Vol 45, No 10 (2019)

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.

For the low-amplitude Cepheid V532 Cyg we have constructed an O − C diagram spanning a time interval of 121 years. The O − C diagram has the shape of a parabola, which has made it possible to determine for the first time the quadratic light elements and to calculate the rate of evolutionary decrease in the period, dP/dt = −0.248 (±0.067) s yr⁻¹, which points to the second crossing of the instability strip. The pulsation stability test proposed by Lombard and Koen (1993) has confirmed that the period decrease is real.

Based on a sample of 7696 nonrecurrent and 566 recurrent sunspot groups, we have investigated the Gnevyshev–Waldmeier rule using the Catalogue of Solar Activity by R.S. Gnevysheva (1954–1978). The maximum recorded sunspot group lifetime is 160 days. The general Gnevyshev–Waldmeier rule for all lifetimes is A_max = (12.1 ± 0.70)LT (A_max is the maximum sunspot group area during the lifetime and LT is the sunspot group lifetime). However, the general rule has turned out to deviate from the derived linear form for the population of small short-living sunspot groups (SSG): it has a significant nonlinear scaling form A_max = (8.02 ± 0.41)LT^{(1.105±0.022)}. For the population of large long-living sunspot groups (LLG) there is a linear form A_max = (12.9 ± 1.1)LT. Allowance only for recurrent sunspot groups with lifetimes more than 40 days gives A_max = (13.93 ± 0.41)LT.