RR Lyrae stars in Galactic globular clusters. VI. The Period-Amplitude relation

We compare theory and observations for fundamental RR Lyrae in the solar neighborhood and in both Oosterhoff type I (OoI) and type II (OoII) Galactic globular clusters (GGCs). The distribution of cluster RR_ab in the PA_V plane depends not only on the metal abundance, but also on the cluster Horizontal Branch (HB) morphology. On average the observed k_puls parameter, 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. 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 RR_ab 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. Synthetic HB simulations show that the PA_V plane can provide accurate cluster distance estimates. The RR_ab 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 ~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 parent HB morphology. Current findings suggest that the PA_V distribution does not seem to be a robust diagnostic for the metal abundance of RR_ab variables. However, the same observables can be used to estimate the absolute magnitude of globular cluster and field RR_ab variables. We show that over the metallicity range -2.4<= [Fe/H] <= 0.0 the M_V(RR)-[Fe/H] relation shows a parabolic behavior.