2.3 Direction to a source

Gravitational wave antennas are linearly-polarized quadrupolar detectors and do not have good directional sensitivity. As a result we cannot deduce the direction to a source using a single antenna. One normally needs simultaneous observation using three or more detectors so that the source can be triangulated in the sky by measuring the time differences in signal arrival times at various detectors in a network. Ground-based detectors have typical separation baselines of 6 L ∼ 3 × 10 m, so that at a wavelength of λ = 3 × 105 m = 1 ms (a frequency of 1 kHz) the network has a resolution of δ𝜃 = λ ∕L = 0.1 rad. If the amplitude SNR is high, then one can localize the source by a factor of 1/SNR better than this.

For long-lived sources, however, a single antenna synthesizes many antennas by observing the source at different points along its orbit around the sun. The baseline for such observations is 2 AU, so that, for a source emitting radiation at 1 kHz, the resolution is as good as Δ 𝜃 = 10−6 rad, which is smaller than an arcsecond.

For space-based detectors orbiting the sun, like LISA, the baseline is again 2 AU, but the observing frequency is some five or six orders of magnitude lower, so the basic resolution is only of order 1 radian. However, as we shall see later, some of the sources that a space-based detector will observe have huge amplitude SNRs in the range of SNR ∼ 103 – 104, which improves the resolution to arcminute accuracies in the best cases.

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