Measuring gravitational radiation

-March 04, 2013

As gravity waves propagate through space, they warp spacetime. The effect is similar to when a pebble is dropped into a pond causing outgoing ripples to warp its surface. Where those ripples are transverse—up-and-down—waves, gravitational waves are tensor waves which expand in one direction while contracting in the perpendicular direction.

Warped space changes lengths and times. If you hold two rulers perpendicular to each other and a gravity wave passes by, one ruler expands as the other ruler contracts. If the amplitude of the gravity wave is large enough, you should be able to measure the expansions and contractions. At least that’s what Einstein predicted and indirect evidence bears it out.

Last time, I told you how high intensity gravitational radiation can be formed by orbiting neutron stars and black holes. Einstein’s theory of general relativity does an awesome job predicting the rate of gravitational energy radiated by the Hulse-Taylor Pulsar. (Check that link, it’s pretty sweet indirect evidence for gravity waves).

To observe gravity waves directly, we need a pair of rulers and the ability to measure tiny changes in their lengths. That is, we need an interferometer; in particular, a LIGO  (laser interferometer gravitational-wave observatory). The US National Science Foundation has built two of them (you always need two so that one can confirm the observation of the other). There’s one in Livingston Louisiana and one in Hanford Washington and they cost $292M to build and about $30M/year to operate.


Figure 1: A Michelson-Morley interferometer (image courtesy of University of Glasgow).

LIGO operates on a brilliantly simple premise. As shown in Figure 1, an interferometer consists of a laser beam and three mirrors. The laser beam first hits a beam splitter. The beam splitter is a half-silvered mirror at a 45 degree angle to the beam. Since it’s half-silvered, half of the beam reflects upward and the remaining half transmits through. The two components of the beam travel down separate legs of the interferometer to a mirror where they are reflected back toward the half-silvered mirror.

The beam that originally reflected from the beam-splitter now transmits toward a detector. The beam that had transmitted through the beam-splitter is now reflected toward the detector. At this point, the two beams overlap into a single beam focused on the detector. The overlapping beams interfere like waves in a bathtub: if a trough coincides with a peak you see a dark spot, and when two peaks or two troughs coincide, you get bright spots, peaks or troughs that are twice as tall (or deep) as the initial wave.

When the length of one leg of the interferometer changes by a full wavelength, the detector sees a dark spot as the peak of one beam coincides with the trough of the other, and then a bright spot as the peaks coincide. A simple interferometer can measure length variations of at least a quarter of the wavelength of the light from the laser. The LIGO interferometers can measure variations of an attometer, 10-18 m, about a thousandth the diameter of a proton.

LIGO started operating in 2000 and has yet to see a gravity wave (because they’re either hella weak or don’t exist).

Beverly Berger, a physicist who used to be the National Science Foundation Program Director for the LIGO Project and is now a collaborator on the experiment, says, “Two neutron stars in orbit with each other are said to be inspiraling. As the system loses energy to gravitational waves, the orbital frequency increases because the neutron stars fall toward each other. This system produces the chirp.”


Figure 2: Livingston Louisiana LIGO installation (image courtesy LIGO).

That chirp lasts about two seconds and should (if Einstein was right) generate gravity waves visible at LIGO. A chirp signal, named after the sound of a bird, consists of a rapid increase in frequency and amplitude over a short period of time. As the gravity chirp passes through the interferometer, it shrinks one arm while expanding the other, creating tiny length variations at increasing frequencies and amplitudes—a tiny, but obvious signature.

By scanning the cosmos, astronomers predict that roughly 0.2 observable inspiraling chirp events should have occurred in the last decade, consistent with the zero that have been seen. However, LIGO has been upgraded to Advanced LIGO and, with ten times its original sensitivity, should either see about 70 events (40 from inspiraling neutron stars, 20 from inspiraling pairs of black holes and 10 from neutron star-black hole systems) or find a problem with general relativity.

Other than confirming yet another one of Einstein’s predictions (he’s yawning in his grave), Berger says, “The idea behind LIGO is to look at the universe with gravitational waves the way that astronomers look at it with electromagnetic waves. We have no idea what it looks like in this gravity dimension."

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