Magnetic Helicity in Solar Active Regions: Some Observational Results Yang Liu (Stanford University)

Outline Helicity Flux Across the Photosphere; Hemispheric Preference of the Sign of Magnetic Helicity; Summary.

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

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

* shear-term dominant; Shear/total = 66% Emergence/total = 34% * Both terms same sign

Helicity buildup in emerging ARs: statistical results (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%

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

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%).

Hemispheric Preference of Helicity Sign The sign of magnetic helicity is expected to have a hemispheric dependence (Here are some tests that examined proxies of helicity). 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);

Hemispheric Preference of Helicity Sign (Proxy of Magnetic Twist) We use a B2z weighted force-free parameter αw, proposed by Hagino & Sakurai (2004), as a proxy of twist for ARs: Preference: 68% in a sample of 236 ARs

Hemispheric Preference of Helicity Sign From Wang Y-M (2013)

Hemispheric Preference of Helicity Sign (Magnetic Helicity) 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 only) in 393 ARs using MDI data. They found 57%--60% of 393 ARs have the signs of injection rates agreeing the hemisphere rule.

Hemispheric Preference of Helicity Sign (Magnetic Helicity) We take a similar approach as Yang et al (2009) but include both terms. Another difference is that our data used were taken in the early phase of Solar Cycle 24 while theirs were in Solar Cycle 23.

Hemispheric Preference of Helicity Sign (Magnetic Helicity) Helicity in emerging ARs: 66% in a sample of 116 emerging ARs

Hemispheric Preference of Helicity Sign (Helicity, Twist, and Writhe in ARs) What does the helicity measured in ARs imply? processes that 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) sign of helicity has a hemisphere preference (weak?).

Hemispheric Preference of Helicity Sign (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 – BUT WHY SO WEAK (66%)? Htotal = TΩ + WΩ + Tα + Wα Htotal = TΩ + WΩ

Hemispheric Preference of Helicity Sign (Helicity, Twist, and Writhe in ARs) Understanding measured twist: relationship of sign between twist and writhe may imply scenarios for twist generation—dynamo origin or emerging origin Scenario 1 (dynamo origin): If flux tubes have initial twist that is high enough to lead to kink instability, part of the twist will convert to writhe. The flux tubes will have twist and writhe of the same sign (Linton et al. 1996; 1998); Scenario 2 (emerging origin): If flux tubes have less twist or no twist initially, Coriolis force (C-effect) and turbulence (Σ-effect) will generate twist by deforming the tubes during their rising (Longcope et al. 1998; Holder et al. 2004). The flux tubes will have twist and writhe of opposite signs (due to helicity conservation).

Hemispheric Preference of Helicity Sign (Helicity, Twist, and Writhe in ARs) Proxy of twist in ARs: we use a B2z weighted force-free parameter αw, proposed by Hagino & Sakurai (2004), as a proxy of twist for ARs. Proxy of writhe in ARs: we use tilt angle (θ) of ARs, normalized by its separation (d) to measure magnetic writhe of ARs (Canfield et al. 2003; Holder et al. 2004):

Hemispheric Preference of Helicity Sign (Helicity, Twist, and Writhe in ARs) Relationship of sign between twist and writhe in ARs: same sign = 122; opposite sign = 114

Hemispheric Preference of Helicity Sign (Helicity, Twist, and Writhe in ARs) AR Number Hemisphere Preference All ARs 236 68% Twist * Writhe > 0 122 52% Twist*Writhe < 0 114 85% These results may suggest that, prior to emergence of magnetic tubes, either the sign of twist (initially strong) doesn’t have a hemispheric preference (kink instability—scenario 1) or the twist is relatively weak (C- & Ω-effects are in work—scenario 2).

Hemispheric Preference of Helicity Sign (Helicity, Twist, and Writhe in Emerging ARs) Examine hemispheric preference of sign of magnetic twist (αw) in two groups of ARs in a sample of emerging ARs (sample size is 116)

Hemispheric Preference of Helicity Sign (Helicity, Twist, and Writhe in Emerging ARs) AR Number Hemisphere Preference All ARs 116 58% Twist * Writhe > 0 61 34% Twist*Writhe < 0 55 84%

Hemispheric Preference of Helicity Sign (Difference between Emerging ARs and other ARs) Sample H. Rule T * W < 0 T*W > 0 Emerg. ARs 116 58% 55 84% 61 34% Other ARs 120 79% 58 88% 62 71%

Hemispheric Preference of Helicity Sign (Difference between Emerging ARs and other ARs)

Summary More questions than conclusions: Interpretation of two term helicity injections; Relationship among helicity, twist, and writhe in ARs; Hemispheric preference examined with different proxies of magnetic helicity – what’s underline link? Physical difference between two-group ARs with same and opposite signs of twist and writhe. Evolving characteristics from emerging ARs toward mature ARs in terms of hemispheric preference examined.

