1. Magneto-hydrodynamic turbulence: from the ISM to discs
Axel Brandenburg (Nordita, Copenhagen)
Collaborators:
Nils Erland Haugen (Univ. Trondheim)
Wolfgang Dobler (Freiburg  Calgary)
Tarek Yousef (Univ. Trondheim)
Antony Mee (Univ. Newcastle)
Talk given at the MPIA in Heidelberg, Tuesday 25. May 2004

2. Brandenburg: MHD turbulence
Sources of turbulence
Gravitational and thermal energy
Turbulence mediated by instabilities
convection
MRI (magneto-rotational, Balbus-Hawley)
Explicit driving by SN explosions
localized thermal (perhaps kinetic) sources
Brandenburg: MHD turbulence

3. Conversion between different energy forms
Examples:
thermal convection
magnetic buoyancy
magnetorotational inst.
Potential
energy
Kinetic
energy
Thermal
energy
Magnetic
energy
Brandenburg: MHD turbulence

4. Galactic discs: supernova-driven turbulence
Microgauss fields:
Korpi et al (1999, ApJ)
Brandenburg: MHD turbulence

5. Huge range of length scales
Driving mechanism:
SN explosions
parsec scale
Dissipation scale
108 cm (interstellar scintillation)
What is the scale of B-field
Linear theory: smallest scale!
Korpi et al. (1999), Sarson et al. (2003)
no dynamo here…
Brandenburg: MHD turbulence

6. Brandenburg: MHD turbulence
Important questions
Is there a dynamo? (Or is resolution too poor?)
Is the turbulent B-field a small scale feature?
How important is compressibility?
Does the turbulence become “acoustic” (ie potential)?
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
Brandenburg: MHD turbulence

7. 1st problem: small scale dynamo
According to linear theory, field would be regenerated at the resistive scale
(Kazantsev 1968)
Schekochihin et al (2003)
Brandenburg: MHD turbulence

8. Forced turbulence: B-field dynamo-generated
Magn.
spectrum
Kin. spectrum
Maron & Cowley (2001)
magnetic peak: resistive scale?
Brandenburg: MHD turbulence

9. Peaked at resistive scale!?
(nonhelical case)
Brandenburg: MHD turbulence

10. Brandenburg: MHD turbulence
Pencil Code
Started in Sept with Wolfgang Dobler
High order (6th order in space, 3rd order in time)
Cache & memory efficient
MPI, can run PacxMPI (across countries!)
Maintained/developed by many people (CVS!)
Automatic validation (over night or any time)
Max resolution currently 10243
Brandenburg: MHD turbulence

11. 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
Brandenburg: MHD turbulence

12. Brandenburg: MHD turbulence
256 processor run at 10243
-3/2
slope?
Haugen et al. (2003, ApJ 597, L141)
1st Result: not peaked at resistive scale -- Kolmogov scaling!
Brandenburg: MHD turbulence

13. 2nd 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 )
Brandenburg: MHD turbulence

14. Bottleneck effect: 1D vs 3D spectra
Why did wind tunnels not show this?
Bottleneck effect: 1D vs 3D spectra
Brandenburg: MHD turbulence

15. Relation to ‘laboratory’ 1D spectra
Dobler et al. (2003, PRE )
Brandenburg: MHD turbulence

16. Third-order hyperviscosity
Different resolution: bottleneck & inertial range
Traceless rate of strain tensor
Hyperviscous heat
3rd order dynamical hyperviscosity m3
Brandenburg: MHD turbulence

17. Comparison: hyper vs normal
height of bottleneck increased
Haugen & Brandenburg (PRE, astro-ph/ )
onset of bottleneck at same position
2nd Result: inertial range unaffected by artificial diffusion
Brandenburg: MHD turbulence

18. 3rd 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!
Brandenburg: MHD turbulence

19. Potential flow subdominant
Potential component more important,
but remains subdominant
Shock-capturing viscosity:
affects only small scales
Brandenburg: MHD turbulence

20. Flow outside shocks unchanged
Localized shocks: exceed color scale
Outside shocks: smooth
Brandenburg: MHD turbulence

21. Dynamos and Mach number
No signs of shocks in B-field
or J-field (shown here)
advection dominates
Brandenburg: MHD turbulence

22. 3rd Result: dynamo unaffected by compressibility and shocks
Depends on Rm of vortical flow component
Bimodal: Rm=35 (w/o shocks), 70 (w/ shocks)
Important overall conclusion:
simulations hardly in asymptotic regime
a need to reconsider earlier lo-res simulations: here discs
Brandenburg: MHD turbulence

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

24. Simulations with stratification
cyclic B-field
alpha-Omega dynamo?
negative alpha
Brandenburg: MHD turbulence

25. High resolution direct simulation
singular!
2563 (direct, new)
323 (hyper, old)
5123 resolution
Brandenburg: MHD turbulence

26. Disc viscosity: mostly outside disc
Brandenburg et al. (1996)
z-dependence of

27. Heating near disc boundary
weak z-dependence of energy density
where
Turner (2004)

28. Magnetic “contamination” on larger scales
Outflow with dynamo field (not imposed)
Disc wind: Poynting flux
10,000 galaxies for 1 Gyr, 1044 erg/s each
Similar figure also for outflows from protostellar disc
Brandenburg: MHD turbulence

29. Brandenburg: MHD turbulence
Unsteady outflow
Disc: mean field model
transport from disc into the wind
von Rekowski et al. (2003, A&A 398, 825)
BN/KL region in Orion:
Greenhill et al (1998)
Brandenburg: MHD turbulence

30. Further experiments: interaction with magnetosphere Alternating fieldline uploading and downloading
von Rekowskii & Brandenburg (A&A)
Similar behavior found by Goodson & Winglee (1999)
Star connected with the disc
Star disconnected from disc

31. Surprises from current research
B-field follows Kolmogorov scaling
Takes lots of resolution: bottleneck, diff-range
Dynamo basically ignores shocks
Future directions
Cosmic ray and thermal diffusion along B-lines
Self-consistent disc winds (proper radiation)
Partially ionized YSO discs
Dynamos at low n/h: do they still work??
Brandenburg: MHD turbulence

32. Examples of such surprises: small magnetic Prandtl numbers
definition
Rm=urms/(hkf)
Is there SS dynamo action
below Pm=0.125?
Comparion w/ hyper
Haugen, Brandenburg, Dobler PRE (in press)
Brandenburg: MHD turbulence