Evolution and period change in RR Lyr variables of the globular cluster M 3

The grid of evolutionary tracks of population II stars with initial masses from $0.81M_{\odot }$ to $0.85M_{\odot }$ and chemical composition of the globular cluster M 3 is computed. Selected models of horizontal branch stars were used as initial conditions for solution of the equations of radiation hydrodynamics and time–dependent convection describing radial stellar oscillations. The boundaries of the instability strip on the Herztsprung–Russel diagram were determined using nearly 100 hydrodynamic models of RR Lyr pulsating variables. For each evolutionary track crossing the instability strip the pulsation period was determined as a function of evolutionary time. The rate of period change of most variables is shown to range within $-0.02\le\dot\Pi\le 0.05~$\mathrm{d}\mathrm{a}\mathrm{y}$/10^6$\mathrm{y}\mathrm{r}$$. Theoretical estimate of the mean period change rate obtained by the population synthesis method is $⟨\dot{\mathrm{\Pi }}⟩=6.0\times {10}^{-3}\mathrm{d}\mathrm{a}\mathrm{y}\mathrm{/}{10}^6\mathrm{y}\mathrm{r}$ and agrees well with observations of RR Lyr variables of the globular cluster M 3.