Analysis of $\alpha$ Centauri AB including seismic constraints

Detailed models of α Cen A and B based on new seismological data for α Cen B by Carrier & Bourban ([CITE]) have been computed using the Geneva evolution code including atomic diffusion. Taking into account the numerous observational constraints now available for the α Cen system, we find a stellar model which is in good agreement with the astrometric, photometric, spectroscopic and asteroseismic data. The global parameters of the α Cen system are now firmly constrained to an age of $t=6.52 \pm 0.30$ Gyr, an initial helium mass fraction $Y_{\mathrm{i}}=0.275 \pm 0.010$ and an initial metallicity $(Z/X)_{\mathrm{i}}=0.0434 \pm 0.0020$. Thanks to these numerous observational constraints, we confirm that the mixing-length parameter α of the B component is larger than the one of the A component, as already suggested by many authors (Noels et al. [CITE]; Fernandes & Neuforge [CITE]; Guenther & Demarque [CITE]): $\alpha_{\mathrm{B}}$ is about 8% larger than $\alpha_{\mathrm{A}}$ ($\alpha_{\mathrm{A}}=1.83 \pm 0.10$ and $\alpha_{\mathrm{B}}=1.97 \pm 0.10$). Moreover, we show that asteroseismic measurements enable to determine the radii of both stars with a very high precision (errors smaller than 0.3%). The radii deduced from seismological data are compatible with the new interferometric results of Kervella et al. ([CITE]) even if they are slightly larger than the interferometric radii (differences smaller than 1%).