1. Overview of dynamos in stars and galaxies
Axel Brandenburg (Nordita, Copenhagen)
Collaborators:
Nils Erland Haugen (Univ. Trondheim)
Wolfgang Dobler (Freiburg  Calgary)
Tarek Yousef (Univ. Trondheim)
Antony Mee (Univ. Newcastle)
Talk given in Cracow, Wednesday 29. Sept 2004

2. turbulent: large-scale and small -scale
Dynamos
kinematic
laminar: fast and slow
turbulent: large-scale and small -scale
nonlinear
self-killing
quenching
self-generating
J.B-driven
Fuchs et al (1999)
Blackman & B (2002)
Fuchs et al (1999)
Blackman & Field (2004)

3. MRI: Local disc simulations
Dynamo makes its own turbulence (no longer forced!)
Hyperviscosity
1283

4. Important questions Does SN turbulence give dynamo?
w/ shear
w/ rotation
Does SN turbulence give dynamo?
Resolution too poor? Or because of shocks?
How important is compressibility?
Does the turbulence become “acoustic”?
Is turbulent B-field a small scale feature?
PPM, hyperviscosity, shock viscosity, etc
Can they screw things up?
Bottleneck effect (real or artifact?)
Does the actual Prandtl number matter?
We are never able to do the real thing
Fundamental questions
 more idealized simulations
Korpi et al (1999)
Sarson et al (2003)

5. 1st Problem: compressibility?
Shocks sweep up all the field: dynamo harder?
-- or artifact of shock diffusion?
Direct and shock-capturing simulations, n/h=1
Direct simulation, n/h=5
 Bimodal behavior!

6. Potential flow subdominant
Potential component more important,
but remains subdominant
Shock-capturing viscosity:
affects only small scales

7. Flow outside shocks unchanged
Localized shocks: exceed color scale
Outside shocks: smooth

8. 2nd problem: small-scale dynamo
Kazantsev (1968)
According to linear theory, field would be regenerated at the resistive scale
Magn.
spectrum
Kin. spectrum
Maron & Cowley (2001)
magnetic peak: resistive scale?

9. Kazantsev spectrum (kinematic)
Opposite limit, no scale separation, forcing at kf=1-2
Kazantsev spectrum confirmed (even for n/h=1)
Spectrum remains highly time-dependent

10. instead: kpeak~Rm,crit1/2 kf ~ 6kf
256 processor run at 10243
-3/2
slope?
Haugen et al. (2003, ApJ 597, L141)
Result: not peaked at resistive scale -- Kolmogov scaling!
instead: kpeak~Rm,crit1/2 kf ~ 6kf

11. 3nd problem: deviations from Kolmogorov?
compensated spectrum
Porter, Pouquet, & Woodward (1998) using PPM, meshpoints
Kaneda et al. (2003) on the Earth simulator, meshpoints
(dashed: Pencil-Code with )

12. Comparison: hyper vs normal
height of bottleneck increased
Haugen & Brandenburg (PRE, 2004)
onset of bottleneck at same position
2nd Result: inertial range unaffected by artificial diffusion

13. Helical MHD turbulence
Helically forced turbulence (cyclonic events)
Small & large scale field grows exponentially
Past saturation: slow evolution
 Explained by magnetic helicity equation

14. Slow saturation
Brandenburg (2001, ApJ)

15. Connection with a effect: writhe with internal twist as by-product
clockwise tilt
(right handed) W
 left handed
internal twist
Talk given at Thinkshop in May 2002
Yousef & Brandenburg
A&A 407, 7 (2003)

16. Revised nonlinear dynamo theory (originally due to Kleeorin & Ruzmaikin 1982)
Two-scale assumption
Production of large scale helicity comes at the price
of producing also small scale magnetic helicity

17. Express in terms of a
 Dynamical a-quenching (Kleeorin & Ruzmaikin 1982)
no additional free parameters
Steady limit:
consistent with
Vainshtein & Cattaneo (1992)
(algebraic
quenching)

18. History of a quenching “catastrophic” a quenching Rm –dependent
(Vainshtein & Cattaneo 1972,
Gruzinov & Diamond )
“conventional” a quenching
e.g., a~B-3, independent of Rm
(Moffatt 1972, Rüdiger 1973)
periodic box simulations:
saturation at super-equipartition,
but after resistive time
(Brandenburg 2001)
open domains: removal of
magnetic waste by helicity flux
(Blackman & Field 2000,
Kleeorin et al )
Dynamical quenching
Kleeorin & Ruzmaikin (1982)

19. Current helicity flux Advantage over magnetic helicity
<j.b> is what enters a effect
Can define helicity density
Rm also in the
numerator

20. Full time evolution Significant field already after kinematic
growth phase
followed by
slow resistive
adjustment

21. Large scale vs small scale losses
Diffusive large scale losses:
 lower saturation level
(Brandenburg & Dobler 2001)
Periodic
box
with LL losses
Small scale losses (artificial)
 higher saturation level
 still slow time scale
Numerical experiment:
remove field for k>4
every 1-3 turnover times
(Brandenburg et al. 2002)

22. Significance of shear a  transport of helicity in k-space
Shear  transport of helicity in x-space
Mediating helicity escape ( plasmoids)
Mediating turbulent helicity flux
Expression for current helicity flux:
(first order smoothing, tau approximation)
Schnack et al.
Vishniac & Cho (2001, ApJ)
Expected to be finite on when there is shear
Arlt & Brandenburg (2001, A&A)

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

24. Helicity fluxes at large and small scales
Negative current helicity:
net production in northern hemisphere
1046 Mx2/cycle

25. Impose toroidal field  measure a
previously:

26. Conclusions Homogeneous dynamos saturate resistively
Entirely magnetic helicity controlled
Inhomogeneous dynamo
Open surface, equator
Still many issues to be addressed
Current helicity flux important
Finite if there is shear
Avoid magnetic helicity, use current helicity