ORBITAL EVOLUTION OF MASS-TRANSFERRING ECCENTRIC BINARY SYSTEMS. II. SECULAR EVOLUTION

Finite eccentricities in mass-transferring eccentric binary systems can be explained by taking into account the mass loss and mass transfer processes that often occur in these systems. These processes can be treated as perturbations of the general two-body problem. The time-evolution equations for the semimajor axis and the eccentricity derived from perturbative methods are generally phase-dependent. The osculating semimajor axis and eccentricity change over the orbital timescale and are not easy to implement in binary evolution codes like MESA. However, the secular orbital element evolution equations can be simplified by averaging over the rapidly varying true anomalies. In this paper, we derive the secular time-evolution equations for the semimajor axis and the eccentricity for various mass loss/transfer processes using either the adiabatic approximation or the assumption of delta-function mass loss/transfer at periastron. We begin with the cases of isotropic and anisotropic wind mass loss. We continue with conservative and non-conservative non-isotropic mass ejection/accretion (including Roche-Lobe-Overflow) for both point-masses and extended bodies. We conclude with the case of phase-dependent mass accretion. Comparison of the derived equations with similar work in the literature is included and an explanation of the existing discrepancies is provided.