## 2. Predicted relationsThe nonlinear convective pulsating models adopted in this paper are
computed with four values of the stellar mass
(5, 7, 9, 11) and three chemical
compositions ( ## 2.1. Period-luminosityFrom the bolometric light curves of our pulsating models and
adopting the grid of atmosphere models provided by Castelli et al.
(1997a,b), we first derive the predicted intensity-weighted mean
magnitude of pulsators for the
This matter has been already discussed in Paper II on the basis of
the predicted and
relations derived under the
assumption of a uniformly populated instability strip. However, since
the Fig. 2 shows the resulting
distribution of fundamental pulsators with the three selected
metallicities. We derive that the pulsator distribution becomes more
and more linear by going toward the infrared and that, aiming at
reducing the intrinsic scatter of
As a whole, each predicted
relation seems to become steeper at the lower metal abundances, with
the amplitude of the effect decreasing from
In closing this section, let us observe that the adopted way to
populate the instability strip allows ## 2.2. Period-color and color-colorThe three methods of deriving the mean color over the pulsation cycle use either (), the average over the color curve taken in magnitude units, or , the mean intensity over the color curve transformed into magnitude, or , the difference of the mean intensities transformed into magnitude, performed separately over the two bands. In Paper IV it has been shown that there are some significant differences between static and synthetic mean colors, and that the predicted () colors are generally redder than colors, with the difference depending on the shape of the light curves, in close agreement with observed colors for Galactic Cepheids. As a matter of example, the predicted difference ranges from 0.02 mag to 0.08 mag, whereas is in the range of 0.014 mag to 0.060 mag. Fig. 4 shows the pulsator synthetic mean colors as a function of
the period for the three different metallicities. Since, given the
finite width of the instability strip, also the
As for the color-color (
## 2.3. Period-luminosity-colorSince the pioneering paper by Sandage (1958), Sandage & Gratton (1963) and Sandage & Tammann (1968), it is well known that if the Cepheid magnitude is given as a function of the pulsator period and color, i.e. if the Period-Luminosity-Color relation is considered, then the tight correlation among the parameters of individual Cepheids is reproduced (see also Laney & Stobie 1986; Madore & Freedman 1991; Feast 1995 and references therein). In Paper II it has been shown that the intrinsic scatter of the
From the least square solutions through the fundamental models we
derive the coefficients ,
and
presented in Table 6, together
with the residual dispersion () of
about the fit. Figs. 6-8 illustrate
the remarkably small scatter of the
In order to complete the theoretical framework for classical
Cepheids, we have finally considered the Wesenheit quantities Table 7 gives the coefficients of the theoretical
reddening-free
Figs. 9-10 show the theoretical Wesenheit quantities as a function
of the period, together with the predicted relations. From a
comparison of Table 7 with Table 2 one derives that the
intrinsic scatter of and
is significantly lower than the
dispersion of
Moreover, the comparison between Figs. 9-10 and Figs. 6-8 discloses
the deep difference between © European Southern Observatory (ESO) 2000 Online publication: February 9, 2000 |