Astron. Astrophys. 324, 121-132 (1997)

5. Discussion and conclusions

The frequency analysis performed by the least-squares method allowed us to obtain a very detailed description of the light curves of the galactic DMCs. With respect to the goals of this first investigation, some conclusions can be extracted directly from the analysis reported in the previous section:

1. The order terms are present in the light curves of all the stars, but often a fit limited to the order is not satisfactory. As regards the component, only AX Vel and GZ Car do not show the 3 harmonic, while TU Cas, U TrA and UZ Cen show also the harmonic. As regards the component, only the first harmonic is observed in its light curve. The coupling terms are observed in a large variety of combinations. The  and  terms are observed in all the stars and also the 2 +  term is rather common. Alcock et al. (1995) and Welch et al. (1996) presented only the order components in their discussion of DMC light curves in the LMC; probably a deeper analysis can yield additional interesting results.
2. The two independent frequencies and  seem to be very stable, in the sense that a reasonable fit can be obtained without admitting their variation. U TrA is the most promising candidate to show such a variation, since a slightly different value was obtained for the oldest subset;
3. In none of the stars a convincing third independent periodicity is detected, even in the cases of TU Cas and BQ Ser, the two claimed candidates;
4. The amplitudes of the modes do not show variations exceeding the error bars, with the exception of the  term in the EW Sct light curve; this star it is the most suitable target for an extensive long-term photometry project carried out by using a very stable instrumentation. Berdnikov (1992) showed how the light curve changes in amplitude over a period when considering different phases of the other period. However, this effect is not real, since it is due to the presence of the cross coupling terms, which Berdnikov did not subtract from the original measurements; when considering these terms, light curves with constant amplitude over each period can be easily constructed, as Fig. 3 shows for BQ Ser. A full set of light curves over the two periods for each DMC can be found in Pardo (1995).

In the introduction we mentioned the separation between classical and s -Cepheids in the space of Fourier parameters; Antonello et al. (1990) ascribed this separation to the different pulsation mode and also invoked the action of a resonance at or near 3.0 d to explain the "Z " shape of the s -Cepheid progression. The very reliable Fourier parameters now at our disposal for the galactic DMCs allow us to give an independent confirmation of these interpretations. Fig. 4 shows the distribution of the values of the galactic DMCs superimposed on the classical and s -Cepheids ones. The values of the DMCs corresponding to the F radial mode occupy the same region as the classical Cepheids and the values of the the 1O radial mode mimic the "Z " shape: note the overlap between DMCs and s -Cepheids in the upper part, the high value at 3.0 d (BQ Ser) and the positioning of the two values belonging to the longest period DMCs (EW and V367 Sct) just on the lower part. It appears quite evident that in the DMCs the light curves of the F -radial mode and the 1O -mode are very similar to the curves of the classical and s -Cepheids, respectively. In turn, this fact proves without any doubt that s -Cepheids are pulsating in the 1O mode and that the value can be considered a powerful discriminant between these modes. It should also be noted that F -mode light curves follow the Hertzsprung progression. A discontinuity is present near 3.0 d in the light curves of 1O pulsators and a resonance effect is the more likely cause.

Fig. 4. The P - plane. Dots: single-mode Classical Cepheids. Triangles: s -Cepheids. Filled dots: Fundamental radial mode of DMCs. Filled triangles with 1 error bars: 1O radial mode of DMCs. Except the 1O radial mode of DMCs, the typical uncertainty of values is well below 0.10 rad

The case of CO Aur deserves particular attention. The ratio between the observed frequencies is 0.8008 and this value is explained by the excitation of the 1O and 2O modes. In the -P plane the value for the term falls in the short period region, where the 1O and F sequences are merging; we can only conclude that the value for this unique (in the Galaxy) pulsator is quite similar to the others. It has not been possible to detect the 2  term, i.e. the  light curve is perfectly sine-shaped. Stellingwerf et al. (1987) predicted an asymmetrical light curve for a 2O pulsator, but this does not seem to be verified in the CO Aur case. It should also be noted that between the single-mode Cepheids there are two stars (V1334 Cyg and DT Cyg) showing a perfectly sine-shaped light curve (Poretti 1994). In view of the close similarity evidenced above between single and double-mode pulsators, further investigation of the pulsating mode of V1334 Cyg and DT Cyg is recommended.

© European Southern Observatory (ESO) 1997

Online publication: May 26, 1998

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