Негауссовские распределения спиральности солнечных магнитных полей в цикле

активности

Kuzanyan KirillKuzanyan Kirill; Sokoloff Dmitry

(IZMIRAN, RAS & Moscow State University)

Gao Yu; Xu Haiqing; Zhang Hongqi;

(NAOC Beijing/Huairou, China)

Takashi Sakurai

(NAOJ Mitaka, Tokyo, Japan)

Simple Dynamo Wave modelMagnetic field

generation (Parker Dynamo)

(A,B): Poloidal/Toroidal fieldcomponents

(Parker 1955)

Correlation of HelicitiesCorrelation of Helicities

observations

Observable !

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.

AR NOAA6619 on 1991-5-11 @ 03:26UT (Huairou)

Photosphetic vector magnetogram Electric current helicity over filtergram

Helicity is naturally very noisy• (e.g.)The average value of current

helicity

HC = −8.7 · 10−3 G2m−1 • the standard deviation 8 · 10−2 G2m−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

“Mean-field” scales

• Smaller than entire astrophysical body (the Sun)

107-109 cm << L << 1011 cm

1-10 days << T << 104 days

• Larger than fluctuation level (granulae)

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: 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

Helicity overlaid with butterfly diagram

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.

dxexFx x

22

2)(

2

1)(

• Gaussian Distribution Function:

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.

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%.

Probability Plots (continued)

More cases for Southern hemisphere.

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)

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

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.

AR 9591

see as an example

Links of non-Gaussian active regions with eruptive events

The active

regions with

most

imbalanced

helicity are

likely to

produce

flares.

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.

Thank You!

Спасибо!