The role of chemical composition in RR Lyrae pulsational properties - I. Periods

We analyse the periods of theoretical radial pulsators, covering the range of total masses, luminosities, effective temperatures and chemical compositions expected for RR Lyrae variables in both galactic fields and globular clusters. We show that for fixed values of the structural parameters (mass, luminosity and effective temperature), the period of fundamental and first-overtone pulsators is independent of the helium content (Y), whereas it slightly increases as the amount of metals (Z) increases. Furthermore, we find that the period along the blue edge for first-overtone pulsation is a function of mass, luminosity and helium content, with a marginal dependence on Z. On these grounds, new linear relations connecting the periods to stellar parameters are derived. Such new relations should allow a more accurate interpretation of the RR Lyrae observed periods and, in particular, they should help in ascertaining the calibration of the mean absolute magnitude of RR Lyrae stars in terms of metal content.