Frequency-Domain Distribution of Astrophysical Gravitational-Wave Backgrounds

Abstract

The superposition of many astrophysical gravitational wave (GW) signals below typical detection thresholds baths detectors in a stochastic gravitational wave background (SGWB). In this work, we present a Fourier space approach to compute the frequency-domain distribution of stochastic gravitational wave backgrounds produced by discrete sources. Expressions for the moment-generating function and the distribution of observed (discrete) Fourier modes are provided. The results are first applied to the signal originating from all the mergers of compact stellar remnants (black holes and neutron stars) in the Universe, which is found to exhibit a $-4$ power-law tail. This tail is verified in the signal-to-noise ratio distribution of GWTC events. The extent to which the subtraction of bright (loud) mergers gaussianizes the resulting confusion noise of unresolved sources is then illustrated. The power-law asymptotic tail for the unsubtracted signal, and an exponentially decaying tail in the case of the SGWB, are also derived analytically. Our results generalize to any background of gravitational waves emanating from discrete, individually coherent, sources.

(v1) Comments welcome. (v2) Updated to match version accepted to PRD

References in corpus (11)

• GWTC-2: Compact Binary Coalescences Observed by LIGO and Virgo During the First Half of the Third Observing Run
• The stochastic gravitational-wave background from massive black hole binary systems: implications for observations with Pulsar Timing Arrays
• Upper Limits on the Isotropic Gravitational-Wave Background from Advanced LIGO's and Advanced Virgo's Third Observing Run
• Open data from the third observing run of LIGO, Virgo, KAGRA and GEO
• Stochastic and resolvable gravitational waves from ultralight bosons
• Gravitational Waves from Global Cosmic Strings and Cosmic Archaeology
• Gravitational-wave confusion background from cosmological compact binaries: Implications for future terrestrial detectors
• Subtraction-noise projection in gravitational-wave detector networks
• Subtracting Compact Binary Foregrounds to Search for Subdominant Gravitational-Wave Backgrounds in Next-Generation Ground-Based Observatories
• Statistical properties of astrophysical gravitational-wave backgrounds
• Statistics of Fourier Modes in Non-Gaussian Fields

Cited by in corpus (2)

• Spectral Variance in a Stochastic Gravitational-Wave Background From a Binary Population
• Detection prospects for the GW background of Galactic (sub)solar mass primordial black holes