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

Abstract

AbstractLinear 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)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.(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.(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.