1. The Nature of Turbulence in Protoplanetary Disks Jeremy Goodman Princeton University jeremy@astro.princeton.edu “Astrophysics of Planetary Systems” Harvard 18 May 2004

2. Why do we care? Spectrum depends on accretion rate only: – from boundary-layer emission Viscosity determines surface density: – not obviously compatible with  viscosity Agglomeration of solids (grains/planetesimals) Gap formation & migration –& planetary eccentricities? Unsteady behaviors –FU Orionis outbursts –Waves and wakes

3. Turbulence/Transport Mechanisms CandidateProCon Magnetorotational Instability (MRI) Robust linear instability. Well studied.  ~10 -2 Uncertain nonthermal ionization required Finite-amplitude hydro instability Independent of ionization. Demonstrated in lab (?) Poorly understood. Not confirmed by simulation SelfgravityCan be local. Reasonably well understood. Q>>1 in T Tauri phase Vertical convectionExpected result of radiative cooling Not driven by shear. Transports J inwards. Radial convection / baroclinic instab. Ditto. Seems to make large vortices,  ~10 -3 Poorly understood. Linear instab. obscure Planetary wakesCalculable. Inevitable at some level. Requires planets. Migration.  <10 -4

4. MRI in Resistive Disks MRI dynamo requires –Re M  1 with imposed field Ionization frac. crucial: –electron-neutral collisions Thermal x e negligible @ T<1000K Nonthermal x e uncertain –Ionization rate: CR, Xrays,… –Recombination: dust, molecular ions, metal ions Other wrinkles: –Layered accretion (Gammie ‘96) –Hall conductivity (Wardle ‘99) Fleming, Stone, & Hawley 2000 Fleming & Stone 2003

5. Resistive turbulence (Fleming et al. 2000)

6. Further remarks on layered MRI If  CR =10 -17 s -1 & dissociative recomb. (after Gammie ‘96) –& accretion rate is too small: then in MMSN,

7. Finite-amplitude hydro instability Richard & Zahn (1999):  outer  inner In MMSN: Richard 2001

8.  r -3/2 “Keplerian” profile found turbulent (Richard 2001)

9. Objections to FAHI Nonlocal: r not H is the lengthscale –H > r >>  r in experiments –H << r ≈  r in accretion disks Also compressible No local linear instability for –But e.g. pipe flow is also linearly stable Not found in local (shearing-sheet) simulations –But  viscosity is explicitly nonlocal –Resolution or numerical Re may be inadequate E.g. Longaretti 2002 Doesn’t explain outbursts (e.g. dwarf novae)

10. Princeton MRI Experiment (H. Ji et al.) B= 0.7 T Re * ~10 7 Re M ~ 1

11. Vortices & Baroclinic Instability Anticyclonic vortices hold together by Coriolis force –Local maximum in P &  –Local minimum in vorticity: & vortensity: Realistically, Wakes of persistent vortices transmit angular momentum Godon & Livio 1999 Klahr & Bodenheimer 2003

12. Baroclinic Instability, continued  disks are typically unstably stratified in radius: –e.g. with dust opacity Growth is nonaxisymmetric –Axisym’ly stable since –Linear growth is only transient due to shear (swing amplification) Self-consistent  ~10 -3 in 2D & 3D is claimed –Klahr & Bodenheimer 2003 Confirmation is needed!

13. A plug for planetary wakes A corotating obstacle---vortex or planet---has a wake –Wavelike angular-momentum transport –Dissipation of gas orbits where wake shocks/damps One planet: –Goodman & Rafikov ‘01; Rafikov ‘02 Many planets: assuming –all metals in planets of equal mass M p –planets distributed like gas Linearized wake in shearing sheet

14. Philosophical remarks Turbulent “viscosity” probably depends on frequency –  turb ~ ,  wake ~ (  r/H)    turb Angular momentum transport need not be turbulent –winds, wakes, … Disks need not be smooth, even on lengthscales  H & timescales  -1 –Surely not on smaller scales! Nelson & Papaloizou ‘04

15. Peroration MRI is the leading candidate but depends on uncertain microphysics and HE irradiation –ISM theorists needed! Finite-amplitude instability should be taken seriously –Higher-resolution simulations –Experiments with d(r 2  )/dr > 0 Baroclinic instability needs to be confirmed –Simulations with independent codes Investigate T (  )