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PH709
Extrasolar Planets
Professor Michael Smith
1
Pulsar Planets
In early 1992, the Polish astronomer Aleksander Wolszczan (with Dale Frail)
announced the discovery of planets around another pulsar, PSR 1257+12.This discovery
was quickly confirmed, and is generally considered to be the first definitive detection of
exoplanets. These pulsar planets are believed to have formed from the unusual remnants
of the supernova that produced the pulsar, in a second round of planet formation, or
else to be the remaining rocky cores of gas giants that survived the supernova and then
spiralled in to their current orbits.

Pulsar timing Pulsars (the small, ultradense remnant of a star that has
exploded as a supernova) emit radio waves extremely regularly as they
rotate. Slight anomalies in the timing of its observed radio pulses can
be used to track changes in the pulsar's motion caused by the presence
of planets.
Observed Properties of Exoplanets: Masses, Orbits, and
Metallicities
Geoffrey Marcy et al…….2005
Summary:
Ongoing 18-year survey of 1330 FGKM type stars at Lick, Keck, and the AngloAustralian Telescopes that offers both uniform Doppler precision (3 m s-1) and long
duration. The 104 planets detected in this survey have minimum masses (M sin i) as
low as 6 M Earth, orbiting between 0.02 and 6 AU.
The core-accretion model of planet formation is supported by four observations:
1) The mass distribution rises toward the lowest detectable masses, dN/dM ~ M -1.0.
2) Stellar metallicity correlates strongly with the presence of planets.
3) One planet (1.3 M Sat) has a massive rocky core, M Core ≈ 70 M Earth.
4) A super-Earth of about 7 M Earth has been discovered.
The distribution of semi-major axes rises from 0.3 – 3.0 AU (dN/d log a) and
extrapolation suggests that about 12% of the FGK stars harbour gas-giant
exoplanets within 20 AU.
The median orbital eccentricity is <e >= 0.25, and even planets beyond 3 AU reside in
eccentric orbits, suggesting that the circular orbits in our Solar System are unusual.
The occurrence “hot Jupiters” within 0.1 AU of FGK stars is 1.2 ± 0.2%.
PH709
Extrasolar Planets
Professor Michael Smith
2
Among stars with one planet, 14% have at least one additional planet, occasionally
locked in resonances.
Kepler and COROT will measure the occurrence of earth-sized planets. 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.
• Planet fraction among ~ solar-type stars exceeds 7%
• Most are beyond 1 AU
• Four very low mass planets have been detected ….20 earth masses.
Other positive detections:
Microlensing: two strong detections, low detection rate imply upper limit of ~1/3 on
the fraction of lensing stars (~ 0.3 Msun) with Jupiter mass planets at radii to which
lensing is most sensitive (1.5 - 4 AU)
Transits: 7 known planets (5 found with OGLE photometrically – dimming).
Interesting upper limit from non-detection of transits in globular cluster 47 Tuc.
Transits + Doppler yields mass and size, hence the density of the planet: 0.2 – 1.4
gm/cm3 : mainly gaseous. In addition, sodium and nitrogen found in their atmospheres.
Eccentricity:
• Except at very small radii, typical planet orbit has significant eccentricity
The eccentricity of an orbit is how much it varies from a perfect circle. A stable orbit
can have an eccentricity anywhere from a perfect circle with an eccentricity of 0, up to a
highly elliptical orbit with an eccentricity up to (but not including) 1. If an orbit had an
eccentricity of 1, it would be parabolic and escape from the system. If it were larger than
1, it would be hyperbolic and also escape from the system.
PH709
Extrasolar Planets
Professor Michael Smith
3
PH709
Extrasolar Planets
Professor Michael Smith
4
Most extrasolar planets reside in non-circular orbits. Of the 90 extrasolar
planets that reside beyond 0.15 AU, their average orbital eccentricity is 0.32.
In contrast, planets orbiting within 0.1 AU of their host star all reside in nearly
circular orbits, no doubt enforced by tidal circularization.
Earth's eccentricity is 0.017, while Jupiter's is 0.094. In our solar system, the planet with
the largest eccentricity is Pluto at 0.244, and Mercury with 0.205. The planet with the
lowest eccentricity is Venus with 0.007. Unless there is some gravitational tugging
