Period–luminosity relations for Galactic Cepheid variables with independent distance measurements

In this paper, we derive the period-luminosity (PL) relation for Galactic Cepheids with recent independent distance measurements from open cluster, Barnes-Evans surface brightness, interferometry and Hubble Space Telescope astrometry techniques. Our PL relation confirms the results from recent works, which showed that the Galactic Cepheids follow a different PL relation to their Large Magellanic Cloud (LMC) counterparts. Our results also show that the slope of the Galactic PL relation is inconsistent with the LMC slope with more than 95 per cent confidence level. We apply this Galactic PL relation to find the distance to NGC 4258. Our result of μ o = 29.49 ± 0.06 mag (random error) agrees at the ∼1.4σ level with the geometrical distance of μ = 29.28 ± 0.15 mag from water maser measurements.