Frequency-Domain Distribution of Astrophysical Gravitational-Wave Backgrounds

TL;DR

This paper introduces a Fourier space method to analyze the frequency distribution of astrophysical gravitational-wave backgrounds, revealing a power-law tail and effects of source subtraction on the noise characteristics.

Contribution

It provides a novel Fourier space framework for the frequency distribution of stochastic gravitational-wave backgrounds from discrete sources, including analytical expressions and implications for data analysis.

Findings

The background from all compact mergers exhibits a -4 power-law tail.

Subtraction of loud sources Gaussianizes the confusion noise.

Analytical derivation of tails for both unsubtracted and subtracted signals.

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.