Study of transient double-mode behaviour of nonlinear models of Cepheids

Nonlinear pulsation models of Cepheids pulsating in first and second overtone modes have been constructed in order to study their transient double-mode behaviour. The purposes were to: (1) verify the possible nonlinear effects on period ratios; (2) compare the general nonlinear characteristics of the theoretical light curves with the observed ones; (3) check the plausibility of the hypothesis of very low metallicity of CO Aur. The analysis of the transient behaviour indicates that the difference between linear and nonlinear period ratios is always negligible, and hence period ratios of linear models can be used for comparisons with observed values. Moreover, the Fourier analysis suggests that, for a given order of fit, some combination frequency terms should be preferentially detected in real stars, and this is confirmed by observations. Finally, the models suggest that first and second overtone double-mode Cepheids with very low metallicity must have much shorter period than CO Aur; this supports the view that CO Aur is compatible only with a standard mass-luminosity relation.