Observing binary inspiral in gravitational radiation: One interferometer.

Close binary systems of compact objects with less than ten minutes remaining before coalescence are readily identifiable sources of gravitational radiation for the United States Laser Interferometer Gravitational-wave Observatory (LIGO) and the French-Italian VIRGO gravitational-wave observatory. As a start toward assessing the full capabilities of the LIGO/VIRGO detector network, we investigate the sensitivity of individual LIGO/VIRGO-like interferometers and the precision with which they can determine the characteristics of an inspiralling binary system. Since the two interferometers of the LIGO detector share nearly the same orientation, their joint sensitivity is similar to that of a single, more sensitive interferometer. We express our results for a single interferometer of both initial and advanced LIGO design, and also for the LIGO detector in the limit that its two interferometers share exactly the same orientation. We approximate the secular evolution of a binary system as driven exclusively by its leading order quadrupole gravitational radiation. Observations of a binary in a single interferometer are described by four characteristic quantities: an amplitude A, a chirp mass M, a time T , and a phase ψ. We find the amplitude signal-to-noise ratio (SNR) ρ of an observed binary system as a function of A and M for a particular orientation of the binary with respect to the interferometer, and also the distribution of SNRs for randomly oriented binaries at a constant distance To assess the interferometer sensitivity, we calculate the rate at which sources are expected to be observed and the range to which they are observable. Assuming a conservative rate density for coalescing neutron star binary systems of 8 × 10−8 yr−1 Mpc−3, we find that the advanced LIGO detector will observe approximately 69 yr−1 with an amplitude SNR greater than 8. Of these, approximately 7 yr−1 will be from binaries at distances greater than 950 Mpc.