Theoretical Period–Radius and Period–Luminosity Relations for Mira Variables with Solar Metallicity

Evolutionary sequences of AGB stars with initial masses on the main sequence \(M_{\textrm{ZAMS}}=1.5\;M_{\odot}\), \(2\;M_{\odot}\), and \(3\;M_{\odot}\) were computed for the initial metallicity \(Z=0.014\). Selected models of evolutionary sequences with envelopes under thermal equilibrium were used as initial conditions for calculation of nonlinear stellar pulsations. The hydrodynamic models of each evolutionary sequence are shown to concentrate along the continuous line in the period–radius and period–luminosity diagrams. The theoretical period–radius and period–luminosity relations differ from one another for different main–sequence star masses because the stellar luminosity of AGB stars depends on the degenerate carbon core mass which increases with increasing \(M_{\textrm{ZAMS}}\). In hydrodynamic models of evolutionary sequences \(M_{\textrm{ZAMS}}=2\) and \(3\;M_{\odot}\) the periods of the first overtone pulsators are \(86\leq\Pi\leq 123\textrm{d}\) and \(174\leq\Pi\leq 204\textrm{d}\), whereas all models of the evolutionary sequence \(M_{\textrm{ZAMS}}=1.5\;M_{\odot}\) oscillate in the fundamental mode. Fairly regular radial oscillations exist in stars with pulsation periods \(\Pi\lesssim 500\) d. In models with longer periods the amplitude rapidly increases with increasing \(\Pi\) and oscillations become irregular.