The effect of metallicity on the Cepheid Period-Luminosity relation from a Baade-Wesselink analysis of Cepheids in the Galaxy and in the Small Magellanic Cloud

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Abstract
We have applied the near-IR Barnes-Evans realization of the Baade-Wesselink method as calibrated by Fouqué & Gieren ([CITE]) to five metal-poor Cepheids with periods between 13 and 17 days in the Small Magellanic Cloud as well as to a sample of 34 Galactic Cepheids to determine the effect of metallicity on the period-luminosity (P-L) relation. For ten of the Galactic Cepheids we present new accurate and well sampled radial-velocity curves. The Baade-Wesselink analysis provides accurate individual distances and luminosities for the Cepheids in the two samples, allowing us to constrain directly, in a purely differential way, the metallicity effect on the Cepheid P-L relation. For the Galactic Cepheids we provide a new set of P-L relations which have zero-points in excellent agreement with astrometric and interferometric determinations. These relations can be used directly for the determination of distances to solar-metallicity samples of Cepheids in distant galaxies, circumventing any corrections for metallicity effects on the zero-point and slope of the P-L relation. We find evidence for both such metallicity effects in our data. Comparing our two samples of Cepheids at a mean period of about 15 days, we find a weak effect of metallicity on the luminosity similar to that adopted by the HST Key Project on the Extragalactic Distance Scale. The effect is smaller for the V band, where we find , and larger for the Wesenheit index W, where we find . For the I and K bands we find and , respectively. The error estimates are 1 σ statistical errors. It seems now well established that metal-poor Cepheids with periods longer than about 10 days are intrinsically fainter in all these bands than their metal-rich counterparts of identical period. Correcting the LMC distance estimate of Fouqué et al. ([CITE]) for this metallicity effect leads to a revised LMC distance modulus of , which is also in excellent agreement with the value of adopted by the Key Project. From our SMC Cepheid distances we determine the SMC distance to be mag irrespective of metallicity.

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