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Helicity : where it comes from and what it tells us

Helicity : where it comes from and what it tells us. Dana Longcope, MSU Anna Malanushenko , MSU/LMSAL. Thanks: Graham Barnes, CoRA B. Ravindra , IIA and …. … advisor extraordinaire. Relative helicity. … are these?. These curves are linked ….

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Helicity : where it comes from and what it tells us

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  1. Helicity: where it comes from and what it tells us Dana Longcope, MSU Anna Malanushenko, MSU/LMSAL Thanks: Graham Barnes, CoRA B. Ravindra, IIA and … Canfield-fest

  2. … advisor extraordinaire Canfield-fest

  3. Relative helicity … are these? These curves are linked … Canfield-fest

  4. Relative helicity Are these coronal field lines twisted about each other? Are they linked with one another? What about gauge-dependence? Canfield-fest

  5. Relative helicity Relative helicity Berger & Field 1984 Finn & Antonsen 1985 Does HR depend on choice of B0? yes Need reference field B0(x) for comparison So what can it tell us? Canfield-fest

  6. Potential field reference • One choice of reference: • potential magnetic field • Advantages: • Potential field is unique (from normal) • Potential field has minimum magnetic energy: •  HR≠0 =>free magnetic energy • minimizing magnetic energy subj. to HR: • can be computed constant from Lagrange multiplier imposing constraint Canfield-fest

  7. Helicity flux: observable Using LCT velocities (Demoulin & Berger 2003) • Track features in LOS m-gram: • Compare to Faraday’s Law featurevelocity: measured Ideal induction: (Berger & Field 1984) reference field Helicity Flux: observed motion Canfield-fest observed field

  8. Measured Velocity (Chae 2001) • AR8011 • F = 1.7 X 1021 Mx2 • S6o latitude • Bz measured: LOS mg • U measured: LCT of Bz • A0 extrapolated Canfield-fest

  9. Measured Velocity (Chae 2001) • Highly variable helicity flux • Up to +3 X 1040 Mx2/day = F2 10-2/day Canfield-fest

  10. Measuring Spin spin braiding dH/dt < 0 for clockwise spin (w<0) 1 12 2 dH/dt < 0 for clockwise motion (if FaFb < 0 ) 2 Internal motion: spin Canfield-fest

  11. Canfield-fest

  12. Source of braiding Braiding: deformation of flux tube axis

  13. Source of spin Natural time scale For twist injection: (Longcope & Welsch2000) propagation of current (twist) within flux tube: torsional Alfven wave Twist moves to balance torques

  14. Measuring Spin P01 Brown et al. 2003 all contributions to dH/dt Canfield-fest Longcope et al. 2007

  15. fit: q = -0.67 x 10-8 m-1 Hbr separation d(t) H Hsp • Helicity dominated by braiding • Northern AR: • H > 0 Hsp < 0 Longcope & Welsch model Canfield-fest

  16. fit: q = +2.3 x 10-8 m-1 Longcope & Welsch model separation d(t) Hsp H Hbr • Helicity dominated by spin • Southern AR: • H > 0 Hsp > 0 Canfield-fest

  17. Canfield-fest

  18. Can this work? 17 Different Low & Lou fields Malanushenkoet al. 2009 Canfield-fest

  19. Spin +braiding make twist Malanushenko et al. 2010 braiding spin+braid Coronal twist Photospheric flux Malanushenko et al. 2010 Canfield-fest

  20. Twist over time aL/2 AR9002 But what happens to free energy? AR9004 Reconnected flux aL/2 Canfield-fest

  21. Twist over time aL/2 EUV loops AR9002 AR9004 aL/2 Canfield-fest

  22. Helicity in the AR How twisted is the field within the grey sub-volume? Ignoring these EG e.g. what is the helicity is in a flux rope? Canfield-fest

  23. Helicity in the AR Which reference field to use? Longcope & Malanushenko 2008 J J unconfined additive Canfield-fest

  24. Advantages of the additive self-helicity D2 Constraint on self-helicity of Di D1 Lagrange multiplier Mag. energy Constrained minimum: piece-wise constant-a Canfield-fest

  25. Hierarchy of energies Constraint:* Field: • Every field line: • footpoint • connectivity B(x) NLFFF ≥ • Domains: • flux • shape • self-helicity Piecewise const.-a Ba(x) ≥ Piecewise potential • Domains: • flux • shape P(x) ≥ • Domains: • flux BFCE(x) MCC ≥ B0(x) potential Ø *other than p-spheric field BC Canfield-fest

  26. Malanushenko et al. 2009 Simulations: Fan & Gibson 2003 Additive helicity drops during instability Canfield-fest

  27. Summary • Relative helicitydepends on reference field • Choosing pot’l field: helicity is proxy for free magnetic energy • Can observe injection of rel. helicity into corona: injection of free energy • Additive rel. helicity leads to piece-wise constant-a field: bound on energy Canfield-fest

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