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The solar dynamo

The solar dynamo. Axel Brandenburg. Importance of solar activity. Solar 11 year sunspot cycle. Sunspots between +/- 30 degrees around equator New cycle begins at high latitude Ends at low latitudes equatorward migration. butterfly diagram. Sunspots. Sunspots. Large scale coherence.

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The solar dynamo

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  1. The solar dynamo Axel Brandenburg

  2. Importance of solar activity

  3. Solar 11 year sunspot cycle • Sunspots between +/- 30 degrees around equator • New cycle begins at high latitude • Ends at low latitudes • equatorward migration butterfly diagram

  4. Sunspots

  5. Sunspots

  6. Large scale coherence Active regions, bi-polarity systematic east-west orientation opposite in the south

  7. 22 year magnetic cycle • Longitudinally averaged radial field • Spatio-temporal coherence • 22 yr cycle, equatorward migration butterfly diagram Poleward branch or poleward drift?

  8. a-effect dynamos (large scale) New loop Differential rotation (faster inside) Cyclonic convection; Buoyant flux tubes Equatorward migration  a-effect

  9. The Sun today and 9 years ago Solar magnetograms: Line of sight B-field from circularly polarized light

  10. Sunspot predictions

  11. Grand minima/maxima?

  12. Cycic Maunder mininum: 10Be record

  13. Long time scales: different oscillators instead of chaos? Saar & Brandenburg (1999, ApJ 524, 295)

  14. News from the 5 min oscillations Discovered in 1960 (Leighton et al. 1962) Was thought to be response of upper atmosphere to convection

  15. Solar granulation Horizontal size L=1 Mm, sound speed 6 km/s Correlation time 5 min = sound travel time

  16. Degree l, order m

  17. 5 min osc are global Franz-Ludwig Deubner (1974) Roger Ulrich (1970)

  18. GONGglobal oscillation network group Since late 1980ties

  19. Current state of the art SOHO Space craft 1993 – now lost in 1998

  20. Only p-modes observed

  21. g-modes • Would probe the center • Are evanescent in the convection zone

  22. RefractionReflection Top: reflection when wavenlength ~ density scale height Deeper down: Sound speed large

  23. Inversion: input/output Duval law Sound speed

  24. Internal angular velocity

  25. Internal angular velocityfrom helioseismology spoke-like at equ. dW/dr>0 at bottom ? dW/dr<0 at top

  26. Cycle dependenceof W(r,q)

  27. In the days before helioseismology • Angular velocity (at 4o latitude): • very young spots: 473 nHz • oldest spots: 462 nHz • Surface plasma: 452 nHz • Conclusion back then: • Sun spins faster in deaper convection zone • Solar dynamo works with dW/dr<0: equatorward migr

  28. Activity from the dynamo

  29. Buoyant rise of flux tubes

  30. A long path toward the overshoot dynamo scenario • Since 1980: dynamo at bottom of CZ • Flux tube’s buoyancy neutralized • Slow motions, long time scales • Since 1984: diff rot spoke-like • dW/dr strongest at bottom of CZ • Since 1991: field must be 100 kG • To get the tilt angle right Spiegel & Weiss (1980) Golub, Rosner, Vaiana, & Weiss (1981)

  31. The 4 dynamo scenarios • Distributed dynamo (Roberts & Stix 1972) • Positive alpha, negative shear • Overshoot dynamo (e.g. Rüdiger & Brandenburg 1995) • Negative alpha, positive shear • Interface dynamo (Markiel & Thomas 1999) • Negative alpha in CZ, positive radial shear beneath • Low magnetic diffusivity beneath CZ • Flux transport dynamo (Dikpati & Charbonneau 1999) • Positive alpha, positive shear • Migration from meridional circulation

  32. Paradigm shifts • 1980: magnetic buoyancy (Spiegel & Weiss) overshoot layer dynamos • 1985: helioseismology: dW/dr > 0  dynamo dilema, flux transport dynamos • 1992: catastrophic a-quenching a~Rm-1(Vainshtein & Cattaneo) Parker’s interface dynamo  Backcock-Leighton mechanism

