Planet Formation Topic: Formation of gas giant planets Lecture by: C.P. Dullemond.

Planet Formation

Topic:

Formation ofgas giant planets

Lecture by: C.P. Dullemond

Two main theories

• Gravitational instability of the gas disk

• Core accretion scenario

Giant Planet Formation byGravitational Instability

Image: Quinn et al.From: http://www.psc.edu/science/quinn.html

Gravitational fragmentation of a gas disk

From earlier chapters weknow that a disk withQ<1 will fragment intoclumps.

Will a clump stay bound?The big discussion: Can a clump cool quickly enough to stay bound?

Let‘s take a clump of polytropic gas of radius R and squeeze it:

If gravity increases faster than the opposing pressure forces: it will continue to collapse.

Will a clump stay bound?

Approximate relation between mass and density:

So the gravity wins out over pressure acceleration upon contraction if:

Since most astrophysical gases have γ>4/3 they will be stable against gravitational collapse, UNLESS the gas cools (and thusthe gas deviates from the strictly polytropic EOS)!


But cooling timescale must be shorter than 1 orbit, otherwise aclump of gas will be quickly dispersed again.

Let‘s calculate the cooling time of a gravitationally unstable (Q=1)protoplanetary disk at radial coordinate R:


In outerdisk: Canfragmentand formGas Giant

Exoplanets: Direct imaging

HR 8799

Credit: Marois et al (2010)

Which mass planets will form?

Since the disk muss be massive to become self-gravitating, theodds are, that the planet will be massive too:

But many clumps can forma planet:

Typically more massive than Jupiter!

Mclump

Mplanet

Giant Planet Formation byCore accretion

Core accretion main idea

• First form a rocky planet (a „core“)• As the rocky core‘s mass increases, it will attract a

hydrogen atmosphere from the disk. A given core mass yields a given atmosphere thickness.

• The core mass can grow when the core+atmosphere accretes planetesimals or pebbles and/or when the atmosphere can cool and thus shrink.

• As the core‘s mass increases further, the mass of the atmosphere will grow faster than linear with core mass.

• Eventually become similar to the core‘s mass, so the additional mass of the gas will attract new gas, which will attract further gas etc: runaway gas accretion!

Attracting a hydrogen atmosphere

Smallest core mass to attract a hydrogen atmosphere:

Bondi radius is the radius from theplanet (core) at which the escapespeed equals the sound speed of the gas

If RBondi < Rcore, then no atmosphere can be kept bound to thecore.

Typically: 10-3...10-2 Mearth

Atmosphere structure

The equations for the atmosphere are very similar to those forstellar structure, just with a fixed core mass added:

If the atmosphere is thick enough, and if it is continuouslybombarded with planetesimals (=heating), then to good approximation it can be regarded as adiabatic:

Outer boundary: R=RBondi. Boundary condition: densityand temperature equal to disk density and temperature.


From: Bachelor thesisGianni Klesse

Varying the mass of thecore


From: Bachelor thesisGianni Klesse

Varying the rateof accretion ofpebbles and/orplanetesimals

Formation of a Gas Giant Planet

Original: Pollack et al. 1996;Here: Mordasini, Alibert, Klahr & Henning 2012

TotalGasSolids



Growth by accretion of planetesimals until the local supply runs out (isolation mass).

TotalGasSolids



TotalGasSolids

Slow accretion of gas (slow, because the gas must radiatively cool, before new gas can be added). Speed is limited by opacities.

The added gas increases the mass, and thereby the size of the feeding zone. Hence: New solids are accreted.

If planet migrates, it can sweep up more solids, accellerating this phase.



Once Mgas > Msolid, the core instability sets in: accelerating accretion of more and more gas

TotalGasSolids



A hydrostatic envelope smoothly connecting core with disk no longer exists. Planet envelope detaches from the disk.

TotalGasSolids



Something ends the gas accretion phase, for example: strong gap opening. „Normal“ planet evolution starts.

TotalGasSolids

Population synthesis

• Put this model into varying disks, at varying positions (Monte Carlo)

• Allow the planet to migrate (which means, incidently, that it can sweep up more solids than before)

• Obtain a statistical sample of exoplanets and compare to observed statistics.

East-Asian Models: Ida & Lin Toward a Deterministic Model of Planetary Formation I...VI (2004...2010)

Bern Models: Mordasini, Alibert, Benz et al. Extrasolar planet population synthesis I...IV (2009...2012)

Kornet et al. (2001...2005), Robinson et al. (2006)

Thommes et al. (2008) [multi-planet: with full N-body]

Predicted initial mass function

Mordasini, Alibert, Benz & Naef 2009

Runaway gas accretion

„Failed cores“ Gas giants

Ice giants

Growth by accretion of planetesimals until the local supply runs out (isolation mass). Note: effect caused by reduced type I migration rate.

Once the faster type II migrationsets in, the core can sweep up fresh material from further inward

Lots of added complexities

Accretion of gas onto GP is a complex 3-D problem

Lubow, Seibert & Artymowics (1999)

Planet Formation Topic: Formation of gas giant planets Lecture by: C.P. Dullemond.

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