Interacting Binaries with Eccentric Orbits. III. Orbital Evolution due to Direct Impact and Self-Accretion

The rapid circularization and synchronization of the stellar components in an eccentric binary system at the onset of Roche lobe overflow is a fundamental assumption common to all binary stellar evolution and population synthesis codes, even though the validity of this assumption is questionable both theoretically and observationally. Here we calculate the evolution of the orbital elements of an eccentric binary through the direct three-body integration of a massive particle ejected through the inner Lagrangian point of the donor star at periastron. The trajectory of this particle leads to three possible outcomes: direct accretion onto the companion star within a single orbit, self-accretion back onto the donor star within a single orbit, or a quasi-periodic orbit around the companion star, possibly leading to the formation of a disk. We calculate the secular evolution of the binary orbit in the first two cases and conclude that direct impact accretion can increase as well as decrease the orbital semimajor axis and eccentricity, while self-accretion always decreases the orbital semimajor axis and eccentricity. In cases where mass overflow contributes to circularizing the orbit, circularization can set in on timescales as short as a few percent of the mass-transfer timescale. In cases where mass overflow increases the eccentricity, the orbital evolution is governed by competition between mass overflow and tidal torques. In the absence of tidal torques, mass overflow results in direct impact can lead to substantially subsynchronously rotating donor stars. Contrary to assumptions common in the literature, direct impact accretion furthermore does not always provide a strong sink of orbital angular momentum in close mass-transferring binaries; in fact, we instead find that a significant part can be returned to the orbit during the particle orbit. The formulation presented in this paper together with our previous work can be combined with stellar and binary evolution codes to generate a better picture of the evolution of eccentric, Roche lobe overflowing binary star systems.