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Prof M Smith
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2 EXOPLANET DETECTION: Prof Michael SMITH
Detecting extrasolar planets
(1)
Direct imaging - difficult due to enormous star / planet flux ratio.
Any optical 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,
Infrared. 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.
Detection may be possible when the planet is especially large
(considerably larger than Jupiter), widely separated from its parent
star, and young (so that it is hot and emits intense infrared
radiation).
(2) Radial velocity
• Observable: line of sight velocity of star orbiting centre of
mass of star - planet binary system.
(3) Astrometry
• Observable: stellar motion in plane of sky
(4) Transits: photometry
• 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
• Observable: light curve of a background star lensed by the
gravitational influence of a foreground star.
• Rare - requires monitoring millions of background stars, and
also unrepeatable
Each method has different sensitivity to planets at various orbital
radii - complete census of planets requires use of several different
techniques
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2.1 Direct Imaging
Direct imaging of planets is difficult because of the enormous
difference in brightness between the star and the planet, and the
small angular separation between them.
Direct detection: must be large and distant from star
Circumstellar dust discs. (Circumstantial evidence.) Disc of
material around the star Beta Pictoris bably connected with a
planetary system. The disk does not start at the star. Rather, its
inner edge begins around 25 AU away, farther than the average
orbital distance of Uranus in the Solar System.
Theoretically, this disk should have lasted for only around 10 million
years. That it has persisted for the 20 to 200 million year lifetime of
Beta Pictoris may be due to the presence of large disk bodies
(i.e., planets) that collide with icy Edgeworth-Kuiper Belt type objects
(dormant comets) to replenish the dust.
Young stars are preferred because young planets are expected to
be more luminous than older planets. In addition, direct imaging is
based on detection of planet luminosity, which must be related to
planet mass or size through uncertain theoretical models.
Some stunning individual systems have been reported (Marois et al.
2010, Lagrange et al. 2010), but the surveys indicate that fewer
planets are found than would be predicted by extrapolating the
power-law (of Eqn. (1) – see next lecture) out to 10-100 AU.
Circumstellar dust discs. (Circumstantial evidence.) 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’
This disk around Beta Pictoris is probably connected with a
planetary system. The disk does not start at the star. Rather, its
inner edge begins around 25 AU away, farther than the average
orbital distance of Uranus in the Solar System.
Its outer edge appears to extend as far out as 550 AUs away from
the star.
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Analysis of Hubble Space Telescope data indicated that planets
were only beginning to form around Beta Pictoris, a very young star
at between 20 million and 100 million years old.
Most dust grains in the disk are not agglomerating to form larger
bodies; instead, they are eroding and being moved away from the
star by radiation pressure when their size goes below about 2-10
microns.
Theoretically, this disk should have lasted for only around 10 million
years. That it has persisted for the 20 to 200 million year lifetime of
Beta Pictoris may be due to the presence of large disk bodies
(i.e., planets) that collide with icy Edgeworth-Kuiper Belt type objects
(dormant comets) to replenish the dust.
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Using high-contrast, near-infrared adaptive optics observations with the Keck
and Gemini telescopes, the team of researchers were able to see three orbiting
planetary companions to HR8799
Young stars are preferred because young planets are expected to
be more luminous than older planets. In addition, direct imaging is
based on detection of planet luminosity, which must be related to
planet mass or size through uncertain theoretical models.
Some stunning individual systems have been reported (Marois et al.
2010, Lagrange et al. 2010), but the surveys indicate that fewer
planets are found than would be predicted by extrapolating the
Direct Spectroscopic Detection? 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
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will retain the same pattern of photospheric absorption lines as in
the direct starlight.
2.2 Planet detection method : Radial velocity
technique
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.
We observe the star. So what can we say about the exoplanet?
X
a
r1
r2
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:
G(M * + m p )
W=
a3
Using a1 M* = a2 mp and a = a1 + a2, then the stellar speed
(v* = a ) in an inertial frame is:
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V* =
Prof M Smith
mp
G(M * + m p )
M*
a
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(assuming mp << M*). i.e. the stellar orbital speed is small …. just
metres 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:
Vobs = V* sin(i)
Hence, measurement of the radial velocity amplitude produces a
constraint on:
mp sin(i)
This assumes stellar mass is well-known, as it will be since to
measure radial velocity we need exceptionally high S/N spectra of
the star.
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Observable yields 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:
Sun due to Earth:
i.e. extremely small running pace
12.5 m/s
0.09 m/s
10 m/s is Olympic 100m
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.
• 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
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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 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.
Radial velocity measurement:
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 over many years are required
For circular orbit:
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51 Peg b was the first known exoplanet
With a 4 day, circular orbit: a hot Jupiter, lying close to the central
star.
Note the large radial velocity shift.
Example of a planet with an eccentric orbit: e=0.67 where
e = 1 – b2/a2 periastron = a (1-e)
a = semi-major axis, b = semi-minor axis
apastron = a (1+e)
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Note the shape, not sinusoidal at all.
Summary: three parameters derived from 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)
Which planets are detectable? Down to a fixed radial velocity
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m p sin i µ a
Prof M Smith
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1
2
Hence, inner massive planets are selected.
2.3 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.
Measure stellar motion in the plane of the sky due to presence of
orbiting planet. Must account for parallax and proper motion of star.
