From Dust to Planetesimals

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

2. Basic Objectives • 1. To find clues on the planet formation mechanisms & time scales • To identify signatures of planet-forming protostellar disks Central Issues • How do planets form so prolifically? • What processes determine the retention factor of heavy elements? • Is the solar system architecture a rule or an exception? Methodology & approach • Spectroscopic and photometric observations • Condensation and coagulation of heavy elements • Dust sedimentation and orbital migration • Fractionation of heavy elements through dust evolution • Transition from protostellar to debris disks

3. Observations: 1 young stars • All stellar material were accreted through protostellar disks. • Sizes and surface density distribution (100 AU, S~r-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?)

4. 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)

5. Observation 3: solar system

6. 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)

7. Vertical settling STOKES REGIME: weak coupling Equation of motion:z’’ = -z -  |z’| z’ In limit < 1, EPSTEIN REGIME: strong coupling Equation of motion: z’’ = - z -  z’ where  is the drag coefficient,  =  c /s s K , > 1

8. 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

9. 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!

10. 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

11. 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

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

13. Dusts in turbulent disks a) Orbital evolution: size dependence (small vs large) b) Turbulent concentration Cuzzi c) Growth & fragmentation Thickness vs radius

14. 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

15. 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

16. Minimum mass nebula S = 10 (a/1AU)-1.5g cm-2 Embryo growth time scale: Extended isolation mass with gas damping: a few Mearth Misolation ~ S1.5a3 (Lissauer, Ida, Kokubo, Sari, etc) Formation of the first gas giant Global enrichment Local enrichment: elemental abundances fractionation (Stevenson,Takeuchi, Youdin)

17. 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 <0.1 My. Termination due to global depletion: limited supply & disk disposal. Local depletion due to gap formation: viscous & thermal conditions. Bryden

18. Metal Enrichment in Gas Giants • More heavy elements are • accreted onto the envelope • than the core • Requirements:) • Local enrichment or • Erosion of massive cores

19. 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)

20. 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

21. Induced core formation (Papaloizou, Kley, Nelson, Artymowicz …) Protoplanet migration (Ida, Levison etc) Modified type I migration of embryos (Ward) Dust migration barrier (Bryden, Rozczyska)

22. 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 => critical core mass. Right bound => tdeolete /tgrowth • Upper bound => gas accretion truncation conditions

23. Self regulated clearing • All stellar material pass through disk accretion • Planets can form inside ice line of massive disks • Inner planets migrate in readily • Most early arrivers were consumed by the stars • The consumed planet were thoroughly mixed • Evidences for self cleaning: resonant planets • tgrowth<tmigrate <tdeplete • Resonant sweeping and clearing • Enhanced formation of multiple planets • Sweeping secular resonance

24. 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]

25. 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 Summary 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.

26. Persistence & depletion of dust Observations: 1) Mm continuum survives for >a few Myr 2) S~r-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

27. Decline in dust continuum Photoevaporation of gas Enhanced orbital decay Takeuchi, Clarke

28. Dust-ring structure klahr 1) Particle accumulation due to radiation pressure 2) Gaps can form through radial drift instability