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

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

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

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

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

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

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

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

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

Brandenburg: MHD turbulence 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 Brandenburg: MHD turbulence

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

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

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 ) Brandenburg: MHD turbulence

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

Relation to ‘laboratory’ 1D spectra Dobler et al. (2003, PRE 026304) Brandenburg: MHD turbulence

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

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 Brandenburg: MHD turbulence

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

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

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

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

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

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

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

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

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

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

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

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

Further experiments: interaction with magnetosphere Alternating fieldline uploading and downloading von Rekowskii & Brandenburg 2004 (A&A) Similar behavior found by Goodson & Winglee (1999) Star connected with the disc Star disconnected from disc

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

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