(such as with the Galilean Satellites) that keeps an orbit eccentric, orbits will usually
circularize with time.
About 10% of the planets found so far have an eccentricity of nearly 0. About 15% have
an eccentricity smaller than Earth's, and over 25% have an eccentricity smaller than
Jupiter's. 45% are smaller than Mercury's eccentricity, and 50% are lower than Pluto's.
The other half have very eccentric orbits; this means that, throughout their years, they
come very close to and very far from their parent star. This will create wide temperature
swings, and for any life like Earth's, this would make survival quite difficult, if not
impossible.
PH709
Extrasolar Planets
Professor Michael Smith
5
Theories:
 Various theories have been proposed to explain the orbital eccentricities, but
none is definitive at the current time. Most proposed mechanisms invoke
gravitationally scattering or perturbations of planets by other planets, perhaps
in resonances, or by interactions with the protoplanetary disk.
Orbital eccentricity as a function of semimajor axis for the 168 known nearby
exoplanets. Planets within 0.1 AU are presumably tidally circularized. Beyond
0.1 AU, the distribution of eccentricities appears essentially uniform between 0
and 0.8. For most Doppler surveys, sensitivity is not a strong function of
eccentricity for 0 < e < 0.8 and a < 3 AU. This plot represents results from many
surveys, and so is drawn from an inhomogeneous sample.
Distribution of Eccentricity:
PH709
Extrasolar Planets
Professor Michael Smith
6
Eccentricity vs planet mass
Distribution of orbital eccentricities as a function of minimum mass for the
130 known nearby exoplanets with M sin i < 13 MJup, excluding those for which
a < 0.1 AU, i.e., those planets which may have been tidally circularized. Highmass exoplanets (M sin i > 5MJup) have a slightly higher median eccentricity
than lower-mass exoplanets. The completeness of Doppler surveys increases
with M sin i and is generally insensitive to eccentricity. This distribution
represents results from many surveys, and so is drawn from an
inhomogeneous.
Ignoring the hot Jupiters, no obvious correlation between planet mass and
eccentricity.
(1) Hot Jupiters have close to circular orbits. All detected planets with semi-major
axis < 0.07 AU have low e. This is similar to binary stars, and is likely due to
tidal circularization.
(2) Remaining planets have a wide scatter in e, including some planets with large e.
Note that the distance of closest approach is a(1-e), and that the effect of
tidal torques scales as separation d-6. The very eccentric planet around
HD80606 (a = 0.438 AU, e = 0.93, a(1-e) = 0.03 AU) may pose some
problems for tidal circularization theory.
PH709
Extrasolar Planets
Professor Michael Smith
Minimum mass as a function of semimajor axis:
7
PH709
Extrasolar Planets
Professor Michael Smith
8
Nothing very striking in these plots:
• Accessible region of mp - a space is fully occupied by detected planets
Get rid of the log (Mj) :
PH709
Extrasolar Planets
Professor Michael Smith
9
Minimum mass as a function of semimajor axis for the 164
known nearby exoplanets with 0.03 < a < 6.5 AU. Doppler surveys
are generally incomplete for exoplanets with a > 3 AU, low-mass
planets (M sin i < 1MJup) beyond 1 AU, and very low-mass planets
(M sin i < 0.1MJup) everywhere. This plot represents results from
many surveys, and so is drawn from an inhomogeneous sample.
Results from radial velocity searches
(1) Massive planets exist at small orbital radii. Closest-in planet is at a = 0.035 AU,
cf Mercury at ~ 0.4 AU. Less than 10 Solar radii.
Best-fit orbit to the radial velocities measured at Keck Observatory
for HD 66428,
with P = 5.4yr, e = 0.5, and M sin i = 3MJup.
Best-fit orbit to the radial velocities measured at Keck Observatory
for HD 11964,
with P = 5.8yr, e ~ 0, and M sin i = 0.6MJup.
PH709
Extrasolar Planets
Professor Michael Smith
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PH709
Extrasolar Planets
Professor Michael Smith
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Account for this by considering only planets with masses large enough to be detectable
at any a < 2.7 AU.
-> dN / dlog(a) rises steeply with orbital radius
Implies that the currently detected planet fraction ~7% is likely to be a substantial
underestimate of the actual fraction of stars with massive planets.
