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 than Lindblad torques Migration time scale ~ 70,000 yr for m p =10 M earth Giant planet formation time  1 Myr

4. Pollack et al. (1996) Tanaka, Takeuchi & Ward (2002) Low mass protoplanets migrate rapidly < 10 5 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 M earth (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 planet migration (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 m p >10 M E

8. 3D simulations with evolving planets  = constant H/r=0.05  =0.005  = constant H/r=0.05  =0.0 Questions: Dead-zones ? Does corotation torque operate in turbulent disc ? m=10 M earth m=20 M earth m=30 M earth m=10 M earth m=20 M earth m=30 M earth Viscous discsInviscid discs

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

10. Gap formation by giant planet forms planet trap for m p < 30 M earth Very low mass planets cannot form mean motion resonances with interior 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 show sustained outward migration (Kley & Crida 2008) Thermal time scale ~ horseshoe libration time scale Now 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 scattering Collisons (~ 1 per run) “Stacked” mean motion resonances Inward migration in lockstep Exotic planet configurations: Horseshoe and tadpole systems (sometimes in MMR with each other)

16. Coorbital planets stable even during significant mass growth - giant coorbital planets can remain stable (Cresswell & Nelson 2008). May be detected by COROT, KEPLER, or RV surveys

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

18. Inward migration occurs on time scale of ~ few x 10 5 year Jovian mass planets remain on ~ circular orbits Heavier planets migrate more slowly than viscous rate due to their inertia A 1 M J planet accretes additional 2 – 3 M J during migration time of ~ few x 10 5 yr

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

20. 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

21. 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) Re m > 100 Dust free disc ~ 50 % of matter turbulent Dusty disc ~ 1 % of matter turbulent Ilgner & Nelson (2006a,b,c)

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

24. Stratified global model H/R=0.1, mp=10 m earth N r x N  x N  = 464 x 280 x 1200

25. Local view – turbulent fluctuations ≥ spiral wakes

26. Planet in laminar disc shows expected inward migration Planet in turbulent disc undergoes stochastic migration

27.  T ~ 20 x type I torque for mp=10 Earth mass  t type 1 ~ 400 t corr  T ~ 200 x type I torque for mp=20 Earth mass  t type 1 ~ 40,000 t corr Run times currently achievable ~ 200 orbits Can treat stochastic migration as a signal to noise problem (assume linear superposition of type I + stochastic torques) Calculate time scale over which type I torque dominates random walk

28. Results show examples where stochastic torques (and migration) contain long-term signal… This is apparently due to persistent features developing in the flow (transient and loosely defined vortices) This example: m p =1 Earth H/R=0.1

30. This example: m p =10 Earth H/R=0.07

33. 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

34. Consider evolution of 1m, 10m, 100m and 1km planetesimals subject to gas drag and stochastic gravitational forcing Aim: Calculate velocity dispersion assuming bodies orbit at ~ 5 AU

35. For runaway growth require planetesimal velocity dispersion to be much smaller than escape velocity from largest accreting objects: For 10 km sized bodies with  =2 g/cm 3 escape velocity=10 m/s Collisional break-up occurs for impact velocities 15 - 30 m/s for bodies in size range 100m - 1km (Benz & Asphaug 1999)

36. 1m-sized bodies strongly coupled to gas. Velocity dispersion ~ turbulent velocities 10m bodies have ~ few x 10 m/s - gas drag efficient at damping random velocities 100m - 1km sized bodies excited by turbulent density fluctuations ~ 50-100 m/s Larger planetesimals prevented from undergoing runaway growth Planetesimal-planetesimal collisions likely to lead to break-up Need 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 ?

37. High mass planets in turbulent discs mp=30 m earth accretes gas and forms gap Migrates inward on viscous time scale ~ 10 5 yr Gas accretion rate enhanced due to magnetic torques

39. 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

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

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

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

44. Compositional Mixing. Before.

45. Compositional Mixing. After. Ocean Planets predicted

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

48. 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

51. GJ876: Already known to have 2 planets in 2:1 resonance Velocity residuals showed periodic variation - 3 rd planet with mass ~ 7.5 Earth masses Gl436 - 22 Earth mass transiting planet lightcurve suggests it is just like Neptune & Uranus Gl581 - Short-period 5 Earth mass planet detected by radial velocity

