# Proto-Planetary Disk and Planetary Formation

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Proto-Planetary Disk and Planetary Formation
Takayuki Tanigawa

Outline What are proto-planetary disks?
Basic property of the proto-planetary disk. Disk shape Rotation velocity Radial density distribution Planetary formation in the disk Dust (~mm) motion Planetesimal (~km) motion Planet (~103km) motion

What are Proto-Planetary Disks?
Disks around young stars. Naturally form when stars are forming. Dissipate within years. Planets can be formed in the disk. Still hard to resolve the planet forming region Fukagawa et al. 2004

Basic property of the disks
How the gas behave in a gravity field. How does the disk shape determine? Rotation velocity of the disks Density distribution of the disks

Gas motion around a star
Particles around a star can rotate with Keplerian motion Rotate on a plane including the star Gas around a star CANNOT rotate with Keplerian motion because of gas pressure

Vertical structure of the disks
Hydrostatic equilibrium z component of star gravitational force Equation of state exp(-x2) Density profile 1/e Disk scale height (thickness)

Shape of the disks Disk aspect ratio The condition of disk flaring
Keplerian angular velocity Sound speed The condition of disk flaring (Not depend on ρ) For typical disks, When when In general cases (like galactic disks) Flat rotation case Disk shape does NOT depend on density, only on the temperature.

Rotation velocity of the gas
Radial force in balance 2D pressure Angular velocity of the gas: v (η≪１) Centrifugal force Sound speed ~ 0.05 Keplerian velocity F Rotation velocity of the gas is slightly slower than Keplerian motion.

Equation of viscous evolution of the disk (a kind of diffusion equation) where (α viscous coefficient) If steady state is assumed (∂Σ/∂t = 0), Steady accretion solution: (q=1/2) Early stage of the disk evolution No accretion solution: Late stage of the disk evolution This radial density distribution have not been confirmed well by observations.

Viscosity in the disks α viscosity (Shakura and Sunyaev 1973)
speed of vortex × disk scale height (from an analogy of the molecular viscosity coefficient) Non-dimensional parameter α depends on physical condition in the disk, if turbulence, α～10-4 – 10-3 if gravitational instability, α～ 1 Ordinal molecular viscosity： random velocity × mean free path Reynolds number Inertial force Viscous force ≫1 Negligible in most cases for astrophysical problems

Summary of the basic disk property
Disk shape Typical disk: Flaring Rotation velocity v Centrifugal force Slightly slower than Keplerian rotation F Radial density distribution

Planetary formation in the disks
4. Solid planets formation 1. Disk formation 2. Dust sedimentation 5. Gaseous planets formation 3. Planetesimal formation 6. Disk dissipation

Importance of solid particles for planetary formation
Terrestrial planets are made from solid. Jovian planets have solid cores which are musts for the formation. Even though solid material is minor component in the disks, solid particles play an critical role for the planetary formation.

Motion of small particles (Dusts)
Drag law in Epstein regime: Vertical component of gravity of the star Balance between the drag and gravity Vertical density distribution We have the terminal velocity Dust particles settles down to the central plane.

Planetesimal formation through gravitational instability of the dust layer

Difficulty for the planetesimal formation

Planetesimal motion Motion is disturbed by mutual gravitational interaction Increase of random velocity by energy exchange > 0 Gravitational scattering Low relative velocity case Increasing rate decreases with the evolution Random velocity evolution stronger interaction High relative velocity case weaker interaction

Terrestrial-planet formation
Planetesimals grows up to be terrestrial planets through the mutual collision Collision cross section Gravitational focusing Gravitational focusing factor Geometrical cross section Growth rate of planets Growth time scale yr

Migration of the planets
Gravitational interaction with the gas become effective. Planets lose angular momentum through the gravitational interaction with the disks. (Tanaka et al. 2002) The velocity of this migration increase with the mass. Planets migrate inward faster than the growth Significant problem of the present theory.

Gaseous planet formation
When the mass of a solid planet reaches 10 Earth masses, the planet starts to capture the disk gas by their strong gravity. Because the quantity of gas material in the disk is much larger than that of solid material, gas planets can generally grow much larger than solid planets. This is why the large planets in extra-solar planets are considered as “gaseous” planets.

Gap formation If planets become large enough, the planets can create a gap in the disk and the growth stop Planet growth is terminated by themselves through the gap formation. The planet in the gap have to move with the disk viscous evolution.

Summary of the planetary formation
Planetary systems are formed in “proto-planetary disks”. . Dust → Planetesimals Settle down to the mid-plane. Gravitational instability of the dust layer. Planetesimal → Solid planets Mutual collision and coalescence. Solid planets → Gaseous planets Gravitational collapse of the atmosphere by the strong gravity of the planets There are still some problems to be addressed. Dust is hard to settle down enough to occur the instability Growth time scale v.s. Migration time scale Dust → planetesimal → solid planet → gaseous planet ここが固まっていない。しっかり考えるべし。

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