Amplitude Fine-Structure in the Cepheid P-L Relation I: Amplitude Distribution Across the RR Lyrae Instability Strip Mapped Using the Accessibility Restriction Imposed by the Horizontal Branch
The largest amplitude light curves for both RR Lyrae (RRL) variables and classical Cepheids with periods less than 10 days and greater than 20 days occur at the blue edge of the respective instability strips. It is shown that the equation for the decrease in amplitude with penetration into the strip from the blue edge, and hence the amplitude fine structure within the strip, is the same for RRL and the Cepheids despite their metallicity differences. However, the manifestation of this identity is different between the two classes of variables because the sampling of the RRL strip is restricted by the discrete strip positions of the horizontal branch, a restriction that is absent for the Cepheids in stellar aggregates with a variety of ages. To show the similarity of the strip amplitude fine structure for RRL and Cepheids we make a grid of lines of constant amplitude in the HR diagram of the strip using amplitude data for classical Cepheids in the Galaxy, LMC, and SMC. The model implicit in the grid, that also contains lines of constant period, is used to predict the correlations between period, amplitude, and color for the two Oosterhoff RRL groups in globular clusters. The good agreement of the predictions with the observations using the classical Cepheid amplitude fine structure also for the RRL shows one aspect of the unity of the pulsation processes between the two classes of variables.