On the sandage period shift effect among field RR lyrae stars

The synthetic horizontal branch (HB) calculations of Lee, Demarque, and Zinn are extended to all HB types over the metallicity range of the Galactic halo. It is shown that the period shifts of the RR Lyrae stars in globular clusters depend sensitively on their HB type as well as metallicity. These models suggest that the disagreement between the slopes, Δ log P(T_eff)/Δ[Fe/H], obtained by Lee, Demarque, and Zinn from their theoretical simulations and the one obtained by Sandage from his recent analysis of Lub's sample of field RR Lyrae stars can be explained if Lub's sample contains many highly evolved stars in the metallicity range of -2.0 ≤ [Fe/H] ≤ -1.6. The analysis of Lee, Demarque, and Zinn did not include these stars. When such an effect is taken into account, the correlation between the period shift and [Fe/H] among the field RR Lyrae stars matches the theoretical model calculations to within the errors, as is the case for the RR Lyraes in globular clusters. It is shown, however, that the mean RR Lyrae luminosity-[Fe/H] relationship is less affected by this effect. The present models for 33 clusters suggest that the best estimate for the mean RR Lyrae luminosity is <M_v^RR> = 0.19[Fe/H] + 0.97 (for Y_HB ≈ 0.22), in excellent agreement with the recent Baade-Wesselink measurements of field RR Lyrae stars. Consequently, a significant correlation is found between age and [Fe/H] among the globular clusters that spans ∼ 4 Gyr (for constant [O/Fe]) over the metallicity range of the Galactic halo. However, the slope of this correlation between age and metallicity will be reduced if [O/Fe] varies steeply with [Fe/H] as recently suggested by Abia and Rebolo.