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 MZAMS =
1.5 M , 2 M  and 3 M  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 MZAMS. In hydrodynamic models of evolutionary sequences
MZAMS = 2 M  and MZAMS = 3 M  the periods of the first overtone pulsators are 86 d ≤ Π ≤ 123 d
and 174 d ≤ Π ≤ 204 d, whereas all models of the evolutionary sequence MZAMS = 1.5 M  oscillate in
the fundamental mode. Fairly regular radial oscillations exist in stars with pulsation periods Π   500 d.
In models with longer periods the amplitude rapidly increases with increasing Π and oscillations become
irregular.