RR Lyrae stars in galactic globular clusters - VI. The period-amplitude relation

Aims. This work uses nonlinear convective models of RR Lyrae stars and evolutionary predictions of low- mass helium burning stellarstructures to constrain the properties of cluster and field RR Lyrae variables. In particular, we address two problems: is the Period-Amplitude ( PAV) plane of fundamental ( RRab) variables a good diagnostic for the metal abundance? Is the MV( RR)-[ Fe/ H] relation of field and cluster variables linear over the whole metal abundance range of [ Fe/ H] similar to - 2.5 to similar to 0? Methods. We perform a detailed comparison between theory and observations for fundamental RR Lyrae variables in the solar neighborhood and in both Oosterho. type I ( OoI) and type II ( OoII) Galactic globular clusters. Results. We show that the distribution of cluster RRab variables in the PAV plane depends not only on the metal abundance, but also on the cluster Horizontal Branch ( HB) morphology. We find that on average the observed pulsation parameter kpuls connecting the period to the visual amplitude increases when moving from metal- poor to metal- rich GGCs. However, this parameter shows marginal changes among OoI clusters with intermediate to red HB types and iron abundances - 1.8 = [ Fe/ H] = - 1.1, whereas its value decreases in OoII clusters with the bluer HB morphology, although these clusters are also the less metal- poor ones of the group. Moreover, at [ Fe/ H] = - 1.7 +/- 0.1 the OoI clusters present redder HB types and larger < k(puls) > values than the OoII clusters. The RRab variables in omega Cen and in the solar neighborhood further support the evidence that the spread in [ Fe/ H], at fixed k(puls), is of the order of +/- 0.5 dex. Using the results of synthetic HB simulations, we show that the PAV plane can provide accurate cluster distance estimates. We find that the RRab variables in OoI and in OoII clusters with very blue HB types obey a well- defined M(V)( RR) - k(puls) relation, while those in OoII clusters with moderately blue HB types present a zero- point that is similar to 0.05 mag brighter. Regarding field variables, we show that with [ Fe/ H] >= - 1.0 a unique M(V)( RR) - k(puls) relation can be adopted, independently of the color distribution of the parent HB star population. Conclusions. Current findings suggest that the PAV distribution is not a robust diagnostic for the metal abundance of RRab variables. However, the same observables can be used to estimate the absolute magnitude of globular cluster and field RRab variables. We show that over the metallicity range - 2.4 = [ Fe/ H] = 0.0 the MV( RR)-[ Fe/ H] relation is not linear but has a parabolic behavior.