Magnetic Tongues, Magnetic Helicity and Twist in Active Regions.

Magnetic Tongues, Magnetic Helicity and Twist in Active Regions.

É. Pariat & P. Démoulin

LESIA, CNRS, Observatoire de Paris, France

Flux Emergence Workshop 2011SSL, Berkeley, CA, USA

22nd August 2011

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Outline

• Introduction: twist in actives regions

• Magnetic tongues

• Magnetic helicity: measurement methods

• Observational properties of injected helicity

• Observed helicity flux distribution

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Global view

( Rust 1994, Low 1997 )

Conjecture : To limit the buildup of Hcorona H has to be ejected via CMEs

ICMEsmagnetic clouds

H cascade to large scales very low dissipation dissipate on the global resistive time scale ( > 100 years )

( Frisch et al. 1975, Berger 1984, Alexakis et al. 2006 )

H is a conserved quantity

( Emonet & Moreno Insertis 1998,Cheung et al. 2006 )

to cross the CZ flux tubes need twist, so H,

observed photospheric H flux : best measurement of H ( the photosphere is the only region where 2D maps of B are measured )

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Evidences of twist

* X-ray sigmoids

( Manoharan et al. 1996, Canfield et al. 1999 )

* coronal loops

* Sunspot whorls

( Hale 1925, Chae 2001, Nakagawa et al. 1971 )

* vector magnetograms

sunspot

B//

* Magnetic tongues

( Lopez et al. 2000 Green et al. 2007 )

* feet/barbs of filaments

( Martin et al. 1994, Aulanier et al. 1999 )

* Shift / J-shape of ribbons

( Moore et al. 1995, Démoulin et al. 1996 )

I.L. Shift

* magnetic clouds

MC

( Bothmer & Schwenn 1998, Dasso et al. 2006 )

( Brown et al. 2003, Schmieder et al. 1996 )

All have H > 0, for H < 0 : mirror symmetry

( Hagyard et al. 1990, Metcalf et al. 2005 )

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Quantitative methods to estimate twist

• (Non-linear) Force Free extrapolation: e.g abest parameters (eg. Pevtsov et al. 02)

• Total Magnetic Helicity

• Properties of UV coronal loops (e.g. Chae & Moon 05)

• Geometrical shape and distribution of coronal loops compared to (N)LFFF model (e.g.

Malanushenko et al. 09, 09b, 11) Anna’s Talk

• Magnetic helicity injection

• Magnetic Tongues (?)

• Shear/Rotation of the polarities (e.g. Magara & Tsuneta 08, Magara 09)

Model-based

Obs-based

What is the amount of twist of the active regions magnetic fields?

(Magara 09)

(Chae & Moon 05)

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Outline

• Introduction: twist in actives regions

• Magnetic tongues

• Magnetic helicity: measurement methods

• Observational properties of injected helicity

• Observed helicity flux distribution

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• Magnetic tongue: extensions of the approximately round magnetic field polarities (López Fuentes et al. 00, Démoulin & Pariat 09, Luoni et al. 11)

• ~ horizontal Taijitu (yin-yang) symbol: ☯• angle formed between the global PIL and the

axis of the main magnetic polarities

• Large scale property of the magnetic field:– Less obvious when considering small scale

structures at the PIL: e.g. sea-serpents– Less obvious but still present in

complex/multipolar AR

Magara & Tsuneta 08

Magnetic TonguesLuoni et al. 11

Hood et al. 2009

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Interpretation of magnetic tongues

• Magnetic tongues: direct signature of the emergence of a twisted flux tube• Elongation is due to the projection of the

azimuthal field on the vertical direction

MDI Magnetograms

AR 8015c

AR 8203

AR 8011

AR 8015b

Luoni et al. 11

Hood et al. 09

H<0

H<0

H<0

H>0

H>0

• Two possible configuration depending only on the chirality/helicity of the twisted FT

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• Typical feature of the early phase of “standard” (i.e. bipolar) active regions emergence

Magnetic Tongues evolution

• Tongue are present while appex of the FT is crossing the photosphere

• Obs. retraction & disappearance of the tongue: projection of the azimuthal field decrease

Luoni et al. 11

Hood et al. 09

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Quantitative estimation?

