1. Anisotropy of current helicity in solar active regions 1)Xu Haiqing, Gao Yu & Zhang Hongqi, NAOC 2) Kirill Kuzanyan, IZMIRAN, Russia 3) Rodion Stepanov, ICMM, Perm, Russia 4) Dmitry Sokoloff, Moscow University, Russia Helicity forever!

2. The role of helicity in dynamos Magnetic Helicity = inviscid invariant Cross helicity = inviscid invariant (Woltjer 1958; Moffat 1969)

3. Magnetic and Current Helicities Magnetic Helicity dissipation rate (e.g., Berger & Field 1984) Relation between current helicity in active regions and mean-field magnetic helicity (Zhang, Moss, Kleeorin, Kuzanyan, Rogachevskii, Sokoloff, Gao, Xu 2012)

4. Correlation of Helicities

5. The Role of Helicities in Dynamo Inviscid integrals magnetic helicity A. B (for turbulent motion, at all scales!) cross-helicity U. B (for no-scale separation MHD) Non-linear back reaction in dynamo self-consistent models

6. Reduction of Vector Magnetic Field from Polarized Light Magnitude (calibration required!) Under the assumption of weak field (calibration required!) the magnetic field is related to the parameters of polarized light. Though some observational problems exist! In real measurements multi-frame averaging is employed to improve the ratio of signal-to- noise.

7. observations Observable !

8. Question How the part of current helicity is really related to the entire quantity??? : How good is local homogeneity approximation? (keep in mind!) ! Observable current helicity is really related to mean magnetic helicity in the model ! (Zhang et al. 2012 ApJ)

9. An estimate for the current helicity of active regions Zhang, Moss, Kleeorin, Kuzanyan, Rogachevskii, Sokoloff, Gao, Xu (2012)

10. Computation of electric current helicity in solar active regions Seehafer (1990); Pevtsov & Canfield (1994); Abramenko et al.(1996);Bao & Zhang(1998); Hagino & Sakurai (2004-05) twist

11. мп,сп,закр magnetic field current helicity twist

12. AR NOAA6619 on 1991-5-11 @ 03:26UT (Huairou) Photosphetic vector magnetogramCurrent helicity over filtergram

13. Helicity is naturally very noisy (e.g.)The average value of current helicity H C = −8.7 · 10 −3 G 2 m −1 the standard deviation 8 · 10 −2 G 2 m −1 (factor 9). changing dramatically on a short range of spatial and temporal scales, related to the size of individual active regions as well as their life time

14. 20 years systematic monitoring of the solar vector magnetic fields in active regions taken at Huairou Solar observing station, China (1987-2006) More observations from Mitaka (Japan) and also Mees, MSFC (USA) etc., but only Huairou data systematically cover 20 years period.

15. Helicity over the solar cycle: Zhang et al. (2010-2012)

16. Important observational properties of helicity: Hemispheric Sign Rule: North=negative; South=positive Systematic reversal of the sign at some latitudes in the beginning and end of the solar cycle

17. Using helicity for constraining dynamo models of the solar cycle We know how helicity behaves with the solar cycle and how migrates over the latitude We need a self-consistent model which is in accord with these observational facts! (after publications of Zhang, Moss, Kleeorin, Rogachevskijj, Sokoloff, Kuzanyan, Gao & Xu, 2003-2012)

18. 2D distributed dynamo with algebraic alpha-quenching, near-surface (example)

19. Definition of current helicity

20. Definition of curl for any vector F Decomposition of current helicity into six parts:

21. Integration by parts: equalities If we assume the magnetic field outside the active region is weak, and so we can use the formula for integration by parts (typical accuracy ~3-5%). Then the derivatives swap.

22. Example of PDF for helicities (hr)

23. Model of turbulent magnetic field after Volegova & Stepanov, 2009 JETP

24. Formulation of the model 1) Random phase of turbulent flow 2) Realistic prescribed energy spectrum with dominating scale 3) Solenoidality condition 4) Prescribed Integral Helicity, so we can set =0 or non-zero.

25. Stepanov et al. (2013), submitted:

26. Isotropic helical case

27. HXHX HYHY HZHZ BXBX BYBY BzBz

28. Non helical case Numerical simulation of turbulent convection

30. Example of PDF for helicities (hr)

31. Observational Example of PDF for helicities: to compare with theory

32. Examples of PDF for helicities hr filtering

33. HzH1H2 Helical Magnetic Field Helical + Potential Magnetic Field Non- Helical Magnetic Field

34. Notice! The addition of potential magnetic field does contribute each of the helicity parts! but it does not contribute to the sum of them, i.e. to the entire helicity

35. Comparison of Helicity parts time-latitudinal averaging

36. Overall data: no immediate link between the helicity parts (H1,H2 weak anti- correlation) H1=H6 H2=H3

37. Contributions to “overall” helicity

38. Notice! At the phases of beginning and end of each cycle there is a certain range of latitudes where the sign of overall helicity changes to the opposite of the one give my hemispheric rule. One may note that during these phases the signs of both pairs of helicity parts are often the same, which makes their joint contribution to the opposite to the hemispheric rule sign

39. Odd and Even parts of Helicity

40. Odd and Even (for the sum)

41. Discussion 1)While we see that the sum of available helicity parts H 1 and H 2 has clear cyclic behaviour, its parts alone are less regular and behave less similar to each other 2)The parts alone much less follow the Hemispheric Sign Rule for Helicity. They disobey the rule at the beginning and the end of the cycle somehow synchronously 3) The Odd parts of the helicity parts look more regular with the cycle than the Even parts

42. Conclusions There are possible causes of anisotropy that require further investigation: 1) Stratification 2) Rotation, Meridional Circulation, Differential rotation (Torsion Oscillations?) 3) Mean magnetic field 4) Data bias

43. Xie-xie! 谢 СПАСИБО!