PH709 Extrasolar Planets Prof Michael Smith 1
Review
http://exoplanet.eu/
http://en.wikipedia.org/wiki/Extrasolar_planet
There are 211 planets listed — 48 in multiple planet systems, 154 in single
planet systems, 4 orbiting pulsars, 1 orbiting a brown dwarf, and 2 free
floating.
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 (1) AU =
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
Fusing stars
There are currently 204 planets known in orbit around fusing stars.
There are currently 156 known planets in single-planet systems and 48 known planets
in 20 multiple-planet systems (14 with two planets, 4 with three and 2 with four).
"Single" here means that only one planet has been detected to date. Since detection
methods are not sensitive to low-mass planets, these stars may have smaller planets that
are below the limits of detectability, or are so far from the star that they have not yet
been observed over an orbital period.
Pulsars
There are currently four known planets orbiting two different pulsars. The planet of PSR
B1620−26 is in a circumbinary orbit around a pulsar and a white dwarf star.
Brown dwarfs
There is currently one known planet orbiting a brown dwarf.
Free floating planets
There is currently one suspected free-floating planet, i.e. it doesn't appear to orbit a star.
PH709 Extrasolar Planets Prof Michael Smith 2
PH709 Extrasolar Planets Prof Michael Smith 3
These lectures:
1. 2-component systems
2. Definitions, planets, disks
3. Detection methods
4. Summary of methods
5. Populations
6. Theory of formation
7. Theory of evolution
PH709 Extrasolar Planets Prof Michael Smith 4
1 Two-Component Systems
Kepler’s Third Law The cubes of the semi-major axes of the planetary orbits
are proportional to the squares of the planets' periods of revolution
Summary: Measuring the mass of a planet
• Kepler‘s third law gives G(M+m) = a3/P2
Since M >> m for all planets, it isn't possible to make precise enough
determinations of P and a to determine the masses m of the planets.
However, if satellites of planets are observed, then Kepler's law can be used.
• Let mp = mass of planet ms = mass of satellite
Ps = orbital period of satellite
as = semi-major axis of satellite's orbit
about the planet.
Then: G(mp+ms) = 42 as3/Ps2
If the mass of the satellite is small compared with the mass of the planet then
mp = 42 as3/(G Ps2)
Example
Europa, one of the Jovian moons, orbits at a distance of 671,000 km from the centre
of Jupiter, and has an orbital period of 3.55 days. Assuming that the mass of Jupiter
is very much greater than that of Europa, use Kepler's third law to estimate the
mass of Jupiter.
Using Kepler's third law:
4 2 a 3
m jupiter meuropa
GP 2
The semi-major axis, a = 6.71 x 105 km = 6.71 x 108 m, and
the period, P = 3.55 x 3600 x 24 = 3.07 x 105 seconds
Since mjupiter >> meuropa, then mjupiter ~ 1.9 x 1027 kg.
PH709 Extrasolar Planets Prof Michael Smith 5
So: we can determine the masses of massive objects if we can detect and follow the
motion of very low mass satellites. That doesn’t lead very far. How can we determine
the masses of distant stars and exoplanets?
BASIC STELLAR PROPERTIES - BINARY STARS
• For solar type stars, single:double:triple:quadruple system ratios are
45:46:8:1.
• Binary nature of stars deduced in a number of ways:
1. VISUAL BINARIES:
- Resolvable, generally nearby stars (parallax likely to be available)
- Relative orbital motion detectable over a number of years
- Not possible for exoplanets!
2. ASTROMETRIC BINARY: only one component detected
3. SPECTROSCOPIC BINARIES:
- Unresolved
- Periodic oscillations of spectral lines (due to Doppler shift)
- In some cases only one spectrum seen
4. ECLIPSING BINARY:
- Unresolved
- Stars are orbiting in plane close to line of sight giving eclipses
observable as a change in the combined brightness with time (‗‘light
curves).
Some stars may be a combination of these.
Visual Binaries
• Angular separation ≥ 0.5 arcsec (close to Sun, long orbital periods - years –
remember: at 1 parsec, 1 arcsec corresponds to 1 AU) – example Sirius:
Also known as Alpha Canis Majoris, Sirius is the fifth closest system to Sol, at
8.6 light-years. Sirius is composed of a main-sequence star and a white
dwarf stellar remnant. They form a close binary, Alpha Canis Majoris A and
B, that is separated "on average" by only about 20 times the distance from
the Earth to the Sun -- 19.8 astronomical units (AUs) of an orbital semi-major
axis -- which is about the same as the distance between Uranus and our Sun
("Sol"). The companion star, is so dim that it cannot be perceived with the
naked eye. After analyzing the motions of Sirius from 1833 to 1844, Friedrich
Wilhelm Bessel (1784-1846) concluded that it had an unseen companion.
