We use color-magnitude diagram synthesis together with theoretical relations from non-linear pulsation models to approach the long-standing problem of the Oosterhoff dichotomy related to the distribution of the mean periods of fundamental RR Lyrae variables in globular clusters .
By adopting the chemical composition determined from spectroscopic observations and a criterion to account for the hysteresis mechanism , we tuned age and mass-loss to simultaneously reproduce the morphology of both the turn-off and the Horizontal Branch of a sample of 17 globular clusters of the Milky Way and of nearby dwarf galaxies in the crucial metallicity range ( -1.9 < [ Fe / H ] < -1.4 ) where the Oostheroff transition is apparent .
We find that the Oosterhoff dichotomy among Galactic globular clusters is naturally reproduced by models .
The analysis of the relative impact of the various involved parameters indicates that the main responsibles of the dichotomy are the peculiar distribution of clusters in the age-metallicity plane and the hysteresis .
In particular , there is a clear connection between the two main branches of the age-metallicity relation for Galactic globular clusters and the Oosterhoff groups .
The properties of clusters ’ RR Lyrae belonging to other Oostheroff groups ( OoInt and OoIII ) are instead not well reproduced .
While for OoIII clusters a larger helium abundance for a fraction of the cluster ’ s stars can reconcile the model prediction with observations , some other parameter affecting both the Horizontal Branch morphology and the RR Lyrae periods is required to reproduce the behavior of OoInt clusters .