The metallicity dependence of the fourier components of RR Lyrae light curves is the Oosterhoff-Arp-Preston period ratio effect in disguise

The correlation of particular Fourier components of the light curves of RR Lyrae variables with metallicity, discovered by Simon and later by Kovacs and his coworkers, is shown to have the same explanation as the period ratios ( period shifts in log P) between RRab Lyrae variables that have the same colors, amplitudes, and light-curve shapes but different metallicities. A purpose of this paper is to demonstrate that the model that predicts the period-metallicity relations in the mediating parameters of colors, amplitudes, and light-curve shapes also explains the Simon-Kovacs et al. correlation between period, phi(31), and metallicity. The proof is made by demonstrating that the combination of the first- and third-phase terms in a Fourier decomposition of RRab light curves, called phi(31) by Simon & Lee, varies monotonically across the RR Lyrae instability strip in the same way that amplitude, color, and rise time vary with period within the strip. The premise of the model is that if horizontal branches at the RR Lyrae strip are stacked in luminosity according to the metallicity, then there necessarily must be a log period shift between RR Lyrae stars with different metallicities at the same phi(31) values. However, there are exceptions to the model. The two metal-rich globular clusters NGC 6388 and NGC 6441, with anomalously long periods of their RR Lyrae stars for their amplitudes, violate the period-metallicity correlations both in amplitudes and in phi(31) values (for NGC 6441 where phi(31) data exist). The cause must be related to the anomalously bright horizontal branches in these two clusters for their metallicities. The effect of luminosity evolution away from the zero-age horizontal branch, putatively causing noise in the metallicity equation, is discussed. It is clearly seen in the amplitude-period correlations but apparently does not exist in the phi(31)-period correlation in the data for the globular cluster M3 analyzed by Jurcsik and coworkers and by Cacciari and Fusi Pecci, for reasons not presently understood. Clarification can be expected from study of precision photometric data of evolved RR Lyrae stars in globular clusters of different metallicity when their Fourier components are known.