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Proto-Planetary DiskProto-Planetary Diskand Planetary Formationand Planetary Formation
Takayuki TanigawaTakayuki Tanigawa
OutlineOutline
What are proto-planetary disks?What are proto-planetary disks?Basic property of the proto-planetary disk.Basic property of the proto-planetary disk.
Disk shapeDisk shapeRotation velocityRotation velocityRadial density distribution Radial density distribution
Planetary formation in the diskPlanetary formation in the diskDust (~mm) motionDust (~mm) motionPlanetesimal (~km) motionPlanetesimal (~km) motionPlanet (~10Planet (~1033km) motionkm) motion
What are Proto-Planetary Disks?What are Proto-Planetary Disks?
Disks around young stars.Disks around young stars.Naturally form when stars are forming.Naturally form when stars are forming.Dissipate within 10Dissipate within 1055-10-1077 years. years.Planets can be formed in the disk.Planets can be formed in the disk.Still hard to resolve the planet forming region
Fukagawa et al. 2004
Basic property of the disksBasic property of the disks
How the gas behave in a gravity field.How the gas behave in a gravity field.How does the disk shape determine?How does the disk shape determine?
Rotation velocity of the disksRotation velocity of the disks
Density distribution of the disksDensity distribution of the disks
Gas motion around a starGas motion around a starParticles around a star can rotate with Keplerian motion
Gas around a star CANNOT rotate with Keplerian motion
Rotate on a plane including the star
because of gas pressure
Vertical structure of the disksVertical structure of the disks
Equation of state
z component of star gravitational force
Density profile
Disk scale height (thickness)
Hydrostatic equilibrium
1/e
exp(-x2)
Shape of the disksShape of the disks
When
The condition of disk flaring
In general cases (like galactic disks)
(Not depend on ρ)
Flat rotation case
Disk shape does NOT depend on density, only on the temperature.
Disk aspect ratio
For typical disks,
Sound speed
Keplerian angular velocity
when
Rotation velocity of the gasRotation velocity of the gasRadial force in balance
(η≪ 1 )
Rotation velocity of the gas is slightly slower than Keplerian motion.
Angular velocity of the gas:
Keplerian velocity
Sound speed
v
F
Centrifugal force
2D pressure
~ 0.05
Radial density distributionRadial density distribution
If steady state is assumed (∂Σ/∂t = 0),
Equation of viscous evolution of the disk (a kind of diffusion equation)
where
Steady accretion solution:
No accretion solution:
This radial density distribution have not been confirmed well by observations.
Early stage of the disk evolution
Late stage of the disk evolution
(q=1/2)
(α viscous coefficient)
Viscosity in the disksViscosity in the disksα viscosityα viscosity (Shakura and Sunyaev 1973)
(from an analogy of the molecular viscosity coefficient)
Non-dimensional parameter α depends on physical condition in the disk,
Ordinal molecular viscosityOrdinal molecular viscosity :
Negligible in most cases for astrophysical problems
Inertial force
Viscous force≫1
Reynolds number
random velocity × mean free path
if turbulence, α ~ 10-4 – 10-3
speed of vortex × disk scale height
if gravitational instability, α ~ 1
Summary of the basic disk propertySummary of the basic disk propertyDisk shape
Rotation velocity
Radial density distribution
~ 0.001-0.01
Typical disk: Flaring
Slightly slower than Keplerian rotation
v
F
Centrifugal force
Planetary formation in the disksPlanetary formation in the disks
1. Disk formation1. Disk formation
2. Dust sedimentation2. Dust sedimentation
3. Planetesimal formation3. Planetesimal formation
4. Solid planets formation4. Solid planets formation
5. Gaseous planets formation5. Gaseous planets formation
6. Disk dissipation6. Disk dissipation
Importance of solid particles for Importance of solid particles for planetary formationplanetary formation
Terrestrial planets are made from solid.Terrestrial planets are made from solid.Jovian planets have solid cores which are Jovian planets have solid cores which are
musts for the formation.musts for the formation.Even though solid material is minor compoEven though solid material is minor compo
nent in the disks, solid particles play an critnent in the disks, solid particles play an critical role for the planetary formation.ical role for the planetary formation.
Motion of small particles (Dusts)Motion of small particles (Dusts)Drag law in Epstein regime:
Dust particles settles down to the central plane.
