Richard H' Durisen

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Gravitational Instabilities
STScI Symposium May 2005 A Decade of Extrasolar
Planets Around Normal Stars

• Richard H. Durisen
• Department of Astronomy
• Indiana University

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BIG QUESTIONS

• DO GRAVITATIONAL INSTABILITIES (GIs) MAKE
  PLANETS?
• Do they make planets by direct fragmentation?
• Do they accelerate core accretion?
• HOW FAST DO GIS TRANSPORT MASS?
• Is transport local or global?
• Do they produce persistent structures, like rings?

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BIG QUESTIONS

• WHEN DO GIs OCCUR?
• Do they occur only in the embedded phase?
• Do they occur in dead zones?
• HOW DO GIs AFFECT SOLIDS?
• Do they mix solids?
• Do they thermally process solids?
• Do they marshall solids into coherent structures?

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Outline of Talk

• What Do We Know?
• Caution about Fragmentation
• Idealized Cooling Laws
• Radiative Cooling
• Special Effects
• Recap of the Big Questions

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What Do We Know?Stability and Onset

• Toomres stability parameter (thin disks)
• for Q cs?/?G? lt 1 ? linear ring instability
• for Q lt 1.5 - 1.7 ? linear spiral instability
• Onset
• growth from noise in a few rotations
• predominance of trailing spiral waves

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What Do We Know? Nonlinear Behavior

• What determines the nonlinear amplitude?
• the amplitude is controlled by the thermal
  physics of the disk
• over long times, a balance is reached between
  heating by irreversible processes and cooling by
  radiation
• Nonlinear outcome
• nonlinear mode coupling gravitoturbulence
• fragmentation occurs for fast radiative cooling
  and for cool isothermal disks
• Nature of the nonlinear waves
• intrinsically 3D (like f-modes)
• surface distortions are important

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What Do We Know? Heating/Cooling and
Fragmentation
Boss 2000 2001
Isothermal
Strong Heating
5MJ?
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What Do We Know? Isothermal Disk Fragmentation
High Resolution Simulation Qmin 1.3 M 1
M? Md 0.09 M? Rd 20 AU Persistent
Dense Clump Forms!
5MJ?
Boss 2000
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What Do We Know? Isothermal Disk Fragmentation
?max 64
Local regions of thin disks fragment for Q lt
1.4
MJ?
?max 128
Pickett et al. 2005
Nelson et al. 2000
Johnson Gammie 2003
Agree about dense clumps forming but not about
how long they live
5MJ?
6 MJ?
?max 256
Mayer et al. 2002 2004
PIckett et al. 2003
Boss 2000
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Caution about Isothermal Fragmentation
Q 1.35 Pickett et al. 2005
No Artificial Viscosity
CQ 15 Artificial Bulk Viscosity
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Idealized Cooling
tcool constant tcool? constant ?
uint/tcool
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Idealized Cooling Mejía et al. 2005
Initial model
R 40 AU Md 0.07M? M 0.5M? ?(r)
r-1/2 Qmin1.8
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Idealized Coolingtcool 2 orp (500 yrs)
constant
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Idealized Coolingtcool 2 orp (500 yrs)
constant
23.5 ORPs
10MJ
9MJ
3MJ
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Idealized CoolingdM/dt Large Variable (tcool
const.)
Net Inflow
Net Outflow
Mass inflow burst 10-5 M?/yr Asymptotic 5x10-7
M?/yr
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Idealized CoolingNonlocal Modes for tcool
constant
The region of net inflow is inside the CR of
strong, persistent m2 modes
Net Outflow Net Inflow
Outer Lindblad Resonance
Dense Rings
Corotation Radius
Inner Lindblad Resonance
m 2 Power Spectrum
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Idealized Coolingtcool? 7.5, Md 0.5Ms
Cooling Phase
Transition Phase
Burst Phase
Asymptotic Phase
Lodato Rice 2005
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Idealized Coolingtcool? 7.5 versus tcool 2
orps
Md 0.05Ms
Md 0.10Ms
Md 0.14Ms
Md 0.25Ms
Mejía et al. 2005
Lodato Rice 2004
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Idealized CoolingGlobal versus Local

• Local Transport by GIs
• Local behavior occurs when
• Md lt 0.5Ms (H lt 0.1r) and
• tcool is local (e.g., tcool? constant)
• Then
• transport is well characterized by a local
  ?-viscosity
• ? 4/9?(?-1)tcool? (Gammie 2001)
• high-order tightly wrapped spirals predominate

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Idealized CoolingGlobal versus Local

• Global Transport by GIs
• Global behavior occurs when
• for any Md, when tcool is global
• for large Md (H gt 0.1r) , when tcool is local
• Then
• transport is not well characterized by a local
  ?-viscosity
• ? gt 4/9?(?-1)tcool? but is very non-uniform in
  space and time
• low-order open spirals predominate
• dense rings form at the edge of GI-activity

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Idealized CoolingDifferent ?(r) for tcool
constant
? r-1
? r-1/2
? r-3/2
Michael et al. 2005
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Radiative CoolingSo What is tcool?

