Optimal Search for an Astrophysical Gravitational-Wave Background
Roughly every 2–10 min, a pair of stellar-mass black holes merge somewhere in the Universe. A small fraction of these mergers are detected as individually resolvable gravitational-wave events by advanced detectors such as LIGO and Virgo. The rest contribute to a stochastic background. We derive the statistically optimal search strategy (producing minimum credible intervals) for a background of unresolved binaries. Our method applies Bayesian parameter estimation to all available data. Using Monte Carlo simulations, we demonstrate that the search is both "safe" and effective: it is not fooled by instrumental artifacts such as glitches and it recovers simulated stochastic signals without bias. Given realistic assumptions, we estimate that the search can detect the binary black hole background with about 1 day of design sensitivity data versus ≈40 months using the traditional cross-correlation search. This framework independently constrains the merger rate and black hole mass distribution, breaking a degeneracy present in the cross-correlation approach. The search provides a unified framework for population studies of compact binaries, which is cast in terms of hyperparameter estimation. We discuss a number of extensions and generalizations, including application to other sources (such as binary neutron stars and continuous-wave sources), simultaneous estimation of a continuous Gaussian background, and applications to pulsar timing.
© 2018 Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Received 5 December 2017; revised manuscript received 23 February 2018; published 16 April 2018. We thank Joe Romano, Letizia Sammut, Tom Callister, Max Isi, Xingjiang Zhu, Pablo Rosado, and Kent Blackburn for helpful comments. R. S. and E. T. are supported by CE170100004. E. T. is supported through ARC FT150100281. LIGO was constructed by the California Institute of Technology and Massachusetts Institute of Technology with funding from the National Science Foundation and operates under cooperative agreement PHY-0757058. This manuscript has LIGO Document ID LIGO-P1700407.
Published - PhysRevX.8.021019.pdf
Submitted - 1712.00688.pdf