Magnetic Helicity in Emerging Active Regions

1. Magnetic Helicity in Emerging Active Regions Yang Liu Stanford University In collaboration with J. T. Hoeksema, M. Bobra, K. Hayashi, A. Norton, X. Sun (Stanford University) and P. W. Schuck (NASA)

2. Outline • Helicity injection into the corona in active regions; • Hemispheric helicity sign rule with HMI data; • Helicity, twist, and writhe in active regions; • Twist and flares in active regions; • Conclusions.

3. 1. Helicity injection into the corona in the active regions • Helicity injection rate: emerging term shear term Bt, Bn (obs), and Vt, Vn (obs + DAVE4VM)

4. * shear-term dominant; Shear/total = 88% Emergence/total = 12%; * Both terms have the same sign. Emerg-term Shear-term

5. An interpretation • Model (Longcope & Welsch 2000): Only a fraction of the twist in the flux tube emerges into the corona. The ``mismatch’’ between the highly twisted field in the subsurface and less twisted field in the corona causes the surface shear flows that propagate the twist from the subsurface to the corona. Longcope & Welsch (2000)

6. An interpretation • Observation (Pevstov et al. 2003): analyzed 6 emerging ARs. The results agree with the model. This is one example for AR9139. Force-free-α: Measure of twist Separation Magnetic Flux Area

7. An interpretation • Simulations (e.g. Magara & Longcope 2003; Manchester et al. 2004; Fan 2009; Fang et al. 2012): results support the model. emergence shearing From Fan (2009)

8. An interpretation • Emerged fields in the corona contain less twist; • Surface shear motions (due to mismatch of the twists between the subsurface highly twisted fields and the emerged less twisted field during flux emergence) build-up the twist in the emerged fields.

9. Helicity buildup in emerging ARs: a survey (A sample of 28 ARs) • Shear-term dominant: • Both terms inject helicity of the same sign in 26 ARs (93%; But see Kusano et al. 2002; Yamamoto et al. 2009 for different cases). H(shear)/H(total): Median = 85% Mean = 86%

10. Helicity flux changes its sign during AR’s emergence. It happens in 12 ARs (43%).

11. Summary of helicity injection in emerging ARs • Shear-term is dominant; • In most ARs (26 of 28 ARs; 93%), emergence-term and shear-term contribute helicity of the same sign; • Helicity flux changes its sign in some ARs during their emergence (12 of 28; 43%).

12. 2. Hemispheric helicity sign rule • We take a similar approach as Yang et al (2009): integrate helicity injection rate over the entire process of AR’s emergence. This calculation is applied to a sample of 28 emerging ARs.

13. 2. Hemispheric helicity sign rule Yes: 61%; No: 39% (28 ARs) Yes: 68%; No: 32%

14. 2. Hemispheric helicity sign rule • Yang et al. (2009) examined the hemisphere rule using helicity. The helicity is computed by integrate over time the helicity injection rate. They collected 58 emerging ARs from MDI data, and found that ~57% follow the hemisphere rule. • Caveat: the helicity flux across the photosphere they used is only part of helicity flux from the shear-term, but this term is dominant (Liu & Schuck 2012). So the result won’t be affected very much by this problem. • Labonte et al. (2007) studied helicity injection rate (again, shear-term) in 393 ARs using MDI data. They found 57%--60% of 393 ARs have the signs of injection rates agreeing the hemisphere rule.

15. 2. Hemispheric helicity sign rule • The hemisphere rule were examined using other different proxies (kind of related to the twist). • Seehafer (1990) found that linear-force-free alpha in ARs has a hemispheric preference in a sample of 16 ARs; Linear-force-free alpha in an AR is deemed to be a proxy of magnetic twist, a fraction of magnetic helicity. • Pevtsov et al. (1995) found ~73% of 65 ARs follow the hemispheric rule. A proxy of magnetic twist, alpha_best (~<Jz/Bz>) was measured (see also Hagino & Sakurai 2004; Hao & Zhang 2011); • Bao & Zhang (1998) found ~83% of 422 ARs follow the hemisphere rule. An index, imbalance of current helicity (ρ=Σ(hc)/Σ|hc|, Abramenko et al. 1996), was calculated (see also Hagino & Sakurai 2004); • The proxies used in aforementioned studies are more or less related to magnetic twist in ARs, but not the magnetic helicity. The level of the sign preference is higher (~73%--83%) than total helicity.

