Vol 45, No 6 (2019)

We have studied a sample containing ~6000 OB stars with proper motions and trigonometric parallaxes from the Gaia DR2 catalogue. The following parameters of the angular velocity of Galactic rotation have been found: Ω₀ = 29.70 ± 0.11 km s^-1 kpc^-1, Ω'₀ = -4.035 ± 0.031 km s^-1 kpc^-2, and Ω ₀ = 0.620 ± 0.014 km s^-1 kpc^-3. The circular rotation velocity of the solar neighborhood around the Galactic center is V₀ = 238 ± 5 km s^-1 for the adopted Galactocentric distance of the Sun R₀ = 8.0 ± 0.15 kpc. The amplitudes of the tangential and radial velocity perturbations produced by the spiral density wave are f_θ = 4.4 ± 1.4 kms^-1 and f_R = 5.1 ± 1.2 kms^-1, respectively; the perturbation wavelengths are λ_θ = 1.9 ± 0.5 kpc and λ_R = 2.1 ± 0.5 kpc for the adopted four-armed spiral pattern. The Sun's phase in the spiral density wave is χ_⊙ = -178° ± 12°.

Evolutionary calculations of population II stars with chemical composition of the globular cluster M3 were carried out under various assumptions about the initial stellar mass (0.809 M_⊙ ≤ M_ZAMS ≤ 0.83 M_⊙ and the mass loss rate parameter in the Reimers formula (0.45 ≤ η_R ≤ 0.55). In general, 30 evolutionary tracks of the horizontal branch stars were computed. Selected models of evolutionary sequences were used as initial conditions for solution of the equations of hydrodynamics that describe radial stellar oscillations. Hydrodynamic models of RR Lyr type stars were computed for the core helium burning stage as well as for the preceding pre-ZAHB stage. Analytic relations for the effective temperature of the instability strip edges as a function of stellar luminosity are obtained. Theoretical histograms of the period distribution of RR Lyr type variables were produced for each evolutionary sequence using Monte-Carlo simulations based on the consistent stellar evolution and nonlinear stellar pulsation calculations. A satisfactory agreement with observations (i.e., the greater number of RRab variables) was found for the evolutionary sequence M_ZAMS = 0.811 M_⊙, ηR= 0.55 with the number fraction of fundamental mode pulsators ≈ 75%. At the same time the mean period of fundamental mode pulsators (〈Π〉₀ = 0.79 day) is substantially greater compared to the observational estimate of 〈Π〉_ab.

The formation of hydrogen emission lines in the magnetospheres of young stars is considered. The magnetosphere is assumed to be formed by a dipolar magnetic field whose axis is aligned with the stellar rotation axis. The radiative transfer in spectral lines is considered in the Sobolev approximation by taking into account the nonlocal radiative coupling. The gas density and temperature distributions in the magnetosphere are taken to be the same as those in Hartmann et al. (1994). The results of our calculations of the Hα and Hβ line intensities and profiles are presented for the case of a slowly rotating star. We separately consider the magnetospheric models in which the infalling gas is heated by radiation from an accretion spot on the stellar surface and the case where the axis of the magnetosphere is tilted with respect to the stellar rotation axis. Rotational modulation of the spectral line profiles with the stellar rotation period is observed in the latter case.

The Gnevyshev—Waldmeier rule relating the lifetimes of sunspot groups and their areas has been verified on an interval of ≈140 years, which exceeds the one used by M.N. Gnevyshev by a factor of 6. The range of lifetimes of recurrent groups under study has been extended from 40 to almost 90 days. The linear form of the Gnevyshev—Waldmeier rule has been confirmed. A more accurate expression for this law is shown to be A_max= (13.0 ± 1.1) LT, where LT is the lifetime of a group in days and A_max is its maximum area in the time of observation measured in millionths of the solar hemisphere. Thus, the conversion factor from the lifetimes to the maximum areas of sunspot groups turns to be larger than that in Gnevyshev (1938) by a factor of ≈1.3.