The distances to open clusters from main-sequence fitting. V. Extension of color calibration and test using cool and metal-rich stars in NGC 6791

We extend our effort to calibrate stellar isochrones in the Johnson-Cousins (BVIC) and the 2MASS (JHKs) filter systems based on observations of well-studied open clusters. Using cool main-sequence (MS) stars in Praesepe, we define empirical corrections to the Lejeune et al. color-effective temperature (T_eff) relations down to T_eff ~ 3600 K, complementing our previous work based on the Hyades and the Pleiades. We apply empirically corrected isochrones to existing optical and near-infrared photometry of cool (T_eff ≳ 5500 K) and metal-rich ([Fe H] = +0.37) MS stars in NGC 6791. The current methodology relies on an assumption that color-T_eff corrections are independent of metallicity, but we find that estimates of color excess and distance from color- magnitude diagrams with different color indices converge on each other at the precisely known metallicity of the cluster. Along with a satisfactory agreement with eclipsing binary data in the cluster, we view the improved internal consistency as a validation of our calibrated isochrones at super-solar metallicities. For very cool stars (T_eff ≳ 4800 K), however, we find that B - V colors of our models are systematically redder than the cluster photometry by .0.02 mag. We use color-T_eff transformations from the infrared flux method and alternative photometry to examine a potential color-scale error in the input cluster photometry. After excluding B - V photometry of these cool MS stars, we derive E (B - V) = 0.105 ± 0.014, [M/H] = +0.42 ± 0.07, (m - M)0 = 13.04 ± 0.08, and the age of 9.5 ± 0.3 Gyr for NGC 6791.