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.

中文翻译：

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最终氦气闪蒸阶段恒星的径向脉动

恒星演化计算是用于人口我与主序列1群众星执行中号_⊙ ≤中号₀ ≤1.5中号_⊙到冷却白矮星的阶段。最终氦闪LTP示于后AGB分发生与初始质量1.3中号_⊙ ≤中号₀ ≤1.32中号_⊙用于过冲参数˚F = 0.016。在更有效的过冲（的情况下˚F = 0.018）的最终氦闪发生在初始质量1.28中号_⊙ ≤中号₀ ≤1.3M的_⊙。在AGB后阶段，质量损失速率参数的五倍变化不会影响最终氦气闪蒸的发生，但会导致进化时间的明显变化。选择的两个进化序列的机型与初始质量中号₀ = 1.3中号_⊙和过冲参数˚F = 0.016和˚F = 0.018在解决流体力学的方程式描述具有有效温度分的径向振荡被用作初始条件Ť _EFF <10 ⁴ K.最大脉动周期Π=117天确定用于进化序列中号₀ = 1.3M的_⊙，f = 0.016与FG Sge时期的观测估计非常吻合。质量，半径，和有效的星的温度是中号= 0.565中号_⊙，- [R = 126 - [R _⊙和Ť _EFF = 4445 K，分别。同时，FG Sge从1960年到1990年这段时期的平均变化率大约比理论估计高出约3倍。