The Luminosity Scale of RR Lyrae Stars Using the Baade-Wesselink Method.

UBVRI and JK photometry and radial velocities have been obtained for 13 field RR Lyrae stars covering a large range of metallicity. The surface brightness version of the Baade-Wesselink (B-W) method has been applied to these stars to determine their absolute magnitudes < M_V>. Using static model atmospheres to provide color-temperature transformations, we find that the RR Lyrae temperature scale can be relatively well defined by the color index V - K. The use of infrared photometry in a B-W analysis reduces the uncertainties because the sensitivity to gravity and metallicity is small. Complications in pulsational velocity determination also have small effects on the < M_V> determination if the analysis is restricted to the phase interval where the temperature change is minimal. Our results show a clear correlation between the luminosities of the RR Lyraes and their metallicities such that:. < M_ V> = 0.20 (+/-0.06) (Fe/H) + 1.05 ( +/-0.14),. with a metal-poor star being more luminous. The typical accuracy of the derived < M _ V> for a single star is 0.20 mag. These RR Lyraes also follow a period-infared luminosity relation, a potentially important distance calibrator. The B-W analysis was extended to four RR Lyraes in globular cluster M4. Our study indicates that an accuracy comparable to the field star < M_ V> determination can be achieved for cluster RR Lyraes. The mean value of < M_ V> for the four stars agree with our field star < M_ V> calibration appropriate to the cluster's metallicity, indicating no fundamental difference in the characteristics between field and cluster RR Lyraes. We find that there is a few tenths of a magnitude intrinsic dispersion in the determined values of < M_ V>, which is expected due to the effect of evolution off the zero-age horizontal branch. In addition, the cluster RR Lyraes obey the < M_ K>-log P relation found for the field stars. Based on our B-W study and other recent RR Lyrae < M_ V> estimates, we conclude that: (1) the surface brightness technique when used with infrared photometry is a reliable method of determining < M_ V> ; (2) < M_ V> is correlated with (Fe/H); and (3) the slope of the < M_ V> - (Fe/H) relation is 0.2. Such a metallicity dependence of < M_ V> implies a variation of globular cluster ages with metallicity, the metal-poor clusters being older by up to 4 Gyr. Our calibrated RR Lyrae luminosity scale is also used to determine the distance to the Galactic center and the distances to nearby galaxies.