1. Extrasolar Planets More that 500 extrasolar planets have been discovered In 46 planetary systems through radial velocity surveys, transit observations, direct imaging and gravitational lensing. The diversity of their configurations was unexpected and challenges theories of planet formation.

4. Planet mass distribution

5. Period – Mass distributions

7. Measurement of the orbital inclination with respect to the stellar equator. The Rossiter-Mclaughlin effect

8. Orbital inclinations for transiting planets: about 1/3 of hot Jupiters have high orbital inclinations or retrograde orbits

9. HR 8799 Four planets ~10 Jupiter masses imaged at 14.5,24, 38, 68 AU (possible resonances)

11. β Pictoris imaged at L′ band (3.78 microns) with the VLT/NaCo instrument in November 2003 (left) and the fall of 2009 (right). Planet mass ~10M J at 12AU > P~15y A Lagrange et al. Science 2010;329:57-59 Published by AAAS

13. Accretion discs In Keplerian (differential rotation)  GM/R 3 Aspect ratio H/R << 1 Hypersonic c = H  << R  Sites of planet formation

14. Schematic disc models (Terquem 2008) Strength of self-gravity measured by Q=  c/  G  ~( M d /M * )(R/H)

15. Planetary accumulation: V. Safronov: Evolution of the protoplanetary cloud and the formation of the earth and planets (1969) Many stages starting from dust grains sticking to formation of planetesimals, growth by runaway Accretion, oligarchic growth to obtain core of several earth masses that can accrete gas.. Long time scale (at a few AU) comparable to disk ages. Difficulties at larger distances….gravitational instability favoured?

16. Gravitational Instability: spiral modes and fragments

17. Tidal Interaction of a protogiant planet with a protoplanetary disc and orbital migration (Lindblad torques): Slower material____________________________ > O < _____________________________Faster material ↓ Centre The outer slower material drags the planet backward and the inner and faster material accelerates it. This frictional interaction causes circularization and orbital migration. The direction is controlled by which material has the stronger interaction. In particular if there is an inner cavity the outer and slower material wins leading to inward migration. For M ≥ 1M J a gap opens in a standard disc ( H/R ~ 0.05, α = 0.005 ). For M ≥ 1M J a gap opens in a standard disc ( H/R ~ 0.05, α = 0.005 ).

18. Schematic illustration of coorbital flow for a low mass protoplanet Due to horseshoe turns if there is a gradient of specific vorticity in the barotropic case or entropy in the adiabatic case the surface density at A’ will not be the same as that at C and that at C’ will not be the same as that at A  Coorbital torque (Horseshoe drag in the baratropic case)

19. Type I Migration (10 5-6 y at 5AU) Surface density in the coorbital region for a 4 M E protoplanet. locally isothermal case (left) adiabatic case with entropy increasing outwards (right) (    r –1/2, T  r –1 ) ( 

20. Type II Migration (evolution time of disk)

21. Runaway (Type III) migration: Coorbital zone with partial gap

22. Summary of the Types of migration For small objects < 0.001 earth masses ….Gas drag determines migration….local fluid effect. For larger objects-----( Direct gravitational interaction with the disc produces the most important migration.) crossover mass is about 10 -(3-4) earth masses. Type I  objects weakly perturb the disc, are fully embedded, m/M < (H/r) 3 Type II: gap forming planet m/M > (H/r) 3  r 2  m/M) (perturbations dominate viscosity) Runaway (Type III): Partial gap forming, disk mass on length scale H should be comparable to m and m/M~ (H /r) 3 In this case dynamics in coorbital zone can give rise to a positive feedback acting on migration…. Possible fast migration in ~ 100 orbits. This case very difficult numerically as it involves partial gaps with a coorbital flow with lots of mass near the planet. Several times more mass than in a minimum mass nebula model needed..

24. Resonant coupling of migrating planets Example of GJ876 (without 3 rd planet) First planet orbits in inner disc cavity. Second planet forms in outer disc. Material between them is cleared by tidal interactions resulting in both orbiting inside the cavity. Second planet is driven inwards due to disc interaction until commensurability is attained. This is subsequently maintained with two planets migrating together.

26. Resonant angles 2        2      Semi-major axes and eccentricities for GJ876

27. Disk migration may allow planets to migrate from the snow line to a close orbit becoming a hot Jupiter and account for resonant systems. However, it cannot account for the observed high eccentricities and inclinations These indicate periods of strong gravitational interaction in a multiplanet system

28. Strong orbital relaxation of N planets and production of high eccentricities Suppose N planets ~ a few M J form rapidly enough for this to occur. Effects noticeable for N as small as 3or 4. Formation through gravitational instability or core accumulation might lead to this. Relaxation as in star clusters with t R = 0.34v 3 /(3√3 G 2 M p ρ ln(Λ)) For N=5, M p = 5M J get t R ~ 100 orbits for scale R = 100 au. Take initial conditions randomly in disc like or spherical annulus 0.1R 1 < R < R 1 with R 1 = 100 au.

29. General outcomes Strong relaxation tends to result in one or two objects taking up the binding energy while the rest are ejected → free floating planets?? Survivors may orbit at 10 – 100 times smaller radii than original cloud and at high mutual inclinations Production of objects that have close encounters or impacts with the central star common for appropriate initial conditions → massive hot Jupiters. Surviving massive planets can generate high eccentricities in interior lower mass objects due to Kozai mechanism.

30. N=4 Outer relaxing planets (8 Jupiter masses). Inner Saturn mass planet starts to circularize

31. 7 Jupiter mass And Saturn mass planet a/A =0.01 coplanar and 60 degree inclination cases

32. Tidal encounters of planets with a central star ( Ivanov and Papaloizou) We need to study the tidal interactions of close orbiting exoplanet ‘Hot Jupiters’ in very eccentric orbits possibly produced by scattering and the approach to orbital circularization. Similar problems for stars captured into highly eccentric orbits around AGN

33. Tidal Encounter on a Parabolic orbit The tidal interaction on a highly eccentric orbit is treated as a sequence of close encounters on a parabolic orbit. Tidal parameter measures Undisturbed body assumed spherically symmetric encounter time/dynamical time:  ~ [M * r P 3 /(MR * 3 )] 1/2 ~  = [M * r P 3 /((M+M * )R * 3 )] 1/2

34. Energy and Angular momentum transferred as a function of  P for  = 8.(2) 1/2 for a coreless model normal modes are excited -mainly inertial modes

35. Tidal Response of Model with R core = 0.25 R * for  and     t = 0.41(upper) and t = 0.78(lower)

36. Tidal Response of Model with R core = 0.5 R * for  and   

37. t c /10 9 y P orb (d) Orbital circularization starting from 10 and 100 AU

38. Tidal interaction between the planet and the central star may account for efficient circularization at periods < ~5 days but many problems remain… Planets may have to survive more than 10* binding energy being dissipated internally. Tides only affect the orbit distribution close to the star. More observations awaited to give improved configuration distributions.