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

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.