Nonlinear Period-Luminosity Relation for the Large Magellanic Cloud   Cepheids: Myths and Truths
  In this paper, we discuss and examine various issues concerning the recent findings that suggested the observed period-luminosity (P-L) relation for the Large Magellanic Cloud (LMC) Cepheids is nonlinear. These include (1) visualizing the nonlinear P-L relation; (2) long period Cepheids and sample selection; (3) outlier removal; (4) issues of extinction; (5) nonlinearity of the period-color (P-C) relation; (6) nonlinear P-L relations in different pass-bands; and (7) universality of the P-L relation. Our results imply that a statistical test is needed to detect the nonlinear PL relation. We then show that sample selection, number of long period Cepheids in the sample, outlier removal and extinction errors are unlikely to be responsible for the detection of the nonlinear P-L relation. We also argue for the existence of a nonlinear P-L relation from the perspective of the nonlinear P-C relation and the non-universality of the P-L relation. Combining the evidence and discussion from these aspects, we find that there is a strong indication that the observed LMC P-L relation is indeed nonlinear in the optical bands (however the K-band LMC P-L relation is apparently linear). This could be due to the internal physical reasons or the external hidden/additional factors. Compared to the non-linear P-L relation, the systematic error in distance scale introduced from using the (incorrect) linear P-L relation is at most at a few per cent level. While this is small compared to other systematic errors, it will be important in future efforts to produce a Cepheid distance scale accurate to one per cent in order to remove degeneracies presented in CMB results. 
C. Ngeow (UIUC) & S. Kanbur (SUNY-Oswego)