On the uncertainty in predicting the stochastic gravitational wave background from compact binary coalescences

TL;DR

This study addresses the challenge of predicting the astrophysical SGWB from CBCs by building a fiducial, multi-population model (BBH, BNS, NSBH) and systematically propagating uncertainties in mass/spin distributions, waveform features, and merger-rate history through Monte Carlo integration. It leverages GWTC-3 posterior samples and hierarchical population inferences to generate 90% credible bands for $\Omega_{GW}(f)$, revealing that the overall bands span about an order of magnitude and are particularly sensitive to the delay-time distribution and metallicity-dependent formation for BBHs, while local merger rates dominate the BNS/NSBH uncertainties. Higher-order GW modes and neutron-star EOS introduce noticeable but smaller shifts in the spectrum, and NSBH spectra depend strongly on the assumed BH upper-mass limit. The framework enables robust interpretation of current LVK upper limits and will inform future detections (e.g., O5), while guiding where astrophysical modeling most affects SGWB forecasts and where further observations can tighten constraints.

Abstract

The stochastic gravitational-wave background from compact binary coalescences is expected to be the first detectable stochastic signal via cross-correlation searches with terrestrial detectors. It encodes the cumulative merger history of stellar-mass binaries across cosmic time, offering a unique probe of the high-redshift Universe. However, predicting the background spectrum is challenging due to numerous modeling choices, each with distinct uncertainties. In this work, we present a comprehensive forecast of the astrophysical gravitational-wave background from binary black holes, binary neutron stars, and neutron star-black hole systems. We systematically assess the impact of uncertainties in population properties, waveform features, and the modeling of the merger rate evolution. By combining all uncertainties, we derive credible bands for the background spectrum, spanning approximately an order of magnitude in the fractional energy density. These results provide thorough predictions to facilitate the interpretation of current upper limits and future detections.

Figures (12)

• Figure 1: Fiducial GWB model contributions from BBH, BNS and NSBH mergers, along with their combined CBC background.
• Figure 2: We show the effect of the uncertainty in the BBH mass model on the energy spectrum. The individual spectra correspond to the GWB according to a single hyperparameter posterior sample. The solid black lines show the combined 90% credible level and the gray line the fiducial BBH background model.
• Figure 3: Comparison of the 90% credible bands of the BBH background spectrum for different mass distribution models.
• Figure 4: Relative change in the amplitude of the BBH GWB, $\Omega_\mathrm{BBH} (f)$, due to the inclusion of spin effects. The curves show deviations from the non-spinning fiducial model at the 90% credible level for two spin distribution models, the Default spin model and the Gaussian spin model.
• Figure 5: Relative increase in the amplitude of the BBH GWB, $\Omega_\mathrm{BBH} (f)$, when higher-order modes are included using the waveform model IMRPhenomXPHM.