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

TL;DR

This work introduces the General Mass Transfer (GeMT) framework, a semi-analytic, orbit-averaged approach to model the secular orbital evolution of mass-transferring binaries across the full range of eccentricities and MT regimes. It builds on prior $\,\delta$-function and emt treatments by treating MT as a perturbation to the instantaneous two-body problem, incorporating a phase-dependent MT rate and a physically motivated Global-$L_1$ prescription for donor ejection. GeMT accounts for both conservative and non-conservative MT and for point-mass and extended-body scenarios, yielding broader regions of orbital widening and eccentricity pumping than previous models, and naturally producing wide, eccentric post-MT binaries that align with observations. The framework is designed for seamless integration into binary evolution and population-synthesis codes, with implications for MT on the main sequence through gravitational-wave progenitors and for a wide array of observed post-interaction binaries.

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.

Figures (18)

• Figure 1: Position of the $L_1$ point, relative to the donor's center of mass, at the periapsis of the binary orbit in units of the instantaneous binary separation. The thick lines are the numerical solutions of Eq. \ref{['eq:Lagrangian_points_2']}. The dotted, dashed, and thin lines illustrate the High-$q$, Low-$f_{\rm don}$, and Global-$L_1$ models, respectively. Blue, orange, and green colors correspond to $f_{\rm don}=0.5,1.0,1.5$, respectively, while $e=0.3$ for all models. Note that the Low-$f_{\rm don}$ prescription is independent of $f_{\rm don}$.
• Figure 2: Position of the $L_1$ point, relative to the donor's center of mass, in units of the semimajor axis $a$, for $q=1$ and $f_{\rm don}=1$ as a function of true anomaly. The thick lines are the numerical solutions of Eq. \ref{['eq:Lagrangian_points']}. From top to bottom, the dotted, dashed and thin lines illustrate the High-$q$, Low-$f_{\rm don}$, and Global-$L_1$ models, respectively. Blue, orange, green and red colors correspond to $e=0.0,0.3,0.6,0.9$, respectively.
• Figure 3: Graphical representation of the mass transfer regimes based on the mass transfer rate formulation by 2019ApJ...872..119H. The white region indicates no mass transfer, i.e. no RLOF. The light blue region corresponds to partial RLOF, where mass transfer occurs during part of the orbit. The light brown region represents full RLOF, with continuous mass transfer throughout the entire orbit.
• Figure 4: Secular rate of change of the semimajor axis as a function of mass ratio $q$, and the donor's level of synchronism $f_{\rm don}$, in the limit of circular orbits. From top to bottom: the GeMT-model in the limit of point masses, extended bodies for $\vec{r}_{\rm acc} = - r_{\rm acc} \hat{\vec{r}}$, the $\delta$-function, and emt models. The values of the relevant parameters are provided in Table \ref{['tab:colormaps_parameters']}.
• Figure 5: Secular rate of change of the semimajor axis in the limit of conservative mass transfer as a function of mass ratio $q$, and eccentricity, $e$. From top to bottom: the GeMT-model in the limit of point masses, extended bodies for $\vec{r}_{\rm acc} = - r_{\rm acc} \hat{\vec{r}}$, the $\delta$-function and emt models. The values of the relevant parameters are provided in Table \ref{['tab:colormaps_parameters']}.