Networks of gravitational wave detectors and three figures of merit

By Bernard F. Schutz. 2011

300 citations recorded by the source corpus.

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 increase than previously thought. I focus on detecting bursts, i.e. short-duration signals, with optimal coherent data-analysis methods. I show that the polarization-averaged sensitivity of any network of identical detectors to any class of sources can be characterized by two numbers—the visibility distance of the expected source from a single detector and the minimum signal-to-noise ratio (SNR) for a confident detection—and one angular function, the antenna pattern of the network. 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 (f.o.m.'s) that characterize the relative performance of different networks. These measure (a) the expected rate of detection by the network and any sub-networks of three or more separated detectors, taking into account the duty cycle of the interferometers, (b) the isotropy of the network antenna pattern, and (c) the accuracy of the network at localizing the positions of events on the sky. I compare various likely and possible networks, based on these f.o.m.'s. Adding any new site to the planned LIGO–VIRGO network can dramatically increase, by factors of 2–4, 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. Including LCGT, LIGO-Australia, and a detector in India gives a network with position error ellipses a factor of 7 smaller in area and boosts the detected event rate a further 2.4 times above the extra-site gain over the original LIGO–VIRGO network. Enlarged advanced networks could look forward to detecting 300–400 neutron star binary coalescences per year.

Subfields: Astronomy and Astrophysics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f4a4a0d9f06e278bcbe1182da748d4702ba82542

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Citations in the corpus

THE RATE OF BINARY BLACK HOLE MERGERS INFERRED FROM ADVANCED LIGO OBSERVATIONS SURROUNDING GW150914 (2016, background): “In each pipeline, the shape of the astrophysical trigger distribution p1(x) is, to a very great extent, universal (Schutz 2011; Chen & Holz 2014); that is, it does not depend on the properties of the source (see Supplement).”
Binary Black Hole Mergers in the First Advanced LIGO Observing Run (2016, unknown): “statistics follow the flat-space, volumetric density p1ðρÞ ∝ ρ−4 [129].”
IDENTIFYING ELUSIVE ELECTROMAGNETIC COUNTERPARTS TO GRAVITATIONAL WAVE MERGERS: AN END-TO-END SIMULATION (2012, methodology): “We use NS-5M BH in this paper. dred square degrees using networks of GW interferometers (Fairhurst 2010; Wen & Chen 2010; Nissanke et al. 2011; Klimenko et al. 2011; Schutz 2011; Veitch et al. 2012; Fairhurst 2012).”
THE FIRST TWO YEARS OF ELECTROMAGNETIC FOLLOW-UP WITH ADVANCED LIGO AND VIRGO (2014, background): “It occurs when the GW phases on arrival support two different binary inclination angles, with the orbital plane nearly facing the observer but with opposite handedness (usually peaked at ι ≈ 30◦ and ι ≈ 150◦; see Schutz 2011).”
DOUBLE COMPACT OBJECTS. III. GRAVITATIONAL-WAVE DETECTION RATES (2015, unknown): “Schutz (2011) described a simple idealized model for the sensitivity of multi-instrument networks.”
WHAT IS THE MOST PROMISING ELECTROMAGNETIC COUNTERPART OF A NEUTRON STAR BINARY MERGER? (2011, unknown): “Kochanek & Piran 1993; Schutz 2011).”
Prospects for observing and localizing gravitational-wave transients with Advanced LIGO, Advanced Virgo and KAGRA (2013, background): “The addition of more detector sites leads to good source localization over the whole sky (Schutz 2011; Veitch et al. 2012; Nissanke et al. 2013; Rodriguez et al. 2014).”
Prospects for Observing and Localizing Gravitational-Wave Transients with Advanced LIGO and Advanced Virgo (2013, background): “As sky localization improves with the development of the detector network [96, 72, 109, 91], these results mark the baseline of performance for the advanced-detector era.”
GWTC-1: A Gravitational-Wave Transient Catalog of Compact Binary Mergers Observed by LIGO and Virgo during the First and Second Observing Runs (2018, background): “In practice, differing fθg do not significantly affect the shape of pðxjAi; fθgÞ over the range of ranking statistics considered here [19].”
Hierarchical analysis of gravitational-wave measurements of binary black hole spin–orbit misalignments (2017, methodology): “We use a roughly astrophysical distribution of systems with sky positions and inclinations randomly chosen, and distances DL distributed uniformly in volume, p(DL) ∝ D2L, such that the distribution of signal-to-noise ratio (SNR) ρ is p(ρ) ∝ ρ−4 (Schutz 2011).”