Evolutionary and Hydrodynamic Models of Short-Period Cepheids

Abstract

Pulsation period evolution during the helium-shell flash in the Mira variable R Hya is investigated using consistent stellar evolution and non-linear stellar pulsation computations. The initial and time-dependent inner boundary conditions for the equations of radiation hydrodynamics describing non-linear stellar oscillations were determined using a grid of TP-AGB model sequences with initial masses on the main sequence 1.5M ⊙ ≤ M ZAMS ≤ 5.0M ⊙ and the initial metallicity Z = 0.014. The setup of initial conditions for hydrodynamic models corresponds to ≈ 100 yr prior to the maximum of the helium-shell luminosity and ensures that the stellar envelope of the evolution model is under both hydrostatic and thermal equilibrium. Solution of the equations of hydrodynamics allowed us to determine the temporal variation of the pulsation period Π(t) during ≈ 500 yr. Within this time interval R Hya is a fundamental mode pulsator. The period temporal dependencies Π(t) calculated for the AGB star models at the beginning of the third dredge-up phase and with masses 4.4M ⊙ < ≈ M < ≈ 4.5M ⊙ are in agreement with observational estimates of the period of R Hya obtained during last two centuries. The mean radius of R Hya pulsation models at the end of the XX century (470R ⊙ < ≈ R < ≈ 490R ⊙ ) agrees with observational estimates obtained using the interferometric angular diameter measurements.

Effects of metallicity on mode switching in Cepheids

“…Thus, there is an opportunity to evaluate the fundamental parameters of this star on the basis of consistent stellar evolution and nonlinear stellar pulsation calculations. However, the earlier attempt to determine the fundamental parameters of CG Cas for the evolutionary sequences with metal abundance Z = 0.02 failed because the upper limit of the first overtone period was found to be shorter than the period of CG Cas (Fadeyev 2020).…”

“…The periods of the fundamental mode Π 0 and the first overtone Π 1 corresponding to oscillation mode switching are described with good accuracy as a function of mean density ρ = M/( 4 3 πR 3 ), where M and R are the mass and the radius of the Cepheid (Fadeyev 2020). This conclusion is based on results of consistent stellar evolution and nonlinear stellar pulsation calculations for Cepheid models with main sequence masses 5.1M ≤ M 0 ≤ 6.1M Therefore, the dependencies Π 0 (ρ) and Π 1 (ρ) for other values of Z remain uncertain.…”