Rethinking mass transfer: a unified semi-analytical framework for circular and eccentric binaries. I. Orbital evolution due to conservative mass transfer

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 semi-analytic framework for the secular orbital evolution of mass-transferring binaries, treating stars either as point-masses or as extended bodies. For the first time, a MT model is applicable to both circular and eccentric orbits and accommodates conservative and non-conservative MT across a broad range of mass ratios and stellar spins. We derive 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 compare our results to previous models and validate them against numerical integrations. Our model predicts eccentric post-MT systems in wider orbits than classical results. Compared to other eccentric MT frameworks we find a broader parameter space for orbital widening and eccentricity pumping. Accounting for extended bodies yields stronger semimajor axis and eccentricity growth at a given mass ratio, and further broadens the parameter space for orbital widening and eccentricity pumping. Whether extended bodies are considered or not, eccentric MT naturally predicts higher eccentricities at longer orbital periods, a correlation observed in numerous post-MT systems, providing a robust mechanism for their formation. Our model can be integrated into binary evolution and population synthesis codes to consistently treat conservative and non-conservative MT in arbitrarily eccentric orbits with applications ranging from MT on the main sequence to gravitational-wave progenitors.