1. Helicity Thinkshop 2009, Beijing Asymmetry of helicity injection in emerging active regions L. Tian, D. Alexander Rice University, USA Y. Liu Yunnan Astronomical Observatory, China

2. Helicity Thinkshop 2009, Beijing Background - observations Well observed on solar photosphere, chromosphere and corona in many different wave- lengths.

3. Helicity Thinkshop 2009, Beijing Why we study helicity ? It is conserved in large scale. It can be traced as the magnetic field flux when it (a) appears as an emerging flux region; (b) forms new loops to fill the corona; (c) erupts to be a flare or a coronal mass ejection (CME); (d) becomes a magnetic cloud when reaches the Earth. Understanding of flare and CME formation mechanism (a) Overload helicity accumulation will inevitably cause a CME occurrence; (b) Different helical flux systems can trigger magnetic reconnection. Helicity output is the key to the solar dynamo Constraints on the dynamo models if take into account the helicity conservation.

4. Helicity Thinkshop 2009, Beijing Helicity measurements - Hc Current helicity H c =∫ v B J dV, and J = ∇ x B Only the vertical component (z) of J can be directly derived from the photospheric magnetic field observations. Sample of vertical current helicity density (h c ) map. From H.Zhang (2001)

5. Helicity Thinkshop 2009, Beijing Helicity measurements - Hm Magnetic helicity H m =∫ v A B dV, and B = ∇ x A Only the transport rate (dHm/dt) can be derived from the photospheric magnetic field observations. Sample of time series magnetic flux change associated with magnetic helicity change. From J.Chae (2001)

6. Helicity Thinkshop 2009, Beijing Analysis of helicity injection rate (dH m /dt) Definition or, simply, i.e., helicity density by LCT method (FWHM=10”, dt=96min) (Pariat 2005)

7. Helicity Thinkshop 2009, Beijing Analysis of helicity injection rate (dH m /dt) Note, using LCT method we can only obtain the total map. Therefore only the total helicity flux density can be obtained, no information is obtained regarding to the contribution from either the advection terms (magnetic field emergence), or from the shear terms (horizontal motions). by horizontal mass motions by emerging flux motions

8. Helicity Thinkshop 2009, Beijing Amount of helicity flux change The amount of helicity flux estimated from the formula should both contributions from the emerging motions and the shear motions. However, many observations display that the surface differential rotation and/or the overall horizontal motions contribute minor to the helicity flux injected from below into the corona ( see review in Tian and Alexander 2009 ), indicating that the flux emergence is the most important origin for the coronal helcity accumulations.

9. Helicity Thinkshop 2009, Beijing Topic : asymmetry of helicity injection flux in emerging active regions Purposes : (1)To physically study why the leading magnetic field of bipolar ARs is often more compact, while the following one, more dispersed. (2)To clear the relation between asymmetry of helicity flux and asymmetry of magnetic flux.

10. Helicity Thinkshop 2009, Beijing First, how about the asymmetry in magnetic flux evolution AR 8227 AR 8214 May-02 03:12UT May-06 03:12UT Jun.-03 03:15UT May-30 03:12UT after one solar rotation cycle MDI data (96m) sample 1

11. Helicity Thinkshop 2009, Beijing The leading polarities always remain more cohesive than the following ones during long- term evolution AR 0656AR 0667 Aug.-10 03:11UT Aug.-13 19:11UT AR 0670 Sep.-06 03:11UT Sep.-09 19:11UT after one solar rotation cycle sample 2

12. Helicity Thinkshop 2009, Beijing Database containing 15 emerging ARs and analysis results

13. Helicity Thinkshop 2009, Beijing Four emerging ARs in southern hemisphere The magnetic flux increase for N and P is imbalanced /asymmetry. The same for the helicity flux. Magnetic flux vs datehelicity flux increaseMagnetic fluxhelicity flux increase

14. Helicity Thinkshop 2009, Beijing Four emerging ARs in northern hemisphere The magnetic flux increase for N and P is imbalanced /asymmetry. The same for the helicity flux.

15. Helicity Thinkshop 2009, Beijing The higher proper motion in the leading polarity, the larger helicity injection by it The correlation between helicity flux increase and magnetic flux increase is very poor. This has two important physical implications: emerging of asymmetric Ω- loop, and more twisted in the leading polarity.

16. Helicity Thinkshop 2009, Beijing In the following work, we use the normalized parameter ΔH/Φ 2, Instead of ΔH, to examine the twist and helicity injection for per unit emerging flux.

17. Helicity Thinkshop 2009, Beijing We select 11 ARs (whose magnetic flux maps were shown in the previous work) AR 0381 (Demoulin & Pariat 2009) is added in the database for comparison. Totally, there are 11 emerging ARs for this analysis. small

18. Helicity Thinkshop 2009, Beijing In the 1 st –3 rd columns are ΔΗ/Φ 2 vs. date, d vs. date, andΔΗ/Φ 2 vs. Φ for every AR The helicity injection is found to saturate when d separation stops.

19. Helicity Thinkshop 2009, Beijing ΔΗ/Φ 2 vs. d, α vs. date The helicity injection is found to delay about 1-2 days after flux emergence. The helicity injection delay may be linked to the emergence of the periphery of the flux rope which contains a low amount of helicity even very twisted. Four ARs with observations at their very beginning to emerge.

20. Helicity Thinkshop 2009, Beijing (1) The leading leg of a presumed Ω-shaped flux tube possesses more twist than that of the following leg prior to its emergence from the interior. (2) The behavior of twist depending on the rate of the flux tube emergence, i.e., the level of rotation of the footpoint of the flux tube will depend upon the rapidity of flux emergence. (3) the leading polarity possesses more helicity so that the leading flux is maintained to be compact and cohesive, due to a stronger tension of the magnetic field, and consequently,is less affected by the convective motions.  Does the leading polarity moves and emerges faster ? Seems yes (because as the field strength in the leading leg becomes proportionately stronger, it becomes more buoyant). It needs MHD simulation to confirm. Discussion: The physical origin of the helicity flux asymmetry

21. Helicity Thinkshop 2009, Beijing (1) The helicity asymmetry, between the leading and following magnetic field, results in the observed magnetic field asymmetry of the two polarities (due to an imbalance in the magnetic tension of the emerging flux tube); (2) The observed imbalance in the helicity asymmetry results from a difference in the speed of emergence between the leading and following legs of an inclined Ω-shaped flux tube; (3) The imbalance in the normalized helicity does not have a relation with the imbalance of opposite-sign magnetic flux. Main conclusions

22. Helicity Thinkshop 2009, Beijing Questions remained (1) Magnetic Helicity would be saturation in some time. However, it is possibly true (?). (2) Injection of magnetic helicity has 1-2 days delay. Why? (3)The force-free parameter (alpha) is too small comparing with observation of vector magnetograms. Why?

23. Helicity Thinkshop 2009, Beijing Questions remained …………. (N) The origin of coronal helicity is still not clear by now; Sunspot rotation possibly plays a very important role in producing and injecting magnetic helicity. (Better methods to measure magnetic helicity need to be developed urgently.) Obviously, more Helicity Thinkshops are expected in the future… And….

24. Helicity Thinkshop 2009, Beijing Thanks!