From Dust to Planetesimals

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From Dust to Planetesimals
D.N.C. Lin
Pascale Garaud, Taku Takeuchi, Cathie
Clarke, Hubert Klahr, Laure
Barrier-Fouchet
Ringberg Castle April 14th, 2004
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Basic Objectives

• 1. To find clues on the planet formation
  mechanisms time scales
• To identify signatures of planet-forming
  protostellar disks

Central Issues

1. How do planets form so prolifically?
2. What processes determine the retention factor of
   heavy elements?
3. Is the solar system architecture a rule or an
   exception?

Methodology approach

1. Spectroscopic and photometric observations
2. Condensation and coagulation of heavy elements
3. Dust sedimentation and orbital migration
4. Fractionation of heavy elements through dust
   evolution
5. Transition from protostellar to debris disks

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Observations 1 young stars

• All stellar material were accreted through
  protostellar disks.
• Sizes and surface density distribution (100 AU,
  Sr-1)
• Gas accretion rate (10-8 M yr-1) after 3-10 Myr
• mm-size dust in the inner mm-size dust in the
  outer disk deplete
• after 3-10 Myr
• Grain phases and size evolution (growth and
  sedimentation)
• Coexistence of hydrogen gas and dust grains (gas
  depletion)
• Debris disk structures (embedded companions?)

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Observation 2 mature stars

• Debris disks (b Pic)
• Apparent correlation between planets and enhanced
  metallicity
• (cause or consequence?)
• Systematic analysis open clusters (photometry
  and spectroscopy)

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Observation 3 solar system
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Theory gas dust evolution

• Gas momentum mass transport
• Dust gas drag, sublimation,
• condensation, radiative scattering
• coagulation, fragmentation
• Fractionation is expected
• Differential evolution

• Evolution of dust
• Laminar limit
• 1) sedimentation (Weidenschilling)
• 2) shearing instability (Weidenschilling
• Cuzzi, Garaud)
• 3) gravitational instability (Goldreich,
• Ward, Sekiya, Youdin, Shu)
• b) Turbulent flow( Supuver, Cuzzi)
• c) Vortical flow (Klahr)

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Vertical settling

• EPSTEIN REGIME strong coupling
• Equation of motion z - z - ? z
• where ? is the drag coefficient,
• ? ? c /?s s ?K , ? gt 1

STOKES REGIME weak coupling Equation of motion
z -z - ? z z In limit ? lt 1,
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Particle evolution in a static disc(small
particles)
At given height, rapid depletion of large
particles successive depletion of smaller and
smaller ones.
At given time, concentration of larger particles
towards thinner and thinner layers around mi-plane
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Shear instability in the dust layer
v 0 (i.e. Keplerian velocity) when D(z) gtgt
1 v -? (i.e. gas velocity) when D(z) ltlt
1 This strong shear in the azimuthal velocity
profile could be unstable!

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Dust layer stability large particle limit
Growth rates

• Dust layer, very thin, composed mostly of very
  large particles uncoupled to the gas !
  Instability affects only the gas, not the
  particles
• Could use Boussinesq shear instability analysis
• But, particles exert a drag on the gas the
  excitation mechanism also provides damping!

Drag neglected Drag taken into account
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Stability criteria
Gravitationally unstable region
Dust to gas mass surface density ratio
Solar nebula
Variations in the critical Richardson number
Thickness to radius ratio
Shearing instability occurs prior the onset of
gravitational instability
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Gravitational instability in turbulent disks
Instability requires heavy elemental enhancement
(Sakeya,Youdin Shu)
Unresolved critical Richardson number in
turbulent disk 0.25 ?
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Dusts in turbulent disks
a) Orbital evolution size dependence (small
vs large) b) Turbulent concentration
Cuzzi c) Growth fragmentation
Thickness vs radius
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Enhanced coagulation

• Orbital decay time is determined by
• the gas density
• Particles growth is determined by the
• dust density
• Overcome the growth barrier, stall,
• and survival of sublimation

• Concentration
• Eddie concentration
• X winds photoevaporation
• Infall to large radii decay
• to sublimation boundaries

Nebula gas solid sublimation temperature
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Sublimation fronts

• Planets compositional
• gradient
• 2) Rapid growth time scale
• efficient retention
• Increases in S helps planets

