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

TL;DR

This paper investigates the impact of shot noise from nearby binary neutron star mergers on the isotropic stochastic gravitational-wave background in the next-generation detector era. It shows that a few loud neighboring events can dominantly shape the BNS foreground and proposes a time–frequency notching technique to mitigate this, replacing a problematic subtraction approach. By comparing cross-correlation measurements to a notched, population-summed model $\Omega_{\mathrm{BNS}}^{z^*}(f)$, the authors quantify the residuals and demonstrate that the overall sensitivity loss for isotropic SGWB searches is small (\lesssim 4\% below 40 Hz and \lesssim 1\% above 40 Hz). The work provides a practical framework for incorporating shot-noise mitigation into Bayesian inference of BNS population hyperparameters and offers a pathway to robustly separate astrophysical foregrounds from cosmological backgrounds in future detectors.

Abstract

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.

Figures (16)

• Figure 1: A schematic comparison between the theoretical analysis and the practical analysis of the CBC foreground energy density. The blue bubble represents the “analysis in theory”, in which an theoretical expression for $\Omega_\mathrm{CBC}(f|\bm\Lambda)$ is shown. This integral has a rigorous one-to-one correspondence between population level hyperparameters $\bm\Lambda$ and $\Omega_\mathrm{CBC}(f|\bm\Lambda)$. The red bubble shows the “analysis in practice”, where the commonly used practical approximation is shown, which replaces the integral with a discrete summation over $N$ simulated events, hence depending on the exact simulation. Additionally, this approximation only holds when $T_\mathrm{obs}\to\infty$ or $N\to\infty$, whereas real observations are typically limited to a duration of $\mathcal{O}(1)$ year. The potential fluctuation of the summation given different realizations of $N$ events must therefore be evaluated. At the bottom, we show the cross-correlation estimator $\widehat{C}(f)$, which measures the observed energy density spectrum of the SGWB. The estimator $\widehat{C}(f)$ and corresponding uncertainty $\widehat{\sigma}(f)$ are defined in the Appendix \ref{['app: CC']}, and we refer to Ref. Romano:2016dpxAllen:1997ad for more details. Due to the factors we list below “Cross-correlation $\widehat{C}(f)$”, $\widehat{C}(f)$ and $\Omega_\mathrm{CBC}(f|\bm\Lambda)$ can potentially deviate from each other. Here STFT refers to the short-time Fourier transform.
• Figure 2: Energy density spectra $\Omega_\mathrm{BNS}(f)$ from two hundred simulated realizations with the identical underlying BNS population. Each gray curve corresponds to a specific realization. The three realizations yielding the highest $\Omega_\mathrm{BNS}(f)$ are highlighted in red, green and blue. For each of these, we also indicate the redshift $z_{\min}$ of the nearest event, which dominates the energy density in that realization. In these three realizations, the nearest event contributes roughly $65\%$(red), $59\%$(green) and $44\%$(blue) to the total $\Omega_\mathrm{BNS}(f)$.
• Figure 3: Similar to Fig. \ref{['fig: BNS_Omega_all']}, but shows the relative deviation in percentage of each spectrum to the mean of two hundred realizations.
• Figure 4: Similar to Fig. \ref{['fig: Deviation_all']}, but now each here subplot corresponds to a different threshold $z^\star$ value. We only show six $z^\star$ values in this plot and the complete version is shown in Fig. \ref{['fig: Deviation_BNS_z_star']}. As $z^\star$ increases, progressively more nearby events are removed from each realization. As a result, the outliers that appears prominently in the $z^\star=0.00$ case gradually disappear, and the overall deviation of each realization from the mean of all two hundred realizations systematically decreases with increasing $z^\star$.
• Figure 5: We aggregate all two hundred realizations from the previous plot to examine the distribution of deviations. We focus on three particular frequencies: 10 Hz, 100 Hz, 200 Hz. The results show that the deviation is largely frequency-independent. We also fit a Gaussian to each of the three frequencies for each subplot in dashed lines, and find that after removing nearby BNS events, the deviations are well characterized by a simple Gaussian, suggesting that the corresponding $\Omega_\mathrm{BNS}^{z^\star}(f)$ also approximately follows a Gaussian distribution. In the upper-left panel, Gaussian curves poorly match the histograms because the distributions have a pronounced long tail extending beyond $100\%$ (also see Fig. \ref{['fig: Deviation_all']}). See Fig. \ref{['fig: Deviation_BNS_z_star_3freqs']} for the complete version.