The mass discrepancy problem in massive stars: an inferential perspective
Bayesian inference has become a standard tool for inferring stellar parameters from stellar evolution models. However, comparatively little attention has been paid to how alternative Bayesian likelihood formulations influence inferred stellar parameters, and the resulting evolutionary mass discrepancy for massive main sequence stars. Here, we investigate the effects of mixing and alternative Bayesian likelihood formulations on the inferred stellar parameters and the resulting evolutionary mass discrepancy. We analysed a sample of seven double-lined eclipsing B type binaries with $β$ Cep components using one pre-computed MESA grid of stellar evolution models and observables such as mass, effective temperature, surface gravity and luminosity. Stellar parameters were inferred within a Bayesian inference method employing nested sampling and piecewise cubic interpolation across the model grid. We compared several inference strategies, including single-star and coeval binary models, with and without dynamical masses included in the likelihood function. Bayesian evidence and Pareto-optimal model selection were used to evaluate the preferred solutions. Our work reinforces that core-boundary mixing is required for all stars. Further, the inferential analysis demonstrates that different likelihood formulations may lead to systematically different inferred mass discrepancies. For the adopted input physics and the small sample of stars, we find that about half of the apparent reduction in the inferred mass discrepancy may arise from the construction of the Bayesian likelihood, while enhanced near-core mixing accounts for the remaining improvement. The preferred coeval solutions further indicate that the systems span central hydrogen mass fraction of $0.632$ -- $0.205$, with ages of $4.25$ -- $12.27$ $\rm Myr$ determined with precisions of $2$ -- $13\%$ under the adopted model input physics.