Eccentric Signatures of Stellar-Mass Binary Black Holes with Circumbinary Disks in LISA

TL;DR

This paper investigates how circumbinary disks influence the evolution and eccentricity of stellar-mass binary black holes, predicting detectable eccentricities in LISA observations that could mimic dynamical formation signatures.

Contribution

It combines advanced disk-driven binary evolution models with gravitational-wave physics to predict eccentricity signatures in LISA-detectable black hole binaries.

Findings

Binaries reach an equilibrium eccentricity between 0.2 and 0.5 due to disk interactions.

Eccentricity decreases rapidly once gravitational wave effects dominate.

LISA may observe binaries with eccentricities around 0.01, depending on initial mass ratio.

Abstract

Stellar-mass binary black holes may have circumbinary disks if formed through common-envelope evolution or within gaseous environments. Disks can drive binaries into wider and more eccentric orbits, while gravitational waves harden and circularise them. We combine cutting-edge evolution prescriptions for disk-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 disk to an equilibrium eccentricity, $0.2\lesssim e_\mathrm{eq} \lesssim0.5$, 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 disks 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.