Helicity as a Constraint on the Solar Dynamo

Alexei A. Pevtsov

If you worry about publicityDo not speak of Current Helicity

Jan Stenflo

Dynamo? Which dynamo?

Type of Dynamo Where it operates?

Flow dominated environment:

Large-scale1

(helical)

CZ/CZ-RZ interface

Small-scale2 (chaotic) CZ-UA interface

Magnetic field dominated environment

Solar/stellar coronae

1 – e.g. mean-field, overshoot region, interface dynamo2 – AKA local, surface, photospheric, turbulent dynamo

(also see Blackman & Ji 2006, MNRAS)

Dynamo in Magnetically Dominated Environment

Magnetically dominated dynamo is observed in laboratory plasma (e.g. Reverse Field Pinch, RFP configuration) : - injection of magnetic helicity (of one sign) drives system away from the relaxed state. - small-scale fluctuations (kink-mode tearing-mode instabilities) - fluctuations produce correlation between fluctuating velocity and magnetic field (EMF, ), which allows the system to evolve back to relaxed state. - helicity evolves toward system-largest spatial scales - sawtooth oscillations in magnetic field - without helicity injection, the field will decay due to resistive decay.

bv

Ji & Prager, 2004

Dynamo in Solar Corona?

(???)Xm LH

-Coronal helicity is supplied from below (Pevtsov et al, 2003, Tian & Alexander 2008)-Time profile of helicity evolution- Impulsive behavior

Helicity injection may play role in coronal heating?

BBz

V

Type of Dynamo Where it operates?

Flow dominated environment:

Large-scale1

(helical)

CZ/CZ-RZ interface

Small-scale2 (chaotic)

CZ-UA interface

Magnetic field dominated environment

Solar/stellar coronae

B

Both flow-driven and mag. field dominated dynamos are driven by finite

term. In flow-driven dynamo

Two types of flow driven dynamos can exist: helical and non-helical. For non-helical dynamo mean turbulent EMF is not required, turbulent velocity is sufficient to amplify magnetic energy via random walk line stretching and shear.

vhelicitykineticatypicallyis ||

Em (active region) ~ 1-10 x 1034 ergEm (network field at granule scale) ~ 1027 ergEk (granulation) ~ 3-6 x 1027 erg

The large-scale (mean field dynamo) generates magnetic fields at scaleslarger than the energy-containing scale of the turbulence, as is, for example, the case in helical turbulence. The small-scale dynamo amplifies magnetic fluctuation energy below the energy-containing scale of the turbulence.

2 types of dynamoMag. Flux of ARs varies with sunspot cycle

Mag. Flux of QS does not

AR and QS magnetic fields may begenerated by separate dynamos.

-AR and QS fields behave differently with solar cycle-QS fields have very short lifetime.

Em (active region) ~ 1-10 x 1034 ergEm (network field at granule scale) ~ 1027 ergEk (granulation) ~ 3-6 x 1027 erg

-Helical dynamo is necessary to generate strong magnetic fields of ARs.-Turbulent dynamo can amplify magnetic field only to 10-20% of kinetic energy.-Numerical simulations: e.g. Cattaneo 1999; Schekochihin et al 2004.-Pm>1 (in numerical simulations), Pm~ 10-6 <<1 (on the Sun)

Helical or not ?

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

effect.dominant aisforceCoriolis1

effect.nohasforceCoriolis1

velocity.angularis

,lengthandvelocitytypical,;2

1

Ro

Ro

LvCoL

vRo

Helical

Chaotic(turbulent)

200026.024/2;100;/100 11 RohhmLhkmv 6.026.024/2;300;/100 11 RohhkmLhkmv

Tornado:Hurricanes:

Pevtsov & Longcope 2007

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

Chaotic (turbulent) dynamo

Pm >1 (in numerical simulations), Pm~10-6 <<1 (on the Sun)Physics of turbulent dynamo is based on random stretching of field lines(assumption that the scale of fluid motions that does the stretching (viscous scale)is larger than the scale of the field that is stretched (resistive scale). For Pm<1, l>l

Cattaneo et al (2003)

ydiffusivit magn.

viscosity

Re

RmPm

Schekochihin et al. 2007

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

N40W00

ASP

- Dependence of scatter on latitude

In agreement with recent modeling by Abbett, et al

Pevtsov & Longcope, 2001, 2007

Helicity Transport and Generation.

enp

enP

e

e

/

/

bBbjbe

BBBJBE

dSdDdt

dH

dDH

tm

m

)2(2

;

AABBE

BA

(Ji, 1999)

Volume rate of change of helicity

Flux of helicity transportacross volume

- mean-field contribution

- fluctuations

bv - Mean E.M.F

Dynamo action converts helicity from the turbulent to the mean field (Seehafer 1995)

BJBBA

bjBba

baba

aabbjBba

AABBJBBA

JBVEJBVE

AABBEBA

EABEEAEB

ABBABA

ABBEBAE

t

t

tt

tt

tt

t

ttt

tt

22

22

;

)2(2)(2)(

)2(2)(2)(

;

)2()(2)(

)(;

)(

)(;

(Blackman & Field, 2002)

Flow of Bihelical fields through the photosphere?

Pevtsov et al.

Pevtsov & Canfield (1999)

Can helicity patches inside sunspots be an indication of dynamo generating bi-helical fields?

Helicity Transport and Generation.

)2()(2)()(2 AABBEAEBBEBA tt

B · A B ·J

BJBΒΑ

bjBba

2k

BBt

t

t

.../~

22

22

2

||

Averaging over closed volume; surface term vanishes (Blackman & Ji 2006):

- Dynamo is driven by - grows- mean magnetic helicity grows- due to helicity conservation, <a.b> grows with opposite sign-<j.b> also grows- quenches α.

0 vv

Magnetic helicity needs to be constantly removed from the dynamo region for dynamo to continue operate.

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).

Pevtsov, A.A.: 2008,"What Helicity Can Tell us About Solar Magnetic Fields",J. Astrophys. Astron., 29, 49-56DOI: 10.1007/s12036-008-0006-1

How These All Might Fit Together?

• Both helical (mean-field) and non-helical (turbulent) dynamo may operate on the Sun. Helical dynamo is necessary to generate strong magnetic fields of active region. Non-helical dynamo may generate network field outside active regions.

• A separate magnetic field/helicity-driven dynamo may operate in the corona.• Mean-field dynamo segregates helicity on two opposite sign components• Helicity needs to be removed from dynamo area to prevent dynamo quenching.• Helicity observed in photosphere is probably created in upper CZN (S-effect

explains large scatter and helicity amplitude; solar cycle variations???).• Helicity is removed from AR:

-gradually by dissipation – coronal heating-via eruption (CMEs, flares).

• 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.