Helicity and Dynamo theory (Solar Magnetic Fields)

1. Helicity and Dynamo theory(Solar Magnetic Fields) Kirill Kuzanyan1,2) 1) IZMIRAN, Russian Academy of Sciences, Moscow, Russia 2) Visiting Professor at National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China

2. Collaboration at National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China • Prof. ZHANG, Hongqi • Prof. Deng, Yuanyong • Dr. Gao, Yu • Dr. Xu, Haiqing • Dr. Yang, Shangbin

3. International Collaboration • Prof. Dmitry Sokoloff, Moscow • Dr. Valery Pipin, Irkutsk, Russia • Prof. Nathan Kleeorin & Igor Rogachevskii, Israel • Dr. David Moss, Manchester, UK • Prof. Axel Brandenburg, NORDITA, Sweden Now in Japan (NAOJ, Mitaka): Prof. T. Sakurai; Dr. K. Otsuji

4. The Butterfly Diagram

5. Basic Physics of the Solar Cycle • Solar dynamo theory Regeneration of magnetic fields due to rotation and turbulent convection • periodic in time • travelling wave Parker 1955 dynamo wave Babcock & Leighton 1961-69 Krause & Rädler 1980 mean-field model

6. Stretch-Twist-Fold Dynamo(after Ya.B.Zeldovich 1960s, also see in H.K.Moffat, 1978)

7. Generation of mean magnetic fields

8. Magnetically Linked Spots

9. Migratory Dynamo wave model Magnetic field generation (Parker Dynamo) E.N. Parker (1955)

10. Simple Mean field dynamo • Parker (1955) was the first to produce quasi-realistic non-axisymmetric velocity distributions with qualitative solutions for B magnetic field • The - mean field dynamo theory was introduced by Steenback, Krause & Raedler (1966) and solutions of these equations supported Parker’s picture.

11. Founders of mean-field dynamo theory Max Steenbeck, Fritz Krause, Karl-Heinz Raedler Potsdam, Germany, 1966 - ….

12. Mean-Field dynamo theory

13. Turbulent Electro-Motive Force

14. Simple Dynamo Wave model Magnetic field generation (Parker Dynamo) (Parker 1955) (A,B): Poloidal/Toroidal field components

16. So, the theory requires cyclonic motions (mirror asymmetry of convection), or the alpha-effect to change sign across the equator and be the same from cycle to cycle!

18. Correlation of Helicities

19. The Role of Helicities in Dynamo • Inviscid integrals magnetic helicity A.B (for turbulent motion, too!) cross-helicity U.B (for classic MHD) • Non-linear back reaction in dynamo self-consistent models

20. observations Observable !

21. 20 years systematic monitoring of the solar vector magnetic fields in active regions taken at Huairou Solar observing station, China (1988-2005…) More observations from Mitaka (Japan) and also Mees, MSFC (USA) etc., but only Huairoudata systematically cover 20 year period!

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

23. Example - Photospheric vector magnetogram of AR 10930 (SOT at Hinode)2006 Dec 11-12 at 23:10:06-00:13:17UT.

24. AR 10930: HC over the filtergram; positive/negative:0.2, 0.5, 1.0, 4.0 G2/m

25. Data Reduction • 983 active regions; 6630 vector magnetograms observed at Huairou Solar Observing Station; • Time average: 2 year bins (1988-2005); • Latitudinal average: 7o bins; So, each bin contains 30+ magnetograms => => independent statistics in each bin: averages with confidence intervals (Student t distribution) We assume the data subsamples equivalent to ensembles of turbulent pulsations, so we gather mean quantities in the sense of dynamo theory

26. Helicity overlaid with butterfly diagram

27. Twist overlaid with butterfly diagram

28. Compare: Qualitatively, the both helical quantities are distributed in a similar manner. So, despite the noisy nature of the data, accuracy of measurements is reliable.

29. The hemispheric sign rule for helicity: Northern hemisphere: mainly negative; Southern hemisphere: mainly positive. Does not change sign from one 11-yr cycle to another! While neither current helicity, nor twist are exactly quadratic with magnetic field

30. Regular inversion of the hemispheric rule: • There are particular latitudes and times over the solar cycle at which the hemispheric rule is inverted, mainly at the raise and fall of the 11-yr cycle • This invertion is statistically significant ! (cf. Bao et al. 2000, see also Sokoloff et al. 2008)

31. Helicity plays an important role in the solar dynamo mechanism! • Current helicity and twist follow the propagation of the magnetic activity dynamo waves recorded by sunspots and “mean” magnetic fields in active regions

32. Simple self-consistent dynamo models with evolution of helicity (dynamical nonlinearity) Kleeorin, Kuzanyan, Moss, Sokoloff, Rogachevskii, Zhang, A&A, 2003; and a series of publications of the authors thereafter in 2005-2011

33. Theoretical butterfly diagram for Parker dynamo: helicity in the solar interior (opposite sign than at surface) Courtesy of D.D. Sokoloff and E. Popova (2009) [with account of meridional circulation)

34. Dynamo model with evolution of Helicity Magnetic field generation (Parker Dynamo) Generation of Helicity Parameterized equation

35. Development of 1D-2D models(Moss,Kleeorin,Rogachevskii, Sokoloff, Kuzanyan et al.) !

36. Choice of Parameter Range (Example) C=0.01- ok! HELICITY C=0.1 too high value LATITUDE

37. Kleeorin et al. 2003EVOLUTION OF HELICITY WITH TIME(Northern HemisphereN) S N HELICITY Sunspot Group Number Magnetic Energy ~1988 ~1997 Diffusion Time Units

38. Estimate of current helicity of active regions Zhang, Moss, Sokoloff, Kuzanyan, Kleeorin, Rogachevskii (2012)

39. 2D model with cross-helicity(after Pipin, Kuzanyan, Zhang & Kosovichev, 2011)

40. Results: model with cross-helicity • He Magnetic field (contour) & Current Helicity (color); Cross-Helicity (colour) (Kuzanyan, Pipin, Zhang 2007).

41. Dynamo Model with Total (small-scale + large scale) Magnetic Field Conservation (Pipin, Sokoloff, Zhang, Kuzanyan 2013 )

42. Results: model with helicity conservation • He Magnetic field & current helicity: comparing the observations and the model (Pipin, Zhang, Sokoloff, Kuzanyan, Gao 2013 )

43. Results: model with helicity conservation • He Magnetic field & current helicity: contour plot (Pipin, Sokoloff, Zhang, Kuzanyan 2013 )

44. СПАСИБО! Thank you! 谢谢！

45. When the night comes with the actionI just know it's time to goCan't resist the strange attractionFrom that giantdynamo.... ABBA "Summer Night City"