Download Lecture 7: Extrasolar Planets 01/08/2013 update: 725 exoplanets

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Lecture 7: Extrasolar Planets
01/08/2013 update: 725 exoplanets (exoplanet.eu)
Resources. For observations, a good starting point is Berkeley extrasolar
planets search homepage http://exoplanets.org/
http://exoplanet.eu/catalog-RV.php
Candidates detected by radial velocity
424 planets
Candidates detected by transits
277 planets
Candidates detected by microlensing or imaging
20 planets from microlensing
14 planets from imaging
Candidate pulsar planets
4 planets
1candidate planet
Kepler Candidate planets
3161 planets
There are 104 planets in systems with more or equal to two planets.
Although few of the planets have been directly imaged, the effects of the
gravity tugging at the stars, as well as the way that gravitation affects can
affect material close to the stars, has been clearly seen.
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Disc of material around the star Beta Pictoris – the image of the bright
central star has been artificially blocked out by astronomers using a
‘Coronograph’
• How can we discover extrasolar planets?
• Characteristics of the exoplanet population
• Planet formation
• Explaining the properties of exoplanets
Rapidly developing subject - first extrasolar planet around an ordinary star
only discovered in 1995 by Mayor & Queloz.
Observations thought to be secure, but theory still preliminary...
Theory: Annual Reviews article by Lissauer (1993) is a good summary of
the state of theory prior to the discovery of extrasolar planets
Definition of a planet
Simplest definition is based solely on mass
• Stars: burn hydrogen (M > 0.075 Msun)
• Brown dwarfs: burn deuterium
• Planets: do not burn deuterium (M < 0.013 Msun)
Deuterium burning limit occurs at around 13 Jupiter masses (1 MJ = 1.9 x
1027 kg ~ 0.001 Msun It is important to realise that for young objects, there
is no large change in properties at the deuterium burning limit. ALL young
stars / brown dwarfs / planets liberate gravitational potential energy as they
contract
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Types of planet
Giant planets (gas giants, `massive’ planets)
• Solar System prototypes: Jupiter, Saturn, Uranus...
• Substantial gaseous envelopes
• Masses of the order of Jupiter mass
• In the Solar System, NOT same composition as Sun
• Presence of gas implies formation while gas was still prevalent
Terrestrial planets
• Prototypes: Earth, Venus, Mars
• Primarily composed of rocks
• In the Solar System (ONLY) orbital radii less than giant planets
Much more massive terrestrial planets could exist (>10 Earth masses),
though none are present in the Solar System. The Solar system also has
asteroids, comets, planetary satellites and rings - we won’t discuss those in
this course.
Detecting extrasolar planets
(1) Direct imaging - difficult due to enormous star / planet flux ratio
(2) Radial velocity
• Observable: line of sight velocity of star orbiting centre of mass of star
- planet binary system
• Most successful method so far
(3) Astrometry
• Observable: stellar motion in plane of sky
• Very promising future method: Keck interferometer, GAIA
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(4) Transits
• Observable: tiny drop in stellar flux as planet transits stellar disc
• Requires favourable orbital inclination
• Jupiter mass exoplanet observed from ground (HD209458b)
• Earth mass planets detectable from space (Kepler, TESS - 2017)
(5) Gravitational lensing
• Observable: light curve of a background star lensed by the gravitational
influence of a foreground star. The light curve shape is sensitive to
whether the lensing star is a single star or a binary (star + planet is a
special case of the binary)
• Rare - requires monitoring millions of background stars, and also
unrepeatable
• Some sensitivity to Earth mass planets
Each method has different sensitivity to planets at various orbital radii
- complete census of planets requires use of several different
techniques
Planet detection method : Radial velocity technique
This is also known as the "Doppler method". Variations in the speed with
which the star moves towards or away from Earth — that is, variations in
the radial velocity of the star with respect to Earth — can be deduced from
the displacement in the parent star's spectral lines due to the Doppler effect.
This has been by far the most productive technique used by planet hunters.
A planet in a circular orbit around star with semi-major axis a
Assume that the star and planet both rotate around the centre of mass with
an angular velocity:
Using a1 M* = a2 mp and a = a1 + a2, then the stellar speed (v* = aΩ) in an
inertial frame is:
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(assuming mp << M*). i.e. the stellar orbital speed is small….just meters per
second!
