A data-analysis strategy for detecting gravitational-wave signals from inspiraling compact binaries with a network of laser-interferometric detectors

TL;DR

This paper presents an efficient data-analysis strategy using maximum-likelihood methods for detecting gravitational waves from inspiraling binaries with a global network of interferometers, optimizing parameter searches and computational costs.

Contribution

It introduces an analytical maximization over four parameters and an efficient Fourier-based approach for the remaining parameters, improving detection strategies for gravitational-wave networks.

Findings

Analytical maximization over four parameters reduces computational complexity.

Fast Fourier Transform accelerates the search over the time of arrival.

Results include sensitivity estimates and source localization for LIGO and VIRGO networks.

Abstract

A data-analysis strategy based on the maximum-likelihood method (MLM) is presented for the detection of gravitational waves from inspiraling compact binaries with a network of laser-interferometric detectors having arbitrary orientations and arbitrary locations around the globe. The MLM is based on the network likelihood ratio (LR), which is a function of eight signal-parameters that determine the Newtonian inspiral waveform. In the MLM-based strategy, the LR must be maximized over all of these parameters. Here, we show that it is possible to maximize it analytically over four of the eight parameters. Maximization over a fifth parameter, the time of arrival, is handled most efficiently by using the Fast-Fourier-Transform algorithm. This allows us to scan the parameter space continuously over these five parameters and also cuts down substantially on the computational costs. Maximization of the LR over the remaining three parameters is handled numerically. This includes the construction of a bank of templates on this reduced parameter space. After obtaining the network statistic, we first discuss `idealized' networks with all the detectors having a common noise curve for simplicity. Such an exercise nevertheless yields useful estimates about computational costs, and also tests the formalism developed here. We then consider realistic cases of networks comprising of the LIGO and VIRGO detectors: These include two-detector networks, which pair up the two LIGOs or VIRGO with one of the LIGOs, and the three-detector network that includes VIRGO and both the LIGOs. For these networks we present the computational speed requirements, network sensitivities, and source-direction resolutions.