CMEs: Taking magnetic helicity
from low corona
into interplanetary space
Mei Zhang
（National Astronomical Observatory, Chinese Academy of Sciences）
Collaborators:
Boon Chye Low, Natasha Flyer (NCAR, Boulder, USA)
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Plan of the Talk
1. Introduction
2. CMEs as a result of magnetic helicity accumulation
in the corona
(Zhang, Flyer & Low 2006, ApJ, 644, 575;
Zhang & Flyer 2008, ApJ, 683, 1160 )
3. Magnetic helicity in the interplanetary space
(Zhang, Flyer & Low 2012, ApJ, 755, 78)
Key observations of CMEs
for modelers to address:
• Why CME takes place?
• Why occasionally, not continuously?
• Why erupts from previously closed regions (active
regions or streamers)?
• Why initiation often associates with surface field
variations such as flux emergence?
We address these questions in terms of magnetic helicity accumulation.
3
Magnetic helicity:
(A：vector potential)
Magnetic helicity is a conserved quantity that describes field topology.
 Magnetic helicity quantifies the twist (self-helicity) and linkage (mutualhelicity) of magnetic field lines.
(Image credit:
T. Sakurai)
Ｈ＝０
Ｈ＝ＴΦ2
Ｈ＝±２Φ1Φ2
 The total magnetic helicity is still conserved in the corona even when
there is a fast magnetic reconnection (Berger 1984).
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Helicity accumulation in the corona:
1. Hemispheric
helicity sign rule:
Positive in southern
hemisphere;
Negative in northern
hemisphere.
(Image credit: A. Pevtsov)
2. Berger (1984)’s
conservation law
=> Magnetic helicity is accumulating
in the corona !
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What are the consequences
of magnetic helicity
accumulation
in the corona?
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We try to understand this by studying axisymmetric nonlinear
force-free fields.
Force-free: Because the corona is very tenuous, the
large-scale field is usually regarded as force-free.
Governing equation:
Boundary condition:
(in Zhang et al. 2006)
With a given boundary condition and a specific
n, all possible solutions with different γ values
can be found. (Flyer et al. 2004, ApJ, 606, 1210 )
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The existence of helicity upper bound
Nonlinear force-free field
calculations indicate that there
may be an upper bound on the
total magnetic helicity that
force-free fields can contain.
(Zhang, Flyer & Low 2006, ApJ, 644, 575)
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Consequence of helicity accumulation (1):
CMEs take place
Existence of total magnetic helicity
upper bound
=> Non-existence of equilibrium field
when H (accumulated) > H (upper bound)
=> Expulsion becomes
unavoidable.
The essence of helicity bound:
The azimuthal field needs confinement that is
provided by the anchored poloridal field. Certain
amount of poloridal flux can only confine a certain
amount of toroidal flux.
(Zhang, Flyer & Low 2006, ApJ, 644, 575)
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Helicity bound: Compare with observations
Boundary condition:
Our upper bound (for dipolar boundary): 0.35 Φp2
Observations: 0.2 – 0.4 Φp2
(Demoulin 2007 in a review)
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Consequences of helicity accumulation (2):
flux-emergence can trigger CME
~ 0.2 Φp2 (bipolar)
~ 0.035 Φp2 (multipolar)
• The upper bound of total magnetic helicity depends on boundary
condition. --- Understand those flux-emergence-triggered or other
boundary-variation-associated CMEs.
• The upper bound of total magnetic helicity (HR/Φp2) of multipolar
fields is 10 times smaller.  Explain why complicated regions
easier to erupt.
(Zhang & Flyer 2008, ApJ, 683, 1160 )
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However, helicity accumulation is still important.
(for boundary variation to trigger CMEs)
91% of 189 CME-source
regions are found to have
small-scale flux emergence,
whereas the same percentage
of small-scale flux emergence
is identified in active regions
during periods with no solar
surface activity.
This means that flux
emergence alone is not a
sufficient condition to trigger
CMEs.
(Zhang Yin et al. 2008, Sol. Phys., 250, 75)
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Consequence of helicity accumulation (3):
Field becomes open up
(self-similar solutions in Low & Lou 1990 )
With more helicity (increasing the index n),
the field becomes fully opened up, forming a
current sheet at the equator and ‘looking like’
potential Aly-limit field (Wolfson 1995).
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(cited by Zhang & Low 2005, ARAA, 43, 103)
However, the field is NOT the potential Aly-limit field.
The three components of the vector magnetic field are different.
