Presentation on theme: "Proto-Planetary Disk and Planetary Formation"— Presentation transcript:
1 Proto-Planetary Disk and Planetary Formation Takayuki Tanigawa
2 Outline What are proto-planetary disks? Basic property of the proto-planetary disk.Disk shapeRotation velocityRadial density distributionPlanetary formation in the diskDust (~mm) motionPlanetesimal (~km) motionPlanet (~103km) motion
3 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 regionFukagawa et al. 2004
4 Basic property of the disks How the gas behave in a gravity field.How does the disk shape determine?Rotation velocity of the disksDensity distribution of the disks
5 Gas motion around a star Particles around a star can rotate with Keplerian motionRotate on a plane including the starGas around a star CANNOT rotate with Keplerian motionbecause of gas pressure
6 Vertical structure of the disks Hydrostatic equilibriumz component of star gravitational forceEquation of stateexp(-x2)Density profile1/eDisk scale height (thickness)
7 Shape of the disks Disk aspect ratio The condition of disk flaring Keplerian angular velocitySound speedThe condition of disk flaring(Not depend on ρ)For typical disks,WhenwhenIn general cases (like galactic disks)Flat rotation caseDisk shape does NOT depend on density, only on the temperature.
8 Rotation velocity of the gas Radial force in balance2D pressureAngular velocity of the gas:v(η≪１)Centrifugal forceSound speed~ 0.05Keplerian velocityFRotation velocity of the gas is slightly slower than Keplerian motion.
9 Radial density distribution 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 evolutionNo accretion solution:Late stage of the disk evolutionThis radial density distribution have not been confirmed well by observations.
10 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 – 10-3if gravitational instability, α～ 1Ordinal molecular viscosity：random velocity × mean free pathReynolds numberInertial forceViscous force≫1Negligible in most cases for astrophysical problems
11 Summary of the basic disk property Disk shapeTypical disk:FlaringRotation velocityv～Centrifugal forceSlightly slower than Keplerian rotationFRadial density distribution
12 Planetary formation in the disks 4. Solid planets formation1. Disk formation2. Dust sedimentation5. Gaseous planets formation3. Planetesimal formation6. Disk dissipation
13 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.
14 Motion of small particles (Dusts) Drag law in Epstein regime:Vertical component of gravity of the starBalance between the drag and gravityVertical density distributionWe have the terminal velocityDust particles settles down to the central plane.
15 Planetesimal formation through gravitational instability of the dust layer 自分自身が良く理解した上で、分散関係式などを説明すべし。Typical size of created planetesimal
17 Planetesimal motionMotion is disturbed by mutual gravitational interactionIncrease of random velocity by energy exchange> 0Gravitational scatteringLow relative velocity caseIncreasing rate decreases with the evolutionRandom velocity evolutionstronger interactionHigh relative velocity caseweaker interaction
18 Terrestrial-planet formation Planetesimals grows up to be terrestrial planets through the mutual collisionCollision cross sectionGravitational focusingGravitational focusing factorGeometrical cross sectionGrowth rate of planetsGrowth time scaleyr
19 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 growthSignificant 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.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.
21 Gap formationIf planets become large enough, the planets can create a gap in the disk and the growth stopPlanet growth is terminated by themselves through the gap formation.The planet in the gap have to move with the disk viscous evolution.
22 Summary of the planetary formation Planetary systems are formed in “proto-planetary disks”..Dust → PlanetesimalsSettle down to the mid-plane.Gravitational instability of the dust layer.Planetesimal → Solid planetsMutual collision and coalescence.Solid planets → Gaseous planetsGravitational collapse of the atmosphere by the strong gravity of the planetsThere are still some problems to be addressed.Dust is hard to settle down enough to occur the instabilityGrowth time scale v.s. Migration time scaleDust → planetesimal → solid planet → gaseous planetここが固まっていない。しっかり考えるべし。