16. 3. Helicity, twist, and writhe in ARs • Firstly, both total helicity and twist show hemisphere rule, suggesting a positive sign-correlation between them. • Checking this with the 28-ARs sample, we found this sign-relationship (89% of 28 ARs have the same sign).

17. 3. Helicity, twist, and writhe in ARs • Secondly, the helicity measured in ARs means: Processes to generate helicity ( ): • Dynamo process; • Processes during rise of flux tubes through CZ (emerging process). • Measurements of the helicity (total helicity) in ARs • During rise, a flux tube is buffeted by convective turbulence (Σ-effect, Longcope et al. 1998, WΣ+TΣ=0) and Coriolis force (C-effect; WC+TC=0). Thus: For a flux tube, H(helicity) = T(twist) + W(writhe) HD = TD + WD HE = TE + WE Htotal = TD + WD + TE + WE Htotal = TD + WD Thus flux tubes (1) have possessed initial helicity before they begin to rise; and (2) this helicity has a sign-hemisphere-preference.

18. 3. Helicity, twist, and writhe in ARs • Additional discussion on Htotal: If we break down the dynamo process into the Ω-effect and α-effect, then, • Kinetic helicity in convection generates magnetic helicity of the same sign in small scale and opposite sign at large scale (Pouquet et al. 1976; Seehafer 1996; Ruzmaikin 1996). The size dividing the small and large scales is the energy-carrying eddy (which is suggested to be 50 Mm in CZ; Brandenburg et al. 2011). If the eddy size is smaller than ARs, Tα + Wα = 0 in ARs. Then, . • The total helicity measured in ARs mainly from the Ω-effect. It agrees with Berger & Ruzmaikin (2000) who predict Ω-effect produces helicity that is consistent with the hemisphere rule. Htotal = TΩ + WΩ+ Tα + Wα Htotal = TΩ + WΩ

19. 3. Helicity, twist, and writhe in ARs • Thirdly, it appears that level of hemispheric helicity preference is lower than hemispheric twist preference. What does it imply? • Measurements of the helicity (Htotal,total helicity), twist (Ttotal, total twist), and writhe (Wtotal, total writhe) in ARs: • Level (Htotal) < level (Ttotal) implies WD has an opposite sign. This should lead to a negative correlation between the signs of Ttotal and Wtotal. • But we got fairly random sign-correlation between Ttotal and Wtotal : 54% positive and 46% negativesample is too small? Htotal = TD + WD, Ttotal = TD + TΣ+ TC, and Wtotal = WD + WΣ+ WC

20. 3. Helicity, twist, and writhe in ARs • Testing emerging process (Σ-effect): This effect, (1) due to kinetic helicity in CZ, is demonstrated to work on the rising flux tubes effectively (2) at the top of CZ (Longcope et al. 1998). If this effect makes appreciable contribution to the twist, we would see a tight temporal correlation between the kinetic helicity in the CZ near the surface and the twist at the photosphere. Guo et al. (2012)

21. 3. Helicity, twist, and writhe in ARs • Testing emerging process (models): Flux emergence models (Longcope et al. 1998; Choudhuri et al. 2004) predict dependence of r -2(r=radius of flux tubes) and α (measure of the twist in flux tubes): i.e., greater twist in smaller tubes. bi-polar active regions (22) All active regions (28)

22. 4. Twist and flare occurrence in ARs • Twist in ARs is related to (1) free energy and (2) magnetic helicity that describes complexity of ARs; • If α-effect and Σ-effect (due to turbulence of convection) make substantial contribution to ARs twist in ARs, the ARs may have mixture signs of twist due to nature of convection turbulence. ARs having Mixture sign helicity may be more flare productive (Kusano et al. 2004).

23. 4. Twist and flare occurrence in ARs • Change of twist and flare occurrencesagree with simulations by Fan (2009) & Fang et al (2012) ? Net Current Helicity over the AR Normalized Time (days) Bobra et al. (2013)

24. Conclusions • Helicity injection into the corona: • Helicity in the active region corona is mainly contributed by the photospheric shearing motion; • In most ARs, the emergence-term and shear-term inject the helicity of the same sign. • A weak hemispheric helicity sign rule is found in the sample of emerging ARs, consistent with previous studies. • Helicity, twist, and writhe in ARs • Magnetic tubes contain helicity before their rise; • This initial helicity has a hemispheric sign-preference; • Signatures that imply appreciable contribution to the ARs’ twist from emergence processes are detected. • There may be evidence that links the twist and flare occurrence in ARs.