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Turbulence simulations showing mean-field dynamos

Turbulence simulations showing mean-field dynamos. Solar paradigm shifts Helicity fluxes Low magnetic Prandtl numbers Mean field coefficients from simulations Axel Brandenburg ( Nordita, Stockholm ). The 4 solar dynamo scenarios. Distributed dynamo (Roberts & Stix 1972)

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Turbulence simulations showing mean-field dynamos

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  1. Turbulence simulations showing mean-field dynamos Solar paradigm shifts Helicity fluxes Low magnetic Prandtl numbers Mean field coefficients from simulations Axel Brandenburg (Nordita, Stockholm)

  2. The 4 solar dynamo scenarios • Distributed dynamo (Roberts & Stix 1972) • Positive alpha, negative shear • Overshoot dynamo (e.g. DeLuca & Gilman 1986) • Negative alpha, positive shear • Interface dynamo (Parker 1993) • 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

  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) 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)

  6. 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!

  7. (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?

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

  9. Upcoming dynamo effort in Stockholm Soon hiring: • 4 students • 3 post-docs • 1 assistant professor • Long-term visitors

  10. Connection with a effect: writhe with internal twist as by-product a effect produces helical field W clockwise tilt (right handed)  left handed internal twist both for thermal/magnetic buoyancy

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

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

  13. 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 Tobias et al. (2008, ApJ) Kapyla et al. (2008, A&A)

  14. Low PrM dynamos Sun PrM=n/h=10-5 Schekochihin et al (2005) Here: non-helically forced turbulence k Helical turbulence

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

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

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

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

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

  20. Earlier results on ht quenching Yousef et al. (2003, A&A)

  21. 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

  22. Conclusion • 11 yr cycle • Dyamo (SS vs LS) • Problems • a-quenching • slow saturation • Solution • Modern a-effect theory • j.b contribution • Magnetic helicity fluxes • Location of dynamo • Distrubtion, shaped by • near-surface shear 1046 Mx2/cycle

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