Models suggest 15-25% of solar-type stars may have planets with masses 0.2 MJ < mp <
10 MJ.
Strong selection effect in favour of detecting planets at small orbital radii, arising from:
- lower mass planets can be detected there
- mass function rises to smaller
masses
Orbital distance distribution of the 167 known nearby exoplanets with
0.03 <a < 10 in logarithmic distance bins. Planets with a > 3AU have
periods comparable to or longer than the length of most Doppler
surveys, so the distribution is incomplete beyond that distance. This
distribution represents results from many surveys, and so is drawn from
an inhomogeneous sample
PH709
Extrasolar Planets
Professor Michael Smith
12
Distribution of periods among the known nearby “hot Jupiters”. There
is a clear “pile-up” of planets with orbital periods near 3 days. Doppler
surveys generally have uniform sensitivity to hot Jupiters, so for massive
planets, there is no important selection effect contributing to the 3-day
pile-up. This distribution represents results from many surveys, and so is
drawn from an inhomogeneous sample.
Observed mass function increases to smaller Mp:
PH709
Extrasolar Planets
Professor Michael Smith
13
Note: the brown dwarf desert!
Minimum mass distribution of the 167 known nearby exoplanets with M sin i <
15 MJup. The mass distribution shows a dramatic decrease in the number of
planets at high masses, a decrease that is roughly characterized by a power law,
dN/dM ~ M-1.16. Lower mass planets have smaller Doppler amplitudes, so the
relevent selection effects enhance this effect. This distribution represents results
from many surveys, and so is drawn from an inhomogeneous sample.
PH709
Extrasolar Planets
Professor Michael Smith
14
Metallicity distribution of stars with and without planets
Left plot: metallicity of stars with planets (shaded histogram) compared to a sample of
stars with no evidence for planets (open histogram) (data from Santos, Israelian &
Mayor, 2001)
Host star metallicity
PH709
Extrasolar Planets
Professor Michael Smith
15
Planets are preferentially found around stars with enhanced metal abundance.
Cause or effect? High metal abundance could:
(a) Reflect a higher abundance in the material which formed the star +
protoplanetary disc, making planet formation more likely.
(b) Result from the star swallowing planets or planetesimals subsequent to
planets forming. If the convection zone is fairly shallow, this can apparently
enrich the star with metals even if the primordial material had Solar abundance.
Detailed pattern of abundances can distinguish these possibilities, but results currently
still controversial.
Lack of transits in 47 Tuc
A long HST observation monitored ~34,000 stars in the globular cluster 47 Tuc looking
for planetary transits.
Locally: 1% of stars have hot Jupiters
~ 10% of those show transits
 Expect 10 -3 x 34,000 ~ few tens of planets
None were detected. Possible explanations:
• Low metallicity in cluster prevented planet formation
• Cluster environment destroyed discs before planets formed
• Stellar fly-bys ejected planets from bound orbits
All of these seem plausible - make different predictions for other clusters.
PH709
Extrasolar Planets
Professor Michael Smith
16
Microlensing Statistics:
Constraint from monitoring of 43 microlensing events. Typically, the lenses are
low mass stars.
At most 1/3 of 0.3 Solar mass stars have Jupiter mass planets between 1.5
AU and 4 AU.
Currently consistent with the numbers seen in radial velocity searches.
PH709
Extrasolar Planets
Professor Michael Smith
17
HST Transit light curve from Brown et al. (2001)
Consistent with expectations - the probability of a transiting system is ~10%.
Measured planetary radius rp = 1.35 RJ:
• Proves we are dealing with a gas giant.
• Somewhat larger than models for isolated (non-irradiated) planets effect of environment on structure.
Precision of photometry with HST / STIS impressive.
Summary of Future Missions
PH709
Extrasolar Planets
Professor Michael Smith
18
….down to earth-like planets.
Kepler: 2008 - Transit method
SIM and Gaia: astrometry
6 Star & Planet Formation & Theory of Exoplanets
1. Intro: Star formation is on-going.
 What is the origin of our solar system? Descartes, Kant,
Laplace: vortices, nebular hypothesis: importance of angular
momentum.
PH709
Extrasolar Planets
Professor Michael Smith
19

