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
• 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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MOTIVATIONS
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Motivations YSO Disks

• Prevalence of Disks Around YSOs
• 50 of young stars have disks
• Disks last 106 - 107 years
• Measured masses range up to 10 the mass of the
  central star
• Mass accretion rates

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Proplyds in the Orion Nebula
2.5 light-years
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Motivation Disk Variability
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Motivation Disk Variability
Infalling envelope
Wind
Disk
Accretion columns
Hartmann 1998
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Motivation Disk Variability
Hartmann 1998
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Motivation Disk Structure
HST
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Motivation Gas Giant Planets

• 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
• Gap-clearing should limit
• Jovians to only a few MJ

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Motivation Gas Giant Planets
Pollack et al. 1996
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What Do GIs Do to Disks?

• When Disk Self-Gravity is Strong
• Can GIs in disks produce permanent bound
  objects?
• Can GIs play an important role in causing inward
  mass transport?
• What are the observable consequences?

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EARLIER STUDIES
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Earlier Studies Toomre (1964)

• Gravitational stability of disks
• Measured by
• Q cs?/?G?
• Cs speed of sound, ? epicyclic frequency,
• G gravitational constant, ? surface density
• for Q
• for Q

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Earlier Studies Tomley et al. (1991, 1994)

• Thermal energetics are critical
• Cooling (Q ?)
• sustains spirals transport
• makes clumps if strong
• Heating (Q ?)
• suppresses instability
• Problem
• done with a 2D particle code

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Earlier Studies Tomley et al. (1991, 1994)
Low Cooling Rate
High Cooling Rate
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METHODOLOGY
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Methodology Equilibrium

• 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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Methodology Equilibrium
Md/M?1/7, Rd/R20?, ?(r) r-1/2
Star
Disk
Pickett, Mejia, Durisen 2002
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Methodology 3D Hydro

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

r 512
? 256
z 64
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Methodology 3D Hydro

• Physics Included
• EOS
• locally isothermal
• locally isentropic
• adiabatic
• with or without bulk viscosity
• Cassen Woolum
• DAlessio Calvet

Green implemented Red in progress
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Methodology 3D Hydro

• Physics Included
• Heating
• artificial bulk viscosity (shock heating)
• alpha-type shear viscosity
• Cooling
• volumetric cooling (const. tcool)
• Eddington grey approximation
• radiative diffusion

Green implemented Red in progress
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Methodology Unique or Unusual

• Full 3D
• Most other GI studies have been thin disk (2D)
  treatments
• Inner Boundary Conditions
• Can include the star
• No reflective boundaries
• Full Physics
• Heating cooling, EOS

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THE FORMATION OF GAS GIANT PLANETS?
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Gas Giants Boss 1998
Solar Nebula Model R 10 AU
Md/M? 0.1 M? 1M? Q outer region Disk
expansion not allowed
Locally isothermal PLANETS FORMED
?6MJ
1MJ?
Boss 1998
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Gas Giants Pickett et al. 2000
Similar Solar Nebula Model Isothermal Evolution
Restricted Expansion
Unrestricted Expansion
30MJ?
Pickett, Durisen, Cassen, Mejia 2000
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Gas Giants Boss 2000
Similar Solar Nebula Model Isothermal Evolution
Restricted Expansion
Unrestricted Expansion
Boss 2000
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Gas Giants Boss 2000
High Resolution Isothermal Evolution Persistent
Dense Clump Forms
5MJ?
Boss 2000
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Gas Giants Pickett et al. 2002
Our Best Isothermal Evolutions
fmax 64
fmax 128
No Persistent Clumps Form
fmax 128
fmax 256
Pickett, Mejía, Durisen 2002
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HEATING COOLING
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Heating Cooling Pickett et al.
Isothermal
Shock Heating
Many Dense Transient Clumps
No Dense Clumps
Pickett, Durisen, Cassen, Mejía 2000
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Heating Cooling Nelson et al.
Isothermal
Heating Cooling
Many Dense Clumps
No Dense Clumps
Nelson, Benz, Ruzmaikina 2000
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Heating Cooling Boss
Radiative Cooling
With Pseudo-Heating
Many Dense Clumps
No Dense Clumps
Boss 2001
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Heating Cooling Mejía et al.
Initial Model For Full Physics Simulations
R 40 AU Md/M 0.7 M 0.5M?
Mejía, Durisen, Pickett, Calvet 2002
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3.48 ORPs
4.01 ORPs
4.44 ORPs
7.46 ORPs
Tcool 2 ORPs Plus Shock Heating
170.6 AU
ORP Outer Rotation Period 250 yr
Pickett, Mejía, Durisen 2002
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3.48 ORPs
4.01ORPs
4.44 ORPs
Tcool 2 ORPs Plus Shock Heating
10.7 AU
84.6 AU
7.46 ORPs
Pickett, Mejía, Durisen 2002
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Heating Cooling Mejía et al.
4.46 ORPs
Radiative Cooling (Eddington approx. grey
atm.) Plus Shock Heating
170.6 AU
DAlessio et al. opacities
Mejía, Durisen, Pickett, Calvet 2002
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Heating Cooling Mejía et al.
? Radiative Cooling ?
? Tcool 2 ORPs
?
Mejía, Durisen, Pickett, Calvet 2002
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Heating Cooling Mejía et al.
Radiative Cooling
Shock Heating
6.5 ORPs
Density
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Heating Cooling Methanol Masers
2000 AU
Durisen, Mejia, Pickett, Hartquist 2001
Massive Protostars sometimes show linear
distributions of methanol (CH3OH) masers.
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Heating Cooling Methanol Masers
2000 AU
Durisen, Mejia, Pickett, Hartquist 2001
Massive Protostars sometimes show linear
distributions of methanol (CH3OH) masers.
These could be due to the central star
illuminating spiral ridges caused by GIs.
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CONCLUSIONS
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Conclusions

• Can GIs in Disks Produce Permanent Bound
  Objects?
• MAYBE
• requires dominance of strong cooling
• and/or a thermal physics boundary
• shock heating tends to suppress it
• Future efforts
• adaptive mesh techniques
• more accurate treatments of heating and cooling

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Conclusions

• Can GIs Play an Important Role in Causing Inward
  Mass Transport?
• DEFINITELY
• violent restructuring when Q first becomes
• persists later and inward at a lower level with
  continued cooling
• Future efforts
• stellar irradiation
• alpha viscosity

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Conclusions

• What Are the Observable Consequences?
• Disk variability
• time-dependent spiral disk distortions
• luminosity outbursts in the disk
• accretion outbursts on the star
• Masers
• Future efforts
• better radiation physics
• ray tracing of stellar illumination

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