1. 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)

2. Plan of the Talk Introduction
CMEs as a result of magnetic helicity accumulation in the corona
(Zhang, Flyer & Low 2006, ApJ, 644, 575;
Zhang & Flyer 2008, ApJ, 683, 1160 )
Magnetic helicity in the interplanetary space
(Zhang, Flyer & Low 2012, ApJ, 755, 78)

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 address 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.
(Image credit: T. Sakurai)
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. Hemispheric helicity sign rule:
Positive in southern hemisphere;
Negative in northern hemisphere.
2. Berger (1984)’s conservation law
(Image credit: A. Pevtsov)
=> Magnetic helicity is accumulating
in the corona !

6. What are the consequences of magnetic helicity accumulation
in the corona?

7. 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 )

8. 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)

9. CMEs take place Existence of total magnetic helicity upper bound
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)

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. flux-emergence can trigger CME
Consequences of helicity accumulation (2):
flux-emergence can trigger CME
~ 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)
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)

13. Consequence of helicity accumulation (3):
Field becomes open up
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).
(self-similar solutions in Low & Lou 1990 )
(cited by Zhang & Low 2005, ARAA, 43, 103)

14. 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)

15. Field lines in 3D are very different.
The field presents Parker-spiral-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)

16. 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.
5. Parker-spiral-like structures will form in the interplanetary space, to accommodate the large amount of magnetic helicity released from the low corona.

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

18. 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)

19. 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)

20. NOAA 10940 (Feb 1, 2007) by SP/Hinode
Strong (umbra) and weak (penumbra) fields show opposite helicity signs.
NOAA (Feb 1, 2007) by SP/Hinode
(Hao & Zhang 2011, ApJ, 733, L27)

21. (More analysis in progress)Bφ
A Convective Babcock-Leighton Dynamo Model (Miesch & Brown 2012) hm
Hemispheric helicity sign rule shows up clearly in magnetic helicity density map.
Current helicity does show cycle variation, with opposite-sign patches presenting. hc
(More analysis in progress)

22. Magnetic Energy Storage as a natural product of coronal evolution
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)

23. Formation of Flux Ropes in the Corona
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)

24. 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.
~ Φp2 (multipolar)
(Zhang & Flyer 2008, ApJ, 683, 1160 )

25. 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).

26. (Wang Dong et al., 2009, Solar Physics, 260, 233）
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） 26