The Nature of Turbulence in Protoplanetary Disks

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

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

4. MRI in Resistive Disks • MRI dynamo requires • ReM 1 with imposed field • Ionization frac. crucial: • electron-neutral collisions • Thermal xe negligible @ T<1000K • Nonthermal xeuncertain • 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=10-17s-1 & dissociative recomb. (after Gammie ‘96) • & accretion rate is too small: then in MMSN,

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

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

9. Objections to FAHI • Nonlocal: rnot 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*~107 ReM ~ 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 Mp • 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(r2)/dr > 0 • Baroclinic instability needs to be confirmed • Simulations with independent codes • Investigate T()