Anisotropy of current helicity in solar active regions

1) Xu Haiqing, Gao Yu & Zhang Hongqi, NAOC

2) Kirill Kuzanyan, IZMIRAN, Russia

3) Rodion Stepanov, ICMM, Perm, Russia

4) Dmitry Sokoloff, Moscow University, Russia

Helicity forever!Helicity forever!

The role of helicity in dynamos• Magnetic Helicity = inviscid invariant

• Cross helicity = inviscid invariant

(Woltjer 1958; Moffat 1969)

Magnetic and Current Helicities• Magnetic Helicity dissipation rate

(e.g., Berger & Field 1984)• Relation between current helicity in active

regions and mean-field magnetic helicity

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

Correlation of HelicitiesCorrelation of Helicities

Reduction of Vector Magnetic Field from Reduction of Vector Magnetic Field from Polarized Light MagnitudePolarized Light Magnitude

Under the assumption of

weak field (calibration (calibration

required!)required!) the magnetic field

is related to the parameters

of polarized light. Though

some observational

problems exist!

In real measurements multi-frame averaging is employed to improve the ratio of signal-to-noise.

12 2 1/ 4

2

cos

sin ( )V

Q U

B C I

B C I I

V Vv

i V V

Q QQ

i Q Q

U UU

i U U

I II

I I

I II

I I

I II

I I

observations

Observable !

Question• How the part of current helicity is really

related to the entire quantity???

: How good is local homogeneity

approximation?

(keep in mind!)

! Observable current helicity is really related to mean magnetic helicity in the model ! (Zhang et al. 2012 ApJ)

Computation of electric current helicity in solar active regions

Seehafer (1990); Pevtsov & Canfield (1994);

Abramenko et al.(1996);Bao & Zhang(1998);

Hagino & Sakurai (2004-05)

twist

мп,сп,закр

magnetic field

current helicity

twist

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

Photosphetic vector magnetogram Current helicity over filtergram

Helicity is naturally very noisy• (e.g.)The average value of current

helicity

HC = −8.7 · 10−3 G2m−1 • the standard deviation 8 · 10−2 G2m−1 (factor 9).changing dramatically on a short range of

spatial and temporal scales, related to the size of individual active regions as well as their life time

20 years systematic monitoring of the solar vector magnetic fields in

active regions taken at Huairou Solar observing station, China

(1987-2006)More observations from Mitaka (Japan) and also Mees, MSFC (USA) etc., but only Huairou data systematically cover 20 years period.

Helicity over the solar cycle: Zhang et al. (2010-2012)

Important observational properties of helicity:

•Hemispheric Sign Rule: North=negative; South=positive

•Systematic reversal of the sign at some latitudes in the beginning and end of the solar cycle

Using helicity for constraining dynamo models of the solar cycle• We know how helicity behaves with the solar

cycle and how migrates over the latitude

We need a self-consistent model which is in accord with these observational facts!

(after publications of Zhang, Moss, Kleeorin, Rogachevskijj, Sokoloff, Kuzanyan, Gao & Xu, 2003-2012)

2D distributed dynamo with algebraic alpha-quenching, near-surface (example)

Definition of current helicity

Definition of curl for any vector F

Decomposition of current helicity into six parts:

Integration by parts: equalities

If we assume the magnetic field outside the active region is weak, and so we can use the formula for integration by parts (typical accuracy ~3-5%). Then the derivatives swap.

Example of PDF for helicities (hr)

Model of turbulent

magnetic field

afterVolegova & Stepanov, 2009 JETP

Formulation of the model

• 1) Random phase of turbulent flow

• 2) Realistic prescribed energy spectrum with dominating scale

• 3) Solenoidality condition• 4) Prescribed Integral Helicity,

so we can set <H>=0 or non-zero.

Stepanov et al. (2013), submitted:

Isotropic helical case

HXHY HZ

BX BY Bz

Non helical case

Numerical simulation of turbulent convection

Ob

serv

atio

nal

Exa

mp

le o

f P

DF

fo

r h

elic

itie

s: t

o c

om

par

e w

ith

th

eory

Hz H1 H2

HelicalMagneticField

Helical + PotentialMagneticField

Non-HelicalMagneticField

Notice!

• The addition of potential magnetic field does contribute each of the helicity parts!

• but it does not contribute to the sum of them, i.e. to the entire helicity

Comparison of Helicity partstime-latitudinal averaging

Overall data: no immediate link between

the helicity

parts (H1,H2

weak anti- correlation)

H1=H6

H2=H3

Contributions to “overall” helicity

Notice!

• At the phases of beginning and end of each cycle there is a certain range of latitudes where the sign of overall helicity changes to the opposite of the one give my hemispheric rule. One may note that during these phases the signs of both pairs of helicity parts are often the same, which makes their joint contribution to the opposite to the hemispheric rule sign

Odd and Even parts of Helicity

Odd and Even (for the sum)

Discussion1) While we see that the sum of available

helicity parts H1 and H2 has clear cyclic behaviour, its parts alone are less regular and behave less similar to each other

2) The parts alone much less follow the Hemispheric Sign Rule for Helicity. They disobey the rule at the beginning and the end of the cycle somehow synchronously

3) The Odd parts of the helicity parts look more regular with the cycle than the Even parts

Conclusions

There are possible causes of anisotropy that require further investigation:

• 1) Stratification

• 2) Rotation, Meridional Circulation, Differential rotation (Torsion Oscillations?)

• 3) Mean magnetic field

• 4) Data bias

Xie-xie! 谢 谢

СПАСИБО!