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Gravitational Wave Observatories

v1.0.1 / 01 mar 02 / greg goebel / public domain

* By the end of the 20th century, astronomers had come to realize that the seemingly stable skies were full of unusual and sometimes violent events whose properties were at the limits of what was known by physics. Optical and radio telescopes were not enough to obtain a detailed understanding of these events, and so astronomers have sought new techniques to probe the Universe.

One of these new techniques is the observation of "gravitational waves" caused by such events. Gravity waves are fluctuations in spacetime that can cause tiny variations in the length of objects as the waves pass by. These variations are so small that so far no one has been able to detect them with any certainty, but new "gravitational wave observatories" are now coming on line that should open the door to the gravitational wave sky.

This document provides a short survey of the principles and details of gravitational wave observatories.

[4] LIGO


* Albert Einstein's General Theory of Relativity, or just General Relativity for short, describes gravity as a curvature of spacetime. One of the implications of General Relativity is that the spacetime distortions set up by a rapid displacement of mass will propagate through the Universe at the speed of light, as gravitational waves.

As such gravitational waves propagate through space, they distort the shape of space by a tiny amount. This means that in principle their passage can be detected by monitoring the motion of carefully isolated test masses. In the early 1960s, Joseph Weber of the University of Maryland at College Park built the first gravitational wave detectors using such principles, and several other detectors similar to his were built in the following decades.

In these detectors, the test masses were huge solid cylindrical bars, usually made of aluminum. The best bar detectors have sensitivities in the range of 1 in 10^18 parts. This sounds impressive, but the motions caused by gravitational waves are very tiny, and no bar detector has ever unambiguously detected a gravitational wave.

Efforts are being made to improve the sensitivity of bar detectors that may allow them to detect the gravitational "fingerprints" of cataclysmic events in the distant cosmos, but another approach, using laser beams and "optical interference" techniques, promises much more sensitivity and flexibility.

This "laser interferometry" approach has now resulted in the US "Laser Interferometer Gravitational Wave Observatory (LIGO)". LIGO was completed in late 1999 and is scheduled to go into operation in mid-2002 after careful setup and calibration. Observatories similar to LIGO are being built overseas, and researchers are considering a space-based follow-on.



* To see how gravitational waves affect matter, suppose a gravitational wave moves through space. Imagine placing a long, flexible rubber hose with a circular cross section along the direction of the wave's travel, and observing the change in the hose at a cross section.

As the wave moves up the hose, it distorts the cross section into a vertical ellipse; then a half wave later into a horizontal ellipse; then a vertical ellipse again; and so on, until the gravitational wave has passed. The cross section of the hose then returns to its normal circular form.

Similarly, suppose four masses are arranged at the four points of a compass in the horizontal plane, and a gravitational wave passes through the plane from above. At one point, the distance between the north-south masses is decreased, and the distance between the east-west masses is increased. A half wave later, the reverse is true.

If the gravitational wave passes through through the masses along the direction of the plane, say in the east-west direction, it has no effect on the masses in the direction of its motion. The east-west masses remain fixed in position, while the distance between the north-south masses increases and decreases as the wave passes through the plane.

If the gravitational wave passes through at other orientations, intermediate effects are produced.

* Gravitational waves are produced by mechanisms analogous to those that produce electromagnetic waves. An electrically charged moving object produces electromagnetic waves in proportion to the electric charge and acceleration of the object. Similarly, a moving mass generates gravitational waves in proportion to its mass and acceleration.

However, Newton's third law of motion, also known as the law of conservation of momentum, specifies that the acceleration of a mass in one direction must be accompanied by an acceleration of another mass in another direction, with momentum, or the product of mass and velocity, in both directions being equal. This means that the other mass generates gravitational waves as well, and the gravitational waves of the two masses tend to cancel each other out.

As the masses are not in the same place, the cancellation is never complete. The amount of gravitational radiation that can escape depends on the arrangement of the masses, measured by what is called its "quadropole moment". A fully symmetrical object like a soccer ball has zero quadropole moment, but an American football has a large quadropole moment, at least for rotation around its short axis.

* Gravitational waves tend to be very weak. For example, the gravitational waves emitted by a 500 tonne steel bar rotating so fast that it is almost flying apart would distort a gravitational wave detector by only one part in 10^40, a change far too small to detect.

