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PH709
Extrasolar Planets - 3
Professor Michael Smith
1
.
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...
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
Most conservative (accepted) possibility:
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Extrasolar Planets - 3
Professor Michael Smith
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• 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.
http://hubblesite.org/newscenter/archive/releases/2003/19
PH709
Extrasolar Planets - 3
Professor Michael Smith
3
PH709
Extrasolar Planets - 3
Professor Michael Smith
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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
3
planetesimal and the star. From Kepler’s law:
P  2
a
G M1  M2 
RHill = (Mp/M*)1/3 a
In this way, the planetesimal acquires mass, and the Hill Radius
grows!
PH709
Extrasolar Planets - 3
Professor Michael Smith
5
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?
Disc ‘Clearing’
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Extrasolar Planets - 3
Professor Michael Smith
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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 - 3
Professor Michael Smith
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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.
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.
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Extrasolar Planets - 3
Professor Michael Smith
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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
• 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!
PH709
Extrasolar Planets - 3
Professor Michael Smith
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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.
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
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Extrasolar Planets - 3
Professor Michael Smith
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(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)
50% of D burned
50% of Li burned
stars
brown
dwarfs
“planets”
Burrows et al. (2001)
THE END
FURTHER¬ READING: NOT PART OF EXOPLANET
COURSE
PH709
Extrasolar Planets - 3
DARWIN – 2020 ? Life?
Professor Michael Smith
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Extrasolar Planets - 3
Professor Michael Smith
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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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Extrasolar Planets - 3
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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.
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
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Extrasolar Planets - 3
Professor Michael Smith
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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
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,
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Extrasolar Planets - 3
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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.

Basic data:
Name:
M.sini:
Radius
Temperature
HD 209458 b
0.69 ± 0.05 MJ
1.32 ± 0.05 RJup
1,130 ± 150 K
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Extrasolar Planets - 3
Professor Michael Smith
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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.
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
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Extrasolar Planets - 3
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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.
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
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Extrasolar Planets - 3
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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.