1. Knots and Bolts of Solar Helicity Dr. Alexei A. Pevtsov “If You are after good publicity, You should not speak about current helicity” – Jan Stenflo

2. Outline Definition of helicity (incl. graphic repr.) Hemispheric helicity rule (observations, origin, cycle variation) Helicity transport Fitting pieces of puzzle together???

3. Knots and Bolts H = 0

4. Knots and Bolts H = 0H= -1

5. Writhe and Twist H = W+T W = -1; T=0 T = -1; W=0

6. Helicities A – vector potential, B – magnetic induction. For liner force-free field (  constant) where  is arbitrary scalar function, where E is magnetic energy -topological invariant -conserves better than energy (Woltjer, 1958; Taylor 1974; Ji et al, 1995) -dynamo, reconnection, stability energy decay – 4-10.5% helicity dissipation – 1.3-5.1% Magnetic Helicity  Current Helicity  Kinetic Helicity 

7. What We Observe Observations: Force-free field (1) : Current helicity density (2) : WL, H-alpha, X-ray Morphology: Abramenko et al, 1996 Bao and Zhang, 1998 Pevtsov et al, 1995, Longcope et al, 1998

8. What We Observe Relative helicity: (e.g. Chae, 2001) (Berger, 1985) Also see Manolis presentation later

9. 466 active regions observed 1988-2000 by Haleakala Stokes Polarimeter  = -0.23, Likelihood of no correlation is 2.5x10 -7 N/(-) S/(+) 69% 75% (cycle 22, Pevtsov et al, 1995) 63% 70% (cycle 23, Pevtsov et al, 2001) Seehafer, 1990 Pevtsov et al, 1995, Abramenko et al, 1996 Longcope et al, 1998, Bao and Zhang, 1998, Pevtsov et al. 2001, Hagino and Sakurai, 2002 60-80%, hemispheric helicity rule

11. Cycle variation? Pevtsov et al 2001 Bao et al, 1999, reverse sign for hc at the beginning Cycle 23 Hagino & Sakurai, 2002, some periods disobey the rule Nandi & Choudhuri 2004 – cycle variation of helicity rule  Lat  best 

13. Zhang, 2006

14. ObservationsRad/MmRef. AR~0.01Pevtsov et al 1995 substructures~0.2Pevtsov etal 1994, Leka et al, 1996 Sources of Twist Joy’s Law0.001Longcope & Klapper 1997 Diff’l rotation0.002Longcope et al 1999  - effect ~0.02Longcope et al 1998 Created in dynamo4 x 10 -5 Charbonneau & Gilman 1998 Holder et al, 2003; Tian et al., 2001 Chae 2001, Green et al 2003 Demoulin et al 2003 – direct action of Coriolis force and differential rotation produce insufficient amount of helicity and cannot explain significant scatter in latitudinal dependency – dynamo does not produce enough helicity.  -effect can do it all? Seehafer et al, 2003 Longcope et al, 1999

15. Nandy, 2006  ~  -0.69 Scatter is latitude-independent Trend, scatter agree with  -effect

16. Helicity Transport For liner force-free field (  constant)where  is arbitrary scalar function Lepping et al (1990) fitted 18 MCs,  =10 -10 m -1, B 0 =0.0002 G,  =10 21 Mx. H MC =(L  /2  )  2 = 5 x 10 42 Mx 2 Larson et al (1995), H MC = 4 x 10 42 Mx 2 Demoulin et al, 2002, AR7978 52 x 10 42 Mx 2 (26 CMEs, 1 rotation) 5 rotations - ? Total helicity ejected by MCs often exceeds coronal helicity (diff. rotation cannot replenish).

17. Helicity Transport via Reconnection Independent flux systems: H m = H 1 + H 2 + H 3 ; e.g. H 1 =0.5H crit ; H 2 =0.4H crit ; H 3 =0.2H crit H m >H crit Canfield & Reardon, 1998 Pevtsov et al 1996

18. Twist in Emerging Flux Tube Longcope and Welsch, 2000: - vortical motions responsible for helicity injection cannot be driven by pressure gradient and cannot be produced by coupling motions of non-mag. plasma -magnetic torque at photosphere-corona transition cannot be countered by pressure gradients.

19. Evolution of ARs and their Helicity - MDI full disk magnetograms -SoHO EIT 195A images - 6 emerging active regions Maleev et al, 2002

20. Modeling Flux Emergence - no twist at emergence - emergence – linear increase in d - d increases in constant rate until t 1

21. Fitted Model Parameters NOAAalpha ramp-up (days) d days Flux (10 20 Mx) Helicity 10 41 Mx 2 d 0 Mm V A m sec -1 85821.731.20304.026.9371 8738…1.79………… 87680.931.80131.325.06182 88171.001.20170.926.7984 91390.801.664412.712.24158 91930.871.8020.123.4560

22. Sunspot Rotation -Kempf, P., Astron. Nachrichten, 1910, Nr. 4429, Bd. 195, 197 -Brown, et al, Solar Phys., 2003, 216, 79 -Pevtsov, A. A. and Sattarov, I.S., Soln. Dannye, 1985, No. 3, 65. Courtesy R. Nightingale

23. Sunspot Rotation (R. Nightingale data) CCWCWBi-direct N31% (70%) 13% (30%) 16% S15% (46%) 17% (54%) 14% * Correct sign of twist; “hemispheric preference” is in agreement with the hemispheric helicity rule * No good correlation between sign of current helicity and direction of rotation

24. Courtesy R. Nightingale

26. Kinetic Helicity and flares See poster by F. Hill et al

27. How These All Might Fit Together? Helicity is created in upper CZN (  -effect explains large scatter and helicity amplitude; solar cycle variations???). Helicity is removed from AR as a result of eruption. Subphotospheric portion of flux tube may serve as “reservoir” of helicity, supplying helicity between flares/CMEs. Sunspot rotation and subphotospheric pattern of kinetic helicity may be indications of helicity transport via torsional waves.

28. Open Questions Evolution of kinetic helicity (before/after flare/flux emergence). Timing of sunspot rotation vs. flare Is helicity of active region determined at their emergence, or maybe, significant amount of helicity can be injected later during AR lifetime?

29. Backup Slides

30. -Overshoot region (DeLuca & Gilman 1991) -Mean-field dynamo (Krause & Radler 1980) -Surface dynamo (Emonet & Cattaneo 2001) Helical Chaotic (turbulent) -Helical dynamo should result in hemispheric preference for sign of helicity -Chaotic (turbulent) dynamo should show no hemispheric sign-preference for helicity. Tornado: Hurricanes:

31. * Sign of vorticity tends to be random in intergranular spaces * In some cases, vorticity reverse sign.

32. N40W00 ASP - Dependence of scatter on latitude In agreement with recent modeling by Abbet, et al

33. Some conclusions Solar magnetic fields exhibit hemispheric sign asymmetry. Presence of solar cycle variations in the hemispheric helicity rule is not clear. Helicity of strong (sunspots) magnetic fields is generated in mid-upper convection zone via  - effect Helicity is constantly transported to the corona via torsional motions and reconnection.

34. Filaments chirality before CRN1970 Filaments chirality after CRN1970 Polar Field Martin et al, 1994 Pevtsov et al, 2003 (82/86%, N/S) Bernasconi et al, 2005 (70/66%)