This report gives a brief summary of what gravitational waves are and why they could be important. It describes several sources of gravitational waves and puts them into three distinct types: burst, periodic, and stochastic sources. It discusses various ways of detecting these waves, and problems associated with such methods, with a focus on two types of ground based detectors: resonant bar, and laser interferometer detectors. There is a look at space based detection systems with an overview of the LISA mission for a space based laser interferometer.
As the many major laser interferometer gravitational wave (GW) detector projects near completion, in terms of construction and noise analysis/reduction, and will soon be operational I am going to look into the possible astrophysical importance of these detectors with regards to our understanding of the workings of the universe, as well as a bit of the history behind them.
The revolution in our understanding of the universe, which could take place as a product of the study of gravitational waves, has been compared to the difference in understanding caused by the introduction of radio astronomy to the purely visual astronomy that had taken place previously. Radio astronomy showed a far more violent universe than was seen before when compared to visual observations. Still, radio waves and light waves are part of the same spectrum, although at wildly different wavelengths, whereas GWs are a completely different phenomenon. This means that study of GWs could prove many times more revolutionary, with it providing information on some of the most violent events in the universe, structure of galaxies and even the formation of the universe.
I am going to try and describe what we understand about the theory of gravitational waves and their production from different sources, although without a thorough mathematical description, as this is beyond the need of this report. I am also going to provide an overview of different types of gravitational wave detector that have been constructed or postulated, along with their theoretical sensitivities and noise sources, with a more detailed look at the laser interferometer type of detector.
What are Gravitational Waves?
When the theory of gravity was first published by Newton in his Philosophiae Naturalis Principia Mathematica in 1686, it was very successful in describing the mechanics of the observed world and especially planetary motions. Within Newton’s equation for gravitational potential, there was no time derivative, meaning that the potential would be felt instantaneously at any distance from its source. Newton’s theory remained as the only description of gravity until Einstein published his Theory of General Relativity in 1915, from which he postulated the existence of gravitational waves. Einstein showed that gravity is actually a product of the curvature/geometry of space-time, which is induced by the distribution of mass and energy. Einstein’s theory included a time derivative in his equations that showed that a gravitational field would propagate at a specific speed, and therefore not act instantly over any distance. If the gravity source were time-varying , it would produce a time varying gravitational field (analogous to an electromagnetic field) which would be a wave in the structure of space-time, propagating away from the source i.e. a Gravitational Wave. The existence of GWs and their emission from various sources has since been studied by many people, using different approximate mathematical treatments, to determine their possible amplitudes, energies and waveforms.
In describing GWs physically and mathematically it is easiest to make some approximations. One of the main things that has to be accounted for is the fact that gravity is non-linear with many contributions to background curvature of space-time. Generally, the lengthscales over which you get variation in the curvature of space-time are much greater than those over which the GWs vary, and therefore the two contributions to the curvature can be split up. Also from the equations it can be shown that, like light, there are two polarisation states of GWs, called + and x polarisations because of the orientation of their force fields. Unlike light, GWs are generally unaffected by their passage through matter and are quadrupolar in manner, which means that they have motion simultaneously in two directions, i.e. stretch or shrink space. GWs can only be emitted by objects or systems which are not spherically symmetric. There are several other approximations and formalisms that are used when describing the emission and propagation of the waves, both of which require different mathematical analyses, but these are too complex to go into here.
In this report I will omit giving any value for the dimensionless amplitude of a GW from a particular source, as these values are liable to vary from source to source and over different distances, and any values given here could well be greatly underestimated or overestimated due to the limited knowledge we have. The one thing that should be known is that the dimensionless amplitude is extremely small for any GW, and they will therefore be very difficult to detect. The energy carried by a GW also varies from source to source.
Sources of Gravitational Waves
Different types of astrophysical event produce different types of gravitational wave; there are burst sources, which produce a pulse of radiation; periodic sources, which produce a continuous, monochromatic GW; and stochastic sources, which are the sources of background GWs. Theoretical models of many different sources have been calculated, although not all these sources are known to actually exist in the universe, but could exist theoretically. Different sources are covered in more detailed below.
