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 (Teff) relations down to Teff ~ 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 (Teff ≤ 5500 K) and metal-rich ([Fe/H]$=+0.37$) MS stars in NGC 6791. The current methodology relies on an assumption that color-Teff 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 (Teff ≤ 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-Teff transformations from the infrared flux method (IRFM) 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.