Orbital evolution of mass-transferring eccentric binary systems. II. Secular Evolution

TL;DR

This paper derives simplified secular equations for the orbital evolution of eccentric binary systems undergoing various mass-loss and transfer processes, aiding long-term binary evolution modeling.

Contribution

It introduces generalized secular evolution equations for semi-major axis and eccentricity considering diverse mass transfer scenarios, including anisotropic winds and phase-dependent accretion.

Findings

Derived secular evolution equations for different mass-loss/transfer processes.

Compared new equations with existing literature and explained discrepancies.

Provided a framework for incorporating mass transfer effects into binary evolution models.

Abstract

Finite eccentricities in mass-transferring eccentric binary systems can be explained by taking into account mass-loss and mass-transfer processes that often occur in these systems. These processes can be treated as perturbations to the general two-body problem. The time-evolution equations for the semi-major axis and the eccentricity derived from perturbative methods are in general phase-dependent. The osculating semi-major axis and eccentricity change over the orbital timescale and they are not easy to implement in binary evolution codes like MESA. However, the secular orbital element evolution equations can be simplified averaging over the rapidly varying true anomalies. In this paper, we derive the secular time-evolution equations for the semi-major 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 RLOF) 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 explanation of the existing discrepancies is provided.