The effect of metallicity on Cepheid Period-Luminosity relations from a
  Baade-Wesselink analysis of Cepheids in the Milky Way and Magellanic Clouds
  The extragalactic distance scale builds on the Cepheid period-luminosity (PL)
relation. In this paper, we want to carry out a strictly differential
comparison of the absolute PL relations obeyed by classical Cepheids in the
Milky Way (MW), LMC and SMC galaxies. Taking advantage of the substantial
metallicity difference among the Cepheid populations in these three galaxies,
we want to establish a possible systematic trend of the PL relation absolute
zero point as a function of metallicity, and determine the size of such an
effect in optical and near-infrared photometric bands. We are using the IRSB
Baade-Wesselink type method as calibrated by Storm et al. to determine
individual distances to the Cepheids in our samples in MW, LMC and SMC. For our
analysis, we use a greatly enhanced sample of Cepheids in the SMC (31 stars) as
compared to the small sample (5 stars) available in our previous work. We use
the distances to determine absolute Cepheid PL relations in optical and
near-infrared bands in each of the three galaxies.} {Our distance analysis of
31 SMC Cepheids with periods from 4-69 days yields tight PL relations in all
studied bands, with slopes consistent with the corresponding LMC and MW
relations. Adopting the very accurately determined LMC slopes for the optical
and near-infrared bands, we determine the zero point offsets between the
corresponding absolute PL relations in the 3 galaxies. We find that in all
bands the metal-poor SMC Cepheids are intrinsically fainter than their more
metal-rich counterparts in the LMC and MW. In the $K$ band the metallicity
effect is $-0.23\pm0.06$~mag/dex while in the $V,(V-I)$ Wesenheit index it is
slightly stronger, $-0.34\pm0.06$~mag/dex. We find some evidence that the PL
relation zero point-metallicity relation might be nonlinear, becoming steeper
for lower metallicities.
