Download Discs and Planets

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 at
14.5 ,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
Sites of planet formation
Accretion
discs
In Keplerian
(differential
rotation)
W = GM/R3
Aspect ratio
H/R << 1
Hypersonic
c=HW
<< RW
Schematic disc
models
(Terquem 2008)
Strength of
self-gravity
measured by
Q= W c/(p G S)
~( 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 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?
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 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 ≥ 1MJ a gap opens in a standard disc ( H/R ~ 0.05,
α = 0.005 ).
Schematic illustration of coorbital
flow for a low mass protoplanet
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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
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5-6
(10
y at 5AU)
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Surface density in the
coorbital region
for a 4 ME protoplanet.
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adiabatic case
with entropy increasing
outwards (right)
locally isothermal
case (left)
( S0
a r –1/2 , T a r –1)
( g = 1.4 )
Type II Migration (evolution time of disk)
Runaway (Type III) migration: Coorbital
zone with
partial gap
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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.
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Type I: objects weakly perturb the disc, are fully embedded, m/M < (H/r)3
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Type II: gap forming planet m/M > (H/r)3
n /(r2 W) < (1/40)( m/M) (perturbations dominate viscosity)
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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 planets
Example of GJ876 (without 3rd planet)
• First planet orbits in inner disc cavity.
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Second planet forms in outer disc. Material between
them is cleared by tidal interactions
resulting in both orbiting inside the cavity.
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Second planet is driven inwards due to
disc interaction until commensurability
is attained. This is subsequently maintained
with two planets migrating together.
Resonant angles 2l1- l2- w1 , 2l1- l2-w2
Semi-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 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
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
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.
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Take initial conditions randomly in disc like
or spherical annulus 0.1R 1 < R < R1
with R1 = 100 au.
General outcomes
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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
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Production of objects that have close
encounters or impacts with the central star
common for appropriate initial conditions
→ massive hot Jupiters.
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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
encounter time/dynamical time:
 ~ [M*rP3/(MR*3)]1/2 ~
= [M*rP3 /((M+M*)R*3)]1/2
Undisturbed body assumed spherically symmetric
Energy and Angular momentum transferred
as a function of W/WP for  = 8.(2)1/2
for a coreless model
normal modes are excited -mainly inertial modes
t = 0.41(upper) and t = 0.78(lower)
Tidal Response of
Model with
Rcore = 0.25 R*
for = 4 and
W/W*= 0.8
Tidal Response of Model
with Rcore = 0.5 R* for  = 4 and
W/W*= 0.8
Orbital
circularization
starting from
tc/109y
10 and 100 AU
Porb(d)
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.