Evolution and pulsations of population I post-AGB stars

Evolutionary calculations of population I stars with initial masses $M_0=1M_{\odot }$, $1.5M_{\odot }$ and $2M_{\odot }$ were carried out up to the stage of the proto–planetary nebula. Selected models of post–AGB evolutionary sequences with effective temperatures $3.6\times 10^3,$\mathrm{K}$\lesssim T_$\mathrm{e}\mathrm{f}\mathrm{f}$\lesssim 2\times 10^4,$\mathrm{K}$$ were used as initial conditions in calculations of self–escited stellar oscillations. For the first time the sequences of hydrodynamic models of radially pulsating post–AGB stars were computed using the self–consistent solution of the equations of radiation hydrodynamics and time–dependent convection. Within this range of effective temperatures the post–AGB stars are the fundamental mode pulsators with period decreasing as the star evolves from $\mathrm{\Pi }\approx 300$ day to several days. Period fluctuations are due to nonlinear effects and are most prominent at effective temperatures $T_{\mathrm{e}\mathrm{f}\mathrm{f}}<5000$K. The amplitude of bolometric light variations is $\mathrm{\Delta }{M}_{\mathrm{b}\mathrm{o}\mathrm{l}}\approx 1$ at $T_$\mathrm{e}\mathrm{f}\mathrm{f}$ \lesssim 6000$Kandrapidlydecreaseswithincreasing$T_$\mathrm{e}\mathrm{f}\mathrm{f}$$. The theoretical dependence of the pulsation period as a function of effective temperature obtained in the study can be used as a criterion for the evolutionary status of pulsating variables suspected to be post–AGB stars.