Magnetic%20Helicity%20Generation%20Inside%20the%20Sun

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Magnetic Helicity Generation Inside the Sun

• Dana Longcope
• Montana State University

Thanks Alexei Pevtsov
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Propagation from
Magnetic Helicity Generation Inside the Sun

• Observations show a clear hemispheric asymmetry
  in the helicity of the coronal magnetic field HR
  lt 0 in the North
• Q Can we therefore conclude that field below the
  solar surface, and in the dynamo, has this same
  asymmetry?

Answer No
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Magnetic Helicity Propagation from Inside the Sun

• Observed trends in photospheric twist
• Implications for state of CZ flux tubes
• Coupling of twist to coronal field
• Observational evidence in emerging AR

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Trend in photospheric twist
Trend abestlt 0 in North abestgt 0 in
South Correlation abest w/ latitude gt 99.9999
466 ARs from Longcope Pevtsov 2003
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Fluctuations in twist
Large latitude-indept scatter ? a created by
turbulence
Linear trend removed (from Longcope, Fisher
Pevtsov 1998)
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The origin of flux
Bipolar active region formed by emergence of FLUX
TUBE from below photosphere
(from Cauzzi et al. 1996)
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Twist in flux tubes
s
s
Field lines twist about axis at a rate q(s,t)
dq/ds Plasma spins about axis at
rate w(s,t) dq/dt
Axis of tube x(s) satisfies thin flux
tube equations (Spruit 1981)
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Dynamics of twist
(from Longcope Klapper 1997)
s
Angular momentum
Unbalanced magnetic torque
q(s)
w(s)
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Dynamics of twist
(from Longcope Klapper 1997)
Field line Kinematics
s
w(s)
Differential spinning
q(s)
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Dynamics of twist
(from Longcope Klapper 1997)
Field line Kinematics
s
w(s)
Differential spinning
q(s)
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Dynamics of twist

• Torsional Alven waves

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Dynamics of twist
(from Longcope Klapper 1997)
Field line Kinematics
s
vs(s)
Axial stretching
q(s)
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Dynamics of twist
(from Longcope Klapper 1997)
Field line Kinematics
s
vs(s)
Axial stretching
q(s)
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Dynamics of twist
Out-of-plane motion of axis
?S(s)
indep. of q or w
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Source of Twist
Helicity Conservation

• Increasing LH
• writhe (dWr/dt lt0 )
• Increasing RH
• twist (dTw/dt gt 0)

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Sa
J
J
B
B
RH
a-effect
S-effect

• Applies to mean fields
• Creates Helicity
• RH eddies ? LH field

• Applies to flux tubes
• Creates Twist
• RH eddies ? RH twist

in the mean field
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Manifestation of S-effect

• Simulation of
• rising flux
• tubes
• Large scatter
• Da
• Latitude-indep.
• Da

( Longcope, Fisher Pevtsov 1998 )
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Coupling flux tube to corona
corona b ltlt 1
(force-free field)
I0
photosphere
I0
surface currents
CZ b gtgt 1
(thin flux tube)
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Coupling flux tube to corona
q(s)
Radial shunting ? S torques 0
(Longcope Weslch 2000)
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Coupling flux tube to corona
Low inertia ? S torques 0 ? Current
matches across interface
q(s)
Twist at end of FT
Coronal twist
(Longcope Weslch 2000)
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Application to Emerging AR
(Longcope Welsch 2000)
Model Assumptions
Model Assumptions

• Initial flux tube uniformly twisted q(s)a/2
• Poles separating d(t) d0 v (t-t0)

Twist propagates into corona
a(t)
d/vA 1 day
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Application to Emerging AR
(Pevtsov, Maleev Longcope 2003)
Model Assumptions

• Initial flux tube uniformly twisted q(s)a/2
• Poles separating d(t) d0 v (t-t0)
• Uniform Alfven speed in tube vA nv
• Coronal helicity H ad F2

? Solution
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Observational Evidence
(Pevtsov, Maleev Longcope 2003)

• Study 6 ARs during emergence
• Find d(t)
• a(t)

8/19 1247
8/19 2047
8/20 447
8/20 2047
8/21 447
8/20 1247
AR9139 SOHO MDI 2000-8-19
d
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Observational Evidence
(Pevtsov, Maleev Longcope 2003)
Fit Model to Data
v264 m/s
a 2 10-8 m-1 vA 158 m/s
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Observational Evidence
(Pevtsov, Maleev Longcope 2003)
AR8582
AR8817
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Implications of model

• Twist exists before emergence
• (i.e. rising tube is twisted)
• Tube Twist propagates into corona
• ? Coronal Helicity

I
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Implications of model

• Twist Helicity q(s) F2 I(s) F ? uniform
• Twist fills in lengthening region
• It DOES NOT favor wider portion

Parker 1979
Longcope Welsch 2000

• Assumes p(r)constant
• Predates Berger Field
• No BG coronal field

• Assumes bgtgt1 ? bltlt1
• Conserves Helicity
• Includes BG coronal field

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Implications of model

• Tube Writhe irrelevant to corona
• Helicity dearth propagates downward

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Summary

• Observed Hemispheric trend
• in p-spheric twist ? coronal HR
• Coronal HR fixed by
• TWIST of anchoring tube
• S-effect produces TWIST in rising FT
• BUT leaves helicity unchanged
• Observed Helicity evolution in
• emerging AR consistent w/ this

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Dynamics of twist
(from Longcope Klapper 1997)
Angular momentum
s
a
q(s)
w(s)
Changing tube radius (Michelle Kwan effect)
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Coupling flux tube to corona
Low-b coronal Equilibrium FFF
High-b CZ Field twisted Thin flux tube
Interface
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Possible sources of twist

1. Initial state of flux tube q(s,0)

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Possible sources of twist

1. Initial state of flux tube q(s,0)
2. External flow twirls tube segment

Creates regions of opposing twist
Requires anomalous friction across flux tube
surface
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Possible sources of twist

1. Initial state of flux tube q(s,0)
2. External flow twirls tube segment
3. Net current driven along flux tube

Violates assumption of isolated flux tube ?
Cannot be a thin flux tube
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Axis-twist coupling
Term required to conserve H Tw Wr
Function of twist
Function of axis
Kinematic eq. for twist depends on axis motion
?
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Photospheric twist w/o Helicity

• Tube crosses photosphere
• Helicity is transported into
• coronal field
• Current in coronal field
• matches twsit in flux tube

• Begin w/ straight untwisted tube
• (H0)
• External flows induce LH writhe
• (dH/dt 0)
• Coupling term S ?RH twist

From the emergence of a flux tube with no net
helicty
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Writhe from Turbulence The S-effect
Twist source
Averaging over turbulence
Spectrum of kinetic helicity
Compare to a-effect
Variance of twist source