For a circular orbit, observe a sin-wave variation of the stellar radial
velocity, with an amplitude that depends upon the inclination of the orbit to
the line of sight:
Hence, measurement of the radial velocity amplitude produces a constraint
on:
mp * sin(i)
(assuming stellar mass is well-known, as it will be since to measure radial
velocity we need exceptionally high S/N spectra of the star).
Observable is a measure of mp sin(i).
-> given vobs, we can obtain a lower limit to the planetary mass
In the absence of other constraints on the inclination, radial velocity
searches provide lower limits on planetary masses
Magnitude of radial velocity:
Sun due to Jupiter: 12.5 m/s
Sun due to Earth: 0.1 m/s
i.e. extremely small - 10 m/s is Olympic 100m running pace
Spectrograph with a resolving power of 105 will have a pixel scale ~ 10-5 c
~ few km/s
Therefore, specialized techniques that can measure radial velocity shifts
of ~10-3 of a pixel stably over many years are required
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High sensitivity to small radial velocity shifts is achieved by:
• comparing high S/N = 200-500 spectra with template stellar spectra
• using a large number of lines in the spectrum to allow shifts of much
less than one pixel to be determined.
• correcting for Earth’s rotation and motion in orbit, accurate timing and
position required
Absolute wavelength calibration and stability over long timescales is
achieved by:
• passing stellar light through a cell containing iodine, imprinting large
number of additional lines of known wavelength into the spectrum
• with the calibrating data suffering identical instrumental distortions as
the data
Error sources:
(1) Theoretical: photon noise limit
• flux in a pixel that receives N photons uncertain by ~ N1/2
• implies absolute limit to measurement of radial velocity
• depends upon spectral type - more lines improve signal
• around 1 m/s for a G-type main sequence star with spectrum recorded
at S/N=200
• practically, S/N=200 can be achieved for V=8 stars on a 3m class
telescope in survey mode
(2) Practical:
• stellar activity - young or otherwise active stars are not stable at the
m/s level and cannot be monitored with this technique
• remaining systematic errors in the observations
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Currently, the best observations achieve:
σ ~ 3 m/s
...in a single measurement. Thought this error can be reduced to around
1…0.6m/s with further refinements, but not substantially further. The very
highest Doppler precisions of 1m/s are capable of detecting planets down to
about 5 earth masses.
Radial velocity monitoring detects massive planets, especially those at
small a, but is not sensitive enough to detect Earth-like planets at ~ 1AU.
Examples of radial velocity data
51 Peg b was the first known exoplanet with a 4 day, circular orbit: a hot
Jupiter, lying close to the central star.
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Example of a planet with an eccentric orbit: e=0.67
Summary of observables
(1) Planet mass, up to an uncertainty from the normally unknown
inclination of the orbit. Measure mp * sin(i)
(2) Orbital period -> radius of the orbit given the stellar mass
(3) Eccentricity of the orbit
Summary: selection function
Need to observe full orbit of the planet: zero sensitivity to planets with
P>Psurvey
For P<Psurvey, minimum mass planet detectable is one that produces a radial
velocity signature of a few times the sensitivity of the experiment (this is a
practical detection threshold)
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Which planets are detectable? For a given radial velocity amplitude:
m p sin i ∝ a
1
2
Hence, inner massive planets are selected.
Current limits:
• Maximum a ~ 3.5AU (i.e. orbital period ~ 7 years)
• Minimum mass ~ 0.5 Jupiter masses at 1AU, scaling with square root
of semi-major axis
• No strong selection bias in favour/against detecting planets with
different eccentricities
Of the first 100 stars found to harbor planets, more than 30 stars host a
Jupiter-sized world in an orbit smaller than Mercury's, whizzing
around its star in a matter of days.
This implies: Planet formation is a contest, where a growing planet must
fight for survival lest it be swallowed by the star that initially nurtured it.
Planet detection method : Astrometry
The gravitational perturbations of a star's position by an unseen companion
provides a signature which can be detected through precision astrometry.
