Reconsidering The Bailey Diagrams of ab-type RR Lyrae Stars, Metallicity-Mediated Evolution as the Direct Cause of the Oosterhoff Phenomenon

We re-examine the Bailey diagrams of fundamental mode RR Lyrae stars from the perspective of horizontal branch (HB) evolution, identifying evolutionary effects as the probable direct cause of the Oosterhoff dichotomy. By establishing empirical relationships between pulsation amplitude and average effective temperature, and utilizing pulsation period relations from nonlinear models, we transform theoretical HB evolutionary parameters into pulsation space and map them onto Bailey diagrams. We find that all pulsating Zero-Age Horizontal Branch stars fall within the Oosterhoff type I (OoI) region, with a pronounced period shift effect observed for relatively metal-rich samples ([Fe/H] > -1). Evolutionary tracks confirm that OoI stars are predominantly early-stage HB stars, while Oosterhoff type II stars are highly evolved objects entering the instability strip late in their HB phase from the blue side. Crucially, metallicity plays a dual role: it directly influences pulsation periods through the period relation, but more fundamentally acts as the first parameter influencing HB morphology. This morphology statistically determines whether HB stars predominantly enter the instability strip during early or late evolutionary stages. Consequently, while evolutionary effects directly govern an individual star's position in the Bailey diagram, the population-level Oosterhoff phenomenon emerges from the interplay between these effects and the metallicity-dependent HB morphology. Our study confirms that evolutionary effects are the direct drivers of the period difference and underscores metallicity's vital role in the statistical emergence of Oosterhoff groups. Continued study of this phenomenon offers key insights into the formation history of the Milky Way and nearby dwarf galaxies.