Evolutionary status of Polaris
Hydrodynamic models of short--period Cepheids were computed to determine the pulsation period as a function of evolutionary time during the first and third crossings of the instability strip. The equations of radiation hydrodynamics and turbulent convection for radial stellar pulsations were solved with the initial conditions obtained from the evolutionary models of population I stars (X=0.7, Z=0.02) with masses from 5.2 to 6.5 Msol and the convective core overshooting parameter 0.1 <= aov <= 0.3. In Cepheids with period of 4 d the rate of pulsation period change during the first crossing of the instability strip is over fifty times larger than that during the third crossing. Polaris is shown to cross the instability strip for the first time and to be the fundamental mode pulsator. The best agreement between the predicted and observed rates of period change was obtained for the model with mass of 5.4 Msol and the overshooting parameter aov=0.25. The bolometric luminosity and radius are L = 1.26e3 Lsol and R = 37.5 Rsol, respectively. In the HR diagram Polaris is located at the red edge of the instability strip.