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Planet Hunting Toolkit III: Radial Velocities March 12, 2009

Posted by CosmicThespian in Toolkit.

In the previous article in this series, I discussed a possible way of getting around the fact that imaging extrasolar planets is incredibly difficult: the wobble imparted on a star by its planets.  However, the current generation of telescopes and instruments can only really make use of the astrometric method in a handful of cases and while future telescopes will be able to leverage astrometric wobble to find Earth-like planets, astronomers can be a bit impatient.  We want to know if there’s anyway to take advantage of what we have now to begin to characterize other planetary systems.  Turns out, there is.

In fact, the method that astronomers use to find the overwhelming majority of exoplanets has a lot in common with how police can catch you for speeding with a radar gun!

Both rely on the concept of doppler shift.  The basic idea is that the speed of a source of a wave (such as an ambulance if we are worried about sound waves, or a flashlight if we’re concerned with light) affects the wavelengths of the waves.  Let me explain with a common example:  Have you ever noticed how the pitch of a train horn changes as a train passes by you?  It starts higher and then dramatically becomes lower once it goes by.  Here’s what’s happening: sound can only travel at a fixed speed through the air (about 700 m.p.h.) – independent of the speed of whatever is making the sound.  When you shout, the sound waves produced by your vocal cords fly off at 700 m.p.h. in all directions.  When a train is moving along at, say, 100 m.p.h. and it blows its horn, the sound doesn’t get to move faster because the train is moving faster.  It’s stuck at 700 m.p.h.  This makes the sound waves “bunch up” in front of the train and get “spread out” behind the train.

Illustration of doppler shift.  When the train is moving, the sound waves in front bunch up; those in back spread out.

Illustration of doppler shift. When the train is moving, the sound waves in front bunch up; those in back spread out.

To take an extreme example, if a jet is moving at the speed of sound (Mach 1), the sound waves can’t get ahead of it because both the jet and the sound waves are traveling at the same speed.  This creates a wall of sound – called a bow shock – in front of the object.  This is what’s responsible for the sonic boom you hear when a plane roars by at Mach 1 or faster.  As the above picture shows, the bunched up sound waves have shorter wavelengths and the stretched out waves have longer ones.  Our ears and brains translate shorter wavelengths into higher pitches and longer wavelengths into lower pitches.  That’s why a train horn sounds higher when it approaches you and then sounds lower once it goes by.

The same thing happens to light waves!  If a star (for example) is moving towards you, all of its light waves get bunched up in front of it thereby making the wavelengths of light shorter.  The opposite happens when a star moves away from you.  Police radar guns take advantage of this by bouncing radar off your car.  By measuring how much shorter the reflected wavelengths are than those that were emitted, the police officer can determine precisely how fast you are driving.

In the Spectra article, I introduced you to the concept of absorption lines (if you haven’t read that article already, you might want to go do that right now!)  If all the wavelengths of light get shorter, that means the absorption lines of a star will appear at shorter wavelengths than we would find them in the lab.  If a star is moving away, the absorption lines show up at longer wavelengths.  Astronomers refer to these two phenomena as blueshift and redshift (because blue is a short wavelength color and red is a long wavelength color).  If we look at a star’s spectrum and find the entire pattern of hydrogen absorption lines (as an example) shifted over to slightly longer wavelengths – that is, if the hydrogen lines are redshifted – we know the star is moving away from us.  In fact, the difference in the observed wavelengths of the absorption lines and those measured in the lab tells you precisely how fast the star is moving away!  If all of the lines are blueshifted, we know the star is moving towards us and how quickly.

The effect of red and blue shifts on absorption lines.

The effect of red and blue shifts on absorption lines.

But what if we find a star where, over time, the lines alternately blueshift and then redshift over and over with a fixed period?  That implies the star is moving towards us and then moving away and then towards….over and over over.  It tells us: the star is wobbling back and forth in space!!!!

This could only happen if there was something we couldn’t see near the star pulling it around.  This, dear reader, is how to find a planet!

This technique of finding planets via the doppler shift (usually called the “radial velocity method”) is responsible for finding the overwhelming majority of planets we know of.  The Extrasolar Planet Encyclopedia (as of the time of this posting) lists 316 of the currently 342 known worlds found this way.  This technique favors larger worlds on short period orbits because these planets produce the largest doppler shifts.  But astronomers have greatly improved on the technology over the past decade which has allowed us to start finding planets several times the mass of the Earth and worlds on multi-year long orbits.  While the vast majority of planets we’ve found thus far are Jupiter-sized worlds orbiting very close to their stars, this is predominately a limitation on the techniques we use and isn’t necessarily an accurate picture of the exoplanetary zoo.

What’s more, the radial velocity technique allows to measure some basic properties of the planet.  By measuring the period of the star’s wobble, we can use Kepler’s Third Law to figure out how far away the planet is from it’s star.  Furthermore, if we know the mass of the star through some other means, than that combined with the star’s velocity and a sprinkling of high school physics can tell us the mass of the planet!  (Actually, it’s a little more complicated than that.  We can really only determine a lower limit for the planet’s mass without knowing something about the tilt of the planet’s orbit relative to the Earth, a topic I may explore further in a later post).

While other techniques can provide astronomers with more information about specific worlds, the radial velocity method is the workhorse method and it is responsible for revealing the wonderous diversity of the exoplanetary zoo.

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