Importance of Shot Noise in the Search for an Isotropic Stochastic Gravitational-Wave Background with Next Generation Detectors

We investigate the impact of shot noise on the stochastic gravitational wave background generated by binary neutron star mergers, and confirm that the overall background can be significantly influenced by relatively few neighboring, loud events. To mitigate the shot noise, we propose a procedure to remove nearby events by notching them out in the time-frequency domain. Additionally, we quantify the cosmic/sample variance of the resulting background after notching, and we study the deviation between the cross-correlation measurement and the theoretical prediction of the background. Taking both effects into account, we find that the resulting sensitivity loss in the search for an isotropic background formed by binary neutron star mergers is minimal, and is limited to $\lesssim 4%$ below 40 Hz, and to $\lesssim 1%$ above 40 Hz.

💡 Research Summary

This paper investigates the impact of shot noise on the stochastic gravitational‑wave background (SGWB) generated by binary neutron‑star (BNS) mergers, with a focus on next‑generation (XG) ground‑based detectors such as Cosmic Explorer and the Einstein Telescope. The authors begin by noting that current LIGO‑Virgo‑KAGRA observations have detected many individual compact‑binary coalescences (CBCs) but have not yet measured an SGWB. Future detectors will be sensitive enough that the astrophysical foreground, dominated by CBCs, will be comparable to or stronger than any cosmological background, making accurate modeling of the foreground essential for extracting sub‑dominant cosmological signals.

The standard theoretical treatment models the CBC foreground as a persistent, Gaussian, stationary background, expressed as an integral over redshift (Eq. 1). In practice, analyses replace the integral with a discrete sum over a finite number of events (Eq. 2), assuming an effectively infinite observation time. The authors argue that for realistic observation periods of order one year, the finite‑sample fluctuations—i.e., shot noise—become a non‑negligible source of uncertainty, especially for BNS where only about half of the events are individually resolvable.

To quantify this effect, the authors adopt a BNS population model identical to their earlier work: component masses uniformly distributed between 1–2 M⊙, zero spin, isotropic sky and orientation, and a merger‑rate density derived from a convolved star‑formation rate and a t⁻¹ delay‑time distribution. The local merger rate is set to 320 Gpc⁻³ yr⁻¹. Using this model they generate 200 independent one‑year realizations, each containing roughly 4.9 × 10⁵ BNS mergers. For each realization they compute Ω_BNS(f) via Eq. 2, employing the IMRPhenomXAS waveform (quadrupole‑only) and the Bilby inference library.

The resulting spectra show a broad distribution: most realizations cluster near the ensemble mean, but a few outliers exhibit dramatically higher energy densities. In the three most extreme cases, a single nearby merger contributes 44–65 % of the total Ω_BNS(f) across the band, leading to deviations of up to 150 % relative to the mean. This demonstrates that the stochastic background is not a smooth, Gaussian quantity but can be dominated by a handful of loud, nearby events—a classic shot‑noise phenomenon previously studied mainly in the context of anisotropic SGWB analyses.

Recognizing that such fluctuations would bias Bayesian inference if one simply used the ensemble‑averaged Ω_BNS(f) as the model, the authors propose two mitigation strategies. The first is a “notching” procedure: in the time‑frequency spectrogram, regions associated with the loudest nearby events are masked out before computing the cross‑correlation estimator. The second is a subtraction method, where the estimated waveform of each identified loud event is removed from the data stream based on its inferred parameters. Both approaches are tested on the simulated data sets.

After applying either mitigation, the authors recompute Ω_BNS(f) and compare it to the original ensemble mean. They find that the residual bias is reduced to below 4 % for frequencies ≤ 40 Hz and below 1 % for frequencies > 40 Hz. This indicates that the loss of sensitivity due to shot‑noise removal is minimal, especially in the most scientifically interesting band (≈ 20–200 Hz) for cosmological SGWB searches.

The paper also examines the discrepancy between the theoretical prediction (Eq. 2) and the measured cross‑correlation spectrum C(f). Real data analysis involves segmenting the strain time series into overlapping short windows, applying a short‑time Fourier transform (STFT), and using a weighted average to account for time‑varying detector noise. These practical steps introduce additional deviations from the simple arithmetic averages assumed in the theoretical expressions. The authors explore how the choice of segment length T and frequency resolution δf affects C(f), and they also assess the impact of estimating the power‑spectral density (PSD) rather than assuming it known. Their findings show that, even when PSD uncertainties are included, the notching procedure still limits sensitivity loss to the few‑percent level.

In conclusion, the study demonstrates that shot noise from a few nearby BNS mergers can dominate the isotropic SGWB estimate for realistic observation times, but that targeted time‑frequency notching (or subtraction) effectively suppresses this bias with negligible impact on overall detector sensitivity. This work provides a concrete, computationally tractable framework for future XG SGWB analyses, enabling more reliable separation of astrophysical foregrounds from the faint cosmological background signals that next‑generation detectors aim to uncover.