Theoretical estimates of the pulsation period change rates in LMC Cepheids are obtained from consistent calculation of stellar evolution and nonlinear stellar pulsation for stars with initial chemical composition X = 0.7, Z = 0.008, initial masses 5M ⊙ ≤ M ZAMS ≤ 9M ⊙ and pulsation periods ranged from 2.2 to 29 day. The Cepheid hydrodynamical models correspond to the evolutionary stage of thermonuclear core helium burning. During evolution across the instability strip in the HR diagram the pulsation period Π of Cepheids is the quadratic function of the evolution time for the both fundamental mode and first overtone. Cepheids with initial masses M ZAMS ≥ 7M ⊙ pulsate in the fundamental mode and the period change rateΠ varies nearly by a factor of two for both crossings of the instability strip. In the period -period change rate diagram the values of Π andΠ concentrate within the strips, their slope and halfwidth depending on both the direction of the movement in the HR-diagram and the pulsation mode. For oscillations in the fundamental mode the half-widths of the strip are δ logΠ = 0.35 and δ logΠ = 0.2 for the first and the secon crossings of the instability strip, respectively. Results of computations are compared with observations of nearly 700 LMC Cepheids. Within existing observational uncertainties ofΠ the theoretical dependences of the period change rate on the pulsation period are in a good agreement with observations.

ReceivedAbstract -Excitation of radial oscillations in population I (X = 0.7, Z = 0.02) red supergiants is investigated using the solution of the equations of radiation hydrodynamics and turbulent convection. The core helium burning stars with masses 8M ⊙ ≤ M ≤ 20M ⊙ and effective temperatures T eff < 4000K are shown to be unstable against radial pulsations in the fundamental mode. The oscillation periods range between 45 and 1180 days. The pulsational instability is due to the κ-mechanism in the hydrogen and helium ionization zones. Radial pulsations of stars with mass M < 15M ⊙ are strictly periodic with the light amplitude ∆M bol ≤ 0. m 5. The pulsation amplitude increases with increasing stellar mass and for M > 15M ⊙ the maximum expansion velocity of outer layers is as high as one third of the escape velocity. The mean radii of outer Lagrangean mass zones increase due to nonlinear oscillations by ≤ 30% in comparison with the initial equilibrium. The approximate method (with uncertainty of a factor of 1.5) to evaluate the mass of the pulsating red supergiant with the known period of radial oscillations is proposed. The approximation of the pulsation constant Q as a function of the mass-to-radius ratio is given. Masses of seven galactic red supergiants are evaluated using the period-mean density relation.

ReceivedAbstract -Instability of population I (X = 0.7, Z = 0.02) massive stars against radial oscillations during the post-main-sequence gravitational contraction of the helium core is investigated. Initial stellar masses are in the range 65M ⊙ ≤ M ZAMS ≤ 90M ⊙ . In hydrodynamic computations of self-exciting stellar oscillations we assumed that energy transfer in the envelope of the pulsating star is due to radiative heat conduction and convection. The convective heat transfer was treated in the framework of the theory of time-dependent turbulent convection. During evolutionary expansion of outer layers after hydrogen exhaustion in the stellar core the star is shown to be unstable against radial oscillations while its effective temperature is T eff > 6700K for M ZAMS = 65M ⊙ and T eff > 7200K for M ZAMS = 90M ⊙ . Pulsational instability is due to the κ-mechanism in helium ionization zones and at lower effective temperature oscillations decay because of significantly increasing convection. The upper limit of the period of radial pulsations on this stage of evolution does not exceed ≈ 200 day. Radial oscillations of the hypergiant resume during evolutionary contraction of outer layers when the effective temperature is T eff > 7300K for M ZAMS = 65M ⊙ and T eff > 7600K for M ZAMS = 90M ⊙ . Initially radial oscillations are due to instability of the first overtone and transition to fundamental mode pulsations takes place at higher effective temperatures (T eff > 7700K for M ZAMS = 65M ⊙ and T eff > 8200K for M ZAMS = 90M ⊙ ). The upper limit of the period of radial oscillations of evolving blueward yellow hypergiants does not exceed ≈ 130 day. Thus, yellow hypergiants are stable against radial stellar pulsations during the major part of their evolutionary stage.