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We determine Period-Luminosity relations for Milky Way Cepheids in theoptical and near-IR bands. These relations can be used directly as referencefor extra-galactic distance determination to Cepheid populations with solarmetallicity, and they form the basis for a direct comparison with relationsobtained in exactly the same manner for stars in the Magellanic Clouds,presented in an accompanying paper. In that paper we show that the metallicityeffect is very small and consistent with a null effect, particularly in thenear-IR bands, and we combine here all 111 Cepheids from the Milky Way, the LMCand SMC to form a best relation. We employ the near-IR surface brightness(IRSB) method to determine direct distances to the individual Cepheids after wehave recalibrated the projection factor using the recent parallax measurementsto ten Galactic Cepheids and the constraint that Cepheid distances to the LMCshould be independent of pulsation period. We confirm our earlier finding thatthe projection factor for converting radial velocity to pulsational velocitydepends quite steeply on pulsation period, p=1.550-0.186*log(P) in disagrementwith recent theoretical predictions. We delineate the Cepheid PL relation using111 Cepheids with direct distances from the IRSB analysis. The relations are byconstruction in agreement with the recent HST parallax distances to Cepheidsand slopes are in excellent agreement with the slopes of apparent magnitudesversus period observed in the LMC.

astronomy and astrophysics

Calibrating the Cepheid Period-Luminosity relation from the infrared  surface brightness technique I. The p-factor, the Milky Way relations, and a  universal K-band relation