Pulsational $M_V$ versus [Fe/H] relation(s) for globular cluster RR Lyrae variables

We use the results from recent computations of updated non-linear convective pulsating models to constrain the distance modulus of Galactic globular clusters through the observed periods of first overtone RRc pulsators. The resulting relation between the mean absolute magnitude of RR Lyrae stars and the heavy element content [Fe/H] appears well in the range of several previous empirical calibrations, but with a non linear dependence on [Fe/H] so that the slope of the relation increases when moving towards larger metallicities. On this ground, our results suggest that metal-poor ([Fe/H]-1.5) variables follow two different linear -[Fe/H] relations. Application to RR Lyrae stars in the metal-poor globular clusters of the Large Magellanic Cloud provides a LMC distance modulus of the order of 18.6 mag, thus supporting the "long" distance scale. The comparison with recent predictions based on updated stellar evolution theory is shortly presented and discussed