(Zhang, Flyer & Low 2012, ApJ, 755, 78)
Field lines in 3D are very
different.
The field presents Parkerspiral-like structures in the
interplanetary space, to
accommodate the large
amount of magnetic helicity
released from low corona.
(Field lines with θ=0.5o, 1o, 2o, 20o
above the equator. )
(Purple: self-similar; Blue: Aly. )
(Zhang, Flyer & Low 2012, ApJ, 755, 78)
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Understanding CMEs in terms of magnetic
helicity accumulation:
1.
2.
Why CME takes place?
• Because the corona has accumulated enough total magnetic
helicity for the eruption.
Why occasionally, not continuously?
• Because the corona needs time to accumulate enough total
magnetic helicity for the eruption.
3.
Why erupts from previously closed regions?
• Because this is where magnetic helicity can be accumulated.
4.
Why initiation often associates with surface field variations
such as flux emergence?
• Because for the changed boundary condition the helicity upper
bound may be reduced, making the already accumulated total
helicity exceeding the new upper bound.
5.
Parker-spiral-like structures will form in the interplanetary
space, to accommodate the large amount of magnetic helicity
released from the low corona.
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Thank you for your attention!
Huairou Solar Observing Station, NAOC
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Hemispheric rule in global magnetic field
The same hemispheric helicity sign rule exists, extending to 60
degrees high in latitudes, and is preserved through the whole
solar-cycle.
(Wang & Zhang 2010, ApJ, 720, 632)
Left: MDI;
(September 1996)
Right: KPVT
(Following the approach in Petvsov & Latushko 2000)
However, complication actually comes in with
active regions….
Hemispheric
helicity sign
rule by SP/Hinode
observation
Do not follow:
end of cycle 23
Follow: beginning
of cycle 24
(Hao & Zhang 2011, ApJ, 733, L27)
Strong (umbra) and weak (penumbra) fields
show opposite helicity signs.
NOAA 10940
(Feb 1, 2007)
by SP/Hinode
(Hao & Zhang 2011, ApJ, 733, L27)
Bφ
A Convective BabcockLeighton Dynamo Model
(Miesch & Brown 2012)
hm
hc
Hemispheric helicity
sign rule shows up
clearly in magnetic
helicity density map.
Current helicity does
show cycle variation,
with opposite-sign
patches presenting.
(More analysis in progress)
Consequences of Helicity Accumulation (4):
Magnetic Energy Storage as a natural
product of coronal evolution
Woltjer (1958) Theorem:
E  0H  Epot
(Even the field is allowed to relax to its
minimum-energy state, it cannot relax to
a potential field!)
E = E – Epot=(E - 0H )+( 0H - Epot)
This implies a storage of a “flare un-releasable” magnetic energy,
increasing with the increasingly accumulated total magnetic helicity.
This is the energy that corona stores uniquely for CMEs!
(Zhang & Low 2005, ARAA, 43, 103)
Consequences of helicity accumulation (5):
Formation of Flux Ropes in the Corona
Taylor relaxation (1972): Turbulent reconnections take place to relax the
field to Woltjer minimum-energy state under helicity conservation.
As a result of Taylor relaxation,
magnetic flux ropes will form
in the corona, as long as
enough total magnetic helicity
has been transported into the
corona.
(Zhang & Low 2003, ApJ, 584, 479)
Consequence of helicity accumulation (6):
• The central part of the field (flux rope) becomes exceeding kink
instability criteria in the process of helicity accumulation.
~ 0.2 Φp2 (bipolar)
Eruptions by kink
instability and by
exceeding helicity
upper bound do not
exclude each other.
~ 0.035 Φp2 (multipolar)
(Zhang & Flyer 2008, ApJ, 683, 1160 )
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For space weather?
Can we monitor the evolution of magnetic helicity and use
it to predict the eruption of CMEs?
In principle: Yes, by observing the photosphere…
--- We can calculate the helicity transfer rate on the
photosphere to monitor the helicity accumulation in the corona.
--- We can estimate the helicity upper bound corresponding
to current boundary flux distribution.
However, needs to fight for accuracy (of vector magnetic field
measurement etc.) and speed (of upper bound calculation).
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Example：Calibrating MDI magnetograms
using SP/Hinode observations
1、Compared to SP/Hionde
observations，MDI also
underestimates magnetic
flux, for both 2007 and 2008
calibration versions.
2、2008 version has
successfully removed the
center-to-limb variation,
whereas 2007 version did
not.
(Wang Dong et al., 2009, Solar Physics, 260, 233）
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