  33. (i) Is magnetic buoyancy a problem? Stratified dynamo simulation in 1990 Expected strong buoyancy losses, but no: downward pumping Tobias et al. (2001)

  34. (ii) Before helioseismology • Angular velocity (at 4o latitude): • very young spots: 473 nHz • oldest spots: 462 nHz • Surface plasma: 452 nHz • Conclusion back then: • Sun spins faster in deaper convection zone • Solar dynamo works with dW/dr<0: equatorward migr Brandenburg et al. (1992) Thompson et al. (1975) Yoshimura (1975)

  35. Near-surface shear layer:spots rooted at r/R=0.95? Benevolenskaya, Hoeksema, Kosovichev, Scherrer (1999) Pulkkinen & Tuominen (1998) • Df=tAZDW=(180/p) (1.5x107) (2p 10-8) • =360 x 0.15 = 54 degrees!

  36. (iii) Problems with mean-field theory? • Catastrophic quenching? • a ~ Rm-1, ht ~ Rm-1 • Field strength vanishingly small? • Something wrong with simulations • so let’s ignore the problem • Possible reasons: • Suppression of lagrangian chaos? • Suffocation from small scale magnetic helicity?

  37. Revisit paradigm shifts • 1980: magnetic buoyancy  counteracted by pumping • 1985: helioseismology: dW/dr > 0  negative gradient in near-surface shear layer • 1992: catastrophic a-quenching  overcome by helicity fluxes  in the Sun: by coronal mass ejections

  38. Flux storage Distortions weak Problems solved with meridional circulation Size of active regions Neg surface shear: equatorward migr. Max radial shear in low latitudes Youngest sunspots: 473 nHz Correct phase relation Strong pumping (Thomas et al.) Arguments against and in favor? Tachocline dynamos Distributed/near-surface dynamo in favor against • 100 kG hard to explain • Tube integrity • Single circulation cell • Too many flux belts* • Max shear at poles* • Phase relation* • 1.3 yr instead of 11 yr at bot • Rapid buoyant loss* • Strong distortions* (Hale’s polarity) • Long term stability of active regions* • No anisotropy of supergranulation Brandenburg (2005, ApJ 625, 539)

  39. Application to the sun:spots rooted at r/R=0.95 Benevolenskaya, Hoeksema, Kosovichev, Scherrer (1999) • Overshoot dynamo cannot catch up • Df=tAZDW=(180/p) (1.5x107) (2p 10-8) • =360 x 0.15 = 54 degrees!

  40. Simulating solar-like differential rotation • Still helically forced turbulence • Shear driven by a friction term • Normal field boundary condition

  41. Simulating solar-like differential rotation • Still helically forced turbulence • Shear driven by a friction term • Normal field boundary condition

  42. Cartesian box MHD equations Magn. Vector potential Induction Equation: Momentum and Continuity eqns Viscous force forcing function (eigenfunction of curl)

  43. Tendency away from filamentary field Cross-sections at different times Mean field

  44. Current helicity and magn. hel. flux Bao & Zhang (1998), neg. in north, plus in south (also Seehafer 1990) Berger & Ruzmaikin (2000) S DeVore (2000) N (for BR & CME)

  45. Magnetic Helicity + J. Chae (2000, ApJ) + - -

  46. Helicity fluxes at large and small scales Negative current helicity: net production in northern hemisphere 1046 Mx2/cycle Brandenburg & Sandin (2004, A&A 427, 13) Helicity fluxes from shear: Vishniac & Cho (2001, ApJ 550, 752) Subramanian & Brandenburg (2004, PRL 93, 20500)

  47. Simulations showing large-scale fields Helical turbulence (By) Helical shear flow turb. Convection with shear Magneto-rotational Inst. Käpyla et al (2008)

  48. Origin of sunspot Theories for shallow spots: (i) Collapse by suppression of turbulent heat flux (ii) Negative pressure effects from <bibj>-<uiuj> vs BiBj

  49. Build-up & release of magnetic twist Coronal mass ejections clockwise tilt (right handed)  left handed internal twist Upcoming work: • Global models • Helicity transport • coronal mass ejections • Cycle forecasts New hirings: • 4 PhD students • 4 post-docs (2yr) • 1 assistant professor • 2 Long-term visitors

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