From Dust to Planetesimals

D.N.C. LinPascale Garaud, Taku Takeuchi, Cathie Clarke, Hubert Klahr, Laure Barrier-Fouchet

Ringberg Castle April 14th, 2004

Basic Objectives1. To find clues on the planet formation mechanisms & time scales2. To identify signatures of planet-forming protostellar disks

Methodology & approach1. Spectroscopic and photometric observations2. Condensation and coagulation of heavy elements3. Dust sedimentation and orbital migration4. Fractionation of heavy elements through dust evolution5. Transition from protostellar to debris disks

Central Issues1. 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?

Observations: 1 young starsa) All stellar material were accreted through protostellar disks.b) Sizes and surface density distribution (100 AU, r-1)c) Gas accretion rate (10-8 M yr-1) after 3-10 Myr d) m-size dust in the inner & mm-size dust in the outer disk deplete after 3-10 Myre) Grain phases and size evolution (growth and sedimentation)f) Coexistence of hydrogen gas and dust grains (gas depletion)g) Debris disk structures (embedded companions?)

Observation 2: mature starsa) Debris disks (Pic)b) Apparent correlation between planets and enhanced metallicity (cause or consequence?)c) Systematic analysis: open clusters (photometry and spectroscopy)

Observation 3: solar system

Theory: gas & dust evolutiona) Gas: momentum & mass transportb) Dust: gas drag, sublimation, condensation, radiative scattering coagulation, fragmentationc) Fractionation is expectedd) Differential evolutionEvolution of dust:a) 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)

Vertical settlingEPSTEIN REGIME: strong couplingEquation of motion: z’’ = - z - z’ where is the drag coefficient,

= c /s s K , 1

STOKES REGIME: weak coupling Equation of motion: z’’ = -z - |z’| z’ In limit < 1,

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

Shear instability in the dust layer

v 0 (i.e. Keplerian velocity) when D(z) >> 1

v ~ - (i.e. gas velocity) when D(z) << 1

This strong shear in the azimuthal velocity profile could be unstable!

Dust layer stability: large particle limit

• 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!

Growth rates

Drag neglected

Drag taken into account

Stability criteria

Dust to gas mass surface density ratio

Thickness to radius ratio

Variations in the critical Richardson number

Solar nebula

Gravitationallyunstable region

Shearing instability occurs prior the onset of gravitational instability

Gravitational instability in turbulent disks

Instability requires heavy elemental enhancement (Sakeya,Youdin & Shu)Unresolved: critical Richardson number in turbulent disk = 0.25 ?

Dusts in turbulent disks

a) Orbital evolution: size dependence (small vs large)b) Turbulent concentration Cuzzic) Growth & fragmentation

Thickness vs radius

Enhanced coagulationa) Orbital decay time is determined by the gas densityb) Particles’ growth is determined by the dust densityc) Overcome the growth barrier, stall, and survival of sublimation

Concentration:1) Eddie concentration2) X winds & photoevaporation3) Infall to large radii & decay to sublimation boundaries

Nebula gas & solid sublimation temperature

Sublimation fronts1) Planets’ compositional gradient2) Rapid growth time scale & efficient retention3) Increases in helps planets

1) Constraints set by stellar metallicity homogenity2) No sharp transition zones3) Coexistence of vapor and solids (observational implications)4) Disk radius is determined by the most-volatile sublimation front

Formation of the first gas giantMinimum mass nebula= 10 (a/1AU)-1.5g cm-2

Embryo growth time scale:

Extended isolation mass withgas damping: a few Mearth

Misolation ~ a3 (Lissauer,Ida, Kokubo, Sari, etc)Global enrichment

Local enrichment: elemental abundances fractionation (Stevenson,Takeuchi, Youdin)

Gas accretionCritical core mass for gas accretion.In Saturn, Uranus, Neptune ~10 MEarth Other dependences: Bombardment rate, radiation transfer, disk response.

Runaway Bondi accretion in <0.1 My.Termination due to global depletion: limited supply & disk disposal.Local depletion due to gap formation:viscous & thermal conditions. Bryden

Metal Enrichment in Gas Giants

More heavy elements are accreted onto the envelope than the coreRequirements:)1) Local enrichment or 2) Erosion of massive cores

Limited Accretion onto CoresMetal enrichment in the envelope

Preheating of Bondi radius & reduction of accretion rate (Edgar)

Kley, Ciecielag, Artymowicz …)Challenge: Saturn-mass planets!

Multiple-giants formation timescale

Time interval between successive gas-giant formation is comparable to the migration time scale

1) KBOs in the solar system, 2) Ups And3) Resonance in GJ 876 & 55 Can

Induced core formation

Dust migration barrier(Bryden, Rozczyska)

Protoplanet migration(Ida, Levison etc)

Modified type Imigration of embryos (Ward)

(Papaloizou, Kley, Nelson, Artymowicz …)

Mass period distribution

Some implications:1) Low mass gas giants form inside ice line migrate in and perish first. 2) Intermediate period planets: migration can be halted by gas depletion: period distribution can provide information on deoletemigrate

3) Ice giants acquire their large mass after gas depletion & do not migrate4) Possibility of an intermediate mass-a desert bounded by rock, ice, and gas giants. 5) Lower bound => critical core mass. Right bound => deolete /growth

Upper bound => gas accretion truncation conditions

t/deplete

Self regulated clearing1) All stellar material pass through disk accretion2) Planets can form inside ice line of massive disks3) Inner planets migrate in readily4) Most early arrivers were consumed by the stars5) The consumed planet were thoroughly mixed

Evidences for self cleaning: resonant planets) growth<migrate <deplete

2) Resonant sweeping and clearing3) Enhanced formation of multiple planets4) Sweeping secular resonance

Metallicity-J CorrelationAbundant 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]

Summary Small dispersion in [Fe/H]:1) Mass of the residual disk is less than 2 mmsn2) Contamination due to late bombardment is less than 5 ME

3) Self regulate dust accretion4) Simultaneous depletion implies dust dragPlanet-stellar metallicity correlation:1) Locally metallicity enhancement2) Sensitive [Fe/H] dependence due to formation3) 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 conditions2) Abundant rocky planets can exist without the presence of gas giants3) 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.

Persistence & depletion of dustObservations:1) Mm continuum survives for >a few Myr2) ~r-1 with a sharp edge3) Simultaneous inner & outer disk depletion

Physical processes1) Dominant scatters have sizes ~mm2) Orbital decay needs replenishment3) Growth drainage: 0.1 sticking probability4) Large particles to the disk centers

Decline in dust continuumPhotoevaporation of gasEnhanced orbital decay

Takeuchi, Clarke

Dust-ring structure

1) Particle accumulation due to radiation pressure2) Gaps can form through radial drift instability

klahr