While very accurate wide-angle astrometry is only possible from space
with a mission like the Space Interferometry Mission (SIM), narrow-angle
astrometry with an accuracy of tens of micro arcseconds is possible from
the ground with an optimised instrument.
Conceptually identical to radial velocity searches. Light from a planet-star
binary is dominated by the star. Measure stellar motion in the plane of
the sky due to presence of orbiting planet. Must account for parallax and
proper motion of star.
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Magnitude of effect: amplitude of stellar wobble (half peak displacement)
for an orbit in the plane of the sky is
 mp 
 × a
a1 = 
M
 *
In terms of the angle:
 m p  a 
 
∆θ = 
 M *  d 
for a star at distance d. Note we have again used mp << M*
Writing the mass ratio q = mp / M*, this gives:
A Jupiter around a Sun at 10pc would produce a wobble with an amplitude
of 0.5 milliarcseconds.
Note:
• Units here are milliarcseconds - very small effect
• Different dependence on a than radial velocity method - astrometric
planet searches are more sensitive at large a
• Explicit dependence on d (radial velocity measurements also less
sensitive for distant stars due to lower S/N spectra)
• Detection of planets at large orbital radii still requires a search time
comparable to the orbital period
Detection threshold as function of semi-major axis
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• Lack of units deliberate! Astrometric detection not yet achieved
• As with radial velocity, dependence on orbital inclination, eccentricity
• Very promising future: Keck interferometer, Space Interferometry
Mission (SIM), ESA mission GAIA, and others
• Planned astrometric errors at the ~10mas level – good enough to detect
planets of a few Earth masses at 1AU around nearby stars
Lecture 8
Planet detection method : Transits - Photometry
Simplest method: look for drop in stellar flux due to a planet transiting
across the stellar disc. Needs luck or wide-area surveys - transits only occur
if the orbit is almost edge-on
For a planet with radius rp << R*, probability of transits is:
Close-in planets are more likely to be detected. P = 0.5% at 1AU, P = 0.1%
at the orbital radius of Jupiter
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What can we measure from the light curve?
(1) Depth of transit = fraction of stellar light blocked
This is a measure of planetary radius, NOT the mass! The method
suffers from a high rate of false detections. A transit detection requires
additional confirmation, typically from the radial-velocity method.
In practice, isolated planets with masses between ~ 0.1 MJ and 10 MJ,
where MJ is the mass of Jupiter, should have almost the same radii (i.e. a
flat mass-radius relation).
-> Giant extrasolar planets transiting solar-type stars produce transits with
a depth of around 1%.
Close-in planets are strongly irradiated, so their radii can be (detectably)
larger. But this heating-expansion effect is not generally observed for
short-period planets.
(2) Duration of transit plus duration of ingress, gives measure of the
orbital radius and inclination
(3) Bottom of light curve is not actually flat, providing a measure of
stellar limb-darkening
(4) Deviations from profile expected from a perfectly opaque disc could
provide evidence for satellites, rings etc
Photometry at better than 1% precision is possible (not easy!) from the
ground. HST reached a photometric precision of 0.0001.
Potential for efficient searches for close-in giant planets
Transit depth for an Earth-like planet is:
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Photometric precision of ~ 10-5 seems achievable from space
May provide first detection of habitable Earth-like planets
NASA’s Kepler mission, and planned successor TESS
A reflected light signature must also exist, modulated on the orbital period,
even for non-transiting planets. No detections yet.
Planet detection method: Gravitational microlensing
Microlensing operates by a completely different principle, based on
Einstein's General Theory of Relativity. According to Einstein, when the
light emanating from a star passes very close to another star on its way to
an observer on Earth, the gravity of the intermediary star will slightly bend
the light rays from the source star, causing the two stars to appear farther
apart than they normally would.
This effect was used by Sir Arthur Eddington in 1919 to provide the first
empirical evidence for General Relativity. In reality, even the most
powerful Earth-bound telescope cannot resolve the separate images of the
source star and the lensing star between them, seeing instead a single giant
disk of light, known as the "Einstein disk," where a star had previously
been. The resulting effect is a sudden dramatic increase in the brightness of
the lensing star, by as much as 1,000 times. This typically lasts for a few
weeks or months before the source star moves out of alignment with the
lensing star and the brightness subsides.
