Observing binary inspiral in gravitational radiation: One interferometer

TLDR

LIGO’s two nearly co‑aligned interferometers provide a joint sensitivity comparable to a single, more sensitive instrument, and the optimal recycling‑frequency parameter depends on whether the goal is to maximize detection rate or measurement precision. The study aims to assess how well individual LIGO/VIRGO‑like interferometers can detect inspiralling binary systems and determine their properties, and to identify the recycling‑frequency values that optimize either detection rate or measurement precision. Using a leading‑order quadrupole radiation model, the authors compute detection rates, observable ranges, and parameter‑precision estimates for single interferometers of initial and advanced LIGO, and examine how these metrics vary with the recycling‑frequency setting. Advanced LIGO is projected to observe roughly 69 neutron‑star binary coalescences per year with SNR > 8, of which about 7 per year will originate from distances beyond 950 Mpc.

Abstract

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 evolution of a binary system as driven exclusively by leading order quadrupole gravitational radiation. To assess the sensitivity, we calculate the rate at which sources are expected to be observed, the range to which they are observable, and the precision with which characteristic quantities describing the observed binary system can be determined. Assuming a conservative rate density for coalescing neutron star binary systems we expect 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. We explore the sensitivity of these results to a tunable parameter in the interferometer design (the recycling frequency). The optimum choice of the parameter is dependent on the goal of the observations, e.g., maximizing the rate of detections or maximizing the precision of measurement. We determine the optimum parameter values for these two cases.