Exoplanets
AST 248
Trappist-1 Planetary System1
Are there other Planets out there?
Yes
We believe most stars harbor
planets ---> planetary
systems
Hard to have planets around
binary stars. Orbits tend to be
unstable
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Exoplanets
An exoplanet is simply a planet that is not in the solar system. Doesn’t orbit the
sun.
● Up until 1990s we didn’t know how common were planets
● First unambiguous detection in 1995. 51 Pegasi b
● Since then, over 4000 exoplanets have been observed
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Needle in a Haystack
Stars are generally ~Billion
times brighter than their
planets
Stellar glare makes it hard to
detect exoplanets.
Need good (big) telescopes
and creative methods
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Reviewing Orbits
We can estimate the mass of the star by assuming circular orbit.
𝑉 is the orbital velocity. 𝑀 is the mass of the star. 𝑟 is the orbital radius
𝑉 =𝐺𝑀
𝑟
With 𝑃 the orbital period. 𝑉 =2𝜋𝑟
𝑃 Really this should be 𝑉 sin(𝑖)where 𝑖 is the inclination of the
orbit
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rV
M
Kepler’s Law
1. Orbits are ellipses (not quite circles)
2. The line connecting the planet to the sun sweep out equal areas in equal times
Planets move faster in their orbit when close to the Sun
3. 𝑎3 = 𝑃2 The orbital period is proportional to the size of the orbit
These Laws apply for all planetary systems where you have one (or many)
exoplanets orbiting a singular star
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Center of Mass
Planets don’t orbit around stars
Orbit around common center of mass.
This picture is exaggerated. Typically it is
close to the star’s center.
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Distance between Star and Planet:
𝑟 = 𝑟⋆ + 𝑟𝑝
Astrometric wobble 𝑟⋆ =𝑀𝑝
𝑀⋆𝑟𝑝
Radial Velocity 𝑣⋆ =𝑀𝑝
𝑀⋆𝑣𝑝
Planetary System Inclination
● Planetary Systems are randomly
orientated relative to us.
● To see Direct Detection, want
face on
● Radial velocity and transits, want
edge on
● This limits what planets we can
detect with a given method. Adds
uncertainty
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Direct and Indirect Observations
● Direct Detection
○ Often coronagraph is used to block star’s light/glare
● Transit Method
○ Planet blocks some of the light of the star
● Detecting Wobbles
○ Astrometry. Star’s path across the sky
○ Doppler Effect. Star’s velocity toward and away from us
○ Pulsar timing
● Gravitational Lensing
○ Weird GR stuff
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Direct
Observation
Indirect
Observation.
Looking at
planet’s effect
on the star
Direct Detection
Coronagraph blocks
starlight. Lowers glare.
Helps to have “face on”
orientation.
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Direct Detection: What info do we get?
Can directly measure distance
between planet and star if we know
distance to the system.
Helps if system is closer to us and if
planets are far from the star
Can repeat observations to watch
exoplanets orbit
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Direct Detection: What type of system is easiest to detect
Large planet (reflects more light)
Far from star (won’t get lost in starlight)
Hot planets (emit more of their own light)
Infrared range is best
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Indirect Observations
● Orbiting planets will affect their host
star
● Changes are small but with good
telescopes we can observe this effect
without ever seeing the planet
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Transits
Planet blocks some of
the light when passing
in front of the star
Light Blocked =Rp2
R⋆2
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Transits Cont.
● Can find multiple planets transiting (slightly more complicated to figure out)
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Trappist-1
Light Curve
Transit Observables
Can directly measure the orbital period (time between dips)
Ratio of Planet’s radius to Star’s radius (size of dips)
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Transit: What type of system is easiest to detect
● Planets close to their star ○ More dips makes it easier to detect
● Larger planets orbiting around smaller stars
○ Makes a larger dip which is again easier to measure.
Note: not particularly easy to see solar system like ours with this method.
Earth’s orbital period is 1 year. Only blocks 0.01% of Sun’s light
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Stars Wobble
● Star’s “wobble” around the
center of mass
● Very small so need careful
measurements to detect
● Finding a wobbling star
implies there is a planet
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Solar System Barycenter
● Small, complex shifts
● Center moves ~1 Solar radius
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Astrometry
Astrometry is the measure of a star’s
position on the night sky.
● Stars are moving
● We are moving around the sun
(parallax)
● Result is we observe stars taking a
curly path.
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Astrometry Method
Detect deviations from this
looping path
Extra deviations are due to
a planet
Wobbling around the center
of mass
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Van der Kamp’s Planet
● 1.6 Mj at 4.4 AU
● Never confirmed
● Attributed to calibration/maintenance of the telescope
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Astrometry: Summary
● Tells us the orbital period
● Overall, difficult to measure
● Easiest to find massive
planets far from their star
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Astrometric wobble 𝑟⋆ =𝑀𝑝
𝑀⋆𝑟𝑝
Detecting More Wobbles: Radial Velocity
● One of the most succesful methods
of detection
● Don’t directly measure the wobble,
but instead detect Doppler shift
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Doppler Effect Review
Things moving toward us have their wavelength shortened (blueshifted)
Things moving away from us have their wavelength extended (redshifted)
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Radial Velocity Method
● Star’s spectra is red/blueshifted
throughout orbit
● Can convert this into a “Radial
Velocity” plot
○ How fast the star is moving
directly away or toward us.
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Radial Velocity: Summary
What can we observe?
○ Gives the period of the orbit
○ Can estimate mass
Easiest to find Massive planets that
are near their star. See many
oscillations
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Radial Velocity 𝑣⋆ =𝑀𝑝
𝑀⋆𝑣𝑝
Puslar Timing
● Rotating neutron stars with
magnetic fields that shine
periodically at earth.
● Regular variations in the pulses
indicate orbiting planet(s)
● Planets around pulsars are
likely uninhabitable. Very
extreme environment
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Gravitational lensing
● General Relativity says light bends around massive
objects (e.g. stars)
● “Lens star” enhances the light of the observed star
● Gives characteristic light curve as it passes by
● Need to look in the right place at the right time to
observe this
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Lens Star
Gravitational Lensing
● Detecting a planet around the lens star comes
from looking at the light curve
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Lens Star
Gravitational Lensing in summary
● What do we observe?
○ Mass of both star and planet
○ Distance between star and planet
● Unlike other methods, is more sensitive to smaller mass planets
● Very random. Need planet/stars to line up just right and be looking at the right
time. Can’t repeat measurement
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Exoplanet Research
● Exoplanet research has exploded in last ~30 years
● Kepler mission, discovered thousands of exoplanets
○ Successor TESS has discovered thousands more
● Researchers use multiple methods (e.g. transit and radial velocity) to get full
picture of a planetary system after it has been discovered
● Better telescopes will be able to find more and smaller planets. Begin observing
the atmospheres of exoplanets
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