2008A&A...477..621N

A number of recent works have suggested that the period-luminosity (PL) relation for the Large Magellanic Cloud (LMC) Cepheids exhibits a controversial nonlinear feature with a break period at 10 days. We aim to test the linearity/nonlinearity of the PL relations in this Research Note for the LMC Cepheids in BVI_cJHK_s band, as well as in the Wesenheit functions. We show that simply comparing the long and short period slopes, together with their associated standard deviations, leads to a strictly larger error rate than applying rigorous statistical tests such as the F-test. We applied various statistical tests to the current published LMC Cepheid data. These statistical tests include the F-test, the testimator test, and the Schwarz information criterion (SIC) method. The results from these statistical tests strongly suggest that the LMC PL relation is nonlinear in BVI_cJH band but linear in the K_s band and in the Wesenheit functions. Using the properties of period-color relations at maximum light and multi-phase relations, we believe that the nonlinear PL relation is not caused by extinction errors.