Detection of Gravitational Waves

3 Detection of Gravitational Waves

Gravitational waves are most simply thought of as ripples in the curvature of space-time, their effect being to change the separation of adjacent masses on earth or in space; this tidal effect is the basis of all present detectors. Gravitational wave strengths are characterised by the gravitational wave amplitude h, given by

where $ΔL$ is the change in separation of two masses a distance $L$ apart; for the strongest allowed component of gravitational radiation the value of $h$ is proportional to the third time derivative of the quadrupole moment of the source of the radiation and inversely proportional to the distance to the source. The radiation field itself is quadrupole in nature and this shows up in the pattern of the interaction of the waves with matter.

The problem for the experimental physicist is that the predicted magnitudes of the amplitudes or strains in space in the vicinity of the earth caused by gravitational waves even from the most violent astrophysical events are extremely small, of the order of 10^–21 or lower [83 ]. Indeed current theoretical models on the event rate and strength of such events suggest that in order to detect a few events per year – from coalescing neutron star binary systems for example – an amplitude sensitivity close to 10^–22 over timescales as short as a millisecond is required. If the Fourier transform of a likely signal is considered it is found that the energy of the signal is distributed over a frequency range or bandwidth which is approximately equal to 1/timescale. For timescales of a millisecond the bandwidth is approximately 1000 Hz, and in this case the spectral density of the amplitude sensitivity is obtained by dividing 10^–22 by the square root of 1000. Thus detector noise levels must have an amplitude spectral density lower than $≃$ 10^–23 Hz^–1/2 over the frequency range of the signal. Signal strengths at the earth, integrated over appropriate time intervals, for a number of sources are shown in Figure 1 .

Figure 1: Some possible sources for ground based and space-borne detectors.

The weakness of the signal means that limiting noise sources like the thermal motion of molecules in the detector (thermal noise), seismic or other mechanical disturbances, and noise associated with the detector readout, whether electronic or optical, must be reduced to a very low level. For signals above $≃$ 10 Hz ground based experiments are possible, but for lower frequencies where local fluctuating gravitational gradients and seismic noise on earth become a problem, it is best to consider developing detectors for operation in space [19 ].

3.1 Initial detectors and their development
3.2 Long baseline detectors on Earth