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  1. Planetary migration - a review Richard Nelson Queen Mary, University of London Collaborators: Paul Cresswell (QMUL),Martyn Fogg (QMUL), Arnaud Pierens QMUL), Sebastien Fromang (CEA), John Papaloizou (DAMTP)

  2. Talk Outline • Type I migration in laminar discs • The role of corotation torques(non linear effects; planet traps; non isothermal effects) • Multiple low mass planets • Protoplanets in turbulent discs: Low mass planets Planetesimals High mass planets • Terrestrial planet formation during/after giant planet migration • Conclusions and future directions

  3. 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 generated by material in horseshoe region- exerts positive torque, but weaker thanLindblad torques • Migration time scale ~ 70,000 yr for mp=10 Mearth • Giant planet formation time 1 Myr

  4. 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 - Reducing dust opacity speeds up gas accretion but migration is always more rapid (e.g. Papaloizou & Nelson 2005, Lissauer et al 2006)

  5. Evidence for type I migration • Short-period low mass planets: 20 planets with m sini < 40 Mearth(e.g. HD69830 Lovis et al 2006, Gl581 Udry et al 2007, GJ436 Butler et al 2005)- but 45 candidates… • Disc models agree T > 1500 K within 0.1AU- dust sublimates • Mass of solids inside 1 AU~ 5 Earth masses for MMSN • Type I migration does occur !- but probably more slowly than predicted by basic theory …….10 Earth mass…….

  6. Stopping/slowing type I migration • MHD Turbulence (see later) • Planet-planet scattering (Cresswell & Nelson 2006) - migration stops if e > H/r • Corotation torques may slow/stop planetmigration (Masset et al 2006) • Planet enters cavity due to transition from ‘dead-zone’ to ‘live zone’ - planet trap(Masset et al. 2005) • Corotation torque in optically thick discs(Pardekooper & Mellema 2007) • Strong magnetic field (Terquem 2002; Fromang, Terquem & Nelson 2005) • Opacity variations: sharp transition in density and temperature (Menou & Goodman 2002) • Eccentric disks (Papaloizou 2002)

  7. Can corotation torques slow type I migration ? (Masset, D’Angelo & Kley 2006) Basic idea - corotation region widens with planet mass and can boost corotation torque For  = const. corotation torque can cause migration reversal for mp>10 ME

  8. 3D simulations with evolving planets Viscous discs Inviscid discs m=30 Mearth m=10 Mearth m=10 Mearth m=30 Mearth m=20 Mearth m=20 Mearth • = constantH/r=0.05 =0.005 • = constantH/r=0.05 =0.0 Questions: Dead-zones ? Does corotation torque operate in turbulent disc ?

  9. Surface density transitions as planet traps • Regions where surface density gradient is positive cause strongpositive corotation torque(Masset, Morbidelli & Crida 2005) • Planets migrate into planet trapand migration is halted Planet stops here 

  10. Gap formation by giant planet formsplanet trap for mp < 30 Mearth Very low mass planets cannot formmean motion resonances withinterior giants (Pierens & Nelson 2008)

  11. Corotation torques in optically thick discs • Corotation torque can exceed Lindblad torques in optically thick discs(Paardekooper & Mellema 2007; Baruteau & Masset 2008; Pardekooper & Papaloizou 2008) • Effect is due to warm gas being advected from inside to outside orbit of planet- and vice versa • Pressure equilibrium leads to modification of density structure in horseshoe region • High density region leads planet, low density region trails it - net positive torque - which saturates

  12. Models with viscous heating and radiative cooling showsustained outward migration (Kley & Crida 2008) Thermal time scale ~ horseshoe libration time scaleNow have a problem of rapid outward type I migration…

  13. Low mass planetary swarms • Consider swarm consisting of between 5 - 20 low mass interacting planets • Question: can interaction within swarm maintain eccentric population and prevent type I migration ? • Answer: No ! • Outcomes: Initial burst of gravitational scatteringCollisons (~ 1 per run)“Stacked” mean motion resonancesInward migration in lockstepExotic planet configurations:Horseshoe and tadpole systems(sometimes in MMR with each other)

  14. Coorbital planets stable even duringsignificant mass growth - giant coorbital planets canremain stable(Cresswell &Nelson 2008) . May be detected byCOROT, KEPLER,or RV surveys

  15. High mass protoplanets • 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

  16. Inward migration occurs on time scale of ~ few x 105 year • Jovian mass planets remain on ~ circular orbits • Heavier planets migrate more slowly than viscous rate • due to their inertia • A 1 MJ planet accretes additional 2 – 3 MJ during migration time of ~ few x 105 yr

  17. Eccentricity Evolution • Disc interaction can cause both growth and damping of e due tointeraction at ELRs, CRs, and COLRs • For Mp > 5 MJup can get disc eccentricity growth- planet eccentricity growth ?(Kley & Dirksen 2005) • Most simulations show e dampingfor Jovian mass planets- but D’Angelo et al (2006) findmost e growth • Origin of exoplanet eccentricities:planet-planet scattering ?(Rasio & Ford; Papaloizou & Terquem 2003; Laughlin & Adams 2004; Juric & Tremaine 2007)

