On the existence of differences in luminosity between horizontal branch stars in globular clusters and in the field

The discrepancy between a long distance-scale derived from Hipparcos-based distances to globular clusters via main-sequence fitting to local subdwarfs, and a short distance-scale derived from the absolute magnitude of field RR Lyraes via statistical parallaxes and the Baade-Wesselink method could be accounted for whether an intrinsic difference of about similar to 0.1-0.2 mag was found to exist between horizontal branch (HB) stars populating the sparse general field and the dense globular clusters. In this paper we discuss the possible existence of such a systematic difference comparing the period-shifts observed for field and cluster RR Lyraes. Various approaches based on different parameters and data sets for both cluster and field variables were used in order to establish the size of such a hypothetical difference, if any. We find that on the whole very small not significant differences exist between the period-metallicity distributions of field and cluster RR Lyraes, thus confirming with a more quantitative approach, the qualitative conclusions by Catelan. This observational evidence translates into a very small difference between the horizontal branch luminosity of field and cluster stars, unless RR Lyraes in globular clusters are about 0.06 M. more massive than field RR Lyraes at same metallicity, which is to be proven.