The evolutionary stage of Betelgeuse inferred from its pulsation periods

Betelgeuse is a well-known bright red supergiant that shows semiregular variations with four approximate periods of 2200, 420, 230, and 185 d. While the longest period was customarily regarded as long secondary period of unknown origin, we identify the ~2200-d period as the radial fundamental mode, and the three shorter periods as the radial first, second, and third overtones. From a linear non-adiabatic pulsation analysis including the pulsation/convection coupling, we have found that these radial pulsation modes are all excited in the envelope of a model in a late stage of the core carbon burning. Models with similar pulsation property have masses of $11\sim 12\, \mathrm{M}_\odot$ ($19\, \mathrm{M}_\odot$ at zero-age main sequence) with luminosities (log L/L_⊙ = 5.27 ~ 5.28) and effective temperatures (log T_eff ≈ 3.53) that are consistent with the range of the observational determinations. We also find that a synthetic light curve obtained by adding the fundamental and the first-overtone mode is comparable with the light curve of Betelgeuse up to the Great Dimming. We conclude that Betelgeuse is likely in the late stage of core carbon burning, and a good candidate for the next Galactic Type II supernova.