Download - Dr. Alexei A. Pevtsov
Dr. Alexei A. Pevtsov
Helicity on the Sun.
If you worry about publicityDo not speak of Current Helicity
Jan Stenflo
Helicity on the Sun:
What is it good for anyway?
Dr. Alexei A. Pevtsov
Outline
• Definition of helicity (incl. graphic repr.)
• Hemispheric helicity rule (observations, origin, cycle variation)
• Helicity transport
• Fitting pieces of puzzle together???
Knots and BoltsH = 0
Knots and BoltsH = 0 H= -1
Writhe and Twist
H = W+T
W = -1; T=0
T = -1; W=0
Helicities BABA ,)()2( 21
)(WTdDH
tubefluxthinm
Eμα H
n BψBdVdVBα
ψ)BdVB(αB dVA H
ψ,B αA αB, B
-m
-m
-
1
21
1
1
2
0;
A – vector potential, B – magnetic induction.
For liner force-free field (constant)
where 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%
dDH c BB dDH k VV
Magnetic Helicity
Current Helicity
Kinetic Helicity
What We Observe
zbest ;
V
m BdVAH Observations: zyx BBBB ,,
Force-free field(1): BB mm EH 12
Current helicity density(2):
zzyyxxc JBJBJBJBBBh
WL, H-alpha, X-ray Morphology:
sinLc
%/; ccc hhh Abramenko et al, 1996Bao and Zhang, 1998
Pevtsov et al, 1995, Longcope et al, 1998
What We Observe
Relative helicity:
Nx
nx
Ny
ny yx
yx
r kkl
nnBdVBAdVBAH
1 1)22
2~
00 (
,2
dxdyBvAdxdyvBAdt
dHzpzp
R )(2)(2(e.g. Chae, 2001)
(Berger, 1985)
466 active regions observed 1988-2000 by Haleakala Stokes Polarimeter= -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)
Seehafer, 1990Pevtsov et al, 1995, Abramenko et al, 1996Longcope et al, 1998, Bao and Zhang, 1998,Pevtsov et al. 2001,Hagino and Sakurai, 2002
60-80%, hemispheric helicity rule
Cycle variation?
Pevtsov et al 2001
Bao et al, 1999, reverse sign for hc at the beginning Cycle 23Hagino & Sakurai, 2002, some periods disobey the ruleNandi & Choudhuri 2004 – cycle variation of helicity rule
Lat
best
LATbest
Zhang, 2006
Observations Rad/Mm Ref.
AR ~0.01 Pevtsov et al 1995
substructures ~0.2 Pevtsov etal 1994, Leka et al, 1996
Sources of Twist
Joy’s Law 0.001 Longcope & Klapper 1997
Diff’l rotation 0.002 Longcope et al 1999
- effect ~0.02 Longcope et al 1998
Created in dynamo 4 x 10-5 Charbonneau & Gilman 1998
Holder et al, 2003;Tian et al., 2001
Chae 2001, Green et al 2003Demoulin 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.-effect can do it all?
Seehafer et al, 2003
Longcope et al, 1999
Nandy, 2006~ -0.69
Scatter is latitude-independentTrend, scatter agree with -effect
Helicity Transport
dxdyByBxBEEμα H
B nψBdVdVBα
ψ)BdVB(αB dVA H
ψ,B αA αB, B
zyx-
m
-m
-
)(,2
0;11
21
1
1
For liner force-free field (constant)
where is arbitrary scalar function
Lepping et al (1990) fitted 18 MCs, =10-10 m-1, B0=0.0002 G, =1021 Mx.HMC=(L/2) 2= 5 x 1042 Mx2 Larson et al (1995), HMC= 4 x 1042 Mx2
Demoulin et al, 2002, AR797852 x 1042 Mx2 (26 CMEs, 1 rotation)5 rotations - ?Total helicity ejected by MCs often exceeds coronal helicity (diff. rotation cannot replenish).
Helicity Transport via Reconnection)0( BnifconstHm
Independent flux systems: Hm= H1+ H2+ H3; e.g. H1=0.5Hcrit; H2=0.4Hcrit; H3=0.2Hcrit Hm>Hcrit
Canfield & Reardon, 1998Pevtsov et al 1996
Twist in Emerging Flux TubeLongcope and Welsch, 2000:
- vortical motions responsible for helicity injection cannot be driven by pressure gradient and cannotbe produced by coupling motions of non-mag. plasma-magnetic torque at photosphere-corona transition cannot be countered by pressure gradients.
Evolution of ARs and their Helicity
- MDI full disk magnetograms-SoHO EIT 195A images- 6 emerging active regions
Maleev et al, 2002
Modeling Flux Emergence
)(
d
v
d
d
dt
d A
- no twist at emergence- emergence – linear increase in d- d increases in constant rate until t1
0)( 0 t
00 )( dtd
ttdttdd
tttttddtd
11010
1010
)(
)()( {
)(t
1000
}][{ )1()(111
tttvttd
d
v
v
dvvttd
ttvA
A /;)(
exp)( 11
11 ][
dH R 2
2 )(
2
2
ww
dt
dH R
Fitted Model ParametersNOAA alpha
ramp-up
(days)
d
days
Flux
(1020 Mx)
Helicity
1041Mx2
d0
Mm
VA
m sec-1
8582 1.73 1.20 30 4.0 26.93 71
8738 … 1.79 … … … …
8768 0.93 1.80 13 1.3 25.06 182
8817 1.00 1.20 17 0.9 26.79 84
9139 0.80 1.66 44 12.7 12.24 158
9193 0.87 1.80 2 0.1 23.45 60
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.
dayVR deg/1517
Courtesy R. Nightingale
Sunspot Rotation(R. Nightingale data)
CCW CW Bi-direct
N 31%
(70%)
13%
(30%)
16%
S 15%
(46%)
17%
(54%)
14%
* 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
Courtesy R. Nightingale
Kinetic Helicity and flares
See poster by F. Hill et al
How These All Might Fit Together?
• Solar magnetic fields exhibit hemispheric sign asymmetry.Helicity (ARs) is created in upper CZN (-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.
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?