1. Magnetic Tongues, Magnetic Helicity and Twist in Active Regions. É. Pariat & P. Démoulin LESIA, CNRS, Observatoire de Paris, France Flux Emergence Workshop 2011 SSL, Berkeley, CA, USA 22nd August 2011

2. Outline Introduction: twist in actives regions Magnetic tongues Magnetic helicity: measurement methods Observational properties of injected helicity Observed helicity flux distribution 22/08/11 - FEW 2011 - E. Pariat2

3. Global view 22/08/11 - FEW 2011 - E. Pariat3 ( Rust 1994, Low 1997 ) Conjecture : To limit the buildup of H corona H has to be ejected via CMEs ICMEs magnetic 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 )

4. Evidences of twist 22/08/11 - FEW 2011 - E. Pariat4 * 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 )

5. Quantitative methods to estimate twist (Non-linear) Force Free extrapolation: e.g  best 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) 22/08/11 - FEW 2011 - E. Pariat5

6. Outline Introduction: twist in actives regions Magnetic tongues Magnetic helicity: measurement methods Observational properties of injected helicity Observed helicity flux distribution 22/08/11 - FEW 2011 - E. Pariat6

7. 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 Tongues 22/08/11 - FEW 2011 - E. Pariat7 Luoni et al. 11 Hood et al. 2009

8. 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 Two possible configuration depending only on the chirality/helicity of the twisted FT 22/08/11 - FEW 2011 - E. Pariat8

9. 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 22/08/11 - FEW 2011 - E. Pariat9

10. 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:  ~arctan(1/2Nt urn ) Uniform twist=  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  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=0.2Nturn=1Nturn=6 22/08/11 - FEW 2011 - E. Pariat10 Luoni et al. 11 Pariat et al. 05

11. Outline Introduction: twist in actives regions Magnetic tongues Magnetic helicity: measurement methods Observational properties of injected helicity Observed helicity flux distribution 22/08/11 - FEW 2011 - E. Pariat11

12. Definition of H ( Barnes 1988, Berger 1988 ) Boundary condition : same magnetogram ( normal component ) (usually potential field ) Coronal field Reference field S S relative magnetic helicity (to a reference field) 22/08/11 - FEW 2011 - E. Pariat12 IF Equivalent

13. Measuring Helicity in AR: extrapolations Direct measurements of magnetic helicity are not possible –Magnetic field almost only estimated in the photosphere –  Magnetic field Extrapolation (Lim et al. 07) 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 A P in a box with the proper condition on A, A P, B & B P Carefull choice of the gauge (DeVore et al. 00, Rudenko & Myshyakov, Thalmann et al. 11, Valori et al 11, 12) 22/08/11 - FEW 2011 - E. Pariat 13 (Thalmann et al. 11 )

14. 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) 22/08/11 - FEW 2011 - E. Pariat14

15. (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 22/08/11 - FEW 2011 - E. Pariat15

16. 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) 22/08/11 - FEW 2011 - E. Pariat16

17. 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 V perp : 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 22/08/11 - FEW 2011 - E. Pariat17 (Lim et al 07)

18. Outline Introduction: twist in actives regions Magnetic tongues Magnetic helicity: measurement methods Observational properties of injected helicity Observed helicity flux distribution 22/08/11 - FEW 2011 - E. Pariat18

19. Differential rotation : theory Differential rotation: Time-independent shearing flow BUT: time dependant input of magnetic helicity + can change of sign east-west bipole H self dominant => H < 0 diff. rot. dH/dt < 0dH/dt > 0 time H 0 ( DeVore 2000, Démoulin et al. 2002 ) north south bipole H = H self + H mutual Competition between: * H self : rotation of each polarity * H mutual : relative rotation of one polarity / the other one with differential rotation : H self. H mutual < 0 H mutual dominant => H > 0 diff. rot. dH/dt > 0 time H 0 dH/dt < 0 22/08/11 - FEW 2011 - E. Pariat19

20. Differential rotation : AR case studies AR 8668 0 without differential rotation only differential rotation Helicity injection rate ( 10 40 Mx 2 h -1 ) H injected < 0 H coronal < 0 ( Démoulin et al. 2002, Nindos et al. 2002, 2003 ) In most ARs, differential rotation cannot provides H coronal 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 H coronal ( Chae et al. 2001, Jeong & Chae 2007, Labonté et al. 07, Tian & Alexander 2008 ) ( Green et al. 2002, Tian & Alexander, 2007 ) 22/08/11 - FEW 2011 - E. Pariat20

21. 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 22/08/11 - FEW 2011 - E. Pariat21 ( Pevtsov 2002 ) H < 0 H > 0 independent 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  effect of the solar rotation Labonté et al. 07

22. AR emergence - H injected ( 10 42 Mx 2 ) Total magnetic flux ( 10 22 Mx ) AR 10831 lowhigh Magnetic tongues: H< 0 Significant helicity injection is delayed ~ 2 days compared to magnetic flux ( Tian & Alexander, 2007 ) lowhigh H injected ( 10 42 Mx 2 ) low high low 22/08/11 - FEW 2011 - E. Pariat22 ( Jeong & Chae 2007 ) Helicity injection follows a low-high-low evolution.

