α Tau is an interesting Red Giant Branch (RGB) star with spectral type K5, yet not well studied. Helium core contraction and hydrogen burning in the shell are occurring in this star. Stars like α Tau are interested to be investigated in order to learn and understand how their evolution processes at the next stage, i.e. Asymptotic Giant Branch (AGB) stage. At AGB stage, a star will suffer stronger oscillations with larger radius than RGB stage. This stage is important because it will be the key-factor on most recent observational data, and Modules for Experiments in Stellar Astrophysics (MESA) and SPECTRUM packages to compute accurate physical parameters and atmospheric models of α Tau at AGB stage. Our computational results show that α Tau will be an AGB star with M = (1.52 ± 0.07) M⊙, Teff = (4545 ± 18) K, and log L = (1.98 ± 0.07) L⊙ at age (2.11 ± 0.27) Gyr. Its radius at this stage is determined to be log R = (1.20 ± 0.92) R⊙. Mass loss at the initial of this stage is still small, i.e. (2.07 ± 0.09) × 10–10 M⊙/yr and it will increase during this stage. The core at this stage contains carbon and oxygen with C/O ∼ 0.26 which shows that α Tau will be type M-AGB. Atmospheric model of α Tau at AGB stage shows that this star will have higher effective temperature and gas pressure than at RGB stage. These conditions will cause the increasing of electron density and Rosseland absorption coefficient in its atmosphere. The hotter atmosphere of AGB stage causes its peak of continuum shifts toward smaller wavelength and yields in three times higher intensity than at RGB stage.
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