A mapping method of age estimation for binary stars: Application to the <i>α</i> Centauri system A and B

Context. Binary and multiple star systems are abundant, and they are important for determining the ages of exoplanet systems and Galactic populations. Given the wealth of data provided by Gaia and the upcoming PLATO mission, it is essential to improve stellar models to obtain accurate stellar ages. Multiple systems reduce the degeneracy in the stellar parameters that control evolution, and they allow better constraints on the physical processes at work in stellar interiors. Aims. Our objective is to apply a mapping technique to estimate the age of a system and the initial chemical composition. We also evaluate the influence of observational uncertainties in mass and heavy-element mixtures on results. Methods. We applied an inverse calibration method to the evolution of a multiple stellar system, assuming that the stars share the same age and initial chemical composition. This approach determines age, the initial mass fractions of helium ( Y ini ) and heavy elements ( Z ini ), as well as the convective mixing-length parameters ( α A and α B ). It uses the observed luminosities ( L A and L B ), radii ( R A and R B ), and surface chemical compositions ( Z / X A and Z / X B ). Results. We used the most recent observational data for M , R , L , and [Fe/H] of α Centauri A and B as input data for our method. We compared two assumptions for the Z / X ratio, following the results for the solar composition. For an assumed high solar Z / X ⊙ = 0.0245, we obtain an age of 7.8 ± 0.6 Ga, Y ini = 0.284 ± 0.004, and Z ini = 0.0335 ± 0.0015. For a low solar Z / X ⊙ = 0.0181, the derived age is 8.7 ± 0.6 Ga, Y ini = 0.267 ± 0.008, and Z ini = 0.025 ± 0.002. Observational errors in the stellar masses of ±0.002 lead to an age error of 0.6 Ga. Overshooting of 0.05 − 0.20 H p at the boundary of the convective core increases the age by 0.6 − 2.1 Ga. Models with higher Z / X and radiative cores, with ages of 7.2 − 7.8 Ga, appear preferable and show better agreement with the observed asteroseismic frequencies.