Eccentric signatures of stellar-mass binary black holes with circumbinary discs in LISA

Abstract

ABSTRACT Stellar-mass binary black holes may have circumbinary discs if formed through common-envelope evolution or within gaseous environments. Discs can drive binaries into wider and more eccentric orbits, while gravitational waves harden and circularize them. We combine cutting-edge evolution prescriptions for disc-driven binaries with well-known equations for gravitational-wave-driven evolution, and study the evolution of stellar-mass binary black holes. We find that binaries are driven by their disc to an equilibrium eccentricity, $0.2\lesssim e_\mathrm{eq}~\lesssim 0.5$, that dominates their evolution. Once they transition to the GW-dominated regime their eccentricity decreases rapidly; we find that stellar-mass binary black holes with long-lived discs will likely be observed in LISA with detectable eccentricities ${\sim} 10^{-2}$ at 0.01 Hz, with the precise value closely correlating with the binary’s initial mass ratio. This may lead stellar-mass binary black holes with CBDs observed in LISA to be confused with dynamically-formed binary black holes.