Metal-rich RR Lyrae variables .2. The pulsational scenario

We present a theoretical investigation on the pulsational behavior of metal-rich RR Lyrae variables over the range of evolutionary parameters suitable for stars with metallicities Z = 0.006, 0.01, and 0.02. With the addition of similar results for metal-poor pulsators, we discuss the theoretical pulsational scenario covering the metallicity range Z = 0.0001-0.02. By connecting pulsational constraints to evolutionary prescriptions for He-burning stars, we discuss the observed behavior of the RR Lyrae population in the Galactic field. We find that the distribution of field ab-type RR Lyrae stars in the period-metallicity plane can be easily understood within the framework of the present theoretical scenario, suggesting that the Oosterhoff dichotomy also affects field variables. Theoretical predictions concerning the amplitude-period diagram are discussed and compared with observational data. We find a general agreement for metal-poor ([Fe/H] < -1.4) RR Lyrae stars, whereas more metal-rich variables show amplitudes smaller than those predicted for pulsators originated from old, low-mass evolving stars. Alternatively, the agreement between theory and observations would ; require that a substantial fraction of metal-rich RR Lyrae variables in the Galactic field were younger than approximate to 2 Gyr. The comparison between the pulsational behavior of RR Lyrae either in the Galactic held or in the Galactic bulge discloses the evidence that, at least as far as RR Lyrae variables are concerned, the metal-rich components of the bulge and of the field population appear quite similar. We finally suggest that the peak at log P similar or equal to -0.55 in the period frequency distribution of first-overtone RR Lyrae stars in the Large Magellanic Cloud, considered as possible evidence for second-overtone pulsators, could be more simply taken as evidence of a metal-rich stellar population.