Gravitational waves emitted by large cosmic objects, such as binary stars, are of course much stronger. The strongest gravitational waves emitted by a binary star can distort an Earth-based gravitational wave detector by one part in 10^20, which is still faint, but possible to detect.

A binary system consisting of a tiny, superdense neutron star in a close orbit with a conventional star could be a strong gravitational wave source. The neutron star tears matter from its visible companion, and this matter emits X-rays as it falls onto the neutron star. The infalling matter may accumulate on the surface of the neutron star unevenly, and also causes it to spin more rapidly, causing the neutron star to emit gravitational waves. Such "X-ray stars" are regarded as good possible targets for a gravitational wave observatory.

Stronger gravitational wave sources are known to exist. In 1974, Russell Hulse and Joseph Taylor of Princeton discovered the first binary star system composed of a pair of neutron stars, orbiting each other in a tight, fast orbit. Two such great masses orbiting at such speed make for an excellent gravitational wave generator. More such binary neutron star systems have been observed.

The orbital period of such binary neutron star systems seems to be slowing down at the rate expected due to loss of orbital energy by gravitational radiation. This is strong, if indirect, evidence for the existence of gravitational waves and for the validity of General Relativity. Hulse and Taylor won the Nobel prize in 1993 for their discovery of the binary neutron star system and its confirmation of General Relativity.

In time, the two stars in such binary neutron star systems will move closer to each other, until they are torn apart or collide with each other. The Hulse-Taylor binary is expected to reach such an end in about 240 million years. This catastrophic event will generate a very strong burst of gravitational waves.

Such collisions are estimated to occur about once every 1,000 years in a galaxy such as the Milky Way. The same sort of collision events in nearby clusters of galaxies would distort an Earth-based gravitational wave detector by one part in 10^22.

A binary star system containing two black holes could be an even more powerful emitter of gravitational waves, but black holes are difficult to detect, and nobody has ever identified a black hole binary. Theoreticians have speculated on the properties of such binaries, and suggest that they may be common in the cores of the spherical "globular clusters" that orbit through the halo of our Galaxy.

Another event that generates a large amount of gravitational radiation is the collapse of a massive star in a supernova explosion, forming a neutron star. Such an event will only send out gravitational waves if it happens asymmetrically, but astrophysicists suspect that is often the case. A supernova occurs in our own Galaxy about once every 30 years, and might set up a strain of one part in 10^18 in an Earth-based gravitational wave detector.

The supernova that was observed in 1987 in the Large Magellanic Cloud, a satellite galaxy of our own Milky Way, should have set up strains of about one part in 10^19, which is just a little beyond the capability of bar detectors. Supernovas in the nearby Virgo Cluster of galaxies appear several times a year, and could cause strains of one part in 10^21. Observation of gravitational waves from a supernova event would provide vital information on the somewhat mysterious processes that take place in the heart of a star as it collapses.

It may be even possible to detect the faint gravitational waves left over from the Big Bang, the primordial explosion that created the Universe, though the traces from the Big Bang may be too faint to ever be observed.



* Building a gravitational wave detector sensitive enough to pick up these extremely faint signals is a challenge. Most of the events described in the previous section would shift a mass by about 10^-21 meter, equivalent to a millionth the diameter of a proton, per meter of separation.

Weber's original bar detector involved two huge solid aluminum cylinders wired with piezoelectric transducers. There were two bars at separate locations, with only signals that affected them both recorded in order to sift out noise. Other bar detectors have been developed and are now operating in the US, Italy, and Australia, but they have produced few convincing results.

A "laser interferometer gravitational wave detector (LGD)" does not measure the distortion of masses as such. Instead, it measures the change in length of a pair of long pathways at a right angle to each other using a laser beam.

Conceptually, the two paths, or "arms", are constructed as long straight pipes, with a mirror attached to a suspended mass at the far ends. A laser beam at the junction of the two pipes is passed through a "beam splitter", a partially silvered mirror at a 45 degree angle to the incident beam, and sent down the pipes. Each split beam hits the mirror at the end of its pipe and bounces back to the junction, where the two are combined and fed to a photodetector system.

If the two recombined beams are perfectly in phase, they will add up, or "constructively interfere", and the photodetector will observe the laser light at a maximum level of brightness. If the two beams are completely out of phase, or antiphase, they will cancel out, or "destructively interfere", and the photodetector will see no laser light. Changes in the relative lengths of the two arms set up patterns of alternating light and dark.

