The solar dynamo

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The solar dynamo

• Axel Brandenburg

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Importance of solar activity
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Solar 11 year sunspot cycle
butterfly diagram

• Sunspots between /- 30 degrees around equator
• New cycle begins at high latitude
• Ends at low latitudes
• equatorward migration

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Sunspots
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Sunspots
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Large scale coherence
Active regions, bi-polarity systematic east-west
orientation opposite in the south
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22 year magnetic cycle

• Longitudinally averaged radial field
• Spatio-temporal coherence
• 22 yr cycle, equatorward migration

butterfly diagram
Poleward branch or poleward drift?
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a-effect dynamos (large scale)
New loop
Differential rotation (faster inside)
Cyclonic convection Buoyant flux tubes
Equatorward migration
? a-effect
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The Sun today and 9 years ago
Solar magnetograms Line of sight B-field
from circularly polarized light
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Sunspot predictions
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Grand minima/maxima?
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Cycic Maunder mininum 10Be record
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Long time scales different oscillators instead
of chaos?
Saar Brandenburg (1999, ApJ 524, 295)
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News from the 5 min oscillations
Discovered in 1960 (Leighton et al. 1962)
Was thought to be response of upper atmosphere to
convection
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Solar granulation

• Horizontal size L1 Mm, sound speed 6 km/s
• Correlation time 5 min sound travel time

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Degree l, order m
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5 min osc are global
Franz-Ludwig Deubner (1974)
Roger Ulrich (1970)
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GONGglobal oscillation network group
Since late 1980ties
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Current state of the art
SOHO Space craft 1993 now lost in 1998
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Only p-modes observed
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g-modes

• Would probe the center
• Are evanescent in the convection zone

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RefractionReflection
Top reflection when wavenlength density scale
height
Deeper down Sound speed large
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Inversion input/output
Duval law
Sound speed
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Internal angular velocity
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Internal angular velocityfrom helioseismology
spoke-like at equ. dW/drgt0 at bottom ? dW/drlt0
at top
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Cycle dependenceof W(r,q)
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In the days 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/drlt0 equatorward migr

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Activity from the dynamo
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Buoyant rise of flux tubes
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A long path toward the overshoot dynamo scenario

• Since 1980 dynamo at bottom of CZ
• Flux tubes buoyancy neutralized
• Slow motions, long time scales
• Since 1984 diff rot spoke-like
• dW/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)
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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

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Paradigm shifts

1. 1980 magnetic buoyancy (Spiegel Weiss) ?
   overshoot layer dynamos
2. 1985 helioseismology dW/dr gt 0 ?
   dynamo dilema, flux transport dynamos
3. 1992 catastrophic a-quenching aRm-1
   (Vainshtein Cattaneo)
   ? Parkers interface dynamo
   ? Backcock-Leighton mechanism

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(i) Is magnetic buoyancy a problem?
Stratified dynamo simulation in 1990 Expected
strong buoyancy losses, but no downward pumping
Tobias et al. (2001)
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(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/drlt0 equatorward migr

Brandenburg et al. (1992)
Thompson et al. (1975)
Yoshimura (1975)
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Near-surface shear layerspots rooted at
r/R0.95?
Benevolenskaya, Hoeksema, Kosovichev, Scherrer
(1999)
Pulkkinen Tuominen (1998)
DftAZDW(180/p) (1.5x107) (2p 10-8)
360 x 0.15 54 degrees!
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(iii) Problems with mean-field theory?

• Catastrophic quenching?
• a Rm-1, ht Rm-1
• Field strength vanishingly small?
• Something wrong with simulations
• so lets ignore the problem
• Possible reasons
• Suppression of lagrangian chaos?
• Suffocation from small scale magnetic helicity?

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Revisit paradigm shifts

1. 1980 magnetic buoyancy
   ? counteracted by pumping
2. 1985 helioseismology dW/dr gt 0 ?
   negative gradient in near-surface shear layer
3. 1992 catastrophic a-quenching ?
   overcome by helicity fluxes
   ? in the Sun by coronal mass ejections

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Arguments against and in favor?
Tachocline dynamos
Distributed/near-surface dynamo

• 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.)

in favor
against

• 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 (Hales polarity)
• Long term stability of active regions
• No anisotropy of supergranulation

Brandenburg (2005, ApJ 625, 539)
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Application to the sunspots rooted at r/R0.95
Benevolenskaya, Hoeksema, Kosovichev, Scherrer
(1999)

• Overshoot dynamo cannot catch up
• DftAZDW(180/p) (1.5x107) (2p 10-8)
• 360 x 0.15 54 degrees!

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Simulating solar-like differential rotation

• Still helically forced turbulence
• Shear driven by a friction term
• Normal field boundary condition

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Simulating solar-like differential rotation

• Still helically forced turbulence
• Shear driven by a friction term
• Normal field boundary condition

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Cartesian box MHD equations
Magn. Vector potential
Induction Equation
Momentum and Continuity eqns
Viscous force
forcing function
(eigenfunction of curl)
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Tendency away from filamentary field
Cross-sections at different times
Mean field
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Current helicity and magn. hel. flux
Bao Zhang (1998), neg. in north, plus in
south (also Seehafer 1990)
Berger Ruzmaikin (2000)
S
DeVore (2000)
N
(for BR CME)
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Magnetic Helicity

J. Chae (2000, ApJ)

-
-
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Helicity fluxes at large and small scales
Negative current helicity net production in
northern hemisphere
1046 Mx2/cycle
Brandenburg Sandin (2004, AA 427, 13)
Helicity fluxes from shear Vishniac Cho (2001,
ApJ 550, 752) Subramanian Brandenburg (2004,
PRL 93, 20500)
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Simulations showing large-scale fields
Helical turbulence (By)
Helical shear flow turb.
Convection with shear
Magneto-rotational Inst.
Käpyla et al (2008)
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Origin of sunspot
Theories for shallow spots (i) Collapse by
suppression of turbulent heat flux (ii) Negative
pressure effects from ltbibjgt-ltuiujgt vs BiBj
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Build-up release of magnetic twist
Coronal mass ejections
clockwise tilt (right handed)
? left handed internal twist

• New hirings
• 4 PhD students
• 4 post-docs (2yr)
• 1 assistant professor
• 2 Long-term visitors

• Upcoming work
• Global models
• Helicity transport
• coronal mass ejections
• Cycle forecasts