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Magneto-hydrodynamic turbulence: from the ISM to discs

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). Sources of turbulence.

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Magneto-hydrodynamic turbulence: from the ISM to discs

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  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)

  2. 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 Korpi et al (1999, ApJ) Microgauss fields: 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. 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 (Kazantsev 1968) • According to linear theory, field would be regenerated at the resistive scale 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. 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

  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. 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, 10243 meshpoints Kaneda et al. (2003) on the Earth simulator, 40963 meshpoints (dashed: Pencil-Code with 10243 ) Brandenburg: MHD turbulence

  14. 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 026304) 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/0402301) 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 unaffectedby 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. 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 magnetosphereAlternating 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

  31. B-field follows Kolmogorov scaling Takes lots of resolution: bottleneck, diff-range Dynamo basically ignores shocks 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?? Surprises from current research Future directions 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

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