Models of Long-Period Variables of the Globular Cluster 47 Tuc

Stellar evolution computations were carried out for stars with a main sequence mass $$M_{\textrm{ZAMS}}=0.86\;M_{\odot}$$ and initial metal abundance $$Z=0.003$$ and $$0.004$$ . Selected models of evolutionary sequences were used for calculation of radial pulsations in the RGB, eAGB and TP–AGB evolutionary stages. Not all pulsating red giants of the globular cluster 47 Tuc are shown to belong to the Mira variables because the lower limit of pulsation periods at the TP–AGB stage is $${\approx}70$$ day, whereas during the eAGB evolutionary stage the periods of radial oscillations range from $${\approx}10$$ to $${\approx}40$$ day. Periods and luminosities of hydrodynamic models of eAGB and TP–AGB pulsating stars locate along the common period–luminosity relation. Small masses of Mira variables in the globular cluster 47 Tuc ( $$0.54\leq M\leq 0.70\;M_{\odot}$$ ) is the main reason for irregular large–amplitude oscillations and the dynamical instability of outer stellar layers at pulsation periods $$\Pi>200$$ day.