Light is deflected by gravitational field of stars, compact objects, clusters
of galaxies, large-scale structure etc.
Simplest case to consider: a point mass M (the lens) lies along the line of
sight to a more distant source
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Define:
• Observer-lens distance
• Observer-source distance
• Lens-source distance
Dl
Ds
Dls
Azimuthal symmetry -> light from the source appears as a ring
...with radius R0 - the Einstein ring radius - in the lens plane.
Gravitational lensing conserves surface brightness, so the distortion of the
image of the source across a larger area of sky implies magnification.
The Einstein ring radius is given by:
Suppose now that the lens is moving with a velocity v. At time t, the
apparent distance (in the absence of lensing) in the lens plane between the
source and lens is r0.
Defining u = r0 / R0, the amplification is:
Note: for u > 0, there is no symmetry, so the pattern of images is not a ring
and is generally complicated. In microlensing we normally only observe
the magnification A, so we ignore this complication...
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Notes:
(1) The peak amplification depends upon the impact parameter, small
impact parameter implies a large amplification of the flux from the
source star.
(2) For u = 0, apparently infinite magnification! In reality, finite size of
source limits the peak amplification.
(3) Geometric effect: affects all wavelengths equally.
(4) Rule of thumb: significant magnification requires an impact
parameter smaller than the Einstein ring radius.
(5) Characteristic timescale is the time required to cross the Einstein ring
radius:
Optical depth to microlensing
Define the optical depth to microlensing as:
This is just the integral of the area of the Einstein ring along the line of
sight to the source. For a uniform density of lenses, can easily show that the
maximum contribution comes from lenses halfway to the source.
Several groups have monitored stars in the Galactic bulge and the
Magellanic clouds to detect lensing of these stars by foreground objects
(MACHO, Eros, OGLE projects). Original motivation for these projects
was to search for dark matter in the form of compact objects in the halo.
Timescales for sources in the Galactic bulge, lenses ~ halfway along the
line of sight:
• Solar mass star ~ 1 month
• Jupiter mass planet ~ 1 day
• Earth mass planet ~ 1 hour
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The dependence on M1/2 means that all these timescales are observationally
feasible. However, lensing is a very rare event, all of the projects monitor
millions of source stars to detect a handful of lensing events.
Lensing by a single star
Lensing by a star and a planet
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Planet detection through microlensing
The microlensing process in stages, from right to left. The lensing star
(white) moves in front of the source star (yellow) doubling its image and
creating a microlensing event. In the fourth image from the right the planet
adds its own microlensing effect, creating the two characteristic spikes in
the light curve. Credit: OGLE
Planet search strategy:
• Monitor known lensing events in realtime with dense, high precision
photometry from several sites
• Look for deviations from single star light curve due to planets
• Timescales ~ a day for Jupiter mass planets, ~ hour for Earths
• Most sensitive to planets at a ~ R0, the Einstein ring radius
• Around 3-5 AU for typical parameters
Sensitivity to planets
Complementary to other methods:
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Actual sensitivity is hard to evaluate: depends upon frequency of
photometric monitoring (high frequency needed for lower masses),
accuracy of photometry (planets produce weak deviations more often than
strong ones)
Very roughly: observations with percent level accuracy, several times per
night, detect Jupiter, if present, with 10% efficiency
Many complicated light curves observed:
The microlensing event that led to the discovery of the new planet was first
observed by the Poland-based international group OGLE, the Optical
Gravitational Lensing Experiment. The microlensing light curve of
planet OGLE–2005-BLG-390Lb
The general curve shows the microlensing event peaking on July 31, 2005,
and then diminishing. The disturbance around August 10 indicates the
presence of a planet. OGLE –2005-BLG-390Lb will never be seen again.
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At around five times the mass of Earth, the new planet, designated OGLE–
2005-BLG-390Lb, is the lowest-mass planet ever detected outside the solar
system. And when one considers that the vast majority of the
approximately 270 extrasolar planets detected so far have been Jupiter-like
gas giants, dozens or hundreds of times the mass of Earth, the discovery of
a planet of only five Earth masses is indeed good news.
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Planet detection method: Direct detection!
