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Helicity and Dynamo theory (Solar Magnetic Fields)PowerPoint Presentation

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

Collaboration 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

International Collaboration Chinese Academy of Sciences, Beijing, China

- 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

The Butterfly Diagram Chinese Academy of Sciences, Beijing, China

Basic Physics of the Solar Cycle Chinese Academy of Sciences, Beijing, China

- 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

Stretch- Chinese Academy of Sciences, Beijing, ChinaTwist-Fold Dynamo(after Ya.B.Zeldovich 1960s, also see in H.K.Moffat, 1978)

Generation of mean magnetic fields Chinese Academy of Sciences, Beijing, China

Magnetically Linked Spots Chinese Academy of Sciences, Beijing, China

Migratory Dynamo wave model Chinese Academy of Sciences, Beijing, China

Magnetic field generation

(Parker Dynamo)

E.N. Parker (1955)

Simple Mean field dynamo Chinese Academy of Sciences, Beijing, China

- 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.

Founders of mean-field dynamo theory Chinese Academy of Sciences, Beijing, China

Max Steenbeck, Fritz Krause, Karl-Heinz Raedler

Potsdam, Germany, 1966 - ….

Mean-Field dynamo theory Chinese Academy of Sciences, Beijing, China

Turbulent Electro-Motive Force Chinese Academy of Sciences, Beijing, China

Simple Dynamo Wave model Chinese Academy of Sciences, Beijing, China

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!

Correlation of Helicities of convection), or the alpha-effect to change sign across the equator and be the same from cycle to cycle!

The Role of Helicities in Dynamo 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

observations of convection), or the alpha-effect to change sign across the equator and be the same from cycle to cycle!

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!

AR NOAA6619 on 1991-5-11 @ 03:26UT (Huairou) fields in active regions taken at Huairou Solar observing station, China (1988-2005…)

Photosphetic vector magnetogram

Current helicity over filtergram

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

AR 10930: H at Hinode)C over the filtergram; positive/negative:0.2, 0.5, 1.0, 4.0 G2/m

Data Reduction at Hinode)

- 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 at Hinode)

Twist overlaid with butterfly diagram at Hinode)

Compare: at Hinode)

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: at Hinode)
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

Regular inversion of the hemispheric rule: at Hinode)

- 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)

Helicity plays an important role in the solar dynamo mechanism!

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

Simple self-consistent dynamo models with evolution of helicity (dynamical nonlinearity)

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

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

Theoretical butterfly diagram for Parker dynamo: helicity in the solar interior (opposite sign than at surface)

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

[with account of meridional circulation)

Dynamo model with evolution of Helicity the solar interior (opposite sign than at surface)

Magnetic field generation

(Parker Dynamo)

Generation of Helicity

Parameterized equation

Development of 1D-2D models the solar interior (opposite sign than at surface)(Moss,Kleeorin,Rogachevskii, Sokoloff, Kuzanyan et al.)

!

Choice of Parameter Range (Example) the solar interior (opposite sign than at surface)

C=0.01- ok!

HELICITY

C=0.1

too high value

LATITUDE

Kleeorin et al. 2003 the solar interior (opposite sign than at surface)EVOLUTION OF HELICITY WITH TIME(Northern HemisphereN)

S

N

HELICITY

Sunspot Group Number

Magnetic Energy

~1988

~1997

Diffusion Time Units

E the solar interior (opposite sign than at surface)stimate of current helicity of active regions

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

2D model with cross-helicity the solar interior (opposite sign than at surface)(after Pipin, Kuzanyan, Zhang & Kosovichev, 2011)

Results: the solar interior (opposite sign than at surface)model with cross-helicity

- He

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

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

Dynamo Model with Total the solar interior (opposite sign than at surface)(small-scale + large scale) Magnetic Field Conservation

(Pipin, Sokoloff, Zhang, Kuzanyan 2013 )

Results: the solar interior (opposite sign than at surface)model with helicity conservation

- He

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

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

Results: the solar interior (opposite sign than at surface)model with helicity conservation

- He

Magnetic field & current helicity: contour plot

(Pipin, Sokoloff, Zhang, Kuzanyan 2013 )

- When the night comes with the action the solar interior (opposite sign than at surface)I just know it's time to goCan't resist the strange attractionFrom that giantdynamo....
ABBA "Summer Night City"

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