Inferring the stochastic gravitational-wave background from eccentric stellar-mass binary black holes with spaceborne detectors

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, Laser Interferometry Space Antenna (LISA), and Taiji can detect the SGWBs from both isolated and GC-formed SBBHs after four years of operation, with the corresponding SNRs 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 SNR by approximately an order of magnitude, it can enable a clear distinction from the strictly power-law background using LISA and Taiji.