Networks of gravitational wave detectors and three figures of merit

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.