We have applied the near-IR Barnes-Evans realization of the Baade-Wesselink method as calibrated by Fouqué & Gieren ( [ ] ) 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 to 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 \pm 0.19 , and larger for the Wesenheit index W , where we find \Delta M _ { W } / \Delta \mbox { [ Fe / H ] } = -0.29 \pm 0.19 .
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 \sigma 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 .
( [ ] ) 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 \pm 0.13 mag irrespective of metallicity .