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Advancements in Solar Dynamo Modelling: Paradigm Shifts & Future Trends

Explore paradigm shifts in solar dynamo modelling from the 1970s to present, discussing magnetic buoyancy, radial diffusion rotation, and quenching effects, emphasizing recent simulations and upcoming research efforts. Discover the implications of axial magnetic fields, radial shear, and the quenching phenomena, as well as the importance of magnetic helicity fluxes and shear-mediated mechanisms. Gain insights into the complexities of solar dynamics and the challenges faced in current modelling approaches, guiding future research directions.

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Advancements in Solar Dynamo Modelling: Paradigm Shifts & Future Trends

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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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