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Astron. Astrophys. 354, 77-85 (2000)

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2. The synthetic curves

In order to test both the accuracy and the consistency of the revised CORS method we adopted the observables predicted by hydrodynamical models of variable stars. The reader interested in a detailed discussion on the physical assumptions adopted to construct these models and on the comparison between theory and observations is referred to BCM, BMS, and BCCM. Among the different sequences of nonlinear models we selected canonical models 2 at solar chemical composition (Y=0.28, Z=0.02) and stellar masses ranging from 5 to 11 [FORMULA]. At fixed stellar mass we generally selected three models which are located in the middle of the instability strip as well as close to the blue and the red edge. The period of the selected models roughly ranges from 3.5 to 106 days. The input parameters and the pulsation periods are summarized in Table 1 which gives, from left to right, (1) the model identification, (2) the stellar mass, (3) the luminosity, (4) the effective temperature, (5) the nonlinear time average radius along a full pulsation cycle, (6) the nonlinear pulsation period.


Table 1. Physical properties of the selected Cepheid models

Theoretical observables have been transformed into the observational plane by adopting the bolometric corrections (BC) and the color-temperature relations by Castelli et al. (1997a,b). We assumed [FORMULA]=4.62 mag. The main difference between the static atmosphere models constructed by the quoted authors and the grid of models computed by Kurucz (1992) is that overshooting was neglected. In fact, they found that for temperatures and gravities typical of the Cepheid instability strip both the color indices and the Balmer profiles of the models constructed by neglecting overshooting are in better agreement with observational data. Unfortunately the set of atmosphere models provided by Castelli et al. (1997a,b) was constructed by adopting a fixed value of microturbulence velocity [FORMULA] km s-1. Even though it has been recently suggested by Bersier et al. (1997) that theoretical colors based on atmosphere models which adopt higher microturbulent velocities are in better agreement with observational data, we plan to investigate the dependence on this parameter as soon as homogeneous sets of atmosphere models constructed by adopting different [FORMULA] values become available.

To account for the effect of the gravity on both magnitudes and colors, the luminosity and temperature variations along the pulsation cycle have been transformed by adopting static and effective gravities 3. In the following the models transformed by adopting [FORMULA] and [FORMULA] will be referred to as "static" and "effective" models, respectively. For each model we have taken into account two magnitudes -V, K- and four colors, namely [FORMULA], [FORMULA], [FORMULA], and [FORMULA]. Fig. 1 shows these curves together with the variations of radius, effective temperature, and gravity for the model at 7 [FORMULA] and [FORMULA] K. The curves plotted in this figure show quite clearly that both magnitude and colors present a negligible dependence on gravity. In fact, even though static and effective gravities attain different values along the cycle and present a difference of the order of 0.05 dex close to the bump phases, the two synthetic curves are almost identical (for a detailed analysis of the dependence of bump Cepheids on static and effective gravities see Sect. 4).

[FIGURE] Fig. 1. Variations along a full pulsation cycle of several theoretical observables for the model at 7 [FORMULA] and [FORMULA] K. This model presents a well-defined bump soon after the phase of luminosity maximum. Solid lines and dots display magnitudes and colors transformed by adopting static and effective gravities respectively.

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© European Southern Observatory (ESO) 2000

Online publication: January 31, 2000