In general: Gravity is fast-acting. Galaxy is old. But young stars
are still being born.

Stars don't live forever, they must continue to be "born".
Where?

Born in obscurity….needed infrared/millimeter/radio
wavelengths.
Gas Disks around Young Stars
During star formation, gas accretion occurs through a geometrically thin
disk that is optically thick. The disks are cooler than the young star, and we
thus see an infrared excess superimposed on the black body stellar
spectrum:
PH709
Extrasolar Planets
Professor Michael Smith
20
PH709
Extrasolar Planets
Professor Michael Smith
21
PH709
Extrasolar Planets
Professor Michael Smith
22
Debris Disks
Debris disks are remnant accretion disks with little or no gas left (just
dust & rocks), outflow has stopped, the star is visible.
Theory: Gas disperses, “planetesimals” form (up to 100 km diameter
rocks), collide & stick together due to gravity forming protoplanets).
Protoplanets interact with dust disks: tidal torques cause planets to
migrate inward toward their host stars. Estimated migration time ~ 2 x
105 yrs for Earth-size planet at 5 AU.
Perturbations caused by gas giants may spawn smaller planets:
Start with a stable disk
around central star.
Jupiter-sized planet forms
& clears gap in gas disk.
Planet accretes along spiral Disk fragments into more
arms, arms become unstable. planetary mass objects.
Spiral density waves continuously produced by the gravity of embedded or
external perturber.
Debris Disks – Outer Disk
AB Aurigae outer
debris disk nearly
face on – see
structure &
condensations
(possible protoplanet formation
sites? Very far
from star) .
(Grady et al. 1999)
Debris: not from original nebula but from recent collisions.
After a few hundred million years, a planetary system is expected to have assumed its
final configuration and has either set the stage for life, or will probably remain barren
PH709
Extrasolar Planets
Professor Michael Smith
23
forever. It is difficult to probe this era. Most of its traces have been obliterated in the
solar system. Only a minority of the nearby stars are so young. Even for them, planets—
and particularly those in the terrestrial planet/asteroidal region—are faint and are lost in
the glare of their central stars.
However, when bodies in this zone collide, they initiate cascades of further collisions
among the debris and between it and other members of the system, eventually grinding a
significant amount of material into dust grains distributed in a so-called debris disk.
Because the grains have larger surface area per unit mass compared to larger bodies, they
(re)radiate more energy and therefore are more easily detected in the IR compared to
their parent bodies. By studying this signal, we can probe the evolution of other planetary
systems through this early, critical stage.
Debris disks are found around stars generally older than 10 Myr, with no signs of
gas accretion (as judged from the absence of emission lines or UV excess) (Lagrange et
al. 2000; Hillenbrand 2005). In the absence of gas drag, a 10 m sized dust grain from
the primordial, proto–planetary nebula cannot survive longer than 1 Myr within 10 AU
of a star due to a number of clearing processes, such as sublimation, radiation pressure,
Poynting-Robertson, and stellar wind drag. Therefore, any main-sequence star older than
10 Myr with an IR excess is a candidate to have circumstellar material supplied through
debris disk processes.
The Birth of the Solar System
The properties of the Solar System hold important clues to its origin

Orbits of the planets and asteroids.

Rotation of the planets and the Sun.

Composition of the planets, especially the strong distinction between
Terrestrial, Jovian, and Icy planets.
Clues from planetary motions:

Planets orbit in nearly the same plane.

Planet orbits are nearly circular.

Planets & Asteroids orbit in the same direction.

Rotation axes of the planets tends to align with the sense of their orbits,
with exceptions.

Sun rotates in the same direction in the same sense.

Jovian moon systems mimic the Solar System.
Clues from planet composition:
Inner Planets & Asteroids:

Small rocky bodies

Few ices or volatiles
PH709
Extrasolar Planets
Professor Michael Smith
24
Major facts for nebula hypothesis:








Coplanar orbits of the planets
All planets have prograde revolution (orbits)
The revolution of rings and natural moons are all prograde (some moons of the
outer planets are not prograde, but these are believed to be captured satellites)
All planets except Venus and Uranus have prograde rotation
The sun contains all the mass
The planets (especially Jupiter and Saturn) contain most of the angular
momentum in the solar system
Small, dense, iron and silicate rich planets in the inner 2 AU. Slow rotors, few
or no moons, no rings, differentiated (molten interiors)
Large, low density, gaseous planets rich in H, He and volatile elements at >= 5
AU

Rapid rotors, many moons, all have ring systems

Abundance gradient. Inner solar system is poor in light volatile gases such as H,
He, but rich in Fe & Ni. Outer solar system is rich in volatiles H, He, etc.
Abundances similar to that of the sun.
Jovian Planets:

Deep Hydrogen & Helium atmospheres rich in volatiles.

Large ice & rock cores
Outer solar system moons & icy bodies:

Small ice & rock mixtures with frozen volatiles.
Formation of the Sun: back to the Primordial Solar Nebula
Stars form out of interstellar gas clouds:

Large cold cloud of H2 molecules and dust gravitationally collapses and
fragments.
Rotating fragments collapse further:

Rapid collapse along the poles, but centrifugal forces slow the collapse
along the equator.

Result is collapse into a spinning disk
PH709

Extrasolar Planets
Professor Michael Smith
25
Central core collapses into a rotating proto-Sun surrounded by a rotating
"Solar Nebula"
Primordial Solar Nebula
The rotating solar nebula is composed of

~75% Hydrogen & 25% Helium

Traces of metals and dust grains
Starts out at ~2000 K, then cools:

As it cools, various elements condense out of the gas into solid form as
grains or ices.

