The Beauty of k2: Probing Stellar Interiors Using Apsidal Motion. I. The Benchmark Massive Binary HD 152248

Over the last decades, several independent studies have shown the need for large convective boundary mixing (CBM) and convective core sizes in massive stars to reproduce a variety of their observed properties. Yet, stars more massive than 20Msun lack a quantitative prescription for CBM as well as an unequivocal constraint on the internal mixing mechanisms acting in them. We use the apsidal motion observed in the twin binary HD152248 - linked to the internal stellar structure constants k2 of the stars - to constrain massive stars' internal density stratification and CBM. We build GENEC stellar models assuming two different angular momentum transports: purely hydrodynamic (hydro) and magneto-diffusive (magnetic). We confront single- and binary-star models to assess the impact of tidal locking on the star's evolution. We investigate the impact of CBM (overshooting), metallicity, initial helium abundance and mass, mass-loss rate, and mixing length parameter on the evolution of stellar parameters. We highlight that k2 from the models are systematically larger than observed ones, the so-called k2-discrepancy. Models predict stars with too low a density contrast between their core and external layers. Both hydro and magnetic models require large step-overshoot of 1.2 to reproduce stellar parameters, including k2. 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 an upper limit on the misalignment angle of stellar rotation axes of ~50{\deg}. Even with such unexpected large angles, the k2-discrepancy is not solved. Even if the mass-loss rate was underestimated by a factor two, it would have no impact on stellar parameters evolution, including k2. It demonstrates that the apsidal motion is a powerful, robust means to probe stellar interiors.