The solar dynamo Axel Brandenburg

2 Importance of solar activity

3 Solar 11 year sunspot cycle Sunspots between +/- 30 degrees around equator New cycle begins at high latitude Ends at low latitudes –equatorward migration butterfly diagram

4 Sunspots

5 Sunspots

6 Large scale coherence Active regions, bi-polarity systematic east-west orientation opposite in the south

7 22 year magnetic cycle Longitudinally averaged radial field Spatio-temporal coherence –22 yr cycle, equatorward migration Poleward branch or poleward drift? butterfly diagram

8  -effect dynamos (large scale) Differential rotation (faster inside) Cyclonic convection; Buoyant flux tubes Equatorward migration New loop    - effect

9 The Sun today and 9 years ago Solar magnetograms: Line of sight B-field from circularly polarized light

10 Sunspot predictions

11 Grand minima/maxima?

12 Cycic Maunder mininum: 10 Be record

13 Long time scales: different oscillators instead of chaos? Saar & Brandenburg (1999, ApJ 524, 295)

14 News from the 5 min oscillations Discovered in 1960 (Leighton et al. 1962) Was thought to be response of upper atmosphere to convection

15 Solar granulation Horizontal size L=1 Mm, sound speed 6 km/s Correlation time 5 min = sound travel time

16 Degree l, order m

17 5 min osc are global Roger Ulrich (1970) Franz-Ludwig Deubner (1974)

18 GONG global oscillation network group Since late 1980ties

19 Current state of the art SOHO Space craft 1993 – now lost in 1998

20 Only p-modes observed

21 g-modes Would probe the center Are evanescent in the convection zone

22 Refraction Reflection Top: reflection when wavenlength ~ density scale height Deeper down: Sound speed large

23 Inversion: input/output Duval lawSound speed

24 Internal angular velocity

25 Internal angular velocity from helioseismology spoke-like at equ. d  /dr>0 at bottom ? d  /dr<0 at top

26 Cycle dependence of  (r,  )

27 In the days before helioseismology Angular velocity (at 4 o 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 d  /dr<0: equatorward migr

28 Activity from the dynamo

29 Buoyant rise of flux tubes

30 A long path toward the overshoot dynamo scenario Since 1980: dynamo at bottom of CZ –Flux tube’s buoyancy neutralized –Slow motions, long time scales Since 1984: diff rot spoke-like –d  /dr strongest at bottom of CZ Since 1991: field must be 100 kG –To get the tilt angle right Spiegel & Weiss (1980) Golub, Rosner, Vaiana, & Weiss (1981)

31 The 4 dynamo scenarios Distributed dynamo (Roberts & Stix 1972) –Positive alpha, negative shear Overshoot dynamo (e.g. Rüdiger & Brandenburg 1995) –Negative alpha, positive shear Interface dynamo (Markiel & Thomas 1999) –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

32 Paradigm shifts i)1980: magnetic buoyancy (Spiegel & Weiss)  overshoot layer dynamos ii)1985: helioseismology: d W /dr > 0  dynamo dilema, flux transport dynamos iii)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) Before helioseismology Angular velocity (at 4 o 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 d  /dr<0: equatorward migr Yoshimura (1975) Thompson et al. (1975) Brandenburg et al. (1992)

35 Near-surface shear layer: spots rooted at r/R=0.95? Benevolenskaya, Hoeksema, Kosovichev, Scherrer (1999) Pulkkinen & Tuominen (1998)  =  AZ  =(180/  ) (1.5x10 7 ) (2  ) =360 x 0.15 = 54 degrees!

36 (iii) Problems with mean-field theory? Catastrophic quenching? –  ~ R m -1,  t ~ R m -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?

37 Revisit paradigm shifts i)1980: magnetic buoyancy  counteracted by pumping ii)1985: helioseismology: d W /dr > 0  negative gradient in near-surface shear layer iii)1992: catastrophic a -quenching  overcome by helicity fluxes  in the Sun: by coronal mass ejections

38 Arguments against and in favor? Flux storage Distortions weak Problems solved with meridional circulation Size of active regions Neg surface shear: equatorward migr. Max radial shear in low latitudes Youngest sunspots: 473 nHz Correct phase relation Strong pumping (Thomas et al.) 100 kG hard to explain Tube integrity Single circulation cell Too many flux belts* Max shear at poles* Phase relation* 1.3 yr instead of 11 yr at bot Rapid buoyant loss* Strong distortions* (Hale’s polarity) Long term stability of active regions* No anisotropy of supergranulation in favor against Tachocline dynamosDistributed/near-surface dynamo Brandenburg (2005, ApJ 625, 539)

39 Application to the sun: spots rooted at r/R=0.95 Benevolenskaya, Hoeksema, Kosovichev, Scherrer (1999) – –Overshoot dynamo cannot catch up  =  AZ  =(180/  ) (1.5x10 7 ) (2  ) =360 x 0.15 = 54 degrees!

40 Simulating solar-like differential rotation Still helically forced turbulence Shear driven by a friction term Normal field boundary condition

41 Simulating solar-like differential rotation Still helically forced turbulence Shear driven by a friction term Normal field boundary condition

42 Cartesian box MHD equations Induction Equation: Magn. Vector potential Momentum and Continuity eqns Viscous force forcing function (eigenfunction of curl)

43 Tendency away from filamentary field Cross-sections at different times Mean field

44 Current helicity and magn. hel. flux Bao & Zhang (1998), neg. in north, plus in south (also Seehafer 1990) Berger & Ruzmaikin (2000) S N DeVore (2000) (for BR & CME)

45 Magnetic Helicity J. Chae (2000, ApJ)

46 Helicity fluxes at large and small scales Negative current helicity: net production in northern hemisphere Mx 2 /cycle Brandenburg & Sandin (2004, A&A 427, 13) Helicity fluxes from shear: Vishniac & Cho (2001, ApJ 550, 752) Subramanian & Brandenburg (2004, PRL 93, 20500)

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

48 Origin of sunspot Theories for shallow spots: (i) Collapse by suppression of turbulent heat flux (ii) Negative pressure effects from - vs B i B j

49 clockwise tilt (right handed)  left handed internal twist Build-up & release of magnetic twist New hirings: 4 PhD students4 PhD students 4 post-docs (2yr)4 post-docs (2yr) 1 assistant professor1 assistant professor 2 Long-term visitors2 Long-term visitors Upcoming work: Global modelsGlobal models Helicity transportHelicity transport coronal mass ejectionscoronal mass ejections Cycle forecastsCycle forecasts Coronal mass ejections