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Helical properties of solar magnetic fields as a proxy of dynamo mechanism: results of

20 years monitoring

K.Kuzanyan1), D.Sokoloff2)

H.Zhang3), Y.Gao3)

1)IZMIRAN, Moscow region, Russia

2)Moscow State University, Russia

3)National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China

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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.

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Simple Dynamo Wave modelMagnetic field

generation (Parker Dynamo)

(A,B): Poloidal/Toroidal fieldcomponents

(Parker 1955)

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• So, the alpha-effect (mirror asymmetry) must change sign across the equator (!?)

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observations

Observable !

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

Positive (negative) values of longitudinal components of the magnetic field are shaded by white (black) in greyscale palette. The transversal magnetic field is shown by blue arrows; the magnitude of the field is proportional to the length of the arrows

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AR 10930: HC over the filtergram; positive/negative: a typical AR.

The filtergram of AR 10930; contours of current helicity HC for positive (negative) values shown in red (green), corresponding to absolute values of 0.2, 0.5, 1.0, 4.0 G2/m, respectively. The field of view is 104''80''.

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• Helicity and twist parameters are extremely fast changing on a short range of spatial and temporal scales, related to the size of individual active regions as well as their life time (or the time of available observations) of several days (sub-surface magnetohydrodynamics).

• Due to this variability the hemispheric rule can be established only in the sense of large scale averages in latitude (here we used 7o) and time (used 2 yr).

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Butterfly Diagram• The distribution of the averaged twist αav

and current helicity hc of solar active regions in the 22nd and 23rd solar cycles (1988-2005), 6630 magnetograms of 983 active regions used.

Let the vertical axis stand for latitude and the horizontal for time (years), plot white/black circles for positive/negative values giving the magnitude by circle sizes. The plot has been overlaid with the butterfly diagrams of sunspots (colours gives the averaged sunspot density).

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Helicity overlaid with butterfly diagram

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Force free factor overlaid with butterfly diagram

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

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Observational Results-1• We note remarkable similarity of the wings

plotted for different tracers (helicity and twist). The analysis of the data for individual tracers shows some similarity between these tracers as well as between the data obtained at different observatories (Huairou, Mitaka and Mees). However, some discrepancy in results obtained at different observatories reflect the noisy nature of the tracers. This confirms the expectation on noisy nature of the mirror asymmetry obtained in direct numerical simulations.

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• The hemispheric rule: mirror asymmetry of the

magnetic field (averaged helical parameters) at the

photospheric level has significant hemispheric

preference.

– on very large amount of observational data!

Northern hemisphere: mainly negative;

Southern hemisphere: mainly positive.

Does not change sign with 11-yr cycle,

while magnetic field changes!

Note: helicity and twist are not immediately

quadratic with magnetic field!

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Sign inversions:

• We have established some particular latitudes and times over the phases of the solar cycle at which the hemispheric sign rule is the opposite, mainly at the raise and fall of the 11-yr cycle, and we have shown that this violation is statistically significant ! (cf. Bao et al. 2000, see also Sokoloff et al. 2008)

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Observational Results-2• We note that there is an approximately two year

time lag between the sunspots and current helicity and twist patterns: helicity and twist patterns come after the one of sunspots. Moreover, the maximum value of helicity often occurs near the edges of the butterfly diagram of sunspots. This is an unexpected result which gives a challenge for dynamo theory because the conventional dynamo theory (Parker's migratory dynamo) predicts the lag of the opposite sign (helicity and twist pattern should appear some 2.7 year before the sunspot pattern).

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Observational Results-3• The wings of helicity and twist butterfly diagrams look steeper

than those ones of sunspots. We also note that there are some areas at the end of the wings where helicity and twist have the "wrong" sign. This is one more challenge for the theory. We may preliminary interpret this phenomenon as penetration of the activity wave from one hemisphere into another "wrong" hemisphere. Something like that can be recognized in sunspot data at the end of Maunder minimum. The other domain of the “wrong” helicity sign located just at the beginning of the wing has been predicted as a result of additional twisting of magnetic tubes arising to form a sunspot group (e.g., Choudhuri et al., 2004).

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?How statistically

significant is the fine structure and evolution

of current helicity with the

solar cycle?(inspired by discussions with

T. Sakurai)

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remind: Data Reduction

• 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;

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Overall data averaged with

standard deviation σ

We can see some evolutional trends but their analysis is hindered by large deviations. Statistical analysis of error level is required.

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Does all data points satisfy Gaussian distribution?

• Let N denote the total number of magnetograms in a sample bin (e.g., 2 years);

dxexFx x

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2)(

2

1)(

• Gaussian Distribution Function:

)( avc orhx • 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. x

x

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Continued …

• 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)/σ is smaller than y equals to P;

• If x is a Gaussian quantity then the plot y vs. x would be a straight line.

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Probability Plots (some cases)

For some cases data distributions are well Gaussian but for some others rather far from Gaussian. However, the data points within 0.2<P<0.8 satisfy the Gaussian distribution quite well! The ratio of numbers of Gaussian to non-Gaussian points is typically about 60% to 40%.

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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 behaviour seems to be closely related to some powerful eruptive events in the solar cycle.

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AR 9591

see as an example

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Current helicity averages over the Gaussian data points (0.2<P<0.8)

Notice similar evolutional trends as for the overall data but with smaller std. deviation.

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Averages over non-Gaussian data points (0.2>P or P<0.8)

Notice: Similar evolutional trends but greater std. deviations for each data bin.

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Result and Discussion

• The non-Gaussian data points are shown to be related to extra-ordinary powerful events in the solar cycle, the evolutional trend of their averages is well similar to those for Gaussian ones. The evolutional 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.

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Averages over all data points, using t-distribution (Student’s) error bars

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Helicity butterfly diagram for Gaussian data points

The hemispheric helicity “rule” is inverted at some latitudes and some phases of the solar cycle . It agrees with earlier studies (Bao et al., 2000; Hagino et al., 2005, see also Choudhuri et al. 2004; cf. Pevtsov et al., 2008).

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Helicity butterfly diagram for non-Gaussian data points

Non-Gaussian part of the data invert the hemispheric helicity “rule” at mainly the same latitudes and during the same time phases as for the Gaussian. But their values are often greater than for non-Gaussian.

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Helicity butterfly diagram for overall data points

The butterfly diagram may reflect the distribution and evolution of helicity in the solar interior at various ranges of scales.

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CONCLUSION

Observational studies of CURRENT HELICITY and TWIST provide a new type of information and additional constrains for dynamo models:

• 1. Hemispheric sign rule: asymmetry ( N- / S+ mainly)• 2. Inversion of the sign at some latitudes+times (but not

the hemispheric asymmetry!)• 3. Phase shift between helicity and sunspot waves• 4. Localisation of strong helicity to edges of butterfly wings• 5. Penetration of helicity waves across Equatoretc.

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Thank You!

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Thank You!

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Discussion• The findings on spatial distribution and

temporal variation of helical properties of the solar magnetic fields indicate global properties of their generation and shed light on the mechanism of the solar dynamo, therefore, provide us with useful constrains on theoretical modelling of the solar activity (e.g. Kleeorin et al. 2003; cf. Choudhuri et al. 2004).

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