Going Further 10.6: Gravitational Wave Observatories

Like other waves, gravitational waves carry energy, and also like other waves, the energy they carry is proportional to the square of their amplitude. However, gravitational waves are extraordinarily difficult to detect.

Gravitational waves are expected to be waves that both stretch and compress the spacetime fabric between a collection of freely falling objects as they pass by the objects. The motion expected for the objects is shown in Figure B.10.6. The motion essentially stretches and compresses a circle of objects such that they are distorted into an ellipse.

Figure B.10.6: As a gravitational wave passes a collection of objects, it distorts their distances from each other. In the figure, a collection of objects that is originally in a circle is distorted into a set of ellipses as the wave passes by. The distortion is not permanent, and the objects return to their original orientation (yellow circles) once the wave is past. Credit: NASA/SSU/ Aurore Simonnet

However, the amplitude of the distortion caused by a gravitational wave is much smaller than our figure shows. The maximum difference in distance between any two of the objects (the diameter of the circle) will not change by more than 1 part in 10²¹. So, if we have a collection of freely falling ball bearings arranged in a circle 1 meter in diameter, a passing gravitational wave would displace some of the ball bearings by at most 10^–21 m. This change is far too small to be measured by any experimental apparatus. But if we could make the circle large enough, perhaps we would be able to measure the displacement of the ball bearings. This is the strategy employed by the National Science Foundation’s Laser Interferometer Gravitational-wave Observatory, or LIGO. LIGO operates telescopes at two physically distinct locations (Hanford, Washington and Livingston, Louisiana). Other countries operate gravitational wave detectors as well, including Italy (VIRGO), Germany (GEO) and Japan (KAGRA). A new facility is also being planned in India, as a joint partnership with the United States.

Figure B.10.7: The Laser Interferometery Gravitational-wave Observatory, or LIGO, consists of two L-shaped interferometers; each interferometer arm is 4 km. One is located near Livingston, LA, and the other near Hanford, WA. This image shows the LIGO interferometer near Livingston, LA. Currently being upgraded, the instruments are expected to again become operational by 2014. Credit: NSF/LIGO

LIGO does not actually use a ring of ball bearings; it uses two delicately suspended mirrors placed where ball bearing would be. Since the maximum effect is obtained when measuring displacements along perpendicular directions, LIGO uses two mirrors that lie along arms, each 4 km long and set apart at a 90 degree angle. Figure B.10.7 shows an aerial view of the LIGO telescope near Livingston, Louisiana. A laser beam is fired into a beam splitter that sends half the light down one arm and half down the other. The mirrors then reflect the light back the way it came, and the beam splitter combines the two beams back into one and sends the combined beam to a detector. Since the light all starts out in the same beam, each beam is in phase at the beginning. Additional mirrors in the arms are used to adjust the phase such that one arm’s beam differs in phase by 180 degrees from the other.

Let's consider a few cases in which we will add together two waves with different phase offsets. In the first case (shown in Figure B.10.8), the two waves are added exactly in phase. In this case, the amplitudes of the waves add, and the resulting wave has an amplitude that is the sum of the two waves. In the second case (Figure B.10.9), the two waves are added exactly out of phase (phase difference of 180 degrees).

In this situation, the two waves cancel each other out and there is no resulting wave detected. Figure B.10.10 shows the results when the two waves are added with a 90 degree phase offset. This produces a resulting wave with an amplitude that is less than the sum of the two individual waves.

Figure B.10.8: Adding together two waves with identical amplitudes and phases (top two panels) produces a resulting wave (bottom panel) that has twice the amplitude of each individual wave and which peaks at the same phase as the original waves.

Figure B.10.9: Adding together two waves with identical amplitudes that are 180 degrees out of phase (top two panels) produces a resulting wave (bottom panel) that has zero amplitude (and therefore does not look like a wave).

Figure B.10.10: Adding together two waves with identical amplitudes that are 90 degrees out of phase (top two panels) produces a resulting wave (bottom panel) that has an amplitude 50% greater than either individual wave and which peaks at a phase between the two original peaks.

Since part of the design of the LIGO interferometer is to set the beams in the different arms to have a 180 degree phase difference, the returning beams should exactly cancel and no light should be seen at the detector. However, if the arm lengths change slightly, then the difference in length will introduce a small difference in phase between beams from different arms and light will be detected. It is this behavior that is exploited by LIGO and that allows it to detect gravitational waves.

In LIGO, small displacements of the mirrors produce a shift in the interference pattern in the laser light. The interferometer is sensitive enough that even the tiny displacements caused by gravitational waves can be measured. For instance, given the 4 km length of the LIGO arms, the maximum displacement (Δl) expected from gravitational waves is:

Δl = ( 10^–21 ) ( 4 km ) ( 10³ m /km ) = 4 x 10^–18 m

This displacement is about 1,000 times smaller than a proton.

This is how things work ideally, but the real world is not ideal and many sources of noise can mimic the signal from gravitational waves. Some of these are simply caused by shakes in the ground that set the mirrors swinging on their suspension cables. LIGO is sensitive not only to earthquakes all over the world, but also the shaking caused by trucks passing on highways miles away and waves crashing on beaches around the world. If that is not bad enough, LIGO can also detect the changing gravitational acceleration caused by the gravity of trucks passing on nearby roads. It is clearly an exquisitely sensitive instrument. Physicists have gone to great effort to minimize the effects of noise on LIGO, upgrading its components starting in 2008 to create Advanced LIGO (aLIGO), with greatly improved sensitivity. They expect that aLIGO will be the first experiment to directly detect gravitational waves from astrophysical sources sometime after 2014.