Planetary formation and migration theory

1. Planetary formation and migration theory Richard Nelson Queen Mary, University of London

2. Theoretical study of planetary formation is increasingly taking twobroadly distinct approaches: fundamental theory and population synthesis Successful explanation of the observed exoplanet population willrequire a sophisticated combination of these approaches Only when the observed population of planets is successfully accounted for will theory be able to make useful predictions for the currentlyundetected population of exoplanets (small masses and/or large orbital radii)A successful theory needs to account for the simultaneous growth and migration of planets

3. Collisional growth of dust whichsettles toward the disc midplane A simple picture of planetary growth Continued growth up to km sizes Runaway growth of largest bodiesassisted by gravitational focusing Oligarchic growth when stirring increasesrandom velocities of the planetesimals Giant planet cores form from continued oligarchic growth beyond the snowline Terrestrial planets form via giant impacts after oligarchic growth ceases because of feeding zone depletion Gas accretes onto rock+ice coreforming giant planet

4. Do the observational data support this simple picture of bottom-up growth ? Fischer & Valenti (2005) Metal rich stars have higher probability of harbouring planets circumstantial evidence which supports core-instability model

5. Planetary migration • Migration of planets can occur because of various processes- Gravitational interaction with protoplanetary disc- Planet-planet scattering- Kozai effect + tidal interaction with central star- Scattering of planetesimals

6. Low mass planets - type I migration • Planet generates spiral waves in disc at Lindblad resonances • Gravitational interaction between planet and spiral wakes causes exchange of angular momentum • Wake in outer disc is dominant (pressure support shifts resonant locations) - drives inward migration • Corotation torque is generated by material in the horseshoe region- exerts positive torque, but weaker than Lindblad torques for a locally isothermal disc • Migration time scale ~ 70,000 yr for mp=10 Mearth • Giant planet formation time > 1 Myr

7. Tanaka, Takeuchi & Ward (2002) Pollack et al. (1996) • Low mass protoplanets migrate rapidly < 105 yr • Gas accretion onto solid core requires > 1 Myr - Difficult to form gas giant planets before they have migrated into star - Reducing dust opacity speeds up gas accretion but migration is always more rapid (e.g. Papaloizou & Nelson 2005, Lissauer et al 2006)

8. Evidence for type I migration • Recently discovered shortperiod Neptunes and super-earths> 50 planets with m sini < 40 Mearth(e.g. Gl 581- 4 planets) • All disc models agree T > 1500 K within 0.1AU- dust sublimates- mass of solids too small within 1 AU- planets must form further out and migrate in • Type I migration does occur !- but probably more slowly than predicted by basic theory

9. Ida & Lin (2008) Type I migration leads to dearth oflow and intermediatemass planets within~ 2 AU, even whenattenuated by x 10 Rapid gas accretionalso reduces number of intermediate massplanets This “planet desert”is inconsistent withobservationsHoward et al (2010)

10. Mordasini et al(2009) Even with type Imigration switchedoff the planet desert is apparent

11. Mordasini et al(2009)A different pop.synthesis modelstill produces a pronounced planet desert

12. Forming hot Neptunes and super-earths via accretion and migration Question: Is it possible to form hot Neptunes and super-earths(or at least the right amount of mass in smaller planets within 1 AU) by combining standard type I migration with oligarchic accretion ? N-body simulations plus type I migration (McNeil & Nelson 2009, 2010)Approximately 15000 planetesimals + approx 100 planetary embryos Dissipating gas disc (time scale ~ 1-2 Myr)

15. Forming Hot Neptunes

17. Although super-earths are formed, no systems containing similar amountsof mass at small radii (such as the systems Gl581 or HD69830) were formed. And all putative giant planet cores migrated inward of 2 AU.

