Orbital Evolution of Binaries in Circumbinary Disks

We present the to-date largest parameter space exploration of binaries in circumbinary disks (CBDs), deriving orbital evolution prescriptions for eccentric, unequal mass binaries from our suite of hydrodynamic simulations. In all cases, binary eccentricities evolve towards steady state values that increase with mass ratio, and saturate at an equilibrium eccentricity $e_{\rm b, eq} \sim 0.5$ in the large mass ratio regime, in line with resonant theory. For binaries accreting at their combined Eddington limit, a steady state eccentricity can be achieved within a few Megayears. Once at their steady state eccentricities, binaries with $q_{\rm b} \gtrsim 0.3$ evolve towards coalescence, while lower mass ratio systems expand due to CBD torques. We discuss implications for population studies of massive black hole binaries, protostars in binary systems, and post-common envelope binaries observed by ground-based gravitational wave detectors.