• Analytically, for a given model of the emerging FT the twist directly sets

– the angle between the tongue and the axis of the polarity: d~arctan(1/2Nturn)

• Uniform twist= d is constant – tongues extension

• Observationally, its extremely difficult to retrieve the twist

– Difficult to define the location of the PIL and the center of polarities

– Tongue only observed during a relatively short period.

– Angle d change because the twist is likely not uniform in the FT

– Extremely difficult to fit a simplistic emerging flux tube model to actual observation

Nturn=0.2 Nturn=1 Nturn=6

Luoni et al. 11

Pariat et al. 05

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Outline

• Introduction: twist in actives regions

• Magnetic tongues

• Magnetic helicity: measurement methods

• Observational properties of injected helicity

• Observed helicity flux distribution

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Definition of H

( Barnes 1988, Berger 1988 )

Boundary condition :

same magnetogram ( normal component )

(usually potential field )

Coronal field

Reference field

SS

relative magnetic helicity (to a reference field)

V

dV)()( PPR BBAAH

IF

Equivalent

Measuring Helicity in AR: extrapolations

• Direct measurements of magnetic helicity are not possible

– Magnetic field almost only estimated in the photosphere

– Magnetic field Extrapolation

y

y

yx

x

x

N

nyxnn

N

n

r kkBH1

2/3222,

1

)(~a (Lim et al. 07)

V

dV)()( PPR BBAAH

• Linear force free field assumption• Use of longitudinal magnetograms only• LFFF Linearized equation (Green et al. 02)

(Green et al. 02)

• Nlfff & Non-force free fields• Needs to numerically integrate A and AP

in a box with the proper condition on A, AP, B & BP

• Carefull choice of the gauge (DeVore et al. 00, Rudenko & Myshyakov, Thalmann et al. 11 , Valori et al 11, 12)

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Measurements precision

• Coronal helicity computation:– Relies on extrapolation methods and are hence subject to their validity &

caveats (DeRosa et al. 09)

• :Very sheared/twisted structures (highest helicity) are the most difficult to obtain

• : Helicity is a large scale quantity stored in large scale structures easier to get

– Different extrapolation methods (Regnier at al. 05) : – H varies by a factor 2• : Helicity computation in a small box is very sensitive to the choice of the

gauge at the boundary: different choice different sign of H (Valori et al. 11)

• : New understanding of how to compute H in a boxed domain (Rudenko & Myshyakov, Thalmann et al. 11 , Valori et al 11, 12)

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(Chae et al. 04)• Magnetic helicity can be estimated by time-

integrating the flux of magnetic helicity through the photosphere. (Chae 01)

• Flux of helicity:

Measuring Helicity in AR: photospheric flux

( Pariat et al. 2005 )A better proxy of the helicity flux density is :

Helicity flux density: summation of the relative rotation of all the elementary flux tubes, weighted by their magnetic fluxes

Magnetogram

+ velocity ( arrows )

Rotation rate

x

x’

B// > 0 B// < 0

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Measuring Helicity in AR: photospheric flux

• How to measure the Helicity flux?– B is given from spectropolarimetry (magnetograms)– U deduced with methods based on Local Correlation Tracking

(November & Simons, 1989)

LCT: basic method to deduce velocities. More sophisticated methods solving the induction equation (Welsh et al. 07) * Induction Method Kusano et al. (2002, 2004) * Inductive LCT Welsch et al. (2004) * Minimum Energy Fit Longcope (2004), Ravindra et al. (2008) * Differential Affine Velocity Estimator Schuck (2005, 2006) * DAVE for Vector Magnetogram Schuck (2008) * Non-linear Affine Velocity Estimator Chae & Sakurai (2008)

