Disk-Regulated Mass Transfer Between Rotating Non-Degenerate Stars: Insights from Be and sdOB Binaries

Mass transfer between non-degenerate stars is a fundamental but still poorly understood process in binary evolution. The commonly used rotationally limited accretion prescription in detailed binary evolution simulations that account for stellar rotation generally yields low accretion efficiencies that are difficult to reconcile with several observational constraints. We present a physically-motivated mass-accretion prescription in which accretion or decretion disks regulate the angular momentum transported to the accretor, thereby allowing for continued accretion at near-critical rotation. The accretion efficiency can be calculated from the conservation of the mass and the angular momentum of the disk. Analytical estimates show that the accretion efficiency depends on stellar rotation and mass ratio for direct impact accretion, and additionally on stellar radius and orbital separation in the disk accretion regime. The overall mass-weighted accretion efficiencies are close to the values expected near the threshold rotation rate, where the accreted specific angular momentum declines sharply. Applying this model to binary evolution simulations, we find that rotationally limited accretion systematically underestimates Be-star masses in Be+subdwarf O/B-type star (sdOB) systems, whereas the disk-star coupling model can produce more massive Be stars that are consistent with observations. The final binary component masses depend not only on accretion efficiency but also core-envelope mass ratio, which itself depends sensitively on the assumed overshooting. We find that our new disk-star coupling model with reduced overshooting yields component masses for Be+sdOB systems that are in closer agreement with observations.

💡 Research Summary

This paper addresses a long‑standing problem in binary stellar evolution: how non‑degenerate stars can continue to accrete mass when they approach critical rotation. The standard “rotationally limited” prescription, widely used in detailed binary evolution codes such as MESA, reduces the accretion rate by a factor of (1 − Ω/Ω_crit). While this approach works reasonably well for close, tidally synchronized systems, it predicts very low mass‑accretion efficiencies (η ≈ 20–30 %) for wide, case‑B mass‑transfer binaries. Observations of Be+sdOB binaries, in which the Be star is a rapidly rotating, mass‑gaining component, contradict these predictions: the Be stars are systematically more massive (≈ 8–12 M_⊙) than the rotationally limited models can produce.

The authors propose a physically motivated alternative: a disk‑star coupling model in which an accretion (or decretion) disk regulates the angular‑momentum flux onto the accretor. The key ingredients are:

1. Accretion geometry – Material leaving the donor through L1 either impacts the accretor directly (if the stellar radius exceeds a minimum circularization radius R_min) or forms a Keplerian disk. In the direct‑impact regime the specific angular momentum of the transferred stream is taken as j_tr = √(G M_a · 1.7 R_min); in the disk regime j_tr = √(G M_a R_a).

2. Rotation‑dependent angular‑momentum uptake – Following the steady‑state thin‑disk solutions of Popham & Narayan (1991), the specific angular momentum actually accreted by the star, j_acc, declines sharply once the surface rotation reaches a threshold Ω/Ω_crit ≈ 0.9. The authors implement a smooth analytic form:
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