Implications of the LISA stochastic signal from eccentric stellar mass black hole binaries in vacuum

Astrophysical formation channels of stellar-mass binary black holes (sBBHs) can induce significant orbital eccentricities in their early inspiral. We analyze the implications on the stochastic gravitational-wave background (SGWB) from unresolved sBBHs, which can be detected with the Laser Interferometer Space Antenna (LISA). We develop an improved SGWB model for the case of an idealized Dirac-delta eccentricity distribution, and extend it to the more astrophysical case of a thermal distribution. Using a fully Bayesian framework, we find that, if all binaries have a high initial eccentricity 𝑒0 ≳0.9 at an orbital frequency of 𝑓orb =10−4  Hz, the resulting SGWB can be robustly distinguished from a background of quasicircular sBBHs. For a thermal eccentricity distribution, the SGWB is consistent with a circular model when binaries form at 𝑓orb =10−5  Hz, but leads to significant systematic biases if formation occurs at 𝑓orb =10−4  Hz. We also show that, when eccentricity is properly accounted for, environmental effects such as dynamical friction can be distinguished from vacuum evolution, but only for sufficiently dense environments with gas densities 𝜌 ≳10−7  g cm−3. Finally, we show that a LISA detection of the sBBH SGWB would place an upper bound on the maximum eccentricity of the sBBH population in the band of ground-based detectors, with direct implications for template modeling and data analysis. Our results highlight the importance of incorporating eccentricity in SGWB modeling to enable accurate astrophysical interpretation of LISA observations.