If a gravitational wave passes through the plane of the two arms vertically, then one arm will increase in length while the other decreases in length, with the changes in length reversing a half wavelength later, and so on. With the gravitational wave passing through the plane of the two arms in the same direction as one of the arm, only one arm changes length. Intermediate effects occur if the gravitational wave passes through in other directions.

With the changes in path length, the sensor will see the laser light going dark, going to a maximum, going dark again, and so on until it returns to a stable level. This pattern of variation, or "interference fringes", can be counted to determine the change in path lengths. The stable position is usually calibrated to be dark in order to reduce the the load on the optical sensor.

Laser interferometry is used in many different contexts for exacting measurements. It essentially measures changes in length as fractions of a wavelength of the laser light used. Interferometers can measure displacements much smaller than the nucleus of an atom.

* It is possible to increase the sensitivity of a laser interferometer system by increasing the laser power and the path length over which the laser travels. The error of measuring the laser beam changes is reduced as the square root of its power, or in simpler terms to cut the error in half, laser power must be increased by four times. Increasing the path length of course increases sensitivity by the same proportion as the increase in path length.

The effective path length can be improved by bouncing the light down each arm several times, or "folding" the light beam. However, the number of bounces is limited, since if the light beam stays in the pipe too long, the passing gravitational wave will have time to change the length of the pipe through one full cycle and cancel out the measurement.

The light beam can be folded using either an "optical delay line" or a "Fabry-Perot cavity". In both cases, there are mirrors at both ends of the pipe. In an optical delay line, the laser light from the splitter passes through a hole in the entrance mirror, bounces back and forth through the pipe a number of times, and then shoots back out the hole in the entrance mirror for measurement.

In a Fabry-Perot cavity, the entrance mirror is partially silvered, allowing light to leak into the pipe and build up through reflections between the partially silvered mirror at the entrance end and the fully silvered mirror at the remote end. The light leaks back out the partially silvered mirror to be recombined.

* The extreme sensitivity of a laser interferometer means that an LGD is also subject to various sources of noise. An LGD can be affected by seismic disturbances; thermal noise in the suspended masses; and disruption of the laser beam by gas molecules.

The mass at the end of each pipe is suspended to damp out seismic noise through inertia, and the structure that supports the suspension is also set on shock mounts. Thermal noise can be reduced by climate control, and the pipes are evacuated to get rid of the gas molecules.

However, some degree of noise is unavoidable. For this reason, a proper gravitational wave observatory should actually consist of two LGDs at remote sites, with communications links between the two sites. Only events that occur at both sites within a short time window will be regarded as valid.

Three LGDs at remote sites are required to provide indication of the direction of a gravitational wave, with the direction "triangulated" from the relative delays in detecting it at the three sites.


[4] LIGO

* The idea of using laser interferometry to detect gravitational waves was dreamt up by Ranier Weiss of the Massachusetts Institute Of Technology (MIT) in the late 1960s, who formed a group to investigate the idea. He initially encountered resistance, later saying: "People threw me out of the room. They were polite about it, but you could see the snickers on their faces."

Nonetheless, he made some converts. Other groups began to experiment with the idea. Joseph Weber and his students performed the first tests of an LGD in 1972. A group was formed in Munich in 1975 to study the concept, and was followed by another in Glascow in 1970s.

In the late 1970s the California Institute of Technology, or Caltech, began a well-funded research effort on LGDs. The work was encouraged by the prestigious physicist Kip S. Thorne of Caltech, who as a student at Princeton had been one of Joseph Weber's fans. In 1983, the Caltech and MIT groups joined hands to form what became the LIGO partnership. The prime movers were Weiss; Thorne; and Ronald Drever of the University of Glascow, who was recruited and brought to Caltech.

The LIGO group built a prototype with 40 meter long arms at Caltech, and submitted a design for LIGO to the US National Science Foundation (NSF) in December 1989. The NSF included LIGO in its budget request for 1991, asking for $47 million USD as a down payment. This was a fairly steep price tag, all the more so because substantially more funding would be needed to complete the project, and there was considerable resistance to the idea. However, the LIGO partnership and their supporters managed to prevail.

