Hydrodynamical models for W Vir pulsating variables

Abstract

We have calculated a grid of hydrodynamical models for W Vir pulsating variable stars with mass M = 0.6M⊙ and bolometric luminosity 200 ≤ Lbol/L⊙ ≤ 1.2 × 103. The positions of the blue edge of the instability strip and the boundary separating the domains of periodic and semi-regular pulsation in the H-R diagram were determined. These two boundaries converge for Lbol ≈ 103L⊙. Two different groups of models can be distinguished in the region of periodic solutions, characterized by oscillations with alternating amplitude and duration of the pulsation cycle. For the first group of models, the alternation of the pulsations occurs over a time interval of two periods of the fundamental mode; this is due to the 2П0=3П1 resonance between the fundamental mode and first overtone. The models of the second group have larger luminosities and are located near the boundary separating the domains of periodic and semiregular pulsations. A discrete Fourier transformation analysis shows that, as we approach the region of semiregular pulsations, additional peaks appear in the spectra of the oscillatory moment of inertia and kinetic energy. These peaks correspond to period doubling bifurcations (a Feigenbaum sequence) of order n≤4. Approximate formulas are presented for the pulsation constant Q as a function of the mass-to-radius ratio (M/M⊙)/(R/R⊙) and the luminosity of the star Lbol.