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Hemispheric Rule of Magnetic Helicity in Solar Active Regions with HMI Data

This study examines the hemispheric rule of the sign of magnetic helicity in solar active regions using a proxy of magnetic twist. It investigates the rule in two groups of active regions with different properties and compares emerging active regions with mature active regions.

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Hemispheric Rule of Magnetic Helicity in Solar Active Regions with HMI Data

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  1. Hemispheric Rule of Magnetic Helicity in Solar Active Regions with HMI Data Yang Liu (Stanford University) Thanks Phil for the great HMI Data!

  2. Outline • Hemispheric rule of the sign of magnetic helicity in solar active regions: test with a proxy of magnetic twist; • Hemispheric rule in two groups of active regions with different properties (twist origin); • Hemispheric rule in emerging active regions and in mature active regions; • Summary.

  3. A Little Bit History … • 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 (14 of 16 ARs follow the hemisphere rule; 86%); Linear-force-free alpha in an AR is deemed to be a proxy of magnetic twist. • 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);

  4. A Little Bit History … • 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.

  5. A Little Bit History … From Wang Y-M (2013)

  6. Hemispheric rule ? ( Pevtsov 2002 ) H < 0 H > 0 independent of solar cycle So, hemispheric preference in quiet sun features (filaments) and in active features (ARs) differs substantially (90% vs. 65%). Why? If HMI data can give a different result? • 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 6 22/08/11 - FEW 2011 - E. Pariat

  7. 1. Hemispheric Rule 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

  8. 2. Hemispheric Rule of Helicity Sign: Two Groups (Relation of Twist and Writhe) • Origin of the twist in ARs seen at the solar surface—dynamo origin or emerging origin: • Scenario 1 (dynamo origin-same sign): 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-opposite sign): 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). Deforming the tubes will produce writhe. To conserve helicity, the same amount of twist with opposite sign will be generated. Thus, the flux tubes will have twist and writhe of opposite signs. The twist follows hemisphere rule.

  9. 2. Hemispheric Rule of Helicity Sign: Two Groups (Relation of Twist and Writhe) • 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):

  10. 2. Hemispheric Rule of Helicity Sign: Two Groups (Relation of Twist and Writhe) Sign Relationship between twist and writhe in ARs: same sign = 122; opposite sign = 114 Proxy of twist: force-free parameter αw Proxy of writhe (Canfield et al. 2003; Holder et al. 2004):

  11. 2. Hemispheric Rule of Helicity Sign: Two Groups (Relation of Twist and Writhe) It suggests that, prior to emergence of magnetic tubes, (1) either the sign of twist (initially strong) doesn’t have a hemispheric preference (kink instability—scenario 1) or (2) the twist is relatively weak (C- & Σ-effects are in work—scenario 2).

  12. 3. Hemisphere Rule: ARs in Difference Phases (Emerging ARs and Mature ARs) T*W < 0: Emerging scenario T*W > 0: Dynamo scenario • Possible reasons that cause the differences: • Evolving characteristics of emerging ARs toward mature phase: change of helicity sign? • Origin of twist in ARs is different for different types of ARs?

  13. Summary ARs (T*W<0) H-Rule = 85% All ARs H-Rule = 68% ARs (T*W>0) H-Rule = 52% It implies that the initial, very strong twist does not have a hemispheric preference.

  14. Summary Emerg ARs: T*W<0 = 84% Emerg ARs = 58% Emerg ARs: T*W>0 = 34% ? Dynamically evolving? All ARs = 68% Mature ARs: T*W>0 = 71% Mature ARs = 79% Mature ARs: T*W<0 = 88%

  15. Summary • The strength of hemisphere rule for CR 24, tested with HMI data, is consistent with previous studies; • It becomes much stronger in a subgroup of ARs with the opposite signs of twist and writhe, while almost no this preference in a subgroup with the same signs; • ARs in different phases have a similar hemispheric preference for the group with the opposite signs of twist and writhe, but differ substantially for the group with the same signs. • Further studies are needed to understand underlying mechanisms that cause those difference.

  16. Thank Phil for his leadership that brought to the solar community such excellent data from WSO, MDI, and HMI!

  17. 2. Hemispheric Preference of Helicity Sign: Magnetic Helicity Helicity in emerging ARs: 66% in a sample of 116 emerging ARs

  18. 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)

  19. 3. Hemispheric Rule in Emerging ARs and Mature ARs: ARs in Different Phases Thus, we have: Proxy of magnetic twist: 68% (236 ARs); Magnetic helicity: 66% (116 emerging ARs). Hemispheric preference in different phases of ARs: Two samples: 116 emerging ARs; 120 other ARs.

  20. Summary • More questions than conclusions: • Relationship among helicity, twist, and writhe in ARs; • What causes the difference between two-group ARs with same and opposite signs of twist and writhe? • What causes the different strength of hemisphere preference in different phases of ARs?

  21. 4. Hemispheric Preference of Helicity Sign: emerging ARs and other ARs Possible reasons causing the differences: Origin of twist in ARs is different for different types of ARs? Stronger field may form deeper in the convection zone (Pevtsov et al. 2011); Helicity flow is stronger in deeper convection zone (Komm et al. 2014); Kinetic helicity in strong field areas has a stronger strength of hemisphere preference (Komm et al. 2014); These suggest weaker field, perhaps forming at the upper part of convection zone, has a weak strength of hemisphere preference; Hypothesis: it’s expected that the emerging ARs (T * W > 0) that don’t follow the hemisphere rule should have less magnetic flux.

  22. 4. Hemispheric Preference of Helicity Sign: emerging ARs and other ARs Possible reasons causing the differences: Origin of twist in ARs is different for different types of ARs?

  23. 3. Hemispheric Rule: ARs in Different Phases (Emerging ARs and Mature ARs) Possible reasons causing the differences: Evolving characteristics of emerging ARs toward mature phase: change of helicity sign? Opposite signs of helicity flux and twist

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