Age and Distance for the Old Open Cluster NGC 188 from the Eclipsing Binary Member V 12

We present time series radial velocity, and photometric observations of a solar-type double-lined eclipsing binary star (V 12) in the old open cluster NGC 188. We use these data to determine the spectroscopic orbit and the photometric elements for V 12. From our analysis, we determine accurate masses (M<SUB>p</SUB> = 1.103 ± 0.007 M <SUB>sun</SUB>, M<SUB>s</SUB> = 1.081 ± 0.007 M <SUB>sun</SUB>) and radii (R<SUB>p</SUB> = 1.424 ± 0.019 R <SUB>sun</SUB>, R<SUB>s</SUB> = 1.373 ± 0.019 R <SUB>sun</SUB>) for the primary (p) and secondary (s) binary components. We adopt a reddening of E <SUB> B-V </SUB> = 0.087 for NGC 188, and derive component effective temperatures of 5900 ± 100 K and 5875 ± 100 K, respectively, for the primary and secondary stars. From their absolute dimensions, the two components of V 12 yield identical distance moduli of V <SUB>0</SUB> - M<SUB>V</SUB> = 11fm24 ± 0fm09, corresponding to 1770 ± 75 pc. Both stars are near the end of their main-sequence evolutionary phase, and are located at the cluster turnoff in the color-magnitude diagram. We determine an age of 6.2 ± 0.2 Gyr for V 12 and NGC 188, from a comparison with theoretical isochrones in the mass-radius diagram. This age is independent of distance, reddening, and color-temperature transformations. We use isochrones from Victoria-Regina (VRSS) and Yonsei-Yale (Y <SUP>2</SUP>) with [Fe/H] = -0.1 and [Fe/H] = 0.0. From the solar metallicity isochrones, an age of 6.4 Gyr provides the best fit to the binary components for both sets of models. For the isochrones with [Fe/H] = -0.1, ages of 6.0 Gyr and 5.9 Gyr provide the best fits for the (VRSS) and (Y <SUP>2</SUP>) models, respectively. We use the distance and age estimates for V 12, together with best estimates for the metallicity and reddening of NGC 188, to investigate the locations of the corresponding VRSS and Y <SUP>2</SUP> isochrones relative to cluster members in the color-magnitude diagram. Plausible changes in the model metallicity and distance to better match the isochrones to the cluster sequences, result in a range of ages for NGC 188 that is more than 3 times that resulting from our analysis of V 12.<p/> WIYN Open Cluster Study. XXXVII.