Which materials condense out when depends on their "condensation
temperature".
Condensation Temperatures
Temp (K)
Elements
>2000 K
Condensate
All elements are gaseous
1600 K
Al, Ti, Ca
Mineral Oxides
1400 K
Iron & Nickel
Metallic Grains – Refractory, Rocky
1300 K
Silicon
Silicate Grains - Rocky
300 K
Carbon,
Oxygen
Carbonaceous grains -Volatiles
300-100 K
Hydrogen,
Nitrogen
Ices (H2O, CO2, NH3, CH4)
The "Frost Line"
Rock & Metals can form anywhere it is cooler than about 1300 K.
Carbon grains & ices can only form where the gas is cooler than 300 K.
Inner Solar System:

Too hot for ices & carbon grains.
Outer Solar System:

Carbon grains & ices form beyond the "frost line".
PH709
Extrasolar Planets
Professor Michael Smith
26
The location of the "frost line" is also a matter of some debate but current
thinking holds that it is probably about 4 AU . A great deal depends on how
much solar radiation can penetrate deep into the outer parts of the primordial
Solar Nebula.
From Grains to Planetesimals to Planets
Grains that have low-velocity collisions can stick together, forming bigger
grains.

Beyond the "frost line", get additional growth by condensing ices onto
the grains.

Grow to where their mutual gravitation assists in the aggregation
process, accelerating the growth rate. Can form km-sized planetesimals
after a few 1000 years of initial growth.

Aggregation of planetesimals into planets
Terrestrial vs. Jovian planet formation.
Terrestrial Planets
Only rocky planetesimals inside the frost line:

Collisions between planetesimals form small rocky bodies.

It is hotter closer to the Sun, so the proto-planets cannot capture H and
He gas.

Solar wind is also dispersing the solar nebula from the inside out,
removing H & He.
Result:

Form rocky terrestrial planets with few ices.
Jovian Planets
The addition of ices to the mix greatly augments the masses of the
planetesimals
These collide to form large rock and ice cores:.

Jupiter & Saturn: 10-15 MEarth rock/ice cores.

Uranus & Neptune: 1-2 MEarth rock/ice cores.
As a consequence of their larger masses & colder temperatures:

Can accrete H & He gas from the solar nebula.

Planets with the biggest cores grow rapidly in size, increasing the
amount of gas accretion.
PH709
Extrasolar Planets
Professor Michael Smith
27
Result:

Form large Jovian planets with massive rock & ice cores and heavy H
and He atmospheres
Moons & Asteroids
Some of the gas attracted to the proto-Jovians forms a rotating disk of material:

Get mini solar nebula around the Jovians

Rocky/icy moons form in these disks.

Later moons added by asteroid/comet capture.
Asteroids:

Gravity of the proto-Jupiter keeps the planetesimals in the main belt
stirred up.

Never get to aggregate into a larger bodies.
Icy Bodies & Comets
Outer reaches are the coldest, but also the thinnest parts of the Solar Nebula:

Ices condense very quickly onto rocky cores.

Stay small because of a lack of material.
Gravity of the proto-Neptune also plays a role:

Assisted the formation of Pluto-sized bodies in 3:2 resonance orbits
(Pluto and Plutinos)

Disperses the rest into the Kuiper Belt to become Kuiper Belt Objects.
Comets and other Trans-Neptunian objects are the leftover icy planetesimals from the
formation of the Solar System.
Mopping up...
The entire planetary assembly process probably took about 100 Million years.
Followed by a 1 Billion year period during which the planets were subjected to heavy
bombardment by the remaining rocky & icy pieces leftover from planet formation.
Light from the Sun dispersed the remaining gas in the Solar Nebula gas into the
interstellar medium.
Planetary motions reflect the history of their formation.
Planets share the same sense of rotation, but have been perturbed from perfect
alignment by strong collisions during formation.
The Sun "remembers" this original rotation. Rotates in the same direction with its
axis aligned with the plane of the Solar System.
PH709
Extrasolar Planets
Professor Michael Smith
28
Planetary compositions reflect the formation conditions.
Terrestrial planets are rock & metal:

They formed in the hot inner regions of the Solar Nebula.

Too hot to capture Hydrogen/Helium gas from the Solar Nebula.
Jovian planets contain ice, H & He:

They formed in the cool outer regions of the Solar Nebula.