Balance between the drag and gravity
We have the terminal velocity
Vertical component of gravity of the star
Vertical density distribution
Planetesimal formation through gravitaPlanetesimal formation through gravitational instability of the dust layertional instability of the dust layer
Typical size of created planetesimal
Difficulty for the planetesimal formaDifficulty for the planetesimal formationtion
Difficulty for the planetesimal formaDifficulty for the planetesimal formationtion
Σ0=2ΣH
Planetesimal motionPlanetesimal motion
Increase of random velocity by energy exchange
Random velocity evolution
Increasing rate decreases with the evolution
Motion is disturbed by mutual gravitational interactionMotion is disturbed by mutual gravitational interaction
Low relative velocity case
High relative velocity case
Gravitational scattering> 0
stronger interaction
weaker interaction
Terrestrial-planet formationTerrestrial-planet formation
Growth time scale
Planetesimals grows up to be terrestrial planets through the Planetesimals grows up to be terrestrial planets through the mutual collisionmutual collision
Collision cross section
Gravitational focusing factor
Geometrical cross section
Gravitational focusing
Growth rate of planets
yr
Migration of the planetsMigration of the planets
Gravitational interaction with the gas Gravitational interaction with the gas become effective.become effective.
(Tanaka et al. 2002)
The velocity of this migration increase with the mass.
Planets lose angular momentum through the gravitational interaction with the disks.
Planets migrate inward faster than the growth
Significant problem of the present theory.
Gaseous planet formationGaseous planet formation When the mass of a solid planet reaches 10 When the mass of a solid planet reaches 10
Earth masses, the planet starts to capture the Earth masses, the planet starts to capture the disk gas by their strong gravity. disk gas by their strong gravity. Because the quantity of gas material in the disk is Because the quantity of gas material in the disk is
much larger than that of solid material, gas planets can much larger than that of solid material, gas planets can generally grow much larger than solid planets.generally grow much larger than solid planets.
This is why the large planets in extra-solar planets are This is why the large planets in extra-solar planets are considered as “gaseous” planets.considered as “gaseous” planets.
Gap formationGap formation
If planets become large enough, the planets can If planets become large enough, the planets can create a gap in the disk and the growth stopcreate a gap in the disk and the growth stop
The planet in the gap have to move with the disk viscous evolution.
Planet growth is terminated by themselves through the gap formation.
Summary of the planetary formationSummary of the planetary formationSummary of the planetary formationSummary of the planetary formation Planetary systems are Planetary systems are formed in “proto-planetary disks”.formed in “proto-planetary disks”.
..
Dust → PlanetesimalsDust → Planetesimals Settle down to the mid-plane.Settle down to the mid-plane. Gravitational instability of the dust layer.Gravitational instability of the dust layer.
Planetesimal → Solid planets Planetesimal → Solid planets Mutual collision and coalescence.Mutual collision and coalescence.
Solid planets → Gaseous planetsSolid planets → Gaseous planets Gravitational collapse of the atmosphere by the strong gravity of the Gravitational collapse of the atmosphere by the strong gravity of the
planetsplanets
There are still some problems to be addressed.There are still some problems to be addressed. Dust is hard to settle down enough to occur the instabilityDust is hard to settle down enough to occur the instability Growth time scale v.s. Migration time scaleGrowth time scale v.s. Migration time scale
Planetary systems are Planetary systems are formed in “proto-planetary disks”.formed in “proto-planetary disks”...
Dust → PlanetesimalsDust → Planetesimals Settle down to the mid-plane.Settle down to the mid-plane. Gravitational instability of the dust layer.Gravitational instability of the dust layer.
Planetesimal → Solid planets Planetesimal → Solid planets Mutual collision and coalescence.Mutual collision and coalescence.
Solid planets → Gaseous planetsSolid planets → Gaseous planets Gravitational collapse of the atmosphere by the strong gravity of the Gravitational collapse of the atmosphere by the strong gravity of the
planetsplanets
There are still some problems to be addressed.There are still some problems to be addressed. Dust is hard to settle down enough to occur the instabilityDust is hard to settle down enough to occur the instability Growth time scale v.s. Migration time scaleGrowth time scale v.s. Migration time scale
Dust → planetesimal → solid planet → gaseous planet Dust → planetesimal → solid planet → gaseous planet