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Astron. Astrophys. 326, 620-628 (1997)

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2. Oscillation parameters

2.1. Period

[FORMULA]  Ceti belongs to a group of well-observed [FORMULA]  Cephei stars. Extensive multicolour Strömgren photometry is presented by Jerzykiewicz et al. (1988). This star has sinusoidal light curves with period [FORMULA]. Unlike most other [FORMULA]  Cephei stars, [FORMULA]  Cet does not show multiple periods or multiple line-profile variations. A hypothetical secondary short-period component, which may be responsible for a marginal night-to-night variation of this star, indicates an amplitude not exceeding [FORMULA], cf. Jerzykiewicz et al. (1988). In the case when only one mode of oscillation is known, pure frequency measurements are not sufficient for unique selection of the stellar model despite identification of the harmonic degree l. This is illustrated in Fig. 1, where the diagram log g vs log [FORMULA] is plotted for stellar models with [FORMULA] [FORMULA] (thin lines) calculated for OPAL opacities with metal content parameter [FORMULA]. The initial hydrogen and helium abundances were adopted as equal to [FORMULA] and [FORMULA], respectively. In Fig. 1, stellar models showing unstable [FORMULA] and [FORMULA] radial modes with period exactly the same as observed for [FORMULA]  Cet ( [FORMULA] ) are indicated as thick lines with filled circles for OPAL opacities and thin lines with open circles for OP opacities, respectively. As one can see, models corresponding to [FORMULA] and [FORMULA] are shifted in log g by about 0.13 dex. Use of OP opacities instead of OPAL opacities results in higher effective temperature for the investigated star, cf. Fig. 1. One can therefore conclude that the proper selection of the stellar model is possible if such parameters as P, [FORMULA] and log g are known with good precision for this star.

[FIGURE] Fig. 1. The diagram log g vs. log [FORMULA] for stellar models of [FORMULA] during the Main Sequence phase of evolution (thin lines). Models showing unstable radial modes with period [FORMULA] are plotted as thick lines with filled circles (for OPAL opacities) and thin lines with open circles (for OP opacities), respectively. Lines marked as [FORMULA] indicate the models best fitting the observed energy flux distribution. The lines a, b and c correspond to E( [FORMULA] ) = [FORMULA], [FORMULA] and [FORMULA], respectively.

2.2. Nonadiabatic observables

The nonadiabatic observables, mentioned in Sect. 1, are the amplitude ratios and the phase differences for various oscillating parameters. We rely on results of model calculations made by Cugier at al. (1994) for photometric data and readers are referred to that work for details. This task involves recent results of stellar evolution calculations and linear nonadiabatic pulsation theory (both taken from Dziembowski and Pamyatnykh's 1993 survey), and well-known stellar atmospheres models (line-blanketed Kurucz's 1979a, b data). Fig. 2a and b show the nonadiabatic observables, viz. Colour amplitude / Visual amplitude [FORMULA] Colour phase - Visual phase for models calculated with OPAL and OP opacities. The lines correspond to unstable [FORMULA] and [FORMULA] radial modes with period equal to [FORMULA].

[FIGURE] Fig. 2. a Nonadiabatic observables of [FORMULA]  Cet (starred symbols) on the diagram colour to light amplitude ratio vs. phase difference. The lines correspond to an unstable [FORMULA] radial mode with period exactly the same as observed for this star ( [FORMULA] ). Stellar models calculated by Dziembowski and Pamyatnykh (1993) for OPAL (thick lines with filled circles) and OP (thin lines with open circles) opacities with [FORMULA] are shown. b The same as Panel a but for stellar models calculated for unstable [FORMULA] radial mode. c The observed (starred symbols) phases of light maxima are plotted together with nonadiabatic models displayed in Panel a. d The same as Panel c but for stellar models shown in Panel b.

According to Jerzykiewicz et al. (1988), the phase lag between the light and radial velocity curves is equal to [FORMULA], and no compelling evidence for variation of this quantity was found. The epochs of maximum light are not entirely independent of wavelength. The u curve lags behind the [FORMULA] and y curves by about [FORMULA], cf. Jerzykiewicz et al. (1988). Fig. 2c and d show that observed phases of the flux maximum (starred symbols) as a function of wavelength offer determination of the effective temperature of [FORMULA]  Cet with high precision. The step in log [FORMULA] of the stellar models shown in these figures is equal to 0.005 dex. Using OPAL opacities with [FORMULA], the observed amplitude ratios and the phase differences lead to the nonadiabatic model shown in Cugier's et al. (1994) Table 2. In particular, the best fit model predicts log [FORMULA] = 4.347 and log g = 3.73.

[TABLE]

Table 2. Journal of the IUE observations.

These values should be verified by "classical" methods of determination of [FORMULA] and log g.

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© European Southern Observatory (ESO) 1997

Online publication: October 15, 1997
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