Transcript The solar dynamo(s) - Center for Magnetic Self Organization

Chicago 2003
The solar dynamo(s)
Fausto Cattaneo
Center for Magnetic Self-Organization in Laboratory
and Astrophysical Plasmas
[email protected]
Chicago 2003
The solar dynamo problem
The solar dynamo is invoked to explain the origin magnetic
activity
Three important features:
• Wide range of spatial scales. From global scale to limit of
resolution
• Wide range of temporal scales. From centuries to
minutes
• Solar activity is extremely well documented
Models are strongly observationally constrained
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Observations
Hale’s polarity law
suggests organization on
global scale.
Typical size of active
regions approx
200,000Km
Typical size of a sunspot
50,000Km
Small magnetic elements
show structure down to
limit of resolution
(approx 0.3")
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Observations: large scale
• Active regions migrate from midlatitudes to the equator
• Sunspot polarity opposite in two
hemispheres
• Polarity reversal every 11 years
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Observations: large scale
PROXY DATA OF SOLAR MAGNETIC ACTIVITY AVAILABLE
10
Be : stored in ice cores after 2 years in atmosphere
14
C : stored in tree rings after ~30 yrs in atmosphere
Beer (2000)
Wagner et al (2001)
Cycle persists through
Maunder Minimum (Beer et al 1998)
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Observations: small scale
Two distinct scales of convection (maybe more)
• Supergranules:
– not visible in intensity
– 20,000 km typical size
– 20 hrs lifetime
– weak dependence on latitude
• Granules:
– strong contrast
– 1,000km typical size
– 5 mins lifetime
– homogeneous in latitude
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Observations: small scale
Quiet photospheric flux
• Network fields
– emerge as ephemeral regions (possibly)
– reprocessing time approx 40hrs
– weak dependence on solar cycle
• Intra-network magnetic elements
– possibly unresolved
– typical lifetime few mins
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General dynamo principle
Any three-dimensional, turbulent (chaotic) flow with high magnetic Reynolds
number is (extremely) likely to be a dynamo.
• Reflectionally symmetric flows:
– Small-scale dynamo action
– Disordered fields; same correlation length/time as turbulence
2
2
B
– Generate | B | but not
• Non-reflectionally symmetric flows:
– Large-scale dynamo; inverse cascade of magnetic helicity
– Organized fields; correlation length/time longer than that of turbulence
– Possibility of
| B |2  B
2
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Rotational constraints
In astrophysics lack of reflectional symmetry associated with
(kinetic) helicity  Coriolis force  Rotation
Introduce Rossby radius Ro (in analogy with geophysical flows)
• Motions or instabilities on scales  Ro “feel’’ the rotation.
– Coriolis force important  helical motions
– Inverse cascades  large-scale dynamo action
• Motions or instabilities on scales < Ro do not “feel” the rotation.
– Coriolis force negligible  non helical turbulence
– Small-scale dynamo action
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Modeling: large-scale generation
Dynamical ingredients
• Helical motions: Drive the α-effect. Regenerate poloidal
fields from toroidal
• Differential rotation: (with radius and/or latitude)
Regenerate toroidal fields from poloidal. Probably
confined to the tachocline
• Magnetic buoyancy: Removes strong toroidal field from
region of shear. Responsible for emergence of active
regions
• Turbulence: Provides effective transport
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Modeling: helical motions
• Laminar vs turbulent α-effect:
– Babcock-Leighton models. α-effect driven by rise and twist of large
scale loops and subsequent decay of active regions. Coriolis-force
acting on rising loops is crucial. Helical turbulence is irrelevant.
Dynamo works because of magnetic buoyancy.
– Turbulent models. α-effect driven by helical turbulence. Dynamo
works in spite of magnetic buoyancy.
• Nonlinear effects:
– Turbulent α-effect strongly nonlinearly
suppressed
– Interface dynamos?
– α-effect is not turbulent (see above)
Cattaneo & Hughes
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Modeling: differential rotation
• Latitudinal differential rotation:
– Surface differential rotation persists throughout the convection zone
– Radiative interior in solid body rotation
Schou et al.
• Radial shear:
– Concentrated in the tachocline; a thin
layer at the bottom of the convection
zone
– Whys is the tachocline so thin? What
controls the local dynamics?
No self-consistent model for the solar differential rotation
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Modeling: magnetic buoyancy
What is the role of magnetic buoyancy?
• Babcock-Leighton models:
– Magnetic buoyancy drives the dynamo
– Twisting of rising loops under the action of the Coriolis force generates
poloidal field from toroidal field
– Dynamo is essentially non-linear
• Turbulent models:
– Magnetic buoyancy limits the growth of the
magnetic field
– Dynamo can operate in a kinematic regime
Wissink et al.
Do both dynamos coexist? Recovery from Maunder minima?
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Modeling: turbulence
How efficiently is turbulent transport?
• Babcock-Leighton models: Turbulent diffusion causes the dispersal of
active regions. Transport of poloidal flux to the poles.
• Interface models: Turbulent diffusion couples the layers of toroidal
and poloidal generation
• All models:
– Turbulent pumping helps to keep
the flux in the shear region
– Turbulence redistributes angular
momentum
– Etc. etc. etc.
Tobias et al.
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Modeling: challenges
No fully self-consistent model exists.
• Self-consistent model must capture all dynamical
ingredients (MHD, anelastic)
• Geometry is important (sphericity)
• Operate in nonlinear regime
• Resolution issues. Smallest resolvable scales are
– in the inertial range
– rotationally constrained
– stratified
Need sophisticated sub-grid models
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Modeling: small-scale generation
cold
g
•
Plane parallel layer of fluid
•
Boussinesq approximation
•
Ra=500,000; P=1; Pm=5
time evolution
Simulations by Lenz & Cattaneo
hot
temperature
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Modeling: physical parameters
Rm 
103
102

Pm=1

simulations

Liquid metal experiments
103
107
Re
• Dynamo must operate in the inertial range of the turbulence
• Driving velocity is rough
• How do we model MHD behaviour with Pm <<1
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Modeling: kinematic and dynamical issues
Re=550, Rm=550
yes
• Does the dynamo still operate?
(kinematic issue)
• Dynamo may operate but become
extremely inefficient (dynamical
issue)
Re=1100, Rm=550
no
Pm=1
Pm=0.5
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Modeling: magneto-convection
• Relax requirement that magnetic field be self sustaining (i.e.
impose a uniform vertical field)
• Construct sequence of simulations with externally imposed
field, 8 ≥ Pm ≥ 1/8, and S =  = 0.25
• Adjust Ra so that Rm remains “constant”
Pm
8.0
4.0
2.0
1.0
0.5
0.25
0.125
Ra
9.20E+04
1.40E+05
2.00E+05
3.50E+05
7.04E+05
1.40E+06
2.80E+06
Nx, Ny
256
256
256
512
512
512
768
Simulations by Emonet & Cattaneo
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Modeling: magneto-convection
B-field (vertical)
vorticity (vertical)
Pm = 8.0
Pm = 0.125
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Modeling: magneto-convection
•
Energy ratio flattens out for Pm < 1
•
PDF’s possibly accumulate for Pm < 1
•
Evidence of regime change in cumulative
PDF across Pm=1
•
Possible emergence of Pm independent
regime
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Summary
Two related but distinct dynamo problems.
• Large-scale dynamo
– Reproduce cyclic activity
– Reproduce migration pattern
– Reproduce angular momentum distribution (CV and tachocline)
– Needs substantial advances in computational capabilities
• Small scale dynamo
– Non helical generation
– Small Pm  turbulent dynamo