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Paradigm shifts in solar dynamo modelling

Paradigm shifts in solar dynamo modelling. Magn. buoyancy, radial diff rot, & quenching  dynamo at the bottom of CZ Simulations: strong downward pumping Radial diff rot negative near surface! Quenching alleviated by shear-mediated helicity fluxes

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Paradigm shifts in solar dynamo modelling

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  1. Paradigm shifts in solar dynamo modelling Magn. buoyancy, radial diff rot, & quenching  dynamo at the bottom of CZ Simulations: strong downward pumping Radial diff rot negative near surface! Quenching alleviated by shear-mediated helicity fluxes Axel Brandenburg (Nordita, Stockholm)

  2. Solar dynamos in the 1970s • Distributed dynamo (Roberts & Stix 1972) • Positive alpha, negative shear • Well-defined profiles from mixing length theory Yoshimura (1975)

  3. 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

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

  5. (ii) Positive or negative radial shear? Benevolenskaya, Hoeksema, Kosovichev, Scherrer (1999) Pulkkinen & Tuominen (1998) • Df=tAZDW=(180/p) (1.5x107) (2p 10-8) • =360 x 0.15 = 54 degrees!

  6. 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. (2003) Yoshimura (1975)

  7. (iii) Quenching in 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?

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

  9. Upcoming dynamo effort in Stockholm Soon hiring: • 4 students • 4 post-docs (2 now) • 1 assistant professor • Long-term visitors

  10. Built-in feedback in Parker loop a effect produces helical field clockwise tilt (right handed)  left handed internal twist both for thermal/magnetic buoyancy

  11. Interpretations and predictions • In closed domain: resistively slow saturation • Open domain w/o shear: low saturation • Due to loss of LS field • Would need loss of SS field • Open domain with shear • Helicity is driven out of domain (Vishniac & Cho) • Mean flow contours perpendicular to surface!

  12. Nonlinear stage: consistent with … Brandenburg (2005, ApJ)

  13. Forced large scale dynamo with fluxes geometry here relevant to the sun 1046 Mx2/cycle Negative current helicity: net production in northern hemisphere

  14. Best if W contours ^ to surface Example: convection with shear  need small-scale helical exhaust out of the domain, not back in on the other side Magnetic Buoyancy? Tobias et al. (2008, ApJ) Käpylä et al. (2008, A&A)

  15. To prove the point: convection with vertical shear and open b.c.s Magnetic helicity flux Käpylä et al. (2008, A&A 491, 353) Effects of b.c.s only in nonlinear regime

  16. Lack of LS dynamos in some cases • LS dynamo must be excited • SS dynamo too dominant, swamps LS field • Dominant SS dynamo: artifact of large PrM=n/h Brun, Miesch, & Toomre (2004, ApJ 614, 1073)

  17. Low PrM dynamoswith helicity do work • Energy dissipation via Joule • Viscous dissipation weak • Can increase Re substantially!

  18. a and wcyc in quenched state

  19. ht(Rm) dependence for B~Beq • l is small  consistency • a1 and a2 tend to cancel • to decrease a • h2 is small

  20. Calculate full aij and hij tensors Response to arbitrary mean fields Calculate Example:

  21. Kinematic a and ht independent of Rm (2…200) Sur et al. (2008, MNRAS)

  22. Time-dependent case

  23. From linear to nonlinear Use vector potential Mean and fluctuating U enter separately

  24. Nonlinear aij and hij tensors Consistency check: consider steady state to avoid da/dt terms Expect: l=0 (within error bars)  consistency check!

  25. Application to passive vector eqn Verified by test-field method Tilgner & Brandenburg (2008)

  26. Shear turbulence Growth rate Use S<0, so need negative h*21 for dynamo

  27. Dependence on Sh and Rm

  28. Direct simulations

  29. Fluctuations of aij and hij Incoherent a effect (Vishniac & Brandenburg 1997, Sokoloff 1997, Silantev 2000, Proctor 2007)

  30. 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

  31. The Future • Models in global geometry • Realistic boundaries: • allowing for CMEs • magnetic helicity losses • Sunspot formation • Local conctrations • Turbulent flux collapse • Negative turbulent mag presure • Location of dynamo • Near surface shear layer • Tachocline 1046 Mx2/cycle

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