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Measurements precision• Photospheric helicity flux measurements:

– Relies on flux transport velocity methods (Welsh et al. 07)

• : Helicity poorly estimated in shootout: wrong sign and/or an order of magnitude difference

• : LCT methods mostly capture Vperp • : Improved methods (e.g. Schuck 08, Chae 08)

– Sensitive to data cadence, resolution, noise levels (e.g. Zhang et al. 08, Yamamoto &

Sakurai 09, Chandra et al. 10, Romano et al. 11, Tian et al. 11) : Helicity given with a factor 2-3

• : Cannot recover helicity flux along the isocontours of B: twisting motions

(high helicity flux) (Green at al. 02)

• : New data set with higher cadence/resolution

• Comparison of helicity flux and coronal helicity computations (Lim et al 07, Park et al. 10) :

Results agree within a factor 2

(Lim et al 07)

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Outline

• Introduction: twist in actives regions

• Magnetic tongues

• Magnetic helicity: measurement methods

• Observational properties of injected helicity

• Observed helicity flux distribution

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Differential rotation : theory

Differential rotation: Time-independent shearing flow BUT: time dependant input of magnetic helicity + can change of sign

east-west bipole

Hself dominant

=> H < 0

diff. rot.

dH/dt < 0 dH/dt > 0

timeH

0

( DeVore 2000, Démoulin et al. 2002 )

northsouthbipole

H = Hself + Hmutual Competition between: * Hself : rotation of each polarity * Hmutual : relative rotation of one polarity / the other one with differential rotation : Hself . Hmutual < 0

Hmutual dominant

=> H > 0

diff. rot.

dH/dt > 0

time

H

0dH/dt < 0

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Differential rotation : AR case studies

AR 8668

0

without differential rotation

only differential rotation

Helicity injection rate ( 1040 Mx2 h-1 )

Hinjected < 0

Hcoronal < 0

( Démoulin et al. 2002, Nindos et al. 2002, 2003 )

In most ARs, differential rotation cannot provides Hcoronal

Helicity injection by differential rotation:

* smaller than the helicity injected by internal motions (typical ~ 1/10 to 1/2 ) * not enough for launched CMEs / MCs * could have the opposite sign than Hcoronal

( Chae et al. 2001, Jeong & Chae 2007, Labonté et al. 07, Tian & Alexander 2008 )

( Green et al. 2002, Tian & Alexander, 2007 )

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Hemispheric rule ?• Due to the solar rotation:

– H<0 in the North – H>0 in the South– Independently of the

solar cycle• True mostly for quiet sun

features!• For active features the

rules is only marginally validated

( Pevtsov 2002 )

H < 0

H > 0independent of solar cycle

• Magnetic helicity studies close to equipartition• Labonté et al. 07: 57-60% of 393 ARs. • Yang et al. 09: 56-57% of 58 emerging ARs.

• Weak correlation likely due to the diff. Rot. at the surface

Why this difference ?

Mechanism generating the twist in emerging flux tube is likely not correlated to the W effect of the solar rotation

Labonté et al. 07

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AR emergence

-H injected ( 1042 Mx2 )

Total magnetic flux ( 1022 Mx )

AR 10831

low high

Magnetic tongues: H< 0

Significant helicity injection is delayed ~ 2 days compared to magnetic flux

( Tian & Alexander, 2007 )

low high

H injected ( 1042 Mx2 )

low

high high

high high

low low low

lowlowlowlow

( Jeong & Chae 2007 )

Helicity injection follows a low-high-low evolution.

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Photospheric flux of magnetic helicitylongitudinal magnetograms 3D MHD simulation

emergence of a twisted flux tube

Helicity flux

simple analytical evolution

( Pariat et al. 2005 )

Helicity flux

Similar peaks of helicity flux

constant vertical velocity emergence of AR 10365

lowhigh

low

low

high

low

low

high

low

H injection evol. can be interpreted by the emergence of a globally twisted FT

( Chae 2004 )( Cheung et al. 2005 )

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AR recurrences

CMEs with low H later on? Rather:Not enough injected helicity measured in evolved ARs ?