  18. Evidence for type II migration • Existence of short period planets (Hot Jupiters) • Resonant multiplanet systems:GJ876 – 2:1 HD82943 – 2:1 55 Cnc – 3:1 HD73526 - 2:1 HD128311 - 2:1

  19. Planets in turbulent discs • Magnetorotational instability vigorous turbulence in discs (Balbus & Hawley 1991; Hawley, Gammie & Balbus 1996, etc…) • Necessary ingredients: (i) Weak magnetic field (ii) • (iii) Sufficient ionisation: X(e-) ~ 10-12 • (iv) Rem > 100 • Dust free disc ~ 50 % of matterturbulent Dusty disc ~ 1 % of matter turbulent Ilgner & Nelson (2006a,b,c)

  20. Stratified disc models • H/R=0.07 and H/R=0.1 discs computed • Locally isothermal equation of state • ~ 9 vertical scale heights Obtain a basic core-halo structure:Dense MRI-unstable disc near midplane, surrounded by magneticallydominant corona (see also Miller & Stone 2000)

  21. Stratified global model H/R=0.1, mp=10 mearth Nr x N x N = 464 x 280 x 1200

  22. Local view – turbulent fluctuations ≥ spiral wakes

  23. Planet in laminar disc shows expected inward migration • Planet in turbulent discundergoes stochastic migration

  24. T ~ 20 x type I torque • for mp=10 Earth mass •  ttype 1 ~ 400 tcorr • T ~ 200 x type I torque for mp=20 Earth mass • ttype 1 ~ 40,000 tcorrRun times currently achievable ~ 200 orbits Can treat stochastic migration asa signal to noise problem(assume linear superposition oftype I + stochastic torques) Calculate time scale over whichtype I torque dominates random walk

  25. Results show exampleswhere stochastic torques (and migration)contain long-termsignal…This is apparently due to persistent featuresdeveloping in the flow(transient and looselydefined vortices) This example:mp=1 EarthH/R=0.1

  26. This example: mp=10 EarthH/R=0.07

  27. Planetesimals in stratified, turbulent discs • Gas in pressure supported disc orbits with sub-Keplerian velocity • Solid bodies orbit with Keplerian velocity • Planetesimals experience head wind (Weidenschilling 1977) • Gas drag induces inward drift & efficient eccentricity damping

  28. Consider evolution of 1m, 10m, 100m and 1km planetesimalssubject to gas drag and stochastic gravitational forcingAim: Calculate velocity dispersion assuming bodies orbit at ~ 5 AU

  29. For runaway growth require planetesimal velocity dispersionto be much smaller than escape velocity from largest accretingobjects: For 10 km sized bodies with =2 g/cm3 escape velocity=10 m/s Collisional break-up occurs for impact velocities 15 - 30 m/sfor bodies in size range 100m - 1km (Benz & Asphaug 1999)

  30. 1m-sized bodies stronglycoupled to gas.Velocity dispersion ~ turbulent velocities10m bodies have<v> ~ few x 10 m/s - gas drag efficient atdamping random velocities100m - 1km sizedbodies excited by turbulent density fluctuations<v> ~ 50-100 m/sLarger planetesimals prevented from undergoing runaway growthPlanetesimal-planetesimal collisions likely to lead to break-upNeed dead-zones to form planets rapidly ? Or leap-frog this phase with gravitational instability ? Or can a relatively small number of bodies avoid catastrophic collisions and grow ?

  31. High mass planets in turbulent discs • mp=30 mearth accretes gas andforms gap • Migrates inward on viscous time scale ~ 105 yr • Gas accretion rate enhanced due to magnetic torques

  32. Terrestrial Planet Formation During Giant Planet Migration • N-body simulations performed (Fogg & Nelson 2005, 2006, 2007) • Initial conditions: inner disk of planetesimals+protoplanets undergoing different stages of `oligarchic growth’ within a viscously evolving gas disc • Giant planet is introduced which migrates through inner planet-forming disc • General outcomes:(i) massive terrestrial planets can form interior to migrating giant(ii) significant outer disk forms from scattered planetesimals and embryos(iii) water-rich terrestrial planets can form in outer disc

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

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

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

  36. Compositional Mixing. Before.

  37. Compositional Mixing. After. Ocean Planets predicted

  38. A case where an inner super-earth forms…

  39. Conclusions and Future Directions • Low mass planets migrate rapidly in laminar discs- but this remains an active research area • Multiple low mass planet systems display:inward resonant migration, horseshoe and trojan systems - observable by COROT or KEPLER ? • Turbulence modifies type I migration and may prevent large-scale inward migration for some planets • Turbulence increases velocity dispersion of planetesimals and may lead to destructive collisions and quenching of runaway growth • Stochastic forces experienced by planets in vertically stratified discs lower in amplitude due to finite disc thickness - work in progress • Water-rich terrestrial planets probably form in “hot Jupiter” systems