Grew large enough to accrete lots of H & He.
.
Lecture 7:
Two obvious differences between the exoplanets and the giant planets in
the Solar System:
• Existence of planets at small orbital radii, where our previous theory
suggested formation was very difficult.
• Substantial eccentricity of many of the orbits. No clear answers to
either of these surprises, but lots of ideas...
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
PH709
Extrasolar Planets
Professor Michael Smith
29

there's too little solid material in the vicinity to built 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
Most conservative (accepted) possibility:
• Planet formation in these extrasolar systems was via the core accretion 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. However, more radical options in which exoplanets form
directly from gravitational instability are also possible.
Gas+dust discs:
Stage 1:
Settling and growth of dust grains: quite well-coupled to gas, rapid only if
turbulent?
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
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 increase the collision cross-section).
Stage 3:
Gas accretion onto core,
Stage 4: Orbital evolution – migration
Giant planets can form at large orbital radii.
Need a migration mechanism that can move giant planets from formation at ~5 AU to a
range of radii from 0.04 AU upwards.
Three theories have been proposed:
• 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.
PH709
Extrasolar Planets
Professor Michael Smith
30
• 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.
• 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
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.
It is thought that 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.
Migration type II - inside an open gap
Interaction tends to clear gas away from location of planet.
PH709
Extrasolar Planets
Professor Michael Smith
31
Result: planet orbits in a gap largely cleared of gas and dust.
Tidal locking of the planet in the gap.
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
PH709
Extrasolar Planets
Professor Michael Smith
32
• At gap edge, flux transferred to planet via gravitational torques, then outward
again to outer disc
• 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
Substantial eccentricities of many exoplanets orbits do not have 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 discovered
• Some (stable) multiple systems are already known
Disadvantages:
• Requires planets to form very close together.
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:
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• 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 END
The COROT instrument will make 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 launch is scheduled in 2006.
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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.
Life?
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Workshop Example: the first transit
1. \Hubble Space Telescope Time-Series Photometry of
the Transiting Planet of HD 2094581
Timothy M. Brown etal
The Astrophysical Journal, 552:699-709, 2001 May 10
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We have observed four transits of the planet of HD 209458 using the STIS spectrograph
on the Hubble Space Telescope (HST). Summing the recorded counts over wavelength
between 582 and 638 nm yields a photometric time series with 80 s time sampling and
relative precision of about 1.1 × 10-4 per sample. The folded light curve can be fitted
within observational errors using a model consisting of an opaque circular planet
transiting a limb-darkened stellar disk. In this way we estimate the planetary radius Rp =
1.347 ± 0.060 RJup, the orbital inclination i = 86 6 ± 0 14, the stellar radius R* = 1.146 ±
0.050 R , and one parameter describing the stellar limb darkening. Our estimated radius
is smaller than those from earlier studies but is consistent within measurement errors and
also with theoretical estimates of the radii of irradiated Jupiter-like planets. Satellites or
rings orbiting the planet would, if large enough, be apparent from distortions of the light
curve or from irregularities in the transit timings. We find no evidence for either
satellites or rings, with upper limits on satellite radius and mass of 1.2 R and 3 M ,
respectively. Opaque rings, if present, must be smaller than 1.8 planetary radii in radial
extent. The high level of photometric precision attained in this experiment confirms the
feasibility of photometric detection of Earth-sized planets circling Sun-like stars.
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The low-mass companion to HD 209458 is the first extrasolar planet found to
transit the disk of its parent star (Charbonneau et al. 2000; Henry et al. 2000).
The primary star (G0 V, V = 7.64, B-V = 0.58; Høg et al. 2000) lies at distance of
47 pc as determined by Hipparcos (Perryman et al. 1997). An analysis of radial
velocity measurements by Mazeh et al. (2000) gave an orbital period of 3.524
days, with Mp sin i = 0.69 ± 0.05 MJup and a = 0.0468 AU, using the derived value
of 1.1 ± 0.1 M for the stellar mass. When combined with the early photometric
light-curve data, the same analysis yielded an orbital inclination i = 86 1 ± 1 6
and a planetary radius Rp = 1.40 ± 0.17 RJup. The planetary radius is at once the
most interesting and the most uncertain of these parameters, largely because of
