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Period-Color and Amplitude-Color Relations for RR Lyraes

We use published OGLE LMC/SMC data to present comprehensive Period-Color (PC) and Amplitude-Color (AC) relations for both fundamental and overtone stars. For fundamental mode stars, we confirm earlier work that the minimum light extinction corrected PC relation in V-I has a shallow slope but with considerable scatter (LMC: $[0.093 \pm 0.019]$ with a standard deviation about this line of 0.116, SMC: $[0.055\pm0.058]$ with a standard deviation about this line of 0.099). We note the high scatter about this line for both the LMC and SMC: either there is some source of uncertainty in extinction or some other physical parameter is responsible for this dispersion. We compare with previous results and discuss some possible causes for this scatter. In contrast, RRc overtone stars do not obey a flat PC relation at minimum light (LMC: $[0.604 \pm 0.041]$ with a standard deviation about this line of 0.109, SMC: $[0.472 \pm 0.265]$ with a standard deviation about this line of 0.091). The fact that fundamental mode RR Lyrae stars obey a flat relation at minimum light and overtone RR Lyrae stars do not is consistent with the interaction of the stellar photosphere and hydrogen ionization front. We compare these results with PC relations for fundamental and first overtone Cepheids. The fact that the PC relations change significantly as a function of phase indicates strongly that Cepheid and RR Lyrae relations can only be understood at mean light when their properties as a function of phase are determined.