Optimal Search for an Astrophysical Gravitational-Wave Background

Abstract

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≈40months 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.

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Plain Language Summary

Over the past few years, astronomy has been revolutionized by the detection of gravitational waves—ripples in the fabric of spacetime—created by merging black holes and neutron stars. However, for every gravitational-wave event that is detected, there are many more that are too far away to be seen with current observatories. We think that every few minutes, a pair of black holes merges somewhere in the Universe. All these mergers contribute to a background hum of gravitational waves, which researchers have sought to detect for years. We have come up with a new, more sensitive way of searching for this background, which may allow researchers to detect it much sooner than previously thought.

We derive an optimal search strategy based on Bayesian parameter estimation. Using simulations, we show that our approach is robust, that it is not fooled by instrumental glitches, and that it can reliably recover simulated signals. When current observatories reach their designed sensitivity, this technique should be able to detect the gravitational-wave background with about one day of data—as opposed to roughly 40 months of data using traditional search methods. As a bonus, this search strategy reveals details about the population of binary black holes. It may eventually be applied to other sources of gravitational waves such as merging neutron stars.

Measuring the gravitational-wave background will allow us to study populations of black holes at vast distances. Someday, the technique may even enable us to see gravitational waves from the big bang, hidden behind gravitational waves from black holes and neutron stars.