1 Mei Zhang （ National Astronomical Observatory, Chinese Academy of Sciences ） Helicity Transport from the convection zone to interplanetary space Collaborators: Boon Chye Low, Natasha Flyer, Mark Miesch (NCAR, Boulder, USA) Yin Zhang, Chuanyu Wang, Juan Hao (NAOC, Beijing, China)

2 Helicity Transport from the convection zone to interplanetary space --- How do we know? Can we measure (or monitor) it?

Plan of the Talk 1.Why helicity? 2.Helicity Transport (Physical process: convection zone – photosphere – corona – interplanetary space) 1) Observation on the photosphere 2) Creation in the convection zone 3) Consequences in the corona 4) In the interplanetary space 3. Concluding remarks

4 Magnetic helicity:  Magnetic helicity quantifies the twist (self-helicity) and linkage (mutual-helicity) of magnetic field lines. Ｈ＝ ０ Ｈ＝Ｔ Φ 2 Ｈ＝ ± ２ Φ 1 Φ 2 Magnetic helicity is a quantity that describes field topology. (A ： vector potential) (Image credit: T. Sakurai)

5 Magnetic helicity:  Helicity much less dissipative than energy  rather transported or redistributed than dissipated  magnetic field (flux and energy) then transported together  avoid treating the difficult process of magnetic reconnection Magnetic helicity is a conserved physical quantity. (A ： vector potential) The total magnetic helicity is still conserved in the corona even when there is a fast magnetic reconnection (Berger 1984).

6 Observation on the photosphere : --- Hemispheric helicity sign rule (Image credit: A. Pevtsov) Magnetic fields are observed to emerge into each hemisphere with a preferred helicity sign: Positive in southern hemisphere; Negative in northern hemisphere. (Pevtsov et al. 1995, Bao & Zhang 1998, Hagino & Sakurai 2005)

Hemispheric rule in global magnetic field Left: MDI; (September 1996) Right: KPVT (Wang & Zhang 2010, ApJ, 720, 632) The same hemispheric helicity sign rule exists, extending to 60 degrees high in latitudes, and is preserved through the whole solar-cycle. (Following the approach in Petvsov & Latushko 2000)

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) However, complication actually comes in with active regions….

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

How to understand this hemispheric helicity sign rule and its solar cycle variation? Example: Making use of Dynamo models

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

12 => Magnetic helicity is accumulating in the corona ! 1. Hemispheric helicity sign rule 2. Berger (1984)’s conservation law In the corona : (Image credit: A. Pevtsov)

13 What are the consequences of magnetic helicity accumulation in the corona?

Consequences of helicity accumulation (1): 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)

15 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) Consequences of helicity accumulation (2): CME takes place

16 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)

17 Helicity bound: Compare with observations Our upper bound (for dipolar boundary): 0.35 Φ p 2 Observations: 0.2 – 0.4 Φ p 2 (Demoulin 2007 in a review) Boundary condition:

18 The upper bound of total magnetic helicity (H R /Φ p 2 ) of multipolar fields is 10 times smaller.  Explain why complicated regions easier to erupt. (Zhang & Flyer 2008, ApJ, 683, 1160 ) ~ 0.2 Φ p 2 (bipolar) ~ Φ p 2 (multipolar) The upper bound of total magnetic helicity depends on boundary condition. --- Understand those flux-emergence-triggered or other boundary-variation- associated CMEs. Consequences of helicity accumulation (3): flux-emergence can trigger CME

19 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)

20 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:

21 In the interplanetary space With more helicity (increasing the index n), the field becomes fully opened up, forming a current sheet at the equator. (Zhang, Flyer & Low 2012, ApJ, 755, 78)

22 The field presents Parker-spiral-like structures in the interplanetary space, to accommodate the large amount of magnetic helicity released from low corona. (Zhang, Flyer & Low 2012, ApJ, 755, 78) (Field lines with θ=0.5 o, 1 o, 2 o, 20 o above the equator. ) (Purple: self-similar; Blue: Aly. )

23 1. Hemispheric helicity sign rule is observed on the photosphere. In both global Sun and active regions. The rule shows solar cycle variation in sunspots. 2. Dynamo models (at least some of them) produce magnetic field consistent with the observed rule. Magnetic helicity better preserved than current helicity. 3.The accumulation of magnetic helicity in the corona Can give rise to flux ropes in the corona. Result in CME as a natural product of coronal evolution. 4.When helicity is dumped into the interplanetary space Parker-spiral-like structures will form. Concluding Remarks

24 1. Hemispheric helicity sign rule is observed on the photosphere. In both global Sun and active regions. The rule shows solar cycle variation in sunspots. 2. Dynamo models (at least some of them) produce magnetic field consistent with the observed rule. Magnetic helicity better preserved than current helicity. Measure by SP/Hinode etc. 3. The accumulation of magnetic helicity in the corona Can give rise to flux ropes in the corona. Result in CME as a natural product of coronal evolution. 4.When helicity is dumped into the interplanetary space Parker-spiral-like structures will form. Measure (or monitor) by coronal magnetism? Concluding Remarks

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

26 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: A family: With the same boundary condition and a specific n, different γ values give fields with different magnetic energy and total magnetic helicity. (in Zhang et al. 2006)

27 The central part of the field (flux rope) becomes exceeding kink instability criteria in the process of helicity accumulation. (Zhang & Flyer 2008, ApJ, 683, 1160 ) Consequence of helicity accumulation (4): ~ 0.2 Φ p 2 (bipolar) ~ Φ p 2 (multipolar) Eruptions by kink instability and by exceeding helicity upper bound do not exclude each other.

(Even the field is allowed to relax to its minimum-energy state, it cannot relax to a potential field!) Woltjer (1958) Theorem: E   0 H   E pot Consequences of Helicity Accumulation (6): 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! Magnetic Energy Storage as a natural product of coronal evolution (Zhang & Low 2005, ARAA, 43, 103) )+( -  E = E – E pot =(E -  0 H  )+(  0 H  - E pot )

29 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. For space weather? However, needs to fight for accuracy (of vector magnetic field measurement etc.) and speed (of upper bound calculation).

30 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 ）