Magnitude of effect: amplitude of stellar wobble (half peak
displacement) for an orbit in the plane of the sky is
æ mp ö
÷÷ ´ a
a1 = çç
è M* ø
In terms of the angle:
æ m p öæ a ö
÷÷ç ÷
Dq = çç
M
è * øè d ø
for a star at distance d. Note we have again used mp << M*
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Prof M Smith
æ m p öæ a ö
÷÷ç ÷
Dq = çç
radians
M
è * øè d ø
The Wobble:
Detection threshold as function of semi-major axis
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2.4 Planet detection method : Transits Photometry
TRANSITS
Currently the most important class of exoplanets are those that
transit the disk of their parent stars, allowing for a determination
of planetary radii.
SELECTION: Of course, while planets close to their parent stars will
preferentially be found, due to their shorter orbital periods and
greater likelihood to transit, planetary transits will be detected at
all orbital separations.
CONFIRMATION: In general, the detection of three successive
transits will be necessary for a confirmed detection, which will limit
confirmed planetary-radius objects to about 1.5 AU.
DENSITIES: The first confirmed transiting planets observed were all
more massive than Saturn, have orbital periods of only a few days,
and orbit stars bright enough such that radial velocities can also be
determined, allowing for a calculation of planetary masses and bulk
densities. A planetary mass and radius allows us a window into
planetary composition (Guillot 2005).
The first transiting planets were mainly gas giants although one
planet, HD 149026b, appears to be 2/3 heavy elements by mass
(Sato et al. 2005; Fortney et al. 2006; Ikoma et al. 2006).
Understanding how the transiting planet mass-radius relations
change as a function of orbital distance, stellar mass, stellar
metallicity, or UV flux, will provide insight into the fundamentals of
planetary
formation,
migration,
and
evolution.
The transit method of planet detection is biased toward finding
planets that orbit relatively close to their parent stars. This means
that radial velocity follow-up will be possible for some planets as the
stellar "wobble" signal is larger for shorter period orbits.
Drop in stellar flux due to a planet transiting across the stellar disc.
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Needs luck or wide-area surveys - transits only occur if the orbit is
almost edge-on
The photometric transit technique can determine the radius of a
planet, but generally not the mass and hence does not immediately
indicate if a transit signal is due to a planet or a binary star system.
r i
a
o
Probability. For a planet with radius rp << R*, probability of a transit-
æ R* ö
Ptransit = sin(q ) » ç ÷
èaø
Close-in planets are more likely to be detected. P = 0.5 % at
1AU, P = 0.1 % at the orbital radius of Jupiter
What can we measure from the light curve?
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(1) Depth of transit = fraction of stellar light blocked
DF æ rp ö
=ç ÷
Fo è R* ø
2
This is a measure of planetary radius! No dependence on
distance from star.
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)
(3)
(4)
Duration of transit plus duration of ingress, gives measure of
the orbital radius and inclination
Bottom of light curve is not actually flat, providing a
measure of stellar limb-darkening
Deviations from profile expected from a perfectly opaque disc
could provide evidence for satellites, rings etc
Transit depth for an Earth-like planet is:
Photometric precision of ~ 10-5 seems achievable from space
THE EFFECT OF A TRANSIT ON RADIAL VELOCITY
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.
• We know that the observed radial velocity depends on
the planetary system inclination to the line of sight ()
• What happens to the line shape when sin i = 1?
• The planet moves across the face of the star, blocking
some of the light (which is blue/red shifted by the
rotation of the star) and changing the line shape –
which makes it look as though the radial velocity is
changing when it isn’t.
This is known as the Rossiter-McLaughlin effect: it yields
the direction of rotation of the star!
Transit timing variation method (TTV) and transit
duration variation method (TDV)
If a planet has been detected by the transit method, then variations
in the timing of the transit provide an extremely sensitive method
which is capable of detecting additional planets in the system with
sizes potentially as small as Earth-sized planets.
Duration variations may be caused by an exomoon.
Orbital phase reflected light variations
Short period giant planets in close orbits around their stars will
undergo reflected light variations changes because, like the
Moon, they will go through phases from full to new and back again.
Since telescopes cannot resolve the planet from the star, they see
only the combined light, and the brightness of the host star seems to
change over each orbit in a periodic manner. Although the effect is
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small — the photometric precision required is about the same as to
detect an Earth-sized planet in transit across a solar-type star —
such Jupiter-sized planets are detectable by space telescopes such
as the Kepler Space Observatory.
3.5 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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DS
θ
Source
DLS
Lens
(Mass M)
Define:
• Observer-lens distance
• Observer-source distance
• Lens-source distance
DL
Observer
Dl
Ds
Dls
Azimuthal symmetry -> light from the source appears as a ring
R0
...with radius R0 - the Einstein ring radius - in the lens plane
relevant time scale is called the Einstein time and it's given by the
time it takes the lens to traverse an Einstein radius.
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Timescales for sources in the Galactic bulge, lenses ~ halfway
along the line of sight:
• Solar mass star ~ 1 month (Einstein radius of order a
few AU)
• Jupiter mass planet ~ 1 day (0.1 AU)
• 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.
• OGLE-2005-BLG-390Lb (Catchy! – OGLE-Year-PlaceNumber)
• Detection of a 5 MEARTH mass planet.
2.6 Timing: Pulsar Planets
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In early 1992, the Polish astronomer Aleksander Wolszczan (with
Dale Frail) announced the discovery of planets around another
pulsar, PSR 1257+12.This discovery was quickly confirmed, and is
generally considered to be the first definitive detection of exoplanets.


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.