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Helicity and Dynamo theory (Solar Magnetic Fields)

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Helicity and Dynamo theory(Solar Magnetic Fields)

Kirill Kuzanyan1,2)

1) IZMIRAN, Russian Academy of Sciences, Moscow, Russia

2) Visiting Professor 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

- 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

- 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

Magnetic field generation

(Parker Dynamo)

E.N. Parker (1955)

- 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.

Max Steenbeck, Fritz Krause, Karl-Heinz Raedler

Potsdam, Germany, 1966 - ….

Magnetic field generation

(Parker Dynamo)

(Parker 1955)

(A,B): Poloidal/Toroidal field

components

- 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!

- 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

Observable !

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.,

but only Huairoudata systematically cover 20 year period!

Photosphetic vector magnetogram

Current helicity over filtergram

- 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

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

- 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

- 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)

- Current helicity and twist follow the propagation of the magnetic activity dynamo waves recorded by sunspots and “mean” magnetic fields in active regions

Kleeorin, Kuzanyan, Moss, Sokoloff, Rogachevskii, Zhang, A&A, 2003;

and a series of publications of the authors thereafter in 2005-2011

Courtesy of D.D. Sokoloff and E. Popova (2009)

[with account of meridional circulation)

Magnetic field generation

(Parker Dynamo)

Generation of Helicity

Parameterized equation

!

C=0.01- ok!

HELICITY

C=0.1

too high value

LATITUDE

S

N

HELICITY

Sunspot Group Number

Magnetic Energy

~1988

~1997

Diffusion Time Units

Zhang, Moss, Sokoloff, Kuzanyan, Kleeorin, Rogachevskii (2012)

- He

Magnetic field (contour) & Current Helicity (color);

Cross-Helicity (colour) (Kuzanyan, Pipin, Zhang 2007).

(Pipin, Sokoloff, Zhang, Kuzanyan 2013 )

- He

Magnetic field & current helicity: comparing the observations and the model

(Pipin, Zhang, Sokoloff, Kuzanyan, Gao 2013 )

- He

Magnetic field & current helicity: contour plot

(Pipin, Sokoloff, Zhang, Kuzanyan 2013 )

Thank you!

谢谢！

- When the night comes with the actionI just know it's time to goCan't resist the strange attractionFrom that giantdynamo....
ABBA "Summer Night City"