A first attempt to connect pulsational amplitudes with stellar parameters has been recently presented by Brocato et al. (1996) who discussed new data for RR Lyrae stars in the globular M5. However, their investigation was necessarily based on the available pulsational computations given by BS for a fixed but unrealistic amount of atmospheric helium (Y=0.30). Similar pioneering results are now being compared with amplitudes computed under the much more realistic assumption Y=0.24 (Pagel 1995; Peimbert 1995).
Figure 9 (click here) shows the bolometric amplitude as a function of the
effective temperature for a star of 0.65 
at
selected stellar luminosity values and for the two labeled
Šassumptions of atmospheric helium Y=0.24 or Y=0.30.
Note that the figure reports only the amplitudes of models which
present a stable limit cycle in the F and/or in the FO.
One finds that the relation between period and temperature obtained by
assuming a helium content Y=0.24 does not differ considerably from
that obtained by assuming a larger helium abundance (Y=0.30).
The small differences in the range of temperatures taken into account
appear as the direct consequence of the different location in the HR
diagram of the corresponding instability regions.
Figure 9: Bolometric amplitude versus effective temperature for
both fundamental and first overtone variables.
The amplitudes plotted in this figure are referred to models
computed by assuming a fixed stellar mass 
and
two different helium abundances Y=0.24 (solid lines) and
Y=0.30 (dashed lines). The sequences of models characterized by
different luminosity levels are marked with different symbols
A relevant feature for Y=0.24 is that the correlation between the amplitudes of F pulsators and the effective temperature becomes more and more independent of stellar luminosity in comparison with the models which present a higher helium abundance (Y=0.30). This is of course a crucial point, since it leads to a direct correlation between F-amplitudes and effective temperatures, as earlier suggested by Sandage (1981). Moreover, one finds that the distributions of FO amplitudes versus effective temperature keeps showing the characteristic ``bell" shape, with the maximum amplitude sensitively dependent on the luminosity level of the pulsators. These amplitudes moving from Y=0.30 to 0.24 do not show systematic differences, since at higher luminosities the two curves are almost identical. At lower luminosities the models with Y=0.30 present pulsational amplitudes which are initially larger and then smaller in comparison with the models characterized by Y=0.24.
Before attempting to match pulsational and evolutionary
prescriptions, it is necessary to evaluate the effects of varying
the stellar mass in the above quoted scenario.
This is shown in Fig. 10 (click here) in which we
report pulsational amplitudes against effective temperatures
but for fixed helium content (Y=0.24) and for two different assumptions
on stellar mass M=0.65 and 
.
Figure 10: Bolometric amplitude versus effective temperature for
both fundamental and first overtone variables.
The amplitudes plotted in this figure are referred to models
computed by assuming a fixed helium content (Y=0.24) and
two different stellar masses 
(solid lines),
and 
(dashed lines).
The sequences of models characterized by
different luminosity levels are marked with different symbols
Figure 10 (click here) shows that a mass increase has little effect on the amplitudes of F-pulsators, whose independence of the luminosity level appears even strengthened for higher masses. On the contrary, at lower luminosities we find that an increase of the stellar mass implies an increase in FO amplitudes. As a point that will be relevant further on, Fig. 10 (click here) supports the suggestion of BS that the amplitude of FO pulsators along the decreasing branch leading to the red limit is largely independent of the stellar luminosity. We further find that, for a given temperature, this amplitude appears moderately dependent on the pulsator mass, increasing when the mass increases. We can find a reason for such a behavior by recognizing that the decreasing branch appears populated by FO pulsators in the OR-region, and by assuming that the pulsational amplitude only depends on the distance in temperature from the red edge. According to such a picture, FO amplitudes are expected to be largely independent of the luminosity for a given mass, while increasing the mass at any given temperature increases the amplitude because the FO boundary shifts toward cooler temperatures, thus increasing the distance of the given temperature from the FO-RE.
Concerning the predicted behavior of stars in GGCs, one may notice that the amplitude distributions shown in Fig. 10 (click here) give two different periods in the OR-region, one along the F and the other along the FO sequence. If the suggestion advanced in the previous section about the efficiency of the hysteresis mechanism is correct, one expects OR-regions populated according to the Oosterhoff type, either by FO (OoII) or by F pulsators (OoI). In terms of the data shown in Fig. 10 (click here) one expects in OoII type clusters the occurrence of a well developed decreasing branch of FO pulsators together with a sequence of F pulsators depopulated in its upper portion. On the contrary, in OoI type clusters one expects a sequence of F pulsators populated up to the largest amplitude, with negligible evidence for the decreasing branch of first overtones.
The discussed scenario
can be safely extended to the case for 
,
as illustrated by data in Fig. 11 (click here). Indeed, both the FO
amplitudes and the width in temperature of the FO region
regularly decrease when passing from 
to 0.65
and 
. Moreover, one finds that F pulsators arrange
even better along the previous amplitude-temperature relation.
As a result, if pulsational prescriptions
given through Figs. 10 (click here) and 11 are taken at their face values,
the observed amplitudes of F pulsators should allow the determination
of stellar effective temperatures with an error of about 
,
if not better, independently of the stellar mass and luminosity.
Figure 11: Pulsational amplitudes versus effective temperature for
three different assumptions on stellar mass. First overtone amplitudes
refer to the common value of luminosity 
.
Fundamental amplitudes are given for 
,
1.81 (
) and 
, 1.81. 1.91
(
)