The extra-galactic Cepheid distance scale from LMC and Galactic period-luminosity relations

In this paper, we recalibrate the Cepheid distance to some nearby galaxies observed by the HST Key Project and the Sandage-Tammann-Saha group. We use much of the Key Project methodology in our analysis but apply new techniques, based on Fourier methods to estimate the mean of a sparsely sampled Cepheid light curve, to published extra-galactic Cepheid data. We also apply different calibrating PL relations to estimate Cepheid distances, and investigate the sensitivity of the distance moduli to the adopted calibrating PL relation. We re-determine the OGLE LMC PL relations using a more conservative approach and also study the effect of using Galactic PL relations on the distance scale. For the Key Project galaxies after accounting for charge transfer effects, we find good agreement with an average discrepancy of -0.002 and 0.075 mag when using the LMC and Galaxy, respectively, as a calibrating PL relation. For NGC 4258 which has a geometric distance of $29.28~\rm mag$, we find a distance modulus of $29.44\pm0.06(\mathrm{random})~\rm mag$, after correcting for metallicity. In addition we have calculated the Cepheid distance to 8 galaxies observed by the Sandage-Tammann-Saha group and find shorter distance moduli by $-0.178~\rm mag$ (mainly due to the use of different LMC PL relations) and $-0.108~\rm mag$ on average again when using the LMC and Galaxy, respectively, as a calibrating PL relation. However care must be taken to extrapolate these changed distances to changes in the resulting values of the Hubble constant because STS also use distances to NGC 3368 and 4414 and because STS calibration of SN Ia is often decoupled from the distance to the host galaxy through their use of differential extinction arguments. We also calculate the distance to all these galaxies using PL relations at maximum light and find very good agreement with mean light PL distances. However, after correcting for metallicity effects, the difference between the distance moduli obtained using the two sets of calibrating PL relations becomes negligible. This suggests that Cepheids in the LMC and Galaxy do follow different PL relations and constrains the sign for the coefficient of the metallicity correction, $\gamma$, to be negative, at least at the median period $\log(P) \approx 1.4$, of the target galaxies.