## 1. IntroductionRR Lyrae stars are fundamental standard candles and the accurate determination of their absolute luminosity has a wide range of applications, including the derivation of the Hubble constant and the determination of globular clusters ages. The results of the HIPPARCOS mission allow in principle a calibration of this luminosity, based on the parallaxes and proper motions. Fernley et al. (1998a, hereafter F98) did that by employing the method of statistical parallax on a sample of 84 RR Lyrae stars (out of the 144 they considered) with [Fe/H] . Combining the statistical parallax result with the absolute magnitude of RR Lyrae itself, computed without applying any Lutz-Kelker (LK) type correction (see Lutz & Kelker 1973, Turon Lacarrieu & Crézé 1977, Koen 1992, Oudmaijer et al. 1998), they derived a zero point of 1.05 0.15 mag for the -[Fe/H] relation, by assuming a slope of 0.18 0.03 (Fernley et al. 1998b). Tsujimoto et al. (1998, hereafter T98) used the statistical parallax method, a maximum likelihood technique and the derived of the star RR Lyrae (with LK correction included) for deriving a combined final value = 0.6-0.7 mag at [Fe/H] = -1.6. Luri et al. (1998, hereafter L98) applied a maximum-likelihood method that takes all available data into account, including parallaxes, proper motions and radial velocities, considering the sample of 144 RR Lyrae stars given in F98. They derived = 0.65 0.23 at an average metallicity of [Fe/H] = -1.51. The results by F98, T98 and L98 imply dimmer RR Lyrae stars by about 0.3 mag with respect to the results from either the Main Sequence fitting technique using HIPPARCOS subdwarfs (see, e.g., Gratton et al. 1997) or recent theoretical Horizontal Branch models (see, e.g., Salaris & Weiss 1998, Caloi et al. 1997). On the other hand, F98, T98 and L98 agree with the results from Baade-Wesselink analyses, which predict a zero point of about 1.00 mag for the -[Fe/H] relation (see, e.g., Clementini et al. 1995). Turon Lacarrieu & Crézé (1977) presented two methods to derive the absolute magnitude of stars from the observed parallaxes, namely using individual LK-corrections and the method of "reduced parallaxes" (hereafter RP) on a sample of stars. The advantages of the RP method are the following: it avoids the biases due to the asymmetry of the errors when transforming the parallaxes into magnitudes, it can be applied to samples which contain negative parallaxes, it is free from LK-type bias if no selection on parallax, or error on the parallax is made (Koen & Laney 1998), and it requires no knowledge about the space distribution of stars. We will apply the RP method to the sample of 144 RR Lyrae stars used by F98, and will derive the zero points of the -[Fe/H] and - relations. Recently, Koen & Laney (1998) also briefly discussed the application of the RP method to RR Lyrae stars. © European Southern Observatory (ESO) 1999 Online publication: July 26, 1999 |