Calibrating the Cepheid Period-Luminosity relation from the near-infrared surface brightness technique

We have applied the near-infrared surface-brightness method to 111 Cepheids in the Milky Way and in the Large and the Small Magellanic Clouds determining distances and luminosities for the individual stars. We find that the K-band Period-Luminosity (PL-)relations for Milky Way and Large Magellanic Cloud Cepheids are almost identical, whereas the zero point of the Wesenheit relation depends significantly on metallicity, metal poor Cepheids being fainter. We determine empirically the relation between the projection factor, p, and pulsational period, P, used for converting the observed radial velocities into the pulsational velocities necessary for applying the near-infrared surface-brightness method. We also determine the p-factor relation on a theoretical basis and find a significantly shallower slope than from our empirical determination, suggesting that there is still some physics related to the method which deserves further investigation. Using the empirical p-factor relation we re-determine the Cepheid PL-relation in the K-band using all 111 Cepheids. We argue that this is the currently best PL-relation for distance determination being largely independent of both metallicity and reddening.