The horizontal-branch stars in globular clusters. I - The period-shift effect, the luminosity of the horizontal branch, and the age-metallicity relation

Synthetic models of the horizontal branches in globular clusters are constructed from a grid of the standard horizontal branch evolutionary tracks. The models are used to study the period shifts at constant T(eff) between RR Lyrae variables in globular clusters of different metallicities and the variation in horizontal-branch luminosity with the Fe/H ratio. The results suggest that the observed differences in the mean periods of the ab variables and the fraction of c-type variables between the two Oosterhoff groups are caused by a difference in the mean luminosity of the ab variables of about 0.18 bolometric mass and by the uneven distribution of variables across the instability strip in the group II clusters.