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Helicity injection in ARs

48 X-flaring ARs345 non-X-flaring ARs

Magnetic flux ( Mx )

Helicity flux over 6 days ( Mx2 )

Twisted flux tube with n turns

• Statistical studies of helicity injection assuming a single twisted flux tube:

– Yamamoto et al. 05: n=0.01-0.02/day• 7 ARs, averaged injection

– Jeong & Chae 07: n=0.07,• 6 ARs followed over a few days

– Labonté et al. 07: n=0.02• 393 ARs over 5-6 days• Very low cad. underestimation

– Tian et al. 08:• 23 sigmoidal ARs: n=0.08 • 18 just emerged ARs: n=0.03

– Yang et al. 09: n=0.04• 58 emerging AR over 2-8 days

( Labonté et al. 2007 )

( Yang et al. 2009 )

(F=(|F+|+|F-|)/2)

H = 0.039 F2

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Helicity accumulation in ARs.

• 1 turn in 100 days (3 Carrington Rotations)• Helicity accumulated in AR over their passage on disk:

• <DH>~0.08-0.2 F2 • Typical instantaneous flux of Helicity in AR:

– <dH/dt> ~ 1042 Mx².day-1 but large variation ; <dH/dt> ~ 10-2 F²/day (F = 1022 Mx)• Total helicity accumulated in AR over several rotation (Démoulin et al. 02, Lim et al. 07)

– <DH>~1-100 x1044 Mx² ; <DH>~ 0.5-2 F²

• Is the normalisation by F2 valid?: Not fully! • Jeong & Chae 07: a=1.3• Labonté et al. 07: a =1.8• Yang et al. 09: a=1.85

– Why? lifetime of ARs increases significantly with their amount of magnetic flux hence helicity accumulation not fully observed for larger ARs

How much helicity is injected in ARs? H=0.005-0.02 F2 /days

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Outline

• Introduction: twist in actives regions

• Magnetic tongues

• Magnetic helicity: measurement methods

• Observational properties of injected helicity

• Observed helicity flux distribution

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Evolution of helicity flux density( Pariat et al. 2006 )

Coherent evolution

28

AR 8210AR 8375

AR 9144

AR 10955

• In most active region, helicitty injection is relatively unipolar: only helicity of one sign is injected!

• Constraint on the emerging flux tube generation mechanism

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Asymmetric injection (?)• Helicity is asymmetricaly injected: 3-10 more

helicity flux in the leading magnetic polarity (Tian & Alexander 09, Tian et al. 11)

• Origin (Fan et al. 09) : stronger field in the leading leg of the Ω-shaped emerging flux tube

– Field lines wind about each other more smoothly more coherent values of the local twist,

– greater Alfvén speed: faster rotation• However… Helicity flux density per unit surface

is not a physically meaningful quantity!!– Helicity flux density is only defined for a given flux

tube: defining a different helicity at both footpoint of a field line is incorrect

– It’s not an asymmetry of Magnetic Helicity• Result is very likely physical because proxies of

helicity flux density may carry more information than magnetic helicity

– Results obtained with 2 proxies of helicity flux density with very different properties puzzling!

– Part of the asymmetry just results may just results from the weighting of in region of higher field strength

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A puzzling magnetic cloud

• Geoeffective magnetic cloud of 20 November 03 a positive helicity (e.g. Gopalswamy et al. 05;Yurchyshyn et al. 05, Möstl et al. 08 )

• AR 10501, at the source of the CME has a global negative helicity.

• How can a negative magnetic helicity AR generate a positive helicity magnetic cloud?

