THE OOSTERHOFF PERIOD EFFECT - LUMINOSITIES OF GLOBULAR-CLUSTER ZERO-AGE HORIZONTAL BRANCHES AND FIELD RR LYRAE STARS AS A FUNCTION OF METALLICITY

The purpose of this paper is to determine the variation of absolute magnitudes of RR Lyrae stars with metal abundance by using the pulsation properties of the variables. It is shown again that the period ratios (expressed as differences in log P, or "period shifts," star by star) for the variables in one globular cluster relative to another at the same temperature are correlated with [Fe/H]. There is explicit discussion of the sensitivity of the correlation to errors in the adopted reddenings. The equivalent analysis of luminosity-to-mass ratios (rather than period shifts) for variables in 10 clusters and for the variables in the field studied by Lub reveal the correlation to he log (L/M0.81) = -0.10[Fe/H] + 1.74 - the same as found by Lub. This equation applies for RR Lyrae stars at the luminosity level that represents the average post-zero-age horizontal-branch evolutionary state. The relation for the zero-age horizontal-branch state is fainter by ∼0.1 mag, reducing the constant to 1.70. The Oosterhoff progression of the ensemble average RRab period in individual clusters is shown to be continuous with [Fe/H], but exhibiting the Oosterhoff separation into two period groups with a period gap at log P(days)= -0.22. The gap is caused by the nonmonotonic behavior of the morphology of the horizontal branch with progressive variation of [Fe/H]. Combining the L/M0.81 relation with several assumptions for the variation of mass with [Fe/H], and applying the bolometric correction, gives MV(RR) = a[Fe/H] + b, where a ranges between 0.19 and 0.39, and b between 0.86 and 1.17 mag, depending on a. The uncertainty in a depends on the adopted mass-[Fe/H] relation which, at present, is largely not known with the necessary precision. The uncertainty in the zero point b is at least 0.2 mag because of uncertainties in (1) the constant in the pulsation equation, (2) the zero point of the color-temperature relation, and (3) the zero point of the mass scale. The value of a is the central issue, because it can be made to carry the cosmogonical burden of whether the age of the globular cluster system in the Galaxy depends on [Fe/H] or is independent of it.