Abstract
Evolution of stars with initial masses \(M_{\textrm{ZAMS}}=1.1\) , \(1.3\) , and \(1.5\;M_{\odot}\) and relative mass abundances of metals \(Z=0.006\) and 0.02 was computed from the main sequence up to the final AGB stage. Selected models of evolutionary sequences were used as initial conditions for solution of the equations of hydrodynamics describing pulsations of red giants, whereas for each evolutionary sequence of Mira variables pulsating in the fundamental mode we determined the theoretical period–luminosity relation. A change in the metal abundance is shown to substantially affect the period–luminosity relation because of significant growth of the slope with decreasing \(Z\) . In particular, Mira variables of the LMC ( \(Z=0.006\) ) with periods from 200 to 300 days are brighter by 0.2–0.5 mag than galactic Mira variables ( \(Z=0.02\) ) with same pulsation periods. The low boundary of fundamental mode pulsations changes from \(\Pi\approx 70\) day for \(Z=0.02\) to \(\Pi\approx 120\) day for \(Z=0.006\) .