52. System Age = 1.5 Myr:

57. t = 80,000 years

58. t = 20,000 years

59. 154,700 years

60. Power spectrum – shows torques have temporal variations ~ run time of simulations Stochastic torques may overcome type I torques over significant time scales for some planets Require longer simulations… Torque distributions σ Naïve application suggests inward migration should be obtained for mp=10

61. Planetesimals in laminar 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

63. Planetesimals in turbulent discs Evolution of 100 - 1000 planetesimals calculated to examine inward drift and velocity dispersion Planetesimal treated as particles that experience gas drag and gravitational force due to disc and central star Sizes: 1m – 1km

64. 1 metre sized planetesimals 1 metre sized objects migrate inward within ~ 30 orbits (300 years) 1m sized boulders become trapped in long-lived vortices - about 50% of particles trapped Tight coupling to gas causes large eccentricities – potentially destructive velocity dispersion ? Neighbouring planetesimals appear to be on very similar orbits

65. Mp = 10 Earth masses

66. Mp = 1 Earth mass

67. 10 metre sized planetesimals Most 10 m size boulders drift inward on time scale of ~ few thousand years – a few drift in more slowly Velocity dispersion remains quite small – coupling too weak to allow individual fluctuations in gas velocity to determine velocity dispersion Danger of destructive collisions: e=0.01 ~ 0.12 km/s at 5 AU Icy 10 m sized bodies fragment with ~ 20 m/s (Benz & Asphaug 1999)

68. 1 km sized planetesimals Results similar to 100 metre sized objects Large velocity dispersion prevents runaway growth of planetesimals to form planetary embryos

69. Stopping type II migration Fortuitous disk removal – form planets late on ? Overlap gaps of ‘Jupiter’ and ‘Saturn’ ? Roche lobe overflow – only works close-in Magnetospheric cavity – only works close-in Switch viscosity off ? – difficult to explain observed distribution of exoplanets – or observed accretion rates onto T Tauri stars

70. 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) Re m > 100 Dust free disc ~ 50 % of matter turbulent Dusty disc ~ 3 % of matter turbulent Ilgner & Nelson (2006a)

72. Low mass planets Consider orbital evolution of: m p =1, 3, 5, 10, 30 Earth mass planets Question: what is effect of turbulence on type I migration ? (Nelson & Papaloizou 2004; Nelson 2005; Laughlin, Adams & Steinaker 2004)

73. Fluctuating torques – suggest stochastic migration

74. Mp = 10 Earth masses

76. Power spectrum – shows torques have temporal variations ~ run time of simulations Stochastic torques may overcome type I torques over significant time scales for some planets Require longer simulations… Torque distributions σ Naïve application suggests inward migration should be obtained for mp=10

77. Planetesimals in laminar 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

78. Planetesimals in turbulent discs Evolution of 100 - 1000 planetesimals calculated to examine inward drift and velocity dispersion Planetesimal treated as particles that experience gas drag and gravitational force due to disc and central star Sizes: 1m – 1km

79. 1 metre sized planetesimals 1 metre sized objects migrate inward within ~ 30 orbits (300 years) 1m sized boulders become trapped in long-lived vortices - about 50% of particles trapped Tight coupling to gas causes large eccentricities – potentially destructive velocity dispersion ? Neighbouring planetesimals appear to be on very similar orbits

80. 10 metre sized planetesimals Most 10 m size boulders drift inward on time scale of ~ few thousand years – a few drift in more slowly Velocity dispersion remains quite small – coupling too weak to allow individual fluctuations in gas velocity to determine velocity dispersion Danger of destructive collisions: e=0.01 ~ 0.12 km/s at 5 AU Icy 10 m sized bodies fragment with ~ 20 m/s (Benz & Asphaug 1999)

81. 100 metre sized planetesimals 100 m sized objects dominated by fluctuations in disc gravity Instead of inward drift undergo `random walk’ on time scales ~ 100 orbits Icy 100m sized objects fragment if ~ 14 m/s ~ 0.24 km/s for e=0.02 at 5 AU Destructive collisions likely as neighbouring orbits randomly orientated

82. 1 km sized planetesimals Results similar to 100 metre sized objects Large velocity dispersion prevents runaway growth of planetesimals to form planetary embryos

86. Migration in optically thick discs Corotation torque can exceed Lindblad torques in optically thick discs (Paardekooper & Mellema 2007) 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 High density region leads planet, low density region trails it - positive torque