1. Helicity and Dynamo theory (Solar Magnetic Fields) Kirill Kuzanyan 1,2 ) 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. When the night comes with the action I just know it's time to go Can't resist the strange attraction From that giant dynamo.... ABBA "Summer Night City"

5. Review of 16 year collaboration studies 1998-2014 Revealing mean-field properties, grouping of current helicity data in active regions with time and latitude (Kuzanyan,Bao,Zhang 2000 Sol.Ph.; Zhang et al. 2010 MNRAS) Relationship between Current Helicity and Twist (Zhang et al. 2002 Astr.Zh.; Sokoloff et al. 2008 Sol.Ph.) Distribution of helicity proxies with depth (Kuzanyan et al. 2003 ChJAA; Zhang et al. 2006 MNRAS) Probing Cross-Helicity in theory (Kuzanyan et al. 2007; Pipin et al. 2011 ApJ) Dynamo models for helicity evolution (Kleeorin et al. 2003 A&A; Sokoloff et al. 2006 AN; Zhang et al. 2012 ApJ; Pipin et al. 2012 ApJ) and more…

6. Current work in progress Gaussian properties of helicity distribution in active regions (Gao, Yu; Sakurai, T. et al.) Anisotropy of helicity in solar active regions (Xu, Haiqing, Rodion Stepanov, Dmitry Sokoloff et al.) Estimate of tilt and helciity and twist in solar active regions (Nathan Kleeorin, Igor Rogachevskii et al.) Comparative study for helicity distributions from data obtained at different instruments: SMFT (Huairou, China), SFT (Mitaka, Japan), SDO HMI, Hinode SP etc. …

7. The Butterfly Diagram

8. 2015-9-3 太阳和太阳风暴 Large scale magnetic field of the Sun 太阳纵向磁场蝴蝶图

9. 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

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

11. Generation of mean magnetic fields

12. Magnetically Linked Spots

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

14. Basic equations of solar magnetism Solar convection zone governed by equations of compressible MHD

15. Solar Parameters (Ossendrijver 2003) 10 20 10 13 10 10 -7 10 5 10 -3 10 -4 0.1-1 10 16 10 12 10 6 10 -7 10 -6 1 1 10 -3 -0.4 BASE OF CZPHOTOSPHERE

16. Induction Equation

17. 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.

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

19. Mean-Field dynamo theory

20. Turbulent Electro-Motive Force

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

23. 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!

25. Correlation of Helicities

26. 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

27. observations Observable !

28. 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., Huairou but only Huairou data systematically cover 20 year period!

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

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

31. AR 10930: H C over the filtergram; positive/negative: 0.2, 0.5, 1.0, 4.0 G 2 /m

32. Data Reduction 983 active regions; 6630 vector magnetograms observed at Huairou Solar Observing Station; Time average: 2 year bins (1988-2005); Latitudinal average: 7 o 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

33. Helicity overlaid with butterfly diagram

34. Twist overlaid with butterfly diagram

35. 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.

36. 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

37. 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)

38. 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

39. 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

40. 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)

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

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

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

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

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

46. 2D model with cross-helicity (after Pipin, Kuzanyan, Zhang & Kosovichev, 2011)

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

48. Results: model with cross-helicity He Magnetic field: contour plot; Cross-Helicity: colour plot ( courtesy of V. Pipin).

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

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

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

52. 52 Hale’s Polarity Law for Transversal Fields magnetic field (G)

53. 53 Observable Properties of Vector Magnetic Fields in Active Regions Cyclic variation 22 years (magnetic cycle!) Longitudinal field component (radial) and one transversal (asimuthal) (asimuthal) are anti-symmetric over the solar equator The other transversal (meridional) component is symmetric over the solar equator Agreement with Hale’s Polarity Rule!

54. 54 Helicity overlaid with butterfly diagram

55. 55 Twist overlaid with butterfly diagram

56. 56 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.

57. 57 THE MAIN RESULT Current helicity and twist follow the propagation of the magnetic activity dynamo waves recorded by sunspots and “mean” magnetic fields in active regions Helicity plays an important role in the solar dynamo mechanism.

58. 58 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

59. 59 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)

60. 60 Observable properties of helicity Anti-symmetric over the solar equator Cyclic variation 11 years (not 22 years!) Time lag with respect to sunspots is about 2 years behind, not ahead! (confront with Parker’s dynamo theory) Systematic sign inversion of helicity (a) at the beginning of the cycle (b) at the end of the cycle

61. 61 Simple self-consistent dynamo model with evolution of helicity (dynamical nonlinear dynamo) Kleeorin, Kuzanyan, Moss, Sokoloff, Rogazhevsky, Zhang, A&A, 2003; and a series of publications of the authors thereafter in 2005-2009

62. 62

63. 63 Choice of Parameter Range (Example) LATITUDE HELICITY C=0.01- ok! C=0.1 too high value

64. 64 Kleeorin et al. 2003 EVOLUTION OF HELICITY WITH TIME ( Northern Hemisphere N ) Diffusion Time Units S N Sunspot Group Number Magnetic Energy HELICITY ~1988~1997

65. 65 Dynamo models help…? or helicity helps the models!? The model which we considered in 2003 was far too simple! Recall the results 2003-2008

66. 66 Development of dynamo models with account of helicity (courtesy of Axel Brandenburg and my co-authors Nathan Kleeorin and Igor Rogachevskii)

67. 67 MHD and magnetic helicity

68. 68 Magnetic helicity conservation How J diverges as   0 Ideal limit and ideal case similar!

69. 69 Production of large-scale helicity forcing produces and Yousef & Brandenburg A&A 407, 7 (2003) But no net helicity production therefore:  alpha effect

70. 70 Effect of helicity fluxes Brandenburg (2005, ApJ) 10 46 Mx 2 /cycle

71. 71 Magnetic helicity flux on the Sun Bao & Zhang (1998), neg. in north, plus in south (also Seehafer 1990) see also Georgoulis, Rust, Pevtsov, Bernasconi, Kuzanyan ApJL (2009) Berger & Ruzmaikin (2000) N DeVore (2000) (for BR & CME)

72. СПАСИБО! Thank you! 谢谢！

73. When the night comes with the action I just know it's time to go Can't resist the strange attraction From that giant dynamo.... ABBA "Summer Night City"