(ed.). Gravitational waves (IOP, 2001)(422s).

Gravitational-wave observables 27the gravitational wave. Essentially in electromagnetism one detects the power inthe radiation, while for gravitational radiation, as we have said before, one detectsthe wave coherently.Let us consider now what we can infer from a detection. If the gravitationalwave has a short duration, of the order of the sampling time of the signal stream,then each detector will usually give just a single number, which is the amplitudeof the wave projected on the detector (a projection of the two polarizations h +and h × ). If the wave lasts more than one sampling time, then this information isa function of time.If the signal lasts for a sufficiently long time, then both the amplitude andthe phase of the wave can be affected by the motion of the detector, which movesand turns with the motion of the Earth. This produces an amplitude and phasemodulation which is not intrinsic to the signal. If the signal’s intrinsic form isunderstood, then this modulation can be used to determine the location of thesource. We distinguish three distinct kinds of signals, from the point of view ofobservations.Bursts have a duration so short that modulation due to detector motion is notobservable. During the detection, the detector is effectively stationary. In thiscase we need at least three, and preferably four, interferometers to triangulate thepositions of bursts on the sky and to find the two polarizations h + and h × . (Seediscussions in Schutz 1989.) A network of detectors is essential to extract all theinformation in this case.Continuous waves by definition last long enough for the motion of thedetector to induce amplitude and phase modulation. In this case, assuming asimple model for the intrinsic signal, we can use the information imprinted onthe signal (the amplitude modulation and phase modulation) to infer the positionand polarization amplitude of the source on the sky. A single detector, effectively,performs aperture synthesis, finding the position of the source and the amplitudeof the wave entirely by itself. However, in order to be sure that the signal is not anartefact, it will be important that the signal is seen by a second or third detector.Stochastic backgrounds can be detected just like noise in a single detector.If the detector noise is well understood, this excess noise may be detected asa stochastic background. This is closely analogous to the way the originalmicrowave background detection was discovered.A more reliable method for detecting stochastic radiation is the crosscorrelationbetween two detectors, which experience the same cosmological noisebut have a different intrinsic noise. Coherent cross-correlation between twodetectors eliminates much detector noise and works best when detectors are closerthan a wavelength.In general, detection of gravitational waves requires joint observing by anetwork of detectors, both to increase the confidence of the detection and toprovide accurate information on other physical observables (direction, amplitudeand so on). Networks can be assembled from interferometers, bars, or both.