Detection of Gravitational Waves
There are several methods by which we expect to be able to observe GWs which all must somehow detect a strain in space caused by the GW. These various methods have different frequency ranges and sensitivities at which they are able to detect. With the various types of detectors a fairly large spectrum of frequencies can be observed. The two main methods at the moment being extensively researched are both ground based and are the resonant bar detectors and the laser interferometer detectors. Both types of detectors are sensitive in the frequency range of a few Hz to a few kHz. In general a detector will consist of two test masses, of which a displacement can be measured between them.
Detection of waves, initially at least will rely on computed waveforms from possible sources, for without these we wouldn’t know what to look for in the results. A physicist called Wai-mo Suen has managed to write a program which is able to solve General Relativity equations for GW emitting systems, which is no mean feat as the equations are very messy and can have thousands of terms in them along with a varying co-ordinate system. With this program and the best supercomputers these waveforms are being calculated by various groups to eventually build up a library of different sources, which can be used as starting points for searches and identifications. Even with the program and supercomputers only the simplest events, such as head on collisions of neutron star (head on collisions are very unlikely, with them generally being glancing), have been accurately calculated so far.
Resonant bar detectors
Resonant bar detectors were the first type of detector used to try and detect GWs, with many initial experiments being carried out by Joseph Weber in the 1960’s (Weber originally thought he had detected GWs due to coincidences in readings from several detectors, but later repeats of the test by other groups found no evidence to support this). Weber’s general form of a bar detector is a heavy cylinder of aluminium, suspended around its circumference, with transducers fixed around the centre of the bar, and all placed inside a vacuum chamber. The bar can be thought of as two masses with a spring between them. A GW incident on the bar will set up mechanical oscillations in the bar, which can be measured as a displacement by the transducers and then be amplified. The type of metal needs to be chosen for a high quality factor, meaning that when excited, the bar will continue to oscillate for a relatively long period, thereby increasing the sensitivity. The main limit on the sensitivity of such a detector is thermal motion of the bar, which will produce a background noise. To try and reduce this effect the bar can be cooled. With liquid helium bar temperatures of 4 K have been achieved. Another way to increase the sensitivity of the bar is to increase its mass which reduces the effect of thermal noise, but there are practical limitations to how heavy a bar can be. Better suspension, to further isolate the bar from external vibrations, has also been developed. There will be other spurious random noise events which would have to be reduced by having two or more detectors working in coincidence. To detect GWs of different polarisation and orientation several differently oriented bars are needed.
There are several groups around the world working with bar detectors and improving the sensitivity of their devices all the time. There were experiments in 1991 to cool the detectors to even lower temperatures. As the sensitivities of the bar become better, the transducers have to become less noisy to achieve the maximum sensitivity. Also being looked into are spherical bars, because these can be more massive and they are resonant in 5 different modes, effectively giving 5 different detectors in one, both factors which will increase sensitivity. There has been work on a form of spherical detector with a truncated icosahedral shape. The current best detectors should be sensitive enough to be able to detect a gravitational collapse within our galaxy with an energy of a few percent of a solar mass, although to get a reasonable event rate for this distances would have to be further, requiring an improvement in energy resolution of the system. This could be achievable with spherical detectors.
A main drawback of resonant bar detectors is that they have only a small frequency range around there fundamental natural frequency, which is a property of the speed of sound in the bar material and their size.
Laser interferometer detectors (beam detectors)
The basic principle of a beam detector is that of a Michelson interferometer, with the mirror being attached to the suspended test masses. Laser light is split by a beam splitter into two perpendicular beams, which each travel a certain distance to the respective mirrors, are reflected and then recombined at the beam splitter. The interference pattern of the resulting recombined beam depends on the difference in path length of two arms. A GW incident on the device will induce a difference in the arm lengths, which will show as a certain interference pattern. Due to the nature of GWs, if they are polarised in the direction of the interferometer arms, they will produce an increase in one arm and a corresponding decrease in the other arm, thereby doubling the difference. There are variations on this simple design to create more sensitive detectors, like simply increasing the arm lengths and the use of Fabry-Perot cavities. There are many potential noise sources in these systems, which will be looked at later, and much time has been spent on analysing them in attempts to reduce their effect. The frequency range from these detectors is wideband.
