Published 20 June 2012 by Markus Pössel

Catching planets with a laser

At my first Lindau meeting, in 2010, I remember one particular bit of information that caught my attention. It was during the lecture by Theodor Hänsch – apparently there is no video in the mediatheque yet -, who was talking about his prize-winning "frequency combs". The principle is simple: Catch a laser pulse between two mirrors, where the poor pulse will endlessly run back and forth, back and forth. If you’re familiar with the basics of relativity, you’ll immediately recognize what this is: Einstein’s "light clock", a conceptually very simple clock that can be used to derive special-relativistic effects such as time dilation or Lorentz contraction (here’s a cute Flash animation which uses light clocks to demonstrate time dilation, and here’s the explanation spelled out).

The point, though, is not to build a real-life version of Einstein’s thought experiment (although that’s a very cool aspect of it), but the following: The light pulse, like any other light pulse, can be thought of as a combination of simple (sine) waves. Which waves do you need to some up to make this kind of pulse? As it turns out, you need precisely those sine waves whose frequencies are multiples of one particular frequency: The frequency defined by the pulse periodically going back and forth in its mirrored prison. Plot these frequencies, and you will get contributions that are evenly spaced: one time the basic frequency, two times, three times, and so on. The result looks like the teeth of a comb – hence the name.

Unsurprisingly, the technical details are more complicated. But do it right, and you obtain a very stable, very precise "frequency grid" against which other frequency measurements can be compared. 

Which brings us to the statement that caught my attention: At one point in the lecture, Hänsch started to talk about exoplanets – planets orbiting stars other than the Sun. Suddenly, there was a direct connection between that lecture and the work of, for instance, a number of my colleagues at the Max Planck Institute for Astronomy who are searching for just those exoplanets.

The connection is the following: When we say that a planet is orbiting a distant star, that is not strictly correct. In reality, the star and its planet both orbit their common center of gravity. Of course, the star has much more mass than the planet. That’s why the center of gravity is very close to, if not inside the star. Hence, the planet is moving quite a lot while the star is wobbling around rather moderately. Still, unless we are seeing the planet’s orbit from the top, the star will move very slightly towards and away from us, the observers. It will not move very fast; if you want to detect the presence of an exoplanet in this way, you will need to be able to measure speeds of around 10 meters per seconds (compare this with the 30 kilometers per second of Earth zipping along its orbit!).

Astronomers have long measured objects’ speeds towards and away from terrestrial observers. The recipe? Spectral lines and the Doppler effect. Spectral lines occur when an object emits lots of light, or alternatively very little light, at certain, well-defined frequencies. The Doppler effect: When an object moves towards you, all of its light is going to be shifted very slightly towards higher frequencies ("blueshift"); when it moves away from you, the shift is towards lower frequencies ("redshift"). The presence of sharply defined spectral lines allows astronomers to track these shifts, and thus the object’s motion towards or away from the observer.

And there you have all the puzzle pieces for the so-called radial velocity method of exoplanet detection: The planet orbiting the star makes the star shift ever-so-slightly as the star, too, orbits the common center of mass. The star’s shifting ever-so-slightly towards and away from terrestrial observers makes the star’s spectral lines Doppler-shift periodically towards slightly higher and lower frequencies. Measure that shift, and you can track the star’s motion; track the motion, and you can detect the exoplanet.

The devil’s in the details. Depending on how light or massive the planet is, the star will move only very little – as little as a few meters per second or even less (compare this with the 30 km/s of Earth zipping along its orbit!). You need to measure very precisely to measure the corresponding shifts of a millionth of a percent or less, and that means: you need very precise standards do measure against! This is where frequency combs come into their own. 

That is what caught my attention back in 2010 in Hänsch’s talk. And just now, with almost perfect timing, just as I’m gearing up for my next Lindau meeting, I came across an announcement by the European Southern Observatory (ESO; full disclosure: a colleague and I help with ESO’s German outreach efforts) describing the first test of a frequency comb coupled with HARPS, a precision spectrograph that has proved a very successful planet hunter. 

The ESO announcement is a bit hazy on the numbers, but it does seem to say that, with the new technique, HARPS should be able to measure speeds in the 10-centimeter-per-second range characteristic for the wobble of a star like the Sun, caused by a planet like the Earth.

Markus Pössel