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

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 $\Delta M_V / \Delta \mbox{[Fe/H]}$ $= -0.21\pm0.19$, and larger for the Wesenheit index W, where we find $\Delta M_{\rm W} / \Delta \mbox{[Fe/H]}$ $= -0.29\pm0.19$. For the I and K bands we find $\Delta M_I / \Delta \mbox{[Fe/H]}$ $= -0.23\pm 0.19$ and $\Delta M_K / \Delta \mbox{[Fe/H]}$ $= -0.21\pm 0.19$, 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 $(m-M)_0 = 18.48\pm 0.07$, which is also in excellent agreement with the value of $(m-M)_0 = 18.50\pm 0.10$ adopted by the Key Project. From our SMC Cepheid distances we determine the SMC distance to be $18.88\pm0.13$ mag irrespective of metallicity.