Multi-wavelength Characteristics of Period-Luminosity Relations

We present a physically motivated explanation for the observed, monotonic increase in slope, and the simultaneous (and also monotonic) decrease in the width/scatter of the Leavitt law (the Cepheid period-luminosity (PL) relation) as one systematically moves from the blue and visual into the near- and mid-infrared. We calibrate the wavelength-dependent, surface-brightness sensitivities to temperature using the observed slopes of PL relations from the optical through the mid-infrared and test the calibration by comparing the theoretical predictions with direct observations of the wavelength dependence of the scatter in the Large Magellanic Cloud Cepheid PL relation. In doing so we find the slope of the period-radius (PR) relation is c = 0.724 ± 0.006. Investigating the effect of differential reddening suggests that this value may be overestimated by as much as 10%; however, the same slope of the PR relation fits the (very much unreddened) Cepheids in IC 1613, albeit with lower precision. The discussion given is general and also applies to RR Lyrae stars, which also show similarly increasing PL slopes and decreasing scatter with increasing wavelength.