2001A&A...371..592B

We present theoretical period - magnitude relationships for Cepheids in different filters for fundamental and first overtone pulsators, completing the work by Alibert et al. (1999A&A...344..551A). The results are provided for different metallicities characteristic of the Magellanic Clouds and the Milky Way. In contrast to the fundamental mode, we find a small metallicity effect on the period - luminosity relationship for the first overtone, due to the sensitivity of the period ratio P₁/P₀ with metallicity. Comparison is made with observations from OGLE and EROS in the Small and Large Magellanic Clouds. We emphasize the constraint on theoretical predictions provided by the combination of both fundamental and first overtone observed sequences. We obtain excellent agreement between models and data in a logP-W_I (Wesenheit index) diagram for a distance modulus for the LMC µ₀=18.60-18.70. We analyse the uncertainties of the fundamental period - magnitude relationships and the consequences on distance determination. We show that an arbitrary shift of the instability strip by 350K in T_eff yields up to 0.45mag effect on M_V at a given period, whereas the effect is less than 0.1 mag in the K-band. Using recent near-IR observations in the Large Magellanic Cloud and our P-M_K relationship, we derive a distance modulus for the LMC in agreement with the value based on W_I data.