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Formation and Evolution of Planetary Systems

Ken Rice (wkmr@roe.ac.uk)

Specialist Topics in Astrophysics: Lecture 3

Alternative Giant Planet FormationAlternative Giant Planet Formation

Gravitational instability model

• Formed as miniature solar systems, condensing from instabilities in the initial solar nebula

• Unstable ring of gas/spiral density waves developed in the SolarNebula

• A Jupiter mass collapsed under its own weight to form a giant planet

Disk of the solar nebula is shrinking

Rings form in nebula But they are unstable

Rings collapse into protoplanets

Protoplanet

Disk InstabilitiesDisk Instabilities

Numerical simulations

Forming Jupiter

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Gravitational InstabilitiesGravitational Instabilities

• Consider energies per unit mass

– Gravity

– Rotation

– Thermal

• Rotation dominates at large R

• Thermal energy dominates at small R

RGR

RG

R

GMEg Σ=Σ=≈ ππ 2

( )2

21

REr Ω=

2

23

sth cTE ≈≈

Conditions for instabilityConditions for instability

• A disc will be gravitationally unstable if gravitational energy dominates over thermal and rotational en energies

– Toomre’s stability criteria

– General Toomre criteria

• To achieve low Q

– Increase mass - Σ– Decrease temperature – cs– Combination of the two

• Disc instability believed to be possible due to

– Cooling

– Mass infall onto disc

1112222

22212

<Σ

Ω⇒<

ΣΩ

⇒<G

c

RG

Rc

EE

EE ss

gg

rth

ππ

2π

π<

ΣΩ=

G

cQ s

FragmentationFragmentation

• Problems

– Requires very massive and cold disc

– Requires rapid cooling to maintain low temperatures.

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QuasiQuasi--steady transportsteady transport

• More likely that disc will undergo a self-gravitating phase when young and massive but not fragment

– Angular momentum transport

PlanetPlanet--Disc interactionsDisc interactions

• Planets form inside gas discs

• Planets must interact with the gas disc

– Exert torques on gas as it flows by – Hill radius

• Induces transport of angular momentum

– Planet migration

• May lead to the opening of a gap in the disc

– Planet can affect region of size ~ Hill radius

31

*3

=M

maR p

H

PlanetPlanet--Disc interactionsDisc interactions

• Gas inside planet

– Flows quicker

– Loses angular

momentum to planet

– Falls inwards and

speeds up its

rotation

• Gas outside planet

– Flows slower than

planet

– Planet loses angular

momentum to gas

– Gas moves outwards

and slows down

Forms spiral arms that transfer angular momentum from inner disc to outer disc.

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Gap FormationGap Formation

• Higher-mass planets clear gaps in the disc

• Gap formation requires that Hill radius > scaleheight (H) of disc

– Low-mass planet – gas flows around Hill radius

– High-mass planets – Hill radius > scaleheight (H) – gap

• Gap size is balance between gravity and viscosity

– Viscosity wants to close the gap

– Gravity from planet wants to open gap

– Exact size depends on resonances with planet (i.e., 2:1 resonance where gas in

disc orbits twice for each planet orbit).

Gaps and Planetary MigrationGaps and Planetary Migration

• As planets grow they drive density waves into the remaining disk

• These waves carry angular momentum and so can push gas away from the planet opening a gap

Simulations by F. Masset

Gap formation simulationGap formation simulation

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LowLow--mass planetsmass planets

• Disc material extends up to the planet – no gap

• Planet excites spiral arms

– Leading inside and trailing outside

– Transport angular momentum through planet

• Net transport removes angular from planet

• Migrates inwards

– Type I migration (no gap)

• Migration rate proportional to the amount of material the feels the planet

– Amount of gas inside Hill sphere

• Lower mass planets migrate more slowly

years 1.0

10planet

Jup5migrate M

Mt =

HighHigh--mass planetsmass planets

• Planets more massive than ~ 0.1 MJupiter open gaps

• Planet depends on disc evolution for migration

– Requires viscosity to replenish areas near disc resonances

• Planet can only migrate on viscous timescales

• Mechanism can bring in Jupiters from 5 AU in < 1 Myr

– Forms hot Jupiters

– What stops them???

years 10 few 52

×≈=νR

tv

Separation distributionSeparation distribution

• Planets form at 5 AU

• Migrate inwards on ~ 0.5 Myr timescales

• If disc removed, planet stalls

• In not, planet plunges into star

– Possible existence of magnetospheric cavity

• Probability of finding planet at radius R is

• Planets spend more time at large radii

– More likely to find them there

2migrate RtPR ∝∝

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ALMAALMA

• 50 12m radio telescope working as an interferometer

– Baseline 150 m – 14 km

• Resolution of 0.01 arcsec at 300 microns

– 1 AU resolution at 100 pc

Directly detecting Directly detecting protoplanetsprotoplanets

50 pc 100 pc

Inferring the presence of planetsInferring the presence of planets

• A migrating planet could clear the inner disc of material

– Gas drag may preferentially remove solid bodies

• Spectral Energy Distribution can be used to infer the distribution of dust in the disc

