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 $-0.02\le\dot\Pi\le 0.05~\mathrm{day}/10^6\mathrm{yr}$. Theoretical estimate of the mean period change rate obtained by the population synthesis method is $\langle\dot\Pi\rangle=6.0\times 10^{-3}~\mathrm{day}/10^6\mathrm{yr}$ and agrees well with observations of RR Lyr variables of the globular cluster M 3.