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

Abstract

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.

Figures (10)

• Figure 1: Computed values of $\delta$ as a function of the central helium fraction $Y_c$ for a mass-gaining 40 $M_\odot$ MS star, based on our Mesa simulations. Three different mass gain onset times are shown: 0.88 Myr (blue), 1.76 Myr (purple), and 2.7 Myr (green). We apply 5-mean smoothing to the data. For each onset time, three mass gain rates are considered, as indicated in the legend.
• Figure 2: Graphical illustration of how the rejuvenation is treated in two cases: when the CNO-processed core mass $M_{c,\mathrm{CNO}}$ remains greater than the convective core mass after accretion (left), and when the convective core mass exceeds $M_{c,\mathrm{CNO}}$ (right). The solid black line represents the helium profile in the star before accretion, with the area underneath it corresponding to the helium mass. The dashed line represents the helium profile of the convective core after rejuvenation. The helium mass inside the expanded convective core (given as $Y_{c,\mathrm{new}}\times M_{c,\mathrm{new}}$) must equal the helium mass originally in the convective core plus the helium mixed in from the surrounding layers (the sum of the colored areas). The profiles and shaded areas are schematic and not drawn to scale.
• Figure 3: Initial core-to-total mass ratio as a function of total stellar mass from Mesa models with varying initial helium abundances. When the total mass is scaled by $h(Y)$ (see Eq. \ref{['eq:h(Y)']}), all points lie on the same curve, described by the fitting function $g(M,Y)$ (see Eq. \ref{['eq:fmix_fitting_function']}). This function predicts the initial convective core mass (initial CNO-processed core mass) based on the star's total mass and initial helium abundance, and is used to determine the convective core mass of uniformly mixed merger products and spun-down chemically homogeneous stars.
• Figure 4: Hertzsprung-Russell diagram showing stellar tracks for various initial masses at $Z=Z_\odot$ with mass loss via stellar winds from Merritt2025 enabled (left) and mass loss disabled (right). Only the MS and HG evolution is shown. Solid lines show the updated stellar tracks when BRCEK formalism is used, and dashed lines are the default stellar tracks from Hurley2000. The luminosity prescription from Shikauchi2024 is enabled only for stars with $M_\mathrm{ZAMS} \geq 15\;M_\odot$.
• Figure 5: Radial evolution of MS stars ($Z=Z_\odot$) losing mass via stellar winds, shown for the Mesa-based Posydon models (dashed black lines), our modified radius (solid blue), and the original radius prescription from Hurley2000 (solid yellow). The ZAMS mass is indicated above each panel. Posydon models are shown up to core-hydrogen exhaustion, with the MS hook omitted. The impact of our modified radius prescription (Eq. \ref{['eq:modified_radius']}) becomes visible in the 80.3 $M_\odot$ model, where the radial evolution changes around 2.5 Myr.