ProtoPlanetary Disk and Planetary Formation

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Proto-Planetary Diskand Planetary Formation

• Takayuki Tanigawa

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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

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What are Proto-Planetary Disks?

• Disks around young stars.
• Naturally form when stars are forming.
• Dissipate within 105-107 years.
• Planets can be formed in the disk.

Still hard to resolve the planet forming region
Fukagawa et al. 2004
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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

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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
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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)
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Shape of the disks
Disk aspect ratio
Keplerian angular velocity
Sound speed
The condition of disk flaring
(Not depend on ?)
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.
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Rotation velocity of the gas
Radial force in balance
2D pressure
Angular velocity of the gas
v
(?1)
Centrifugal force
Sound speed
0.05
Keplerian velocity
F
Rotation velocity of the gas is slightly slower
than Keplerian motion.
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Radial density distribution
Equation of viscous evolution of the disk (a kind
of diffusion equation)
where
(a viscous coefficient)
If steady state is assumed (?S/?t 0),
Steady accretion solution
(q1/2)
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.
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Viscosity in the disks
a viscosity (Shakura and Sunyaev 1973)
speed of vortex disk scale height
(from an analogy of the molecular viscosity
coefficient)
Non-dimensional parameter a depends on physical
condition in the disk,
if turbulence, a10-4 10-3
if gravitational instability, a 1
Ordinal molecular viscosity
random velocity mean free path
Reynolds number
1
Negligible in most cases for astrophysical
problems
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Summary of the basic disk property
Disk shape
Typical disk
Flaring
Rotation velocity
v
0.001-0.01
Centrifugal force
Slightly slower than Keplerian rotation
F
Radial density distribution
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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
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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.

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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.
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Planetesimal formation through gravitational
instability of the dust layer
Typical size of created planetesimal
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Difficulty for the planetesimal formation
S02SH
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Planetesimal motion
Motion is disturbed by mutual gravitational
interaction
Increase of random velocity by energy exchange
gt 0
Gravitational scattering
Low relative velocity case
Increasing rate decreases with the evolution
Random velocity evolution
stronger interaction
High relative velocity case
weaker interaction
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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
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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.
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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.

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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.
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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