Orbital Evolution of Mass-transferring Eccentric Binary Systems. I. Phase-dependent Evolution

Observations reveal that mass-transferring binary systems may have non-zero orbital eccentricities. The time evolution of the orbital semimajor axis and eccentricity of mass-transferring eccentric binary systems is an important part of binary evolution theory and has been widely studied. However, various different approaches to and assumptions on the subject have made the literature difficult to comprehend and comparisons between different orbital element time evolution equations not easy to make. Consequently, no self-consistent treatment of this phase has ever been included in binary population synthesis codes. In this paper, we present a general formalism to derive the time evolution equations of the binary orbital elements, treating mass loss and mass transfer as perturbations of the general two-body problem. We present the self-consistent form of the perturbing acceleration and phase-dependent time evolution equations for the orbital elements under different mass loss/transfer processes. First, we study the cases of isotropic and anisotropic wind mass loss. Then, we proceed with non-isotropic ejection and accretion in a conservative as well as a non-conservative manner for both point masses and extended bodies. We compare the derived equations with similar work in the literature and explain the existing discrepancies.