• Mixed helicity signs in the southern filaments

Global negative helicity accumulation in AR 10501

M flares

Wind Data: Positive helicity MC Grad-Shafranov reconstruction

Möstl et al. 08

Chandra et al. 10

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Mixed helicity in filaments

• Topological analyze: existence of a close connectivity domain where is the South filament

• Helicity injection in the south filament: localized positive injection.

• Ejected South filament forms the observed magnetic cloud

Localized positive helicity acc. in South filament

South Filament

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Mixed helicity in filaments

• Filament in AR 9862– Eruption on

01/11/01– Mixed sign of

helicity during the eruption

• Helicity injection:– Whole active

region: H<0– Injection in

filament footpoints: H<0

• Mixed helicity: larger energy may be released (e.g Linton et al. 01).

– Filament eruption in mixed helicity region (Kusano et al. 04)

BBSO Ha, 31/10/01 MDI

Helicity mapWhole AR: H>0

A+B: H<0

( Romano et al. 2011 )

Conclusion

H stored in the corona, then ejected via CMEs

tachocline photosphere corona interplanetary space

H in ICMEs & Magnetic Clouds

B emergence & H transfert

dynamo : produce H <0 & H >0

Observedphotospheric H flux

Hcorona frommagneticextrapolation

HMC frommagnetic cloud modelling

Helicity budget ( H is a conserved quantity )

Dynamo :coupling of the hemisphere north: H < 0 south: H > 0but why dominance of only 60 % ?

Maps of H injected in ARsWhy some ARs have H < 0, and some H > 0 ? constraints on the solar dynamo

Flux of helicity through the photosphereH=0.005-0.02 F2/days constraint for models

Does all the helicity of emerging FT cross the photosphere ?Is there H accumulating bellow?

Helicity storage in the solar coronaImproved method to compute H in 3D domain

Why CME rate is constant over several carrington rotation while H injection decrease?

Mixed helicity regions few examples of mixed helicity region associated with large eruptions Is the eruptivity of

mixed helicity region particular?

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Flux density of magnetic helicity

Flux density :

All previous studies with GA maps : simultaneous injections of both sign of magnetic helicity. True ?

( Chae 2004 )( Nindos et al. 2003 )

GA & Bn

( Kusano et al. 2002 )

GA & velocityGA & velocity

Does it had a physical meaning ?

Total H flux : well established physical meaning

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Simplest example: a translated magnetic flux tube

=> GA is NOT a good proxy of the flux density ! ( Pariat et al. 2005 )

GA introduces fake signal of both signs in equal amount Only the total flux of helicity is reliable

u

Flux tube

u

Photosphere

While nohelicity is injected !

GA

Bn > 0

( Kusano et al. 2002 )

Example of an observed AR -->

u

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Flux density of magnetic helicity

+

=> Double integration on the magnetogram

( Pariat et al. 2005 )

A better proxy of the helicity flux density is :

Helicity flux density: summation of the relative rotation of all the elementary flux tubes, weighted by their magnetic fluxes

Magnetogram

+ velocity ( arrows )

Rotation rate

x

x’

B// > 0 B// < 0

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Corona

Photosphere

emergence

Magnetic helicity flux : theory

emergence horizontal motionsHelicity flux

Phostosphere

B

Can always define :

=>

Corona

Photosphere

emergence

Simple interpretation of : photospheric footpoint motion of magnetic flux tubes

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Which velocities are measured by LCT ?

* The footpoint motions of flux tubes : ( suppose simple emergence )

( Démoulin & Berger 2003 )

=> Full helicity flux from longitudinal magnetogram time series ( close to centre disk )

But emergence is a complex phenomena e.g. it involves magnetic reconnection

( Magara 2004, Pariat et al 2005, Archontis et al. 2007 )

* Mostly the horizontal motions : ( Ravindra et al. 2008, Shuck 2008 )

=> Miss a large part of the helicity flux !

This conclusion comes from testing LCT with an anelastic MHD simulation

Limitation: B field dominated by the convection => similar to super-granule cells

Would need an AR-like B field to test LCT