For each given value of the stellar mass the modal stability of the
envelope models has been explored at selected luminosity levels
(
)
and by assuming a step of 100 K in the effective temperature.
Figure 1 (click here) shows the topology of the instability strip for
, as compared with similar boundaries but for
the mass values
M=0.65 or 
already reported in Bono et al.
(1995). Table 1 (click here) gives luminosities and effective
temperatures along the newly computed boundaries. One finds that the
topology of the instability strip for the mass value 
discloses the same overall features of the instability strip of RR Lyrae
models characterized by larger mass values.
From the same figure it can be seen quite clearly that the width of the
region where only the FO presents a stable limit cycle
increases as the stellar mass increases.
Figure 1 (click here) also shows the location of some FO models
for 
which present a stable limit cycle at
effective temperatures lower than the FO red edge.
These models define a FO stability isle in a
region of the
instability strip where only F pulsators should be
characterized by a stable limit cycle.
A similar but specular finding was obtained by BS. Indeed, they found some F models showing a stable limit cycle in the region of the instability strip where only FO pulsators might be present. The approach to limit cycle stability of these models due to the peculiarities of the dynamical and convective structure will be discussed in a forthcoming paper (Bono et al. 1996).
Figure 1: The location into the HR diagram of the instability strip
for 
is compared with previous results for
larger values of stellar mass and fixed chemical composition.
At the lower luminosities, and for each assumed
mass value, moving from higher to lower effective temperatures the
different curves show: the FO blue edge (FO-BE), the F blue edge (F-BE),
the FO red edge (FO-RE) and the F red edge (F-RE). Asterisks mark the
location of some models for 
which are
characterized by a stable first overtone limit cycle in the region
of the instability strip where only fundamental pulsators should be
present. See text for further details
Table 1: Fundamental and first overtone instability boundaries for
In order to achieve a good accuracy throughout all phases of the pulsation cycle, a variable time step has been adopted: the number of time steps necessary for covering a period ranges roughly from 400 to 600. Before being able to provide any sound conclusion concerning the modal stability and the dependence of the light and velocity curve morphologies on physical parameters and chemical composition, the pulsation characteristics have to approach a limiting amplitude. To accomplish this goal the local conservation equations and the convective transport equation for each case were integrated in time until the initial velocity perturbation settles down and the pulsation behavior (amplitudes, periods) approaches a limit cycle stability.
The time interval necessary for the
radial motions to approach their asymptotic amplitudes ranges from
one thousand to ten thousand pulsational cycles. As a general
rule, we assumed the direct time integration to be
roughly equivalent to the inverse of the linear growth rate.
Therefore, the nonlinear unstable models of the present survey
are all characterized, over two consecutive periods, by a periodic
similarity of the order of or lower than 
.
The range of luminosities covered by the different series of models
was chosen so as to largely cover the theoretical prescriptions from
HB evolutionary models.
For variable stars these models foresee a minimum Zero Age Horizontal
Branch (ZAHB) luminosity
for Z=0.0001 and 
for Z=0.001 respectively. At the same time, the canonical
HB evolutionary
scenario predicts the occurrence of variable stars which are evolving
within the instability strip at moderately larger luminosities.
Figure 2 (click here) presents an atlas of theoretical light curves
of F pulsators for two consecutive periods.
These models were computed by assuming a mass
. The light curves of FO pulsators referred to the
same sequences of models are reported in Fig. 3 (click here).
Figures 4 (click here) and 5 show the same quantities of Figs. 2 (click here) and
3 but are referred to the sequences in which a mass value
was adopted.
Both light and velocity curves for the models discussed in this
paper are available upon request to the authors.
Figure 2: Theoretical light curves of the four sequences of fundamental
pulsators for the stellar mass 
. Each plot shows
the bolometric amplitude for two consecutive periods and the
effective temperature of the model. The luminosity level
of the four sequences are also reported
Figure 3: Same as Fig. 2, but the light curves are referred to
the four sequences of first overtone pulsators
Figure 4: Theoretical light curves of the four sequences of fundamental
pulsators for the stellar mass 
. Each plot shows
the bolometric amplitude for two consecutive periods and the
effective temperature of the model. The luminosity level
of the four sequences are also reported
Figure 5: Same as Fig. 4, but the light curves are referred to the
four sequences of first overtone pulsators
From the calculated light curves we find that the overall morphology, as well as the occurrence of secondary features like ``Bumps" or ``Dips" over the pulsation cycle closely follows the theoretical scenario suggested by BS which is based on models computed by adopting a different helium abundance (Y=0.30). The overall agreement concerning the occurrence of secondary features both in theoretical and observational light curves has been already discussed by Walker (1994) by presenting the photometry of RR Lyrae stars in the galactic globular M68.