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Proto-Planetary Disk and Planetary Formation Takayuki Tanigawa.

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Presentation on theme: "Proto-Planetary Disk and Planetary Formation Takayuki Tanigawa."— Presentation transcript:

1 Proto-Planetary Disk and Planetary Formation Takayuki Tanigawa

2 Outline 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 shape Disk shape Rotation velocity Rotation velocity Radial density distribution Radial density distribution Planetary formation in the disk Planetary formation in the disk Dust (~mm) motion Dust (~mm) motion Planetesimal (~km) motion Planetesimal (~km) motion Planet (~10 3 km) motion Planet (~10 3 km) motion

3 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 years. Dissipate within 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

4 Basic 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 disks Rotation velocity of the disks Density distribution of the disks Density distribution of the disks

5 Gas motion around a star Particles 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

6 Vertical structure of the disks Equation of state z component of star gravitational force Density profile Disk scale height (thickness) Hydrostatic equilibrium 1/e exp(-x 2 )

7 Shape 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

8 Rotation velocity of the gas Radial force in balance (η ) 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

9 Radial 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)

10 Viscosity in the disks α viscosity α 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 viscosity Ordinal molecular viscosity Negligible in most cases for astrophysical problems Inertial force Viscous force 1 Reynolds number random velocity × mean free path if turbulence, α – speed of vortex × disk scale height if gravitational instability, α 1

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

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

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

14 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

15 Planetesimal formation through gravitational instability of the dust layer Typical size of created planetesimal

16 Difficulty for the planetesimal formation Σ 0 =2Σ H

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

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

19 Migration of the planets Gravitational interaction with the gas become effective. Gravitational interaction with the gas 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.

20 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. 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. 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. This is why the large planets in extra-solar planets are considered as gaseous planets.

21 Gap formation If planets become large enough, the planets can create a gap in the disk and the growth stop If planets become large enough, the planets can create 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.

22 Summary of the planetary formation Planetary systems are formed in proto-planetary disks. Planetary systems are formed in proto-planetary disks.. Dust Planetesimals Dust 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 planets Solid planets Gaseous planets Gravitational collapse of the atmosphere by the strong gravity of the planets Gravitational collapse of the atmosphere by the strong gravity of the planets 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 instability Dust is hard to settle down enough to occur the instability Growth time scale v.s. Migration time scale Growth time scale v.s. Migration time scale Planetary systems are formed in proto-planetary disks. Planetary systems are formed in proto-planetary disks.. Dust Planetesimals Dust 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 planets Solid planets Gaseous planets Gravitational collapse of the atmosphere by the strong gravity of the planets Gravitational collapse of the atmosphere by the strong gravity of the planets 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 instability Dust is hard to settle down enough to occur the instability Growth time scale v.s. Migration time scale Growth time scale v.s. Migration time scale Dust planetesimal solid planet gaseous planet


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