Helicity: where it comes from and what it tells us Dana Longcope, MSU Anna Malanushenko, MSU/LMSAL 8/11/10Canfield-fest Thanks: Graham Barnes, CoRA B. Ravindra, IIA and …

… advisor extraordinaire 8/11/10Canfield-fest

Relative helicity These curves are linked … … are these? 8/11/10Canfield-fest

Relative helicity Are these coronal field lines twisted about each other? Are they linked with one another? What about gauge-dependence? 8/11/10Canfield-fest

Relative helicity Need reference field B 0 (x) for comparison Relative helicity Berger & Field 1984 Finn & Antonsen 1985 Does H R depend on choice of B 0 ? So what can it tell us? 8/11/10Canfield-fest yes

Potential field reference One choice of reference: potential magnetic field Advantages: Potential field is unique (from normal) Potential field has minimum magnetic energy:  H R ≠0 =>  free magnetic energy minimizing magnetic energy subj. to H R : can be computed constant from Lagrange multiplier imposing constraint 8/11/10Canfield-fest

Helicity flux: observable Using LCT velocities (Demoulin & Berger 2003) Track features in LOS m-gram: Track features in LOS m-gram: Compare to Faraday’s Law Compare to Faraday’s Law (Berger & Field 1984) Helicity Flux: feature velocity: measured 8/11/10Canfield-fest Ideal induction: observed motion observed field reference field

Measured Velocity (Chae 2001) AR8011 AR8011 F = 1.7 X Mx 2 F = 1.7 X Mx 2 S6 o latitude S6 o latitude B z measured: LOS mg B z measured: LOS mg U measured: LCT of B z U measured: LCT of B z A 0 extrapolated A 0 extrapolated 8/11/10Canfield-fest

Measured Velocity (Chae 2001) Highly variable helicity flux Highly variable helicity flux Up to +3 X Mx 2 /day = F /day Up to +3 X Mx 2 /day = F /day 8/11/10Canfield-fest

8/11/10 Measuring Spin spin braiding 1 2 22  12 Canfield-fest dH/dt < 0 for clockwise spin (  <0) dH/dt < 0 for clockwise motion (if  a  b < 0 ) Internal motion: spin

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Source of braiding Braiding: deformation of flux tube axis

Source of spin Natural time scale For twist injection: (Longcope & Welsch 2000) propagation of current (twist) within flux tube: torsional Alfven wave Twist moves to balance torques

8/11/10 Measuring Spin Brown et al all contributions to dH/dt P01 Canfield-fest Longcope et al. 2007

8/11/10 separation d(t) Longcope & Welsch model H br H sp H Helicity dominated by braiding Northern AR: H > 0 H sp < 0 fit: q = x m -1 Canfield-fest

8/11/10 separation d(t) Longcope & Welsch model H br H sp H Helicity dominated by spin Southern AR: H > 0 H sp > 0 fit: q = +2.3 x m -1 Canfield-fest

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Can this work? 8/11/10Canfield-fest Malanushenko et al Different Low & Lou fields

Spin + braiding make twist 8/11/10Canfield-fest braiding spin+braid Photospheric flux Coronal twist Malanushenko et al. 2010

Twist over time 8/11/10Canfield-fest AR9004 AR9002 But what happens to free energy?  L/2 Reconnected flux

Twist over time 8/11/10Canfield-fest AR9004 AR9002  L/2 EUV loops

Helicity in the AR 8/11/10Canfield-fest EG How twisted is the field within the grey sub-volume? Ignoring these e.g. what is the helicity is in a flux rope?

Helicity in the AR 8/11/10Canfield-fest Which reference field to use? unconfinedadditive J J Longcope & Malanushenko 2008

Advantages of the additive self-helicity Constraint on self-helicity of D i Lagrange multiplier Mag. energy Constrained minimum: piece-wise constant-  8/11/10Canfield-fest D1D1 D2D2

Hierarchy of energies 8/11/10Canfield-fest NLFFF Piecewise const.-  Domains: flux shape self-helicity Every field line: footpoint connectivity Piecewise potential Domains: flux shape MCC Domains: flux Field: Constraint:* potential Ø ≥ ≥ ≥ ≥ *other than p-spheric field BC B(x)B(x) B(x)B(x) P(x)P(x) B FCE (x) B0(x)B0(x)

8/11/10Canfield-fest Malanushenko et al Additive helicity drops during instability Simulations: Fan & Gibson 2003

Summary Relative helicity depends 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-  field: bound on energy 8/11/10Canfield-fest