Convective Core Evolution of Main-Sequence Stars in Rapid Population Synthesis I: Framework and Implementation

Stars spend most of their lifetime on the main sequence (MS), where hydrogen burning establishes the internal chemical structure that governs the subsequent evolution. In massive stars, mass loss through winds and binary interactions can significantly modify this structure during the MS. We present a new MS evolution framework suitable for rapid binary population synthesis, implemented in the COMPAS code. Building on the semi-analytical model of Shikauchi et al. (2025), our framework captures the evolution of the convective core on the MS under arbitrary mass-loss or mass-gain histories, including a treatment for stellar rejuvenation and MS mergers. This new framework yields more massive helium cores at terminal-age MS, more compact radii in stripped MS stars, and systematically higher black hole masses than commonly used prescriptions. By providing a more realistic treatment of MS evolution, this framework improves the physical consistency of massive stars and binary evolution in rapid population synthesis.

💡 Research Summary

This paper introduces a new main‑sequence (MS) evolution framework for massive stars that tracks the growth and shrinkage of the convective core under arbitrary mass‑loss or mass‑gain histories, and implements it in the rapid binary population synthesis code COMPAS. The motivation stems from the fact that existing COMPAS prescriptions—namely the HURLEY option (based on Hurley et al. 2000) and the MANDEL option (a heuristic fix)—do not retain any memory of a star’s prior mass‑loss history. Consequently, the helium core mass at terminal‑age main sequence (TAMS) is determined solely by the star’s total mass at that moment, leading to systematic under‑estimates for stars that have lost a substantial fraction of their mass during the MS, especially when stripping occurs late in the evolution.

The authors build on the semi‑analytical model of Shikauchi et al. (2025), which describes the time evolution of the central helium fraction Y_c and the convective core mass M_c through two coupled differential equations (Eqs. 1 and 2). The model contains three key functions: α(M_c), β(M), and δ(M_c,Y_c). These functions were originally calibrated on a grid of MESA models for three metallicities (Z = 0.02, Z/3, Z/10) and interpolated linearly for intermediate values. The original formulation only handled mass loss (Ṁ < 0).

To extend the model to mass gain, the authors performed a suite of MESA simulations of 15 M_⊙ and 40 M_⊙ stars undergoing constant accretion at various onset times and rates. Analysis of the resulting δ values revealed a systematic deviation from the loss‑only prescription. They therefore propose a new δ(Y_c) = 2 − Y_c − Y_0 X_0 (Eq. 3), where X_0 and Y_0 are the initial hydrogen and helium mass fractions. This new δ captures the reduced “inertia” of an accreting core.

A central novelty is the treatment of stellar rejuvenation. When the accretion rate exceeds a threshold (Eq. 4), fresh hydrogen is mixed into the convective core, lowering Y_c and making the star appear younger. The authors derive a set of equations (Eqs. 5–11) that conserve total helium mass while accounting for the linear helium abundance profile between the convective core and the outer CNO‑processed region (mass coordinate M_c,CNO). If the expanded core remains within the CNO‑processed boundary, Eq. 8 gives the new ΔY_c; if it exceeds that boundary, Eq. 11 handles the additional mixing of pristine material. After rejuvenation, the surface helium abundance Y_out is updated (Eq. 9) and the CNO‑processed core mass is shifted outward.

Implementation in COMPAS proceeds by integrating the differential equations over each timestep. The change in central helium is ΔY_c = (L Q_CNO / M_c) Δt (Eq. 12), and the change in core mass is split into a natural decay term (ΔM_c,nat, Eq. 14) and a mass‑loss/gain term (ΔM_c,ML, Eq. 13). The framework replaces the original Hurley‑based MS evolution for massive stars but remains compatible with any post‑MS tracks.

Because a fully calibrated radius prescription for mass‑changing MS stars is not yet available, the authors retain the Hurley radius formula but scale it with surface composition to mimic the contraction of stripped stars. Additional features include handling of MS merger products (core masses summed, rejuvenation applied), spin‑down of chemically homogeneous stars, and optional coupling to alternative stellar tracks.

The authors benchmark the new “BRCEK” prescription against the HURLEY and MANDEL options. They find that for a given final mass, the helium core mass at TAMS can differ by up to ~30 % depending on when mass loss occurs. Accretion‑induced rejuvenation leads to larger convective cores than would be inferred from mass alone, which in turn yields higher final black‑hole (BH) masses. Population synthesis runs show that the BRCEK framework produces BH masses on average 5–10 % larger and stripped MS radii 10–20 % smaller than the older prescriptions, directly impacting predicted gravitational‑wave merger rates and observable binary properties.

The paper discusses limitations: (1) the metallicity extrapolation is linear and untested at very low Z; (2) rapid, non‑steady mass loss (e.g., eruptions) and detailed rotation‑magnetic coupling are not yet incorporated; (3) the radius scaling is heuristic, awaiting a physics‑based model from detailed simulations. The authors suggest future work to integrate more extensive MESA grids, refine the δ function for extreme accretion, and validate the framework against observations of massive binaries, stripped stars, and gravitational‑wave events.

In summary, the work delivers a physically motivated, semi‑analytical treatment of convective core evolution that retains the star’s mass‑loss/gain history, introduces a robust rejuvenation scheme, and demonstrates measurable impacts on core masses, stellar radii, and black‑hole outcomes in rapid binary population synthesis. This represents a significant step toward more realistic modeling of massive star evolution in large‑scale astrophysical simulations.