1. Magnetic Helicity Generation Inside the Sun
Dana Longcope
Montana State University
Thanks: Alexei Pevtsov

2. Magnetic Helicity Generation Inside the Sun
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

3. 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

4. Trend in photospheric twist
abest< 0
in North
abest> 0
in South
Correlation:
abest
w/ latitude
> %
466 ARs from Longcope & Pevtsov 2003

5. Fluctuations in twist
Large latitude-indep’t scatter  a created by turbulence
Linear trend removed
(from Longcope, Fisher & Pevtsov 1998)

6. The origin of flux Bipolar active region formed by emergence of
FLUX TUBE
from below photosphere
(from Cauzzi et al. 1996)

7. Twist in flux tubes 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)

8. Dynamics of twist Angular momentum: s Unbalanced magnetic torque q(s)
(from Longcope & Klapper 1997) s
Angular momentum:
Unbalanced magnetic
torque
q(s)
w(s)

9. Dynamics of twist Field line Kinematics s w(s) Differential spinning
(from Longcope & Klapper 1997)
Field line Kinematics s
w(s)
Differential spinning
q(s)

10. Dynamics of twist Field line Kinematics s w(s) Differential spinning
(from Longcope & Klapper 1997)
Field line Kinematics s
w(s)
Differential spinning
q(s)

11. Dynamics of twist
Torsional Alven waves

12. Dynamics of twist Field line Kinematics s vs(s) Axial stretching q(s)
(from Longcope & Klapper 1997)
Field line Kinematics s
vs(s)
Axial stretching
q(s)

13. Dynamics of twist Field line Kinematics s vs(s) Axial stretching q(s)
(from Longcope & Klapper 1997)
Field line Kinematics s
vs(s)
Axial stretching
q(s)

14. Dynamics of twist
Out-of-plane
motion of axis
S(s)
indep. of q or w

15. Source of Twist Helicity Conservation Increasing LH
writhe (dWr/dt <0 )
Increasing RH
twist (dTw/dt > 0)

16. S=a a-effect S-effect RH Applies to mean fields Creates Helicity*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

17. Manifestation of S-effect
Simulation of
rising flux
tubes
Large scatter Da
Latitude-indep.
( Longcope, Fisher & Pevtsov 1998 )

18. Coupling flux tube to corona
corona: b << 1
(force-free field)
I=0
photosphere
I=0
surface
currents
CZ: b >> 1
(thin flux tube)

19. Coupling flux tube to corona
q(s)
Radial shunting
 S torques = 0
(Longcope & Weslch 2000)

20. 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)

21. 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

22. 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

23. Observational Evidence
(Pevtsov, Maleev & Longcope 2003)
Study 6 ARs during emergence
Find d(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 d

24. Observational Evidence
(Pevtsov, Maleev & Longcope 2003)
Fit Model to Data
v=264 m/s
a = m-1
vA = 158 m/s

25. Observational Evidence
(Pevtsov, Maleev & Longcope 2003)
AR8582
AR8817

26. Implications of model Twist exists before emergence
(i.e. rising tube is twisted)
Tube Twist propagates into corona
 Coronal Helicity I

27. 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

28. Implications of model Tube Writhe: irrelevant to corona
Helicity dearth propagates downward

29. 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

30. Dynamics of twist Angular momentum: s a q(s) w(s) Changing tube radius
(from Longcope & Klapper 1997)
Angular momentum: s a
q(s)
w(s)
Changing tube radius
(Michelle Kwan effect)

31. Coupling flux tube to corona
Low-b coronal
Equilibrium: FFF
High-b CZ
Field: twisted
Thin flux tube
Interface

32. Possible sources of twist
Initial state of flux tube: q(s,0)

33. 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

34. 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”

35. Axis-twist coupling Term required to conserve H = Tw + Wr
Function of twist
Function of axis
Kinematic eq. for twist
depends on axis motion 

36. Photospheric twist w/o Helicity*
Begin w/ straight untwisted tube
(H=0)
External flows induce LH writhe
(dH/dt =0)
Coupling term S RH twist
Tube crosses photosphere
Helicity is transported into
coronal field
Current in coronal field
matches twsit in flux tube
* From the emergence of a flux tube with no net helicty

37. Writhe from Turbulence: The S-effect
Twist source
Averaging over turbulence:
Spectrum of kinetic helicity
Compare to a-effect:
Variance of twist source: