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Magnetic Helicity Generation Inside the Sun. Dana Longcope Montana State University. Thanks: Alexei Pevtsov. Propagation from. Magnetic Helicity Generation Inside the Sun. Observations show a clear hemispheric asymmetry in the helicity of the coronal magnetic field: H R < 0 in the North

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magnetic helicity generation inside the sun

Magnetic Helicity Generation Inside the Sun

Dana Longcope

Montana State University

Thanks: Alexei Pevtsov

slide2

Propagation from

Magnetic Helicity Generation Inside the Sun

Observations show a clear hemispheric asymmetry in the helicity of the coronal magnetic field: HR < 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

magnetic helicity propagation from inside the sun
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
trend in photospheric twist
Trend in photospheric twist

Trend:

abest< 0

in North

abest> 0

in South

Correlation:

abest

w/ latitude

> 99.9999%

466 ARs from Longcope & Pevtsov 2003

fluctuations in twist
Fluctuations in twist

Large latitude-indep’t scatter  a created by turbulence

Linear trend removed

(from Longcope, Fisher & Pevtsov 1998)

the origin of flux
The origin of flux

Bipolar active region

formed by emergence of

FLUX TUBE

from below photosphere

(from Cauzzi et al. 1996)

twist in flux tubes
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)

dynamics of twist
Dynamics of twist

(from Longcope & Klapper 1997)

s

Angular momentum:

Unbalanced magnetic

torque

q(s)

w(s)

dynamics of twist1
Dynamics of twist

(from Longcope & Klapper 1997)

Field line Kinematics

s

w(s)

Differential spinning

q(s)

dynamics of twist2
Dynamics of twist

(from Longcope & Klapper 1997)

Field line Kinematics

s

w(s)

Differential spinning

q(s)

dynamics of twist3
Dynamics of twist
  • Torsional Alven waves
dynamics of twist4
Dynamics of twist

(from Longcope & Klapper 1997)

Field line Kinematics

s

vs(s)

Axial stretching

q(s)

dynamics of twist5
Dynamics of twist

(from Longcope & Klapper 1997)

Field line Kinematics

s

vs(s)

Axial stretching

q(s)

dynamics of twist6
Dynamics of twist

Out-of-plane

motion of axis

S(s)

indep. of q or w

source of twist
Source of Twist

Helicity Conservation

  • Increasing LH
  • writhe (dWr/dt <0 )
  • Increasing RH

twist (dTw/dt > 0)

slide16
S=a

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 RHtwist

* in the mean field

manifestation of s effect
Manifestation of S-effect
  • Simulation of
  • rising flux
  • tubes
  • Large scatter
  • Da
  • Latitude-indep.
  • Da

( Longcope, Fisher & Pevtsov 1998 )

coupling flux tube to corona
Coupling flux tube to corona

corona: b << 1

(force-free field)

I=0

photosphere

I=0

surface

currents

CZ: b >> 1

(thin flux tube)

coupling flux tube to corona1
Coupling flux tube to corona

q(s)

Radial shunting

 Storques= 0

(Longcope & Weslch 2000)

coupling flux tube to corona2
Coupling flux tube to corona

Low inertia 

Storques= 0

 Current matches

across interface

q(s)

Twist at end of FT

Coronal “twist”

(Longcope & Weslch 2000)

application to emerging ar
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

application to emerging ar1
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

observational evidence
Observational Evidence

(Pevtsov, Maleev & Longcope 2003)

  • Study 6 ARs during emergence
  • Findd(t)
  • a(t)

8/19 12:47

8/19 20:47

8/20 4:47

8/20 20:47

8/21 4:47

8/20 12:47

AR9139

SOHO MDI

2000-8-19

d

observational evidence1
Observational Evidence

(Pevtsov, Maleev & Longcope 2003)

Fit Model to Data

v=264 m/s

a = 2 10-8 m-1

vA = 158 m/s

observational evidence2
Observational Evidence

(Pevtsov, Maleev & Longcope 2003)

AR8582

AR8817

implications of model
Implications of model
  • Twistexists before emergence
  • (i.e. rising tube is twisted)
  • Tube Twist propagates into corona
  •  Coronal Helicity

I

implications of model1
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 b>>1  b<<1
  • Conserves Helicity
  • Includes BG coronal field
implications of model2
Implications of model
  • Tube Writhe: irrelevant to corona
  • Helicity dearth propagates downward
summary
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
dynamics of twist7
Dynamics of twist

(from Longcope & Klapper 1997)

Angular momentum:

s

a

q(s)

w(s)

Changing tube radius

(Michelle Kwan effect)

coupling flux tube to corona3
Coupling flux tube to corona

Low-bcoronal

Equilibrium: FFF

High-bCZ

Field: twisted

Thin flux tube

Interface

possible sources of twist
Possible sources of twist
  • Initial state of flux tube: q(s,0)
possible sources of twist1
Possible sources of twist
  • Initial state of flux tube: q(s,0)
  • External flow “twirls” tube segment

Creates regions of opposing twist

Requires anomalous “friction”

across flux tube surface

possible sources of twist2
Possible sources of twist
  • Initial state of flux tube: q(s,0)
  • External flow “twirls” tube segment
  • Net current driven along flux tube

Violates assumption of isolated flux tube

 Cannot be a “thin flux tube”

axis twist coupling
Axis-twist coupling

Term required to conserve H = Tw + Wr

Function of twist

Function of axis

Kinematic eq. for twist

depends on axis motion

photospheric twist w o helicity
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
  • (H=0)
  • External flows induce LH writhe
  • (dH/dt =0)
  • Coupling term SRH twist

* From the emergence of a flux tube with no net helicty

writhe from turbulence the s effect
Writhe from Turbulence: The S-effect

Twist source

Averaging over turbulence:

Spectrum of kinetic helicity

Compare to a-effect:

Variance of twist source: