Statistical properties of current

helicity and twist distribution in the

solar cycle by high resolution data

from SOT/SP on board Hinode

K. Otsuji1)

, T. Sakurai1)

, K. Kuzanyan1,2*)

1) National Astronomical Observatory of Japan

2) IZMIRAN, Russian Academy of Sciences, Russia

PASJ, in press 12/2014 (astro-ph arXiv:1410.7532)*) contact email: kuzanyan@gmail.com (Kirill Kuzanyan)

Kyoto University, 2015/01/13

The role of helicity in dynamoMagnetic helicity • inviscid invariant in MHD

Current helicity

observational proxy of mean magnetic helicity in solar active regions (Zhang et al. 2012)

• signature of the alpha-effect (Seehafer 1994)

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Plan of the talk1. Introduction: History of helicity computationReview of recent studies from Hinode2.1. Review of available data for active regions,

selection by FOV and strong fields & filling factor (FF)

2.2. Sensitivity & errors: cut-off values, FF,=examples, cf. ground-based data

2.3. Disambiguation methods. Errors= disambiguation, current errors = examples

3. Helical parameters which we compute4. Butterfly diagrams of helical parameters

5. Smoothing and altering Bz, Bt cut-off values for simulating ground-based data.

6. Conclusions

Computation of helicity and the hemispheric rule

• Seehafer 1990: 16 active regions (the hemispheric rule: North-/South+ ) for helicity

• Pevtsov et al.

1994-1995:

69 ARs

More results on hemispheric rule

Bao & Zhang 1998: 422 ARs Zhang, Bao, Kuzanyan 2002

More results on hemispheric ruleHagino & Sakurai 2004-2005

• Variation with the solar cycle also reported by Hagino & Sakurai 2005

Variations of the hemispheric rule with the solar cycle (Bao et al. 2000)

Butterfly diagram for helicity

used 6600+ ARs : Zhang et al. 2010, see also Zhang et al. 2012

Compare: Qualitatively, the both helical quantities are distributed in similarly

(after Zhang et al. 2010)

Results involving Hinode

• Tiwari et al. 2009

Sample of 43 magnetograms: hemispheric sign rule is not confirmed

• Hao & Zhang M. 2011

Sample of 64 active region magnetograms from Hinode SOT/SP: most of data for cycle 24 do not follow the hemispheric rule

Purpose of this study

• Develop a systematic approach to studies of cyclic variations of helical parameters with Hinode or any other data

• Give a statistically significant result on the hemispheric sign rule for helicity over the solar cycle, potentially useful for dynamo theory

Data availability and selection• Hinode SOT SP level2 data

– Available from http://www.csac.hao.ucar.edu/

• MERLIN code– Milne-Eddington gRid Linear Inversion Network

• Data period: 2006-2012• Data selection criteria

1. Near disk center (<30deg) => ignore projection effects

2. FOV>10,000 [arcsec2]

3. area(|B|>1kG)>1,000[arcsec2]

4. area(FF=0)/FOV < 0.05 (about 90% of overall data)

– Ratio of strong fields=area(|B|>1kG)/FOV~0.1-0.2

Selected: 558 magnetograms of 80 Active Regions 12

Properties of SP level2 data

• Pixel size: ~0.3 arcsec for both slit and scan direction for most of magnetograms

• Scan duration: 1~2 hours• 180°ambiguity: not resolved

• Typical noise level

– ~50-70G for Bx and By (established!)

– ~3-5G for Bz (established!)

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Excluding unreliable data pixels – Inclination angle is almost 0°or 180°– Filling Factor (magnetic filling fraction)=0– Erroneously-disambiguated pixels

• Pixel-By-Pixel difference in azimuth: 160°<|Δφ|< 200°

• Spuriously high derivatives |Curl(B)z|>3×10-3 [G/m]

– Corresponding approximately |ΔBx,y|>700G

• Difference between each value of Bx, By

and its 3-pixel median < 100G 14

Calculation of Helical Parameters • (Curl B)z

• Current helicity density

• Twist– Local twist (Bao and Zhang 1998)

– Average twist (Hagino and Sakurai 2004)

– Global twist (Tiwari 2009)15

Bz Local twist Helicity

Example distribution of current helicity and local twist

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Variety of ranges for the magnetic field strength and image resolution (seeing, by

Gaussian convolution, FWHM)

• Range of magnetic fields

– BL: weak(3-300G), medium(300-1000G),

strong(1000-3000G), all (>3G)

– BT: weak(50-150G), medium(150-500G),

strong(500-2000G), all (>50G)

• Image resolution (seeing), FWHM– 0”, 0.5”, 2”, 2”+BT sqrt(filling factor)∝

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NOAA 10938 helicity (No smoothing)2007-01-16, latitude +2.9

BT=|BL|/2

Northern hemisphere: large BL H>0, large BT H<0 18

NOAA 11017 helicity (No smoothing)2009-06-04, latitude +27.0

BT=|BL|/2

Northern hemisphere: large BL H>0, large BT H<0 19

NOAA 11041 helicity (No smoothing)2010-01-25, latitude -25.1

BT=|BL|/2

Southern hemisphere: large BL H<0, large BT H>0 20

Smoothing of magnetic field values (2”)

Smothed from1/6” -> 2” (12 times)

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Effect of smoothing on helicity

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Effect of smoothing on local twist

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Statistical effect on current helicity distribution with time (2006-2012)

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Statistical effect on twist distribution with time (2006-2012), cycles 23-24

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Conclusions• We found different properties of helicity through the

strong and weak values of magnetic field components:

• current helicity for the weak magnetic fields (absolute field strength < 300 G) follows the so-called hemispheric sign rule [N-/S+], no smoothing

• the pattern of current helicity fluctuates and violates the hemispheric sign rule when strong magnetic fields are considered, smoothing 2.0"

• the weak and inclined fields better conform to and the strong and vertical fields tend to violate the hemispheric rule

...important clues to understanding the solar dynamo and formation and evolution of solar active regions…

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Future plans

a) Account of projection effects;  

b) Account of cross-correlations between consequent magnetograms of the same active region to reveal statistical behavior with time;  

c) Study of helicity in quiet regions (much more data available)

С Новым Годом!

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Happy New Year!