The Cepheid period-luminosity (P-L) relation is regarded as a linear relation (in log[P]) for a wide period range from ~2 to ~100 days. However, several recent controversial works have suggested that the P-L relation derived from the Large Magellanic Cloud (LMC) Cepheids exhibits a non-linear feature with a break period around 10 days. Here we review the evidence for linear/non-linear P-L relations from optical to near infrared bands. We offer a possible theoretical explanation to account for the nonlinear P-L relation from the idea of stellar photosphere - hydrogen ionization front interaction.
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