A mapping method of age estimation for binary stars: Application to the $\alpha$ Centauri system A and B

TL;DR

This paper presents a method to estimate stellar ages and initial compositions of binary stars using inverse calibration, applied to the Alpha Centauri system, considering observational uncertainties and different chemical assumptions.

Contribution

It introduces a mapping technique for age estimation of binary stars that accounts for chemical composition and observational errors, improving stellar modeling accuracy.

Findings

Estimated ages of Alpha Centauri A and B around 7.8-8.7 Gyr.

Initial helium and metal fractions determined with uncertainties.

Models with higher metallicity and radiative cores fit observed data better.

Abstract

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. 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. 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 ($\alpha_A $ and $\alpha_B$). It uses the observed luminosities ($L_A$ and $L_B$), radii ($R_A$ and $R_B$), and surface chemical compositions ($Z/X_A$ and $Z/X_B$). We used the most recent observational data for $M$, $R$, $L$, and $[Fe/H]$ of $\alpha$ 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 $Z/X_\odot =0.0245$, we obtain an age of $7.8 \pm 0.6$ Ga, $Y_{ini} = 0.284 \pm 0.004$, and $Z_{ini} = 0.0335 \pm 0.0015$. For a low solar $Z/X_\odot = 0.0181$, the derived age is $8.7 \pm 0.6$ Ga, $Y_{ini} = 0.267 \pm 0.008$, and $Z_{ini} = 0.025 \pm 0.002$. Observational errors in the stellar masses of $\pm$0.002 lead to an age error of 0.6 Ga. Overshooting of $0.05-0.20H_p$ 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.