Using high-resolution hydrodynamics simulations, we show that equal-mass binaries accreting from a circumbinary disk evolve toward an orbital eccentricity of e≃0.45, unless they are initialized on a nearly circular orbit with e≲0.08, in which case they further circularize. The implied bi-modal eccentricity distribution resembles that seen in post-AGB stellar binaries. Large accretion spikes around periapse impart a tell-tale, quasi-periodic, bursty signature on the light curves of eccentric binaries. We predict that intermediate-mass and massive black hole binaries at z≲10 entering the \emph{LISA} band will have measurable eccentricities in the range e≃10−3−10−2, if they have experienced a gas-driven phase. On the other hand, GW190521 would have entered the LIGO/Virgo band with undetectable eccentricity ∼10−6 if it had been driven into the gravitational wave regime by a gas disk.
@article{arxiv.2010.09707,
title = {Equilibrium eccentricity of accreting binaries},
author = {Jonathan Zrake and Christopher Tiede and Andrew MacFadyen and Zoltán Haiman},
journal= {arXiv preprint arXiv:2010.09707},
year = {2021}
}