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.

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Eclipsing binaries (EBs) are unique targets for measuring accurate stellar properties and constraining stellar evolution models. In particular, it is possible to measure masses and radii at the few percent level for both components of a double-lined spectroscopic EB (SB2-EB). On the one hand, detached EBs hosting at least one star with detectable solar-like oscillations constitute ideal test objects to verify the ability of ensemble asteroseismology to derive stellar properties. On the other hand, the oscillations and surface activity of stars that belong to EBs offer unique information about the evolution of binary systems. This paper builds upon previous works dedicated to red giant stars (RG) in EBs; so far 20 known systems have been discovered by the NASA Kepler mission. We report the discovery of 16 RGs in EBs, which are also from the Kepler data, leading to a total of 36 confirmed RG stars in EBs from the original Kepler mission. This new sample includes three SB2-EBs with oscillations, resulting in a total of 14 known SB2-EBs with an oscillating RG component. This sample also includes six close systems in which the RG display a clear surface activity and complete oscillation suppression. Based on dedicated high-resolution spectroscopic observations (Apache Point Observatory, Observatoire de Haute Provence), we focus on three main aspects. Firstly, from the extended sample of 14 SB2-EBs, we confirm that the simple application of the asteroseismic scaling relations to RGs overestimates masses and radii of RGs by about 15% and 5%. This bias can be reduced by employing either new asteroseismic reference values for RGs or model-based corrections of the asteroseismic parameters. Secondly, we confirm that close binarity leads to a high level of photometric modulation (up to 10%) and a suppression of solar-like oscillations. In particular, we show that it reduces the lifetime of radial modes by a factor of up to 10. Thirdly, we use our 16 new systems to complement previous observational studies that aimed to constrain tidal dissipation in interacting binaries. We confirm the important role of the equilibrium tide in binary evolution, but we also identify systems with circular orbits despite relatively young ages, which suggests the need to explore complementary tidal dissipation mechanisms in the future. Finally, as a by-product, we report the measurements of mass, radius, and age of three M-dwarf companion stars.