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 which predicts the period-metallicity relations is 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 and 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 Lyraes with different metallicities at the same Phi_31 values. However, there are exceptions to the model. (...)