Magnetohydrodynamic turbulence: from the ISM to discs

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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)

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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

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Conversion between different energy forms
Examples thermal convection magnetic
buoyancy magnetorotational inst.
Potential energy
Kinetic energy
Thermal energy
Magnetic energy
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Galactic discs supernova-driven turbulence
Korpi et al (1999, ApJ)
Microgauss fields
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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
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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
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1st problem small scale dynamo

• According to linear theory, field would be
  regenerated at the resistive scale

(Kazantsev 1968)
Schekochihin et al (2003)
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Forced turbulence B-field dynamo-generated
Magn. spectrum
Kin. spectrum
Maron Cowley (2001)
magnetic peak resistive scale?
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Peaked at resistive scale!?
(nonhelical case)
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Pencil Code

• Started in Sept. 2001 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

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Kazantsev spectrum (kinematic)
Opposite limit, no scale separation, forcing at
kf1-2
Kazantsev spectrum confirmed (even for n/h1)
Spectrum remains highly time-dependent
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256 processor run at 10243
-3/2 slope?
Haugen et al. (2003, ApJ 597, L141)
1st Result not peaked at resistive scale --
Kolmogov scaling!
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2nd problem deviations from Kolmogorov?
compensated spectrum
Porter, Pouquet, Woodward (1998) using PPM,
10243 meshpoints
Kaneda et al. (2003) on the Earth simulator,
40963 meshpoints (dashed Pencil-Code with 10243 )
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Bottleneck effect 1D vs 3D spectra
Why did wind tunnels not show this?
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Relation to laboratory 1D spectra
Dobler et al. (2003, PRE 026304)
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Third-order hyperviscosity
Different resolution bottleneck inertial range
Traceless rate of strain tensor
Hyperviscous heat
3rd order dynamical hyperviscosity m3
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Comparison hyper vs normal
height of bottleneck increased
Haugen Brandenburg (PRE, astro-ph/0402301)
onset of bottleneck at same position
2nd Result inertial range unaffected by
artificial diffusion
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3rd Problem compressibility?
Shocks sweep up all the field dynamo harder?
-- or artifact of shock diffusion?
Direct and shock-capturing simulations, n/h1
Direct simulation, n/h5
? Bimodal behavior!
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Potential flow subdominant
Potential component more important, but remains
subdominant
Shock-capturing viscosity affects only small
scales
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Flow outside shocks unchanged
Localized shocks exceed color scale
Outside shocks smooth
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Dynamos and Mach number
No signs of shocks in B-field or J-field (shown
here)
advection dominates
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3rd Result dynamo unaffectedby compressibility
and shocks

• Depends on Rm of vortical flow component
• Bimodal Rm35 (w/o shocks), 70 (w/ shocks)

Important overall conclusion simulations
hardly in asymptotic regime

• a need to reconsider earlier lo-res simulations
  here discs

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MRI Local disc simulations
Dynamo makes its own turbulence (no longer
forced!)
Hyperviscosity 1283
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Simulations with stratification
cyclic B-field alpha-Omega dynamo? negative alpha
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High resolution direct simulation
singular!
2563 (direct, new)
323 (hyper, old)
5123 resolution
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Disc viscosity mostly outside disc
Brandenburg et al. (1996)
z-dependence of
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Heating near disc boundary
weak z-dependence of energy density
where
Turner (2004)
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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
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Unsteady outflow
Disc mean field model
transport from disc into the wind
von Rekowski et al. (2003, AA 398, 825)
BN/KL region in Orion Greenhill et al (1998)
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Further experiments interaction with
magnetosphereAlternating fieldline uploading and
downloading
von Rekowskii Brandenburg 2004 (AA)
Similar behavior found by Goodson Winglee (1999)
Star connected with the disc
Star disconnected from disc
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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??

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Examples of such surprises small magnetic
Prandtl numbers
definition Rmurms/(hkf)
Is there SS dynamo action below Pm0.125?
Comparion w/ hyper
Haugen, Brandenburg, Dobler PRE (in press)