Inferring the Stochastic Gravitational-Wave Background from Eccentric Stellar-mass Binary Black Holes with Spaceborne Detectors

TL;DR

This work addresses the SGWB produced by eccentric stellar-mass binary black holes and its detectability with spaceborne detectors. It develops a Bayesian framework, including a simplified likelihood to efficiently combine data from A/E/T channels and account for the Galactic foreground, to perform model selection and parameter estimation for three SBBH formation channels. The study finds that isolated-evolved and GC-formed SBBHs yield backgrounds that are effectively indistinguishable from a power-law, while AGN-formed SBBHs exhibit a spectral turnover that can be clearly distinguished from a power-law background by LISA and Taiji, enabling precise constraints on distortion parameters and amplitude. The results underline both the promise and limitations of null-channel Bayesian methods, and point toward cross-correlation networks (e.g., LISA+Taiji) as a robust approach for robust SGWB detection in the presence of foregrounds and noise uncertainties.

Abstract

The stochastic gravitational-wave background (SGWB) from eccentric stellar-mass binary black holes (SBBHs) holds crucial clues to their origins. For the first time, we employ a Bayesian framework to assess the detectability and distinguishing features of such an SGWB with spaceborne detectors, while accounting for contamination from the Galactic foreground. Our analysis covers eccentric SBBHs from three formation channels: isolated binary evolution, dynamical assembly in globular clusters (GCs), and in active galactic nuclei (AGNs). We find that TianQin, LISA, and Taiji can detect the SGWBs from both isolated and GC-formed SBBHs after 4 years of operation, with the corresponding signal-to-noise ratios of around 10, 60, and 170. However, these backgrounds are spectrally degenerate with a strictly power-law SGWB. Furthermore, highly eccentric SBBHs formed in AGNs yield an SGWB marked by a spectral turnover and sharp decline. While this feature lowers the signal-to-noise ratio by approximately an order of magnitude, it can enable a clear distinction from the strictly power-law background using LISA and Taiji.

Figures (4)

• Figure 1: Transfer functions for the TDI channels as a function of the dimensionless frequency $u = (2\pi fL)/c$. The blue and orange lines correspond to the $A/E$ and $T$ channels, respectively.
• Figure 2: Probability distribution of orbital eccentricity for three different formation channels at an initial GW frequency $f_{\rm GW}$ of $10\,\rm Hz$. The gold, green, and red lines correspond to the field, GC, and AGN cases, respectively.
• Figure 3: Energy spectral density $\Omega_{\rm gw}$ of the Galactic foreground and the SGWB from different SBBH populations, compared with the PLIS curves for TianQin, LISA, and Taiji for a 4-year operation period at $\rho_{\rm th}=1$. The cyan solid line represents the Galactic foreground (FG). The black solid, gold dashed, green dotted, and red dash-dotted lines correspond to the strictly power-law background and the eccentric backgrounds from the field, GC, and AGN cases, respectively.
• Figure 4: Reconstructed energy spectral density $\Omega_{\rm gw}$ from 4-year simulated datasets for LISA (left panel) and Taiji (right panel). The cyan and red lines correspond to the 4-year Galactic foreground and the SGWB from SBBHs in AGN, respectively. For comparison, a strictly power-law background is also shown as a black line. The posterior distributions (shaded 1-$\sigma$ and 2-$\sigma$ regions) and their medians (dashed lines) are compared against the true values (solid lines), illustrating the frequency-dependent reconstruction accuracy of each detector. A cutoff frequency of $0.05\,\rm Hz$ is marked by the gray dash-dotted line for reference.