On the use of field RR Lyrae as Galactic probes: I. The Oosterhoff dichotomy based on fundamental variables

Abstract

We collected a large data set of field RR Lyrae stars (RRLs) by using catalogues already available in the literature and Gaia DR2. We estimated the iron abundances for a sub-sample of 2,382 fundamental RRLs ($\\Delta$S method: CaIIK, H$\\beta$, H$\\gamma$ and H$\\delta$ lines) for which are publicly available medium-resolution SDSS-SEGUE spectra. We also included similar estimates available in the literature ending up with the largest and most homogeneous spectroscopic data set ever collected for RRLs (2,903). The metallicity scale was validated by using iron abundances based on high resolution spectra for a fundamental field RRL (V~Ind), for which we collected X-shooter spectra covering the entire pulsation cycle. The peak ([Fe/H]=-1.59$\\pm$0.01) and the standard deviation ($\\sigma$=0.43 dex) of the metallicity distribution agree quite well with similar estimates available in the literature. The current measurements disclose a well defined metal-rich tail approaching Solar iron abundance. The spectroscopic sample plotted in the Bailey diagram (period vs luminosity amplitude) shows a steady variation when moving from the metal-poor ([Fe/H]=-3.0/-2.5) to the metal-rich ([Fe/H]=-0.5/0.0) regime. The smooth transition in the peak of the period distribution as a function of the metallicity strongly indicates that the long-standing problem of the Oosterhoff dichotomy among Galactic globulars is the consequence of the lack of metal-intermediate clusters hosting RRLs. We also found that the luminosity amplitude, in contrast with period, does not show a solid correlation with metallicity. This suggests that period-amplitude-metallicity relations should be cautiously treated.