Distance to the Large Magellanic Cloud: The RR Lyrae stars

New photometry and spectroscopy for more than a hundred RR Lyrae stars 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, the local reddening, the luminosity-metallicity relation, and the distance to the LMC. The average apparent luminosity of the RR Lyraes with complete V and B light curves is [V(RR)] = 19.412 +/- 0.019 (sigma = 0.153), [B (RR)] = 19.807 +/- 0.022 (sigma = 0.172) in our field A (62 stars) and [V (RR)] = 19.320 +/- 0.023 (sigma = 0.159), [B (RR)] = 19.680 +/- 0.024 (sigma = 0.163) in our field B (46 stars). The average V apparent luminosity of the clump stars in the same areas is 0.108 and 0.029 mag brighter than the RR Lyrae level ([V-clump] = 19.304 +/- 0.002 and 19.291 +/- 0.003, in field A: 6728 stars, and B: 3851 stars, respectively). Metallicities from low-resolution spectra obtained with the Very Large Telescope have been derived for 101 RR Lyrae stars, finding an average value of [Fe/H] = -1.48 +/- 0.03 (sigma = 0.29, on the Harris metallicity scale). An estimate of the reddening within the two fields was obtained (1) from the Sturch method applied to the fundamental-mode pulsators (RRab's) with known metal abundance and (2) from the colors of the edges of the instability strip defined by the full sample of RR Lyrae variable stars. We obtained E (B-V) = 0.116 +/- 0.017 and 0.086 +/- 0.017 mag in fields A and B, respectively, with a clear-cut indication of a 0.03 mag differential reddening between the two fields. We find that reddening in field A is 0.028 mag smaller than derived by OGLE-II in the same area. On average, the new reddenings are also 0.035 mag larger than derived from Cepheids with projected distances within 2degrees from the centers of our fields. The new metallicities were combined with the apparent average V-0 luminosities to determine the slope of the luminosity-metallicity relation for the RR Lyrae stars. We derived DeltaM(V) (RR) /Delta[ Fe/H] = 0.214 +/- 0.047, with no clear evidence for the change in slope at [Fe/H] = -1.5, as recently suggested by evolutionary/pulsation and horizontal-branch models. The dereddened apparent average luminosity of the RR Lyraes defined by the present photometry is [V(RR)](0) = 19.064 +/- 0.064 at [Fe/H] = -1.5. When coupled with the absolute magnitude derived from the Baade-Wesselink and the statistical parallaxes methods (M-V(RR) = 0.68 +/- 0.15 and 0.76 +/- 0.13 mag at [Fe/H] = -1.5), both methods known to favor the short distance scale, this value leads to distance moduli for the LMC of mu(LMC) = 18.38 +/- 0.16 and mu(LMC) = 18.30 +/- 0.14, respectively. If we use instead the absolute magnitude from the new main-sequence fitting of Galactic globular clusters from Gratton et al. [M-V (RR) = 0.61 +/- 0.07 mag at [Fe/H] = -1.5], we derive mu(LMC) = 18.45 +/- 0.09. The average I apparent luminosity of the clump stars derived by the present photometry is [I-clump] = 18.319 +/- 0.002 and 18.307 +/- 0.003, in field A (sigma = 0.190, 6728 stars) and B (sigma = 0.184, 3851 stars), respectively. These values, once corrected for our new reddening estimates, lead to [I](0) = 18.12 +/- 0.06 mag and move the clump distance modulus to the LMC to 18.42 +/- 0.07 and 18.45 +/- 0.07 when Udalski or Popowski metallicity-I luminosity relations for the clump stars are adopted. All these values are only 1sigma shorter than provided by the Population I distance indicators and make it possible to reconcile the short- and long-distance scale on a common value for the distance modulus of the LMC of mu(LMC) = 18.515 +/- 0.085 mag.