On the light curve - luminosity relation of RR Lyrae stars

We use a large sample of RRab stars in globular clusters and in the Sculptor dwarf galaxy to decipher the relation between the Fourier decomposition and the luminosity. For fixing the zero point of the relation, we use the latest Baade-Wesselink (BW) results. It is shown that the most plausible representation of the absolute brightness (in V color) consists of a linear expression of the period and of the Fourier parameters A_1 and Phi_31 (computed also from the V light curve). We derive an average M_V = Alpha [Fe/H] + Beta relation from all the available Fourier data. Our results exclude any values of Alpha larger than 0.19, in agreement with most of the BW and evolutionary studies. We give age and reddened distance modulus estimations for the clusters entering in our analysis