Photometric: 2005 image of 2M1207 (blue) and its planetary companion,
2M1207b, one of the first exoplanets to be directly imaged, in this case
from the Very Large Telescope array in Chile
Infrared image of 2M1207 (blue) and its planet 2M1207b, as viewed by the
Very Large Telescope. As of September 2006 this was the first confirmed
extrasolar planet to have been directly imaged.
Spectroscopic? The starlight scattered from the planet can be distinguished
from the direct starlight because the scattered light is Doppler shifted by
virtue of the close-in planet's relatively fast orbital velocity (~ 150 km/sec).
Superimposed on the pattern given by the planet's albedo changing slowly
with wavelength, the spectrum of the planet's light will retain the same
pattern of photospheric absorption lines as in the direct starlight.
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Located just 500 light-years away toward the constellation Scorpius, this star is only
slightly less massive and a little cooler than the Sun. But it is much younger, a few
million years old compared to the middle-aged Sun's 5 billion years. This sharp infrared
image shows the young star has a likely companion positioned above and left - a hot
planet with about 8 times the mass of Jupiter, orbiting a whopping 330 times the EarthSun distance from its parent star. The young planetary companion is still hot and
relatively bright in infrared light due to the heat generated during its formation by
gravitational contraction. In fact, such newborn planets are easier to detect before they
age and cool, becoming much fainter. Though over 300 extrasolar planets have been
found using other techniques, this picture likely represents the first direct image of a
planet belonging to a star similar to the Sun.
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Fomalhaut (sounds like "foam-a-lot") is a bright, young, star, a short 25
light-years from planet Earth in the direction of the constellation Piscis
Austrinus. In this sharp composite from the Hubble Space Telescope,
Fomalhaut's surrounding ring of dusty debris is imaged in detail, with
overwhelming glare from the star masked by an occulting disk in the
camera's coronagraph. Astronomers now identify, the tiny point of light in
the small box at the right as a planet about 3 times the mass of Jupiter
orbiting 10.7 billion miles from the star (almost 23 times the Sun-Jupiter
distance). Designated Fomalhaut b, the massive planet probably shapes and
maintains the ring's relatively sharp inner edge, while the ring itself is
likely a larger, younger analog of our own Kuiper Belt - the solar system's
outer reservoir of icy bodies. The Hubble data represent the first visiblelight image of a planet circling another star.
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In the twelve years previous to 2008, over 300 candidate planetary systems
have been found orbiting nearby stars. None, however, were directly
imaged, few showed evidence for multiple planets, and many had a Jupitersized planet orbiting inside the orbit of Mercury. Last week, however,
together with recent images of Fomalhaut b, the above picture was released
showing one of first confirmed images of planets orbiting a distant Sun-like
star. HR 8799 has a mass about 1.5 times that of our own Sun, and lies
about 130 light years from the Sun -- a distance similar to many stars easily
visible in the night sky. Pictured above, a 10-meter Keck telescope in
Hawaii captured in infrared light three planets orbiting an artificially
obscured central star. The 8-meter Gemini North telescope captured a
similar image. Each planet likely contains several times the mass of Jupiter,
but even the innermost planet, labelled d, has an orbital radius near the
equivalent of the Sun- Neptune distance. Although the HR 8799 planetary
system has significant differences with our Solar System, it is a clear
demonstration that complex planetary systems exist, systems that could
conceivable contain an Earth-like planet.
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A mere 50 light-years away, young star Beta Pictoris became one of the
most important stars in the sky in the early 1980s. Satellite and groundbased telescopic observations revealed the presence of a surrounding outer,
dusty, debris disk and an inner clear zone about the size of our solar system
-- strong evidence for the formation of planets. Now, infrared observations
from European Southern Observatory telescopes incorporated in this
composite offer a detection of a source in the clear zone that is most likely
a giant planet orbiting Beta Pic. Designated Beta Pictoris b, the new source
is more than 1,000 times fainter than the direct starlight that has been
carefully subtracted from the image data. It is aligned with the disk at a
projected distance that would place it near the orbit of Saturn if found in
our solar system. Confirmation that the new source is a planet will come if
future observations can demonstrate that the source moves in an orbit
around the star. When confirmed, it will be the closest planet to its parent
star directly imaged ... so far.
