Proto-Planetary Disk and Planetary Formation Takayuki Tanigawa.

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