Clues in Bailey Diagrams Indicate that the Horizontal Branch Evolutionary Effect Is the Direct Reason for Oosterhoff Phenomenon

Abstract: Noticing the potential relationship between the pulsation amplitude of fundamental mode RR Lyrae stars and their average effective temperatures, we derived the relation between them from observational data. Using these relationships, we present the zero-age horizontal branch lines and corresponding evolutionary tracks in the Bailey diagrams. We first find that the trends of zero-age horizontal branch lines are consistent with the distributions of Oosterhoff I RR Lyrae stars, and there is a period shift effect in relatively metal-rich samples ([Fe/H] > -1). Main results show that evolutionary effects are the direct cause of the Oosterhoff dichotomy. The vast majority of Oosterhoff I RR Lyrae stars are in the early stage of horizontal branch evolution, while most of the Oosterhoff II stars are near the end of the horizontal branch phase. Our Bailey diagrams can intuitively explain some Oosterhoff phenomena (e.g., long-period RR Lyrae stars in the metal-rich globular clusters NGC 6388 and NGC 6441), and also have the potential to become an important tool for in-depth study of RR Lyrae stars. Further research is needed on the Oosterhoff dichotomy to explore the formations and evolutionary processes of the Milky Way and its substructures.