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PH709
Extrasolar Planets - 6
Professor Michael Smith
1
Two obvious differences between the exoplanets and the giant
planets in the Solar System:
A) Existence of planets at small orbital radii, where our
previous theory suggested formation was very difficult.
B) Substantial eccentricity of many of the orbits. No clear
answers to either of these surprises, but lots of ideas...
The Problem: It is very difficult to form planets close to the
stars in a standard theory of planet formation using minimum
mass solar nebula, because


it's too hot there for grain condensation and
there's too little solid material in the vicinity to build
protoplanet's core of 10 ME (applies to r~1 AU as well).

problematic to build it quickly enough (< 3 Myr)

there's too little gas to build a massive envelope
PH709
Extrasolar Planets - 6
Professor Michael Smith
2
Disk gravitational instability theory.
The more radical option in which exoplanets form directly from
gravitational instability are also possible.
This depends on the Jeans Mass. The Toomre parameter
expresses the condition associated wit a disk: a disk needs to be
sufficiently massive to be gravitationally unstable to overcome
the shearing effects.
http://www.astro.virginia.edu/class/whittle/astr553/Topic06/L
ecture_6.html
Jeans Length L :
 > L =  cs2 / (G )
Toomre parameter Q:
Q = cs /  G ) < 1.5
where  is the surface density of the disk (mass per unit area)
and  is the epicyclic frequency:
2
= 4 2 + R d2/dR
and the angular rotation speed is
1. :(R) = GM/R3
2. Rigid body: (R) = constant, 
= 2 uniform density)
3. Keplerian:(R) = 1/R 3/2,

