Period-luminosity relations for Cepheid variables: from mid-infrared to multi-phase

This paper discusses two aspects of current research on the Cepheid period-luminosity (P-L) relation: the derivation of mid-infrared (MIR) P-L relations and the investigation of multi-phase P-L relations. The MIR P-L relations for Cepheids are important in the James Webb Space Telescope era for the distance scale issue, as the relations have potential to derive the Hubble constant within similar to 2% accuracy-a critical constraint in precision cosmology. Consequently, we have derived the MIR P-L relations for Cepheids in the Large and Small Magellanic Clouds, using archival data from Spitzer Space Telescope. We also compared currently empirical P-L relations for Cepheids in the Magellanic Clouds to the synthetic MIR P-L relations derived from pulsational models. For the study of multi-phase P-L relations, we present convincing evidence that the Cepheid P-L relations in the Magellanic Clouds are highly dynamic quantities that vary significantly when considered as a function of pulsational phase. We found that there is a difference in P-L relations as a function of phase between the Cepheids in each of the Clouds; the most likely cause for this is the metallicity difference between the two galaxies. We also investigated the dispersion of the multi-phase P-L relations, and found that the minimum dispersions do not differ significantly from the mean light P-L dispersion