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

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

Two main theories Gravitational instability of the gas disk Core accretion scenario

Giant Planet Formation by Gravitational Instability

Image: Quinn et al. From: http://www.psc.edu/science/quinn.html Gravitational fragmentation of a gas disk From earlier chapters we know that a disk with Q<1 will fragment into clumps.

Will a clump stay bound? The big discussion: Can a clump cool quickly enough to stay bound? Lets 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 thus the gas deviates from the strictly polytropic EOS)!

Will a clump stay bound? But cooling timescale must be shorter than 1 orbit, otherwise a clump of gas will be quickly dispersed again. Lets calculate the cooling time of a gravitationally unstable (Q=1) protoplanetary disk at radial coordinate R:

Will a clump stay bound? In outer disk: Can fragment and form Gas 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, the odds are, that the planet will be massive too: But many clumps can form a planet: Typically more massive than Jupiter! M clump M planet

Giant Planet Formation by Core accretion

Core accretion main idea First form a rocky planet (a core) As the rocky cores 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 cores mass increases further, the mass of the atmosphere will grow faster than linear with core mass. Eventually become similar to the cores 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 the planet (core) at which the escape speed equals the sound speed of the gas If R Bondi < R core, then no atmosphere can be kept bound to the core. Typically: 10 -3...10 -2 M earth

Atmosphere structure The equations for the atmosphere are very similar to those for stellar structure, just with a fixed core mass added: If the atmosphere is thick enough, and if it is continuously bombarded with planetesimals (=heating), then to good approximation it can be regarded as adiabatic: Outer boundary: R=R Bondi. Boundary condition: density and temperature equal to disk density and temperature.

Atmosphere structure From: Bachelor thesis Gianni Klesse Varying the mass of the core

Atmosphere structure From: Bachelor thesis Gianni Klesse Varying the rate of accretion of pebbles and/or planetesimals

Formation of a Gas Giant Planet Original: Pollack et al. 1996; Here: Mordasini, Alibert, Klahr & Henning 2012 Total Gas Solids

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). Total Gas Solids

Formation of a Gas Giant Planet Original: Pollack et al. 1996; Here: Mordasini, Alibert, Klahr & Henning 2012 Total Gas Solids 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 M gas > M solid, the core instability sets in: accelerating accretion of more and more gas Total Gas Solids

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. Total Gas Solids

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. Total Gas Solids

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 migration sets 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)

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