PH709 Extrasolar Planets Prof Michael Smith 6
Hubble Space Telescope :
• Observations:
Relative positions:
= angular separation = position
Absolute positions: Harder to measure orbits of more massive star A and
less massive star B about centre of mass C which has proper motion µ.
PH709 Extrasolar Planets Prof Michael Smith 7
Declination
Motion of centre of mass
N = proper motion µ
Secondary
B
E Primary C
Right Ascension A
NB parallax and aberration must also be accounted for.
• RELATIVE ORBITS:
- TRUE orbit:
q = peri-astron distance (arcsec or km)
Q = apo-astron distance (arcsec or km)
a = semi-major axis (arcsec or km)
a = (q + Q)/2
- APPARENT orbits are projected on the celestial sphere
Inclination i to plane of sky defines relation between true orbit and apparent
orbit. If i≠0° then the centre of mass (e.g. primary) is not at the focus of the
elliptical orbit.
Measurement of the displacement of the primary gives inclination and true
semi-major axis in arcseconds a".
i i
Incline by 45° Apparent orbit
True orbit
• If the parallax p in arcseconds is observable then a can be derived from a".
Earth
B
radius
of Earth's
orbit a
a" p
Sun A
r = distance of binary star
For i=0° a = a"/p" AU (In general correction for i≠0 required).
PH709 Extrasolar Planets Prof Michael Smith 8
Now lets go back to Kepler‘s Law …
• From Kepler's Law, the Period P is given by
2 3
2 4 a
P =
G (mA + mB)
For the Earth-Sun system P=1 year, a=1 A.U., mA+mB~msun so 4π2/G = 1
3
2 a
P =
(mA + mB)
provided P is in years, a in AU, mA, mB in solar masses.
The total system mass is determined:
a" 3 1
mA + mB = ( )
p P2
• ABSOLUTE ORBITS:
B
B
d rB
A
c
* e
f q Q
rA
A
Semi-major axes aA = (c+e)/2
aB = (d+f)/2
Maximum separation = Q = c + f
Minimum separation = q = d + e
So aA + aB = (c+d+e+f)/2 = (q + Q)/2 = a
a = aA + a B (1)
(and clearly r = rA + rB)
From the definition of centre of mass, mA rA = mB rB ( mA aA = mB aB)
mA/mB = aB/aA = rB/rA
So from Kepler‘s Third Law, which gives the sum of the masses, and Equation
(1) above, we get the ratio of masses, ==> mA, mB. Therefore, with both, we
can solve for the individual masses of the two stars.
Spectroscopic Binaries
PH709 Extrasolar Planets Prof Michael Smith 9
• Orbital period relatively short (hours - months) and i≠0°.
• Doppler shift of spectral lines by component of orbital velocity in line of sight
(nominal position is radial velocity of system):
wavelength wavelength
Time Time
2 S tars observable 1 S tar observable
PH709 Extrasolar Planets Prof Michael Smith 10
See: http://instruct1.cit.cornell.edu/courses/astro101/java/binary/binary.htm
• Data plotted as RADIAL VELOCITY CURVE:
recession recession
+ +
v v
(km s-1)
0 (km s-1) 0
time time
- -
ABSOLUT E RELATIVE
approach approach
•Shape of radial velocity curves
depends on orbital eccentricity and
orientation
• If the orbit is tilted to the line of sight
(i rA sin i
} a sin i
vB sin i => rB sin i
So can only deduce (mA + mB) sin3 i = (a sin i)3/P2 (3)
For a spectroscopic binary, only lower limits to each mass can be derived,
unless the inclination i is known independently.
DETAILED DERIVATION
********************************************************
1. Assume a planet and star, both of considerable mass, are in circular
orbits around their centre of mass. Given the period P, the star‘s orbital
speed v* and mass M*, the mass of the planet, Mp is given by
Mp3/ (M* + Mp)2 = v*3 P / (2 G)
Note that there are 9 unknowns: P, a*, ap, M*, Mp, v*, vp, a, M - 9
variables
However,
a = a* + ap
M = M*+ Mp
Centre of mass; M* a* = mp ap
Kepler‘s law relates: P, a, M
P = 2 a*/v*
P = 2 ap/vp
….so that is 6 equations.
Note: we usually only know vr* = v* sin I and we assume the planet
mass is small.
PH507 Astrophysics Dr. S.F. Green 12
Eclipsing Binaries
• Since stars eclipse, the orientation is
i ~ 90°
• For a circular orbit:
1, 1' FIRST CONTACT
2, 2' SECOND CONTACT
3, 3' THIRD CONTACT
4, 4' FOURTH CONTACT
4' 3' 2' 1'
v 1 2 3 4
Observer in plane
• Variation in brightness with time is LIGHT CURVE.
