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Astron. Astrophys. 354, 610-620 (2000)

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3. Comparison with Galactic Cepheids

The principal aim of this paper is to present a wide homogeneus theoretical scenario for Cepheid studies. The analysis of observed pulsational properties is out of our present intentions, but it seems necessary to verify the reliability of our models against well studied variables. For this purpose, we take into consideration the sample of calibrating Galactic Cepheids studied by Gieren et al. (1998, [GFG]) and by Laney & Stobie (1994, [LS]). To the intensity mean BVJK magnitudes we add the [FORMULA] magnitudes as derived from [FORMULA] mag, where the magnitude-weighted [FORMULA] colors are by Caldwell & Coulson (1987). Such a constant correction, suggested by GFG, is confirmed (see Fig. 11) from our synthetic mean colors. Note that, according to GFG, we excluded SV Vul, GY Sge and S Vul for problems with a variable period and EV Sct, SZ Tau and QZ Nor for uncertainty with regard to the pulsation mode.

[FIGURE] Fig. 11. Predicted difference between [FORMULA] and [FORMULA] colors for fundamental pulsators with different masses and chemical compositions. The solid line refers to a difference of -0.03 mag.

Before analyzing the calibrating Galactic Cepheids, let us briefly consider the recent results on Magellanic Clouds Cepheids provided by the OGLE II microlensing survey (Udalski et al. 1999). The final [FORMULA] and [FORMULA] relations given by these authors for Cepheids with [FORMULA], are [FORMULA] and [FORMULA], with a LMC distance modulus [FORMULA] mag. The data in Table 3 with [FORMULA] yield [FORMULA] and [FORMULA], namely a predicted slope in close agreement with OGLE measurements but a zero-point which is brighter by roughly 0.24 mag, suggesting [FORMULA] mag, a value which fits the recent upward revision of the LMC distance derived from field red clump stars (Zaritsky 1999).

As for the [FORMULA] relation presented by Udalski et al. (1999), we find that its slope (-3.28) is in fair agreement with the results (-3.17) of our models with [FORMULA] (see also the lower panel of Fig. 12). Conversely, the OGLE [FORMULA] relation discloses a significative difference with respect to our predicted relations. As shown in the upper panel of Fig. 12, it seems that the OGLE color-term is not able to fully remove the effect of the finite width of the instability strip (as a matter of comparison, see the lower panel of Fig. 7). At the moment we cannot explain such a disagreement and we expect the release of LMC and SMC data to test the full set of our predictions.

[FIGURE] Fig. 12. (lower panel) Wesenheit quantities of fundamental pulsators in comparison with the OGLE WPL relation. (upper panel) OGLE PLC relation applied to fundamental pulsators.

Passing to the Galactic Cepheids, Fig. 13 and Fig. 14 show the predicted linear PL relations with Z=0.02 (dotted line) in comparison with the calibrating Cepheids (dots) from LS and GFG, respectively. Note that both the reddening and true distance modulus given by the authors are adopted. We find a fair agreement in the infrared, whereas in the V and I bands the observed Cepheids with the longer periods appear brighter than the predicted relations. This could suggest that these luminous variables have lower metallicities than the currently adopted value Z=0.02 (see Fry & Carney 1997) or be near the blue edge of the instability strip. One could also suspect that the predicted slopes with Z=0.02 are smaller than the actual ones. This seems supported by Fig. 15 where the steeper PL relations provided by Udalski et al. (1999) are taken into account.

[FIGURE] Fig. 13. Calibrating Galactic Cepheids (dots) in comparison with predicted PL relations with Z=0.02 (dotted line). Data from Laney & Stobie (1994 [LS]).

[FIGURE] Fig. 14. Calibrating Galactic Cepheids (dots) in comparison with predicted PL relations with Z=0.02 (dotted line). Data from Gieren et al. (1998 [GFG]).

[FIGURE] Fig. 15. Calibrating Galactic Cepheids (dots) from Laney & Stobie (1994 [LS]) and Gieren et al. (1998 [GFG]), in comparison with OGLE PL relations for LMC and SMC Cepheids (dashed-dotted line).

However, in order to remove the effects of the finite width of the instability strip, let us apply our predicted PLC relations to the calibrating Cepheids. Figs. 16-17 disclose that predictions and observed data are now in a better agreement. Meanwhile, there are some evidences that the calibrating Galactic Cepheids lie on the average below the theoretical PLC relations with Z=0.02. In other words, our predicted relations yield somehow larger true distance moduli than those given by LS and GFG. Specifically, the left panels of Fig. 18 show that the difference between LS and GFG data and the results of our predicted [FORMULA] relation with Z=0.02, by adopting the reddening values listed by these authors, have a significant period dependence. This trend cannot be ascribed to our color and period term since a quite similar behavior is present in the right panels which refer to the [FORMULA] relation given by Udalski et al. (1999). Notwithstanding the different values of the period and color terms, one finds a similar trend, with the OGLE relation suggesting smaller distances than those listed by LS and GFG.

[FIGURE] Fig. 16. As in Fig. 13, but for predicted PLC relations.

[FIGURE] Fig. 17. As in Fig. 14, but for predicted PLC relations.

[FIGURE] Fig. 18. True distance modulus of Galactic Cepheids from the [FORMULA] relation in comparison with Laney & Stobie (1994 [LS]) and Gieren et al. (1998 [GFG]) data. The left panel refer to the predicted relation with Z=0.02, while the right panels refer to the OGLE result for LMC and SMC Cepheids.

On the other hand, we show in Fig. 19 that the BVI reddenings  4 derived from the predicted color-color relation with Z=0.02 are slightly lower than those given by LS and GFG. The origin of the discrepancy could be found in Fig. 20, where our predicted color-color relation with Z=0.02 (dotted line) is plotted together with the two quadratic relations given by Dean et al. (1978) for the intrinsic color-color locus of the Galactic Cepheids (solid line and dashed line). Since observational studies generally adopt the solution depicted with the solid line, the reason for which our predicted CC relation yields slightly smaller BVI reddenings is explained. This could provide the key to understand the difference in the true distance moduli.

[FIGURE] Fig. 19. Galactic Cepheids BVI reddenings from predicted CC relations with Z=0.02 in comparison with LS93 (circles) and LS94 (dots) values.

[FIGURE] Fig. 20. Predicted [FORMULA] relation with Z=0.02 (dotted line) in comparison with the intrinsic locus of Galactic Cepheids. The solid line and the dashed line refer to the labelled solutions, as given by Dean et al. 1978.

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© European Southern Observatory (ESO) 2000

Online publication: February 9, 2000