Magnetic Helicity Generation Inside the Sun

Magnetic Helicity Magnetic Helicity Generation Inside the SunGeneration Inside the Sun

Dana LongcopeDana Longcope

Montana State UniversityMontana State University

Thanks: Alexei PevtsovThanks: Alexei Pevtsov

Observations show a clear hemispheric Observations show a clear hemispheric asymmetry in the helicity of the coronal asymmetry in the helicity of the coronal magnetic field: magnetic field: HHRR < 0 in the North < 0 in the North

Q: Can we therefore conclude that field Q: Can we therefore conclude that field below the solar surface, and in the below the solar surface, and in the dynamo, has this same asymmetry?dynamo, has this same asymmetry?

Answer: NoAnswer: No

Magnetic Helicity Magnetic Helicity Generation Inside the SunGeneration Inside the Sun

Propagation fromPropagation from

• Observed trends in photospheric twistObserved trends in photospheric twist• Implications for state of CZ flux tubesImplications for state of CZ flux tubes• Coupling of twist to coronal fieldCoupling of twist to coronal field• Observational evidence in emerging ARObservational evidence in emerging AR

Magnetic Helicity Propagation from Inside

the Sun

Trend in photospheric Trend in photospheric twisttwist

466 ARs from Longcope & Pevtsov 2003

Trend:Trend:bestbest< 0< 0in Northin North

bestbest> 0> 0in Southin South

Correlation:Correlation:bestbest

w/ w/ latitudelatitude> 99.9999%> 99.9999%

Fluctuations in twistFluctuations in twist

Large latitude-Large latitude-indep’t scatter indep’t scatter

created by created by turbulenceturbulence

Linear trend removed Linear trend removed (from Longcope, (from Longcope, Fisher & Pevtsov Fisher & Pevtsov

1998)1998)

The origin of fluxThe origin of flux

(from Cauzzi et al. 1996)

Bipolar active regionBipolar active regionformed by emergence offormed by emergence ofFLUX TUBEFLUX TUBEfrom below photospherefrom below photosphere

Twist in flux tubesTwist in flux tubes

Axis of tube:Axis of tube: xx(s)(s)satisfies thinsatisfies thinflux tubeflux tubeequationsequations(Spruit 1981)(Spruit 1981)

Field lines Field lines twisttwist about axis at a rate about axis at a rate q(s,t) “=“ d/ds

Plasma Plasma spinsspins about axis at rate about axis at rate(s,t) “=“ d/dt

ss

ss

Dynamics of twistDynamics of twist

dt

da

as

q

dt

dA

2v2

Angular Angular momentum:momentum:

UnbalanceUnbalanced magneticd magnetic

torquetorque

(from Longcope & Klapper 1997)

q(s)q(s)

(s)(s)

ss

Dynamics of twistDynamics of twist(from Longcope & Klapper 1997)

q(s)q(s)

(s)(s)

s

qssdt

dq

v

ksv

s ˆˆ

Differential spinningDifferential spinning

Field line Field line KinematicsKinematics ss

s

qssdt

dq

v

ksv

s ˆˆ


2

22A2

2

vdt

d

s

qq

Torsional Alven waves

dt

da

as

q

dt

dA

2v2


q(s)q(s)

vvss(s)(s)

ss

s

qssdt

dq

v

ksv

s ˆˆ

Field line Field line KinematicsKinematics

Axial stretchingAxial stretching

s

qssdt

dq

v

ksv

s ˆˆ


Out-of-Out-of-planeplanemotion of motion of axisaxis

ss

indep. of q or indep. of q or

Source of TwistSource of Twist

dt

dWr

dt

dTw

Increasing LHIncreasing LHwrithewrithe (dWr/dt <0 ) (dWr/dt <0 ) Increasing RHIncreasing RHtwisttwist (dTw/dt > 0) (dTw/dt > 0)

