Resonance Effects in Fundamental Mode, First-Overtone, and Double-Mode Cepheids

Abstract

Linear adiabatic periods, period ratios and frequencies of Cepheid models with. P₀ less than about 10 days have been computed, taking into account standard and nonstandard mass-luminosity relations and the new (or augmented) opacities. A comparison of the results with the observed properties of Cepheids has yielded the following conclusions:

(a)

1. A non-standard mass-luminosity relation is needed in order to have good agreement between observed stars and models on the temperature-period (or luminosity) diagram; ‘standard’ models have much lower temperatures and luminosities than observed stars.

2. (b) The linear models predict the following resonances: f₂/f₀ = 2 (well known) at P₀ ∼ 10 days, f₄/f₀ = 3 at P₀ ∼ 6.8 days, f₄/f₁ = 2 at P₁ ∼ 3.2 days, and f₁ + f₀ = f₃ at P₀ ∼ 6.5 days.

3. (c) All these resonances yield effects which have been observed in light curves of Cepheids at the predicted periods: f₂/f₀ = 2 and f₄/f₀ = 3 in classical Cepheids; f₄/f₁ = 2 in first-overtone Cepheids; and f₄/f₁ = 2 and f₁ + f₀ = f₃ in double-mode Cepheids.

The discussion will include comparison with the results obtained with nonlinear models by Moskalik et al. (1992) for fundamental-mode Cepheids, and by Aikawa (1992) for first-overtone Cepheids.