Rethinking mass transfer: A unified semianalytical framework for circular and eccentric binaries

I. Orbital evolution due to conservative mass transfer

¹ Anton Pannekoek Institute for Astronomy, University of Amsterdam Amsterdam 1098 XH, The Netherlands
² School of Physics and Astronomy, Cardiff University Cardiff CF24 3AA, United Kingdom
³ Institute of Astronomy, KU Leuven Celestijnenlaan 200D B-3001 Leuven, Belgium
⁴ Leuven Gravity Institute, KU Leuven Celestijnenlaan 200D box 2415 3001 Leuven, Belgium

^★ Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 9 April 2025
Accepted: 15 November 2025

Abstract

Mass transfer (MT) is a fundamental process in stellar evolution. While MT in circular orbits is well studied, observations indicate that it also occurs in eccentric ones, where theoretical models are limited. We present a new semianalytic framework for the secular orbital evolution of mass-transferring binaries that treats stars as either point masses or extended bodies. For the first time, a MT model is applicable to both circular and eccentric orbits and accommodates conservative and nonconservative MT across a broad range of mass ratios and stellar spins. We derived secular orbit-averaged equations describing the orbital evolution by treating MT, mass loss, and angular momentum (AM) loss as perturbations to the general two-body problem. Assuming conservative MT, we compared our results to previous models and validated them against numerical integrations. Our model predicts eccentric post-MT systems in wider orbits than classical results. Compared to other eccentric MT frameworks, the parameter space for orbital widening and eccentricity pumping we find is broader. When extended bodies are accounted for, a stronger semimajor axis and eccentricity growth are obtained at a given mass ratio, and the parameter space is further broadened for orbital widening and eccentricity pumping. Regardless of whether extended bodies are considered, eccentric MT naturally predicts higher eccentricities at longer orbital periods. This correlation has been observed in numerous post-MT systems, and thus eccentric MT provides a robust mechanism for their formation. Our model can be integrated into binary evolution and population synthesis codes to consistently treat conservative and nonconservative MT in arbitrarily eccentric orbits. The applications range from MT on the main sequence to gravitational-wave progenitors.