: 20000809_2018
Figure 8.2
N11W11
EIT: 20001025
C3: 20001025_1242
Figure 8.2
N06W61
C3:20020415_0742
Figure 9.1.
C3:20020417_1038
EIT 20020415_0750 S15W01
EIT 20020417_1106 S14W34
EIT: 20000415
C3: 20020415_0742
Figure 9.2
S15W01
EIT: 20020417
C3: 20020417_1038
Figure 9.3
S14W34
Figure 10.1.
C3: 20031028_1142
EIT 20021028_1154 S16W02
C3: 20031029_2142
EIT 20031029_2154 S15W02
EIT: 20031028
C3: 20031028_1142
Figure 10.2
S16W02
EIT: 20031029
C3: 20031029_2142
S15W02
C3: 20040725_1718
EIT 20040725_2006 N04W30
C3: 20050513_1742
EIT 20050513_2352 N12E11
Figure 11.1.
EIT: 20040725
C3: 20040725_1718
Figure 11.2
N04W30
EIT: 20050513
C3: 20050513_1742
Figure 11.3
N12E11
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 |χ| increases and β decreases.
• When the base major axis located near Zc axis, the
shift is away from X’c axis with greater value than
when the base major axis near Yc axis. If β 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.
• Therefore, when an observed halo major axis is
located near X’c 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 Y’c 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 β, χ, ωy and ωz 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.