We propose a methodological framework to perform forward asteroseismic modeling of stars with a convective core, based on gravity-mode oscillations. These probe the near-core region in the deep stellar interior. The modeling relies on a set of observed high-precision oscillation frequencies of lowdegree coherent gravity modes with long lifetimes and their observational uncertainties. Identification of the mode degree and azimuthal order is assumed to be achieved from rotational splitting and/or from period spacing patterns. This paper has two major outcomes. The first is a comprehensive list and discussion of the major uncertainties of theoretically predicted gravity-mode oscillation frequencies based on linear pulsation theory, caused by fixing choices of the input physics for evolutionary models. Guided by a hierarchy among these uncertainties of theoretical frequencies, we subsequently provide a global methodological scheme to achieve forward asteroseismic modeling. We properly take into account correlations amongst the free parameters included in stellar models. Aside from the stellar mass, metalicity and age, the major parameters to be estimated are the near-core rotation rate, the amount of convective core overshooting, and the level of chemical mixing in the radiative zones. This modeling scheme allows for maximum likelihood estimation of the stellar parameters for fixed input physics of the equilibrium models, followed by stellar model selection considering various choices of the input physics. Our approach uses the Mahalanobis distance instead of the often used χ 2 statistic and includes heteroscedasticity. It provides estimation of the unknown variance of the theoretically predicted oscillation frequencies.

Context. Space asteroseismology reveals that stellar structure and evolution models of intermediate-and high-mass stars are in need of improvement in terms of angular momentum and chemical element transport. Aims. We aim to probe the interior structure of a hot massive star in the core-hydrogen burning phase of its evolution. Methods. We analyse CoRoT space photometry, Gaia DR2 space astrometry, and high-resolution high signal-to-noise HERMES and HARPS time-series spectroscopy of the slowly rotating B2V star HD 170580. Results. From the time-series spectroscopy we derive v sin i = 4±2 km s −1 , where the uncertainty results from the complex pulsational line-profile variability that was so far ignored in the literature. We detect 42 frequencies with amplitude above five times the local noise level. Among these we identify five rotationally split triplets and one quintuplet. Asteroseismic modelling based on CoRoT, Gaia DR2 and spectroscopic data leads to a star of M ∼ 8 M near core-hydrogen exhaustion and an extended overshoot zone. The detected low-order pressure-mode frequencies cannot be fit within the uncertainties of the CoRoT data by models without atomic diffusion. Irrespective of this limitation, the low-order gravity modes reveal HD 170580 to be a slow rotator with an average rotation period between 73 and 98 d and a hint of small differential rotation. Conclusions. Future Gaia DR3 data taking into account the multiplicity of the star, along with long-term TESS photometry would allow to put better observational constraints on the asteroseismic models of this blue evolved massive star. Improved modelling with atomic diffusion, including radiative levitation, is needed to achieve compliance with the low helium surface abundance of the star. This poses immense computational challenges but is required to derive the interior rotation and mixing profiles of this star.