Knots and Bolts of Solar Helicity

Dr. Alexei A. Pevtsov

“If You are after good publicity,You should not speak about current helicity” – Jan Stenflo

Outline

• Definition of helicity (incl. graphic repr.)

• Hemispheric helicity rule (observations, origin, cycle variation)

• Helicity transport

• Fitting pieces of puzzle together???

Knots and BoltsH = 0

Knots and BoltsH = 0 H= -1

Writhe and Twist

H = W+T

W = -1; T=0

T = -1; W=0

Helicities BABA ,)()2( 21

)(WTdDH

tubefluxthinm

Eμα H

n BψBdVdVBα

ψ)BdVB(αB dVA H

ψ,B αA αB, B

-m

-m

-

1

21

1

1

2

0;

A – vector potential, B – magnetic induction.

For liner force-free field (constant)

where is arbitrary scalar function

, where E is magnetic energy

-topological invariant-conserves better than energy (Woltjer, 1958; Taylor 1974; Ji et al, 1995)-dynamo, reconnection, stability energy decay – 4-10.5% helicity dissipation – 1.3-5.1%

dDH c BB dDH k VV

Magnetic Helicity

Current Helicity

Kinetic Helicity

What We Observe

zbest ;

V

m BdVAH Observations: zyx BBBB ,,

Force-free field(1): BB mm EH 12

Current helicity density(2):

zzyyxxc JBJBJBJBBBh

WL, H-alpha, X-ray Morphology:

sinLc

%/; ccc hhh Abramenko et al, 1996Bao and Zhang, 1998

Pevtsov et al, 1995, Longcope et al, 1998

What We Observe

Relative helicity:

Nx

nx

Ny

ny yx

yx

r kkl

nnBdVBAdVBAH

1 1)22

2~

00 (

,2

dxdyBvAdxdyvBAdt

dHzpzp

R )(2)(2(e.g. Chae, 2001)

(Berger, 1985)

Also see Manolis presentation later

466 active regions observed 1988-2000 by Haleakala Stokes Polarimeter= -0.23, Likelihood of no correlation is 2.5x10-7

N/(-) S/(+)

69% 75% (cycle 22, Pevtsov et al, 1995)63% 70% (cycle 23, Pevtsov et al, 2001)

Seehafer, 1990Pevtsov et al, 1995, Abramenko et al, 1996Longcope et al, 1998, Bao and Zhang, 1998,Pevtsov et al. 2001,Hagino and Sakurai, 2002

60-80%, hemispheric helicity rule

Cycle variation?

Pevtsov et al 2001

Bao et al, 1999, reverse sign for hc at the beginning Cycle 23Hagino & Sakurai, 2002, some periods disobey the ruleNandi & Choudhuri 2004 – cycle variation of helicity rule

Lat

best

LATbest

Zhang, 2006

Observations Rad/Mm Ref.

AR ~0.01 Pevtsov et al 1995

substructures ~0.2 Pevtsov etal 1994, Leka et al, 1996

Sources of Twist

Joy’s Law 0.001 Longcope & Klapper 1997

Diff’l rotation 0.002 Longcope et al 1999

- effect ~0.02 Longcope et al 1998

Created in dynamo 4 x 10-5 Charbonneau & Gilman 1998

Holder et al, 2003;Tian et al., 2001

Chae 2001, Green et al 2003Demoulin et al 2003

– direct action of Coriolis force and differential rotation produce insufficient amount of helicity and cannot explain significant scatter in latitudinal dependency– dynamo does not produce enough helicity.-effect can do it all?

Seehafer et al, 2003

Longcope et al, 1999

Nandy, 2006~ -0.69

Scatter is latitude-independentTrend, scatter agree with -effect

Helicity Transport

dxdyByBxBEEμα H

B nψBdVdVBα

ψ)BdVB(αB dVA H

ψ,B αA αB, B

zyx-

m

-m

-

)(,2

0;11

21

1

1

For liner force-free field (constant)

where is arbitrary scalar function

Lepping et al (1990) fitted 18 MCs, =10-10 m-1, B0=0.0002 G, =1021 Mx.HMC=(L/2) 2= 5 x 1042 Mx2 Larson et al (1995), HMC= 4 x 1042 Mx2

Demoulin et al, 2002, AR797852 x 1042 Mx2 (26 CMEs, 1 rotation)5 rotations - ?Total helicity ejected by MCs often exceeds coronal helicity (diff. rotation cannot replenish).

