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.

In the late summer of 2015 all the upgrades and careful preparations paid off. On September 14, 2015 at approximately 09:50 UTC, LIGO detected the first directly observed gravitational wave signal. The signal was created by the merging of two black holes into a single, more massive, black hole. As the black holes spiraled closer together, their orbital period decreased, and the gravitational waves emitted by the system increased proportionally in frequency as a result. Additionally, the amplitude of the waves also increased. The wave pattern seen by LIGO is shown in Figure B10.11. It shows the strain, discussed below, vs. time.

Figure B.10.11: The gravitational wave signals from LIGO Hanford and LIGO Livingston are shown in these plots, which have strain vs. time in each detector. Overplotted are theoretical templates from a computer simulation. At the bottom the signals from the simulation and both detectors are plotted together; the time delay between the two sites has been removed. Image Credit: Caltech/MIT/LIGO Lab

Notice how the strain increases with time. This is because the strength of the waves (their amplitude) is growing as the merger progresses. Notice also that the successive waves are squeezed closer and closer together as the two black holes approach one another. This is because the orbital frequency is increasing - the black holes are orbiting around each other faster as they approach. When the two black holes merge, the gravitational waves quickly "ring down" as the newly formed single black hole settles into equilibrium. It is rotating, but rotating single black holes do not emit gravitational waves, so the signal ceases.

But what is strain? And how does LIGO measure it?

Strain is a measure of differential stretching; it is defined as the change in length of an object divided by its un-stretched length. So if an object starts out one meter long and it gets stretched by one centimeter, the strain on it would be 1 cm / 100 cm = 0.01. Notice that strain has no units because it is a change in length (in meters, for instance) divided by a length in the same unit of measure.

Figure B.10.12: This video demonstrates how the LIGO observatories work. Gravitational waves alternately stretch and shrink the arms of the interferometer, causing the returning laser beams from each arm to alter their relative phases, and this alternating light signal allows LIGO scientists to determine the strain in each arm. Animation by T. Pyle, Caltech/MIT/LIGO Lab

LIGO consists of what is called a Michelson interferometer. In somewhat simplified terms, it has two arms, each 4 km long, that are situated at right angles from one another. See Figures B10.7 and B1012. In each arm there is a vacuum tube, and within that tube a laser beam is fired. The laser is created by shining a single laser beam onto a beam splitter, and the beam splitter sends half the beam down one arm and half the beam down the other. The beams run down the length of each arm and are reflected back by mirrors. Additional optical components in the arms tune the phase of the two beams (the alignment of their peaks and troughs) so that they are 180 degrees out of phase when they arrive at the photo detector. This causes the two beams to exactly cancel, and so no light is seen at the photo detector, as discussed above.

This kind of arrangement is extremely sensitive to changes in path length of the two beams. If one of the arms suddenly becomes longer (or shorter) than the other, the beams will no longer line up perfectly. As a result, they will not cancel each other, and a bit of light will be seen at the detector.

This is exactly how LIGO and other interferometer-based gravitational wave detectors work. As a gravitational wave passes by, it will alternately stretch one arm while shrinking the other. Then, half a phase later it will shrink the first arm and stretch the other. By measuring how the brightness at the photo detector changes, the strain of each arm can be deduced. This is what is plotted in Figure A1.

LIGO actually consists of two identical interferometers: one in Louisiana and one in Eastern Washington state. Any signal from a gravitational wave emitting source should be seen in both detectors - the Earth and other objects are transparent to gravitational waves. However, there will be a small time delay of a few milliseconds between one detector and the next. This is related to the light travel time between the two and can be used to deduce a rough location for the emitter.

The detection of gravitational waves by LIGO is the first test of general relativity in the strong-field limit. Other tests have been done in much weaker fields around Earth or the Sun, or near white dwarfs. But the fields around these two black holes were much stronger, making this detection an important indication that general relativity is valid at least up to the field strengths probed by this merger event. Detailed modeling of the ring down phase of the merger will probe even stronger fields.

There is another important aspect of this first detection of gravitational waves. It opens a new view of the Universe for us. While some of the sources LIGO is expected to detect should also be visible in x-rays or gamma-rays, mergers like the one seen on September 14, with two merging black holes, are bright in gravitational waves, but they are expected to be completely invisible in electromagnetic waves. Without LIGO and similar instruments we would thus not even know about such events. Interestingly, the NASA Fermi Gamma-ray Space Telescope detected a weak burst of gamma-rays 0.4 seconds after the LIGO detection. The Fermi observation cannot accurately locate the origin of the gamma-rays in the sky, so it is not known if the burst is related to the gravitational wave source. Still, it is an interesting coincidence, and perhaps only that. Further detections should eventually tell us if merging black holes are accompanied by outburst of electromagnetic waves, perhaps as a result of some small amount of matter that is orbiting them. In any event, LIGO and similar experiments will reveal an entire new realm of the Universe, one that we have been utterly blind to until now.

With only two detectors it is difficult for LIGO to pinpoint the location of gravitational waves. However, soon LIGO will have company. The VIRGO detector in Italy near Pisa is another Michelson interferometer. It has arms three kilometers long and is expected to come online sometime in 2016. KAGRA is under construction in Japan. With additional detectors in India set for construction, in the future it will be possible to detect fainter signals and to localize their sources with better precision.

The direct detection of gravitational waves has been exciting for scientists and science enthusiasts worldwide. First, it is the most precise measurement ever made, and it detected the weakest signal ever detected. It also confirmed the last major prediction of general relativity in a spectacular fashion while ushering in a new tool for observing the Universe. But it has one thing in common with the indirect method used by Hulse and Taylor to study their pulsar.

When the two black holes merged, they formed a single black hole. Observations show that one of the merging objects had a mass of 29 solar masses, and the other a mass of 36 solar masses. When the merger was over, the remaining single black hole had a mass of 62 solar masses. If you compare the total mass before and after you will note that 3 solar masses is missing. Where did it go? That was the energy carried away by the gravitational waves. So just as Hulse and Taylor were able to deduce the presence of gravitational waves by the slow trickle of energy out of the binary pulsar system they studied, we could deduce the existence of gravitational waves by the much more dramatic loss of energy in this merging black hole system – assuming we had some way of seeing it at all. But we don’t have to. LIGO has shown us the waves themselves.