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Unraveling Turbulence in Protoplanetary Disks: Insights and Mechanisms

Explore the intriguing dynamics of protoplanetary disks through the lens of turbulence and transport mechanisms. Delve into the role of MRI dynamo, ionization fraction, vortices, and wakes on planetary system formation. Uncover the complexities of turbulent viscosity and angular momentum transport in these cosmic environments.

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Unraveling Turbulence in Protoplanetary Disks: Insights and Mechanisms

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  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()

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