Helicity Transport via Reconnection)0( BnifconstHm

Independent flux systems: Hm= H1+ H2+ H3; e.g. H1=0.5Hcrit; H2=0.4Hcrit; H3=0.2Hcrit Hm>Hcrit

Canfield & Reardon, 1998Pevtsov et al 1996

Twist in Emerging Flux TubeLongcope and Welsch, 2000:

- vortical motions responsible for helicity injection cannot be driven by pressure gradient and cannotbe produced by coupling motions of non-mag. plasma-magnetic torque at photosphere-corona transition cannot be countered by pressure gradients.

Evolution of ARs and their Helicity

- MDI full disk magnetograms-SoHO EIT 195A images- 6 emerging active regions

Maleev et al, 2002

Modeling Flux Emergence

)(

d

v

d

d

dt

d A

- no twist at emergence- emergence – linear increase in d- d increases in constant rate until t1

0)( 0 t

00 )( dtd

ttdttdd

tttttddtd

11010

1010

)(

)()( {

)(t

1000

}][{ )1()(111

tttvttd

d

v

v

dvvttd

ttvA

A /;)(

exp)( 11

11 ][

dH R 2

2 )(

2

2

ww

dt

dH R

Fitted Model ParametersNOAA alpha

ramp-up

(days)

d

days

Flux

(1020 Mx)

Helicity

1041Mx2

d0

Mm

VA

m sec-1

8582 1.73 1.20 30 4.0 26.93 71

8738 … 1.79 … … … …

8768 0.93 1.80 13 1.3 25.06 182

8817 1.00 1.20 17 0.9 26.79 84

9139 0.80 1.66 44 12.7 12.24 158

9193 0.87 1.80 2 0.1 23.45 60

Sunspot Rotation-Kempf, P., Astron. Nachrichten, 1910, Nr. 4429, Bd. 195, 197-Brown, et al, Solar Phys., 2003, 216, 79

-Pevtsov, A. A. and Sattarov, I.S., Soln. Dannye, 1985, No. 3, 65.

dayVR deg/1517

Courtesy R. Nightingale

Sunspot Rotation(R. Nightingale data)

CCW CW Bi-direct

N 31%

(70%)

13%

(30%)

16%

S 15%

(46%)

17%

(54%)

14%

* Correct sign of twist; “hemispheric preference” is in agreement with the hemispheric helicity rule* No good correlation between sign of current helicity and direction of rotation

Courtesy R. Nightingale

Kinetic Helicity and flares

See poster by F. Hill et al

How These All Might Fit Together?

• Helicity is created in upper CZN (-effect explains large scatter and helicity amplitude; solar cycle variations???).

• Helicity is removed from AR as a result of eruption.

• Subphotospheric portion of flux tube may serve as “reservoir” of helicity, supplying helicity between flares/CMEs.

• Sunspot rotation and subphotospheric pattern of kinetic helicity may be indications of helicity transport via torsional waves.

Open Questions

• Evolution of kinetic helicity (before/after flare/flux emergence).

• Timing of sunspot rotation vs. flare

• Is helicity of active region determined at their emergence, or maybe, significant amount of helicity can be injected later during AR lifetime?

Backup Slides

effect.dominant aisforceCoriolis1

effect.nohasforceCoriolis1

velocity.angularis

,lengthandvelocitytypical,,2

o

o

o

R

R

LvL

vR

-Overshoot region (DeLuca & Gilman 1991)-Mean-field dynamo (Krause & Radler 1980)-Surface dynamo (Emonet & Cattaneo 2001)

Helical

Chaotic(turbulent)

-Helical dynamo should result in hemispheric preference for sign of helicity-Chaotic (turbulent) dynamo should show no hemispheric sign-preference for helicity.

200026.024/2;100;/100 011 RhhmLhkmv

6.026.024/2;300;/100 011 RhhkmLhkmv

Tornado:

Hurricanes:

* Sign of vorticity tends to be random in intergranular spaces* In some cases, vorticity reverse sign.

N40W00

ASP

- Dependence of scatter on latitude

In agreement with recent modeling by Abbet, et al

Some conclusions• Solar magnetic fields exhibit hemispheric sign

asymmetry.• Presence of solar cycle variations in the

hemispheric helicity rule is not clear.• Helicity of strong (sunspots) magnetic fields is

generated in mid-upper convection zone via -effect

• Helicity is constantly transported to the corona via torsional motions and reconnection.

Filaments chiralitybefore CRN1970

Filaments chiralityafter CRN1970

Polar Field

Martin et al, 1994Pevtsov et al, 2003 (82/86%, N/S)Bernasconi et al, 2005 (70/66%)