1. Magneto-rotational instability Axel Brandenburg (Nordita, Copenhagen)

2. 2 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

3. 3 Alfven and slow magnetosonic waves Vertical field B 0 Dispersion relation Alfven frequency:

4. 4 Alfven and slow magnetosonic waves Alfven slow magnetosonic

5. 5 March 23, 1965: Gemini 3 Gus Grissom & John Young: docking with Agena space craft

6. 6 Analogy with tidal disruption, etc. Space craft experiment MRI (Balbus & Hawley 1991) Tidal disruption of a star

7. 7 Shearing sheet analysis linear analysis: variable wave number Rayleigh quotient with Boris Dintrans (Toulouse)

8. 8 Comparison with inviscid simulations Only reliable till t<18

9. 9 Shearing sheet simulations Dynamo makes its own turbulence Hyperviscosity 128 3

10. 10 High resolution direct simulation 512 3 resolution singular!

11. 11 Simulations with stratification cyclic B-field alpha-Omega dynamo? negative alpha

12. 12 Vertical stratification Brandenburg et al. (1996) z-dependence of

13. 13 Heating near disc boundary Turner (2004) weak z-dependence of energy density where

14. 14 Dan Lathrop’s new MRI experiment

15. 15 Dan Lathrop’s new MRI experiment

16. 16 Preliminary simulations 1000 G (Ha=73) 2000 G (Ha=146) 500 G (Ha=37)  = 48 Hz (  R i 2 / = 375)

17. 17 Pencil Code Started in Sept. 2001 with Wolfgang Dobler High order (6 th order in space, 3 rd 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 1024 3

18. 18 256 processor run at 1024 3

19. 19 Wallclock time versus processor #

20. 20 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)

21. 21 Pencil Code check ins

22. 22 Transfer equation & parallelization Analytic Solution: Ray direction Intrinsic Calculation Processors

23. 23 The Transfer Equation & Parallelization Analytic Solution: Ray direction Communication Processors

24. 24 The Transfer Equation & Parallelization Analytic Solution: Ray direction Processors Intrinsic Calculation

25. 25 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

26. 26 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)

27. 27 Unsteady outflow transport from disc into the wind BN/KL region in Orion: Greenhill et al (1998)

28. 28 Application: magnetic contamination of galaxy cluster 10,000 galaxies for 1 Gyr, 10 44 erg/s each Similar figure also for outflows from protostellar disc

29. 29 Further experiments: interaction with magnetosphere Alternating fieldline uploading and downloading Star connected with the discStar disconnected from disc Similar behavior found by Goodson & Winglee (1999) von Rekowskii & Brandenburg 2004 (A&A)

30. 30 Similar behavior found by Goodson & Winglee cf. field line opening: Uzdensky (2002), Pudritz & Matt (2004)

31. 31 Open questions Radiation transfer with scattering where QPOs (vertical disc oscillation?) –In resonance with vert/rad epicycle freq? Viscous instability