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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, severalrecent controversial works have suggested that the P-L relation derived fromthe Large Magellanic Cloud (LMC) Cepheids exhibits a non-linear feature with abreak period around 10 days. Here we review the evidence for linear/non-linearP-L relations from optical to near infrared bands. We offer a possibletheoretical explanation to account for the nonlinear P-L relation from the ideaof stellar photosphere - hydrogen ionization front interaction.

Non-Linear Cepheid Period-Luminosity Relation and the Interaction of Stellar Photosphere with Hydrogen Ionization Front