Planet Formation

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

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

3. Giant Planet Formation by Gravitational Instability

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

5. 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.

6. 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)!

7. Will a clump stay bound? But cooling timescale must be shorter than 1 orbit, otherwise a clump 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:

8. Will a clump stay bound? In outer disk: Can fragment and form Gas Giant

9. Exoplanets: Direct imaging HR 8799 Credit: Marois et al (2010)

10. 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: Mplanet Mclump But many clumps can form a planet: Typically more massive than Jupiter!

11. Giant Planet Formation by Core accretion

12. 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!

13. Smallest core mass to attract a hydrogen atmosphere: Attracting 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 RBondi < Rcore, then no atmosphere can be kept bound to the core. Typically: 10-3...10-2 Mearth

14. 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=RBondi. Boundary condition: density and temperature equal to disk density and temperature.

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

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

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

18. Formation of a Gas Giant Planet Total Gas Growth byaccretionofplanetesimalsuntilthelocalsupplyruns out (isolationmass). Solids Original: Pollack et al. 1996; Here: Mordasini, Alibert, Klahr & Henning 2012

19. Formation of a Gas Giant Planet Total Slow accretionof gas (slow, becausethe gas must radiatively cool, beforenew gas canbeadded). Speed is limited byopacities. Gas Solids If planet migrates, itcansweepupmoresolids, accelleratingthisphase. The added gas increasesthemass, andtherebythesizeofthefeedingzone. Hence: New solidsareaccreted. Original: Pollack et al. 1996; Here: Mordasini, Alibert, Klahr & Henning 2012

20. Formation of a Gas Giant Planet Total Gas OnceMgas > Msolid, thecoreinstabilitysets in: acceleratingaccretionofmoreandmore gas Solids Original: Pollack et al. 1996; Here: Mordasini, Alibert, Klahr & Henning 2012

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

22. Formation of a Gas Giant Planet Total Gas Something endsthe gas accretionphase, for example: strong gapopening. „Normal“ planet evolutionstarts. Solids Original: Pollack et al. 1996; Here: Mordasini, Alibert, Klahr & Henning 2012

23. Population synthesis • Putthismodelintovaryingdisks, atvaryingpositions (Monte Carlo) • Allowthe planet tomigrate (whichmeans, incidently, thatitcansweepupmoresolidsthanbefore) •  Obtain a statistical sample ofexoplanetsandcomparetoobservedstatistics. East-Asian Models: Ida & LinTowarda Deterministic Model of Planetary Formation I...VI (2004...2010) Bern Models: Mordasini, Alibert, Benz et al.Extrasolar planet populationsynthesis I...IV (2009...2012) Kornetet al. (2001...2005), Robinson et al. (2006) Thommes et al. (2008) [multi-planet: withfull N-body]

24. Predictedinitialmassfunction Growth byaccretionofplanetesimals untilthelocalsupplyruns out (isolation mass). Note: effectcausedbyreduced type I migration rate. Oncethefaster type II migration sets in, thecorecansweepup fresh material fromfurther inward Runaway gas accretion „Failed cores“ Gas giants Icegiants Mordasini, Alibert, Benz & Naef 2009

25. Lots of added complexities Accretion of gas onto GP is a complex 3-D problem Lubow, Seibert & Artymowics (1999)