AST101 - Lecture 22 (Radial Velocity)

How can learn about a planet’s rings through the transit method

• Can see extra small dips during transit

• Use small variations in the light curve of the bottom of a transit to make surface maps of an exoplanet

• If there was just a disk it’d just be flat

  • Can see variations in the light curve at the bottom to see what else is blocking out the light

  • Learn if there’s earthquake the way the light curves

What is the purpose of the Transit Exoplanet Survey Satellite (TESS)

• Will look for transit toward 500,000 stars covering 85% of the sky

What is the problem with Kepler’s First Law

It orbits the sun in an eliptical patterns with the sun at one focus, but it’s a bit wrong as it orbits their common center of mass

What is the doppler effect?

• Sources moving towards you shift to higher frequency (shorter wavelength)

• Sources moving away from you shift to lower frequency (longer wavelength)

• Only measures line of sight

• Object moving away directly measure all of its speed

• Moving across our line of sight

  • Measure none of its speed

• Moving diagonally measure only part of its speed

• In all cases, the only part of the motion we can measure is the radial velocity

What is the center of mass

• Point where one could put a fulcrum to keep system balance

• For the Sun and the Earth, the center of mass is almost at the center of the Sun, as it’s much more massive

What is the orbits of stars like?

• Most stars are much more massive than their planets

• Therefore, center of mass is close to but not at the center of the star

• From our perspective star wobbles toward and away from us

What is the doppler method?

Exoplanet moves in a large orbit but exoplanet is too faint to see

• Parent star moves in a tiny orbit and is bright enough to see

• Use doppler effect applied to the spectrum of the star to measure the radial velocity (wobble) of the star as it orbits the center of the mass

  • Measure the mass and where it is in its orbit

• The fact that the sun wobbles is that there’s a planet making it wobble by changing it’s center of mas

  • The amount of wobble changes how much shift is seen

What is 51Pegasi B?

• Exoplanet revealed off the doppler shifts of the star of 51 pegasi

• Radial velocity peaked around 60ms

• This was the first extrasolar planet to be discovered around a Sun-like star

What does the doppler method tell us

• Tell us we found an exoplanet

• Orbit cannot be face on

• Calculate the orbit period

  • Big dip and little dip

  • Except sun exoplanet to do a wobble in one period

• Using kepler third law we can use the period to calculate the distance of the exoplanet from its parent star

  • From the semi-major axis that we got from the orbital period

• The velocity change gives us the star’s speed, which if we know the star’s mass, tells us the exoplanets mass

What are some characteristics of 51 Pegasi B?

• 4 day orbital period

• 0.053 AU semi major axis

• Mass 0.47M

• Half the mass of Jupier 7 times closer to the Sun orbited 4 days

• Named hot jupiter

What are hot jupiters?

• Proven to be the most common type of exoplanet found in both transit and Doppler searcher for exoplanets

• At odds with the nebular theory

• Form in outer solar system but move inward via planetary migration

  • Interaciton with another object

  • Wind from the hot star pushes it

  • Migrated slowly towards the star

What are Hot Jupiters so Common?

• Doppler: Heavy and close-in means they produce a large wobble in their parent star

• Transit: Large and close-in means they produce a deep transit in the parent star light curve

• Observational bias

• Close-in means wobbles or transit repeat themselves quickly

• With better instruments the fraction of these should go down

How does the inclination of a planet be a problem?

• Easier to find things that are edge-on

• One catch to the doppler method is that we can only measured the radial velocity

• If the orbit is edge-on we see all the star’s motion

• Hard to tell exactly what the angle is

• If the orbit is inclined, we can see some of the star’s motion

• If the orbit is face on, we don’t see any of the star’s motion (can’t detect the exoplanet

• Can only find with the doppler method

  • Lower limit on true doppler velocity

  • Know the minimum possible mass of the exoplanet

  • If the exoplanet also transit we know it must be nearly edge-on and so we know its actual mass

What are the strengths of the doppler method?

• Does not need continuous monitoring

• Works for any orientation of the exoplanet’s orbit (beside face on)

• Very good for massive planets in close-in orbits

What are the weaknesses of the Doppler Method?

• Needs a big telescope to measure spectra and doppler shifts

• Can only measure a minimum mass unless inclination is known

• Can only study one star a time

• Biased toward close-in exoplanets

What can we learn by comining the transit and doppleer method?

• Transit measures size and inclination’

• Doppler gives us an exoplanet’s mass

• Measure the density by combining which we can begin to figure out its interior composition

• Graph plot mass (horizontal) vs size (vertical axis)

• Dotted lines show various possible densities

• Solar system planets are shown in green

• Selected transiting exoplanets are shown in red