Gravitational Instabilities in Protoplanetary Disks

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Gravitational Instabilities in Protoplanetary
Disks

• Annie C. Mejía
• Astronomy Department
• Indiana University

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Collaborators

• Nuria Calvet
• Harvard-Smithsonian
• Pat Cassen
• NASA-Ames Research Center
• Paola DAlessio
• UNAM
• Richard H. Durisen
• Indiana University
• Tom Hartquist
• University of Leeds
• Brian K. Pickett
• Purdue University Calumet
• John Rosheck
• Indiana University
• Dotty Woolum
• Cal State Fullerton

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OBSERVATIONS
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Disk Statistics

• Prevalence of Disks Around Young Stars
• gt 50 of young stars have disks
• Disks last 106 - 107 years
• Measured masses range up to gt 10 the mass of the
  central star
• Mass accretion rates lt 10-8 to 10-4 M? per year

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Proplyds in the Orion Nebula
STSCI
2.5 light-years
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5
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STSCI
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6
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Disk Edge-on
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Disk Face
HST
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THEORY
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Disk Structure
Infalling envelope
Wind
Disk
Accretion columns
Hartmann 1998
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Disk Evolution
Hartmann 1998
STSCI
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Gas Giant Planet Formation

• Gas Giant Planets are Hard to Form
• They must form while there is
  H He, i.e., in
  106 - 107 years
• Core-accretion takes too
  long for Saturn, Uranus,
  Neptune

STSCI
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Gas Giant Planet Formation
Pollack et al. 1996
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Gravitational Instabilities

• GIs
• Spiral distortions in a self-gravitating disk
• Appear wherever ? is high and T is low

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EARLIER STUDIES
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Toomre (1964)

• Gravitational stability of disks
• Measured by
• Q cs?/?G?
• Cs speed of sound, ? epicyclic frequency,
• G gravitational constant, ? surface density
• for Q lt 1 ? ring instability
• for Q lt 1.5 - 2 ? spiral instability

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Tomley et al. (1991, 1994)

• Thermal energetics are critical
• Cooling (Q ?)
• Sustains spirals transport
• Makes clumps if it is strong
• Heating (Q ?)
• Suppresses instability

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Tomley et al. (1991, 1994)
Low Cooling Rate
High Cooling Rate
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Pickett et al. (1998, 2000)

• Different EOS
• Locally
• Isothermal
• Locally
• Isentropic
• Adiabatic
• With AV

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Pickett et al. (1998, 2000)

• Different resolutions
• r,?,z 128,64,16
• Double r and z
• Double ?

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Cooling, Heating Fragmentation
Gammie Fragmentation occurs when tcool
3/?.
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THE FORMATION OF GAS GIANT PLANETS
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Isothermal Solar Nebula
Solar Nebula Model R 10 AU
Md/M? 0.1 M? 1M? Q lt 1 in the
outer region Disk
expansion not allowed
Locally isothermal Planets formed
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Isothermal Solar Nebula
Pickett et al. 2000
Boss 2000
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Isothermal High Resolution
Boss 2000 High Resolution Isothermal
Evolution Persistent Dense Clump Forms
Pickett et al 2002 Our Best Isothermal Evolution
s No Persistent Clumps Form
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SPH Simulations

• Solar Nebula Model
• R 20 AU
• Md/M? 0.1
• M? 1M?
• Qmin 1.4
• Locally isothermal
• Adiabatic as
• disk fragments
• Planets formed

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METHODOLOGY
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Equilibrium 2D Models

• How to make a star/disk model
• Self-consistent field method
• Hachisu 1987
• Force balance ? potential
• Polytropic EOS P ??
• Md/M?, Rd/R?, ?(r) r-p
• With or without the star

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Equilibrium 2D Models
Md/M?1/7, Rd/R? 20, ?(r) r-1/2
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3D Hydro Code

• Numerical characteristics
• 2nd order in space and time
• Eulerian
• Fixed cylindrical grid (r,?,z)
• (128,64,16) to (512,256,64)
• 105 to 8x106 cells
• Runs in parallel on a SUN E10000

r 512
? 256
z 64
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3D Hydro Code

• Physics included
• Solves
• Poissons equation
• Equations of hydrodynamics
• Equation of state
• EOS
• Locally isothermal
• Locally isentropic
• Adiabatic

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3D Hydro Code

• Physics included
• Heating
• Artificial viscosity (shock heating)
• Stellar irradiation
• ?-type shear viscosity
• Cooling
• Volumetric cooling (const. tcool)
• Eddington grey approximation
• Flux-limited diffusion radiative cooling

implemented in progress coming soon
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3D Hydro Code

• Stellar irradiation, flux-limited diffusion
  radiative cooling
• Radiative cooling in the atmosphere (?lt2/3)
• Diffusion approximation (with flux limiter) in
  the interior of the disk (??2/3)
• Irradiation (T? 4000 K, R? 2 R?)
• DAlessio (2001) opacities, amax1?m

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SIMULATIONS
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Initial Model
Initial model for full physics simulations
R 40 AU Md 0.07M? M 0.5M? ?(r)
r-1/2 Qmin1.8
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tcool2 ORP (500 yr)
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tcool2 ORP (500 yr)
23.5 ORPs
10MJ
9MJ
3MJ
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tcool2 ORP (500 yr)
6 ORPs
23.5ORPs
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tcool2 ORP (500 yr)
Internal Energy (erg)
Luminosity (L?)
Time (ORP)
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Various Constant tcool Disks
tcool 2 ORP
tcool 1/4 ORP
tcool 1 ORP
12 ORPs
?
18 ORPs
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Irradiation, Flux Diffusion Radiative Cooling
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Irradiation, Flux Diffusion Radiative Cooling
4 ORPs
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SUMMARY AND CONCLUSIONS
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Simulations

• GIs play an important role in causing mass
  transport
• Violent restructuring when Q first becomes lt 1.5
• Persists later at a lower level with continued
  cooling
• Rings of several MJ formed in the constant tcool
  cases, but no fragmentation so far

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Planet Formation

• Thermal energetics are critical
• Isothermality favors fragmentation
• Must include the effects of cooling and heating
• Clump formation requires dominance of strong
  cooling
• Shock heating tends to suppress it
• High azimuthal resolution necessary

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Future Efforts

• Shear viscosity
• Opacities with different maximum grain sizes.
• SEDs
• Adaptive mesh refinement

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