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Abstract

Circumbinary disks are found in a variety of astrophysical scenarios, spanning binary star formation to accreting supermassive black hole binaries. Depending on the characteristics of the system, the interaction with a circumbinary disk can either damp or excite the binary's eccentricity and can also widen or shrink the orbit. To predict the outcome of the long-term disk-binary interaction, we present a new formalism based on the results of recent suites of hydrodynamic simulations, which resolve the complex geometry of the gas in the vicinity of the binary and fully account for the gravitational and accretion forces. We released a python package, spindler, that implements our model. We show that - under the assumed thin disk model with a fixed thickness and viscosity prescription - accretion onto the binary depletes the disk mass before inducing a significant change in the orbital separation or the mass ratio, unless the mass reservoir feeding the disk is comparable to the mass of the binary. This finding implies that, in most scenarios, an interaction with a circumbinary disk is not an efficient mechanism to shrink the orbit of the binary. However, the interaction can excite the eccentricity up to an equilibrium value, and induce a statistical correlation between the mass ratio and eccentricity, as long as the mass of the disk is at least a few percent of the mass of the binary. We consider the applicability of our model to a variety of astrophysical scenarios: during star formation, in evolved stellar binaries, triples, and in supermassive black hole binaries. We discuss the theoretical and observational implications of our predictions.