From Dust to Planetesimals
D.N.C. Lin
Pascale Garaud, Taku Takeuchi,
Cathie Clarke, Hubert Klahr,
Laure Barrier-Fouchet
Ringberg Castle
April 14th, 2004
Basic Objectives
1. To find clues on the planet formation mechanisms & time scales
2. 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.
2.
3.
4.
5.
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
Observations: 1 young stars
a)
b)
c)
d)
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
e) 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 stars
a) Debris disks (b 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 evolution
a) Gas: momentum & mass transport
b) Dust: gas drag, sublimation,
condensation, radiative scattering
coagulation, fragmentation
c) Fractionation is expected
d) Differential evolution
Evolution 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 settling
EPSTEIN REGIME: strong coupling
Equation of motion: z’’ = - z - m z’
where m is the drag coefficient,
m =  c /s s K , m > 1
STOKES REGIME: weak coupling
Equation of motion: z’’ = -z - m |z’| z’
In limit m < 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
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
Stability criteria
Gravitationally
unstable region
Dust to gas
mass surface
density ratio
Variations in
the critical
Richardson number
Solar
nebula
Thickness to radius ratio
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
Cuzzi
c) Growth & fragmentation
Thickness vs radius
Enhanced coagulation
a) Orbital decay time is determined by
the gas density
b) Particles’ growth is determined by the
dust density
c) Overcome the growth barrier, stall,
and survival of sublimation
Concentration:
1) Eddie concentration
2) X winds & photoevaporation
3) Infall to large radii & decay
to sublimation boundaries
Nebula gas & solid sublimation temperature
Sublimation fronts
1) Planets’ compositional
gradient
2) Rapid growth time scale
& efficient retention
3) Increases in S helps planets
1) 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
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)
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
Metal Enrichment in Gas Giants
More heavy elements are
accreted onto the envelope
than the core
Requirements:)
1) Local enrichment or
2) Erosion of massive cores
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)
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
Induced core formation
(Papaloizou, Kley, Nelson, Artymowicz …)
Protoplanet
migration
(Ida, Levison etc)
Modified type I
migration of
Dust migration barrier embryos (Ward)
(Bryden, Rozczyska)
Mass period distribution
t/tdeplete
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 tdeolete /tmigrate
3) Ice giants acquire their large mass after gas depletion & do not migrate
4) Possibility of an intermediate mass-a desert bounded by rock, ice, and
gas giants.
5) Lower bound => critical core mass. Right bound => tdeolete /tgrowth
Upper bound => gas accretion truncation conditions
Self regulated clearing
1)
2)
3)
4)
5)
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
1) tgrowth <tmigrate <tdeplete
2) Resonant sweeping and clearing
3) Enhanced formation of multiple planets
4) Sweeping secular resonance
Metallicity-J 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]
Summary
Small dispersion in [Fe/H]:
1) Mass of the residual disk is less than 2 mmsn
2) Contamination due to late bombardment is less than 5 ME
3) Self regulate dust accretion
4) Simultaneous depletion implies dust drag
Planet-stellar metallicity correlation:
1) Locally metallicity enhancement
2) Sensitive [Fe/H] dependence due to formation
3) 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.
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
1) Dominant scatters have sizes ~mm
2) Orbital decay needs replenishment
3) Growth drainage: 0.1 sticking
probability
4) Large particles to the disk centers
Decline in dust continuum
Photoevaporation of gas
Enhanced orbital decay
Takeuchi, Clarke
Dust-ring structure
klahr
1) Particle accumulation due to
radiation pressure
2) Gaps can form through radial
drift instability