• Timing of events gives information on sizes of stars and orbital elements.
PH507 Astrophysics 13
LECTURE 2
• Shape of events gives information on properties of stars and relative
temperatures. If smaller star is hotter, then:
Case 1 Smaller star is hotter
Case 2 Larger star is hotter
F
or
magnitude
Secondary minimum
Primary minimum
time
Case 1 t' t'
1 2 t' t' 2t t 4 t t
3 4 1 3
Case 2 t1 t
2 3t 4 t 1 2 t' t' 3 4 t' t'
PH507 Astrophysics 14
• If orbits are circular: minima are symmetrical ie t2-t1 = t4-t3 = t2'-t1' = t4'-t3';
minima are half a period apart; eclipses are of same duration.
Asymetrical and/or unevenly spaced minima indicate eccentricity and
orientation of orbit.
• For a circular orbit: t1 t2 t3 t 4
Distance = velocity x time
2RS = v (t2 - t1) (4)
and 2RL
2RS + 2RL = v (t4 - t1) => 2RL =
v(t4 - t2) (5)
2RS
RS/RL = (t2 - t1) / (t4 - t2) (35)
• Light curves are also affected by:
Non-total eclises No flat minimum
Limb darkening "rounds off"
(non-uniform eclipses
brightness)
Ellipsoidal stars
"rounds off"
(due to
proximity) maxima
Reflection effect
(if one star is
very bright)
PH507 Astrophysics Professor Glenn White 15
Eclipsing-Spectroscopic Binaries
• For eclipsing binaries i ≥ 70° (sin3i > 0.9)
• If stars are spectroscopic binaries then radial velocities are known.
So: masses are derived,
radii are derived,
ratio of temperatures is derived
Examine spectra and light curve to determine which radius corresponds with which
mass and temperature:
• Since Luminosity L = 4 R2 T4, the ratio of Luminosities is derived from
2 4
LA RA TA
= RB TB
LB
Summary
Type Observed Derived
Visual p, motion on sky a, e, i, mA, mB
Apparent magnitudes LA, LB
Spectroscopic velocity curves MA/MB, (MA+MB)sin3i, a sin i
Eclipsing light curves e, i, RS/RL
Eclipsing/ light + velocity curves MA, MB, RA, RB, TA/TB, a, e, i,
Spectroscopic distance LA, LB, TA, TB
PH709 Extrasolar Planets Professor Michael Smith 16
2 Extrasolar Planets or Exoplanets
134 other stars are now known to possess planetary systems. 157 planets have
been discovered. Although none 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 influence material close to the stars, has been clearly
detected.
Circumstellar dust discs: 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‘ A bulge in the image of dust from the star Beta Pictoris 18 light years away
could indicate the presence of a planet orbiting it, claims Nasa scientist Sally Heap.
Analysis of earlier pictures from the Hubble Space Telescope indicated that planets were only
beginning to form around Beta Pictoris, a very young star at between 20 million and 100 million
years old. ESO ADONIS adaptive optics system at the 3.6-m telescope. It shows (in
false colours) the scattered light at wavelength 1.25 micron (J band)
• How can we discover extrasolar planets?
• Characteristics of the exoplanet population
• Planet formation: theory
• Explaining the properties of exoplanets
Rapidly developing subject - first extrasolar planet around an ordinary star only
discovered in 1995 by Mayor & Queloz.
Resources. For observations, a good starting point is Berkeley extrasolar planets search
homepage
http://exoplanets.org/
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
PH709 Extrasolar Planets Professor Michael Smith 17
Simplest definition is based solely on mass
• Stars: burn hydrogen (M > 0.075 Msun)
• Brown dwarfs: burn deuterium
• Planets: do not burn deuterium (M 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.
3 Detecting extrasolar planets
(1) Direct imaging - difficult due to enormous star / planet flux ratio
The ultimate goal of any extrasolar planet search must surely be obtaining an
image of such a planet directly. This is fraught with difficulties since planets do
not emit light, so any image would have to be captured with starlight reflected
by the planet's atmosphere or surface. This will depend of course on the albedo
of the planet, which is hard to determine unless another detection method, such
as transits, is used as well. In any case, the light from the star will swamp that of
the planet by a factor of 109 in the optical, so it seems that concentrating upon
the infrared region would have the best chance of success. In the infrared, the
PH709 Extrasolar Planets Professor Michael Smith 18
difference in the emission strength between a star and a planet is 107 (Angel &
Woolf, 1997) since planets radiate strongly in the infrared and stellar emission is
weaker in this region than in the optical.
