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

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

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

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

(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!

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)

(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?

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

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

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

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!

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

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

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)

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

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)

Low PrM dynamos with helicity do work Energy dissipation via Joule Viscous dissipation weak Can increase Re substantially!

a and wcyc in quenched state

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

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

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

Time-dependent case

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

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

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

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

Dependence on Sh and Rm

Direct simulations

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

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

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