Evolutionary status and fundamental parameters of the Cepheid V1033 Cyg

On the basis of consistent stellar evolution and nonlinear stellar pulsation calculations the Cepheid V1033 Cyg is shown to be the post--main sequence star at the first crossing of the instability strip during gravitational contraction of the helium core. The observed light variability of V1033 Cyg is due to radial oscillations in the fundamental mode. The best agreement (within one percent) between recent observations and the theoretical estimate of the period change rate was obtained for the evolutionary sequence with stellar mass $M=6.3M_\odot$ and helium and heavier element fractional abundances $Y=0.28$ and $Z=0.022$, respectively. The age of the star, the luminosity, the radius, the effective temperature and the surface gravity are $t_\mathrm{ev}=5.84\times 10^7$ yr, $L=2009L_\odot$, $R=45.6R_\odot$, $T_\mathrm{eff}=5726 \mathrm{K}$, $\log g=1.92$.