1. Coronal Mass Ejection As a Result of Magnetic Helicity Accumulation
Mei Zhang
（National Astronomical Observatory of China）
Collaborators:
BC Low (HAO/NCAR)
Natasha Flyer (SCD/NCAR)
References:
Zhang, Flyer & Low 2006, ApJ, 644, 575
Zhang & Flyer 2008, ApJ, 683, 1160

2. 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.

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

4. Magnetic helicity: (A：vector potential)
Magnetic helicity is a conserved quantity that describes field topology.
 Magnetic helicity quantifies the twist (self-helicity) and linkage (mutual-helicity) of magnetic field lines.
Ｈ＝ＴΦ2
Ｈ＝±２Φ1Φ2
Ｈ＝０
 The total magnetic helicity is still conserved in the corona even when there is a fast magnetic reconnection (Berger 1984).

5. Magnetic helicity is accumulating in the corona!
Helicity accumulation 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
(Image credit: A. Pevtsov)
2: Berger (1984)’s law
Magnetic helicity is accumulating in the corona!

6. What is the consequence of magnetic helicity accumulation
in the corona?

7. 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.
Governing equation:
Boundary condition:
The family: With the same boundary condition, different γ values give fields with different magnetic energy and total magnetic helicity.

8. Consequence of helicity accumulation (1):
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)

9. 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.
The existence of total magnetic helicity upper bound means
Expulsion becomes unavoidable.
(Zhang, Flyer & Low 2006, ApJ, 644, 575)

10. Helicity bound: Compare with observations
Boundary condition:
Our upper bound (for dipolar boundary): 0.35 Φp2
Observations: 0.2 – 0.4 Φp (Demoulin 2007 in a review)

11. Consequence of helicity accumulation (2):
~ 0.2 Φp2 (bipolar)
~ 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 )

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

13. Consequence of helicity accumulation (3):
The central part of the field becomes exceeding kink instability criteria in the process of helicity accumulation.
~ 0.2 Φp2 (bipolar)
~ Φp2 (multipolar)
(Zhang & Flyer 2008, ApJ, 683, 1160 )

14. 3D numerical simulation by Fan and Gibson:
(Fan & Gibson 2007, ApJ, 668, 1232 )
Case K: Erupt via kink instability
Self-helicity: -1.4 Φp2
Case T: Erupt via torus instability
Self-helicity: Φp2
The two distinct cases of eruption have roughly the same amount of total magnetic helicity!

15. Understanding CMEs in terms of magnetic helicity accumulation:
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.

16. For space weather?
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.
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)
With current techniques we probably could measure the coronal magnetic field, but these fields are measured at the solar limb, not on the disk.

17. 1、How accurate are the measured vector magnetic fields?
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? 17

18. (Wang Dong et al., 2009, Sciences in China, in press）
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） 18

19. (Wang Dong et al., 2009, Solar Physics, in press）
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） 19

20. Thank you for your attention! Huairou Solar Observing Station, NAOC