The Distances to Open Clusters from Main‐Sequence Fitting. IV. Galactic Cepheids, the LMC, and the Local Distance Scale

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Abstract
We derive the basic properties of seven Galactic open clusters containing Cepheids and construct their period-luminosity (P-L) relations. For our cluster main-sequence fitting we extend previous Hyades-based empirical color-temperature corrections to hotter stars using the Pleiades as a template. We use BVI_{C}JHK_{s} data to test the reddening law, and include metallicity effects to perform a more comprehensive study for our clusters than prior efforts. The ratio of total to selective extinction R_V that we derive is consistent with expectations. Assuming the LMC P-L slopes, we find = -3.93 +/- 0.07 (statistical) +/- 0.14 (systematic) for 10-day period Cepheids, which is generally fainter than those in previous studies. Our results are consistent with recent HST and Hipparcos parallax studies when using the Wesenheit magnitudes W(VI). Uncertainties in reddening and metallicity are the major remaining sources of error in the V-band P-L relation, but a higher precision could be obtained with deeper optical and near-infrared cluster photometry. We derive distances to NGC4258, the LMC, and M33 of (m - M)_0 = 29.28 +/- 0.10, 18.34 +/- 0.06, and 24.55 +/- 0.28, respectively, with an additional systematic error of 0.16 mag in the P-L relations. The distance to NGC4258 is in good agreement with the geometric distance derived from water masers [Delta (m - M)_0 = 0.01 +/- 0.24]; our value for M33 is less consistent with the distance from an eclipsing binary [Delta (m - M)_0 = 0.37 +/- 0.34]; our LMC distance is moderately shorter than the adopted distance in the HST Key Project, which formally implies an increase in the Hubble constant of 7% +/- 8%.