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)
Boulder, 14 August 2008

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 >  dynamo dilema, flux transport dynamos
1992: catastrophic a-quenching a~Rm (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)
Yoshimura (1975)
Thompson et al. (2003)

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)
Talk given at Thinkshop in May 2002
 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
Negative current helicity:
net production in northern hemisphere
1046 Mx2/cycle

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?
Käpylä et al. (2008, A&A)
Tobias et al. (2008, ApJ)

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 dynamos with 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 Use S<0, so need negative h*21 for dynamo
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 >  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