– Hot dust close to the star

– Cooler dust further out

• A deficit of near infrared flux suggests the presence of an inner gap

– May only be a gap in the dust

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Orbital eccentricitiesOrbital eccentricities

• Many extrasolar planets have high eccentricities

– Disc migration should keep eccentricities low

• Could be due to scattering

– Multiple planet systems

– Once gas is removed planets can interact

• Chaotic orbits

– Orbit crossing

– Close encounters and ejections

– Survivors left with high eccentricities

• Instability if

≈∆

+≈∆∆+<short term 3.0

termlong 4.2)1(

31

31

2112

qqaa

Timescales for Planet FormationTimescales for Planet Formation

• Giant planets must have formed in about 10 million yrs

– Studies of young stars show that by 10 million yrs they have blown away their gas disks

– Since Jovian planets are largely gaseous, growth will have ceased when the gas was expelled from the Solar System

• Terrestrial planets probably took longer to form because their growth does not require large amounts of gas

• The Sun reached the main sequence (began fusing hydrogen in its core) after about 30 million yrs

• The entire process of planetary formation took about ~100 million yrs (about 2% of the present age of the Solar System)

What happened to all the gas?What happened to all the gas?

• The inner planets were not massive enough to accrete the lightest gases of the Solar Nebula

• Just prior to nuclear ignition, a star will enter the “T Tauri” phase, when the stellar wind is very strong

• This pressure pushed the gas out into space leaving the inner protoplanetsand the already formed outer giants

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Origin of Planetary SatellitesOrigin of Planetary Satellites

• Remnants of an accretion disk (e.g. Galilean satellites)

– Different composition with radius

– Circular, low inclination orbits

– Even spacing of orbits

• Asteroid captures (e.g. Phobos and Deimos)

– Composition similar to asteroids or comets

– Eccentric and high inclination orbits

• Large captures (e.g. one suggested hypothesis for the origin of the Moon)

Last Stages of Planet FormationLast Stages of Planet Formation

The last stages were undoubtedly dominated by violent collisions between planets and planetesimals in various phases of growth (left) resulting in a molten

Earth and the formation of the Moon (right)

Solar System AnomaliesSolar System Anomalies

• Venus rotates “backwards” with respect to the Sun and its orbit around the Sun

– It is postulated that a large planetesimal crashing off-centre could have disrupted

Venus and altered its rotation direction

• Uranus rotates on its side

– Probably hit by a large planetesimal and knocked on its side

• Pluto has a highly inclined orbit (18 degrees)

– May have originated in a collision or near collision with a massive planetesimal

– Pluto is actually not a “planet” but a “Kuiper Belt object, so the inclined orbit is

not that unusual

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Star and Planet Formation SummaryStar and Planet Formation Summary

PlanestimalPlanestimal hypothesishypothesis

• Minimum mass solar nebula (MMSN)

• Disc evolves viscosly

• Collisional growth

• Isolation mass (applies to both the core and final mass – envelope + core)

2-

5.1

MMSN m kg AU 1

42000−

=Σ r

Hcsαν = ν

2Rtv =

gsosw

o

osw

p FRVV

VRV

dt

dms

2

2

esc2 1 πρπρ =

+=

( )( ) 2

1

23

31

isolation

*

2

isolation

*

2

isolation

3

43

422M

am

M

maRam H

σπσπσπ =⇒

==

This is all consist with the fact that solar system planets all orbit in the same plane and in the same direction, and with the fact that exoplanetsare found preferentially around metal-rich stars.

• Type I – low-mass planets – very rapid????

– May be influenced by turbulence and may be more of a random walk.

• Type II – gap opening – high-mass planets

– Evolves with the disc - viscously

• Type II migration explains ‘hot Jupiters’ and the radial distribution of planets

MigrationMigration

years 1.0

10planet

Jup5

migrate M

Mt =

years 10 few 52

×≈=νR

tv

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EccentricityEccentricity

• Surprising – solar system planets have very low eccentricities.

• Exoplanet eccentricities possibly due to planet-planet scattering

– Interactions eject planets

– Remaining planets have increased eccentricities

– Free-floating planets???

• Solar system may be unusual!!!

– The properties of the exoplanet systems may be due to selection effects.

ConclusionsConclusions

• The “planetesimal hypothesis” provides a viable theory for the growth of terrestrial planets, the cores of giant planets and other smaller bodies

• Growth of giant planets probably happens fast otherwise gas is lost from the nebula

– Still some support for an instability mechanism for the formation of gas giants.

• The formation of planetesimals is one of the weakest parts of the theory

– Interaction with disc gas can produce a drag force that removes planetesimals –

not clear how this is solved.

• Most of the observed structure in the Solar System and exoplanets has been explained (with the exception of a few anomalies that are not too well understood…)