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

Axel Brandenburg (Nordita, Stockholm)

Solar dynamos in the 1970sDistributed dynamo (Roberts & Stix 1972)Positive alpha, negative shearWell-defined profiles from mixing length theoryYoshimura (1975)

Paradigm shifts1980: magnetic buoyancy (Spiegel & Weiss) overshoot layer dynamos1985: helioseismology: dW/dr > 0 dynamo dilema, flux transport dynamos1992: catastrophic a-quenching a~Rm-1 (Vainshtein & Cattaneo) Parkers interface dynamo Backcock-Leighton mechanism

(i) Is magnetic buoyancy a problem?Stratified dynamo simulation in 1990Expected strong buoyancy losses,but no: downward pumpingTobias 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 helioseismologyAngular velocity (at 4o latitude): very young spots: 473 nHzoldest spots: 462 nHzSurface plasma: 452 nHzConclusion back then:Sun spins faster in deaper convection zoneSolar dynamo works with dW/dr

(iii) Quenching in mean-field theory?Catastrophic quenching?? a ~ Rm-1, ht ~ Rm-1Field strength vanishingly small!?!Something wrong with simulationsso lets ignore the problemPossible reasons:Suppression of lagrangian chaos?Suffocation from small-scale magnetic helicity?

Simulations showing large-scale fieldsHelical turbulence (By)Helical shear flow turb.Convection with shearMagneto-rotational Inst.Kpyl et al (2008)

Upcoming dynamo effort in StockholmSoon hiring:4 students4 post-docs (2 now)1 assistant professorLong-term visitors

Built-in feedback in Parker loopboth for thermal/magnetic buoyancya effect produceshelical fieldclockwise tilt(right handed) left handedinternal twist

Interpretations and predictionsIn closed domain: resistively slow saturationOpen domain w/o shear: low saturation Due to loss of LS fieldWould need loss of SS fieldOpen domain with shearHelicity 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 fluxesgeometryhere relevantto the sunNegative current helicity:net production in northern hemisphere 1046 Mx2/cycle

Best if W contours ^ to surfaceExample: convection with shearKpyl et al. (2008, A&A)Tobias et al. (2008, ApJ) need small-scale helicalexhaust out of the domain,not back in on the other sideMagneticBuoyancy?

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

Lack of LS dynamos in some casesLS dynamo must be excited

SS dynamo too dominant, swamps LS fieldDominant SS dynamo: artifact of large PrM=n/hBrun, Miesch, & Toomre(2004, ApJ 614, 1073)

Low PrM dynamoswith 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 tensorsResponse to arbitrary mean fields Example:Calculate

Kinematic a and ht independent of Rm (2200)Sur et al. (2008, MNRAS)

Time-dependent case

From linear to nonlinearMean and fluctuating U enter separatelyUse vector potential

Nonlinear aij and hij tensorsConsistency check: consider steady state to avoid da/dt termsExpect:l=0 (within error bars) consistency check!

Application to passive vector eqnVerified by test-field methodTilgner & Brandenburg (2008)

Shear turbulenceGrowth rateUse S

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 shifts1980: magnetic buoyancy counteracted by pumping1985: helioseismology: dW/dr > 0 negative gradient in near-surface shear layer1992: catastrophic a-quenching overcome by helicity fluxes in the Sun: by coronal mass ejections

The FutureModels in global geometryRealistic boundaries: allowing for CMEs magnetic helicity lossesSunspot formationLocal conctrationsTurbulent flux collapseNegative turbulent mag presureLocation of dynamoNear surface shear layerTachocline1046 Mx2/cycle

Boulder, 14 August 2008Talk given at Thinkshop in May 2002