Astron. Astrophys. 363, 593-600 (2000)

1. Introduction

Features of observed light and velocity curves of pulsating stars must contain information about the stellar physical status, and this motivates the widespread application of Fourier decomposition techniques to regular variable stars. Simon & Lee (1981) performed the Fourier decomposition of the Cepheid light curves, and found a sharp rise of the relative phase (or phase difference) and a remarkable dip of the ratio of amplitudes of the low order Fourier components in the vicinity of the period 10 days. Velocity curves then were analyzed with the same technique by Simon & Teays (1983), and the lower order Fourier components showed a similar behavior.

Many theoretical nonlinear models were calculated with various physical assumptions and different hydrodynamic codes to explain this feature, which is also called Hertzsprung progression (Hertzsprung, 1926). A modal resonance between the second overtone and the fundamental mode, first proposed by Simon & Schmidt (1976), was identified as responsible for it. However the mass of canonical evolutionary models, such as those obeying the mass-luminosity relation M-L obtained by Becker et al. (1977), had to be reduced to about 60% to realize this resonance in the observed period range, which is called bump mass discrepancy. Non-linear calculations have succeeded in reproducing the main features of light and velocity curves (see e.g. Buchler et al. 1990), and the introduction of the OPAL opacity confirmed these positive results, and also considerably reduced the bump mass discrepancy (Moskalik et al. 1992).

While the mass-discrepancy of double-mode Cepheids was resolved with the OPAL opacity (Moskalik at al. 1992; Kanbur & Simon 1994), there are still some unsolved problems of nonlinear pulsations for shorter period Cepheids. The double-mode behavior seems to be now reproducible thanks to the introduction of turbulent convection (e.g. Buchler & Kollath 1999), and this should be in part also the case of the resonance in the first overtone pulsators between the first and the fourth overtone modes (for this problem, see Antonello & Aikawa 1993, 1995; Schaller & Buchler 1993). Feuchtinger et al. (2000) constructed convective models for the first overtone pulsators and succeeded in reproducing the observed feature of the resonance. But the positive results are limited to Cepheids in Galaxy, and presently it is not possible to reproduce the features observed in Cepheids of low metallicity galaxies such as the Magellanic Clouds (e.g. Buchler & Kollath 1999).

There have not been so many calculations of nonlinear pulsations for longer period Cepheids. Carson & Stothers (1984) pointed out that the amplitude variation with pulsation periods in their nonlinear models based on the canonical M-L relation did not fit the observations. On the other hand, Davis et al. (1981) claimed that the light curve features in X Cygni (16.4 d) could be explained only by a model based on this relation. Simon & Kanbur (1995) made a large number of nonlinear models and tried to compare them with obervations using the Fourier parameters.

The comparison of model output with observations seems to be more difficult for longer period Cepheids than for shorter period ones, because the modal couplings are a crucial mechanisms for explaining many features in shorter period Cepheids, but we do not know what are the mechanisms in longer period Cepheids. We propose that oscillations with considerably strong non-adiabaticity is one of the possible keys to characterize the pulsation in longer period Cepheids.

In this paper, we shall investigate features of light and velocity variations in nonlinear pulsation models of longer period Cepheids systematically, and compare them with observations. Antonello & Morelli (1996) published a large set of Fourier components of observed light curves. Kovács et al. (1990) published Fourier components of observed velocity curves also for longer period Cepheids, and we shall supplement it with other available data for two stars.

In Sect. 2 we describe our nonlinear pulsation modelling, we compare our results with observations in Sect. 3, we briefly discuss several interesting features in nonlinear models in Sect. 4 and make conclusions in Sect. 5.

© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000
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