Work on LIGO was directed at first by Caltech physicist Robbie Vogt, who was later replaced by another Caltech physicist, Barry Barrish. Barrish had worked on detector systems for the cancelled Superconducting Supercollider (SSC), and in fact the LIGO project benefited from the death of the SSC by acquiring many highly professional SSC "refugees".

Completing LIGO took the rest of the decade and a total of $365 million USD in NSF funding. Two facilities were formally inaugurated in November 1999, and are now being calibrated. One facility is at Livingston, Louisiana, near Baton Rouge; and the other is at Hanford, in south-central Washington state.

* Each LIGO facility has an LGD with arms 4 kilometers long, implemented as pipes 1.2 meters in diameter. The pipes are made of stainless steel, specially treated to remove traces of hydrogen that might leach out, and evacuated to 10^-12 atmosphere. The vacuum in the pipes is one of the largest vacuums on Earth, with a total volume at each facility of 10,600 cubic meters, more than the internal space of eight Boeing 747 jumbo jets. Each LGD's mirrors is made of fused silica, and the test masses supporting them hang on quartz threads. The entrance mirrors are partially silvered, allowing each pipe to act as a Fabry-Perot cavity.

Events detected by LIGO will only be considered possibly valid if they happen within 10 milliseconds of each other, which is the maximum travel time of a gravitational wave between the two facilities, which are 3,030 kilometers apart. The Hanford facility also has a second LGD sharing the same pipes as the main LGD, but with mirrors at the midpoint of the pipe, not the ends. If the main LGD actually registers a real gravitational wave rather than noise, the half-size LGD should register a similar but smaller signal.

Despite the cost of LIGO, somewhat surprisingly researchers are not sure it will detect gravitational waves in the short term. However, in 2005 improvements will begin to upgrade the system to the improved "LIGO 2" configuration, which most expect will be able to detect gravitational waves.

LIGO 2 will feature more powerful lasers; greater seismic noise immunity, possibly using electronic feedback systems; and mirrors made of single-crystal sapphire. LIGO 2 is expected to be 15 times more sensitive than the current LIGO 1. Researchers are already considering ideas for LIGO 3, such as cryogenically cooled mirrors.



* LIGO is the first major LGD observatory coming on line, but others are following close behind. An Italian-French group is now constructing the VIRGO observatory near Pisa in Italy, which will have three kilometer long interferometer arms. While the shorter arms imply less sensitivity than LIGO, VIRGO developers feel they have a superior seismic isolation system that may compensate.

A British and German group is working near Hanover, Germany, on an LGD named GEO with 600 meter arms. The Japanese have built an LGD named TAMA near Tokyo that has 300 meter long arms, and hope to scale it up in a few years. The Australian Consortium for Interferometric Gravitational Astronomy (ACIGA) is also considering an LGD of similar scale to LIGO. Once a third LGD facility comparable to the two LIGO facilities comes on line, gravitational wave hunters will be able to locate the position of gravitational wave sources in the sky.

* The true next generation LGD system will likely be space based. Gravitational wave researchers are now promoting the "Laser Interferometer Space Antenna (LISA)", which would consist of three satellites spaced in a triangle with sides 5 million kilometers long. LISA would be used to sense low-frequency gravitational waves, and would be intended to detect activities in black hole systems.

Conceptually, each LISA satellite would look like a ring with a Y-shaped core, containing a laser and telescope assembly to allow it to link up with the other two satellites. The test masses in the satellites would be cubes 4 centimeters on a side, floating freely inside the satellite.

LISA is being investigated jointly by NASA and the European Space Agency (ESA). The project has not been formally started yet, but backers hope to launch a test system soon, and have the full LISA array in space by 2010.



* I was a bit frustrated to have to list the acronyms VIRGO, GEO, and TAMA without explaining what they actually stood for. I did find websites for all the LGD projects mentioned in this text, and they were full of many details, but if they explained what the acronyms stood for, that information was buried deeper than I could find on a quick exploration.

* Sources include:

I didn't really plan on writing this document. I'd had notes from the articles by Jeffries and Waldrop cited above for the better part of a decade, gathering dust, when I came across Irion's article and decided to organize the materials I had and update them.

* Revision history:

   v1.0   / gvg / 01 jun 00
   v1.0.1 / gvg / 02 mar 02 / Minor cosmetic update.
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