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
  We determine Period-Luminosity relations for Milky Way Cepheids in the
optical and near-IR bands. These relations can be used directly as reference
for extra-galactic distance determination to Cepheid populations with solar
metallicity, and they form the basis for a direct comparison with relations
obtained in exactly the same manner for stars in the Magellanic Clouds,
presented in an accompanying paper. In that paper we show that the metallicity
effect is very small and consistent with a null effect, particularly in the
near-IR bands, and we combine here all 111 Cepheids from the Milky Way, the LMC
and SMC to form a best relation. We employ the near-IR surface brightness
(IRSB) method to determine direct distances to the individual Cepheids after we
have recalibrated the projection factor using the recent parallax measurements
to ten Galactic Cepheids and the constraint that Cepheid distances to the LMC
should be independent of pulsation period. We confirm our earlier finding that
the projection factor for converting radial velocity to pulsational velocity
depends quite steeply on pulsation period, p=1.550-0.186*log(P) in disagrement
with recent theoretical predictions. We delineate the Cepheid PL relation using
111 Cepheids with direct distances from the IRSB analysis. The relations are by
construction in agreement with the recent HST parallax distances to Cepheids
and slopes are in excellent agreement with the slopes of apparent magnitudes
versus period observed in the LMC.
