Abstract
We report the mean metallicity and absolute magnitude of RR Lyrae stars in a sample of 37 globular clusters, calculated via the Fourier decomposition of their light curves and ad hoc semi-empirical calibrations, in an unprecedented homogeneous approach. This enabled a new discussion of the metallicity dependence of the horizontal branch (HB) luminosity, as a fundamental distance indicator. The calibration for the RRab and RRc stars should be treated separately. For the RRab the dispersion is larger and non-linear. For the RRc stars the correlation is less steep, very tight and linear. The relevance of the HB structural parameter $\mathcal L$, is highlighted and we offer a non-linear calibration of the form MV([Fe/H], $\mathcal L$). Excellent agreement is found between values of [Fe/H] and MV from the light curve decomposition with spectroscopic values and distances obtained via Gaia-DR3 and HST. The variables census in 35 clusters includes 326 stars found by our program.
