Turbulence simulations showing mean-field dynamos

1
Turbulence simulations showing mean-field dynamos

• Solar paradigm shifts
• Helicity fluxes
• Low magnetic Prandtl numbers
• Mean field coefficients from simulations
• Axel Brandenburg (Nordita, Stockholm)

2
The 4 solar dynamo scenarios

• Distributed dynamo (Roberts Stix 1972)
• Positive alpha, negative shear
• Overshoot dynamo (e.g. DeLuca Gilman 1986)
• Negative alpha, positive shear
• Interface dynamo (Parker 1993)
• 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

3
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

4
(i) Is magnetic buoyancy a problem?
Stratified dynamo simulation in 1990 Expected
strong buoyancy losses, but no downward pumping
Tobias et al. (2001)
5
(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)
6
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!
7
(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?

8
Simulations showing large-scale fields
Helical turbulence (By)
Helical shear flow turb.
Convection with shear
Magneto-rotational Inst.
Käpyla et al (2008)
9
Upcoming dynamo effort in Stockholm

• Soon hiring
• 4 students
• 3 post-docs
• 1 assistant professor
• Long-term visitors

10
Connection with a effect writhe with internal
twist as by-product
a effect produces helical field
W
clockwise tilt (right handed)
? left handed internal twist
both for thermal/magnetic buoyancy
11
Nonlinear stage consistent with
Brandenburg (2005, ApJ)
12
Forced large scale dynamo with fluxes
geometry here relevant to the sun
1046 Mx2/cycle
Negative current helicity net production in
northern hemisphere
13
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
Tobias et al. (2008, ApJ)
Kapyla et al. (2008, AA)
14
Low PrM dynamos
Sun PrMn/h10-5
Schekochihin et al (2005)
Here non-helically forced turbulence
k
Helical turbulence
15
Calculate full aij and hij tensors
Response to arbitrary mean fields
Calculate
Example
16
Kinematic a and ht independent of Rm (2200)
Sur et al. (2008, MNRAS)
17
From linear to nonlinear
Use vector potential
Mean and fluctuating U enter separately
18
Nonlinear aij and hij tensors
Consistency check consider steady state to avoid
da/dt terms
Expect
l0 (within error bars) ? consistency check!
19
Rm dependence for BBeq

1. l is small ? consistency
2. a1 and a2 tend to cancel
3. making a small
4. h2 small

20
Earlier results on ht quenching
Yousef et al. (2003, AA)
21
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

22
Conclusion

• 11 yr cycle
• Dyamo (SS vs LS)
• Problems
• a-quenching
• slow saturation
• Solution
• Modern a-effect theory
• j.b contribution
• Magnetic helicity fluxes
• Location of dynamo
• Distrubtion, shaped by
• near-surface shear

1046 Mx2/cycle