Period Color and Amplitude Color relations for MACHO project LMC RR   Lyraes
  In this paper, we analyze period color and amplitude color relations at minimum, mean and maximum $V$ band light for 6391 RRab stars in the Large Magellanic Cloud obtained by the MACHO project. Specifically, we find that color and amplitude are nearly independent of period at minimum light but that there exists a definite relation between period and color and amplitude and color at maximum light. These two properties are easily explained by the application of the Stefan Boltzmann law and the interaction of the photosphere and hydrogen ionization front at minimum light. When we examine the slope of the period color relation as a function of phase, we find that the slope varies significantly with phase and is small for a wide range of phases around minimum light. This suggests that another factor that needs to be considered when trying to understand RR Lyrae observed properties is their behavior at different phases during a pulsation cycle. 
S. M. Kanbur and I. Fernando