On the Old Open Clusters M67 and NGC 188: Convective Core Overshooting, Color‐Temperature Relations, Distances, and Ages

The color‐magnitude diagram of M67 is used to constrain the value of the parameter Fover in its ≈1.3 M⊙ turnoff stars: Fover is effectively the fraction of the maximum possible extent of convective core overshooting predicted by the Roxburgh (1989, A&A, 211, 361) criterion. Isochrones that treat overshooting using the parameterized Roxburgh criterion are able to reproduce the morphology of the cluster turnoff, including the luminosity of the gap, if Fover ≈ 0.07 (assuming current best estimates for the reddening and metallicity). Previous studies have derived values of Fover near 0.5 in open clusters of similar metallicity but having turnoff masses ≥1.55 M⊙, indicating that the overshooting parameter is a strong function of mass in the lowest mass stars that retain convective cores throughout the main‐sequence phase. NGC 188 appears to be too old for core overshooting to play any role in the evolution of stars that are currently in the core H‐burning phase, but the availability of well‐calibrated BVRI photometry for this system, together with Landolt photometric standards, provides valuable tests of the color‐Teff relations that apply to [Fe/H] ≈ 0.0 stars. Our analysis of color‐color diagrams, in particular, suggests that the Castelli (, A&A, 346, 564) V−R and V−I transformations for lower gravity stars are more realistic than those published recently by VandenBerg & Clem (2003, AJ, 126, 778). The same color‐color diagrams also indicate that the differences in recent (V−I,V) diagrams for M67 appear to be due, at least in part, to the difficulty of defining the standard VRI photometric system. The ages of M67 and NGC 188 that have been derived in this study are 4.0 and 6.8 Gyr, respectively, which is consistent with other modern determinations.