Background

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Helicity on the Sun.
If you worry about publicity Do not speak of
Current Helicity Jan Stenflo
Dr. Alexei A. Pevtsov
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Helicity on the Sun

• What is it good for anyway?

Dr. Alexei A. Pevtsov
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Outline

• Definition of helicity (incl. graphic repr.)
• Hemispheric helicity rule (observations, origin,
  cycle variation)
• Helicity transport
• Fitting pieces of puzzle together???

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Knots and Bolts
H 0
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Knots and Bolts
H 0
H -1
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Writhe and Twist
W -1 T0
H WT
T -1 W0
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Helicities
Magnetic Helicity
?
A vector potential, B magnetic induction.
?Current Helicity
?
For liner force-free field (a constant)
Kinetic Helicity
where Y is arbitrary scalar function
, where E is magnetic energy

• topological invariant
• conserves better than energy (Woltjer, 1958
  Taylor 1974 Ji et al, 1995)
• dynamo, reconnection, stability
  energy decay 4-10.5
• 
  
  helicity dissipation 1.3-5.1

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What We Observe
Observations
Force-free field(1)
Pevtsov et al, 1995, Longcope et al, 1998
Current helicity density(2)
Abramenko et al, 1996 Bao and Zhang, 1998

WL, H-alpha, X-ray Morphology
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What We Observe
Relative helicity
(Berger, 1985)
(e.g. Chae, 2001)
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Seehafer, 1990 Pevtsov et al, 1995, Abramenko et
al, 1996 Longcope et al, 1998, Bao and Zhang,
1998, Pevtsov et al. 2001, Hagino and Sakurai,
2002 60-80, hemispheric helicity rule
466 active regions observed 1988-2000 by
Haleakala Stokes Polarimeter r -0.23, Likelihood
of no correlation is 2.5x10-7
N/(-) S/() 69 75 (cycle 22, Pevtsov
et al, 1995) 63 70 (cycle 23, Pevtsov et
al, 2001)
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Cycle variation?
Bao et al, 1999, reverse sign for hc at the
beginning Cycle 23 Hagino Sakurai, 2002, some
periods disobey the rule Nandi Choudhuri 2004
cycle variation of helicity rule
abest
g
Lat
g lt 0
Pevtsov et al 2001
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Zhang, 2006
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Longcope et al, 1999
Holder et al, 2003 Tian et al., 2001
Chae 2001, Green et al 2003 Demoulin et al 2003
Seehafer et al, 2003

• direct action of Coriolis force and differential
  rotation produce insufficient
• amount of helicity and cannot explain
  significant scatter in latitudinal dependency
• dynamo does not produce enough helicity.
• - S-effect can do it all?

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• Nandy, 2006
• F-0.69
• Scatter is latitude-independent
• Trend, scatter agree with S-effect

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Helicity Transport
Lepping et al (1990) fitted 18 MCs, a10-10 m-1,
B00.0002 G, F1021 Mx. HMC(La/2p) F2 5 x 1042
Mx2 Larson et al (1995), HMC 4 x 1042
Mx2 Demoulin et al, 2002, AR7978 52 x 1042 Mx2
(26 CMEs, 1 rotation) 5 rotations - ? Total
helicity ejected by MCs often exceeds coronal
helicity (diff. rotation cannot replenish).
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Helicity Transport via Reconnection
Independent flux systems Hm H1 H2 H3 e.g.
H10.5Hcrit H20.4Hcrit H30.2Hcrit
HmgtHcrit
Pevtsov et al 1996
Canfield Reardon, 1998
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Twist in Emerging Flux Tube

• Longcope and Welsch, 2000
• vortical motions responsible for helicity
  injection
• cannot be driven by pressure gradient and cannot
• be produced by coupling motions of non-mag.
  plasma
• magnetic torque at photosphere-corona transition
• cannot be countered by pressure gradients.

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Evolution of ARs and their Helicity

• - MDI full disk magnetograms
• SoHO EIT 195A images
• 6 emerging active regions

Maleev et al, 2002
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Modeling Flux Emergence

• no twist at emergence
• emergence linear increase in d
• d increases in constant rate until t1

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Fitted Model Parameters
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Sunspot Rotation

• Kempf, P., Astron. Nachrichten, 1910, Nr. 4429,
• Bd. 195, 197
• -Brown, et al, Solar Phys., 2003, 216, 79
• Pevtsov, A. A. and Sattarov, I.S., Soln. Dannye,
  1985,
• No. 3, 65.

Courtesy R. Nightingale
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Sunspot Rotation(R. Nightingale data)
Correct sign of twist hemispheric preference
is in agreement with the hemispheric helicity
rule No good correlation between sign of
current helicity and direction of rotation
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Courtesy R. Nightingale
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Kinetic Helicity and flares
See poster by F. Hill et al
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How These All Might Fit Together?

• Solar magnetic fields exhibit hemispheric sign
  asymmetry.
• Helicity (ARs) is created in upper CZN (S-effect
  explains large scatter and helicity amplitude
  solar cycle variations???).
• Helicity is removed from AR as a result of
  eruption.
• Subphotospheric portion of flux tube may serve as
  reservoir of helicity, supplying helicity
  between flares/CMEs.
• Sunspot rotation and subphotospheric pattern of
  kinetic helicity may be indications of helicity
  transport via torsional waves.

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Open Questions

• Evolution of kinetic helicity (before/after
  flare/flux emergence).
• Timing of sunspot rotation vs. flare
• Is helicity of active region determined at their
  emergence, or maybe, significant amount of
  helicity can be injected later during AR
  lifetime?