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Astron. Astrophys. 333, L35-L38 (1998)

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3. Discussion

After examining the Fourier parameters we suspected the existence of a Hertzsprung-type progression for long-period Cepheids. In Fig. 1 we have plotted the radial velocity and light curves of the Cepheids with period longer than 45 d. It is possible to see that the velocity curve differs from the `normal' shape at [FORMULA] d, it becomes progressively more symmetric and then takes again the `normal' shape after [FORMULA] d. The light curves tend to become more symmetric with increasing period, and between 90 and 134 d the shape changes near the maximum, with the possible presence of a small bump and flat or secondary maximum. The low order Fourier parameters are plotted in Fig. 2 and compared with those of long-period Cepheids in the Galaxy. The data for the galactic Cepheids were taken from Kovacs et al. (1990), Aikawa & Antonello (1997) and Antonello & Morelli (1996). There is a scatter or change of phase differences [FORMULA] of the radial velocity curves in the period range 90 - 134 d, while the [FORMULA] values of light curves are quite uniform and the [FORMULA] values are scattered. In the same period range the amplitude ratios [FORMULA] are rather small, both for radial velocity and light curves. These results remind in part what occurs in fundamental mode Cepheids with [FORMULA] d and in first overtone mode Cepheids with [FORMULA] d; the main difference is the uniformity of [FORMULA] values of the light curves in the present case.

[FIGURE] Fig. 1. Sequences of radial velocity (left panel) and light (right panel) curves of long-period Cepheids in Magellanic Clouds; the periods are reported.

[FIGURE] Fig. 2. Low order phase differences [FORMULA] and amplitude ratios [FORMULA] of radial velocity (left panel) and light (right panel) curves of long-period Cepheids in Magellanic Clouds (filled squares) and Galaxy (crosses)

Before offering the possible interpretation, some remarks are needed: a) the number of stars in our sample is poor, and we have not discriminated between SMC and LMC Cepheids; b) the accuracy of the photometric measurements is not very high and the problems related to the period changes cannot be avoided when selecting the data set for the analysis, if the observations span many years; c) the CORAVEL radial velocity data were obtained in a short time span (less than five years), but three Cepheids, namely HV 837, HV 11157 and HV 883, are binary, and their pulsation curves were derived by Imbert (1994) by correcting for the orbital motion. In spite of these warnings, we think the progression of the curves is real and it is related to a resonance mechanism. The linear adiabatic models indicate [FORMULA] between the fundamental and the first overtone mode as a possible candidate. Some years ago, Petersen (1989) discussed this theoretical case using the old opacities, and suggested that the resonance center should be expected at [FORMULA] d. As a matter of fact, the adiabatic models seem to indicate that the lower overtones tend to satisfy almost simultaneously the relation [FORMULA], or, in other words, their frequencies tend to be coincident with the harmonics of the fundamental mode frequency. However, according to the linear nonadiabatic models these resonances should not occur in the observed period range, since the strong nonadiabaticity gives very different periods and period ratios from adiabatic model results (Aikawa, private communication).

From the comparison of galactic and Magellanic Cloud Cepheids it is possible to note that, even if rather scattered, the distribution of amplitude ratio values differs according to the galaxy: in the Magellanic Clouds, for [FORMULA] d, the [FORMULA] values can be larger than in the Galaxy. This result is probably related to the analogous differences of pulsation amplitude among Cepheids in different galaxies, studied for example by van Genderen (1978). The low number of stars do not allow to study possible differences between LMC and SMC.

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© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998