uncertainty in the value of the stellar radius R*. Knowledge of Rp is important
because it allows inferences about the planet's composition and evolutionary
history (Guillot et al. 1996; Guillot 1999; Burrows et al. 2000). Unfortunately, the
measured quantity that emerges most easily from the photometric transit data is
the ratio Rp/R*, and residual errors in the astrometry and effective stellar
temperature suffice to make the estimate of R*, and hence Rp, uncertain by about
10%. Additional small errors in Rp result from uncertainties about the stellar
limb darkening.
2 An Upper Limit on the Albedo of HD 209458b: Direct Imaging
Photometry with the MOST Satellite
Rowe et al.
The Astrophysical Journal, Volume 646, Issue 2, pp. 1241-1251
We present space-based photometry of the transiting exoplanetary system HD
209458 obtained with the Microvariablity and Oscillations of Stars (MOST)
satellite, spanning 14 days and covering 4 transits and 4 secondary eclipses. The
HD 209458 photometry was obtained in MOST's lower precision direct imaging
mode, which is used for targets in the brightness range 6.5>=V>=13. We
describe the photometric reduction techniques for this mode of observing, in
particular the corrections for stray earthshine. We do not detect the secondary
eclipse in the MOST data, to a limit in depth of 0.053 mmag (1 sigma). We set a
1 sigma upper limit on the planet-star flux ratio of 4.88×10-5 corresponding to
a geometric albedo upper limit in the MOST bandpass (400-700 nm) of 0.25. The
corresponding numbers at the 3 sigma level are 1.34×10-4 and 0.68, respectively.
HD 209458b is half as bright as Jupiter in the MOST bandpass. This low
geometric albedo value is an important constraint for theoretical models of the
HD 209458b atmosphere, in particular ruling out the presence of reflective
clouds. A second MOST campaign on HD 209458 is expected to be sensitive to
an exoplanet albedo as low as 0.13 (1 sigma), if the star does not become more
intrinsically variable in the meantime.
3. Subaru HDS Transmission Spectroscopy of the
Transiting Extrasolar Planet HD 209458b
Narita et al 2005
Publications of the Astronomical Society of Japan, Vol.57, No.3, pp. 471-480
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We have searched for absorption in several common atomic species due to the
atmosphere or exosphere of the transiting extrasolar planet HD 209458b, using
high precision optical spectra obtained with the Subaru High Dispersion
Spectrograph (HDS). Previously we reported an upper limit on Halpha
absorption of 0.1% (3 sigma) within a 5.1Å band. Using the same procedure, we
now report upper limits on absorption due to the optical transitions of Na D, Li,
Halpha, Hbeta, Hgamma, Fe, and Ca. The 3 sigma upper limit for each
transition is approximately 1% within a 0.3Å band (the core of the line), and a
few tenths of a per cent within a 2Å band (the full line width). The wide-band
results are close to the expected limit due to photon-counting (Poisson)
statistics, although in the narrow-band case we have encountered unexplained
systematic errors at a few times the Poisson level. These results are consistent
with all previously reported detections and upper limits, but are significantly
more sensitive.
Remarks:
22 Mar 05: Direct thermal emission found with Spitzer by Deming et al (2005)
4 Feb 04: Oxygen and Carbon detected in the atmosphere (Vidal-Madjar et al
2004)
Nov 01: Na detected in the planet atmosphere (Charbonneau et al 2001)
12 Mar. 03: Detection of an extended cometary-shaped atmosphere (Vidal
Madjar et al 2003)
Infrared radiation from an extrasolar planet
Deming et al 2005
Nature, Volume 434, Issue 7034, pp. 740-743
A class of extrasolar giant planets-the so-called `hot Jupiters' (ref. 1)-orbit within
0.05AU of their primary stars (1AU is the Sun-Earth distance). These planets
should be hot and so emit detectable infrared radiation. The planet HD209458b
(refs 3, 4) is an ideal candidate for the detection and characterization of this
infrared light because it is eclipsed by the star. This planet has an anomalously
large radius (1.35 times that of Jupiter), which may be the result of ongoing
tidal dissipation, but this explanation requires a non-zero orbital eccentricity (~
0.03; refs 6, 7), maintained by interaction with a hypothetical second planet.
Here we report detection of infrared (24µm) radiation from HD209458b, by
observing the decrement in flux during secondary eclipse, when the planet
passes behind the star. The planet's 24-µm flux is 55 +/- 10µJy (1sigma), with a
brightness temperature of 1,130 +/- 150K, confirming the predicted heating by
stellar irradiation. The secondary eclipse occurs at the midpoint between
transits of the planet in front of the star (to within +/- 7min, 1sigma), which
means that a dynamically significant orbital eccentricity is unlikely.
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Extrasolar Planets
Professor Michael Smith
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Basic data:
HD 209458 b
Name:
0.69 ± 0.05 MJ
M.sini:
1.32 ± 0.05 RJup
Radius
1,130 ± 150 K
Temperature
0.045 AU
Semi-major axis:
3.52474541 ± 0.00000025 d.
Orbital period:
0.0
Eccentricity:
83
Omega (deg):
T_peri (Mid-transit time - HJD): 2 452 854.825415 ± 0.000060
86.1 ± 0.1
Inclination:
8 History of Planet Formation Speculation
There is little early history surrounding the general subject.
In 1584, when the Catholic monk Giordano Bruno asserted that there were "countless suns