• Treatments to Date
• 2D
• Nelson et al. 2000
• Johnson Gammie 2003
• 3D
• Boss (2001, 2002, 2004)
• Mejia (2004), Cai (2006), Boley (2007)
• Major Issue
• Boss sees fast cooling due to convection
  independent of opacity
• Mejia/Cai see slow cooling dependent on opacity

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Radiative Cooling Johnson Gammie 2003
Thin-disk shearing box simulations with one-zone
radiative cooling
No Frag.
Conclusions Opacity boundaries
may be important. You cannot predict
fragmentation from the initial tcool
alone. Fragmentation occurs for
lttcoolgt? lt 1 -10.
?c0 initial cooing time
Opacity Gap
lt?cgt average sustained cooing time
Frag.
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Radiatve Cooling Mejía et al. 2005 Cai et al.
2005
z (AU)

• Stellar /or Envelope Irradiation, Flux-Limited
  Diffusion Optically Thin Radiative Cooling
• Irradiation by starlight or envelope (T 15 to
  120K) can be on or off
• DAlessio (2001) opacities, a-3.5 with amin
  0.005 ? and variable amax (1 ? to 1 mm)
• Match optically thin and thick regions with an
  Eddington grey atmosphere at ? 2/3

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Radiative CoolingMejía Disk with Realistic
Cooling
Mejía et al. 2005, Cai et al. 2005
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Realistic CoolingWhat are the tcools?
Mejía et al. 2005, Cai et al. 2005
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Realistic CoolingBoss versus Mejía/Cai
Boss Disk Mejía/Cai Code Mejía/Cai BCs
Boss Disk Mejía/Cai Code Boss BCs
Boss Disk Boss Code
Cai et al. 2005
Boss 2001
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Realistic CoolingBoss versus Mejía/Cai
? (g cm-2)
Dense Cold Ring For Boss BC
Cai et al. 2005
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Realistic CoolingEnvelope Irradiation of Mejía
Disk
No Envelope Irradiation
Irradiation Tenv 15K
Irradiation Tenv 25K
Irradiation Weakens and can Suppress GIs
Cai et al. 2005
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Realistic CoolingMetallicity and Grain Size
Solar amax 1?
2.0 Solar amax 1?
0.5 Solar amax 1?
Solar amax 1mm
Higher Z Higher amax Suppress GIs
Cai et al. 2005
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Special Effects
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Special Effects Spiral Waves as Hydraulic Shock
Jumps
Hydraulic jumps associated with spiral shocks can
lead to breaking waves!
This has implications for mixing and
processing of solids
Boley et al. 2005, Boley Durisen 2005
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Special Effects Dense Rings, Lindblad
Resonances, Planets
Durisen et al. 2005
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Special EffectsMixing Marshalling of Solids
Boss 2004 Fast mixing into spirals of small
particulates added to disk at high altitude
Rice et al. 2004 Rapid concentration of 50cm
particles into GI spirals
See also Haghighipour Boss 2003
Durisen et al. 2005 Mejía 2005
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Special EffectsLayered Accretion the Dead
Zone
GIs result in outbursts for large ltdM/dtgt
Armitage et al. 2002
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Special EffectsGIs and MRI in 3D
Low GI Stress Phase
High GI Stress Phase
GI stresses weaken oscillate due to MRI
Fromang et al. 2005
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BIG QUESTIONS

• DO GRAVITATIONAL INSTABILITIES (GIs) MAKE
  PLANETS?
• Do they make planets by direct fragmentation?
• Do they accelerate core accretion?

Probably not, real tcools are too long.
They are suppressed by irradiation.
They probably do by marshalling solids
into dense structures (like rings).
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BIG QUESTIONS

• HOW DO GIS TRANSPORT MASS?
• Is transport local or global?
• Do they produce persistent structures, like rings?

It depends on tcool(r) and Md/Ms.
Effective ? can be large.
FU Ori rates possible in bursts.
At edges of GI active regions, yes. This
is most likely for global GIs.
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BIG QUESTIONS

• WHEN DO GIs OCCUR?
• Do they occur mainly in the embedded phase?
• Do they occur in dead zones?

Perhaps not, because they can be
stabilized by envelope irradiation and
finite thickness.
In some cases, they may not occur until
the envelope dissipates.
Yes, probably, but more work is needed!
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BIG QUESTIONS

• HOW DO GIs AFFECT SOLIDS?
• Do they mix solids?
• Do they thermally process solids?
• Do they marshall solids into coherent structures?

You bet they do.
You bet they do.
You bet they do.
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Other Points to Take with You

• Proper treatment of radiative cooling is critical
  for modeling GIs and understanding their
  effects.
• Spiral waves in disks are intrinsically 3D with
  interesting consequences.
• GIs probably assist planet formation by creating
  dense structures and marshalling solids into them.