Radial Pulsations of Stars at the Stage of the Final Helium Flash

Abstract

Stellar evolution calculations were performed for population I stars with masses on the main sequence 1 M_⊙ ≤ M₀ ≤ 1.5 M_⊙ up to the stage of a cooling white dwarf. The final helium flash LTP is shown to occur in post-AGB stars with initial masses 1.3 M_⊙ ≤ M₀ ≤ 1.32 M_⊙ for the overshooting parameter f = 0.016. In the case of more effective overshooting (f = 0.018) the final helium flash occurs at initial masses 1.28 M_⊙ ≤ M₀ ≤ 1.3 M_⊙. Fivefold variations of the mass loss rate parameter at the post-AGB stage do not affect the occurrence of the final helium flash, but lead to noticeable changes of the evolutionary time. Selected models of two evolutionary sequences with an initial mass M₀ = 1.3 M_⊙ and overshooting parameters f = 0.016 and f = 0.018 were used as initial conditions in solving the equations of hydrodynamics describing the radial oscillations of stars with effective temperatures T_eff < 10⁴ K. The maximum pulsation period Π = 117 days determined for the evolutionary sequence M₀ = 1.3 M_⊙, f = 0.016 is in a good agreement with observational estimates of the period of FG Sge. The mass, radius, and effective temperature of the star are M = 0.565 M_⊙, R = 126R_⊙ and T_eff = 4445 K, respectively. At the same time, the average rate of change in the period of FG Sge from 1960 to 1990 exceeds its theoretical estimate approximately by a factor of 3.