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.

Planet mass distribution

Period – Mass distributions

Measurement of the orbital inclination with respect to the stellar equator.

The Rossiter-Mclaughlin effect

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

HR 8799 Four planets ~10 Jupiter masses imaged at14.5 ,24, 38, 68 AU (possible resonances)

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 ~10MJ at 12AU > P~15y

A Lagrange et al. Science 2010;329:57-59

Published by AAAS

Accretion discs

In Keplerian(differential

rotation)GM/R3

Aspect ratio H/R << 1

Hypersonicc = H << R

Sites of planet Sites of planet formationformation

Schematic disc models

(Terquem 2008)

Strength of self-gravity

measured by

Q= c/G

~( Md/M*)(R/H)

Planetary accumulation:

V. Safronov: Evolution of the protoplanetary cloud and the formation of the earth and planets (1969)

Many stages starting from dust grains stickingto formation of planetesimals, growth by runawayAccretion, 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?

Gravitational Instability: spiral modes and fragments

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 The outer slower material drags the planet backward and the inner and faster material accelerates it. This frictional inner and faster material accelerates it. This frictional

interaction causes circularization and orbital migration. The interaction causes circularization and orbital migration. The direction is controlled by which material has the stronger direction is controlled by which material has the stronger

interaction . In particular if there is an inner cavity the outer interaction . In particular if there is an inner cavity the outer and slower material wins leading to inward migration. and slower material wins leading to inward migration.

For M ≥ 1MFor M ≥ 1MJ J a gap opens in a standard disc ( H/R ~ 0.05, a gap opens in a standard disc ( H/R ~ 0.05, αα = = 0.005 ).0.005 ).

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)

Type I Migration (105-6 y at 5AU)• •

• • Surface density in the • coorbital region• for a 4 ME protoplanet.• • locally isothermal • case (left)

• adiabatic case• with entropy increasing• outwards (right) • • ( r –1/2 , T r –1)• • ( •

Type II Migration (evolution time of disk)

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

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

r2 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..

Resonant coupling of migrating planetsExample of GJ876 (without 3rd 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.

Resonant angles 22Semi-major axes and eccentricities for GJ876

Disk migration may allow planets to migrate from the snow line to a close orbit becoming a hot Jupiter andaccount for resonant systems.

However, it cannot account for theobserved high eccentricities and inclinations

These indicate periods of stronggravitational interaction in a multiplanet system

Strong orbital relaxation of N planetsand 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

tR = 0.34v3/(3√3 G2 Mp ρ ln(Λ))

• For N=5, Mp = 5M J get tR ~ 100 orbits for scale R = 100 au.

• Take initial conditions randomly in disc like

or spherical annulus 0.1R 1 < R < R1

with R1 = 100 au.

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.

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

7 Jupiter mass And Saturn mass planet

a/A =0.01

coplanar and 60 degree inclination cases

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

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*rP3/(MR*

3)]1/2 ~ = [M*rP

3 /((M+M*)R*3)]1/2

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

Tidal Response of Model with

Rcore = 0.25 R*

for and

t = 0.41(upper) and t = 0.78(lower)

Tidal Response of Model with Rcore = 0.5 R* for

and

tc/109y

Porb(d)

Orbital circularization

starting from

10 and 100 AU

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.