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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

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

relative helicity
Relative helicity

… are these?

These curves are linked …

Canfield-fest

relative helicity1
Relative helicity

Are these coronal field lines twisted about each other?

Are they linked with one another?

What about gauge-dependence?

Canfield-fest

relative helicity2
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

potential field reference
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

helicity flux observable
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

measured velocity
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

measured velocity1
Measured Velocity

(Chae 2001)

  • Highly variable helicity flux
  • Up to +3 X 1040 Mx2/day = F2 10-2/day

Canfield-fest

measuring spin
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

source of braiding
Source of braiding

Braiding: deformation of flux tube axis

source of spin
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

measuring spin1
Measuring Spin

P01

Brown et al. 2003

all contributions to dH/dt

Canfield-fest

Longcope et al. 2007

slide15

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

slide16

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

can this work
Can this work?

17 Different Low & Lou fields

Malanushenkoet al. 2009

Canfield-fest

spin braiding make twist
Spin +braiding make twist

Malanushenko et al. 2010

braiding

spin+braid

Coronal twist

Photospheric flux

Malanushenko et al. 2010

Canfield-fest

twist over time
Twist over time

aL/2

AR9002

But what happens to free energy?

AR9004

Reconnected flux

aL/2

Canfield-fest

twist over time1
Twist over time

aL/2

EUV loops

AR9002

AR9004

aL/2

Canfield-fest

helicity in the ar
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

helicity in the ar1
Helicity in the AR

Which reference field to use?

Longcope & Malanushenko 2008

J

J

unconfined

additive

Canfield-fest

slide24

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

hierarchy of energies
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

slide26

Malanushenko et al. 2009

Simulations: Fan & Gibson 2003

Additive helicity drops during instability

Canfield-fest

summary
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