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Magneto-rotational instability. Axel Brandenburg ( Nordita, Copenhagen ). Discs and disc viscosity. Magnetorotational instability (MRI) how does it work? simulations and experiments Vertical stratification and radiation Heating near disc surface Star/disc coupling and outflows
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Magneto-rotational instability AxelBrandenburg (Nordita, Copenhagen)
Discs and disc viscosity • Magnetorotational instability (MRI) • how does it work? • simulations and experiments • Vertical stratification and radiation • Heating near disc surface • Star/disc coupling and outflows • Field lines open up, enhanced outflow
Alfven and slow magnetosonic waves Vertical field B0 Dispersion relation Alfven frequency:
Alfven and slow magnetosonic waves Alfven slow magnetosonic
March 23, 1965: Gemini 3 Gus Grissom & John Young: docking with Agena space craft
Analogy with tidal disruption, etc. Tidal disruption of a star Space craft experiment MRI (Balbus & Hawley 1991)
Shearing sheet analysis with Boris Dintrans (Toulouse) linear analysis: variable wave number Rayleigh quotient
Comparison withinviscid simulations Only reliable till t<18
Shearing sheet simulations Dynamo makes its own turbulence Hyperviscosity 1283
High resolution direct simulation singular! 5123 resolution
Simulations with stratification cyclic B-field alpha-Omega dynamo? negative alpha
Vertical stratification Brandenburg et al. (1996) z-dependence of
Heating near disc boundary weak z-dependence of energy density where Turner (2004)
Preliminary simulations W/2p = 48 Hz (WRi2/n = 375) 2000 G (Ha=146) 500 G (Ha=37) 1000 G (Ha=73)
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 so far 10243
CVS maintained • pserver (password protected) • Public (check-out only), private (ci/co, 20 people) • Set of 12 test problems • Nightly auto-test (different machines, web) • Before check-in: run auto-test yourself • Mpi and nompi dummy module for single processor machine (or use lam-mpi on laptops)
Intrinsic Calculation Ray direction Transfer equation & parallelization Processors Analytic Solution:
Analytic Solution: Communication Ray direction The Transfer Equation & Parallelization Processors
Analytic Solution: Intrinsic Calculation Ray direction The Transfer Equation & Parallelization Processors
Current implementation • Plasma composed of H and He • Only hydrogen ionization • Only H- opacity, calculated analytically No need for look-up tables • Ray directions determined by grid geometry No interpolation is needed
Disc and outflow (YSOs) Disc temperature relative to halo is free parameter: Here about 3000K Cooler disc: more vigorous evolution von Rekowskii et al 2003 (A&A)
Unsteady outflow transport from disc into the wind BN/KL region in Orion: Greenhill et al (1998)
Application: magnetic contamination of galaxy cluster 10,000 galaxies for 1 Gyr, 1044 erg/s each Similar figure also for outflows from protostellar disc
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
Similar behavior found by Goodson & Winglee cf. field line opening: Uzdensky (2002), Pudritz & Matt (2004)
Open questions • Radiation transfer with scattering • where • QPOs (vertical disc oscillation?) • In resonance with vert/rad epicycle freq? • Viscous instability