Hubble Space Telescope Fine Guidance Sensor Parallaxes of Galactic Cepheid Variable Stars: Period-Luminosity Relations^*

We present new absolute trigonometric parallaxes and relative proper motions for nine Galactic Cepheid variable stars: ℓ Car, ζ Gem, β Dor, W Sgr, X Sgr, Y Sgr, FF Aql, T Vul, and RT Aur. We obtain these results with astrometric data from Fine Guidance Sensor 1r, a white-light interferometer on the Hubble Space Telescope. We find absolute parallaxes in milliarcseconds: ℓ Car, 2.01 ± 0.20 mas; ζ Gem, 2.78 ± 0.18 mas; β Dor, 3.14 ± 0.16 mas; W Sgr, 2.28 ± 0.20 mas; X Sgr, 3.00 ± 0.18 mas; Y Sgr, 2.13 ± 0.29 mas; FF Aql, 2.81 ± 0.18 mas; T Vul, 1.90 ± 0.23 mas; and RT Aur, 2.40 ± 0.19 mas; average σ_π/π = 8%. Two stars (FF Aql and W Sgr) required the inclusion of binary astrometric perturbations, providing Cepheid mass estimates. With these parallaxes we compute absolute magnitudes in V, I, K, and Wesenheit W_VI bandpasses, corrected for interstellar extinction and Lutz-Kelker-Hanson bias. Adding our previous absolute magnitude determination for δ Cep, we construct period-luminosity relations (PLRs) for 10 Galactic Cepheids. We compare our new PLRs with those adopted by several recent investigations, including the Freedman and Sandage H₀ projects. Adopting our PLR would tend to increase the Sandage H₀ value, but leave the Freedman H₀ unchanged. Comparing our Galactic Cepheid PLR with those derived from LMC Cepheids, we find the slopes for K and W_VI to be identical in the two galaxies within their respective errors. Our data lead to a W_VI distance modulus for the LMC m - M = 18.50 ± 0.03, uncorrected for any metallicity effects. Applying recently derived metallicity corrections yields a corrected LMC distance modulus of (m - M)₀ = 18.40 ± 0.05. Comparing our PLR to solar-metallicity Cepheids in NGC 4258 results in a distance modulus 29.28 ± 0.08 that agrees with one derived from maser studies.