Very Accurate Distances and Radii of Open Cluster Cepheids from a Near‐Infrared Surface Brightness Technique

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Abstract
We have obtained the radii and distances of 16 galactic Cepheids supposed to be members in open clusters or associations using a new optical and two near-infrared calibrations of the surface brightness (Barnes-Evans) method. We find excellent agreement of the radii and distances produced by both infrared techniques, which use the V, V - K (K on the Carter system) and the K, J - K magnitude-color combinations, respectively, with typical random errors that are as little as ~2%. We discuss possible systematic errors in our infrared solutions in detail and conclude that the typical total uncertainty of the infrared distance and radius of a Cepheid is about 3% in both infrared solutions, provided that the data are of excellent quality and that the amplitude of the color curve used in the solution is larger than ~0.3 mag. The optical V, V - R distance and radius of a given Cepheid can deviate by as much as ~30% from the infrared value because of large systematic and random errors caused by microturbulence and gravity variations: these affect the optical but not the infrared colors. We find excellent agreement of our infrared radii with the infrared radii derived previously for these variables by Laney & Stobie from an application of the maximum likelihood technique, which further increases our confidence that the total errors in our infrared solutions are not larger than ~3%. In an Appendix we discuss the relative advantages and disadvantages of our infrared surface brightness technique and the maximum likelihood technique. We compare the adopted infrared distances of the Cepheid variables to the zero-age main-sequence-fitting (ZAMS-fitting) distances of their supposed host clusters and associations (assuming a Pleiades distances modulus of 5.57) and find an unweighted mean value of the distance ratio of 1.02 ± 0.04. A detailed discussion of the individual Cepheids shows that the uncertainty of the ZAMS-fitting distances varies considerably from cluster to cluster. We find clear evidence that four Cepheids are not cluster members (SZ Tau, T Mon, U Car, and SV Vul), while we confirm cluster membership for V Cen and BB Sgr, for which former evidence for cluster membership was only weak. After rejection of nonmembers, we find a weighted mean distance ratio of 0.969 ± 0.014, with a standard deviation of 0.05, which demonstrates that both distance indicators are accurate to better than 5%, including systematic errors, and that there is excellent agreement between both distance scales.
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