0)ˆ(

sdt

dq vks

Helicity Helicity ConservatiConservati

onon

0 vv 0)ˆ(

s

vks

• Applies to Applies to mean mean fieldsfields• Creates Creates HelicityHelicity** • RHRH eddies eddies LH LH fieldfield

• Applies to Applies to flux flux tubestubes• Creates Creates TwistTwist • RHRH eddies eddies RHRH twisttwist

BB

JJ

RHRH

effecteffect effecteffect

* in the mean field* in the mean field

J

B

Manifestation of -effect

• Simulation of Simulation of rising fluxrising flux tubestubes• Large scatter Large scatter • Latitude-Latitude-indep. indep.

( Longcope, Fisher & Pevtsov 1998 )( Longcope, Fisher & Pevtsov 1998 )

Coupling flux tube to Coupling flux tube to coronacorona

CZCZ: : >> 1 >> 1

coronacorona: : << 1 << 1

I=0I=0

I=0I=0

photospherephotosphere

surfacesurfacecurrentscurrents

(force-free field)(force-free field)

(thin flux tube)(thin flux tube)


q(s)

(Longcope & Weslch 2000)

Radial shuntingRadial shunting

torquestorques = 0= 0

s

q

2Av

t


q(s)

Low inertia Low inertia

torquestorques = 0= 0 Current matchesCurrent matches across interfaceacross interface

(Longcope & Weslch 2000)

02

zq

Coronal “twist”Coronal “twist”

Twist at end of FTTwist at end of FT

Application to Emerging Application to Emerging ARAR(Longcope & Welsch 2000)(Longcope & Welsch 2000)

Model AssumptionsModel Assumptions

• Initial flux tube: uniformly twisted:Initial flux tube: uniformly twisted: qq(s)=(s)=• Poles separating:Poles separating: d(t) = dd(t) = d00 + v (t-t + v (t-t00))

Twist Twist propagates propagates into coronainto corona

(t)(t)d/vA ~ 1 day


Application to Emerging Application to Emerging ARAR(Pevtsov, Maleev & Longcope 2003)(Pevtsov, Maleev & Longcope 2003)

)1(

0

11

)(

d

dt

• Initial flux tube: uniformly twisted: qInitial flux tube: uniformly twisted: q(s)=(s)=• Poles separating:Poles separating: d(t) = d d(t) = d00 + v (t-t + v (t-t00))

• Uniform Alfven speed in tubeUniform Alfven speed in tube: : vvAA= = vv• Coronal helicity:Coronal helicity: H = H = d d 22


SolutionSolution

Observational EvidenceObservational Evidence(Pevtsov, Maleev & Longcope 2003)(Pevtsov, Maleev & Longcope 2003)

• Study 6 ARs during emergenceStudy 6 ARs during emergence• FindFind d(t)d(t)• (t)(t) 8/19 12:478/19 12:47 8/19 20:478/19 20:47 8/20 4:478/20 4:47

8/20 12:478/20 12:47 8/20 20:478/20 20:47 8/21 4:478/21 4:47

dd

AR9139AR9139SOHO MDISOHO MDI2000-8-19 2000-8-19


Fit Model to DataFit Model to Data

)1(

0

11

)(

d

dt

v=264 m/sv=264 m/s

= 2 10= 2 10-8-8 m m-1-1

vvAA = 158 m/s = 158 m/s


AR8582AR8582

AR8817AR8817

Implications of modelImplications of model• TwistTwist exists exists beforebefore emergence emergence (i.e. rising tube is twisted) (i.e. rising tube is twisted) • Tube Tube TwistTwist propagates into corona propagates into corona Coronal HelicityCoronal Helicity

II

Implications of modelImplications of model• Twist Helicity Twist Helicity q(s) q(s) 22 ~ ~ I(s)I(s) uniform uniform• Twist Twist fills infills in lengthening region lengthening region It It DOES NOTDOES NOT favor wider portion favor wider portion