= point mass)
4. Flat rotation; :(R) = 1/R,

= 2 1/2 
To form a solid core, the heavy elements must settle.
Cooling is important for object to collapse – not clear this
occurs sufficiently fast.
PH709
Extrasolar Planets - 6
Professor Michael Smith
3
Core-accretion Theory. Most conservative (accepted)
possibility:
• Planet formation in these extrasolar systems was via the
“core-accretion gas-capture” model – i.e. same as dominant
theory for the Solar System
• Subsequent orbital evolution modified the planet orbits to
make them closer to the star and / or more eccentric.
We will focus on this option.
PH709
Extrasolar Planets - 6
Professor Michael Smith
4
PH709
Extrasolar Planets - 6
Professor Michael Smith
5
Stage 1:
Settling and growth of dust grains: quite well-coupled to gas.
Rapid growth if turbulent motion increase collision rate?
Grains settle toward the mid-plane of the gas disk.
Gas orbits slightly slower than Keplerian, because the gas
pressure is higher nearer the centre, providing an outward force
in additional to the centrifugal force.
Friction between gas and dust causes grains to decelerate and
move in.
From pebbles to planetesimals (km size): inward drift due to gas
drag.
So the pebble must grow quickly to avoid spiraling in.
Stage 2:
Planetesimal to rocky planet/gas-giant core: independent of gas.
It is a slow process – gravitational dynamics (gravity increases
the collision cross-section).
Stage 3:
Gas accretion onto core
When is the gas/dust bound to the planetesimal rather than the
star?
The Hill radius is found by equating the orbital periods of the
planetesimal and the star. From Kepler’s law:
P = 2p
a3
G (M1 + M2 )
RHill = (Mp/M*)1/3 a
PH709
Extrasolar Planets - 6
Professor Michael Smith
6
In this way, the planetesimal acquires mass, and the Hill Radius
grows!
Stage 4: Orbital evolution – migration
Giant planets can form at large orbital radii.
Need a migration mechanism that can move giant planets from
formation site at ~5 AU to a range of radii from 0.04 AU upwards.
Three theories have been proposed:
• 1. Gas disc migration: planet forms within a protoplanetary
disc and is swept inwards with the gas as the disc evolves and
material accretes onto the star. The most popular theory, as by
definition gas must have been present when gas giants form.
• 2. Planetesimal disc migration: as above, but planet
interacts with a disc of rocks rather than gas. Planet ejects the
rocks, loses energy, and moves inwards.
• 3. Planet scattering: several massive planets form –
subsequent chaotic orbital interactions lead to some (most)
being ejected with the survivors moving inwards as above.
Gas disc migration
•
migration from larger radii offers a plausible way to form giant
planets at small radii, but:
–
–
–
why did the migration stop?
why are the planetary semi-major axes distributed over a
wide range?
why did migration not occur in the solar system?
PH709
Extrasolar Planets - 6
Professor Michael Smith
7
Disc ‘Clearing’
Planet interacts with gas in the disc via gravitational force.
Strong interactions at resonances, e.g. where
disc = nplanet,
with n an integer. For example the 2:1 resonance, where n = 2,
which lies at 2-2/3 rp = 0.63 rp
Resonances at r < rp: Disc gas has greater angular velocity
than planet. Loses angular momentum to planet -> moves
inwards
Resonances at r > rp: Disc gas has smaller angular velocity
than planet. Gains angular momentum from planet -> moves
outwards.
Migration type I - no gap
If the object has too small a mass to open a gap, it will drift inwards.
The analysis of Type I migration relies on the (near) exact cancelling
of the various torques. The planet, unless more massive than the
surrounding disk, follows the disk's viscous flow.
The intrinsic imbalance of torques from the inner and outer disk
determines this.
It is very rapid, and may shift the protoplanetary core to arbitrarily
small distance from the star in the allotted ~3 Myr time frame.
PH709
Extrasolar Planets - 6
Professor Michael Smith
8
Migration type II - inside an open gap
Interaction tends to clear gas away from location of planet.
Result: planet orbits in a gap largely cleared of gas and dust.
Tidal locking of the planet in the gap.
PH709
Extrasolar Planets - 6
Professor Michael Smith
9
This process occurs for massive planets (~ Jupiter mass) only.
Earth mass planets remain embedded in the gas though
gravitational torques can be very important source of orbital
evolution for them too.
How does this lead to migration?
1. Angular momentum transport in the gas (viscosity) tries to close
the gap (diffusive evolution of an accretion disc).
2. Gravitational torques from planet try to open gap wider.
3. Gap edge set by a balance:
-> Internal viscous torque = planetary torque
4. Planet acts as an angular momentum ‘bridge’:
• Inside gap, outward angular momentum flux transported by
viscosity within disc
• At gap edge, flux transferred to planet via gravitational
torques, then outward again to outer disc
PH709
Extrasolar Planets - 6
Professor Michael Smith
10
• Outside gap, viscosity again operative
Typically, gap extends to around the 2:1 resonances interior and
exterior to the planet’s orbit.
As disc evolves, planet moves within gap like a fluid element in the
disc – i.e. usually inwards.
Inward migration time ~ few x 105 yr from 5 AU.
Mechanism can bring planets in to the hot Jupiter regime.
This mechanism is quantitatively consistent with the distribution of
exoplanets at different orbital radii – though the error bars are still
very large!
Eccentricity generation mechanisms
The substantial eccentricities of many exoplanets orbits do not have
a completely satisfactory explanation. The theories can be divided
into groups corresponding to different formation mechanisms:
(A) Direct molecular cloud fragmentation
(B) Protostellar disk fragmentation theories
(C) Companion star-planet interaction (in double star like 16
