Optimal Search for an Astrophysical Gravitational-Wave Background

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 (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 one 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 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.

Estimating the angular power spectrum of the gravitational-wave background in the presence of shot noise

“…where we have used (5) and (8), and have introduced the shorthand · · · S,Ω ≡ · · · S Ω . 6 5 The lack of correlation between time intervals is due to the acausal relationship between distant GW sources, while the lack of correlation between different m is due to statistical isotropy.…”

“…With an ever-growing number of compact binary coalescences (CBCs) being catalogued [3,4], attention is now increasingly turning toward other, as-yetundetected, GW observables, such as the stochastic GW background (SGWB). The SGWB is a persistent, pseudorandom GW signal, formed from the incoherent superposition of many GW sources throughout cosmic history [5,6], which can be searched for by cross-correlating data between multiple GW detectors [7,8].…”

Gravitational wave detection without boot straps: A Bayesian approach

“…However, if the rate of astrophysical signals is sufficiently small, then we can make the following approximation as in Smith and Thrane [6]:…”

Time-dependence of the astrophysical stochastic gravitational wave background

“…3 indicates that characterizing the time variability of the SGWB signal is a useful probe to understand different populations of binary GW source and their event rates respectively. The time variability of the SGWB signal is a independent avenue along with other existing methods to detect the GW event rates from the individual GW sources and SGWB signal (Messenger & Veitch 2013;Farr et al 2015;Smith & Thrane 2018). These frameworks (Messenger & Veitch 2013;Farr et al 2015;Smith & Thrane 2018) are able to measure the rates from the GW data and can successfully distinguish between the background and individual signal.…”