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ASTR 200 : Lecture 21
Exoplanet Detection Basics
Assemble yourselves into work groups of 3­5 people
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Extrasolar (or Exoplanet) detection
• This is a subject that had a long history, full of `what
turned out to be incorrect' claims.
• It is technically very challenging to detect planets
around other stars.
Three main techniques currently
1) Radial velocity (spectral) method on parent star
2) Transit method
3) Direct imaging method
There are also a few via other techniques
4) Pulsar timing
5) Gravitational microlensing
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Spectral method
• Assume there is a Jupiter-mass planet (10 -3 the mass of
the Sun) in an orbit around a 1-solar mass star, with
orbital a=4 au.
• Assume we see the planet's orbit 'edge on' (i=90 deg)
• The star/planet is a binary star, but we only see the light
from the star.
(a) How fast is the planet moving (km/s) in its orbit?
(b) How fast is the star moving (km/s) in its orbit
around the center of mass?
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Stellar radial velocity method
• Assume there is a Jupiter-mass planet (10 -3 the mass of
the Sun) in an orbit around a 1-solar mass star, with
orbital a=4 au. Planet speed~15 km/s, star ~15 m/s
• Assume we see the planet's orbit 'edge on' (i=90 deg)
• The star/planet is a binary star, but we only see the light
from the star.
(c) What will be the period of the star's Doppler shift
pattern for its spectral lines?
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(d) What will be the wavelength shift for a visible line
(say with wavelength 500 nm)
Stellar radial velocity method
• Assume there is a Jupiter-mass planet (10 -3 the mass of
the Sun) in an orbit around a 1-solar mass star, with
orbital a=4 au. Planet speed~15 km/s, star ~15 m/s
• Assume we see the planet's orbit 'edge on' (i=90 deg)
• The star/planet is a binary star, but we only see the light
from the star.
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(c) What will be the period of the star's Doppler shift
pattern for its spectral lines? P=a3/2 so P=8 yr
(d) What will be the wavelength shift for a visible line?
v
15m/s
−6
−5
Δ λ=λ =(500 nm)
=25 x 10 nm∼3 x10 nm
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c
3 x10 m/s
Signal of jovian planets around other stars
• Expected signal was thus :
– Stellar radial velocity ~10 m/s
– Periods of roughly 1-2 decades
– Need to, by luck or by doing a large number of target
star, find one where planetary orbit is roughly edge on
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The BIG surprise
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Stellar radial velocity method
• Assume the Jupiter-mass planet orbiting a 1-solar mass
star has orbital semimajor axis a=0.04 au (not 4 au)
(e) Now what will be the period of the star's Doppler
shift pattern for its spectral lines?
(f) What is the orbital speed of the star in its orbit
around the center of mass?
(g) What will be the wavelength shift for a visible line
(say with wavelength 500 nm)?
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This was a big surprise
• There are jovian mass planets in orbits around
stars, but closer than the distance at which
Mercury orbits the Sun
• These objects are called 'hot Jupiters' because their
equilibrium temperatures will be high.
• Conventionally, many (but not all) astronomers
believe that these planets formed further out away
from the star (past the snow line) but then migrated
into their current position
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Hot
Jupiters
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Transiting planets
• Technique of watching the light output of a star, and
observing a dimming because a planet moves in front
of the star and blocks some of the light coming to Earth
• Suppose we were near some star that lies along the
ecliptic plane, and that one of our Solar System's
planets passed in front of the star. What fraction of the
star's light would be blocked if the planet was
– (a) Jupiter ?
– (b) Earth
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It is just the fractional area covered
• Light blocked is
f=
2
p
2
⊙
πR
πR
2
Rp
=(
)
R⊙
• So the star's intensity is now I '=I −fI =I (1−f )
which as a fraction is
2
Rp
I'
= 1−f = 1−( )
I
R⊙
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An exoplanet transit
• Say this was Earth transiting our Sun as viewed by
an astronomer elsewhere in the the galaxy.
Roughly how long (minutes? hours? days?) would
the transit last?
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The Kepler space telescope was built
explicitly to do just this
• Stared at one field for a few years, measuring the
`photometry' (amount of light arriving) of ~100,00
stars
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Mostly transiting
planets, mostly from Kepler
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Directly imaging planets
• Why doesn't one just take a picture??
• Perhaps it is angular separation. Ground based
telescopes have trouble separating object if they are
closer in angular separation than 0.5”
– Suppose one was an astronomer on a planet in the Alpha
Centauri system, 1.3 pc from the Sun, looking back at the
Sun-Jupiter system.
– What is the angular separation of Jupiter when Jupiter is
as far away as possible (in an angular sense) from the
Sun?
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Directly imaging planets
• So, the problem is NOT angular separation, when it
comes to looking for planets within ~10 pc from the
Sun
• The problem is CONTRAST. One is looking for a
faint object near a bright one (the star). Analogy is to
see a firefly near a streetlamp; the light of the firefly is
easy to see in the dark, but hard when there is lots of
nearby light
• This is why there are techniques used to block or
cancel out the light of the star
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HR
8799
4 planets
around a
star 40pc
away
Imaging is
in the near
infrared
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Mostly directly imaged
giant planets
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Reflected light
• What is the ratio of reflected optical light from
Jupiter to that of the Sun? Take A_jup=0.5,
R_jup=70,000 km, a_jup=5.2 au
Thermal planetary light
• What about the THERMAL planetary light?
• Turns out contrast is better in the IR
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