23. Photospheric flux of magnetic helicity longitudinal magnetograms3D 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 velocityemergence of AR 10365 low high low high low high low H injection evol. can be interpreted by the emergence of a globally twisted FT 22/08/11 - FEW 2011 - E. Pariat23 ( Chae 2004 ) ( Cheung et al. 2005 )

24. AR recurrences CMEs with low H later on? Rather: Not enough injected helicity measured in evolved ARs ? 22/08/11 - FEW 2011 - E. Pariat24

25. Helicity injection in ARs 48 X-flaring ARs 345 non-X-flaring ARs Magnetic flux ( Mx ) Helicity flux over 6 days ( Mx 2 ) 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 )  =(|  + |+|  - |)/2) 22/08/11 - FEW 2011 - E. Pariat25 H = 0.039  

26. Helicity accumulation in ARs.  1 turn in 100 days (3 Carrington Rotations) Helicity accumulated in AR over their passage on disk: ~0.08-0.2   Typical instantaneous flux of Helicity in AR: – ~ 10 42 Mx².day -1 but large variation ; ~ 10 -2  ²/day (  = 10 22 Mx) Total helicity accumulated in AR over several rotation (Démoulin et al. 02, Lim et al. 07) – ~1-100 x10 44 Mx² ; ~ 0.5-2  ² Is the normalisation by   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    /days 22/08/11 - FEW 2011 - E. Pariat26

27. Outline Introduction: twist in actives regions Magnetic tongues Magnetic helicity: measurement methods Observational properties of injected helicity Observed helicity flux distribution 22/08/11 - FEW 2011 - E. Pariat27

28. Evolution of helicity flux density ( Pariat et al. 2006 ) Coherent evolution 22/08/11 - FEW 2011 - E. Pariat28 AR 8210 AR 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

29. 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 22/08/11 - FEW 2011 - E. Pariat29

30. 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 22/08/11 - FEW 2011 - E. Pariat30 Möstl et al. 08 Chandra et al. 10

31. 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 22/08/11 - FEW 2011 - E. Pariat31

32. 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 H , 31/10/01 MDI Helicity map Whole AR: H>0 A+B: H<0 ( Romano et al. 2011 ) 22/08/11 - FEW 2011 - E. Pariat32

33. Conclusion H stored in the corona, then ejected via CMEs tachocline photosphere coronainterplanetary space H in ICMEs & Magnetic Clouds B emergence & H transfert dynamo : produce H 0 Observed photospheric H flux H corona from magnetic extrapolation H MC from magnetic cloud modelling Helicity budget ( H is a conserved quantity ) Dynamo : coupling of the hemisphere north: H < 0 south: H > 0 but why dominance of only 60 % ? Maps of H injected in ARs Why some ARs have H 0 ?  constraints on the solar dynamo Flux of helicity through the photosphere H=0.005-0.02   /days  constraint for models Does all the helicity of emerging FT cross the photosphere ? Is there H accumulating bellow? Helicity storage in the solar corona Improved 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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35. Flux density of magnetic helicity Flux density : All previous studies with G A maps : simultaneous injections of both sign of magnetic helicity. True ? ( Chae 2004 ) ( Nindos et al. 2003 ) G A & B n ( Kusano et al. 2002 ) G A & velocity Does it had a physical meaning ? Total H flux : well established physical meaning 22/08/11 - FEW 2011 - E. Pariat35

36. Simplest example: a translated magnetic flux tube => G A is NOT a good proxy of the flux density ! ( Pariat et al. 2005 ) G A introduces fake signal of both signs in equal amount Only the total flux of helicity is reliable u Flux tube u Photosphere While no helicity is injected ! GAGA B n > 0 ( Kusano et al. 2002 ) Example of an observed AR --> u 22/08/11 - FEW 2011 - E. Pariat36

37. 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 22/08/11 - FEW 2011 - E. Pariat37

38. Corona Photosphere emergence Magnetic helicity flux : theory emergencehorizontal motionsHelicity flux Phostosphere B Can always define : =>=> Corona Photosphere emergence Simple interpretation of : photospheric footpoint motion of magnetic flux tubes 22/08/11 - FEW 2011 - E. Pariat38

39. 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 22/08/11 - FEW 2011 - E. Pariat39