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)

Hemispheric rule of sign: Summary. The strengths of two groups in other class ARs are not significantly different in comparison with β-class ARs. Possible reasons: 1. sample size is small; 2. difficulty in determining tilt angle (that is used to compute writhe)—α-class ARs have unipole structure while γδ-class ARs have multi-pole structure.

Hemispheric rule ? H < 0 H > 0 Due to the solar rotation: ( Pevtsov 2002 ) Due to the solar rotation: H<0 in the North H>0 in the South Independently of the solar cycle True mostly for quiet sun features! For active features the rules is only marginally validated H < 0 Why this difference ? H > 0 independent of solar cycle Magnetic helicity studies  close to equipartition Labonté et al. 07: 57-60% of 393 ARs. Yang et al. 09: 56-57% of 58 emerging ARs. Weak correlation likely due to the diff. Rot. at the surface Mechanism generating the twist in emerging flux tube is likely not correlated to the W effect of the solar rotation 22/08/11 - FEW 2011 - E. Pariat Labonté et al. 07

Hemispheric helicity sign rule The sign of magnetic helicity is expected to have a hemispheric dependence. Yang et al. (2009) tried to examine the hemispheric rule using magnetic helicity. The helicity is computed from helicity flux across the photosphere. They collected 58 emerging ARs, 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 not the total helicity flux. There is also the work of Labonté et al. 2007. Yang only focused on « emerging » AR. While this is right, as you wrote in your previous paper « to be fair, the DAVE-helicity tracks the total helicity fairly well though. DAVE-helicity flux is fairly close to the total helicity flux. It caught about 76% of the total helicity accumulated in the corona in that 6-day period for AR11072, and 83% for AR11158 in that 5-day period.” I doubt that using only LCT methods, without vector magnetograms would change the average sign. This means that Yang results cannot be disregarded and I personnaly take them as solid in term of statistics of the helicity rule

Hemispheric rule: (scenarios) There are several scenarios. Background mean poloidal field (Choudhuri 2003; Choudhuri et al. 2004): predicts reversal of the sign preference at the beginning of solar cycle:

Hemispheric rule: (scenarios) There are several scenarios. Σ-effect (the turbulent convection in convection zone—ultimately due to Coriolis force; Longcope et al. 1998); The Coriolis force on the rising flux tubes (e. g. Holder et al. 2004). I’m not sure that I understand the scenarios: you want to explain why there shall be an hemispheric rule? Or why it should not be 100%? There are some people (Stein et al. 2012) that actually do not suppose that magnetic flux is generated at the tachoclyne bit rather locally in the upper convection zone. Helicity = twist + writhe 57% 61%

I’m not sure i fully understand your point on the different scenarios. To me the idea about the helicity rule mostly comes from initial studies of the W effect. In mean field dynamo theory W effect creates a global helicity which is null but which is distributed with different sign in both hemisphere: negative in N and positive in S with no change with solar cycles. This helicity is for a large part injected at large (sun) scale in the open field and in the solar wind. This is confirmed by the work of Bieber et al. 87, Berger & Ruzmaikin 00. The scientific community made the hypothesis that the field found in active regions are due to somehow similar process (not necessarily W effect directly) and have thus tried to confirm it in observations. However, one should remember at this point that it is still unclear how the magnetic field that eventually constitute the AR generated. And we don’t know where its helicity is given or modified

For the formation of the AR field most of the community suppose that the flux tubes are formed at the tachoclyne though not really knowing how. There are no proper simulations & theory of flux tube formation Some people believe (e.g. Stein 2012 and colleague) that AR are formed locally in the upper convection zone by local dynamo For the formation of helicity we can imagine scenarios Field and helicity are formed in the upper convection zone altogether Flux tubes are formed at the tachoclyne with signed helicity Possible modification of helicity as it rises up! FT are formed at the tachoclyne with no helicity Helicity is acquired while rising Helicity is acquired in the upper convection zone Different processes can appears at different stages.

Hence different processes can appears at different stages. To me, what your and previous results suggest is that the mechanisms that generates helicity is not directly related to the helicity rule, hemispheric segregating mechanisms are second order Is likely to be random at the first order The slight hemispheric preference (and not rule) may be given directly at the formation site of the AR, or given latter as the flux tube are transported up toward the atmosphere

Relationship between magnetic helicity and force-free-alpha in ARs Do you think that alpha measures mostly twist? Why? It seems to me that some other methods have used the alpha from linear force free extrapolation. These one are based on larger scale field lines and therefore may mesure mostly writhe Helicity = twist + writhe Flux tube contains H initially. Initial H hemisphere-dependent.

Conclusions 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. A relationship between twist and size of magnetic tubes is found in a sample of active regions having a bipolar structure.