• Constraints set by stellar
• metallicity homogenity
• 2) No sharp transition zones
• 3) Coexistence of vapor and solids
• (observational implications)
• 4) Disk radius is determined by the
• most-volatile sublimation front

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Formation of the first gas giant
Minimum mass nebula S 10 (a/1AU)-1.5 g
cm-2 Embryo growth time scale Extended
isolation mass with gas damping a few
Mearth Misolation S1.5 a3 (Lissauer, Ida,
Kokubo, Sari, etc)
Global enrichment
Local enrichment elemental abundances
fractionation (Stevenson,Takeuchi, Youdin)
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Gas accretion
Critical core mass for gas accretion. In Saturn,
Uranus, Neptune 10 MEarth Other dependences
Bombardment rate, radiation transfer, disk
response.
Runaway Bondi accretion in lt0.1 My. Termination
due to global depletion limited supply disk
disposal. Local depletion due to gap
formation viscous thermal conditions.
Bryden
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Metal Enrichment in Gas Giants

• More heavy elements are
• accreted onto the envelope
• than the core
• Requirements)
• Local enrichment or
• Erosion of massive cores

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Limited Accretion onto Cores
Metal enrichment in the envelope
Challenge Saturn-mass planets!
Kley, Ciecielag, Artymowicz )
Preheating of Bondi radius reduction of
accretion rate (Edgar)
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Multiple-giants formation timescale
1) KBOs in the solar system, 2) Ups And 3)
Resonance in GJ 876 55 Can
Time interval between successive gas-giant
formation is comparable to the migration time
scale
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Induced core formation
(Papaloizou, Kley, Nelson, Artymowicz )
Protoplanet migration (Ida, Levison
etc) Modified type I migration of embryos (Ward)
Dust migration barrier (Bryden, Rozczyska)
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Mass period distribution
t/tdeplete

• Some implications
• Low mass gas giants form inside ice line migrate
  in and perish first.
• Intermediate period planets migration can be
  halted by gas depletion
• period distribution can provide information
  on tdeolete /tmigrate
• Ice giants acquire their large mass after gas
  depletion do not migrate
• Possibility of an intermediate mass-a desert
  bounded by rock, ice, and
• gas giants.
• Lower bound gt critical core mass. Right bound gt
  tdeolete /tgrowth
• Upper bound gt gas accretion truncation
  conditions

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Self regulated clearing

1. All stellar material pass through disk accretion
2. Planets can form inside ice line of massive disks
3. Inner planets migrate in readily
4. Most early arrivers were consumed by the stars
5. The consumed planet were thoroughly mixed

• Evidences for self cleaning resonant planets
• tgrowth lttmigrate lttdeplete
• Resonant sweeping and clearing
• Enhanced formation of multiple planets
• Sweeping secular resonance

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Metallicity-hJ Correlation
Abundant Z shorten growth time scales
increases Mcore
A large fraction of hot Jupiters must have
perished early
Tidal disruption and period cut off
Remaining puzzle why is the retention efficiency
invariant of Fe/H
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Summary

• Small dispersion in Fe/H
• Mass of the residual disk is less than 2 mmsn
• Contamination due to late bombardment is less
  than 5 ME
• Self regulate dust accretion
• Simultaneous depletion implies dust drag
• Planet-stellar metallicity correlation
• Locally metallicity enhancement
• Sensitive Fe/H dependence due to formation
• Some contaminations are expected

Planetary ubiquity and diversity 1) The current
mass period distribution of extra solar planets
can be used to infer the formation
conditions 2) Abundant rocky planets can exist
without the presence of gas giants 3)
Protostellar disks may have been repeated cleared
through the formation, migration, and
stellar consumption of planets. 4) Many planetary
systems may have high dynamical filling factors.
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Persistence depletion of dust
Observations 1) Mm continuum survives for gta
few Myr 2) Sr-1 with a sharp edge 3)
Simultaneous inner outer disk depletion

• Physical processes
• Dominant scatters have sizes mm
• Orbital decay needs replenishment
• Growth drainage 0.1 sticking
• probability
• 4) Large particles to the disk centers

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Decline in dust continuum
Photoevaporation of gas Enhanced orbital decay
Takeuchi, Clarke
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Dust-ring structure
klahr
1) Particle accumulation due to radiation
pressure 2) Gaps can form through radial
drift instability