Orbital evolution of mass-transferring eccentric binary systems. I. Phase-dependent evolution

TL;DR

This paper develops a comprehensive formalism for modeling the phase-dependent orbital evolution of eccentric binary systems undergoing mass transfer and loss, addressing inconsistencies in previous approaches.

Contribution

It introduces a self-consistent set of equations for orbital element evolution considering various mass-loss and transfer processes, unifying different models.

Findings

Derived phase-dependent evolution equations for eccentric binaries.

Compared new equations with existing literature, clarifying discrepancies.

Provided a framework for incorporating these equations into binary population synthesis.

Abstract

Observations reveal that mass-transferring binary systems may have non-zero orbital eccentricities. The time-evolution of the orbital semi-major 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 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 been ever 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 to the general two-body problem. We present the self-consistent form of the perturbing acceleration and the 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 the non-isotropic ejection and accretion in conservative as well as non-conservative manner for both point masses and extended bodies. Comparison of the derived equations with similar work in the literature is made and explanation of the existing discrepancies is provided.