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Astron. Astrophys. 363, 601-604 (2000)

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3. Theory versus observation

We used the same definitions of the weighted phases (or phase differences) [FORMULA] and the relative amplitude ratios, [FORMULA], and the same procedures of the Fourier fitting as in Paper I.

Fig. 2 shows the weighted phases and relative amplitude ratios of theoretical light and velocity curves for various model sequences, compared with observations. The observed parameters which are presently available concern LMC and SMC Cepheids with [FORMULA] d (Antonello 1998). Since for shorter period Cepheids only light curve data would be available, we decided to take into account the short period Cepheids in Galaxy as a reference. The comparison with the theoretical models will be instructive in any case, since it is known that for [FORMULA] d the [FORMULA] and [FORMULA] values are roughly similar in Galaxy, LMC and SMC. On the other hand, nothing can be said for the present about the higher order Fourier parameters of LMC and SMC Cepheids.

[FIGURE] Fig. 2. Weighted phases, [FORMULA] and relative amplitude ratios, [FORMULA] of theoretical light curves (left panels) and velocity curves (right panels) against period, compared with observations of Cepheids in Galaxy (crosses) and Magellanic Clouds (filled squares). Short dashed line: sequence (a), -200 K; continuous line: sequence (a), -400 K; dotted line: sequence (b), -200 K; long dashed line: sequence (b), -400 K

We summarize here the main results of the comparison.

  • For both M-L relations, the theoretical models reproduce the global features of the trends of observed Fourier components, in particular in the radial velocity case. On the whole, the comparison between models and observations of Cepheids with [FORMULA] d in Magellanic Clouds indicates that it is not possible to choose reliably between sequence (a) and sequence (b) models as the best ones. In this period range, [FORMULA] values of radial velocity curves appear to be probably sensitive to [FORMULA]. Some discrepancies occur in the light curve case for [FORMULA] at P near 100 d, since the observations suggest some structure which is not reproduced by models.

  • The main differences between the Fourier components of the two model sequences are the locations of the effects related to the resonance [FORMULA] (e.g. dips of [FORMULA] values), which are shifted towards longer periods for sequence (a) models. Since there are no significant differences among the light curve parameters of Galaxy and Magellanic Cloud Cepheids for [FORMULA] d, the almost flat distribution of [FORMULA] values of theoretical light curves is openly against the observational results (see e.g. Buchler 1998).

  • Theoretical velocity curves have a sharper response at the 10 days resonance than light curves. Taking into account also the results reported in Paper I, we can conclude that the theoretical radial velocities are less sensitive to different metallicities than theoretical light curves; it would be interesting to check this result with radial velocity observations of LMC and SMC Cepheids with period near 10 d.

  • Antonello (1998) found a new progression of the light and radial velocity curves of longer P Cepheids, and suggested the resonance [FORMULA] at [FORMULA] d as the responsible mechanism for this effect. The present models offer probably half of the required theoretical support to this interpretation. The radial velocity phase differences for [FORMULA] d increases in a way which recalls what occurs at [FORMULA] d, and similarly also the amplitude ratios; unfortunately, it is not possible to get limit cycles for longer P and to verify the complete similarity. As regards the light curves, there is an interesting hint that [FORMULA] reaches a minimum value in this P range, which is expected in case of a resonance; on the other hand the light curve phase differences are structureless, but there are similar problems also for the 10 d resonance. This is an interesting problem theoretically on resonance phenomena under strong non-adiabatic pulsation, if the feature comes from the mode resonance.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000