Parker 1979Parker 1979

• Assumes p(r)=constantAssumes p(r)=constant• Predates Berger & Field Predates Berger & Field • No BG coronal fieldNo BG coronal field

Longcope & Welsch 2000Longcope & Welsch 2000

• Assumes Assumes >>1 >>1 <<1<<1• Conserves HelicityConserves Helicity• Includes BG coronal fieldIncludes BG coronal field

Implications of modelImplications of model• Tube Tube WritheWrithe: : irrelevant irrelevant to coronato corona• Helicity Helicity dearth dearth propagates downwardpropagates downward

Summary• Observed:Observed: Hemispheric trend Hemispheric trend in p-spheric twist in p-spheric twist coronal Hcoronal HRR

• Coronal HCoronal HR R fixed byfixed by TWISTTWIST of anchoring tube of anchoring tube

• -effect produces -effect produces TWISTTWIST in rising FT in rising FT BUT leaves BUT leaves helicityhelicity unchanged unchanged

• Observed:Observed: Helicity evolution in Helicity evolution in emerging AR consistent w/ thisemerging AR consistent w/ this


q(s)q(s)(s)(s)

ss

dt

da

as

q

dt

dA

2v2

Angular Angular momentum:momentum:

Changing tube Changing tube radiusradius(Michelle Kwan (Michelle Kwan effect)effect)

aa


LowLow-- coronalcoronalEquilibrium: Equilibrium: FFFFFF

HighHigh-- CZCZField: twistedField: twistedThin flux tubeThin flux tube

InterfaceInterface

Possible sources of twistPossible sources of twist1.1. Initial state of flux tube: Initial state of flux tube: q(s,0)q(s,0)

Possible sources of twist1.1. Initial state of flux tube: Initial state of flux tube: q(s,0)q(s,0)

2.2. External flow External flow “twirls”“twirls” tube segment tube segment

Creates regions of opposing twistCreates regions of opposing twist

Requires anomalous “friction”Requires anomalous “friction” across flux tube surfaceacross flux tube surface

Possible sources of twistPossible sources of twist1.1. Initial state of flux tube: Initial state of flux tube: q(s,0)q(s,0)

2.2. External flow External flow “twirls”“twirls” tube segment tube segment

3.3. Net current driven along flux tubeNet current driven along flux tube

Violates assumption of isolated flux tubeViolates assumption of isolated flux tube Cannot be a “thin flux tube”Cannot be a “thin flux tube”

Axis-twist couplingAxis-twist coupling

sdt

dq

vks )ˆ(

Term required to conserve Term required to conserve H = Tw + WrH = Tw + Wr

dssqTw )(2

2

Function of twistFunction of twist

dssdt

dWr

vks )ˆ(

2

2

Function of axisFunction of axis

Kinematic eq. for twistKinematic eq. for twist depends on axis motiondepends on axis motion

dt

dWr

dt

dTw

Photospheric twist w/o Helicity*Photospheric twist w/o Helicity*

* From the emergence of a flux tube with no net helicty* From the emergence of a flux tube with no net helicty

•Begin w/ straight untwisted tubeBegin w/ straight untwisted tube (H=0)(H=0)•External flows induce LH writheExternal flows induce LH writhe (dH/dt =0)(dH/dt =0)•Coupling term Coupling term RH twistRH twist

•Tube crosses photosphereTube crosses photosphere•Helicity is transported intoHelicity is transported into coronal fieldcoronal field•Current in coronal fieldCurrent in coronal field matches twsit in flux tubematches twsit in flux tube

Writhe from Turbulence: The Writhe from Turbulence: The -effect-effect

s

e

vks )(

dkkFkc )(5

12

dkkFa cee )(

3

1vv

Twist sourceTwist source

Averaging over turbulence:Averaging over turbulence:

Spectrum of kinetic helicity

Compare to Compare to -effect:-effect:

2222 )(|| dkkEkkVariance of twist source:Variance of twist source:

Magnetic Helicity Generation Inside the Sun

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