Networks of gravitational wave detectors and three figures of merit (1102.5421v2)

Abstract: This paper develops a general framework for studying the effectiveness of networks of interferometric gravitational wave detectors and then uses it to show that enlarging the existing LIGO-VIRGO network with one or more planned or proposed detectors in Japan (LCGT), Australia, and India brings major benefits, including much larger detection rate increases than previously thought... I show that there is a universal probability distribution function (pdf) for detected SNR values, which implies that the most likely SNR value of the first detected event will be 1.26 times the search threshold. For binary systems, I also derive the universal pdf for detected values of the orbital inclination, taking into account the Malmquist bias; this implies that the number of gamma-ray bursts associated with detected binary coalescences should be 3.4 times larger than expected from just the beaming fraction of the gamma burst. Using network antenna patterns, I propose three figures of merit that characterize the relative performance of different networks... Adding {\em any} new site to the planned LIGO-VIRGO network can dramatically increase, by factors of 2 to 4, the detected event rate by allowing coherent data analysis to reduce the spurious instrumental coincident background. Moving one of the LIGO detectors to Australia additionally improves direction-finding by a factor of 4 or more. Adding LCGT to the original LIGO-VIRGO network not only improves direction-finding but will further increase the detection rate over the extra-site gain by factors of almost 2, partly by improving the network duty cycle... Enlarged advanced networks could look forward to detecting three to four hundred neutron star binary coalescences per year.

• The paper introduces three figures of merit—triple detection rate, sky coverage, and directional precision—to evaluate and optimize gravitational wave detector networks.
• It derives a universal signal-to-noise distribution and defines 'visibility distance' to quantify improvements in sensitivity for burst signals.
• The analysis highlights significant benefits from expanding the network with additional detectors, enhancing detection rates and source localization accuracy.

Overview of "Networks of Gravitational Wave Detectors and Three Figures of Merit"

The article by Bernard F. Schutz presents a comprehensive framework for evaluating and optimizing networks of interferometric gravitational wave detectors. The work primarily entails examining the effectiveness of extending the current LIGO-VIRGO network by incorporating additional detectors such as the proposed LCGT in Japan, and potential detectors in Australia and India. The author introduces three figures of merit designed to evaluate how such networks improve sensitivity, isotropy, and sky localization capabilities in gravitational wave detection.

Key Contributions and Findings

The paper outlines a thorough approach to measure the performance and potential enhancements that additional detectors bring to gravitational wave networks. This evaluation focuses on short-duration signals, commonly referred to as bursts. The methodological innovations presented are densely technical yet pivotal for guiding the design and implementation of enhanced gravitational wave detection networks.

1. Universal Detection Distribution and Sensitivity Improvement: The author derives a universal probability distribution of signal-to-noise ratio (SNR) for detected events, revealing that the first detected gravitational wave is likely to have an SNR approximately 1.26 times the search threshold. This implies a nuanced understanding of detection sensitivity improvements.
2. Detection Volume and Visibility Distance: Schutz proposes the concept of "visibility distance," a key parameter representing the potential detection range of gravitational signals for a given source. This parameter aids in isolating and enhancing network performance by focusing on the geometric contribution to sensitivity, independently of detector technology specifics.
3. Figures of Merit:
   • Triple Detection Rate (3DR): This figure estimates the effectiveness of networks by considering the rate of events detected using subnetworks of three or more detectors. It accounts for operational duty cycles, which are significant given the delicacy and potential downtimes of current detectors.
   • Sky Coverage (SC): This measure assesses the isotropy of the network's antenna pattern. An isotropic network covers diverse sky locations uniformly, which may be critical for comprehensive surveys and for detecting sources that are isotropic across the celestial sphere.
   • Directional Precision (DP): Aimed at evaluating the network's accuracy in localizing gravitational wave sources, DP considers the relative baselines between detectors, showcasing how additional detectors enhance triangulation and source localization accuracy.
4. Implications for Network Expansion: Analysis indicates remarkable benefits in adding detectors to existing infrastructure:
   • Adding any new site, including detectors in Asia or Australia, can double the event detection rate through enhanced coherent data analysis and null-stream methods.
   • Specifically, moving one LIGO detector to Australia or adding LCGT in Japan not only boosts detection rates but drastically improves sky localization precision by increasing baseline lengths within the network.

Practical and Theoretical Implications

The findings have profound implications for future gravitational wave astronomy, both in guiding the strategic development of detector placements and enhancing analytical methodologies for maximizing data yield from gravitational wave events. Practically, deploying additional detectors as suggested could increase the detection rate of neutron star binary coalescences to potentially hundreds per year, transforming the observational capabilities of gravitational wave astronomy.

On a theoretical level, the research adopts a universal framework to address detection probabilities, inclination biases in system observations, and to quantify error reductions in source localization. These advancements are instrumental for designing robust frameworks to ensure that large-scale network investments return optimal scientific insights.

Future Prospects

The paper projects a promising future where extended networks enable us to tap into multitudes of cosmic phenomena with unprecedented detail and frequency. As gravitational wave detection technology evolves, the insights provided here will remain integral to pushing the boundaries of our astrophysical knowledge. Integrating these approaches could redefine data processing methodologies to safeguard against false signals while maximizing accurate and valuable detections.

In sum, Bernard Schutz’s paper lays out a clear, methodical approach to improving gravitational wave detectors' networks, enabling a significant enhancement in detection capabilities and scientific returns.