1. Dec. 2, 2008 Bangalore, India Active region emergence and its effect on the solar corona Dana Longcope Montana State University, Bozeman, MT Isaac Klapper B. Ravindra* Brian Welsch § George Fisher (UCB) Alex Pevtsov (NSO) Thanks MSU * Presently IIA § Presently UCB

2. Dec. 2, 2008 Bangalore, India Typical AR: 8968 movie Active regions: where they come from Babcock 1961 MDI

3. Dec. 2, 2008 Bangalore, India separate grow   

4. Dec. 2, 2008 Bangalore, India   various sizes...... same story

5. Dec. 2, 2008 Bangalore, India Outline 1.Dynamics of emergence 2.Twist (helicity) in emerging tubes 3.Transport of helicity into the corona by emerging tubes How do these emerging flux tubes affect the corona?

6. Dec. 2, 2008 Bangalore, India Dynamics of rising flux tubes Isolated tube, pressure-confined, “thin”  a << H p Isolated tube, pressure-confined, “thin”  a << H p Axis of tube: space curve x(s,t) Axis of tube: space curve x(s,t) Dynamical equations: Spruit 1981, Choudhuri & Gilman 1987 Dynamical equations: Spruit 1981, Choudhuri & Gilman 1987

7. Dec. 2, 2008 Bangalore, India Model evolution of AR tubes Initialize tube at base of CZ Follow evolution of emerging tube - thin FT eqns. Predict configuration of observed AR Fan et al. 1994 D’Silva & Choudhuri 1993

8. Dec. 2, 2008 Bangalore, India A Rising Flux Tube Deflection of rising tube by Coriolis effect  tilted pair of spots

9. Dec. 2, 2008 Bangalore, India Hale’s polarity law Joy’s law for tilt angles (D’Silva & Choudhuri 1993) p-f asymmetry (Fan et al. 1993) post-emergence velocities (Moreno-Insertis et al 1994) Statistical dispersion (Longcope & Fisher 1996) Thin flux tube successes: Moreno-Insertis et al. 1994 D’Silva & Choudhuri 1993

10. Dec. 2, 2008 Bangalore, India Flux Tube Twist Flux tubes must be twisted in order to rise (Parker 1979) untwisted twisted Moreno-Insertis & Emonet 1996 Abbett et al. 2000

11. Dec. 2, 2008 Bangalore, India (courtesy T. Magara & Hinode) (from Nakagawa et al. 1971)... and AR fields are twisted

12. Dec. 2, 2008 Bangalore, India Evidence that flux tubes emerge already twisted: Flux (  ) and current increase together (Leka et al. 1996 )   curr.

13. Dec. 2, 2008 Bangalore, India How twisted are the tubes? a best introduced by Pevtsov, Canfield & Metcalf (1995) calc B ^ (a) by extrapolating calc B ^ (a) by extrapolating B z w/ fixed value of a B z w/ fixed value of a vary a until B ^ (a) best vary a until B ^ (a) best matches observed B ^ matches observed B ^ i.e. minimize i.e. minimize

14. Dec. 2, 2008 Bangalore, India How twisted are the tubes? ~ 3 x 10 -9 m -1 ~ 3 x 10 -9 m -1 varies /w latitude varies /w latitude Da best ~ 10 -8 m -1 independent of latitude independent of latitude Linear trend removed (from Longcope, Fisher & Pevtsov 1998)

15. Dec. 2, 2008 Bangalore, India Twist in flux tubes Field lines twist about axis at a rate q(s,t) “=“ d q /ds Plasma spins about axis at rate w (s,t) “=“ d q /dt Axis of tube: BzBz J v s  v  =  r a  = 2q B  = qr B z Piddington 1978

16. Dec. 2, 2008 Bangalore, India Twist in flux tubes Axis of tube: BzBz J v s  Evolution of twist & spin (Longcope & Klapper 1997) k

17. Dec. 2, 2008 Bangalore, India Dynamics of twist Out-of-plane motion of axis  S( s ) indep. of q or w

18. Dec. 2, 2008 Bangalore, India Axis-twist coupling Increasing LH writhe (dWr/dt <0 )  Increasing RH twist (dTw/dt > 0)

19. Dec. 2, 2008 Bangalore, India Writhe from Turbulence: The S-effect (Longcope, Fisher & Pevtsov 1998) Twist source Averaging over turbulence: Spectrum of kinetic helicity Variance of twist source:

20. Dec. 2, 2008 Bangalore, India S-effect vs.  -effect Spectrum of kinetic helicity Compare to a -effect:

21. Dec. 2, 2008 Bangalore, India Cause of the observed twist Observed properties Observed properties  Twist in CZ flux tube  Twist in CZ flux tube  LH twist in North  LH twist in North  ~ 3 x 10 -9 m -1  ~ 3 x 10 -9 m -1  25% violation of trend  25% violation of trend  Da ~ 10 -8 m -1  Da ~ 10 -8 m -1  Da indep. of latitude  Da indep. of latitude Writhe from CZ turbu- lence: The S -effect Kinetic helicity: Kinetic helicity: RH writhe in North RH writhe in North ~ 3 x 10 -9 m -1 ~ 3 x 10 -9 m -1 Fluctuates (turbulence) Fluctuates (turbulence) Level indep. of latitude Level indep. of latitude Da ~ 10 -8 m -1 Da ~ 10 -8 m -1

