Distance to the Large Magellanic Cloud: The RR Lyrae Stars

(abridged) New photometry and spectroscopy for more than a hundred RR Lyraestars in two fields located close to the bar of the Large Magellanic Cloud(LMC) are used to derive new accurate estimates of the average magnitude, thelocal reddening, the luminosity-metallicity relation, and of the distance tothe LMC. Metallicities from low resolution spectra obtained with the VLT havebeen derived for 101 RR Lyr's; the average value is [Fe/H]=-1.48+/-0.03(sigma=0.29). An estimate of the reddening was obtained with 2 differentmethods, and we found: E(B-V)=0.116+/-0.017, and 0.086+/-0.017 mag in field Aand B, respectively. The dereddened apparent average luminosity of the RRLyrae's defined by the present photometry is _0=19.064+/-0.064 at[Fe/H]=-1.5. We determine the slope of the luminosity-metallicity relation forthe RR Lyrae stars: Delta[M_V(RR)]/ Delta[Fe/H]=0.214+/-0.047, with no clearevidence for a change in slope at [Fe/H]=-1.5. When coupled with the absolutemagnitude derived from the Baade-Wesselink and the statistical parallaxesmethods, both methods known to favour the short distance scale, this valueleads mod(LMC)=18.38+/- 0.16 and 18.30+/-0.14, respectively. If we use insteadthe absolute magnitude from the new Main Sequence Fitting of Galactic globularclusters [M_V(RR)=0.61+/-0.07 mag at [Fe/H]=-1.5] we derivemod(LMC)=18.45+/-0.09. The average I luminosity of the clump stars isI_0=18.12+/-0.06, and moves the clump distance modulus to the LMC tomod(LMC)=18.42+/-0.07 and 18.45+/-0.07 when two metallicity-I relations areused. All these values are only 1 sigma shorter than provided by the Pop Idistance indicators, and allow to reconcile the short and long distance scaleon a common value for the distance modulus of the LMC of 18.515+/-0.085 mag.