The beauty of <i>k</i> ₂ : Probing stellar interiors using apsidal motion

Context. Over the last two decades, several independent studies have shown the need for large convective boundary mixing and convective core sizes in massive stars to reproduce a variety of their observed properties. Yet, stars more massive than 20 M ⊙ lack a quantitative prescription for convective boundary mixing as well as an unequivocal constraint on the internal mixing mechanisms acting in them. Aims. We take advantage of the fact that massive stars evolve mainly in binaries to constrain convective boundary mixing. We use the apsidal motion observed in main-sequence binary stars – linked to the internal stellar structure constants k 2 of the stars – to constrain massive stars’ internal density stratification and convective core sizes. In this first paper of a series, we develop the methodology and aim to identify the models that reproduce the stellar parameters of the benchmark twin massive binary HD 152248. Methods. We built stellar evolution models with the GENeva Evolutionary Code ( GENEC ) assuming two different angular momentum transport schemes: purely hydrodynamic and magneto-diffusive models. We confronted single- and binary-star models to assess the impact of tidal locking on the star’s evolution. We investigated the impact of convective boundary mixing (overshooting), metallicity, initial helium abundance, initial mass, mass-loss rate, and mixing length parameter on the evolution of stellar parameters. Results. We highlight the k 2 discrepancy between models and observations: the k 2 from the models are systematically larger than the observed ones. Models predict stars with too low a density contrast between their core and external layers. Both purely hydrodynamic and magneto-diffusive models require large step-overshoot parameters of 1.2–1.3 to reproduce the stellar parameters, including k 2 . Other parameters have almost no impact. Given the efficiency of tides to synchronise systems, the assumption of pseudo-synchronisation is sound for this system. It sets a constraint on the misalignment angle of stellar rotation axes of 45° −52° maximum. Even with such large angles – unexpected as alignment happens on the same timescale as synchronisation – it does not solve the k 2 discrepancy and a large step-overshoot parameter of at least 1.0 is necessary to reproduce the observations. Conclusions. Reproducing k 2 and the apsidal motion rate simultaneously with stellar parameters requires enhanced core boundary mixing. It acts as increasing the main-sequence lifetime of the star and lowering the rate of radius expansion: the star has more time to contrast its core-envelope density profile. Even if the mass-loss rate were underestimated by a factor of two, it would have no impact on stellar parameters’ evolution, including k 2 . It demonstrates that the apsidal motion is a powerful, robust means to probe stellar interiors.