Observing binary inspiral in gravitational radiation: One interferometer

TL;DR

The paper analyzes the capability of a single LIGO/VIRGO-like interferometer to detect and characterize inspiralling binaries using leading-order quadrupole radiation. By connecting the detector noise PSD to the SNR and the Fisher-information-like covariance matrix through frequency-domain moments, it quantifies how well ${\cal A}$, ${\cal M}$, ${\psi}$, and ${T}$ can be measured and how the recycling frequency influences performance. It provides concrete forecasts for detection rates and ranges for initial and advanced LIGO designs, highlighting a large improvement in the advanced era (e.g., ~69 detections per year with ${\rho}>8$, including a significant fraction beyond 950 Mpc) and showing that ${\cal M}$ can be determined with extraordinary precision. The work also discusses optimal instrument configurations for different goals and acknowledges the limitations of the quadrupole approximation, arguing for future inclusion of higher-order post-Newtonian effects to enhance information extraction from gravitational-wave observations.

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.

Figures (7)

• Figure 1: The noise power spectral density (PSD) $S_h(f)$ for the (anticipated) initial LIGO interferometers configured for standard recycling with a knee frequency of 300 Hz. The solid line shows the total PSD, while the dashed lines show the important physical limits and environmental influences that contribute to the total. For more detail, see Sec. \ref{['subsec:noise']} and table \ref{['tbl:instruments']}.
• Figure 2: The noise power spectral density (PSD) $S_h(f)$ for the (anticipated) advanced LIGO interferometers configured for standard recycling with a knee frequency of 100 Hz. The solid line shows the total PSD, while the dashed lines show the important physical limits and environmental influences that contribute to the total. In the limit that the two LIGO interferometers have identical orientations and we ignore the information available owing to gravitational wave burst arrival time differences, the (advanced design) LIGO detector noise PSD $S_h(f)$ is $1/2$ the value shown here. For more detail, see Sec. \ref{['subsec:noise']} and table \ref{['tbl:instruments']}.
• Figure 3: The sensitivity of a LIGO-like interferometer to the gravitational radiation from a coalescing binary system depends on the detailed characteristics of the interferometer through several moments of the inverse of the its power spectral density (PSD) $S_h(f)$. In particular, the signal-to-noise ratio (SNR) $\rho^2$ depends on a moment of $S_h^{-1}(f)$. Here we show how this moment (normalized to its value at a recycling frequency of 100 Hz) varies with the choice of interferometer recycling frequency. To maximize the rate at which sources are detected this quantity should be maximized. For more details see \ref{['subsec:snr-discussion']}.
• Figure 4: We define the range function ${\cal R}_\gamma$ of a LIGO-like interferometer as the distance ${d_L}$ within which a fraction $\gamma$ of the observable sources are expected to lie. We also define a characteristic distance ${\cal R}$, such that the total rate of observable sources is $4\pi{\cal R}^3\dot{{\cal N}}/3$, where $\dot{{\cal N}}$ is the rate density of sources (which we assume to be uniform). A conservative estimate of ${\cal R}$ for an advanced LIGO-like interferometer is 420 Mpc. Here we show $\gamma$ as a function of ${\cal R}_\gamma/{\cal R}$. For further discussion see Sec. \ref{['subsec:range']}.
• Figure 5: The fractional standard deviation $\sigma_{\cal M}/\widehat{\cal M}$ of the measured mass ${\cal M}$ depends on the distance to the source, the relative orientation of the source and the interferometer, and a factor $\Sigma_{\cal M}(f_c)$ that depends on the interferometer configuration ( i.e., the recycling frequency $f_c$; cf. eqn. \ref{['defn:Sigma-M']} and Sec. \ref{['subsec:cij']}). Here we show $\Sigma_{\cal M}$ as a function of $f_c$ for initial and advanced LIGO-like interferometers. In order to maximize the precision with which ${\cal M}$ can be determined, the recycling frequency should be chosen to minimize $\Sigma_{{\cal M}}$. The corresponding recycling frequency differs from that which should be chosen to maximize the rate of sources detected ( cf. fig. \ref{['fig:f7/3']}). For more details, see Sec. \ref{['subsec:cij']}.