Equilibrium eccentricity of accreting binaries

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, quasiperiodic, bursty signature on the light curves of eccentric binaries. We predict that intermediate-mass and massive black hole binaries at z ≲ 10 entering the LISA band will have measurable eccentricities in the range of 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.