Magnetic Helicity Generation Inside the Sun

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

2. 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 Trend: abest< 0 in North abest> 0 in South Correlation: abest w/ latitude > 99.9999% 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 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)

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

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

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

13. Dynamics of twist (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 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

17. Manifestation of S-effect • Simulation of • rising flux • tubes • Large scatter • Da • Latitude-indep. • Da ( 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  Storques= 0 (Longcope & Weslch 2000)

20. 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)

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 • 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

24. Observational Evidence (Pevtsov, Maleev & Longcope 2003) Fit Model to Data v=264 m/s a = 2 10-8 m-1 vA = 158 m/s

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

26. Implications of model • Twistexists 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 (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-bcoronal Equilibrium: FFF High-bCZ 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* • 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

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