1. Негауссовские распределения спиральности солнечных магнитных полей в цикле активности Kuzanyan Kirill Kuzanyan Kirill; Sokoloff Dmitry (IZMIRAN, RAS & Moscow State University) Gao Yu; Xu Haiqing; Zhang Hongqi; (NAOC Beijing/Huairou, China) Takashi Sakurai (NAOJ Mitaka, Tokyo, Japan)

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

4. Correlation of Helicities

5. observations Observable !

6. 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.

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

8. AR 10930: H C over the filtergram; positive/negative: 0.2, 0.5, 1.0, 4.0 x 10 -3 G 2 /m

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

10. 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

11. Turbulent Diffusion and Scales Spatial and time scales are linked by turbulent diffusivity (eta) = L 2 / (tau) For the Sun (eta) ~ 10 12 -10 14 cm 2 /s check it on a range of scales and times “ Mean ” scales are less than entire scales of the object but big enough, compared with “ the background ”, and so observable

12. “Mean-field” scales Smaller than entire astrophysical body (the Sun) 10 7 -10 9 cm << L << 10 11 cm 1-10 days << T << 10 4 days Larger than fluctuation level (granulae)

13. Observations and 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

14. Helicity overlaid with butterfly diagram

15. 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 ahead, not behind! (confront with dynamo theory) Systematic sign inversion of helicity (a) at the beginning of the cycle (b) at the end of the cycle

16. Is current helicity evolving with the solar cycle? Is the physical nature of the photospheric current helicity related with the solar cycle: Photospheric current helicity is a proxy of the  -effect operating at the bottom of solar convection zone (?)  IT EVOLVES with the solar cycle! (e.g., Kleeorin et al.,2003 etc) Current Helicity is a product of convective turbulence in the solar convection zone (?)  It Does Not Evolve! (Longcope, Fisher & Pevtsov, 1998)

17. Statistical properties of current helicity distribution in solar active regions 983 active regions; 6630 vector magnetograms observed at Huairou Solar Observing Station; Time ranges from 1988 to 2005; Time average: 2 year data bins; Latitudinal: Northern hemisphere and Southern hemisphere;

18. How close are data points to Gaussian distribution? Let N denote the total number of magnetograms in a sample bin (e.g., 2 years); Let n be the number of magnetograms in the same bin for which the current helicity is smaller than X. Then the probability of that the current helicity is smaller than X is P=n/N. Gaussian Distribution Function:

19. Normal Probability Paper method Assume ξ is a Gaussian quantity with the same mean value μ and std.σ as for the observable current helicity distribution. Then the probability that (ξ- μ)/σis smaller than y equals to P; If x is a Gaussian quantity then the plot y(x) vs. x is a straight line.

20. Probability Plots (some cases) For some cases data distributions are well Gaussian but for some other rather far from Gaussian. However, we choose the data points within 0.2<P<0.8 as close to Gaussian distribution! The ratio of numbers of Gaussian to non-Gaussian points is typically about 60% to 40%.

21. Probability Plots (continued) More cases for Southern hemisphere.

22. Multi-modal Gaussian distribution Example of multi- modal Gaussian distribution: two Gaussians (1) Weak values close to zero (2) Strong values agreed with global properties (Southern hemisphere 1993)

23. Helicity butterfly diagram for Gaussian vs. non-Gaussian points Non-Gaussian part of data disobey the hemispheric helicity “rule” at the same latitudes and during the same time phases as for the Gaussian. But their values are often greater than for non-Gaussian. This manifests helicity at various ranges of scales. Gaussian data Non- Gaussian data

24. Why non-Gaussian? 1991-05-07---1991-05-12 AR 6615 (Jeongwoo Lee et al. 1998) 2001-08-26---2001-09-01 AR 9591 15 C flare, 2 M Flare and 1 X Flare only on 2001-08-26 (see Active Region Monitor). Non-Gaussian points seem to be closely related to some powerful eruptive events in the solar cycle.

25. AR 9591 see as an example

26. Links of non-Gaussian active regions with eruptive events The active regions with most imbalanced helicity are likely to produce flares.

27. Result and Discussion Even though the non-Gaussian data points are shown to be related to some extra- ordinary powerful events in the solar cycle, the evolutionary trend of their averages is well similar to those for Gaussian ones. The evolutionary trends of the both Gaussian and non-Gaussian data may imply that helicity for both groups of data is generated by the same mechanism of the solar (mean-field) dynamo though maybe at different time-spatial scales.

28. Thank You! Спасибо!