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 $e \simeq 0.45$, unless they are initialized on a nearly circular orbit with $e \lesssim 0.08$, 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 $z \lesssim 10$ entering the LISA band will have measurable eccentricities in the range $e \simeq 10^{-3} - 10^{-2}$, if they have experienced a gas-driven phase. On the other hand, GW190521 would have entered the LIGO/Virgo band with undetectable eccentricity $\sim 10^{-6}$ if it had been driven into the gravitational wave regime by a gas disk.