Classically and Asteroseismically constrained 1D Stellar Evolution Models of $\alpha$ Centauri A and B using Empirical Mixing Length Calibrations

TL;DR

This study models the binary system Alpha Centauri A and B using classical and asteroseismic data, exploring different physics assumptions and calibrating the mixing length parameter to match observations, resulting in consistent optimal values and an estimated age of 5.3 Gyr.

Contribution

It provides a comprehensive analysis of stellar models for Alpha Centauri A and B with empirical mixing length calibrations under various physics assumptions, confirming the trend of sub- and super-solar mixing lengths.

Findings

Optimal mixing lengths are 0.932 and 1.095 times solar for Alpha Centauri A and B.

Models fit observations within 3 sigma for 31 out of 150,000 tracks.

Estimated system age is 5.3 ± 0.3 Gyr.

Abstract

The bright, nearby binary $\alpha$ Centauri provides an excellent laboratory for testing stellar evolution models, as it is one of the few stellar systems for which we have high-precision classical (mass, radius, luminosity) and asteroseismic ($p$-mode) observations. Stellar models are created and fit to the classical and seismic observations of both stars by allowing for the free variation of convective mixing length parameter $\alpha_{\text{MLT}}$. This system is modeled using five different sets of assumptions about the physics governing the stellar models. There are 31 pairs of tracks (out of ${\sim} 150,000$ generated) which fit the classical, binary, and seismic observational constraints of the system within $3\,\sigma$. Models with each tested choice of input physics are found to be viable, but the optimal mixing lengths for Cen A and Cen B remain the same regardless of the physical prescription. The optimal mixing lengths are $\alpha_{\text{MLT,A}} /\alpha_{\odot}= 0.932$ and $\alpha_{\text{MLT,B}}/\alpha_{\odot} = 1.095$. That Cen A and Cen B require sub- and super-solar mixing lengths, respectively, to fit the observations is a trend consistent with recent findings, such as in Kervella et al. (2017), Joyce and Chaboyer (2018), and Viani et al. (2018). The optimal models find an age for $\alpha$ Centauri of $5.3 \pm 0.3$ Gyr.