Cyg)
(D) Classical giant planet formation with planet-planet
interaction
(E) Resonant disk-planet interaction
(D) Scattering among several massive planets
Assumption: planet formation often produces a multiple system
which is unstable over long timescales:
• Chaotic evolution of a, e (especially e)
• Orbit crossing
• Eventual close encounters -> ejections
• High eccentricity for survivors
Advantages:
• Given enough planets, close together, definitely works
• Can produce very eccentric planets (cf e=0.92 example)
• Some (stable) multiple systems are already known
Disadvantages:
• Requires planets to form very close together.
PH709
Extrasolar Planets - 6
Professor Michael Smith
11
Is it plausible that unstable systems formed in a large
fraction of extrasolar planetary systems?
• Collisions may produce too many low e systems
(E) Disc interactions
Assumption: gravitational interaction with disc generates eccentricity
Advantages:
• Same mechanism as invoked for migration
• Works for just one planet in the system
• Theoretically, interaction is expected to increase
eccentricity if dominated by 3:1 resonance
Disadvantages:
• Gap is only expected to reach the 3:1 resonance for
brown dwarf type masses, not massive planets. Smaller
gaps definitely tend to circularize the orbit instead.
• Seems unlikely to give very large eccentricities
(B) Protoplanetary disc itself is eccentric
Assumption: why should discs have circular orbits anyway?
Eccentric disc -> eccentric planet?
Not yet explored in much depth. A possibility, though again seems
unlikely to lead to extreme eccentricities.
Scattering theory is currently most popular,
possibly augmented by interactions with other planets in
resonant orbits.
THE PLANET ITSELF
Luminosity evolution (theory)
PH709
Extrasolar Planets - 6
50% of D burned
Professor Michael Smith
12
50% of Li burned
stars
brown
dwarfs
“planets”
Burrows et al. (2001)
THE END
FURTHER¬ READING: NOT PART OF EXOPLANET
COURSE
DARWIN – 2020 ? Life?
PH709
Extrasolar Planets - 6
Professor Michael Smith
13
PH709
Extrasolar Planets - 6
Professor Michael Smith
14
7 Summary of (Future) Missions
CoRoT is a space project:
Convection, Rotation and Transits
The COROT instrument makes it possible, with a method called
stellar seismology, to probe the inner structure of the stars, as well
as to detect many extrasolar planets, by observing the periodic
micro-eclipses occurring when these bodies transit in front of their
parent star.
Its objective is double:
- study stellar interiors
- detect planets analogous to the Earth orbiting around other stars
than the Sun.
A Russian Soyuz 2-1B rocket lifted the satellite into a circular polar orbit with an
altitude of 827 km on 27 December 2006. It will carry a telescope able to
observe continuously many stars during very long periods and to measure very
accurately the variations of their brightness.
http://corot.oamp.fr/
PH709
Extrasolar Planets - 6
Professor Michael Smith
15
….down to earth-like planets.
Kepler: 2009 - Transit method, occurrence of earth-sized planets.
http://www.kepler.arc.nasa.gov/
PH709
Extrasolar Planets - 6
Professor Michael Smith
16
Concept Study
Mar 2001 to July 2001
Discovery selection Dec. 21, 2001
Phase B
Feb 2002 to Oct 2004
Phase C/D
Nov 2004 to Oct 2008
Launch
February 2009
Commissioning Launch + 30 days
Phase E
Flight operations For 3.5 years from end of commissioning
Data analysis
For 5 years from end of commissioning
The Kepler instrument 0.95-meter diameter telescope.
It has a very large field of view for an astronomical telescope —105 square
degrees— or about the area of both your hands held at arm's length, in order to
observe the necessary large number of stars.
It stares at the same star field for the entire mission and continuously and
simultaneously monitors the brightnesses of more than 100,000 stars for the
life of the mission—3.5 years.
The diameter of the telescope needs to be large enough to reduce the noise from
photon counting statistics, so that it can measure the small change in brightness
of an Earth-like transit. The design of the entire system is such that the combine
differential photometric precision over a 6.5 hour integration is less than 20
ppm (one-sigma) for a 12th magnitude solar-like star including an assumed
stellar variability of 10 ppm. (This is a conservative, worse-case assumption of a
grazing transit.
A central transit of the Earth crossing the Sun lasts 13 hours. And about
75% of the stars older than 1 Gyr are less variable than the Sun on the time scale
of a transit. )
The photometer must be space-based to obtain the photometric precision
needed to reliably see an Earth-like transit and to avoid interruptions caused by
day-night cycles, seasonal cycles and atmospheric perturbations, such as,
extinction associated with ground-based observing.
Space Interferometry Mission SIM and Gaia: astrometry
The Space Interferometry Mission (SIM) will detect planets with masses as
low as 3 M Earth orbiting within 2 AU of stars within 10 pc, and it will
measure masses, orbits, and multiplicity. The candidate rocky planets will
be amenable to follow-up spectroscopy by the “Terrestrial Planet Finder”
and Darwin.
PH709
Extrasolar Planets - 6
Professor Michael Smith
17
TPF: Direct imaging detection and spectroscopic characterization of
nearby Earthlike planets will be undertaken by the Terrestrial
Planet Finder missions.
The TPF Coronagraph (TPF-C), planned for launch in 2014, will
operate at visible wavelengths. It will suppress the light of the
central star to unprecedented levels, allowing it to search for
terrestrial planets in ~150 nearby planetary systems. TPF-C will be
followed about five years later by the TPF Interferometer (TPF-I).
TPF-I will operate in the mid-IR and will survey a larger volume of
our solar neighborhood, searching for terrestrial planets around as
many as 500 nearby stars.