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

• 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

Basic Physics of the Solar Cycle• Solar dynamo theory

Regeneration of magnetic fieldsdue to rotation and turbulent convection

• periodic in time• travelling wave

Parker 1955 dynamo waveBabcock & Leighton 1961-69Krause & Rädler 1980 mean-field model

Stretch-Twist-Fold Dynamo(after Ya.B.Zeldovich 1960s, also see in H.K.Moffat, 1978)

Generation of mean magnetic fields

Magnetically Linked Spots

Migratory Dynamo wave model

Magnetic field generation (Parker Dynamo)

E.N. Parker (1955)

Simple Mean field dynamo

• 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

Max Steenbeck, Fritz Krause, Karl-Heinz RaedlerPotsdam, Germany, 1966 - ….

Mean-Field dynamo theory

Turbulent Electro-Motive Force

Simple Dynamo Wave modelMagnetic field

generation (Parker Dynamo)

(A,B): Poloidal/Toroidal fieldcomponents

(Parker 1955)

• 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 HelicitiesCorrelation of Helicities

The Role of Helicities in Dynamo

• 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

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 HuairouHuairou data systematically cover 20 year period!

AR NOAA6619 on 1991-5-11 @ 03:26UT (Huairou)

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: HC over the filtergram; positive/negative: 0.2, 0.5, 1.0, 4.0 G2/m

Data Reduction• 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

Twist overlaid with butterfly diagram

Compare: 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

Regular inversion of the hemispheric rule:

• 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)

Cou

rtes

y of

D.D

. S

okol

off

and

E.

Pop

ova

(200

9)

[with account of meridional circulation)

Dynamo model with evolution of HelicityMagnetic field

generation (Parker Dynamo)

Parameterized equation

Generation of Helicity

Development of 1D-2D models (Moss,Kleeorin,Rogachevskii, Sokoloff, Kuzanyan et al.)

!

Choice of Parameter Range (Example)

LATITUDE

HELICITY

C=0.01- ok!

C=0.1

too high value

Kleeorin et al. 2003

EVOLUTION OF HELICITY WITH TIME(Northern Hemisphere N)

Diffusion Time Units

S

N

Sunspot Group Number

Magnetic Energy

HELICITY

~1988 ~1997

Estimate of current helicity of active regions

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

2D model with cross-helicity(after Pipin, Kuzanyan, Zhang & Kosovichev, 2011)

Results: 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

(Pipin, Sokoloff, Zhang, Kuzanyan 2013 )

Results: 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 conservation

• He

Magnetic field & current helicity: contour plot

(Pipin, Sokoloff, Zhang, Kuzanyan 2013 )

СПАСИБО!

Thank you!

谢谢！

•When the night comes with the actionI just know it's time to goCan't resist the strange attractionFrom that giant dynamo....

ABBA "Summer Night City"