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Mei Zhang

（ National Astronomical Observatory of China）

Coronal Mass Ejection

As a Result of

Magnetic Helicity Accumulation

Collaborators:

BC Low (HAO/NCAR)

Natasha Flyer (SCD/NCAR)

References:

1. Zhang, Flyer & Low 2006, ApJ, 644, 575

2. Zhang & Flyer 2008, ApJ, 683, 1160

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In This Talk

I will present our understandings of CMEs in terms of

magnetic helicity accumulation:

CMEs are the unavoidable products of coronal

evolution as a result of magnetic helicity

accumulation.

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• 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?

Key observations of CMEs for modelers to address:

We intend to answer these questions in terms of magnetic helicity accumulation.

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Magnetic helicity:

Magnetic helicity quantifies the twist (self-helicity) and linkage

(mutual-helicity) of magnetic field lines.

Ｈ＝０

Ｈ＝ＴΦ2

Ｈ＝ ±２ Φ1Φ2

Magnetic helicity is a conserved quantity that describes field

topology.

(A ： vector potential)

The total magnetic helicity is still conserved in the corona even when

there is a fast magnetic reconnection (Berger 1984).

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Magnetic helicity is accumulating in the corona!

1: Magnetic fields are

observed to emerge into each

hemisphere with a preferred

helicity sign, positive/negative

in the southern/northern

hemisphere

2: Berger (1984)’s law

Helicity accumulation in the corona:

(Image credit: A. Pevtsov)

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What is the consequence of

magnetic helicity accumulation

in the corona?

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We try to understand this by studying families of nonlinear force-free fields.

Force-free: Because the corona is very tenuous, the large-scale field is usually regarded as force-free.

Boundary condition:

Governing equation:

The family: With the same boundary condition, different γ values give fields with different magnetic energy and total magnetic helicity.

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Our 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)

Consequence of helicity accumulation (1):

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The existence of total magnetic

helicity upper bound means

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

Our upper bound (for dipolar boundary): 0.35 Φp2

Observations: 0.2 – 0.4 Φp2 (Demoulin 2007 in a review)

Boundary condition:

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• 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 )

~ 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.

Consequence of helicity accumulation (2):

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The upper bound of total magnetic helicity depends on boundary

condition. --- Understand those flux-emergence-triggered or other boundary-

variation-associated CMEs

However, helicity accumulation is still important.

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.

(Zhang Yin et al. 2008, Sol. Phys., 250, 75)

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• The central part of the field becomes exceeding kink instability criteria in the process of helicity accumulation.

(Zhang & Flyer 2008, ApJ, 683, 1160 )

Consequence of helicity accumulation (3):

~ 0.2 Φp2 (bipolar)

~ 0.035 Φp2 (multipolar)

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3D numerical simulation by Fan and Gibson:

Case K: Erupt via kink instability

Self-helicity: -1.4 Φp2

Case T: Erupt via torus instability

Self-helicity: -0.63 Φp2

The two distinct cases of eruption have roughly the same amount of total magnetic helicity!

(Fan & Gibson 2007, ApJ, 668, 1232 )

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1. Why CME takes place?

• Because the corona has accumulated enough total magnetic helicity for the eruption.

2. 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.

Understanding CMEs in terms of magnetic helicity accumulation:

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Can we monitor the evolution of magnetic helicity and use it to

predict the eruption of CMEs?

In principle: Yes. But……

Practical problems: To calculate magnetic helicity we need to know coronal magnetic field, but so far we still cannot measure coronal magnetic field directly with good temporal and spatial resolutions.

1. Extrapolating coronal magnetic field using photospheric field measurements based on force-free assumption is subjected to several unsolved problems. (For example, no-forcefreeness on the photosphere, 180-degree

ambiguity, the existence of smooth solutions)

2. With current techniques we probably could measure the coronal magnetic field, but these fields are measured at the solar limb, not on the disk.

For space weather?

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Even for extrapolating coronal magnetic field using photospheric

magnetic field measurements based on force-free assumption,

there are still a few problems.

For example：

1 、 How accurate are the measured vector magnetic fields?

2 、 How large are the CME source regions?

3 、 How accurate are the extrapolated coronal magnetic fields

and how would it be influenced by the accuracy of photospheric

magnetic field measurements?

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Example1 ： Calibrating Huairou vector

magnetograms using SP/Hinode observations

Compared to SP/Hinode

observations ， current

Huairou calibrations still

under-estimate magnetic

fluxes.

And there is a center-to-

limb variation.

(Wang Dong et al., 2009, Sciences in China, in press）

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Example2 ： 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, in press）

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Thank you for your attention!

Huairou Solar Observing Station, NAOC