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Helicity and Dynamo theory (Solar Magnetic Fields). Kirill Kuzanyan 1,2 ) 1) IZMIRAN, Russian Academy of Sciences, Moscow, Russia 2) Visiting Professor at National Astronomical Observatories, Chinese Academy of Sciences, Beijing, China.

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Helicity and dynamo theory solar magnetic fields

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
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
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
The Butterfly Diagram Chinese Academy of Sciences, Beijing, China


Basic physics of the solar cycle
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 t wist f old dynamo after ya b zeldovich 1960s also see in h k moffat 1978
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
Generation of mean magnetic fields Chinese Academy of Sciences, Beijing, China


Magnetically linked spots
Magnetically Linked Spots Chinese Academy of Sciences, Beijing, China


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

Magnetic field generation

(Parker Dynamo)

E.N. Parker (1955)


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


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


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

Magnetic field generation

(Parker Dynamo)

(Parker 1955)

(A,B): Poloidal/Toroidal field

components



Correlation of helicities
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
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
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
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 c over the filtergram positive negative 0 2 0 5 1 0 4 0 g 2 m
AR 10930: H at Hinode)C over the filtergram; positive/negative:0.2, 0.5, 1.0, 4.0 G2/m


Data reduction
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




Compare
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
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
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
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
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 moss kleeorin rogachevskii sokoloff kuzanyan et al
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
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 evolution of helicity with time northern hemisphere n
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 stimate of current helicity of active regions
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 after pipin kuzanyan zhang kosovichev 2011
2D model with cross-helicity the solar interior (opposite sign than at surface)(after Pipin, Kuzanyan, Zhang & Kosovichev, 2011)


Results model with cross helicity
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 small scale large scale magnetic field conservation
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 model with helicity conservation
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 model with helicity conservation1
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 )


СПАСИБО! the solar interior (opposite sign than at surface)

Thank you!

谢谢!


  • 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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