18. In N-body simulations type I migration causes modest sizedprotoplanets to migrate into star unless they form very late indisc life timeBut without some type I migration it will be impossible toexplain hot super earths or hot Neptunes Recent work suggests that disc turbulence(Nelson & Papaloizou 2004), and/or thermal effects (Paardekooper & Mellema 2006) may modify migration of low mass planets

19. Low mass planets migrating in turbulent discs Angular momentum transport which causes mass accretion in protoplanetary discs is probably due to turbulence MHD turbulence is generated by the magnetorotational instability (Balbus & Hawley 1991) Migration of low mass planets in turbulent discs examined using MHD simulations (Nelson & Papaloizou 2004; Nelson 2005)

21. Local view – turbulent fluctuations ≥ spiral wakes

22. Planet in laminar disc shows expected inward migration • Planet in turbulent discundergoes stochastic migrationQuestion: can stochastic torques counterbalance underlying type I migration torques on long time scales ? - long term simulationssuggest that the fluctuatingtorques eventually averageout allowing inward migration to occur

23. For intermediate mass planets, stochastic torques eventuallyaverage out, and underlying type I migration drives inwarddrift over 1000 orbits time scalesRecent work examining stochastic forcing of embedded bodieswithin a dead zone indicate that stochastic forces are reduced by~ factor 20 Unlikely that turbulence will prevent type I migration

24. Corotation torques  • Corotation torques arise when gas interacts with planet while performing horseshoe orbits • Conservation of either specific vorticity (vorticity/density) and/or entropy during U-turn causes change in density structure near planet • In optically thick discs corotation torque can exceed Lindblad torques - stalling or evenreversing type I migration(Paardekooper & Mellema 2007; Baruteau & Masset 2008; Pardekooper & Papaloizou 2008) • Cooler gas is transported from outside to inside orbit of planet during a horseshoe orbit(and vice versa) • Pressure equilibrium leads to modification of density structure in horseshoe region • High density region leads planet, low density region trails it – giving a net positive torquue 

25. Effect of entropy gradient in disc

26. Evolution of the torque with radiative diffusion To prevent the entropy-related corotation torque from saturating,require that local thermal and viscous diffusion times ~ horseshoe libration time

27. Planets initially migrate to the zero migrationline. As gas disc disperses, this line moves inslowly toward star If thermal relaxation time << horseshoe libration time migrate inward If thermal relaxation time >> horseshoe libration time migrate inward If thermal relaxation time ~ horseshoe libration time migrate outward

28. Mordasini et al - in prep.

29. N-body simulations of oligarchic growth of planets withmigration and corotation torques included have been performed (McNeil & Nelson – in prep.)

35. N-body simulations + migration torques taken from Paardekooper et al (2010) Hellary & Nelson (in prep.)

38. Allowing corotation torques to diminish when eccentricity growscauses evolution to resemble caseswith unattenuated type I migration - Successful growth requiresprotoplanets to become isolated from one another during oligarchicgrowth

39. Conclusions • Combination of fundamental theory and population synthesis modelshave potential to explain observed exoplanet distributions • Successful accounting for observed exoplanets is necessary before theory can make predictions about unobserved classes of planet • At present, theory can explain individual systems (e.g. resonant multiplanet systems) but cannot account for the gross properties of exoplanet distributions • Need to improve understanding of migration processes- how do planets evolve in the dead zone of a turbulent protoplanetarydisc subject to stellar heating and turbulent dissipation ? • Need to understand mass growth of intermediate mass planets- what prevents rapid gas accretion turning Neptunes into Jupiters ? • Significant progress expected on time scale of 2 – 3 years

40. Terrestrial Planet Formation During Giant Planet Migration • N-body simulations performed (Fogg & Nelson 2005, 2006, 2009) • Initial conditions: inner solids disk undergoing different stages of `oligarchic growth’ within a viscously evolving gas disc • Giant planet is introduced which migrates through inner planet-forming disc

42. Compositional Mixing. Before.

43. Compositional Mixing. After. Ocean Planets predicted

44. Continued accretion in the scattered disk. Initial condition.

45. Continued accretion in the scattered disk. t + 1 Myr.

46. Continued accretion in the scattered disk. t + 6 Myr.

47. Stopping giant planet migration at different radii  different planetarysystem architectures are produced - often with planets in habitable zone

48. Conclusions • The theory of planet formation is developing at a very rapidly pace • There remain many unanswered questions relating to the growth of planets and their migration, providing excellent opportunities for PhD research …

49. There are two competing models for explaining how giant planets form:Gravitational instability model- the protostellar disc fragments to form giant planets directlyCore accretion model- a large core composed of rock + ice forms first, andthen accretes a massive gaseous envelope

50. High mass protoplanets in laminar discs • When planets grow to ~ Jovian mass they open gaps:(i) The waves they excite become shock waves when RHill > H(ii) Planet tidal torques exceed viscous torques • Inward migration occurs on viscous evolution time scale of the disk