Planet Formation Topic: Connecting to the solar system Lecture by: C.P. Dullemond.
Planet Formation Topic: Formation of gas giant planets Lecture by: C.P. Dullemond.
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Transcript of 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)!
Will a clump stay bound?
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:
Will a clump stay bound?
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.
Atmosphere structure
From: Bachelor thesisGianni Klesse
Varying the mass of thecore
Atmosphere structure
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
Formation of a Gas Giant Planet
Original: Pollack et al. 1996;Here: Mordasini, Alibert, Klahr & Henning 2012
Growth by accretion of planetesimals until the local supply runs out (isolation mass).
TotalGasSolids
Formation of a Gas Giant Planet
Original: Pollack et al. 1996;Here: Mordasini, Alibert, Klahr & Henning 2012
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.
Formation of a Gas Giant Planet
Original: Pollack et al. 1996;Here: Mordasini, Alibert, Klahr & Henning 2012
Once Mgas > Msolid, the core instability sets in: accelerating accretion of more and more gas
TotalGasSolids
Formation of a Gas Giant Planet
Original: Pollack et al. 1996;Here: Mordasini, Alibert, Klahr & Henning 2012
A hydrostatic envelope smoothly connecting core with disk no longer exists. Planet envelope detaches from the disk.
TotalGasSolids
Formation of a Gas Giant Planet
Original: Pollack et al. 1996;Here: Mordasini, Alibert, Klahr & Henning 2012
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)