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Pulsar Planets
In early 1992, the Polish astronomer Aleksander Wolszczan (with Dale
Frail) announced the discovery of planets around a 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.
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4 Detecting extrasolar planets: summary
RV, Doppler technique (v = 3 m/s)
Astrometry: angular oscillation
Photometry: transits - close-in planets
Microlensing:
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Lecture 9: The extrasolar planet population
http://exoplanet.eu/
The planets are listed with indications of their approximate masses as
multiples of Jupiter 's mass (MJ = 1.898 × 1027 kg) or multiples of Earth's
mass (ME = 5.9737 × 1024 kg), and have approximate distances in
astronomical units (1AU = 1.496 × 108 km, distance between Earth and
Sun) from their parent stars.
According to astronomical naming conventions, the official designation for
a body orbiting a star is the star's catalogue number followed by a letter.
The star itself is designated with the letter 'a', and orbiting bodies by 'b', 'c',
etc.
DISTRIBUTIONS:
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Metallicity:
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 Anglo-Australian 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.
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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 20AU.
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 of “hot Jupiters” within 0.1 AU of FGK stars is 1.2 ± 0.2%.
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.
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• 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: 8 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: 55 known planets. 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.
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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 zero.
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 has 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.
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 semi major 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 0.0 and 0.8. For most Doppler surveys,
sensitivity is not a strong function of eccentricity for 0<e<0.8 and a<3AU.
This plot represents results from many surveys, and so is drawn from an
inhomogeneous sample.
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Distribution of Eccentricity:
Eccentricity vs. planet mass
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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. High-mass 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 sample.
Ignoring the hot Jupiters, there is 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.
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Minimum mass as a function of semi major axis:
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Nothing very striking in these plots:
• Accessible region of mp - a space is fully occupied by detected
planets
Get rid of the log (Mj) :
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Minimum mass as a function of semi major 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.
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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.
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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
This 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
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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
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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 pileup. This distribution represents results from many surveys, and so is drawn
from an inhomogeneous sample.
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Observed mass function increases to smaller Mp:
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 relevant selection effects enhance this effect. This
distribution represents results from many surveys, and so is drawn from an
inhomogeneous sample.
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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)
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Host star metallicity
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 ([M/H]=-0.7 --- high for a GlCl)
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.
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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.
This is currently consistent with the numbers seen in radial velocity
searches.
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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 Current/Future Missions
CoRoT is a space project in Astrophysics - Convection, Rotation and
Transits
Its objective is double:
- study the stellar interiors
- detect planets analogous to the Earth orbiting around other stars than the
Sun.
The satellite will orbit at an altitude of 896 km. It will carry a telescope
able to observe continuously many stars during very long periods and to
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measure very accurately the variations of their brightness. ALREADY 25
PLANETS DISCOVERED!
http://corot.oamp.fr/
Figure 1. Transit of a planet (decrease of the luminosity of the hosting star
when the planet passes in front of it) as observed by Corot. The parent star
is a Sun-like star. The planet is a very hot giant planet, similar to Jupiter but
orbiting its star in 1.5 day, and with an estimate of the radius between 1.5
time and 1.8 time Jupiter's radius (given Corot's excellent photometric data,
most of the uncertainty is in fact due to the uncertainty on the radius of the
parent star, which is still preliminary). Thanks to combined spectroscopic
observations from the ground, the mass of the planet has also been
measured around 1.3 time that of Jupiter.
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….down to earth-like planets.
Kepler: 2008 - Transit method
SIM and Gaia: astrometry
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Lectures: Star 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.
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)
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• 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.
• 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:
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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 (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)
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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 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 µm 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, PoyntingRobertson, and stellar wind drag (Backman & Paresce 1993; Chen et al.
2005a). 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 tend 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.
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Clues from planet composition:
Inner Planets & Asteroids:
•
•
Small rocky bodies
Few ices or volatiles
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
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
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Condensate
>2000 K
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".
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.
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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.
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.
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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.
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.
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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
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
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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 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 crosssection).
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.
• 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.
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• 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
Ωdisc = nΩplanet,
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.
Result: planet orbits in a gap largely cleared of gas and dust.
Tidal locking of the planet in the gap.
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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
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• 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
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(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.