THE VERTICAL HEIGHT OF THE HORIZONTAL BRANCH - THE RANGE IN THE ABSOLUTE MAGNITUDES OF RR LYRAE STARS IN A GIVEN GLOBULAR-CLUSTER

The observed range of apparent magnitudes of RR Lyrae variables in a given cluster is shown to be real, resulting from evolution away from the zero-age horizontal branch (ZAHB). The demonstration is made using data on periods, temperatures, and magnitudes of cluster variables in M3, M4, M15, M92, NGC 6171, NGC 6723, NGC 6981, and ω Cen by showing that in a given cluster the RR Lyrae stars that are brighter than others of the same color have longer periods by the amounts expected from the larger radii calculated as if the brighter luminosities that are observed are real, rather than caused by measuring errors. A similar result using period shifts at constant amplitude for variables in a given cluster show that the effect is not due to differential reddening. The intrinsic HB width determined in this way varies with metallicity. In the low-metallicity clusters M15 and NGC 5053, the total HB spread is 0.2 mag, rising to ∼0.6 mag in metal-rich clusters such as M4. In the special case of ω Cen, the abnormally large width of 0.7 mag is caused by the combination of the two effects of evolution away from the ZAHB and the dependence of the luminosity level of the ZAHB on metallicity. The intrinsic spread in the absolute magnitude of an ensemble of RR Lyrae stars, say in a general field, caused by the two effects just mentioned complicates their use either as distance indicators or in studies that relate the luminosity zero points of Population I Cepheids and RR Lyrae stars, say in M31 or IC 1613. In galaxies where RR Lyrae stars are found only near the limit of detection, the metallicity distribution and the incompleteness of the sampling into the RR Lyrae luminosity function must be known if the resulting bias errors are to be avoided in the inferred distances or in the determination of relative period-luminosity zero points.