3.1 Man-made sources

One source can unfortunately be ruled out as undetectable: man-made gravitational radiation. Imagine creating a wave generator with the following extreme properties. It consists of two masses of 103 kg each (a small car) at opposite ends of a beam 10 m long. At its center the beam pivots about an axis. This centrifuge rotates 10 times per second. All the velocity is nonspherical, so 2 vnonsph in Equation (9View Equation) is about 105 m2 s–2. The frequency of the waves will actually be 20 Hz, since the mass distribution of the system is periodic in time with a period of half the rotation period. The wavelength of the waves will, therefore, be 1.5 × 107 m, similar to the diameter of the earth. In order to detect gravitational waves, not near-zone Newtonian gravity, the detector must be at least one wavelength from the source, say diametrically opposite the centrifuge on the Earth. Then the amplitude h can be deduced from Equation (9View Equation): h ∼ 5 × 10−43. This is far too small to contemplate detecting! The story changes, fortunately, when we consider astrophysical sources of gravitational waves, where nature arranges for masses that are 1027 times larger than our centrifuge to move at speeds close to the speed of light!

Until observations of gravitational waves are successfully made, one can only make intelligent guesses about most of the sources that will be seen. There are many that could be strong enough to be seen by the early detectors: star binaries, supernova explosions, neutron stars, the early universe. In this section, we make rough luminosity estimates using the quadrupole formula and other approximations, which are usually accurate to within factors of order two, and, very importantly, they show how key observables scale with the properties of the systems. Where appropriate we also make use of predictions from the much more accurate modelling that is available for some sources, such as binary systems and black hole mergers. The detectability depends, of course, not only on the intrinsic luminosity of the source, but on how far away it is. Often the biggest uncertainties in making predictions are the spatial density and event rate of any particular class of sources. This is not surprising, since our information at present comes from electromagnetic observations, and as our earlier remarks about the differences between the mechanisms of emission of gravitational and electromagnetic radiation make clear, electromagnetic observations may not strongly constrain the source population.


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