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We identified and characterized the largest (536) RR Lyrae (RRL) sample in aMilky Way dSph satellite (Sculptor) based on optical photometry data collectedover $\sim$24 years.  The RRLs display a spread in V-magnitude ($\sim$0.35 mag) which appearslarger than photometric errors and the horizontal branch (HB) luminosityevolution of a mono-metallic population. Using several calibrations of twodifferent reddening free and metal independent Period-Wesenheit relations weprovide a new distance estimate $\mu$=19.62 mag ($\sigma_{\mu}$=0.04 mag) thatagrees well with literature estimates. We constrained the metallicitydistribution of the old population, using the $M_I$ Period-Luminosity relation,and we found that it ranges from -2.3 to -1.5 dex. The current estimate isnarrower than suggested by low and intermediate spectroscopy of RGBs($\Delta$[Fe/H] $\le$ 1.5).  We also investigated the HB morphology as a function of the galactocentricdistance. The HB in the innermost regions is dominated by red HB stars and byRRLs, consistent with a more metal-rich population, while in the outermostregions it is dominated by blue HB stars and RRLs typical of a metal-poorpopulation. Our results suggest that fast chemical evolution occurred inSculptor, and that the radial gradients were in place at an early epoch.

Variable Stars in Local Group Galaxies. I: Tracing the Early Chemical Enrichment and Radial Gradients in the Sculptor dSph with RR Lyrae Stars