and countless earths all rotating around their suns," he was accused of heresy. But even in
Bruno's time, the idea of a plurality of worlds wasn't entirely new. As far back as ancient
Greece, humankind has speculated that other solar systems might exist and that some
would harbor other forms of life.
All the attention has
been focused upon the origin of a single stellar system. As outlined below, some
renowned individuals have contemplated the origin and early development of
the solar system. Many of the ideas will resurface in modern theories.
Rene Descartes proposed a Theory of Vortices in 1644. He postulated that
space was entirely filled with swirling gas in various states. The friction
between the vortices `filed' matter down and funnelled it towards the eye of
the vortex where it collected to form the Sun. Fine material
formed the heavens on being expelled from the vortex while heavy material
was trapped in the vortex. Secondary vortices around the planets formed the
systems of satellites.
Emanuel Swedenborg put forward a Nebula Hypothesis in 1734. The Sun was
formed out of a rapidly rotating nebula. The planets were the result of
condensations from a gauze ejected out of the Sun. The germinal idea for his
nebular hypothesis came from a seance with inhabitants of Jupiter.
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Georges Buffon suggested an Impact Theory in 1745. He proposed that a
passing comet grazed the Sun and tore some material out of it. This cooled and
formed the Earth. Apparently, Buffon had in mind a comet as massive as the
Sun and an encounter corresponding to a modern tidal theory.
Immanuel Kant (1755) and Pierre Simon de Laplace (1796) independently
proposed the Nebular Hypotheses, amongst the oldest surviving scientific
hypotheses. They involved a rotating cloud of matter cooling and contracting
under its own gravitation. This cloud then flattens into a revolving disk
which, in order to conserve angular momentum, spins up until it sheds its outer
edge leaving successive rings of matter as it contracts. Kant tried to start from
matter at rest whereas Laplace started with an extended mass already rotating.
Charles Messier (1771 recorded the shapes of astrophysical nebulae which were
suggestive of disks around stars in which new planets might be forming.
Even though these nebulae turned out to be galaxies, the Kant-Laplace
hypothesis still survives.
George Darwin, son of Charles Darwin, conjured up a Tidal Hypothesis in
1898. Extrapolating back in time, to four million years ago, the moon was
pressed nearly against the Earth. Then, one day, a heavy tide occurred in the
oceans which lifted the moon out.
Thomas Chamberlin (1901) and Forest Moulton (1905) proposed a
planetesimal hypothesis.
They postulated that the materials now composing the Sun, planets, and
satellites, at one time existed
as a spiral nebula, or as a great spiral swarm of discrete particles. Each particle
was in elliptic motion about the central nucleus.
James Jeans (1916) and Harold Jeffreys proposed a new Tidal Hypothesis in
1917 while World War I was in progress. A passing or grazing star is supposed
to have pulled out a long cigar-shaped strand of material from the Sun. The
cigar would fragment to form the planets with the larger planets at
intermediate distances.
Modern History
In the 1930s, it was realised that stars are powered through most of their lives
by thermonuclear reactions which convert hydrogen to helium.
Lyman Spitzer's 1939 refutation of tidal theory brought down the JeansJeffreys' hypothesis. He showed that the material torn out of the Sunby nearcollisions would be hot and so would then rapidly expand and never contract
into planets.
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Henry Russell's Binary and Triple Star Theories (1941) resemble Buffon's
passing star theory. The Sun was originally part of a binary system and the
second star of this system then underwent a very close encounter
with a third star. The encounter ejected a gaseous filament in which the planets
formed.
Fred Hoyle put forward a Supernova Hypothesis in 1944. Hoyle, inspired by
Lyttleton's system, set up a system in which the Sun companion star was a
supernova. The outburst would have to be sufficient to break up the binary
system yet leave sufficient remains to form the planets.
Fred Whipple promoted the Dust Cloud Hypothesis in 1946, applicable to the
origin of all stars. The pressure of light rays from stars pushed dust into clouds,
and chance concentrations condensed into stars. A smaller dust cloud was then
captured with a much greater angular momentum, enough to form the planets.
Whipple had thus proposed a mechanism to trigger stars.
Carl von Weizsaecker revived the Nebula Hypothesis in 1944. An extended
envelope surrounds the forming Sun. Large regular turbulent eddies form in a
disk containing one tenth of a solar mass. He realised the significance of
supersonic motion and magnetic coupling of the dust to the gas.
Dirk ter Haar (1950) discarded the large regular vorticesand found that
gravitational instabilities would also be ineffective in the thick solar nebula. He
thus proposed collisional accretion into condensations. The problem he raised,
however, was that the turbulence would decay before sufficient collisions
would build up the condensations. The turbulence would have to be driven but
there was no apparent driver. This problem was to return again in the 1990s but
on a much larger scale.