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 Gravitational-Wave Transient Catalogue (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.

中文翻译：

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天体物理引力波背景的频域分布

许多低于典型探测阈值的天体物理引力波（GW）信号的叠加使探测器处于随机引力波背景（SGWB）中。在这项工作中，我们提出了一种傅里叶空间方法来计算离散源产生的随机引力波背景的频域分布。提供了矩生成函数的表达式和观察到的（离散）傅立叶模式的分布。结果首先应用于源自宇宙中所有致密恒星遗迹（黑洞和中子星）合并的信号，发现该信号表现出$-4$幂律尾。该尾部在引力波瞬态目录（GWTC）事件的信噪比分布中得到了验证。然后说明了明亮（响亮）合并的减去在多大程度上使未解决的源产生的混淆噪声高斯化。未减去信号的幂律渐近尾部以及 SGWB 情况下的指数衰减尾部也是通过分析得出的。我们的结果可以推广到任何由离散的、单独相干的源发出的引力波背景。