22. Dec. 2, 2008 Bangalore, India Twist: Photosphere vs. Corona  best and  for 140 ARs  best and  for 140 ARs Found  best correlated with  Found  best correlated with  a best ~ a in coronal field Force-free-field w/ constant-  Pevtsov, Canfield & McClymont (1997)

23. Dec. 2, 2008 Bangalore, India Coupling flux tube to corona Low- b coronal Equilibrium: FFF High- b CZ Field: twisted Thin flux tube

24. Dec. 2, 2008 Bangalore, India Coupling flux tube to corona Balance of net torque Current matches across interface (Longcope & Weslch 1998) a  a =2q in corona in tube

25. Dec. 2, 2008 Bangalore, India Coupling flux tube to corona Imbalanced torque (shunted current)  spin shunt spinning

26. Dec. 2, 2008 Bangalore, India Brown et al. 2003 Flux tube twist  sunspot rotation Evershed 1910 1 deg/hr movie

27. Dec. 2, 2008 Bangalore, India Twist Creates Spin TRACE White Light channelTRACE 171A (1MK) (Courtesy D. Alexander) movie

28. Dec. 2, 2008 Bangalore, India Spin from Emergence Twist propagates Twist propagates into corona into corona simple model: Longcope & Welsch 1998

29. Dec. 2, 2008 Bangalore, India Spin from Emergence Twist propagates Twist propagates into corona into corona Twist-rarefaction Twist-rarefaction waves propagates waves propagates inward to CZ inward to CZ simple model: Longcope & Welsch 1998

30. Dec. 2, 2008 Bangalore, India Spin from Emergence Twist propagates Twist propagates into corona into corona Twist-rarefaction Twist-rarefaction waves propagates waves propagates inward to CZ inward to CZ Characteristic Characteristic time-scale for time-scale for adjustment: adjustment: d/v A ~ 1 day simple model: Longcope & Welsch 1998

31. Dec. 2, 2008 Bangalore, India Spin from Emergence Observation: Pevtsov, Maleev & Longcope 2003 Fit Model to Data v=264 m/s a = 2 10 -8 m -1 v A = 158 m/s

32. Dec. 2, 2008 Bangalore, India Spin from Emergence AR8582 AR8817 Observation: Pevtsov, Maleev & Longcope 2003

33. Dec. 2, 2008 Bangalore, India Measured Velocity (Chae 2001) = +3 X 10 40 Mx 2 /day = F 2 10 -2 /day B z measured: LOS mg U measured: LCT of B z U measured: LCT of B z A 0 extrapolated A 0 extrapolated

34. Dec. 2, 2008 Bangalore, India Measuring Spin partition m-gram v(x) from LCT cf WL rotation from Brown et al. 2003 Longcope, Ravindra & Barnes 2007

35. Dec. 2, 2008 Bangalore, India Measuring Spin spinbraiding 1 2 22  12

36. Dec. 2, 2008 Bangalore, India Measuring Spin Brown et al. 2003 all contributions to dH/dt P01

37. Dec. 2, 2008 Bangalore, India separation d(t) Longcope & Welsch model H br H sp H Helicity dominated by braiding Northern AR: H > 0 H sp < 0 fit: q = -0.67 x 10 -8 m -1

38. Dec. 2, 2008 Bangalore, India separation d(t) Longcope & Welsch model H br H sp H Helicity dominated by spin Southern AR: H > 0 H sp > 0 fit: q = +2.3 x 10 -8 m -1

39. Dec. 2, 2008 Bangalore, India Helicity Injection

40. Dec. 2, 2008 Bangalore, India Long term helicity injection AR  t (hrs )  H/  2 (10 -2 day -1 ) ref 8011400.0030.18 Chae (2001) 81001200.020.4 Kusano et al. (2002) 8668500.031.4 Chae et al. (2001) 9165800.26.0 Nindos & Zhang (2002) 103651200.051.0 Chae, Moon & Park (2004) 106961320.020.4 Lim et al. (2007) (from van Driel-Gesztelyi, Demoulin & Mandrini, 2003)

41. Dec. 2, 2008 Bangalore, India Helicity Flux in ARs Differential rotation: –Th. (DeVore 2000):  ~ 3 X 10 -3 /day –Obs. (Demoulin et al 2002)  ~ 3 X 10 -4 Proper motions: (observations) –LCT (van Driel-Gesztelyi et al. 2003)  ~ 10 -2 – Sunspot rotation (Brown et al 2003)  ~ 10 -1

42. Dec. 2, 2008 Bangalore, India Summary ARs created by emergence of flux tubes Tubes consist of twisted flux -- twisted by turbulence during rising (  -effect) Helicity of twist propagates into corona Observed proper motions (rotating sunspots) consistent with twist propagation