Orbital evolution of eccentric interacting binary star systems

We provide a comprehensive description of the long-term (secular) orbital evolution of eccentric interacting binary systems. The evolution of circular interacting binary systems is a well studied phenomenon, but observations have shown the existence of a small but significant number of eccentric interacting binary systems. We begin by extending the commonly accepted Roche formalism for binary interacting to include eccentric orbits and asynchronously rotating stars. Using this, we calculate orbital trajectories for particles ejected from a Roche lobe-filling donor star at the periastron of the eccentric orbit. These particles admit of three possible trajectories: direct impact onto the secondary star, self accretion back onto the donor star, and the formation of a disk about the accretor. We provide a proscription for determining a priori the trajectory of the particle given the initial system parameters, as well as describe the secular evolution of the system for each of the three cases described above. We find that these orbital evolution timescales are comparable to the mass transfer timescale which can be significantly longer than expected from the literature. Furthermore, while it is commonly assumed that any mass transfer interactions will act to circularize the orbit, we find that there are regimes of parameter space where mass transfer can cause an increase in eccentricity, and can do so at a timescale comparable to the circularization timescale created by tidal interactions. The formalism presented here can be incorporated into binary evolution and population synthesis models to create a self-consistent treatment of mass transfer in eccentric binaries.