2020ApJ...893..106M

We study the process of runaway, unstable Roche lobe overflow in coalescing binary systems and its dependence on the properties of the binary involved. We create three-dimensional hydrodynamic models of binary coalescences and follow them through a phase of increasing Roche lobe overflow until the accretor is engulfed by the donor at the onset of a common-envelope phase. In these models, we vary binary properties of mass ratio, donor structure and spin, and equation of state through the gas adiabatic index. We compare the numerical results to semianalytic models of binary orbit evolution based on mass and angular momentum exchange between two point masses. Using our hydrodynamic simulations, we measure the key parameters: the donor mass-loss rate and the angular momentum exchanged per unit mass loss from the donor. Using these calibrations, the semianalytic model closely reproduces the escalating mass loss and runaway orbital decay observed in the hydrodynamic models. The semianalytic model accurately reproduces the major differences in orbit evolution that arise with varying mass ratio and donor structure. We encapsulate the semianalytic model in a publicly released Python package, RLOF. We apply this model to the observed period decay and subsequent merger of the binary V1309 Sco and find that it can simultaneously reproduce the observed orbital decay and time of outburst. We further demonstrate that there is a relationship between the period derivative and second derivative that can be a useful metric for evaluating candidate merging binaries.