Abstract
The purpose of this paper is to predict the temperature at the fundamental blue edge (FBE) of the instability strip for RR Lyrae (RRL) variables from the pulsation equation that relates temperature to period, luminosity, and mass. Modern data for the correlations between period, luminosity, and metallicity at the FBE for field and cluster RRL stars are used for the temperature calculation. The predicted temperatures are changed to B - V colors using an adopted color transformation. The predicted temperatures at the FBE become hotter as [Fe/H] changes from 0 to -1.5, and thereafter cooler as the metallicity decreases to -2.5. The temperature range over this interval of metallicity is Δ log Te = 0.04, or 640 K at 6900 K. The predicted color variation is at the level of 0.03 mag in B - V over most of this range. The predictions are compared with the observed RRL colors at the FBE for both the field and cluster variables, showing general agreement at the level of 0.02 mag in (B - V)0, which, however, is the uncertainty of the reddening corrections. The focus of the problem is then reversed by fitting a better envelope to the observed FBE relation between color and metallicity for metallicities smaller than -1.8, which, when inserted in the pulsation equation, gives a nonlinear calibration of the absolute magnitude of the average evolved level of the horizontal branch (HB) of MV = 1.109 + 0.600([Fe/H]) + 0.140([Fe/H])2, where the zero point has been set by the observed RR Lyrae stars in the LMC at ⟨V⟩0 = 19.064 by Clementini et al. for [Fe/H] = -1.5, and using an adopted LMC modulus of (m - M)0 = 18.54 from Tammann et al. that is independent of the LMC Cepheids. This equation gives MV = 0.52 at [Fe/H] = -1.5.
However, the calibration fails for the extreme second-parameter clusters NGC 6388 and NGC 6441. Proof that the MV absolute magnitudes for their RR Lyrae variables are ∼0.4 mag brighter than the calibration equation predicts is from the unusually long periods for given amplitudes at their high metallicities of [Fe/H] ∼ -0.5. All second-parameter clusters are believed to violate the equation, but less severely than these two extreme examples. An additional complication in using RRL stars as distance indicators at the 0.1 mag level is shown by the difference of Δ log P = 0.029 ± 0.007 in the position of the envelope locus at the shortest periods for the observed period-metallicity correlation between the field and cluster variables. The field variables have shorter periods than cluster variables at the envelope. This requires the cluster RRL stars to be 0.09 mag brighter than the field variables at the same temperature and mass, or to have a temperature difference of Δ log Te = 0.008 at fixed luminosity and mass. The field and cluster variables also differ in the near absence of cluster RR Lyrae stars in the -1.7 > [Fe/H] > -2.0 metallicity interval, whereas the field variables show no such gap. A test is proposed for different origins for the field and the cluster variables by comparing the morphology of the HBs in the local dwarf spheroidal galaxies with that in the Galactic globular clusters in the inner halo and by relating the differences with the relevant second-parameter indicators.