(2) Radial velocity
• Observable: line of sight velocity of star orbiting centre of mass of star - planet
binary system
• Most successful method so far - all early detections
(3) Astrometry
• Observable: stellar motion in plane of sky
• Very promising future method: Keck interferometer, GAIA, SIM
(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 (2007 launch. NASA
Discovery mission), Eddington)
(5) Gravitational lensing: first success in 2004
• 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
s
Each method has different sensitivity to planets at various orbital radii - complete
census of planets requires use of several different techniques
PH709 Extrasolar Planets Professor Michael Smith 19
Planet detection method : Radial velocity technique
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 ) in an inertial
frame is:
(assuming mp 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
PH709 Extrasolar Planets Professor Michael Smith 20
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
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.
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
Currently, the best observations achieve:
~ 3 m/s
...in a single measurement. Thought that this error can be reduced to around 1 m/s with
further refinements, but not substantially further. The very highest Doppler precisions
of 1 m/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 ~ 1 AU.
PH709 Extrasolar Planets Professor Michael Smith 21
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.
Example of a planet with an eccentric orbit: e=0.67
Summary: observables
PH709 Extrasolar Planets Professor Michael Smith 22
(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 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:
PH709 Extrasolar Planets Professor Michael Smith 26
Photometric precision of ~ 10-5 seems achievable from space
May provide first detection of habitable Earth-like planets
NASA‘s Kepler mission, ESA version Eddington
A reflected light signature must also exist, modulated on the orbital period,
even for non-transiting planets. No detections yet.
Lecture 4:
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
Define:
• Observer-lens distance Dl
• Observer-source distance Ds
• Lens-source distance Dls
PH709 Extrasolar Planets Professor Michael Smith 27
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...
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:
PH709 Extrasolar Planets Professor Michael Smith 28
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
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
PH709 Extrasolar Planets Professor Michael Smith 29
Lensing by a star and a planet
PH709 Extrasolar Planets Professor Michael Smith 30
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
What has this to do with planets?
Binaries can also act as lenses
Light curve for a binary lens is more complicated, but a characteristic is the presence of
sharp spikes or caustics. With good enough monitoring, the parameters of the binary
doing the lensing can be recovered.
Orbiting planet is just a binary with mass ratio q 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.
PH709 Extrasolar Planets Professor Michael Smith 40
Nothing very striking in these plots:
PH709 Extrasolar Planets Professor Michael Smith 41
• Accessible region of mp - a space is fully occupied by detected planets
• Ignoring the hot Jupiters, no obvious correlation between planet mass and
eccentricity...
Minimum mass as a function of semimajor axis for the 164
known nearby exoplanets with 0.03 3 AU, low-mass
planets (M sin i 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 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 45
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 46
Note: the brown dwarf desert!
Minimum mass distribution of the 167 known nearby exoplanets with M sin i = 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.
PH709 Extrasolar Planets Professor Michael Smith 52
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 53
PH709 Extrasolar Planets Professor Michael Smith 54
PH709 Extrasolar Planets Professor Michael Smith 55
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 Jupiter-sized planet forms Planet accretes along spiral Disk fragments into more
around central star. & clears gap in gas disk. 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 proto-
planet 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 56
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 (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 tends to align with the sense of their orbits,
with exceptions.
Sun rotates in the same direction in the same sense.
PH709 Extrasolar Planets Professor Michael Smith 57
Jovian moon systems mimic the Solar System.
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".
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Condensation Temperatures
Temp (K) Elements 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
Carbon,
300 K Carbonaceous grains -Volatiles
Oxygen
Hydrogen,
300-100 K Ices (H2O, CO2, NH3, CH4)
Nitrogen
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.
PH709 Extrasolar Planets Professor Michael Smith 59
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.
Never get to aggregate into a larger bodies.
PH709 Extrasolar Planets Professor Michael Smith 60
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.
.
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.
PH709 Extrasolar Planets Professor Michael Smith 61
• 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, or
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 ( moves inwards
Resonances at r > rp: Disc gas has smaller angular velocity than planet. Gains
angular momentum from planet -> moves outwards.
PH709 Extrasolar Planets Professor Michael Smith 63
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
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. The planet, unless more massive than the
surrounding disk, follows the disk's viscous flow.
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?
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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 a 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!
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)
PH709 Extrasolar Planets Professor Michael Smith 65
(D) Classical giant planet formation w/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
• 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:
• Same mechanism as invoked for migration
• Works for just one planet
• 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
(3) 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
PH709 Extrasolar Planets Professor Michael Smith 66
8 History of Planet Formation Speculation
There is little early history surrounding the general subject. 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
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
PH709 Extrasolar Planets Professor Michael Smith 67
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 Jeans-
Jeffreys' hypothesis. He showed that the material torn out of the Sunby near-
collisions 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
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,
PH709 Extrasolar Planets Professor Michael Smith 68
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.