The optimal search for an astrophysical gravitational-wave background

TL;DR

This paper develops an optimal Bayesian search method for detecting the stochastic gravitational-wave background from unresolved binary black hole mergers, improving sensitivity and enabling population analysis.

Contribution

It introduces a Bayesian parameter estimation framework for stochastic background detection, surpassing traditional cross-correlation methods in sensitivity and providing population insights.

Findings

The method is robust against instrumental artefacts like glitches.

It can detect the background with about one day of data at design sensitivity.

It independently constrains merger rates and black hole mass distributions.

Abstract

Roughly every 2-10 minutes, 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 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 artefacts 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 one day of design sensitivity data versus $\approx 40$ 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 hyper-parameter 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.