In the late 1970’s and 1980’s prototypes of beam detectors ranging in size from 1-40 m were made to test and improve the design. Some detectors were able to achieve about five times greater sensitivity than the best bar detectors at the time. There are several teams currently working on beam detectors with arm lengths in the km scale. The most advanced and biggest project is LIGO (Laser Interferometer Gravitational-Wave Observatory) which is jointly run by Caltech and MIT and shall be talked about more extensively later. Others include VIRGO (Italian and French) with a 3km detector, GEO-600 (German and British) with a 600m detector, and TAMA-300 (Japanese) with a 300m detector. The set-up of these detectors can be changed when trying to detect waves from different sources, i.e. at different wavelengths, due to noise sources being different under different regimes. When all these detectors come on-line they will be able to co-operate in coincidence searches, and also provide positional information of sources with a precision of up to 0.5°.
Noise in laser interferometers
The noise sources in any GW detector are one of the most important things to be considered for analysis, as these can be large given the weakness of GWs, and if the noise was not taken into account no coherent signal could ever be seen. Here I shall go over some of the noise sources for beam detectors and what can be done to reduce them.
LIGO is an American based laser interferometer project, which will eventually consist of two 4km arm length interferometers at different locations in the US. The facilities started construction in 1992 and were supposed to come on-line for observing before the turn of the century, unfortunately this didn’t happen and LIGO still has yet to make any observations. The LIGO facilities, which have a large L shape, have been designed so that they can accommodate a number of different interferometers of 2 and 4km arm length, and so that different experiments can be fitted for observing various sources. The test masses and optical paths are all housed in vacuum chambers to prevent the air molecules causing unnecessary noise. There is also the opportunity of fitting more advanced detector systems. In its first stage of operation LIGO will not work at full sensitivity using the full arm lengths, with initial testing being made with the 2km arm lengths, making it comparable to the other projects such as GEO-600. The most recent development is the “first lock” of a 2km detector at the Hanford, Washington site in October 2000. This involved the first time laser light had been resonated throughout the entire system, with the mirrors also being locked into position to great precision. Now this has been done, work can be begun on tuning the detector to its maximum sensitivity. There will have to be a great deal of testing but it is hoped that the detector will eventually be able to start proper scientific observing in 2002. The next step will be to bring on line the 4km detector in Louisiana, and then the 4km in Washington. When these are up and running they will combine to make the most sensitive GW detector we have. One of the main sources that such detectors will be looking for, due to their probable relatively high event rate and strong emission, are the coalescence of neutron star and black hole binaries.
The Japanese TAMA300 detector was the first of this new generation of interferometers to achieve full lock, which was in May 1999, and has already carried out a short search. Improvement on this instrument are continuing. The recording of data from all the interferometers has been standardised to a format developed by the VIRGO team, to aid comparisons between detectors.Space-based detectors
Although as of yet gravitational waves have not been detected experimentally, they have been inferred to exist with close observance to general relativity’s predictions. This happened when two astronomer, Hulse and Taylor, discovered a binary system with one object being a pulsar and the other being another massive compact object, most likely a neutron star. After years of observation of this system, and study of its rotation, it has been shown to be losing energy as if it were radiating it away via GWs. This system has now been studied for over 25 years, providing very accurate data that fits very well with general relativity, and could be said to prove the theory.
A couple of things that could be established fairly quickly by observing GW from a extragalatic sources, if accompanied by electromagnetic radiation, are whether GWs travel at the speed of light and a more accurate value for Hubble’s constant.
There is still lots of effort to be put in and progress to be made in the search for GWs, but this needs to continue with current projects and new projects such as LISA. This new way of looking at the universe will open up the world of physics and astronomy with many new possibilities. It will provide a way of probing the origins of the universe, and events that could show how structure formed within the universe. It could also show objects that have yet to even be predicted, but will mainly offer new insight and understanding of objects from which little knowledge can be gleaned by electromagnetic radiation. Along with all of this GW studies could be a way to prove, improve or overthrow one of the biggest scientific breakthroughs of the twentieth century: general relativity. These goals are within sight and with enough interest and investment could provide a scientific revolution.
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