Gravitational wave spectrum

Whereas astrophysical electromagnetic waves are typically much smaller than their sources, ranging from a few kilometres down to sub-nuclear wavelengths, gravitational waves are larger than their sources, with wavelengths starting at a few kilometres and ranging up to the size of the Universe. A gravitational perturbation larger than the Universe would not be called a wave because it would not have any detectable oscillation; in fact, it would not be detectable at all.

The diagram below shows the amplitudes of some known and expected sources across the full gravitational-wave spectrum, along with the sensitivities of some current and planned detectors. The horizontal axis 𝑓𝑔𝑤 (or λ𝑔𝑤) is straightforward, but the vertical axis requires some explanation: we want to define a characteristic strain 𝑐 that can be compared to a detector noise 𝑛 to indicate a source's detectability. This necessarily depends on the nature of the source's waveform ℎ(𝑡) and how it can be identified in the detector output.

The signal-to-noise ratio of a given source in a given detector is (approximately) given by 𝑐/ℎ𝑛. Typically this depends on the observation time 𝑇. In the following diagram we assume a canonical value of 𝑇 = 1 year: for continuous sources, this sets the number of cycles of integration 𝑁; for transient sources, we show the final 1 year of the signal from the loudest transient that we expect to occur in a given 1 year period. (For gravitational-wave frequencies below 1/year we treat 𝑁≈1: signals are only detectable if their instantaneous strain exceeds the estimated noise.)

Sources:

Detectors:

Future detectors:


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