viscous stress tensor: T r!

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1 Accretion in a rotating system is only possible if matter looses its angular momentum! viscous stress tensor: T r! mass ang. mom. Viscosity could do this, but molecular viscosity is far too low. Thus one invokes turbulent viscosity! 11/15/2011 Hubert Klahr - Planet Formation - MPIA 23

2 Possibilities for Turbulence and angular momentum transport: 1. Non-Linear Shear Instability: Richard et al. 2003? 2. Self Gravity: Toomre 1964 (+) 3. Thermal Convection: Ryu & Goodman Magneto (Rotational) Instability: Balbus & Hawley 1992 (+) 5. Baroclinic Instabilities: Klahr & Bodenheimer 2003 (+) Dependent on time and location within the disk, i.e. ionization state and temperature structure, one has most likely a mix of 2,4 and 5! 11/15/2011 Hubert Klahr - Planet Formation - MPIA 24

3 Ionized accretion disk around a black hole! 11/15/2011 Hubert Klahr - Planet Formation - MPIA 25

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9 MRI: a.k.a - Rockets in an earth orbit accelerate when they break! B 11/15/2011 Hubert Klahr - Planet Formation - MPIA 31

10 MRI: a.k.a - Rockets in an earth orbit accelerate when they break! B 11/15/2011 Hubert Klahr - Planet Formation - MPIA 32

11 Magneto Rotational Instability (MRI) drives turbulence in accretion disks 12/13/2009 Hubert Klahr - Planet Formation - MPIA 33 Simulation by Mario Flock using the Pluto code.

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15 because it is a reliable source for turbulence. Box: Disk: 12/13/2009 Hubert Klahr - Planet Formation - MPIA 37

16 Development of MHD Turbulence From initial perturbation to saturation of the turbulence Colors: gas density yellow = high blue! = low Standard magneto rotational instability simulation ala Balbus and Hawley 12/13/2009 Hubert Klahr - Planet Formation - MPIA 38

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18 At least part of a proto planetary disk may not be ionized enough for MRI to work! MHD Dead Zone Sano, Miyama,"Umebayashi &Nakano 2000 Fromang, Terquem, & Balbus 2002 Semenov, Wiebe, & Henning /15/2011 Hubert Klahr - Planet Formation - MPIA 40

19 Transition from MRI-active to dead zones: 2D axissymmetric simulation of active/dead zone interaction. Dzyurkevich, Turner, Flock & Klahr, submitted. Wünsch, Gawryszczak, Klahr & Rozyczka, /15/2011 Hubert Klahr - Planet Formation - MPIA 41

20 Transition from MRI-active to dead zones: Dzyurkevich, Turner, Flock & Klahr, Fully active disk Threshold at 6.5 AU DEAD Threshold at 4.5 AU DEAD Contour plots of Elsasser number: (less then unity means vertical field is stable to MRI) Our resolution: (Hawley et al. 1995)

21 Natalia Dziurkevich (in prep.): Active (Blue) and Dead (Yellow/Orange) Zones 12/13/2009 => Planetesimals Hubert are Klahr - needed Planet Formation in - MPIA the Dead Zone. 43

22 Baroclinic Effects on Earth: Formation of Hurricanes 12/13/2009 Hubert Klahr - Planet Formation - MPIA 44

23 Geophysical Baroclinic Instability 12/13/2009 Hubert Klahr - Planet Formation - MPIA 45

24

25 Stable: low rotation small radial temperature gradient

26 Unstable:high rotation stronger radial temperature gradient

27 Geophysical Baroclinic Instability: Astrophysical Baroclinic Instability in disks:! WARM COLD gz =! 2 z g z 12/13/2009 Hubert Klahr - Planet Formation - MPIA!"R -3/2-1.0<<Ri 49 2 <0

28 Thermal disk wind: Vertically stable Brunt-Vaissala Freq.: 12/13/2009 Hubert Klahr - Planet Formation - MPIA 50 compare: Klahr 2004

29 Thermal disk wind: Vertically stable: compare: Klahr /13/2009 Hubert Klahr - Planet Formation - MPIA 51

30 Baroclinic Instability in disks...is a local instability picking up on the global radial entropy gradient in the disk. Usually closer to the star it is warmer. T ~ R^ without rotation there would simply be convection. Shear and rotation prevent a linear convective instability (Solberg-Hoiland criterium). => Baroclinic Disk ground state = Heat (Entropy) gradient plus coriolis forces create thermal wind, e.g. vertical shear. Unfortunately growth time of classical B.I. is longer then shear time. 12/13/2009 Hubert Klahr - Planet Formation - MPIA 52

31 Pluto Code: 1024^2; WENO3-RK3; HLLE; FARGO 12/13/2009 Hubert Klahr - Planet Formation - MPIA 53

32 Pluto Code: 1024^2; WENO3-RK3; HLLE; FARGO 12/13/2009 Hubert Klahr - Planet Formation - MPIA 54

33 Pluto Code: 1024^2; WENO3-RK3; HLLE; FARGO 12/13/2009 Hubert Klahr - Planet Formation - MPIA 55

34 Pluto Code: 1024^2; WENO3-RK3; HLLE; FARGO 12/13/2009 Hubert Klahr - Planet Formation - MPIA 56

35 Literature overview 2003 Klahr and Bodenheimer: A radial entropy gradient drives turbulence in 2D and 3D (Radiation) Hydro Simulations of Protoplanetary disks Klahr: The radial Entropy gradient does not drive a LINEAR instability. Maybe NONLINEAR? 2005a,b;2006 Johnson and Gammie: find NO instability in their 2D shearing sheet simulations... But it was WITHOUT radiative cooling. 2007a,b Petersen, Stewart and Julien: find that radiative cooling or thermal diffusion is essential for the non-linear evolution of the instability. 2D Anelastic High Reynolds number simulations = no angular momentum transport. Re = Lesur & Papaloizou: Independent Confirmation of non-linear instability + elliptic instability does not destroy vortices in 3D 2010 Paardekooper,!Lesur,!Papaloizou Vortex Migration in Protoplanetary Disks 2011 Lyra & Klahr: Baroclinic and MHD interplay. 12/13/2009 Hubert Klahr - Planet Formation - MPIA 57

36 Waves in B.I. vs. MRI!"#$!%&'())*'( It will be difficult to distinguish via observations....,0.,+ 1 B.I. (left) MRI (right) Heinemann and Papaloizou ,0 12/13/2009 ï+,- ï+,. +,+ / +,. Hubert Klahr - Planet Formation - MPIA 58