Unifying stochastic and deterministic signals: a practical search for the intermittent binary black-hole background

Abstract

Over the past decade, the Advanced LIGO, Advanced Virgo, and KAGRA detectors have detected nearly 400 compact binary mergers, most of which are stellar-mass binary black-hole (BBH) mergers. Nevertheless, most mergers in the Universe are too weak to be individually detected at current sensitivity levels. Since a BBH merger in band is much shorter than the average time between successive mergers, the population of these subthreshold events gives rise to an intermittent background of gravitational waves (GWs). This GW background is guaranteed to exist, but it has not yet been detected with current stochastic or deterministic searches. Here we propose a fast and accurate likelihood-based search for this background, which unifies the standard model-agnostic cross-correlation search and a fully deterministic, template-based search in a single likelihood. Our search is based on a truncated likelihood ratio, which is fully marginalized over the extrinsic parameters of the individual mergers, and which represents the data in two detectors as an expansion in terms of approximate sufficient statistics. These statistics are higher-order cross-moments of the data, weighted by geometrical factors that generalize the standard overlap reduction function (ORF) used in cross-correlation searches. We show that almost all the Bayesian evidence and information on the BBH merger population comes from correlations between frequency bins induced by individual mergers and is captured in the higher-order generalized ORFs. Consequently, any likelihood function that does not take these inter-frequency correlations into account is necessarily suboptimal. We validate our search on one year of simulated Advanced LIGO data, and find that a catalog-informed analysis, which uses information from both the detected and unresolved mergers, can infer the peak of the redshift distribution of the population of BBH mergers.