RR Lyrae Stars in Galactic Globular Clusters. II. A Theoretical Approach to Variables in M3

We present predicted relations connecting pulsational (period and amplitude of pulsation) and evolutionary (mass, absolute magnitude, and color) parameters, as based on a wide set of convective pulsating models of RR Lyrae stars with Z = 0.001, Y = 0.24, and mass and luminosity suitable for the "old" (age > 8 Gyr) variables observed in globular clusters. The relations are collated with sound constraints on the mass of pulsators, as inferred from up-to-date evolutionary models of horizontal-branch stars, in order to provide a self-consistent theoretical framework for the analysis of observed variables. The theoretical predictions are tested through a detailed comparison with measurements of RR Lyrae stars in the globular cluster M3. We show that the predicted relations satisfy a variety of observed data, thus providing a pulsational route to the determination of accurate distances to RR Lyrae-rich globular clusters with intermediate metal content. We show that current uncertainties on the intrinsic luminosity of up-to-date horizontal-branch models, as due to the input physics used in the computations by the different authors, have a quite low influence (~0.02-0.03 mag) on the pulsational distance modulus. On the contrary, the effect of the different bolometric corrections adopted to convert bolometric luminosity into absolute magnitude is of the order of ~0.05-0.06 mag. The pulsation models are also used to perform some valuable tests on the physics adopted in current stellar evolution computations. We show that the constraints inferred by pulsation theory support the large value of the mixing-length parameter (l/Hp = 1.9-2.0) adopted to fit observed red giant branches, but that, at the same time, they would yield that the luminosity of the horizontal-branch updated models is too bright by ~0.08 ± 0.05 mag, if helium diffusion and metal diffusion are neglected. Conversely, if element diffusion is properly taken into account, then there is a marginal discrepancy of ~0.04 ± 0.05 mag between evolutionary and pulsational predictions.