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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