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

Technical Summary: Disk-Regulated Mass Transfer Between Rotating Non-Degenerate Stars

Problem Statement
Mass transfer between non-degenerate stars is a critical yet poorly understood process in binary evolution. A central uncertainty is the accretion efficiency—the fraction of transferred mass retained by the accretor. Standard binary population synthesis (BPS) and detailed stellar evolution simulations (e.g., using MESA) typically employ a "rotationally limited" accretion prescription. In this framework, accretion is restricted once the accretor approaches its critical breakup rotation rate, often leading to very low accretion efficiencies.

However, observational constraints from Be-star binaries, particularly Be+subdwarf O/B-type (sdOB) systems, suggest significantly higher accretion efficiencies (often $\gtrsim 30\%$ to $>50\%$). Existing rotationally limited models systematically underestimate the masses of Be stars in these systems and fail to reproduce the observed parameter space of Be+sdOB binaries. Furthermore, previous studies indicate that neither rotationally limited nor thermally limited prescriptions alone can satisfy the efficiency requirements derived from observed Be+sdOB populations.

Methodology
The authors propose a physically motivated "disk-star coupling" mass-accretion prescription to address these discrepancies. The core physical mechanism posits that an accretion or decretion disk regulates the angular momentum transported to the accretor, allowing mass accretion to continue even when the star rotates near its critical limit.

1. Angular Momentum Regulation: Drawing on the steady-state thin disk solutions of Popham & Narayan (1991), the authors model the specific angular momentum accreted by the star ($j_{acc}$) as a function of the stellar rotation rate ($\Omega/\Omega_{crit}$).

   • At low rotation rates, $j_{acc}$ is approximately the Keplerian value at the stellar surface.
   • As the star approaches a threshold rotation rate (adopted as $\Omega/\Omega_{crit} \approx 0.9$), the disk's shear stress allows angular momentum to be transported outward from the star into the disk. Consequently, $j_{acc}$ decreases sharply, potentially becoming negative, enabling continued mass accretion without the star exceeding its critical rotation.
   • The authors implement a smoothed functional form for $j_{acc}$ to ensure numerical stability in 1D simulations, avoiding discontinuities that would arise from a strict threshold.

2. Conservation Laws and Efficiency Calculation: The model assumes that excess angular momentum extracted from the star is transported through the disk and removed via mass loss at the disk's outer edge ($R_{out}$). By applying conservation of mass and angular momentum, the accretion efficiency ($\eta = \dot{M}_{acc}/\dot{M}_{tr}$) is calculated self-consistently. The efficiency depends on the ratio of the specific angular momentum at the disk edge to that at the accretion radius.

3. Simulation Framework: The authors implemented this prescription within the POSYDON framework, utilizing MESA (Modules for Experiments in Stellar Astrophysics) to evolve binary models.

   • They disabled the implicit wind scheme used to prevent supercritical rotation, relying instead on explicit rotationally enhanced winds and the reduced accretion rate in the supercritical regime to restore subcritical rotation.
   • A grid of binary models was simulated with solar metallicity, varying primary masses ($2-9 M_\odot$), mass ratios ($0.4-0.95$), and orbital periods.
   • The study also investigated the impact of core overshooting treatments (comparing standard POSYDON settings with a reduced overshooting prescription) on the final component masses.

Key Contributions and Results

• Analytical Estimates: The authors derived analytical expressions for accretion efficiency. They show that in the disk-accretion regime, efficiency depends on stellar rotation, mass ratio, and the ratio of stellar radius to Roche-lobe radius. In the direct-impact regime, it depends on rotation and mass ratio. The overall mass-weighted accretion efficiencies are found to be close to values expected near the threshold rotation rate, where the accreted specific angular momentum declines sharply.
• Binary Evolution Comparison:
  • Rotationally Limited Model: In this standard model, accretors reach critical rotation after accreting only a small fraction of the transferred mass ($\sim 0.2 M_\odot$ in a test case), leading to low efficiencies ($<10\%$ for most systems). This results in Be stars that are systematically less massive than observed.
  • Disk-Star Coupling Model: This model allows accretors to accrete significantly more mass (e.g., $\sim 1.6 M_\odot$ in the rapid phase of the test case) with efficiencies reaching $\sim 40-60\%$. The disk extracts angular momentum, allowing the star to expand and accrete while remaining near the critical rotation threshold.
• Reproduction of Observations:
  • When applied to Be+sdOB systems, the rotationally limited model fails to produce Be stars with masses consistent with observations, particularly for wide-orbit (Case B) systems.
  • The disk-star coupling model produces Be stars with masses that cover a significant portion of the observed range.
  • The authors found that the final component masses are sensitive to the assumed overshooting. A model combining the disk-star coupling prescription with reduced overshooting yields component masses for Be+sdOB systems that are in closer agreement with observations than the standard high-overshooting models.
• Orbital Periods: While the disk-star coupling model increases mass retention, the resulting orbital periods are comparable to or slightly longer than those in the rotationally limited model. This is because the more conservative mass transfer reduces the total mass lost from the system, leading to more extreme mass ratios that accelerate orbital expansion, partially counteracting the angular momentum loss from the disk edge.

Significance and Claims
The paper claims that the discrepancy between observed Be+sdOB binary properties and current simulation results can be resolved by adopting a disk-regulated mass transfer model. The authors argue that:

1. Rotationally limited accretion prescriptions systematically underestimate Be-star masses in Be+sdOB systems.
2. A disk-star coupling mechanism, which allows for the regulation of angular momentum transport, enables higher accretion efficiencies consistent with observational constraints (specifically the requirement for efficiencies $>50\%$ in many systems).
3. The combination of this new accretion prescription with reduced core overshooting provides a more physically consistent explanation for the observed masses and orbital periods of Be+sdOB binaries.

The authors acknowledge that the actual efficiency depends on uncertain factors such as disk structure, magnetic fields, and the specific conditions of disk formation and mass loss (e.g., via L2 points or hot spots). However, they conclude that the disk-star coupling model offers a necessary physical mechanism to explain the existence of massive Be stars in wide binaries where tidal spin-down is inefficient.